THE BARYON CENSUS IN A MULTIPHASE INTERGALACTIC MEDIUM: 30% OF THE BARYONS MAY STILL BE MISSING

For low-redshift cosmology and galaxy formation rates, it is important to account for all the baryons synthesized in the Big Bang. Cosmologists have noted a baryon deficit in the low-redshift universe (Fukugita et al. 1998) relative to the predicted density synthesized in the Big Bang. Although this deficit could arise from an incomplete inventory, it could also challenge our understanding of the thermodynamics of structure formation and the response of the gas to accretion shocks and galactic outflows. Recent analysis (Komatsu et al. 2011) of the spectrum of acoustic peaks in the cosmic microwave background (CMB) obtained by the Wilkinson Microwave Anisotropy Probe found that baryons comprise a fraction Ω_b = 0.0455 ± 0.0028 of the critical matter energy density of the universe, ρ_cr = (9.205 × 10⁻³⁰ g cm⁻³) h²₇₀, where h₇₀ is the Hubble constant (H₀) in units of 70 km s⁻¹ Mpc⁻¹. This 4.6% baryon fraction corresponds to a mean comoving density $\overline{\rho }_b = \Omega _b \rho _{\rm cr} = 4.24 \times 10^{-31}$ g cm⁻³ and a hydrogen number density n_H = 1.90 × 10⁻⁷ cm⁻³, assuming a primordial helium mass fraction Y_p = 0.2477 (Peimbert et al. 2007).

Unfortunately, the observed baryon inventories in the low-redshift universe are uncertain. Theoretical estimates of the physical state of the gas are complicated by the formation of galaxies and large-scale structure and feedback from star formation in the form of ionizing radiation, metals, and outflows. Galaxy surveys have found ∼10% of these baryons in collapsed objects such as galaxies, groups, and clusters (Salucci & Persic 1999; Bristow & Phillipps 1994; Fukugita & Peebles 2004). Over the last 15 years, substantial reservoirs of gas have been found in the intergalactic medium (IGM), in the halos of galaxies, and in the circumgalactic medium (CGM). There are often semantic problems in defining the CGM, as gas blown out of galaxies or material within the virial radius (Tumlinson et al. 2011; Prochaska et al. 2011). Of the remaining 80%–90% of cosmological baryons, approximately half can be accounted for in the low-z IGM (Shull 2003; Bregman 2007; Danforth & Shull 2008; Danforth 2009) including the warm-hot IGM (or WHIM). Ultraviolet spectroscopic surveys of Lyα and O vi have identified substantial numbers of absorbers (Danforth & Shull 2008; Tripp et al. 2008; Thom & Chen 2008), but claimed detections of hotter gas in X-ray absorption by O vii (Nicastro et al. 2005a, 2005b) remain controversial (Kaastra et al. 2006; Yao et al. 2012). Unfortunately, X-ray spectra still have not confirmed the potential large reservoir of baryons at T > 10⁶ K, suggested by cosmological simulations.

An inefficient distribution of collapsed baryons versus distributed matter is a prediction of nearly all cosmological simulations of large-scale structure formation (Cen & Ostriker 1999, 2006; Davé et al. 1999, 2001; Smith et al. 2011; Tepper-García et al. 2011). These N-body hydrodynamical simulations suggest that 10%–20% of the baryons reside in collapsed objects and dense filaments, with the remaining 80% distributed over a wide range of phases in baryon overdensity ($\Delta _b = \rho _b / \overline{\rho }_b)$ and temperature (T). Thermodynamic considerations suggest that shock-heated WHIM at z < 1 is a natural consequence of gravitational instability in a dark-matter-dominated universe. This hot gas is augmented by galactic-wind shocks and virialization in galaxy halos.

In this paper, we improve the analysis of baryon content in both photoionized and shocked-heated IGM phases and assess the accuracy of observational and theoretical estimates. Because Lyα absorption surveys probe the neutral component of diffuse, photoionized filaments, assessing the baryon content requires a correction for the neutral fraction, f_H i. We derive more accurate photoionization corrections, both from cosmological simulations and analytic models. The analytic models are updated, accounting for the (1 + z)^4.4 rise in the metagalactic ionizing background out to z ≈ 0.7, the (1 + z)³ increase in absorber density, and changes in cosmological proper length, dℓ/dz. Our simulations also correct the O vi surveys for ionization fraction ($f_{{\rm O\,\mathsc{vi}}}$) and metallicity (Z/Z_☉). Finally, we use our critically evaluated catalog (Tilton et al. 2012) of H i and O vi absorption lines from our Hubble Space Telescope (HST) Legacy Archive Project on IGM data taken by the HST and the Far-Ultraviolet Spectroscopic Explorer (FUSE).

To constrain the distribution of Z and $f_{{\rm O\,\mathsc{vi}}}$, we use cosmological hydrodynamic simulations of IGM heating, cooling, and metal transport to find the column-density-weighted average for their product, $(Z / Z_{\odot }) f_{{\rm O\,\mathsc{vi}}}$. Whereas previous work assumed constant values, Z/Z_☉ = 0.1 and $f_{{\rm O\,\mathsc{vi}}} =0.2$, our new simulations provide spatially averaged corrections for metallicity, O vi ionization fraction, and covariance of IGM parameters (T, ρ, Z). Our computed mean value $\langle (Z / Z_{\odot }) f_{{\rm O\,\mathsc{vi}}} \rangle = 0.01$ is half the previously assumed value, thereby doubling previous estimates of the baryon census traced by O vi. In Section 2, we describe the simulations and their results for the O vi distribution in column density, gas temperature, baryon overdensity, metallicity, and ionization fraction. In Section 3, we assess the corrections for ionization and metallicity, applied to the O vi and Lyα absorbers, and we derive values of Ω_b from recent surveys of IGM and CGM phases. Variations in these factors are produced by WHIM thermodynamics, gas temperature (T), baryon overdensity (Δ_b), and O vi column density ($N_{{\rm O\,\mathsc{vi}}}$). In Section 4, we summarize the current baryon census with uncertainties on each component. Our conclusions and recommendations for future work are given in Section 5.

The primary simulation analyzed in this work is run $50\_1024\_2$ of Smith et al. (2011) with "distributed feedback" implemented with the adaptive-mesh refinement (AMR) + N-body code Enzo (Bryan & Norman 1999; O'Shea et al. 2005a). To check convergence and robustness of our results, we also looked at run $50\_1024\_1$ with "local feedback." The simulations have a box size of 50 h⁻¹ Mpc comoving, with 1024³ grid cells and dark matter particles, yielding a dark matter mass resolution of 7 × 10⁶ M_☉ and spatial cells of 49 h⁻¹ kpc (comoving). We have employed a sophisticated treatment of metal cooling and heating (Smith et al. 2008, 2011). Radiative cooling is included by solving for the non-equilibrium chemistry and cooling of atomic H and He, coupled to tabulated metal cooling rates computed as a function of density, metallicity, temperature, electron fraction, and redshift in the presence of an ionizing metagalactic radiation background. To mimic the effects of reionization, we included a spatially uniform, but redshift-dependent radiation background given by Haardt & Madau (2001). The radiation background influences the gas through photoheating and photoionization, whose effects are included in the cooling of both the primordial and metal species.

The spatial and temporal injection of feedback is governed by the rate at which thermal energy and metals are placed into the grid by star particles. A major difference between our metal injection and that used by Oppenheimer & Davé (2009) is the degree of metal mixing. In their smoothed particle hydrodynamics (SPH) formulation, Oppenheimer and Davé inject unmixed metals into a "particle," using a galactic-wind formulation. In our grid code, described below and in Smith et al. (2011), the metals are injected along with mass and energy, distributed in both space and time, and assumed to be fully mixed. Mass and energy are either placed into a single cell ("local feedback") or 27 cells ("distributed feedback"). The subsequent metal transport is achieved by pressure gradients across cells, rather than by explicit addition of kinetic energy by galactic winds. Our standard results are based on the distributed method. We use a modified version of the star formation routine of Cen & Ostriker (1992). Star particles, representing the combined presence of a few million solar masses of stars, are formed when the following three conditions are met: (1) the total density of a grid cell is above a certain threshold, (2) a convergent flow exists (negative velocity divergence), and (3) the cooling time is less than the dynamical time. If all three conditions are satisfied, a "star particle," representing a large collection of stars, is formed within the grid cell with a total mass m_* = f_*m_cell(Δt/t_dyn). Here, f_* ≈ 0.1 is the star formation efficiency, m_cell is the baryon mass in the cell, t_dyn is the dynamical time, and Δt is the hydrodynamical time step. Subsequently, this much mass is also removed from the grid cell as the star particle is formed, ensuring mass conservation. Although the star particle is formed instantaneously within the simulation, feedback occurs over a longer timescale, which more accurately reflects the gradual process of star formation.

The rate of star formation, and hence the rate at which thermal energy and metals are injected into the grid by the star particle, peaks after one dynamical time and then decays exponentially. Stellar feedback is represented by the injection of thermal energy and the return of gas and metals to the grid, in amounts proportional to Δm_sf. A fraction (25%) of the stellar mass is returned to the grid as gas. The thermal energy and metals returned to the grid are e = (Δm_sf)c² and m_metals = (Δm_sf)y, where ≈ 10⁻⁵ is the ratio of rest-mass energy to thermal energy and y ≈ 0.025 is the metal yield. The distributed feedback method (Smith et al. 2011) distributed over a 27-cell cube was designed to mitigate the overcooling that occurs when feedback is deposited into a single grid cell. This raises the temperature, gas density, and cooling rate to unphysically high values. Overcooling also causes the winds that should be transporting metals into the IGM to fizzle out and remain confined to their sites of origin. Smith et al. (2011) showed that this model is able simultaneously to provide good matches to the global star formation history and the observed number density per unit redshift of O vi absorbers (Danforth & Shull 2008). The local feedback method was significantly less successful.

To follow the cosmic star formation rate (SFR) history and the resulting injection of feedback, we have chosen to use Enzo 1024³ unigrid hydrodynamics without mesh refinement. We believe these "unigrid" calculations offer the most efficient use of scarce computational resources. With a box size of 50 h⁻¹ Mpc, we have a comoving spatial resolution of 49 h⁻¹ kpc, sufficient to resolve cosmic-web filaments and gravitational shocks throughout the IGM. This resolution may create some issues for resolving small galaxies at high redshift, which could affect the results for metallicity production and transport compared to AMR. However, our previous experiments (Smith et al. 2011) showed that AMR does not necessarily provide a better computation of the global SFR. In our simulations, star formation seems to be dependent on the force resolution on the root grid. Stars do not form in the lower-resolution simulations because the halos do not collapse correctly at early times when there is no refinement occurring in the box. By the time refinement happens, it is already too late; the collapse of the halos has already been delayed, owing to the poor force resolution. We have verified this by running simulations, with and without AMR, at the same resolution on the top grid. We find almost the exact same star formation history. For this reason, we decided to use constant high resolution everywhere and put our computational resources into a large unigrid: 1024³ in this paper, moving to 1536³ in recent work (Shull et al. 2012a) following the reionization epoch at z ≈ 6–20. By keeping a fixed (comoving) unigrid, we have less spatial resolution close to galaxy halos. In future studies, we intend to explore the effects of adding AMR around star-forming halos.

Post-processing of the simulations was carried out using the data analysis and visualization package yt², documented by Turk et al. (2011). Our Enzo unigrid simulations (Smith et al. 2011), post-processed in the current paper, are among the best current work in describing the temperature, metallicity, and ionization state of the hot gas (WHIM) and photoionized gas. Our results have been checked for convergence and they are robust. These tests are discussed extensively in Smith et al. (2011) using several runs with different box sizes, resolutions, and modes of feedback (local and distributed), finding consistent results. In the current project, we seek to understand the thermal and ionization state of the IGM, including the distribution and covariance of metallicity, temperature, and O vi ionization fraction. In our simulations, the physical properties of O vi absorbers and the degree to which they trace the WHIM are in good agreement with other recent simulations (Tepper-García et al. 2011; Cen & Chisari 2011). However, they differ significantly from those of Oppenheimer & Davé (2009) and Oppenheimer et al. (2012), who found that O vi and Ne viii originate almost exclusively in warm (T ≈ 10⁴ K) photoionized gas. The SPH models by Oppenheimer & Davé (2009) and Davé et al. (2011) find IGM phases with markedly different temperatures and metallicities, but these results likely arise from their metal-injection schemes and the lack of mixing. Tepper-García et al. (2011) suggested that much of this difference arises because Oppenheimer & Davé (2009) neglected the effect of photoionization on metal-line cooling. Oppenheimer et al. (2012) investigated this claim by running additional simulations in which photoionization reduced the metal cooling. This reduction resulted in a small, but insufficient number of O vi absorbers associated with WHIM gas. Instead, they point to the fact that they do not include the mixing of metals from their galactic-wind particles, allowing feedback to take the form of cold, heavily enriched clouds.

Differences between AMR and SPH cosmological simulations have been analyzed in several studies. O'Shea et al. (2005b) compared the SPH code GADGET with the Eulerian grid code Enzo. Cosmological simulations run with dark matter only agree quite well, provided that Enzo is run with a sufficiently fine root grid; otherwise, low-mass halos are suppressed. For adiabatic gas dynamics, these authors found discrepancies in distributions of temperature, mass, and entropy in regions of low overdensity. In their comparison of simulations, these developers of both SPH and grid codes argued that "these discrepancies are due to differences in the shock-capturing abilities of the different methods." Similar concerns were expressed by Vazza et al. (2007), who noted the different phase diagrams of shocked cells in grid codes compared to SPH.

In examining the various interpretations of the high ions (O vi and Ne viii), we have identified several key differences between the two codes: the Oppenheimer–Davé SPH code and our grid-based approach with Enzo. Other simulations (Cen & Ostriker 2006; Cen & Chisari 2011; Tepper-García et al. 2011; Smith et al. 2011; Cen 2012) find different results on IGM temperature and ionization state. Our current 1024³ simulations have better hydrodynamic resolution throughout the IGM than those of Tepper-García et al. (512³) and Davé & Oppenheimer (384³), but the schemes for feedback and mixing of metals differ. On the other hand, we have not employed the AMR capabilities of Enzo, which gives us less resolution around the galaxy halos. The disagreements between IGM temperatures and ionization mechanisms appear to arise from four effects: (1) different methods of injecting energy and metals (mixed or unmixed); (2) overcooling of unmixed, metal-enriched gas at high density and high metallicity; (3) differences in shock capturing (and shock-heating) between SPH and grid codes; and (4) differences in photoionization rates through the assumed radiation fields at hν = 100–250 eV. All four possibilities merit careful comparative studies, although we believe the resolution of this O vi controversy may ultimately hinge on understanding the nature of galactic winds and their ability to mix heavy elements into the IGM. Additional work is therefore needed to understand the hydrodynamic and resolution differences in the treatment of shocks and interfaces between hot and cold gas. Our future studies will attempt to distinguish between effects of hydrodynamics (code resolution) and feedback (injection of mass, energy, and metals).

In this section, we provide a brief overview of the current observations of the baryon census at low redshift. We then present improvements in measuring the baryons in the two major components of the IGM: the WHIM as probed by O vi absorbers (Section 3.1) and the diffuse Lyα absorbers probed by H i (Section 3.2). Our improvements include both analytic models and numerical simulations, which allow us to understand the spatial variations of temperature, density, and metallicity throughout the IGM.

Observations of the 'Lyα forest" of absorption lines suggest that it contains ∼30% of the low-z baryons (Penton et al. 2000, 2004; Lehner et al. 2007; Danforth & Shull 2008). Another 30%–40% is predicted by simulations to reside in shock-heated gas at 10⁵ K to 10⁷ K (WHIM). These two components account for 60%–70% of the cosmological baryons. However, owing to its low density, the WHIM is difficult to detect in emission (Soltan 2006). More promising are absorption-line studies that use the high ionization states of abundant heavy elements with resonance lines in the far-ultraviolet (C iv, N v, O vi), extreme ultraviolet (O iv, O v, Ne viii), and soft X-ray (O vii, O viii, N vi, Ne ix). Gas in the temperature range 5 < log T < 6 can also be detected in broad Lyα absorption (Richter et al. 2004; Danforth et al. 2010) arising from trace amounts of neutral hydrogen with neutral fractions $-6.6 < \log f_{{\rm H\,\mathsc{i}}} < -4.8$. By far, the most effective surveys of the low-z WHIM were obtained from the O vi lines at 1031.926 Å and 1037.617 Å (Danforth & Shull 2005, 2008; Tripp et al. 2008; Thom & Chen 2008), which probe the temperature range 10^5.3–5.7 K in collisionally ionized gas. Danforth & Shull (2008) measured the column densities of 83 O vi absorbers and estimated that 8.6% ± 0.8% of the baryons reside in this phase, assuming constant correction factors for the metallicity (Z ≈ 0.1 Z_☉) and O vi ionization fraction ($f_{{\rm O\,\mathsc{vi}}} = 0.2$). A few detections of Ne viii have also been reported (Savage et al. 2005, 2011; Narayanan et al. 2009, 2011; Meiring et al. 2012) probing somewhat hotter gas (log T ≈ 5.7 ± 0.2).

To detect even hotter portions of the WHIM at log T > 6 probably requires searches for trace metal absorption lines from highly ionized C, O, or Ne. These weak X-ray absorption lines are difficult to detect with the current throughput and spectral resolution of spectrographs on Chandra and XMM-Newton (Yao et al. 2012). Possible X-ray detections of hotter gas at (1–3) × 10⁶ K have been claimed, using absorption lines of helium-like O vii λ21.602 (Nicastro et al. 2005a, 2005b, 2008; Buote et al. 2009; Fang et al. 2010; Zappacosta et al. 2010) and hydrogenic O viii λ18.969 (Fang et al. 2002, 2007). Most of these Chandra detections remain controversial and unconfirmed by the XMM-Newton satellite (Kaastra et al. 2006; Williams et al. 2006; Rasmussen et al. 2007). For example, recent analyses of spectroscopic data on Mrk 421 fail to detect any WHIM gas at the claimed redshifts (z = 0.01 and 0.027), either in broad Lyα absorption (Danforth et al. 2011) from high signal-to-noise (S/N) data from the cosmic origins spectrograph (COS) on the HST or in O vii (Yao et al. 2012) in Chandra data.

The post-processed results of our simulations relevant to O vi and H i are illustrated in Figures 1–8. Figure 1 shows the distribution of baryons in the two-dimensional phase space of baryon temperature and overdensity (log T, log Δ_b) color-coded by baryon mass fraction. Figure 2 shows the neutral fraction, f_H i, also plotted versus log T and log Δ_b. The commonly found features in these phase-space plots include the diffuse Lyα absorbers (T = 10^3.0–4.5 K and Δ_b = 10⁻² to 10^+1.5), a condensed phase (Δ_b > 10³), and a shocked-heated plume of WHIM (T = 10^5–7 K and Δ_b = 10⁰–10^2.5). Most of the narrow Lyα absorbers are believed to be photoionized, although broad Lyα absorbers (BLAs) may arise in the collisionally ionized WHIM, becoming detectable when $\log f_{{\rm H\,\mathsc{i}}} > -6.5$. The gas traced by O vi and BLAs resides at temperatures 5 < log T < 6, marked in Figure 3 for the cumulative distribution of mass and metals versus temperature. The two curves show results from our simulations with distributed feedback (energy injected into 27 cells) and local feedback (single cell). Figure 4 shows the cumulative mass distribution of O vi versus column density and indicates that a significant fraction of O vi is traced by weak absorbers with $\log N_{{\rm O\,\mathsc{vi}}} \le 13.5$ (equivalent width W_λ < 40 mÅ for the stronger 1032 Å line).

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Our simulations track many O vi properties, including metallicity, temperature, and ionization fraction. Figures 5 and 6 show the range and covariance of the two correction factors used in the baryon census: metallicity in solar units (Z/Z_☉) and O vi ionization fraction $f_{{\rm O\,\mathsc{vi}}}$. The ionization fraction includes the effects of both collisional ionization and photoionization, as discussed by Smith et al. (2011). Figure 5 color-codes these distributions in column density, $N_{{\rm O\,\mathsc{vi}}}$, while Figure 6 illustrates their distribution in temperature and baryon overdensity. In multiphase gas, several mechanisms can produce O vi (113.87 eV is needed to ionize O v) including collisional ionization at log T > 5 and photoionization by the (EUV) metagalactic background. The dashed line in Figure 6 shows the locus of points (log T and log Δ_b) at which collisional ionization equals photoionization. This calculation is based on O v collisional ionization rates from Shull & Van Steenberg (1982). The O v photoionization rate was derived assuming a cross section σ(E) = (0.36 × 10⁻¹⁸ cm²)(E/113.87 eV)^−2.1 and the EUV radiation field at 8–10 ryd from Figure 13 of Haardt & Madau (2012).

Figure 7 shows the distribution of the product, $(Z /Z_{\odot }) f_{{\rm O\,\mathsc{vi}}}$, throughout the simulation grid. Color-coded by O vi mass fraction, this product exhibits a bimodal distribution with temperature and baryon overdensity. In the deepest-red portions representing high O vi mass fraction, one finds regions with large values, $(Z / Z_{\odot }) f_{{\rm O\,\mathsc{vi}}} \approx 10^{-1.3}$, in high-density filaments with Δ_b ≈ 100, and regions with lower values, $(Z /Z_{\odot }) f_{{\rm O\,\mathsc{vi}}} \approx 10^{-2.5}$ at Δ_b ≈ 10. In converting the column densities of O vi absorbers to baryons, one should not adopt single corrections for metallicity and ionization fraction. Instead, as described in Section 3.1, we apply statistical corrections based on the correlation of the product $(Z /Z_{\odot }) f_{{\rm O\,\mathsc{vi}}}$ with O vi column density (Figure 8).

3.1. Warm-hot IGM Probed in O vi Absorption

We can use the simulations to derive the distribution of metallicity and O vi ionization fraction throughout the multiphase IGM. Both quantities vary throughout the grid in the simulated IGM. Moreover, the product $(Z/Z_{\odot }) f_{{\rm O\,\mathsc{vi}}}$ correlates with $N_{{\rm O\,\mathsc{vi}}}$ (Figure 8) with weaker absorbers having systematically lower values. This is primarily an effect of spatial variations in the metallicity, but also variations in the O vi ionization fraction produced by spatial fluctuations in WHIM temperature and contributions from photoionizing radiation on low-density IGM. The baryon content in O vi-traced WHIM is then given by an integral over O vi column density (N), with the corrections for metallicity and ionization fraction placed inside the integral:

$$\begin{equation} \Omega _b^{{\rm (O\,\mathsc{vi})}} = \left[ \frac{\mu _b H_0}{c \rho _{\rm cr} {\rm (O/H)}_{\odot }} \right] \int _{N_{\rm min}}^{N_{\rm max}} \frac{d {\cal {N}} (N)}{dz} \, \frac{N}{ Z_{\rm O} (N) \, f_{{\rm O\,\mathsc{vi}}}(N) } \, dN. \end{equation} \tag{ 1 }$$

Here, μ_b = 1.33m_H is the mean baryon mass per hydrogen nucleus, accounting for helium. Earlier surveys that used O vi as a baryon tracer assumed constant values of the ionization fraction, $f_{{\rm O\,\mathsc{vi}}} = 0.2$ (its maximum value in collisional ionization equilibrium at log T_max = 5.45), and metallicity, Z/Z_☉ = 0.1, relative to the solar oxygen abundance, (O/H)_☉ = 4.90 × 10⁻⁴ (Asplund et al. 2009).

From our simulations (Figure 8), the product of metallicity and O vi ionization fraction has a statistical power-law dependence on O vi column density, scaling as N^γ,

$$\begin{equation} (Z/Z_{\odot }) f_{{\rm O\,\mathsc{vi}}} = (0.015)(N_{{\rm O\,\mathsc{vi}}} /10^{14}\,{\rm cm}^{-2})^{0.70} \;. \end{equation} \tag{ 2 }$$

Integrating over the observed distribution $d{\cal {N}} / dz \propto N^{-\beta }$, we find

$$\begin{equation} \Omega _b^{{\rm (O\,\mathsc{vi})}} \propto \int _{N_{\rm min}}^{N_{\rm max}} \, N^{1 - \gamma - \beta } \; dN \propto \big[ N_{\rm min}^{2-\gamma -\beta } - N_{\rm max}^{2-\gamma -\beta } \big] \;. \end{equation} \tag{ 3 }$$

For γ ≈ 0.70 and the observed β ≈ 2.0 (Danforth & Shull 2008), the integral increases at the low end as N^−0.7_min. The column-density-weighted mean of the product $f_{{\rm O\,\mathsc{vi}}} \, (Z / Z_{\odot }) = 0.01$, a factor of two smaller than previously assumed. For our standard integration range, $13.0 \le \log N_{{\rm O\,\mathsc{vi}}} \le 15.0$, this correction doubles the number of baryons in the O vi-traced WHIM, compared to previous assumptions. As noted earlier, we found similar results in all our simulations.

Previous O vi surveys and baryon estimates were quantified by an absorption-line frequency, $d{\cal N}/dz$, per unit redshift and an O vi-traced baryon fraction, $\Omega _b^{{(\rm O\,\mathsc{vi})}} / \Omega _b$. Using 40 O vi absorbers seen with FUSE, Danforth & Shull (2005) found $d{\cal N}/dz \approx 17\pm 3$ for column densities $13.0 \le N_{{\rm O\,\mathsc{vi}}} \le 14.5$. The 10¹³ cm⁻² lower limit corresponds to 12.5 mÅ equivalent width in O vi λ1032. The 2005 FUSE census gave an O vi-traced baryon fraction of at least 4.8% ± 0.9% (statistical error only) for a correction factor $f_{{\rm O\,\mathsc{vi}}} \, (Z / Z_{\odot }) = 0.02$. Danforth & Shull (2008) used HST/STIS data on 83 O vi absorbers to find $d{\cal N}/dz \approx 15.0^{+2.7}_{-2.0}$ integrated down to 30 mÅ, with $d{\cal N}/dz \approx 40^{+14}_{-8}$ integrated to 10 mÅ. Their derived WHIM baryon fractions were 7.3%  ±  0.8% and 8.6%  ±  0.8%, integrated to 30 mÅ and 10 mÅ, respectively. Tripp et al. (2008) found a similar line frequency, $d{\cal N}/dz \approx 15.6^{+2.0}_{-2.4}$, for 51 intervening O vi absorption systems integrated to 30 mÅ, while Thom & Chen (2008) found $d{\cal N}/dz \approx 10.4\pm 2.2$ for 27 O vi absorbers down to 30 mÅ. The latter survey was more conservative, requiring detection of both the stronger O vi line at 1032 Å and the weaker line at 1038 Å. They also had fewer sight lines (16) and a smaller number of O vi absorbers (27) in their survey. Their line frequency is smaller than those in other O vi surveys, perhaps because of small-number statistics and the two-line detection requirement.

As part of a Hubble Archive Legacy Project (PI: Shull, HST-AR-11773.01-A), the Colorado group has re-analyzed HST/STIS data on IGM absorption lines (Tilton et al. 2012), finding 746 H i absorbers and 111 O vi absorbers. Through a critical evaluation of data in the literature and comparison to high-S/N COS spectra when available, we corrected line identification errors in Danforth & Shull (2008) and other surveys. The O vi line frequency from Tilton et al. (2012) is $d{\cal N}/dz \approx 22.2^{+3.2}_{-2.4}$ integrated to 30 mÅ equivalent width in O vi λ1032, with a slope β = 2.08 ± 0.12. Down to 10 mÅ, they find $d{\cal N}/dz \approx 42.0^{+10.7}_{-6.3}$. This new survey provides more reliable baryon fractions for the O vi-traced WHIM of 7.2% ± 0.8% (integrated down to 30 mÅ equivalent width) and 8.6% ± 0.7% (to 10 mÅ), using the old correction factor, $f_{{\rm O\,\mathsc{vi}}} \, (Z / Z_{\odot }) = 0.02$. Taken as a whole, these O vi surveys suggest a WHIM baryon fraction of 8%–9%, assuming the old values of metallicity and ionization fraction. With our new correction factors, $f_{{\rm O\,\mathsc{vi}}} \, (Z / Z_{\odot }) = 0.01$, the baryon fractions double. We therefore adopt an O vi-traced baryon fraction of 17% ± 4%, where we have increased the error to account for systematic uncertainties. There are also corrections for possible double-counting: for example, strong BLAs with metals may contain detectable O vi, and some Lyα forest absorbers may contain photoionized O vi. These issues are discussed in Section 4.1.

The value of $\Omega _b^{{(\rm O\,\mathsc{vi})}}$ is dominated by weak absorbers with $N_{{\rm O\,\mathsc{vi}}} < 10^{13.5}$ cm⁻², where absorption-line statistics become uncertain. An accurate O vi census requires measuring even weaker O vi λ1032 absorption lines with $N_{{\rm O\,\mathsc{vi}}} < 10^{13}$ cm⁻² corresponding to equivalent widths $W_{\lambda } = (12.5\ {\rm m\AA})(N_{{\rm O\,\mathsc{vi}}}/10^{13}$ cm⁻²). Deep spectroscopic surveys in O vi can also ascertain where the distribution of O vi absorbers flattens (Figure 4).

3.2. Diffuse Lyα Absorbers

In this section, we describe the ionization corrections needed to translate H i (Lyα) absorption surveys into baryon content. As with O vi, we use simulations to derive the distribution of hydrogen neutral fraction, f_H i, throughout the multiphase IGM. We then compare our numerical results to those from analytic calculations. The numerical simulation results are based on the distribution of f_H i over the grid of phase-space parameters (log T, log Δ_b) in our 1024³ simulations with 50 h⁻¹ Mpc boxes. Summing the baryon masses over this grid, subject to various cuts in f_H i, T, and Δ_b, we derive baryon fractions corresponding to the Lyα forest, BLAs (WHIM), hot gas, and condensed gas.

Table 1 shows the parameter cuts and results of this exercise for models with both local and distributed feedback (Smith et al. 2011). The rows are arranged to cover a three-decade range in neutral fraction, from $-7 < \log f_{{\rm H\,\mathsc{i}}} < -4$, plus gas outside that range (hot gas at log T > 6.3 and condensed gas with $\log f_{{\rm H\,\mathsc{i}}} > -4$). For both feedback schemes, photoionized Lyα forest absorbers generally have neutral fractions in the range $-6 < \log f_{{\rm H\,\mathsc{i}}} < -4$, with temperatures classified as "warm" (3 < log T < 5). These diffuse Lyα absorbers comprise 32.3% and 34.4% of the baryons for the distributed and local feedback schemes, respectively. Both runs have ∼82% of the gas with $\log f_{{\rm H\,\mathsc{i}}} < -7$ (undetectable in Lyα absorption) residing in the WHIM, with the remainder in hot (∼10%) and condensed (∼8%) phases. Gas with $-7 < \log f_{{\rm H\,\mathsc{i}}} < -6$ should be detectable as BLAs. In the simulations, these absorbers have a 2:1 ratio of WHIM to warm phase, with almost none in the other phases. Gas with $-5 < \log f_{{\rm H\,\mathsc{i}}} < -4$ is almost entirely in the warm phase (∼97%).

Table 1. Baryon Content Probed by f_H i in Simulations

Primary Thermal Phases	Range in fH i	Baryon Contenta	Baryon Contenta
		(Distributed Feedback)	(Local Feedback)
WHIM (log T > 6.3)	$-10 < \log f_{{\rm H\,\mathsc{i}}} < -7$	28.3% of baryons	25.2% of baryons
WHIM (5 < log T < 6.3) + Warm	$-7 < \log f_{{\rm H\,\mathsc{i}}} < -6$	29.4% of baryons	27.8% of baryons
Warm photoionized Lyα forest	$-6 < \log f_{{\rm H\,\mathsc{i}}} < -5$	25.8% of baryons	27.4% of baryons
Warm photoionized Lyα forest	$-5 < \log f_{{\rm H\,\mathsc{i}}} < -4$	6.5% of baryons	7.0% of baryons
Condensed phase (log Δb > 3)	$-4 < \log f_{{\rm H\,\mathsc{i}}} < 0$	10.0% of baryons	12.6% of baryons
Total baryons		100%	100%

Note. ^aCuts on grid (Figure 2) are in neutral fraction (f_H i), baryon overdensity (Δ_b), and temperature (T) as shown in first column. Warm phase refers to photoionized gas at 3 < log T < 5. WHIM refers to gas at 5 < log T < 7, where Lyα absorbers with 5 < log T < 6 are detectable as broad Lyα absorbers (b > 40 km s⁻¹ with $\log f_{{\rm H\,\mathsc{i}}} > -6.5$). Last two columns give fraction of baryons in each phase, as traced by f_H i. We use the 1024³ simulations in 50 h⁻¹ Mpc boxes, with both local and distributed feedback.

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These numerical estimates that ∼33% of the baryons are traced by the Lyα agree well with our analytic calculations. To better elucidate this comparison, we describe the formalism (Penton et al. 2000) in more detail, including assumptions for the photoionization corrections to the H i (Lyα) absorbers. In photoionization equilibrium, the density of neutral hydrogen in low-density gas depends on the ionizing background, gas density, and electron temperature, all of which evolve with redshift and have spatial fluctuations,

$$\begin{equation} n_{{\rm H\,\mathsc{i}}} = \frac{n_e \, n_{\rm H} \, \alpha _{\rm H}^{(A)}(T) }{ \Gamma _{\rm H} } \;. \end{equation} \tag{ 4 }$$

Here, n_e = (1 + 2y) = 1.165n_H is the electron density for fully ionized gas, n_H is the total density of hydrogen nuclei, and y = n_He/n_H = [(Y/4)/(1 − Y)] ≈ 0.0823 is the helium-to-hydrogen ratio by number, assuming Y = 0.2477 helium abundance by mass. For the low values of n_H and N$_{{\rm H\,\mathsc{i}}}$ in IGM absorbers, we adopt the hydrogen case-A radiative recombination rate coefficient, α^(A)_H(T) ≈ (2.51 × 10⁻¹³ cm³ s⁻¹)T_4.3^−0.726, scaled to an electron temperature T = (10^4.3 K) T_4.3 characteristic of low-metallicity IGM (Donahue & Shull 1991). The H i photoionization rate depends on the metagalactic radiation field, with specific intensity $I_{\nu } = I_0 (\nu / \nu _0)^{-\alpha _s}$ referenced to the Lyman limit, hν₀ = 13.6 eV. Here, 〈α_s〉 ≈ 1.6–1.8 is the mean QSO spectral index between 1.0–1.5 ryd (Telfer et al. 2002; Shull et al. 2012b). The frequency-integrated photoionization rate is given by the approximate formula, Γ_H ≈ [4πI₀σ₀/h(α_s  +  3)] ≈ (2.49 × 10⁻¹⁴ s⁻¹) I₋₂₃(4.8/α_s  +  3), where I₀ = (10⁻²³ erg cm⁻² s⁻¹ Hz⁻¹ sr⁻¹)I₋₂₃. Hereafter, we combine the two parameters, I₀ and α_s, into a single scaling parameter, Γ₋₁₄ = (Γ_H/10⁻¹⁴ s⁻¹), for the hydrogen photoionization rate. Previous calculations of the low-z ionizing intensity (Shull et al. 1999) found Γ_H ≈ 3.2^+2.0_{− 1.2} × 10⁻¹⁴ s⁻¹ and noted that low-z observational constraints were consistent with values in this range. More recent calculations (Haardt & Madau 2012) are consistent with this value and other estimates at z ≈ 0. Figure 9 illustrates current estimates of the intensity of the metagalactic ionizing radiation field starting at 1 ryd (H i photoionization edge), continuing to 4 ryd (He ii edge) and beyond, including ionization potentials needed to produce some of the higher metal ions, such as C iv (47.87 eV = 3.52 ryd), O vi (113.87 eV = 8.37 ryd), O vii (138.08 eV = 10.15 ryd), Ne viii (207.2 eV = 15.24 ryd), and O viii (739.11 eV = 54.35 ryd).

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The Lyα absorbers are thought to arise as fluctuations in dark matter confined clumps or filaments, which we approximate as singular isothermal spheres with density profiles, n_H(r) = n₀(r/r₀)⁻² normalized to a fiducial radius r₀. For a sight line passing through an absorber at impact parameter p, the total baryon mass within radius r = p is M_b(p) = 4πμ_bn₀r²₀p, where μ_b = (1 + 4y)m_H ≈ 1.33m_H is the mean baryon mass per hydrogen. The H i column density can be derived, using the density-squared dependence of $n_{{\rm H\,\mathsc{i}}}$ and integrating through the cloud along path length ℓ at impact parameter p, where ℓ² = r² − p². We substitute p = rcos ϕ and ℓ = ptan ϕ for the angle ϕ between the directions of p and r,

$$\begin{eqnarray} N_{{\rm H\,\mathsc{i}}} (p) &=& \left[ \frac{ \alpha _{\rm H}^{\rm (A)} \, (1 + 2y)}{ \Gamma _{\rm H} } \right] 2 \int _{0}^{\infty } n_0^2 \left(\frac{r}{r_0} \right) ^{-4} \; dl \nonumber\\ &=& \left[ \frac{ \pi n_0^2 \, r_0^4 \, \alpha _{\rm H}^{\rm (A)} \, (1 + 2y)}{2 \, \Gamma _{\rm H} \, p^3 } \right] \;. \end{eqnarray} \tag{ 5 }$$

Solving for the quantity n₀r²₀, we can express the absorber mass within r = p as

$$\begin{eqnarray} M_b(p) &=& 4 \pi \mu _b \, p^{5/2} \left[ \frac{2 \, \Gamma _{\rm H} \, N_{{\rm H\,\mathsc{i}}}(p) }{ \pi (1 + 2y) \alpha _{\rm H}^{\rm (A)} } \right]^{1/2} \nonumber\\ &=& (1.09 \times 10^9 \, M_{\odot }) \left[ N_{14}^{1/2} \, \Gamma _{-14}^{1/2} \, p_{100}^{5/2} T_{4.3}^{0.363} \right] \;. \end{eqnarray} \tag{ 6 }$$

In the above formula, we have scaled the impact parameter p = (100 kpc)p₁₀₀ using a 100 kpc characteristic scale length of Lyα absorbers at fiducial column density $N_{{\rm H\,\mathsc{i}}} = (10^{14}\;{\rm cm}^{-2}) N_{14}$; see Penton et al. (2000), and references therein.

Next, we calculate the baryon density in the Lyα absorbers as a fraction of the cosmological closure density, ρ_cr = (3H²₀/8πG) at z = 0. Because our Lyα survey extends to z = 0.4, we include corrections for cosmological evolution in the space density of absorbers, ϕ(z), and the hydrogen photoionization rate, Γ_H(z). We begin with the standard expression for the number of absorbers per unit redshift,

$$\begin{equation} \frac{d{\cal N}}{dz} = \left[ \frac{c}{(1+z) H(z)} \right] \pi [p(z)]^2 \, \phi (z) \;, \end{equation} \tag{ 7 }$$

where H(z) = H₀[Ω_m(1 + z)³ + Ω_Λ]^1/2 is the Hubble parameter at redshift z in a flat ΛCDM cosmology, and the absorber space density is ϕ(z) = ϕ₀(1 + z)³. The absorption-line frequency and impact parameter p correspond to the H i column density and absorber mass given in Equations (5) and (6). The baryon mass density in Lyα absorbers at redshift z is written as the product of absorber mass, M_b, times the absorber space density, ϕ(z), integrated over the distribution in H i column density. We define the closure parameter, $\Omega _b^{{(\rm H\,\mathsc{i})}} = \rho _b(0) / \rho _{\rm cr}(0)$ at z = 0, where ρ_b(z) = ρ_b(0)(1 + z)³. Assembling all the terms, we find a closure parameter in Lyα absorbers of column density $N_{{\rm H\,\mathsc{i}}}$,

$$\begin{eqnarray} \Omega _b^{{(\rm H\,\mathsc{i})}} &=& \frac{ \phi _0 M_b }{\rho _{\rm cr}} = \frac{32 (2 \pi)^{1/2}}{3} \left[ \frac{\mu _b G}{c H(z) (1+z)^2} \right] \nonumber\\ && \times \left[ \frac{ \Gamma _{\rm H}(z) p(z) N_{{\rm H\,\mathsc{i}}} }{ (1+2y) \alpha _{\rm H}^{\rm (A)} } \right] ^{1/2} \;. \end{eqnarray} \tag{ 8 }$$

Recent calculations of the metagalactic ionizing background (Haardt & Madau 2012) show that the hydrogen photoionization rate rises rapidly from redshifts z = 0 to z = 0.7. We have fitted the rate to the convenient formula Γ_H(z) = (2.28 × 10⁻¹⁴ s⁻¹)(1 + z)^4.4. We have little data on the redshift evolution of the characteristic absorber scale length, p, other than theoretical expectations for the gravitational instability of filaments in the cosmic web. In the following calculation, we assume that p = (100 kpc)p₁₀₀ remains constant with redshift and rewrite Equation (8) as an integral over column density,

$$\begin{eqnarray} \Omega _b^{{(\rm H\,\mathsc{i})}} &=&(9.0 \times 10^{-5}) \frac{ h_{70}^{-1} p_{100}^{1/2} \; T_{4.3}^{0.363} (1+z)^{0.2}}{ [\Omega _m (1+z)^3 + \Omega _{\Lambda }]^{1/2} } \nonumber\\ && \times \int _{N_{\rm min}}^{N_{\rm max}} \frac{ d {\cal N} (\log N_{{\rm H\,\mathsc{i}}}) }{dz} N_{14}^{1/2} \; d(\log \, N_{{\rm H\,\mathsc{i}}}) \;. \end{eqnarray} \tag{ 9 }$$

The ionization rate, Γ_H(z)∝(1 + z)^4.4, enters Equation (8) as the square root, almost exactly compensating for the (1 + z)² factor in the denominator.

We can now use Lyα surveys to evaluate their contribution to the baryon census from our analytic formalism. Ultraviolet spectrographic surveys of low-redshift absorbers provide the distribution of H i column densities in the diffuse Lyα forest (Penton et al. 2000, 2004; Danforth & Shull 2008; Lehner et al. 2007; Tilton et al. 2012). Penton et al. (2004) applied photoionization corrections to a survey of 187 Lyα absorbers over redshift path length Δz = 1.157 and found a distribution in H i column density, f(N)∝N^−β with β = 1.65 ± 0.07 and a 29% ± 4% contribution to the total baryon content. Danforth & Shull (2008) surveyed 650 Lyα absorbers with HST/STIS over the range $12.5 \le \log N_{{\rm H\,\mathsc{i}}} \le 16.5$ with total path length Δz = 5.27. Their H i distribution was similar, with β = 1.73 ± 0.04 and a fractional contribution of 28.7% ± 3.7% (statistical errors only) to the baryon census. Although the formulas for baryon fractions were stated correctly (Equations (7)–(10) in Danforth & Shull 2008), the values listed in their Tables 12 and 13 were computed with incorrect cosmological corrections and overestimated values of Ω_b for H i and O vi. Our new HST archive survey (Tilton et al. 2012) properly includes these effects, as well as the redshift evolution of Γ_H(z), to find β = 1.68 ± 0.03 for 746 Lyα systems with column densities between $12.5 < \log N_{{\rm H\,\mathsc{i}}} < 16.5$ over path length Δz = 5.38.

The new derivation (Tilton et al. 2012) of $\Omega _b^{{(\rm H\,\mathsc{i})}}$ is consistent with 24%–30% of the baryons residing in the Lyα forest and partial Lyman-limit systems. This value, derived using the analytic formalism above, agrees fairly well with estimates of 32%–34% from our numerical simulations (Table 1). For the current census, we adopt an Lyα forest baryon fraction of $\Omega _b^{{\rm (H\,\mathsc{i})}} = 28\%\ \,{\pm}\, 11$%. The latter error bars include systematic effects, as we discuss in Section 4.

We now summarize the current status of the low-z baryon census and describe the individual baryon contributions, together with previous estimates and uncertainties. Figure 10 shows a pie chart of the current observable distribution of low-redshift baryons in various forms, from collapsed structures to various phases of the IGM, CGM, and WHIM. These slices show the contributions, Ω⁽ⁱ⁾_b/Ω_b^(tot), to the total baryon content from components (i). Measurements of Lyα, O vi, and BLAs, together with more careful corrections for metallicity and ionization fraction, can now account for ∼60% of the baryons in the IGM. An additional 5% may reside in circumgalactic gas, 7% in galaxies, and 4% in clusters. This still leaves a substantial fraction, 29% ± 13%, unaccounted for. We have assigned realistic errors on each of the "slices of the baryon pie," most of which involve systematic uncertainties in the parameters needed for the ionization corrections, metallicity, and geometric factors (cloud size). It is possible that the baryon inventory could change as a result of better determinations of these parameters. However, most numerical simulations including ours (Figure 3) suggest that a substantial reservoir (∼15%) of hot baryons exists in the hotter WHIM (T > 10⁶ K).

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4.1. Components of Baryon Content

4.2. Error Budgets

Here, we summarize the current status of the error budgets for the major contributors to uncertainty in the diffuse Lyα forest baryon census. Many of the parameters enter the formula for $\Omega _b^{{\rm (H\,\mathsc{i})}}$ as the square root, a weak dependence (see Equation (6)) arising because recombination theory predicts that $N_{{\rm H\,\mathsc{i}}} \propto n_{\rm H}^2$ for highly ionized absorbers. Thus, the total baryon mass (proportional to n_H) depends on a weight factor N^1/2₁₄. From this formulation, we can conduct an error-propagation analysis to arrive at the overall uncertainty on the Lyα contribution to Ω_b in Equation (9). This quantity depends on five parameters, which we list below with assigned errors.

• 1.  
  Distribution of H i column densities. Danforth & Shull (2008) measured the distribution of H i column densities, $d{\cal {N}} / dz \propto N_{{\rm H\,\mathsc{i}}}^{-\beta }$. Based on 650 low-redshift Lyα absorbers, they found a slope β = 1.73 ± 0.04 and a baryon content of 29% ± 4% of Ω_b, integrated over $12.5 \le \log N_{{\rm H\,\mathsc{i}}} \le 16.5$. Our new survey (Tilton et al. 2012) finds β = 1.68 ± 0.03 and a contribution of 28% ± 4% from the Lyα forest plus partial Lyman-limit systems to the baryon fraction. We assume 15% uncertainty in the column-density distribution statistics, which are increasingly uncertain at $\log N_{{\rm H\,\mathsc{i}}} < 13.0$. Extending the $N_{{\rm H\,\mathsc{i}}}^{-1.7}$ distribution from log N = 12.5–12.0 would add another 3% to the baryon fraction (from 28% to 31%) if there is no change in slope.
• 2.  
  Hydrogen photoionization rate. This rate, Γ_H, depends on the radiation field normalization at 1 ryd (I₀) and spectral slope (α_s) between 1.0–1.5 ryd. Previous AGN composite spectra found indices ranging from α_s = 1.76 ± 0.12 (Telfer et al. 2002) to α_s = 0.56^+0.38_{− 0.28} (Scott et al. 2004). New HST/COS composite spectra of AGNs find an index α_s = 1.59 ± 0.20 (Shull et al. 2012b), close to the Telfer et al. (2002) value for radio-quiet AGNs. Our calculations also take into account the (1  +  z)^4.4 rise in Γ_H(z) from z = 0 to z = 0.7, a fit to the recent calculations of Haardt & Madau (2012). We estimate the joint error on Γ_H as ±50% from models of the metagalactic radiation field from quasars and galaxies (Shull et al. 1999; Haardt & Madau 2012).
• 3.  
  Characteristic scale length of absorbers. The characteristic impact parameter, p₁₀₀, at $N_{{\rm H\,\mathsc{i}}} \approx 10^{14}$ cm⁻² in units of 100 kpc, is inferred by direct and indirect means, including comparing "hits and misses" of Lyα absorbers along nearby sight lines (Bechtold et al. 1994) and the cumulative distributions of absorbers with nearest-neighbor galaxies (Stocke et al. 1995; Shull et al. 1998). The frequency of Lyα absorption lines per unit redshift also implies 200–300 kpc absorber cross sections, when associated with the space density of galaxies down to luminosities L ≈ 0.01–0.03 L* (Shull et al. 1996; Stocke et al. 2006; Prochaska et al. 2011). We adopt an uncertainty of ±50% on p₁₀₀.
• 4.  
  Electron temperature. Temperature (T_e) enters through the square root of the hydrogen recombination rate coefficient, α^(A)_H∝T^−0.726. Models of IGM photoelectric heating (Donahue & Shull 1991) predict a range from 5000 K to 30,000 K. For z < 0.4, with small expected variations from photoionization, we adopt an uncertainty of ±30%.
• 5.  
  Hubble constant. This parameter has been measured as H₀ = 72 ± 8 km s⁻¹ Mpc⁻¹ (Freedman et al. 2001) and H₀ = 73.8 ± 2.4 km s⁻¹ Mpc⁻¹ (Riess et al. 2011), using distance scales based on Cepheids in galaxies with Type Ia supernovae. To be conservative, we adopt an error of ±5%.

From standard error-propagation formulas, we write the relative error on $\Omega _b^{{(\rm H\,\mathsc{i})}}$ as the quadrature sum of relative errors on the five parameters, weighted by the square of the exponents (1, 0.5, or 0.363) as they appear in the scaling (see Equation (9)):

$$\begin{eqnarray} \left(\frac{\sigma _{\Omega }}{\Omega } \right) ^2 &=& \left(\frac{\sigma _N}{N} \right)^2 + \left(\frac{\sigma _h}{h} \right)^2 + \left(\frac{\sigma _N}{N} \right)^2 + (0.5)^2 \nonumber\\ && \times \left[ \left(\frac{\sigma _{\Gamma }}{\Gamma } \right)^2 + \left(\frac{\sigma _p}{p} \right)^2 \right] + (0.363)^2 \left(\frac{\sigma _T}{T} \right)^2. \quad \end{eqnarray} \tag{ 10 }$$

This formula gives a relative error (σ_Ω/Ω) = 0.40, so that we can express $\Omega _b^{{(\rm H\,\mathsc{i})}} / \Omega _b^{(\rm tot)} = 0.28 \pm 0.11$. Most (77%) of the error budget comes from uncertainties in the ionizing radiation field (Γ_H) and characteristic absorber size (p₁₀₀).

What observations and theoretical work are needed to make progress on the baryon census, both in sensitivity and in accuracy? First, we need more precise UV absorption-line surveys to measure O vi and Lyα absorbers to lower column densities. As described in Section 3, the numbers of absorbers in current surveys become increasingly uncertain at column densities $\log N_{{\rm H\,\mathsc{i}}} < 13.0$ and $\log N_{{\rm O\,\mathsc{vi}}} < 13.5$. The current surveys integrate below these levels, but our experience using COS to re-examine earlier Lyα and O vi detections with FUSE, GHRS, and STIS, suggests that some of these weak absorbers are unconfirmed with high-S/N data. In our HST Archive Legacy Project, Tilton et al. (2012) re-analyzed O vi and Lyα data from HST/STIS to provide critically evaluated column densities for $N_{{\rm H\,\mathsc{i}}}$ and $N_{{\rm O\,\mathsc{vi}}}$, and their absorption-line frequencies, $d {\cal {N}}/dz$. The new O vi data were included, together with our fits to $f_{{\rm O\,\mathsc{vi}}} \, (Z/Z_{\odot })$, to yield more accurate values of $\Omega _b^{{\rm (O\,\mathsc{vi})}}$.

With the 10-fold increase in UV sensitivity of COS on HST, we should be able to do even better. We hope to use HST/COS to obtain high-quality data (S/N ⩾30) to search for additional baryons in weak absorbers and constrain the predicted flattening in the column density distributions of H i and O vi. Scaled to column densities (10¹³ cm⁻²)N₁₃, these lines have equivalent widths of (12.5 mÅ)N₁₃ for O vi λ1032 and (54.5 mÅ)N₁₃ for Lyα. These weak-absorber surveys will require HST/COS sensitivity to 4 mÅ equivalent widths, which is achievable at S/N = 30 toward many bright AGN background targets. We can also use COS to obtain better detections and statistics for BLAs and the Ne viii doublet (λλ770.4, 780.3). The Ne viii lines are potentially more reliable probes of hot, collisionally ionized gas than O vi, since Ne viii requires 207 eV to produce and is likely to be less contaminated by photoionization. The lower solar neon abundance, (Ne/O)_☉ ≈ 0.15, makes the Ne viii lines weak, and redshifts z > 0.47 are needed to shift them into the HST/COS band. The BLAs have considerable promise for WHIM probes, as they do not require corrections for metallicity. They do require determining the neutral fraction, f_H i, through careful modeling of the gas temperature and ionization conditions.

It would also be helpful to verify the claimed X-ray detections of O vii in the WHIM (Nicastro et al. 2005a, 2005b) which are not confirmed in other data (e.g., Kaastra et al. 2006; Rasmussen et al. 2007) or in re-analysis of the same data (Yao et al. 2012). The most critical observations for the WHIM census may require a next generation of X-ray spectrographs to measure the weak absorption lines of O vii λ21.602, O viii λ18.969, and other He-like and H-like lines of abundant metals (C v, C vi, N vi, N vii). As discussed by Yao et al. (2012), this requires high-throughput spectrographs (E ≈ 0.3–1.0 keV) with energy resolution E/ΔE > 4000 sufficient to resolve O vii absorbers with mÅ equivalent width. For weak lines, the predicted O vii equivalent widths are $W_{\lambda } = (2.88\ {\rm m\AA})\, (N_{{\rm O\,\mathsc{vii}}}/10^{15}\ {\rm cm}^{-2})$.

Finally, the IGM simulations can be improved in several aspects, in order to use them as more reliable predictors of IGM parameters. In this paper, we computed individual (cell-by-cell) values of metallicity Z and ionization fractions, f_H i and $f_{{\rm O\,\mathsc{vi}}}$, together with their statistical variations and covariance. Our simulations (Smith et al. 2011) were performed with somewhat larger box sizes (50 h⁻¹ Mpc) and on a larger 1024³ grid compared with previous studies of low-z IGM thermodynamics. Our O vi conclusions appear to be robust, as gauged by convergence tests and runs with different methods of injecting feedback from star formation into the grid. Post-processing these simulations allowed us to provide more accurate corrections for the product $(Z / Z_{\odot }) f_{{\rm O\,\mathsc{vi}}}$ as a function of column density $N_{{\rm O\,\mathsc{vi}}}$. These statistics can be performed for other key ions (O vii, Ne viii). We will extend our simulations through higher resolution, addition of discrete ionizing sources, and radiative transfer. We also will explore the correct mixture of collisional ionization and photoionization in the WHIM, a project that requires understanding the implications of different feedback mechanisms for injecting mass, thermal energy, and metals into the CGM. How these metals mix and radiate likely determines the thermodynamics of the surrounding IGM. Because there still exist considerable differences between how simulations treat the thermal state of the IGM, we will continue to push to higher resolution to capture the low-mass galaxies which are important for metal production and mass injection.

This work was supported by NASA grant NNX08AC14G for COS data analysis and an STScI archival legacy grant AR-11773.01-A. Our theoretical work and numerical simulations were supported by the Astrophysical Theory Program (NNX07-AG77G from NASA and AST07-07474 from NSF) at the University of Colorado, Boulder. We thank Eric Hallman, Michele Trenti, John Stocke, Joshua Moloney, and Evan Tilton for helpful comments on the manuscript, and Mark Voit and Joel Bregman for discussions on hot gas in clusters and galaxy halos.