LUCE INTEGRATA DA
POPOLAZIONI STELLARI.
Fondamenti Teorici
Laura Greggio - OAPd
Proprieta’ delle popolazioni stellari rilevanti per la
determinazione di Eta’ ,Metallicita’ e Massa di insiemi
di stelle dalla loro Luce Integrata
Lectures on Stellar Populations
Why should it work
Young populations are bright
Old populations are faint
Young populations are hot
Old populations are cool
Metal poor populations are hot Metal rich populations are cool
Lectures on Stellar Populations
Integrated Colors hold the Key
Young populations are BLUE
Metal poor populations are BLUE
Old populations are RED
Metal rich populations are RED
From Colors
AGE, Z
MASS
From Magnitudes + Lectures on Stellar Populations
Age – Z degeneracy: a taste of it
Turn-Off region can be reproduced with either Young and Metal Rich
or Old and Metal Poor populations
RGBs are mostly dependent on Z
Break degeneracy by considering more ‘COLORS’
Lectures on Stellar Populations
Population Synthesis Technique
Compute integrated spectrophotometry of Stellar Systems by adding up the
light of each star
Used to recover information like AGE and Z of Stellar Populations
Pioneered by Beatrice Tinsley (1980)
Bruzual 1983 – tracks only up to Helium ignition
Arimoto & Yoshii 1986; Guiderdoni & Rocca-Volmerange 1987 – collection of tracks from different authors
(models of Galaxy formation and evolution)
Renzini & Buzzoni (1986); Buzzoni (1989) – use FCT for Post MS stages
Charlot & Bruzual (1991) - almost homogeneous set of tracks (Maeder & Meynet 1987)
+ updates
Worthey 1994 – schematic evolution for PMS; only populations older than 1 Gyr
Bressan, Chiosi and Fagotto 1994 – use Padova tracks
+ updates
Maraston 1998 – use FCT
+ updates
IMPORTANT IS:
• Include ALL RELEVANT evolutionary phases
• Parametrize the “unknown” + Nail the parameter with appropriate
observables
Lectures on Stellar Populations
SSP Bolometric Light: Isochrone Synthesis
md
SSP
L
One isochrone of given (AGE,Z) is {m, L, Te}
  L (m) (m)dm
mi
 ( m)  A  m 2.35
IMF:
 ( m)  A 
m 1.3
0.5  m
Salpeter
m  0.5
 2.3
m  0.5
Kroupa
ms
A is the scale factor:
 m ( m)dm  M
SSP
0
mi
A
M 0SSP
ms
 m[ ( m) / A]dm
mi
The total light of an SSP is directly proportional to
the mass ORIGINALLY transformed into Stars
Lectures on Stellar Populations
MASS RETURN
dM 
  ( t )  R ( t )
dt
R ( t )  
ms
mTO
 ( m ) ( t   m )( m  wm )dm
t
M(env)
M (t )dt

1  
0
t

 (t )dt
0
SSP give back to the ISM a substantial fraction
of their initial mass:
after 15 Gyr the fraction is 30% (Salpeter) 45% (Kroupa)
Lectures on Stellar Populations
Stellar Mass along the Isochrone
md
SSP
L
In the Post-MS phases
the stellar mass is a poor variable
  L (m) (m)dm
mi
The evolutionary mass is almost the
same along the whole Post-MS
portion of the isochrone
Lectures on Stellar Populations
FCT Approximation: substitute L(m,) with L(mTO,t)
m2
n1, 2    ( m )dm   ( m1.5 )m1, 2
m1
m1, 2
dt
 ev
dm
1
t1, 2 ( m1.5 )
m1.5
 ( m1.5 )   ( mTO )
approximations:
valid for PMS phases
dtev
dm

m1.5
dtev
dmTO
tev ( m1.5 )  tev ( mTO )
m2
m1
mTO
 TO t j  b( )t j
nPMS
  ( mTO ) m
j
b( )
j
is the Stellar Evolutionary Flux:
# of leaving the MS per unit time
is the considered PMS evolutionary
phase
Lectures on Stellar Populations
Fuel Consumption Theorem
SSP
LSSP  LSSP
MS  LPMS 
mTO

L
 ( m) ( m)dm 
mi
n j  b( )t j
n L
j
j
PMS
b() is the stellar evolutionary flux at the TO (# per year)
tj is the lifetime of the PMS phase j
tj Lj = energy radiated in the j-th phase ~ nuclear energy released in the j-th phase
 Fj = [m(H) + 0.1 m(He)]j
n
x
-5
10 erg/particle
SSP
L
L
SSP
MS
L
SSP
PMS
mTO
NA
x
Mo/Lo
x (sec in 1 yr)-1
6 1023 particles
0.5 (gr sec)/erg
(3.15 107)-1
with b() in 1/yr
 L ( m ) ( m )dm  9.75  10 b( ) F j ( mTO ) F in solar masses
PMS
mi
L in solar luminosities


10

The contribution to the total luminosity of any PMS stage is proportional to the
Amount of equivalent fuel burned during that stage.
Approximations:
 ( m ), m ev , t j , F j
all evaluated @ the turn off mass instead of
@ the evolutionary mass
Lectures on Stellar Populations
PMS Luminosity
L  LMS  9.75  1010 b( )  Fj (mTO )
PMS
@ TO
(Maraston 98)
PMS luminosity decreases as age increases
because the evolutionary flux decreases:
less and less stars enter the PMS phase, in spite of the IMF
Lectures on Stellar Populations
L(MS) and L(PMS) – dependence on overshooting
Maraston 04
•b(τ) almost insensitive on oversh.
dominated by the derivative of the TO mass
•MS Luminosity is higher,
PMS Luminosity is lower for
tracks with overshooting
more H burned on the MS
•Transitions shifted at older ages
Lectures on Stellar Populations
Lbol : dependence on IMF
L
mTO
 L ( m) ( m)dm  9.75  10

10
 ( mTO ) m TO
mi
 F (m
j
PMS
TO
)
Flatter IMF yields more rapid evolution
Of both the MS and the PMS luminosity
For stars with m>0.5 Mo
1Mo SSPs in stars between 0.1 and 120 Mo
Lectures on Stellar Populations
Contributions of phases
•Only at young ages does the MS
provide most of the bolometric light
•Past 1 Gyr most of the light comes from
the MS (TO) plus RGB
Lectures on Stellar Populations
Advantages of FCT
•Fuel is a better variable in PMS phases
•Fuel formulation allows us to include uncertain evolutionary stages and parametrize the effect
•SSP models are easily checked
L j  9.75  1010 b( ) F j
Lj
Lbol
 9.75  1010 B( ) F j
B( )  b( ) / Lbol
Specific Evolutionary Flux
(stars per year per solar Luminosity)
Almost independent of age:
Older than 1 Gyr it’s about
2 10-11 stars/yr/Lo
Lectures on Stellar Populations
TP AGB Phase
The evolution of stars through the TP AGB phase is difficult to compute;
AGB Termination depends on Mass Loss
Envelope models by Marigo describe the evolution through Thermal Pulses
These models can be used with the tracks by Girardi, and isochrones can be computed
Ip
The models need specification of
several parameters, among which
•The core mass-luminosity relation
•Conditions for 3rd dredge up
•Envelope Burning
•the Mass Loss Rate
Lectures on Stellar Populations
Lj
Lbol
 9.75  1010 B( ) Fj
Maraston 1998
TP AGB Phase: empirical
Marigo e Girardi 2001
Lectures on Stellar Populations
Test of FCT on M3
(Renzini and Fusi Pecci, 1988, ARAA 26, 199)
nSSP
 B( )  LT  t j
j
Lj  9.75  1010 LT B( )Fj
LT  30000 Lo
Lectures on Stellar Populations
B( )  2.15  10 11
Test on MC Cs
Lj
Lbol
 9.75  1010 B( ) Fj
Data from Ferraro et al. 1995:
Intermediate age clusters in the LMC
Empirical luminosities
Fuel consumption
Increase through the
RGB phase transition
Lectures on Stellar Populations
What have we learnt
• SSPs fade as they age
Mass to Light ratio is low in young, high in old systems
• The bolometric Light of an SSP is always proportional to the mass
that went into stars in the Burst of SF
The mass in stars of a stellar population secularly decreases because of
the mass return
• FCT: the contribution to the bolometric luminosity of any PMS phase
is proportional to the amount of fuel burned in that phase
A reasonable and useful approximation
• At ages older than about 1 Gyr most of the SSP bolometric light
originates from the MS(TO) plus the RGB (by similar amounts)
HB, AGB, SGB make a smaller contribution
Lectures on Stellar Populations
What have we learnt
• At ages older than about 1 Gyr the specific evolutionary flux is about
2 10-11 stars/yr/Lo, almost insensitive to Age and IMF
Useful in a number of applications , e.g. estimate of number of stars in a PMS
phase from the sampled luminosity; crowding conditions of a frame from
surface brightness.
• When tracks with overshooting are used: b() is unchanged, the MS
luminosity is larger, the PMS lower; various transitions are shifted at
older ages
• Flatter IMFs lead to faster fading of SSP light
This applies to both the MS and the PMS contributions.
Lectures on Stellar Populations