4.1. Past and present X-ray instruments
With the advent of the Chandra and XMM-Newton observatories, high resolution X-ray spectroscopy of a wide variety of cosmic sources became feasible for the first time. Among the possible results most eagerly speculated upon was the detection of intergalactic absorption lines from highly ionised metals in the continuum spectra of bright extragalactic sources. After all, one of the most striking results from the Einstein observatory had been the detection of a very significant broad absorption feature at ~ 600 eV in the spectrum of PKS 2155-304 with the Objective Grating Spectrometer (Canizares & Kruper 1984). Ironically, if interpreted as intergalactic H-like O Ly absorption, redshifted and broadened by the expansion of the Universe, the strength of the feature implied the presence of a highly ionised IGM of near-critical density, a possibility that has of course definitively been discounted since then.
The High Energy Transmission Grating Spectrometer (HETGS; Canizares et al. 2005) and the Low Energy Transmission Grating Spectrometer (LETGS; Brinkman et al. 2000) on Chandra, and the Reflection Grating Spectrometer (RGS) on XMM-Newton (den Herder et al. 2001) were the first instruments to provide sensitivity to weak interstellar and intergalactic X-ray absorption lines. The 'traditional' ionisation detectors (proportional counters, CCD's) do not have sufficient energy resolution for this application. But the angular resolution provided by an X-ray telescope can be used to produce a high resolution spectrum, by the use of diffracting elements. Laboratory X-ray spectroscopy is typically performed with crystal diffraction spectrometers, and the use of crystal spectrometers for general use in astrophysics was pioneered on the Einstein observatory (e.g. Canizares et al. 1979). The Focal Plane Crystal Spectrometer indeed detected the first ever narrow X-ray absorption line in a cosmic source, the 1s - 2p absorption by neutral oxygen in the interstellar medium towards the Crab (Canizares & Kruper 1984). Previous grating spectrometers (the Objective Grating Spectrometer on Einstein and the two Transmission Grating Spectrometers on EXOSAT) had only limited resolution and sensitivity. But there is no fundamental limit to the resolution of a diffraction grating spectrometer, and the high angular resolution of the Chandra telescope has allowed for high resolution spectroscopy using transmission gratings. The focusing optics on XMM-Newton have more modest angular resolution, but they are used with a fixed array of grazing incidence reflection gratings, which produce very large dispersion angles and thus high spectral resolution. The HETGS provides a spectral resolution of = 0.0125 Å over the 1.5-15 Å band with the high line density grating, and = 0.025 Å over the 2-20 Å band with the medium line density grating. The LETGS has = 0.05 Å over the 2-170 Å band, while the RGS has = 0.06 Å over the 5-38 Å band. These numbers translate to resolving powers of R = 400-1500 in the O K band, and with a sufficiently bright continuum source, one should be able to detect equivalent widths of order 0.1-0.5 eV (5-20 mÅ), or below in spectra with very high signal-to-noise. The predictions for H- and He-like O resonance absorption line strengths are generally smaller than these thresholds, but not grossly so, and so a search for intergalactic O was initiated early on. Given that the current spectrometers are not expected to resolve the absorption lines, the only freedom we have to increase the sensitivity of the search is to increase the signal-to-noise ratio in the continuum, and it becomes crucial to find suitable, very bright sources, at redshifts that are large enough that there is a reasonable a priori probability of finding a filament with detectable line absorption.
As we will see when we discuss the results of the observational searches for X-ray absorption lines, the problem is made considerably more difficult by the very sparseness of the expected absorption signature. Frequently, when absorption features of marginal statistical significance are detected in astrophysical data, plausibility is greatly enhanced by simple, unique spectroscopic arguments. For instance, for all plausible parameter configurations, an absorbing gas cloud detected in N V should also produce detectable C IV absorption; or, both members of a doublet should appear in the correct strength ratio if unsaturated. In the early stages of Ly forest astrophysics, it was arguments of this type, rather than the crossing of formal statistical detection thresholds alone, that guided the field (e.g., Lynds 1971). But for the 'X-ray Forest' absorption, we expect a very different situation. The detailed simulations confirm what simple analytical arguments had suggested: in most cases, Intergalactic absorption systems that are in principle detectable with current or planned X-ray instrumentation will show just a single absorption line, usually the O VII n = 1-2 resonance line, at an unknown redshift. When assessing the possibility that a given apparent absorption feature is 'real', one has to allow for the number of independent trial redshifts (very roughly given by the width of the wavelength band surveyed, divided by the nominal spectral resolution of the spectrometer), and with a wide band and a high spectral resolution, this tends to dramatically reduce the significance of even fairly impressive apparent absorption dips. For instance, an apparent absorption line detected at a formal '3 significance' (or p = 0.0015 a priori probability for a negative deviation this large to occur due to statistical fluctuation) with Chandra LETGS in the 21.6-23.0 Å band pales to '1.7 ' if we assume it is the O VII resonance line in the redshift range z = 0 - 0.065; with N 30 independent trials, the chances of not seeing a 3 excursion are (1 - p)N = 0.956, or: one will see such a feature one in twenty times if one tries this experiment (we are assuming a Gaussian distribution of fluctuations here). If we allow for confusion with O VIII Ly at higher redshift, or even other transitions, the significance is even further reduced. And the larger the number of sources surveyed, the larger the probability of false alarm. Clearly, more reliable statistics on intervening X-ray absorbers and detections at higher significance are desired, but the required high-quality data will not be available until the next-generation X-ray facilities such as XEUS and Constellation X are installed (see Paerels et al. 2008 - Chapter 19, this volume).
Nevertheless, even with these odds, the above discussed high-ion measurements are important observations to do with the currently available instruments Chandra and XMM-Newton. Given the predicted strengths of the absorption lines (e.g., Chen et al.2003; see also Sect. 5.1), attention has naturally focused on a handful of very bright BL Lac- and similar sources. Below, we discuss the results of the searches. Note that the subject has recently also been reviewed by Bregman (2007).
4.2. Intervening WHIM absorbers at low redshift
The first attempt at detecting redshifted X-ray O absorption lines was performed by Mathur et al. (2003) with a dedicated deep observation (470 ks) with the Chandra LETGS of the quasar H 1821+643, which has several confirmed intervening O VI absorbers. No significant X-ray absorption lines were found at the redshifts of the O VI systems, but this was not really surprising in view of the modest signal to noise ratio in the X-ray continuum. Since it requires very bright continua to detect the weak absorption, it is also not surprising that the number of suitable extragalactic sources is severely limited. Early observations of a sample of these (e.g. S5 0836+710, PKS 2149-306; Fang et al. 2001; PKS 2155-304, Fang et al. 2002) produced no convincing detections. Nicastro and his colleagues then embarked on a campaign to observe Mrk 421 during its periodic X-ray outbursts, when its X-ray flux rises by an order of magnitude (e.g. Nicastro 2005). The net result of this has been the accumulation of a very deep spectrum with the Chandra LETGS, with a total of more than 7 million continuum counts, in about 1000 resolution elements. Nicastro et al. (2005) have claimed evidence for the detection of two intervening absorption systems in these data, at z = 0.011 and z = 0.027. But the spectrum of the same source observed with the XMM-Newton RGS does not show these absorption lines (Rasmussen et al. 2007), despite higher signal-to-noise and comparable spectral resolution (Mrk 421 is observed by XMM-Newton for calibration purposes, and by late 2006, more than 1 Ms exposure had been accumulated). Kaastra et al. (2006) have reanalysed the Chandra LETGS data, and find no significant absorption. Other sources, less bright but with larger redshifts, have been observed (see for instance Steenbrugge et al. (2006) for observations of 1ES 1028+511 at z = 0.361), but to date no convincing evidence for intervening absorption has materialised.
Observations have been conducted to try and detect the absorption by intergalactic gas presumably associated with known locations of cosmic overdensity, centred on massive clusters. Fujimoto et al. (2004) attempted to detect absorption in the quasar LBQS 1228+1116, located behind the Virgo cluster. An XMM-Newton RGS spectrum revealed a marginal feature at the (Virgo) redshifted position of O VIII Ly, but only at the ~ 95% confidence level. Likewise, Takei et al. (2007) took advantage of the location of X Comae behind the Coma cluster to try and detect absorption from Coma or its surroundings, but no convincing, strong absorption lines were detected in a deep observation with XMM-Newton RGS. The parallel CCD imaging data obtained with EPIC show weak evidence for Ne IX n = 1-2 line emission at the redshift of Coma, which, if real, would most likely be associated with WHIM gas around the cluster, seen in projection (the cluster virial temperature is too high for Ne IX). In practice, the absence of very bright point sources behind clusters, which makes absorption studies difficult, and the bright foregrounds in emission, will probably make this approach to detecting and characterizing the WHIM not much easier than the random line-of-sight searches.
The conclusion from the search for intergalactic X-ray absorption is that there is no convincing, clear detection for intervening absorption. This is, in retrospect, not that surprising, given the sensitivity of the current X-ray spectrometers, the abundance of suitably bright and sufficiently distant continuum sources, and the predicted properties of the WHIM.
4.3. The Milky Way halo and Local Group gas
The first positive result of the analysis of bright continuum spectra was the detection of O VII and O VIII n = 1 - 2 resonance line absorption at redshift zero. Nicastro et al. (2002) first identified the resonance lines in the Chandra LETGS spectrum of PKS 2155-304 (O VII n = 1 - 2, n = 1 - 3, O VIII Ly, Ne IX n = 1 - 2). Rasmussen et al. (2003) detected resonance absorption in the XMM-Newton RGS spectra of 3C 273, Mrk 421, and PKS 2155-304. Since then, at least O VII n = 1 - 2 has been detected in effectively all sufficiently bright continuum sources, both with Chandra and XMM-Newton; a recent compilation appears in Fang et al. (2006). Portions of a deeper spectrum that shows the zero redshift absorption are shown in Fig. 7.
Figure 7. Chandra LETGS spectrum of Mrk 421. Crosses are the data, the solid line is a model. The labels identify z 0 absorption lines in Ne, O, and C. The vertical tick marks indicate the locations of possible intergalactic absorption lines. From Williams et al. (2005).
Nicastro et al. (2002) initially interpreted the absorption as arising in an extended intergalactic filament. The argument that drives this interpretation is based on the assumption that O VI, O VII, and O VIII are all located in a single phase of the absorbing gas. The simultaneous appearance of finite amounts of O VI and O VIII only occurs in photoionised gas, not in gas in collisional ionisation equilibrium, and this requires that the gas has very low density (the photoionisation is produced by the local X-ray background radiation field; for a measured ionisation parameter, the known intensity of the ionising field fixes the gas density). The measured ionisation balance then implies a length scale on the order of l ~ 10 (Z0.1)-1 Mpc, where Z0.1 is the metallicity in units 0.1 Solar. This is a very large length, and even for 0.3 Z metallicity, the structure still would not fit in the Local Group (and it is unlikely to have this high a metallicity if it were larger than the Local Group). In fact, the absorption lines should have been marginally resolved in this case, if the structure expands with a fair fraction of the expansion of the Universe.
Rasmussen et al. (2003) constrained the properties of the absorbing gas by dropping the O VI, and by taking into account the intensity of the diffuse O VII and O VIII line emission as measured by the Wisconsin/Goddard rocket-borne Quantum X-ray Calorimeter (XQC) experiment (McCammon et al. 2002). The cooling timescale of O VI-bearing gas is much smaller than that of gas with the higher ionisation stages of O, and this justifies the assumption that O VI is located in a different, transient phase of the gas. With only O VII and O VIII, the medium can be denser and more compact, and be in collisional ionisation equilibrium. Treating the measured O VII emission line intensity as an upper limit to the emission from a uniform medium, and constraining the ionisation balance from the measured ratio of O VII and O VIII column densities in the lines of sight to Mrk 421 and PKS 2155-304, Rasmussen et al. derived an upper limit on the density of the medium of ne 2 × 10-4 cm-3 and a length scale l 100 kpc.
Bregman (2007) favours a different solution, with a lower electron temperature and hence a higher O VII ion fraction. If one assumes Solar abundance and sets the O VII fraction to 0.5, the characteristic density becomes ne ~ 10-3 cm-3, and the length scale (l ~ 20 kpc) suggests a hot Galactic halo, rather than a Local Group intragroup medium.
Arguments for both type of solution (a small compact halo and a more tenuous Local Group medium) can be given. The most direct of these is a measurement of the O VII line absorption towards the LMC by Wang et al. (2005) in the spectrum of the X-ray binary LMC X-3, which indicates that a major fraction of the O VII column in that direction is in fact in front of the LMC. Bregman (2007) points out that the distribution of column densities of highly ionised O on the sky is not strongly correlated with the likely projected mass distribution of the Local Group, and that the measured velocity centroid of the absorption lines appears characteristic of Milky Way gas, rather than Local Group gas. On the other hand, a direct measurement of the Doppler broadening of the O VII gas, from the curve of growth of the n = 1 - 2 and n = 1 - 3 absorption lines in the spectrum of Mrk 421 and PKS 2155-304 (Williams et al. 2005, Williams et al. 2007), indicates an ion temperature of Ti 106.0-6.3 K (Mrk 421) and Ti 106.2-6.4 K (PKS 2155-304), and these values favour the low-density, Local Group solution. Regardless, the prospect of directly observing hot gas expelled from the Galactic disk, or measuring the virial temperature of the Galaxy and/or the Local Group is exciting enough to warrant further attention to redshift zero absorption and emission.
Finally, the spectrum of Mrk 421 shows the expected z = 0 innershell O VI absorption, at 22.019 Å, both with Chandra and with XMM-Newton. There has been some confusion regarding an apparent discrepancy between the O VI column densities derived from the FUV and from the X-ray absorption lines, in the sense that the X-ray column appeared to be significantly larger than the FUV column (Williams et al. 2005). Proposed physical explanations for this effect involve a depletion of the lower level of the FUV transitions (1s2 2s) in favour of (at least) 1s2 2p, which weakens the 1032, 1038 Å absorption but does not affect the 1s - 2p X-ray absorption. However, it requires very high densities to maintain a finite excited state population, and, more directly, the measured wavelength of the X-ray line is actually not consistent with the wavelength calculated for 1s - 2p in excited O VI, off by about 0.03-0.05 Å, on the order of a full resolution element of both the Chandra LETGS and the XMM-Newton RGS (Raassen 2007, private communication). The conclusion is that the discrepancy is due to an authentic statistical fluctuation in the X-ray spectrum - or, more ironically, to the presence of a weak, slightly redshifted O VII absorption line.