Abstract
The intergalactic medium (IGM) is the dominant reservoir of baryons at all cosmic epochs. In this paper, we investigate the evolution of the IGM from z= 2 → 0 in (48 h−1 Mpc)3, 110-million particle cosmological hydrodynamic simulations using three prescriptions for galactic outflows. We focus on the evolution of IGM physical properties, and how such properties are traced by Lyα absorption as detectable using Hubble's Cosmic Origins Spectrograph (COS). Our results broadly confirm the canonical picture that most Lyα absorbers arise from highly ionized gas tracing filamentary large-scale structure. Growth of structure causes gas to move from the diffuse photoionized IGM into other cosmic phases, namely stars, cold and hot gas within galaxy haloes, and the unbound and shock-heated warm-hot intergalactic medium (WHIM). By today, baryons are comparably divided between bound phases (35 per cent in our favoured outflow model), the diffuse IGM (41 per cent) and the WHIM (24 per cent). Here we (re)define the WHIM as gas with overdensities lower than that in haloes (
today) and temperatures T > 105 K, to more closely align it with the ‘missing baryons’ that are not easily detectable in emission or Lyα absorption. Strong galactic outflows can have a noticeable impact on the temperature of the IGM, though with our favoured momentum-driven wind scalings they do not. When we (mildly) tune our assumed photoionizing background to match the observed evolution of the Lyα mean flux decrement, we obtain line count evolution statistics that broadly agree with available (pre-COS) observations. We predict a column density distribution slope of 
for our favoured wind model, in agreement with recent observational estimates, and it becomes shallower with redshift. Winds have a mostly minimal impact, but they do result in a shallower column density slope and more strong lines. With improved statistics, the frequency of strong lines can be a valuable diagnostic of outflows, and the momentum-driven wind model matches existing data significantly better than the two alternatives we consider. The relationship between column density and physical density broadens mildly from z= 2 → 0, and evolves as 
for diffuse absorbers, consistent with previous studies. Linewidth distributions are quite sensitive to spectral resolution; COS should yield significantly broader lines than higher resolution data. Thermal contributions to linewidths are typically subdominant, so linewidths only loosely reflect the temperature of the absorbing gas. This will hamper attempts to quantify the WHIM using broad Lyα absorbers, though it may still be possible to do so statistically. Together, COS data and simulations such as these will provide key insights into the physical conditions of the dominant reservoir of baryons over the majority of cosmic time.
1 INTRODUCTION
Diffuse intergalactic hydrogen produces numerous weak redshifted H i Lyα (1216 Å) absorption features along lines of sight to distant bright objects such as quasars, the phenomenon known as the Lyα forest (Lynds 1971; Sargent et al. 1980). Advances in sensitive high-resolution spectroscopy and theoretical understanding of structure formation have led to the currently favoured paradigm for the origin of the Lyα forest (Cen et al. 1994; Zhang, Anninos & Norman 1995; Hernquist et al. 1996; Miralda-Escudé et al. 1996): it arises from highly photoionized intergalactic hydrogen (Gunn & Peterson 1965) tracing uncollapsed large-scale structure in the Cosmic Web. The general properties of the Lyα forest are well-described by the Fluctuating Gunn–Peterson Approximation (FGPA; Weinberg, Katz & Hernquist 1997a; Croft et al. 1998), in which a tight relation between density and temperature in cosmologically expanding photoionized gas (Hui & Gnedin 1997) leads to a tight correlation between the Lyα optical depth and the underlying mass density at each location along the line of sight (LOS). At z≳ 2, where the Lyα transition falls into the observed-frame optical, this approximation is quite good, and it can be used to infer the mean baryon density (Rauch et al. 1997; Weinberg et al. 1997b) and the matter fluctuation spectrum, which in turn provides constraints on cosmological parameters (Croft et al. 1999, 2002; McDonald et al. 2000, 2006; Viel, Haehnelt & Springel 2004; Viel et al. 2008).
In this paper, a successor to Davé et al. (1999, 2001), we use cosmological hydrodynamic simulations to model the IGM and the Lyα forest at lower redshifts. Here, the Lyα transition falls in the ultraviolet (UV), requiring more difficult space-based observations. Furthermore, the physical description of the Lyα forest departs more strongly from the FGPA, because filamentary structures begin to grow so large as to heat a significant fraction of intergalactic gas to well above photoionization temperatures (Davé et al. 1999). This results in the emergence of the warm-hot intergalactic medium (WHIM; Cen & Ostriker 1999; Davé et al. 1999, 2001; Cen & Ostriker 2006), which contains a substantial fraction of all baryons today. Additionally, the evolving relationship between matter overdensity and Lyα column density is such that at low z, a given overdensity produces a lower column density absorber: roughly speaking, a 1014.5 cm−2 line at z≈ 2.5 is physically analogous to a 1013 cm−2 line at z= 0 (Davé et al. 1999). This shift results in many fewer Lyα forest absorbers to a given sensitivity limit, i.e. a much thinner forest of lines. All these factors make the low-z Lyα forest more difficult to characterize both observationally and theoretically, and not as useful for constraining cosmology (Zhan et al. 2005). But the intergalactic medium (IGM) at low z still contains the vast majority of baryons in the Universe, so understanding the low-z Lyα forest and the WHIM remains a central challenge to assembling a complete picture of cosmic baryon evolution.
One of the original Key Projects of Hubble Space Telescope was to understand the low-z Lyα forest. The faint object spectrograph (FOS), despite being unable to fully resolve Lyα absorbers, provided critical insights into the nature of the low-z Lyα forest. For example, even the earliest observations showed that the number density evolution of Lyα absorbers must slow dramatically between z > 2 and z= 0 (Bahcall et al. 1991; Morris et al. 1991). Initially, it was suggested that low-z absorbers might represent a different population than those at high z, with the high-z systems tracing the Cosmic Web and the low-z systems arising in galaxy haloes (Bahcall et al. 1996). This idea was supported by the apparently tight connection between column density and galaxy impact parameter (Chen et al. 1998). However, Davé et al. (1999) showed that all these observations can be fully accommodated within the structure formation model of the Lyα forest. The change in number density evolution can be explained as an ionization effect (Theuns, Leonard & Efstathiou 1998), since the dominant source of metagalactic flux (quasars) diminishes rapidly at z≲ 2 (Haardt & Madau 2001), countering the effect of the declining mean density of baryons. The relationship between Lyα equivalent width and galaxy impact parameter arises because the IGM is denser around galaxies owing to matter clustering. Subsequent higher resolution quasar spectroscopy using the Space Telescope Imaging Spectrograph (STIS) has generally confirmed these interpretations, and STIS Lyα forest data are well-described by structure formation models (Davé & Tripp 2001). Hence the low-z Lyα forest is not fundamentally different than the high-z one, although the relationship of neutral hydrogen absorption to large-scale structure has shifted.
The installation of the Cosmic Origins Spectrograph (COS) on Hubble should usher in a new age for the study of the low-z Lyα forest. The dramatically increased sensitivity over STIS will enable a more robust characterization of the z≲ 1 IGM, and it will enable study of Lyα absorbers at overdensities comparable to that detectable at high z. COS will also enable tomographic probes of the IGM at transverse separations that will provide interesting constraints on the large-scale coherence of Lyα absorbers (e.g. Casey et al. 2008). All these data will provide theoretical studies with new opportunities to understand the low-z IGM, and new challenges for models to meet.
An advantage of low-z IGM work compared to high z is that the galaxy population around low-z absorbers can be studied to much greater depth. The relation between the two provides unique insights into how the early and late stages of gravitational collapse are connected, and how the baryons have decoupled from the dark matter via shock heating and radiative cooling. The galaxy–absorber connection can be studied through the individual association of galaxies with absorbers or by statistical measures such as correlation functions. This is the subject of a subsequent paper in this series (Kollmeier et al., in preparation). Another paper in this series (Oppenheimer et al., in preparation) will deal with metal-line absorbers detectable using COS, and their relationship to galaxies and large-scale structure.
In this paper, we employ state-of-the-art cosmological hydrodynamic simulations to study the z≲ 1 IGM as traced by the Lyα forest and WHIM. Where appropriate we include comparisons with existing data and predictions for COS. Our new simulations have 216 times more particles and 80 times more volume compared to our previous studies in Davé et al. (1999) and Davé & Tripp (2001), and they include more sophisticated physical processes compared to those works and more recent studies such as Paschos et al. (2009). For example, our simulations now include metal-line cooling and a well-constrained heuristic model for galactic winds that enrich the IGM and regulate star formation in accordance with observations. While we will not discuss chemical enrichment in this work (see e.g. Oppenheimer & Davé 2008), the energy input from such outflows can non-trivially impact the thermal conditions in the IGM, particularly around galaxies. Tornatore et al. (2010) investigated the IGM in simulations similar to ours with the further addition of feedback from black holes, showing that it can significantly impact WHIM properties.
In Section 2 we describe our cosmological hydrodynamic simulations and the generation and analysis of artificial spectra. In Section 3 we describe the physical conditions of the IGM from z= 2 → 0, including how Lyα absorbers trace large-scale structure and the emergence of WHIM gas. In Section 4, we present statistics of Lyα absorbers and their evolution. We also present comparisons to STIS data and predictions for COS, and study the impact of differences in spectral resolution and noise. In Section 5, we discuss how Lyα absorbers trace the physical conditions of the low-z IGM, including wide absorbers that trace WHIM gas. We summarize and discuss the implications of our results in Section 6.
2 SIMULATIONS
2.1 The code and input physics
We employ our modified version (Oppenheimer & Davé 2008) of the N-body+hydrodynamic code gadget-2 (Springel 2005). gadget-2 uses a tree-particle-mesh algorithm to compute gravitational forces on a set of particles, and an entropy-conserving formulation (Springel & Hernquist 2002) of Smoothed Particle Hydrodynamics (SPH; Gingold & Monaghan 1977; Lucy 1977) to simulate pressure forces and shocks on the gas particles. We include radiative cooling from primordial gas assuming ionization equilibrium (following Katz, Weinberg & Hernquist 1996) and metal-line cooling based on Sutherland & Dopita (1993). Star formation follows a Schmidt (1959) Law calibrated to the Kennicutt (1998a,b) relation; particles above a density threshold where subparticle Jeans fragmentation can occur are randomly selected to spawn a star with half their original gas mass. The interstellar medium (ISM) is modelled through an analytic subgrid recipe following McKee & Ostriker (1977), including energy returned from supernovae (Springel & Hernquist 2003a).
Kinetic outflows are also included emanating from all galaxies that are forming stars. Gas particles eligible for star formation are randomly selected to be in an outflow. Outflowing particles have their velocity augmented by vw in a direction given by v×a, where v and a are the comoving velocity and acceleration of the particle, respectively. The ratio of the probabilities to be in an outflow relative to that for forming into stars is given by η, the mass loading factor. Hydrodynamic forces on wind particles are ‘turned off’ until the particle reaches one-tenth the threshold density for star formation, or a maximum time of 20 kpc/vw. This hydrodynamic delay allows wind particles to escape their host galactic discs, mimicking the effect of ‘chimneys’ in the ISM that are unresolvable in cosmological simulations but would allow the escape of gas in real galaxies. The choices for vw and η, including their possible dependence on galaxy or halo properties, define the ‘wind model’.
We consider three wind models. The first has no winds, ‘nw’. This model fails a number of observational tests, including overproducing cosmic star formation (e.g. Davé et al. 2001; Balogh et al. 2001) and failing to enrich the IGM (Oppenheimer & Davé 2006), but it serves as a baseline model to assess the impact of outflows on the diffuse IGM.
The second wind model uses constant values of η= 2 and vw= 680 km s−1 for all outflows from every galaxy; we call this our ‘constant wind’ (cw) model. The cw model is similar to that used in Springel & Hernquist (2003b), Tornatore et al. (2010) (though their wind speed is somewhat lower) and the OverWhelmingly Large Simulations (OWLS; Wiersma et al. 2009). This model uses all the supernova energy (assuming a Chabrier IMF) to drive kinetic winds. Doing so suppresses cosmic star formation to be broadly in agreement with observations, with the added benefit of yielding resolution-converged results (Springel & Hernquist 2003b). In detail, it fails to enrich the IGM in agreement with high-z C iv absorbers (Oppenheimer & Davé 2006) or to enrich galaxies in accordance with observations of the mass–metallicity relation (Davé, Finlator & Oppenheimer 2007), but it is still a physically reasonable scenario that captures some of the main effects implied by the observations.
Our preferred model, which we refer to as ‘vzw’, uses scalings expected for momentum-driven winds (Murray, Quatert & Thompson 2005), though we note that such scalings can be generated by other physical mechanisms (Dalla Vecchia & Schaye 2008). Here, 
, and η=σ0/σ, where σ is the velocity dispersion of the host galaxy. We estimate σ from the galaxy's stellar mass following Mo, Mao & White (1998), using an on-the-fly friends-of-friends galaxy finder, as described in Oppenheimer & Davé (2008). The scaling factor fL is randomly chosen for each ejection event in the range 1.05–2, based on observations of local starbursts by Rupke, Veilleux & Sanders (2005). This choice also gives outflow velocities consistent with that seen in z∼ 1 (Weiner et al. 2009) and z∼ 2–3 (Steidel et al. 2004) star-forming galaxies. The ejection speeds are generally comparable to the galaxy escape velocities at low redshifts, but because wind particles are slowed by hydrodynamic interactions with surrounding gas, they typically do not escape their host galactic haloes, at least in more massive systems. σ0 is a free parameter adjusted to broadly match the cosmic star formation history; here we choose σ0= 150 km s−1. This yields η∼ 1 for L∼L* galaxies at z∼ 2, which is in agreement with the constraints inferred from z∼ 2 galaxies by Erb (2008).
The key features of our momentum-driven wind model are the higher mass-loading factors and lower ejection velocities in lower mass galaxies. This model has displayed repeated and often unique success at matching a range of cosmic star formation and enrichment data. This includes observations of IGM enrichment as seen in z∼ 2–4 C iv absorbers (Oppenheimer & Davé 2006, 2008), z∼ 0 O vi absorbers (Oppenheimer & Davé 2009) and z∼ 6 metal-line absorbers (Oppenheimer, Davé & Finlator 2009). Concurrently, it also matches the galaxy mass–metallicity relation (Davé et al. 2007; Finlator & Davé 2008), and the enrichment levels seen in z= 0 intragroup gas (Davé, Oppenheimer & Sivanandam 2008). It also suppresses star formation in agreement with high-redshift luminosity functions (Davé, Finlator & Oppenheimer 2006) and the cosmic evolution of UV luminosity at z∼ 4–7 (Bouwens et al. 2007). In contrast to the nw and cw models, the vzw model approximately reproduces the observed z= 0 stellar mass function of galaxies up to luminosities L∼L*, though it still predicts excessive stellar masses for higher mass galaxies (Oppenheimer et al. 2010). The numerical implementation of this model – with probabilistic, one-at-a-time particle ejection and the temporary turn-off of hydrodynamic forces – is only a heuristic representation of the underlying physics, and there are significant numerical and physical uncertainties associated with the hydrodynamic interactions between wind and ambient-halo particles and the mixing of outflows with the surrounding gas. None the less, this heuristic model appears to distribute matter and energy into the IGM and regulate galaxy growth in broad accord with observations.
While we leave a detailed discussion of metals to a forthcoming paper in this series, the simulations include a sophisticated chemical evolution model that follows four individual species (C, O, Si, Fe) from three sources: Type II SNe, Type Ia SNe and stellar mass loss from AGB stars. The former instantaneously enriches star-forming particles, whose metallicity can then be carried into the IGM via outflows (described below). Type Ia modelling is based on the fit to data by Scannapieco & Bildsten (2005), with a prompt component tracing the star formation rate and a delayed component (with a 0.7 Gyr delay) tracking stellar mass. Stellar mass loss is derived from Bruzual & Charlot (2003) population synthesis modelling assuming a Chabrier (2003) IMF. Delayed feedback adds energy and metals to the three nearest gas particles; Type Ia add 1051 erg per SN, while AGB stars add no energy, only metals. We use Limongi & Chieffi (2005) yields for Type II SNe; yields for Type Ia and AGB stars come from various works (see Oppenheimer & Davé 2008, for details).
2.2 Simulations
The primary simulations used here are those described by Oppenheimer et al. (2010), using the three outflow models outlined above. Each simulation contains 3843 gas and 3843 dark matter particles, in a random periodic volume of 48 h−1 Mpc (comoving) on a side with a gravitational softening length (i.e. spatial resolution) of 2.5 h−1 kpc (comoving, Plummer equivalent). We assume a cosmology concordant with WMAP-7 constraints (Jarosik et al. 2010), specifically Ωm= 0.28, ΩΛ= 0.72, h≡H0/100 km s −1 Mpc−1= 0.7, Ωb= 0.046, n= 0.96 and σ8= 0.82. This yields gas and dark matter particle masses of 3.56 × 107 M⊙ and 1.81 × 108 M⊙, respectively. The initial conditions are generated with an Eisenstein & Hu (1999) power spectrum at z= 129, in the linear regime, and evolved to z= 0; they are identical for all simulations. Our naming convention is r[boxsize]n[number of particles per side][wind model], where the initial letter ‘r’ indicates the particular choice of cosmology above. Hence our models are r48n384nw, r48n384cw and r48n384vzw15, where the postscript 15 on vzw indicates our choice of σ0= 150 km s−1.
To investigate the effects of the numerical resolution and box size, we also employ a simulation with 5123 gas and 5123 dark matter particles, in a random periodic volume of 96 h−1 Mpc (comoving) on a side with a gravitational softening length of 3.75 h−1 kpc (r96n512vzw15). This simulation is run with the same momentum-driven wind model as our 48 h−1 kpc case, and we will refer to it as ‘vzw-96’. Compared to vzw-48, it has an eight times larger simulation volume but 3.375 times worse mass resolution. Hence, it tests both sensitivity to box size and numerical resolution, although the dynamic range in either sense is not dramatically large.
2.3 Generating spectra
Spectra are generated using our spectral generation code specexbin, which casts lines of sight at an angle to the simulation axes, allowing continuous and non-repeating lines of sight to be generated through the periodic simulation volumes. We generate 70 such continuous spectra from z= 2 to z= 0. specexbin calculates optical depths in H i and a variety of metal ions; here we will only be concerned with Lyα. For line statistics we will typically consider three redshift ranges, namely z= 0–0.2 (which we will call ‘z= 0’), z= 0.9–1.1 (‘z= 1’) and z= 1.8–2 (‘z= 2’). In each interval, the total path length for the 70 spectra is Δz= 14. This is comparable to the path length to be obtained by e.g. the program of the COS GTO team.
The procedure for calculating optical depths is described by Oppenheimer & Davé (2008). In brief, the algorithm is to (i) calculate the neutral fraction of each gas particle based on the density, temperature and the assumed photoionizing flux (discussed below); (ii) smooth the neutral hydrogen density on to randomly chosen lines of sight in real space; (iii) calculate H i optical depths assuming ionization equilibrium and optically thin gas using cloudy96 (Ferland et al. 1998) and (iv) use the H i-weighted peculiar velocity as well as Hubble flow to rebin the real-space optical depths into redshift space. This produces a table of optical depths versus redshift along each LOS. Concurrently, for each ionic absorption species specexbin outputs the optical depth-weighted temperature, density and metallicity, which are used to quantify the physical conditions in each identified absorber. For lines of sight that parallel box axes, specexbin produces the same Lyα absorption spectra as tipsy1 (Hernquist et al. 1996). As reported by Peeples et al. (2010), the Lyα flux power spectra computed from tipsy spectra at z= 3 are indistinguishable from those produced by the independent spectral extraction code of Lidz et al. (2010), confirming the robustness of the procedure to the details of numerical implementation.
Extracted spectra are converted from optical depths to fluxes, resampled to a pixel scale of 6 km s−1, and convolved with the COS line spread function2 (LSF). Specifically, we use the far-UV (FUV) G130M LSF at 1450 Å. The LSF varies only very slightly with wavelength in the FUV channel, but is substantially different (and narrower) in the NUV channel. Nevertheless, we keep the LSF fixed at all wavelengths so as to avoid introducing any artificial evolution from the varying LSF. Generally, the FUV LSF is somewhat broader than had been originally expected, with its central peak having an equivalent 1σ Gaussian width of ≈ 17 km s−1, and it also has substantial non-Gaussian wings. Finally, we add Gaussian random noise to the simulated spectra assuming a signal-to-noise ratio (S/N) of 30 per pixel. This is comparable to the highest quality data that will be obtained with COS.
The shape and amplitude of the metagalactic photoionizing flux are still not well constrained, particularly at lower redshifts. We assume that the flux is spatially uniform, which is probably a good approximation in the diffuse and optically thin Lyα forest. We take the spectral shape from that predicted by Haardt & Madau (2001) using the population of observed quasars and star-forming galaxies (their ‘Q1G01’ model). This model assumes a 10 per cent escape fraction of ionizing radiation from galaxies and is broadly consistent with available constraints (e.g. Scott et al. 2002).
We adjust the amplitude of the metagalactic flux to match the observed evolution of the mean flux decrement (
) in the Lyα forest. A modest post-processing adjustment recovers essentially the identical answer to running the entire simulation with a different ionizing background, since the dynamics of Lyα forest gas are negligibly affected by photoionization (Weinberg et al. 1998). The amount of adjustment varies slightly among our simulations, since the outflows have a small but non-negligible impact on the Lyα forest. In practice, we multiply all the optical depths by a factor fτ before we convert to flux, then measure 
, and iteratively adjust fτ until we obtain a good match to 
. In the optically thin approximation (excellent in this case), this procedure is equivalent to multiplying the strength of the ionizing background by 1/fτ. While in principle we could have fτ be a function of redshift, this was not seen to be necessary to within the accuracy of available data, and so we simply determine a constant fτ individually for each simulation.
The resulting evolution of the mean flux decrement in the Lyα forest is shown in the top panel of Fig. 1. The values of fτ are indicated in the parentheses within the legend; they are close to unity, indicating that the original Haardt & Madau (2001) metagalactic flux amplitude is viable to within current observational uncertainties. In all cases, the resulting 
is a reasonable match to observations by Kirkman et al. (2007), who measured the flux decrement evolution using data compiled from Hubble's FOS at z≲ 1.5 and the Keck telescope's High Resolution Echelle Spectrograph (HIRES) at z≳ 1.5. The simulations appear to have a somewhat higher flux decrement at 1 ≲z≲ 1.5, but in this regime the low resolution of FOS and the increased blending owing to a thicker Lyα forest (as compared to z∼ 0) are more likely to result in continuum placement errors that would cause the flux decrement to be biased low. Hence, we do not consider these discrepancies serious as yet, though they are worth revisiting when better data become available from COS.
Top: mean flux decrement (
) evolution from z= 2 → 0 in our three simulations. Data points are from Kirkman et al. (2007). The numbers in parentheses are the values of fτ by which the optical depths are multiplied in each simulation to obtain the agreement with data as shown. Bottom: 
evolution that matches the mean flux for the vzw (green) and nw (blue) runs. The cw run (not shown) is identical to nw. These are simply the Haardt & Madau (2001) values divided by fτ. Data points show proximity effect measurements from Scott et al. (2002).
The bottom panel of Fig. 1 shows the evolution of the H i photoionization rate 
that yields the mean flux evolution in the top panel. Since we multiply the Haardt & Madau (2001) model by a constant factor, the shapes of the curves are identical to their model. The amplitude is multiplied by f−1τ, so vzw is slightly higher than nw; cw is identical to nw since it has the same fτ. All the models are consistent with the available observational constraints as they are fairly uncertain (see Davé & Tripp 2001, for more constraints); here we show proximity effect measurements from Scott et al. (2002). If we take the z= 1.4 measurement of 
at face value and modify 
to match it, this would result in an increase in 
by 0.2 dex at z= 1.4, and a subsequent recovery back to the original track by z= 1.6. This would be an odd detour in its evolution, implying a peak in photoionizing flux at z∼ 1.5 along with a secondary peak at z∼ 2–2.5 as in the original Haardt & Madau (2001) evolution. In this case, the peak epoch of Jν would no longer correspond to the peak epoch of high-luminosity quasars, although lower luminosity quasars peaking at lower redshifts could provide a significant contribution (Shankar, Weinberg & Miralda-Escudé 2009).
It is interesting that the constant wind and no-wind cases have identical values of fτ, while the vzw case is lower. In the simplest view, winds tend to add energy to the IGM, resulting in less Lyα absorption, and hence one needs smaller optical depths and a lower fτ. In detail, however, because 
is dominated by marginally saturated absorbers, the relevant issue is whether the winds are heating gas giving rise to those absorbers in particular. It turns out that vzw, owing to its smaller wind speeds from typical galaxies, tends to deposit energy closer to galaxies where strong absorbers arise, while cw tends to deposit energy far away in more diffuse gas, as we will discuss in Section 3. Hence we believe that although cw adds more energy to the IGM overall, this does not impact 
nearly as much as in vzw.
Fig. 2 shows an example spectrum from z= 0.3 to 0. 4 along an identical LOS through our three wind simulations. The Lyα forest is fairly sparse at these epochs, but many very weak lines exist that could be detected given sufficient observational capabilities. The mean absorption is similar by construction, but there are distinct variations evident particularly between the cw case and the other two. The expanded segment in the right-hand panels highlights a region that shows significant differences among all three wind models. The density structure is mostly independent of outflows, though small differences are evident, but the IGM temperature can be significantly impacted by wind energy. The constant wind case shows a higher temperature almost everywhere along the LOS, while the temperatures for vzw and nw are fairly similar. However, the fact that optical depths are not very sensitive to temperature makes these differences difficult to pick out in the observed spectra. Overall, winds do not have a strong impact on the physics or absorption properties along typical lines of sight, as we will demonstrate more quantitatively with Lyα absorber statistics.
Example of a section of noise-free simulated spectra (Δz= 1), with an expanded region shown on the right, comparing three of our outflow models. Top panel shows Lyα absorption, middle shows density relative to the cosmic mean and bottom shows temperature. The colour code is nw (blue) plotted on bottom, cw (red) above and vzw (green) on top; e.g. redshifts showing only green correspond to locations where models are identical. The density structure is similar in all models, with the vzw having slightly more absorption overall. The cw model clearly produces a warmer IGM and the most deviations in optical depth; the other two show smaller differences.
3 IGM PHYSICAL CONDITIONS
3.1 Cosmic phase diagram
The left-hand panels of Fig. 3 shows cosmic phase diagrams of baryons, i.e. overdensity versus temperature, in our fiducial vzw run at redshifts from 2 → 0. The trends shown are familiar. At the lowest densities there is a tight density–temperature relation set by a competition between photoionization heating and adiabatic cooling owing to Hubble expansion. At roughly the cosmic mean density, shock heating begins on collapsing filamentary structures, creating a plume of hotter gas. At higher densities, radiative cooling becomes effective, creating the spur of dense gas that fuels star formation in galaxies. The other wind models look qualitatively similar.
Left-hand panels: cosmic phase-space diagram for gas particles in the vzw run at z= 2, 1, 0 (2000 randomly subsampled gas particles). We divide the baryons into four categories: diffuse, condensed, hot halo and WHIM. This is done using a temperature cut at 105 K to separate the former two from the latter two, and a density cut given by equation (1) to separate the bound baryons (condensed and hot halo gas) from the intergalactic baryons (diffuse and WHIM). Temperature histograms are along the y-axis for each phase and the total (black), with median values indicated by the tick marks. The percentage of mass in each phase is listed in each panel; additionally, the fraction in stars is shown in magenta. Right panels: same, for the other simulations (nw, cw and vzw-96), all at z= 0.
Two perhaps unfamiliar features are the shelf of gas sitting at T≈ 104 K, which is metal-enriched gas outside of star formation regions (we truncate all cooling at 104 K), and the upwards-curving plume of the densest gas, which is a consequence of the two-phase ISM implementation of Springel & Hernquist (2003a). The temperature in the two-phase regime is given by a mass-weighted average of the subgrid hot phase, assumed to be at 108 K, and the mass-dominant cold phase at 1000 K. Neither of these features is physical; they simply represent computational conveniences.
From redshift 2 to 0, we see the growth of galaxies and large-scale structure playing out in the cosmic phase diagram. The denser phases become more heavily populated, as does the plume of shock-heated WHIM gas, though the hotter phases are still clearly populated even at z= 2. The hottest gas also grows most substantially owing to the formation of large potential wells at late times. The diffuse gas extends into lower overdensity regions at late times, as voids become more empty, and its temperature drops with time as the physical density and photoionization rates go down. The overall cosmic gas temperature distribution becomes broader with time, and shifts to slightly higher temperatures, driven by the increasing fraction in WHIM and hot halo gas. These trends have all been noted and described in previous works (e.g. Davé et al. 1999).
3.2 Redefining cosmic baryon phases
In Fig. 3, we have also subdivided our baryons into four cosmic phases. The subdivisions are slightly different than conventional ones (e.g. Davé et al. 2001), in which diffuse baryons are at T < 105 K, WHIM gas is 105 < T < 107 K, hot gas is T > 107 K and condensed baryons are at a fairly high overdensity. Our new divisions are intended to be more physically motivated, particularly in the case of the WHIM, though in practice they do not represent dramatic changes.
) at the boundary of a virialized halo. To determine this, we note that for reasonable choices of the Navarro, Frenk & White (1996) concentration parameter c, the density at the virial radius is roughly one-third the mean enclosed density.3 We thus obtain (Kitayama & Suto 1996)
We further separate the ‘hot’ phases (WHIM and hot halo gas) from ‘cool phases’ (diffuse and condensed gas) by a temperature threshold of Tth= 105 K, the same value used in earlier definitions. At high densities, all gas that is star forming is included in the condensed phase, although the subgrid two-phase model creates a mean gas particle temperature that can exceed T > Tth. At IGM densities, this represents the temperature above which the H i neutral fraction starts to drop dramatically, making Lyα absorption a poor tracer of its baryonic content (though as we will see later, wide Lyα absorbers can still trace this gas). Furthermore, since photoionization cannot easily heat gas to these temperatures, it demarcates gas that has been shock-heated by large-scale structure. From Fig. 3, one can see that some gas at T= 104–105 K is also shock-heated above the photoionization locus, but the locus itself extends to T≈ 105 K, at least at z≥ 1.
With these divisions, we have four phases as follows:
Diffuse (T < Tth, δ < δth),
WHIM (T > Tth, δ < δth),
Hot halo (T > Tth, δ > δth),
Condensed (T < Tth, δ > δth),
with the qualification that two-phase star-forming gas is ‘condensed’ regardless of temperature. The most significant departure from previous definitions is that of the WHIM gas. Unlike the common definition in which 105–107 K gas is WHIM regardless of density, the WHIM gas in our definition is truly intergalactic, in the sense that it is not within the boundaries of a galaxy or its halo. Also, since hot gas is most commonly detected in X-ray emission, which roughly scales as ∝ρ2T1/2 (neglecting metal-line emission for the sake of this argument), this lower density gas is more likely to be ‘missing’ from current observational censuses. For instance, our definition removes hot gas in galaxy groups at T≲ 1 keV from being part of the WHIM; such gas can be detected in soft X-rays (Mulchaey 2000) because its high density (relative to truly intergalactic gas) leads to significant emission, albeit at faint levels. Hence, our revised definition more closely reflects the idea that the WHIM is the repository of the ‘missing’ cosmic baryons. Eliminating the upper limit of T= 107 K for the WHIM has minimal impact, since very little gas with δ < δth has such high temperatures.
3.3 Winds and the phase diagram
The right-hand panels of Fig. 3 show the z= 0 cosmic phase diagram for our other simulations: nw, cw and vzw-96. Comparing vzw-96 to vzw, we see some subtle differences particularly in the high-temperature gas. The hot halo gas extends to slightly higher temperatures, owing to larger haloes being able to form in the 96 h−1 Mpc volume; this causes a slightly higher median temperature for this phase, from 106.46 to 106.55 K. Similarly, the WHIM gas extends to slightly higher temperatures, causing a comparable increase in median WHIM temperature. The cooler phases show no appreciable physical differences. There is also a feature in the condensed phase at 
corresponding to a slightly different implementation of the two-phase cut-off in this run, but this does not affect any of our results.
The no-wind case also shows some differences with respect to vzw. Although the distribution of WHIM gas in phase space is similar, the median temperature increases slightly from 105.77 to 105.85 K, just as in the vzw-96 case but for a different reason. Here, the main effect is that with no outflows, the IGM is almost completely unenriched (Oppenheimer & Davé 2008). Hence, there is no metal cooling in this regime, which yields somewhat higher temperatures. For the same reason, the condensed phase shows almost no particles at the 104 K metal cooling floor.
The constant wind model noticeably pushes WHIM gas into a lower density regime compared to vzw, but its median temperature is lower (105.69 K) since the diffuse IGM is more enriched (Oppenheimer & Davé 2006). In contrast, the hot phase temperature is higher by ≈ 0.15 dex, reflecting the significant IGM heating that occurs when winds from all galaxies, even small ones, are emanating at 680 km s−1. These results are qualitatively similar to those from Tornatore et al. (2010) who explore a similar wind model, and they further note that black hole feedback (as they implement it) causes even more heating of particularly low-density gas. It is also similar to results from mesh hydrodynamic simulations by Cen & Ostriker (2006), who found that winds increase the mass fraction in the WHIM by 20 per cent. Hence, it is possible to non-trivially impact the cosmic distribution of baryons in phase space with plausible outflows.
3.4 Baryon phase evolution
We now quantify the trends in the cosmic phase diagram by examining the evolution of baryons in each phase amongst our various simulations. As is apparent from Fig. 3, baryons progressively move from the diffuse phase into WHIM and hot halo gas, owing to the hierarchical growth of large potential wells. The condensed phase gas is supplied predominantly from cold mode accretion but also some cooling from halo gas (Kereš et al. 2009), and this provides the fuel to grow the cosmic stellar content. By z= 0, baryons are comparably divided between diffuse, WHIM and the various bound phases, as was found in Davé et al. (2001). However, the new definition of the WHIM yields somewhat less WHIM gas and more diffuse gas, tilting the balance towards diffuse gas overall. The precise balance between the diffuse and WHIM phases is also sensitive to the adopted value of Tth, as one can see from Fig. 3.
Fig. 4 (top-left panel) shows the fraction of baryons in each cosmic phase from z= 4 → 0 in our vzw run. We additionally show the evolution of baryons in stars. Qualitatively, the behaviour is very similar to that seen in all cosmological hydrodynamic simulations (Davé et al. 2001), as discussed above. The next five panels of Fig. 4 show a comparison of individual phase evolution for our three wind prescriptions, plus our large-volume vzw-96 run. The upper-right panel shows the evolution of the global stellar content, i.e. the integral of cosmic average star formation rate density versus redshift (Madau 1998), in each wind run. Note that these values account for stellar evolution which returns material back into the gas phase. The no-wind case produces by far the most stars, which is the well-known result that without strong feedback, there is a severe overcooling problem (Davé et al. 2001). A stellar baryon fraction today of ∼20 per cent far exceeds current observational values of <10 per cent (e.g. Bell et al. 2003). Although we do not show it here, this case is also poorly resolution-converged, as pointed out by Balogh et al. (2001), and hence the problem would be worse at higher resolution.
Top left: evolution from z= 4 → 0 of baryon fraction in various cosmic phases, including stars, in our fiducial vzw run. Next five panels: evolution of baryon fraction in stars (upper right), and then the various baryonic phases in order of their location in ρ−T space: WHIM (middle left), hot halo (middle right), diffuse (lower left) and condensed (lower right), in our three wind models (green, blue, red lines), along with the larger-volume vzw-96 simulation (cyan).
By contrast, both wind models do a good job of suppressing star formation. Their globally averaged star formation rates are almost identical down to z∼ 2, which is by design as the wind prescriptions are tuned to reproduce the observed star formation rates up to this epoch. At lower redshifts, there start to be greater differences. Because the vzw model has more recycling of wind material back into galaxies, it provides more fuel for late-time star formation (Oppenheimer et al. 2010). None of our simulations includes a prescription (e.g. AGN feedback) to truncate star formation in the most massive systems as observed, which would lower the predicted stellar fractions particularly at late times. The resolution dependence of global star formation is mitigated by the presence of outflows, as shown by Springel & Hernquist (2003b) for the cw case, and as shown here by comparing vzw and vzw-96. Both wind models are generally consistent with the currently favoured values of the stellar baryon content today of 4–8 per cent (Baldry, Glazebrook & Driver 2008).
The middle left panel shows WHIM evolution, which displays significant variations, particularly between models with and without galactic winds. The modest wind speeds of the vzw model do not heat much gas to WHIM temperatures compared to the purely gravitational (nw) case, but there is still some heating evident at high z, which diminishes to z= 0. The cw case shows a significant amount of WHIM gas even at z= 4, and the WHIM fraction increases faster than in the other cases down to z∼ 1. At this point the supply of wind energy abates, and the WHIM fraction levels off and actually falls slightly to z= 0. Tornatore et al. (2010) found less dramatic effect on the WHIM fraction with similar simulations, although the energy input from their winds is half of ours. These differences highlight an important point: galactic winds can in principle have a strong effect on the evolution of WHIM gas. The winds in our favoured model do not substantially affect the WHIM, but faster winds in plausible variant models can do so. Measuring the evolution of the global WHIM content could provide constraints on the large-scale thermal impact of outflows. Such measurements will be challenging given the difficulty of quantifying the WHIM even at the present epoch, but the redshifting of some UV tracer lines to longer wavelengths could potentially facilitate such measurements.
The middle-right panel shows hot bound gas evolution. In general, this is dominated by gravitational heating from large potential wells, as indicated by the no-wind model. The vzw case produces more hot bound gas at late times, as it removes material from galaxies and places it into their surrounding hot haloes. Since the wind speed scales with escape velocity, large galaxies can have outflow velocities that exceed the wind speed of the cw model, which provides greater heating in their large haloes. The cw model removes a significant amount of hot gas at early times because its high-speed winds can escape smaller potential wells, but at late times the potential wells become deep enough to retain the gas, and its hot phase rises more quickly. Still, even by z= 0 this model does not produce as much hot bound gas as the vzw model. The vzw-96 and vzw simulations are very similar again, showing that simulation volume effects are not important even for large potential wells in terms of their global mass content.
In the lower-left panel, the diffuse phase shows similar trends in all the models. The vzw winds have little impact on the diffuse gas content, as their typically modest velocities do not produce substantial IGM heating. The cw winds lower the diffuse gas fraction at high z by shock heating some IGM gas above 105 K. This heating produces noticeable broadening of high-z metal lines, leading to worse agreement (relative to vzw) with observed C iv linewidths (Oppenheimer & Davé 2006). At late times, heating of the low-density IGM declines because of the reduced global star formation and the trapping of the constant-vw winds by deeper potential wells, causing the diffuse phase fraction to return to the no-wind value by z∼ 0.5. The box size has a negligibly small impact on this phase – the cyan vzw-96 curve is hidden by the overlaid green vzw curve at all but the highest redshifts.
The bottom-right panel shows the condensed phase evolution. The overall trend for this phase is to increase at early epochs as material accumulates in haloes, then decrease towards later times as galaxies convert gas to stars more rapidly than they accrete fresh gas. The fraction of condensed gas is ≲10 per cent at all times and ≲6 per cent today, in all the models. The cw model shows a fixed offset to lower condensed gas fractions relative to the no-wind model, since it expels a constant amount of material out of the star-forming regions, and most of this material ends up outside of haloes owing to the large wind speed. The vzw model shows qualitatively different behaviour from the others, with less redshift evolution. Mostly this difference reflects the late-time reaccretion of wind material, more prominent in the vzw model because of lower wind speeds (Oppenheimer et al. 2010). We note the qualitative similarity of the evolution of this phase (which contains most of the cosmic neutral gas) with the observed evolution of cosmic H i gas from Damped Lyα systems (Wolfe, Gawiser & Prochaska 2005), being roughly constant from z∼ 3 → 0. 5 and then dropping to z= 0.
Returning to Fig. 3, the histograms along the vertical axis show the temperature distribution of baryons at z= 2, 1, 0. The overall trend follows the movement of baryons within the cosmic phase diagram, namely that the median temperature increases with time. In detail, the diffuse phase actually moves towards lower temperatures because of the changing balance between photoionization heating and adiabatic cooling. The WHIM gas extends up to higher temperatures at low z, and the hot bound gas also becomes hotter on average as larger potential wells form. The median cosmic gas temperature today is ≈ 105 K.
Overall, the cosmic evolution of baryon phases reflects the hydrodynamic and radiative processes associated with the growth of structure. Winds have a significant impact, particularly on the stellar phase (by design) and on the WHIM phase (if the winds are strong enough). They also impact the bound phases (hot halo and condensed), since these lie close to galaxies where winds play a more important dynamical role. The diffuse phase is mostly unaffected by winds. The complex dynamical interplay between outflows and hierarchical growth is an important factor in the cosmic history of baryons, and improved observational constraints and theoretical predictions will be required to fully characterize it.
4 LYα ABSORBER OBSERVABLES
We now investigate the statistics of Lyα absorbers in our simulated COS-like spectra, and present comparisons when appropriate to existing pre-COS data. We consider the canonical statistics of the column density and linewidth distributions, as well as the evolution of the number density of lines. To obtain line statistics, we fit our simulated spectra with Voigt profiles using AutoVP (Davé et al. 1997), yielding an H i column density (NH i), Doppler linewidth (b) and redshift for each absorber. Owing to the sparseness of the low-z Lyα forest, the fits are generally unambiguous, and tests have shown that AutoVP obtains line parameters very similar to that from other Voigt profile fitters (e.g. VPFIT) when the lines are unsaturated. We use the continuum directly provided by the simulations, as we assume that observed spectra can be fit with an accurate continuum in the relatively sparse low-z Lyα forest. We also examine the impact of varying the assumed S/N and spectral resolution of our simulated spectra. Note that AutoVP provides ‘raw’b-parameters uncorrected for instrumental resolution. In our COS-resolution spectra, with a Gaussian width of 17 km s−1, we therefore expect essentially no lines with 
. Since it turns out that the vzw-96 absorber statistics are indistinguishable from the vzw case (as anticipated by the close agreement in IGM physical properties), we do not show this model herein.
4.1 Column density distributions
Fig. 5 shows column density (left-hand panels) and b-parameter (right-hand panels) distributions for absorbers at z= 0, 1, 2. As mentioned previously, these three bins correspond to all lines within redshift ranges z= 0–0.2, z= 0.9–1.1 and z= 1.8–2, respectively, identified with AutoVP in our 70 random lines of sight. Results are shown for all three of our outflow models. The column density distribution (CDD) 
has been multiplied by NH i to remove some of the steep power-law scaling (discussed below), which enhances the visibility of the differences among models. It also results in a dimensionless number that reflects the relative number of lines per unit redshift at a given NH i.
Column density (left) and b-parameter (right) distributions at z= 0 (top), z= 1 (middle) and z= 2 (bottom) for our three simulations. The CDD have been multiplied by NH i to improve visibility of the differences between models. The thick cyan line shows a fit to data from Penton et al. (2004) at z≈ 0, namely log f(NH i) = 10.3–1.65 log NH i, over their fitted range of 
; dotted lines on either side indicate their 1σ quoted uncertainty of ±1.0 in log f(NH i). Thick black and magenta lines show best fits for CDDs from STIS data from Lehner et al. (2007) and Davé et al. (2001), respectively. The same lines are reproduced at the other redshifts for reference, showing that there is modest evolution in the CDD amplitude from z= 2 → 0. The turnover at NH i < 1013 cm−2 arises from incompleteness in recovering lines at the assumed S/N and resolution (see Section 4.4). Linewidth distributions are shown for all lines with NH i > 1013 cm−2, i.e. our complete sample at COS resolution and an assumed S/N = 30. Tick marks above each curve indicate median b values.
The CDD shows the usual power-law behaviour, above the completeness limit at 
that results from our adopted S/N and resolution (see Section 4.4). Characterizing the CDD as a power law with 
, and fitting between 1013 < NH i < 1014.5 cm−2, we obtain values of β=−1.88, − 1.70, − 1.80 for the nw, vzw and cw models at z= 0, respectively, with an uncertainty of approximately ± 0.1 on each. Hence, all the slopes are formally consistent with each other, although given that the exact same LOS are being analyzed, one can conclude that the nw model produces a steeper slope than the wind models, and that the vzw model produces the shallowest slope. We note that all the slopes are shallower than the slope −2.04 ± 0.23 obtained in the simulation by Davé et al. (2001) (though within formal uncertainties), which was most analogous to the no-wind case here. We will show in Section 4.4 that higher spectral resolution tends to produce a somewhat steeper slope, so this could explain part of the difference. Paschos et al. (2009) found a slope of −1.84 ± 0.02 using a fixed mesh simulation with 75 kpc resolution and no galactic outflows, which basically agrees with our no-wind case.
These are several pre-COS set of low-z Lyα forest data for comparison. One sample, from Penton, Stocke & Shull (2004), contains 187 somewhat heterogeneous Lyα absorbers, mostly at z≲ 0.1, from Hubble/STIS and Goddard High Resolution Spectrograph data. A more uniform and higher resolution sample of 341 absorbers out to z≲ 0.4 was obtained by Lehner et al. (2007) using only STIS data, and included Far-Ultraviolet Space Explorer data to help constrain the properties of saturated Lyα absorbers. We also show earlier results from Davé et al. (2001), who analysed two STIS spectra using AutoVP. The fits to all their resulting CDDs are shown as the thick lines in the upper-left panel of Fig. 5; black for Lehner et al. (2007), magenta for Davé et al. (2001) and cyan with ±1σ uncertainties shown as the dashed lines for Penton et al. (2004). The slope obtained by Penton et al. (2004) is −1.65 ± 0.07, which is statistically different from that of Lehner et al. (2007) (−1.84 ± 0.06) or Davé et al. (2001) (−2.04 ± 0.23). As we will show in Section 4.4, at least part of the difference likely owes to spectral resolution, since higher resolution data yield steeper slopes. For this reason it is not straightforward to compare to the COS predictions presented here to these data, but broadly the slope and amplitude predicted by the current simulations are in agreement given the various uncertainties. A careful comparison against upcoming COS data should provide more discrimination between models.
At higher column densities, Penton et al. (2004) found that their data showed a characteristic ‘dip’ in the CDD at 
, which they point out persists from high z (see their fig. 9). Lehner et al. (2007) likewise saw that the CDD slope is shallower at NH i > 1014.4 cm−2 than for smaller systems. We see a hint of the onset of such a dip in all our simulations, but we cannot accurately trace it out to 
, since we quickly run out of absorbers owing to the rarity of high-NH i absorbers along our randomly chosen LOS. The origin of this dip is unclear. It occurs at a column density close to that expected for overdensities near the boundaries of galaxy haloes, which leads us to speculate that perhaps these absorbers probe the outer parts of galaxy haloes where (at least in larger haloes) some of the gas might be shock-heated to a temperature where it would not absorb in H i. At even higher columns, one would then probe through denser halo regions where H i condenses out again, owing to self-shielding, causing a ‘recovery’ back to the original CDD. We leave a detailed examination of this conjecture for future work.
The redshift evolution of the CDD shows a steady march upwards in line counts at a given 
). The overall steady evolution reflects the evolution of the mean flux decrement over this redshift range, and hence is dependent on our procedure of adjusting the ionizing background strength to match 
. The incompleteness at 
becomes more severe at higher z, as line blending becomes more common. Recall that we have fixed our resolution and LSF to the COS far-UV (FUV) channel at all z, which underestimates the data quality that is obtainable at z∼ 1 (where the COS NUV channel has a narrower LSF, albeit with lower sensitivity) and at z∼ 2 (where one can trace the Lyα forest in the optical). This makes it difficult to compare slopes across a fixed NH i range, but if we restrict ourselves to 1013.4−1014.6 cm−2 where the CDD is reasonably complete at all z, we obtain slopes for the vzw model of −1.89, −1.71 and −1.54 at z= 0, 1, 2, respectively. The CDD is clearly getting steeper with time, broadly matching the observed CDD slope evolution from high z (∼− 1.5; e.g. Kim, Cristiani & D'Odorico 2001; Janknecht et al. 2006) to low z.
The CDDs are remarkably insensitive to the outflow model at lower column densities. Wind dynamics, despite enriching the IGM and depositing energy over large scales in quite different ways, have little impact on the diffuse H i distribution. As shown by Oppenheimer & Davé (2008) and Kollmeier et al. (2003, 2006), the typical extent of galactic winds (∼ 100 kpc physical) generally does not extend into the diffuse Lyα forest. This was noted in the earliest simulation studies of Lyα absorption that explored outflows (Theuns et al. 2002). However, there are significant differences for stronger absorbers, as outflows (particularly in the vzw case) deposit more cool gas in the outskirts of haloes, which increases the Lyα absorbing cross-section. This yields significantly more sub-Lyman limit systems and slightly shallower CDD slopes, and it is also reflected in the number counts of strong lines as we will show in Section 4.3.
4.2 b-parameter distributions
The right-hand panels of Fig. 5 show the b-parameter distributions for our three wind models at z= 0, 1, 2. The histograms show the usual Gaussian distribution with an extended tail to higher linewidths. The median b-parameter for each model is indicated by the tick mark above the curves. The typical value is around 40 km s−1 at all z, with a slight trend to become smaller at high z.
The linewidths are significantly wider than what was found using STIS data (e.g. Davé et al. 2001; Williger et al. 2010). Simulations by Davé et al. (2001) predicted a median b that depended on NH i with a typical value of 25 km s−1, in good agreement with their STIS data. Lehner et al. (2007) determined a median b= 30 km s−1, also from STIS data. Paschos et al. (2009) used simulated spectra with approximately 5 km s−1 resolution and obtained a similar b-parameter distribution. We will show in Section 4.4 that the larger b values predicted in this work are mostly a result of the poorer spectral resolution of COS relative to STIS. Our simulated linewidths are more comparable to those obtained using Goddard High Resolution Spectrograph (GHRS) (∼ 18 km s−1 resolution; Penton et al. 2004). Owing to this sensitivity to instrumental characteristics, we do not conduct any detailed comparison with data here. Nevertheless, we will show in Section 5 that linewidths still contain some information about the underlying temperature of the absorbing gas. It may be possible to extract better constraints on linewidths using higher order Lyman lines through a curve-of-growth analysis or through simultaneous fitting of multiple transitions (e.g. Lehner et al. 2007), but we leave such a study for the future.
The linewidths, like the CDDs, show almost no sensitivity to outflow model. This is perhaps more surprising, given that the various wind models heat the IGM to different levels (see Fig. 4), with cw clearly providing substantial heating. In Section 5.4, we will show that the b-parameters are only loosely correlated with temperature, reflecting the dominance of other sources of line broadening such as Hubble flow and instrumental resolution. In detail, the cw model does have marginally higher median b values of 43.0, 39.4 and 38.2 km s−1 at z= 0, 1, 2, respectively, as compared to vzw which has 42.3, 38.2 and 36.2 km s−1 (almost identical to nw), so the expected effect is present but small. We will also show in Section 4.4 that b-parameters are highly sensitive to spectral resolution, and hence comparisons of data to models (or to other data sets) must carefully account for such effects.
4.3 Absorber evolution
The evolution of Lyα absorbers provides insights into the interplay between cosmic expansion, photoionization and the growth of structure. One simple statistical characterization of this evolution is the redshift-space number density of absorbers along the LOS, d N/d z. d N/d z is usually measured within a specified column density range. Early data from FOS (Weymann et al. 1998) showed a dramatic change in the evolution rate of strong (
) absorbers between z≳ 2 and z≲ 1. However, subsequent higher quality data have muddled the situation. Owing to the paucity of such strong absorbers, there appears to be substantial cosmic variance for dN/dz among the various sightlines. Moreover, more recent data with substantially higher resolution generally show a significantly lower dN/dz compared to the FOS results, presumably because higher resolution enables more accurate deblending of strong lines. It appears that large redshift path length and high spectral resolution are both necessary to obtain an accurate estimate of dN/dz for strong absorbers; COS should provide this combination.
Fig. 6 shows the evolution of dN/dz for our three outflow models. The top panel shows dN/dz for NH i > 1014 cm−2 lines, while the bottom shows 
absorbers. Overlaid are a compilation of data taken from Williger et al. (2010). For strong lines, the points across the top of the panel are the Key Project FOS results (Weymann et al. 1998). The others come from higher resolution data sets, and are all significantly lower than the FOS results. In general, the simulations show a relatively slow decline in dN/dz, with little evidence for any kind of ‘break’ in evolution as was seen in the FOS data. Theuns et al. (1998) and Davé et al. (1999) emphasized that the decline of the UV background at z < 2 slows the evolution of the forest relative to a constant Ultraviolet Background (UVB) case. The steadiness of evolution in Fig. 6 relative to fig. 3 of Davé et al. (1999) is partly a consequence of the narrower redshift range and partly a consequence of adopting a UVB that declines more slowly at low redshift because of contributions by galaxies.
LOS number density of Lyα absorbers (dN/dz), as a function of redshift. Top panel shows the evolution of absorbers with NH i > 1014 cm−2, while bottom panel shows 
. Data from various sources compiled by Williger et al. (2010) are indicated.
The strong absorbers show a clear discrimination between outflow models by z= 0, with twice as many NH i > 1014 cm−2 absorbers in the vzw model as in the no-wind case. The cw model is intermediate. This shows that our favoured outflow model is ejecting more gas into the vicinity of galaxies where strong absorbers arise, and that this gas is remaining relatively cool. The difference arises because the momentum-driven wind model ejects more material from lower mass galaxies at lower wind speeds, thereby providing a reservoir of cooler gas that can cause strong Lyα absorption. This is qualitatively the same effect that causes this model to provide a larger amount of DLA absorption and broader DLA kinematics, as described by Hong et al. (in preparation). The vzw case shows the best agreement with recent z∼ 0 data, which is directly tied to its somewhat shallower CDD slope, although the uncertainties are still large enough to preclude any firm discrimation. COS should yield a good observational determination, providing an important diagnostic of galactic outflows.
The weaker absorbers show much less sensitivity to outflows, indicating that winds do not substantially disturb gas at the densities giving rise to 
absorbers. A reasonable fit for all the models is given by d N/d z∝ (1 +z)0.7, which is significantly shallower than the evolution at high z (e.g. Davé et al. 1999). However, all the models generically fail to reproduce the apparent break in evolution at z∼ 1 (Janknecht et al. 2006). This can be traced directly to the evolution of the mean flux decrement 
(Fig. 1), which the models overpredict around z∼ 1 by the same factor of 2 that they overpredict dN/dz. In fact, the two observational data sets are not unrelated, as 
is most sensitive to absorbers just below the logarithmic portion of the curve of growth, namely 
. If we adjusted the UVB intensity to reproduce the Kirkman et al. (2007),
measurements at z= 1−1.5, then we would predict a break in dN/dz evolution at log (1 +z) ≈ 0.35. Improved statistics will thus provide valuable constraints on the evolution of the UVB, perhaps demonstrating significant departures from the Haardt & Madau (2001) predictions.
In summary, the evolution of Lyα absorbers will in principle provide strong constraints on the evolution of the ionizing background (for weaker lines), and perhaps on the nature of outflows (for stronger lines). However, accurate constraints require larger data sets with good resolution, which COS should provide.
4.4 The effects of instrumental resolution and noise
Instrumental resolution and noise characteristics of the data can have a non-trivial impact on the derived statistics of Lyα absorbers. This can lead to some confusion when cross-comparing different samples, or when comparing simulations to data without carefully matching such characteristics. In this section we use our simulations to briefly investigate how COS-resolution data would compare to an equivalent sample of higher STIS-resolution data, and how the Lyα forest would appear if it were possible to greatly boost the S/N of COS data. These are idealized experiments, not readily achievable with current instruments, but they illustrate the trends one should keep in mind when intercomparing samples.
Fig. 7 shows the CDD and b-parameter distributions for the vzw model at z≈ 0 for our simulated spectra convolved with a COS LSF at S/N = 30 and 100, and with a 7 km s−1 Gaussian (with 3 km s−1 pixels) intended to roughly mimic STIS resolution. The higher S/N or resolution both extend the CDDs to lower column densities with an unbroken power law, showing that our COS-resolution sample with S/N = 30 is essentially complete to NH i= 1013 cm−2. Coincidentally, increasing the S/N to 100 at COS resolution is roughly equivalent, in terms of CDD completeness, to having STIS resolution with S/N = 30. At the high-NH i end, STIS resolution produces quite a few more strong lines. We caution that different Voigt profile fitting algorithms can significantly affect the parameters derived for saturated lines, so one must be careful in interpreting this plot. However, it does indicate that some of the variations seen in dN/dz for strong lines may owe to different instrumental characteristics for the various data sets. Examination of the true column densities in the simulated absorbers shows that the high column density systems identified in the STIS-resolution spectra are generally real; at COS resolution AutoVP mischaracterizes them as lower column density systems with larger b-parameters (and thus less saturation). Finally, the slope of the CDD at 1013 < NH i < 1014.3 cm−2 is steeper in the case of higher S/N or resolution; for the former, we obtain a slope of −1.73 (as opposed to −1.70 for the original vzw case), and for the latter we get −1.82. Hence, high resolution produces a significantly steeper CDD slope, which can help explain why the CDD slopes in Davé & Tripp (2001) are steeper.
Effects of S/N and spectral resolution on Voigt profile parameter distributions in our fiducial vzw run at z= 0. COS resolution assumes the COS LSF in the FUV channel, which is ≈ 17 km s−1 Gaussian width (1σ), while STIS resolution assumes a Gaussian with 7 km s−1 width. Top panel shows CDDs multiplied by NH i, demonstrating that the turnover at low NH i at 1013 cm−2 owes to a lack of sensitivity; either increasing S/N or resolution allows one to probe further. There are also differences at the high-NH i end. Bottom panel shows the b-parameter distributions; these are not very sensitive to S/N variations, but are dramatically sensitive to spectral resolution. Here we also show the result of convolving the linewidths identified in the STIS-resolution spectra with a 22 km s−1 Gaussian to illustrate the effect of moving from STIS to COS resolution; this demonstrates that much of the line broadening in the COS-resolution case owes to its coarser spectral resolution.
The b-parameter distribution shows strong sensitivity to spectral resolution, but increasing S/N does not have a major impact on b-parameters. At STIS resolution, the median b-parameter is below 30 km s−1, and the distribution roughly agrees with that found in Davé et al. (2001). At COS resolution, lines are significantly broader, resulting in a median greater than 40 km s−1 and a much more prominent tail to high b values. The cyan dot–dashed curve in Fig. 7 shows the result of taking each line in the STIS-resolution distribution and increasing its b-parameter by adding 
in quadrature to account for the difference in resolution between COS and STIS. The peak of the distribution moves much closer to that of the COS distributions, suggesting that for many lines the larger COS b-parameter is a simple consequence of convolving the line with a broader LSF. However, the COS distributions still have many more lines at b≥ 60 km s−1, showing that these broad lines must arise mainly from blends that cannot be resolved by the COS FUV channel. Because of the effects of line blending, we think it is generally better to test models by applying the LSF to simulated spectra rather than attempting to correct measured b-parameters on a line-by-line basis. The exception might be in cases where higher order Lyman series lines provide additional constraints on the b-parameters via curve-of-growth analysis. More generally, this illustrates that the b-parameters are particularly sensitive to spectral resolution, and any comparisons between data sets, or between data and models, should take special care to match the instrumental LSF.
5 LYα ABSORBER PHYSICAL CONDITIONS
We now examine the relationship between absorber properties and the physical conditions of the absorbing gas, namely its temperature, density and ionization state. The relatively simple nature of Lyα forest absorption, particularly for weaker absorbers, results in fairly tight relationships that offer insights into the evolution of baryons in the IGM.
To assign densities and temperatures to individual absorbers, we find the location of peak absorption and assign to the absorber the H i-weighted ρ and T of the nearest pixel. This is not a perfect procedure, as, e.g. the width of the line might be determined by coincident hotter gas superposed on stronger absorption from colder gas. But it gives a reasonable idea of the physical conditions present in the absorbing gas. To better isolate real trends, we only consider absorbers whose formal χ2 errors for NH i and b as reported by AutoVP are fractionally less than 20 per cent, which mostly removes very weak absorbers whose parameters are not well-determined. For studying linewidths, we include only absorbers with NH i > 1013 cm−2, for which we have a relatively complete sample. We focus on the momentum-driven wind case and point out where substantial differences arise in the other wind models.
5.1 Absorbers in phase space
Fig. 8 shows how Lyα absorbers populate and trace cosmic phase space (here shown as temperature versus hydrogen number density). In each panel except the upper left, our simulated absorbers between z= 0 and 0.2 are indicated as circles, placed using their H i-weighted densities and temperatures. Solid lines demarcate the phase boundaries as defined in Section 3.2 and shown in Fig. 3, and the vertical dotted line indicates the cosmic mean density of hydrogen. Our absorber sample overlaps the shading, which represents the simulated distribution of H i. However, because random sightlines sample the Lyα forest in a volume-weighted fashion, there are more weak Lyα absorbers tracing lower densities even though most of the cosmic H i resides in rare, strong absorbers tracing the condensed phase. Conversely, absorbers are not detectable at densities below nH= 10−6 cm−3, where the vast majority of the IGM volume exists, and this detectability threshold is the reason that the low-z Lyα forest is observed to be sparsely populated.
Cosmic phase diagrams for the vzw run at z= 0.1. Upper left shows all baryons, coloured by H i fraction. Other panels are shaded by 
, binned in 0.1 × 0.1 dex pixels. Solid lines demarcate the four cosmic phases as in Fig. 3, while the dotted line indicates the cosmic mean density. In each panel, the circles show the locations of z= 0–0.2 absorbers in phase space, with the area of the circle proportional to NH i (see lower-left panel for scale). The colour scale in each panel corresponds to different quantities: ionization fraction (upper right), total hydrogen column density NH (middle left), absorber size (middle right), NH i (lower left) and linewidth (lower right).
The upper-left panel displays the cosmic distribution of baryons in phase space, colour-coded by ionization fraction. The remaining five plots contain up to three additional dimensions of information within two-dimensional cosmic phase space: shading for global H i content (i.e. the product of the intensity and colour maps in the top-left panel), circle size scaled to absorber NH i and circle colour for the various quantities, as follows: neutral fraction (upper right), total hydrogen column (middle left), absorber path length (middle right), NH i (lower left) and linewidth (lower right). It is clear that there are strong correlations amongst the various physical and observational quantities. In subsequent sections, we will quantify some of these trends in more detail and attempt to connect observables to physical quantities within this plane.
The H i neutral fraction in the upper-right panel is computed for each absorber as an optical depth-weighted neutral fraction from all SPH particles that contribute to the absorption. Note that we assume ionization equilibrium; this is expected to be a very good approximation in the Lyα forest. It is clear that, as expected, the IGM is highly ionized, with the weakest absorbers showing neutral fractions of ∼ 10−6 cm−3. Neutral fractions increase towards lower temperature and higher density, such that absorbers at ∼ 1014 cm−2 (the typical absorber at the crossing point of the phase division lines) show a neutral fraction of ∼ 10−5 cm−3. The neutral fraction increases rapidly along the condensed phase, leading quickly to very strong absorbers.
The middle-left panel of Fig. 8 shows the total hydrogen column density NH, computed by dividing NH i by the neutral fraction. A remarkable trend emerges that the vast majority of Lyα forest absorbers have NH between 1018 cm−2 and 1019 cm−2, except for the hottest or densest absorbers. This trend was noted observationally in a small sample by Prochaska et al. (2004), which they pointed out was in general agreement with simulation predictions from Davé et al. (2001). Here, the trends of NH versus overdensity can be more clearly seen; it is double-valued in the sense that NH is lower at both low and high overdensities, and it peaks at intermediate overdensities, particularly at high temperatures.
The middle-right panel shows an estimated size of Lyα absorbers, obtained by dividing NH by the physical density. Weak absorbers (∼ 1013 cm−2) have sizes up to ∼ 1 Mpc, and this quickly drops to ∼ 100 kpc for ∼ 1014 cm−2. This is broadly consistent with the large coherence lengths observed in quasar pair sightlines (e.g. Dinshaw et al. 1998; Casey et al. 2008), though the elongated geometry of absorbing structures also affects apparent coherence lengths. The sizes are consistent with analytic estimates by Schaye (2001) from assuming that Jeans smoothing establishes the structure of the low-density IGM [see Peeples et al. (2010) for evaluation of this hypothesis against simulation results, albeit at higher redshift]. The absorber lengths drop rapidly with increasing overdensity, such that strongest absorbers in the condensed phase have sizes ∼ 1 kpc or less. This explains why absorbers from this phase are rarely seen despite the substantial reservoir of neutral gas in the condensed phase – their cross-section is remarkably small.
The two lower panels consider absorber observables NH i and b. The lowest column density systems lie along the low-density, high-temperature envelope of detectable H i. The trend of increasing NH i towards low temperatures and high densities mimics that in the ionization fraction, such that the typical absorber at the bound/unbound division has 
(and lower at higher temperatures). The strongest absorbers generally arise in condensed phase gas, though they are rare in these random LOS.
The b-parameters in the lower-right panel also show trends in phase space, but they are not as distinct as with column densities. Narrower lines tend to arise in lower density and lower temperature gas, but there is a significant scatter. Wide lines can occur in hot gas, but such gas can also contain narrower lines. Wide lines can also occur in very strong absorbers that are heavily saturated, arising in condensed gas. Overall, b-parameters trace temperatures fairly loosely, a point we will quantify further in Section 5.4.
Overall, Lyα absorption along random lines of sight can trace present-day baryons from close to the mean overdensity up to overdensities of ∼ 104 or more, and to temperatures well above 105 K. There are strong trends of ionization fraction and absorber size, which together with the underlying baryon distribution in phase space yield a strong trend of physical parameters versus column density, and a weaker but still noticeable trend versus linewidths. In the next two sections we explore these trends more quantitatively, to better understand how observables obtained from COS spectra can reveal the physical conditions of the absorbing gas.
5.2 Column density versus physical density
The evolution in the relationship between column density NH i and overdensity δ is governed by the interplay between cosmic expansion, which lowers the physical density (at a given δ) and thus lowers the recombination rate, and evolution of the UV background, which drops at lower redshifts and thus lowers the photoionization rate. Davé et al. (1999) showed that much of the observed evolution in the Lyα forest can be understood through the evolution in this relation, because this interplay causes a given strength absorber to correspond to a higher overdensity at lower redshift. Complications arise because, by z= 0, a significant amount of IGM gas is heated collisionally by shocks rather than by photoionization, resulting in departures from the FGPA (Zhan et al. 2005). Nevertheless, this 
relation is central to understanding the physics of the Lyα forest in a structure formation context.
Fig. 9 shows that a fairly tight 
relation is established at all redshifts, as found by previous studies. The three panels show this relation for the momentum-driven wind model at z= 0, 1, 2. Absorbers are categorized by cosmic phase, with a colour code following Fig. 4, namely diffuse (blue), WHIM (green), hot halo (red) and condensed (cyan). The lower envelope reflects gas that is purely photoionized, as shock heating will move absorbers to lower NH i for a given overdensity by lowering the neutral fraction.
Baryonic physical density in units of the cosmic mean (
) versus column density NH i for absorbers from the momentum-driven wind model, at z= 0 (top), z= 1 (middle) and z= 2 (bottom). In each panel, the solid line shows the relation from equation (3) at z= 0 (black), z= 1 (magenta) and z= 2 (cyan). Absorbers are colour-coded as diffuse (blue), WHIM (green), hot (red) or condensed (cyan). Point sizes are scaled ∝b.
The WHIM absorbers generally have somewhat higher density at a given NH i, since the gas has been shock-heated; this trend is exacerbated for the hot halo absorbers. As a result, at overdensities above 10 or so, corresponding to 
at z∼ 0, there begin to be significant departures from equation (3). The departures from this relation also become more prominent with time, since more IGM gas becomes shock-heated. Condensed phase gas typically gives rise to the strongest Lyα absorption systems seen at the highest overdensities. At z= 2 there is a shelf at the lowest densities, largely because the underdense absorbers have larger velocity widths and are thus more difficult to identify at fixed NH i and S/N.
Equation (3) is similar in form to the (by-eye) fits presented in Davé et al. (1999, 2001). Differences arise because the ionizing background strength employed here is slightly different, and here we consider only the diffuse absorbers. We have checked that the above equation holds reasonably well for the diffuse absorbers in the no-wind and constant-wind cases (when the fτ factor is included), since these absorbers are essentially unaffected by outflows. The other wind models are qualitatively similar in terms of their other phases as well, though in detail there are minor differences that we will discuss in the following sections. The insensitivity to winds further emphasizes the fundamental nature of the 
relationship in describing the physics of the Lyα forest.
5.3 Absorption phase
We now examine the cosmic phase of Lyα absorption as a function of column density. Fig. 10 shows a sum over H i column density for lines in bins of NH i for our momentum-driven wind model. At both low (
) and high (
) redshifts, there is a clear transition in which total H i absorption is dominated by diffuse absorbers at low NH i and by condensed absorbers at high NH i. The transition occurs at 
for 
and ≈ 1014.5 cm−2 for 
. WHIM and hot halo absorbers are subdominant at all column densities, though they are much more common at 
than at 
. While the column density demarcation is less clear for these phases than for diffuse/condensed, WHIM absorbers typically have NH i < 1014 cm−2, while hot halo absorbers sometimes have larger NH i.
Summed column densities per unit path length as a function of column density, subdivided by absorber phase. The top panel shows absorbers in the range z= 0–0.5, and the bottom panel shows z= 1.5–2.
While the broad trends are similar for other wind models, in detail there are substantial differences particularly for absorption in bound phases. If we consider absorbers from 
at z= 0–0.5, then the cw model contains only half the absorption, and nw only ≈40 per cent of the absorption, relative to vzw. This reiterates the result in Fig. 6 that high-NH i absorbers provide the most sensitive probe of galactic outflows in the Lyα forest.
In summary, the low-z Lyα forest contains absorbers from all cosmic phases, but diffuse absorbers dominate at 
and condensed absorbers dominate at higher NH i. WHIM and hot phase absorbers are present, but highly subdominant in total absorption. Next, we assess whether linewidths add enough information to pinpoint the absorbers arising in WHIM and hot halo gas.
5.4 Linewidths and temperatures
In the absence of other sources of line broadening, the b-parameters will reflect the temperature of the underlying absorbing gas. A particularly promising application of this is tracing the missing baryons with wide Lyα lines because, unlike relying on high-ionization metal lines such as O vi (e.g. Tripp, Savage & Jenkins 2000) or O vii (e.g. Nicastro et al. 2005), H i linewidths are independent of metallicity. However, in practice, linewidths are not dominated by thermal broadening (Weinberg et al. 1997c), although the thermal contribution is higher at low z (Davé & Tripp 2001). Here, we investigate the relation between linewidths and temperature in our simulations, to better understand how robustly one can trace the WHIM, and hotter IGM gas in general, using wide Lyα lines.
Fig. 11 (top panel) shows the distribution of absorbers’b-parameters versus temperature from our momentum-driven wind simulation at z≈ 0 (other wind models are similar). Absorbers are colour-coded by cosmic phase as in Fig. 4. Recall that we do not fit a continuum to the simulated spectra, hence there is no additional uncertainty in this regard in the identification of broad absorbers in the models. However, such uncertainties may be important when analysing observations, as broad absorbers may be partially ‘fit out’ when fitting a continuum to unnormalized data. There is a definite trend for wider absorbers to arise in hotter gas, as shown by the running median (magenta curve), but there is also substantial scatter as indicated by error bars which show 1σ dispersion values about the median. Hence, a wide Lyα line is more likely to arise in hotter gas, but it does not always do so.
Top: temperature versus b-parameter for Lyα absorbers, colour-coded by absorber phase, from the vzw simulation at z= 0. Symbol size is scaled by 
. Diagonal solid line shows the relation for pure thermal broadening; some absorbers are narrower than ‘allowed’ owing to uncertainties in Voigt profile fitting and the assigning of temperatures to individual absorbers. Histograms in b and T are shown along the bottom and side, respectively, divided by absorber phase, with tick marks above the curves identifying the median values. For visibility of the other phases, the diffuse-phase histograms have been reduced by five times; otherwise, it would dominate at essentially all b values. Magenta curve shows a running median, with 1σ dispersion, for the entire sample. Bottom: like top, but showing H i column density in place of temperature.
If lines were purely thermally broadened, then the H i linewidth would be related to the temperature by 
. This relation is shown as the solid diagonal line. A small fraction of WHIM and hot absorbers are narrower than allowed by thermal broadening, either because of b-parameter uncertainties in the Voigt profile fits or because of uncertainties in assigning temperatures to absorbers as described above. Generally, however, most absorbers’ widths significantly exceed the thermal broadening value. The running median shows a similar trend as the thermal broadening track, but it is higher by a factor of 1.5–3 in b, until a turnover at the very largest b values. For the narrow diffuse absorbers, we obtain the same result as in Davé & Tripp (2001) that thermal broadening contributes equally to other sources (in quadrature) in setting the linewidths. For wider absorbers, the thermal contribution becomes smaller. In general, the dominant contribution to the b-parameters is not thermal broadening, but rather Hubble broadening in the expanding gas or line blending owing to limited spectral resolution as discussed in Section 4.4.
Along the bottom and side of Fig. 11 are displayed absorber histograms in b and T for each cosmic phase, with the median values indicated by tick marks. The diffuse-phase histogram has been multiplied by 1/5 along each axis for visibility. The ones along the temperature axis show the expected behaviour, with hotter phases having higher median temperatures. The increasing T with b is broadly reflected in the histograms along the b-axis as well, with WHIM and hot absorbers being at higher b values than diffuse and condensed ones. However, the scatter between b and T is quite significant; the histograms of the various phases span a wide range in b and have a substantial overlap. Moreover, the diffuse absorbers essentially dominate at all b values (remember that this histogram has lowered by five times) simply because they are so numerous, despite the fact that their median linewidth is substantially smaller than all the other phases. Hence, it is unfortunately not straightforward to assign a gas temperature purely from the b-parameter. A key implication is that searches for WHIM gas with COS by selecting only broad Lyα lines is likely to pick up a significant fraction of diffuse absorbers, and care must be taken to avoid double-counting baryons in such studies.
Both the column density and linewidth provide some guidance in determining the cosmic phase of the absorbing gas. It stands to reason then that combining the two observables may provide more accuracy in identifying the cosmic phase. The bottom panel of Fig. 11 shows the absorbers in NH i−b, colour-coded by absorber phase. Broad, weak absorbers with b > 60 km s−1 and NH i < 1014 cm−2 include a relatively large fraction of WHIM absorbers. However, a significant fraction of absorbers in this range are still diffuse, and many WHIM or hot halo absorbers have lower b-parameters than this threshold.
In summary, the linewidths trace temperature only fairly loosely, and for any individual absorber it is difficult to pinpoint the cosmic phase purely from observables. Nevertheless, one can assign phases probabilistically based on their location (NH i, b), at the penalty of introducing some model dependence. With the large ensembles of absorbers expected to be obtained with COS, this approach can provide some constraints on the content of all baryonic phases as traced by Lyα absorption.
6 CONCLUSIONS
We study the low-redshift IGM as traced by Lyα absorbers in 48 h−1 Mpc, 2 × 3843 particle cosmological hydrodynamic simulations with three prescriptions for galactic outflows. This work builds on our previous works of a decade ago, namely Davé et al. (1999, 2001), by employing simulations with 216 times more particles and 80 times more volume, using improved numerical methodology, and most significantly, testing the impact of large-scale galactic outflows on the IGM as traced by Lyα absorption. Our scenario for the nature and evolution of Lyα forest absorbers from z= 2 → 0 remains basically unchanged: most absorbers arise in low overdensity, highly photoionized gas that traces uncollapsed large-scale filaments. Davé et al. (1999) argued that much of the observed evolution in the Lyα forest can be understood in terms of the evolving relationship between H i column density and the overdensity of the absorbing gas; our latest simulations yield a similar slope and evolution of this relation. Outflows are found to have a small impact on the diffuse IGM, but they do have a significant effect on bound-phase absorbers that arise nearer to galaxies. Our statistical results for Lyα forest absorbers are obtained by applying the AutoVP line fitter (Davé et al. 1997) to artificial spectra with a resolution and S/N similar to those expected for typical COS observations.
Our main results are as follows.
Baryons at z∼ 0 are divided comparably amongst the diffuse phase, the WHIM and the bound phases (condensed, hot halo and stars), The WHIM here is defined as low-density (outside of haloes) gas with T > 105 K, a notable change from previous definitions that impose a maximum temperature but not a maximum density. In detail, our favoured momentum-driven outflow model has 41 per cent in diffuse gas, 35 per cent in bound phases and 24 per cent in WHIM at z= 0, with values for other wind models and redshifts shown in Fig. 4.
Our favoured momentum-driven wind (vzw) model shows similar evolution in diffuse (unbound) IGM baryonic phases to the no-wind (nw) case. In contrast, the condensed, hot halo and stellar fractions are all noticeably different between those two, and between either of these models and the constant wind (cw) model. Furthermore, cw significantly heats the IGM, resulting in more WHIM and less condensed and diffuse gas.
The vzw model at COS resolution shows a CDD with a power-law slope of −1.70. The slope is slightly steeper for nw and cw, and it is steeper for higher resolution spectra. While formally all slopes are within ∼ 2σ of each other, recall that the lines of sight are identical through each simulation, so the differences are fairly robust.
The shallower vzw slope arises because it produces more strong (NH i > 1014 cm−2) lines at z= 0, which agrees better with observations of dN/dz evolution. Weaker lines show no differences in dN/dz among wind models, but they do indicate a discrepancy around z∼ 1 that may reflect deviations from the Haardt & Madau (2001) ionizing background evolution.
The linewidth (b) distribution shows a median around ∼ 40 km s−1 at COS resolution, and it is insensitive to the wind model. It is highly sensitive to spectral resolution, even at large b values, and much of the broadening owes to instrumental resolution (note that our b-parameters are not corrected for this).
Diffuse Lyα absorbers follow a relation between NH i and overdensity given by
, in general agreement with our previous findings. This results in a region of a given overdensity giving rise to a lower column density systems at higher redshift. Departures from this relation become more prominent at low z owing to an increased amount of shock heating.The bulk of Lyα absorbers have total hydrogen columns of ∼ 1018−19 cm−2, reflecting the trend that the low-NH i absorbers are more ionized (neutral fraction ∼ 10−6 cm−3) and larger (hundreds of kpc), while high-NH i absorbers are less ionized (neutral fraction ∼ 10−3 cm−3) and smaller (few kpc).
Linewidths only loosely reflect the temperature of the absorbing gas, because typically linewidths are 1.5 to 3 times the thermal broadening value. Hence, wide lines do not exclusively track WHIM or hot gas, though trends in ρ and T with both b and NH i could be used to assign absorbers to a particular cosmic phase in a statistical sense.
Improved dN/dz statistics for weak lines (NH i < 1014 cm−2) will improve determinations of the UV background intensity at z < 2. Improved statistics at higher column densities can provide strong tests of galactic outflow models.
The installation of COS on Hubble promises a great leap forward in our understanding of low-redshift Lyα absorption and the IGM from which it arises. Besides testing the basic paradigm of the Cosmic Web origin for weak Lyα forest absorbers, COS Lyα data will provide constraints on the baryon content in various cosmic phases, ionizing background evolution and the nature of galactic outflows. Additional constraints will be provided by the distribution of IGM metals that can be probed to much greater precision with COS (the subject of Paper II in this series) and by the relation between galaxies and absorption systems (covered in Paper III). The combination of these constraints with overall Lyα absorber statistics will provide powerful diagnostics for the mechanisms of galactic outflows. Comparisons of theory and observations in the coming years will critically test our prevailing paradigms and prescriptions, thereby providing valuable insights into the evolution of the majority of baryons over cosmic time.
In detail, 
, which is approximately 1/3 for low values of concentrations corresponding to objects just undergoing collapse.
We thank M. Fardal, D. Kereš, N. Lehner, M. Peeples and J. Schaye for helpful conversations, and G. Williger for providing us the data shown in Fig. 6 in electronic form. The simulations used here were run on University of Arizona’s SGI cluster, ice. Support for this work was provided by NASA through grant numbers HST-GO-11598 and HST-AR-11751 from the Space Telescope Science Institute, which is operated by AURA, Inc. under NASA contract NAS5-26555. This work was also supported by the National Science Foundation under grant number AST-0847667. Computing resources were obtained through grant number DMS-0619881 from the National Science Foundation. DW acknowledges support from NSF grant AST-0707985 and from an AMIAS membership at the Institute for Advanced Study. NK acknowledges support from NASA through ADP grant NNX08AJ44G.
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