Stellar Populations
Karina Caputi
Physics of Galaxies 2019-2020 Q4 Rijksuniversiteit Groningen Stellar evolution as key for galaxy evolution
Galaxy evolution is the integrated consequence of stellar evolution
For a single star, the evolution depends on its initial mass
The evolution of a galaxy depends on the initial mass distribution of all its stars
initial mass function (IMF)
Picture credit: ESO Lecture Three: ~2% of galaxy mass in stellar light Stellar Populations
What defines luminous properties of galaxies face-on
edge-on
https://www.astro.rug.nl/~etolstoy/pog16/
The effect of star formation, spiral arms, gas, dust Sparke & Gallagher, chapter 1, 2 18th April 2016
Stellar properties Stellar Properties: Three main physical properties define a star:
2 4 • Effective Temperature Teff L 4 R T e The continuum of a star is a black-body curve, with T ~ Teff
Stellar Populations = Stars in Galaxies max =[2.9/T (K)] mm
2 • Surface Gravity log g pressure of stellar photosphere g = G M / R ionisation balance, pressure broadening, molecular abundance
• Metallicity Z or [Fe/H] or chemical composition, elements heavier than He
individual elements cause absorption lines where atoms intercept light from the centre of the star a star with [Fe/H] = -2 has 1% as much Fe as the Sun Spectral variation versus Teff
Temperature (Teff) Surface Gravity (log g) A-stars Cool, <3500K
0.15M⦿
~4 500K log g ~ 4
0.8M⦿
~6 000K log g ~ 2 1M⦿
~11 000K log g ~ 0 2M⦿
40M⦿ Hot, ~30 000K
blue red
Strength of spectral line depends on Teff of star & also abundance of that element Stars like the Sun are ~72% H; 26% He and 2% "metals"
Metallicity (Z or [Fe/H]) Metallicity (Z or [Fe/H]) K-giant stars The Sun
[Fe/H] = -2.35
[Fe/H] = -1.47
[Fe/H] = -0.92
SiI Zr ZrI ZrI Subaru/HDS, R ~ 90k NiI VI TiI FeI FeI chemical elements in the Sun FeI TiI CaI
FeI BaII FeI FeI
GIRAFFE, R ~ 20k Spectral variation versus surface gravity
Temperature (Teff) Surface Gravity (log g) A-stars Cool, <3500K
0.15M⦿
~4 500K log g ~ 4
0.8M⦿
~6 000K log g ~ 2 1M⦿
~11 000K log g ~ 0 2M⦿
40M⦿ Hot, ~30 000K blue red
Strength of spectral line depends on Teff of star & also abundance of that element Stars like the Sun are ~72% H; 26% He and 2% "metals"
Metallicity (Z or [Fe/H]) Metallicity (Z or [Fe/H]) K-giant stars The Sun
[Fe/H] = -2.35
[Fe/H] = -1.47
[Fe/H] = -0.92
SiI Zr ZrI ZrI Subaru/HDS, R ~ 90k NiI VI TiI FeI FeI chemical elements in the Sun FeI TiI CaI
FeI BaII FeI FeI
GIRAFFE, R ~ 20k Temperature (Teff) Surface Gravity (log g) A-stars Cool, <3500K
0.15M⦿
~4 500K log g ~ 4
0.8M⦿
~6 000K log g ~ 2 1M⦿
~11 000K log g ~ 0 2M⦿
40M⦿ Hot, ~30 000K
blue red
Strength of spectral line depends on Teff of star & also abundance of that element Stars like the Sun are ~72% H; 26% He and 2% "metals" Spectral variation versus metallicity
Metallicity (Z or [Fe/H]) Metallicity (Z or [Fe/H]) K-giant stars The Sun
[Fe/H] = -2.35
[Fe/H] = -1.47
[Fe/H] = -0.92
SiI Zr ZrI ZrI Subaru/HDS, R ~ 90k NiI VI TiI FeI FeI chemical elements in the Sun FeI TiI CaI
FeI BaII FeI FeI
GIRAFFE, R ~ 20k Stellar classification according to spectra
Standard spectral classification: OBAFGKM
Decreasing Teff sequence Quick Stellar Classification Stellar Types & Ages
Standard Spectral Class - based on presence of strong absorption , OBAFGKM which was later found to be also a sequence of decreasing Teff. • 1-9, are temperature sub-classes (hot-cool) Numbers 1-9 - temperature sub-classes The Sun is a G2V star 0.15M⦿ • I-V, luminosity class, decreasing log g (hot-cool) >10Gyr ~4 500K
Classification determined without metallicity... Quick Stellar Classification 0.8M⦿ Stellar Types & Ages Numbers I-V - luminosity sub-classes ~6 000K (decreasing log g) 1M⦿ ~8Gyr
~1.5Gyr Standard Spectral Class - based on presence of strong absorption , OBAFGKM ~11 000K 2M⦿ which was later found to be also a sequence of decreasing Teff. ~5Myr • 1-9, are temperature sub-classes (hot-cool) 40M⦿ The Sun is a G2V star 0.15M⦿ • I-V, luminosity class, decreasing log g blue red >10Gyr OBAFGKM... ~4 500K
Classification determined without metallicity... 0.8M⦿
Integrated Stellar Populations ~6 000K
1M⦿ ~8Gyr Spectra are time consuming to obtain ~1.5Gyr in large numbers ~11 000K 2M⦿
~5Myr 40M⦿
MAGNITUDES & COLOURS blue red
OBAFGKM...
Elliptical Galaxy O’Connell 1986 PASP, 98, 163
Integrated Stellar Populations
Spectra are time consuming to obtain in large numbers
MAGNITUDES & COLOURS
Elliptical Galaxy O’Connell 1986 PASP, 98, 163 Quick Stellar Classification Stellar Types & Ages
Standard Spectral Class - based on presence of strong absorption , OBAFGKM which was later found to be also a sequence of decreasing Teff. • 1-9, are temperature sub-classes (hot-cool) The Sun is a G2V star 0.15M⦿ • I-V, luminosity class, decreasing log g >10Gyr ~4 500K
Classification determined without metallicity... 0.8M⦿
~6 000K
1M⦿ ~8Gyr
~1.5Gyr ~11 000K 2M⦿
~5Myr 40M⦿
blue red
OBAFGKM...
Galaxy = integrated stellar populations Integrated Stellar Populations
Spectra are time consuming to obtain in large numbers
MAGNITUDES & COLOURS
Elliptical Galaxy O’Connell 1986 PASP, 98, 163 Stellar spectra in different broad-band filters Comparing to Atmospheric Transmission Compare to stellar spectra
U B V R
Notice that stars of different temperatures have very different spectra, so they have different fluxes through the filters and therefore they have different colors.
Photometric calibration is defined to correct for all effects and determine true magnitude of a star in a perfect telescope above the Earth's atmosphere. Stellar spectra
Spectrum of an Elliptical galaxy Spectra of late-type galaxies
U B V R I U B V R I Comparing to Atmospheric Transmission Compare to stellar spectra
U B V R
Notice that stars of different temperatures have very different spectra, so they have different fluxes through the filters and therefore they have different colors.
Photometric calibration is defined to correct for all effects and determine true magnitude of a star in a perfect telescope above the Earth's atmosphere. Spectrum of a typical elliptical galaxy Stellar spectra
Spectrum of an Elliptical galaxy Spectra of late-type galaxies
U B V R I U B V R I Comparing to Atmospheric Transmission Compare to stellar spectra
U B V R
Notice that stars of different temperatures have very different spectra, so they have different fluxes through the filters and therefore they have different colors.
Photometric calibration is defined to correct for all effects and determine true magnitude of a star in a perfect telescope above the Earth's atmosphere. Stellar spectra Spectrum of a typical star-forming galaxy
Spectrum of an Elliptical galaxy Spectra of late-type galaxies
U B V R I U B V R I AtmosphericComparing transmission to Atmospheric Transmission Compare to stellar spectra
U B V R
Notice that stars of different temperatures have very different spectra, so they have different fluxes through the filters and therefore they have different colors.
Photometric calibration is defined to correct for all effects and determine true magnitude of a star in a perfect telescope above the Earth's atmosphere. Stellar spectra
Spectrum of an Elliptical galaxy Spectra of late-type galaxies
U B V R I U B V R I The k-correction K-correction Converting apparent to absolute magnitudes L Correcting for red-shifting of light out of wavelength region True flux: F = so we need the distance D to the stars 4 D2 We receive flux f at our telescopes from an object at distance d. If we wanted instead to know what the flux F is of that object if it were at distance D, then D 2 f = F d The difference in magnitudes m (of f) at d and M (of F) at D is then f d m M = 2.5 log = 5 log F D We always pick D to be 10 parsecs (10 pc), so if d is measured in parsecs, then m M = 5 log(d[pc]) 5 If d is measured in 106 pc=1 Mpc, then m M = 5 log(d[Mpc]) + 25
m–M is called the distance modulus and is sometimes written µ=m–M This is most important for high-redshift galaxies. If it is not taken into account conclusions can easily be in error. ...and M is called the absolute magnitude
Nearly ~120 000 stars in Hipparcos catalogue Apparent vs. Absolute mags within ~100pc of the Sun Evolutionary Timescales Stars burn hydrogen into helium for most of their lifetimes, until they exhaust the H in bright their cores, how long does this take?
12 Let’s call E the amount of energy released by H burning during its main-sequence lifetime, τms
If the star’s luminosity on the main sequence is L, then, E = L τms 10 So if we can determine E, we can determine τms 4H He + 0.7% mass of 4H in energy ESA Hipparcos satellite, launched 1989 main sequence 2 8 The amount of energy released by converting a mass dM of H into He is dE=0.007c dM
magnitude red giant branch So if a fraction α of the total mass of the star M is burned into He before core H- exhaustion, then E=0.007c2 αM
absolute absolute 6 2 so the main-sequence lifetime is MS =0.007 Mc /L
4 Typically, α=0.1, so: 1 MS = 10M/M (L/L ) Gyr 2 4 -0.5 0 0.5 1 1.5 2 From the equations of stellar structure, for the main sequence: L M faint B-V 3 Thus we have the main-sequence lifetime as a function of mass: MS = 10A(M/M ) Gyr blue colour red Perryman et al. 1995, A&A, 304, 69 So a star ten times the mass of the sun lives for ~1/1000 of the time: ~10 Myr! Stellar Evolution models in HR diagram Evolutionary Timescales Stellar Evolution Models
The main-sequence lifetime is a crucial timescale: it is a clock. By measuring the magnitude and colour of the main sequence turnoff (MSTO or just TO) we can determine the age of a stellar population – and therefore something about A set of stellar models all with the its evolution same composition
The brighter and bluer the MSTO, the younger the population, because brighter, bluer MS stars are more massive
Isochrones - single age stellar populations Globular clustersExamples of globular clusters
A set of stellar models all with the Similar sequences same age and same composition 4.5 Myr
The resulting track in an HR diagram All MW GCs are old, and their CMDs are very or a CMD is called an isochrone similar. They vary primarily due to composition The exact location of the features in differences the HR diagram depends age • “metallicity” [Fe/H] •age ➔ • He content • metallicity, • variations of other elements • a quantity related to He or other 14 Gyr element abundances. main-sequence • Age is an important but secondary turnoffs consideration Evolutionary Timescales Stellar Evolution Models
The main-sequence lifetime is a crucial timescale: it is a clock. By measuring the magnitude and colour of the main sequence turnoff (MSTO or just TO) we can determine the age of a stellar population – and therefore something about A set of stellar models all with the its evolution same composition
The brighter and bluer the MSTO, the younger the population, because brighter, bluer MS stars are more massive
Isochrones in HR diagram
Isochrones - single age stellar populations Globular clustersExamples of globular clusters
A set of stellar models all with the Similar sequences same age and same composition 4.5 Myr
The resulting track in an HR diagram All MW GCs are old, and their CMDs are very or a CMD is called an isochrone similar. They vary primarily due to composition The exact location of the features in differences the HR diagram depends age • “metallicity” [Fe/H] •age ➔ • He content • metallicity, • variations of other elements • a quantity related to He or other 14 Gyr element abundances. main-sequence • Age is an important but secondary turnoffs consideration Open Clusters Open Clusters low mass, relatively small (~10 pc diameter) clusters of stars in the Galactic disk containing <103 stars. Useful for studying the evolution of the properties of the MW’s disk Because open clusters live in the disk of our Milky Way, they are subject to strong tides and shearing motions
Because they are so small and contain few stars, they also evaporate quickly Open Clusters Open Clusters low mass, relatively small (~10 pc diameter) clusters of Therefore they do not live very long unless they are very stars in the Galactic disk containing <103 stars. Useful for studying the evolution of the massive — so most of them are quite young The Pleiades cluster is a good exampleproperties of an of open the MW’scluster. disk Because open clusters live in the disk of our Milky Way, The “fuzziness” is starlight reflected from interstellar dust they are subject to strong tides and shearing motions
Because they are so small and contain few stars, they also evaporate quickly All stars in an open cluster are Which of these clusters is the youngest? Therefore they do not live very long unless they are very at the same distance, massive — so most of them are quite young The• Pleiades cluster is a good example of an open cluster. Which is the oldest? The “fuzziness” is starlight reflected from interstellar dust • formed at the same time have the same composition All stars in an open cluster are • Which of these clusters is the youngest? • at the same distance, Very useful for testing stellar evolution models! Which is the oldest? • formed at the same time • have the same composition Very useful for testing stellar evolution models!
The effect of age in CMDsThe effect of age in CMDs The effect of metallicity Isochrones - single age Isochrones - single age The effect of metallicity The effect of metallicity • Isochrones: stellar populations – theoretical distribution of group of• starsI sochroneswith the : stellar populations Stellar temperatures and luminosities 12 Gyr same age When populations get old, the also depend on composition. isochrones “pile up” at very similar Stellar temperatures and luminosities – example: fromluminosities 4 Myr to and 10.6 temperatures Gyr – theoretical distlog(age) ribution of group of stars with theThis is an opacity effect: more metals mean more 12 Gyr When populations get old, the absorption, especially in the blue (it’s reradiated also depend on composition. (the labels give the log(age)). same age into the IR), so stars become cooler (redder) and • It is easy to determine ages for isochrones “pile up” at very similar dimmer young populations – example: fromluminosities 4 Myr to and 10.6 temperatures Gyr log(age) This is an opacity effect: more metals mean more [Fe/H]=-2 • but not for old populations! absorption, especially in the blue (it’s reradiated (the labels give the log(age)). [Fe/H]=0 into the IR), so stars become cooler (redder) and • “Age dating” GCs is difficult! • It is easy to determine ages for dimmer young populations [Fe/H]=+0.5 • "Old" isochrones are much closer together than the "younger" isochrones Age-metallicity degeneracy [Fe/H]=-2 Putting it together • but not for old populations! [Fe/H]=0 -> Easy to measure the age of a young population but The absolute V magnitude of the MSTO varies as • log(age) “Age dating” GCs is difficult! difficult for an old pop [Fe/H]=+0.5 Age-metallicity degeneracy MV (MSTO) = 2.7 log(t/Gyr)Putting + 0.3[Fe/ H]it +together 1.4 • "Old" isochrones are much closer together than the Both age and metallicity affect isochrones, "younger" isochrones and so MS turnoff required to separate 3x lower age their effects on stellar populations. 2x higher [Fe/H] The absolute V magnitude of the MSTO varies as age-metallicity degeneracy Uncertainties: -> Easy to measure the age of a young population but Difficult to measure the location of the main sequence turnoffs log(age) MV (MSTO) = 2.7 log(t/Gyr) + 0.3[Fe/H] + 1.4 difficult for an old pop Both age and metallicity affect isochrones, Only MS turnoff Distance uncertainties cause large age uncertainties: changes! and so MS turnoff required to separate 3x lower age 10% distance uncertainty ➔ 0.2 mag uncertainty in distance modulus ➔ 0.2 mag their effects on stellar populations. 2x higher [Fe/H] uncertainty in MSTO magnitude ➔ 20% uncertainty in age Uncertainties: Difficult to measure the location of the main sequence turnoffs Only MS turnoff Distance uncertainties cause large age uncertainties: changes! 10% distance uncertainty ➔ 0.2 mag uncertainty in distance modulus ➔ 0.2 mag uncertainty in MSTO magnitude ➔ 20% uncertainty in age
The Luminosity Function An Example: Solar Neighbourhood
Hipparcos CMD: stars within 100 pc of the Sun: bright
We can construct a luminosity function: dN (MV )dM = The luminosity function Φ(Mv) describes how many stars of each luminosity are present in a Vmax given volume (e.g., pc3). The Luminosity Function where Vmax is the volume over whichAn stars Example: Solar Neighbourhood with Mv could be seen
Hipparcos CMD: stars within 100 pc of the Sun: bright faint We can construct a luminosity function:blue red dN (MV )dM = The luminosity function Φ(Mv) describes how many stars of each luminosity are present in a Vmax given volume (e.g., pc3).
where Vmax is the volume over which stars with Mv could be seen
faint blue red Statistical Properties The stellar luminosity function (LF)
The stellar luminosity function is a measure of the number density of stars per unit of volume and per unit of luminosity (or absolute magnitude)
dN = (M,V ) dMdV
If the distribution of stars of different luminosities is homogeneous in space:
dN =[ (M) dM][⌫(V ) dV ]
Generally, source surveys are apparent-magnitude limited, so the resulting LF is affected by Malmquist bias
This means that the mean absolute magnitude of the In practice this means that the effective volume in which we see observed sample is brighter than the mean absolute brighter objects is LARGER than the effective volume in which we see magnitude of the total stellar population fainter objects. LF for different spectral-type stars 1997ESASP.402..279H
stellar LF has Gaussian shape
Houk et al. (1997) An Example: Solar Neighbourhood An Example: Solar Neighbourhood
Thus we can also determine the mass-to-light ratio of the Solar Neighbourhood: proportion of massive stars to dim low mass stars all stars 3 • the V-band luminosity density is 0.053L pc Hipparcos limit 3 only MS • the mass density is (including white dwarfs) 0.039M pc • combining, the mass-to-light ratio in solar units is M/LV 0.67 M /L ! This is a lower limit to the total mass per unit luminosity (in a given band)
Note this is the present-day luminosity function (PDLF), which is the LF we see after the This is the result (in black). high-mass stars have evolved away • Most of the stars are faint. • If we weight by the luminosity of the stars: nearly all of the light is in bright stars • If we weight by the mass of the stars: most of the stellar mass is in low-mass stars
The initial mass function (IMF) The Initial Mass Function (IMF) The Initial Mass Function (IMF)
A critical input for stellar population models crucial to understand the formation and evolution of galaxies is the initial mass function, usually shortened to IMF. To determine ψ(MV), we need to determine dN This specifies the distribution of mass in stars immediately after a star formation event: the immediately after a star- number of stars dN with masses between M and M+dM is dN = N0 (M)dM formation event to get the initial luminosity We normalize ψ(M) such that N0 is the total function Φ0 M (M)dM = M number of solar masses formed in the event: Z dN = (M) dM
If the system has been forming stars at a constant rate (roughly true for the MW disk) since time t, then t/ for (M)