Download Resolved SPs : simulations

The Simulator
(AT FIXED METALLICITY)
y
r
 n( r )dr   n( y)dy
Random Extraction of Mass-Age pair
rn
yn
r random in 0↔1
y
r 
 n( y)dy
yn
yx
 n( y)dy
yn
Place Synthetic Star on HRD
Convert (L,Teff) into (Mag,Col)
Apply Photometric Error
NO
YES
Test to STOP
Notify: Astrated Mass,
# of WDs,BHs,TPAGB..
Lectures on Stellar Populations
June 2006
EXIT
Interpolation between tracks: lifetimes
Lectures on Stellar Populations
June 2006
Interpolation between Tracks:
L and Teff of low mass stars
Lectures on Stellar Populations
June 2006
Interpolation between Tracks:
L and Teff of intermediate mass stars
Lectures on Stellar Populations
June 2006
Photometric Error: Completeness
NGC 1705
(Tosi et al. 2001)
Completeness levels:
0.95 % thick
0.75 % thin
0.50 % thick
0.25% thin
Lectures on Stellar Populations
June 2006
Photometric errors: σDAO and Δm
Lectures on Stellar Populations
June 2006
Crowding
# of stars j in one resolution element (r.e.)
Probability of j+j blend is
where Sj is the srf density of j stars
and σr.e. is the area intercepted
 n 2j
Degree of Crowding in the frame
With Nr.e resolution elements is
Sj
n j  S j   r .e .
crow 
n2j  N r . e .
n j  N r .e .
2
 n j  2.4  10 5  S j  rsq. e''.d Mpc
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.
 r .e .  (0.5) 2
In Phoenix (DSp) we detect >4200 RC stars/Kpc2: with OmegaCAM crow is 0.1 already at 2 Mpc
Lectures on Stellar Populations
June 2006
Another way to put it:
(Renzini 1998)
# of blends in my frame is
# of j stars in my frame (if SSP) is
# of blends in my frame becomes
n2j  N r .e .
n j  B( )  L  t j
( B( )  Lr . e .  t j )  N r . e . 
2
where L is the lum sampled
by the r.e.
B 2 t 2j  L2frame
N r .e .
# of blends increases with the square of the Luminosity and decreases
with the number of resolution elements
Lectures on Stellar Populations
June 2006
Pixels and Frames: Example
LB  10 0.4(  B  AB mod M Bo )
Lbol  2.5 LB
B(15Gyr )  2.2  10 11
t LPV  0.25 Myr
t RGBT  5 Myr
(1)
(2)
(3)
(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
Lectures on Stellar Populations
June 2006
How Robust is the Result?
The statistical estimator does not account for systematic errors
Theoretical
Transformed
Errors Applied
EACH STEP BRINGS ALONG ITS OWN UNCERTAINTIES
THE SYSTEMATIC ERROR IS DIFFUCULT TO GAUGE
Lectures on Stellar Populations
June 2006
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 Gy
This is valid for all the PMS boxes, with
different proportionality factors
N box
 M stars(   0 )
j
Perform the exercise for all isochrones
M stars( )
Lectures on Stellar Populations
June 2006
Methods for Solution: Blind Fit
used by Hernandez, Gilmore and Valls Gabaud
Harris 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
Ages: 1112 Gyr
[M/H]:-1.75  -1.65
Lectures on Stellar Populations
June 2006
PARTIAL CMD
•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
ni
m 
PLR    i  exp( ni  mi )
i  ni 
fit  2 ln PLR  2 ( mi  ni  ni ln
i
•Minimize fit -- get best fit
+ a quantitative measure of the quality of the fit
Lectures on Stellar Populations
June 2006
ni
)
mi
My prejudice:
•The model CMDs may NOT contain 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 same
accuracy as the fit to the entire
CMD.”
If wrong Z is used, the blind method will give a solution,
but not THE SOLUTION
Lectures on Stellar Populations
June 2006
Methods for Solution: Tailored Fit
Count the stars in the diagnostic boxes:
Their number scales with the mass in
Stars in the corresponding age range
Construct partial CMD constrained to reproduce
the star’s counts within the boxes.
The partial CMDs are coherently populated also
with stars outside the boxes
Between 10 and 50 Myr
Younger than 10 Myr
Between 50 Myr
and 1 Gyr
Lectures on Stellar Populations
June 2006
•
Compare the total simulation to the data
Use your knowledge of
Stellar evolution to improve
the fit AND decide where
you cannot improve, and
where you need a perfect
match
The two methods should
be viewed as complementary
Lectures on Stellar Populations
June 2006
Simulation
Lectures on Stellar Populations
June 2006
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.
Lectures on Stellar Populations
June 2006