New Astronomy Reviews 46 (2002) 541–545www.elsevier.com/ locate/newar

Radioactive isotopes in star forming regions*˜ ¨Miguel Cervino , R. Diehl, K. Kretschmer, S. Pluschke

¨Max-Planck-Institut f ur extraterrestrische Physik, 85741Garching, Germany

Abstract

We examine the isotope production in star forming regions through a model of stellar-group population synthesis26 60 2 1evolution. From this we obtain the light-curves ofg-ray line emission due to radioactive decay of Al, Fe and the e e

annihilation line. We discuss in particular, the effects of the dispersion due to the discreteness of the stellar populations. Weconclude that when predictedg-ray line observations are combined with other multi-wavelength measurements, one canefficiently constrain the age of a stellar population, and help to identify the primary nucleosynthesis sources of theradio-isotopes. 2002 Elsevier Science B.V. All rights reserved.

PACS: 98.20.Af; 98.35.Ac; 26.20.1f; 26.30.1kKeywords: Gamma-ray lines; Synthesis models; Chemical evolution

1. About evolutionary synthesis codes star formation has been assumed. We have used theSN radioisotopic yields from Woosley and Weaver

Evolutionary synthesis models are a useful tool to (1995) for stars that do not reach the Wolf–Rayet26understand the observed emission of Al and the (WR) phase and the yields from Woosley et al.

determination of the primary nucleosynthesis sources (1995) for WR stars.¨of this radio-isotope; see also Pluschke et al., this Two main sources of dispersion exist: First, the

volume. The production of such radioisotopes is uncertainties in the ejected chemical yields in stellardominated by the stellar winds and the occurrences winds and SN, and second, statistical effects relatedof supernovae (SN) in the cluster of massive stars. In to the discreteness of the stellar population. Note thatFig. 1 (left panel) we show the Supernova Rate evolutionary synthesis codes assume a smoothly-(SNr), normalized to the total mass of the stellar filled IMF, which is however only a good approxi-

6cluster, obtained from an updated version of our mation for clusters with more than 10 M trans-(

population synthesis code presented earlier in Cer- formed into stars. This situation is illustrated in the˜vino et al. (2000). We have used the evolutionary right panel of Fig. 1 where an analytical IMF and the

tracks by Meynet et al. (1997) with solar metallicity results of 3 Monte Carlo simulations of the IMF are3and enhanced mass loss rates. For the results pre- shown for a cluster with 10 M transformed into(

sented here we use a power-law Initial Mass Func- stars.tion (IMF) with a slope equal to the Salpeter value in So, in order to establish conclusions about thethe mass range 2–120 M . An instantaneous burst of origin of radio-isotopes, it is necessary to know the(

corresponding theoretical light-curves and relatedquantities (i.e. the mean theoretical value),and to*Corresponding author.

˜E-mail address: mcervino@obs-mip.fr (M. Cervino). obtain an estimation of the dispersion due to the

1387-6473/02/$ – see front matter 2002 Elsevier Science B.V. All rights reserved.PI I : S1387-6473( 02 )00198-7

˜542 M. Cervino et al. / New Astronomy Reviews 46 (2002) 541–545

Fig. 1. Left panel: Temporal evolution of the predicted supernova rate. Right panel: Analytical and Monte Carlo simulations of the IMF for3a cluster where 10 M has been transformed into stars.(

discreteness of the stellar population. We point out 2. Emission line fluxes and flux ratiosthat our code is different from the one presented in

26 60 2 1¨the contribution by Stefan Pluschke et al. (these 2.1. Al and Fe g-emission lines, and the e eproceedings), yet both codes obtain similar results. annihilation line

¨(Also the work by Pluschke (2001) includes thedispersion due to the discreteness of the stellar We have obtained the expected 1.809 MeV and

26 60population, using Monte Carlo simulations of their 1.173/1.332 MeV luminosity from the Al and Feevolutionary code). decays, respectively. In Fig. 2 (left panel) we show

26 60Fig. 2. Left panel: Temporal evolution of the predicted 1.809 MeV and 1.173/1.332 MeV luminosity from the Al and Fe decays,respectively. Right panel: Temporal evolution of the predicted 511 keV luminosity for different escape fractions of the positrons produced by56Co decay.

˜M. Cervino et al. / New Astronomy Reviews 46 (2002) 541–545 543

the temporal evolution of the luminosities, normal- shown in the left panel of Fig. 3. Four phases can beized to the mass of gas transformed into stars in the distinguished: (i) the stellar wind phase up to 3 Myrsynthetic cluster. The figure shows that a star form- with a steep rise of the ratio, (ii) the Type Ib/cing region reaches a peak in the 1.809 MeV lumin- supernova phase (from WR stars) from 3 to 7 Myrosity at the time when massive WR stars are present with a faltering of the slope, (iii) the Type II(from 3 to 4 Myr) and slowly decays for larger ages: supernova phase from 7 to 37 Myr with a stepthe lower the initial mass, the lower the production around 7 Myr and a tail of positive slope, and (iv)

26of Al in the final SN explosion. The 1.173/1.332 the decay phase, beyond 37 Myr. Note that the ratioMeV luminosity shows a more constant behavior varies over more than 4 orders of magnitude during

60until |19 Myr, the SN yields for Fe do not depend the evolution of the cluster, and it is not very26 O7Vas strongly on mass as the Al yields do. For lager sensitive to the value of the IMF slope. So,Y 26

ages (i.e. initial masses lower than 12 M ) the becomes a useful parameter to constrain the age of(601.173/1.332 MeV luminosity (and the Fe yield) the starburst. Alternatively, if the age is known

decreases monotonically until an age of 38 Myr, otherwise (e.g. inferred from observations of otherwhereafter the SN activity fades away. phenomena at other wavelengths), we can constrain

Additionally, we have derived the expected 511 the contribution of massive stars to the observed26 O7VkeV luminosity from the stellar cluster, from the mass of Al, expressed throughY . As an exam-26

22 O7Vradioactive decays of Na (with a branching ratio ple, the value ofY obtained for the Cygnus261 26 44 24for the formation of e of 0.905), Al (0.85), Ti region is about 1310 . This value is in accord with

56 5(0.95), Co (0.19). A mean-life of 5310 years has our model predictions if the region is dominated by a1been assumed for the e . The annihilation gamma- cluster formed 4–6 Myr ago.

ray yield has been corrected by a factor 0.575, taking In the right panel of Fig. 3 we show the ratio of1into account that each e produces two 511 keV the luminosity of the 1.809 MeV line and the

photons with an efficiency of 28.75% (the remaining integrated kinetic energy,E , released by the cluster.k

71.25% produce continuum emission). In Fig. 2 The kinetic energy increases with time, and so, the(right panel) we show the temporal evolution of the ratio decreases. Again, this ratio is independent frompredicted 511 keV luminosity for different escape the mass transformed into stars, and can be used to

56fractions of positrons produced by Co decay. The characterize any cluster whatever its mass. The56mean-life of the Ni in the chain released kinetic energy can be related to the radius of

56 56 56 1Ni→ Co→ Fe1e is 111 days. Note that is is the (super)bubble formed by the star formationstill a matter of debate which fraction of positrons process. One may use a hydro-dynamical model (seeescape the SN envelope rather than decaying inside. ¨Pluschke, 2001), or interpret optical (Ha filaments)

or radio (HI emission) loop structures. Their ratiovaries over three orders of magnitude during the

O7V2.2. Equivalent O7 V star yields, Y and L cluster evolution. Possibly this ratio can also be used26

(1.809 MeV) over E ratio to constrain the age of the stellar cluster; at least,kO7Vtogether withY and other observables it will test26

From the observed proportionality of the 1.809 the self-consistency of the predictions.MeV g-line emission with radio-thermal emission,

¨Knodlseder (1999) introduced anequivalent O7 V26 O7star Al yield, Y , defined as the ratio of the mass26

26of Al ejected by cluster members over the ionizing 3. Uncertainties due to the discreteness of theluminosity, normalized to the number of stars of stellar population

O7V 21spectral type O7 V (logQ 549.05 ph s ). Such0

a ratio has the advantage to be independent of the The dispersion due to the discreteness of stellarmass normalization, i.e. the values can be compared populations must be considered when the output of afor any cluster system whatever its size may be. synthesis code is compared with real stellar clusters.

26 O7VThe evolution of the specific Al yieldY is Such a dispersion can be estimated analytically using26

˜544 M. Cervino et al. / New Astronomy Reviews 46 (2002) 541–545

O7VFig. 3. Left panel: Temporal evolution of the predictedY ratio. Right panel: Temporal evolution of the predicted L(1.809 MeV) overE26 k

ratio.

˜the prescriptions of Buzzoni (1989), Cervino et al. So, for a given amount of mass transformed into(2001); we chose a Monte Carlo (MC) sampling stars, there is an intrinsic dispersion around eachmethod instead. As a example, we show in Fig. 4 the mean parameter value obtained from any synthesisprobability density function of the radioisotope yield code, due to the fact that we do not knowexactly the

O7VY , obtained from 1000 MC simulations of 100 initial masses of all the stars in the cluster. One way26

stars in the mass range 8–25 M assuming a to overcome such uncertainty is to use ratios of(

Salpeter IMF slope. Fig. 4 shows the relative disper- observable quantities:20.5sion obtained analytically in units of M , where M Let us assume an observableu 5 x /y. The re-(

is the amount of mass transformed into stars in the sulting equation for the relative error is:cluster. These figures show that a considerable

22 2 ss s cov(x, y)dispersion develops in the early evolution due to the yu x] ] ] ]]]. 1 22 (1)2 2 2small number statistics at the high-mass end. During x yu x y

the subsequent evolution, the relative uncertaintyremains roughly constant, with a shallow minimum In this case an important result appears: the relativearound 5–10 Myr followed by a slight increase for error of the ratio can be lower than the individuallater times. errors of the quantities involved. How much the error

O7VFig. 4. Left panel: Probability density functions ofY for a set of 1000 Monte Carlo simulations. Right panel: Analytical relative error of26O7V 20.5Y in units of M .26 (

˜M. Cervino et al. / New Astronomy Reviews 46 (2002) 541–545 545

in the ratio can be reduced depends on the co- observed systems must be taken into account in anyvariance term. As a trivial example, the computed comparison with real data. We have also shown that

26 26ratio of the Al flux over the Al itself will be ratios of different quantities are better suited toalways equal to 1 without any dispersion at all. So, constrain the physical properties of the systems. We

O7Vthe predictions of correlated quantities likeY , are in the process of extending this work to find26

L(1.809 MeV) over E ratio, or the profile of the more correlations with other observed quantitiesk26 (such as individual stellar populations, X-ray emis-Al line can be a better diagnostic to constrain the

26 sion and optical emission lines) and to better con-origin of the Al, because two quantities comingstrain the physical properties of the systems wherefrom the same source are related in the parameter of

26 the models can be applied.consideration. Analogously, the ratios of the Alflux with observables in other wavelengths (likeX-ray emission of Ha filaments) can be also useful.

References

Buzzoni, A., 1989. ApJS 71, 871.4. Conclusions˜ ¨Cervino, M., Knodlseder, J., Schaerer, D., von Ballmoos, P.,

Meynet, G., 2000. A&A 363, 970.We have shown properties related tog-ray emis-˜Cervino, M., Vals-Gabaud, D., Luridiana, V., Mas-Hesse, J.M.,

sion lines from model predictions based on the 2001. A&A (accepted, astro-ph/0109435).computation of evolutionary synthesis. Such model ¨Knodlseder, J., 1999. ApJ 510, 915.

Meynet, G., Arnould, M., Prantzos, N., Paulus, G., 1997. A&Acodes present the advantage to obtain correlations320, 460.between phenomena in different wavelength ranges,

¨Pluschke, S., 2001. PhD Thesis TU Munchen.used to constrain the evolutionary status of theWoosley, S.E., Langer, N., Weaver, T., 1995. ApJ 448, 315.

studied systems and the relative importance of Woosley, S.E., Weaver, T., 1995. ApJS 101, 181.massive stars for theg-line emission. The dispersiondue to the discreteness of stellar populations in the