short-period line profile variations in the be star ε cap

Mon. Not. R. Astron. Soc. 321, 131±142 (2001)

Short-period line profile variations in the Be star e Cap

L. A. Balona1w and W. A. Lawson2

1South African Astronomical Observatory, PO Box 9, Observatory 7935, Cape, South Africa2School of Physics, University College UNSW, Australian Defence Force Academy, Canberra, ACT 2600, Australia

Accepted 2000 August 25. Received 2000 August 1; in original form 2000 March 6

A B S T R A C T

We present new high-dispersion spectroscopic data for the Be star e Cap. The purpose of

these data is to study the short-period line profile variations. By using a two-dimensional

period-finding technique, we confirm that the photometric period of 0.99 d is present in the

helium line profiles. We show that the variations are not easily explained by non-radial

pulsation and suggest that corotating circumstellar material is responsible.

Key words: line: profiles ± stars: early-type ± stars: emission-line, Be ± stars: individual:

e Cap.

1 I N T R O D U C T I O N

e Cap (HR 8260, HD 205637, HIP 106723) is a B3Ve shell star

with a considerable record of short- and long-term variations.

Occultation observations show that the star is a close binary (Abt

& Cardona 1984). Rivinius, SÏ tefl & Baade (1999) obtained an

orbital period of about 95 d. Pedersen (1979) found a period of

0.9775 d from spectrophotometry of the He i 4026 AÊ line. Cuypers,

Balona & Marang (1989) showed that the short-period light

variations in e Cap could be phased with a period P � 1:03 d:Mennickent, Vogt & Sterken (1994) found a quasi-period of about

780 d in the photometry, the star being redder when fainter.

Porri & Stalio (1988) reported central quasi-emission features

in the helium lines. These central quasi-emission peaks seem to be

related to an edge-on circumstellar disc that is optically thin in the

continuum, has a small spatial extent and little intrinsic line

broadening. A study of Be stars showing such features has recently

been undertaken by Rivinius et al. (1999) and confirms the model

of Hanuschik (1995) for the formation of shell lines in circum-

stellar discs in Keplerian rotation.

In spite of the fact that Be stars have been studied intensively

for over a century, we still do not understand the mechanism for

formation of the circumstellar disc. The periodic variations in the

light and line profile variations in Be stars seem to provide a clue,

but we do not fully understand what is causing the periodic

variations. One idea is that it is caused by non-radial pulsation and

another that it is caused by occultation by corotating circumstellar

clouds.

We observed e Cap as part of a project to understand periodic

variability in Be stars. The star is bright and is known to show

periodic light variations. Since most Be stars have periods close to

1 d, the intention was to obtain high-dispersion spectroscopy from

South Africa (SAAO) and Australia (Mt Stromlo and Siding

Spring Observatories ± MSSSO). Unfortunately, bad weather at

MSSSO greatly reduced the usefulness of these results. The

SAAO data are exclusively used in the investigation of the period

and line profile variations. The MSSSO data were useful in the

investigation of the He i 6678 line. In spite of this unfortunate

circumstance, we feel that the data are sufficient to determine the

period and the nature of the line profile variations.

2 O B S E RVAT I O N S

Observations at SAAO were obtained using the GIRAFFE eÂchelle

fibre-fed spectrograph attached to the Cassegrain focus of the

1.9-m telescope during 1998 September 1±15. The GIRAFFE

spectrograph has a resolving power of about 32 000. The

wavelength range for these observations was 4080±5790 AÊ spread

over 51 orders. The 1024 � 1024 TEK charge-coupled device

(CCD) chip gives a resolving power of 0.06±0.08 AÊ pixel21. A

Th±Ar arc lamp was used for wavelength calibration with arc

spectra taken at regular intervals to calibrate possible drifts.

Flatfielding was accomplished by illuminating the camera with

uniform light using a tungsten filament lamp and a diffusing

screen. The blaze correction was determined by measuring the

response across each order when the fibre was illuminated by a

tungsten lamp. Exposure times were in the range 5±20 min for a

signal-to-noise (S/N) ratio of about 200. A total of 114 spectra of

e Cap was obtained (see Table 1).

The MSSSO data were obtained with the CoudeÂ±eÂchelle slit

spectrograph of the 1.9-m telescope during 1998 September 3±6

and October 1±8. Owing to unforeseen circumstances, we were

unable to use the same wavelength range as on the SAAO

spectrograph. The MSSSO spectra covered 6240±7190 AÊ spread

over 14 orders with a dispersion of about 0.07 AÊ pixel21. The

detector was a 4096 � 2048 SITe CCD employed at 2 � 2

prebinning, giving a resolving power of about 48 000. A Th±Ar

arc lamp was used for wavelength calibration. Flatfielding and

blaze correction was accomplished by illuminating the slit with a

tungsten lamp. Exposure times were 15 or 20 min for a S/N ratio

q 2001 RAS

w E-mail: [email protected]

of about 100. A total of 27 spectra of e Cap was obtained

(Table 1).

3 P H Y S I C A L PA R A M E T E R S O F T H E S TA R

There are substantial line profile variations in the helium lines of

about 2 per cent in intensity. In Fig. 1 we present mean line

profiles of all the helium and hydrogen lines that were measured.

The Balmer lines show that the strong shell spectrum is still

present. From the variation and the asymmetry of the lines, it is

clear that all lines are affected by the circumstellar material to

some degree. The He i 5016 and 4921 lines are strongly blended

with lines of Fe ii originating in the shell. The central quasi-

emission feature studied by Rivinius et al. (1999) is weakly

present in the He i 4471 and 6678 lines. This can be compared

with the profiles of the same two lines shown in Porri & Stalio

(1988). The Fe ii shell lines are prominent; the mean profiles of

the strongest ones are shown in Fig. 2.

The projected rotational velocity of e Cap is given as

250 km s21 by Slettebak (1982) from a visual estimate of

photographic spectra. To what extent this value is influenced by

circumstellar material is, of course, problematic. We attempted to

determine v sin i from those helium lines that appear to be

relatively symmetric. This was done by using an intrinsic line

profile calculated using the spectrum line synthesis code (Gray &

Corbally 1994) and a uniformly bright spherical star with linear

limb darkening coefficient u � 0:30: The value of v sin i and

radial velocity, Vr, were the only two free parameters. The

equivalent width was constrained to be the same as the observed

equivalent width (EW). Results of a calculation by nonlinear least-

squares fit is shown in Table 2 and the fits are shown by the

Table 1. Observing log for the SAAO andMSSSO. The Julian day is with respect toJD 245 1000; N is the number of spectra ofe Cap obtained on that night.

SAAO MSSSOJD N JD N

58 13 59 159 8 60 160 11 62 162 3 63 663 11 87 164 15 89 465 10 90 366 14 91 167 3 92 468 9 93 369 5 94 270 271 10

Figure 1. The mean line profiles of several He i lines and Ha , Hb and Hg . The dotted profiles are fits using rotationally broadened Gaussian profiles.

132 L. A. Balona and W. A. Lawson

q 2001 RAS, MNRAS 321, 131±142

Figure 2. The mean line profiles of some Fe ii shell lines.

Figure 3. Periodograms of StroÈmgren b data from the LTPV catalogue. The frequency is in cycle d21 and the amplitude in magnitudes. The range of Julian

date relative to JD 244 0000 is shown in each panel.

Short-period line profile variations in e Cap 133

q 2001 RAS, MNRAS 321, 131±142

dashed lines in Fig. 1. The mean value is v sin i � 286 km s21;which is the value adopted here. The dispersion in the calculated

v sin i is large, indicating a strong contribution owing to the

circumstellar material, even in those lines which do not show

emission or incipient emission.

The Hipparcos parallax is 4:92 ^ 0:91 mas which, coupled with

an apparent magnitude V � 4:49 ^ 0:05 and E�B 2 V� � 0:04

(Zorec & Briot 1991), gives MV � 22:2 ^ 0:4: The apparent

magnitude is the mean of 625 photometric measurements obtained

between 1985 and 1992 at the SAAO. All Be stars are subject to

large, irregular light variations. The quoted error in V is the

standard deviation of the mean, which is a taken as a measure of

the scatter in V. The absolute magnitude based on its spectral type

is about MV � 22:2 (Balona & Crampton 1974), the same as

given by the Hipparcos parallax.

The radius can be derived from the absolute magnitude if we

have an estimate of the effective temperature. For a spectral type

of B3 and assuming an uncertainty of half a subtype, we have

log Teff � 4:28 ^ 0:04; BC � 21:9 ^ 0:2 from Popper (1980),

where BC is the bolometric correction. These values, together with

the Hipparcos parallax give a radius of R=R( � 5:3 ^ 1:5: The

value assumed by Porter (1996) for a B3 emission-line star is

R=R( � 4:7: The radius calibration of Balona (1995) gives

R=R( � 4:2; 5.8 and 7.4 for B3 luminosity classes V, IV and III,

respectively. The Hipparcos parallax probably gives our best

estimate for the luminosity, so the radius derived from the

luminosity and effective temperature is probably more reliable

than one derived from a spectral classification calibration.

Rapid rotation will give a somewhat larger equatorial radius: at

critical rotation the equatorial radius will be about 1.5 times larger

than the polar radius (Porter 1996). Assuming an expansion of

1.25 in the radius gives R=R( � 6:6 ^ 1:9; which we will adopt

as the equatorial radius of e Cap. The expected period of rotation

is then P � 1:3 ^ 0:3 d; assuming i � 908 and a rms error of about

50 km s21 for the projected rotational velocity. The critical

rotational velocity for a B3 star is about 460 km s21 (Porter

1996), which implies a minimum period of rotation of about 0.7 d

and an angle of inclination i . 378:

4 P E R I O D F I N D I N G ± P H OT O M E T RY

Cuypers et al. (1989) showed that the short-period light variations

in e Cap could be phased with a period P � 1:03 d: Because it is

so close to 1 d, this period must be regarded as uncertain. The

Hipparcos data shows a sharp decrease in brightness �H � 4:58�in 1990 June, followed by a slow recovery to H � 4:41 over the

next few years. These data are not suitable for determining periods

of the order of 1 d. Balona (1993) reported a linear increase in

brightness of nearly 0.1 mag during 1992 September. Superimposed

upon this, there is a sinusoidal variation with period close to 1 d

and an amplitude of 0.03 mag. This type of variability, in which a

sudden increase in brightness is associated with short-period

variations, has also been seen in k CMa (Balona 1990) and can be

understood in terms of a localized outburst rotating with the star.

The star has also been observed extensively as part of the Long-

term Photometry of Variables project (Manfroid et al. 1991;

Sterken et al. 1993). We chose seasons where the long-term

Table 3. The three most significant frequencies extracted froman analyses of the line profiles. The first column gives thewavelength of the line. the other columns give the frequencyin cycle d21. The quantities that are analysed are the radialvelocity, Vr, equivalent width, EW, and the first four moments.

Line Vr EW M1 M2 M3 M4

He i 4144 3.03 0.11 2.03 0.11 0.85 0.1112.13 0.45 0.85 0.19 1.98 0.1910.12 0.20 6.75 2.16 2.05 1.15

Hg 4340 0.35 1.14 1.19 0.14 0.17 0.130.89 2.01 0.42 0.50 0.61 0.500.19 0.75 1.30 7.85 1.53 0.20

He i 4388 2.01 0.12 2.03 2.01 2.02 2.004.29 0.31 0.08 0.60 0.08 0.590.29 1.60 2.43 2.76 1.73 1.13

He i 4471 3.03 0.07 1.05 0.04 0.05 0.041.21 1.17 1.12 0.12 1.13 0.125.04 2.09 0.90 2.01 0.80 2.00

Mg ii 4481 2.00 2.00 0.32 0.88 0.41 0.872.05 0.07 0.40 0.95 0.33 0.39

16.01 0.13 2.04 0.39 1.78 0.25

Fe ii 4583 2.01 2.03 2.02 0.38 0.12 0.390.50 0.13 0.12 0.50 2.01 0.344.41 0.41 2.09 0.33 1.55 1.12

He i 4713 3.02 0.13 0.08 0.12 0.24 0.125.05 1.86 0.22 0.74 0.10 0.220.87 0.22 0.31 0.19 3.26 0.31

Hb 4861 0.64 1.02 1.05 0.13 1.05 1.120.12 0.89 0.90 0.33 0.92 0.321.43 0.20 1.19 1.75 1.19 0.85

He i 4921 1.04 0.13 0.88 0.13 0.88 0.120.13 1.04 1.76 0.95 0.75 5.680.61 0.61 0.35 5.68 4.70 0.94

He i 5016 1.04 0.11 0.11 0.11 0.10 0.110.24 1.88 2.03 2.10 1.87 2.091.55 2.11 2.12 1.17 0.26 1.17

He i 5047 3.02 0.12 0.95 0.18 0.05 0.191.92 0.05 0.31 0.44 0.16 0.445.02 0.29 0.45 0.90 0.65 0.91

Fe ii 5169 2.01 2.00 2.01 2.00 2.00 0.970.34 0.07 0.21 0.06 0.45 0.071.08 0.35 4.01 3.36 3.99 3.35

Fe ii 5197 0.09 2.01 0.23 2.01 0.13 0.122.04 0.46 5.84 0.12 1.24 2.011.90 10.10 0.71 4.28 3.64 4.27

Fe ii 5316 2.05 0.07 0.09 2.01 0.38 0.056.20 2.02 3.02 0.05 3.01 2.020.83 3.80 0.60 2.88 0.31 1.14

Table 2. Results of fitting a rotationallybroadened intrinsic profile to some He i linesusing a nonlinear least-squares solution. Thevalue of v sin i is in km s21 and s is the rmserror of the intensity. The radial velocity, Vr, isin km s21 and the equivalent width, EW, in AÊ .

Line v sin i Vr s EW

He i 4144 271 211.2 0.0034 0.68He i 4388 318 236.0 0.0039 0.78He i 4471 270 1.0 0.0041 1.33


q 2001 RAS, MNRAS 321, 131±142

Figure 4. The EW variation of some helium lines and the Hg and Hb lines (in AÊ ).

.01.

02.

03.

04.

05.

0Fr

eque

ncy

Figure 5. Grey-scale images of the periodogram at fixed wavelengths across the line profiles of He i lines at 4144 (left), 4388, 4471 and 4922 AÊ (right). The

ticks along the X-axis are spaced at intervals of 100 km21. The frequency is in cycle d21.


q 2001 RAS, MNRAS 321, 131±142

variability, typical of Be stars, appears to be small and calculated

the periodograms. The periodogram is calculated by fitting the

best sinusoid at each frequency and plotting the resulting

amplitude as a function of frequency. The data are successively

prewhitened with the frequency of highest amplitude (equivalent

to minimum scatter) to obtain possible further Fourier compo-

nents. The results shown in Fig. 3 tend to confirm that there is a

periodicity near 1 d. The exact period is severely distorted by the

1-d aliasing problem.

5 P E R I O D F I N D I N G : S P E C T R O S C O P Y

Period analysis of the light curve seeks to find periodicities in the

luminosity of the star through a given passband. In the case of

spectroscopic measurements, one ought to strive to measure quan-

tities that likewise have physical significance. The spectroscopic

line profile behaves in a complex manner and it is not at all clear

which quantity best measures the period. A very common

technique is to analyse the intensity at fixed wavelengths across

the rectified line profile, but no physical meaning can be attached

to such measurements. We prefer to attack the problem in as many

different ways as possible. We therefore measured the following

quantities for each line profile:

(i) the wavelength at minimum intensity (the mode), which we

will call the `radial velocity';

(ii) the equivalent width or zeroth moment;

(iii) the centroid (first moment), second, third and fourth

moments.

The physical meaning of the radial velocity is not clear, but

each of the moments can be related to the pulsational parameters

as described by Balona (1987).

In Table 3 we show for each line the three frequencies of

-400.-200. 0. 200. 400.4144

.0.2

.4.6

.81.

01.

21.

4P

hase

-400.-200. 0. 200. 400.4388

.0.2

.4.6

.81.

01.

21.

4

-400.-200. 0. 200. 400.4471

.0.2

.4.6

.81.

01.

21.

4P

hase

-400.-200. 0. 200. 400.4921

.0.2

.4.6

.81.

01.

21.

4

Figure 6. Grey-scale images of the difference profiles of four He i phased with frequency f � 1:01 cycle d21: The velocity axis is in km s21; epoch of phase

zero is HJD 245 1000.000. In this and other grey-scale figures, light areas represent excess emission, dark areas excess absorption relative to the mean line

profile.


q 2001 RAS, MNRAS 321, 131±142

highest amplitude in the radial velocity, EW and first four

moments. It is clear that a frequency close to f � 2:0 cycle d21 or

its 1-d aliases is present in most lines and usually has the largest

amplitude. In addition, a frequency of about 0.14 cycle d21 is

present in the EW and is also visible in some of the other

quantities. The strong variation in EW may be caused by the effect

of circumstellar material on the line profiles. The variation for

some helium lines is shown in Fig. 4. The nature of the EW

variation is complex; some lines show an antiphase variation.

Finally, in Fig. 5 we show grey-scale plots of the periodogram

of the intensities at fixed wavelengths across the line profiles of

four helium lines. Once again, it is evident that a periodicity is

present at about 2.0 cycle d21 or the 1-d alias.

We conclude from the analysis of the photometry and

spectroscopy that there are very strong reasons to believe that a

periodicity exists in e Cap which is close to 1 or 0.5 d. Because the

period is so close to 1 or 0.5 d, data from MSSSO would have been

particularly important. Unfortunately, the few spectra of He i 6678

from MSSSO are not useful for this purpose. Some constraint on

the choice between 1 or 0.5 d could have been obtained by

examining the variations during a night. Unfortunately, the short

summer nights allow only, at most, one quarter or half a cycle to be

observed, which is too short to allow any constraint on the period.

It is important to note that the star does not behave in a simple

way and one cannot assume that the variation is simply a

superposition of a large number of sinusoidal variations (as may

be expected from a pulsating star). There is no evidence for

coherent periods except for the two frequencies at 0.14 and

2.0 cycle d21. The former frequency may be spurious as the

observations only cover barely two cycles.

6 T W O - D I M E N S I O N A L P E R I O D A N A LY S I S

In the previous section we attempted a period search for a one-

dimensional quantity such as magnitude, radial velocity, a moment

-400.-200. 0. 200. 400.4144

.0.2

.4.6

.81.

01.

21.

4P

hase

-400.-200. 0. 200. 400.4388

.0.2

.4.6

.81.

01.

21.

4

-400.-200. 0. 200. 400.4471

.0.2

.4.6

.81.

01.

21.

4P

hase

-400.-200. 0. 200. 400.4921

.0.2

.4.6

.81.

01.

21.

4

Figure 7. Grey-scale images of the difference profiles of four He i phased with frequency f � 2:02 cycle d21: The velocity axis is in km s21; epoch of phase

zero is HJD 245 1000.000.


q 2001 RAS, MNRAS 321, 131±142

of the line profile, etc. If the variations are strictly periodic, or if

there is one dominant period, it is possible to obtain a better

estimate of the period by examining grey-scale plots of difference

profiles phased according to a given test period. A `difference

profile' is obtained when the line profile at a given time is divided

by the mean profile. This technique allows the visualization of

line profile variations in two dimensions: time and wavelength.

Unlike a one-dimensional quantity, such as magnitude, there is

now the additional constraint that the time variation must lead to a

continuous, coherent pattern. The phase diagram at the correct

period must show definite structures varying continuously with

time. At other periods the structure dissolves into a random

pattern. This additional constraint is important in producing better

discrimination among the aliases and therefore a more reliable

indication of the true period.

The procedure consists in constructing a phase diagram of the

difference spectra as a function of wavelength for a trial period

and visually inspecting the diagram for coherent structures. The

period is increased by a small amount and another diagram

produced and inspected. Since we know that the most likely period

is near 1 or 0.5 d, we confined the search around these two

periods. We prefer to use velocity instead of wavelength, the

velocity being calculated relative to the laboratory wavelength of

the line in question. This allows different lines to be compared

more easily.

It became quite clear that the correct period corresponds rather

closely to a frequency f � 1:01 cycle d21 �P � 0:99 d�: The phase

diagrams are still reasonably coherent at f � 1:00 and 1.02 d21,

but quickly degenerate into a random distribution outside this

range. In particular, the alias frequency f � 0:99 cycle d21 does

not produce satisfactory coherence of the pattern. All helium lines

show the same pattern. In Fig. 6 we show the pattern for f �1:01 d21 for four He i lines. A coherent pattern is also produced at

twice this frequency, f � 2:02 d21; which is shown in Fig. 7 for

the same lines.

The pattern is quite clear and easy to interpret. It appears to

be caused by two structures situated more or less diametrically

opposite one another (either clouds or NRP waves). For the

f � 2:02 d21 case, however, the structures appear to persist for

longer than half a period. If the structures are corotating, this can

only occur if the angle of inclination of the rotational axis, i, is

tilted towards the observer and not equator-on. Because of its shell

spectrum, e Cap is likely to have a high angle of inclination. The

choice of f � 1:01 d21 produces features that are visible for only

half a cycle and is consistent with an equator-on geometry. This

argument does not apply if the structures are caused by NRP

perturbations. The fact that two structures are present, nicely

explains why f � 2:02 d21 is the dominant frequency in the line

profiles.

Although the phase coverage with f � 1:01 d21 is no more than

40 per cent of a cycle, we believe that the variation of the pattern

of the difference spectra with time cannot be understood in any

other way. The possibility that the true frequency is 2.02 cycle d21

is not entirely excluded. However, we note that the 1-d alias of the

photometric period (1.03 cycle d21) found from the multilongitude

observations of Cuypers et al. (1989) can be identified with

the 1-d period, but is incompatible with a period near 0.5 d. A

re-analysis of the data shows no sign of a period frequency at

2 cycle d21. On this basis, we consider that the true period is very

likely to be f � 1:01 cycle d21:The pattern for the Balmer lines is less distinct (Fig. 8). This

effect is also seen in h Cen (Balona 1999) and arises from the fact

that the line core is formed further from the star compared

with the helium lines. The patterns in the Fe ii are even less

distinct (Fig. 9). There appears to be no definite periodicity in

these shell lines.

7 M O D E L L I N G

In order to obtain some indication of what pulsational parameters

would be required, we fitted the He i 4144 and 4388 line profiles

by a simple NRP model, which assumes that the eigenfunction can

be expressed by a single spherical harmonic of degree ` and

azimuthal order m. This is not a very good approximation in a

rapidly rotating star where the period in the corotating frame may

-400.-200. 0. 200. 400.4340

.0.2

.4.6

.81.

01.

21.

4P

hase

-400.-200. 0. 200. 400.4862

.0.2

.4.6

.81.

01.

21.

4Figure 8. Grey-scale images of the difference profiles of Hg (left) and Hb (right) phased with frequency f � 1:01 cycle d21: The velocity axis is in km s21;

epoch of phase zero is HJD 245 1000.000.


q 2001 RAS, MNRAS 321, 131±142

be long. However, it is clear that NRP, if present, is not the only

factor involved in the line profile variations. The contribution

owing to circumstellar material cannot be modelled. Instead of the

crude NRP model, we could have used a sophisticated code and

detailed synthetic line profiles. While this is perfectly justified in a

star in which the circumstellar material is less intrusive or

virtually absent (as in 28 CMa, for example; see Balona et al.

1999), it is hardly appropriate in this case. All we can hope for is a

rough estimate of the mode and pulsational parameters and for this

purpose the simple NRP model is adequate. We ignore the effect

of temperature variations arising from pulsation in this model. The

horizontal velocity amplitude was calculated using the normal

result obtained from the pressure boundary condition.

The observed line profiles were phased with either the f � 1:01

or 2.02 d21 periodicities and binned together. Fig. 10 displays the

observed line profiles assuming f � 1:01 d21; while in Fig. 11

f � 2:02 d21 is used. In order to obtain the best-fitting pulsational

parameters, we performed a direct fit of the model to the observed

line profiles for fixed (`, m). A grid of models covering all

physically plausible parameter values was constructed and the rms

deviation between the observed and calculated profiles deter-

mined. This gives a first approximation to the global minimum for

the particular (`, m). Using these values as starting parameters, the

difference between the observed and calculated profiles was again

minimized. We allowed the angle of inclination and the

pulsational amplitude and phase as the only free parameters.

Results are shown in Table 4.

The table shows that there is no consistent (`, m) which gives

the best fit for the two lines for either f � 1:01 or 2.02 cycle d21.

This is, in any case, fairly obvious by inspection of Figs 10 and 11

where the difference in line profile shapes between He i 4144 and

4388 is quite striking. Also, even the best-fitting parameters of

Table 4 fail to reproduce the line profile variations with any degree

of accuracy, as can be seen in the figures. It is also clear that this is

not a result of the accuracy of the model calculations. The most

likely explanation for the large difference in behaviour between

-400.-200. 0. 200. 400.4583

.0.2

.4.6

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01.

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4P

hase

-400.-200. 0. 200. 400.5169

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01.

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4

-400.-200. 0. 200. 400.5197

.0.2

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01.

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4P

hase

-400.-200. 0. 200. 400.5316

.0.2

.4.6

.81.

01.

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4

Figure 9. Grey-scale images of the difference profiles of the shell Fe ii lines at 4583, 5169, 5197 and 5316 AÊ phased with frequency f � 1:01 cycle d21: The

velocity axis is in km s21; epoch of phase zero is HJD 245 1000.000.


q 2001 RAS, MNRAS 321, 131±142

the lines is the influence of circumstellar material, as already

mentioned. For this reason, line profile fitting, by itself, cannot be

used to test for NRP in this star.

8 C O N C L U S I O N S

The fact that quasi-emission peaks are seen in some of the helium

lines in e Cap suggests that the circumstellar disc is affecting the

line profiles. This conclusion is further strengthened by the

inconsistent projected rotational velocities obtained from different

helium lines and the EW variability of these lines. The large

difference in line profile shape between He i 4144 and 4388 shown

in Fig. 10 shows that circumstellar material is severely distorting

the line profiles of one or both these lines. It seems that at least for

some helium lines the line profile is formed at various levels

above the photosphere. The difference profiles do, however, show

very similar patterns for all the helium lines (Figs 6 and 7). This

seems to us to be an indication that the periodicity arises not in the

photosphere, but some distance above it in the circumstellar

material.

From the periodograms of a variety of one-dimensional

spectroscopic parameters, there is strong evidence for a periodi-

city near f � 1:0 or 2.0 cycle d21. By inspection of two-

dimensional phase diagrams, we show that the frequency can be

refined to f � 1:01 or 2.02 cycle d21 and that the ambiguity

caused by 1-d aliasing is much reduced. The multilongitude

photometric data of Cuypers et al. (1989), is consistent with a

period near 1 d but not 0.50 d. There are no constraints for the

NRP model, which is consistent with either period. Inspection of

phased grey-scale plots of difference spectra shows that for

corotating clouds the 0.50-d period implies a low angle of

inclination. In this model the grey-scale plot for the 0.99-d period

agrees with the high angle of inclination expected from the

presence of shell lines.

The period of 0.99 d is in good agreement with the expected

period of rotation of the star and is consistent with the well-known

correlation between projected rotational velocity and the photo-

metric period in Be stars (Balona 1990, 1995). While we are

confident that the period is close to 1 d rather than 0.5 d, our phase

coverage is poor and a final resolution of the problem must await

multilongitudinal simultaneous observations.

Periodic variations in Be stars have been interpreted in terms of

NRP or rotational modulation of some kind. There are two stars

that are crucial to the understanding of the mechanism giving rise

to the periodic variations: m Cen and h Cen. By far the strongest

case for NRP is in the line profile variations of m Cen (Rivinius

et al. 1998). This star is interpreted as a multiperiodic non-radial

pulsation with four closely spaced periods near 0.505 d and two

near 0.28 d. The times of maximum beat amplitude correspond to

outbursts, suggesting a close link between NRP and the mass loss

mechanism. This, however, is not the only interpretation of the

observations (Balona et al. 2000). On the other hand, h Cen shows

a complex pattern in the difference profiles of the helium lines

which repeats with the well-determined photometric period

(Balona 1999). The pattern is at variance with what might be

Figure 10. Line profiles of the helium lines at 4144 and 4388 AÊ phased with f � 1:01 cycle d21 and binned. The dashed lines are the best-fitting NRP profiles

from Table 4. For the 4144 line the mode is �`;m� � �1; 1� and for 4388 it is (2, 0).


q 2001 RAS, MNRAS 321, 131±142

expected from NRP and are interpreted in terms of corotating

circumstellar clouds by Balona (1999).

Balona (1993) reported periodic light variations in e Cap

during an outburst phase. These observations are very similar

to those reported in k CMa (Balona 1990), which has better

coverage of the outburst. In the latter star a sharp rise in

brightness, is accompanied by periodic light variations with the

typical 1-d period. The periodic variation was absent before

the outburst, indicating that NRP cannot be responsible for the

subsequent periodic variations during the outburst. This strongly

suggests that the outburst is the cause of the periodic variations,

not the other way round, as Rivinius et al. (1998) propose for

m Cen.

In e Cap we have shown that the observations can be

understood as corotation, at least qualitatively. A quantitative

model must await a fuller understanding of the physical conditions

and geometry of the putative clouds. Our attempt to fit NRP line

profiles failed owing to the severe distortion of the lines by

circumstellar material. If NRP is present, then its effect has to be

in some way transmitted to the circumstellar material to account

for the line profile variations which are visible even in helium

lines which are heavily affected by this material.

Figure 11. Line profiles of the helium lines at 4144 and 4388 AÊ phased with f � 2:02 cycle d21 and binned. The dashed lines are the best-fitting NRP profiles

from Table 4. For the 4144 line the mode is �`;m� � �2;21� and for 4388 it is �1;21�:


q 2001 RAS, MNRAS 321, 131±142

AC K N OW L E D G M E N T S

LAB and WAL thank the Directors of SAAO and MSSSO for the

allocation of telescope time. WAL thanks Steve James, Marco

Maldoni, Eric Mamajek and Paul O'Neil for their assistance with

observing.

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This paper has been typeset from a TEX/LATEX file prepared by the author.

Table 4. Pulsational parameters for best-fitting models. Foreach mode (`, m), the inclination, i (degrees), pulsationalamplitude, Vr (km s21), and phase, f r (rad), is given. Thefinal column gives the goodness of fit in arbitrary units(smaller values imply a better fit). For the He i 4144 AÊ linewe assumed v sin i � 290 km21; while for He i 4388 AÊ weassumed v sin i � 320 km21: For both lines a Gaussianintrinsic line profile with rms width 20 km21 was assumed.

He i 4144, f � 1:01 d21:(`, m) i Vr f r s

(0,0) 85 2 2.8 0.403(1,21) 30 12 5.1 0.370(1,0) 45 2 1.2 0.397(1,1) 30 109 2.0 0.324(2,21) 85 6 5.0 0.712(2,22) 35 118 6.2 0.329(2,0) 45 1 0.8 0.403(2,1) 30 18 2.3 0.374(2,2) 30 2 0.0 0.402

He i 4144, f � 2:02 d21:(`, m) i Vr f r s

(0,0) 85 4 1.0 0.479(1,21) 30 1 4.6 0.444(1,0) 80 23 1.2 0.436(1,1) 30 57 1.0 0.437(2,22) 40 10 1.2 0.437(2,21) 85 17 1.0 0.364(2,0) 50 38 1.1 0.394(2,1) 30 3 0.0 0.482(2,2) 30 22 1.1 0.479

He i 4388, f � 1:01 d21:(`, m) i Vr f r s

(0,0) 60 2 5.0 0.572(1,21) 35 17 6.1 0.528(1,0) 35 2 3.1 0.583(1,1) 50 2 4.1 0.572(2,22) 35 151 5.5 0.485(2,21) 35 5 4.6 0.566(2,0) 65 23 0.9 0.377(2,1) 85 40 1.3 0.473(2,2) 35 2 6.3 0.573

He i 4388, f � 2:02 d21:(`, m) i Vr f r s

(0,0) 85 27 1.5 0.597(1,21) 35 1 4.8 0.552(1,0) 85 11 1.8 0.629(1,1) 35 69 1.9 0.613(2,22) 35 1 0.2 0.641(2,21) 85 2 0.3 0.647(2,0) 65 45 4.3 0.649(2,1) 35 18 1.0 0.615(2,2) 35 2 5.0 0.646


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short-period line profile variations in the be star ε cap

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