The Baryon Census in a Multiphase Intergalactic Medium: 30% of the Baryons May Still Be Missing

The Baryon Census in a Multiphase Intergalactic Medium: 30% of the Baryons May Still Be Missing

Abstract

Although galaxies, groups, and clusters contain % of the baryons, many more reside in the photoionized and shocked-heated intergalactic medium (IGM) and in the circumgalactic medium (CGM). We update the baryon census in the (H i) Ly forest and warm-hot IGM (WHIM) at  K traced by O vi  absorption. Using robust cosmological simulations of heating, cooling, and metal transport, we improve the O vi baryon surveys with spatially averaged corrections for metallicity () and O vi ionization fraction (). Statistically, their product correlates with column density, , with a -weighted mean of 0.01, which doubles previous estimates of WHIM baryon content. We also update the Ly forest contribution to baryon density out to , correcting for the increase in absorber density, the rise in photoionizing background, and cosmological proper length . We find substantial baryon fractions in the photoionized Ly forest (%) and WHIM traced by O vi and broad-Ly absorbers %). The collapsed phase (galaxies, groups, clusters, CGM) contains %, leaving an apparent baryon shortfall of %. Our simulations suggest that % reside in hotter WHIM ( K). Additional baryons could be detected in weaker Ly and O vi absorbers. Further progress requires higher-precision baryon surveys of weak absorbers, down to minimum column densities  cm,  cm,  cm, using high-S/N data from high-resolution UV and X-ray spectrographs.

Subject headings:
cosmological parameters — observations — intergalactic medium — quasars: absorption lines

1. Introduction

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, Hogan, & Peebles 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 (WMAP) found that baryons comprise a fraction of the critical matter-energy density of the universe, , where is the Hubble constant () in units of 70 km s Mpc. This 4.6% baryon fraction corresponds to a mean comoving density, g cm, and a hydrogen number density , assuming a primordial helium mass fraction (Peimbert et al. 2007).

Baryon inventories in the low redshift universe are uncertain. They are often complicated by the formation of galaxies and large-scale structure and by the 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- IGM (Shull 2003; Bregman 2007; Danforth & Shull 2008; Danforth 2009) including the warm-hot IGM (or WHIM). Ultraviolet spectroscopic surveys of Ly and O vi have identified substantial numbers of absorbers (Danforth & Shull 2008; Tripp et al. 2008; Thom & Chen 2008), but claimed detections of hotter in X-ray absorption by O vii (Nicastro et al. 2005) 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  K, suggested by cosmological simulations.

An inefficient distribution of collapsed baryons vs. 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-Garcia 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 ( and temperature (). Thermodynamic considerations suggest that shock-heated WHIM at 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 Ly absorption surveys probe the neutral component of diffuse, photoionized filaments, assessing the baryon content requires a correction for the neutral fraction, . We derive more accurate photoionization corrections based on the rise in the metagalactic ionizing background out to , as well as the increase in absorber density and changes in cosmological proper length, . We also use cosmological simulations to correct the O vi surveys for ionization fraction () and metallicity . Finally, we use our group’s critically evaluated catalog of H i and O vi absorption lines (Tilton et al. 2012) from our HST Legacy Archive project on IGM data taken by the Hubble Space Telescope (HST) and Far Ultravolet Spectroscopic Explorer (FUSE).

To constrain the distribution of and , we use cosmological hydrodynamic simulations of IGM heating, cooling, and metal transport to find the column-density weighted average for their product, . Whereas previous work assumed constant values, and , our new simulations provide spatially averaged corrections for metallicity, O vi ionization fraction, and covariance of IGM parameters (, , ). Our computed mean value 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 Ly absorbers, and we derive values of from recent surveys of IGM and CGM phases. Variations in these factors are produced by WHIM thermodynamics, gas temperature (), baryon overdensity (), and O vi column density (). In Section 4 and two Appendices, we summarize the current baryon census with uncertainties on each component.

2. Cosmological Simulations of the Whim

The primary simulation analyzed in this work is run of Smith et al. (2011) with “distributed feedback” and performed with the adaptive-mesh-refinement + N-body code Enzo (Bryan & Norman 1997; O’Shea et al. 2004). To check convergence and robustness of our results, we also looked at other runs, particularly run with “local feedback”. Post-processing of the simulations was carried out using the data analysis and visualization package yt2, documented by Turk et al. (2011). The simulation has a box size of Mpc comoving, with 1024 grid cells and dark matter particles, giving it a dark-matter mass resolution of and spatial cells of kpc. 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 influence of the radiation background through photoheating and photoionization is included in the cooling of both the primordial and metal species.

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 (Smith et al. 2011), and they are robust. We have tested the results from several runs with different box sizes, resolutions, and modes of feedback (local and distributed), finding similar results, as described later. Our use of unigrid (rather than adaptive-mesh-refinement) hydrodynamics was deliberate, to provide optimal hydrodynamic resolution of the IGM and WHIM. It is well established that SPH (smooth particle hydrodynamic) codes provide poor hydrodynamic resolution of shocks and instabilities. Agertz et al. (2007) noted that Eulerian grid-based methods are able to resolve and treat important dynamical instabilities such as Kelvin-Helmholtz or Rayleigh-Taylor, whereas these processes are poorly resolved by SPH techniques. Vazza et al. (2007) pointed to the significantly different phase diagrams of shocked cells in grid codes compared to SPH, with sizable differences in the morphologies of accretion shocks between grid and SPH methods.

We have employed a sophisticated treatment of metal cooling and heating (Smith, Sigurdsson, & Abel 2008; Smith et al. 2011). The SPH models by Davé & Oppenheimer (2009) and Davé et al. (2011) find IGM phases with markedly different temperatures and metallicities, but we believe these results arise from their metal-injection schemes and the lack of mixing. None of the other major simulation groups (Cen & Ostriker 2006; Cen & Chisari 2011; Tepper-Garcia et al. 2011; Smith et al. 2011; Cen 2012) can reproduce their results on IGM temperature and ionization state. Our simulations have better hydrodynamic resolution than all of the Tepper-Garcia et al. simulations () and Davé & Oppenheimer models (). Our paper was the only one to test for convergence, and we concluded that our models were robust. It has sometimes been suggested that the use of “unigrid” Enzo calculations casts doubt on the validity of the results for metallicity production and transport, compared to adaptive-mesh-refinement (AMR). Just the opposite is true. In fact, AMR does not provide a better computation of the global star formation rate, as we examined (Smith et al. 2011). In these 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 high resolution everywhere and put our computational resources into a large unigrid: in this paper, and moving to in recent work at (Shull et al. 2012a).

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: the total density of a grid cell is above a certain threshold, a convergent flow exists (negative velocity divergence), and the cooling time is less than the dynamical time. Star particles return feedback to the grid in the form of metal-enriched gas and thermal energy. We use a distributed-feedback method (Smith et al. 2011) in which material and energy are distributed over a 27-cell cube (three cells on a side) centered on the location of the star particle. This is done to mitigate the over-cooling that occurs when feedback is deposited into a single grid cell, which raises the temperature, gas density, and cooling rate to unphysically high values. Over-cooling 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). If all three above conditions are satisfied, a “star particle,” representing a large collection of stars, is formed within the grid cell with a total mass, . Here, is the star-formation efficiency, is the baryon mass in the cell, is the dynamical time, and is the hydrodynamical timestep. 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 is assumed to occur over a longer time scale, which more accurately reflects the gradual process of star formation. Stellar feedback is represented by the injection of thermal energy and the return of gas and metals to the grid, in amounts proportional to . We assume that a fraction (25%) of the stellar mass is returned to the grid as gas. The thermal energy and metals returned to the grid are and , where is the ratio of rest-mass energy to thermal energy and is the metal yield. The rate of star formation and rate at which thermal energy and metals are injected into the grid by the star particle peak after one dynamical time, then decays exponentially.

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-Garcia et al. 2011; Cen & Chisari 2011). However, they differ significantly from those of Oppenheimer & Davé (2009, 2011), who found that O vi and Ne viii originate almost exclusively in warm ( K) photoionized gas. Tepper-Garcia 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.

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 smooth particle hydrodynamic (SPH) code and our grid-based approach with Enzo. The disagreement between the IGM temperatures and ionization mechanisms appear to arise from four effects: (1) Different methods of injecting energy and metals (mixed or unmixed); (2) Over-cooling of unmixed, metal-enriched gas at high density and high metallicity; (3) Differences in shock capturing (and shock-heating) between SPH and grid codes; (4) Differences in photoionization rates through the assumed radiation fields at 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 IGM.

3. Census of Baryons in Different Thermal Phases

Figure 1.— Distribution of IGM in temperature and baryon overdensity , color-coded by baryon mass fraction. This distribution shows the same thermal phases seen in simulations by other groups and commonly labeled as warm (diffuse photoionized gas), WHIM, and condensed.

The “Lyman- forest” of absorption lines appears to contain 30% of the low- baryons (Penton et al. 2000, 2004; Lehner et al. 2007). Another 30–40% is predicted by simulations to reside in shock-heated gas at  K to  K (WHIM). Owing to its low density, the WHIM is difficult to detect in emission (Soltan 2006). More promising are absorption-line studies, using 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). The low- WHIM has most effectively been surveyed in 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  K in collisionally ionized gas. Danforth & Shull (2008) measured the column densities of 83 O vi absorbers and estimated that % of the baryons reside in this phase, assuming constant correction factors for the metallicity () and O vi ionization fraction (). A few detections of Ne viii have also been reported (Savage et al. 2005; Narayanan et al. 2009, 2011; Meiring et al. 2012) probing somewhat hotter gas. Weak X-ray absorption lines are difficult to detect with the current throughput and spectral resolution of spectrographs on Chandra and XMM/Newton. Possible X-ray detections of hotter gas at  K have been claimed, using absorption lines of helium-like O vii  (Nicastro et al. 2005a,b, 2008; Buote et al. 2009; Fang et al. 2010; Zappacosta et al. 2010) and hydrogenic O viii  (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). Recent analyses of spectroscopic data on Mrk 421 fails to detect any WHIM gas at the claimed redshifts ( and 0.027), either in broad Ly absorption (Danforth et al. 2011) from high-S/N data from the Cosmic Origins Spectrograph (COS) on the Hubble Space Telescope (HST) or in O vii (Yao et al. 2012) in Chandra data.

The post-processed results of our simulations relevant to O vi are illustrated in Figures 1–7. Figure 1 shows the temperature-density phase diagram of the multiphase IGM, color-coded by baryon mass fraction. The commonly found features in () plots include the diffuse Ly absorbers ( K and to ), a condensed phase (), and a shocked-heated plume of WHIM ( K and to ). The gas traced by O vi resides at , marked in Figure 2 for the cumulative distribution of mass and metals vs. temperature in our simulations. The two curves show results from simulations with distributed feedback (energy injected into 27 cells) and local feedback (single cell). The similarity of the mass distribution curves is evidence of model robustness. Figure 3 shows the cumulative mass distribution of O vi versus column density, indicating that a significant fraction of O vi is traced by weak absorbers with (equivalent width  mÅ for stronger 1032 Å line).

Our simulations show a large range of O vi properties, including metallicity, temperature, and ionization fraction. Figures 4 and 5 show the range and covariance of the two correction factors: metallicity in solar units and O vi ionization fraction . The ionization fraction includes the effects of both collisional ionization and photoionization, as discussed by Smith et al. (2011). Figure 4 color-codes these distributions in , while Figure 5 illustrates their distribution in temperature and baryon overdensity. The wide range of physical conditions in which O vi exists demonstrates the multiphase character of this ionized gas. The mechanisms that produce O vi (113.87 eV is needed to ionize O v) include collisional ionization at and photoionization by the hard (EUV) metagalactic background. The dashed line in Figure 5 shows the locus of points ( and ) 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 and the EUV radiation field at 8–10 ryd from Figure 13 of Haardt & Madau (2012).

Figure 6 shows the distribution of the product, , throughout the simulation. Color-coded by O vi mass fraction, this plot exhibits bimodality of this product with temperature and baryon overdensity. In the deepest-red portions, representing high O vi mass fraction, one finds regions with large values, , in high-density filaments with , and other regions with lower values, at . In converting the column densities of O vi absorbers to baryons, one therefore should not adopt single corrections for metallicity and ionization fraction. However, as we discuss in Section 3.1, one can apply statistical corrections that correlate the product with O vi column density (Figure 7). Integrating over the O vi column-density distribution, we find that this product is a factor of two lower than the previously assumed value of 0.02. This doubles the fraction of WHIM baryons traced by O vi from 8–9% to %.

Figure 2.— Cumulative distributions of IGM mass (top panel) and metals (bottom panel) vs. temperature from our simulations, run with both “local and distributed” feedback (Smith et al. 2011). We only show IGM baryons with overdensities ; the remaining mass and metals are in galaxies and collapsed phase. Vertical dashed lines mark the temperature range ( K to  K) probed by O vi and Ne viii, and horizontal lines show intercepts for the two distributions.
Figure 3.— Cumulative distribution of O vi by mass from our WHIM simulation, for column densities to cm. Solid black line shows cumulative mass fraction, labeled on left vertical axis. Gray histogram shows cumulative number of O vi absorbers, labeled on right vertical axis. Red points show observed cumulative column-density distribution (Danforth & Shull 2008) labeled on right vertical scale. A significant fraction of O vi-traced WHIM resides in weak absorbers, although the distribution flattens at .
Figure 4.— Distribution of IGM metallicity and O vi ionization fraction color-coded by O vi column density. Note the wide range and covariance of individual factors, whose product, , correlates with O vi column density (color bar along right).
Figure 5.— Distribution of IGM temperature versus baryon overdensity, , color-coded by O vi mass fraction. In this phase space, we identify the WHIM ( K), warm, diffuse photoionized gas ( K and ), and condensed gas (). Dashed line shows locus at which collisional ionization equals photoionization (collisional ionization dominates above the dashed curve).
Figure 6.— Distribution of the metallicity-ionization product, , versus baryon overdensity, , color-coded by O vi mass fraction. The broad distribution of the product, from 0.001 to 0.1 has local enhancements (deep red) in low-metallicity regions (overdensities ) and high-metallicity regions (). The column density weighted mean of this product is 0.01 (Figure 7).
Figure 7.— Values of the product, , for the WHIM simulation with distributed feedback overlaid with a power-law fit (solid red line) to the ensemble, . Results from simulations with local feedback are similar. Integrating over the observed distribution in , we find a weighted value of 0.01. Horizontal (blue) line shows previously assumed value of 0.02 for this product ( and ). Typical variance () about this fit is 0.3–0.4 dex, shown by red dashed lines.

3.1. Warm-Hot IGM Probed in O vi Absorption

As noted, the metallicity and O vi ionization fraction vary throughout the grid in the simulated IGM. Figures 6 and 7 show that the product correlates with , 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 given by an integral over O vi column density (), now with the corrections for metallicity and ionization fraction placed inside the integral:

(1)

Here, 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, (its maximum value in collisional ionization equilibrium at ) and metallicity, , relative to the solar oxygen abundance, (O/H) (Asplund et al. 2009).

From our simulations (Figure 7), the product of metallicity and O vi ionization fraction has a statistical power-law dependence on O vi column density, scaling as ,

(2)

Integrating over the distribution , we find

(3)

For and the observed (Danforth & Shull 2008), the integral increases at the low end as . The column-density weighted mean of the product , a factor of two smaller than previously assumed. For our standard integration range, , 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, , per unit redshift and an O vi-traced baryon fraction, . Using 40 O vi absorbers seen with FUSE, Danforth & Shull (2005) found for column densities . The  cm lower limit corresponds to 12.5 mÅ equivalent width in O vi . The 2005 census gave an O vi-traced baryon fraction of at least % (statistical error only) for a correction factor . Danforth & Shull (2008) used HST/STIS data on 83 O vi absorbers to find integrated to 30 mÅ, with integrated to 10 mÅ. Their derived WHIM baryon fractions were % and %, integrated to 30 mÅ and 10 mÅ, respectively. Tripp et al. (2008) found a similar line frequency, for 51 intervening O vi absorption systems integrated to 30 mÅ, while Thom & Chen (2008) found 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 much 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 or owing to the two-line requirement.

As part of a Hubble Archive Legacy project (PI: Shull, HST-AR-11773.01-A), the Colorado group has reanalyzed 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 integrated to 30 mÅ, with a slope . This new survey provides more reliable baryon fractions for the O vi-traced WHIM of % (integrated down to 30 mÅ equivalent width) and % (to 10 mÅ), using the old correction factor, . Taken as a whole, these O vi surveys suggest a WHIM baryon fraction of 8–9%, assuming the old values for metallicity and ionization fraction. With our new correction factors, , the baryon fractions double. We therefore adopt an O vi-traced baryon fraction of %, where we have increased the error to account for systematic uncertainties. The value of is dominated by weak absorbers with  cm, where the absorption-line statistics become uncertain. An accurate O vi census will require measuring even weaker O vi  absorption lines, with column densities below  cm, corresponding to equivalent widths  cm). Deep spectroscopic surveys in O vi can also ascertain where the distribution of O vi absorbers flattens (Figure 3).

3.2. Diffuse Photoionized Ly Filaments

In this subsection, we provide details on the assumptions, described briefly in Penton et al. (2000), for the photoionization corrections to the H i (Ly) 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 throughout the IGM:

(4)

Here, is the electron density for fully ionized gas, is the total density of hydrogen nuclei, and is the helium-to-hydrogen ratio by number, assuming helium abundance by mass. For the low values of and N in IGM absorbers, we adopt the hydrogen case-A radiative recombination rate coefficient, , scaled to an electron temperature characteristic of low-metallicity IGM (Donahue & Shull 1991). The H i photoionization rate depends on the metagalactic radiation field, with specific intensity referenced to the Lyman limit,  eV. Here, 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, , where erg cm s Hz sr. Hereafter, we combine the two parameters, and , into a single scaling parameter, , for the hydrogen photoionization rate. Previous calculations of the low- ionizing intensity (Shull et al. 1999) found and noted that low- observational constraints were consistent with values in this range. More recent calculations (Haardt & Madau 2012) are consistent with this value and other estimates at . Figure 8 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).

Figure 8.— Compilation of the mean AGN spectral energy distribution (SED), pinned at 1 ryd, with erg cm s Hz sr and two different flux distributions, . Previous composite spectra from small numbers of AGN are shown in red (HST) and light blue (FUSE), with slopes (Telfer et al. 2002) and (Scott et al. 2004). Soft X-ray data are from ROSAT observations of AGN in the Lockman Hole (Hasinger 1994) normalized at keV (73.53 ryd) with spectral slope . The ionization potentials of H i and He ii and ionization energies to produce key metal ions are shown as arrows. The metagalactic backgrounds are from Haardt & Madau (2001, 2011).

The Ly absorbers are thought to arise as fluctuations in dark-matter confined clumps or filaments, which we approximate as singular isothermal spheres with density profiles, normalized to a fiducial radius . For a sight line passing through an absorber at impact parameter , the total baryon mass within radius is , where is the mean baryon mass per hydrogen. The H i column density can be derived, using the density-squared dependence of and integrating through the cloud along pathlength at impact parameter , where . We substitute and for the angle between the directions of and ,

(5)

Solving for the quantity , we can express the absorber mass within as

(6)

In the above formula, we have scaled the impact parameter using a 100-kpc characteristic scale length of Ly absorbers at fiducial column density ; see Penton et al. (2000) and references therein.

Next, we calculate the baryon density in the Ly absorbers as a fraction of the cosmological closure density, at . Because our Ly survey extends to , we include corrections for cosmological evolution in the space density of absorbers, , and the hydrogen photoionization rate, . We begin with the standard expression for the number of absorbers per unit redshift,

(7)

where is the Hubble parameter at redshift in a flat CDM cosmology, and the absorber space density is . The absorption-line frequency and impact parameter correspond to the H i column density and absorber mass given in Equations (5) and (6). The baryon mass density in Ly absorbers at redshift is written as the product of absorber mass, , times the absorber space density, , integrated over the distribution in H i column density. We define the closure parameter, at , where . Assembling all the terms, we find a closure parameter in Ly absorbers of column density ,

(8)

Recent calculations of the metagalactic ionizing background (Haardt & Madau 2012) show that the hydrogen photoionization rate rises rapidly from redshifts to . We have fitted the rate to the convenient formula . We have little data on the redshift evolution of the characteristic absorber scale length, , other than theoretical expectations for the gravitational instability of filaments in the cosmic web. In the following calculation, we assume that remains constant with redshift. We rewrite Equation (8) as an integral over column density,

(9)

The ionization rate, , enters Equation (8) as the square-root, almost exactly compensating for the factor in the denominator.

From UV spectrographic surveys of intergalactic Ly absorbers, we now have a reasonable understanding of the distribution of H i column densities in the diffuse Ly 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 Ly absorbers over redshift pathlength and found a distribution in H i column density with and a % contribution to the total baryon content. Danforth & Shull (2008) surveyed 650 Ly absorbers with HST/STIS over the range with total pathlength . Their H i distribution was similar, with and a fractional contribution of % (statistical errors only) to the baryon census. Although the formulae 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 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 , to find for 746 Ly systems with column densities between over pathlength . Their new derivation of is consistent with 24-30% of the baryons residing in the Ly forest and partial Lyman-limit systems. For the current census, we adopt a baryon fraction of %. The latter error bars include systematic effects, discussed in greater detail in Appendix A.

4. Baryon Census and Future Surveys

We now summarize the current status of the low- baryon census and discuss requirements for future surveys. Details of the individual baryon contributions are described in Appendix B, giving previous estimates and uncertainties. Figure 9 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, , to the total baryon content from components (). Measurements of Ly, O vi, and broad Ly absorbers, together with more careful corrections for metallicity and ionization fraction, can now account for % of the baryons in the IGM. An additional 5% may reside in circumgalactic gas, 7% in galaxies, and 4% clusters. This still leaves a substantial fraction, %, 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 2) suggest that a substantial reservoir (%) of hot baryons exists in the hotter WHIM ( K).

Figure 9.— Compilation of current observational measurements of the low-redshift baryon census (Section 3.3). Slices of the pie-chart show baryons in collapsed form (galaxies, groups, clusters), in the circumgalactic medium (CGM) and intercluster medium (ICM) and in cold gas (H i and He i). Reservoirs include diffuse photoionized Ly forest and WHIM traced by O vi and broad Ly absorbers. Blended colors (BLAs and O vi) have combined total of %, accounting for double-counting of WHIM at  K with detectable metal ions. The collapsed phases (galaxies, CGM, ICM, cold neutral gas) total %. Formally, % of the baryons remain unaccounted for. Our simulations (Figure 2) suggest that an additional 15% reside in X-ray absorbing gas at  K. Additional baryons may be found in weaker lines of low-column density O vi and Ly absorbers. Deeper spectroscopic UV and X-ray surveys are needed to resolve this issue.

What observations and theoretical work are needed to make progress on error bars or baryon detections? First, we need more precise UV absorption-line surveys to measure O vi and Ly absorbers to lower column densities. As described in Section 3, the numbers of absorbers in current surveys become increasingly uncertain at column densities and . The current surveys integrate below these levels, but our experience using COS to re-examine earlier Ly 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) reanalyzed O vi and Ly data from HST/STIS to provide critically evaluated column densities for and , and their absorption-line frequencies, . The new O vi data were included, together with our fits to , to yield more accurate values of .

With the ten-fold increase in UV sensitivity throughput of Cosmic Origins Spectrograph on HST, we should be able to do even better. We hope to use HST/COS to obtain high-quality data (S/N ) 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 , these lines have equivalent widths of (12.5 mÅ) for O vi  and (54.5 mÅ) for Ly. 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 broad Ly absorbers (BLAs) and the Ne viii doublet (). 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), makes the Ne viii lines weak, and redshifts 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, , 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. 2005) 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 , O viii , 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 ( keV) with energy resolution sufficient to resolve O vii absorbers with mÅ equivalent width. For weak lines, the predicted O vii equivalent widths are .

Finally, the IGM simulations can be improved in several aspects, in order to use them as even more reliable predictors of IGM parameters. In this paper, we computed individual (cell-by-cell) values of metallicity and ionization fraction , together with their statistical variations and co-variance. Our simulations (Smith et al. 2011) were performed with somewhat larger box sizes ( Mpc) and on a larger grid, compared with previous studies of low- 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, , as a function of column density, . 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 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 and Evan Tilton for comments on the manuscript, and Mark Voit for discussions on hot gas in clusters and galaxy halos.

Appendix A: Ly Forest Baryon Content and Error Analysis

Here, we summarize the current status of the error budgets for the major contributors to uncertainty in the diffuse Ly forest baryon census. Many of the scalings enter the formula for as the square root, a weak dependence arising because recombination theory predicts that for highly ionized absorbers. Thus, the total baryon mass (proportional to ) depends on a weight factor (see equation [6]). From this formulation, we can conduct an error-propagation analysis, to arrive at the overall uncertainty on the Ly contribution to 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, . Based on 650 low-redshift Ly absorbers, they found a slope and a baryon content of % of , integrated over . Our new survey (Tilton et al. 2012) finds and a contribution of % from the Ly-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 . Extending the distribution from to 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, , depends on the radiation field normalization at 1 ryd () and spectral slope () between 1.0–1.5 ryd. Previous AGN composite spectra found indices ranging from (Telfer et al. 2001) to (Scott et al. 2004). New HST/COS composite spectra of AGN find an index (Shull et al. 2012b), close to the Telfer et al. (2001) value for radio-quiet AGN. Our calculations also take into account the rise in from to , a fit to the recent calculations of Haardt & Madau (2012). We estimate the joint error on as % 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, , at  cm in units of 100 kpc, is inferred by direct and indirect means, including comparing “hits and misses” of Ly absorbers along nearby sight lines and the cumulative distributions of absorbers with nearest-neighbor galaxies (Stocke et al. 1995; Shull et al. 1998). The frequency of Ly absorption lines per unit redshift also implies 200–300 kpc absorber cross sections, when associated with the space density of galaxies down to luminosities (Shull et al. 1996; Stocke et al. 2006; Prochaska et al. 2011). We adopt an uncertainty of on .

  4. Electron temperature. Temperature () enters through the square root of the hydrogen recombination rate coefficient, . Models of IGM photoelectric heating (Donahue & Shull 1991) predict a range from 5000 K to 30,000 K. For , with small expected variations from photoionization, we adopt an uncertainty of %.

  5. Hubble constant. This parameter has been measured as km s Mpc (Freedman et al. 2001) and km s Mpc (Riess et al. 2011), using distance scales based on Cepheids in galaxies with Type Ia supernovae. To be conservative, we adopt an error of %.

From standard error-propagation formulae, we write the relative error on 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):

(10)

This formula gives a relative error , so that we can express . Most (77%) of the error budget comes from uncertainties in the ionizing radiation field () and characteristic absorber size ().

Appendix B: Current Baryon Census

The following paragraphs summarize our current knowledge of the baryon-content in various components and thermal phases of the IGM.

  • Photoionized Ly Absorbers. For this paper, we adopt % based on the results of Danforth & Shull (2008), our new survey (Tilton et al. 2012), and the systematic uncertainties discussed in Section 3.2. The mid-range distribution in column densities, , is fairly well characterized, but the numbers of high-column absorbers are small. Their contribution to remains uncertain owing to corrections for their size and neutral fraction. At the low end of the column-density distribution, there could be modest contributions to the baryon content from weaker Ly absorbers. In current surveys, their numbers are increasingly uncertain at (our integration was down to 12.5). For a power-law distribution with , extending the distribution from down to 12.0 would increase the baryon fraction by another 10% (from 28% to 31%). For this paper (Figure 9), we adopt % based on the results of Danforth & Shull (2008), Tilton et al. (2012), and the systematic uncertainties discussed in Section 3.2.

  • WHIM (O vi-traced). Previous FUSE surveys of intergalactic O vi absorbers (Danforth & Shull 2005; Tripp et al. 2006) found lower limits of 5% and 7%, respectively for the contribution of this gas to the baryon inventory. These surveys assumed metallicity and ionization fraction . In 2008, three O vi surveys with HST/STIS (Danforth & Shull 2008; Tripp et al. 2008; Thom & Chen 2008) probed to lower O vi column densities. Based on the survey of 83 O vi absorbers (Danforth & Shull 2008) and our more recent analysis of 111 O vi absorbers (Tilton et al. 2012), we adopt a baryon fraction %. The factor-of-two increase arises primarily from our revised corrections, , for metallicity and O vi ionization fraction (see Section 3.1). There may be some, as yet undetermined, overlap of photoionized O vi with the Ly forest.

  • WHIM (BLA-traced). Broad Ly absorbers (BLAs) were proposed (Richter et al. 2004, 2006; Lehner et al. 2006, 2007) as repositories of a substantial fraction of the low-redshift baryons. BLAs are defined as Ly absorbers with Doppler parameters  km s, corresponding to temperatures for pure thermal broadening with  km s). Owing to the large abundance of hydrogen, a small neutral fraction (H i) remains detectable in Ly up to  K, although high-S/N is required to measure the broad, shallow absorption. As a result, the surveys of BLAs differ considerably. In their survey of seven AGN sight lines, Lehner et al. (2007) found a BLA frequency of for absorbers with 40 km s  km s and . They claimed that 20% of the baryons reside in BLAs. A more recent survey (Danforth et al. 2010) came to different conclusions. Surveying BLA candidates along seven AGN sight lines observed by HST/STIS, their BLA absorption-line frequency per unit redshift was , comparable to that of the O vi absorbers but 40% lower than that found by Lehnert et al. (2007). After correction for possible (20–40%) overlap between BLA and O vi (metal-bearing) absorbers, the corresponding baryon fraction is . For Figure 9, we adopt a value of %, with an increased error reflecting the uncertain detection statistics. We apply their metallicity-based correction to obtain a blended total (approximately 1/4 overlap) of % for the O vi/BLA-traced WHIM over the temperature range .

  • WHIM (X-ray absorber-traced). Our simulations (Figure 2) and those of Cen (2012) suggest that % of the baryons could be contained in hotter WHIM, at  K. Some of this gas could be detectable in X-ray absorption lines of trace metals (O vii, O viii, Ne ix, NeX, etc.). However, most of these weak absorption lines are below the detection limits of current X-ray spectrographs (Yao et al. 2012). The suggested absorption systems are too few in number to provide good statistics, and many are unconfirmed.

  • Galaxies. Salucci & Persic (1999) found that galaxies contribute 7% of the baryons. More recent discussion by Fukugita & Peebles (2004) estimated 6%. In Figure 9, we assume that galaxies contribute % of the baryons.

  • Groups and Clusters. The integrated cluster mass function of Bahcall & Cen (1993) was used by Fukugita et al. (1998) to find that the baryon contribution of clusters of galaxies consists of and . Adjusting for , we find a cluster contribution of or 6.8% of the baryons. Fukugita & Peebles (2004) revised the hot-baryon contribution to or 4% of the baryons, owing to a redefinition of cluster mass (Reiprich & Böhringer 2002). For the total contribution of galaxy clusters, including their hot gas, we adopt a fraction % of the baryons.

  • Cold H I (and He I) Gas. Zwaan et al. (2003) and Rosenberg & Schneider (2003) conducted blind H i surveys in the 21-cm line that probe the mass density in neutral atomic gas. The HIPASS survey (Zwaan et al. 2003) found . Following the discussion of Fukugita & Peebles (2004), which augments the H i measurements by the expected accompanying cold He i and H, we plot the total cold gas mass in Figure 9 as % of the baryons.

  • Circumgalactic Medium (CGM). X-ray spectra of AGN taken with both Chandra and XMM/Newton detected strong O vii absorbers at (see Bregman 2007; McKernan et al. 2005; Wang et al. 2005; Fang et al. 2006). The typical detected column densities, cm, correspond to ionized hydrogen column densities cm assuming a length-scale  kpc and mean metallicity of 20% solar. Several arguments suggest that the Galactic O vii resides in a thick disk or low scale-length halo (5–10 kpc; see Yao & Wang 2005). Such a reservoir holds which is % of the in Milky Way baryons. Bregman (2007) suggested that a hot gaseous medium with mass might extend throughout the Local Group. Such a reservoir is also 2% of the baryonic mass of the Local Group, assuming total mass and 12% baryon fraction (McGaugh et al. 2010). However, the Milky Way halo and Local Group may not be typical of other star-forming galaxies. Recent COS studies of 42 galaxies (Tumlinson et al. 2011) found that large (150 kpc) oxygen-rich halos of star-forming galaxies are major reservoirs of galactic metals. Additional CGM could extend to distances of 100-200 kpc from galaxies with higher specific star formation rates (Stocke et al. 2006). Savage et al. (2010) detected hot circumgalactic gas () in H i-free O vi absorption associated with a pair (perhaps small group) of galaxies at , at impact parameters  kpc. They note that the absence of H i absorption with broad O vi suggests a “rare but important class of low- intergalactic medium absorbers”.

    Prochaska et al. (2011) took this idea further, suggesting that all the O vi arises in the “extended CGM of sub- galaxies”. Their mass estimate associates the O vi absorption with H i around galaxies () having constant hydrogen column densities,  cm, over the full 200–300 kpc extent, as gauged by AGN-galaxy impact parameters. They estimated that these extended halos could contain a mass , which would represent % of the baryon masses of present-day sub- galaxies. They further assert that gas at these large distances is gravitationally bound and virialized. We question the realism of constant-, virialized gas at such large distances from dwarf galaxies. Previous nearest-neighbor studies low- O vi absorbers and galaxies (Stocke et al. 2006; Wakker & Savage 2009) found correlations with galaxies (at 800 kpc) and with dwarf () galaxies (at 200 kpc). For Figure 9, we adopt a CGM contribution of %, recognizing that the CGM reservoir is still poorly understood.

Footnotes

  1. affiliation: now at Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824
  2. http://yt.enzotools.org/

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