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Astro 6590: Galaxies and the UniverseLecture #2 (Wed Sep 3, 2008)

• Extinction and reddening• Overview of stars• Star counts• Luminosity functions• Malmquist bias• Overview of the H-R diagram• Color magnitude diagrams (CMDs)• Overview of stellar evolution in the CMD• Spectroscopic parallax• Overview of stellar spectra• Overview of galaxy spectra• The 4000 Å break• Initial mass function• Star formation rate• Overview of population synthesis• Case studies: Palomar 11, Sex A, LGS3

Photometric observationsWhat we observe is:

• extincted/fainter• absorbed/reddened• redshifted• projected• convolved• evolved

mobs = mintrinsic + ∆mext + ∆mza) Extinction by the Earth’s atmosphere (airmass)b) Extinction within the Milky Way (Galactic extinction)c) Extinction within external galaxy (internal extinction)d) Redshift due to Hubble expansion (“K correction”)

ExtinctionAtmospheric extinction

Interstellar extinctionLet αλ be the scattering cross section at wavelength λ; the optical depth τλ at distance d is:

τλ = ∫ αλ n(s) dsObserved flux fobs,λ relative to the emitted f0,λ => fobs,λ = f0,λ e-τ

Since = 10-0.4 = e- => star dimmed by∆m = 1.086 τλ

f0,λfobs,λ

(m0-mobs) τλ

d0

The importance of dust• Star formation: stars form from dusty molecular clouds• Dust scatters and absorbs light

• Effective absorber of photons of λ ≤ a (a = size of grain)• Most grains have a > ~ 0.1 μ => UV more effected

“classical” dust grains: a ~ 0.1 μ and N > 104 atoms“small” dust grains: N < 100 atomsPAH’s (Polycyclic Aromatic Hydrocarbons) N ~ 50 atoms

Leger and Puget (1984): Large planar molecules• Galactic Center: AV ~ 30 mag => 1 photon in 1012 penetrates

A2.2μ~ 2.5 mag => 1 photon in 10 penetrates• Dust polarizes light

• Observed starlight is linearly polarized due to population of paramagnetic dust grains partially aligned with IS B-field.

Spectra fit by modified Planck curves Iν ∝ εν Bν(T) and εν ∝ νn

Wien’s law: λpeak = 250 μ (20 K/T)

5 μ1000K50 μ100K250 μ20K

λpeak ~ 1mmT = 5K

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Interstellar extinction and reddening

• In a galaxy only ~10-22 of the volume is occupied by stars.• The interstellar medium (ISM) provides 5-10% of the baryonic

mass of the MW in form of gas mixed with tiny solid particles: dust grains.

• Dust strongly affects the properties of astrophysical objects.• Dust particles interact with photons (absorbtion, scattering,

polarization). This is particularly effective in optical-UV.• The optical depth τ of the ISM is

• In magnitude units:Aλ ≡ -2.5 log10 = 1.086 τλ

x τλ = αλ ∫ n(x‘) dx‘ = αλN(x)where N(x) is the column density of scattering and absorbing particles along the l.o.s.X

0

IλIλo

The extinction in magnitudes is numerically ≈ the optical depth of l.o.s.For dust grains: αλ = ndQA(λ)σd where nd = dust

grain density, QA(λ) = absorption efficiency (non-dimensional) and σd is the geometric cross section of the grain.

Interstellar Reddening and Color Excess

Blue light is absorbed more than red lightUse observed vs expected color index to infer extinction

Color excess: E(λ1 – λ2) = difference between observed color index and intrinsic color index

e.g. E(B-V) = (B-V) – (B-V)0 = AB - AV

Interstellar reddening

Apparent magnitude: m1(λ) = M1(λ) + 5 log d1 + A1(λ)m2(λ) = M2(λ) + 5 log d2 + A2(λ)

where 1 = ‘reddened’ star; 2 = ‘comparison’ starif M1(λ) = M2(λ) => Δm(λ) = 5 log (d1/d2) + A(λ)

for λ1 and λ2: Enorm = (Δm(λ) - Δm(λ2)) / (Δm(λ1) - Δm(λ2))= (A(λ) - A(λ2)) / (A(λ1) - A(λ2))= E(λ - λ2) / E(λ1- λ2)

where Enorm = normalized extinction

Extinction curve:

E(λ-V) A(λ) - A(V) ⎧ A(λ) ⎫ A(V)= = RV ⎨ - 1 ⎬ => RV =

E(B-V) E(B-V) ⎩ A(V) ⎭ E(B-V)

Ratio of total to selective extinction

Galactic extinction law: determination of Rλ•Consider two *s of the same spectral type (same intrinsic SED), one nearby, unreddened by extinction and the other further away and reddened. Observe their mags at several λs to get color excesses: e.g., E(U-V), E(B-V), E(R-V), E(I-R) etc.

Color excesses will depend on amount of reddening of reddened *•Normalize to unity E(B-V)

and plot E(λ-V) as f(λ):

•It has been shown that along •l.o.s. not crossing dense clouds:

RV ≈ 3.2 ± 0.02

Johnson 1965

Level of reddening curve extrapolated to 0 absorption at λ = ∞

E(X

-V)

AV

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Extinction lawsExtinction law = A(λ)/A(V)

Parameterization: the average Rv-dependent Extinction Law

A(λ)/A(V) = a(x) + b(x)/Rv(x= λ-1)

Rv affects the shape of the extinction curves(particularly at the shorter wavelengths)

Cardelli, Clayton & Mathis (1989, ApJ 345, 245) show plots of Aλ/AV as a f(RV), where

(a) as λ → UV, the ratio Aλ/AV ↑(b) at fixed λ in the UV, Aλ/AV ↑ as RV ↓

The differences among different lines of site become more dramatic as λ → UV

Cardelli et al’’s extinction law

Cardelli et al. 1989; Mathis 1990 ARAA

A bump around2175 Å => graphite resonance?

Serious deviationfor x > 7 μm-1

Shapeindependent ofRv in the NIR

U.B.V bandsfor reference

Shown for 3 different l.o.s.

Major IR instruments/missions

IRAS (InfraRed Astronomical Satellite) : Jan 1983 launch• 90% of sky at 12, 25, 60 and 100 μ• ULIRGs: emit most of their light in FIR• IR “cirrus”: diffuse, high latitude, 100 μ• Often use 2 component model

1. T ~ 170K, n=1: hot dust, associated with SF2. T ~ 30K, n=2: cool dust, associated with cirrus

COBE (Cosmic Background Explorer): Nov 1989 launch• FIRAS: precision measurement of CMB spectrum• DMR: search for CMB anisotropies on 7º scale• DIRBE: cosmic IR background (absolute brightness) in 10

bands from 1.25 to 240 μNIR bands (1-5 μ): starlightMIR bands (12, 25, 60 μ): interplanetary dust, warm IS dust (T ~ 40-60K)FIR bands (100, 140, 240 μ): Galactic, cool IS dust

100 μ: T ~ 20-25K; 140,240μ: T ~ few tens of K.

Corrections to observed magnitudes

using the DIRBE instrument on COBE

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Star counts, LFs etc Galactic longitude and latitude

Binney & Tremaine

Star counts in the Milky Wayν(r,l,b,M,S): space density of stars of absolute magnitude M and spectral type S at distance r in the direction l,b. A(m,l,b,S): star counts of stars of spectral type S in direction l,bAlong any l.o.s. (l,b) then, assume that:

ν(d,M,S) dM dV = Φ(M,S) dM DS(r) dV

where dV is a volume element, dM is an increment of absolute magnitude, DS(r) is the relative density function (density of stars of spectral type S at distance r in units of the corresponding stellar density in the solar nbhd) and Φ(M,S) is the luminosity function (actual number of *s of M and S per cubic pc in the solar neighborhood).

Most methods for determining L.F. involve counting the number dN/dm of objects that have m in the range (m, m+dm) and that lie in some area of the sky. The star count function then is

A(m) ≡

What do we expect the star counts to show?

dNdm

Star countsA(m,S): star counts of stars of spectral type S in a direction l,bIf some * has M, it will appear to have m if it is a distance r:

M = 5 log r + a(r) + M – 5where a(r) is the absorption in magnitudes along the l.o.s.

In a field subtending ω, stars in the distance interval (r, r+dr) occupy a volume dV = ωr2dr. Hence from this volume, we obtain a contribution to the star counts at apparent magnitude m of

dA(m,S) = Φ(m+5-5log r – a(r),S) DS(r) ωr2drStars at another m’ and r’ will make a similar contribution.Thus, the total # of *s A(m,S) is obtained by summing over all distances or, equivalently, over stars of all M distribute along the l.o.s. in such a way that m = const.

A(m,S) = ω ∫ Φ[m+5-5log r-a(r),S] DS(r) r2drFor general star counts, lumping all spectral types, we get

A(m) = ω ∫ Φ[m+5-5log r-a(r)] D(r) r2dr

Mihalas & Binney 4-2

∞0

∞0

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Stellar luminosity functionThe general luminosity function then is

Φ(M) ≡ Σ Φ(M,S) and D(r) is the total # of *s of all types per unit V at distance r, inunits of the total # of all types per unit V in the solar nbhd.

=> This is true only if the LF is constant along the l.o.s. (same as in solar nbhd).

Mihalas & Binney 4-2

What do you know about the Hipparcossatellite?

Galaxy luminosity functions

Solid line shows the Schechter fit for L* ~ 8x109h-2 L⊙

Luminosity functions

• Elliptical Gals brightest• Sa’s brighter than most Sc’s

Malmquist bias

See BM 3.6.1 for derivation (and basis for homework problems)

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Malmquist bias: practical implications

Roberts & Haynes 1994, ARAA 32, 115

What do you notice?

How do you explain it?

Malmquist bias: practical implications

HIPASS Completeness Limit

HIPASS Limit

HIPASS bandwidth

RG, MH & ALFALFA collaboration

Selection function

Example: Suppose you want to investigate the galaxy density in some some sample which has a limiting magnitude mlim (or flim).Nearby, you will detect all of the galaxies brighter than Mlim (or Llim), but further away, you will ONLY detect the bright galaxies (M<Mlim (or L>Llim).

.

ϕ(x): “selection function”: an estimate of the probability that a galaxy brighter than Mlimat distance x>R is included in the sample:

ϕ(x) = ∫ Φ(M)dM

∫ Φ(M)dM

M(x)

Mlim

-∞

-∞

e.g., Huchra & Geller 1982, ApJ 257, 423

ϕ(x<R) =1

Hipparcos CMDHipparcos satellite

Along the MS:

L ∝ M3.5

What do you know about this satellite?

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Temperatures of stars Spectral class, color and Teff

M5M0K5K0G5G0F5

F0A5A0B5B0O5

Spectral Class

+10.0+9.0+7.3+5.9+5.1+4.4+3.4

+2.6+2.0+0.7-1.1-4.1-5.7

M.S. MV

+1.63+1.45+1.18+0.89+0.70+0.58+0.42

+0.27+0.130.00-0.16-0.31-0.35B – V

Reln between (B-V) and Teff from Fowler 1996, ApJ

Different types offset 0.3 dex

Color-magnitude diagrams (CMDs)The horizontal axis of the H-R diagram can be represented in different ways:

• Spectral class• Effective surface temperature• “Color index”: difference in brightness measured in

separate (wavelength) filters

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Basic relations Stellar spectral types

Stellar luminosity classes

Why?

The method of “spectroscopic parallax”

1. Observe the star’s apparent brightness.

2. Observe the star’s spectrum; determine its spectral class and luminosity class.

3. Place the star on the H-R diagram; estimate its luminosity.

4. Use luminosity and apparent brightness to get distance.

Also works for star clusters, galaxies

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Color-magnitude diagrams (CMDs)

•Also useful as a distance indicator • Extragalactic distance scale discussion (later)

Evolution of High Mass Stars• A high mass star also shines by burning hydrogen when it is on

the Main Sequence, but• The sequence of fusion reactions (still 4H => He) is

different (the “C-N-O cycle” not the proton-proton chain).• Although a high mass star has more hydrogen to begin with, it

burns its hydrogen must faster than a low mass star does.• High mass stars have shorter Main Sequence lifetimes than

low mass stars.

• The basic sequence of Post Main Sequence Evolution is the same for high and low mass stars, until the star reaches the Red Supergiant Phase.

• In a low mass star, the carbon-oxygen core cannot burn further.• In a high mass star, the core temperature and density are so

high that further burning sequences take place.

Evolutionary tracks in the H-R diagram

Girardi et al 2000, AApSuppl 141, 371

• These are tracks only for low mass stars (mass indicated at initial point of post-MS evolution)

• The timescale for the complete track is 25 Gyr.

• Only the high mass stars are really interesting!

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Evolution depends on metal abundance

Girardi et al 2000, AApSuppl 141, 371

• Age range goes from log (t/yr) = 7.8 to 10.2 at equally spaced intervals of ∆log (t/yr) of 0.3

• Left: metal poor population; Right: solar abundance

X+Y+Z=1

Galaxy colors and stellar evolution• Stars have masses in range ~0.07 to 50 M• Main Sequence: stable H-burning phase

• Main sequence lifetime

τMS ≈ 1010 yrs

~ 1010 yrs

or ~ 1010 yrs

L* ~ L

L* ~ 50 for M* > 10M

R* ~ R

M*M

M*M

M*M

((( )

)) α

2.2

0.7

α ~ 5 for M* < 1Mα ~ 3.9 for 1 < M* < 10M

M*L

M*M

L*L

(((

)))

-2.5

-5.7

Galaxy colors in various photometric systems

Fukugita, Shimasaku & Ichikawa 1995, PASP 107, 945

Colors along the Hubble sequence

Roberts & Haynes 1994, ARAA, 32, 115Circles: RC3-UGC sampleSquares: RC3-Local Supercluster sample

Fukugita, Shimasaku & Ichikawa 1995, PASP 107, 945

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Galaxy colors in various photometric systems

Fukugita, Shimasaku & Ichikawa 1995, PASP 107, 945

Galaxy spectra

Kennicutt 1992 ApJS, 79, 255

Spectral line measuresQuick review: RG will discuss in more detail in a week or two

Equivalent width: measure of the strength of the spectral line relative to the neighboring continuum.

• W (in Å): width of a box reaching up (or down) to the continuum that has the same area as the spectral line

W = ∫ dλ

• Broadening of the spectral line arises from:1. Natural broadening (QM)2. Doppler broadening (thermal/motions)3. Pressure/collisional broadening

Fc – FλFc

Other terms to review: curve of growth, Voigt profile, Lorentz profile, damping wings.

What is 2MASS?

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Galaxy spectra Common (rest-frame optical) spectral

Optical spectrum: Elliptical galaxy

N. Vogt

4000 Åbreak

4000Å Balmer Break DB

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Main Sequence Turnoff: Age Estimator

Open clusters: span range of ages

CMDs of OCs of different ages

Hyades cluster

Pinsonneault et al. 2004, ApJ 600, 936

Distance : 46.34 pc

(m-M) = 3.33

Age: 550 Myr

Hyades cluster

Pinsonneault et al. 2004, ApJ 600, 936

Distance : 46.34 pc

(m-M) = 3.33

Age: 550 Myr

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Hyades cluster

Pinsonneault et al. 2004, ApJ 600, 936

Main stages of stellar evolution in CMD

Palomar 11

Lewis et al. 2006, AJ 131, 2538

Distance: 14.3 kpc

VTO ~ 20.88 ± 0.06

(V-I)TO ~ 1.03 ± 0.01

Discovered in 1955 by A.G. Wilson on POSS plates

Palomar 11

Lewis et al. 2006, AJ 131, 2538

Distance: 14.3 kpcVTO ~ 20.88 ± 0.06(V-I)TO ~ 1.03 ± 0.01

Age = 10.4 ± 0.5 Gyr

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Galaxies: Not a single population

Star clusters: assume all stars formed at the same time

Galaxies: a complex mixture of stars formed at different times

• Star formation rate• Initial mass function

What determines the CMD/spectrum?

• The star formation rate SFR and how it may vary with time, SFR(t)

• Is SFR constant? Decreasing over time?• A “starburst”? Episodic bursts?

• The initial mass function IMF, which stipulates the number of stars per mass interval per unit volume that are created.

• ξ(M) = = Const M-(1+x)

• In the solar neighborhood, we have the “Salpeter” IMF, x = 1.35 (Salpeter 1955)

• Other models (Miller; Miller & Scalo) allow multiple slopes over different mass ranges

• Need to specify the upper and lower mass cutoffs

Is the IMF everywhere/time the same?

dNdM

Initial Mass Function (IMF)Higher mass *s are less abundance than lower mass *s;=> logarithmic decrease in the number of higher mass *s

# *s per unit M per unit V

ξ(M) = M = ∝ Mx

d ln(M) = dM M = M*/M⊙

x = = -2.35 => Salpeter (1955) IMF

Sometimes written as ξ(M) ∝M-(1+x)

• Salpeter IMF derived for solar nbhd, current epoch• Other parameterizations have been proposed

• Scalo (1986) allowed for changes in slope x with MM -2.45 for M > 10 MM -3.27 for 1 < M < 10 MM -1.83 for 0.2 <M < 1 M

• Major questions today: • Is the IMF the same everywhere in the MW?• Has the IMF evolved over time?

ξ(M) ∝

dNdM

dNd ln(M)

1M

dlogξd log(M)

(Initial) Mass Function

• ξ(M) = c M-(1+x) (Beware of different definitions!)

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Kroupa (Science 2002) IMFΦ(M) = dN/dM = 1/M ξ(M) ∝ Mx with

- 2.7 for 1.0 ≤ M < 120- 2.3 for 0.5 ≤ M < 1.0- 1.3 for 0.08 ≤ M < 0.5- 0.3 for 0.01 ≤ M < 0.08

x =

# of *s w/ masses in (M, M+dM) formed at a given time in a given volume

Star formation rate (SFR)Suppose start with initial mass of gas Mg,0

SFR => R(t,τ) = rate at which the mass of gas is convertedinto stars per unit time

Constraint: ∫ R(t,τ) dt = Mg,0

Star formation models:• Constant SFR until some time t = τ, then halt

R(t,τ) = 0 < t ≤ τ

R(t,τ) = 0 t ≥ τ

• Exponential

R(t,τ) = exp (-t/τ)

∞

0

Mg,0

τ

Mg,0

τ

If τ is short:“burst”

Stellar Mass from Colors

Bell et al. 2005, ApJ 625, 23

Sextans ADwarf Irregular

D=1.44 Mpc

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CMD of Sextans A

Actively forming stars for last 2.5 Gyr; increased rate < 100 Myr ago. Some old stars (but images not deep enough to track details)SF found in 3 zones (high NHI); youngest is single region < 20 Myr old

Also Dolphin et al. 2003, AJ 126, 187

CMD of Sextans A

Also Dolphin et al. 2003, AJ 126, 187

LGS 3Miller et al 2001, ApJ 562, 713

• Stellar population dominated by old, metal poor stars but….• Handful of young blue stars + HI gas• Transition object between dSph and dI?

D = 760 kpc

Small amount of HI (2 x 105 M⊙)

LGS 3Miller et al 2001, ApJ 562, 713

• Stellar population dominated by old, metal poor stars but….• Handful of young blue stars + HI gas• Transition object between dSph and dI?

Stellar population and star formation history vary with radial position in the galaxy

Most of the young stars are in central 63 pc where the SFR has been fairly constant. Elsewhere: declining SFR

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LGS 3 versus Sex A Galaxy spectra

• Redshift

• Velocity dispersion/rotational velocity

• Star formation rate

• AGN activity

• Abundances

Observing galaxy spectra

The observed spectrum of a galaxy, made up of a large # of *s, (assumed here, for simplicity, to be identical) can be described as

G(u) = ∫ dvlos F(vlos) · S(u – vlos)where u = c ln λ is the wavelength expressed in logarithmic units

S is the spectrum of the star in the same unitsF(vlos) describes the distribution of the stellar line-of-sight

velocities within the portion of the galaxy observed.

Note: this is a convolution integral. In practice, it is therefore possible to extract F(vlos) from an observed G(u) if a suitable template stellar spectrum S is available.

But need “suitable” spectrum => mix of types

Spectral evolution

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Understanding spectra as evolution

Bruzual & Charlot, 1993 ApJ 405, 5382003 MNRAS 344, 1000

Basic assumptions:• Galaxies can be treated as closed systems• Chemical enrichment is not important after stars form• The SFR is either a burst or a smooth function of time,

independent of stellar mass; it determines the spectral and luminosity evolution of the galaxy

• The IMF is a simple function of the stellar mass (independent of galaxy age)

• The effect of dust and gas on the observed spectra can be treated separately

We will look at B&C again later

Models vs. Data: Spirals

• Increasing SF time scales produce good fits for increasingly late-type Spirals

• Note good fit of 4000 Å break and main absorption features in all cases

BC93 Fig. 7Bruzual & Charlot 1993, ApJ 405, 538

Models vs. Data: Ellipticals

• Best-fitting age model and composite elliptical spectrum

• Fairly good fit over entire spectral range

• Note UV-rising branch, highlighting importance of accurate AGB modeling

• ELLIPTICALS: The oldest objects formed stars within 1-2 Gyr of the BB and have had little SF since. “RED AND DEAD”

• Instantaneous burst models

BC93 Fig. 5

SF Histories – The Extremes

BC93 Fig. 4a BC93 Fig. 4d

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Sloan Digital Sky Survey:

SDSS filters:Ultraviolet (u) 3543 ÅGreen (g) 4770 “Red (r) 6231 “Near IR (i) 7625 “IR (z) 9134 “

SDSS color-color diagram

Baldry et al.

SDSS color-magnitude diagram SDSS color-magnitude diagram

Baldry et al.

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Blue and red sequence LF’s

Baldry et al. (2004)

Brightest gal’s are redMost gal’s are blue