Stellar populations

• Both luminosity and spectrum depends on stellar content of the galaxy, and understanding these is the subject of stellar populations.

• Use stellar evolution theory to interpret differences in stellar pops between galaxies
  • consider the spectrum of a galaxy to be the sum of a set of simple stellar populations (SSPs)
  • SSPs are single-age, single-metallicity population.
  • Spectrum of a SSP depends three quantities: the age, metallicity and IMF, plus an understanding of stellar evolution and atmospheres.
  • try to determine the relative amplitudes of all possible SSPs in a given galaxy spectrum, and hence get the star formation history. Note that SFH is combination of age distribution, metallicity distribution, and initial mass function (time dependent?)

• quick review of stellar evolution
  • Stellar evolution gives model tracks (evolution as function of time for a given mass)
  • MS, SGB, RGB (note relative constancy of tip luminosity with stellar mass), HB, AGB, PAGB, WD (or SN), advanced stages for higher mass stars.
  • What is going on inside the star at each stage? Hydrogen and helium burning sequences: HB morphology, red clump stars, blue loop stars.
  • cross section of properties at fixed time across a range of masses is an isochrone (e.g., Renzini fig 1.6)).
  • Age effects (show model isochrones)
  • Metallicity effects: atmosphere effects and internal effects. Observed metallicity effects: RGB, HB morphology. (show model isochrones)
  • Other effects? Second-parameter problem (show second parameter data). Extreme HB stars. Age? He abundance? Heavy element abundances? Density? Rotation?
  • Potential importance of binaries/interactions: SNIa and blue-stragglers.

• Integrated luminosity of a population
  • since post-MS evolution is fast compared to MS evolution for all masses, it is true that at any given time when the most luminous stars are the most evolved stars the luminosity is given predominantly by stars of (nearly) a single mass. (true for all except youngest ages, see Renzini 1.1),

• Do SSPs get brighter or fainter as they age?
  • To determine the luminosity of a stellar population, consider the number of stars evolving off the MS, or equivalently, dying, which is given by the evolutionary flux:
    
    $$b(t) = \psi(M_{TO}) \vert Mdot\vert$$
    
    
    measured in number of stars per year, where $\psi$ is the IMF, and $\vert Mdot\vert$ is the time derivative of the turnoff mass. ( Renzini 1.1).
  • one can see that the IMF is critical in determining the luminosity evolution of a galaxy.
  • Once one reaches an age where most massive stars have died, all stars of lower mass reach comparable luminosity (tip of RGB), hence luminosity of population depends on number of red giants
  • For typical IMF, number of stars increases slower towards lower mass than rate of generation of turnoff stars decreases

• Integrated mass of a population
  • Mass contribution depends on IMF
    • ``classical'' Salpeter IMF (power law with $dN/dM \propto M^{-2.35}$) and others (Pagel Fig 3).
    • Widely used determination of local IMF is by Kroupa, Tout, and Gilmore, who find $dN/dM\propto M^{-2.7}$ for $M>1$ Msun, $dN/dM\propto M^{-2.2}$ for $0.5>M>1 Msun$, $dN/dM\propto M^{-1.3}$ for $M<0.5$ Msun. For our purposes we'll assume that $\xi(M)$ is normalized to unit mass, i.e., $\int m \xi dm = 1$.
    • For all measured IMFs, bulk of the mass is in relatively low mass stars ($<1$ Msun).
  • Empirically, no strong evidence for variations of IMF as functions of, e.g., metallicity.
  • No well-established theory for predicting IMF

• Since most of integrated mass is in low mass, unevolved, faint, stars, while most of luminosity comes from the more massive, brighter stars, stellar populations can be parameterized in terms of stellar mass-to-light ratio
  • definition in terms of solar mass-to-light ratio.
    
    $$M/L\equiv {(M/Msun) \over (L/Lsun)}$$
    
    

  • Absolute value of M/L depends strongly on IMF; relative values characterize different stellar pops for fixed IMF.
  • Typical synthetic M/L ratios for individual stars:

    Mass	$M/L_V (ZAMS)$
    0.3	27
    0.5	14
    1.0	1.57
    2.0	0.12
    4.0	0.012

  • M/L for simple stellar populations (solar metallicity and KTG IMF)

    Population age (Gyr)	$M/L_V$
    0.1	0.14
    1	0.5
    2	0.8
    3	1.1
    5	1.5
    10	2.3
    15	3.0

  • M/L composite populations with constant SFR (solar metallicity and KTG IMF):

    Population age range	$M/L_V$
    0.1-10	1.5
    0.1-15	2.0

  • stellar M/L ratio depends on luminosity bandpass; less variation as one goes to near-IR bandpasses

  • Note: people also talk about total mass to light ratios, i.e., including dark matter

• Integrated spectrum of a population
  • need to know the relative contributions of each stage of evolution
  • number of stars in each post-MS stage is determined by the time spent in each stage:
    
    $$N_j = b(t) t_j$$
    
    
    and although the flux is sensitive to the IMF, the relative contributions of each stage are not, at least for older populations (Renzini fig 1.5).
  • For all except the youngest population, the later stages of stellar evolution provide a majority of the light.
  • Consequently, many properties are nearly independent of the IMF, including the integrated spectrum and the relative contributions of various evolutionary stages.
  • Integrated spectra can be predicted from stellar evolutionary models

• Potential problems with synthetic integrated spectra:
  • stellar isochrone uncertainties, due to opacities, convection, diffusion, mass loss, atmospheres, etc.; tend to be larger at later stages of evolution (luminous stages!)
  • missing evolutionary stages (e.g. HB, AGB, PAGB)
  • missing components in models, e.g., SMR stars
  • solar element abundance distribution
  • interacting binary stars

• Some existing evolutionary synthesis compilations/codes:
  • Bruzual & Charlot (e.g. MNRAS 344, 1000 (2003))
  • Worthey ApJS 95, 107, 1994
  • Bertelli et al., A&AS 106,275,
  • Vazdekis
  • Starburst99, includes HII region contribution, i.e. emission line fluxes
  • others
  • BC models try to include all stages of evolution, use observed spectra for atmospheres at solar metallicity but models at other metallicities. Bertelli et al have all metallicities, need to use model atmospheres for most cases. Worthey uses older isochrones (diff opacities), model atmospheres, appoximations for later stages of evolution.
  • Charlot, Worthey, Buzzoni paper: just from stellar physics alone, ages are uncertain to 25-50%.

• Dependence of color and luminosity on time ( BC Fig 1) for a single burst
  • luminosity variation is combination of IMF plus rate of evolution for lower masses.
  • color evolution comes from changing mix of stellar population

• Spectral evolution ( BC Fig 4) for a variety of star formation rates.
  • Note similarity of SEDs at older ages for SSPs
  • Even more similar for extended SF histories
  • Note potential power of UV

• dependence of contributor on wavelength ( burst (BC Fig 9) and constant SF rate (BC Fig 10)).

• dependence on stellar models ( Worthey 33 and Worthey 34, Charlot et al Fig 2).

• Even with perfect models, there's still a problem separating age and metallicity because of similar effect of age and metallicity: the age-metallicity degeneracy (for integrated light).
  • Increasing Z makes stars cooler, as does making them older. Different color indices all behave in the same way, so even with multiple colors, one can't distinguish age and metallicity. ( Worthey Fig 46-49). Worthey 3/2 law ; most indices are degenerate in age and metallicity, with
    
    $$\Delta(log age)/\Delta(log Z) \sim 1.5$$
    
    
    (Worthey Table 6).
  • Breaking the degeneracy with line indices, e.g. H lines + others.
    • Issue: emission contamination in H$\beta$ (and other indices)

  • This degeneracy is a problem even for a single SSP. For a combination of SSPs the situation is worse. Here one is dominated by the brightest contributor which may be a small contributor by mass!

• Perhaps obtaining absolute ages in this way will not be fruitful. However, all is not lost: probably there is useful information in determining age spread among a set of objects.

• Issues with different element abundance ratios. Note variations in abundance ratios between solar neighborhood stars and globular clusters.