Download The Stellar Population Synthesis Technique Charlie Conroy Princeton

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:
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•
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•
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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)