Stellar Objects: Composite Stellar Populations 1 Composite Stellar Populations 1 Definition and problems Definition and Problems A Composite Stellar Population (CSP) is a collection of stars formed at different time and with different initial chemical compositions. Clearly, the properties of a CSP depends on the star formation rate (SFR) — the amount (total stellar mass) formed as a function of time — and the initial chemical composition (or Age Metallicity Relation - AMR) of the stars. The SFR and AMR together are called the star formation history (SFH). If the SFH is known, together with the IMF, the CSP of a system (e.g., a galaxy or its bulge) is then determined. But in general, the SFH is not known a priori, depending the gas accretion and removal from this system as well as the star formation efficiency and the stellar mass ejection back to the ISM (stellar feedback). None of these processes are well understood. The stellar feedback itself can in principle be inferred from the stellar evolution modeling, although how it affects the other processes is still unclear. Therefore, a study of the CSP draws on results of stellar evolution and on ideas of galaxy formation; thus it stands at a boundary between these two major areas of astronomical research. Here we discuss two simple examples of such studies. 2 One-zone instantaneous recycling model 2.1 Major assumptions • Primary metals such as O, Ne, and S (in contrast to N, which largely < results from secondary production), produced by massive stars (t ∼ 50 Myr), are returned to the ISM with a yield of p, which is independent of Z. O, Ne, and S, among other elements, are ”primary” products of stellar nucleosynthesis, whose yields depend relatively little on the abundances in the progenitor star. Stellar Objects: Composite Stellar Populations 2 • The returned metals are mixed in the galaxy thoroughly and rapidly. Heavy elements are dispersed by flows propelled by supernova explo- sions and stellar winds, as well as differential rotation, large scale flows induced by bars, etc. The timescale of the mixing is probably much shorter than that of the star formation. (The star formation in the solar neighborhood is fairly steady over the past 8-10 Gyr.) • The mass Ms in the remnants of massive stars and in low-mass stars remains locked within them throughout the galaxy’s lifetime. • The gas inflow to (or outflow from) a galaxy has a rate that is propor- tional to the star formation rate, i.e., δMf = νδMs. 2.2 Model Construction From mass conservation, δMs + δMg = νδMs, (1) therefore, δM δM = − g . (2) s 1 − ν The mass Mh of heavy elements in the gas can then be expressed as p − Z + νZ δM = pδM − ZδM + νZ δM = − f δM , (3) h s s f s 1 − ν g where the metallicity is defined as M Z = h . (4) Mg The increase of the metal abundance of the gas is then δMhMg − δMgMh p + νZf − νZ δMg δZ = 2 = − . (5) Mg 1 − ν Mg Stellar Objects: Composite Stellar Populations 3 A couple of simple cases: • Inflow (ν > 0): Assuming Zf is independent of Z and is equal to Z(t = 0), p M (t) ν/(1−ν) Z(t)= 1 − g . (6) ν Mg(t = 0) < • Closed-box or outflow (ν ∼ 0): Assuming Zf is equal to Z(t), p M (t = 0) Z(t)= Z(t = 0)+ ln g . (7) 1+ |ν| n Mg(t) o Clearly, the outflow only reduces the effective yield of metals returned to the gas. When ν = 0, we recover the close-box model as described in §10.1 of the text book. In this case, the total mass of stars formed before time t Ms(< Z)= Mg(0) − Mg(t)= Mg(0) 1 − exp{−[Z − Z(0)]/p} . (8) 2.3 Model applications • The simple closed-box model gives a good fit to the metallicity distri- butions of G and K giant stars of the Galactic bulge. −2 • Near the Sun, the Galactic disk contains 30 − 40M⊙ pc of stars, −2 −2 together with about 13M⊙ pc in gas, for a total of ∼ 50M⊙ pc . The average abundance in the gas is about Z(now) ≈ 0.7Z⊙ Assuming Z(t =0)=0 and ν = 0, we have Z(now) = pln(50/13). (9) So p ≈ 0.5Z⊙. • The Sun is more metal rich than the local disk gas → incomplete mixing and/or inflow of metal-poor gas. Stellar Objects: Composite Stellar Populations 4 Events involving massive stars are concentrated in young star clusters, leading to the potential for localized enrichment. Infall of primordial (or not so primordial) gas from the environment of a galaxy may involve accretion of gas clouds or dwarf galaxies, possibly leading to localized depressions of heavy element abundances. • The solar neighborhood G-dwarf problem: the closed-box model over- estimates of metal poor stars (Z < Z⊙/4)) if Z(t = 0) = 0: M (< Z⊙/4) 1 − exp[−Z⊙/4p] s = ≈ 0.52, (10) Ms(< 0.7Z⊙) 1 − exp[−0.7Z⊙/p] compared to the observed fraction of ≈ 0.25 for a sample of G dwarf stars in the solar neighborhood. → pre-enrichment of the gas and/or late infall of metal-poor gas . • Globular clusters contain little gas and a lot of stars that all have the same metal-poor composition. → single generation of star and effective ejection of the rest of gas. • The high O/Fe ratio in the halo and thick disk. This suggests a brief formation period, early in the history of the Galaxy. The thin disk has lower O/Fe and a metallicity distribution consistent with prompt initial enrichment (perhaps from the thick disk) combined with infall of extragalactic gas. • Characteristic abundances increase with galactic luminosity. This trend embraces irregulars as well as spirals. This trend may in- volve the escape of nucleosynthesis products in winds from galaxies with low escape velocities. Indeed, effective yields for low surface brightness galaxies as a class fall below those for normal galaxies. • Galaxies in the Virgo cluster core, with marked H I deficiencies, are more metal rich than spirals with normal H I content located in the periphery of the cluster and in the field. This may result from the curtailment of metal-poor infall onto galaxies in the cluster core, where they are immersed in the hot cluster medium. In contrast, infall continues onto spirals in the cluster periphery and in the field, restraining the increase in abundances with time. Stellar Objects: Composite Stellar Populations 5 The evolution of galaxies is a complicated issues and is not well understood. Our Galaxy and other nearby galaxies provides the necessary test-beds for understanding various important physical, chemical, and dynamical pro- cesses, which are essential for us to interpret observations of more distant galaxies. 3 Star formation history based on CMD fits Statistical comparison of observed and synthetic CMDs can be used to de- termine the SFH and AMR, plus other parameters such as extinction and distance to a CSP. Basic assumptions: 1) stellar models are sufficiently accurate as the function of mass, age, and metallicity and available for all the populations presented in the observed CSP; 2) the prescribed IMF is realistic and independent of age and metallicity; and 3) data quality is sufficiently good with errors measured or modeled. In addition, the distance modulus and extinction of the observed CSP are often assumed a priori, which could in principle be determined via the same fitting procedure. The observed CMD is divided onto a grid with N cells of specified or variable sizes in both the magnitude and color directions; each cell contains No(i) counts, where i = 1, ..., N. The morphology of the CMD can be used to provide useful limiting ranges of the age t and metallicity Z of the CSP. The model synthetic CMD of the CSP can be expressed as a linear combina- tion of a set of elementary stellar populations. Each elementary population j is assumed to have a uniform distribution of age and metallicity within inter- vals ∆t and ∆Z. The sizes of ∆t and ∆Z, centered around n discrete values of age t and m metallicities, are determined by the limited counting statistics and photometric errors of the observed CMD as well as the uncertainties in j the theoretic modeling. The CMD of such an elementary population Ne (i) can be most conveniently generated using MC techniques. The synthetic CMD can be expressed as j Ns(i) = ΣjajNe (i)+ f(i) (11) Stellar Objects: Composite Stellar Populations 6 where j runs from 1 to n × m and the weight aj is to be determined, while f(i) is the number of interlopers (foreground and background stars) in each of the CMD cell i and is typically estimated with the CMD of an observation off the CSP. Other effects one needs to consider include unresolved binaries and blending, which broaden the CMD. One way to account for the binary effect, for ex- ample, is to randomly assign a fixed fraction of stars with companions. For such a selected star with a mass of Mpr, the mass of the companion Mcomp is drawn according to Mcomp = [ran(1 − qc)+ qc]Mpr (12) where qc is the minimum value of the ratio Mcomp/Mpr and is usually assumed to be 0.7 and ran is a random number with a flat distribution between 0 and 1. So Mcomp has a value between 0.7Mpr and Mpr. The magnitude in a generic −0.4MA(1) −0.4MA(2) band A is then MA = −2.5log[10 + 10 ], where MA(1) and MA(2) are the magnitudes of the system components.