communications in asteroseismologycomm. in asteroseismology vol. 141, 2002 multiplefrequenciesofµ2...

Communications in Asteroseismology

Volume 141January, 2002

Editor: Michel Breger, Turkenschanzstraße 17, A - 1180 Wien, AustriaLayout and Production: Wolfgang Zima and Renate Zechner

Editorial Board: Gerald Handler, Don Kurtz, Jaymie Matthews, Ennio Porettihttp://www.deltascuti.net

COVER ILLUSTRATION:Representation of the COROT Satellite, which is primarily devoted to under-standing the physical processes that determine the internal structure of stars,and to building an empirically tested and calibrated theory of stellar evolution.Another scientific goal is to observe extrasolar planets.

British Library Cataloguing in Publication data.A Catalogue record for this book is available from the British Library.

All rights reservedISBN 3-7001-3002-3ISSN 1021-2043

Copyright c© 2002 byAustrian Academy of Sciences

Vienna

Contents

Multiple frequencies of θ2 Tau: Comparison of ground-based and spacemeasurements

by M. Breger 4

PMS stars as COROT additional targetsby M. Marconi, F. Palla and V. Ripepi 13

The study of pulsating stars from the COROT exoplanet field databy C. Aerts 20

10 Aql, a new target for COROTby L. Bigot and W. W. Weiss 26

Status of the COROT ground-based photometric activitiesby R. Garrido, P. Amado, A. Moya, V. Costa, A. Rolland, I. Olivares

and M. J. Goupil 42

Mode identification using the exoplanetary cameraby R. Garrido, A. Moya, M. J.Goupil, C. Barban, C. van’t Veer-Menneret,

F. Kupka and U. Heiter 48

COROT and the late stages of stellar evolutionby T. Lebzelter, H. Pikall and F. Kerschbaum 51

Pulsations of Luminous Blue Variablesby E. A. Dorfi and A. Gautschy 57

By-product of the V1162 Ori multisite campaign: the new δ Scuti starGSC 4778 00324

by P. Lampens, P. van Cauteren, P. Niarchos, K. Gazeas, V. Manimanis,

T. Arentoft, P. Wils, A. Bruch, R. Garrido and R. Shobbrook 65

Strømgren photometry of SX Phe = HD 223065by A. Stankov, D. Sinachopoulos, E. Elst and M. Breger 72

Comm. in Asteroseismology

Vol. 141, 2002

Multiple frequencies of θ2 Tau: Comparison ofground-based and space measurements

M. Breger

Institut fur Astronomie, Univ. Wien, Turkenschanzstr. 17, A–1180 Wien, Austria

Abstract

The satellite photometry of the δ Scuti star θ2 Tau obtained with the Wide-Field Infrared Explorer (WIRE) led to the detection of 12 frequencies of pulsation(Poretti et al. 2002). We examine the available ground-based photometry in theliterature to check whether these frequencies are also present. The re-analysis ofthe 1986 Delta Scuti Network data leads to 10 statistically significant frequen-cies (amplitude signal/noise ratio greater than 4.0). 9 of these 10 frequenciesare in excellent agreement with those detected from space, while the 10th fre-quency is seen as a peak in the WIRE residuals, though not at a statisticallysignificant level. Previous reports on amplitude variability are confirmed.

Introduction

A number of lengthy observing campaigns covering individual δ Scuti variableshave shown that the majority of these pulsating variables on and near themain sequence pulsate with a large number of simultaneously excited nonradialp modes. Furthermore, long-term variability of the pulsation amplitudes ofthese nonradial modes with a time scale of years has been discovered for many,but not all of these nonradial pulsators. The Delta Scuti Network specializesin multisite observations of these stars. The network is a collaboration ofastronomers located at observatories spaced around the globe in order to avoidregular, daily observing gaps. So far, 21 campaigns have been carried out. Themost recent campaign covered BI CMi, for which 29 frequencies of pulsationderived from 1024 hours (177 nights) of photometry were discovered (Bregeret al. 2002).

The variability of the star θ2 Tau was discovered by Horan (1977, 1979)and confirmed by Duerbeck (1978). In order to study the multiple frequencies

M. Breger 5

in this star, the Delta Scuti Network undertook two campaigns (Breger et al.1987, 1989). The data could be supplemented by additional measurementsby Kovacs & Paparo (1989). Altogether, five frequencies of pulsation weredetected and interpreted to be due to mainly nonradial pulsation. The sizeand distribution of the frequencies suggested p modes with values of ` = 0 to2, since higher ` values would not be seen photometrically due to cancellationeffects across the stellar surface. A mode with a higher ` value was also detectedspectroscopically by Kennelly & Walker (1996). Furthermore, the Delta ScutiNetwork reobserved θ2 Tau during 1994, but the data are at present unpublishedbecause of unresolved instrumental difficulties at a few of the participating sites(in the former Soviet republics). Furthermore, satellite data have also nowbecome available (see below).

θ2 Tau is a 140.728 d binary system with known orbital elements (Ebbig-hausen 1959, Torres, Stefanik & Latham 1997). The two components havesimilar temperatures. The primary component is evolved (A7III), while thesecondary is fainter by 1.10 mag (Peterson, Stefanik & Latham 1993) and stillon the main sequence. Both stars are situated inside the instability strip. It wasshown by Breger et al. (1989) that the dominant pulsation modes originate inthe primary component because the predicted orbital light-time effects for theprimary match the observed shifts in the light curves of up to several minutes.This conclusion agrees with the expectations from the values of the observedfrequencies (12 – 15 cd−1). These are compatible with those expected froman evolved star (i.e., the primary) and incompatible with those expected formain-sequence δ Scuti stars (i.e., the secondary star in the binary system). Wenote here that for frequency analyses, the light-time corrections in the binarysystem need to be applied to all data covering more than a few weeks.

The 2000 satellite data

During 2000 August, θ2 Tau was monitored extensively with the star camera onthe Wide-Field Infrared Explorer satellite (WIRE). This remarkable, pioneeringstudy from space led to the discovery of 12 independent frequencies of pulsationdown to the 0.5 mmag level (Poretti et al. 2002). The satellite data are freeof the 1 cd−1 aliasing often present in ground-based data, but include aliasingat the orbital frequency of 15 cd−1. The 12 detected frequencies include the5 frequencies previously found from the ground, but with different amplitudes.The difference in the effective wavelengths between the space and ground-based data can be expected to lead to different amplitudes between the studies.However, the relative strengths between the modes also changed severely, whichconfirms the existence of amplitude variability in θ2 Tau.

Poretti et al. also report a frequency of 26.19 cd−1 and regard this frequency

6 Multiple frequencies of θ2 Tau

as a spurious term caused by the length of the duty cycle. This explanationmay be too cautious: we find that some of the terrestrial data also show thisvariability with an identical frequency value. This may be due to pulsation ofthe fainter secondary. The pulsation of the secondary will be examined in detailat a future time and is consequently ignored in the rest of this paper (whichconcentrates on the main frequency region of variability.)

The 1982 – 1986 ground-based photometric data

The question arises whether these frequencies determined from the satellite dataare also present in the ground-based data. A re-examination of the old datais in order for an additional reason: The published multifrequency analyseswere performed at a time at which experimentally determined limits for theextraction of frequencies from multisite photometric data were unavailable andthe statistical criteria for the acceptance or rejection of additional modes wereless developed. Inspection of Figs. 3 and 4 in Breger et al. (1989) confirmsthat the published five-frequency solution does remove almost all the power inthe power spectra. Could there exist additional statistically significant peaks?

One of the most important questions in the examination of multiperiodicityconcerns the decision as to which of the detected peaks in the power spectrumcan be regarded as variability intrinsic to the star. Due to the presence ofnonrandom errors in photometric observations and because of observing gaps,the predictions of standard statistical false-alarm tests give answers which areconsidered by us to be overly optimistic. In a previous paper (Breger et al.1993) we have argued that a ratio of amplitude signal/noise = 4.0 provides auseful criterion for judging the reality of a peak. This corresponds to a powersignal/noise ratio of 12.6. Subsequent analyses comparing independent datasets have confirmed that this criterion is an excellent predictor of intrinsic vs.possible noise peaks, as long as it is not applied to very small data sets or atlow frequencies, where the errors of measurement are far from random. In thepresent study, the noise was calculated by averaging the amplitudes (oversam-pled by a factor of 20) over 5 cd−1 regions centered around the frequency underconsideration.

The following data are available: 1982: 10 nights, 1983: 27 nights (somemultisite), 1985: 3 nights, 1986: 17 nights (many multisite).

New pulsation frequency analyses of the available data in various annual andmultiyear combinations were performed with a package of computer programswith single-frequency and multiple-frequency techniques (programs PERIOD,Breger 1990, PERIOD98, Sperl 1998). These programs utilize Fourier as wellas multiple-least-squares algorithms. The latter technique fits a number ofsimultaneous sinusoidal variations in the magnitude domain and does not rely

M. Breger 7

on prewhitening. For the purposes of presentation and initial searches, however,prewhitening is required if the low-amplitude modes are to be seen. Therefore,in the presentation of the results (see below), the various power spectra arepresented as a series of panels, each with additional frequencies removed relativeto the panel above.

The results of the multiperiodicity analyses of the 1982–1986 data can besummarized as follows:

(i) Little additional information beyond the published five-frequency solutioncan be extracted out of the 1982/1983 data.

(ii) Considerable more information is available in the 1986 November datadue to the multisite nature and the extremely high accuracy of the data.

(iii) Adding the three nights from 1985 (Kovacs & Paparo 1989) to the 1986data does not lower the noise level in the power spectrum of the combined datanor improve the significance level of the detected frequencies.

(iv) Due to the different quality of the annual data sets and possible ampli-tude variability, the combined 1982–1986 solution shows higher noise than the1986 data alone.

We therefore select the 1986 data (only) for a more detailed re-analysis.

Multiple frequencies present in the 1986 photometric data

During 1986 November, coordinated photoelectric measurements of the starθ2 Tau were obtained at four observatories on three continents. The cam-paign represented the 3rd campaign of the Delta Scuti Network. The followingtelescopes were used:

(i) the 0.6 meter telescope of Sierra Nevada Observatory, Spain (observerR. Garrido),

(ii) the 0.6 meter reflector of Xinglong Station of Beijing Observatory, China(observers Huang Lin, Jiang Shi-yang and Guo Zi-he),

(iii) the 0.9 meter telescope of McDonald Observatory, Texas, USA (ob-server M. Frueh)

(iv) the 0.5 meter reflector at Piszkesteto, the mountain station of KonkolyObservatory, Hungary (observer M. Paparo).

Photomultiplier detectors were used together with V or Stromgren y filters.The spectral window of the data is very clean, because the measurements wereobtained on three continents. In particular, the 1 c/d aliasing, common inground-based measurements, is quite small (see Fig. 1).

The power spectrum of the 1986 θ2 Tau data was computed from frequencyvalues of zero to the Nyquist frequency. Here we have already applied the orbitallight-time corrections for the primary, although this correction is not critical forthe 21 d duration of the observations. The highest power levels of the stellar


0

20

40

f3

f2

f1Ground-baseddata of θ2 Tau (1986)

0

1

-3 -2 -1 0 1 2 3

Spectral Window

10 11 12 13 14 15 16

0

2

4

f4

Frequency in cycles per day

Pow

er in

mill

imag

2

Data - 3f(3 frequencies prewhitened)

Figure 1: Power spectra of the 1986 measurements of θ2 Tau. The top panel showsthe spectral window, while the bottom panel presents the results after prewhiteningthe three dominant frequencies found in the middle panel.

M. Breger 9

0.0

0.5

1.0 f7

f6f5Data - 4f

10 11 12 13 14 15 16

0.0

0.2

Significance level

Frequency in cycles per day

Pow

er in

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imag

2

Data - 10f

0.0

0.2

0.4

0.6

f9f8Data - 7f

0.0

0.2

0.4

f10Data - 9f

Figure 2: Power spectrum of the 1986 measurements of θ2 Tau after successiveprewhitening of the previously detected frequencies. The four panels show the resultsafter prewhitening 4, 7, 9 and 10 frequencies, f1 to f10, determined in previous panels.The curve in the bottom panel represents the statistical significance limit. Peaksbelow the limit are rejected.


Table 1: The frequency spectrum of θ2 Tau

Ground-based (1986) WIRE (2000)Frequency Amplitude Frequency Amplitude

cd−1 millimag S/N cd−1 millimag

f1 13.23 6.5 44 13.23 2.5f2 13.69 5.0 33 13.70 6.5f3 13.48 2.5 17 13.49 1.3f4 14.32 2.3 15 14.32 3.2f5 12.17 1.2 8.2 12.13 0.6f6 14.61 1.1 7.5 14.61 0.7f7 12.84 1.0 6.9 12.83 1.5f8 11.74 0.8 5.7 11.73 0.6

- - 11.77 1.5f9 12.38 0.8 5.4 12.40 0.8f10 13.81 0.7 4.5 - -

- - 10.86 1.1- - 12.70 0.7

data are found in the 10 to 16 cd−1 region. Since this is also the frequencyrange in which the frequencies from the satellite photometry were detected, weconcentrate on this region. Fig. 1 also shows that the four dominant frequenciesare found at 13.23, 13.69, 13.48 and 14.32 cd−1. The four modes are old friendsand were already found in previous analyses.

Fig. 2 shows the power spectra after the dominant four frequencies wereprewhitened through a simultaneous four-frequency least-squares optimizationto the data. These solutions optimize the frequency values, amplitudes, phasesof ten sinusoids and determine the overall zero-point. The analysis was repeatedafter prewhitening multifrequency solutions containing more frequencies. Alto-gether, 10 frequencies exceeding the significance limits could be detected. Forthe five frequencies known to high precision from the previous Delta Scuti Net-work campaigns, we have used the previous frequency values.

The adopted frequencies and amplitudes are shown in Table 1. The newten-frequency solution fits the observed data well and leads to residuals of only±2.0 mmag per single observation.

M. Breger 11

Comparison between the ground-based and satellite results

The re-analysis of the 1986 ground-based photometry has increased the numberof frequencies from 5 to 10. Table 1 shows the excellent agreement between theresults of the ground-based and satellite data sets: 9 frequencies are identical.

Two frequencies found in both data sets deserve additional comments:(i) The values determined for f5 are 12.17 and 12.13 cd−1, respectively. The

difference of 0.04 cd−1 is not significant, since both data sets are ∼ 20 d long(i.e., 1/T ∼ 0.05 cd−1).

(ii) The WIRE satellite photometry led to the detection of a close frequencypair at 11.73 and 11.77 cd−1. The ground-based data only reveals only a singlemode, f8, at 11.74 cd−1. Without additional data, we are unable to resolve theproblem. Although the frequency pair is near the limit of frequency resolution,one cannot automatically reject the result without additional tests (e.g., see thediscussion on close frequencies in δ Scuti stars by Breger & Bischof 2002). Itis conceivable that due to an accidentally favorable phasing of the two modesduring one of the two data sets, the pair was detected in only that data set.Amplitude variability of one of the two modes in the pair is also a possibleexplanation.

There exist three other frequencies, which are found at statistically signifi-cant levels in only of the two data sets:

(i) The 1986 data reveals an additional mode at 13.81 cd−1, which has notbeen seen before. The power spectrum of the WIRE residuals shows a peak at13.83 cd−1 (see Fig. 6 of Poretti et al. 2002) and is therefore probably alsopresent in that data set.

(ii) The mode at 12.70 cd−1 found by WIRE may also be present in the1986 ground-based data. A peak is seen at that value, but below the level ofsignificance. We have tested the possibility that the small amount of 1 cd−1

aliasing with the peak at 11.74 cd−1 might affect the amplitude. Multifrequencysolutions with both or even three frequencies (11.73, 11.77 and 12.70 cd−1)fail to raise the amplitude significantly.

(iii) The mode at 10.86 cd−1 found by WIRE is not present in the 1986data, although it is near a small cluster of power in the residuals (see bottompanel of Fig. 2).

Conclusion

The re-analysis of the previously published photometry obtained from observa-tories situated on the ground leads to excellent agreement with the results foundby the WIRE satellite: 9 frequencies are detected independently in both datasets at a high level of statistical significance. The 9 modes show considerable


amplitude variability between 1986 and 2000.Two additional modes are presentwith statistically significant amplitudes in one data set and definite peaks inthe power spectrum of the other data set. The WIRE mode at 10.86 cd−1 wasnot seen in 1986. Amplitude variability is the most probable explanation.

Acknowledgments. This investigation has been supported by the AustrianFonds zur Forderung der wissenschaftlichen Forschung under project numberP14546-PHY. It is a pleasure to acknowledge helpful discussions with EnnioPoretti.

References

Breger, M. 1990, Communication in Asteroseismology (Vienna), 20, 1Breger, M. 1993, in ’Stellar Photometry - Current Techniques and FutureDevelopments’, ed. Butler, C. J., Elliott, I., Cambridge University Press, 106Breger, M. 2000, ASP Conf. Ser., 210, 1Breger, M., Bischof, K. 2002, A&A, in pressBreger, M., Lin, H., Jiang, S.-Y., et al. 1987, A&A 175, 117Breger, M., Garrido, R., Lin, H., et al. 1989, A&A 214, 209Breger, M., Stich, J., Garrido, R., et al. 1993, A&A 271, 482Breger, M., Handler, G., Garrido, R., et al. 1999, A&A 349, 225Breger, M., Garrido, R., Handler, G., et al. 2002, MNRAS 329, 531Duerbeck, H. W. 1978, IBVS, 1412, 1Ebbighausen, E. G. 1959, Pub. Dom. Astrophys. Obs. 11, 235Horan, S. 1977, IBVS 1232, 1Horan, S. 1979, AJ 84, 1770Kennelly, E. J., Walker, G. A. H. 1996, PASP 108, 327Kovacs, G., Paparo, M. 1989, MNRAS 237, 201Peterson, D. M., Stefanik, R. P., Latham, D. W. 1993, AJ 105, 2260Poretti, E., Buzasi, D., Laher, R., et al. 2002, A&A 382, 157Sperl, M. 1998, Communications in Asteroseismology (Vienna) 111, 1Torres, G., Stefanik, R. P., Latham, D. W. 1997, ApJ 485, 167


Vol. 141, 2002

PMS stars as COROT additional targets

M. Marconi1, F. Palla2, V. Ripepi1

1Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy2Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy

Abstract

The importance of pre-Main Sequence (PMS) δ Scuti studies is discussed andrecent developments both from the theoretical and observational point of vieware reviewed. The open problems in the current status of knowledge of theseyoung pulsators are mainly connected to the limitations of short time baselineground observations. COROT could definitely help to solve these problems byallowing accurate and continuous observations. A list of possible PMS δ Scuticandidates for a COROT additional program has been identified and exploratoryground-based observations are planned.

Introduction

PMS stars with masses M ≥ 1.5M¯, called Herbig Ae/Be stars, cross thepulsation instability strip during their contraction toward the main sequence.The estimated crossing times range from ∼ 0.05 τKH (1.5M¯) to ∼ 0.1 τKH

(4M¯), where τKH is the Kelvin-Helmholtz timescale. In spite of the relativelyshort crossing time, a number of Herbig stars have the appropriate values ofcolors to fall within the instability strip boundaries of the well known evolvedvariable stars.

The existence of pulsating stars among intermediate Herbig stars was origi-nally suggested by Breger (1972) who discovered two PMS pulsator candidatesin the young open cluster NGC 2264. This initial finding was confirmed by sub-sequent observations of a δ Scuti-like pulsation in the Herbig Ae stars HR5999(Kurtz & Marang 1995) and HD104237 (Donati et al. 1997).

This evidence stimulated the first theoretical investigation of the PMS in-stability strip, based on nonlinear convective hydrodynamical models (Marconi

14 PMS stars as COROT additional targets

& Palla 1998). As a result, the topology of the PMS instability strip for thefirst three radial modes was identified and a list of possible PMS pulsatingcandidates was provided on the basis of spectral types.

New observational studies were then devoted to the search for δ Scuti-typephotometric variations with periods of minutes to several hours and amplitudesless then few tenth of magnitudes among Herbig stars inside or close to thetheoretical instability boundaries.

Kurtz & Muller (1999) reobserved HD104237 and confirmed its photomet-ric variability; Marconi et al. (2000) identified two new PMS pulsating stars,namely HD35929 and V351 Ori; Pigulski et al. (2000) discovered the pulsatingnature of two members (BL50 and HP57) of NGC 6823; Kurtz & Catala (2001)confirmed the δ Scuti pulsation and periodicity of HR5999; Kurtz & Muller(2001) identified the PMS δ Scuti star HD142666; Marconi et al. (2001) pro-vided new observations and frequency information on V351Ori; finally, Pinheiroet al. (2001) observed the pulsational variation of the luminosity of V346 Ori.

In order to properly understand the nature and intrinsic properties of PMSδ Scuti stars, an extensive comparison of the observed pulsation propertieswith theoretical predictions is required (e.g. Marconi et al. 2000, 2001). Inparticular, the comparison between empirical and theoretical periods and period-ratios is expected to provide important constraints on stellar mass, whereasthe comparison of the position in the color-magnitude diagram suggested byobservations and/or the pulsational analysis with PMS and post-MS tracks mayallow to constrain the evolutionary state.

Position of PMS δ Scuti stars in the HR diagram

The main characteristics, including the observed frequencies, of the ten knownor suspected δ Scuti stars are reported in Table 1. For most of these objects, thereported periodicities are affected by the uncertainty due to the 1 day alias, sothat they may not represent the actual periods. Moreover, for some objects theobservations are too scarce and the errors too large to allow accurate frequencydeterminations.

However, let’s assume that the published frequencies are indeed correct andcompare them with the predictions of linear non adiabatic pulsation models(see Marconi et al. 2000, 2001 and references therein). Such a comparisonallows us to constrain the position of observed stars in the HR diagram, asshown in Fig. 1. In fact, at fixed solar composition, the mass, luminosity, andeffective temperature are varied in order to simultaneously satisfy the observedperiodicities and the PMS evolutionary constraint.

It is worth noting that the solution of such a fitting procedure is unique

M. Marconi, F. Palla and V. Ripepi 15

Table 1: Known or suspected PMS δ Scuti stars.Star F1 F2 V (mag) Sp. Type

V351Ori 15.49±0.23 11.89±0.24 8.9 A7V346Ori 34.2±4.9 21.2±3.8 10.1 A5HD104237 33.0±0.2 8.1 A5HR5999 4.81±0.01 7.0 A7HP57 12.7256±0.0002 15.5244±0.0003 14.6BL50 13.9175±0.0005 9.8878±0.0009 14.5

V588 Mon 9.09±0.82 9.75 A7V599 Mon 8.06±0.39 10.3 F2HD142666 21.43±3.00 8.8 A8HD35929 5.10±0.13 8.1 A5

Figure 1: Position in the HR diagram of observed PMS δ Scuti stars, as predicted onthe basis of linear nonadiabatic computations. The PMS evolutionary tracks by Palla& Stahler 1993 and the nonlinear instability strip by Marconi & Palla (1998), for thethree lowest radial modes, are shown for comparison.

only for candidates for which several periodicities are available from observa-tions (V351 Ori, V346Ori, HP57, BL50). In fact, two relations are needed to


Table 2: The position in the HR diagram and the pulsation mode(s) of PMS δScuti stars. The modes are indicated with F (Fundamental), FO (First Overtone),SO (Second Overtone), TO (Third Overtone), FoO (Fourth Overtone), FiO (FifthOvertone).

Star M/M¯ log L/L¯ log Te Source mode(s)V351Ori 1.8 1.142 3.866 Marconi et al. 2001 F,FOV346Ori 1.5 0.74 3.863 Pinheiro et al. 2001 F,SOHD104237 2.2 1.5 3.93 van den Ancker 1998 FiOHR5999 4.0 2.12 3.845 Marconi & Palla 1998 SOHP57 2.0 1.25 3.857 this paper FO/SOBL50 2.5 1.6 3.86 this paper SO/FoO

V588 Mon 3.5 2.05 3.913 this paper TOV599 Mon 2.5 1.51 3.84 this paper FOHD142666 1.7 1.03 3.88 Natta et al. 1997 FOHD35929 3.4 1.92 3.857 Marconi et al. 2000 FOHD35929 3.8 2.06 3.851 Marconi et al. 2000 SO

properly disentangle the luminosity and effective temperature contributions toperiods, the mass being determined via comparison with the evolutionary tracks.In case of a single observed periodicity, the comparison with the nonlinear in-stability strip (e.g. for HR5999, see Marconi & Palla 1998) and/or independentinformation on the intrinsic parameters (e.g. for HD104237 and HD142666)are taken into account and used to remove degeneracies. The predicted pulsa-tion modes for all the selected candidates are reported in Table 2 together withreferences for the luminosity and effective temperature values. For HD35929,the solutions found by Marconi et al. (2000) are reported (see also Fig. 1).

We also notice that a certain ambiguity on the evolutionary state holds forstars close to the MS (e.g. V351 Ori). In this region of the HR diagram thePMS and post-MS tracks are not well separated at fixed stellar masses. Insuch cases a nonradial pulsation analysis could help solve the problem, as nicelydiscussed by Suran et al. (2001).

As a final comment on Fig. 1, it is interesting to note that only two stars(V588 Mon and HD104237) bluer than the second overtone blue edge of thetheoretical instability strip are actually predicted to pulsate in overtones higherthan the second one.

How COROT could help

The 1 day alias problem affecting most of the observed PMS δ Scuti starscould be easily removed with continuous observations. If these observationsare made from space, the additional uncertainty due to weather conditions is


Table 3: PMS δ Scuti candidates for COROT observations.Star RA(J2000) Dec(J2000) V Sp. Type

RNO63 06 07 52.41 -05 16 04.4 13.3 F6eLKH338 06 10 47.05 -06 12 47.9 15.1 F2eLKH339 06 10 54.43 -06 14 39.4 13.6 F2eV588Mon 06 39 05.90 09 41 03.4 9.75 A7V589Mon 06 39 28.45 06 42 04.8 10.3 F2VSB2 06 39 41.55 09 34 40.2 13.33 F7W121 06 40 56.50 09 54 10.4 10.8 F8e

V360Mon 06 41 06.18 09 36 22.9 13.29 F8eVV Ser 18 28 47.96 00 08 39.7 11.87 B,AePar21 19 29 00.81 09 38 38.7 14.16 A5

also removed. In the case of COROT, a high photometric precision is alsoforeseen, such that accurate period measurements and the identification of lowamplitude pulsations will be possible.

PMS δ Scuti candidates for COROT observations

According to the adopted Scenario 4 of the COROT (Center=102.5 deg, i.e.RA=6h 50min, see Minutes of the 6th Scientific Committee) mission, the twopossible fields in the Galactic anticenter and center directions are those reportedin Figs. 2 and 3. On the basis of these fields, we have identified a list of PMScandidates (open circles in Figs. 2 and 3) by searching in the Herbig catalogue(The, Winter & Perez 1994). The coordinates, V-magnitudes, and spectraltypes of the selected candidates are listed in Table 3.

Unfortunately, none of the PMS candidates is located close to the maintargets of the asteroseismological project (filled circles in Figs. 2 and 3). Forthis reason, we propose these objects as the targets of a COROT additionalprogram. The first three objects of the list (RNO63, LKH338, LKH339) areso close to each other that they can be observed within a single COROT field.The fourth and the fifth stars are the two PMS δ Scuti stars already discoveredby Breger (1972) in NGC2264 (also shown in the figure). We notice thatthese two stars are the brightest ones in the list. The three following objects(VSB2, W121, V360 Mon) are again observable within a single field. Most ofthese candidates are too faint (V>9 mag) to be observed in the Astroseismologyprogram configuration and too bright (V<16.5 mag) for the Exoplanet programsetup. However, fainter magnitudes than V=9 mag are probably measurable inthe Astroseismological configuration even by loosing a bit in precision (1 partover 10,000 is enough for our goals).


Figure 2: Position of PMS δ Scuti candidates (open circles) in the anticenter directionCOROT field. The main targets of the asteroseismological project (filled circles) areshown for comparison.

Figure 3: As in Fig. 2 but in the Galactic center direction

Up to now, only V588 Mon and V589 Mon are known to be δ Scuti-likevariable stars, but the search for variability in the other candidates by means ofground based observations is planned.


Conclusions

With the recent development of both observational and theoretical studies, PMSδ Scuti stars have become an important tool for understanding the structureand the evolutionary properties of young intermediate-mass stars. The numberof known or suspected pulsating PMS objects has significantly increased duringthe last few years, but for most of them the detected periodicities are quiteuncertain due to alias problems and/or poor data number. Continuous andaccurate observations from space, as those expected with the advent of theCOROT mission, would definitely overcome these problems. In this paper, wehave proposed PMS δ Scuti stars as the targets of a COROT additional programand provided a list of suitable candidates.

Acknowledgments. We kindly thank the COROT working group on PMSδ Scuti stars: C. Catala, J.M. Alcala, E. Antonello, S. Bernabei, M. Breger,E. Covino, D.F.M. Folha, M.J. Goupil, L. Mantegazza, E. Paunzen, F.J.G.Pinheiro, E. Poretti, W. Weiss, F. Zerbi, K. Zwintz.

References

Breger, M. 1972, ApJ 171, 539Donati, J.-F., Semel, M., Carter, B. D., Rees, D. E., Cameron, A. C. 1997,

MNRAS 291, 658Kurtz, D. W., Catala, C. 2001, A&A 369, 981Kurtz, D. W., Marang, F. 1995, MNRAS 276 191Kurtz, D. W., Muller, M. 1999, MNRAS 310, 1071Kurtz, D. W., Muller, M. 2001, MNRAS 325, 1341Marconi, M., Palla, F. 1998, ApJ 507, L141Pigulski, A., KoÃlaczkowski, Z., Kopacki, G. 2000a, AcA 50, 113Marconi, M., Ripepi, V., Alcala, J. M., Covino, E., Palla, F., Terranegra, L. 2000,

A&A 355, L35Marconi, M., Ripepi, V., Bernabei, S., Palla, F., Alcala, J. M., Covino, E.,

Terranegra, L. 2001, A&A 372, L21Natta, A., Grinin, V. P., Mannings, V., Ungerechts, H. 1997, ApJ 491, 885Palla, F., Stahler S. W. 1993, ApJ 418, 414Pinheiro, F. J. G., Marconi, M., Ripepi, V., Folha, D., Palla, F. 2001,

IAU Coll. 185, in pressSuran, M., Goupil, M., Baglin, A., Lebreton, Y., Catala, C. 2001, A&A 372, 233The, P. S., de Winter, D., Perez, M. R. 1994, A&AS 104, 315van den Ancker, M. E., The, P. S., de Winter, D. 1996, A&A 309, 809


Vol. 141, 2002

The study of pulsating stars from the COROTexoplanet field data

C. Aerts

Instituut voor Sterrenkunde, Catholic University of Leuven, Belgium

Abstract

In this paper we present our proposal to search for periodically variable starsin the exoplanet field data. In order to do so one first has to perform a quasi-automated frequency search in the data. Once the periodically variable starsare found, they have to be classified, e.g. by means of a statistical schemeanaloguous to the one we developed for the classification of new B-type variablesdiscovered from the HIPPARCOS data.

After the classification of the variable stars, we plan to study the β Cep starsand the slowly pulsating B stars (SPBs) with the goal to derive constraints ontheir internal structure.

Goal of the project

In this project we propose to make full use of the COROT exoplanet field datafor asteroseismology. The observation strategy adopted by the planet hunters isideally suited for asteroseismology of some classes of pulsators, i.e. this project isa free by-product of the search for planets within the COROT framework. Theindividual integration times of 32 seconds for the CCD frames of the exoplanetfield will in any case result in a time sampling of the order of minutes during5 consecutive months. This is largely sufficient to derive very accurately thepulsation frequencies for several types of κ driven modes in main-sequence stars,such as the β Cep stars, the slowly pulsating B stars (hereafter termed SPBs),the γ Doradus stars and most δ Scuti stars. The expected photometric accuracywill be at least an order of magnitude higher than the one of current ground-based datasets of such types of stars.

COROT is by far better suited to perform our project than MOST andMONS. MOST will observe only a few very bright stars, while the MONS

C. Aerts 21

Field Monitor will gather data for a few thousand stars, which will be observedduring one month. COROT is therefore the only mission resulting in data with atotal time base significantly longer than a month. Particularly, main-sequencegravity-mode pulsators, i.e. γ Doradus stars and SPBs, cannot be studies byMOST and MONS, as they have beat periods of several months or even years.

The concrete goal of our project is twofold: 1) the search for, and classifi-cation of, new variable stars; 2) the derivation of detailed frequency spectra ofthe new variables and their physical interpretation.

Search for new variables

The discovery of new variables in the COROT exoplanet fields will be quitestraightforward in view of the excellent time sampling. Such high temporalresolution is beyond comparison with e.g. the one of the HIPPARCOS mis-sion. The long time base of the data of the latter mission already allowed thediscovery of thousands of new periodically variable stars, despite the relativelypoor sampling (Eyer, 1998). This led to the publication of the HIPPARCOScatalogue of periodic variable stars (van Leeuwen et al. 1997, Grenon et al.1997).

A considerable amount of new variables will be found among the 30 000stars which will all be monitored during 5 months by COROT. The applica-tion of classical period search algorithms will result in the detection of manynew periodically variable stars of different kinds. In view of the high-temporalresolution and the high duty cycle, Fourier analysis will suffice to perform thefrequency search.

Classification of the new variables: discriminant analysis

The newly discovered periodic variables need to be classified, i.e. the origin oftheir variability has to be decided upon. Waelkens et al. (1998) have developed aclassification scheme for the new HIPPARCOS B-type variables. Their methodis based upon multivariate discriminant analysis. With this method, one makesuse of different known parameters of the stars. One of these parameters isof course the frequency. Besides this quantity, Waelkens et al. (1998) usedthe Geneva parameters X, Y, Z. These parameters are reddening-free quantitiesderived from the Geneva colours. Since the COROT exoplanet data will containthree colours, the method developed by Waelkens et al. is also applicable to theCOROT data after minor modification. It was also already successfully appliedby Aerts et al. (1998) in their search for new γ Doradus candidates from theHIPPARCOS data.

22 The study of pulsating stars from the COROT exoplanet field data

The essential ingredients of discriminant analysis are the following: In gen-eral, multivariate classification schemes use the knowlegde of stellar parametersin an n-dimensional space. The classification of new variables is best done intwo steps: the assignment of a new variable to a known class according to adistance measure and subsequently a check through bivariate plots. Discrim-inant analysis is only possible when prototypes of classes are available, suchthat a “definition” of a known class can be formulated. The unknown ob-jects will then be assigned to one of these so-called calibration classes. Thisassignment is obtained by the determination of discriminating axes in the mul-tidimensional space, in such a way that optimal separation of the predefinedclasses is attained. For each star the Mahalanobis or generalised distance tothe discriminating axes is used for assignment to one of the definition classes.However, stars with a relatively large Mahalanobis distance still might have adifferent origin of variability than those of the class to which they were as-signed. A definite classification is then made by means of bivariate plots withinthe n-dimensional parameter space. The stars with a large Mahalanobis dis-tance having also another position in bivariate plots compared to the calibrationstars are probably of a different nature and cannot be assigned to one of thecalibration classes. A typical example could be a Be star, a CP star or a su-pergiant. For these stars it is often not possible to provide a clear definition ofthe class as there are e.g. very different timescales in the variability of Be stars,there are supergiants with and without microvariations, etc. It is better not touse them as calibration classes. All new variables of such kind will then at firstbe assigned to a wrong class but their different nature will be derived from thelarge Mahalanobis distance and/or a deviating position in the bivariate plots.

Before applying the discriminant analysis one needs to choose the parame-ters to be used for the definition of the classes. In the framework of our proposalthese are the frequency and the three COROT colours. This implies that wehave to determine the COROT colours for the known variables of the differenttypes of pulsators, in order to find the definition of each class.

Interpretation of the variability

A next step in our project consists of the detailed interpretation of the frequen-cies in terms of asteroseismology. In order for this to be possible, we are obligedto limit ourselves to the multiperiodic variables with correct mode identification.The latter remains a serious problem for κ driven modes outside the asymptoticregime. As we will be dealing with faint stars having long beat periods, spec-troscopic mode identification methods will not be of any help. The best wayto identify modes from frequency spectra is in that circumstance the detectionof rotationally- or magnetically-induced frequency multiplets.

C. Aerts 23

Figure 1: Frequency analysis of the simulated signal for the typical β Cep star with atime span of 20 days (top) and of 5 months (bottom). The dashed lines indicate theinput frequencies.

We have performed some preliminary simulations in order to derive the ca-pabilities of COROT with respect to the detection of multiple periods. In viewof our expertise we have limited the simulation study to pulsating B stars, i.e.β Cep stars and SPBs. We have simulated a periodic signal typical for a β Cepstar and an SPB respectively. For none of these stars the mode selection mech-anism is understood and we have no idea how many modes are excited. TheWIRE data of β Crucis have clearly indicated that more modes are excited thanthought up to now from ground-based photometry in this β Cep star (Cuyperset al. 2002). This is also the case for the δ Scuti star θ2 Tauri (Poretti et al.2002). Taking these recent results into account we have selected 10 frequenciesout of the pool of observed frequencies for the two classes of stars for our simu-lation. For the prototypical β Cep star it concerns frequencies between 3 and 6c d−1 and for the SPB between 0.3 and 0.8 c d−1. We have included observeddoublet and triplet frequencies. The amplitudes were taken between 50µmagand 20mmag, which is the maximum amplitude observed for such stars. Nonoise was added at this stage.

24 The study of pulsating stars from the COROT exoplanet field data

Figure 2: Frequency analysis of the simulated signal for the typical SPB with a timespan of 20 days (top) and of 5 months (bottom). The dashed lines indicate the inputfrequencies.

We generated light curves with the following two different time samplings :

1. every 3 minutes during 20 days,

2. every 20 minutes during 5 months.

Such sampling is quite conservative as COROT should do better.The Fourier spectra for the simulated signals of the β Cep star, respectively

SPB, are shown in Figs. 1 and 2. We are particularly interested to see whetherCOROT would be able to result in the detection of the multiplets. This willnot be the case for the data obtained during the exploratory phases, as can bederived from the upper panels of Figs. 1 and 2. The runs of 5 months do resulteasily in the derivation of the multiplet frequencies of the β Cep star, which isvery important. This will imply that the COROT data will in principle allowus to derive the internal rotation law in stars that will end their lives as type IIsupernovae. Most of the close frequencies of the SPB are also recovered, albeitnot all of them. This corresponds to the well-known fact that the beat periodsof such stars can be of the order of a year. At least 7 of the 10 frequencies areeasily recovered, though, in our exercise.

C. Aerts 25

Of course, our very basic simulations have to be redone, by convolving thegenerated signal with a realistic noise-budget valid for COROT. This will bedone in a forthcoming study. However, the simple exercise allows us to derivethe following conclusions :

• the time span of the COROT exploratory programme is too short todisentangle the frequencies of pulsating B stars;

• rotational splittings will easily be found for β Cep stars in the SISMO coreprogramme, as the sampling is much better than the one we have takenin this study; the core programme will also allow the detection of a verylarge fraction of the excited gravity modes of SPBs;

• the exoplanet data are ideally suited for detecting the larger-amplitudemodes of β Cep stars and of SPBs.

All the conclusions for the SPB-type pulsations are also valid for the gravitymodes in γ Doradus stars. We did not include such stars in the simulation asthe observational inventory available for them does not reach the same level ofcompleteness as the ones of the β Cep stars and SPBs.

Future work

We have already stressed the potential of the COROT exoplanet data for as-teroseismology of massive stars at previous COROT meetings. With our basicstudy provided here, we have shown that our goal is indeed feasible. In the nearfuture we will perform a more extensive simulation study with a realistic noisebudget. We will particularly concentrate on the derivation of the detection limitof modes for the exoplanet data. One of the other main goals of this futuresimulation study is to derive the optimal rebinning for the analysis of gravitymodes in SPBs and γ Doradus stars.

References

Aerts, C., Eyer, L., Kestens, E. 1998, A&A 337, 790Cuypers, J., Aerts., C., Buzasi, D., Catanzarite, J., Conrow, T., Laher, R. 2002, in

ASP Conf. Ser., Vol. 259, Radial and Nonradial Pulsations as Probes of StellarPhysics, eds. C. Aerts, T.R. Bedding and J. Christensen-Dalsgaard,(San Francisco ASP), in press

Eyer, L. 1998, PhD Thesis, Geneva ObservatoryGrenon, M. et al. 1997, ESA SP-1200, Volume 12Poretti, E., Buzasi, D., Laher, R., Catanzarite, J., Conrow, T. 2002, A&A,

in press (astro-ph/0111361)van Leeuwen, F. et al. 1997, ESA SP-1200, Volume 11Waelkens, C., Aerts, C., Kestens, E., Grenon, M., Eyer, L. 1998, A&A 330, 215


Vol. 141, 2002

10 Aql, a new target for COROT

L. Bigot1, W. W. Weiss2

1Observatoire de la Cote d’Azur, BP 4229, Nice, France.2Institut fur Astronomie, Univ. Wien, Turkenschanzstr. 17, 1180 Wien, Austria.

Abstract

The satellite COROT (e.g., Baglin & Foing 1999) will be devoted to the seismicinvestigation of stars. It will provide new insights into our knowledge of stellarstructure. Among the variable stars, the group of roAp stars is unique. Indeed,the oscillations of these stars are dominated by the effects of magnetic fields,which are typically three orders of a magnitude higher than in the Sun. Thestudy of the oscillations in roAp stars provides a chance to test and to improveour knowledge of the structure of these extremely peculiar stars. The spiritof this article is to argue in favor of 10 Aql (HD 176232, HR 7167) as aninteresting target for COROT. We then present basic aspects of roAp stars andin particular recent theoretical developments concerning the magnetic field androtation effects on the mode properties. We also propose an interpretation ofthe frequencies already observed for this star.

The Ap and roAp stars

The group of Ap stars is one of the most studied. They are Main Sequencestars of about 2 M¯ but with spectra showing abnormal lines of some elements.These peculiarities were first discovered more than a century ago and were thefirst application of spectroscopy to stellar astrophysics. During the twentiethcentury these stars indeed revealed strongly abnormal chemical composition,with spectral lines of some rare elements enhanced by several order of magnitude(Morgan 1933, Adelman 1973, Preston 1974). The most abnormal lines concernthe rare elements like Europium, Chromium, Strontium (7000 < Teff < 10000)and Lithium (10000-14000 K). The elements of the iron peak are in turn of solarabundances. These elements are concentrated in some spots (and even rings) atthe surface of the star. This has been observed by Doppler imaging techniques

L. Bigot and W. W. Weiss 27

(e.g. Piskunov & Rice 1993). All these features were unexplained during thefirst part of the 20th century.

Babcock (1947) made a crucial discovery to explain the physical processesthat occur in Ap stars. Indeed, he was the first to underline a Zeeman splittingof spectral lines, proof for the presence of a strong magnetic field. The typicalstrengths of the fields present in Ap stars are of the order of kilogauss, say atleast 2 or 3 orders of magnitudes higher than the value of the global field of theSun. These magnetic fields first appeared to be dipolar. The variability of theobserved field was explained by the model of the oblique rotator (Babcock 1949,Stibbs 1950) which claimed that the axis of symmetry of the field is inclined tothe rotation axis, so that as the star rotates the observer sees different aspectsof the same field. The inclination, β, between the magnetic and rotation axesis discussed in Landstreet & Mathys (2000). They show that slowly rotatingAp stars are characterized by small values of β. There is now clear evidencefor non-dipolar components of fields in Ap stars (e.g. Landstreet 1980, Mathys1987, Landstreet 1992, Mathys & Hubrig 1997, Landolfi et al. 1998).

Recently, Hubrig et al. (2000a) showed that the magnetic field in Ap starsbecomes detectable after some time spent on the Main Sequence, roughly after30%, which indicates that this abnormal intense magnetic field may be relatedto a special stage in the life of the star.

The chemical peculiarities in Ap stars were explained by the presence ofthese huge fields. Indeed, the intense field is supposed to stabilize the externallayers of the star against turbulent mixing. In the stable upper layers, thechemical elements are then subject to the balance between the gravitationalsettling and the radiative pressure (Michaud 1970). The elements which areconcentrated in their line forming regions appear then overabundant.

Kurtz (1978) made an important and unexpected discovery in the late sev-enties. In studying the effective temperature of Przybylski’s star, he was thefirst to detect a rapid light variation of about 12 min in an Ap star. This wasclear evidence for the presence of acoustic oscillations. This discovery was un-expected because it was wrongly thought before that the huge magnetic fieldwould suppress any type of oscillations. These Ap stars are the only stars ofthe Main Sequence to show the same short periods as the Solar-like stars, i.e.from about 5 to 15 min. Kurtz (1982) named them the rapidly oscillating

Ap (roAp) stars. However, with typical amplitudes from 0.3 to about 8 mmag(Johnson B filter), the oscillations in the roAp stars are three orders of magni-tudes higher than those in the Sun. Their number has grown to 32 (Martinezet al. 2001).

From the time of their discovery these stars showed multiplets with peaksexactly separated by the rotation frequency, Ω, of the star. Kurtz (1982) thenproposed the model of the oblique pulsator which states that the axis of sym-

28 10 Aql, a new target for COROT

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DOV

PNNV

SPB

DBV

DAV

Mira

Irr

EC14026

Ceph

Solar like

δ Scuti

RR Lyrae

γ

β Ceph

roAp

Log T

-2

0

2

4

6

5.0 4.5 4.0 3.5

Doradus

eff

Figure 1: Representation of the Hertzsprung-Russell diagram for variable stars. TheroAp stars are located on the Main Sequence at the intersection with the δ Scutiinstability strip. From Christensen-Dalsgaard & Dziembowski (2000).

metry of the mode is aligned with the magnetic axis of the star, i.e. is inclinedfrom the rotation axis. Then, exactly as in the model of the oblique rotator,the observer sees different aspects of the same mode during the rotation of thestar. There is a double light variation, one with a short time scale due to theoscillations (few minutes) and one longer due to the rotation of the star (fewdays). In the frequency domain, the modulation by rotation makes each modeof degree ` to appear as a multiplet with (2` + 1) components separated byexactly the rotation frequency. This fact has been confirmed for several roApstars by comparison with the rotation periods obtained from mean light vari-ations due the spots (e.g. Kurtz & Marang 1988, Kurtz et al. 1990, 1996)and is the best evidence in favor of the model of the oblique pulsator. An-other property of these oscillations is a phase jump by π radians exactly at the


amplitude minima. This aspect is evidence for dipole (` = 1) modes. Thisvariation indeed corresponds to the fact that the observer sees alternatively thetwo hemispheres of the mode with opposite phases (one in contraction, one inexpansion).

The source of these oscillations is still not clearly established. The shortperiods of the pulsations could lead us toward the stochastic excitation due tothe turbulence in the outer layers of the stars, as for the Sun. However, thelarge amplitudes (∼ mmag) cannot be explain by this process. Dziembowski &Goode (1996) show that for large number of nodes, the oscillations are drivenby the κ-mechanism of the hydrogen ionization zone, and not by the He II zoneas in the δ Scuti stars. The frontier between the roAp stars and the Ap starswhich do not show rapid light variations, the non oscillating Ap (noAp) stars, isnot clear. Indeed, the two classes of stars have similar magnetic field strengths,similar color indexes, etc. However, Hubrig et al. (2000b) point out a significantdifference in their masses, which are somewhat larger in the noAp stars. Thismay have important consequences in the excitation mechanism. Balmforthet al. (2000) proposed a kappa-mechanism depending on the latitude, as aconsequence of the suppression of convective turbulence at the magnetic poles.They show that the excited modes can be in some cases aligned with themagnetic field.

Reviews on roAp stars are available in Weiss (1986), Unno et al. (1989),Matthews (1991) and Kurtz (1990, 2000).

A model for roAp star pulsation

The model generally accepted to interpret pulsations in roAp stars is the modelof the oblique pulsator (Kurtz 1982, Dziembowski & Goode 1985, Kurtz &Shibahashi 1986, Bigot & Dziembowski 2002). We are now going to describethe basic aspects of this model and its consequences on the interpretation ofthe seismic data. We consider only the main component of the magnetic field,say the dipole one. The non-perturbative treatment of the effects of a dipolemagnetic field on acoustic modes has been done by Dziembowski & Goode(1996), Bigot et al. (2000) and Cunha & Gough (2000). These studies showshifts of frequencies of the order of several µHz for fields of about 1 kG. Thereis also a significant damping of the oscillations by dissipation of Alfvenic waves.We will ignore here this effect. In roAp stars the axis of symmetry of the mag-netic field generally differs from the axis of rotation. Therefore, their combinedeffects on acoustic modes lead to a coupling of spherical harmonics, see Fig. 2represented for dipole modes. In the context of roAp stars, only the coupling inthe azimuthal order m matters. We may then write the general displacement


Ω

Observer

B

A

ω−Ω ω ω+Ω

−1

A 1

A 0

Mode axis

β

i

Figure 2: Representation of the model of the oblique pulsator in the special case of adipole mode. This axis of symmetry of this mode generally differs from both rotationand magnetic axes. Then the inertial observer sees a variation of the aspect of thismode as the star rotates. This leads to the presence of a triplet in the spectrum.

vector as a linear combination of the (2`+ 1) unperturbed eigenvectors

~ξ =∑

m=−`

αm~ξm, (1)

with αm coefficients to be determined. This degenerate perturbation formalismwas first applied by Dziembowski & Goode (1985) in this context of roAp stars.It can be shown then that the equation of oscillation leads to the followingeigenvalue problem

∑

m=−`

αm

Ojm − ω2δjm

= 0 j = −`, ..., `, (2)

where Ojm is the projection of the sum of the rotational, Lorentz and the usualadiabatic operators on unperturbed eigenvectors. The system (2) has (2`+ 1)eigenvalues ω and (2` + 1) eigenvectors αm which are orthogonal. For therotational operator we take into account both Coriolis and centrifugal forces.The latter is the dominant effect of the rotational shift of frequency and istypically two orders of magnitude higher than the Coriolis force. This is mainlydue to the presence of large radial orders for which the modes are more sensitiveto the centrifugal force. However, the effects of the Coriolis force are essentialto keep an asymmetry in the problem and cannot be neglected. This asymmetryleads to unequal coefficients for the coupling, i.e. |αm| 6= |α−m|, see Bigot &Dziembowski (2002) for more details.


Once the solutions of equation (2) are found, one has to express them inthe reference frame of the observer in order to compare with observations. Thisreference frame is defined with the polar axis along the line-of-sight. It is wellknown (e.g. Kurtz 1982) that the fluctuations of luminosity of each eigenmodeexpressed in the observer’s system writes as the multiplet

δL

L∝

∑

m=−`

Am` cos(ω −mΩ)t, (3)

with consecutive peaks separated exactly by the rotation rate Ω. The amplitudesof the multiplet are given by

Am` = d

(`)m0(i)

∑

j=−`

αmd(`)m0(β), (4)

where d(`)jm are expressed in term of the Jacobi polynomials (e.g. Edmonds

1960), and i is the angle between the line of sight and the axis of rotation. Itcan be shown that the inequality of side peaks Am 6= A−m, often observed inroAp stars, is only due to the asymmetry introduced by the Coriolis force. TheLorentz and the centrifugal forces have a mirror symmetry that cannot lead tothis inequality.

The case of dipole modes

The case of dipole modes (` = 1) is of special importance to interpret pulsationsin roAp stars, since these modes are the most observed ones. In that case,recently Bigot & Dziembowski (2002) have shown that the effects of rotation,mainly due to centrifugal force, are sufficient to tilt the axis of symmetry of thismode from the magnetic axis. The geometrical picture of the dipole mode isthat during the pulsation cycle its axis of symmetry moves in a plane inclinedfrom both the rotation and magnetic axes. In general, the maximum of thedisplacement vector describes an ellipse in that plane. In Fig. (3) we representthe fundamental parameters of the dipole mode, say the angle δ between thenormal of the mode plane and the rotation axis, the ellipticity ψ defined asthe arctan of the ratio between the major and semi axes of the ellipse and thedimensionless frequency of the mode σ = (ω−ωmag

1 )/DΩ2+1/3, where DΩ2

is the shift due to centrifugal force and ωmag1 is the magnetic shift without

rotation for m = 1. These parameters are plotted as functions of the obliquityangle β and for different values of the quantity µ = (ωmag

0 − ωmag1 )/DΩ2,

which measures the strength of the magnetic field; |µ| increases with B. Weshow clearly on this figure that the dipole modes are very dependent on the


Figure 3: The fundamental parameters of the dipole modes σ, δ and ψ as function ofthe obliquity angle β and for different values of µ (see text). The three types of linescorrespond to the three solutions of the system (2). The magnetic effects dominateover the rotational effects on the mode if |µ| > 1. The last quantity D measuresthe alignment of the mode axis with the magnetic axis: D = 0 means alignmentand D = 1 means orthogonality with the magnetic axis. From Bigot & Dziembowski(2002).

value of β and on the magnetic strength (through µ). We see that in generalthere is no preference for alignment of the dipole axis with the magnetic axis.The reason is that in roAp stars the centrifugal effects are in general comparableto the magnetic effects of the m components of the mode, and therefore aresufficient to affect the inclination of the mode.


Amplitudes of the side lobes (` = 1)

For the moment, no rotational side lobes have been detected in 10 Aql. Thismight be due to the probable small rotational frequency Ω/2π. From v sin i <5 km s−1 (Hoffleit 1982), R = 2.42R¯, and an arbitrary assumption i = 70degwe get Ω/2π = 0.5 µHz, which is very small. That is probably the reason whywe have not yet detected the rotational multiplets in 10 Aql.

We hope that with the improved accuracy of COROT, we will resolve therotational side lobes of the modes and get important constraints on this star.With this idea, we now illustrate the effects of the magnetic field on the am-plitudes of the dipole modes. We plot in Fig. (4) the amplitudes of the tripletas functions of the parameter µ. The magnetic effects are larger than the ro-tational effects on the mode, when |µ| À 1. We also consider two differentvalues of β, the angle between the axes of the magnetic field and rotation. Fig.(4) shows that the magnetic field has a strong influence on the amplitudes ofthe triplet. For 10 Aql, we are certainly in the regime |µ| > 1. There is also animportant dependence on β. Therefore, we see that a comparison between theobserved values of the triplet and these calculations can lead to an estimate ofB and β for this star.

Analysis of the frequencies in 10 Aql

The roAp stars are excellent candidates for asteroseismology. From their pulsa-tions we can potentially estimate their radii, luminosities, mean densities, ages,magnetic fields, rotation rates, inclinations i and β. These variable stars canthen be used as tests for stellar structure models and for dynamo theories.

One of the most important criteria to select a target for an asteroseismicspace mission is the number of modes that we can expect for this star. Theshort periods of oscillations in roAp stars allow us to use the formalism of theasymptotic theory for p-modes (e.g. Tassoul 1980) to interpret their spectra.The non-magnetic and non-rotational frequencies are then given by

ν = ∆0

(

n+`

2+ ε

)

, (5)

with ε a small constant depending on the stellar structure. The fundamentalspacing ∆0 between two consecutive radial orders n and n+ 1 is defined by

∆0 =

2

∫ R

0

dr

cS

−1

∼< ρ >∼M1/2R−3/2, (6)

with cS the sound speed. This quantity has been calculated for several stellarmodels by Saio & Shibahashi (1985). They found that these values are between


Figure 4: Amplitudes of the triplet (A0, A1, A−1) normalized to the unity as functionof the magnetic field and for two different values of β = 10deg (left) and 40 deg(right). The meaning of lines is A0 (full line) , A1 (dashed), A−1 (dot-dashed) andD (dotted).

20 and 100 µHz. From its value we can get an estimate on the mean densityof the star, which is then a constraint on the stellar model. About half of theroAp stars are multiperiodic. One of them is in the field of COROT in thenorthern hemisphere. This star is 10 Aql (HD 176232, HR 7167). It is a F0SrEu star whose recent spectroscopic investigation is available in Ryabchikovaet al. (2000). The variability of this star has been discovered by Heller &Kramer (1990) who showed three distinct eigenmodes whose frequencies areν1 = 1435.99, ν2 = 1385.37 and ν3 = 1239.26 µHz. Their amplitudes are lessthan 0.5 mmag (Johnson B filter). These amplitudes are much larger than thesolar amplitudes but they are quite small for roAp stars which have generally∆B > 1 mmag. These three modes are very close to the noise detection ∼ 0.2


Figure 5: The three detected frequencies in 10 Aql, ν1 = 1435.9, ν2 = 1385.4 andν3 = 1239.2 µHz. Note also the low amplitudes (∆B < 0.5 mmag) of the eigenmodes.From Heller & Kramer (1990).

mmag. The main source of this noise is the scintillation of the sky. Therefore itis a great advantage to observe these stars from space. There are others roApstars which show small amplitudes like HR 1217 (Kurtz et al. 1989) or γ Equ(Martinez et al. 1996), and in these cases they exhibit more than one mode.In turn, the roAp stars which show large amplitudes, like HR 3831 (Kurtz etal. 1997) or α Cir (Kurtz et al. 1994) have only one single mode. Thereforesince 10 Aql has similar amplitudes to HR 1217 and γ Equ we expect thatthere are many modes hidden in the noise of detection. The satellite COROTwill considerably decrease this noise and will be able then to discover a largenumber of eigenmodes.

The geometrical nature of the modes already detected in 10 Aql is not yetclearly established. In most roAp stars (e.g. Kurtz 1990, 1998) the modesresponsible of the oscillations are dipole (` = 1) modes. We can expect thesame nature of pulsation in 10 Aql.

In order to interpret oscillations and to prepare the space mission, we haveto choose a stellar evolutionary model for this star. The metallicity Z is cer-tainly one of the most undetermined parameters regarding the extreme chemicalcomplexity of the outer layers. There is no reason to choose solar metallicity


for an Ap star, since the Sun is known to be metal deficient compared withits neighborhood. Therefore, following Saio & Shibahashi (1985), we considerZ = 0.03. The effective temperature and luminosity are given by Matthews etal. (1999). The latter is obtained from Hipparcos measurements. They are:Teff = 8000±100 K and L = 21.4±0.6 L¯. The model is also constrained bythe large frequency separation observed in 10 Aql, i.e. ∆12 = ν1 − ν2 = 50.6µHz. The overshooting is supposed to be 0.2Hp, with Hp the pressure scaleheight. The stellar model is calculated with the CESAM evolutionary codedeveloped at the Observatoire de la Cote d’Azur (Morel 1997). The modelwhich reproduces well all these constraints is: M = 2.11M¯, R = 2.42R¯,X = 0.70, Z = 0.03 and a central fraction of hydrogen Xc = 0.4. We founda spacing of ∆0 = 50.15 µHz and a cut-off frequency equal to 1510 µHz (seeAudard et al. 1998 for a discussion of the limit of frequencies for trappedacoustic modes in roAp stars). These results that we obtain are comparablewith the observations of Heller & Kramer (1990). We note that the largestobserved frequency is close to the cut-off frequency. In Figs (6), (7) and (8) werepresent the three frequencies which are closest to the observed ones, assum-ing that they correspond to a same degree ` = 1. They have respectively theradial orders n = 24, 27, and 28. We note that the calculated non magneticfrequencies (full lines) differ from the observed ones (dot-dashed lines) by sev-eral µHz, up to about 8 µHz. However, it is now well known (Dziembowski &Goode 1996, Bigot et al. 2000, Cunha & Gough 2000) that the magnetic fieldis responsible for an important shift of frequency in roAp stars. It also breaksthe degeneracy of frequencies which depend on |m|. In Fig. (6), (7) and (8)we place the frequencies corresponding to the radial orders n = 24, 27 and 28affected by two different values of the magnetic field B = 0.5 and 0.8 kG. Thebest value of B that reproduces the data is 0.8 kG. We then get an agreementwith the three observed frequencies within ∼ 0.3 µHz. This value of B agreeswith the estimate given in Ryabchikova et al. (2000) from spectroscopy. Thefrequencies ν1 and ν2 correspond to the modes (n = 27, ` = 1,m = 0) and(n = 28, ` = 1,m = 0) and ν3 correspond to (n = 24, ` = 1, |m| = 1). Wenote that the shifts introduced by the field are quite large. This is due to thefact that these frequencies are close to the cut-off frequency.

We emphasize here that the non-obvious observed inequality ∆obs23 = νobs

2 −νobs3 6= k∆obs

12 = k(νobs1 − νobs

2 ), with k integer, is well explain by the effectof the magnetic field and the shift that it produces. The magnetic spacingsthat we obtain for B = 0.8 kG are ∆mag

12 = νmag1 − νmag

2 = 50.4 µHz and∆mag23 = νmag

2 − νmag3 = 146.8 µHz which are close to the values observed by

Heller & Kramer (1990).


Figure 6: Positions of the frequency ν3 without a magnetic field (full line) and forB = 0.5 kG with m = 0 (dotted line) and for B = 0.8 kG with m = 0 (dashed line)and |m| = 1 (dot(×3)dashed line). The observed value is plotted with a dot-dashedline.

Conclusion

The roAp star 10 Aql is a very interesting target for the asteroseismic spacemission COROT. The observations from the ground already lead to three eigen-modes with large radial orders. We have shown that the positions and ampli-tudes of the eigenmodes in the spectrum of oscillations are strongly influencedby the magnetic field, which by our estimation is close to 0.8 kG. The lackof accurate measurements leads to an absence of rotational sidelobes. Theinterest in COROT is to improve the resolution of observations, to resolve themultiplets and to discover a large number of modes hidden in the noise. As wehave shown, the amplitudes will lead to a determination of the magnetic field


Figure 7: Same as Fig. (6) for the frequency ν2.

and the obliquity angle between the rotation and magnetic axes, which thenwould be a constraint for dynamo theories for Ap stars.

Acknowledgments. L.B. thanks the ”Societe de Secours des Amis desSciences” for financial support during the preparation of this article.

References

Adelman, S. J. 1973, ApJ 183, 95Audard N., Kupka F., Morel P., Provost J., Weiss W. W., 1998, A&A 335, 954Babcock, H. W. 1947, ApJ 105, 105Babcock, H. W. 1949, Obs 69, 191Baglin, A., Foing, B. H. 1999, AdSpR 24, 145Bagnulo, S., Landolfi, M., Landi Degl’Innocenti, M. 1999, A&A 343, 865


Figure 8: Same as Fig. (6) for the frequency ν1.

Balmforth, N. J., Cunha, M. S., Dolez, N., Gough, D. O., Vauclair, S. 2001,MNRAS 323, 362

Bigot, L., Provost, J., Berthomieu, G., Dziembowski, W. A., Goode, P. R. 1999,RoAJS 9, 129

Bigot, L., Provost, J., Berthomieu, G., Dziembowski, W. A., Goode, P. R. 2000,A&A 356, 218

Bigot, L., Dziembowski, W. A. 2002, A&A, accepted

Christensen-Dalsgaard, J., Dziembowski, W. A. 2000, in Variable stars as essential

astrophysical tools, ed. Cafer Ibanoglu, Kluwer Academic Publishers,Dordrecht, Boston, NATO science series. Series C, Mathematical and physicalsciences; vol. 544, p. 1

Cunha, M. S., Gough, D. 2000, MNRAS 319, 1020Dziembowski, W. A., Goode, P. R. 1985, ApJ 296, L27


Dziembowski, W. A., Goode, P. R. 1996, ApJ 458, 338Edmonds, A. R. 1960, Angular Momentum in Quantum Mechanics, second

edition, Princeton Univ. PressHeller, C. H., Kramer, K. S. 1990, MNRAS 246, 699Hoffleit, D., 1982, Bright Star Catalogue, 4th edn, Yale University ObservatoryHubrig, S., North, P., Mathys, G. 2000a, ApJ 539, 352Hubrig, S., Kharchenko, N., Mathys, G., North, P. 2000b, A&A 355, 1031Kurtz, D. W. 1982, MNRAS 200, 807Kurtz, D. W., Shibahashi, H. 1986, MNRAS 223, 557Kurtz, D. W., Marang, F. 1988, MNRAS 231, 565Kurtz, D. W., Matthews, J. M., Martinez, P., Seeman, J., Cropper, M.,

Clemens, J. C., Kreidl, T. J., Sterken, C., Schneider, H., Weiss, W. W.,Kawaler, S. D., Kepler, S. O. 1989, MNRAS 240, 881

Kurtz, D. W. 1990, ARA&A 28, 607Kurtz, D. W., van Wyk, F., Marang, F. 1990, MNRAS 243, 289Kurtz, D. W., Sullivan, D. J., Martinez, P., Tripe, P. 1994, MNRAS 270, 674Kurtz, D. W., van Wyk, F., Roberts, G., Marang, F., Handler, G., Medupe, R.

1997, MNRAS 287, 69Kurtz, D. W., Marang, F., van Wyk, F., Roberts, G. 1996, MNRAS 280, 1Kurtz, D. W. 2000, in in Variable stars as essential astrophysical tools, ed. Cafer

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Vol. 141, 2002

Status of the COROT ground-based photometricactivities

R. Garrido1, P. Amado1, A. Moya1, V. Costa1, A. Rolland1, I. Olivares1 andM. J. Goupil2

1.-Instituto de Astrofisica de Andalucia, Apdo. 3004, Granada, Spain2.-DASGAL, UMR CNRS 8633, Observatoire de Paris-Meudon, France

Abstract

We report photometric observations made at the Observatorio de Sierra Nevadaof the secondary targets in the input catalogue of COROT. These observationsconsist of Stromgren –uvby- and Crawford –Hβ– measurements of stars inScenarios 1, 2 and 4. The cooler stars are being measured in the CaII H&Kphotometric system. We present here the present status of observations andreductions together with some preliminary results on the monitoring of photo-metric variability for some selected stars.

Introduction

In order to have an homogeneous data base of the secondary targets (up to8 mag) it was decided to perform photometric and spectroscopic observationsof the preliminary COROT selected fields. Here we present the photometricobservations carried out in the four band –uvby- Stromgren system, where asusual:

(b− y) is basically a temperature indicatorm = (v − b)− (b− y) is a metallicity indicatorandc = (u− v)− (v − b) is a luminosity indicatorand in the Crawford –Hβ– system whereHβ is another independent temperature indicator for most of the star sam-

ple, hence the reddening will be calculated using the Hβ index.The use of the CaII H&K band has been introduced since it is more

than two times more sensitive to metallicity changes than m1, with sensitivity

R. Garrido et al. 43

Figure 1: V versus (b − y) color diagram. (b − y) is unreddened. Stars fainter than8 mag. are probably missidentifications of multiple systems.

increasing to lower temperatures, as shown by Twarog and Anthony-Twarog(1991).

Figure 2: c versus (b− y) color diagram. Colors are unreddened.

44 Status of the COROT ground-based photometric activities

Figure 3: m versus (b− y) color diagram. Colors are unreddened.

Instrumentation

All the Stromgren and Crawford observations were made with a photoelectricphotometer able to work in two modes: in the Stromgren mode, it measuressimultaneously the four uvby bands and in the Crawford mode, it measuressimultaneously two bands nw (narrow and wide) centered on the Hβ line.This photometer is attached to a 0.9m telescope on Sierra Nevada Obser-vatory, property of the IAA (CSIC) situated near the city of Granada. Thebuilding contains two domes hosting two telescopes. CaII H&K observa-tions were made with a CCD camera attached to the other telescope with adiameter of 1.5m. Details of this instrumentation can be downloaded fromhttp://www.iaa.es/osn/principal/html.

Catalogue observations

The observations we present here began in early 2000 when it was not yet knownthe final scenario chosen for COROT, at that time there was two possibilities:one starting at α = 5h37m (and 12h later) called scenario 1 and other startingat α = 7h19m (and 12h later) called scenario 2. We decided to observe bothscenarios in order to have more physical information on the possible targets tohelp in the final selection. After some discussions during the meeting of theScientific Committee held in Paris in spring 2001 an intermediate scenario wasfinally decided for COROT: scenario 4, starting at α = 6h03m and ending at7h31m (and 12h later) , always within an equatorial band of ±10 degrees. This


Figure 4: Photometric variability of HD 49434. Stars are magnitude differences be-tween HD 49434 and HD 48922. Points are for HD 49933 minus HD 48922.

Figure 5: Power spectra of both photometric series shown in Figure 4.

final scenario has some stars in common with scenarios 1 and 2 but most of thestars were new.

Before the decision was taken to select scenario 4 most of the stars inscenarios 1 and 2 were observed. In particular for scenario 1, 539 stars out of661 were observed in the Stromgren and Crawford systems and 78 out of 144 inthe CaII H&K system. For scenario 2 these numbers were: 442 out of 458and 69 out of 128. We started the new observations for scenario 4 in summer2001 and all the visible stars in the season were observed in Stromgren and

46 Status of the COROT ground-based photometric activities

Table 1: Fitted frequencies of HR 6534.

ν(µHz) Amp (mag) phase(rad) νi/ν0 νi/ν1158.92 0.0022 ± 0.0003 3.40 ± 0.16 1 -207.45 0.0039 ± 0.0004 4.57 ± 0.09 0.77 1237.38 0.0018 ± 0.0004 1.47 ± 0.19 0.67 0.87291.95 0.0022 ± 0.0004 4.84 ± 0.16 0.56 0.71353.76 0.0029 ± 0.0003 0.25 ± 0.12 0.45 0.59

Crawford systems: a total of 155 objects. No observations were made in theCaII H&K system during this summer.

In conclusion, 155 out of 419 stars have been observed in scenario 4 in theStomgren and Crawford systems and 105 out of 187 stars were observed inthe CaII H&K system. We expect to finish all the observations in summer2002, including the remaining stars from scenarios 1 and 2 in order to have anhomogeneous catalogue to compare with spectroscopic observations made alsofor stars of these two scenarios.

We present in Figure 1, 2 and 3 some preliminary and partial results of thephotometric reductions now in progress.

Figure 6: (b+v) photometric variations of HR 6534.


Table 2: Frequency of the fundamental radial mode and period ratios for radialmodes of a 1.75M¯ model with no rotation (v = 0) and with a rotational veloc-ity of v = 100 km/s and v = 255 km/s.

v (km/s) log Teff ν0 (µHz) P1/P0 P2/P0 P3/P0 P4/P0 P5/P00 3.90 207.2 0.772 0.6305 0.533 0.458 0.399

100b 3.90 210.6 0.777 0.633 0.536 0.462 0.3980 3.89 188.2 0.772 0.628 0.530 0.456 0.398

100b 3.89 191.2 0.782 0.627 0.534 0.460 0.397250a 3.89 203.4 0.787 0.643 0.545 0.473 0.416250b 3.89 221.2 0.884 0.736 0.635 0.553 0.488

a no degenerate coupling included

tb degenerate coupling included

Photometric monitoring

Some bright stars from scenarios 1, 2 or 4 were observed to be slightly vari-able in spectroscopy by Claude Catala and then selected to be monitored inphotometry. From these HD 171834, HD 164259, HD 46304, HD 174866 andHD 180868 were found to be “non-variable” during one night of observation(6 hours aproximately) at the level of 2 mmags rms (see Figure 5b for a typicalpower spectrum of a “non-variable” star). Only HD 49434 showed some pho-tometric variability as can be seen in Figure 4. This long term variability, seepower spectrum in Figure 5, is typical for the newly discovered γ Dor stars asdiscussed in Bruntt et al. (2002).

One of the comparison stars to test variability turned out to be a new δ Scutistar: HD 159170 = HR 6534. Light curves are plotted in Figure 6. The star isclearly multiperiodic and a preliminary Fourier solution is shown in Table 1.

Period ratios seem to indicate that HR 6534 is a pure radial pulsator but thestar has a rotational velocity of 255 kms−1 and when high rotation is includedin the pulsation model the radial overtones do not show anymore the classicalperiod ratios as shown in Table 2. More observations have been made during2001 from OSN and from SAT in La Silla in order to confirm these results thatwill be discussed in a forthcoming paper by Garrido et al. 2002.

Unfortunateley HR 6534 (or “Orianita” as MJG wants it to be renamed) isoutside the scenario 4 (α = 17h33m30s and δ = -05d44m41s)

References

Anthony-Twarog, B. J., Twarog, B. A. 1995, AJ 109, 2828Bruntt, H., Catala, C., Garrido, R., Rodriguez, E. 2002, in preparationGarrido, R., Goupil, M. J., et al. 2002, in preparation


Vol. 141, 2002

Mode identification using the exoplanetary camera

R. Garrido1, A. Moya1, M. J.Goupil2, C. Barban2, C. van’t Veer-Menneret2,F. Kupka3 and U. Heiter3

1.-Instituto de Astrofisica de Anadalucia, Apdo. 3004, Granada, Spain2.-DASGAL, UMR CNRS 8633, Observatoire de Paris-Meudon, France

3.-Institut fur Astronomie, Universitat Wien, Austria

Abstract

Numerical simulations are presented, which show that color information, assupplied by the exoplanetary camera of COROT, can be relevant to discriminateamong several spherical degrees ` of the non-radial oscillations of δ Scuti stars.

Introduction

Multiperiodic δ Scuti stars show power spectra indicating that they pulsate ina mixing of radial and non-radial modes. Whereas period ratios can be usedas an indication of the radial order n for radial modes they are not useful forthe non-radial ones. Rotation and evolution –the so called “avoided crossing”phenomenon– complicate even more any mode identification. Spectroscopy –through line profile variations– and photometry –through the use of amplituderatios and phase differences of different colors– have been widely utilized astechniques for mode identification. Here we will focus on the capability ofthe explanetary camera in COROT to supply color information which can berelevant for mode identification.

Numerical simulations

In front of the exoplanetary camera a bi-prism device will supply colored spottedimages which will give three colors. These colors will depend on the spectraltype of the considered star and on the position over the CCD plane. The fullspot will be divided into three parts called “blue”, “green” and “red”, containing20%, 20% and 60% respectively of the total flux.


Figure 1: Amplitude ratio vs phase differences between “blue” and “green” bandsof the exoplanetary camera of COROT for a model atmosphere of T = 7500 K,log g = 4.0 and periods close to a pulsation cosntant of Q = 0.035d. Regions forevery ` value contain predictions for phase lags between 90 and 135 degrees and valuesof R between 0.25 and 1.00.

The Kurucz model atmospheres have been improved in the way explained indetail in Heiter et al. (2002), basically by a better treatment of the convectionand a larger number of shells in order to obtain good derivatives with respectto temperature and gravity.

The linearised formula given by Watson (1988) has been used to computethe diagrams shown in Figure 1 and 2. Regions for different ` have beenevaluated for an improved model atmosphere of T = 7500 K, log g = 4,Pop I and a period region around the fundamental radial mode –pulsationconstant Q = 0.035 d– following the paper by Garrido et al. (1990). Basicallythe predictions are based on calculations assuming a phase lag –angle betweentemperature and radius variations– between 90 and 135 degrees and an R value–a parameter measuring the non-adiabaticity of the atmosphere– between 0.25and 1.00.

From these figures we can see a clear separation for high ` orders, givingvery different regions in the amplitude ratio vs phase differences plane. For thelowest ` orders this separation is less evident but we expect that the accuracyat which COROT will supply light curves allows a precision for amplitudes and

50 Mode identification using the exoplanetary camera

Figure 2: Same as figure 1 but for the central region.

phases sufficient to discriminate among several ` orders and hence to help doingasteroseismology of these stars.

References

Garrido, R., Garcia-Lobo, E., Rodriguez, E. 1990, A&A 234, 262Heiter, H., et al. 2002, in preparationWatson, R. D. 1988, Ap&SS 140, 255


Vol. 141, 2002

COROT and the late stages of stellar evolution

T. Lebzelter, H. Pikall, F. Kerschbaum

Institut fur Astronomie, Turkenschanzstrasse 17, A-1180 Vienna, Austria

Abstract

Small amplitude variability is observed during the late stages of stellar evolutionof low- to intermediate-mass stars. In this paper we discuss the occurrence ofsmall-amplitude variations in the upper right part of the HRD, namely amongthe AGB and post-AGB stars, and we propose two observing programs for theCOROT Additional Program.

AGB and post-AGB evolution

After exhaustion of central hydrogen, stars of low to intermediate mass evolveinto red giants. The ascent on the first giant branch (RGB) is followed by aphase of helium core burning and a phase of helium and hydrogen shell burning,the latter being called the Asymptotic Giant Branch phase (AGB). This phase ischaracterized by cool, highly extended stellar atmospheres/envelopes. Pulsationis a critical aspect of the late stages of stellar evolution. Regular, semiregularand irregular variations have been found in the light and velocity changes ofthese stars. Based on regularity, period and amplitude three types of variableshave been defined: Miras, Semiregular variables (SRVs) and Irregular variables(Lb). Pulsation affects the structure of the stellar atmosphere. Expansionleads to conditions better suited for the formation of dust. Mass loss and dustproduction are related and important tests for stellar evolution While variabilityis probably mainly due to pulsation, it may be affected by other sources. Theattempt to understand the irregularities in the light change of these stars isone of the main aspects currently investigated in these objects (Percy 1997,Lebzelter et al. 2000, Kerschbaum et al. 2001, Percy et al. 2001).

The AGB phase terminates when the star reaches a very high mass loss rate.While losing the remainder of its atmosphere, the degenerated core is uncoveredand the effective temperature rises shifting the objects to the “left” in the HRD.

52 COROT and the late stages of stellar evolution

When all nuclear sources of energy are used up, the final (core-)contractionis inevitable and the objects arrive at the white dwarf (WD) cooling track,which is characterized by decreasing luminosity and temperature. A numberof interesting phases are associated with these final steps in stellar evolution.Here we want to focus on three classes of objects: RCrB stars (RCB), Hydrogendeficient Carbon-stars (HdC) and Extreme Helium Stars (eHe). All three groupsare characterized by the absence of Hydrogen. While for the first two groups His underabundant by a factor of 10−4 to 10−8 (number density), some objectsamong the eHes have a larger fraction of H.

Following Iben et al. (1996) two evolutionary scenarios are thought to lead tothe RCrB phenomenon: One possibility is the merging of two, close degeneratedobjects – like WD or even Neutron stars – in a binary system (double degeneratescenario, DD). Recent calculations of WD-evolution with He-accretion (Saio &Jeffery 2001) support this idea. The accreted material is heated and compressedby shocks which starts the nuclear fusion. He Shell burning releases enoughluminosity to virtually move the star to the upper right corner of the HRD.Alternatively a final Helium flash can produce enough luminosity to expand theenvelope so the object appears as a cool supergiant again. Helium flashes occurregularly during the final stages of AGB evolution, but in some cases a very lateFINAL flash may happen after the star has lost its envelope and is already onthe WD cooling track (final flash scenario, FF). Both scenarios lead again to acool, extended envelope, so that these stars are found close to the AGB.

According to Clayton (1996) all RCB have an infrared excess, while for noneof the HdC was an infrared excess observed. IRAS data imply dust temperaturesin the range of 650–900 K (Walker 1986). There is evidence for old, fossil dustshells with large spatial dimensions, implying an age of 104 to 105 years forthe shell around R CrB itself (Gillett et al. 1986), but without a connection tothe recent mass loss, which is responsible for the declines. The emisson in theinfrared is changing but not correlated to the big declines. Measurements ofthe polarisation support the existence of dust.

Beside the obvious large amplitude variations in RCB, the declines, whichare due to phases of heavy mass loss and the emission of dust in puffs directly inthe line of sight, small amplitude pulsation is observed in these stars. However,investigation of these variations has just begun and their origin and type ofpulsation is not yet known. Typical pulsation periods are 30–110 days for RCBand HdC and between 0.1 and a few days for the eHe (Weiss et al. 1996, andreferences therein). Feast (1996) points out that the turnover timescales for afew large convection cells are of the same order for cool objects, but there isdoubt if the change in brightness can be explained by these.

T. Lebzelter, H. Pikall and F. Kerschbaum 53

Open questions

AGB stars

Our interest in COROT concerning AGB stars is motivated by two open ques-tions that require precise photometry with a high time resolution. At firstglance, neither requirement seems necessary for investigations of AGB stars, asthe variations in these objects typically occur on a time scale of several tens ofdays up to several years with amplitudes between 0.1 and 8 magnitudes.

However, the definition of the variability region in the HRD, where the AGBstars are located, can be established by much smaller variations on much smallertimescales. AGB variables are not located within the classical instability stripbut seem to form a separate instability region. The blue border of this region isnot known yet. Several investigations detected small amplitude variability in lateK- and early M-type giants, i.e. on the left side of the AGB. Jorissen et al. (1997)and Fekel et al. (2000) showed that small amplitude variability is common inthis kind of stars. Semiregular and irregular variables with amplitudes of morethan 0.1 mag are found also among early M-type giants (e.g. Lebzelter 1999a).Edmonds & Gilliland (1996) found variable K-giants in the globular cluster 47Tuc with period lengths of a few days and amplitudes of about 10 mmag. Koen& Laney (2000) detected short time variations (periods of a few days) in Mgiants, although part of their results may be due to problems with the Hipparcosdata they used (Kerschbaum et al. 2000). A more detailed investigation of thevariability in this region of the HRD is necessary to derive the origin of theobserved variability and to deduce the parameters for the onset of pulsationamong cool giants.

Also for the classical, large amplitude AGB variables, photometry with hightime resolution is needed. It is suspected that these stars show also variationsthat do not origin from stellar pulsations. Opposite to what is found in Sun-likestars, the surface of a cool AGB giant should be covered only by a few largeconvective cells (Schwarzschild 1975; Freytag et al. 1997). Their occurrenceand motion may be echoed in small amplitude changes of the star (e.g. Lebzelter1999b). Beside that several investigators report the observation of short timeoutbursts in MIRAS (Maffei & Tosti 1995, de Laverny et al. 1998). For a fewhours the star’s brightness changes by up to several 0.1 mag. The mechanismof these outbursts is not understood yet.

Both kinds of variations, due to surface structures and due to outbursts,happen on a short time scale and may be detectable only with high precisionphotometry. Due to the lack of appropriate models an accurate prediction ofthe time scales and amplitudes of these variations cannot be made.


Post-AGB stars

The small amplitudes of the pulsation detected or expected in the groups ofpost-AGB stars described above should predestine these objects for high preci-sion continuous photometry offered by COROT. Periods have been derived onlyfor a small fraction (2) of the known objects, all with rather big uncertainties,so there is a clear demand for a detailed study of these stars.

The determination of exact stellar parameters like effective temperature,luminosity, mass and the chemical composition are needed to calculate detailedmodels of these objects – both for evolutionary and pulsational aspects. TheHipparcos mission could not determine distances to any of the objects, becausemany of the objects were not bright enough, but the detection of RCB in theLMC during the MACHO-project (Alcock et al. 1996) supported high luminosi-ties. Estimates of the brightness were MV ≈ −4 to −5. This however doesn’tconstrain evolutionary models (which could shed light on the object’s masses)sufficently. Atmospheric abundances, derived from detailed static modeling ofthe atmospheres, simultaneously yield values for temperatures and surface grav-ities (Asplund et al. 2000, Pandey et al. 2001). Pulsation theory relates theperiod of pulsation to the star’s mean density regarding the pulsation mode,which makes it important to measure the period with high accuracy, but pe-riods of the order of 30-110 days are hard to observe, due to seasonal effects.The temporal change of period is an indication if the star is contracting orexpanding, but prior to that the period has to be established.

High luminosity in stellar envelopes allows strange modes, which can growon very short timescales, comparable to a few of their pulsation periods. Mak-ing it simple, one could say, that such envelopes tend to show instabilities ofgreater order and manifold than low-luminosity objects. The reason derivespartly from the fact that the Kelvin-Helmholtz timescale becomes comparableto the dynamical timescale for very high luminosities. Linear theory showedthat a density inversion enables mode trapping in the outer parts of the en-velopes [REFERENCE?]. Stellar winds are thought to be driven by differentmechanisms, but high luminosities help anyway, if the matter is not heated, butaccelerated. The connection between pulsation, wind and dust formation is stillnot understood. While dust formation and dust driven winds can be modeledsimultaneously (Hofner 1999), the influence on the pulsation has not been in-vestigated so far. This also leads to the question if all RCB are pulsating, andwhat the correlation of systematic period variations to the evolution of theseobjects is.

Another important question is: How does convection work in cool super-giants? As for AGB stars, which are in many ways similar to the RCB andHdC, short time variations with low amplitudes are expected. In the case ofsome eHe stars the question arises: Is the observed irregularity intrinsic or due

T. Lebzelter, H. Pikall and F. Kerschbaum 55

to shortcomings in the observations.

Perspectives

Within the course of the Additional Program we propose two observing pro-grams. M giants and AGB stars are found all over the sky so that we aim tomeasure the light variability of both kinds of stars that are in the final fields ofview of COROT. The data will contribute to both questions discussed for theAGB stars above. We plan to combine these observations with spectroscopicmeasurements and photometric follow up studies from the ground.

The second observing proposal aims to measure the light change of at leastone post-AGB object with high photometric precision. It turned out that anumber of stars from the three groups described in this paper would be closeto the planned field of view of COROT. One star, FH Sct – an RCB – willbe in the Exoplanetary Field if one of the prime targets is observed in theasteroseismology field. No pulsational period has been derived for this star yet.The apparent brightness is V = 12.2 mag and therefore FH Sct fits perfectly inthe sensitivity range of the instrument. For both proposals the ExoplanetaryField offers sufficient time resolution.

Acknowledgments. TL is supported by the Austrian Science Fund ProjectP14365-PHY. We wish to thank W.W.Weiss for organizing the COROT ScienceWeek in Vienna.

References

Alcock, C., Allsman, R. A., Alves, D. R., et al. 1996, ApJ 470, 583Asplund, M., Gustafsson, B., Lambert, D. L., Rao, N. K. 2000, A&A353, 287Clayton, G. C. 1996, PASP 108, 225Clayton, G. C. 2001, AP&SS 275, 143de Laverny P., Mennessier, M. O., Mignard, F., Mattei, J. A. 1998, A&A 330, 169Edmonds, P. D., Gilliland, R. L. 1996, ApJ 464, L157Feast, M. W. 1986, in Hydrogen Deficient Stars and Related Objects, ed. K. Hunger

(Dordrecht, Reidel), p. 151Fekel, F. C., Henry, G. W., Henry, S. M. 2000, in Garcia Lopez, R. J., Rebolo, R.,

Zapatero Osorio, M. R. (eds.), 11th Cambridge Workshop on CoolStars, Stellar Systems and the Sun, ASP Conf. Ser. 223, 925

Freytag, B., Holweger, H., Steffen, M., Ludwig, H.G. 1997, in Paresce, F. (ed.),Science with the VLT interferometer”, ESO Astrophys.Symp., Springer, p. 316

Gillett, F. C., Backman, D. E., Beichman, C., Neugebauer, G. 1986, ApJ 310, 842Hofner, S. 1999, A&A 346, L9Iben, I., Tutukov, A. V. & Yungelson, L. R. 1996, ApJ 456, 750Jorissen, A., Mowlavi, N., Sterken, C., Manfroid, J. 1997, A&A 324, 578


Kerschbaum, F., Lebzelter, T., Lazaro, C. 2001, A&A 375, 527Koen, C., Laney, D. 2000, MNRAS 311, 636Lawson, W. A. & Cottrell, P. L. 1997, MNRAS 285, 266Lebzelter, T. 1999a, A&A 346, 537Lebzelter, T. 1999b, A&A 351, 644Lebzelter, T., Kiss, L. L., Hinkle, K. H. 2000, A&A 361, 167Maffei, P., Tosti, G. 1995, AJ 109, 2652Pandey, G., Kameswara Rao, N., Lambert, D. L., et al. 2001, MNRAS 324, 937Percy, J. R. 1997, JAAVSO 25, 93Percy, J. R., Wilson, J. B., Henry, G. W. 2001, PASP 113, 983Saio, H. 1995, MNRAS 277, 1393Saio, H. & Jeffery, C. S. 2000, MNRAS 313, 671Schwarzschild, M. 1975, ApJ 195, 137Walker, H. J. 1986, in Hydrogen Deficient Stars and Related Objects, ed. K. Hunger

(Dordrecht, Reidel), p. 407Walker, H. J. 1994, CCP7 Newslett. 21, 40Weiss, A., Fried, R., Olson, C. E. 1996, A&AS 116, 31Woitke, P., Goeres, A. & Sedlmayr, E. 1996, A&A 313, 217


Vol. 141, 2002

Pulsations of Luminous Blue Variables

E. A. Dorfi1, A. Gautschy2

1Institut fur Astronomie, Turkenschanzstr. 17, A-1180 Wien, Austria,[email protected]

2ETH-Bibliothek, Ramistr. 101, Ch-8092 Zurich, [email protected]

Abstract

From simulations of massive stars we find regular low-amplitude radial pulsa-tions can be excited. Such pulsations were encountered during core hydrogenburning as well as during the early core helium burning stage of evolution. Forfour selected models we present light curves in the V-band. The results are dis-cussed with the aim to guide observations to identify and monitor such regularlypulsating variable massive stars in nature.

Introduction

The COROT mission offers the possibility for high-precision measurements ofphotometric variations of stars. With increasing accuracy more and more do-mains with light variability are being identified on the Hertzsprung-Russell (HR)diagram. This applies in particular to the high-luminosity regime where the lu-minous blue variables (LBVs) are located. The results from the HIPPARCOSmission (Eyer & Grenon 1997) demonstrated that almost all stars with luminos-ity class lower than III show noticeable light variability (above some 10 mmag)of some as yet unknown origin.

From the observational point of view the nature of LBV variability is still notwell understood. On timescales of years and months, eruption-like outburstshave been reported but small amplitude, quasi-regular photometric variationshave also been detected on timescales of several days (e.g. Nota & Lamers(1997) for a summary on LBV properties). Due to the small number of knownLBVs (see Table 1) and the insufficient observational coverage, the physicalnature of either the micro-variability or the outbursts is not clear up to date.Based on a search through the literature the latest discovery of a new LBV

58 Pulsations of Luminous Blue Variables

Table 1: Known luminous blue variables (after Bohannan 1997 and Shemmer et al.2000)

Galaxy # LBVs

Milky Way 5 η Car, P Cyg, AG Car, HR Car, HD160529LMC 6 S Dor, R71, R127, HD269582, R110, R143SMC 1 R40M31 4 AE And, AF And, Var A-1, Var 15M33 4 Var B, Var C, Var 2, Var 38, B416NGC2403 5 V12, V22, V35, V37, V38M81 3 I1, I2, I3M101 3 V1, V2, V10NGC1058 1 SN1961V

has been reported by Shemmer et al. (2000) for the star B416 located in M33.Hence, photometric satellite missions like COROT could offer a unique oppor-tunity to gain new insights into the physical mechanism operating in the mostluminous stars.

The theoretical results of the LBV-phase have been strongly debated and thesuggested models range from strange mode instabilities (Kiriakidis et al. 1993)to an oscillatory dynamically unstable pulsation for stars near to the Eddingtonlimit (Stothers & Chin 1993). However, none of the models presented are ableto explain the micro-variability, the eruptive outbursts or the stellar winds alsoobserved during the LBV phase. According to Leitherer (1997) the observation-ally deduced mass loss rates for LBVs not undergoing a major outburst rangefrom 10−4M¯ yr−1 for ηCar to 6 ·10−7M¯ yr−1 for R71 (see also Table 1).The final outflow velocities are typically around 200 km/s.

In this short contribution we want to focus on the most luminous stars, theso-called LBVs (luminous blue variables) or S Dor variables. Since the observednumber of such variables is rather small, theoretical predictions of the variabilitybecome more important.

We have performed radial non-linear pulsation computations for these starsby applying the full set of the radiation hydrodynamics equations (RHD, e.g.Mihalas & Mihalas 1984). The initial models are computed from usual stellarevolution calculations where the corresponding evolutionary paths are plottedin Fig. 1. The pulsational models investigated belong to massive stars at thestage of either core hydrogen buring or early core helium burning. The numer-ical method used for the non-linear pulsation simulations is described in detailin Dorfi (1998). In the dynamical computations the radiative transfer is per-formed by using the Rosseland-mean OPAL92-opacity for the radiative flux and

E. A. Dorfi and A. Gautschy 59

Table 2: Table of LBV model parameters and pulsation properties

Name M L Teff P ∆R/R ∆u us ∆mV

[M¯] [103L¯] [K] [days] [km/s] [km/s] [mag]

M20C 20 66 27 100 0.290 0.033 63 0.11M45 45 537 33 890 0.575 0.080 248 48 0.11M60H 60 933 34 680 1.611 0.368 598 211 0.27M60C 60 900 18 000 4.086 0.281 356 114 0.26

the Planck-mean for the corresponding radiation energy equation. The calcu-lated profiles (density, temperature, etc.) are taken as input for a frequency-dependent radiative transfer. After folding the obtained spectra with the filterpassbands we get e.g. the V-light curves presented in Fig. 1. To enhance thestructural differences the areas below the observable light curves have beenfilled with grey colour.

Theoretical light curves of LBVs

The properties of the LBV models discussed in this paper are summarized inTable 2. The models exhibit rather regular pulsations (cf. Fig. 1) with pe-riods P shown in column 5. The relative changes of the photospheric radius∆R/R are given in column 6 indicating that only the masses above 30M¯ showpronounced radial oscillations with velocity variations ∆u (column 7). Thesemotions go along with strong shock waves running through the atmosphereand the shock speed us is given in column 8. Finally, the last column statesthe changes in the visual magnitude ∆mV, which allows a direct comparisonwith observed LBVs. According to the results we emphasize the non-adiabaticnature of the pulsations, where large velocity amplitudes are accompanied bysmall luminosity variations of the order of about 0.1mag. For light curves indifferent passbands we refer to Dorfi & Gautschy (2000). Due to the dom-inance of the radiation pressure these oscillations are mainly confined to theouter layers. From a comparison with linear stability analysis they seem to berather regular radial modes (for a review e.g. Gautschy & Saio 1995).

The temporal evolution of a pulsating star (model: M60H) is plotted inFig. 2 through the motion of different mass shells over two pulsational cycles.The period of the outer (observable) shell is P = 1.611 days. In contrast tothis periodicity the inner shells are oscillating with half of that period, namelyP = 0.805 days. This short period corresponds exactly to the pulsation periodobtained from a linear stability analysis which causes also the most prominent


Figure 1: The HRD showing the location of luminous blue variables together withstellar evolution calculations. The grey shaded inserts exhibit the theoretical V-lightcurves of the LBV model calculations around their mean V-magnitude as a functionof the pulsation phase, summarized in Table 2. Note that the magnitude scale ofthe upper panels is twice that of the lower ones. The upper models have masses of60M¯, the lower ones 45M¯ (right) and 20M¯ (left), respectively.


peak in a power spectrum of the inner mass shells (Dorfi & Gautschy 2000).However, the non-linear reactions of the outermost layers induce a longer pe-riodicity visible for an external observer because the motions of the upper at-mosphere are dominated by two strong shock waves seen at phases 0.35 and0.7. These outward running waves travel at speeds of us = 136 km/s andus = 211 km/s. The Mach numbers of these shocks vary between 5 and 8.After the acceleration event the mass shells are moving basically along ballistictrajectories characterized by the dynamical time scale of the stellar envelope.Clearly, such shock compressions heat the thermal gas and the correspondingfeatures are imprinted on the light curves. Due to the low optical depth in theouter layers no phase shift of the features is introduced in the light curves ifobserved in different passbands.

Rad

ius

[R

]

Time in pulsation periods

Figure 2: The paths of different mass shells as a function of the pulsation period showthe ballistic behavior of the outermost atmosphere (M = 60M¯, L = 933 000L¯,Teff = 34 680K). For an observer this motion pattern leads to periodic luminosityvariations with P = 1.611 days whereas the internal pulsation period is close to 0.8days (see text for more details).

Atmospheres of pulsating LBVs

The non-linearities of the pulsations increase with the mass of the star andthe effects described in this section will occur for masses above 30M¯. Asalready seen in the light curves (Fig. 1) and the mass shells (Fig. 2) the at-


mospheric motions are characterized by the shock waves leading to prominentperturbations of the outgoing stellar radiation. Since the waves deposit energyand momentum into the outermost stellar regions, the whole density and tem-perature stratification changes. Consequently, the location of the photospheredefined through

L = 4πσR2T 4eff (1)

can be shifted by large values. Taking the mean value over a pulsational cy-cle, the effective temperature changes e.g. for model M60C from the initialhydrostatic value of Teff = 18 000K to 20 700K. Caused by the large amountof radiation pressure, the density inversion of the hydrostatic model cannot bemaintained in dynamical models, which allows one to see deeper into the stellaratmosphere. The non-monotonic gradients in the dynamic atmospheres alsopermit sudden frequency-dependent changes of the optical depth meaning thatnot all the radiation leaving the star has to come from the same atmosphericlayer. Both effects, the compression of the gas by the shock waves as well asthe non-monotonic behavior of the photosphere, are responsible for the compli-cated structure of the light curves (Fig. 1). However, as demonstrated in Fig. 2the underlying mass motions can exhibit a much simpler pattern.

Figure 3 illustrates these changes of the observable parameters comparinga hydrostatic with a dynamical atmosphere in the case of a pulsating LBV with60M¯. The thick solid line represents the initial model where the dominance ofthe radiative forces (Fig. 3, lower right panel) generate an unavoidable densityand gas pressure inversion situated around 80R¯ (Fig. 3, left panels). Thegrey shaded areas depict the upper and lower boundaries of physical quantitiesduring a pulsational cycle. The resulting dynamic structure differs in many as-pects from the hydrostatic stratification since outwards of 30R¯ shock wavesare propagating through the stellar layers. Correspondingly, the density, tem-perature and pressure stratification leads to a different appearance of such apulsating star relative to a hydrostatic configuration. This dynamic atmosphere(outside of 30R¯ for model M60C) exhibits radial structures, which cannotbe encompassed by the initially hydrostatic structure which is based on staticequilibrium conditions. In particular, the aforementioned density inversion cannever be supported in such a dynamical environment. The effective photo-spheric radius shrinks from R = 97.4R¯ to a mean value oscillating aroundRdyn = 74.2R¯. Since the mean luminosity L has to remain constant we getfrom Eq. (1) how the temperature of the dynamical atmospheres Tdyn relatesto the initial hydrostatic value of Teff by

Tdyn = Teff

√

R

Rdyn. (2)


Figure 3: The difference between hydrostatic and hydrodynamic models for the modelM60C (M = 60M¯, L = 900 000L¯, Teff = 18 000K). The thick solid line plots theinitial hydrostatic structure, the grey shaded areas show the variation of the density,velocity as well as gas and radiation pressure during a fully developed pulsational cycle.

Inserting the aforementioned values for the radii we obtain from the last equa-tion Tdyn = 20 620K in agreement with the averaged value of the non-linearsimulations of 20 700K. Due to the fact that the atmosphere is extended,thin and rather transparent the main effect comes from the inward shift of theeffective photosphere allowing such a simple description of an overall bluer ap-pearance of the LBV. The shock waves running through the atmosphere withhigh Mach numbers (see us in Table 2) affect mainly the light curves as depictedin Fig. 1.

Conclusions

Summarizing a large number of non-linear pulsation computations (e.g. Dorfiet al. 2001) we emphasize that in general the observations of variable stars withlarge amplitude pulsations cannot be interpreted by simple hydrostatic atmo-spheric models. The stratification of the outer stellar layers is strongly modifiedby the shock waves, which heat and accelerate the atmospheric material. Al-though the small number of galactic LBVs makes it very unlikely that such


stars will be observed within the COROT mission it should be pointed out thatthe deduced stellar parameters of stars with large amplitude pulsations haveto analyzed through dynamical atmospheres and not by adopting hydrostaticmodel atmospheres.

The short life time of about 104 years (based on statistics) of the LBVphenomenon makes observational studies more difficult. Nevertheless, it isnecessary to obtain regular sampled photometric data with accuracies of theorder of 0.01mag together with a time resolution of much less than one day.Since we have found very regular pulsating stars in the non-linear computationsa careful monitoring would be essential to verify or disprove these predictedoscillations. If the observations of such stars are not done with an appropriatesampling the predicted pulsations can either be overlooked or interpreted assome kind of irregular flickering. To investigate the pulsational properties ofLBVs well-sampled photometric data would be of great importance.

Acknowledgments. This project was supported by the Fonds zur Forderungder Wissenschaften (FWF) under project number S7305-AST.

References

Bohannan, B. 1997, in Luminous Blue Variables: Massive Stars in Transition, Eds.A. Nota and H. J. G. L. M. Lamers, ASP Conf. Series Vol. 120, p.3

Dorfi, E. A. 1998, 27th Saas Fee Course, Springer, Berlin, p.263Dorfi, E. A., Gautschy, A. 2000, ApJ 545, 982Dorfi, E. A., Feuchtinger, M. U., Hofner, S. 2001, in Stellar Pulsation - Nonlinear

Studies, Eds. D. Sasselov and M. Takeuti, ASSL, Kluwer, Dordrecht, p.137Eyer, L., Grenon, M. 1997, in HIPPARCOS - Venice ‘97, ESA SP-402, p.467Gautschy, A., Saio, H. 1995, ARA&A 33, 75Kiriakidis, M., Fricke, K. J., Glatzel, W. 1993, MNRAS 264, 50Leitherer, C. 1997, in Luminous Blue Variables: Massive Stars in Transition, Eds.

A. Nota and H. J. G. L. M. Lamers, ASP Conf. Series Vol. 120, p.58Mihalas, D., Mihalas, B. W. 1984, Foundations of Radiation Hydrodynamics, Oxford

University Press, New YorkNata, A., Lamers, H. J. G. L. M. (Eds.) 1997, Luminous Blue Variables: Massive

Stars in Transition, ASP Conf. Series Vol. 120Shemmer, O., Leibowitz, E. M., Szkody, P. 2000, MNRAS 311, 698Stothers, R. B., Chin, C.-W. 1993, ApJ 408, L85


Vol. 141, 2002

By-product of the V1162 Ori multisite campaign: thenew δ Scuti star GSC 4778 00324

Lampens, P.1, Van Cauteren, P.2,5, Niarchos, P.3, Gazeas, K.3,Manimanis, V.3, Arentoft, T.1,4, Wils, P.5, Bruch, A.6, Garrido, R.7,

Shobbrook, R.8

1Koninklijke Sterrenwacht van Belgie, Ringlaan 3, 1180 Brussels, Belgium2Beersel Hills Observatory (BHO), Laarheidestraat, 3, 1650 Beersel, Belgium

3Section of Astrophysics, Astronomy and Mechanics, University of Athens, 15783Zografos, Athens, Greece

4Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium5Vereniging Voor Sterrenkunde (VVS), Belgium

6Laboratorio Nacional de Astrofısica, C.P. 21, 37500-000, Itajuba - MG - Brazil7Instituto de Astrofısica de Andalucıa, CSIC, Apdo. 3004, 18080 Granada, Spain8Research School of Astronomy and Astrophysics, Australian National University,

Weston Creek PO, ACT 2611, Australia

Introduction

Among the comparison stars used to monitor the intriguing intermediate am-plitude δ Scuti V1162 Ori two new variable stars have been discovered in thesame field. One of them is GSC 4778 00324, for which short-period variabilitywith an amplitude of about 0.01 mag with respect to the ”official” comparisonstar had been reported previously (Van Cauteren and Lampens, 2000). Thisvariability was also the cause for the first claim of multiperiodicity for V1162 Ori(Hintz et al. 1998). The colour indices obtained by Handler (2000) put thenew variable star in the middle of the δ Scuti instability strip. Therefore wedecided to monitor GSC 4778 00324 taking as much as possible advantage fromthe international multisite campaign on V1162 Ori itself (Arentoft et al. 2001).In various cases the effective field-of-view was too small to allow simultaneousmeasuring with the main target and a few participants secured data by dedi-cating some extra time. However, the bulge of the data discussed here comesfrom those smaller telescopes with a sufficiently large chip that allow to simul-taneously obtain data on both δ Scuti stars (Belgium and Greece). Figure 1shows the field with the identification of the known and the new variable stars.The δ Scuti candidate is called ”New 1”. The star called ”New 2” is a new

66 The new δ Scuti star GSC 4778 00324

eclipsing binary with an orbital period very close to an integer multiple of oneday. The present contribution reflects the contents of a poster, presented atIAU Symp. 185 (Lampens et al. 2002), in more detail and reports on the finaldata analysis for the new δ Scuti star.

Figure 1: The field of V1162 Ori (8x12 arcmin2) and the newly detected variablestars.

Data and reduction

The observations were collected between October 1999 and March 2001. Allobservations used here were made using a standard V filter. Occasionally theR filter was used. The reduction was performed by each individual observingteam. In some cases the packages MOMF (Kjeldsen and Frandsen 1992; byTA) or MIRA AP (Axiom Research Inc.; by PVC) were used. Table 1 lists theindividual contributions. We mention the name of the observer, the location ofthe observatory, the number of measurements, an identifier for the comparisonstar and the mean data string length. In total we have made use of 2949 datapoints for the analysis of GSC 4778 00324 (V= 10.26; b-y = 0.20). In principlethe same comparison star as used for the V1162 Ori campaign was adopted(GSC 4778 00019, V= 9.73; B-V = 1.55). Arentoft et al. (2001) have shownthat this comparison star shows nightly zero-point shifts but only at the level of0.01-0.02 mag such that this will not affect the frequency search in the rangeof interest (see below). In addition all differential data have been rescaled tothe same mean difference in magnitude. The time base length of the completedata sets is 520 days. This allows a theoretical frequency resolution of 1.5/Tor 0.0029 cycles/day.

P. Lampens et al. 67

Table 1: Logbook of observations of GSC 4778-00324

Name Observatory Nr of data Comp.star Mean length Remark

(S=GSC4778) (days)

Bruch OPD 432 S 285 0.158 C2 usedGarrido Sierra Nevada 23 S 019 0.073

Lampens et al. Hoher List 53 S 019 0.080Niarchos et al. Athens Univ. 2467 S 019 0.103

Shobbrook Siding Spring 13 S 019 0.120Sterken ESO 105 S 019 0.093

Van Cauteren Beersel Hills 1054 S 019 0.106

All 4147 S 019 95.7 hrs T=520 d

Frequency analyses

The same criteria as for the final data selection of V1162 Ori were applied alsoin this case (Arentoft et al. 2001). The analysis was performed in three steps:(a) on the (northern) winter 1999-2000 data set, (b) on the (northern) winter2000-2001 data set, and (c) on the complete data set. In all cases the datapoints were weighted in proportion to the inverse square of the residuals on anight-to-night basis. In each set up to three frequencies could be identified.We are confident that the two most dominant frequencies are secure as theyare common to each individual analysis and have signal-to-noise ratios wellabove 4. Figure 2 illustrates the frequency search for the complete data set.Figure 2a illustrates the periodogram of the original data, the subsequent framesshow the periodograms after prewhitening with the most dominant frequencyof the previous frame. Whereas there is no doubt about the main frequencyat 12.28 cycles/day, some ambiguity arises concerning the second frequency.In our previous analysis (Lampens et al. 2002) we adopted the frequency at16.62 c/d as the most probable second frequency since it appeared to be veryslightly more dominant in the yearly analyses in which all the data points weretreated equally. However, Figure 2b now shows that the 1/day alias frequencyat 15.62 cycles/day is slightly stronger (the corresponding amplitude is larger by1 mmag). This, together with the symmetry of the alias pattern in Figure 2b (5distinguishable peaks at each side of the adopted peak), causes us to identify thelatter as the most probable second frequency. After simultaneous prewhiteningwith the two most dominant frequencies, the remaining standard deviation is6.7 mmag. The nightly rms values of the data usually range from 3 to 10 mmag.Considering the possible contribution of slight zero-point shifts in the shortestdata sets, this may reflect the overall precision of the differential data. Butthe periodogram in Figure 2c still exhibits additional power in the range 10-15 cycles/day. Possible values for a third frequency together with the most


dominant frequencies are summarized in Table 2, presenting the final results ofthe analysis. Depending on the choice for the second frequency (either 15.62or 16.62 cycles/day) the third frequency assumes quite distinct values and itsvalue is therefore uncertain even though it was identified with a signal-to-noiseratio larger than 4 in most cases. The ratio between the two most dominantfrequencies is either 0.74 (16.62 c/d) or 0.79 (15.62 c/d).

0 5 10 15 20 250

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0 5 10 15 20 250

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0 5 10 15 20 250

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0 5 10 15 20 250

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

Figure 2: Periodograms of successive frequency searches (a-d: from left to right).

Figure 3 illustrates two of the associated mean light curves. The V am-plitudes are of order of several millimags only. It must be remarked that thesolutions presented here are incomplete as there exists at least one string ofdata for which the fit is not quite satisfactory (on JD 2451575). The best


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−0.05

−0.04

−0.03

−0.02

−0.01

0

0.01

0.02

0.03

0.04

0.05

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−0.05

−0.04

−0.03

−0.02

−0.01

0

0.01

0.02

0.03

0.04

0.05

Figure 3: Phase diagrams at the frequencies of 12.28 c/d (left) and 15.62 c/d (right)after prewhitening for the other frequency.

solution in terms of largest reduction of the standard deviation is flagged (1) inTable 2. The long, continuous data set obtained in Brazil (Table 1) was used asan independent test of the proposed frequency solution. Figure 4 shows the yetunused data as well as the two-frequency fit from solution (1). We readjustedthe phases in order to have a perfect match between the calculated and the


Table 2: Frequency analyses for GSC 4778 00324

Season Nr Ident. Freq. Ampl. Phase S/N Remarkc/d mag 2πrad

1999-2000 1546 f1 12.2801 0.0041 0.960 7.8 weighted dataf2 15.6157 0.0034 0.927 5.6 RSS = 6.3 mmagf3 11.7173 0.0023 0.317 4.3 uncertain

2000-2001 1403 f1 12.2802 0.0048 0.6712 7.4 weighted data

f2 16.6215 0.0038 0.8272 6.9 RSS = 6.7 mmag

f3 13.2568 0.0027 0.3672 4.4 uncertain

(1) 1999-2001 2949 f1 12.2810 0.0041 0.136 8.1 weighted dataf2 15.6169 0.0036 0.135 6.8 strong alias at 16.62 c/df3 10.5852 0.0021 0.421 4.7 RSS = 6.3 mmag

(2) 1999-2001 2949 f1 12.2810 0.0042 0.118 8.2 weighted dataf2 16.6171 0.0027 0.611 4.8 strong alias at 15.62 c/df3 12.9543 0.0021 0.802 3.9 RSS = 6.5 mmag

2 Phases corrected for the origin difference between data sets

observed light curve. The standard deviation of the residuals dropped by 24%to the level of 6.4 mmag. This shows that the quality of the presently avail-able data set is probably not sufficient to permit the identification of additionalfrequencies with amplitudes as small as 2-3 mmag.

514.68 514.7 514.72 514.74 514.76 514.78 514.8 514.82

−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

0.015

0.02

0.025

Figure 4: Observations from OPD, Brazil, and two-frequency fit (JD 2451514).


Conclusions

A by-product of the international multisite campaign on V1162 Ori is theserendipitous discovery of a pulsating star of very small amplitude and withvariable light curve among the comparison stars in the field. GSC 4778 00324has the colours of a typical δ Scuti star. This star was frequently observedduring the 1999-2000 and 2000-2001 seasons, mainly from Greek and Belgiansites. The final frequency analysis, based on assigning weights to the data,confirms the δ Scuti type and the presence of at least two and probably threefrequencies in the range 10-15 cycles/day. V amplitudes are of order 4 mmagor smaller. The proposed frequency solutions are incomplete but the presentlyavailable data set does not permit the identification of more frequencies. In it-self it is remarkable that observations from non-ideal sites in the vicinity of largeEuropean cities (Athens and Brussels) allow to detect and monitor such subtlevariations and can effectively contribute to the analysis of these small-amplitudemultiperiodic pulsating stars.

Acknowledgments. This research was supported by project G.0265.97of the Belgian Fund for Scientific Research (FWO) - Flanders. T. Arentoft(TA) acknowledges financial support by the Flemish Ministry for Foreign Policy,European Affairs, Science and Technology, under contract BIL 98/11/52 andby the National Research Foundation of South Africa. We thank C. Sterkenfor providing us with observations of the new variable star. R.R. Shobbrook,Honorary Visiting Fellow at the Australian National University, acknowledgessupport from Mount Stromlo and Siding Spring Observatories. P. Lampens andP. Van Cauteren (PVC) thank Prof. Dr. W. Seggewiss for granting telescopetime at the Hoher List Observatory (University of Bonn, Germany). We alsothank M. Sperl for updated versions of the programme Period98.

References

Arentoft, T. et al. 2001, A&A 374, 1056Handler, G. 2000, IBVS 4817Hintz, E., Joner, M. & Kim, C. 1998, PASP 110, 689Kjeldsen, H. & Frandsen, S. 1992, PASP 104, 413Lampens, P. et al. 2002, poster in Proceedings of IAU Coll. 185 on Radial andNonradial Pulsations as Probes of Stellar Physics, Leuven, Belgium, 26-31 July,

2001. ASP Conference Series, eds. C. Aerts, T. Bedding &J. Christensen-Dalsgaard, in press.

Van Cauteren, P. & Lampens, P. 2000, IBVS 4849


Vol. 141, 2002

Strømgren photometry of SX Phe = HD 223065

A. Stankov1, D. Sinachopoulos2, E. Elst3, M. Breger1

1 Institut fur Astronomie, Turkenschanzstrasse 17, 1180 Vienna, Austria2 Institute of Astronomy and Astrophysics, National Observatory of Athens, I.

Metaxa and Bas. Pavlou, 15236 Athens, Greece3 Koninklijke Sterrenwacht van Belgie, Ringlaan 3, 1180 Uccle, Belgium

Abstract

We present the analysis of more than 220 photometric measurements of thevariable star SX Phe. The observations were made with the Johnson V andthe four Strømgren (u, v, b, y) filters. An analysis of the parameters δc1 andδm1 is presented. The behavior of δc1 during the luminosity variations of thestar corresponds to that expected from the standard luminosity calibrations byCrawford (1979) with δV = −10δc1. The behavior of the metallicity index,δm1, does not correspond to the expectations from the standard calibrations.

Introduction

SX Phe stars are a Pop. II subgroup of the δ Scuti stars. In order to shedlight on the variability of SX Phe and related stars, many studies of SX Phehave been undertaken since the report on our previous observations (Elst 1978).Rodriguez et al. (1990) used Strømgren photometry to study the behavior ofthe δm1 index for SX Phe stars. In addition, Garrido et al. (1990) used uvby

photometry for the identification of pulsation modes (modal discrimination) ofthe pulsating δ Scuti stars. The observations presented here were obtained toprovide deeper understanding of the variability of SX Phe in the Strømgrenfilters.

Observations and data reduction

The ESO 50cm telescope was used to monitor SX Phe during the nights of1992 October 18 and 31, as well as 1992 November 1. HD 223011 was used as

A. Stankov et al. 73

28.5 28.6 28.7 28.8

7.4

7.2

7.0

6.8

SX Phoenicis

V

HJD [2448900+]

27.5 27.6 27.7 27.8

7.4

7.2

7.0

6.8

14.5 14.6 14.7 14.8

7.4

7.2

7.0

6.8

Figure 1: Photometry of SX Phe in V

a comparison star. The photometer of the 50cm ESO telescope is only a single-channel photometer. Consequently, the measurements through the four filterswere not obtained simultaneously, as was the case in Garrido et al. (1990).Due to technical problems, we had to use two different photomultipliers for our

74 Strømgren photometry of SX Phe = HD 223065

observations. During the first night we used a HAMAMATSU and during theother two nights a EMI 9789QB tube.

In addition, we observed 16 bright photometric standard stars each nightfor transforming our observations into the standard uvby system. The SNOPYsoftware on theHP 1000 computer was used for this transformation. The com-parison star did show any significant variability during this period. From thestatistical fluctuations of its reduced magnitudes and indices we estimate thatthe accuracy of a single HD 223011 measurement is σV = 0.006, σ(b−y) =0.005, σm1

= 0.008, σc1= 0.007 mag.

7.5 7.4 7.3 7.2 7.1 7.0 6.9 6.80.02

0.04

0.06

0.08

0.10

0.12

0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.200.070

0.075

0.080

0.085

0.090

0.095

0.100

G c1

V

G m1

(b-y)

Figure 2: Left pannel: δc1 versus V ; dotted line: expected slope from calibrationsfrom Crawford. Right pannel: δm1 versus (b− y).

Since SX Phe is about 0.9 magnitudes fainter than the comparison star, weexpect that the accuracy of measurement is lower for SX Phe. More than 10000counts per exposure (30 seconds each) of SX Phe were collected in each filterduring the first night using the HAMAMATSU photo-multiplier. The efficiencyof the EMI 9789QB tube was somewhat lower.

Table 1 lists the measurements of SX Phe, while Figure 1 shows the lightcurves of SX Phe obtained during three nights.

Variations of the Stromgren parameters during the pulsationalcycles

Crawford (1979) has presented calibrations of these parameters, based on alarge number of different stars. A pulsating star such as SX Phe changes itsluminosity and temperature during its pulsation cycle, but is not affected bya variable abundance. This provides an excellent opportunity to check thesecalibrations whether also apply the atmospheric changes during pulsation.


We can now turn to the variations of the metallicity parameter for A/F stars,δm1, and the luminosity parameter, δc1. The observed variations are shown inFig. 2. For δc1, we derive a slope of δV /δc1 = 9.8, in good agreement with theexpected value of 9.0 derived for different stars by Crawford. The two slopesare also shown in Fig. 2, where the Crawford slope is displaced vertically forgreater clarity.

The right panel of Fig. 2 shows the relation between δm1 and color, b− y.A definite non-zero slope is found. A comparison with the standard valuesgiven by Crawford (1979), describing the variation of δm1 with temperature,shows very poor agreement. A logical, but incorrect, interpretation would bethat the metal content changes during the cycle! We note here that SX Pheis extremely metal-poor and that the calibrations were set up for stars withnear-solar abundances. The calibrations, therefore, cannot be expected to holdfor SX Phe.

The behavior of SX Phe confirms the observed behavior of two other (metal-poor) SX Phe stars, KZ Hya and CY Aqr (Rodriguez et al. 1990).

References

Crawford, D. L. 1979, AJ 84, 1858Elst E. 1978, A&AS 32, 161Garrido, R., Garcia-Lobo, E., Rodriguez, E. 1990, A&A 234, 262Rodriguez, E., Rolland, A., Lopez de Coca, R., et al. 1990, Rev. Mexic.

Astron. Astrof. 21, 386


Table 1: Measurements of SX Phe

HJD +244 8900 V (b-y) m1 c114.4976 7.400 .185 .076 .78114.5134 7.417 .163 .096 .76314.5280 7.097 .097 .123 .92014.5332 7.069 .108 .123 .93814.5376 7.151 .122 .126 .900

14.5426 7.263 .152 .098 .86314.5468 7.337 .162 .097 .82114.5518 7.397 .179 .086 .79314.5560 7.439 .181 .089 .77114.5605 7.465 .187 .082 .760

14.5650 7.471 .182 .080 .75814.5691 7.441 .174 .081 .75014.5731 7.331 .135 .093 .78614.5771 6.989 .022 .138 .94814.5820 6.792 .057 .138 1.036

14.5842 6.851 .074 .138 1.03714.5882 7.033 .114 .126 .96314.5922 7.181 .140 .109 .90514.5962 7.301 .161 .096 .85114.6001 7.371 .175 .082 .821

14.6040 7.417 .182 .084 .79214.6079 7.450 .188 .080 .77314.6118 7.467 .188 .077 .76714.6166 7.465 .180 .088 .74514.6206 7.433 .168 .085 .757

14.6244 7.344 .143 .107 .77714.6282 7.166 .087 .118 .88214.6320 6.994 .075 .137 .96814.6360 7.007 .095 .126 .977

continued on next page


continued from previous page

HJD +244 8900 V (b-y) m1 c114.6399 7.090 .114 .123 .947

14.6438 7.186 .139 .125 .89214.6476 7.273 .155 .115 .85414.6515 7.335 .163 .116 .82314.6564 7.387 .173 .102 .80914.6604 7.411 .183 .096 .783

14.6643 7.429 .182 .092 .78114.6682 7.431 .175 .111 .75414.6720 7.428 .174 .105 .75914.6759 7.412 .168 .107 .76114.6798 7.383 .157 .114 .780

14.6839 7.327 .144 .115 .81514.6880 7.251 .120 .130 .85714.6918 7.192 .116 .131 .89014.6958 7.173 .121 .127 .90314.6997 7.193 .136 .115 .898

14.7037 7.238 .141 .126 .85714.7076 7.291 .156 .115 .83514.7115 7.339 .166 .109 .81714.7153 7.380 .172 .106 .80014.7209 7.433 .180 .098 .783

14.7249 7.453 .182 .098 .77614.7289 7.461 .181 .101 .75714.7342 7.442 .171 .098 .76414.7391 7.353 .135 .113 .78914.7436 7.084 .068 .134 .925

14.7481 6.899 .071 .140 1.01214.7527 6.972 .100 .140 .99814.7574 7.151 .135 .136 .90514.7622 7.296 .161 .107 .860




HJD +244 8900 V (b-y) m1 c114.7647 7.346 .171 .101 .82914.7694 7.401 .183 .091 .81214.7742 7.451 .186 .105 .77114.7789 7.470 .191 .094 .75814.7834 7.466 .184 .088 .76327.5212 7.411 .200 .085 .783

27.5309 7.460 .197 .084 .76527.5324 7.460 .190 .092 .75727.5374 7.419 .166 .103 .75327.5390 7.381 .166 .091 .77127.5438 7.209 .101 .117 .86827.5455 7.097 .072 .130 .93627.5496 6.974 .085 .132 .99927.5512 6.982 .095 .128 1.00227.5560 7.078 .121 .126 .95927.5575 7.119 .128 .127 .934

27.5592 7.167 .136 .119 .92027.5640 7.276 .154 .117 .86827.5655 7.306 .159 .114 .85527.5672 7.329 .164 .117 .83227.5719 7.379 .171 .117 .800

27.5734 7.401 .168 .112 .80127.5751 7.404 .179 .104 .79427.5799 7.421 .191 .093 .78227.5818 7.427 .181 .106 .77127.5834 7.434 .177 .113 .755

27.5884 7.433 .171 .109 .77527.5900 7.425 .174 .106 .77027.5916 7.423 .169 .111 .76227.5963 7.399 .156 .116 .77527.5979 7.378 .146 .126 .787




HJD +244 8900 V (b-y) m1 c127.6007 7.337 .134 .129 .81827.6046 7.254 .121 .133 .85927.6062 7.228 .119 .132 .87727.6078 7.208 .119 .134 .88627.6124 7.188 .125 .130 .895

27.6140 7.194 .133 .120 .90627.6157 7.207 .131 .134 .88127.6199 7.251 .142 .121 .87727.6215 7.270 .143 .127 .86427.6232 7.289 .155 .119 .850

27.6280 7.346 .164 .106 .82527.6295 7.360 .170 .104 .81127.6312 7.382 .169 .105 .81027.6350 7.414 .173 .110 .78327.6366 7.426 .181 .103 .77327.6382 7.443 .180 .103 .76827.6400 7.445 .180 .107 .77127.6416 7.448 .189 .095 .76527.6433 7.461 .180 .103 .75927.6451 7.471 .174 .105 .766

27.6468 7.467 .175 .112 .74127.6484 7.459 .178 .101 .75927.6533 7.410 .155 .105 .78327.6548 7.377 .134 .126 .77227.6564 7.323 .127 .118 .801

27.6604 7.093 .079 .114 .93527.6620 6.990 .061 .138 .97027.6636 6.943 .065 .136 1.00127.6684 6.960 .089 .139 1.00527.6700 7.004 .107 .130 .991

27.6716 7.069 .111 .141 .945continued on next page



HJD +244 8900 V (b-y) m1 c127.6762 7.214 .151 .112 .89427.6778 7.255 .155 .121 .86327.6794 7.296 .160 .120 .83627.6842 7.374 .178 .105 .808

27.6858 7.389 .183 .099 .80627.6874 7.403 .188 .103 .78727.6923 7.456 .188 .094 .78427.6939 7.464 .188 .104 .76027.6978 7.464 .193 .091 .758

27.6994 7.459 .192 .088 .76527.7033 7.439 .169 .099 .75927.7050 7.406 .164 .105 .75527.7089 7.258 .120 .109 .80727.7107 7.119 .068 .113 .895

27.7146 6.804 .051 .143 1.02127.7163 6.808 .065 .139 1.03527.7201 6.916 .094 .141 1.02227.7218 6.982 .118 .132 .97827.7257 7.133 .142 .115 .93727.7296 7.249 .156 .113 .86927.7335 7.332 .173 .104 .82327.7374 7.377 .185 .097 .81127.7414 7.411 .189 .094 .77327.7454 7.428 .190 .099 .759

27.7493 7.426 .191 .085 .76727.7533 7.411 .183 .089 .76127.7573 7.376 .167 .106 .75728.5088 7.373 .181 .109 .76928.5104 7.388 .190 .094 .774

28.5121 7.406 .181 .106 .75528.5171 7.418 .193 .096 .733




HJD +244 8900 V (b-y) m1 c128.5188 7.425 .186 .094 .74228.5204 7.414 .189 .096 .72428.5254 7.391 .169 .099 .747

28.5270 7.369 .182 .078 .76128.5286 7.356 .157 .101 .76528.5337 7.240 .132 .098 .84528.5353 7.202 .111 .118 .86928.5369 7.157 .118 .105 .902

28.5410 7.120 .125 .102 .93028.5426 7.125 .122 .110 .92228.5442 7.144 .116 .126 .89728.5489 7.192 .136 .111 .88628.5505 7.216 .141 .109 .881

28.5521 7.232 .149 .106 .86028.5537 7.256 .151 .107 .84328.5579 7.304 .163 .102 .81328.5595 7.319 .167 .100 .80528.5611 7.332 .173 .094 .801

28.5656 7.374 .174 .096 .78528.5672 7.381 .178 .099 .76528.5691 7.398 .180 .088 .78228.5729 7.412 .184 .087 .77428.5745 7.420 .177 .097 .76028.5761 7.421 .179 .099 .75028.5777 7.431 .176 .095 .75628.5824 7.429 .168 .094 .76328.5841 7.416 .173 .090 .75928.5857 7.405 .163 .099 .761

28.5900 7.343 .146 .098 .79128.5916 7.302 .138 .100 .81028.5934 7.257 .122 .109 .837




HJD +244 8900 V (b-y) m1 c128.5980 7.118 .100 .118 .91328.5996 7.091 .095 .122 .927

28.6012 7.072 .099 .121 .93928.6050 7.092 .108 .125 .93328.6067 7.110 .124 .118 .91528.6084 7.157 .117 .125 .91128.6130 7.250 .149 .099 .857

28.6146 7.281 .150 .108 .82328.6162 7.309 .158 .094 .82628.6202 7.353 .175 .090 .78928.6218 7.384 .165 .095 .79728.6234 7.394 .175 .089 .785

28.6280 7.432 .185 .074 .77828.6296 7.439 .189 .075 .76328.6312 7.453 .182 .079 .75628.6351 7.459 .170 .089 .74428.6367 7.464 .175 .096 .736

28.6383 7.456 .172 .087 .75028.6429 7.377 .144 .099 .75328.6445 7.316 .125 .097 .79128.6461 7.219 .087 .107 .83928.6499 6.847 .039 .126 1.005

28.6516 6.805 .051 .120 1.04228.6532 6.809 .066 .116 1.05428.6548 6.854 .065 .137 1.04028.6596 7.057 .117 .117 .95928.6613 7.110 .134 .111 .92928.6629 7.175 .134 .115 .89728.6672 7.299 .164 .099 .83828.6688 7.338 .167 .094 .82728.6740 7.411 .176 .083 .810




HJD +244 8900 V (b-y) m1 c128.6757 7.417 .187 .083 .788

28.6796 7.456 .184 .088 .76228.6812 7.469 .186 .089 .76128.6857 7.473 .195 .070 .77528.6874 7.471 .179 .091 .75228.6913 7.446 .164 .090 .757

28.6930 7.407 .167 .079 .77328.6968 7.290 .123 .109 .81228.6984 7.191 .103 .104 .87228.7030 6.953 .073 .132 .97928.7046 6.957 .076 .138 .984

28.7092 7.042 .100 .132 .97028.7108 7.091 .112 .129 .94028.7155 7.212 .149 .102 .88728.7172 7.252 .147 .113 .85528.7213 7.327 .168 .114 .834

28.7259 7.375 .188 .101 .80228.7299 7.408 .192 .098 .78128.7339 7.423 .192 .094 .78628.7380 7.433 .174 .121 .75328.7420 7.429 .179 .107 .75728.7459 7.415 .170 .114 .77128.7499 7.377 .160 .106 .79628.7538 7.323 .142 .126 .816

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