Annu. Rev. Astron. Astrophys. 1998. 36: 267-316
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Observations of absorption by the He I and HeII Lyman series provide another, independent source of information on the state of the intergalactic medium and the UV background radiation (Sargent et al 1980). Comparing the Doppler parameters of the HeII 304 Å and HI 1215 Å lines it is in principle possible to use the difference in atomic masses to measure the contributions from bulk and thermal motions to the line broadening separately, so theories of the kinematics of the cosmic gas can be tested. The far-UV HeII Lyman edge at 228 Å probes the intensity of the UV background at much shorter wavelengths than the HI edge. As the photoionization rates are dominated by the intensity of the ionizing radiation near the respective ionization edges, measurements of the HeII and HI column densities can then in principle fix the spectral shape of the UV background in the vicinity of two points, 228 Å and 912 Å. This comparison can be done as a function of wavelength (or redshift) so it is possible to measure the spatial spectral fluctuations of the UV background caused by local UV sources and by fluctuations in the intergalactic absorption, and, perhaps at higher redshifts, to study the progress of reionization (e.g., Shapiro & Giroux 1987; Donahue & Shull 1987; Miralda-Escudé & Rees 1993; Shapiro et al 1994; Madau & Meiksin 1994; Giroux et al 1995).

In a photoionized optically thin gas HeIII is the dominant ionization state; the remaining He is expected to be mostly in the form of singly ionized HeII. For realistic spectral intensity distributions (except for the very soft UV background caused by decaying neutrinos, Sciama 1990) HeI is undetectable in the optically thin clouds of the Lyalpha forest proper, although it should be present in Lyman limit systems (Miralda-Escudé & Ostriker 1992). Indeed, HeI yielded the first detection of helium at high redshift, when absorption by its 504 Å line was found in HST FOS data of several optically thick (z ~ 2) metal systems towards the bright QSO HS1700+64 (Reimers et al 1992, Reimers & Vogel 1993). The ionization state of HeI is less easy to interpret because of the possible presence of internal sources of radiation, and unknown shielding effects.

The HeII Ly alpha Forest

Because of its relative strength, HeII 304 Å is likely to be a better tracer of the low density baryon distribution than even HI Lyalpha.

The principal observable of the HeII Lyalpha forest is the ratio of the Gunn-Peterson optical depths of HeII to HI:

Equation 18     (18)

where NHeII and NHI are the column densities of HeII and HI, respectively (Miralda-Escudé 1993). The last equation is valid for an optically thin gas, where the ionization equilibrium is governed by photoionisation and both H and He are highly ionized. JHeII and JHI are the intensities of the ionizing radiation field weighted with the frequency dependence of the photoionization cross-sections. Thus the relative strength of the GP troughs are only dependent on the ratios of the ionizing fluxes, a situation which can be cast in terms of the column density ratio eta or the ratio of the intensities at the absorption edges, the softness parameter SL (Madau & Meiksin 1994),

Equation 19     (19)

The HeII/HI ratio eta can range from values of a few, to a thousand, depending on the spectral slope of the ionizing radiation. The shape of the ionizing spectrum depends on the relative mix between "hard" (AGNs) and "soft" (stellar) sources, and on the details of radiative transfer by the intergalactic medium (Bechtold et al 1987; Shapiro & Giroux 1987; Miralda-Escudé & Ostriker 1990; Meiksin & Madau 1993; Giroux & Shapiro 1996, Haardt & Madau 1996).

Thus a HeII 304 Å Gunn-Peterson trough should appear more prominent than the corresponding HI trough (Miralda-Escudé 1993), allowing for a more sensitive measurement of the distribution of gas in low density regions. For the actual HeII forest of discrete absorption lines a relation similar to equation (18) holds, where tau is now replaced by taueff as defined earlier (Miralda-Escudé 1993):

Equation 20     (20)

This relation gives the optical depths for a Lyalpha forest of individual lines above a certain optical depth threshold, assuming that the column density distribution of HI Lyalpha lines is a power law with index beta. The Doppler parameters are bHeII and bHI. Clearly, together with the strong HeII GP effect there should be a HeII forest stronger than the corresponding HI Lyalpha forest by a similar factor.

OBSERVATIONS     Only a small fraction of all QSOs are suitable for a search for HeII absorption. The short wavelength of 304 Å requires an object to be redshifted to at least z > 2 - 3 for the HeII line to enter the far UV bands accessible to the Hubble Space Telescope (HST), or the Hopkins Ultraviolet Telescope (HUT). The QSO has to be bright enough for a spectrum to be taken, and most importantly, there must be flux down to the wavelength range of interest. The average blanketing of the spectrum by Lyalpha lines (the "Lyman valley", Møller & Jakobsen 1990) and especially the total blackout imposed by individual intervening Lyman limit systems below 912 Å in their rest frame renders the large majority of QSOs useless for a HeII search (Picard & Jakobsen 1993), and surveys of known QSOs for residual UV flux (e.g. Jakobsen et al 1993) have to be mounted to select suitable candidates.

To date there are five detections of the HeII forest. A HeII absorption "break" blueward of the HeII emission line was first seen with the HST FOC far UV prism by Jakobsen et al, 1994 in the LOS to Q0302-003 (zem = 3.29), leading to an estimate for the mean optical depth, tauHeII = 3.2+infty-1.1. The object was reobserved at higher resolution with the GHRS instrument by Hogan et al (1997) (tauHeII approx 2, beyond the proximity effect region). Tytler et al. (1995) obtained tauHeII = 1.0 ± 0.2, later corrected to tauHeII > 1.5 (Tytler & Jakobsen, unpublished) in the LOS to Q1937-69 (zem = 3.18). Davidsen et al (1996), observed the object HS1700+6416 with HUT to obtain tauHeII = 1.0 ± 0.2, at < z > = 2.4. Reimers et al (1997), in the LOS to HE2347-4342 (zem = 2.89) find the HeII absorption to consist of patches with a high continuous GP component, tauHeII = 4.8+infty-2 in addition to the contribution expected from the discrete lines, which alternate with regions with less GP absorption tauHeII approx 3.

INTERPRETATION     Given the large uncertainties, all tau measurements to date seem to be consistent with each other, if the expected increase in the optical depth with redshift is taken into account. Constraining the strength and shape of the ionizing radiation from the absorbed flux requires a knowledge of the clumpiness of the gas, because of the exponential dependence of the absorbed flux on the optical depth. According to equations (18) and (20) the relative strengths of the absorption by HI and HeII depend on the amount of bulk motion relative to thermal motion, and on the column density distribution function (slope and possible cutoff at low column density), and the relative contribution from a diffuse absorption trough. Arguments have been put forward both against (Songaila et al 1995) and in favor (Hogan et al 1997; Reimers et al 1997; Zheng et al 1998) of the existence of such a trough in addition to the line absorption expected from translating the known HI Lyalpha forest into a HeII forest. If the proponents of additional trough absorption are correct this may also imply that the HI column density distribution function has been over-corrected for confusion, and does not extend to as low a column density as previously assumed. Superficially this argument sounds like the return of the lines-versus-trough debate familiar from the HI Gunn-Peterson effect, but there is new information to be gained by studying the detailed structure of the low density HeII absorption. The larger optical depth of HeII highlights very low density structure in voids, which may be too weak to be usefully constrained with optical HI Lyalpha forest spectra. Eventually such observations will constrain the spatial fluctuations of the ionizing radiation field and the density field in a large fraction of the volume of the the universe. The question of whether the spatial variations of the diffuse absorption can be (or should be) parametrized as "lines" may have to await the arrival of better data. In any case, the finding of a substantial amount of HeII absorption from voids is an important consistency check for hierarchical structure formation models (Zhang et al 1995, 1997; Croft et al 1997a).

At the time of this writing the spectral shape of the radiation field is still not well constrained (Sethi & Nath 1997; Reimers et al 1997; Zheng et al 1998). An interesting twist has been added by the detection of patchy HeII absorption, which is inconsistent with a uniform radiation field. Reimers et al (1997) invoke incomplete reionization of HeII as a possible explanation, an effect predicted to produce saturated absorption troughs (Meiksin & Madau 1993). However, it is hard to tell how strongly saturated the troughs really are. The observations may still be consistent with a fully re-ionized HeII, if the troughs are caused by local fluctuations in the HeII ionizing background (Miralda-Escudé 1997).

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