Galaxy Classification 2/17/05

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Lecture 4

• Galaxy Classification 2/17/05

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Todays Lecture

• Galactic Center Overview
• Galaxy Classification

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Dark Matter Halo Summary

• M 55 ? 1010 Msun
• L0
• Diameter 200 kpc
• Composition unknown!

90 of the mass of our Galaxy is in an unknown
form MACHOS are not likely to make up most of it.
This could be a topic for your final project
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The Galactic Center Summary of Observations
The center of the galaxy is impossible to view
directly at visible wavelengths because of the
great amount of extinction caused by the
interstellar dust along the line of sight.
However, longer wavelength radiation can
penetrate the dust and some fine images of the
galactic center region have been obtained at
infrared and radio wavelengths.
This image shows a view of about 50 degrees along
the galactic plane obtained by IRAS at a
relatively long wavelengths. This is a false
colour image that shows infrared emission due to
dust primarily. Clearly this dust is concentrated
in the the galactic plane and shows a very strong
enhancement around the center of the galaxy as
shown in the inset closeup on the right.
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Galactic Center (central 10 pc) Contains

• Population of young stars
• Interstellar material including both ionized gas
  (HII regions) and molecular clouds which orbit
  the Center in a ring with an inner radius of
  about 2 pc. Hot dust is also observed.
• Strong magnetic fields (milligauss) compared with
  elsewhere in Galaxy
• A compact radio source called SgrA that
  coincides with the dynamical center of the Galaxy

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Stars in central region of Galaxy
This image is a composite of photographs obtained
in the infrared bands of 1.6, 2.2 and 3.8
microns. This field of view of this image is
about 0.3 pc (1 light year). The radio source Sgr
A is located in the middle of the bluish
"y"-shaped asterism near the center of the
picture. The colours are assigned to indicate the
band where the flux is highest (red corresponds
to longer wavelength emission). These stars are
all extremely young, massive objects and are
heavily reddened by dust along the line sight.
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Gas in Central Region of Galaxy
This image shows the "mini-spiral" at the center
of the Milky Way. This is a radio image obtained
at the VLA (Very Large Array) near Socorro NM.
The observations were made at a wavelength of 6cm
and the emission is from ionized gas at the
galactic center. The image covers about 40" on
the sky corresponding to the inner 10pc or so.
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Radio image of Central Square Degree
Radio image at 20 cm showing the large scale
filaments which are probably due to synchrotron
emission along magnetic field lines. The blob in
the middle of the picture is the region
surrounding the point-like radio source, Sgr A,
(the dark point at right-center in this blob)
which is believed to mark the nucleus of the
Galaxy. Synchrotron emission is a characteristic
of Active Galactic Nuclei (AGN). The relativistic
particles are believed to derive their energy
from processes associated with accretion onto the
Black Hole which is thought to reside at the
center of the Milky Way.
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How does our Galaxy compare with others?
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• Properties of Galaxies
• The Extragalactic ZOO
• Some Catalogs of Objects
• Morphological Classification - Hubble Sequence
• Properties of Spirals, Irregulars, Ellipticals

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Some Catalogs of Objects

• Messier Catalog (Charles Messier 1781)

103 bright objects (galaxies, nebulae, SNRs,
glob. Clusters)

• New General Catalog (Herschels and Dreyer in
  1926)

8000 objects (galaxies, nebulae, SNRs, glob.
Clusters)

• IC Index Catalog, supplement to the above

another 7000 entries.
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The Extragalactic Zoo
Galaxies come in 3 major shapes Spirals,
Ellipticals and Irregulars
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Overall Brief Comparison Between Types
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Hubble Classification System
Spiral Galaxies Two forms - Barred and
Non-barred
(1) the size of the nuclear bulge relative to the
flattened disk (Lbulge/Ldisk) (2) the pitch
angle of the spiral arms (early types are
tightly wound) (3) the degree of resolution
into stars and H II regions of the arms and/or
disk
Modern Sequence S0, Sa, Sb, Sbc, Sc. Scd, Sdm,
Sm, Im, Ir
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Note of Caution

• Importance of wavelength on classification
• K-correction

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• Elliptical galaxies are designated "E," where
  refers to their apparent flattening
• 10(1 - b/a)
• Apparently round ellipticals are E0s
• The flattest ellipticals observed are E7s.

• In between the ellipticals and the spirals are
  the S0s which have
• very large bulges
• weak disks
• no spiral structure

Irregulars are ones that dont fit in any other
class
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The Hubble type (or T) can be shown to correlate
with

• bulge/disk luminosity ratio
• relative H I content M(H I)/L(B)
• mass concentration
• stellar population
• nuclear properties
• chemical abundances in the ISM
• star formation history and integrated stellar
  spectrum

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Properties of Spirals
Surface Brightness
The disc has an exponential surface brightness
profile,
Or, we can re-write in terms of magnitudes
The central surface brightness (r0) is
surprisingly constant across spirals. For types
Sc and earlier
Freemans Law
The surface brightness profile of the bulge is
m(r) me 8.3268(r/re)1/4-1
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Observations Properties of Individual Galaxies
Spirals
The stars in the disc are approximately circular
orbits. Apart from a steep rise near the galactic
center, the rotation speeds are remarkably
constant with radius, out to well beyond the
visible extent of the disc. Shown are rotation
ccurves of spiral galaxies as a function of
radius for different morphological classes.
For all Hubble types, note that
Vmax
L
For a given L, early types, have larger Vmax
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Observations Properties of Individual Galaxies
Spirals
The relationship between rotation speed and
luminosity for disc galaxies is known as the
Tully-Fisher relation. The Tully-Fisher relation
for different morphological classes is shown. For
the population as a whole
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Radius increases with Luminosity

• logR25 -0.249MB-4.00

R25 is the radius of the disk corresponding to a
surface brightness level of 25 mag arcsec-2 in B
in units of kpc
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Spirals show color gradients bulges are redder
than disks
Combined effects of age and metallicity
variations (bulges are older and more metal rich)
Also, metallicity is correlated with total
luminosity
Ellipticals
Spirals and Irregulars
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Spirals show increase in globular cluster
contribution to total light as you go to earlier
types
The specific frequency is largest for giant
ellipticals
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SummarySpirals Rotation Curves

• Rotation curves similar across Hubble types
  (importance of dark matter)
• As L goes up so does Vmax (Tully-Fischer
  Relationship)
• For a given L, early-types have larger Vmax
• Sa Vmax 299 km/s (163-367 km/s)
• Sb Vmax 222 km/s (144-330 km/s)
• Sc Vmax 175 km/s (99-304 km/s)

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Summary Spirals
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Summary Spirals
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Properties of Ellipticals
Current outstanding questions

• What are their intrinsic shapes?
• Do they have massive halos?
• Do they contain supermassive central black holes?
  
• What is the origin of the r1/4 law?
• What is the origin of the fundamental plane''?
• Are ellipticals dynamically similar to the
  bulges, or the halos, of spiral galaxies?
• What causes the distinction between ellipticals
  and spirals?
• When and how were elliptical galaxies formed, and
  on what time-scale?

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Properties of Ellipticals

• Look simple but are very complex
• Elliptical-shaped smooth, few clumps of blue
  few patches of dust
• No disk

• Huge range of luminosities (6 orders of
  magnitude!)
• Huge range of masses (6 orders of magnitude)
• Huge range of sizes (0.1 - gt 100 kpc diameters)
  and shapes
• Wide range of rotation (luminous ones slow
  rotation, less luminous faster rotation and
  denser stellar cusps at centers)

Considered fossil records of formation
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Hubble type not helpful for EllipticalsDistinctio
ns made based on size, luminosity, surface
brightness

• cD Galaxies
• Large and dense (1 Mpc)
• Found in centers of clusters
• MB -22 mag to -25 mag
• Mass 1013 - 1014 M?
• Lots of globular clusters
• Very high mass to light ratios (750 M? / L?) gt
  dark matter

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• Normal Ellipticals
• Intermediate size centrally condensed (1-200 kpc)
• MB -15 mag to -23 mag
• Mass 108 - 1013 M?
• Lots of globular cluster contribution to light
  but fewer than in cDs
• High mass to light ratios (7-100 M? / L?)

• Dwarf Ellipticals (dE)
• Fundamentally different objects
• Low surface brightness
• Smaller sizes (1-10 kpc)
• MB -13 mag to -19 mag
• Mass 107 - 109 M?
• Smaller globular cluster specific freq. But
  still larger than for spirals
• Lower metallicity systems

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• Dwarf spheroidals (dSph)
• Extremely low-luminosity
• Only detected near us
• Smallest sizes (0.1-0.5 kpc)
• MB -8 mag to -15 mag
• Mass 107 - 108 M?

• Blue Compact Dwarf Galaxies (BCDs)
• Unusually blue for ellipticals (B-V 0 to 0.3
  bluer than spirals)
• Have large abundance of gas (15-20 of entire
  mass)
• Low mass to light ratios (lowest 0.1 M? / L?)
• Small sizes (lt 3 kpc)
• MB -14 mag to -17 mag
• Mass 109 M?

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Observations Properties of Individual Galaxies
Ellipticals
Normal and cD Galaxies The surface brightness
profile typically has no strong features and
continues to rise (but with a declining gradient)
all the way into the core of the galaxy. It is
often well-fit by a Vaucouleurs R1/4 profile
where Ie I(Re) and Re is the effective radius
containing half the projected light. This is the
surface brightness profile for the bulges of
spirals.
As mass decreases, surface brightness transitions
to more exponential fall-off (dEs and dSph)
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Observations Properties of Ellipticals
Magnitude vs. effective radius
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Observations Properties of Ellipticals
Gas and Dust?

• Most gas is hot (107 K) - 108 - 109 M?
• Some gas is warm (104 K) - 104 - 105 M?
• Some gas is cold (102 K) - 107 - 109 M?

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Color gradients are found in ellipticals too
central is redder than are regions farther out.
Also, metallicity is correlated with total
luminosity
Ellipticals
Spirals and Irregulars
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Side note How do you find the mass of an
elliptical?
Not much gasNot much rotationHow do we
determine mass?
The velocity dispersion and the Virial theorem
(derived on the board)
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Applications of the Virial Theorem
The Virial Theorem has important implications in
statistical mechanics of classical systems.
Consider a system of N particles described by
their position vectors, ri, and their momentum
vectors, pi m , for i 1N. We will assume
that their positions and momenta are bounded,
i.e. there are maximum values of each. We may
then define the quantity
The time derivative of S is
The average of dS/dt over a time interval t is
Since S is bounded (because r and p have finite
maxima), the time average of dS/dt can be made
vanishingly small by considering a long time
interval t in which to average. Therefore, we may
equate
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Applications of the Virial Theorem
The left hand side is just twice the time average
of kinetic energy and we may utilize Newtons
second law on the right hand side
The Virial Theorem was first studied by
Claussius. He called the right-hand side of the
above equation the virial of the system. It has
some important applications. We will study one
Gravitation.
From potential theory, we may substitute the
relation F -?U to get
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Applications of the Virial Theorem
For a central, power-law force, i.e. F(r) ? rn,
the potential is of the form
U krn1
Therefore,
Hence,
For the gravitational force, n -2 such that
F(r) ? r-2, and the potential is U(r) kr-1 and
the Virial Theorem requires
The total energy is the sum of kinetic and
potential energies
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Applications of the Virial Theorem
The average of dS/dt over a time interval t is
Since S is bounded (because r and p have finite
maxima), the time average of dS/dt can be made
vanishingly small by considering a long time
interval t in which to average. Therefore, we may
equate
For a stable, closed system, the moment of
inertia is constant, i.e. on the time average the
shape of the galaxy is not changing and hence the
left-hand side of the equation vanishes
For a spherical distribution of N stars, the time
average will be constant. We may drop the time
averaging and arrive at
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Applications of the Virial Theorem
Where U is the gravitational potential energy
Consider a spherical uniform distribution of of
N stars each of mass m confined to a radius R.
The total mass of the collection is M Nm. The
Observations of distant galaxies only allows us
to measure the radial velocities of collections
of a galaxy, not the individual motions of stars.
We assume that at any instant there is an equal
probability of galactic motion in any direction.
Since there are three degrees of motion, but we
are selectively only able to observe one of the
three directions, the radial component of the
velocity vector represents one-third of the total
velocity.
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Applications of the Virial Theorem
Therefore,
Now let us study in more detail the gravitational
potential of this spherical cluster of mass M
Nm of radius R. Instead of the gravitational
potential of the point mass, we can consider the
slightly more complex arrangement of point masses
distributed uniformly within a shell of thickness
dr and mass dm (Sdmi).
r
dr
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Applications of the Virial Theorem
Thus, if Mr is the total mass contained within
the shell of radius r, then the potential energy
of a mass m located outside of the shell, i.e. r
gt R is
Integrating over all shells from r 0 to R, the
total gravitational potential energy as a
function of radial distance from the center of
the cluster becomes
At this point we would need to know the mass
distribution M(r) to integrate. For simplicity,
let us assume the density r is a constant equal
to the average
Now we know the mass distribution M(r)
We may now integrate
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Applications of the Virial Theorem
The Virial Theorem would tell us that the total
kinetic energy of the stars averages in time to be
We may solve for the radial velocity dispersion,
sr2, from our previous result of 3Nmsr2 -3MTOT
sr2 U
Since we used the Virial Theorem in the
derivation we call the mass term the virial mass.
This calculation is for the mass density, r, a
constant and a spherical, not a cylindrical
distribution. However, we can learn from the
approach that a virial mass is defined when one
observes the velocity dispersion in a galaxy
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Observations Properties of Individual Galaxies
Ellipticals
One of the most important observed scaling
relations for elliptical galaxies is the
Faber-Jackson relation between the luminosity and
the line-of-sight velocity dispersion,
The above scaling relations are only approximate.
A much tighter relation is found by combining L,
s, and Re. Elliptical lie close to a fundamental
plane in this 3-dimensional space,
There is a clear relationship between
luminosity, velocity distribution, and radius
(surface brightness). What is the origin of
this??
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The fundamental plane for elliptical galaxies.