Absorption signatures of warm-hot gas at low redshift: Broad H i Lyα Absorbers

Thorsten Tepper-García, Philipp Richter, Joop Schaye, Craig M. Booth, Claudio Dalla Vecchia, Tom Theuns
Institut für Physik und Astronomy, Universität Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam, Germany
Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The Netherlands
Department of Astronomy & Astrophysics, The University of Chicago, Chicago, IL 60637, USA
Kavli Institute for Cosmological Physics and Enrico Fermi Institute, The University of Chicago, Chicago, IL 60637, USA
Max Planck Institut für Extraterrestrische Physik, Giessenbachstraße 1, 85748 Garching, Germany
Institute for Computational Cosmology, Department of Physics, University of Durham, South Road, Durham, DH1 3LE, UK
Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium
E-mail: tepper@astro.physik.uni-potsdam.de
Accepted 2012 June 14. Received 2012 May 14; in original form 2012 January 26
Abstract

We investigate the physical state of H i absorbing gas at low redshift () using a subset of cosmological, hydrodynamic simulations from the OWLS project, focusing in particular on broad () H i Ly absorbers (BLAs), which are believed to originate in shock-heated gas in the warm-hot intergalactic medium (WHIM). Our fiducial model, which includes radiative cooling by heavy elements and feedback by supernovae and active galactic nuclei, predicts that by nearly 60 per cent of the gas mass ends up at densities and temperatures characteristic of the WHIM and we find that half of this fraction is due to outflows. The standard H i observables (distribution of H i column densities , distribution of Doppler parameters , correlation) and the BLA line number density predicted by our simulations are in remarkably good agreement with observations.

BLAs arise in gas that is hotter, more highly ionised and more enriched than the gas giving rise to typical Ly forest absorbers. The majority of the BLAs arise in warm-hot () gas at low () overdensities. On average, thermal broadening accounts for at least 60 per cent of the BLA line width, which in turn can be used as a rough indicator of the thermal state of the gas. Detectable BLAs account for only a small fraction of the true baryon content of the WHIM at low redshift. In order to detect the bulk of the mass in this gas phase, a sensitivity at least one order of magnitude better than achieved by current ultraviolet spectrographs is required. We argue that BLAs mostly trace gas that has been shock-heated and enriched by outflows and that they therefore provide an important window on a poorly understood feedback process.

keywords:
cosmology: theory — methods: numerical — intergalactic medium — quasars: absorption lines — galaxies: formation
pagerange: Absorption signatures of warm-hot gas at low redshift: Broad H i Ly AbsorbersAbsorption signatures of warm-hot gas at low redshift: Broad H i Ly Absorberspubyear: —-

1 Introduction

The analysis of intervening H i Ly absorption in the spectra of distant quasars (QSO) has become an extremely powerful tool to study the spatial distribution of the diffuse intergalactic medium (IGM) that follows the large-scale distribution of cosmological filaments, and to constrain the baryon content of the IGM as a function of redshift. At redshifts , more than 95 per cent of the baryonic matter resides in the form of photo-ionised, diffuse gas giving rise to the “Ly forest” in the spectra of distant QSOs (e.g. Rauch et al., 1997). As a consequence of expansion, the Ly forest thins out, and at the contribution of the Ly forest to the total baryon budget has decreased to per cent (e.g. Penton et al., 2004; Lehner et al., 2007). At the same time, the formation of galactic structures and the gravitational heating of the IGM by collapsing large-scale filaments lead to a gradually increasing amount of shock-heated intergalactic gas at temperatures , which is referred to as the warm-hot intergalactic medium (WHIM, Cen & Ostriker, 1999; Theuns et al., 1998; Davé et al., 2001; Bertone et al., 2008).

Since collisional ionisation determines the ionisation state of the shock-heated IGM, the neutral gas fraction in the WHIM is significantly lower, by at least one order of magnitude, than in the photo-ionised IGM of the same density (e.g. Richter et al., 2008). Because of this very small neutral hydrogen fraction in the WHIM, most of the recent observational campaigns to study warm-hot intergalactic gas at low redshift have concentrated on intervening absorption by highly ionised metals in ultraviolet (UV) spectra of bright QSOs. In particular, five-times ionised oxygen (O vi) has been used extensively to trace shock-heated intergalactic gas at low redshift and to constrain the baryon content of the WHIM (e.g. Tripp et al., 2000; Richter et al., 2004; Danforth et al., 2006; Danforth & Shull, 2008; Thom & Chen, 2008b; Tripp et al., 2008; Danforth et al., 2010). However, because O vi predominantly traces metal-enriched gas in a critical (in terms of ionisation balance) temperature regime at , and because the metals may well be poorly mixed on small scales (Schaye et al., 2007) the interpretation of intervening O vi absorbers is still controversial (e.g. Oppenheimer & Davé, 2009; Tepper-García et al., 2011; Smith et al., 2011). In particular, it is not yet clear whether O vi absorbers predominantly arise in photo-ionised (e.g. Thom & Chen, 2008a) or collisionally ionised gas (e.g. Danforth & Shull, 2008), or in complex absorbing structures with cool gas intermingled with warm-hot gas (Tripp et al., 2008).

An alternative to highly ionised metals as tracers of warm-hot gas is offered by H i absorption. Due to the low neutral hydrogen fraction expected from collisional ionisation at temperatures , Ly absorption from shock-heated WHIM filaments is expected to be very weak. In addition, H i absorption lines arising in gas at temperatures are expected to be relatively broad because of the effect of thermal broadening. Such broad () and shallow ( or ) Ly absorption features, the so-called Broad Ly Absorbers (BLAs; Richter et al., 2006a), are hence difficult to identify in the UV spectra of QSOs because of the limited signal-to-noise (S/N) and the low resolution of spectral data obtained with current space-based UV spectrographs.

In spite of being observationally challenging, directly detecting the small amounts of neutral hydrogen in the WHIM in absorption is a feasible task. The first systematic studies of BLAs at low redshift have been conducted using high-resolution Hubble Space Telescope (HST) Space Telescope Imaging Spectrograph (STIS) spectra of bright QSOs (Richter et al., 2004; Sembach et al., 2004; Richter et al., 2006a; Williger et al., 2006; Lehner et al., 2007; Danforth et al., 2010). These studies indicate that BLAs may indeed account for a substantial fraction of the baryons in the WHIM at . They also show, however, that identification and interpretation of broad spectral features in UV spectra with limited data quality is afflicted with large systematic uncertainties. In particular, the effects of non-thermal broadening and unresolved velocity-structure in the lines lead to the occurrence of broad spectral features that do not necessarily arise in gas at high temperatures. The Cosmic Origins Spectrograph (COS; Green et al., 2012), a new UV spectrograph which has recently been installed on HST, is expected to substantially increase the number of BLA candidates at low redshift. Due to the limited spectral resolution of COS , the systematic uncertainties in identifying thermally broadened H i lines in the WHIM temperature range will nevertheless remain.

To investigate the physical properties and spectral signatures of BLAs at low redshift, Richter et al. (2006b) have studied broad H i absorption features using a cosmological simulation based on a grid-based adaptive mesh refinement (AMR) method (Norman & Bryan, 1999). Their simulation reproduces the observed BLA number density and supports the idea that BLAs trace (at least in a statistical sense) a substantial fraction of shock-heated gas in the WHIM at temperatures . However, since this (early) simulation ignored several important physical processes that are expected to affect the thermal state of this gas phase (i.e. energetic feedback, radiative heating and cooling by hydrogen and metals), it is important to re-assess the frequency and physical properties of BLAs using state-of-the-art cosmological simulations with more realistic gas physics.

In this paper, we present a systematic study of BLAs at low redshift based on a set of cosmological simulations from the OverWhelmingly Large Simulations (OWLS) project (Schaye et al., 2010). This work complements our previous study on intervening O vi absorbers and their relation to the WHIM based on a slightly different set of OWLS simulations (Tepper-García et al., 2011, henceforth Paper I). The main features of the simulations we use are briefly described in Sec. 2. As we have done in Paper I for the case of low redshift O vi absorbers, we compare the predictions from our fiducial model to a set of standard H i observables, and discuss various physical properties of the general H i absorber population in Sec. 3. Given the dependence of the WHIM mass fraction predicted by simulations on the particular implementation of the relevant physical processes reported in the past (e.g. Cen & Ostriker, 2006), we investigate the impact of different physical models on the thermal state of the various gas phases in our simulations in Sec. 4. In this section we also present and discuss the results on the physical properties of the absorbing gas traced by BLAs. Finally, we summarise our main findings in Sec. 5. In the Appendix we include: a full description of our fitting algorithm (Appendix A); a detailed calculation of the observability of H i absorbing gas in terms of optical depth as a function of density and temperature (Appendix B); a discussion of the convergence of our results with respect to the adopted physical model (Appendix C), and with respect to the adopted resolution and simulation box size (Appendix D).

2 Simulations

The simulations used in this work are part of a large set of cosmological simulations that together comprise the OWLS project, described in detail in Schaye et al. (2010, and references therein). Briefly, the simulations were performed with a significantly extended version of the -Body, Tree-PM, Smoothed Particle Hydrodynamics (SPH) code gadget iii – which is a modified version of gadget ii (last described in Springel, 2005) –, a Lagrangian code used to calculate gravitational and hydrodynamic forces on a system of particles. The initial conditions were generated from an initial glass-like state (White, 1996) with cmbfast (version 4.1; Seljak & Zaldarriaga, 1996) and evolved to redshift using the Zeldovich (1970) approximation.

The reference model, dubbed REF, in the OWLS framework adopts a flat CDM cosmology characterised by the set of parameters as derived from the Wilkinson Microwave Anisotropy Probe (WMAP) 3-year data111These parameter values are largely consistent with the WMAP 7-year results (Jarosik et al., 2011), the largest difference being the value of , which is lower in the WMAP 3-year data than allowed by the WMAP 7-year data. (Spergel et al., 2007). This model includes star formation following Schaye & Dalla Vecchia (2008), metal production and timed release of mass and heavy elements by intermediate mass stars, i.e. asymptotic giant-branch (AGB) stars and supernovae of Type Ia (SNIa), and by core-collapse supernovae (SNIIe) as described by Wiersma et al. (2009b). It further incorporates kinetic feedback by SNIIe based on the method of Dalla Vecchia & Schaye (2008), as well as thermal feedback by SNIa (Wiersma et al., 2009b). Radiative cooling by hydrogen, helium and heavy elements is included following the method of Wiersma et al. (2009a). The ionisation balance for each SPH particle is computed as a function of redshift, density, and temperature using pre-computed tables obtained with the photoionisation package cloudy (version 07.02.00 of the code last described by Ferland et al., 1998), assuming the gas to be optically thin and exposed to the Haardt & Madau (2001) model for the X-Ray/UV background radiation from galaxies and quasars. It is worth noting that a simulation run that adopts the REF model, although with a slightly different set of values for the cosmological parameters (from WMAP7), has been shown to reproduce the H i absorption observed at in great detail (Altay et al., 2011).

Along with REF, we consider three further models from the OWLS suite respectively referred to as NOSN_NOZCOOL, NOZCOOL, and AGN. All these models differ from the reference model in one or more respects. NOSN_NOZCOOL neglects kinetic feedback by SNIIe, and the calculation of radiative cooling assumes primordial abundances. It is the most simple model in terms of input physics, and it is similar (and hence useful for comparison) to the simulation used by Richter et al. (2006b). The model NOZCOOL assumes primordial abundances when computing radiative cooling, and the model AGN includes feedback by active galactic nuclei (AGN) based on the model of black hole growth developed by Booth & Schaye (2009, see also ).

All these simulations were run in a cubic box of co-moving Mpc on a side, containing dark matter (DM) particles and equally many baryonic particles. The initial mass resolution is (DM) and (baryonic). The gravitational softening is set to co-moving kpc and is fixed at proper kpc below .

In this study, we choose AGN as our fiducial model since it is the most complete model in terms of input physics. In addition to reproducing various standard H i statistics (see Appendix C), this model has been shown to reproduce: the observed mass density in black holes at ; the black hole scaling relations (Booth & Schaye, 2009) and their evolution (Booth & Schaye, 2011); the observed optical and X-ray properties, stellar-mass fractions, star-formation rates (SFRs), stellar-age distributions and the thermodynamic profiles of groups of galaxies (McCarthy et al., 2010); and the steep decline in the cosmic star formation rate below (Schaye et al., 2010; van de Voort et al., 2011). Note that, while the H i statistics predicted by the AGN model are very similar to the predictions of the other models considered here (see Appendix C), there are notable differences in the temperatures of the gas traced by BLAs (see Fig. 11). We will address this point in more detail in Sec. 4.4. Table 1 briefly summarises the relevant features of the models described above. For a more detailed description of these (and other) models that are part of the OWLS project, see Schaye et al. (2010).

3 The general H i absorber population

In this section we test the predictions of our fiducial model (AGN) against observations using a set of well-measured H i observables: the H i column density distribution function (CDDF), the distribution of H i line widths, and the correlation between H i column density and line width.

3.1 Synthetic spectra

For a meaningful comparison to existing data, we generate 5000 random sightlines (1000 at five redshifts spanning the range with step ) through the simulation box covering a total redshift path , corresponding to an absorption path length .

We use the package specwizard written by Schaye, Booth, & Theuns to generate a synthetic spectrum for each sightline containing absorption by H i Ly only. Briefly, we draw a random physical sightline across the simulation box of size , which is simply defined as the line between a given point on opposite faces of the box, and the collection of SPH particles with projected distances to this line smaller than their smoothing length. Next, we calculate the ionisation balance for each SPH particle as a function of redshift, density, and temperature, which we do using precomputed tables obtained with the photoionisation package cloudy (version 07.02 of the code last described by Ferland et al., 1998), assuming the gas to be optically thin and exposed to the Haardt & Madau (2001) model for the X-Ray/UV background radiation from galaxies and quasars. We divide the physical sightline into pixels of constant width , where and are the Hubble constant in units of and the expansion factor at the box’s redshift , respectively, and compute the smoothed ion density , the ion density-weighted gas temperature, and the ion density-weighted peculiar velocity at each pixel. Proper distance bins of width along the sightline are transformed into velocity bins of width , where is the Hubble parameter at redshift ; ion number densities are transformed into ion column densities via , and gas temperatures into Doppler parameters using ., where is Boltzmann’s constant and is the ion’s mass. The H i optical depth at each pixel is computed assuming a thermal (i.e. Gaussian) profile, taking peculiar velocities into account, as described by Theuns et al. (1998, their Appendix 4). Finally, the optical depth spectrum is transformed into a continuum-normalised flux via .

We convolve our spectra with a Gaussian line-spread function (LSF) with a full width at half-maximum (FWHM) = 7 and re-sample our spectra onto pixels. We add Gaussian noise to each spectrum assuming a flux dependent root-mean-square (rms) amplitude given by , where S/N is the adopted signal-to-noise ratio. We assume a minimum, i.e. flux-independent noise level . This implies that our algorithm will underestimate the true column density of absorption features with a flux of the order of (or lower than) , which corresponds to a logarithmic central optical depth (see Appendix A). Our choice of a perhaps unrealistically low value for thus allows us to reduce the gap between the true and the fitted column density of saturated lines.

We generate three sets of spectra, adopting S/N=10, S/N=30, and S/N=50, respectively. The spectra with S/N=10 and S/N=30 thus closely match the properties of the large sample thus far obtained with HST/STIS; these will be used in Secs. 3.2, 3.3, and 3.4 to test the predicted H i observables against observations; the synthetic spectra with S/N=50 are intended to investigate the physical properties of the H i absorbing gas following a statistical approach, in the remaining sections of the paper.

Fitting of our 5000 synthetic spectra using the procedure described in Appendix A yields a total of 93430, 66705, and 28649 components for S/N =50, 30, and 10, respectively. The resulting line-number densities and their corresponding Poisson uncertainties are (S/N=50), (S/N=30), and (S/N=10). For reference, the sample of 341 Ly absorbers at identified in seven FUSE+STIS spectra with average S/N by Lehner et al. (2007) along an unblocked redshift path yields at , which agrees (within the Poisson uncertainties) with our result at a similar S/N.

3.2 Column-density distribution function

In Fig. 1 we show the column-density distribution function (CDDF), , obtained from our spectra with S/N=10 (red) and S/N=30 (blue) spanning the redshift range , together with results from different observations at similar redshifts using spectra with comparable (average) S/N values. Assuming that the CDDF can be parametrized in the form of a single power-law, , we find () for S/N=10 (S/N=30) for logarithmic column densities in the range (). The lower limit in approximately corresponds in each case to the completeness limit as given by eq. (6), while the upper limit roughly indicates the column density above which our fitting algorithm underestimates the true H i column density due to the minimum noise-level adopted (see Appendix A).

The slope we obtain is in fairly good agreement with the slope measured from different observations. For Lehner et al. (2007, their table 7) measure a range of values for absorbers in selected column-density intervals between and , and line widths or . If we extend the fitted column density range to , we find and for S/N=10 and S/N=30, respectively. Williger et al. (2010) use a subsample from the Lehner et al. (2007) data and their own data at , and find . Davé et al. (2001) measure for absorbers with column densities at a median redshift . Note, however, that a significantly shallower slope is found by Penton et al. (2004) who identify 109 Ly absorbers at along 15 STIS spectra with , and measure for logarithmic H i column densities in the range .

The amplitude of the CDDF resulting from the analysis of our synthetic spectra adopting different S/N is also in remarkable agreement with the observations. Note that the amplitude comes out naturally from our simulation, i.e. the CDDF has not been normalised to match the data in any way (even though that could have been justified because of uncertainties in the intensity of the UV background). At column-densities , our predicted amplitude agrees well with the data all the way down to the lowest column densities measured, . At , the amplitude of our predicted CDDF appears slightly lower (or its slope is steeper) than the result by Lehner et al. (2007). Note, however, that their data point at highest measured column-density bin has a rather large uncertainty. On the other hand, it is very likely that our choice of fitting parameters leads us to underestimate the amplitude of the predicted CDDF at by underestimating the true column density of saturated lines, as explained in Appendix A. A comparison between the true and the fitted H i column densities integrated along each sightline reveals that our fitting procedure indeed yields integrated H i column densities which are systematically lower than the true total column density, in particular for (see inset in Fig. 1). This could explain the difference between our predicted CDDF and the result by Lehner et al. (2007) at the high- end.

3.3 Line width distribution

Fig. 2 shows the distribution of Doppler parameters, , obtained from our synthetic spectra for S/N=10 and 30 spanning the redshift range , together with the line width distributions obtained from data with comparable S/N values and redshifts by Lehner et al. (2007, green data points) and Danforth & Shull (2008, orange data points). The median values of our predicted distributions are , , and for S/N = 10, 30, and 50 (not shown), respectively. All of these agree well with the median value found by Heap et al. (2002), , by Shull et al. (2000), , and with the median value for the full Lehner et al. (2007) sample. Note that all of these values are significantly larger than the median value measured by Davé & Tripp (2001). Our simulation shows a lower fraction of broad () absorbers when compared to the Lehner et al. (2007) -value distribution, but our results compare well to the line width distribution from Danforth & Shull (2008).

The predicted median -values indicate that a lower S/N value systematically shifts the line width distribution to slightly larger values. Yet, the number of components with relative to the total number of components identified in each case decreases from to per cent when the adopted S/N value decreases from 50 to 10. Here, two competing mechanisms are at work: On the one hand, a low S/N value results in a stronger blending of narrow components into (artificial) broad features. On the other hand, since broader lines are shallower (at a given column density), and thus more difficult to detect at low S/N, the number of broad components detected decreases with decreasing S/N. Compared to a higher S/N value, the net effect of a low S/N value is to yield a smaller number (both relative and absolute) of broad absorption features (at a given resolution and sensitivity).

3.4 The b\scriptsize H\,{\tiny I}−N\scriptsize H\,{\tiny I} distribution

Last, we compare the distribution obtained from our simulated spectra with S/N=30 and S/N=10 to two different sets of observations used for the comparison of our predicted CDDF and the line width distribution discussed in the last sections. To this end, we bin the lines from observations and from our synthetic spectra in using , and compute the median -value, and 25-/75-percentiles in each bin. The result is shown in Fig. 3. The distribution from our simulated spectra matches the observations well within the uncertainties. Even the drop in observed at low in the Davé & Tripp (2001) is well reproduced by our simulation. Note that lines with identified in spectra with S/N=30 generally have larger widths. This is a consequence of the fact that, at a fixed column density, lines with a given width are shallower with respect to narrower lines, and they can only be detected if the S/N is high enough.

Summarising, we conclude that the H i observables predicted by our fiducial model are in excellent agreement with observations. This agreement may be surprising in view of the uncertainty in the input physics used in our simulation. However, in Appendix C we show that these results are quite robust against the model variations with respect to our fiducial model considered here (see Sec. 4.1). We now proceed with the analysis of the physical conditions in low- H i absorbers.

3.5 Physical state of the H i absorbing gas

In this section we present and discuss the physical properties of the gas detected via H i absorption in our fiducial model (AGN; see Tab. 1). The method we use is similar to the method described in Paper I, in which we used optical-depth weighted quantities. Briefly, to compute the desired H i optical-depth weighted quantity (e.g. density) associated with a given absorption line, we first compute the optical-depth weighted density in redshift space along the sightline as in Schaye et al. (1999). Next, we compute the average of the optical-depth weighted density over the line profile, weighted again by the optical depth in each pixel and assign this last weighted average to the line. In concordance with Paper I, in the following we shall denote quantities weighted by H i optical depth by adding a corresponding subscript; thus, for example, the H i optical-depth weighted temperature is denoted by . We refer the reader to Sec. 5.1 of Paper I for a more detailed description about our method for computing optical depth-weighted quantities.

For simplicity, we obtain a new line sample of H i absorbers identified in synthetic spectra with S/N=50 generated from 5000 sightlines across a simulation box at a single redshift 222Note that our chosen redshift is slightly higher than the median redshift of most H i absorption-line studies at low redshift (e.g. in Lehner et al., 2007). Although some evolution does take place from , we do not expect the choice of this particular redshift to affect our conclusions in any significant way. , , spanning a total redshift path , which corresponds to an absorption path length . These spectra have been fitted following the method described in Appendix A.

We restrict our analysis to “simple”, i.e. single-component, absorbers, unless stated otherwise, We define an absorber as ‘simple’ if the velocity distance from its centre to any other component along the same sightline satisfies , where . Absorption lines that do not satisfy this condition are referred to as ‘complex’.

Table 2 contains various statistical and physical quantities resulting from the analysis of these new line sample, such as the relative number of identified components, the relative number of simple absorbers, the line-number density, , the total baryon content333The total baryon content in H i is computed via in H i, , and the total baryon content in gas traced by H i, (see also Sec. 4.5). Note that the statistical and physical properties of this new sample are very similar to the corresponding properties of the line sample discussed in Secs. 3.23.4.

3.5.1 Physical density and absorber strength

As previously noted by several studies (e.g. Schaye et al., 1999; Davé et al., 1999), there exists a tight correlation between H i column-density, , and overdensity444The mean baryonic density in our model is . , , of the absorbing gas usually parametrized in the form of a power-law, . Due to variations in the (local) ionising radiation field, the influence of other heating mechanism (shocks), and other factors such as the geometry of the absorbing structures, etc., this relation has an intrinsic scatter, which decreases with increasing redshift (Davé et al., 1999).

The relation between overdensity and H i column density for the diffuse IGM has been derived analytically by Schaye (2001), who assuming local hydrostatic equilibrium555The assumption of ‘local hydrostatic equilibrium’ implies that the size of a self-gravitating gas cloud is of the order of the local Jeans length. and optically thin gas finds

 logΔ∝23+α\leavevmode\nobreak (1−2b)(logN\scriptsize H\,{\tiny I}−92log(1+z)). (1)

In the above equation, is the slope of the temperature-density relation, , which results from the balance between photo-heating and adiabatic cooling (Hui & Gnedin, 1997), and is the power of the temperature in the expression for the H i recombination rate coefficient which behaves as . If re-ionisation of the IGM takes place at sufficiently high redshifts, its imprints on the thermal state of the IGM are eventually washed out, and the slope of temperature-density relation is expected to reach an asymptotic limit determined by the temperature dependence of the H i recombination rate. More specifically, at low redshift . We find666We compute the recombination rate coefficient for recombination case A numerically, and fit a power law in the given temperature range. in the temperature range , and hence . Inserting this value into eq. (1) gives . Thus, the value of the amplitude in the relation decreases with redshift, implying that absorbers of a given column density trace gas at higher overdensities at lower redshift.

In Fig. 4 we show the relation resulting from our fiducial model for all simple H i absorbers identified in spectra with different S/N values at . The turn-over in overdensity at column densities below the sensitivity limit (eq. 6) for each adopted S/N is caused by errors in the measured below this limit. Note also the deviation of the relation from a single power-law at column densities (indicated by the shaded area), which corresponds approximately to the column density for which the Ly line saturates. This is in part due to the inability of our algorithm to properly fit saturated lines.

Performing a least-square, error-weighted fit to the S/N=50 result for column densities above the corresponding sensitivity limit (; see eq. 6) and restricted to , we find and , normalised to . The resulting slope for S/N=30 (S/N=10) is () in the logarithmic column density range (), where the lower column density limit is given by eq. (6). A power-law with the theoretical expected slope 0.738 and arbitrary amplitude has been included in this figure for reference (black, dashed line).

For comparison, Davé et al. (2010, their equation 3) find and at , for absorbers arising in gas with temperatures in their simulation. If we restrict our sample to single-component absorbers with , we find and . We note that we do not rescale the amplitude of the UV background in our simulation, while Davé et al. (2010) adjust its amplitude by a factor 3/2 to bring their predicted evolution of the H i optical depth into better agreement with observations.

3.5.2 Gas temperature and line width

A matter of interest is to which extent the measured H i line width can be used to estimate the temperature of the H i absorbing gas. We explore this by comparing the H i thermal line width, , computed from the optical depth-weighted gas temperature, , to the total H i line width, , as a function of the line strength as given by the optical depth at the line centre, . The optical depth at the line centre is computed using the H i column density and the H i line width inferred from a Voigt profile fit to the line (see Appendix A). We bin the ratio in , and plot in Fig. 5 the median value and the 25-/75-percentiles in each bin as a function of , for all single component absorbers identified in our synthetic spectra with different S/N values at .

We see that thermal broadening becomes increasingly important with increasing line strength (or H i column density), and it contributes with at least 50 per cent to the total line width, i.e. , irrespective of the line strength and the adopted S/N value. The temperature of gas giving rise to absorption lines with central optical depths in the range (corresponding to strong lines) on average contributes with at least 90 per cent to the total line width, i.e. . The lower value shown by highly saturated lines, i.e. lines with (gray, shaded area) is most probably due to the uncertainty in the fit parameters of such lines. These results suggest, in view of the tight relation discussed above, that absorption arising in low density gas is subject to more significant non-thermal (i.e. Hubble) broadening than gas at higher density. This is consistent with the idea that low density, unbound gaseous structures are subject to the universal expansion, while gas at higher densities residing closer to galaxies may have detached from the overall expansion. We find (not shown) that the line width correlates well with the gas temperature for , but that it is a poor indicator of the thermal state of the gas for lower column densities.

Fig. 5 shows also that lines with central optical depths corresponding to H i column densities below the formal completeness limit for each adopted S/N value (indicated by the arrows) as given by eq. (6) have, on average, , which is un-physical. These lines correspond to absorption by gas at high temperatures, which gives rise to very shallow and extremely broad features that are (incorrectly) fitted with several components, thus yielding line widths that are narrower than allowed by the gas temperature.

In the central optical depth range typical for BLAs detected in spectra with S/N=50, (see Sec. 4.2.1) indicated by the hatched area, the contribution of thermal broadening to the line width amounts to 60 to 90 per cent. If non-thermal processes (e.g. turbulence) contribute to the line broadening in such a way that the total line width is given by , where is the non-thermal broadening (as would be the case for a purely Gaussian turbulence field), then the ratio of non-thermal broadening to total line width can be important, even though the thermal contribution is substantial. Take as an example the maximum, average thermal broadening to total line ratio for BLAs ; this value together with implies .

3.5.3 The (N\scriptsize H\,{\tiny I},\leavevmode\nobreak b% \scriptsize H\,{\tiny I})-plane

A deeper insight into the physical state of gas giving rise to H i absorption identified in real QSO spectra can be gained by studying the relation between selected physical quantities and the line observables, and , simultaneously. We have followed such an approach in Paper I in order to study the physical conditions of O vi absorbing gas, and now apply it to study gas traced via H i absorption. We focus on four quantities: gas temperature , neutral hydrogen fraction , total hydrogen column density , and gas metallicity . Note that gas temperature and metallicity are ‘true’ optical depth-weighted quantities, while total hydrogen column-density and ionisation fraction are ‘derived’ quantities. For instance, the neutral fraction is computed using the optical depth-weighted hydrogen particle density, , and the optical depth-weighted gas temperature, using pre-computed tables obtained with the photoionisation package cloudy (version 07.02 of the code last described by Ferland et al., 1998), as described in Sec. 2.

For each of these physical quantities we proceed as follows: First we compute the desired physical quantity, e.g. , for each of the simple absorbers in our S/N=50 line sample. We then divide the -plane into cells, and compute the median value for the desired quantity using the values of all absorbers with values in that cell. Fig. 6 displays the result for temperature (top-left), neutral hydrogen fraction (top-right), metallicity (bottom-left), and total hydrogen column density (bottom-right). The colour code indicates the median value of the corresponding physical quantity. For reference, we include contours (white solid curves) showing the distribution by number of the simple H i absorbers on the -plane. These contours enclose, starting from the innermost, 20, 40, 60, 80, and 90 per cent of the total number of H i components. The dashed horizontal and diagonal lines at the top-right corner of each panel indicate, respectively, the BLA selection criteria and (Richter et al., 2006a) adopting S/N=50.

There are several interesting features in this figure. First, all four physical quantities appear to have a relatively simple dependence on and . The temperature of the gas (top-left panel), for example, shows a positive correlation with the line width, which appears to be tighter for absorbers at a given (range), in agreement with the results presented in Sec. 3.5.2. In this respect, note the population of narrow (), low-column density () absorbers with high () optical depth-weighted temperatures. These correspond to the absorbers with column densities below the formal completeness limit and with , previously discussed.

The neutral hydrogen fraction (top-right panel) increases with , but strongly decreases with . This can be interpreted as a temperature-dependence, given the positive correlation between and . Correspondingly, the total hydrogen column density (bottom-right panel) increases with both and . The bottom-left panel shows that the (local) metallicity of the gas is strongly correlated with the line width. Given the correlation between gas temperature and line width shown the top-left panel, this suggests that there is a correlation between gas temperature and (local) gas metallicity. This correlation is very likely a consequence of strong feedback. Indeed, high-temperature, high-metallicity absorbers could be tracing shock-heated, enriched outflows in the surroundings of galaxies that have not had enough time to mix with the surrounding gas and to cool down, whereas low-temperature, low-metallicity absorbers could be tracing both gas that has not yet been impacted by outflows, and wind material that has been ejected at redshifts high enough for it to cool down and to dilute its metal content in the ambient gas.

The BLA selection regime defined by the dashed lines in each panel reveals a population of H i absorbers tracing highly ionised () gas with median temperatures , median (local) metallicities , and total hydrogen column densities , which is almost an order of magnitude higher than the total hydrogen column density of typical Ly forest absorbers (see also Fig. 12). According to our previous interpretation of the correlation, these results suggests that BLAs may be tracing galactic outflows. We will come back to this point in Sec. 4.4.2.

The results presented in this section indicate that the H i column density of unsaturated absorbers is a reliable tracer of the underlying physical density of the gas giving rise to the detected H i Ly absorption. Moreover, the temperature of the absorbing gas may be roughly estimated from the measured line width, as suggested by the average contribution of thermal broadening to the total line width of these absorbers. Finally, H i absorbers subject to the commonly adopted BLA selection criteria trace gas which appears to be physically distinct from the gas traced by typical Ly forest absorbers.

4 The warm-hot diffuse gas

In the next sections we explore in detail the effect of feedback and metal-line cooling on the physical state (i.e. density and temperature) of the gas in our simulations. Also, we investigate the H i absorption signatures of warm-hot diffuse gas, and the physical properties of the gas traced by broad H i absorption features (BLAs) identified in synthetic QSO absorption spectra. For this purpose, we use the H i sample from our fiducial model AGN presented in Sec. 3.5, and generate similar samples for all the other model runs. Comparison between model predictions and observations (whenever possible) are done exclusively for our fiducial run.

4.1 Model-dependence of the predicted warm-hot gas mass

On super-galactic scales, two mechanisms are able to shock-heat intergalactic gas to temperatures : a) galactic outflows driven by SNII explosions and by AGN activity; b) accretion shocks caused by infall onto the potential wells of dark matter halos. We have selected four model runs from the OWLS project, NOSN_NOZCOOL, NOZCOOL, REF, and AGN, to investigate the effect of each of these mechanisms on the properties of diffuse gas and its imprints on simulated absorption spectra. Note that these models have already been described in Sec. 2 (see also Tab. 1).

We are interested in the predicted distribution of gas mass among the various (gas) phases –in particular the warm-hot diffuse phase– defined in Tab. 3. We adopt a temperature threshold at (or ) and a density threshold at to distinguish these gas phases. The density threshold has been chosen so as to roughly separate unbound gas from collapsed structures (at ). The temperature threshold is motivated by the bi-modality in the gas mass distribution predicted by the models considered here (see below). Note that our value is somewhat below the ‘canonical’ but to some extent arbitrary commonly adopted to distinguish cool from warm-hot intergalactic gas (but see Wiersma et al., 2010).

The distribution of gas mass as a function of temperature and (over-)density predicted by the different models is presented in Fig. 7. The coloured areas show the cumulative gas mass (in per cent) indicated by the colour bar on the right. The vertical (horizontal) solid line in each panel indicates the density (temperature) threshold separating the various phases. Star-forming gas, which is defined as gas with physical densities (or777The relation between hydrogen particle density and (baryonic) overdensity is given by eq. (B) in Appendix B. at ), is shown to the right of the blue, vertical dashed line in each panel. The percentage included in each separate region indicates the baryonic mass in the corresponding (gas) phase relative to the total baryonic mass. In particular, the number (orange) in the top-left corner of each panel gives the mass fraction of gas with and , i.e. warm-hot diffuse gas. The starred percentage indicates in each case the baryonic mass confined in stars. Note that our adopted temperature threshold seems appropriate to separate cool, photo-ionised from shock-heated gas; the gas mass distribution at is clearly bimodal, with two phases having significant gas mass fractions above and below . The dotted contours indicate the neutral hydrogen fraction, , as function of density and temperature at ; it has been computed using pre-computed cloudy tables as described in Sec. 2. The logarithmic -value is indicated next to the corresponding contour in the top-left panel.

The sequence of models given by moving clock-wise from the top-left panel is essentially a sequence of increasing feedback strength (and model complexity). The mass fraction in warm-hot diffuse gas in the model NOSN_NOZCOOL (top-left panel) indicates that by roughly 30 per cent of the gas mass is shock-heated to temperatures by gravity alone. In the absence of any feedback on galactic scales, a large fraction of the gas that is accreted via gravitational infall at higher redshifts is able to cool and fuel star formation, with nearly 15 per cent of the gas mass ending up in stars by . The cool, photo-ionised diffuse gas at and in this model contains roughly 40 per cent of the total gas mass.

Moving on to the top-right panel (model NOZCOOL), we see that nearly 45 per cent of the baryonic mass in the simulation is in the form of warm-hot diffuse gas as a consequence of the kinetic energy released by supernova explosions. This corresponds to an absolute increase in mass of 15 per cent in this gas phase compared to NOSN_NOZCOOL. At the same time, the mass fraction in the cool diffuse IGM predicted by NOZCOOL decreases with respect to NOSN_NOZCOOL, but by a far smaller amount ( per cent in absolute terms). Thus, about 10 per cent of the gas mass that ends up in the WHIM by must be removed from a gas phase other than the cool diffuse IGM. The significantly lower mass in stars in the NOSN_NOZCOOL model compared to the NOZCOOL model strongly suggests that at higher redshifts supernova feedback shock-heats and blows a significant fraction of the ISM out of halos, which ends up in the WHIM by .

Including radiative cooling by heavy elements (model REF; bottom-right panel) has a negligible effect on the WHIM and the cool diffuse IGM, suggesting that metal-line cooling in the these gas phases is inefficient, either because their density is low, or the metals they contain are not yet well mixed, or perhaps because the level of enrichment is low, or a combination of them all. Interestingly, the REF model predicts a much higher mass fraction in stars and star-forming gas with respect to NOZCOOL, in spite of including SN feedback. The corresponding decrease in mass in warm-hot gas at high densities (which can be considered as the intra-group and intra-cluster medium; ICM), suggests that some of the gas in this phase is accreted and fuels star formation. However, the exact evolutionary path of the gas in phase space might be more complex than this.

Perhaps the most remarkable result is the fact that feedback from AGN has a very strong impact on the thermal state of the diffuse gas. Indeed, comparison of the bottom panels shows that an additional per cent of the total gas mass in the simulation is shock-heated to temperatures above and pushed into regions of low density (), such that by nearly 60 per cent of the gas mass ends up in the WHIM. A comparison of the mass distributions among the different phases predicted by REF and AGN suggests that half of the additional WHIM mass, i.e. per cent, at is removed at higher redshifts mainly from the ISM (thus reducing the mass in stars at by a factor ), and from the ICM. The remaining per cent of the WHIM mass apparently comes from the IGM. Comparison of the gas mass fractions in the warm-hot diffuse phase between the models NOZCOOL and AGN suggests that SN and AGN contribute roughly a similar amount to the baryon content of the WHIM. Equally important, the gas mass in this gas phase predicted by the models NOSN_NOZCOOL ( per cent) and AGN ( per cent) indicates that (strong) feedback (both by SN and AGN) may be able to shock-heat an amount of gas comparable to the gas shock-heated via gravitational infall. This results thus indicate that it is crucial to understand feedback processes on super-galactic scales before being able to make any reliable predictions about the baryon content of warm-hot gas in the Universe.

Consider finally the hydrogen neutral fraction indicated by the dotted contours. The logarithmic value of is indicated next to the corresponding contour in the top-left panel, and they are identical in all the other panels. At a fixed temperature, the neutral hydrogen fraction increases with density, since the ionisation state of the gas is dominated by photo-ionisation. However, at sufficiently high densities, i.e. at , collisional ionisation dominates and the neutral hydrogen fraction depends only on the gas temperature, resulting in contours running parallel to the -axis. In either case, the neutral hydrogen fraction steeply decreases with temperature at all densities (see also Richter et al., 2008; Danforth et al., 2010). As a consequence, the gas at densities and temperatures characteristic of the warm-hot diffuse gas is expected to be highly ionised. In particular, the model AGN predicts that the vast majority of the gas in the WHIM contains a neutral hydrogen fraction . This has important implications for the detectability of this gas phase via H i absorption which will be discussed in detail in Sec. 4.2.1.

4.2 Observability of (warm-hot) gas using (broad) H i absorption

In this section we explore to what extent the actual gas mass (distribution) in the cool and warm-hot diffuse phases are traced by the H i detected in absorption. In particular, we investigate the thermal state of the gas traced by absorbers selected in terms of their line width, albeit only on a statistical basis. At the same time, we invert the approach and inquire about the spectral signatures (and physical properties) of H i absorbers arising in warm-hot gas. Even though we are interested primarily in broad absorbers, we include narrow absorbers in our analysis as well. This allows for a more robust interpretation of our results. We define the following classes of H i absorbers in terms of their spectral and/or physical properties:

1. NLA: H i absorber components with Doppler parameters . We adopt the notation introduced by Lehner et al. (2007).

2. BLA: H i absorber components with Doppler parameters that satisfy the sensitivity limit introduced by Richter et al. (2006a) and adopted in other studies (Danforth et al., 2010; Williger et al., 2010)

 ⎛⎜⎝N\scriptsize H\,{\tiny I}/cm−2b% \scriptsize H\,{\tiny I}/kms−1⎞⎟⎠≥3×1012(S/N)−1.

This limit is equivalent to a H i Ly central optical depth

 τ0≥2.27(S/N)−1. (2)

We feel that using a detection limit in terms of is more intuitive than the limit in terms of , in particular for small values of , since in this limit . Henceforth, we will use eq. (2) instead of the limit in terms of as our second BLA selection criterion; also, all corresponding results will be expressed in terms of rather than .

3. hot-BLA: BLAs with optical-depth weighted temperatures . This class is defined in order to isolate BLAs genuinely tracing warm-hot gas. Note that our adopted temperature threshold is lower than the actual temperature implied by Doppler parameters assuming pure thermal broadening888The thermal width of an H i line arising in gas at is . . This is, however, not an issue since as we have shown ins Sec. 3.5.2, the line width of BLAs is never entirely set by thermal broadening.

As in previous sections, all the results presented here refer to simple absorbers as defined in Sec. 3.5, unless stated otherwise. Tab. 4 gives an overview of the statistics of simple absorbers in each of the classes defined above, for all four models considered here. An example of such a simple (broad) H i absorber is shown in Fig. 8. The top panel shows the spectrum (black) and corresponding fit (red) centred at a H i Ly line with and . The next panel shows the smoothed overdensity (black) and the H i optical depth-weighted overdensity (red dashed) along the sightline. Note the relative simple density structure of the absorbing gas. The smoothed (black) and H i optical depth-weighted (red dashed) temperatures are shown in the third panel (from the top). Clearly, the gas giving rise to the BLA shown in the top panel has a temperature . As a consequence of the high temperature, the absorbing gas is highly ionised, with a total H i column density , and it represents thus a significant baryon reservoir. The slight off-set between the BLA and the density peak of the absorbing gas is due to its (small) peculiar velocity along the sightline (bottom panel).

4.2.1 Spectral sensitivity

Before we investigate the physical and statistical properties of BLAs in our simulations, we need to assess how setting a fixed sensitivity limit as given by eq. (2) may bias the detection of warm-hot gas. Under rather simple assumptions, it is possible to model the H i Ly central optical depth, , of H i absorbing gas as a function of its temperature and density. This allows one to put constraints on the physical state of the gas phase traced using H i absorption, given a set of instrumental limitations that lead to a minimum detection (or sensitivity) limit. Conversely, following this approach it is possible to estimate the sensitivity needed to detect gas at a given temperature and density. We describe the basic assumptions and give a detailed calculation of our model in Appendix B. In particular, we show that it depends on the assumed size of the absorbing structure. With no better estimate at hand, we assume the absorbers to have a linear size999Note that the simulation runs we use do resolve the Jeans length, in particular at the relatively low densities consider here. of order the local Jeans length (Schaye, 2001, see also eq. 12). Note that we have already showed in Section 3.5.1 that this assumption can account for the relation predicted by the simulations. Also, our model neglects non-thermal broadening, implying that all sensitivities in terms of given henceforth are strict lower limits.

We now investigate the relation between the gas mass distribution in our simulations and the gas mass detected in H i absorption. For each of the BLAs in the line sample obtained for each model considered here, we estimate and , and plot the resulting distribution on the plane. The result is shown in Fig. 9. The coloured areas indicate the cumulative number fraction (in per cent) of BLAs at a given density and temperature. The gray solid contours correspond in each case to the gas mass distribution shown in Fig. 7. Note that for the contours the axes indicate the actual gas overdensity and gas temperature. We plot in each panel a series of black dashed contours which indicate the central optical depth, , as a function of and as given by eq. (13). The corresponding contour values are indicated next to each curve only in the top-left panel, but they are identical for all the other panels. Note in particular the thick dashed contour (magenta) which indicates our adopted sensitivity limit as given by eq. (2) for S/N=50, i.e. (or ).

One notable feature in this figure is the bi-modality of the distribution of gas traced by broad H i absorbers, irrespective of the model. We see in each case a population of BLAs tracing gas at low temperatures () and overdensities , and a second population tracing warm-hot gas at and overdensities . Note, however, that the amplitude of the distribution varies from model to model. Comparing the gray contours to the coloured distribution we see clearly that the H i detected in absorption traces only a fraction of the gas mass in the simulations. In particular, the model AGN (bottom-left panel) shows a large fraction of gas mass at and which is not detected in H i absorption. The same is true for the models NOZCOOL and REF, although at slightly different temperatures and overdensities. Consideration of the thick dashed contour reveals that this is a selection effect, i.e. the gas is simply not detectable at our adopted sensitivity limit. As discussed above, this comes about because the gas at such high temperatures and relative low densities is extremely ionised, with neutral hydrogen fractions , and its absorption simply falls below our adopted detection threshold (cf. Fig. 14).

Thus, in our fiducial model BLAs detected in spectra with S/N=50 typically have , while the bulk of the gas mass at and is predicted to give rise to absorption with . The fact that we do detect in absorption some of the gas at temperatures and densities which correspond to sensitivities slightly smaller than our adopted value (i.e. to the left of the thick dashed contour) reflects the simplicity of the assumptions that go into modelling the absorption strength in terms of and . Nevertheless, the expected and actual detections are fairly consistent with each other. Based on this, we estimate that in order to detect most of the baryonic mass in the WHIM using thermally broadened H i absorption, spectra with very high S/N are required that allow detection at the level, which is roughly an order of magnitude lower than the typical sensitivities adopted in BLA studies (Richter et al., 2006a; Danforth et al., 2010; Williger et al., 2010) .

4.3 BLA number density

Since our adopted sensitivity limit matches the value used to identify BLA candidates in real QSO spectra, we may directly compare the predicted and observed line frequencies. Applying the selection criteria described above (i.e. and ) to our AGN H i line sample obtained from spectra with S/N=50 at results in 6120 BLA candidates, which corresponds to a line-number density , where the quoted uncertainty is pure Poissonian. The number densities of BLAs identified in spectra with S/N=30 and S/N=10 are given in Tab. 5. For completeness, we also include in this table the corresponding numbers for NLAs. Note that the absolute number of BLAs decreases while the relative number of simple BLAs increases with decreasing S/N. This is due to a low S/N causing line blending and increasing the line widths, as discussed in Sec. 3.3 (see also Richter et al., 2006a, their figure 2).

In Fig. 10 we compare the cumulative BLA number density as a function of predicted by our fiducial run obtained from spectra with various S/N values to the available observational results obtained from QSO spectra at comparable redshifts and with similar (average) S/N. The arrows indicate the BLA sensitivity limit in terms of for the corresponding S/N value as given by eq. (2). The predictions for simple BLAs are indicated by the solid lines. Since our definition of simple absorbers is somewhat arbitrary, we include the corresponding predictions for all, i.e. simple and complex, BLA candidates as well (dashed lines). These two sets of lines thus span our predicted line-frequency range for .

It is noteworthy that our predictions are broadly consistent with the observed range of BLA number densities. For example, our prediction for S/N=30 (blue solid) agrees with the results by Lehner et al. (2007, green data points). These authors find in their data with an average , discarding lines with associated line-parameter errors larger than 40 per cent, a fraction of single-component BLAs close to 30 per cent and a mean (averaged over 7 sightlines) line-number density at (equivalent to ), and at (or ). Both our S/N=50 (black) and S/N=30 (blue) predictions match the result by Danforth et al. (2010, orange data point), who find at () along seven sightlines at , spanning a total redshift path , with . Their sample consists of 15 single-component BLAs and 48 BLAs with uncertain velocity structure. Williger et al. (2010, magenta data point) estimate their detection limit at (or ) and obtain and for their full and single-component BLA samples, respectively, along a single sightline () and corresponding spectrum with S/N=20 – 30. Finally, Richter et al. (2006a, black data point) measure using their reliable sample of single-component BLAs, detected along four sightlines at (), at a sensitivity (or ), in spectra with an average .

4.4 Physical properties of broad H i absorbers

In Sec. 3 we discussed the relation between the physical conditions of the gas traced by typical H i absorbers and their line observables (, ) using our fiducial model. We now focus on the physical conditions of the gas giving rise to H i absorbers identified as simple BLAs in our synthetic spectra at ; these correspond to single-component H i absorbers falling within the region defined by the polygon in Fig. 6 which is defined through two criteria: a) the line width satisfies ; b) the central optical depth obeys eq. (2), i.e. .

Given the importance of broad H i absorbers as potential WHIM tracers, and the dependence of the predicted WHIM mass fraction on the adopted physical model, we next explore the relation between the measured line width and the temperature of the absorbing gas using the models introduced in Sec. 2. We further use our fiducial model (AGN) to investigate the ionisation state, neutral hydrogen fraction, and metallicity of the gas traced by different classes of H i absorbers. Finally, we estimate the baryon content of the gas traced by BLAs using all models, but compare our results to observations using only the model AGN.

4.4.1 Temperature distribution of (broad) lines

In Fig. 11 we show the distribution of temperatures of the gas traced by both BLAs (red histograms) and NLAs (blue histograms) identified our spectra with S/N = 50 at obtained from different models. The dashed, vertical line in each panel indicates the temperature threshold adopted to separate cool from warm-hot gas (see Tab. 3).

In all models, the temperature distribution of the gas traced by NLAs shows that lines with Doppler parameters preferentially arise in gas at temperatures with a peak at , as expected from their width. The few lines which are narrower than allowed by the temperature of the absorbing gas (i.e. the section of the blue histogram to the right of the vertical, dashed line) are mostly weak lines that fall below the formal completeness limit, as discussed in Sec. 3.5.2. But some of these lines are real detections, which suggest that gas at different temperatures overlaps in velocity space (due to redshift-space distortions), and some of it may even overlap in position space, indicating the existence of multi-phase absorbing structures. In models with feedback (NOZCOOL, REF, AGN), the temperature distribution of the gas traced by NLAs is broader than in the model without feedback (NOSN_NOZCOOL), and the fraction of lines with ‘un-physical’ widths is higher. This can be explained as follows. Outflows driven by SNe and AGN follow the path of least resistance in space, thus escaping into the voids while leaving the cooler, denser filaments intact (Theuns et al., 2002). With increasing feedback strength, the cross-section of such high-temperature outflows increases as well, and so does the chance for a random sightline to intersect both cool, dense filaments and shock-heated material, with their corresponding absorption overlapping from time to time along the spectrum.

Note that the NLA temperature distributions in the models NOZCOOL and REF are very similar to each other, and the same is true for the corresponding BLA temperature distributions. Moreover, the fraction of hot-BLAs is only slightly lower in REF than in NOZCOOL. This indicates that metal-line cooling is of secondary importance in setting the thermal state of the gas phase traced by (broad) H i absorbers.

In contrast to narrow H i absorbers, broad H i lines trace gas around two different temperatures, and , irrespective of the model (red histograms). Clearly, BLAs arising in gas at low temperatures must be subject to substantial non-thermal broadening, such as bulk flows and/or Hubble broadening101010Note that our simulations lack the resolution to capture small-scale turbulence within the gas. . Since the line width of an H i absorber with arising in gas at is completely dominated by non-thermal broadening, its linear size (assuming the line width is entirely due to Hubble broadening) must be , which is consistent with the Jeans length of a filament with a mean density and temperature (eq. 12).

Interestingly, the fraction of BLAs tracing gas at low () and high () temperatures is very different in each model, as can be judged qualitatively by the shape of the corresponding histograms and quantitatively by the percentage included in each panel which gives the fraction of hot-BLAs, i.e. BLAs tracing gas with . In fact, the ratio of BLAs tracing cool gas to those tracing warm-hot gas appears to be very sensitive to feedback strength. In principle, this could be used to constrain feedback models observationally. The caveat is that a statistically significant sample of confirmed BLAs would be required for which the gas temperature can be measured reliably. In our fiducial model (AGN), which includes the strongest feedback, the majority of the BLAs trace gas at , with little contamination by non-thermally broadened lines. In fact, two out of three BLA candidates arise in gas at temperatures .

The bi-modal character of the gas temperature distributions for BLAs predicted by the model NOSN_NOZCOOL is also consistent with previous results. Richter et al. (2006b) find in a simulation that included a model similar to our NOSN_NOZCOOL that per cent of the BLAs trace gas at , and a significant fraction gas at . The quantitative difference between theirs and our result for NOSN_NOZCOOL is probably caused by the difference in the simulation methods used. Using a linear model to fit the thermal to total line width, Richter et al. (2006b) find that (no error quoted). We note that we do not find such a tight correlation between and , but if we perform a linear fit between these two quantities, we find111111For reference, the corresponding results for S/N=30 and S/N=10 are and , respectively. . This is consistent with the result presented in Sec. 3.5.2 that thermal broadening on average contributes with (at least) 60 per cent to the total line width of BLAs.

Lehner et al. (2007) argue that broad H i lines may trace both cool and warm-hot gas, but that the majority of BLAs trace gas at if their width is dominated by thermal broadening. As mentioned in the previous paragraph, thermal broadening accounts for a significant fraction to the total line width of single-component, broad H i absorbers. Thus, our simulations are consistent with the result inferred from observations that these absorbers do preferentially trace gas at high temperatures, at least in models with (some type of) feedback.

In summary, we find that in the absence of feedback BLA samples are contaminated by a large fraction of non-thermally broadened lines. Conversely, the fraction of broad H i absorption lines tracing gas at temperatures increases when feedback is included. For instance, our fiducial model predicts that, in a statistical significant sample, 67 per cent of the BLAs trace gas at . Our results thus strongly support the idea that reliable BLAs detected in real absorption spectra are genuine tracers of gas at such high temperatures.

4.4.2 Neutral hydrogen fraction, total hydrogen column density, and metallicity

In Fig. 12 we show the distribution of neutral hydrogen fraction (left panel), total hydrogen column density (middle panel), and (local) metallicity (right panel) of the gas traced by narrow absorbers (blue), BLAs (red), and hot-BLAs (orange) identified in spectra with S/N=50 obtained from our fiducial model. The vertical dashed line indicates in each case the corresponding median value.

In general terms, the physical properties of the gas traced by BLAs and hot-BLAs show similar distributions and comparable median values, but they are somewhat different from the corresponding properties of the gas traced by NLAs. For example, the median neutral hydrogen fraction of gas traced by NLAs is , which is slightly higher than the neutral hydrogen fraction of the gas traced by (hot-)BLAs, . This is expected since, as we have shown previously, the temperature of gas giving rise to broad H i absorption is, on average, higher than the temperature of gas giving rise to narrow H i absorbers. Furthermore, the median total hydrogen column density of the gas detected via (hot-)BLAs is , which is several times larger than the median total hydrogen column density of the gas traced by NLAs, , and its distribution extends out to significantly larger values, , as compared to . This is due to several factors. First, as shown in Figs. 14 and 9, high-temperature gas detected via H i absorption at a fixed sensitivity necessarily has a higher density with respect to gas at lower temperatures. Also, a higher density implies an average higher as a consequence of the correlation. Finally, gas at high temperature has a lower neutral hydrogen fraction, which in turn yields higher total hydrogen column densities for a given . The high(-er) total hydrogen density of the gas traced by broad H i absorbers implies that its baryon content is considerable. We will come back to this point in more detail in Sec. 4.5.

Quite interesting is the difference between the gas metallicity distributions. While the metallicity of the gas traced by NLAs shows a broad distribution with a tail extending to very low values and a median , the metallicity distribution of the gas traced by broad absorbers is narrow, with most values falling in the range , centred around . On average, the metallicity