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The Stellar Population Synthesis Technique Charlie Conroy Princeton Outline • Introduction to stellar population synthesis (SPS) – What’s the matter? • The effects of SPS uncertainties on derived properties – Stellar evolution – Dust – The initial mass function (IMF) • The challenge of comparing models of galaxy evolution to observations • Where do we go from here? Galaxies, then and now Perez-Gonzalez et al. 2007 Galaxy stellar mass function from z~4 to z~0 How are these physical properties derived? Fontana et al. 2006 Stellar Population Synthesis: Overview • Stellar population synthesis (SPS) utilizes the fact that galaxies are made of dust and stars – We simply need to know the number of stars as a function of their mass, age, and metallicity – Starlight attenuated by dust • Focus on UV, optical, near-IR data, and so ignore dust emission • SPS provides the fundamental link between theory/models and observations – Used extensively in extragalactic astrophysics Stellar Population Synthesis - I • Single/simple stellar populations (SSPs): (IMF x spectra) star clusters t=106.6 yrs Van Dokkum 2008 IMF t=1010 yrs Stellar evolution Stellar Population Synthesis - II • Composite stellar populations (CSPs): SFR x SSP x dust galaxies An example: a galaxy made of two populations: Integrate over stellar ages t’ Stellar Population Synthesis: Challenges SPS Model: IMF, spectral library, stellar evolution, SFH, dust, metallicity fit parameters of model to data Observations: Spectral energy distributions, magnitudes, etc. physical properties • But how robustly can we make this transformation between observables and physical properties?? – How do uncertainties in SPS propagate into uncertainties in physical properties? • Systematic vs. statistical uncertainties – What inputs do we need to know better in order to make this translation more precise? – Are some combination of observables better (more robust) than others? The Propagation of Uncertainties: I • Recent work has shown that the stellar masses estimated from different SPS models do not agree – Offsets of a factor of ~2 – The effect is a function of the age of the stars • Worse at higher redshift (Maraston et al. 2006) – Thought to be due to the differing treatment of the thermally-pulsating AGB (TP-AGB) phase Systematic shifts arise from different SPS models Maraston et al. 2006 The Propagation of Uncertainties: II • LRG optical color evolution has been challenging to model – Solution has two parts: 1. 2. Include a small amount of very metal-poor stars Theoretical stellar spectral libraries are substantially flawed Theoretical spectral library Empirical spectral library Empirical spectral library + 3% metal-poor stars Maraston et al. 2008 The Propagation of Uncertainties: III • The theoretical spectral libraries are in error, even at Zsol Maraston et al. 2008 (some of) the elephants in the room: 1. Stellar evolution TP-AGB, HB, BS, post-AGB, WR, overshooting, binaries, etc. • 2. Dust Extinction law Molecular clouds vs. cirrus dust; optical depths, transition times Geometry of dust (clumpiness) very important • • • 3. Metallicity evolution and distribution Rarely discussed, but an effect that must be there • 4. IMF • 5. Effects normalization, and SED shape - degenerate with SFH Stellar spectral libraries • • 6. No comprehensive (i.e. usable; only solar Z) empirical library Theoretical libraries have known, substantial flaws Non-solar abundance patterns (α-enhancement) • Impacts both stellar evolution and the libraries Data • ~8,000 galaxies with z<0.05 – GALEX+SDSS+2MASS matched photometry • Redshifts from SDSS – Structural measurements, including inclination (b/a) • provided by Mike Blanton Stellar Evolution Uncertainties • Assume “Padova” 2007 stellar evolution calculations • Introduce parameters: – fbhb: fraction of blue horizontal branch stars • Extended HBs common at low metallicity, also seen at higher Z • Neglected in nearly all SPS modeling – Sbs: specific frequency of blue straggler stars • • • • Several scenarios for their existence May be very common in the field Ubiquitous in GCs (where Sbs~a few) Neglected in nearly all SPS modeling – ΔT: shift in log(T) along TP-AGB phase • T extremely uncertain owing to the complexities of this phase. Low T means a very complex atmosphere, including dust formation – ΔL: shift in log(L) along TP-AGB phase • To control uncertain phases of stellar evolution, i.e. parameterize our ignorance Stellar Evolution: TP-AGBs Data on star clusters in the LMC Zsol SSP evolution TP-AGB onset Conroy, Gunn & White 2008 SSP evolution Stellar Evolution: Blue Stragglers and HB • Effects become important in the blue and UV because these are hot stars Horizontal branch Blue stragglers Conroy, Gunn & White 2008 The Propagation of Uncertainties Conroy, Gunn & White 2008 Default assumptions Marginalize over uncertainties An Example: fitting GALEX+SDSS+2MASS photometry at z~0 Dependence of physical properties (x-axis) on the uncertainties in stellar evolution (y-axis) 68% CL 95% CL Stellar Evolution: Systematic Trends ~400 z~0 galaxies • See systematic trends as sample size grows Fitting to large datasets may actually inform stellar evolution models, dust models, etc. Conroy, Gunn & White 2008 • A Parametric Dust Model Lets construct a flexible dust model: • Two dust components: 1. dust around young stars with optical depth τ1 i.e. stars embedded in molecular cloud 2. dust around old stars with optical depth τ2 i.e. cirrus dust a) old dust can be clumpy, with gaussian PDF characterized by dispersion σclump • Transition between the two occurs at a time tesc • The attenuation curve will be a power-law: λ-δ (will also explore MW extinction) Dust: Attenuation Curves • Dust assumptions are hugely important – Attenuation curve depends on: • Size distribution of grains – Metallicity – Intensity of UV radiation • Geometry (scattering) • In general, we do not know what the attenuation law “should” be! • UV bump is an important feature in MW, LMC, SMC extinction curves, and shows considerable variation amongst environments. Should this feature be included in attenuation curves in SPS? Should it be marginalized over? – – If UV bump is carried by PAHs (e.g. Weingartner & Draine 2001), then we might expect variation in bump strength for different galaxies because PAH fraction varies from galaxy to galaxy (Draine et al. 2008) No evidence for UV bump from local starburst galaxies (Calzetti et al.), but seen at high-z (e.g. Eliasdottir et al.) Effects of Dust Assumptions on Mass Estimates: I – Stellar mass dependence on galaxy inclination – Should be uncorrelated – But heavily-used public stellar mass catalogs do show a correlation – Fitting with a sufficiently flexible dust model resolves this issue – Vary τ2, τ1, use MW extinction curve face-on edge-on Conroy et al. in prep • One example: face-on edge-on Maller et al. 2008 Effects of Dust Assumptions on Mass Estimates: II • Degeneracies of physical parameters with attenuation law for a single galaxy • These degeneracies are typical 68% CL 95% CL Dust Uncertainties: MC disruption times • The timescale for molecular cloud (MC) disruption, tesc, is not wellconstrained observationally Plausibly ranges from 106.5 < tesc < 107.5 yrs – Will depend on metallicity, intensity of UV radiation (e.g. local SFR), etc. – Standard model assumes tesc=107 yrs 7.5 yrs tesc=106.6 yrs Log(M/L)0 Log(M/L)0 tesc=10 Conroy et al. in prep Δ[ Log(M/L)] • Difference between standard and modified assumption for tesc Constraints on Attenuation: I • Pick out the same galaxies at various epochs – “Same” in the sense of similar metallicity, V-band opacity, SFR, etc. • • Observed colors will map out the SED In particular, will be very sensitive to the presence of the UV bump Constraints on Attenuation: II • Evolution of observed B-R color from DEEP2 survey • Data favor no UV bump Calzetti MW w/ bump MW w/ bump MW w/o bump MW w/o bump Dust vs. Inclination • Best-fit results for ~6,000 z<0.05 SDSS+GALEX+2MASS galaxies IMF Uncertainties IMF is extremely difficult to measure in the solar neighborhood Conventional wisdom: IMF uncertainties are important in only two respects: – Overall shift in normalization of stellar masses – Luminosity evolution for a passively evolving system IMF constraints from MW, LMC Kroupa 2001; Scalo 1998 Luminosity evolution depends on the slope of the IMF at the mainsequence turn-off mass, which is ~1 Msun for old systems Logarithmic slope of IMF • • IMF Uncertainties: Luminosity Evolution • Rate of passive luminosity evolution very sensitive to IMF • Directly impacts conclusions regarding galaxy evolution Passive luminosity evolution at z<1 Conroy, Gunn & White 2008 IMF uncertainty at ~1Msun Wake et al. 2006 – Known since the late 70s (Tinsley & Gunn), but has since been approximately forgotten LRG evolution since z=0.6 IMF Uncertainties: SSPs • • • IMF has a marginal effect on the colors of SSPs, except for nearIR colors at intermediate ages Large effect on M/L These results (esp in the optical) have lead many to believe that the IMF does not have an important effect on the derived properties of galaxies, aside from an overall normalization Zsol SSP evolution for different IMFs Slope = 1.3 Recall Salpeter (1955) IMF: dn/dM ~ M-2.3 Slope = 3.3 IMF Uncertainties: SFR estimates • • Fit observed galaxies with varying assumptions for the logarithmic slope of the IMF at high masses (>2Msun) Derived SFRs depend sensitively on the IMF – There is a clear, and strong degeneracy between the IMF and SFR – The dependence of SFR and IMF is linear - not a constant shift – IMF effects near-IR colors at intermediate ages (due to AGB) for SSPs – IMF degenerate with SFR Log[IMF(>2Msun)]=1.5 Log[IMF(>2Msun)]=3.5 Log(M/L)0 Log(M/L)0 Conroy et al. in prep Conclusion: Conventional wisdom regarding IMF is not correct (see also Marchesini et al. 2008) Δ[ Log(SFR)] • Difference between standard and modified assumption for IMF slope The Way Forward • • Interesting physical parameters depend on a number of uncertain inputs in the SPS technique Solution: fit observed galaxies with an SPS code that explicitly marginalizes over the uncertain inputs – This approach will provide robust catalogs of derived data products – The characterization of errors via MCMC will all be crucial in the interpretation of these results • • – Will help constrain TP-AGB, HB, etc. Mass function at z=0 Data from Li & White 2009 Best-fit Schechter Best-fit Schechter, taking errors into account Behroozi, Conroy, Wechsler, in prep • Need comprehensive, empirical stellar libraries Careful attention to dust modeling, include UV through far-IR (Akari will help here) Surface brightness fluctuations are a unique probe of the stellar populations The challenge of comparing models of galaxy formation to observations Croton et al. 2006 Luminosity function • We want to compare galaxy evolution models to observations • The SPS technique is used to translate the physical outputs from these models into observational predictions • How hard is it to make this translation? K-band b-band Synthetic Galaxies • Consider two star formation histories – A “passive” galaxy with no on-going star formation – An actively star-forming galaxy • Consider the expected colors of these synthetic galaxies as a function of the uncertain aspects in SPS – Our model will be: • • • • • • • • • τ2 & IMF fixed 0.5<τ1<1.5 6.6<log(tesc/yrs)=7.5 0.4<δ<1.3 0.0<σclump<1.0 -0.1<ΔT<0.1 -0.2<ΔL<0.2 0.0<fbhb<0.2 0<Sbs<2 Synthetic Galaxies: Uncertain Colors • Marginalize over all uncertainties (with optimistic priors), except for the IMF and τ2 SF galaxy passive galaxy Conroy, White, & Gunn in prep τ2=1.0 τ2=0.3 τ2=0.0 τ2=0.3 Conclusions & The Future • The SPS technique requires a number of uncertain inputs, including: – Stellar evolution, the IMF, assumptions about metallicity distributions, dust models, etc. • These uncertainties propagate into, and introduce substantial systematics in the derived physical properties, including: – Stellar masses, mean ages, SFRs, metallicities • A solution is to fit the observations taking these substantial uncertainties into account (marginalization) – Produce new, robust catalogs of derived properties with the tools we’ve developed • Eventually return to the uncertain inputs, and hope to reduce uncertainties with future observations – Revival of interest in stellar evolution, stellar spectral libraries, IMF constraints w/ Jim Gunn (Princeton) & Martin White (Berkeley)