5.1
Dust
Is strong Ly emission really
expected from a PG? A PG can be thought
of as a giant H II region. A typical Ly
photon in an
ionization-bounded H II region is resonantly scattered
~ 106-107 times before it leaks out
(Osterbrock 1962).
It follows that even a tiny admixture of dust in an H II region will
erase nearly all Ly
emission,
because the total path travelled by
Ly
photons is
N
103X longer than the
``straight through'' radius of the H II region.
This expectation appeared to be borne out by early ultraviolet
observations of starburst galaxies with IUE. Starburst or H II
region galaxies might
have been expected to be prodigious emitters of Ly; yet the
first observations of these objects
(Meier and
Terlevich 1981;
Hartmann, Huchra,
and Geller 1984;
Deharveng,
Joubert, and Kunth 1986;
Hartmann et
al. 1988) showed that their Ly
emission was weak, absent,
or sometimes even in absorption. Thus they appeared to be excellent
candidates for the type of excess absorption that might be associated
with resonant scattering. The implication for PG searches was clear:
searches for Ly
emission from
PGs were doomed to failure.
Neverthless, it now appears that this simple picture of quenched
Ly emission from starburst
galaxies and PGs may be oversimplified,
for several reasons. Neufeld (1991) has argued that scattering
in a multiphase medium results in a much larger equivalent
width of Ly
than would result
from resonant scattering in
a homogeneous medium - possibly even exceeding the strength of
Ly
that would be expected
without resonant scattering.
The empirical evidence also no longer supports resonant scattering. An
analysis of a larger sample of IUE observations of low redshift
star-forming galaxies (including recent observations by
Terlevich et
al. 1993) suggests that the observed line strength ratio
Ly/H
is consistent with that
expected from normal
recombination theory and reddening laws
(Calzetti and
Kinney 1992,
Valls-Gabaud 1993),
but much larger than would be the case were
resonant scattering of importance. There are also several classes of
astronomical objects (other than QSO's) at large redshift known to have
observable Ly
. Some (although
not all) radio galaxies are known to
possess strong Ly
emission, as
do several companions to QSOs
(Djorgovski et
al. 1985,
1987;
Steidel et
al. 1991;
Hu et al. 1991).
(In the latter case it is unclear whether the observed Ly
is excited
internally or by the QSO itself.) One or two damped Ly
absorbers have
now been detected in Ly
, as
have some companions to damped Ly
absorbers.
Furthermore, van
den Bergh (1990) has inspected CCD images
(Pierce 1988)
of 105 galaxies in the Ursa Major and Virgo clusters, and has
noted that galaxies with metallicities [Fe/H] < -1 exhibit essentially
no dust absorption. Thus a phase will always exist early in the
history of a PG during which time it will be dust free. For a constant
star formation rate (e.g., BW87), and for a final PG gas metallicity Z
1/3 Z
(as suggested by the maximum
metallicity
of the halo and the minimum metallicity of the disk), it follows that
as much as ~ 30% of the lifetime of the PG phase may be spent in
a relatively dust-free state (see also De Propris et
al. 1993). This
suggests an empirical correction to the predicted numbers of observable
Ly
emitting PGs that we
conservatively estimate to be of order a factor 10 in surface density.
Finally, it is of interest to compare the predicted far-IR flux from
dust-quenched PGs with observations (see also
Djorgovski and
Weir 1990;
Bond, Carr, and
Hogan 1991;
Bond and Myers
1994;
Blain and Longair
1993a,
b;
Wright et
al. 1993).
The COBE experiment has set an
upper limit of ~ 0.03 µerg cm-2 s-1
sr-1 cm on
spectral distortions in the CMB blackbody spectrum over the wavenumber
range 2-20 cm-1 (wavelengths 0.5-5 mm). Now, the total background
flux from PGs is expected to be S 2/(1 + z) µerg cm-2
s-1 sr-1 [from Eq. (5), assuming a flat spectrum for
rest
> 912Å, and
Z
10-34 g
cm-3].
The re-emitted spectra of starburst galaxies (e.g., Arp 220,
M82,
F10214+4724) all appear to peak in I
near 100µm. Hence a
reasonable estimate for the peak sub-mm-mm flux density from PGs is
Ik
S/k
0.02 µerg
cm-2 s-1 sr-1 cm,
if these PGs are completely shrouded in dust. (A more
detailed calculation, taking into account the energy distribution of
starburst galaxies, gives Ik a factor 2 smaller.) This can be
compared with the upper limit on spectral distortions in the CMB
blackbody of < 0.03 in the same units
(Mather et
al. 1993). In other
words, a substantial fraction of galaxy formation activity could be
hidden by dust, without violating COBE constraints on spectral
distortions in the CMB blackbody fit
(7).
The overall conclusion of this section is that some fraction
of PGs 10% should be
visible in Ly
P. Although dust shrouding
in the late stages of PGs appears very probable, it does not significantly
affect the current observational constraints.
5.2
Angular Extent
The limits quoted for emission line sources in
Section 4 were for
point sources. Since virtually all observations referred to were
acquired under sky noise (or detector noise) limited conditions, it
follows that the limiting flux for PGs will vary roughly as
1 / sqrt()
1/
, where
is a
measure of the characteristic angular diameter of a PG. The
characteristic size expected for PGs is quite uncertain (cf.
Section 2.4); we will assume a maximum
angular diameter of 5", corresponding
to about 30-40 kpc for z = 2-5 (h50 = 1,
0 = 1), and also
corresponding roughly to the characteristic size of the z = 1.8 radio
source 3C326.1
(McCarthy et
al. 1987). This is roughly
5X larger than typical seeing disks at ground-based
observatories, resulting in a shift of the data points to the left in
Figs. 7 and
8 (i.e., towards brighter limiting
fluxes).
Whether this angular extent is reasonable for a PG is unclear. For example, dissipation could result in a large concentration of gas towards the center of a proto-elliptical, something that agrees with the high luminosity and phase-space densities of ellipticals at the present epoch (Carlberg 1986), as well as the strong nuclear concentration of starbursts in nearby galaxies (Kormendy and Sanders 1992). The question of the angular size of PG's will only be resolved when a substantial population of these objects has been discovered.
5.3
Other Complications
Biasing (Kaiser 1986) could lead to a strong clustering of galaxy formation sites, and hence a relatively small volume filling factor for PG's. Such an effect is in fact seen in dissipative n-body simulations (e.g., Evrard, Summers, and Davis 1994). It was this complication that De Propris et al. (1993) sought to avoid by searching for PG's near known structures at intermediate redshift (e.g., QSO's); however, the null results of some of the other work cited above could be caused by a random placement of fields. Clearly this should be considered when designing future PG search strategies (see discussion in Section 6.1).
Another possibility that must be seriously considered is that we have completely miscalculated the expected optical appearance of PG's. For example, suppose that most proto-bulges and proto-ellipticals go through a luminous AGN phase immediately after commencing star formation (Djorgovski 1994). In this case PG's have already been found, and conventional PG searches are doomed! Or, suppose that the IMF of the initial burst of star formation were radically different from the Salpeter (1955) IMF. This could could result in very different properties of PG's (e.g., no emission lines in the case of an upper mass cutoff, or an extremely brief luminous PG phase for an IMF biased towards massive stars).
5.4
Revised Comparison of Observational Limits
with Models
Figure 9 shows a revised comparison of the
observational limits on Ly
emission from PGs with models. This figure differs from
Fig. 8 in
that we have increased the individual flux upper limits by 0.7 in log
LLy
to allow for
resolved structure (Section 5.3), and have
moved the predicted model surface densities down by a factor of 10X in
surface density to simulate the effect of dust absorption during 90%
of the lifetime of a PG (Section 5.2).
Figure 9. As in Fig. 8, except that the effects of dust have been allowed for by reducing the predicted density of the model by 10X, and the effects of a 5" object size have been taken into account by increasing the observed flux limits by 5X. See Section 5.3 for further details.
The corrections that were adopted above for angular size and dust are quite uncertain, and are probably at or near the extremes of what would be considered reasonable. Nevertheless, the result is clear: with the above corrections there no longer appears to be a significant discrepancy between model predictions and observations. There remain other effects discussed above (clustering of PG's, confusion of AGN's and PG's) that are not taken into account in Fig. 9. In other words, the fact that we have not found a pervasive population of emission line PGs to date is probably not surprising.
7 A somewhat different conclusion was reached by
Djorgovski
(1992). However, if his parameters are changed to match
our calculation (efficiency of energy production from
nuclear reactions = 0.01,
X = 0.01,
* = 0.001
from the initial starburst), the agreement with our conclusion
is reasonable. Back.