Lecture 03:

• Stars • Resolved stellar populations

Refs: SG 1.1, 2.1-2.3, MBW 10.1-10.3, R. Smith’s Course on Stellar Populations: http://astro.dur.ac.uk/~rjsmith/stellarpops.html

HR diagram

• Stars occupy a position based on their mass and move along the plot based on their age

• Stars within 100pc from the Sun (Hipparcos satellite). Densest regions are populated for longer times

SG fig 2.2

A few numbers • Remember what Teff is. Strongly

related to peak wavelngth in continuum spectrum.

• MS parameters (M, R, L) for fixed Z are bound by «simple» scaling relations.

• MS lifetime shorter for higher mass.

• Stars below 1.5MA are brighter in pMS phase

• MS luminosity dominated by high mass, blue stars (if present)

• Numbers change with Z (low Z means lower opacity…)

• Mass distribution is important for integrated galaxy spectra

SG, tab. 1.1

Scaling relations

• Mass-Luminosity and Size-Luminosity relations on MS:

𝑅 ∝ 𝑅⊙𝑀𝑀⊙

𝛼, 𝐿 ∝ 𝐿⊙

𝑀𝑀⊙

𝛽;𝛼 = 0.7,𝛽 = 5 for M < 2M⊙

(only at first order, second order corrections may be important – see MBW 10.1.4).

• MS lifetime/mass dependence:

Log 𝜏𝑀𝑀10𝐺𝐺𝐺� = 1.015 − 3.49 Log

𝑀𝑀⊙

+ 0.83 𝐿𝐿𝐿𝑀𝑀⊙

2

• 𝐿𝑀𝑀 ∝ 𝑇𝑒𝑒𝑒𝑏 ,𝑏 = 4.1 ÷ 8.6 • Notice the strong dependence on mass mass is the key parameter for

stellar evolution (along with Z)

Scaling relations

Evolutionary tracks • Track evolution of a

star in T, L plane as a function of initial mass.

• Computed through stellar evolution models

Evolutionary tracks • Track evolution of a

star in T, L plane as a function of initial mass.

• Computed through stellar evolution models

Metallicity

• 𝑍⊙ = 0.02, Mass fraction of heavy elements, can be as low as 10-6

• 𝑍𝐴 = 𝑍(𝐴/𝐻) computed as

Log 𝑛𝐴𝑛𝐵

/ 𝑛𝐴𝑛𝐵 ⊙

• Lower Z implies lower opacitydifferent tracks in L-T diagram

Stellar spectra • Rouhgly similar to a

blackbody + peculiar features (lines, breaks) depending on chemistry, evolutionary status

• Continuum determined by Teff according to Wien’s law: peak wavelength moves to higher lambda for lower temps.

• Temperature determines also the ionization level at surface, hence the presence and strength of line features due to absorption by neutral atoms

Stellar spectra • Rouhgly similar to a

blackbody + peculiar features (lines, breaks) depending on chemistry, evolutionary status

• Continuum determined by Teff according to Wien’s law: peak wavelength moves to higher lambda for lower temps.

• Temperature determines also the ionization level at surface, hence the presence and strength of line features due to absorption by neutral atoms

Stellar spectra • Rouhgly similar to a

blackbody + peculiar features (lines, breaks) depending on chemistry, evolutionary status

• Continuum determined by Teff according to Wien’s law: peak wavelength moves to higher lambda for lower temps.

• Temperature determines also the ionization level at surface, hence the presence and strength of line features due to absorption by neutral atoms

Reminder: • Hot opaque body emits continuous spectrum • Hot low density gas emits a sequence of emission lines • Cold low density gas, back-illuminated by an opaque bodycontinuous

spectrum with absorption (darker) lines

Stellar spectra • Rouhgly similar to a

blackbody + peculiar features (lines, breaks) depending on chemistry, evolutionary status

• Continuum determined by Teff according to Wien’s law: peak wavelength moves to higher lambda for lower temps.

• Temperature determines also the ionization level at surface, hence the presence and strength of line features due to absorption by neutral atoms

Stars in the solar neighborhood The Hipparcos satellite has measured the distance modulus through trig. Parallax for 15000 stars within 100pc from the Sun. From m-M relation + B-V colorslocal HR diagram Notice MS + Red Clump He burning pMS stars + 4 WDs + Hertzsprung gap Observational issues: • Distance errorsvertical

scattering • Dust extinction • Dust emission

Soon to be updated by GAIA

Luminosity functions present day Luminosity function:

Φ 𝑀 =𝑑𝑑

𝑑𝑀𝑑𝑑

M: abs mag in selected band

SG fig. 2.3

As with galaxy lum. Func., faint end and bright end are difficult to measure: dim objects may elude the count and bright objects may be rare. When weighting counts with luminosity, rare luminous stars dominate: may affect luminosity of a galaxy, depending on SFH. Faint K and M stars contribute largely to mass. LF changes depending on the observed band

Sun

Luminosity functions

SG fig. 2.4

Computed back from Present day through stellar evolution models. Faint K objects have longest times on MS: Initial LF mathces present LF. Brighter, most massive stars evolve faster and move out of MS before we observe them. Exercise: how to estimate ILF from PDLF at constant SFR?

Initial Luminosity function:

Ψ 𝑀 =𝑑𝑑

𝑑𝑀𝑑𝑑

M: abs mag in selected band

Luminosity functions

SG fig. 2.4

Assume constant SFR �̇�𝑀𝑆𝑆 for a time 𝜏𝑔𝑔𝑔. At a given magnitude 𝑀𝑉 , a star stays on MS for a time 𝜏𝑀𝑀. Then:

𝜏𝑔𝑔𝑔 ≤ 𝜏𝑀𝑀 → 𝑑𝑖𝑛 = �̇�𝑀𝑆𝑆𝜏𝑔𝑔𝑔 , 𝑑𝑜𝑜𝑜 = 0 → 𝜙(𝑀𝑉)𝜓(𝑀𝑉)

= 𝑁𝑖𝑖−𝑁𝑜𝑜𝑜𝑁𝑖𝑖

=1

𝜏𝑔𝑔𝑔 > 𝜏𝑀𝑀 → 𝑑𝑖𝑛 = �̇�𝑀𝑆𝑆𝜏𝑔𝑔𝑔 , 𝑑𝑜𝑜𝑜 = �̇�𝑀𝑆𝑆 𝜏𝑔𝑔𝑔 − 𝜏𝑀𝑀 →𝜙(𝑀𝑉)𝜓(𝑀𝑉)

=𝑑𝑖𝑛 − 𝑑𝑜𝑜𝑜

𝑑𝑖𝑛=𝜏𝑀𝑀𝜏𝑔𝑔𝑔

Initial mass function

We can convert ILF to IMF from an empirical or modeled M-L relation. Thus we get the number of stars born with mass in a given mass interval. Ex. 1: Salpeter IMF:

𝜉 𝑀 𝑑𝑀 = 𝜉0𝑀𝑀0

−2.35

𝑑𝑀/𝑀⊙

(surprisingly robust for many stellar populations at masses above 0.5𝑀⊙ ) Ex. 2: Scalo IMF For M ≥ 0.2 𝑀⊙:

ξ (M) ≈ M-2.45 for M > 𝑀⊙. ξ (M) ≈ M-3.27 for 1 𝑀⊙ > M > 10 𝑀⊙.

ξ (M) ≈ M-1.83 for M < 0.2 𝑀⊙ Note: IMFs are commonly normalized at 1 𝑀⊙ The IMF is a key ingredient to simulate the birth and evolution of a stellar population (stellar population synthesis), a necessary step to predict a galaxy spectrum and its evolution.

Initial mass function

Not trivial to measure: • Need single populations • Massive O and B stars found

only in young environments, with plenty of dust

• Globular clusters made only of old stars

Not trivial to model: • Is it universal? • Does it evolve with time? • Does it depend on

environment? • Key open problem in

modern astrophysics.

Age dating For Simple Stellar Populations (SSPs), modeling of stellar evolution together with IMF and metallicity information allow to simulate isochrones in the HR diagram, providing estimates of ages from MS turnoff.

Age dating For Simple Stellar Populations (SSPs), modeling of stellar evolution together with IMF and metallicity information allow to simulate isochrones in the HR diagram, providing estimates of ages from MS turnoff.

NOTES: It works only if no new stars are born after initial burst. Thus the need for SSPgood for globular clusters and ellipticals. Age/metallicity are degenerate (see MBW 10.1.4), since stars with higher metallicity evolve faster. Stars with same 𝜏Z3/2 have virtually identical spectra apart from fine features which must be investigated carefully (spectral indices)

Age dating For Simple Stellar Populations (SSPs), modeling of stellar evolution together with IMF and metallicity information allow to simulate isochrones in the HR diagram, providing estimates of ages from MS turnoff.

Age dating For Simple Stellar Populations (SSPs), modeling of stellar evolution together with IMF and metallicity information allow to simulate isochrones in the HR diagram, providing estimates of ages from MS turnoff.

Age dating For Simple Stellar Populations (SSPs), modeling of stellar evolution together with IMF and metallicity information allow to simulate isochrones in the HR diagram, providing estimates of ages from MS turnoff.

Chavez & Bertone, Astrophys Sp Sci, 335, p. 193 (2011)

Galaxies are not SSPs… • Different regions show different ages and metallicity • Need to resolve individual stars in the galaxies to prove

this (only available for MW and local group galaxiesmostly S and Irr, only one E2 and some dEs)

LMC, Marigo et al., A&A 403, 225 (2003)

Galaxies are not SSPs…

• Most galaxies/stellar pops unresolved:

From R. Smith course: http://astro.dur.ac.uk/~rjsmith/stellarpops.html

Only broadband colors, luminosity distribution and average spectroscopic features available

Galaxies are not SSPs…

• Most galaxies/stellar pops unresolved:

From R. Smith course: http://astro.dur.ac.uk/~rjsmith/stellarpops.html

We are left with a bunch of integrated data, often degenerate with respect to key parameters of population(s)

Galaxies are not SSPs… • Solution (sort of): relate the integrated galaxy spectrum to

the spectral features of its populationstellar population synthesis, spectral synthesis.

• Problem: lines in real spectra depend on environment (e.g. pressure broadening) and spectral features are often «smeared». Unable to define clearly the continuum.

From R. Smith course: http://astro.dur.ac.uk/~rjsmith/stellarpops.html