Download Properties of Elliptical Galaxies The first step in investigating the

Properties of Elliptical Galaxies
The first step in investigating the evolution of galaxies is to understand the properties of those galaxies today. We’ll start with the
elliptical galaxies. We can summarize their properties as follows:
1) In general, elliptical galaxies, as projected on the sky, have complete 2-dimensional symmetry. The question of whether these objects are symmetric in practice, or are tri-axial is open (though
dynamical modeling suggests that triaxiality can only last for a
short time). Some ellipticals have “fine structure,” such as very
weak ripples, shells, and boxy (not elliptical) isophotes. These signatures are weak, but real. In general, those ellipticals with fine
structure are slightly bluer than equivalent galaxies without fine
structure.
2) The apparent flattening of elliptical galaxies is given in the Hubble
classification scheme as En, where n is defined in terms of the
apparent semi-major axis, a, and semi-minor axis, b, as
n = 10(a − b)/a
(14.01)
Ellipticals range in flattening from E0 (round) to E7. No elliptical
is flatter than E7. The data are not consistent with the hypothesis
that all ellipticals are E7 and appear flattened by the effects of
random viewing angles. Most likely there is a spread of flattenings
centered around E3, or thereabouts.
3) Rotation is not important in most elliptical galaxies. That is, E7
galaxies are not flattened due to rapid rotation.
4) There is little or no star formation in elliptical galaxies. However,
the spectral energy distribution of some ellipticals turns up in the
ultraviolet. (In other words, since elliptical galaxies are made up of
old stars, the composite spectrum of an elliptical should look like
that of a ∼ 4, 000◦ K star. However, many ellipticals are brighter
at 1500 Å than they are at 2000 Å.)
Above are low-resolution ultraviolet spectra of elliptical galaxies in
the wavelength range bewteen 1200 A and 3500 A. Note how the
spectral energy distribution of some galaxies, such as NGC 221,
4382, and 4111 declines at shorter wavelengths: this is expected
if most of the stars being observed have blackbody peaks in the
red or infrared. However, some galaxies, such as NGC 1399, 4552,
4649, and 1407 have ultraviolet upturns. Some of the stars in these
galaxies are extremely hot: the prevailing theories are that the hot
component is made up of very blue horizontal branch stars.
5) There is very little cold interstellar medium in elliptical galaxies.
However, there is x-ray gas at a temperature of about T ∼ 106 K.
One can easily see where this gas comes from. The stars in an
elliptical galaxy must be losing mass. If the stars are moving
isotropically at vrms ∼ 200 km s−1 , then the atoms of lost material,
if thermalized, will have a temperature of
3
1
2
mH vrms
∼ kT =⇒ T ∼ 106 degrees K
2
2
(14.02)
6) Ellipticals are almost always found in dense environments. The
few field ellipticals that exist may have swallowed their neighbors.
The plots above show how the fraction of spiral and elliptical galaxies change with the local density. In high density environments
(such as the centers of clusters), elliptical and lenticular galaxies
are common, and very few normal spiral galaxies exist. Conversely,
very few ellipticals and S0’s are present in the field.
7) Most ellipticals have weak radial color gradients: they are redder
on the inside than they are on the outside. This may be due to age
(older stars have a redder turn-off mass), or metallicity (metal-rich
stars are intrinsically redder than their metal-poor counterparts).
8) Elliptical galaxies populate a “fundamental plane” in luminositysurface brightness-velocity dispersion space. But there are many
other reflections of this plane. For example,
• Elliptical galaxy luminosity correlates with color. Large ellipticals are redder than small ellipticals.
• Elliptical galaxy color correlates with absorption line strength.
Redder galaxies have stronger absorption features.
• Elliptical galaxy absorption features correlate with the UV upturn. Galaxies with strong absorption features have larger UV
excesses.
• Elliptical galaxy UV excess correlates with the number of planetary nebulae in the galaxy. Galaxies with large UV excesses have,
relatively speaking, fewer planetary nebulae.
These classic plots display elliptical galaxy color index (y-axis) versus galaxy luminosity. The absolute magnitudes have been scaled
to the distance of Virgo, so that you should substract about 31
from the x-axis to get true absolute magnitudes. Note the correlation: bright elliptical galaxies are redder than small elliptical
galaxies.
9) There are several laws that re-produce the observed luminosity
profile of an elliptical galaxy. The most famous is the de Vaucouleur r1/4 -law. Under the law, the surface brightness of an elliptical galaxy, I (units of ergs cm−2 s−1 arcsec−2 ), as a function
of the distance from the galaxy center, r, is given by
µ
log
I
Ie
(µ
¶
= −3.33071
r
re
¶1/4
)
−1
(14.03)
The key scaling variables in this equation are re and Ie . The
scaling length re is called the effective radius: it is the radius that
encloses half the total light from the galaxy. The variable Ie is
the surface brightness of the galaxy at radius re . Note that with
a little math, (14.03) can be transformed to the form
m = a + b r1/4
(14.04)
where m is the surface brightness of the galaxy (in magnitudes per
square arcsec), and a is the central surface brightness.
Properties of Spiral Galaxies
The properties of spiral galaxies can be summarized as follows:
1) Most spiral galaxies can be de-composed into a elliptical galaxylike bulge, and an exponential law disk. In other words, in the
absense of a bulge, the surface brightness of a spiral galaxy is
simply
µ ¶
I
= e−r/rd
(14.05)
I0
where I0 is the galaxy’s central surface brightness in units of
ergs cm−2 s−1 arcsec−2 and rd is the scale length of the exponential. Not all spiral galaxies have a bulge, and some galaxies are
not easily de-composed into bulge plus disk.
2) The stellar density perpendicular to the disk of a galaxy can also
be parameterized as an exponential. However, the vertical scale
length differs for different types of stars. Below are some rough
vertical scale lengths for stars in solar neighborhood
Object
O stars
Cepheids
B stars
Open Clusters
Interstellar Medium
A stars
F stars
Planetary Nebulae
G Main Sequence Stars
K Main Sequence Stars
White Dwarfs
RR Lyr Stars
Scale Length (pc)
50
50
60
80
120
120
190
260
340
350
400
2000
3) For a long time, it was thought that the central surface brightness
of spiral disks was approximately the same for all galaxies (B ∼
21.7 mag arcsec−2 ). This is now known to be a selection effect.
(It is easier to see high surface brightness objects than low surface
brightness objects.) While the central surface brightness of spiral
galaxies seldom gets brighter than B ∼ 21.7, the distribution of
central surface brightnesses fainter than this is roughly flat.
4) Bright spirals are more metal rich than faint spirals. Similarly,
early-type (Sa, Sb) spirals are, in general, more metal-rich than
equivalent late-type (Sc, Sd) spirals.
5) Most spirals have radial metallicity gradients, such that their central regions are more metal-rich than their outer disks. These
gradients are more pronounced in late-type spirals.
6) The rotation curves of most spiral galaxies are flat with radius.
(That is, the rotation speed stays the same.) Spirals in clusters do
show some evidence for truncation in their gas and mass profile.
7) Most spirals obey the Tully-Fisher relation. Those that don’t are
usually “peculiar” in some way.
Properties of Dwarf Galaxies
Dwarf galaxies have very different properties from either spiral or
elliptical galaxies. Normally, dwarf galaxies are defined as objects
with absolute B magnitudes fainter than −16. There are three
types of dwarf galaxies: dwarf ellipticals (dE), dwarf spheroidals
(dSph), and dwarf irregulars (dI). Unfortunately, astronomers are
very sloppy in their terminology, so it is sometimes hard to understand which type is being talked about.
Dwarf Ellipticals are the low luminosity extension of normal
giant elliptical galaxies; they obey the same relation as their larger
counterparts. An example of a dwarf elliptical is M32. (Actually,
M32 is more compact than a normal elliptical, since it has been
tidally stripped of its outer stars by M31.)
Dwarf Spheroidals are gas-poor, diffuse systems whose density
profile is closer to an exponential disk than an r1/4 law. These
objects do not fall on the elliptical galaxy fundamental plane, and,
in the Morgan classification scheme, would be given the letter “D”
instead of “E”. Examples are NGC 147 and the Leo I dwarf.
Dwarf Irregulars are low-luminosity extensions to spiral galaxies. In general, these objects are brighter than the dSph galaxies
since they have active star formation, but if their star formation
were to cease, they might evolve into a dSph. The Small Magellanic Cloud is a dwarf irregular.
Dwarf galaxies have the following properties:
1) Dwarf galaxies are typically very metal poor (but not as metalpoor as a Pop II globular cluster).
2) Dwarf galaxies show evidence for more than one burst of star formation. (As we’ll see, this is a curious feature.)
3) Dwarf galaxies can be “nucleated.” Their nuclei are sometimes
interpreted as being a small bulge.
4) The mass-to-light ratio of dwarf spheroidals (as measured from the
virial motion of their stars) can be extremely large!
Galaxy Clusters
Before proceeding further, we should now digress slightly and consider the types of classifications of galaxy clusters. There are three
main classification schemes for clusters.
For the very richest clusters, there is the system that George Abell
devised. In the mid 1950’s Abell eyeballed the newly taken Palomar Sky Survey plates, and identified the richest clusters in the
sky. He located the third brightest galaxy in the cluster, estimated its magnitude (m3 ), estimated the brightness of a galaxy 2
magnitudes fainter than the third brightest galaxy (m3 + 2), and,
after estimating and subtracting off the “background”, counted
the number of galaxies with magnitudes between m3 and m3 + 2.
The Abell Richness Class was then determined by the number
of galaxies in this range.
Richness
# of Galaxies
Richness
# of Galaxies
0
1
2
30 – 49
50 – 79
80 – 129
3
4
5
130 - 199
200 - 299
> 300
Complementing the Abell Richness classification is the BautzMorgan classification. This system describes how condensed a
cluster is by the existence (or lack there-of) of a cD galaxy. Clusters with a large, centrally located cD galaxy are classified as
Bautz-Morgan I; clusters whose brightest galaxies are intermediate
between a cD and a normal elliptical galaxy have the Roman numeral II, and clusters with no dominant galaxies are Bautz-Morgan
type III clusters.
Finally, these is the Rood-Sastry classification scheme, which
seeks to organize the evolutionary state of rich cluster in a tuningfork type diagram. At the base of the tuning fork are the regular,
roughly spherical cD clusters. Binary clusters (type B) are next:
these are similar to cD clusters, except that the cluster is dominated by two bright, central galaxies, rather than one. After type
B, the tuning fork divides. On one side are the roughly spherical systems: “C” clusters, in which the bright galaxies are located
near the cluster core, and “I” clusters, which are irregular in shape
with no well defined center. On the other side of the tuning fork
are “L” or linear clusters, in which all the bright galaxies lie along
a line, and “F” clusters, which are distinctly flattened.
The Galaxy Luminosity Function
One of the key pieces in the study of galaxies and galaxy evolution
is the galaxy luminosity function. Traditionally, the number of
galaxies versus absolute luminosity (or absolute magnitude), φ,
has been parameterized by the Schechter luminosity function
∗
α
φ(L)dL = φ∗ (L/L∗ ) e−L/L d(L/L∗ )
(14.06)
Note the form of the equation. For faint galaxies with L ¿ L∗ , the
exponential term goes to 1, and the luminosity function asymptotes to a power law with slope α. At the bright end, where
L > L∗ , the exponential term dominates, and the number of galaxies rapidly goes to zero. The variable φ∗ normalizes the function
and defines the overall density of galaxies in the universe. Note
that L∗ , the absolute luminosity of a bright galaxy at the point of
the exponential cutoff, is often given in terms of magnitudes, i.e.,
M ∗.
Typical numbers for the key parameters of the Schechter function
are α ≈ −1, M ∗ ∼ −21, and φ∗ ∼ 0.002 galaxies per cubic Megaparsec. Note that since there is no cutuff at the faint end of the
Schechter function, the power-law slope of the Schechter function
at faint magnitudes (formally) implies that the total number of
galaxies is infinite. However, the total galaxy luminosity implied
by the Schechter function,
Z
Z
∞
φ(L)LdL =
0
0
∞
α
∗
φ∗ L (L/L∗ ) e−L/L d(L/L∗ ) = φ∗ L∗ Γ(α+2)
(14.07)
is finite. (In the above equation, Γ is the gamma function.)
Finally, if one writes the Schechter function in terms of magnitude,
instead of luminosity, the equation is
φ(M )dM = 0.921φ∗ X α+1 e−X dM
where
X = 100.4(M
∗
−M )
(The proof is left to the enthusiastic student.)
(14.08)
(14.09)
Galaxy Counts
One of the most basic observations an astronomer can perform to
study the evolution of galaxies in the universe is to count galaxies.
The premise of the experiment is straightforward. One can determine the number of galaxies versus apparent magnitude simply by
counting galaxies on plates. One can also predict the number of
galaxies versus apparent magnitude by assuming that galaxies are
distributed throughout the universe and follow the Schechter luminosity function. A simple(?) integral along the line-of-sight then
predicts the observed counts. Any difference between the expected
and observed galaxy counts may be evidence for evolution.
Of course, the experiment is much easier said than done. First,
one needs to perform the integration, i.e., if φ(M ) is the Schechter
function, then
Z
∞
φ(m − 5 log r + 5)dV
N (m)dm =
(14.10)
0
where dV represents the volume element over which the integration
is taking place. For a Euclidean, non-expanding universe, this
would simply be dV = 4πr2 dr. However, in the real world, the
volume element is a complicated function of q0 and z.
A more serious problem is that at large redshifts, galaxies become
difficult to see, due to surface-brightness dimming, and due to
redshifting. The second effect is the most important. For example,
elliptical galaxies are significantly fainter in the ultraviolet than
they are in the optical; Consequently, at large redshifts, they will
be extremely faint. To correct for this, one must know the galaxy’s
spectral energy distribution (SED), and apply a K-correction.
However, the K-correction for spiral galaxies is different from that
of ellipticals, so one also needs to know the fraction of galaxies of
each type. And, of course, if there is evolution in the galaxy types,
the result will be wrong.
A few years ago, the analysis of galaxy counts indicated a strong
excess of faint blue galaxies over the predictions of models. The
immediate interpretation was that evolution had been detected in
the form of a new, large population of star-forming galaxies at
moderate redshifts. A perhaps better explanation came later: it
is possible that the intrinsic luminosity function of galaxies is not
a Schechter function, and there is an excess of faint galaxies over
and above what is predicted from the Schechter function. In this
case, the faint blue fuzzies are nearby dwarf irregular galaxies.