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Last-modified: $Date: 2003/04/27 00:12:18 $
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URL: http://sciastro.astronomy.net/
Posting-frequency: semi-monthly (Wednesday)
Archive-name: astronomy/faq/part8
Subject: Introduction
sci.astro is a newsgroup devoted to the discussion of the science of
astronomy. As such its content ranges from the Earth to the farthest
reaches of the Universe.
However, certain questions tend to appear fairly regularly. This
document attempts to summarize answers to these questions.
This document is posted on the first and third Wednesdays of each
month to the newsgroup sci.astro. It is available via anonymous ftp
from <URL:ftp://rtfm.mit.edu/pub/usenet/news.answers/astronomy/faq/>,
and it is on the World Wide Web at
<URL:http://sciastro.astronomy.net/> and
<URL:http://www.faqs.org/faqs/astronomy/faq/>. A partial list of
worldwide mirrors (both ftp and Web) is maintained at
<URL:http://sciastro.astronomy.net/mirrors.html>. (As a general note,
many other FAQs are also available from
<URL:ftp://rtfm.mit.edu/pub/usenet/news.answers/>.)
Questions/comments/flames should be directed to the FAQ maintainer,
Joseph Lazio (jlazio@patriot.net).
Subject: H.00 Galaxies, Clusters, and Quasars (QSOs)
[Dates in brackets are last edit.]
H.01 How many stars, galaxies, clusters, QSO's etc. in the
Universe? [1997-08-06]
H.02 Is there dark matter in galaxies? [1997-12-02]
H.03 What is the Hubble constant? What is the best value? [1995-07-19]
H.04 How are galaxy distances measured? [1995-06-29]
H.05 When people speak of galaxies X billion light years, does
this mean they are that far away now or were that far away
when the light left them? [1997-08-06]
H.06 What are QSO's ("quasars")? [1995-06-29]
H.07 Are the QSO's really at their redshift distances? [2003-02-18]
H.08 What about apparent faster-than-light motions? [1995-06-29]
H.09 What's the Local Group? [1999-05-19]
For an overall sense of scale when talking about galaxies, see the
Atlas of the Universe, <URL:http://anzwers.org/free/universe/>.
Subject: H.01 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.
------------------------------
Subject H.01.1 How many stars are there in the Milky Way?
Author: William Keel <keel@bildad.astr.ua.edu>
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).
Subject: H.01.2 How many galaxies in the Universe?
Author: William Keel <keel@bildad.astr.ua.edu>
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.
Subject: H.01.3 How many globular clusters in the Milky Way?
Author: William Keel <keel@bildad.astr.ua.edu>
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.
Subject: H.01.4 How many open clusters?
Author: William Keel <keel@bildad.astr.ua.edu>
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).
Subject: H.02 Is there dark matter in the Universe?
Author: Will Sutherland <w.sutherland1@physics.oxford.ac.uk>,
William Keel <keel@bildad.astr.ua.edu>
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.
Subject: 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. There is also
the question of reconciling the very small (1 part in 100,000)
observed fluctuations in the cosmic microwave background with the
"lumpy" galaxy distribution seen at the present day; dark matter helps
nicely to match these two facts because the density fluctuations grow
more rapidly with time in a higher-density Universe. Finally, the
theory of inflation (which is an "optional extra" to the standard big
bang model) usually predicts that the universe should have exactly the
critical density, which could require as much as 95% of the mass in
the Universe to be dark.
It is worth mentioning the possibility of non-standard gravity
theories, which attempt to explain the above list of observations
without dark matter. It turns out that modifying the inverse-square
law of gravity does not work well, essentially because the dark matter
problem extends over so many different lengthscales. Modifying the F =
ma law has been tried, e.g., by Milgrom, but relativistic versions of
this theory have not been found, and most cosmologists are reluctant
to abandon Einstein's GR which is elegant and well tested (at least on
solar system scales).
Subject: H.02.2 How much dark matter is there?
A convenient way of quoting mass estimates is via Omega, the ratio of
the density contributed by some objects to the "critical density" = 3
H^2 / 8 pi G, where H is the Hubble constant and G is the universal
constant of gravitation. The critical density is the amount of matter
that would be just sufficient to stop the expansion of the Universe
and is 10^{-29} g/cm^3. (Of course, portions of the Universe have a
higher density than this, e.g., you, but this is an average density.)
The visible stars in galaxies contribute about 1 percent of critical
density, i.e., Omega_stars ~ 0.01; dark halos around galaxies
contribute Omega_halos ~ 0.05; mass estimates from clusters tend to
give Omega_clus ~ 0.2 (assuming the ratio of dark matter to stars is
the same in clusters as everywhere else); and theoretical
considerations (i.e., inflation) favor Omega_total = 1. The gap
between 0.05 and 0.2 can be explained if galaxy halos extend further
out than we can measure the rotation curves, but if Omega_total = 1 we
may require extra dark matter in intergalactic space.
It's also interesting to consider the dark matter density "locally."
Within a few hundred parsecs of the Sun, this is about 0.01 Solar
masses per cubic parsec, or about 0.3 proton masses per cm^3; that's
only about 1/10 of the density of visible matter (mostly stars);
though it's much larger than critical density because we live in a
galaxy. However, because the stars are in a thin disk while the dark
matter is more spherical, if you take an 8 kpc radius sphere centred
on the Galaxy and passing through the Sun, roughly half the mass in
this sphere is dark matter If you consider a larger sphere, e.g., out
to the Large Magellanic Cloud at 50 kpc radius, over 80% of the mass
in it is dark matter. This estimate was first made by Jan Oort, and
the estimate of the *total* mass density near the Sun is today termed
the Oort limit in his honor.
Subject: H.02.3 What is the dark matter?
Since it's detected in a negative sense---not visible in gamma rays,
X-rays, ultraviolet, visible light, infrared, millimeter, or radio
regimes, and it doesn't block light either---it's a theoretical happy
hunting ground. First, let's list some things that can't make the
dark matter. Most forms of gas are excluded, because atomic hydrogen
would be seen in 21cm radiation, and hot gas would be seen in X-rays
and/or distort the spectrum of the CMB. Cold molecular gas is a
possibility, but it would tend to collapse into visible stars.
"Snowballs" made of solid hydrogen would evaporate due to the CMB, and
larger snowballs would leave too many craters on the Moon or be seen
as high-speed comets. "Rocks" are unlikely because there haven't been
enough stars to make the heavy elements. Faint red stars are excluded
because they're not seen in deep images e.g., the Hubble Deep Field.
This leaves two main classes of dark-matter candidate: large objects
called MACHOs and subatomic particles, some of which are called WIMPs.
MACHOs stands for Massive Compact Halo Objects; examples are
"interstellar Jupiters" or "brown dwarfs," which are lumps of mostly
hydrogen less than 0.08 Solar masses; objects this small don't get hot
enough to fuse hydrogen into helium, and so would be extremely faint
and hard to find. Other varieties of MACHOs are dead stars, such as
old white dwarfs or neutron stars, and black holes.
The second class is some form of sub-atomic particle; if so, there'd
be millions of these passing through us every second, but they'd
hardly ever interact with normal matter, hence the term "weakly
interacting massive particles" or WIMPs. Many varieties of these have
been suggested; the only one of these that certainly exists is the
neutrino, but neutrinos may not have any mass. The number of
neutrinos made in the Big Bang is similar to the number of CMB photons
(few hundred per cm^3), so if they have a small mass (around 30 eV = 6
x 10^-5 electron masses) they could contribute most of the dark
matter. However, computer models indicate that galaxies form much too
late in a neutrino-dominated universe. Another possibility is the
"axion" which is a hypothetical particle invented to solve a strange
"coincidence" in particle physics (called the strong CP problem).
The most popular WIMP at the moment is the "neutralino" or "lightest
supersymmetric particle"; supersymmetry is a popular way to unify the
strong and electroweak forces (also known as a Grand Unified Theory),
which has some (tentative) experimental support. Supersymmetry
predicts an unobserved new particle or "superpartner" for every known
particle; the lightest of these should be stable, and lots of them
would be left over from the Big Bang. These probably weigh about
30-500 proton masses.
An important piece of evidence here is "primordial nucleosynthesis,"
which explains the abundances of He-4, Deuterium, He-3 and Li-7
produced a few minutes after the Big Bang; in order to obtain the
observed abundances of these elements, the density of baryons (i.e.,
"ordinary" matter) must be Omega_baryon ~ 0.02--0.1. Since Omega_stars
~ 0.01, there are probably some dark baryons, but if Omega_total = 1
(as inflation predicts) most of the dark matter is probably WIMPs.
Subject: H.02.4 Searches for Dark Matter
There are many searches now underway for the dark matter.
For MACHOs, the most promising method is "gravitational microlensing,"
where we wait for a MACHO to pass between us and a distant star, and
the gravity of the MACHO bends the starlight into two images. These
images are too close together to resolve, but add up to more light, so
the star appears to brighten and then fade back to normal as the MACHO
passes by. The shape is quite distinctive, and the brightening
happens only once so does not look like a variable star. The
probability of such a close-enough approach is very low, so millions
of stars must be monitored to have a chance of finding these
events. The Large Magellanic Cloud is the most popular target. A
number of groups---MACHO, EROS, OGLE, among others---have been doing
this for several years, and have found a number of good candidate
microlensing events. At the moment, it is too early to say that
MACHOs have definitely been discovered, but it looks as though the
"brown dwarf" objects are just about excluded, while perhaps as much
as 50% of the dark matter could be in larger objects roughly 0.5 solar
masses, e.g., white dwarfs.
There is an axion search recently started at Lawrence Livermore Labs,
which uses a huge superconducting magnet to convert axions (if they
exist) into microwave photons. For the big bang neutrinos, there is
currently no hope of detecting them because they have far less energy
than the well-known solar neutrinos (see FAQ entry E.01). However, if
a neutrino mass could be measured by lab experiments, we could
calculate their contribution to the dark matter.
For the supersymmetric particles, there are broadly three ways at
detecting them: i) Direct detection by watching a crystal down a deep
mine, and waiting for a WIMP to bounce off a nucleus in it with
observable results such as scintillation or heating of the crystal.
Very roughly 1 WIMP per day should hit each kg of detector, but the
tricky part is discriminating these from natural radioactivity. The
WIMPS should have a preferred direction (due to the orbit of the Sun
around the galaxy), but we'll have to wait for next-generation
experiments to measure this. ii) Indirect detection, whereby WIMPs
get captured in the Sun, and then a WIMP + anti-WIMP annihilate into
super-high energy (GeV) neutrinos which could be detected in huge
volume detectors, e.g., Antarctic ice or ocean water. iii) Create
WIMPs directly at next-generation accelerators like LHC, measure their
properties and then calculate how many should have been produced in
the Big Bang.
With all these searches, there is a good chance that in the next 10
years or so we may find out what constitutes dark matter.
Further reading:
Astronomy magazine, Oct. 1996 issue contains many dark matter articles.
The Center for Particle Astrophysics home page at
<URL:http://physics7.berkeley.edu/> has several links including the
Question of Dark Matter page.
The MACHO home page at <URL:http://wwwmacho.mcmaster.ca/> has info on
the MACHO project and links to many other dark matter searches.
For cosmology background, see Ned Wright's Cosmology Tutorial at
<URL:http://www.astro.ucla.edu/~wright/cosmoall.htm>.
A more technical conference summary is at
<URL:http://xxx.lanl.gov/abs/astro-ph/9610003>.
Krauss, L., _The Fifth Essence_, Basic Books, NY 1989.
Silk, J., _The Big Bang_, Freeman, San Francisco, 1988.
Peebles, P.J.E., _Principles of Physical Cosmology_, Princeton, 1992
(advanced)
Subject: H.03 What is the Hubble constant? What is the best value?
Author: Steve Willner <swillner@cfa.harvard.edu>,
Joseph Lazio <jlazio@patriot.net>
By 1925, V. M. Slipher had compiled radial velocities for 41 galaxies.
He noticed that their velocities were quite a bit larger than typical
for objects within our Galaxy and that most of the velocities
indicated recession rather than approach. In 1929, Edwin Hubble (and
others) recognized the simple relationship that recession velocity is
on average proportional to the galaxy's distance. (His distance
measure was the apparent magnitude of the brightest individually
recognizable stars.) This proportionality is now called "Hubble's
Law," and the constant of proportionality is known as the "Hubble
constant," H (often written "Ho," i.e., H subscript zero).
The Hubble constant also has the property of being related to the age
of the Universe, which undoubtedly explains some of the interest in
its value. It is a constant of proportionality between a speed
(measured in km/s) and a distance (measured in Mpc), so its units are
(km/s)/Mpc. Since kilometers and megaparsecs are both units of
distance, with the correct factor, we can convert megaparsecs to
kilometers, and we're left with a number whose units are (km/s)/km.
If we take 1/H, we see that it has units of seconds, that is 1/H is a
time. We might consider 1/H to be the time it takes for a galaxy
moving at a certain velocity (in km/s) to have moved a certain
distance (in Mpc). If the galaxies have always been moving exactly as
they now are, 1/H seconds ago all of them were on top of us!
Of course the proportionality isn't exact for individual galaxies. Part
of the problem is uncertainties in measuring the distances of galaxies,
and part is that galaxies don't move entirely in conformity with the
"Hubble Flow" but have finite "peculiar velocities" of their own. These
are presumably due to gravitational interactions with other, nearby
galaxies. Some nearby galaxies indeed have blue shifts; M 31 (the
Andromeda galaxy) is a familiar example.
In order to measure the Hubble constant, all one needs a distance and a
redshift to a galaxy that is distant enough that its peculiar velocity
does not matter. Measuring redshifts for galaxies is easy, but
measuring distances is hard. (See the next question.) The Hubble
constant is therefore not easy to measure, and it is not surprising that
there is controversy about its value. In fact, there are generally two
schools of thought: one group likes a Hubble constant around 55
(km/s)/Mpc, and another prefers values around 90 (km/s)/Mpc.
When converted to an age of the Universe, H = 55 (km/s)/Mpc corresponds
to an age of about 19 billion years and H = 90 (km/s)/Mpc is an age of
11 billion years (again if the velocities are constant).
A measure of how difficult it is to determine the Hubble constant
accurately can be seen by examining the different values reported. A
search by Tim Thompson <tim@lithos.Jpl.Nasa.Gov> for the period
1992--1994 found 39 reported values for H in the range
40--90 (km/s)/Mpc.
The linear relation between distance and recession velocity breaks down
for redshifts around 1 and larger (velocities around 2E5 km/s). The
true relation depends on the curvature of space, which is a whole other
topic in itself (and has no clear answer). The sense, though, is that
infinite redshift, corresponding to a recession velocity equal to the
speed of light, occurs at a finite distance. This distance is the
"radius of the observable Universe." Nothing more distant than this can
be observed, even in principle.
Subject: H.04 How are galaxy distances measured?
Author: Martin Hardcastle <m.hardcastle@bristol.ac.uk>
Galaxy distances must be measured by a complicated series of inferences
known as the distance ladder. We can measure the distances to the
nearest stars by parallax, that is by the apparent motion of the star in
the sky as a result of the Earth's motion round the Sun. This technique
is limited by the angular resolution that can be obtained. The
satellite Hipparcos will provide the best measurements, giving the
parallax for around 100,000 stars. At present parallax can be used
accurately to determine the distances of stars within a few tens of
parsecs from the Sun. [ 1 parsec = 3.26 lt yrs.]
Statistical methods applied to clusters of stars can be used to extend
the technique further, as can `dynamical parallax' in which the
distances of binary stars can be estimated from their orbital
parameters and luminosities. In this way, or by other methods, the
distance to the nearest `open clusters' of stars can be estimated;
these can be used to determine a main sequence (unevolved
Hertzsprung-Russell diagram) which can be fitted to other more distant
open clusters, taking the distance ladder out to around 7 kpc.
Distances to `globular clusters', which are much more compact clusters
of older stars, can also have their distances determined in this way
if account is taken of their different chemical composition; fitting
to the H-R diagram of these associations can allow distance estimates
out to 100 kpc. All of these techniques can be checked against one
another and their consistency verified.
The importance of this determination of distance within our own galaxy
is that it allows us to calibrate the distance indicators that are used
to estimate distances outside it. The most commonly used primary
distance indicators are two types of periodic variable stars (Cepheids
and RR Lyrae stars) and two types of exploding stars (novae and
supernovae). Cepheids show a correlation between their period of
variability and their mean luminosity (the colour of the star also plays
a part) so that if the period and magnitude are known the distance can
in principle be calculated. Cepheids can be observed with ground-based
telescopes out to about 5 Mpc and with the Hubble space telescope to at
least 15 Mpc. RR Lyrae stars are variables with a well-determined
magnitude; they are too faint to be useful at large distances, but they
allow an independent measurement of the distance to galaxies within 100
kpc, such as the Magellanic Clouds, for comparison with Cepheids. Novae
show a relationship between luminosity at maximum light and rate of
magnitude decline, though not a very tight one; however, they are
brighter than Cepheids, so this method may allow distance estimates for
more distant objects. Finally, supernovae allow distance determination
on large scales (since they are so bright), but the method requires some
input from theory on how they should behave as they expand. The
advantage of using supernovae is that the derived distances are
independent of calibration from galactic measurements; the disadvantage
is that the dependence of the supernova's behaviour on the type of star
that formed it is not completely understood.
The best primary distance indicators (generally Cepheids) can be used
to calibrate mainly empirical secondary distance indicators; these
include the properties of H II regions, planetary nebulae, and
globular clusters in external galaxies and the Tully-Fisher relation
between the width of the 21-cm line of neutral hydrogen and the
absolute magnitude of a spiral galaxy. These can all be used in
conjunction with type Ia supernovae to push the distance ladder out to
the nearest large cluster of galaxies (Virgo, at around 15--20 Mpc)
and beyond (the next major goal is the Coma cluster at around 5 times
farther away). Other empirical estimators such as a galaxy
size-luminosity relation or a constant luminosity for brightest
cluster galaxies are of uncertain value.
The goal in all of this is to get out beyond the motions of our local
group of galaxies and determine distances for much more distant
objects which can reasonably be assumed to be moving along with the
expansion of the universe in the Big Bang cosmology. Since we know
their velocities from their redshifts, this would allow us to
determine Hubble's constant, currently the `holy grail' of
observational cosmology; if this were known we would know the
distances to _all_ distant galaxies directly from their recession
velocity. Sadly different methods of this determination, using
different steps along the distance ladder, give different results;
this leads to a commonly adopted range for H of between 50 and 100
km/s/Mpc, with rival camps supporting different values. There are a
number of ongoing attempts to reduce the complexity of the distance
ladder and thus the uncertainty in H. One has been the recent (and
continuing) use of the Hubble Space Telescope to measure Cepheid
variables directly in the Virgo cluster, thereby eliminating several
steps; this leads to a high (80--100) value of H, although with large
uncertainty (which should hopefully be reduced as more results
arrive). Other groups are working on eliminating the distance ladder,
with its large uncertainty and empirical assumptions, altogether, and
determining the distances to distant galaxies or clusters directly,
for example using the Sunyaev-Zeldovich effect together with X-ray
data on distant clusters or using the time delays in gravitational
lenses. The early results tend to support lower values of H, around
50.
Subject: H.05 When people speak of galaxies X billion light years
away, does this mean they are that far away now or were that
far away when the light left them?
Author: William Keel <keel@bildad.astr.ua.edu>
Distance is indeed a slippery thing in an expanding universe such as ours.
There are at least three kinds of distances:
* angular-diameter distance---the one you need to make the usual
relation
sine(angular size) = linear size/distance
work;
* luminosity distance---makes the typical relationship
observed flux = luminosity / 4 pi (distance**2)
work; and
* proper distance---the piece-by-piece distance the light actually
travelled.
Of the three, the proper distance is perhaps the most sensible of the
three. In this case, distance doesn't mean either when the light was
emitted or received, but how far the light travelled. Since the
Universe expands, we have been moving away from the emitting object so
the light is catching up to us (at a rate set by the rate of expansion
and our separation from the quasar or whatever at some fiducial
time). You can of course turn this distance into an extrapolated
distance (where the quasar or it descendant object is "today") but
that gets very slippery. Both special and general relativity must be
taken into account, so simultaneity, i.e., "today," has only a limited
meaning. Nearby galaxies are pretty much where we see them; for
example, the light from the Andromeda galaxy M31 has been travelling
only about 0.01% of the usually estimated age of the Universe, so its
distance from us would have changed by about that fraction, if nothing
but the Hubble expansion affected its measured distance (which is not
the case, because gravitational interactions between the Andromeda
galaxy and our Galaxy affect the relative velocity of the two
galaxies).
To muddy the waters further, observers usually express distances (or
times) not in light-years (or years) but by the observable quantity
the redshift. The redshift is, by definition, the amount by which
light from an object has been shifted divided by the emitted or
laboratory wavelength of the light and is usually denoted by z. For
an object with a redshift z, one can show that (1+z) is the ratio of
the scale size of distances in the Universe between now and the epoch
when the light was given off. Turning this into an absolute distance
(i.e., some number of light-years) requires us to plug in a rate for
the expansion (the Hubble constant) and its change with time (the
deceleration parameter), neither of which is as precisely known as we
might like.
As a result ages and distances are usually quoted in fairly round
numbers. If the expansion rate has remained constant (the unrealistic
case of an empty Universe), the age of the Universe is the reciprocal
of the Hubble constant. This is from 10--20 billion (US, 10^9) years
for the plausible range of Hubble constants. If we account for the
matter in the Universe, the Universe's age drops to 7--15 billion
years. A quick estimate of the look-back time (i.e., how long the
light from an object has been travelling to us) for something at
redshift z is
t = (z/[1+z])*1/H0
for Hubble constant H0. For example, the author has published a paper
discussing a cluster of galaxies at z=2.4. For the press release we
quoted a distance of 2.4/3.4 x 15 billion light-years (rounded to 11
since that 15 is fuzzy).
Subject: H.06 What are QSO's ("quasars")?
Author: Martin Hardcastle <m.hardcastle@bristol.ac.uk>
"Quasi-stellar objects" (or QSO's) are defined observationally as
objects that appear star-like on photographic plates but have high
redshifts (and thus appear extragalactic; see above). The luminosity
(if we accept that the redshift correctly indicates the distance) of a
QSO is much larger than that of a normal galaxy, and many QSO's vary on
time scales as short as days, suggesting that they may be no more than a
few light days in size. QSO spectra typically contain strong emission
lines, both broad and narrow, so that the redshift can be very well
determined. In a few cases, a nebulosity reminiscent of stars in a
normal galaxy has been detected around a QSO. Quasars (a shortened
version of "quasi-stellar radio source") were originally discovered as
the optical counterparts to radio sources, but the vast majority of
QSO's now known are radio-quiet. Some authors reserve the term "quasar"
for the radio-loud class and use the term "QSO" generically; others
(especially in the popular literature) use "quasar" generically.
In the standard model, QSO's are assumed to lie at the centre of
galaxies, and to form the most extreme example of the class of active
galactic nuclei (AGN); these are compact regions in the centre of
galaxies which emit substantially more radiation in most parts of the
spectrum than would be expected from starlight. From the energy
output in QSO's, together with some guess at their lifetime (about
10^8 years) the mass of the central engine can be estimated as of
order 10^7 solar masses or more (this is consistent with estimates of
the masses of other, related types of AGN). A compact, massive object
of this kind is most likely (on our current understanding of physics)
to be a black hole, and most astronomers would accept this as the
standard assumption. The luminosity ultimately derives from matter
falling into the black hole and gravitational potential energy being
converted to other forms, but the details are unexplained and very
much an active research topic.
Subject: H.07 Are the QSO's really at their redshift distances?
Author: Martin Hardcastle <m.hardcastle@bristol.ac.uk>
It's often suggested that QSOs are not at the distances that would be
inferred from their redshifts and from Hubble's law; this would avoid
the enormous powers and necessity for general-relativistic physics in
the standard model. Many arguments of this type are flawed by a lack
of consideration of the other types of galaxies and active galactic
nuclei (AGN): unless it's believed that _no_ galaxy is at its redshift
distance, i.e., that the whole concept of redshift is wrong, then we
know that there are objects very similar to QSOs which _are_ at their
redshift distances. (Cosmological theories that overthrow the whole
idea of redshift and the big bang are beyond the scope of this
discussion, although several have been proposed based on the apparent
spatial association of objects with very different redshifts.)
Another argument favoring QSOs being at their redshift distance comes
from gravitational lensing. Gravitational lenses occur when two
objects are nearly aligned, and the mass of the foreground object
lenses (magnifies and/or distorts) the background object. In every
gravitational lens for which redshifts are known, the galaxy (or
galaxies) acting as the lens has a lower redshift than the galaxy
being lensed.
A recent analysis of data available from the 2-degree field (2dF
survey) also showed no evidence for a connection between galaxies and
QSOs. This analysis is particularly significant because the people
who carried out the analysis spoke to proponents on both sides of the
argument *before* conducting their analysis (Hawkins, Maddox, &
Merrifield 2002, Mon. Not. R. Astron. Soc., vol. 336, p. L13).
More generally, though, like many arguments in science, this one also
has an element of aesthetics. The proponents of the standard model
argue that the physics we know (general relativity, special
relativity, electromagnetism) is sufficient to explain QSOs, and that,
by Occam's razor, no model introducing new physics is necessary. Its
opponents argue either that there are features of QSOs which cannot be
explained by the standard model or that the predictions of the
standard model (and, in particular, its reliance on supermassive black
holes) are so absurd as clearly to require some new physics. A good
deal of bad science has been put forward (on both sides) on sci.astro.
Readers should be aware that the scientific community isn't as
insanely conservative as some posters would have them believe, and
that a number of other possibilities for QSO physics were considered
and rejected when they were first discovered. For example, the
frequent suggestion that the redshifts of QSOs are gravitational does
not work in any simple model. Species having different ionization
potentials ought to exist at different distances from the central
source and thus should have different redshifts, but in fact emission
lines from all species are observed to have the same redshift.
For examples of claims of galaxy-QSO associations, see papers by
Stockton, either of the Burbidges, or Arp. For additional, technical
discussions of why these conclusions are not valid, see papers by
Newman & Terzian; Newman, Terzian, & Haynes; and Hawkins, Maddox, &
Merrifield (2002).
Subject: H.08 What about apparent faster-than-light motions?
Author: Martin Hardcastle <m.hardcastle@bristol.ac.uk>
The apparently faster-than-light motions observed in the jets of some
radio-loud quasars have misled a number of people into believing that
the speed of light is not really a limit on velocity and that
astrophysics has provided a disproof of the theory of relativity. In
fact, these motions can be easily understood without any new physics;
you just need trigonometry and the idea of the constancy of the speed of
light.
Consider the situation shown in the diagram below. A blob B of
radio-emitting plasma starts at O and moves with velocity v at some
angle a to our line of sight. At a time t, B has moved across the sky
a distance vt sin a. The light from when it was at O has travelled a
distance ct towards us (c is the speed of light). But the light from
its position at time t only has to travel an additional distance
(ct - vt cos a) to reach us. Thus we measure the time between the two
events as (distance / speed of light) = t(1 - (v/c) cos a). If we
derive an apparent velocity by dividing the (measurable) transverse
motion of the source by the measured time difference, we get
vt sin a v sin a
v(apparent) = ------------------ = ---------------
t(1 - (v/c) cos a) 1 - (v/c) cos a
^ O ^
| |\ |
| | \ |
| | \ vt cos a
| | a \ |
ct | \ |
| | \ |
| | B v
| | ^
| | ct - vt cos a
v | v
\_____I_____/
(Earth, radio telescope)
This apparent velocity can clearly be greater than c if a is small and
v is close to c. There are other independent reasons for believing
that the jets in radio-loud quasars have velocities close to c and are
aligned close to the line of sight, so that this explanation is a
plausible one.
Subject: H.09 What's the Local Group?
Author: Hartmut Frommert <spider@seds.org>,
Christine Kronberg <smil@lrz.uni-muenchen.de>
This is "our" group of galaxies. It was first recognized by Hubble,
in the time of the first distance determinations and redshift
measurements.
The Local Group contains the Andromeda Galaxy (M31) and its satellites
M32 and M110, as well as the Triangulum galaxy (M33). Other members
(over 30 in all) include our Milky Way Galaxy, the Large and the Small
Magellanic Cloud (LMC and SMC), which have been known before the
invention of the telescope (as was the Andromeda Galaxy), as well as
several smaller galaxies which were discovered more recently. These
galaxies are spread in a volume of nearly 10 million light years
diameter, centered somewhere between the Milky Way and M31.
Membership is not certain for all these galaxies, and there are
possible other candidate members.
Of the Local Group member galaxies, the Milky Way and M31 are by for
the most massive, and therefore dominant members. Each of these two
giant spirals has accumulated a system of satellite galaxies, where
* the system of the Milky Way contains many (nearby) dwarf galaxies,
spread all over the sky, namely Sag DEG, LMC, SMC, and the dwarf
galaxies in Ursa Minor, Draco, Carina, Sextans (dwarf), Sculptor,
Fornax, Leo I and Leo II; and
* the system of the Andromeda galaxy is seen from outside, and thus
grouped around its main galaxy M31 in Andromeda, containing bright
nearby M32 and M110 as well as fainter and more far-out NGC 147 and
185, the very faint systems And I, And II, And III, and, possibly, And
IV.
The third-largest galaxy, the Triangulum spiral M33, may or may not be
an outlying gravitationally bound companion of M31, but has itself
probably the dwarf LGS 3 as a satellite.
The other members cannot be assigned to one of the main subgroups, and
float quite alone in the gravitational field of the giant group
members. The substructures of the group are probably not
stable. Observations and calculations suggest that the group is highly
dynamic and has changed significantly in the past: The galaxies around
the large elliptical Maffei 1 have probably been once part of our
galaxy group.
As this shows, the Local Group is not isolated, but in gravitational
interaction, and member exchange, with the nearest surrounding groups,
notably:
* the Maffei 1 group, which besides the giant elliptical galaxy Maffei
1 also contains smaller Maffei 2, and is associated with nearby IC
342. This group is highly obscured by dark dust near the Milky Way's
equatorial plane.
* the Sculptor Group or South Polar Group (with members situated
around the South Galactic pole), dominated by NGC 253;
* the M81 group; and
* the M83 group.
In the future, interaction between the member galaxies and with the
cosmic neighborhood will continue to change the Local Group. Some
astronomers speculate that the two large spirals, our Milky Way and
the Andromeda Galaxy, may perhaps collide and merge in some distant
future, to form a giant elliptical. In addition, there is evidence
that our nearest big cluster of galaxies, the Virgo Cluster, will
probably stop our cosmological recession away from it, accelerate the
Local Group toward itself so that it will finally fall and merge into
this huge cluster of galaxies.
A table of the currently known Local Group member galaxies is at
<URL:http://www.seds.org/messier/more/local.html>. A (somewhat
technical) review of the Local Group is at
<URL:http://arXiv.org/abs/astro-ph/?0001040>.
Subject: Copyright
This document, as a collection, is Copyright 1995--2003 by T. Joseph
W. Lazio (jlazio@patriot.net). The individual articles are copyright
by the individual authors listed. All rights are reserved.
Permission to use, copy and distribute this unmodified document by any
means and for any purpose EXCEPT PROFIT PURPOSES is hereby granted,
provided that both the above Copyright notice and this permission
notice appear in all copies of the FAQ itself. Reproducing this FAQ
by any means, included, but not limited to, printing, copying existing
prints, publishing by electronic or other means, implies full
agreement to the above non-profit-use clause, unless upon prior
written permission of the authors.
This FAQ is provided by the authors "as is," with all its faults.
Any express or implied warranties, including, but not limited to, any
implied warranties of merchantability, accuracy, or fitness for any
particular purpose, are disclaimed. If you use the information in
this document, in any way, you do so at your own risk.
|
with stars, then every direction you looked would eventually end on
the surface of a star, and the whole sky would be as bright as the
surface of the Sun.
Why would anyone assume this? Certainly, we have directions where we look that are dark because something that does not emit light (is not a star) is between us and the light. A close example is in our own solar system. When we look at the Sun (a star) during a solar eclipse the Moon blocks the light. When we look at the inner planets of our solar system (Mercury and Venus) as they pass between us and the Sun, do we not get the same effect, i.e. in the direction of the planet we see no light from the Sun? Those planets simply look like dark spots on the Sun.
Olbers' paradox seems to assume that only stars exist in the universe, but what about the planets? Aren't there more planets than stars, thus more obstructions to light than sources of light?
What may be more interesting is why can we see certain stars seemingly continuously. Are there no planets or other obstructions between them and us? Or is the twinkle in stars just caused by the movement of obstructions across the path of light between the stars and us? I was always told the twinkle defines a star while the steady light reflected by our planets defines a planet. Is that because the planets of our solar system don't have the obstructions between Earth and them to cause a twinkle effect?
9-14-2024 KP