hubble arranged his sequence on a tuning fork diagram...
TRANSCRIPT
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
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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”.
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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”.
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• 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.
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Ellipticals
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Spirals
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Spirals
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Barred Spirals
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Lenticulars
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Irregulars
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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.
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ULIRGS (Ultraluminous IR Galaxies)
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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.
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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.
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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.
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Rotation Curves of Spiral Galaxies
Observations !v ~ constant (r0)
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Rotation Curves of Spiral Galaxies
Rubin, Thonnard, & Ford, 1978, ApJ, 225, L107
Vera Rubin (b1928)
Responsible for most of the work
on the “galaxy rotation rate”
problem.
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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
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Rotation Curves of Spiral Galaxies
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
Rotation Curves of Spiral Galaxies
Rubin et al. 1985, ApJ, 289, 81Thursday, August 9, 2012
Rotation Curves of Spiral Galaxies
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
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Rotation Curves of Spiral Galaxies
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
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Rotation Curves of Spiral Galaxies
Pierce & Tully (1992)
21 cm flux vs. Velocity
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Rotation Curves of Spiral Galaxies
Pierce & Tully (1992)
MB MR
MI MH
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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
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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.
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Ellipticals
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Elliptical Galaxies
M 87Giant Elliptical
Mass ~ 3 x 1012 M⊙
Size is ~10 x diameter of Milky Way
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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.
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Elliptical Galaxies - Classifications
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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
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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
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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 ?
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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
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Elliptical Galaxies - Dynamics
Compare rotational velocity, vrot, to velocity
dispersion, σ :
Ellipticals with high V/σ
Ellipticals with lowV/σ
Davies et al. 1983, ApJ 266, 41
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Elliptical Galaxies - Dynamics
ATLAS3D: Emsellem et al. 2011, MNRAS, 414, 888
ellipticity
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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
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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)⊥
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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.
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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)
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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
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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.
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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
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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
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Fundamental Plane projections Kormendy & Djorgovski 1989, ARAA, 27, 235
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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
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Where does the Fundamental Plane come from ?
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
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Where does the Fundamental Plane come from ?
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
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Where does the Fundamental Plane come from ?
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
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Supermassive Blackholes in Galaxies
M 87Giant Elliptical
Mass ~ 3 x 1012 M⊙
Size is ~10 x diameter of Milky WayThursday, August 9, 2012
Supermassive Blackholes in Galaxies
M 87Giant Elliptical
Mass ~ 3 x 1012 M⊙
Size is ~10 x diameter of Milky Way
Jet of material emitted by nucleus
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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.)
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Supermassive Blackholes in Galaxies
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Correlation between SMBH Mass and Galaxy Properties
Gebhart et al. 2000, ApJ,
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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)
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