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 Galaxies (8/9)

H.01 How many stars, galaxies, clusters, QSO's etc. in the Universe?
H.02 Is there dark matter in galaxies?
    

H. How many stars, galaxies, clusters, QSO's etc. in the Universe?

The various parts of this question will be considered separately.
Also, rather consider how many stars there are in the Universe, we'll
consider how many stars there are in the Milky Way.  The number of
stars in the Universe can be estimated by multiplying the number of
stars in the Milky Way by the number of galaxies in the Universe.

H.01.1 How many stars are there in the Milky Way?

My standard answer in introductory astronomy classes is "about as many
as the number of hamburgers sold by McDonald's." Being more precise
requires an extrapolation, because we can't see all the individual
stars in the Milky Way for two reasons---distance and dust absorption.

Both factors make stars appear dimmer. Observations at visible
wavelengths are limited to a region of (more or less) 5000 light-years
radius about the Sun, with a few windows in the intervening dust
giving us glimpses of more distant areas (especially near the Galactic
center). Our map of the Galaxy gets correspondingly more sketchy with
distance. Guided somewhat by observations of other spiral galaxies, we
think that the overall run of star density with radius is fairly well
known. Getting a total stellar head count is more of a problem,
because the stars that we can see to the greatest distances are also
the rarest. Measurements of the relative numbers of stars with
different absolute brightness (known in the trade as the luminosity
function) shows that, for example, for every Sun-like star there are
about 200 faint red M dwarfs. These are so faint that the closest,
Proxima Centauri, despite being closer to the Sun than any other
(known) star, takes very large binoculars or a telescope to find.  So,
to get the total stellar population in the Milky Way, we must take the
number of luminous stars that we can see at large distances and assume
that we know how many fainter stars go along with them. Recent numbers
give about 400,000,000,000 (400 billion) stars, but a 50% error either
way is quite plausible. Much of the interest in "brown dwarfs" stems
from a similar issue---a huge number of brown dwarfs would not change
how bright the Galaxy appears (at visible wavelengths), but would
change its total mass quite substantially. Oddly enough, within a
particular region, we probably know the total mass and luminosity
rather more accurately than we do just how many stars are producing
that light (since the most common stars are by far the dimmest).

H.01.2 How many galaxies in the Universe?

A widely-distributed press release about the Hubble Deep Field
observations, <URL:http://oposite.stsci.edu/pubinfo/PR/96/01.html>,
reported the discovery of a vast number of new galaxies.  The
existence of many galaxies too faint to be hitherto detected was no
surprise, and calculations of the number of galaxies in the observable
Universe and searches for how they change with cosmic time must always
allow for the ones we can't detect, through some combination of
intrinsic faintness and great distance. What was of great interest in
the Hubble Deep field (and similar) data was just how any faint
galaxies were detected and what their colors and forms are. Depending
on just what level of statistical error can be tolerated, catalogs of
galaxies in the Hubble Deep Field list about 3000. This field covers
an area of sky of only about 0.04 degrees on a side, meaning that we
would need 27,000,000 such patches to cover the whole sky.  Ignoring
such factors as absorption by dust in our own Galaxy, which make it
harder to see outside in some directions, the Hubble telescope is
capable of detecting about 80 billion galaxies (although not all of
these within the foreseeable future!).  In fact, there must be many
more than this, even within the observable Universe, since the most
common kind of galaxy in our own neighborhood is the faint dwarfs
which are difficult enough to see nearby, much less at large
cosmological distances. For example, in our own local group, there are
3 or 4 giant galaxies which would be detectable at a billion
light-years or more (Andromeda, the Milky Way, the Pinwheel in
Triangulum, and maybe the Large Magellanic Cloud). However, there are
at least another 20 faint members, which would be difficult to find at
100 million light-years, much less the billions of light years to
which the brightest galaxies can be seen.

H.01.3 How many globular clusters in the Milky Way?

We are on firmer ground with this one, since globular clusters are
fairly large and luminous. The only places where our census in the
Milky Way is incomplete are regions close to the galactic disk and
behind large amounts of absorbing dust, and for the fainter clusters
that are farthest from the Milky Way just now. The electronic version
of the 1981 Catalogue of Star Clusters and Associations. II. Globular
Clusters by J. Ruprecht, B. Balazs, and R.E. White lists 137 globular
clusters in and around the Milky Way. More recent discoveries have
added a handful, especially in the heavily reddened regions in the
inner Galaxy. As a rough estimate accounting for the regions that
cannot yet be searched adequately, our galaxy should have perhaps 200
total globulars, compared with the approximately 250 actually found
for the larger and brighter Andromeda galaxy.

H.01.4 How many open clusters?

Here we must extrapolate again, since open clusters can be difficult
to find against rich star fields in the plane of the Milky Way, and
since richer clusters may be identified farther away than poor
ones. The electronic version of the catalogue of open cluster data
compiled by Gosta Lynga, Lund Observatory, Box 43, S-221 00 Lund,
Sweden, 1987 version, lists 1111 identified open clusters in our
galaxy. There are certainly at least ten times this number, since we
have trouble seeing even rich open clusters more than about 7000
light-years away in most directions through the obscuring dust in the
plane of our Galaxy. This effect is especially acute since young star
clusters are strongly concentrated to this plane (no coincidence since
the gas from which new clusters are formed is associated with dust).

H.  Is there dark matter in the Universe?

Dark matter is matter that is detected by its gravitational effect on
other matter rather than because of its electromagnetic radiation
(i.e., light).  This might be because of one of two reasons: 1. The
matter may emit light, but the light is so faint that we cannot detect
it; an example of this kind of matter is interstellar planets.  2.
The matter might not interact with light at all; an example of this
kind of matter is neutrinos.

The first astronomical instances of "dark matter" were probably the
white dwarf Sirius B and the planet Neptune.  The existence of both
objects was inferred by their gravitational effects on a nearby object
(Sirius A and the planet Uranus, respectively) before they were seen
directly.

H.02.1 Evidence for dark matter

There are many independent lines of evidence that most of the matter
in the universe is dark.  Essentially, many of these measurements rely
on "weighing" an object such as a galaxy or a cluster of galaxies by
observing the motions of objects within it, and calculating how much
gravity is required to prevent it flying apart.

(1) Rotation patterns in spiral galaxies.
(2) Velocities of galaxies in clusters.
(3) Gravitational lensing.
(4) Hot gas in galaxies and clusters.
(5) Large-scale motions. 

(1) Rotation patterns in spiral galaxies. The disks of spirals are
full of stars and gas in nearly circular coplanar orbits, making them
wonderful tracers for the gravitational field in which they move.  In
centrally-concentrated masses, such as within the solar system (where
most of the mass is concentrated in the Sun), the
velocity-vs.-distance relation approaches Kepler's 3rd Law, velocity^2
= constant * central mass / distance.  Once we sample outside the
central concentration of stars, using observations of the 21cm line
emitted by neutral hydrogen clouds, spiral galaxies violate this
velocity-distance relation quite flagrantly; velocity=constant is a
good approximation (hence the moniker "flat rotation curves").  A
sample picture and rotation curve is at
<URL:http://crux.astr.ua.edu/gifimages/ngc5746.html>. To get this
pattern, one needs a mass distribution that goes as density
proportional to 1/radius^2, much fluffier than the observable stars
and gas in the galaxy, and in an amount that may be 10 or more times
the total mass we can account for with stars, dead stellar remnants,
gas, and dust.  There were hints of this issue for a while, but it was
a series of observations by Vera Rubin and collaborators in the
mid-1970's that really rubbed our noses in it.

(2) Velocities of galaxies in clusters.  Galaxies in clusters have
random orbits.  By measuring the dispersion for, e.g., 100 galaxies in
the cluster, one finds typical dispersions of 1000 km/s. The clusters
must be held together by gravity, otherwise the galaxies would escape
in less than 1 billion years; cluster masses are required to be at
least 10 times what the galaxies' stars can account for.  This problem
was first demonstrated in 1938 by Fritz Zwicky who studied the
galaxy-rich Coma cluster.  Zwicky was very bright, very arrogant, and
highly insulting to anyone he felt was beneath him, so this took a
long while to sink in. Today we know that virtually all clusters of
galaxies show the same thing.

(3) Gravitational lensing. General relativity shows that we can treat
gravity (more precisely than in Newtonian dynamics) by considering it
as a matter-induced warping of otherwise flat spacetime. One of the
consequences of this is that, viewed from a distance, a large enough
mass will bend the paths of light rays.  Thus, background objects seen
past a large mass (galaxy or cluster of galaxies) are either multiply
imaged or distorted into "arcs" and "arclets."  Some beautiful
examples can be seen at
<URL:http://www.stsci.edu/pubinfo/PR/96/10/A.html>,
<URL:http://www.stsci.edu/pubinfo/PR/95/14.html>, and
<URL:http://www.stsci.edu/pubinfo/PR/95/43.html>.  When we know the
distances of foreground and background objects, the mass inside the
lensing region can be derived (and for some of these multi-lens
clusters, its radial distribution). Same old story - we need a lot
more mass in invisible than visible form.

(4) Hot gas in galaxies and clusters. A real shocker once X-ray
astronomy became technologically possible was the finding that
clusters of galaxies are intense X-ray sources. The X-rays don't come
from the galaxies themselves, but from hot, rarefied gas at typically
10,000,000 K between the galaxies.  To hold this stuff together
against its own thermal motions requires - you guessed it, huge
amounts of unseen material.

It is worth noting that these last three methods all give about the
same estimate for the amount of dark matter in clusters
of galaxies.  

(5) Less direct evidence also exists: On larger scales, there is
evidence for large-scale "bulk motions" of galaxies towards
superclusters of galaxies, e.g., the Great Attractor.