Hubble arranged his sequence on a tuning fork diagram...

Hubble went on in his paper “Extra-Galactic Nebulae” to propose that galaxies (nebulae) be classified as ellipticals, spirals, and irregulars.

This is today known as the Hubble Sequence.

Hubble arranged his sequence on a tuning fork diagram. Originally he (incorrectly) hypothesized that galaxies evolved from the Left to the Right of this sequence.

Early types Later types

Thursday, August 9, 2012

Hubble subdivided spiral sequences into Sa, Sab, Sb, Sbc, Sc (Scd, Sd), and SBa, SBab, SBb, SBbc, SBc (SBcd, SBd). Two characteristics dictate this (1) the bulge-to-disk ratio and (2) how tighltly wound the spiral arms are. Spirals with high

bulge-to-disk ratios (Lbulge/Ldisk > 0.3) and tightly wound arms are the “a” subclass. The lower sequence has nuclear “bars”.


Irregulars: galaxies lacking organized structure.

Hubble subdivided spiral sequences into Sa, Sab, Sb, Sbc, Sc (Scd, Sd), and SBa, SBab, SBb, SBbc, SBc (SBcd, SBd). Two characteristics dictate this (1) the bulge-to-disk ratio and (2) how tighltly wound the spiral arms are. Spirals with high

bulge-to-disk ratios (Lbulge/Ldisk > 0.3) and tightly wound arms are the “a” subclass. The lower sequence has nuclear “bars”.


• Elliptical Galaxies: E’s. Galaxies with nearly elliptical isophotes with no clearly defined substructure. - Defined by “ellipticity”, ε=1 - b/a. a=semimajor axis, b=semiminor axis.

0 < ε<0.7. - Notation for Morphological Class is En, where n = 10ε. E4 has b/a~0.6.

E0 has b/a~1.

• Spiral Galaxies. Normal Spirals: S’s; Barred Spirals: SB’s. - In each class, a alphabetic sequence ordered based on brightness of

bulge/disk (and “tightness” of spiral arms, but they are correlated): a (bright bulge, tight arms), ab, b, bc, c, cd, d (faint or no bulge, open arms).- Sa and SBa are “Early type” spirals. Sd and SBd are “late type”. - Milky Way is thought to be a SBbc.

• Irregular Galaxies (Irr’s). Galaxies with weak (Irr I) or no (Irr II) structure. - Sometimes classify compared to Magellanic clouds, such as Sdm, Sm, Im. - Large Magellanic Cloud is SBm.

• S0 Galaxies, also called “Lenticular”. Transition (?) between spiral and elliptical galaxies. Two types: S0 and SB0. Contain bulge and large disk with no spiral arms.


Ellipticals


Spirals


Barred Spirals


Lenticulars


Irregulars


Spectral Energy Distributions of Galaxies

“Normal” galaxies have SEDs (flux density per wavelength) that are composites of stellar spectra (Planck functions). Other galaxies have SEDs that depart from

these. Including AGN, IR-luminous galaxies, etc.


ULIRGS (Ultraluminous IR Galaxies)


Spiral Galaxies

•Compared to Ellipticals, cover smaller range in Absolute Magnitude (-16 > M(B) > -23) and Mass (109 M⊙◉☉⨀ < M < 1012 M⊙◉☉⨀ ).

•Decreasing bulge-disk luminosity with morphological type: L(bulge)/L(disk)~0.3 for Sa’s to L(bulge)/L(disk) ~ 0.05 for Sc’s.

• Increasing “opening” angle for Spiral arms with morphological type: ~6o for Sa’s to ~18o for Sc’s.

•Bars are not uncommon. Frequency is uncertain, possibly as many as 70% of spirals have a bar (including the Milky Way?) Bars redistribute angular momentum of stars, gas, and dark matter. By perturbing oribts, gas can be driven to galaxy centers.


Spiral Galaxies - Brightness Profiles

•The light profile of Spiral Galaxy Disks follows an exponential distribution

µdisk(R) = µ0 + 1.09�

R

hr

�

•The light profile of Spiral Galaxy Bulges follow an r1/4 distribution

µbulge(R) = µe + 8.3268

��R

hr

�1/4

− 1

�

•Where μ is the surface brightness in, with μ ~ -2.5 log(I), in units of mag arcsec-2.


Rotation Curves of Spiral Galaxies

Wavelength

Blue

shift

ed

Reds

hifte

d

656 nm (Hα)

Spiral galaxies do rotate.

Measure “rotation curve” by measuring doppler shifted light from spectral lines as a function of galacticentric

distance.



Observations !v ~ constant (r0)



Rubin, Thonnard, & Ford, 1978, ApJ, 225, L107

Vera Rubin (b1928)

Responsible for most of the work

on the “galaxy rotation rate”

problem.


Dark Matter distribution in galaxies.

Navarro-Frenk-White (NFW) profile:

For Spiral Galaxies, we can extend the relation between Mass and Velocity over the whole galaxy using the “maximum” rotational velocity, V, at R=size of galaxy:

2



There is a relationship between the Maximum rotation velocity and the Galaxy’s Absolute

Magnitude (Luminosity).

This relation is now referred to as the Tully-Fisher Relation, after Brent Tully and

Richard Fisher who first determined it in 1977.

They derived:

MB = -9.95 log10 ( vmax ) + 3.15 (Sa)

MB = -10.2 log10 ( vmax ) + 2.71 (Sb)

MB = -11.0 log10 ( vmax ) + 3.31 (Sc)

As with other quantities, this relation is tightened when using Infrared magnitudes:

MH = -9.50( log10 VR - 2.50) - 21.67

Rubin et al. 1985, ApJ, 289, 81Thursday, August 9, 2012


Rubin et al. 1985, ApJ, 289, 81Thursday, August 9, 2012


Derivation of the Tully-Fisher Relation.

Maximum Rotation rate is related to velocity by:

L ∝ vαmax α � 4with

The Flat Rotation Curve implies M =v2maxR

GRewrite this in terms of the M/L

ratio: L = (M/L)−1 v2maxR

GRewrite the Radius, R, in terms of the

mean surface brightness : �I� = L/R2

L =�

M

L

�−2 �1

G2�I�

�v4max



If the Mass to Light Ratios and average surface brightness are the same for spiral galaxies, then this gives the Tully Fisher Relation, L ~ v4.

There *is* variation in the mass-to-light ratios and surface brightnesses of Spirals, but they are about the same for Spirals of the same

Morphological Classification.

L =�

M

L

�−2 �1

G2�I�

�v4max



Pierce & Tully (1992)

21 cm flux vs. Velocity



Pierce & Tully (1992)

MB MR

MI MH


Luminosity-Metallicity RelationZaritsky, Kennicutt, Huchra 1994, ApJ, 420, 87

More luminous galaxies have high metallicities. The more luminous galaxies have had more metal enrichment.

Milky Way

Metallicity (metal fraction) of gas

Metallicity of stars

Sun

Sun


Mass-Metallicity Relation

Tremonti et al. 2004, ApJ, 613, 898

More luminous means more mass to first order. Higher-mass galaxies have had more metal enrichment.


Ellipticals


Elliptical Galaxies

M 87Giant Elliptical

Mass ~ 3 x 1012 M⊙

Size is ~10 x diameter of Milky Way


Elliptical Galaxies - Classifications

•Normal Ellipticals - includes “Giant Ellipticals” (gE’s), and “normal” E’s. Range in magnitude from -15 < M(B) < -23 (cf. spiral galaxies, which have much smaller range). Diameter’s range from 1-200 kpc. Often includes S0 galaxies.

•cD Galaxies. (Brightess of the “D” Ellipiticals in the antiquated “Yerkes morphological classification”). Extremely luminous, M(B) > -25, large (R ~ 1 Mpc). Found only in the centers of dense galaxy clusters. Extended light profiles (see below), and high M/L.

•Dwarf Ellipticals. (dE’s) Differ from E’s in that they have smaller surface brightness, fainter magnitudes (-13 < M(B) < -19), and lower metallicity.

•Blue Compact Dwarfs (BCDs). Similar in morphological appearnce to E’s and dE’s, but clearly bluer in color, with appreciable gas content.

•Dwarf Spheroidals. (dSph) similar to dE’s, have magnitudes down to M(B) ~ -8 mag. Because they are so faint, only found (so far) in local group.


Elliptical Galaxies - Classifications


Ellipticals - Brightness Profiles•The light profile of normal Ellipticals is similar to that of Spiral

Galaxy Bulges -- follow an r1/4 distribution. Also called “de Vaucouleur’s” Profile

Surface-brightness profile of NGC 4472Kim et al. 2000, MNRAS, 314, 307


Ellipticals - Brightness Profiles•The light profile of normal Ellipticals is similar to that of Spiral

Galaxy Bulges -- follow an r1/4 distribution. Also called “de Vaucouleur’s” Profile

Schombert 1986, ApJS, 60, 603


Elliptical Galaxies - Dynamics

Compare rotational velocity, Vrot, to velocity dispersion, σ :

What the heck is σ ?

This is the velocity dispersion, which is the average of radial velocities in a galaxy.

Why are Elliptical Galaxies not Round ? What holds them up ?


Elliptical GalaxiesWhat the heck is σ ?

This is the velocity dispersion, which is the average of radial velocities in a galaxy.

telescope

elliptical galaxy (made of lots of stars on radial, keplerian orbits)

continuum

wavelength

flux

Δλ

λ0

Absorption line: many stars at

different velocities



Compare rotational velocity, vrot, to velocity

dispersion, σ :

Ellipticals with high V/σ

Ellipticals with lowV/σ

Davies et al. 1983, ApJ 266, 41



ATLAS3D: Emsellem et al. 2011, MNRAS, 414, 888

ellipticity


Elliptical Galaxies

Stars in Elliptical Galaxies are “thermalized”. Stars are collisionalless partcles on radial orbits. Act like statistical ensemble of particles

that interact only via their gravity

If all stars started out in circular orbits, how long does it take for a galaxy to “thermalize” ?

Consider the relaxation timescale pair collisions in a system of N stars of total mass M = N m, with extent R, and mean stellar density, n = 3N/(4πR3).

Define the “relaxation” timescale to be the average time it takes a star to change its velocity by 90o due to pair collisions.

K =12M�v2� =

12Mσ2

1 =32kT


Elliptical Galaxies

Consider a star (star 1)passing another one (star 2), with impact parameter b. Star 1 attains a velocity component perpendicular to

the incoming direction of:

v(1)⊥ ≈ aδt ≈

�Gm

b2

� �2b

v

�=

2Gm

bv

(star 1)

(star 2)

Star 1 goes through many collisions, accumulating velocity components.

After a time t, the velocity is v⊥ =�

i

v(i)⊥


Elliptical Galaxies

(star 1)

(star 2)

The expectation value of the perpendicular velocity component is:

�v⊥� =�

i

�v(i)⊥ � = 0

because the direction of each “kick” is random. But, the mean square velocity does not vanish:

�|v⊥|2� =�

i

�v(i)⊥ · v(i)

⊥ � =�

i

��v(i)⊥

��2� �= 0

The perpendicular velocity performs a random walk.


Note the integral is not defined at b=0 or b=∞. We have to chose bmin and bmax, in which case the definite integral is proportional to ln(bmin / bmax).

Because the stellar system (galaxy) has some extent, we take bmax=R.

Because our approximation for breaks down if it is on the same order as v (the velocity) we choose bmin accordingly:

Elliptical GalaxiesTo computer the sum over all collisions, convert the sum to an integral where we integrate over all impact parameters b. During time t, all stellar collisional

partners with b between b and b+db are locatedin a cylindrical shell of volume element (2πb db)(vt):

v⊥

bmin = 2Gm/v2

Therefore: bmax/bmin = Rv2/(2Gm)


Lastly, according to the Virial Theorem, Ug = 2 K, which implies GM/R =G (N m)/R = v2, in which case bmax / bmin = N.

Elliptical Galaxies

bmax/bmin = Rv2/(2Gm)

Therefore:

We define the relaxation timescale to be the time it takes for the mean square velocity to equal v, the typical velocity of a star in the system:

��v2⊥(trelax)

�� = v2


Elliptical Galaxies

We define the relaxation timescale to be the time it takes for the mean square velocity to equal v, the typical velocity of a star in the system:

��v2⊥(trelax)

�� = v2

Therefore:

Now, consider, typical galaxies have R/v ~ 108 yr and ~1011-1013 stars.

Typical trelax for galaxies is > age of the Universe. Therefore, pair collisions do not play any role in galaxy evolution. We will return to this point when we

discuss galaxy formation.


Elliptical GalaxiesAll elliptical galaxies have a relationship between their central radial-velocity dispersion,

σ, and their absolute magnitude. This is the Faber-Jackson relation, L ~ σ4.

Sandra Faberb. 1944

This is a consequence of the Virial Theorem.

cD EllipticalsMass ~ 1013-1014 M⊙

Diameter ~ 300-1000 kpc

“Normal” EllipticalsMass ~ 108-1013 M⊙

Diameter ~ 1-200 kpc

“Dwarf” EllipticalsMass ~ 107-108 M⊙

Diameter ~ 1-10 kpc


Tighter fit to the data uses the radius (size) of the galaxy. This is the “fundamental plane” of elliptical galaxies. L ~ σ2.65 re0.65.

The effective radius is related to the surface brightness, which is not constant over all types of Ellipticals. You can rewrite the “fundamental plane” as

re ~ σ1.24 Ie-0.82

cD Ellipticals

giant & normal Ellipticals

dwarf Ellipticals


Fundamental Plane projections Kormendy & Djorgovski 1989, ARAA, 27, 235


Where does the Fundamental Plane come from ?

Consider a cloud of particles of radius R, total mass, M, and initial constant density,

ρ0 = M/(4/3)πR3

Integrate over all “shells” to get total potential energy

R

drThe gravitational potential energy on a spherical shell of thickness dr at a

distance r isr

dUg = −GMr 4πr2ρ

rdr

Ug = −4πG

� R

0Mr ρr dr

For “constant” density, Mr =43πr3ρ0



R

drr

Ug = −4πG

� R

0Mr ρr dr

For “constant” density, Mr =43πr3ρ0

Integral becomes,

Ug = −4πG

� R

0(4/3πr3ρ0) ρ0r dr

Solving gives

Ug = −16π2

15Gρ2

0R5 ρ0 = M/(4/3πR3)

Inserting

Gives the total gravitational potential energy.

Ug = −35

GM2

R



From the Virial Theorem, 2K + Ug = 0. Therefore:

The Luminosity and Surface brightness are related:

The total gravitational potential energy.

Ug = −35

GM2

R

The Kinetic Energy is:

L = 2πR2e�I�e

Combining these gives: Re ∝ L

�I�eRe∝ L

�I�eσ2

M=

�M

L

�−1 σ2

�I�e



Re ∝ L

�I�eRe∝ L

�I�eσ2

M=

�M

L

�−1 σ2

�I�eTo agree with the fundamental plane observation, this must equal:

Re ∝�

M

L

�−1 σ2

�I�e∝ σ1.4

�I�0.85e

Rewriting in terms of the M/L ratio, using σ ~ M2/R and I ~ L/R2

�M

L

�∝ σ0.6

�I�0.15e

∝ M0.3

R0.3e

R0.3e

L0.15

The effective Radii cancel in the above. Therefore, the fundamental place is reproduced if either :

�M

L

�∝M0.2

�M

L

�∝ L0.25


Supermassive Blackholes in Galaxies


Mass ~ 3 x 1012 M⊙

Size is ~10 x diameter of Milky WayThursday, August 9, 2012



Mass ~ 3 x 1012 M⊙

Size is ~10 x diameter of Milky Way

Jet of material emitted by nucleus


Supermassive Blackhole in M87

rotational velocity

velocity dispersion, σ ≈ FWHM / 2.35

Modeling gives Virial Mass of (3.2+/-0.9) x 109 M⊙ within r < 0.05” = 3.5 pc.

Macchetto et al. 1997

(This density is 1.8 x 107 M⊙ pc-3. Recall, the solar neighborhood has 0.05 M⊙ pc-3.)


Correlation between SMBH Mass and Galaxy Properties

Gebhart et al. 2000, ApJ,


Correlation between SMBH Mass and Galaxy Properties

Correlations of dynamically measured black hole masses and bulk properties of host galaxies. (a) Black hole mass, MBH, versus stellar velocity dispersion for 65 galaxies.(b) Black hole mass versus V -band bulge luminosity for 36 early type galaxies with direct dynamical measurements of MBH.

McConnell, Ma, Gebhardt et al. (2012, Nature, 480, 215)


Hubble arranged his sequence on a tuning fork diagram...

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