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Star Populations and Star Formation

• As comprehensive as Cold Dark Matter Theory is, it cannot tell us much about the leading tracer of dark matter, regular, baryonic matter.

• Galaxy dynamics can tell a lot about a galaxy’s evolution, but many other clues are available:

• patterns in stellar populations

• chemical abundance patterns

• Although stars and the ISM have to follow the laws of physics, it is much more difficult to carry out ab initio computations in these areas than it is for a dynamical model of a galaxy where usually only gravity needs to be taken into account

• Consequently, observations and empirical data play a large role in our understanding of the composite nature of the regular matter in galaxies.

Think of a galaxy as an ecosystem!

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Stellar Populations in Galaxies

• Goals– reconstruct the fossil record of star formation, heavy element

formation, and galaxy formation– delineate systematic trends in stellar content and evolutionary

properties of galaxies vs type, mass, bulge/disk/halo/nucleus, radius, environment

– reconcile results with lookback studies of high-redshift galaxies– understand underlying physical processes that drive star

formation, galaxy evolution– reconcile results with predictions of theoretical scenarios,

models, and numerical simulations

• Diagnostics: what are “stellar populations”?– age– chemical abundances (absolute and differential)– stellar orbits

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Topics• The Solar neighborhood

– basics of star formation– stellar statistics, luminosity function, IMF – disk population: ages, abundances, orbits

• The Galactic halo and bulge– field stars– formation scenarios: instantaneous collapse vs hierarchical formation– globular clusters and the fossil record

• Resolved stellar populations in nearby galaxies– Magellanic Clouds– Local group galaxies

• Integrated stellar populations in galaxies– diagnostics of star formation rates and histories– spectral and evolutionary synthesis techniques– star formation properties of the Hubble sequence– starbursts: physical nature and triggering– environmental influences on galaxy evolution

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Star Formation Basics I

It is simple to show from stellar theory that stars have formed recently in many galaxies:

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MainSequence 3

10 yrs(M[M ])

τ ≈

(above correct for M<~10M )

Look at typical MS lifetimes:

O star M= 30 M τ = 2-3x106 yrs

K star M= 0.7 M τ = 3x1010yrs

So many generations of massive stars may have come and gone since a galaxy formed while all the low mass stars ever formed are still around.

-- Note that in a typical “old” galaxy like a giant elliptical, the main sequence turn-off is at about 0.9 M or G5.

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Star Formation Basics II• Look at how stars form in sufficient depth

to see what might influence the action on galaxy scales

Deeply embedded protostar

Agglomeration & planetesimals Mature planetary system

Circumstellar disk

B,V,I

Globule before a protostar forms

Jet from a circumstellar disk returning energy to a cloud

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Jean’s Mass and Cloud Collapse

2

4

2

43

3 32 2

Jeans 1 4 12 3 2

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Jeans 12

GMP M,R = mass,radius of cloud4 R

R computed from ave distance between particlesGMnkT= n=particle density, m=mass of a particle3M4

4 nm

9 k TM2 nGm

TM 18 M fn

=π

⎡ ⎤π ⎢ ⎥π⎣ ⎦

⎛ ⎞= ⎜ ⎟

π ⎝ ⎠

= 3or a molecular hydrogen cloud, n in particles/cm

Cloud must be very cold and very dense for low mass stars to form, easier to form high mass stars. Magnetic fields and turbulence can hinder cloud collapse.

Gravitational force must overcome gas pressure for a cloud to collapse:

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Modes of Star Formation I: Sequential SF / Self-Propagating SF

• Many regions in the Milky Way show evidence for previous star formation to have triggered subsequent star formation (Orion is a good example)

• Clouds can be compressed by radiation pressure or SN shocks or shocks/pressure gradients from expanding HII regions

• Spiral patterns caused by rotational shear

• Does not predict a clear relationship between properties across a spiral arm

What causes the first star formation?

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Modes of Star Formation II: Density Wave Star Formation

But it has been hard to find direct evidence of density-wave triggered star formation -- M51 best studied case.

Look at the sequence implied:

1. Leading edge of density wave will have compressed molecular gas clouds

2. Immediately behind will be a region with very young stars

3. Further behind older stars will be found

M99

Gonzalez & Graham 1996 ApJ

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M51 I: Visible-Hα Imaging

Scoville et al. 2001

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M51 II: CO Imaging

CO contours superposed on visible light image of M51 (Aalto et al. 1999). Spatially resolved velocities revealed streaming motions expected from spiral density waves although velocities are very high.

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Grand Design versus Flocculent Spirals

• Flocculent <=> propagating star formation• Grand design <=> spiral density wave-induced SF

NGC4414 - a flocculent spiral.

M74 - a grand design spiral

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Modes of Star Formation III: Bimodal Star Formation

• In the Milky Way, regions of high and low mass star formation are frequently distinct– compare the Taurus cloud (no OB stars) with Orion (lots of OB stars)

• A number of observations suggest that a larger proportion of high mass stars formed early in the Universe– Could account for the “G Dwarf” problem in the Milky Way = why are there so

few low metallicity G dwarfs?– Could explain why intracluster gas so metal-rich

• Some extreme starburst galaxies show suppressed low mass star formation

• Pop III stars almost surely were preferentially very high mass stars (difficult for pure hydrogen to cool)

• Recent theoretical work has shown that variations in magnetic fields and turbulence inside molecular clouds could lead to bimodal star formation

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Factors Controlling Star Formation

• Need raw material– star formation rate will depend on the amount of gas

• Need gas agglomerated into clouds– clumps of gas need to cool to collapse => easier with

more heavy elements (higher metallicity)• Triggers to help clouds collapse

– may be needed to overcome magnetic field pressure– possibilities include

• nearby hot stars or supernovae (sequential star formation)• spiral density waves• gravitational instabilities in spiral disks but need to avoid

situtations where differential rotation (shear) would tear clouds apart

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One More Set of Ingredients: Stellar Evolution

• Stellar evolutionary time scales provide ages for clusters in the Milky Way and also useful for galaxies– Later we’ll see that caution is

needed when looking at the integrated light of galaxies

• Consider what colors a single age stellar population would have– Need to know the relative

numbers of stars with mass = Initial Mass Function

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Schmidt Law: Connecting Gas to a Global SFR

• How to bridge the gap from what is seen in individual clouds in the MW, for example, to galaxy-wide properties such as the star formation rate (SFR) and stellar birth history?– How does the SFR vary from galaxy to galaxy?– What factors control the SFR: This is the key we are really

looking for since understanding the physics of the SFR would unravel a lot of galaxy evolution.

• First step in by Schmidt ApJ 1959:ngas for Schmidt's original workSFR n=2 ∝ ρ

Kennicutt 1989 recast this relation in terms of surface density since that is the observable in other galaxies so

where N is used to distinguish the surface density index from the volume density index. How can this relation be measured? Is n=2 universal? How does the constant of proportionality vary?

NgasSFR a= Σ

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Deriving the Schmidt Law• Need to measure the current star formation rate and the current

gas densities; data on the history of these quantities also highly desirable

• What are the observables: (many of these most useful for history)– Number of stars currently on the main sequence – Number of giant branch stars (not very useful because the giant phase

is relatively short)– Number of white dwarfs – Amounts of atomic and molecular gas– Metallicity– Very young star clusters – Other information that is available: 1. stellar evolution rates; 2.

fractions of gas returned to the ISM as a result of stellar evolution; 3. chemical yields from SN and other stellar evolution

• Many processes lock up material that won’t or can’t be recycled into stars (eg., formation of stars with M<~ 0.9 M , white dwarfs) so gas density must declining with time

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SFR and Gas Density Data I

• Schmidt’s study looked at primarily the solar neighborhood. Due to technology limitations, he could not rely on emission line surveys and had to deduce the SFR by analyzing stellar luminosity functions – difficult to execute but yielded a formalism that is useful for looking at the SFR history

• Kennicutt 1989 executed an improved study of the relationship between SFR and gas density:– Hα used as a surrogate for the SFR (but note extinction may be a

problem)– HI, CO used to measure the gas density (conversion of CO mass to

H2 mass problematic and by necessity assumed to be a constant)– Radial profiles of Hα, HI, and CO were available for 15 galaxies

ranging from S0 to Sc– HI and CO data also included velocities for derivation of rotation

curves.

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SFR and Gas Density Data II

Lines are for N=1 and N=2

Kennicutt found that the Hα surface brightness correlates most strongly with HI surface mass density, not with the molecular surface mass density. Slope is N~1.4

But local star formation studies obviously show that stars form from molecular clouds, not from HI clouds.

CO data sets show excellent correlation between CO mass and SFR.

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Kennicutt investigated a number of possibilities to resolve the discrepancy between the CO results and his Hα results. For example, as shown above he found good correlation between stellar scale lengths and Hαbut much poorer between Hα and CO.

SFR and Gas Density Data III

From Young and Scoville 1991

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What Gives?

• Looking at integrated indicators of properties may just show that bigger galaxies have more of everything

• Plot at left suggests that if the gas density falls below a threshold, star formation is suppressed.

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Martin and Kennicutt 2001: Improvements

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Density Thresholds

Martin and Kennicutt 2001 confirmed the earlier results with much higher quality data and a larger sample.

Hα

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More on Thresholds

NGC 5236

Hα

gas

Gas densityCritical density

Toomre Q parameter for stellar disk:

2gas

crit Q 2crit

=velocity dispersion =epicyclic freqQ(R)

gas surface densityG

(R) V V dV= (R)= (R)= 2G (R) R R dR

σ κσκ=

µ =π µ

µ ⎛ ⎞σκµ α α κ +⎜π µ ⎝ ⎠

If gas density is higher than the critical density, then gravitational instabilities will cause clouds to collapse and stars to form.The velocity dispersion in a disk does not vary much with R while κ varies as 1/R (see Sept 13 lec. notes).=> Surface density drops faster than 1/R so it drops below the critical density at some R so this may explain the “edges” of stellar disks.

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Physical Insight into Q

• By considering a local region in a disk, one can show that Toomre’s Q criterion is the disk analogue to Jean’s criterion for cloud collapse– Rotation, velocity dispersion provide pressure-like terms that can

counteract the gravitational force– See B&T p. 310-315 and p. 362-363

• Other interesting results include– Stability criteria for purely gaseous disks are close to those for

stellar disks– Stability is only a weak function of disk thickness

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Subcritical Disks

• Martin and Kennicutt also noted that some galaxies are forming stars in regions where the disk is definitely subcritical: NGC 2403 is a clear example.

• Rather than the Coriolis force being the key to whether a cloud can collapse, if the shear is small enough, clouds may have time to collapse so a shear criterion is needed in addition to a rotation criterion.

shearcrit

2.5A d A=-0.5RG dR

σ Ωµ ≈

π

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More on the SFR: What’s its History?• Collection of stars, stellar remnants, and enriched gas represent the

integrated history of star formation in a galaxy– Low mass galaxies may lose enriched gas due to SN

V

V

V

V V

t(M ) Maximum possible age for a star still on the MS(M ) Observed luminosity function for stars on the MS(M ) = Luminosity function for all stars ever formed

N(M , t) number of stars in M 0.5 to

=ϕ =ψ

= −

V

V

V

VV

1

V V 1-t (M )

M 0.5 on MS formed up to time tAssume (M ) is independent of time, t=0 time of galaxy formation, t=1 is nowdN(M , t) (M ) f(t) f(t) = star formation rate

dt

(M ) (M ) f (t)dt

+ψ

= ψ

ϕ = ψ ∫

ϕ(Mv) is observable, ψ(MV) can be estimated from open clusters (its equivalent to the initial mass function) so f(t) can be estimated.

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The Solar Neighborhood

• begin with fundamental stellar statistics

• Hipparcos parallax survey provides database for >20000 stars out to ~100 pc

• key statistical properties are luminosity, mass functions

• key evolutionary diagnostics are ages, kinematics, abundances

cf. Kovalevsky 1998, ARAA, 36, 99

Perryman et al. 1997, The Hipparcos Catalog, and A&A, 323, L49

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Luminosity Function

Reid, Gizis, Hawley 2002, AJ, 124, 2721

(for faintest stars IR magnitudes needed)

LF = number of stars per unit volume per magnitude bin

29Maeder, Meynet 1988, A&AS, 76, 411

Mass-Luminosity Relations

converts luminosity function to present day mass function (PDMF)

30Reid et al. 2002

Solar Neighborhood Mass Function