In the previous Sections we have described several possible scenarios for galaxy formation. It is reasonable to ask whether any aspects of these theories will survive for a significant length of time, or whether our knowledge of galaxy formation is still so patchy that even basic ideas might be completely overturned by new observations. Of course, any judgement on the relative merits of current theories is bound to be subjective, so we would caution the reader that the views expressed below are unlikely to be shared by all research workers.
In this article, we have taken the approach that the cosmological
density parameter
and the
initial shape of the fluctuation spectrum
are effectively free parameters for theories of galaxy formation, to
be constrained by observations. Dynamical arguments
(Section 2.4)
suggest that
lies somewhere between the limits
0.1
1, but the
large. uncertainty means that we can attempt to make theories with
any value of
within this range.
However, there is an alternative view that the only natural value
for the cosmological density is
= 1. Suppose
that the present cosmological density parameter were
= 0.1. At
early times, for example at the GUT epoch when
T ~ 1015 GeV, the density parameter
would have been equal to unity except for one part in
~ 1050. Any
larger deviation would lead to a universe which either has a
negligible present density or to a closed universe which would have
recollapsed before stars and galaxies could have formed. Rather than
appeal to such finely tuned conditions (perhaps motivated by anthropic
arguments, e.g.
Barrow, 1982)
in the early universe, it seems preferable to find a fundamental
principle which requires
= 1. One
idea, due to
Gunn (1981)
utilizes phase transitions in grand unified theories (see
Guth, 1982,
for an introductory review). In Guth's inflationary scenario (see also
Linde, 1982;
Albrecht and Steinhardt,
1982)
the embryo universe expands exponentially by many orders of
magnitude as it supercools below the critical temperature of a GUT
phase transition. The flatness of the universe may be explained
because the energy density remains constant during the expansion phase
while the curvature term k / R2
decreases exponentially. By the time the
exponential phase is over, the curvature term is likely to be
negligible so the present value of
should be
extremely close to
unity. In addition, inflationary scenarios may help to explain why the
density of GUT monopoles is much less than the density of nucleons
(Guth, 1982;
see also
Preskill, 1979)
and may provide an explanation
of scale-free (n = + 1) primordial fluctuations, though
recent work indicates a spectrum with an excessively large amplitude
(Hawking, 1982;
Guth and Pi, 1982;
Bardeen et al., 1983).
Despite the difficulties with the inflationary model, it is
impressive that we can now contemplate quantitative calculations to
answer such fundamental questions.
Grand unification theories favour adiabatic perturbations, although
as described in Section 9.1 entropy
perturbations may arise from
primordial shear or vorticity. The most natural hypothesis, however,
is that only the adiabatic mode is present. We would argue that the
Zel'dovich scale-free spectrum is the only spectrum that is likely to
arise naturally in the early universe (see
Press, 1980;
Zel'dovich, 1980;
Kibble, 1976;
and the papers on inflationary models referred to
above). This is because we require an amplitude of
/
~
10-4 on
galactic scales to produce galaxies by gravitational instability. Any
other power-law spectrum must be truncated to avoid divergent
curvature fluctuations and requires that a theory for the origin of
fluctuations involves a characteristic mass scale comparable to that
of a galaxy. The Zel'dovich spectrum neatly avoids this difficulty.
If we take these arguments at all seriously, we are required to
build a theory of galaxy formation using a scale-free adiabatic
spectrum with the cosmological density parameter set to unity. This
provides a severe constraint. The pancake theory, assuming massless
neutrinos, is ruled out since it predicts order unity fluctuations in
the mass density on scales much larger than the coherence-length of
the galaxy distribution. The pancake theory, including massive
neutrinos, also faces a problem in accounting for galaxy clustering
(cf. Eq. 5.24b) unless galaxies form at very recent epochs
(z 1)
which would seem to be unreasonable
(White, Frenk and Davis,
1983; and
Kaiser, 1983b).
The remaining possibility is that "cold" weakly
interacting particles (e.g. gravitinos or axions) provide the
dominant contribution to the mass density. As reviewed in
Section 9.3,
this leads to a non-power law fluctuation spectrum. The details of
galaxy formation and clustering within this theory are only just
beginning to be worked out (e.g.
Peebles, 1983)
but we would expect
that many of the features of hierarchical clustering models discussed
in previous sections, such as radiative cooling processes, angular
momentum and dissipative collapse are applicable in this context. If,
ultimately, the theory is found not to work, we will have to revise
our opinions as to the "naturalness" of the initial conditions.
Understanding the formation of galaxies and clusters requires an understanding of the physics of the very early universe. Particle physicists are likely to provide galaxy formers with a variety of new ideas in the next few years. We expect that galaxy formers will come up with a few surprises for particle physicists as well.
Acknowledgements
G.E. acknowledges the hospitality of the Astronomy Department at Berkeley where part of this review was written and to King's College, Cambridge, for financial support. We thank Rebecca Elson, Nick Kaiser, Nigel Sharp and Brent Tully for their comments on parts of the manuscript. We are especially grateful to Carol Loretz for her skillful job in typing the manuscript and to Richard Sword for preparing the Figures. We would like to thank our various colleagues who have helped shape our ideas on galaxy formation. Dick Bond, Mike Fall, Craig Hogan, Colin Norman and Mike Wilson deserve a special mention. This work was supported in part by DOE contract ATO3-82ER40069 and by a NASA grant, NGR 05-003-578.