of more complex systems like galaxies. A simple stellar population is dened as an assembly

Transcription

1 Chapter 4 SIMPLE STELLAR POPULATIONS 4.1 Introduction Simple stellar populations (SSP) are the basic tool to understand the spectro-photometric properties of more complex systems like galaxies. A simple stellar population is dened as an assembly of coeval, initially chemically homogeneous, single stars. Four main parameters are required to describe a SSP, namely its age (t), composition (Y,Z) and the initial mass function (IMF). In nature, the best examples of SSP's are star clusters. Galaxies are certainly not SSP's because stars of dierent metallicity, age are present, and binary systems are also common objects. However, a complex population can always be expanded in a series of SSP's, and therefore the case of a SSP must be understood before addressing more complex systems. In this thesis dierent sets of SSPs are calculated starting from the grids of isochrones described in the previous chapter x 3, which cover a wide range of chemical composition and ages. All the gures presented in this chapter refers to the VW- isochrones and SSPs with = 0:45 (see previous chapter for more details), for dierent assumptions refers to the appendix A. 4.2 Fundamentals of population synthesis In this section is described, in some detail, the procedure followed to determine integrated spectral properties of SSPs. Aim of this procedure is to obtain a representative stellar population of singleburst from which the galaxies spectra can be calculated convolving the integrated spectral energy distribution (ISED) of the SSPs with the adopted star formation history of the galaxy. In order to calculate the ux emitted by a SSP, the isochrones in the CMD must be constructed. The more accurate this calculation, the more precise are the uxes for the whole galaxy. Itis worth recalling that the precise shape of an isochrone depends on the properties of the underlying evolutionary tracks, while the relative number of stars in dierent portions of the isochrone is governed by the assumed initial mass function (IMF), (M), and the lifetimes of the stars present 37

2 38 CHAPTER 4. SIMPLE STELLAR POPULATIONS in the isochrone in dierent evolutionary stages. To this aim we have adopted the large grid of isochrones with ne age spacing, calculated by thepadova group and described in the previous chapter (section x 3.2.1). The isochrones span the age range from a few 10 6 yr to yr and all evolutionary phases from the ZAMS up to the either the stage of C-ignition or PN formation, depending upon the mass of the most evolved star in the isochrone. The isochrone coordinate (log T e and log L=L )must be translated into observables like color indices and magnitudes in the Johnson-Cousins system (U, V, B, R, I, J, K, L, M, N and 1550). The integrated monochromatic ux at the generic wavelength () along the isochrone with age 0 and metallicity Z has been calculated weighting it on the initial mass function associated to the given mass M. To this aim the isochrone has been divided into elemental portions of log L=L and log T e : to which correspond suitable intervals of: logl=l and log T e log M=M log g and N = (M)M the latter being the number of stars per interval of initial mass. The isochrones used in this study are obtained assuming the Salpeter IMF express as where =2:35 and A is taken equal to one. dn=dm = (M) =A M ; The total mass of the SSP ( R M u M l (M)MdM) is obtained deriving the lower limit of the IMF from the following condition: R Mu M (M)MdM R = Mu M l (M)MdM (4.1) with the fraction of the total mass in form of stars stored in the IMF above M which isthe minimum mass contributing to the nucleosynthetic enrichment of the interstellar medium (ISM) over a time-scale comparable to the total lifetime of a galaxy. This mass is approximately equal to 1M. The real lower mass limit of the IMF (M l ) adopted to calculate the integration above is equal to 0.15M. The spectral energy distribution (SED) in ergs sec ;1 A ;1 to be associated to the stars in isochrone element is obtained by interpolating the spectral energy distributions of the adopted spectral library, as a function of gravity, T e, and metallicity. Finally, the SED is normalized to the emitting surface of the stars in the isochrone element and to the number of such stars N. By integrating the contribution of each isochrone element along the whole isochrone, the ISED, ssp ( 0 Z), of a SSP of any age and metallicity has been derived. This is given by:

3 4.3. INTEGRATED SPECTRA AND COLORS OF SSPS 39 ssp ( 0 Z)= Z Mu M l (M)f (M 0 Z)dM (4.2) where f (M 0 Z) is the monochromatic ux of a star of mass M, metallicity Z(t) and age given by 0. (M) is the Salpeter IMF. The integrated ux ssp ( 0 Z) refers to an ideal SSP of total mass 1M whose component stars distribute in mass according to the IMF over the range M l M u. The total luminosity of a SSP is obtained by integrating ssp ( 0 Z)over the whole range of wavelengths L SSP ( 0 Z)= Z 1 ssp ( 0 Z)d (4.3) from which the integrated absolute bolometric magnitude immediately follows: 0 M bol = ;2:5log L SSP L + M bol (4.4) where M bol is taken equal to The integrated Johnson-Cousins UBVRIJKLMN absolute magnitude of a SSP are obtained by convolving the ISED with the response function of each bandpass. To this aim, the ISED has been convolved with the V bandpass and the bolometric correction (BC) calculated according to the denition given by Kurucz (1992). This BC has been renormalized to the solar value (BC = ;0:08). All the other magnitudes ( i )have been obtained from the colors ( i ; V ) normalized to those of Vega. 4.3 Integrated spectra and colors of SSPs Many properties of stellar models do depend on the chemical composition (metallicity). Indeed at increasing metallicity, the mean sequence Turn-o gets redder and fainter, the T e range covered by the sub-giant branch (SGB) decreases, and the RGB bend toward lower T e. The core Heburning phase (in HB, clump, or loop as appropriate to a star's mass) in general gets redder at increasing metal content. For the purposes of illustration in Fig. 4.1) we show a few isochrones of young age at varying metal content. The evolution of high metallicity stars of low mass is a subject of interest because of their potential ability toprovide the correct explanation of the UV-excess observed in elliptical galaxies (see chapter 6). The high metallicity(aboutz )low-mass stars, after a normal He-burning phase (red-hb), skip the standard TP-AGB and soon after the early AGB phase is completed, proceed toward the WD regime. These stars are named P-EAGB. At even higher metallicity (3Z ), the old HB stars of normal mass (say M ) can spend a signicant fraction of the core Heburning phase at high T e and subsequently skip the entire AGB phase to directly evolve toward the WD regime (Brocato et al., 1990 Horch et al., 1992). These stars are named Hot-HB and

4 40 CHAPTER 4. SIMPLE STELLAR POPULATIONS Figure 4.1: The isochrones HR diagram for the high- mass stars with four dierent values of the metallicity, Z=0.0004, Z=Z, Z=0.05 and Z=0.1, solid, dotted, dashed and long-dashed lines respectively at the age of 10 7 yr ( 10M ) AGB-manque (cf. Greggio & Renzini (1990)). Fig. 4.2 shows isochrones corresponding to models of this type for purposes of illustration. The physical explanation is that for a given M HB, both the lower hydrogen content intheenvelope, and the enhanced CNO processing in the H-burning shell, because of the high metallicity, concur to burn out the envelope much faster than in stars of the same mass but lower metallicity and hence helium content (we remind the reader that these models are calculated assuming Y=Z equal to 2.5). These morphological properties of the stellar tracks reect especially on the ISED and hence on the integrated colors of the SSP. Figs. 4.3 and 4.4 show the spectral energy distribution of SSP at the age of yr and yr, for dierent metallicities as indicated, in the wavelength range from 100 to 6,000A. In Fig. 4.3 the UV region is dominated by the ux emitted by young massive stars, whereas in Fig 4.4 the UV region is dominated by dierent emitters depending on the metal content. In the case of low metallicity the stars contributing to the UV ux are the classical P-AGB objects. Whereas at increasing metallicity the contribution from AGB-manque and H-HB gets more and

5 4.3. INTEGRATED SPECTRA AND COLORS OF SSPS 41 Figure 4.2: The isochrones HR diagram for the low- and intermediate- mass stars with four dierent values of the metallicity. Z=0.0004, Z=Z, Z=0.05 and Z=0.1, solid, dotted, dashed and long-dashed lines respectively at the age of 10 9 yr ( 1M ). The AGB-manque phase is indicated. more important up to the extreme case of Z=0.1 in which the UV ux is almost entirely generated by this type of objects. An extent grid of SSPs have been calculated according to the dierent sets of isochrones (see section x 3.2.1). The library of integrated magnitudes and colors of the SSP's covers the same range of ages and chemical compositions as for the library of isochrones. The output of these SSPs are described in appendix x A where comparison between the dierent sets are also given for the solar metallicity. According to our denition of SSP and adopted normalization, all integrated magnitudes (cf. appendix A) refer to the ideal case of a SSP with normalization constant equal to 1 (Eqs. 4.2 and 4.1). Before applying these magnitudes to real SSPs, such as star clusters, the magnitudes must be suitably scaled to the total mass of the system by re-normalizing the IMF. In view of the discussion below itisworth looking at the color evolution of SSPs with particular attention to the possible appearance of the so-called phase transitions as named by Renzini & Buzzoni (1986). According to the Fuel Consumption Theorem the onset in a SSP of two par-

6 42 CHAPTER 4. SIMPLE STELLAR POPULATIONS Figure 4.3: The ISED for SSPs with dierent metallicity. Z=0.0004, Z=Z, Z=0.05 and Z=0.1, solid, dotted, dashed and long-dashed lines, respectively at the age of yr. The standard contribution from the PN and loop phases is in the wavelength range between 1,0002,000A. ticular groups of stars, namely RGB and AGB, should manifest itself with sudden variations in the integrated colors. Let consider for instance the integrated (V{K) color for four SSPs with dierent chemical composition, i.e., [Z=0.0004,Y=0.23], [Z=0.02,Y=0.28], [Z=0.05,Y=0.352], and [Z=0.1,Y=0.475] shown in Fig. 4.5 panel a). The arrows indicate the ages at which thephase- transitions of AGB and RGB stars should occur. It goes with out saying that these ages depend on the type of stellar models in use. The portion of the curves between the two arrows is dominated by the properties of AGB stars, in particular by those during the thermally pulsing regime, i.e., the evolutionary rate, lifetime and maximum luminosity. The AGB stars can develop only in the SSPs older than 10 8 yr which corresponds to the AGB-transition phase. At the age of about 10 9 yr the phase transition of RGB stars should occur. No sign of this phase can be seen in the (V{K) color. This can be explained by means of the Fuel Consumption Theorem (see Renzini & Buzzoni (1986) for all details), which shows that the relative bolometric luminosity oftheagb stars tends to decrease in coincidence with the increasing contribution from the RGB stars. The opposite trends tend to balance each

7 4.3. INTEGRATED SPECTRA AND COLORS OF SSPS 43 Figure 4.4: The ISED of a SSP with dierent metallicity. Z=0.0004, Z=Z, Z=0.05 and Z=0.1, solid, dotted, dashed and long-dashed lines, respectively at the age of 10 Gyr. The AGB-manque and the H-HB stars contribute especially in the UV region. other with the net eect that no variations in the color are expected. Indeed the reddening of the (V{K) color can be seen in panel a) of Fig.4.5. The remarkable change in (V{K) color at the onset of AGB stars could in principle be used to date a SSP if detected in real star clusters and in a wider context to date a more complex system like a galaxy provided it resembles a SSP (for instance an elliptical galaxy). As it will be discuss in much more detail below this variation in the (V{K) color caused by rst AGB stars in a galaxy occurs too early on in a galaxy's life to be detectable in cosmological context. From this point of view, much more interesting is the variation in the (1550{V) color caused by appearance of hot-hb and AGB-manque stars of high metallicity which is expected to occur much later in the galaxy history (at the age of several Gyr) and thus to be perhaps detectable at relatively low redshift. The situation is shown in panel b) of Fig As the SSP ages the color (1550{V) get redder and redder till it suddenly bluens at critical ages that depends on the metallicity assoonaspost-agb, Hot-HB and AGB-manque are formed in the stellar population.

8 44 CHAPTER 4. SIMPLE STELLAR POPULATIONS Figure 4.5: The colors evolution of a SSP with dierent metallicities, Z=0.0004, Z=Z, Z=0.05 and Z=0.1, solid, dotted, dashed and long-dashed lines, respectively, for the (V{k) color panel a) and (1550{V) panel b). The appearance of the AGB and RGB stars is indicated 4.4 Integrated absorption line spectral indices Line strength indices are perhaps the best tool (Worthey, 1992) for discriminating age from metallicity eects, and casting light on the chemical composition of elliptical galaxies and hence their past star formation history. Pioneering studies in this sense, involving spectral features in the visual range applied to stellar populations studies, have been rst undertaken by Spinrad & Taylor (1969), Spinrad & Taylor (1971) and Taylor (1971) who have derived metal-abundances in galactic stars using a large set of indices covering stellar spectra from UV up to near infrared. Since then many studies have dened and analyzed the line strength indices over the whole range of wavelengths from UV (Rose (1984) and Rose (1985a) for the galactic stars Rose (1985b) for elliptical galaxies) up to the infrared (Frogel et al., 1980). In the optical region many eorts have been made to obtain systematic analysis of the narrow band indices to reproduce these indices in galaxies adopting the EPS models (Faber, 1973 Faber & Franch, 1980 Burstein et al., 1984 Faber et al., 1985 Worthey,

9 4.4. INTEGRATED ABSORPTION LINE SPECTRAL INDICES Worthey et al., 1992 Gorgas et al., 1993 Gonzales, 1993 Worthey et al., 1994). In order to predict feature strengths in the integrated light of galaxies it is necessary to know thebehavior of the features in stars very well. This can be accomplished completely theoretically, empirically, or by some mixture of the two. Examples of theoretical studies are Mould (1978), Johnson et al. (1982), Tripicco & Bell (1990), Gulati et al. (1993) and Barbuy et al. (1992). Furthermore, a large set of observations have been collected for stars of dierent spectral type by (Spinrad & Taylor, 1971 Aaronson et al., 1978 Cohen, 1978 Mould & McElroy, 1978 Faber et al., 1985 Peletier, 1989 Buzzoni et al., 1992 Buzzoni et al., 1993b Gorgas et al., 1993 Worthey, 1992 Worthey et al., 1992) and (Worthey et al., 1994), who derived empirical calibrations of the indices as a function of key stellar parameters (T e,gravity, [Fe/H]). The denition of these empirical tting functions has been an important step to cope with population synthesis and derive the integrated values expected for SSPs. The empirical tting function of 21 indices derived by Worthey (1992) as a function of the stellar parameters have been adopted in this thesis to generate integrated indices for SSPs and elliptical galaxies. To illustrate the sensitivity of line strength indices to dierent kinds of star in the HRD we show in artistic way how main sequence, sub giant andrgb stars contribute to H, Mg 2, and Fe indices. This is displayed in Fig. 4.6 for a typical globular cluster NGC 1851 (Saviane 1997 private communication). Specically H is mainly sensitive to turnoo stars, while the base of the RGB mainly contributes to the iron (Fe5207 and Fe5335) features. The Mg 2 indices carries information mainly on the upper part of the RGB and AGB Line strength indices: denition The most popular library and calibration of line strength indices is by the Lick Observatory group (cf. Worthey (1992) and references therein) who have obtainedarich and homogeneous set of stellar and galactic spectra, on which theyhave dened their set of indices and associated tting function to be used in studies of population synthesis. The spectra range from 4,000A to 6,400A, with resolution of 8.2A. The assembled library includes about 400 stars covering a large range of gravities, metallicities and temperatures, which allowustoevaluate the dependence on these basic parameters. It is worth recalling that their sample includes both the M type stars (very important to understand old and metal-rich populations) and the hot stars (that are very important to study dierent sources of ux). The standard denition of the line strength comes from Faber et al. (1977) and Burstein et al. (1984). Two pseudo-continuum are dened on either side of a central bandpass which include the feature to be measured. The average ux on these side bands, F Cr (red) and F Cb (blue), is interpolated to the midpoint of the central bandpass. The dierence between the interpolated pseudo-continuum and central bandpass ux F I, dene the index. In Table 4.1 the pseudo-

10 46 CHAPTER 4. SIMPLE STELLAR POPULATIONS Figure 4.6: A simplied sketch of the sensitive index dependence in the CMD of NGC1851 given me by Saviane 1997 private communication continuum denition are summarized. The location of the index pass bands are illustrated in Fig For clarity, the location of the continuum pass bands are not included. In Fig. 4.8 we show the synthetic ux of a SSP with Z=0.02 and age of 10 Gyr to which we have superimposed the three pass bands dening the Mg 2 index and its pseudo-continuum. The indices are dened in two ways. Molecular bands are expressed in magnitudes, while atomic features are expressed in A. Explicitly, in either an index (I) bandpass or a continuum (C) bandpass, the average bandpass ux is calculated F band = Z 2 1 F d ( 2 ; 1 ) (4.5) The continuum for the index is then the run of the ux dened by drawing a line from the midpoint of the blue continuum level (F Cb ) to the midpoint of the red continuum level (F Cr ). This denition is slightly dierent from that of Burstein et al. (1984). An equivalent width is EW =( 2 ; 1 ) 1 F I ; F C A (4.6)

11 4.4. INTEGRATED ABSORPTION LINE SPECTRAL INDICES 47 Figure 4.7: Index pass bands are shown as a shaded boxes for ve dierent indices(h,mg 2,Mg b, Fe5270 and Fe5335 as indicated) overlap to the synthetic spectra for a SSP with Z=0.02 and age 10Gyr. Mg b has nearly the same bandpass as Mg 2, but slightly narrowed. It is shown as dierent shaded box to distinguish it from Mg 2. and an index measured in magnitudes is FI I = ;2:5log F C mag (4.7) Worthey (1992) has empirically calibrated the 21 indices as a function of the atmospheric parameters: T e (or (V{K)), surface gravity (logg), and metallicity (given by [Fe/H]). Worthey (1992) has used two separate polynomial function for each index to cover the range of temperatures from 3,570 to 13,260 K as a function of T e ( e = 5040 T e ), gravity and metallicity. The regions of validity are from 3,570 to 5,160 K for the cool functions, and from 5,040 to 13,260 K for the hot functions. There is a small region of temperature overlap which insures a relatively smooth transition between the two regimes. Cool stars were t with polynomials in(log e ), hot stars with polynomials in ( e ). In some cases the indices have been expressed in exponential form, that is, in a form I = C 1 +expp ( e log g [Fe=H]), where P indicates a polynomial. See

12 48 CHAPTER 4. SIMPLE STELLAR POPULATIONS Figure 4.8: Denition of a spectral index. The three bands dening the Mg 2 index are shown inside the shaded boxes the straight solid line represents the pseudo-continuum. An index is measured by comparing the ux in the pseudo-continuum (A) and the average ux in the central bandpass (B) the Table 7 and 8 in Worthey (1992) for all details. For the stars even cooler than 3,570 K, Worthey (1992) has adopted the M dwarfs and M giants exist in the stellar library. Since no metallicity sensitivity has been detected in the indices of these stars, Worthey (1992) has given a simple quadratic ts for the indices as a function of the temperature only. For the M giant a quadratic ts as a function of the temperature (not V{K) has been given, instead quadratic ts as a function of (V{K) (not temperature) for the M dwarfs stars. The Lick spectral indices have been designed to study old stellar population, indeed the bluer dwarf stars in the sample have (V{K)1 (spectral type F4 and log T e ' 3:8) which correspond to the turn o age of 4 Gyr. The tting function are so useful to interpret the integrated spectra of stellar system older that same Gyr, such as globular cluster and elliptical galaxies. For this reason the integrated spectra of the SSPs in this thesis was been synthesized by usingisochrones younger than 10 8 yr.

13 4.4. INTEGRATED ABSORPTION LINE SPECTRAL INDICES 49 It is worth recalling that the tting function obtained by Worthey (1992) include the eect of the iron abundances of the adopted sample. The relative abundances of the other -elements with respect to the iron could be not solar, and vary as a function of [Fe/H] according to the chemical enrichment of the solar neighborhood, and this can change from systems to systems Integrated line strength indices of SSP To construct synthetic indices for SSPs we follow the same scheme as used for the integrated spectra. For every combination of the T e, g and [Fe/H], that means a given star in the isochrone, the corresponding spectra has been assigned from the stellar spectral library described in x 4.2. From this spectra the average uxes in the contunumm bandpass F Cr and F Cb,have been calculated for each of the 21 indices. The mean ux in the central bandpass F I has been derived adopting the analytic ts of Worthey (1992) and Worthey et al. (1994) for the same values T e, g and [Fe/H] (Eqs. 4.6, 4.7). If F I and F C aretheuxinthecentral bandpass and in the contunumm, respectively, the integrated uxes for a single SSP, i.e. of a coeval, chemically, homogeneous assembly of stars with age 0 and metallicity Z, and for each indices are: F I ssp ( 0 Z)= F C ssp ( 0 Z)= Z MU M L (M)F I (M 0 Z)dM (4.8) Z MU M L (M)F C (M 0 Z)dM (4.9) where F I (M 0 Z) and F C (M 0 Z) are the uxes for a star of mass M, metallicity Z(t) and age 0. In order to present results independent of the particular choice made for the IMF normalization, the SSP indices have been calculated adopting the Salpeter IMF as given in Eq. 4.2, and xed lower and upper limit of the integration, M l =0.15M and M u =120M respectively. Knowing the integrated uxes for a SSP, the denition of each index (Eqs. 4.6, 4.7) is applied to get back the integrated index. Ihave calculated these for each sets of SSP, and tabulations for these are give in appendix B. For care of brevity, I will present tabulations only for solar metallicity, all the others tabulation will be available on request. The gures below refer to the SSPs with solar metallicity with mass-loss during the RGB phase given by = 0:45 and according to Vassiliadis & Wood during AGB phase. In Fig 4.9 the index-age relationships for the indices log H,Mg 2,Mg 1,Mg b,fe5207 and Fe5335 are shown together with the combined index log [MgFe] as dened by (Gonzales, 1993): [MgFe] = p hfei Mg b (4.10) in a SSP of Z=0.02. For all indices it is evident a turnover around the age of 18 Gyr. Can be pointed out the inverse trend of the H index.

14 50 CHAPTER 4. SIMPLE STELLAR POPULATIONS Figure 4.9: The line strength indices as a function of the age for a SSP with solar metallicity. Panel a) shows the log H, Mg 2,Mg 1, and log [MgFe] indices whereas panel b) shows the Irons, and Mg b indices. The correlation between H and [MgFe] for SSPs with dierent metallicities is shown in Fig The age goes from 1 Gyr to beyond 15 Gyr in steps of log t=0.05 as indicated. The dip and the loop-like structure in the SSPs with the lowest and highest metallicity are caused by the onset of the HB and appearance of the H-HB stars, respectively. The inspection of the indices values (see tabulations in appendix B) and the comparison with similar results obtained by Gonzales (1993) show that excellent agreement exists between the two studies. For sake of provisional comparison, the data of Re/2- and Re/8-aperture from the Gonzales (1993) sample are shown in Fig It is soon evident that the locus drawn by the observations has the same slope of the SSPs with metallicity comprised between Z=0.02 and Z=0.05. It is worth underlying that at increasing metallicity the loop-like structure become more and more evident, which mayplayanimportant role in the interpretation of these data (see also chapter x 8). In brief the interesting possibility arises that galaxies with strong H could be very old systems with very high metallicity as opposed to the obvious alternative that these systems have suered from star formation in a recent past (see chapter x 8). These results are in contradiction to with those

15 4.4. INTEGRATED ABSORPTION LINE SPECTRAL INDICES 51 Figure 4.10: Single stellar populations of dierent metallicities in the H -[MgFe] plane. Along each SSP the age varies from 1 to above 15 Gyr as indicated. The full and open dots are the Re/8-data and Re/2-data of (Gonzales, 1993). obtained by Gonzales (1993), using the H and [MgFe] indices which seem to suggest a broad range for galactic ages.

16 52 CHAPTER 4. SIMPLE STELLAR POPULATIONS Table 4.1: Index denitions Name Index Bandpass Continua Units Measures error 01 CN mag CN,FeI CN mag CN,FeI Ca A CaI,FeI,FeII G A CH,FeI Fe A FeI,TiII Ca A CaI,FeI,NiI, TiII 07 Fe A FeI,TiI, FeII,TiII 08 Fe A FeI,TiI,CrI, MgI,NiI 09 H A H,FeI Fe A FeI,NiI,TiI Mg mag MgH,FeI,NiI Mg mag MgH,Mgb FeI 13 Mg b A Mg b Fe A FeI,CaI Fe A FeI Fe A FeI,CrI Fe A FeI,NiI,MgI Fe A FeI,CrI Na D A NaI TiO mag TiO TiO mag TiO