ASTR2100

1
27. The Structure of the Universe Goals 1.
Examine the various techniques used to establish
distances to galaxies, noting the strengths and
weaknesses of each. 2. Note how the nature of the
universe is revealed by both the spatial
distribution of galaxies and their 3-dimensional
mapping using radial velocity distances. 3. Note
how clusters and superclusters of galaxies
delineate the spongy nature of the universe at
large scales.
2
The Extragalactic Distance Scale The techniques
used to establish distances to galaxies are
varied, although each depends directly or
indirectly upon a local calibration of distances
based upon trigonometric parallaxes for stars
and/or star cluster main-sequence fitting. The
method of measuring trigonometric parallaxes has
a long and colourful history that seems unlikely
to end. The Hipparcos mission of the mid 90s was
intended to supplant the old technique of
measuring absolute parallaxes for stars through
the intermediary of relative parallaxes, but
seems to have run afowl of systematic errors of
its own. The problem is only now coming to light.
Hipparcos parallaxes also suffer from a magnitude
limit near 10, which means that many important
types of stars were not on the program of
observation. The technique of calibrating
distances using open cluster main-sequence
fitting has been more reliable overall.
3
Evidence for a robust calibration of the Cepheid
period-luminosity relation from cluster
Cepheids is seen in the figures. Cluster
Cepheids and Cepheids with Parallaxes from the
Hubble Space Telescope (old style and solid)
define the same PL relation.
4
Evidence for a systematic error in Hipparcos
parallaxes for Cepheids is also seen. The
cluster PL calibrations validity is demonstrated
by the fact that it matches the distance to the
galaxy NGC 4258 found geometrically from
masers. Cepheid distances generally use a
Wesenheit (reddening-free) relation rather than
PLC (period- luminosity-colour) relation.
5
A typical Wesenheit formula is where the lt gt
brackets denote intensity means of the
corresponding magnitudes. Wilson-Bappu
Effect. The Wilson-Bappu effect is a direct
correlation between the luminosity of a star and
the width of the central emission core of the
single-ionized calcium K-line in late-type stars
(spectral types G and K). Since it appears to
apply to bright giants as well as dwarfs, it
spans a large range of luminosity. The
relationship is typically calibrated using
parallaxes, but is much less accurate (typically
0.6 magnitude) than cluster main-sequence
fitting, so sees very limited applications in
calibration work. The central emission reversal
in Ca II K-line cores originates in
optically-thin spectral lines from overlying
chromospheric gas.
6
The Cepheid Distance Scale. Despite the solid
nature of the calibration of the Cepheid PL
relation, problems still arise. The manner of
extracting photometric magnitudes for crowded
stars in distance galaxies is not without
criticism, and many existing relationships rely
upon Magellanic Cloud Cepheids as calibrators
rather than Galactic calibrators. The Galactic
calibration of the Cepheid PL relation is
supported not only by HST parallaxes and cluster
parallaxes, but also by calibrations tied to the
Baade-Wesselink method, which uses Cepheid
photometry in combination with radial velocity
variations to deduce Cepheid luminosities
directly. Magellanic Cloud Cepheid suffer from
two problems (i) an uncertain distance to the
LMC (the most commonly-used distance modulus is
18.50), and (ii) the question of a metallicity
dependence on Cepheid luminosities. Galactic
Cepheids have metallicities like those in nearby
spiral galaxies, whereas LMC Cepheids are
metal-poor by comparison.
7
RR Lyrae Variables and Type II Cepheids. These
types of Cepheids are lower-mass (0.5-2.0 M?)
pulsators that also appear to obey a PL relation,
but one that is less luminous than that for
classical Cepheids. Their lower luminosities
reflect their origin from older, often
metal-poor, lower-mass stars, but it also means
that they are more difficult to detect than
classical Cepheids in nearby galaxies. Often they
are simply ignored. But see the recent work of
Dan Majaess on a calibration of the PL relation
for Type II Cepheids, and how it confirms the
distances to nearby galaxies established from
classical Cepheids. The variables are often
detected in the same surveys of nearby galaxies
made to measure the brightness changes of their
classical Cepheids, and a number of other
researchers have begun to make use of them as
secondary distance calibrators for the sample of
Cepheid calibrating galaxies.
8
Type II Cepheids in nearby galaxies, taken from
published observations of variable stars in the
galaxies by Dan Majaess. In each case the
upper two relations represent expectations for
classical and overtone Cepheids, while the lower
line represents a Wesenheit relation for Type
II Cepheids. Note that some Type II
Cepheids have pulsation periods as long as some
classical Cepheids, and are about as luminous.
Their potential as standard candles for the
extragalactic distance scale is very real.
9
M Supergiants and Type C Semiregular
Variables. These stars are pulsating M
supergiants with periods often in excess of 1-2
years. Yet they also appear to obey a PL
relation, making them particularly valuable as
distance candles. They are more luminous than
Cepheids, and are apparently more numerous in
spiral galaxies, but little work has been done to
use them as calibrators.
10
M supergiants saw use as distance indicators
differently 30 years ago when stellar
evolutionary models by the Geneva group revealed
that very massive stars (M gt 25 M?) never make it
to the red side of the HR diagram during
post-main-sequence evolution. Humphreys noted an
upper limit for M supergiant luminosities near
MV 7.5 (Mbol 9.5), which can be used as a
standard candle provided that either photometry
or spectroscopy is available for the brightest
stars in a galaxy to identify the M supergiants
(BV 1.7).
11
H II Regions. Sandage and Tammann expended
considerable effort to establish the diameters of
H II regions as a standard candle 40 years ago,
but the technique was never particularly
reliable. The diameter of an H II region depends
in a complicated fashion on the masses of the
stars in the driving cluster at its core as well
as its ages (older H II regions have had time to
expand) and the density of gas in its
surroundings. The technique has died out in
recent years, which is probably a good thing.
There is an obvious limit to its usefulness as a
standard candle in any event, since the H II
region must be resolved as such for the technique
to apply.
12
Type Ia Supernovae. There are several different
types of supernovae, distinguishable by
differences in their light curves and the
spectral lines they display near maximum light.
The spectral features and light curve shapes have
been organized over the years into types I and
II, where type I supernovae lack hydrogen lines
and Type II do contain hydrogen lines. Subtypes
are recognized by differences in their light
curves or spectra, and are summarized
below Supernova Type Spectra Ia Lacks H and
displays a Si II line at 615.0 nm near peak
light Ib He I line at 587.6 nm and no Si II line
at 615 nm Ic Weak or no He lines and no Si II
line at 615 nm IIP Reaches a plateau in its
light curve IIL Displays a linear decrease in
its light curve Type II supernovae are the
expected terminal stage in the evolution of
massive stars, while Type I supernovae may have a
variety of origins. Type Ia supernovae are the
objects of interest as extragalactic distance
indicators.
13
Several means exist for creating Type Ia
supernovae. All share a common underlying
mechanism, deflagration of a CO white dwarf
bumped over the Chandrasekhar limit ( 1.38 M?
for a non-rotating star) through mass accretion
in a close binary system. The CO white dwarf is
no longer able to support itself through electron
degeneracy pressure and begins to collapse. Many
believe the upper mass limit is not formally
attained. Increasing temperature and density
inside the core ignite carbon fusion as the star
approaches the limit (to within about 1) before
collapse is initiated. Within a few seconds, a
substantial fraction of the stars matter
undergoes nuclear fusion, releasing enough energy
(12 1044 J) to unbind the star in a supernova
explosion. An outwardly expanding shock wave is
generated, reaching velocities of order
5,00020,000 km/s, 0.03c. A significant increase
in luminosity occurs, the supernova reaching an
absolute magnitude of 19.3 with little
variation. The last property is what makes them
so valuable as distance indicators.

14
In order to be used as a distance indicator, a
Type Ia supernova must first be identified as
such (spectroscopy), then it must be followed
photometrically in order to establish a
reasonably complete light curve. Maximum light
for the supernova may have been unobserved, but
the light curve is regular enough that the time
of light maximum can usually be established
reliably.
15
Light curve shape for Type Ia supernovae in
different wavebands, and the relationship between
decline rate and maximum luminosity. Templates
are frequently used to match the light curve in
order to attain a best fit overall.
16
Example (textbook). The Type Ia supernova SN
1963p in the galaxy NGC 1084 had an apparent blue
magnitude of B 14.0 at maximum light. Calculate
the distance to the supernova for an extinction
of AB 0.49. (B AB) MB 5 log d 5 ,
so log d (B AB MB 5)/5 (14.0 0.49
19.3 5)/5 37.81/5 7.562 So d
107.562 36.5 Mpc So why does the textbook give
41.9 Mpc???
17
Novae. Novae are less luminous than supernova
and originate differently, enough to produce a
range of luminosities at light maximum. They are
also created in close binary systems when a
compact white dwarf accumulates mass from its
companion. In the case of novae, the white dwarf
is not near the Chandrasekhar limit and the
accreted gas undergoes thermonuclear burn-off
near the surface of the white dwarf. More massive
white dwarfs are also smaller, producing greater
compression of the accreted mass and a hotter,
briefer explosive response that produces a
brighter nova of shorter duration. There is a
moderately tight relation between Mmax and rate
of decline first noted by Arp in 1956 for M31
novae. They are roughly as luminous as the most
luminous Cepheids.
18
Globular Cluster Luminosity Functions. This
technique was described previously in Chapter 25,
and has been used as a secondary means of
establishing distances to galaxies as distant as
the Virgo cluster. Application of the technique
involves fitting a Gaussian profile to counts of
globular clusters as a function of apparent
magnitude, using the derived width and location
of maximum of the fitted profile to deduce both
the richness of the globular cluster population
for the galaxy and its distance modulus relative
to the maximum derived for Milky Way globulars.
Of course the globulars must first be
distinguished from stars. Application to Virgo
cluster galaxies by Harris is indicated in the
figure.
19
Planetary Nebulae Luminosity Functions. Evolution
ary tracks are displayed for stars evolving from
the asymptotic giant branch (AGB) through the
central star of planetary nebula (PN) stage, for
M 0.535, 0.569, 0.597, 0.633, 0.677, 0.754,
and 0.900 M? (bottom to top), compared with the
location of actual central stars of PN. At the
high mass end the evolution is too fast to
permit creation of a PN. The most probable mass
is 0.6-0.7 M?, typical of white dwarfs.
20
The upper luminosity limit is also seen in the
maximum luminosities of the PNe themselves, and
can be used as a distance indicator, as indicated
here for M31 and Leo group PNe. The PNe are
detected through narrow band photometry and then
counted as a function of magnitude. The
luminosity cutoff is well-defined, and PN
distances compare well with Cepheid distances.
PNe have also been used to estimate the distance
to the Galactic centre.
21
Surface Brightness Fluctuation Method. Surface
brightness fluctuation (SBF) is a secondary
distance indicator used to estimate distances to
galaxies. The technique uses the fact that
galaxies are made up of a finite number of stars.
The number of stars in any small patch of the
galaxy will vary from point to point, creating a
noise-like fluctuation in the surface brightness
distribution. While the various stars present in
a galaxy will cover an enormous range in
luminosity, the SBF can be characterized as if
all stars had the same brightness, which is the
luminosity-weighted integral over the luminosity
distribution of stars. Older elliptical galaxies
have fairly consistent stellar populations, thus
the typical fluctuation star closely
approximates a standard candle. In practice,
corrections are required to account for
variations in age or metallicity from galaxy to
galaxy.
22
The SBF pattern is measured from the power
spectrum of the residuals left behind from a deep
galaxy image after a smooth model of the galaxy
has been subtracted. The SBF pattern is evident
as the transform of the point spread function in
the Fourier domain. The amplitude of the spectrum
gives the luminosity of the fluctuation star.
Since the technique depends on a precise
understanding of the image structure of the
galaxy, extraneous sources such as globular
clusters and background galaxies must be excluded
from the analysis, as well as areas of
interstellar dust absorption. In practice it
means that SBF works best for elliptical galaxies
or the bulges of S0 galaxies, since spiral
galaxies generally have complex morphologies and
extensive dust features. SBF is calibrated by
use of fiducial Cepheid Period-Luminosity
relation (P-L) based on observations of variables
located in the Large Magellanic Cloud (Tonry
1991).
23
An example of the surface brightness
fluctuation technique applied to galaxies in
various cluster groups, including the Local
Group. Note that the relationship has a
distinct shape for galaxies of comparable
distance.
24
The Tully-Fisher Relation. The Tully-Fisher
relation was introduced in Chapter 25. Its
application to the determination of distances
to spiral galaxies requires a calibration,
usually using galaxies whose distances are
established using Cepheids or other techniques.
Note that any recalibration of distances to the
claibrating galaxies affects secondary
techniques like the TF relation. The TF
relation in various passbands is illustrated at
right.
25
The D-s Relation. The Faber-Jackson
relationship, which expresses the power-law
correlation between an elliptical galaxys
luminosity and its internal velocity dispersion,
was also introduced in Chapter 25. The technique
displays considerable scatter (see figure at
right), however, so a modification has been
developed in recent years that is referred to
as the D-s relation.
26
Two groups conducting surveys of elliptical
galaxies arrived independently at a new result
the FJ correlation could be tightened
considerably by the addition of a third
parameter, namely surface brightness. In its
modern incarnation, the new correlation has
become known as the Dn-s relation a power-law
correlation between the luminous diameter Dn and
the internal velocity dispersion se,
namely where ? 1.20 0.10 according to some
researchers. More broadly, the Dn-s relation and
its variants may be viewed as manifestations of
the Fundamental Plane (FP) of elliptical
galaxies, a planar region in the 3-dimensional
space of structural parameters in which normal
ellipticals are found. One expression of the FP
relates effective diameter to internal velocity
dispersion and central I-band surface
brightness where a 1.44 0.04 and ß 0.79
0.04.
27
Two versions of the Fundamental Plane for Virgo
cluster and Coma cluster elliptical galaxies.
28
Brightest Galaxies in Clusters. Studies of
clusters of galaxies (e.g. Schechter 1976)
indicate that the magnitude of the brightest
galaxy in a cluster, or better yet, the 10th
brightest galaxy in a cluster, is tightly
constrained in luminosity, hence making it a
good distance indicator.
29
The technique has become more sophisticated in
recent years (see below), although less
complicated versions can be just as reliable.
Below is the Hubble diagram for the Lauer
Postman (1992) BCG sample. Apparent magnitude
within rm is plotted against log redshift. The
straight line plotted through the points has
slope 5, the relation expected for a linear
Hubble flow.
30
An example of a calibration of m10 (magnitude of
the 10th brightest cluster galaxy) versus log
redshift (z) for some galaxy surveys (lower
left), and how that translates into a study of
galaxy cluster ellipticity e as a function of
implied redshift z (lower right). Note how more
distant galaxy clusters tend to be less
spherically symmetric than nearby galaxy
clusters.
31
Eclipsing Binaries. In 1994 a group including Ed
Guinan (Villanova) proposed the use of
extragalactic eclipsing binaries with
well-determined physical properties as standard
candles to improve the extragalactic distance
scale. The advent of high quantum efficiency/low
noise CCDs makes it possible to obtain high
precision light and radial velocity curves for
the more luminous OB-type eclipsing binaries in
the Magellanic Clouds with even small to moderate
size (12m) telescopes. That can lead to the
determination of distance moduli (m-M)0 to the
LMC and SMC with precisions of about 0m.15 for
individual binaries. The distances are
essentially free from the assumptions made using
other distance indicators. The technique makes
use of Wilson-Devinney code models for eclipsing
binaries, but is otherwise independent of
parallax and proper motion data.
32
Application of the technique to an eclipsing OB
system in M33 by Bonanos et al. (2006). Note
precision of 0m.12, after correction for
reddening.
33
Gravitational Lens Time Delay and H0. When a
quasar is viewed through a gravitational lens,
multiple images are seen. The light paths from
the quasar that form the images have different
lengths that differ by approximately d?(cos ?1
cos ?2) where ?s are the deflection angles and d
is the distance to the quasar. Since quasars are
time variable sources, the path length difference
can be measured by looking for a time-shifted
correlated variability in the multiple
images. By 1996 the time delay had been
measured in 4 quasars, giving H0 63 12
km/s/Mpc, H0 42 km/s/Mpc, although another
analysis of the same data gave H0 60 17
km/s/Mpc, H0 52 11 km/s/Mpc, H0 63 15
km/s/Mpc, and H0 71 20 km/s/Mpc.
34
The time delay in separate images A and B of the
double QSO 0957561.
35
The more usual form of gravitational lensing by a
rich cluster of galaxies.

36
Sunyaev-Zeldovich Effect and H0. Hot gas in
clusters of galaxies distorts the spectrum of the
cosmic microwave background observed through the
cluster. The hot electrons in a cluster scatter a
small fraction of the cosmic microwave background
photons and replace them with photons of slightly
higher energy. The difference between the CMB
seen through the cluster and the unmodified CMB
seen elsewhere on the sky can be measured.
Actually only about 1 of the photons passing
through the cluster are scattered by the
electrons in the hot ionized gas in the cluster,
and those photons have their energies increased
by an average of about 2. That leads to a
shortage of low energy photons of about 0.01?0.02
0.0002 or 0.02, which gives a decrease in the
brightness temperature of 500 mK. At high
frequencies ( 218 GHz) the cluster appears
brighter than the background. The effect is
proportional to the number density of electrons,
the thickness of the cluster along the line of
sight, and the electron temperature.
37
The parameter that combines those factors is
called the Kompaneets y parameter, y t(kT/mc2),
where t is the optical depth or the fraction of
photons scattered, while (kT/mc2) is the electron
temperature in units of the rest mass of the
electron. The X-ray emission IX from the hot gas
in the cluster is proportional to the square of
the number density of electrons, the thickness of
the cluster along our line of sight (LOS), and
the electron temperature and X-ray frequency. As
a result, the ratio y2/IX constant ?
(Thickness along LOS) ? f(T) If the thickness
along the LOS is assumed to be the same as the
diameter of the cluster, the observed angular
diameter can be used to find the distance. The
technique is very difficult, but recent work with
closely packed radio interferometers operating at
30 GHz has given precise measurements of the
radio brightness decrement for 18 clusters only
a few have adequate X-ray data. A recent
Sunyaev-Zeldovich determination of the Hubble
constant gave 77 10 km/s/Mpc from 38 clusters.
38
Distance Indicator Summary. From textbook,
although results suspect.
39
The Expansion of the Universe With the
distances to nearby galaxies established via the
various techniques outlined in the previous
section, with highest weight to those using the
Cepheids and Type Ia supernovae, it is found that
there is a correlation of the Doppler shift of a
galaxys spectrum with distance. The effect was
first noted by Slipher in 1914, but was later
elaborated upon by Hubble in 1929 and by Hubble
and Humason in 1934. The relationship is linear
for nearby galaxies, and corresponds to an
increase in a galaxys velocity of recession v
with increasing distance d. Known as the Hubble
Law, it is generally described as where H0 is
the Hubble constant , always cited in units of
km/s per Mpc, i.e. km s1 Mpc1. Typical current
values have been found to lie in the range 50100
km s1 Mpc1, with best values lying around 72
km s1 Mpc1.
40
Redshift-Distance Relation. Cluster elliptical
galaxies of different redshift, and how that
correlates with distance (distances recalibrated
for figure at right).
41
The Hubble Law is not a peculiarity of our local
galactic neighbourhood, but reflects an actual
expansion of space, referred to as the Hubble
flow. Individual galaxies can display their own
peculiar velocities within the Hubble flow, as
well as translational effects arising from the
gravitational attraction of nearby superclusters.
Velocities and distances are often found with the
standard Doppler equation and For
large velocities (approaching c), the
relativistic velocity and distance equations
become and
42
Cosmological redshifts include the effects of any
change in the rate of expansion of the universe
relative to distant epochs, namely
through The value of the Hubble constant has
undergone a lot of change since the time of
Hubble, who originally estimated it to be 500 km
s1 Mpc1. The results of the Hubble Key Project
to measure H0 using Cepheids in nearby galaxies
has produced a value of H0 72 8 km s1 Mpc1
(Freedman et al. 2000). That result is
essentially identical to a value of H0 71 4 km
s1 Mpc1 deduced from minute fluctuations in the
cosmic microwave background by the Wilkinson
Microwave Anisotropy Probe (WMAP) satellite. To
take into account possible future changes, many
astronomers use a dimensionless constant h, where
43
The nature of the Hubble Law indicates that the
universe is expanding. Given that observed
feature, it is natural to conclude that at some
distant epoch all of the observable mass in the
universe originated at some unique point in a
creation event. The term Big Bang originated
with Fred Hoyle in 1949, who was describing the
difference between steady state cosmology and big
bang cosmology to listeners on a BBC radio
program. Since the rate of expansion of the
universe is established, it is possible to
determine its age since the Big Bang, provided
that the expansion rate has been constant. The
resulting time is called the Hubble time, and
corresponds to That value is usually taken
to be a good estimate for the age of the universe.
44
Clusters of Galaxies Astronomers consider that,
on the largest scales, the universe is
homogeneous and isotropic, which is known as the
cosmological principle, namely all points in
space ought to experience the same physical
development, correlated in time in such a way
that all points at a certain distance from an
observer appear to be at the same stage of
development. In that sense, all spatial
conditions in the universe must appear to be
homogeneous and isotropic to an observer at all
times in the future and in the past. Homogeneous
implies the same everywhere, while isotropic
implies having the same properties in all
directions viewed. On small scales that is
clearly not the case, since galaxies spatially
tend to clump into groups, clusters, and
superclusters of ever-increasing dimension,
numbers, and mass.
45
Typical properties of galaxy groupings Type Memb
ers Diameter s (km/s) M/M? M/L Group lt50 1
Mpc 150 1013 200 Cluster 50/gt1000 5
Mpc 800-1000 1015 300
46
The Local Group. The schematic of the Local
Group has dashed lines of constant radius about
the system barycentre between M31 and the Milky
Way. Note the spatial proximity of M33 to M31,
and the satellites of M31 and the MW.
47
Other Groups Within 10 Mpc. Although there are
40 galaxies (and probably many more of low
luminosity) lying within a concentration roughly
1 Mpc across containing the Milky Way, LMC, SMC,
M31, and M33, with the NGC 3109/Sextans Group
debated with regard to its inclusion, there are a
variety of other nearby galaxy groups within 10
Mpc. That includes the Sculptor Group (1.8 Mpc),
the M81 Group (3.1 Mpc), the Centaurus Group (3.5
Mpc), the M101 Group (7.7 Mpc), the M66 Group
(9.4 Mpc), the M96 Group (9.4 Mpc), and the NGC
1023 Group (9.5 Mpc). The locations of the above
groups relative to the Milky Way are depicted in
the figure, which is plotted in supergalactic
coordinates with the y-axis in the direction of
the Virgo Cluster. Note that the local
concentrations of galaxies are also associated
with regions of low galaxy density, termed voids.
That characteristic is also seen on larger scales.
48
The local concentrations of galaxies, relative to
the Mily Way at (0, 0), as plotted in
supergalactic cordinates.
49
Virgo Cluster. The Virgo Cluster is the nearest
rich cluster, located on the Virgo/Coma Bernices
boundary 16 Mpc distant, containing 3,000
galaxies or more within a region 3 Mpc across.
The image below contains M86 (top left), M84 (top
right), and NGC 4388 (bottom).
50
Some of the galaxies in the Virgo Cluster
actually have blueshifted velocities relative to
the Milky Way, because of their large orbital
speeds about the cluster barycentre. Many of the
spirals in the cluster exhibit evidence of being
stripped of gas from their outer regions. X-ray
spectra of the cluster centre can be represented
by a single-temperature plasma in which the
temperature of the intracluster medium decreases
with radius from 0' to 50', and becomes almost
constant beyond the 50' radius. The metal
abundances also decrease with radius from 0' to
40', then become constant beyond 40'. The X-ray
image of the cluster at right is centred on the
peculiar galaxy M87, which appears to dominate
the dynamics of the intracluster medium in the
Virgo cluster.
51
Evidence for ram pressure stripping of gas and
dust in Virgo cluster galaxies is evident in HST
images of the spiral galaxies NGC 4522 (left) and
NGC 4402 (right).
52
Wu Tremaine (2006, ApJ, 643, 210) estimate a
mass of 2.4 ? 1012 M? within 32 kpc of M87
according to the dynamics of its globular cluster
system. Does it reach 3 ? 1013 M? within 300
kpc (textbook)?
53
Coma Cluster. The Coma cluster is an even richer
cluster of galaxies lying 15 north of the Virgo
cluster, 90 Mpc distant, and 6 Mpc across. It
may contain of order 10,000 galaxies or more, but
most are too faint to be detected.
54
The mass of the Coma cluster is often estimated
using the Virial Theorem, as in Example 27.3.1 of
the textbook. Let us examine the technique
critically. The standard formulation is where
ltTgt is the average kinetic energy of the galaxies
and ltUgt is their average potential. Both terms
are readily evaluated to produce the
relationship where M is the mass of the
cluster, ltRgt is its average radius, and ltv2gt is
the velocity dispersion of its member galaxies.
The equation can be rearranged to evaluate the
mass of a cluster in terms of its radius and
velocity dispersion
55
Note that the textbook uses 5 rather than 2
in the numerator. That is to account for the fact
that the radial velocity dispersion accounts for
only the line-of-sight component and not
transverse motions. The same equation is used to
estimate the masses of Galactic star clusters,
but with 2 or 3 not 5. Given the
uncertainties associated with measurements of vR
for galaxies, it is not clear that any increment
is needed. For open cluster studies, the equation
is usually evaluated as ltRgt 3 Mpc and
ltv2gt½ 977 km/s result in a value of M 1.3 ?
1015 M? for the Coma cluster. The total
luminosity of 5 ? 1012 L? is affected only at the
few percent level by dwarf galaxies lying at the
sky limit, so the mass-to-light ratio is 260
M?/L?, rather than 660.
56
The Coma cluster is a strong source of X-rays
that originate from a rich intergalactic medium.
The thermal bremsstrahlung spectrum of the
cluster (below) is matched by model temperature
of 8.8 ? 107 K. Rough estimates for some of the
parameters leads to an estimate for the gas
mass of in other words, 10 of the
total mass estimated for the cluster, which is
fairly typical.
57
The X-ray spectrum of the hot gas also displays
emission lines from highly ionized states of
iron, oxygen, and neon i.e. Fe XXV, Fe XXVI, O
VII, O VIII, Ne IX. Since the iron can only
originate from the gas ejected into the
interstellar medium from supernovae explosions,
the implication is that the material in the
intracluster medium of the Coma cluster has been
produced through collisions between galaxies and
ram-pressure gas stripping of the clusters
spiral and irregular galaxies. When galaxies
move through the intracluster gas at speeds of
several thousand km/s, ram pressure stripping
is very important, as also noted for some of
the spirals in the Virgo cluster.
58
The Local Supercluster. The Coma cluster lies
roughly in the same direction as the Virgo
cluster, but beyond it. The Virgo cluster is part
of a larger conglomeration of galaxy groups that
includes the Local Group and other galaxy groups
lying towards the Virgo cluster. The
supercluster of galaxies is 70 Mpc across
centred on the Virgo cluster, with the Coma
cluster lying just beyond. The Local Group
appears to experience a Virgocentric flow
towards the supercluster barycentre.
59
There appears to be a larger streaming motion of
the Local Group and the Virgo cluster relative to
the Hubble flow towards the constellation of
Centaurus. This peculiar motion is on the order
600 km/s. There is another supercluster, the
Hydra-Centaurus supercluster, lying in that
direction, but it apparently suffers its own
streaming motion along that line-of-sight. The
presence of a Great Attractor 45 Mpc distant was
postulated by Alan Dressler and Sandra Faber in
the 1980s on the basis of radial velocity
perturbations (below).
60
The Shapley concentration is a supercluster of
20 rich galaxy clusters 200 Mpc distant that
also lies roughly in this direction, although
beyond the distance estimated for the Great
Attractor. Estimates of galaxy distances tied to
Type Ia supernovae indicate that streaming
motions disappear at distances in excess of 90
Mpc, in fact that they apparently may not exist
at all! This is perhaps a topic worthy of further
investigation.
61
Bubbles, Voids, and Strands. Extensive surveys
have been made of galaxies, e.g., example the
Palomar Sky Survey and its extension. The
location and brightnesses of galaxies near the
SGP indicate the patchy nature of their
distribution.
62
Redshift surveys in selected bands of sky
further accentuate the patchy nature of the
distribution of galaxies, which is marked by
bubbles containing very few galaxies surrounded
by denser strands rich in clusters and
superclusters of galaxies.
63
The CfA survey of Huchra and Geller.
64
The CfA survey of Huchra and Geller.
65
The 2dF Galaxy Redshift Survey. The largest voids
measure 100 Mpc across.
66
A remaining question is whether or not this
fractal nature of the distribution of galaxies
continues or is truncated beyond a specific
redshift, beyond which the homogeneity of the
universe reasserts itself. The origin of the
strands is hotly debated.
67
The rich
68
The curious