astro 6590: galaxies and the universehosting.astro.cornell.edu/academics/courses/astro6590/... ·...

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Astro 6590: Galaxies and the UniverseSee http://www.astro.cornell.edu/academics/courses/astro6590

• Professors Martha Haynes & Riccardo Giovanelli• MW 1:25-2:40 SSB 301• 4 credits• Some ability to solve straightforward numerical problems• Background in astronomy helpful, but not required• Books:

• “Galactic Astronomy”, Binney & Merrifield• “Galactic Dynamics”, Binney & Tremaine• Papers from the literature available electronically through

CU library• Regular assignments will include problems, in class presentations

and a final (major) project• All subject to change/negotiation


Find lecture notes by clicking on date

Readings/RefsRead the sections in the textbooks;You should read all the papers… at least, someday

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Part B: For Your Eyes Only


Part B: For Your Eyes Only

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Constituents of the Milky Way

The Milky Way is known in a fair amount of detail, and both the gas and stars split cleanly into different populations or phases.

Stars:

Disk: 5 x 1010 M

Bulge: ~ 1010 M

Halo: ~109 M

Globulars: ~108 M

Gas:

H2 clouds: ~109 M

HI gas: 4 x 109 M

HII regions: ~108 M

Dark matter:

Halo: 2 x 1012 M

Definition: what is a galaxy?• A galaxy is a self-gravitating collection of about 106 to 1011

stars, plus an amount up to 1/2 of as much by mass of gas, and about 10X as much by mass of dark matter. The stars and gas are about 70% hydrogen by mass and 25% helium, the rest being heavier elements (called "metals").

• Typical scales are: masses between 106 to 1012 M (1 solar mass is 2 x 1030 kg), and sizes ~ 1-100 kpc (1 pc = 3.1 x 1016

m). Galaxies that rotate have Prot ~ 10-100 Myr at about 100 km/s. The average separation of galaxies is about 1 Mpc.

• Between galaxies there is very diffuse hot gas, called the intergalactic medium (IGM); in clusters this is called theintracluster medium (ICM). It was much denser in the past before galaxies formed, accreted the gas and converted it into stars.

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73 % - dark energy or cosmological constant23 % - dark matter, probably CDM

Ωbaryons = 0.045+/-0.004 ~ (1/6) Ωmatter

Coronal + diffuse IG gas ~0.037Cluster IGM ~ 0.002

Stars ~ 0.003

Cold Gas ~ 0.0008 (~2/3 atomic)

“HI contributes only a piffling fraction of cosmic matter”

R. Giovanelli, 2008

Fukugita & Peebles 2004, ApJ 616, 643

Cosmic Inventory

Key points about galaxiesJ.E. Gunn, 1981, “Astrophysical Cosmology” Vatican Symposium

1. Galaxies are easily discernible as discrete entities whereas groups and clusters are not.

2. The specific angular momenta of galaxies correlate closely with optical morphology.

• Scaling relations (Fundamental plane/Tully-Fisher relation)3. The morphological types of galaxies are related to the density

of galaxies in their immediate neighborhood.• Morphology-density relation

4. The luminosity function (LF) of galaxies is distinctly non-Gaussian with a long tail extending to low luminosities.

5. There are large peaks in the density distribution of matter and these in turn surround the visible portions of galaxies.

• Dark matter!

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Properties of galaxies and clusters of galaxies which must be explained.

1. Galaxies are easily discernible as discrete entities, whereas groups and clusters are not.• Characteristic sizes?• Topologies?• Origin?• On what scale does the cosmological principle hold?

If we select a star at random in the universe, it would nearly always be possible to identify its parent galaxy with significant confidence. The same is not true of galaxies and “parent”groups of galaxies.

Virial Theorem: -2<K.E.> = <P.E.>

Free-fall time: tff = 3π 132 Gρ

½

time

• Do hierarchical models predict this behavior?

• Can they give us any insight into what is going on?

• How did the structures we see today form and evolve?

Hierarchical models

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Wechsler et al.

cluster halo

‘Milky Way’ halo

Cosmic hierarchies

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Coma Cluster = A1656

cz ~ 7000 km/s => D ~ 100 Mpc

Often used as “prototypical rich cluster”

Identifying clusters of galaxies

RG et al. 1997 (SCI)1 RA = Abell radius ~ 1.5 h-1 Mpc

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The redshift dimensionNot only do redshifts help the identification of group or cluster

members, they also prove useful to indicate masses, identify substructure and detail evolutionary processes at work

e.g. use Virial Theorem to estimate mass of cluster of galaxiesObserve many radial velocities: vr P(x,μ,σ) = exp -1

σ√2π1 x – μ2 σ[ ]( ) 2


2. The specific angular momenta of galaxies correlate closely with optical morphology.

• Bare spheroid: ~ 240 kms-1 kpc <= elliptical• Spheroid in disk: ~ 600 “ <= bulge• Disk galaxy: ~4000

a. Elliptical galaxies do not rotate fast enough to explain their flattening.

b. Scaling relations: Radii and internal velocities correlate with L

L ∝Vrot n~4L ∝ Rγ, γ ~ 2 (~const SB)

L ∝ σ4

log Re = 0.36(<I>e/μB) + 1.4 log σ0

Tully-Fisher relationFaber-Jackson relation“Fundamental plane” (later)

SpiralsEllipticals

n

Why?

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Spiral Galaxies: Tully-Fisher Relation

Giovanelli et al. 1997W ~ 2 Vrot

Why?

Template Rotation Curves

Catinella et al. 2006 ApJ

Not just the amplitude, but the shape is correlated

with luminosity

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Morphological Classification

Morphological classification schemes

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Galaxy Zoo

Ellipticals: E0 to E7

Type E0 Type E3 Type E6

Hubble 1936, “The Realm of the Nebulae”

En, n=0 to 7, where n = 10 (1 – b/a)

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Spiral sequence

Type Sa Type Sb Type Sc

To first order, the tightness of a spiral galaxy’s arms is correlated with the size of its nuclear bulge.

• In addition: Sa’s are usually brighter, rotate faster and have less current SFR than Sc’s

• Sa’s show a diversity of B/D ratios; Sc’s only small ones.

The barred spiral sequence

Type SBa Type SBb Type SBc

• Origin of bars: do all spirals have bars? Why/why not?• Relationship to SMBH

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The nearby spiral galaxy M83 in blue light (L) and at 2.2μ (R)

• We easily see these spiral arms because theycontain numerous bright O and B stars which illuminate dust in the arms.

• However, stars in total seem to be evenly distributed throughout the disk.

• The density contrast is only of order 10%.The blue image shows young star-forming regions and is affectedby dust obscuration. The NIR image shows mainly the old stars and is unaffected by dust. Note how clearly the central bar can be seen in the NIR image.

Spiral arms

Variations in spiral morphology

Flocculent spirals (fleecy)

Grand-design spirals (highly organized)

• Spiral structure varies greatly in detail.• The cause of this is not really

understood• Grand design spirals seem to have

nearby companions – driven by interactions

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3. The morphological mix is related to the density of galaxies in the local surroundings.

=> Morphological segregation

Morphology-density relationDressler, 1980

Holds over 6 orders of magnitude of galaxy density

Field:E:S0:Sp = 10:10:80

Why?

Kauffmann et al. 1999VIRGO/GIF simulationssee also Benson et al. 2001; Springel et al. 2001

Hierarchical simulationsshow a clear correlationbetween color/morphologyand density, in qualitativeagreement with observations

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Elliptical versus Spiral

Ellipticals SpiralsSmooth light distribution Arms, disk, bulgeBrightest stars are red Brightest are blueLittle/no star formation On-going star formationLittle/no cool/cold gas Molecular + atomic gasRandom motions Circular rotation in disk

Found in cluster cores Avoid cluster cores

Morphological segregation:Initial conditions or evolution?

Lenticulars = S0’s

Ellipticals SpiralsSmooth light distribution Arms, disk, bulgeBrightest stars are red Brightest are blueLittle/no star formation On-going star formationLittle/no cool/cold gas Molecular + atomic gasRandom motions Circular rotation in disk

Found in cluster cores Avoid cluster cores

S0: Spiral-like: disk+bulge, rotation

Elliptical-like: little gas/star formation; no spiral structure

Evolution along the Hubble sequence?

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VCC: Virgo Cluster Catalog Sandage, Binggeli & Tammann1985AJ 90, 1759

• LF = The number of objects (stars, galaxies) per unit volume of a given luminosity (or absolute magnitude)

Φ(L) = dN/dL dV

• Bright galaxies are rare … But can be detected to large distances.

• Faint galaxies can only be seen nearby.

• Binggeli, Sandage & Tammann:Compared LFs of Virgo Cluster Catalog (VCC) and local field



LF: Number density of galaxies per unit Lφ(L)dL ~ Lα eL/L* dL

φ(M)dM ~ 10-0.4(α+1)M exp(-100.4(M*-M)) dL

Press-Schechter (1974) formalism plus CDM fluctuation spectrum predicts faint

end slope α = -1.8

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Luminosity function• The L.F. gives the number of galaxies per unit volume per

luminosity (or magnitude) interval.

• Schechter (1980) expressed the LF as an analytic function with both a power law and an exponential:

log L

ϕ(L)

α = faint end slopeL* = luminosity at “knee” of L.F.

Bright galaxies are rare.Low L galaxies only seen nearby.

cD’stoo bright!

Elliptical galaxies display a variety of sizes and masses

• Giant elliptical galaxies can be 20 times larger than the Milky Way

• Dwarf elliptical galaxies are extremely common and can contain as few as a million stars

M31 - Andromeda

M32

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Key points of cosmology (later)The dominant motion in the universe is the smooth linear

expansion known as “Hubble’s Law”.• Hubble (1923): galaxy spectra are redshifted• “redshift” = z = ∆ λ / λ• Hubble’s law (1926): v = H d

where V is the observed recessional velocityd is the distance in Mpc

The metric for a homogeneous and isotropic model universe is:

where R(t) is the scale factor, and dσ2 is the metric for constant curvature in 3-D space:

ds2 = dt2 - dσ2R2(t)

c2

dσ2 = + r2 (dθ2 + sin2θ dφ2)dr2

1 – kr2

k : the curvature constant

k=0 => R(t) ∝ t2/3 => Einstein-deSitter universe

Quantitative Morphology

Photometric surface brightness profile (at projected radius R)

“de Vaucouleurs’ profile”:I(R)= I(Re) exp-7.67[(R/Re)¼ - 1]where Re is the “effectiveradius” and L(<Re)=½ Ltotal

“exponential profile”:I(R)= I(0) exp[-R/Rd]

where Rd is the “exponential scalelength”.

Works for spiral disks

Works for ellipticals and for bulges

Spiral: I(R) = Ibulge(R) + Idisk(R)… [+ Ibar(R)]

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Quantitative Morphology

For z2 = r2 - R2 and dz = r dr/(r2 - R2)½:

I(R) = j(r) dz = 2

This is an Abel integral equation with solution:

j(r) =

For certain I(R), j(r) can be expressed algebraically. For smooth (fitted) profiles, the integral can be evaluated directly. For noisy data, use the Richardson-Lucy iterative inversion algorithm (B&M 4.2).

“Sersic profile”:I(R)= I(Re) exp-b[(R/Re)1/n - 1]

where n is the “Sersic index” => n=1 and b=1.67 (disk)n=4 and b=7.67 (deVauc)

In general, we want to derive the luminosity density j(r) from the surface brightness I(R):

∫-∞

∞ ∞∫R

j(r) r dr(r2 - R2)1/2

∫R

∞-1 dI dRπ dR (R2 - r2)1/2

For Monday’s class

I will post the slides tomorrow.

Please look at them in advance of class, so I can speed through the first half.

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