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5.1 Dust

Is strong Lyalpha emission really expected from a PG? A PG can be thought of as a giant H II region. A typical Lyalpha 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 Lyalpha emission, because the total path travelled by Lyalpha photons is sqrtN approx 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 Lyalpha; 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 Lyalpha 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 Lyalpha emission from PGs were doomed to failure.

Neverthless, it now appears that this simple picture of quenched Lyalpha 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 Lyalpha than would result from resonant scattering in a homogeneous medium - possibly even exceeding the strength of Lyalpha 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 Lyalpha/Hbeta 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 Lyalpha. Some (although not all) radio galaxies are known to possess strong Lyalpha 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 Lyalpha is excited internally or by the QSO itself.) One or two damped Lyalpha absorbers have now been detected in Lyalpha, as have some companions to damped Lyalpha 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 approx 1/3 Zsmsun (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 Lyalpha 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 approx 2/(1 + z) µerg cm-2 s-1 sr-1 [from Eq. (5), assuming a flat spectrum for rest lambda > 912Å, and rho Z appeq 10-34 g cm-3]. The re-emitted spectra of starburst galaxies (e.g., Arp 220, M82, F10214+4724) all appear to peak in Inu near 100µm. Hence a reasonable estimate for the peak sub-mm-mm flux density from PGs is Ik approx S/k approx 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 gtapprox 10% should be visible in LyalphaP. 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(Deltaomega) propto 1/Deltatheta, where Deltatheta 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, Omega0 = 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 Lyalpha 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 LLyalpha 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).

9 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 epsilon = 0.01, Delta X = 0.01, Omega* = 0.001 from the initial starburst), the agreement with our conclusion is reasonable. Back.

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