COSMOLOGY
(1b) Radiative Shocks in Protogalaxies and the Origin of
Globular Clusters
The suggestion has been made that globular clusters formed within
protogalaxies by gravitational instability in the compressed gas resulting from
radiative shocks with velocities of the order of the virial velocity of
the protogalaxy or from thermal instability in gas at the virial temperature.
[e.g. Fall and Rees 1985, ApJ, 298, 18;
Kang, Shapiro, Fall, and Rees 1990, henceforth KSFR].
Under such circumstances, gas which cools to 10^4K and, thereafter,
remains at 10^4K for a time longer than its internal free-fall time
will lead to gravitational instability with a characteristic mass comparable
to those of globular clusters. Detailed calculations
by Kang and Shapiro (
KSFR; and
1992)
of the thermal
and chemical evolution and radiative transfer in metal-free gas overtaken
by such shocks, however, showed that the success of this model for globular
cluster formation depends upon the presence of a strong UV or soft X-ray
source within the protogalaxy in order to suppress nonequilibrium H_2
formation in the postshock gas. Without such suppression, H_2 line
excitation rapidly cools the gas from 10^4K to 10^2K before
gravitational imprint of the globular cluster mass is accomplished.
For galaxies like our own, for example, gravitationally-induced motions
during and after the build-up of the protogalaxies would have led naturally
to shocks of velocity v_s~300 km s^-1 in
gas of preshock densities n_H,1=0.1-1cm^-3
during the protogalactic stage. The level of external radiation flux
required to suppress H_2 formation and cooling in this case implies
a total luminosity in excess of ~10^45 erg s^-1
for either an AGN-type source or early-type stars. This led KSFR to suggest
that such a radiation source was generically present in all protogalaxies
during the globular cluster formation epoch, in what remains today as
one of the leading theories of the origin of globular clusters.
Motivated by new observational evidence from studies of Faraday
rotation in Damped Lyman Alpha (DLA) quasar absorption line systems,
that interstellar magnetic fields of microgauss strength were already present
in protogalaxies by a redshift of order 3,
Shapiro, Clocchiati, and Kang (1992)
generalized the radiative shock calculations described
above to include the effects of a magnetic field.
The MHD conservation equations were solved
along with the rate equations for nonequilibrium
ionization, recombination, molecular formation and dissociation,
and the equations of radiative transfer for steady state MHD shocks of velocity
300 km/s in a gas of preshock densities
n_H,1=0.1-1 cm^-3, and magnetic field strengths
B_1=0.1-6 microgauss. As in the previous, nonmagnetized calculations
described above,
external sources of UV and soft X-ray radiation were included,
such as might be
present within the protogalaxy. The magnetic field was shown to limit the
degree of postshock compression, and, thereby, to reduce the level
of external radiation flux required to suppress H_2 formation and
cooling. For example, if the growth time for gravitational instability
in the compressed postshock layer at 10^4K is that given by linear
perturbation analysis of a thin sheet, then while
the total luminosity of the
external source in the nonmagnetized case must exceed
~10^45 erg/s for either an AGN-type source or early-type
stars, the magnetized case only requires luminosities
~10^44 erg/s or lower, as long as
B_1>1.6(n_H,1)^1/2 microgauss.
This new study involving radiative MHD shocks inside protogalaxies also
took care to reanalyse the effects of the thin-sheet geometry of the
postshock layer which cooled to 10^4 K on the gravitational
instability and fragmentation of that layer and demonstrated that the
characteristic mass scale subject to gravitational instability is
increased by the presence of the magnetic field. While the thin-sheet geometry
for the nonmagnetized case already boosts the mass scale above the value
estimated by the spherical Jeans mass, to about 10^7 M_solar,
the mass scale in the magnetized case is even higher, as high as
10^8 M_solar.
This theory of shock-induced formation of globular clusters inside
protogalaxies was described in an invited review by
Shapiro (1993)
in the book on The Globular Cluster-Galaxy Connection which resulted
from the Eleventh Santa Cruz Summer Workshop in Astronomy and Astrophysics
on this topic. In that review, new calculations not published elsewhere
were presented of radiative shocks of different shock velocities and
gas densities appropriate for protogalaxies of different mass.
Previous calculations had focused on shocks of velocity 300 km/s
in gas of density 0.1-1 cm^-3 appropriate for protogalaxies of mass
like that of the Milky Way. These new calculations showed
how the threshold luminosity required to suppress H_2 formation
varies with the mass of the protogalaxy. Fall and Rees had previously
argued that the same final spherical Jeans mass of 10^6 M_solar
would result in gas which cools isobarically to 10^4 K from the
virial velocity of a protogalaxy of mass different from that of the Milky Way,
as long as the protogalaxy obeys the well-known Faber-Jackson or Tully-Fisher
relations and the mass-to-light ratio is independent of mass.
The new calculations in
Shapiro (1993) demonstrated that the
threshold value of UV luminosity required to suppress H_2 decreases with
decreasing protogalaxy mass, faster than the decrease in
mass. As a result, if there were enough luminosity inside a Milky Way
type galaxy to suppress H_2 and form globular clusters by
gravitational instability behind radiative shocks, then
small-mass protogalaxies would also have succeeded in forming them, even
more easily, in fact.