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1 Galaxy Classification
2 Spirals
3 Ellipticals
4 Comparison
5 Multiwavelength
6 Spiral Rotation and Arms
7 Barred Spirals
8 Dwarf Galaxies
9 Galaxy Luminosity Function
1. Galaxy Classification
External galaxies occur in a wide variety of shapes and sizes. In
the first systematic attempt to quantify their morphology,
Hubble produced his "tuning fork" diagram in the 1920s:
The Zoo: Sloan Digital Sky Survey
http://www.galaxyzoo.org/
Four main types of galaxies –
Hubble proposed a scheme for classifying galaxies
in his 1936 book, The Realm of the Nebulae
 Ellipticals (20%)(E)
 Lenticulars (SO or SB0)
 S01, S02, S03 – strength of dust
absorption, S01 has none
 SB01, SB02, SB03 – prominence of bar
 Spirals (77%)– normal (S) (SA) or barred (SB)
 Sa – Sc depending on bulge/disk ratio,
tightness of spiral arms, and gas content
 Irregulars (3%)(do not fit into above category)
Galaxies on the left are designated early type galaxies, and
those toward the right are called "late types." These labels arise
because Hubble believed that this diagram represents an
evolutionary sequence. We now believe otherwise.
A detailed description of Galaxy classifications can be found at:
http://nedwww.ipac.caltech.edu/level5/Haynes/Haynes_contents.html
2 Spiral Galaxies
2.1 Classification
de Vaucouleurs introduced several important features:
 Continuity of barred and non-barred spirals (through mixed
types SA-SAB-SB)
 Continuity of spirals into irregulars Sc-Scd-Sd-Sdm-Sm-Im
(m means Magellanic, the LMC being the prototype):
 Rings. Galaxies are divided into those possessing ring-like
structures (denoted ‘(r)’) and those without rings (denoted ‘(s)’).
So-called ‘transition’ galaxies are given the symbol (rs).
Hoag’s object: (183Mpc)
Spiral galaxies have outstretched, curving arms suggestive of a whirlpool
or pinwheel. Hubble distinguished different sub-classes according to the
tightness of the arms and the size of the nucleus. He called these Sa, Sb,
and Sc.
▪
▪
▪
▪
Sa - tightly-wound, smooth arms, and a bright central disc
Sb - better defined spiral arms than Sa
Sc - much more loosely wound spiral arms than Sb
Sd - very loose arms, most of the luminosity is in the arms and
not the disc



Normal spiral galaxies are designated S* or SA*. Barred
spiral galaxies are designated SB*
Definite spiral structures are seen in some 61% of
galaxies. These structures often extend throughout most of
the galaxy’s visible disk, which have scale lengths to 15
kpc or more.
Although individual galaxies often show irregularities in
the light distribution within the spiral patterns the
underlying spiral geometry is highly regular.
Logarithmic Spirals: The "*" is chosen from a, b or c, and was
originally classified on the basis of the pitch angle of the spiral
arms:
The derivative r'(θ) is proportional to the parameter b. In other
words, it controls how "tightly" and in which direction the spiral
spirals.
In the extreme case that b = 0, the spiral becomes a circle of
radius a.
Conversely, in the limit that b approaches infinity the spiral
tends toward a straight line.
o
Note that late-type spiral galaxies (Sc's) also tend to
have:
 smaller bulges
 more "grand design" spiral structure
M65 Sa :
Triangulum, 900kpc, M33, SA(s)cd:
M51a and M51b – whirlpool SA(s)bc + SB0pec, 7 Mpc
M31,
780kpc,
Andromeda
SAb
2.2 Irregular
Irregular galaxies come in two types:
• Irr I which are in some sense a logical extension of the
Hubble tuning fork, having characteristics "beyond" those of
class Sc - high gas content, dominant presence of a young
population.
Irr I galaxies may show bar-like structures and incipient
spiral structure like the Large Magellanic Cloud, below. Such
galaxies are sometimes referred to as "Magellanic Irregular"
galaxies.
NGC1427a:
The LMC Large Magellanic Cloud
•
Irr II which are galaxies which defy classification
because of some form of disturbance. M82, shown below, is
undergoing an intense period of star-formation.

Certain galaxies lack either an obvious spiral structure or
nuclear bulge, appearing instead as a random collection of
stars with no obvious order.
These are designated "Irr" for "irregular."
Make up a few % of the field galaxy population
Generally smaller, sizes of a few kpc
Absolute magnitudes of –13 to –20

Masses of 108 to 1010 Msun
o




.
2.3 Spiral Properties
 As a fiducial, the Milky Way
 Radial Scale Length of 3-4 kpc
 Blue Luminosity of ~ 1.5 x 1010 L
 Absolute blue magnitude, -20.7
 Total Mass of ~1011 – 1012 M
(depending on how much dark matter there is).
About 90% of galaxies in the field are spirals
Most spirals are found in the field (in groups)
Spiral galaxy scale lengths run from ~1 kpc (dwarfs) to
~50 kpc
Absolute magnitudes ranging from –16 to –23, that’s a
factor of ~1000 in luminosity!
Masses ranging from 109 to 1012 M
Surface Brightness. At large radii, face-on disk galaxies
typically have exponential luminosity profiles; the log of the
surface brightness falls as a linear function of radius, or
The total luminosity of an exponential disc profile
I(R) = Io exp(-R/Ro)
is given by 2I o Ro2 ,
where I0 is the (extrapolated) surface brightness at the center of
the disk, and R0 is the disk's exponential scale length.
At smaller radii, the luminosity profile may deviate either above
or below the exponential line; the former are known as `Type I'
profiles, the latter as `Type II' ( Barred Spirals).
Observations of edge-on disks show that most of the luminosity
comes from a rather thin component which is reasonably well-fit
by
2
I(z) =
where
z
I(z=0) sech2 (z/2zo)
.
sech(z)=2/[exp(z)+exp(-z)].
Colours. The integrated colours of disk galaxies reveal trends
with morphological type; S0 and Sa galaxies are red, while Sc
and Sd galaxies are blue. These trends reflect different rates of
star formation; broadband colors are sensitive to the average
star formation rate over the last 108 years.
2.4 Barred spirals
A large fraction of disk galaxies have bars: narrow linear structures
crossing the face of the galaxy.
In barred S0 galaxies the bar is often the only structure visible in the disk.
In types SBa and later the bar often connects to a spiral pattern extending
to larger radii (e.g. NGC 1300). Viewed face-on, bars typically appear to
have axial ratios of 2.
The surface brightness within the bar is often fairly constant. Some bars
appear to be ‘squared off’ at the ends. The true 3-D shapes of bars are
difficult to determine, but many appear to be no thicker than the disks
they occur in; if so then bars are the most flattened triaxial systems
known
Bars in edge-on galaxies are hard to detect photometrically; however,
kinematic signatures of barred potentials have been used to infer their
presence in some edge-on systems. What is noteworthy is that such edgeon bars appear to be associated with boxy or peanut-shaped bulges.
M58 SBb:
3 Elliptical Galaxies
When you have seen one elliptical galaxy, you have pretty much seen
them all. Here is a picture of one such system, the nearby elliptical M32:


An elliptical galaxy shows no spiral structure and can vary from
almost round (what Hubble called E0) to almost cigar shaped
(called E7).
This classification is based on our perspective from Earth and not
on the actual shape. So, elliptical galaxies are designated "E#,"
where # refers to their apparent flattening:
o # = 10(1 - b/a)
M89: E0
M59 E5





Apparently round ellipticals are E0s
The flattest ellipticals observed are E7s.
Do not have perfect elliptical isophotes – typical
deviations of a few %
Deviations from ellipses can be classified as disky or
boxy(peanut)
Boxy galaxies tend to be more luminous, slower rotators

Disky: normal and low luminosity ellipticals, which have nearly
isotropic random velocities but are flattened due to rotation.

3-D shapes – ellipticals are predominantly triaxial
ellipsoids:
Oblate: A = B > C (a flying saucer)
Prolate: A > B = C (a cigar)






Triaxial A > B > C
(A,B,C are intrinsic axis radii)
Find that galaxies are mildly triaxial:
A:B:C ~ 1 : 0.95 : 0.65 (with some dispersion ~0.2)
Triaxiality is also supported by observations of isophotal twists in
some galaxies (would not see these if oblate or prolate)
It was once thought that the shape of ellipticals varied from spherical to highly
elongated. The Hubble classification of elliptical galaxies ranges from E0 for
those that are most spherical, to E7, which are long and thin.
It is now recognized that the vast majority of ellipticals are of middling
thinness, and that the Hubble classifications are a result of the angle with
which the galaxy is observed.

In between the ellipticals and the spirals are the S0s which have
o very large bulges
o weak disks
o no spiral structure
Surface Brightness. Many normal bright (Mv < -17) elliptical
galaxies and the bulges of spirals have a projected luminosity
distribution that follows a de Vaucouleurs. (or R1/4) law. The
surface brightness, I, of the bulge of the galaxy (measured in
units of L pc-2) shows a radial dependence according to:
where Re is the radius of the isophote containing half the
total luminosity, and Ie is the surface brightness at Re.
This is often referred to as a r1/4 law – and the distribution is sometimes
called a de Vaucouleurs profile.

Note that this law is a purely empirical fit with no physical
basis. However, any theory of elliptical galaxy formation must
reproduce it.
Cores of Ellipticals
• Seeing corrections are important; moreover, it's generally not
possible to make corrections without some assumptions about
the underlying luminosity distribution
• Few E galaxies actually have flat luminosity profiles at small
radii; instead, the profiles rise inward to the last measured
point .
• Cores may exhibit unusual kinematics; for example, about a
quarter of all elliptical galaxies have cores which appear to
counter-rotate with respect to the rest of the galaxy .
• Although such `kinematically decoupled' cores are generally
not photometrically distinct, several E galaxies with
decoupled cores have features in their line-strength profiles
coincident with the kinematically decoupled regions .
• A few nearby E galaxies have nuclear star clusters with
densities much higher than the cores they reside in; some of
these nuclei may be rotating, disk-like systems.
Shapes of Ellipticals
• Projected axial ratios range from b/a = 1 to ~0.3, but not
flatter (Schechter 1987).
• Apparent ellipticity is generally a function of projected
radius, with a wide range of profiles.
• Isophotal twists are common. Because it is highly unlikely
that intrinsically twisted galaxies could be dynamically stable,
such twists are generally interpreted as evidence for
triaxiality .
• Elliptical galaxies are not elliptical; isophotes may depart
significantly from perfect ellipses. A Fourier analysis of
isophotal radius in polar coordinates implies that most E
galaxies are either `boxy' or `disky' .
Kinematics of Ellipticals
• The rotation velocities of bright E galaxies are much too
low to account for the flattenings we observe; fainter E
galaxies, however, rotate at about the rates implied by their
shapes (Davies 1987).
• E galaxies may exhibit minor-axis rotation; more generally,
the apparent rotation axis and the apparent minor axis may be
misaligned. While in most galaxies these misalignments are
modest, a few galaxies appear to rotate primarily about their
minor axes.

Larger galaxies have fainter effective surface brightnesses. Mathematically
speaking:
effective radius, and

As
(Djorgovski & Davis 1987) where Re is the
is the mean surface brightness interior to Re.
, we can substitute the previous correlation and see that
and therefore:
meaning that more
luminous ellipticals have lower surface brightnesses.


More luminous elliptical galaxies have larger central velocity
dispersions. This is called the Faber-Jackson relation (Faber &
Jackson 1976). Analytically this is:
.
Shells & Other `Fine Structures'
• The surface brightnesses of E galaxies do not always decline
smoothly with radius. When a smooth luminosity profile is
subtracted from the actual surface brightness, `shells' or
`ripples', centered on the galaxy, are seen.
• The fraction of field E galaxies with shell-like features is at
least 17% and possibly more than 44%.
• The colours of shells indicate that they are composed of stars.
In many cases the shells are somewhat more blue than the
galaxies they occupy.
• Shell systems have a variety of morphologies; some galaxies
have shells transverse to the major axis and interleaved on
opposite sides of the center of the galaxy, while other
galaxies have shells distributed at all position angles .
• Profile subtraction sometimes reveals other kinds of
structures in E galaxies, including embedded disks, linear
features or `jets' (not the jets seen in AGNs!), `X-structures',
etc..
Gas & Dust in Ellipticals
• When examined with sufficient resolution, 25% to more than
40% of E galaxies show features due to dust absorption.
• The dust lanes seen in E galaxies imply that the absorbing
material is distributed in rings or disks. Dust lanes may be
aligned with either the major or minor axes, or they may be
warped.
• E galaxies contain modest amounts of cool and warm gas,
although not as much as is found in S galaxies. A few E
galaxies have extended disks of neutral hydrogen.
• X-ray observations indicate that many ellipticals contain
10^9 to 10^10 solar masses of gas at temperatures of ~10^7
K; this hot gas typically forms a pressure-supported
`atmosphere' around the galaxy.
Tidal Features
• Elliptical galaxies in rich galaxy clusters often exhibit
luminosity profiles which fall below a de Vaucouleurs law at
large radii. Such downturns are often attributed to tidal
truncation in the mean field of the cluster (K82).
• In contrast, E galaxies with close companions often have
luminosity profiles which rise above a de Vaucouleurs law at
large radii. These features may be plausibly blamed on tidal
interactions.
• E galaxies in closely interacting systems sometimes exhibit
outer isophotes which are visibly egg-shaped and/or offset
with respect to the centers of their galaxies. Again, tidal
effects are strongly implicated (K82, Borne et al. 1988).
• On very deep exposures, some E galaxies are seen to have
`plumes' or `tails', while others (e.g. NGC 5128) show rather
irregular luminosity distributions. Tail-like features may be
signatures of major mergers involving one or more
dynamically cold disk galaxies (Schweizer 1987).
4 Galaxy Constituents:

Spiral galaxies contain:
o stars (population I and II) , gas, dust


Elliptical galaxies contain:
o stars (population II only – (i.e. old) stars)
Irregular galaxies are harder to classify. They usually contain:
o stars (population I (young stars) – in other words there are
significant amounts of gas in the galaxy which is being
transformed into young stars – with ages as short as a few
million years) and some population II) , star-forming regions
, gas (a higher proportion than in spirals)
The Large Magellanic Cloud at optical wavelengths
Mass M
Absolute mag
Luminosity L
M/L (M / L
=1)
Diameter (kpc)
Stellar
population
Ellipticals
105 - 1013
-9 -> -23
3 x 105 - 1011
100
Spirals
10 – 4 x 1011
-15 -> -21
108 – 2 x 1010
2 – 20
Irregulars
108 – 3 x 1010
-13 -> -18
107 - 109
1
1 – 200
II and old I
5 - 50
I in arms, II
and old I
overall
Yes
1 – 10
I, some II
83
4
Presence
of Almost none
dust
Total fraction
13
%
9
Yes
E
Colour
Red
S0
Sa
Red
Sb

Sc
Blue
Sd Irr
Blue
Stellar
Old Old +
Old +
Intermediate
Population
Intermediate Intermediate +
+ Young
Young
Star Form zero low
higher
high
Rate
HI (gas) Zero/ low
modest
high highest
low
dust
Zero/
Higher
highest
Lower
low
(less
metals)
Dynamics Bulge/halo Disk dominated, so
dom.
rotation
The Colour-Magnitude Diagram:
Colour: Large automated imaging surveys are better at
defining a galaxy's colour rather than morphology.
it is more natural to describe a galaxy as being on the
‘red sequence’ or ‘blue sequence’ rather than being an
‘early type’ or ‘late type’.
This interpretation also has the advantage that galaxy
colours are directly related to the star formation, dust and
metal-enrichment history of the galaxy and can thus be
more readily interpreted in theoretical models
The bimodal distribution of red and blue galaxies as seen in
analysis of Sloan Digital Sky Survey data[2] and even in de
Vaucouleurs' 1961 analyses of galaxy morphology.
Three features:
the red sequence,
the green valley
the blue cloud.
The red sequence includes most red galaxies which are
generally elliptical galaxies. The blue cloud includes most blue
galaxies which are generally spirals. In between the two
distributions is an underpopulated space known as the green
valley which includes a number of red spirals.
Unlike the comparable HR diagram for stars, galaxy properties
are not necessarily completely determined by their location on
the color-magnitude diagram. The diagram also shows
considerable evolution through time.
Colour (U-R) versus stellar mass relations for different
environments.
Panel (a): void-like environments while
Panel (f) cluster-like environments.
[Conclude: Hubble sequence applies to other properties.]
5 Multiwavelength Views of Galaxies
Our view of is greatly affected by the observing wavelength –
the infrared penetrates deeper than optical radiation.
M101, a nearby Sc galaxy:
The Whirlpool: M51…below Chandra (X-ray) and ISO (mid-IR):
The x-ray image (left) highlights the energetic central regions of
the two interacting galaxies. Much of the diffuse glow is from multimillion degree gas. Many of the point-like sources in the x-ray
image are due to black holes and neutron stars in binary star
systems.
Mid-IR light (right) is well-suited to studying star formation and
tracing dust in spiral galaxies. This image not only shows the galaxy
cores and spiral arms, but nicely illustrates the knots of star
formation occurring in the arms of M51.
M104: (SAa, 9 Mpc) Spitzer's infrared view of the starlight, piercing
through the obscuring dust, is easily seen, along with the bulge of
stars and an otherwise hidden disk of stars within the dust ring.
NGC253 at infrared,optical and X-ray wavelengths
M81 at optical wavelengths and using the 21cm wavelength HI tracer of
atomic hydrogen gas. The spiral structure is clearly shown in this image,
which shows the relative intensity of emission from neutral atomic hydrogen
gas. In this pseudocolor image, red indicates strong radio emission and blue
weaker emission.
6 SPIRAL ROTATION
Basic components of Spirals reviewed:
 Disks:
metal rich stars and ISM, nearly circular
orbits with little random motion, spiral patterns
 Bulge: metal poor to super-rich stars, high stellar
densities, mostly random motion – similar to
ellipticals
 Bar: present in 50 % of disk galaxies, long lived, flat,
linear distribution of stars
 Nucleus: central (<10pc) region of very high mass
density, massive black hole or starburst or nuclear
star cluster
 Stellar halo: very low surface brightness (few % of
the total light), metal poor stars, GCs, low-density
hot gas, little/no rotation
 Dark halo: dominates mass (and gravitational
potential) outside ~10kpc, nature unknown?
 Luminosity profiles: (1D):
 Exponential disk: I(r) = I0 exp(-r/rd)
 rd= disk scale length, typically ~2-6 kpc
 Light falls off sharply beyond Rmax ~3-5rd
 In the central regions, also see light from the bulge
 Bulge follows the r1/4-law, like ellipticals
Vertical disk structure:
 The surface brightness perpendicular to the disk is
also described by a exponential or better by a sech
law
 I(z) = I(0) exp(-|z|/z0)
 I(z) = 0.25 I(0) sech2 (-z/2z0) …… recall
sech(z)=2/[exp(z)+exp(-z)]
 z0 is the scale height of the vertical disk
 Different populations have different scale heights. In
the Milky Way:
 Young stars & gas ~ 50pc
 Old thin disk ~ 300-400 pc (older stars, like the
sun)
 Thick disk ~1 – 1.5 kpc (older, metal-poor
stars)
Best interpretation of many of these is a trend in star
formation history
 Early type spirals formed most of their stars early
on (used up their gas, have older/redder stars)
 Late type spirals have substantial on-going starformation, didn’t form as many stars early-on (and
thus lots of gas left)
 Spirals are forming stars at a few Msun per year,
and we know that there is ~a few x 109 Msun of HI
mass in a typical spiral
Rotation curves of other galaxies
On the left, a spiral galaxy image, with spiral arms delineated by HII
regions.
On the right, the light from a narrow strip running along the major axis of
the galaxy has been spread into a spectrum, between about 6500 and 6800
Angstroms.
The rotation of the galaxy is seen in the emission lines from H alpha at 6563
Angstroms (the brightest line), as well as other fainter lines in this region due to [NII].
HII regions appear reddish in this image because of the prominence of the H alpha
line in the red region of the spectrum.
We can measure rotation curves via:
 HI mapping: 21cm emission from atomic hydrogen
 Via optical spectroscopy: Optical absorption lines
from the stellar component or Optical emission lines
from hotter gas. ◦
More luminous galaxies have higher rotation velocities, later
type galaxies have slower rise in velocity
 rotational velocity is constant, so that means M  r
beyond limits of stellar disks, which are showing an
exponential drop off in light (and thus mass) anyway!
Tully-Fisher Relation:
Tully & Fisher (1977) found that
L Vmax
where  ~ 4
The Tully-Fisher relation for spiral galaxies, (and the Faber-Jackson relation
for ellipticals), follow from the dynamics if we assume constant mass-to-light
ratio and surface brightness.
Plot the maximum circular velocity of spiral galaxies
against their luminosity in a given band:
Find that L and Vmax are
closely correlated
Tully-Fisher relation
Smallest scatter when L is
measured in the red or the near-infrared wavebands
m Vrot
/R=GMm/R
2
2
2
so M is proportional to Vrot R
• the observed flux or Luminosity L of a galaxy
◦ can be determined photometrically
▪ eg. simply integrating the surface brightness to determine the
total flux or Luminosity from the galaxy.
◦ which is a function of the (visible) mass
(more massive - more stars - more emission)
Assuming all galaxies have the same M/L ratio and the
same surface brightness, then the relation L is
proportional to Vrot4
In part, Tully-Fisher relation reflects simple gravitational
dynamics of a disk galaxy (see problem 5.10 in textbook).
Estimate the luminosity and maximum circular velocity of
an exponential disk of stars.
Luminosity
Empirically, disk galaxies have an exponential surface
brightness profile:

I(R) I(0) exp[-R / hR]
…with central surface brightness I(0) a constant. Integrate
this across annuli to get the total luminosity:
L 2R I(0) exp[R/ hR] dR
Can integrate this expression by parts, finding:

L I(0)hR2
2
i.e. for constant central surface brightness, luminosity
scales with the square of the scale length.
Spiral Structure

The most obvious feature in a spiral galaxy is its spiral structure:
o Here, for example, is M101 with clear ‘grand design’ spiral
arms:
Flocculent spiral: NGC 4414

Structure is made up from young, bright stars
Because disk galaxies rotate differentially, the orbital period is
an increasing function of radius R. Thus if spiral arms were
material features then differential rotation would would soon
wind them up into very tightly-coiled spirals. The expected pitch
angle of material arms in a spiral galaxy like the Milky Way is
only about 0.25 degrees. In fact, pitch angles measured from
photographs range from about 5 degrees for Sa galaxies to 20
degrees for Sc galaxies (Kennicutt 1981). The most likely
implication is that spiral arms are not material features.
First ingredient for producing spiral arms is differential
rotation. For galaxy with flat rotation curve:

V(R) constant
(R) V
R
Angular R1
velocity
Any feature in the disk will be wrapped into a trailing spiral
pattern due to differential rotation.
o
o
Open spiral structure cannot be maintained in this
way.
This problem is usually known as the winding
dilemma
In the 1950's it was thought that magnetic fields could be the
mysterious generators of spiral structure.





The stars in a spiral arm cannot always be the same stars:
o Very rapidly, spiral structure will wind up very
tightly.
There are different types of spiral arms
o “Grand-Design” – two well-defined spiral arms
(10%)
o Multiple-arm spirals (60%)
o Flocculent spirals – no well-defined arms at all,
“ratty” (30%)
Are spiral arms leading or trailing?
What is the nature of the arms?
The solution to this dilemma was finally sorted out by Lin
& Shu in 1963.
o Their solution was to assume that:
 Stars follow slightly elliptical orbits
 The orientations of these orbits are correlated:
o
As is apparent from the above figure, this
arrangement produces a spiral density wave: spiral
arms are caused by a density perturbation that moves
along at a speed different from the speed of the
objects within it. The density wave resists the
spiral’s tendency to wind up and causes a rigidly
rotating spiral pattern
o

Properties of spiral arms can be explained if they are
not rotating with the stars, but rather density waves:
• Spiral arms are locations where the stellar orbits
are such that stars are more densely packed.
• Gas is also compressed, possibly triggering star
formation and generating population of young stars.
• Arms rotate with a pattern speed which is not equal
to the circular velocity - i.e. long lived stars enter and
leave spiral arms repeatedly.


…..so, young bright stars should lie in front of the
highest density regions
High densities also compress the magnetic fields, which
produces a maximum in the radio continuum emission in
regions of highest density.
So, bright stars should appear "down stream" from the peak
in the radio continuum emission.
This effect is, indeed, observed, and so the density wave
theory is vindicated!
In the inner parts of disks, stars are moving faster than the
pattern speed and overtake the density wave.
In the outer parts, stars move more slowly than the pattern
speed, and the spiral arms over take the stars

o
o
o
o
o
o
• Pattern speed is less than the circular
velocity
material travels around undisturbed elliptical
orbits, but sometimes many orbits come close
together, so the density increases.

The only remaining question is why orbits arrange
themselves in correlated ellipses.
o the answer is self organization:
This feedback loop can also generate the bars in SB
galaxies
o Such a runaway process is called a dynamical
instability
o Note that this process only works if there is enough
mass in the disk for the perturbations to modify the
gravitational field
 In early-type spirals (Sa's) where most of the
mass is in the bulge not the disk, the instability
will be partly suppressed.
 This suppression explains the anti-correlation
between bulge size and strength of spiral
structure.
Spiral arm pattern is amplified by resonances between the
epicyclic frequencies of the stars (deviations from
circular orbits) and the angular frequency of the spiral
pattern
o Spiral waves can only grow between the inner and
outer Linblad resonances (p =  -/m ; p =  +
/m ) where =the epicyclic frequency (frequency of
radial oscillations) and m is an integer (the # of spiral
arms)
o

Define the epicyclic frequency via:

2(R) 1/R 3 d/dR  R22 
o
For a point mass gravitational field,
.
Stars outside this region find that the periodic pull of
the spiral is faster than their epicyclic frequency,
they don’t respond to the spiral and the wave dies out
o Resonance can explain why 2 arm spirals are more
prominent
Note that density wave theory does not explain flocculent
spirals. Those can be explained by self-propagating star
formation:
o Star forming regions produce supernovae, which
shocks the gas, which triggers more star formation,
etc, etc, etc
o Differential rotation stretches out the regions of star
formation into trailing, fragmentary arms
o No global symmetry (as observed)
o

7. Barred Galaxies
e.g. NGC 1300:
Half of all disk galaxies show a central bar which contains up to
1/3 of the total light
Bars are almost as flat as surrounding disks.
S0 galaxies can have bars – a bar can persist in the absence of gas
Bar patterns are not static, they rotate with a pattern speed, but
unlike spiral arms they are not density waves. Stars in the bar stay
in the bar.
The asymmetric gravitational forces of a disk allow gas to lose angular
momentum (via shocks) compressing the gas along the edge of the bar. The
gas loses energy (dissipation) and moves closer to the center of the galaxy.
8. Dwarf Galaxies
Dwarf Elliptical
Faint, M > -18, Low-luminosity: 106 – 1010 L
Low-mass: 107 – 1010 M
Small in size, ~few kpc
Often low surface brightness, so they are hard to find!
Why are dwarf galaxies important??
Majority of galaxies are dwarfs!! There are probably lots of these, in
the Local Group there are >30!
Dwarf galaxies may be remnants of galaxy formation
process: “proto-dwarf” gas clouds came together to
form larger galaxies (hierarchical formation)
Dwarf galaxies are currently being “absorbed” by larger
galaxies
Dwarf galaxies are relatively simple systems, not merger
products
Different types of dwarf galaxies
Dwarf ellipticals (dE): Note that these are structurally very
different from luminous E’s.
Gas-poor, old stellar
population. Note that many dE’s have nuclei (dE,N).
Dwarf spheroidals (dSph): Gas-poor, diffuse systems.
Low luminosity (low surface brightness end of dE’s.
Dwarf irregulars (dIrr): Extreme end of late type spirals.
Active, on-going star-formation but low surface brightness
(like dSph’s). Gas-rich. Note that there are no dwarf
spirals!!
In the Local Group, we can study the resolved stellar
population (color magnitude diagrams) to determine the star
formation histories of dwarf galaxies
Dwarf ellipticals are generally old (stars formed > 10 Gyr
old), but some may have had more recent (a few Gyr ago)
weaker episodes of star formation
Dwarf irregulars tend to have quasi-continuous star
formation (perhaps interspersed with bursts).
Lower
luminosity dIrr’s more likely to have a bursty history
Environmental effects may play a role (e.g., tidal
stripping removing gas from dSph’s)
No two galaxies have the same star formation history
Dwarfs do not contain dark matter…..however:
 Dwarf Spheroidal, Leo I :
 Leo I
Low Surface brightness galaxies (LSB)
 Very difficult to detect!
 Need dedicated surveys
 Recent automated CCD surveys suggest there may be more
LSB galaxies than all the other types of galaxy put together
Peculiar Galaxies
 In particular, interacting galaxies
 Many cataloged by Arp in 1966
9. Galaxy Luminosity Function
Count the number of galaxies as a function of luminosity
(or absolute magnitude)
Useful for:
 Understanding galaxy formation (distribution by
luminosity implies distribution by mass – how many
galaxies of a given type and mass were formed
 Galaxy evolution models – either must reproduce
observed LFs (hierarchal formation models) or
assume them (and work backwards in time). Can
also measure evolution in LFs vs. redshift!
 Galaxy Properties
Schechter (1976) found that
 (L)dL = *(L/L*) exp{-L/L*}d(L/L*)
 (L)dL = number of galaxies per unit volume
with luminosities between L and L+dL
 Where L* = 1.9 x1010h72-2 Lsun is a
characteristic luminosity cutoff,  is the powerlaw slope at the faint end, * is the normalization
(# galaxies/Mpc3)
 This function is a power law for L< L* , but cuts
off rapidly for L > L*
Usually measured in magnitude:
 (M)dM = (0.4 ln10)x * x 10 0.4(+1)(M*-M) x
exp{-10 0.4(M*-M)}dM
* = 0.45 x10-2h723 Mpc-3
Schechter Function by galaxy type and environment
Field – dominated by Spirals, faint end dIrr
Clusters – many more E/S0 galaxies, faint end dE, more dwarfs than
in field
Approximate Schechter values:
M* ~ -20.5 (in B), depends on H0
L* ~ 2 x 1010 L (~Milky Way)
 ~ -1 to –1.5 , often take -1 . 2 5
Normalization is uncertain!
Integrating the Luminosity Function
n* = 8 x 10-3 Mpc-3
L* = 1.4 x 1010 Lsun

…where Lsun = 3.9 x 1033 erg s-1 is the Solar luminosity.
Illustrative
1. Total Number of Galaxies:
If we integrate the Schechter function, we get the total
number of galaxies (per Mpc3), we find:
 N = ∫0 (L)dL = * L* (+1)
 Where  is the gamma function, (j+1)=j! when j is
an integer
 If <-1, (+1) is undefined (!), and N is infinite!!
2. Total Luminosity of Galaxies:
We can also integrate to find the total luminosity
 total lum = ∫0 L (L)dL = * L* (+2), which
diverges if  < -2
 so the total amount of light is finite! (Phew!!)
Dominated by galaxies with L ~ L* for typical value of
.
Mass function of galaxies
For stars, measurements of the luminosity function can be
used to derive the Initial Mass Function (IMF).
For galaxies, this is more difficult:
• Mass to light ratio (M/L) of the stellar population
depends upon the star formation history of
the galaxy.
• Image of the galaxy tells us nothing about the amount
and distribution of the dark matter.
More difficult measurements are needed to try and get at
the mass function of galaxies.