The Simulator

Lectures on Stellar PopulationsJune 2006

The Simulator

Random Extraction of Mass-Age pair

(AT FIXED METALLICITY)

Place Synthetic Star on HRD

Convert (L,Teff) into (Mag,Col)

Apply Photometric Error

Test to STOP

y

y

r

r nn

dyyndrrn )()(

r random in 0↔1

x

n

n

y

y

y

y

dyyn

dyyn

r

)(

)(

EXITYESNO Notify: Astrated Mass,

# of WDs,BHs,TPAGB..


Interpolation between tracks: lifetimes


Interpolation between Tracks: L and Teff of low mass stars


Interpolation between Tracks:L and Teff of intermediate mass stars


Photometric Error: Completeness

NGC 1705(Tosi et al. 2001)

Completeness levels:0.95 % thick0.75 % thin0.50 % thick0.25% thin


Photometric errors: σDAO and Δm


Crowding

..erjj Sn

2jn

2''..

5

..

..2

104.2 Mpcsq

erjjerj

erj dSnNn

Nncrow

# of stars j in one resolution element (r.e.)

jS

2.. )5.0( er

where Sj is the srf density of j stars and σr.e. is the area intercepted

Probability of j+j blend is

Degree of Crowding in the frameWith Nr.e resolution elements is

depends on SFH:

In VII Zw 403 (BCD) we detect with HST 55 RSG, 140 bright AGB and 530 RGT(1) stars/Kpc2

Observed with OmegaCAM we get crow=0.1 at 17,10 and 5.6 Mpc for the 3 kinds resp.

In Phoenix (DSp) we detect >4200 RC stars/Kpc2: with OmegaCAM crow is 0.1 already at 2 Mpc


Another way to put it:(Renzini 1998)

..2

erj Nn

jj tLBn )(

..

222

..2

.. ))((er

framejerjer N

LtBNtLB

# of blends in my frame is

# of j stars in my frame (if SSP) is where L is the lum sampledby the r.e.

# of blends in my frame becomes

# of blends increases with the square of the Luminosity and decreaseswith the number of resolution elements


Pixels and Frames: Example

)mod(4.010 BoBB MABL 11102.2)15( GyrBBbol LL 5.2

MyrtLPV 25.0 MyrtRGBT 5

(2)(3)

(1)

(4)

(1) A.O.: σ(r.e.) ≈ 0.14x0.14 ….. nRGT ≈ 8 in one r.e.(2) HST: σ(r.e.) ≈ 0.06x0.06…..nRGTxnRGT≈2e-04 … N(r.e.)≈1e+05(3) …………………………………………≈ 2e-05…..(4) GB : σ(r.e.)≈0.3 sq.arcsec….n RGTxnRGT≈0.044…N(r.e.)≈1.3e+04


How Robust is the Result?The statistical estimator does not account for systematic errors

Theoretical Transformed Errors Applied

EACH STEP BRINGS ALONG ITS OWN UNCERTAINTIESTHE SYSTEMATIC ERROR IS DIFFUCULT TO GAUGE


Why and How Well does the Method Work?

Think of the composite CMD as a superposition of SSPs,

each described by an isochrone

The number of stars in is proportional to the Mass that went into stars at τ ≈0.1 GyThis is valid for all the PMS boxes, with different proportionality factors

)( 0 starsboxj MN

Perform the exercise for all isochrones

)(starsM


Methods for Solution: Blind Fit

used by Hernandez, Gilmore and Valls GabaudHarris and Zaritsky (STARFISH)

Cole; Holtzman; Dolphin

Dolphin 2002, MNRAS 332,91: Review of methods and description of Blind fit

•Generate a grid of partial model CMD with stars in small ranges of ages and metallicities•Construct Hess diagram for each partial model CMD•Generate a grid of models by combining partial CMDs according to SFR(t) and Z(t)

DATA PURE MODEL PARTIAL CMD

Ages: 1112 Gyr[M/H]:-1.75 -1.65


•Use a statistical estimator to judge the fit: mi is the number of synthetic objects in bin i ni is the number of data points in bin i

i i

iiii

ii

n

i i

i

m

nnnmPLRfit

mnn

mPLR

i

)ln(2ln2

)exp(

•Minimize fit -- get best fit + a quantitative measure of the quality of the fit


My prejudice:

•The model CMDs may NOT contain the solution

If wrong Z is used, the blind method will give a solution,but not THE SOLUTION

•The method requires a lot of computing: Does this really improve the solution? (apart from giving a quantitative estimate of the quality of the fit)

Dolphin: “ The solution with RGB+HB was extremely successful, measuring…the SFH with nearly the sameaccuracy as the fit to the entireCMD.”


Methods for Solution: Tailored Fit

Count the stars in the diagnostic boxes:Their number scales with the mass inStars in the corresponding age range

Younger than 10 Myr

Between 10 and 50 Myr

Between 50 Myr and 1 Gyr

Construct partial CMD constrained to reproducethe star’s counts within the boxes.The partial CMDs are coherently populated alsowith stars outside the boxes


• Compare the total simulation to the data

Use your knowledge ofStellar evolution to improvethe fit AND decide where you cannot improve, andwhere you need a perfectmatch

The two methods shouldbe viewed as complementary


Simulation


What have we learnt

When computing the simulations we should pay attention to

• The description of the details in the shape of the tracks, and the evolutionary lifetimes (use normalized independent variable)• The description of photometric errors, blending and completeness (evaluate crowding conditions: if there is more than 1 star per resolution element the photometry is bad; crowding condition depends on sampled luminosity, size of the resolution element and star’s magnitude)

Different methods exist to solve for the SFH:

the BLIND FIT is statistically good, but does not account for systematic errors; it seems too complicated on one hand,

could miss the real target of measuring the mass in stars on the other;

the TAILORED FIT goes straight to the point of measuring the mass in stars of the various components of the stellar population; it’s unfit for automatic use; the solution reflects the prejudice of the modeler; the quality of the fit is judged only in a rough way.

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