7. REIONIZATION OF THE IGM

The history of the transition from a neutral universe to one that is almost fully ionized can reveal the character of cosmological ionizing sources and constrain the star formation activity at high redshifts. The existence of a filamentary, low-density intergalactic medium (IGM), which contains the bulk of the hydrogen and helium in the universe, is predicted as a product of primordial nucleosynthesis [8] and of hierarchical models of gravitational instability with ``cold dark matter'' (CDM) [6], [26]. The application of the Gunn-Peterson constraint on the amount of smoothly distributed neutral material along the line of sight to distant objects requires the hydrogen component of the diffuse IGM to have been highly ionized by z 5 [49], and the helium component by z 2.5 [9]. From QSO absorption studies we also know that neutral hydrogen accounts for only a small fraction, ~ 10%, of the nucleosynthetic baryons at early epochs [29]. It thus appears that substantial sources of ultraviolet photons were present at z 5, perhaps low-luminosity quasars [22] or a first generation of stars in virialized dark matter halos with T_vir ~ 10⁴-10⁵ K [40], [21], [38]. The existence of a decline in the space density of bright quasars at redshifts beyond ~ 3 was first suggested by [39], and has been since then the subject of a long-standing debate. In recent years, several optical surveys have consistently provided new evidence for a turnover in the QSO counts [23], [57], [48], [28]. The interpretation of the drop-off observed in optically selected samples is equivocal, however, because of the possible bias introduced by dust obscuration arising from intervening systems. Radio emission, on the other hand, is unaffected by dust, and it has recently been shown [50] that the space density of radio-loud quasars also decreases strongly for z > 3. This argues that the turnover is indeed real and that dust along the line of sight has a minimal effect on optically-selected QSOs (Figure 4, left panel). The QSO emission rate of hydrogen ionizing photons per unit comoving volume is shown in Figure 4 (right panel) [34]. It is important to notice that the procedure adopted to derive this quantity implies a large correction for incompleteness at high-z. With a fit to the quasar luminosity function (LF) which goes as (L) L^-1.64 at the faint end [43], the contribution to the emissivity converges rather slowly, as L^0.36. At z = 4, for example, the blue magnitude at the break of the LF is M_* -25.4, comparable or slightly fainter than the limits of current high-z QSO surveys. A large fraction, about 90% at z = 4 and even higher at earlier epochs, of the ionizing quasar emissivity is therefore produced by sources that have not been actually observed, and are assumed to be present based on an extrapolation from lower redshifts.

Figure 4. Left: comoving space density of bright QSOs as a function of redshift. The data points with error bars are taken from [23] (filled dots), [57] (filled squares), [48] (crosses), and [28] (filled pentagon). The empty triangles show the space density of the Parkes flat-spectrum radio-loud quasars with P > 7.2 x 1026 W Hz-1 sr-1 [25]. Right: comoving emission rate of hydrogen Lyman-continuum photons (solid line) from QSOs, compared with the minimum rate (dashed line) which is needed to fully ionize a fast recombining (with gas clumping factor C = 30) Einstein-de Sitter universe with b h250 = 0.08. Models based on photoionization by quasar sources appear to fall short at z = 5. The data point shows the estimated contribution of star-forming galaxies at z 3, assuming that the fraction of Lyman continuum photons which escapes the galaxy HI layers into the intergalactic medium is fesc = 0.5 (see [34] for details).

Galaxies with ongoing star-formation are another obvious source of Lyman continuum photons. Since the rest-frame UV continuum at 1500 Å (redshifted into the visible band for a source at z 3) is dominated by the same short-lived, massive stars which are responsible for the emission of photons shortward of the Lyman edge, the needed conversion factor, about one ionizing photon every 10 photons at 1500 Å, is fairly insensitive to the assumed IMF and is independent of the galaxy history for t >> 10⁷ yr. Figure 4 shows the estimated Lyman-continuum luminosity density of galaxies at z 3. ⁽²⁾ The data point assumes a value of f_esc = 0.5 for the unknown fraction of ionizing photons which escapes the galaxy HI layers into the intergalactic medium. A substantial population of dwarf galaxies below the detection threshold, i.e. having star-formation rates < 0.3 M yr^-1 Mpc^-3, and with a space density in excess of that predicted by extrapolating to faint magnitudes the = 1.38 best-fit Schechter function, may be expected to form at early times in hierarchical clustering models, and has been recently proposed by [38] and [34] as a possible candidate for photoionizing the IGM at these epochs. One should note that, while highly reddened galaxies at high redshifts would be missed by the dropout color technique (which isolates sources that have blue colors in the optical and a sharp drop in the rest-frame UV), it seems unlikely that very dusty objects (with f_esc << 1) would contribute in any significant manner to the ionizing metagalactic flux.

As the hydrogen mean recombination timescale, _rec, at high redshifts is much smaller than the then Hubble time [34], it is possible to compute at any given epoch a critical value for the photon emission rate per unit cosmological comoving volume,

(8)

independently of the (unknown) previous emission history of the universe: only rates above this value will provide enough UV photons to ionize the IGM by that epoch. Here _H(0) is the mean hudrogen density of the expanding IGM at the present-epoch, and C is the ionized hydrogen clumping factor. One can then compare our determinations of _ion to the estimated contribution from QSOs and star-forming galaxies. The uncertainty on this critical rate is difficult to estimate, as it depends on the clumpiness of the IGM (scaled in the expression above to the value inferred at z = 5 from numerical simulations [18]) and the nucleosynthesis constrained baryon density. The evolution of the critical rate as a function of redshift is plotted in Figure 4. While _ion is comparable to the quasar contribution at z 3, there is some indication of a deficit of Lyman continuum photons at z = 5. For bright, massive galaxies to produce enough UV radiation at z = 5, their space density would have to be comparable to the one observed at z 3, with most ionizing photons being able to escape freely from the regions of star formation into the IGM. This scenario may be in conflict with direct observations of local starbursts below the Lyman limit showing that at most a few percent of the stellar ionizing radiation produced by these luminous sources actually escapes into the IGM [30]. ⁽³⁾ If, on the other hand, faint QSOs with (say) M_AB = -19 at rest-frame ultraviolet frequencies were to provide all the required ionizing flux, their comoving space density would be such (0.0015 Mpc^-3) that about 50 of them would expected in the HDF down to I_AB = 27.2. At z 5, they would appear very red in V - I as the Ly forest is shifted into the visible. This simple model can be ruled out, however, as there is only a handful (7) of sources in the HDF with (V - I)_AB > 1.5 mag down to this magnitude limit.

It is interesting to convert the derived value of _ion into a ``minimum'' SFR per unit (comoving) volume, _* (hereafter we assume _b h²₅₀ = 0.08 and C = 30):

(9)

(The conversion factor assumes a Salpeter IMF with solar metallicity). The star-formation density given in equation (9) is comparable with the value directly ``observed'' (i.e., uncorrected for dust reddening) at z 3 [35].

³ Note that, at z = 3, Lyman-break galaxies would radiate more ionizing photons than QSOs for f_esc 30%. Back.