[sci.astro] Galaxies (Astronomy Frequently Asked Questions) (8/8)
From: lazio@spacenet.tn.cornell.edu
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Subject: [sci.astro] Galaxies (Astronomy Frequently Asked Questions) (8/8)
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Date: Wed, 06 Aug 97 0:49:59 GMT
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Summary: This posting address frequently asked questions about
galaxies, clusters, and QSO's.
Last-modified: $Date: 1997/08/07 00:13:42 $
Version: $Revision: 2.4 $
URL: http://astrosun.tn.cornell.edu/students/lazio/sci.astro.html
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 also available via anonymous
ftp in the directory <URL:ftp://seti.tn.cornell.edu/pub/lazio/> and it
is on the World Wide Web at
<URL:http://astrosun.tn.cornell.edu/students/lazio/sci.astro.html>.
Like many other FAQs it is also available from
<URL:ftp://rtfm.mit.edu/pub/usenet/news.answers>,
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and their worldwide mirrors.
Questions/comments/flames should be directed to the FAQ maintainer,
Joseph Lazio (lazio@spacenet.tn.cornell.edu).
------------------------------
Subject: Copyright
This document, as a collection, is Copyright 1995,1996 by T. Joseph
W. Lazio (lazio@spacenet.tn.cornell.edu). 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
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This FAQ is provided by the authors "as is," with all its faults.
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this document, in any way, you do so at your own risk.
------------------------------
Subject: H.00 Galaxies, Clusters, and QSO's
[Dates in brackets are last edit.]
H.01 How many stars, galaxies, clusters, QSO's etc. in the
Universe? [97-08-06]
H.02 Is there dark matter in galaxies?
H.03 What is the Hubble constant? What is the best value? [95-07-19]
H.04 How are galaxy distances measured? [95-06-29]
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? [97-08-06]
H.06 What are QSO's ("quasars")? [95-06-29]
H.07 Are the QSO's really at their redshift distances? [97-04-16]
H.08 What about apparent faster-than-light motions? [95-06-29]
------------------------------
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 galaxies?
------------------------------
Subject: H.03 What is the Hubble constant? What is the best value?
Author: Steve Willner <swillner@cfa.harvard.edu>,
Joseph Lazio <lazio@spacenet.tn.cornell.edu>
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 interesting 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 <mjh22@mrao.cam.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 <mjh22@mrao.cam.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 <mjh22@mrao.cam.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 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 QSO's which _are_ at their redshift distances. Cosmological
theories which 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.
[For additional reading, see
Stockton, A. 1978, ApJ, 223, 747-757, "The Nature of QSO Redshifts"
Stockton, A. 1980, in "Objects of High Redshift", Proceedings of IAU
Symp. 92, eds. G. O. Abell \& P. J. E. Peebles (Dordrecht:
Reidel) pp. 89-97, "Association between QSOs and Groups of
Galaxies"
In these papers Stockton determines the redshifts of galaxies seen
near QSOs. He finds that galaxies seen near QSOs generally have
comparable redshifts to the QSO.]
Like many arguments in science, this one is to some extent based on
aesthetics. The proponents of the standard model argue that the
physics we know (general relativity, special relativity,
electromagnetism) is sufficient to explain QSO's, and that by Occam's
razor no model introducing new physics is necessary. Its opponents
argue either that there are features of QSO's 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 QSO's are gravitational
doesn't 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.
------------------------------
Subject: H.08 What about apparent faster-than-light motions?
Author: Martin Hardcastle <mjh22@mrao.cam.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.
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