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Population synthesis models
From stellar evolution models to synthetic populations in the Milky Way
L´eo Girardi
OAPadova INAF – Italy LIneA – Rio de Janeiro – Brazil
GAIA/ITN School, Tenerife, Sep. 2013
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Lecture 4 scheme
Lecture goals:
how to simulate the Milky Way a simple code
MW components
overview of main features in optical and near-IR CMDs To read:
Reviews: Bahcall 1986, Ivezi´c et al. 2012 Codes: Robin et al. 2003, Girardi et al. 2005
The basic problem
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...Simulating the stars along a given line of sight (l.o.s.; pencil beam survey) You can see this problem in 2 ways:
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1.. it is equivalent to take a simulated external galaxy and spread it along the l.o.s., reddening the components according to a given reddening–distance relation.
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2.. it is equivalent to simulate many external galaxies, each one at a different distance and extinction along the l.o.s.
Both ways work.
1 is by far the easiest to code and good enough for many applications, but assumes galaxy components are homogeneous along the l.o.s.
2 is more general, and if well coded will not cost much more than 1 in terms of computing time.
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The equation of stellar statistics
The number counts of Galactic stars in a given bin of apparent magnitude [mλ, mλ+ dmλ] – where λ stands for a passband – and towards an element of galactic coordinates (`, b) and solid angle dΩ, is given by the fundamental equation of stellar statistics
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N(mλ, `, b) = dmλ
Z ∞
0
dr r2ρ(r)L(Mλ, r) dΩ (1)
where r is the line-of-sight distance, and ρ(r) is the stellar density as a function of the position r = (`, b, r ).
r (in parsecs) is related to the absolute and apparent magnitudes M0,λand mλ, and to the interstellar absorption Aλ, by
M0,λ= mλ− 5 log r − Aλ(r ) + 5 .
L(M0,λ, r) is the intrinsic distribution of stellar absolute magnitudes, i.e. the intrinsic luminosity function (LF) of the stars considered at r.
The equation of stellar statistics
The ultimate goals of star count models:
describe the stellar densities ρ(r) for the largest possible volume to a lesser extent, determineL(Mλ, r)
The way to reach these goals:
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First assume the functional forms of ρ andL, and then compare the results of Eq. (1) to observed number counts in several Galaxy fields. Then change parameters, iterate...
A number of assumptions help in simplifying the task. The first one is to recognize that the Galaxy can be separated in a few distinct components, such as the disc, halo, and bulge:
ρ = ρd+ ρh+ ρb, (2)
each one of these components having a simple expression for their density. The second one is to start by assuming an intrinsic LFL which is virtually independent of (or weakly varying with) r, i.e.
L(Mλ, r) =L(Mλ) for each component.
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The intrinsic luminosity function L(M)
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1.. Earlier models (e.g. Bahcall & Soneira 1980, 1984; Gilmore & Reid 1983; M´endez &
van Altena 1996, 1998) assume empiricalL(M), derived from e.g. star counts in globular clusters or in the Solar Neighbourhood. To cope with difficulties, non-physical assumptions started being adopted, e.g. different scale heigths for
“red” and “blue” stars.
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2.. Latest models (Besan¸con, TRILEGAL, Galaxia) assume a theoreticalL(M), derived from sets of evolutionary tracks together with suitable distributions of stellar masses, ages, and metallicities. Difficulties are dealt via changes in other parameters, e.g.
age and metallicity distributions.
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The latter method belongs to the family of “evolutionary population synthesis”models.
Brings along great advantages, for instance the simulation of metallicity gradients, scale lengths increasing with age, other observables (e.g. stellar radii, mass loss), etc. At the price of
more parameters to adjust
trusting in stellar evolution models (and who doesn’t?)
Example: TRILEGAL v1.5 scheme
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Example: TRILEGAL web interface
http://stev.oapd.inaf.it/trilegal
allows to specify photometric system, extinction, and all geometric parameters,...
Example: TRILEGAL web interface
output table
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Other popular codes
Besan¸con (Robin et al. 2003, http://model.obs-besancon.fr/), also makes population synthesis but using different stellar data, includes kinematics and a mass model for the disk(s), good calibration (especially for 2MASS) but few photometric systems
GALFAST (Juri´c et al. 2008), based on stellar densities derived from SDSS photometric parallaxes, uses a givenL (it’s not strictly population synthesis), is being used in the forecast of LSST, pioneers use of GPUs to greatly speed simulations
Galaxia (Sharma et al. 2011), population synthesis based on same stellar models as TRILEGAL, uses efficient algorithms to sample stars in arbitrary volumes.
Input databases
Evolutionary tracks and spectra:
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Input databases
The intrinsic CMDs andL that follow for the disk and halo:
Input databases
The intrinsic CMDs andL that follow for the disk, in the optical and near-IR:
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Galaxy components
Galaxy components
Rough motivations for these components:
exponential dust layer: not very well justified, but works fine as long as we’re not looking right at the Galactic Plane – say for|b| > 5◦
radial exponential disks: that’s what we see in external spirals: the surface brightness decreases exponentially (Freeman lectures)
vertical sech2disks: that’s expected for isothermal disks. Not justified for a superposition of disks with increasing scale height with age. (Freeman lectures) oblate power-law halo: more general than classical r−1/4spheroids, and empirically shown to provide much better fits (e.g. Juri´c et al. 2008)
triaxial bulge: that’s also empirical (COBE/DIRBE results by Drew et al.), gives good initial description, but other structures are now emerging (Gerhard and Freeman lectures)
and the missing components: disk warp and flare, spiral arms, ...
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As you see, there’s a great deal of questionable approximations in these ρ(r) – as well as in theirL. Overall, the approach works and is useful, but has to be largely improved.
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Distributions of distance moduli
Make product of ρ and r2, and apply N(µ) dµ = N(r ) dr .
Example: thin disk and halo towards NGP (were them observed with 100 % completeness):
If we observe a sample of stars with similar luminosity (e.g. red clump/HB), disk ones will dominate at µ0.13 mag (r < 4 kpc), halo ones at µ0&13 mag
but this also heavily depends on wavelength, color cuts, etc.
Model calibration
The classical approach is, roughly:
define a set of photometric data complete within a given magnitude range start with “well-accepted parameter values”, e.g R = 8 kpc, hR= 2.5 kpc, etc., and simulate the star counts
first adjust the density scale, that is Σ or ρ , just increasing/decreasing them until Nobserved/Nmodeled' 1
then start adjusting other geometric parameters (power-law indexes and scale lengths), by comparing different l.o.s. and magnitude ranges
iterate
do it for subsamples dominated by different components, i.e. low-|b| for thin disk, high-|b| for thick disk and halo, small |b| and small ` for bulge
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Model calibration
do it for subsamples dominated by different components, i.e. low-|b| for thin disk, high-|b| for thick disk and halo, small |b| and small ` for bulge
Girardi et al 2005.
2MASS data: all-sky, little affected by reddening, and dominated by the thin disk even at very high|b|
Model calibration
do it for subsamples dominated by different components, i.e. low-|b| for thin disk, high-|b| for thick disk and halo, small |b| and small ` for bulge
Girardi et al 2005.
Very deep optical surveys: dominated by thin disk, then thick, then halo, as we go to
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Model calibration
red and blue samples may sample different components (ans usually different distances)
The Hipparcos local sample
is the thin disk local stellar density OK?
check with a complete sample drawn from Hipparcos catalog
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Optimization of model parameters
A preferable approach:
define a list of N lines-of-sight and bins of the CMD to deal with, build the data vector n = (n1, n2, . . . , nN)
define the model unknown parameters θ and their initial guess values, and compute the model values νi(θ)
use an optimizer routine that migrates across the θ space until the the model-data likelihood is maximised. For Poisson statistics it is
l = 2 XN
i =1
νi(θ)− ni+ niln ni
νi(θ)
(3) Examples: Vanhollebeke et al 2009 bulge calibration using 2MASS+OGLE data
Optimization of model parameters
Examples: Vanhollebeke et al 2009 bulge calibration using 2MASS+OGLE data
best-fit parameters
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Background galaxies
For high S/N observations, they set the faintest magnitude that can be probed.
For ground-based optical observations, limit is R∼ 22.5 (e.g. Groenewegen et al. 2002) For HST optical observations, limit is at least I ∼ 24 (probably I ∼ 26 with latest ACS and WFC3). But this coincides with limit for having significant numbers of MW stars per pointing (e.g. M´endez & Guzm´an 1998 for HDF)
Stellar content in some main surveys
.With present tools, any photometric survey can be easily simulated.
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Simulations tell us things the photometry alone does not provide: e.g. the likely distributions of stellar ages, masses, and distances. Are they reliable?
A partial answer tomorrow. See Allende Prieto lectures for main survey descriptions.
Here’s a quick overview of things that we are reasonably sure, about the stellar populations probed by some major MW surveys:
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Stellar content in 2MASS
Probes the coolest stars. Little affected by extinction.
Stellar content in 2MASS
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Over most of Polar Caps, 2MASS CMDs reveal just 2 vertical features (VF).
TRILEGAL disk & halo, Marigo et al. 2003
M67 by 2MASS, Sarajedini et al.
2009
The interpretation: these CMDs are dominated by nearby dwarfs.
Blue VF is caused by the intermediate-age to old turn-offs in the thin disk.
Red VF is caused by the kink that solar-metallicity stars of 0.4 M have in near-IR colours. It simply reflects the formation of deep near-IR H2O absorption lines at
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Stellar content in 2MASS
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Closer to the Galactic Plane, and Bulge, the VFs become much more spread in colour, with a fan of red stars, and a slight “doubling” of the blue sequence.
The red fan are the distant cool & luminous giants sampled across the disk(s).
The main red sequence is no longer caused by dwarfs, but by red clump stars!
The bluest fuzzy sequence are the youngest main sequence stars (that were absent at high|b|).
Very close to the GP, all sequences get messier because of extinction.
Stellar content in the SDSS imaging
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Three main structures, again sampling different MW components: thick disk turn-off (blue bright), halo turn-off (blue faint), and low-mass thin disk (red faint)
de Jong et al. 2010: used the blue features to calibrate thick disk + halo parameters in an objective way.
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Tomorrow’s lecture
Beyond optical-IR star counts:
modeling huge spectroscopic surveys modeling big asteroseismic surveys some other interesting applications
No homework, sorry.
Tomorrow’s lecture
Beyond optical-IR star counts:
modeling huge spectroscopic surveys modeling big asteroseismic surveys some other interesting applications No homework, sorry.
