Coincidences between OVI and OVII Lines: Insights from High Resolution Simulations of the Warm-Hot Intergalactic Medium
CCoincidences between OVI and OVII Lines: Insights from HighResolution Simulations of the Warm-Hot Intergalactic Medium
Renyue Cen ABSTRACT
With high resolution (0 . h − kpc), large-scale, adaptive mesh-refinement Eu-lerian cosmological hydrodynamic simulations we compute properties of O VI andO VII absorbers from the warm-hot intergalactic medium (WHIM) at z = 0. Ournew simulations are in broad agreement with previous simulations with ∼
40% ofthe intergalactic medium being in the WHIM. Our simulations are in agreementwith observed properties of O VI absorbers with respect to the line incidence rateand Doppler width-column density relation. It is found that the amount of gasin the WHIM below and above 10 K is roughly equal. Strong O VI absorbers arefound to be predominantly collisionally ionized. It is found that (61% , , = (12 . − , − , >
14) have
T < K.Cross correlations between galaxies and strong [N(OVI) > cm − ] O VI ab-sorbers on ∼ − σ upper limit on the mean column density of coincidental O VII lines atthe location of detected O VI lines by Yao et al. is above our predicted value by afactor of 2 . −
4. The claimed observational detection of O VII lines by Nicastroet al, if true, is 2 σ above what our simulations predict. Subject headings:
Methods: numerical, absorption lines, Galaxies: evolution,missing baryons, intergalactic medium
1. Introduction
Physical understanding of the thermodynamic evolution of the intergalactic medium(IGM) has been substantially improved with the aid of ab initio cosmological hydrodynamicsimulations. One of the most robust predictions is that 40 −
50% of all baryons in the presentuniverse is in the WHIM of temperature 10 − K and overdensity 10 −
300 (e.g., Cen & Princeton University Observatory, Princeton, NJ 08544; [email protected] a r X i v : . [ a s t r o - ph . C O ] M a y > ≥ − K) and densities. It is likely, at least forlarge galaxies, that a significant fraction of the CGM falls into the same temperature rangeof the WHIM. Of particular interest is some of the CGM that has been heated up by starformation feedback shocks to the WHIM temperature range (e.g., Cen & Ostriker 2006; Cen& Chisari 2011). In the present analysis we define WHIM as gas of temperature 10 − Kwith no density limits. Most of the WHIM gas is truly intergalactic with overdensity < T ≤ K) portion, has nowbeen fairly convincingly confirmed by a number of observations in the FUV portion of QSOspectra from HST and FUSE, through the O VI λλ T ∼ × K when collisionally ionized (e.g., Tripp et al. 2000; Tripp & Savage 2000; Oegerleet al. 2000; Savage et al. 2002; Prochaska et al. 2004; Sembach et al. 2004; Danforth & Shull2005; Danforth et al. 2006; Danforth & Shull 2008; Tripp et al. 2008; Thom & Chen 2008a,b;Cooksey et al. 2008) and Ne VIII λλ T ∼ × K incollisional ionization equilibrium (Savage et al. 2005, 2006; Narayanan et al. 2009, 2011; Trippet al. 2011) as well as broad Ly α absorption lines (BLAs) (Danforth et al. 2010; Savage et al.2011a,b). In agreement with simulations, the part of WHIM detected in O VI absorption isestimated to constitute about 20-30% of total WHIM. The detection of Ne VIII lines alongat least some of the sight lines with O VI detection provides unambiguous evidence for theWHIM origin, instead of lower temperature, photoionized gas, under physically plausibleand observationally constrained situations.X-ray observations performed to search for X-ray absorption of the higher temperatureportion ( T ≥ K) of the WHIM associated with known massive clusters have also beensuccessful. An XMM-Newton RGS spectrum of quasar LBQS 1228+1116 revealed a featureat the Virgo redshifted position of O VIII Ly α at the 95% confidence level (Fujimoto et al.2004). Using XMM-Newton RGS observations of an AGN behind the Coma Cluster, theSeyfert 1 X Comae, Takei et al. (2007) claimed to have detected WHIM associated with theComa cluster. Through the Sculptor Wall Buote et al. (2009) and Fang et al. (2010) havedetected WHIM O VII absorption at a column greater than 10 cm − . There is evidence ofdetection in soft X-ray emission along the filament connecting clusters A222 and A223 at z = 0 .
21 that may be associated with the dense and hot portion of the WHIM (Werner et al. 3 –2008).However, the search for X-ray absorption of WHIM along random lines of sight turnsout to be elusive. Early pioneering observations (Fang et al. 2001, 2002, S5 0836+710,PKS 2149-306, PKS 2155-304) gave the first O VII detection (O VIII for PKS 2155-304),which has not been convincingly confirmed subsequently (Cagnoni et al. 2004; Williamset al. 2007; Fang et al. 2007). Mathur et al. (2003) performed a dedicated deep observation(470 ks) with the Chandra LETGS of the quasar H 1821+643, which has several confirmedintervening O V I absorbers, but found no significant ( >> σ ) X-ray absorption lines atthe redshifts of the O V I systems. Nicastro et al. (2005a,b) embarked on a campaign toobserve Mrk 421 during its periodic X-ray outbursts with the Chandra LETGS with a totalof more than 7 million continuum counts and presented evidence for the detection of twointervening absorption systems at z = 0 .
011 and z = 0 . z = 0 .
011 and z = 0 .
027 yields intriguing evidence of two large-scale filaments at the respective redshifts,one of which has only 5 −
10% probability of occurring by chance (Williams et al. 2010).Observations of 1ES 1028+511 at z = 0 .
361 by Steenbrugge et al. (2006) yield no convincingevidence for X-ray WHIM absorption.What is perceived to be more disconcerting is the lack of detection of O VII absorbers atthe redshifts of detected O VI absorbers along some random lines of sight. This is because,overall, the O VII line is predicted to be the most abundant and anecdotal evidence suggestssubstantial coincidence between O VI and O VII (e.g., Cen & Fang 2006). A statisticallysignificant upper limit placed on the mean column density of O VII absorbers at the locationsof a sizeable set of detected O VI absorbers using stacking techniques by Yao et al. (2009)prompts them to call into question the very existence of the high temperature ( T ≥ K)portion of the WHIM, although the limited sensitivity and spectral resolution of the currentX-ray observations may render any such conclusions less than definite.Therefore, at this juncture, it is pressing to statistically address this lack of significantcoincidence between O VI and O VII absorbers and other issues theoretically, through higherresolution simulations that are necessary in order to well resolve the interfaces of multi-phasemedia. This is the primary purpose of this paper. We use two simulations of high resolution 4 –of 0 . h − kpc and box size of 20 − h − Mpc to perform much more detailed characterizationof O VI and O VII lines to properly compare to extant observations. This high resolution isto be compared with 83 h − kpc resolution in our previous simulations (Cen & Ostriker 2006;Cen & Fang 2006), 25 − h − kpc resolution in Smith et al. (2011) and Shull et al. (2011),1 . − . h − kpc in Oppenheimer et al. (2012) and 1 . − . h − kpc in Tepper-Garc´ıa et al.(2011), resolves the Jeans scale of WHIM by 2-3 orders of magnitude and interfaces betweengas phases of different temperatures in a multi-phase medium. It is useful to distinguish,in the case of SPH simulations, between the gravity force resolution and the resolutionof the hydrodynamics solver, with the latter being worse than the former by a factor oforder a few. It is also useful to keep in mind the initial cell size or interparticle separation,because in both SPH and adaptive mesh refinement (AMR) simulations not all regions areresolved by the maximum resolution. Calling this “mean region resolution” ∆ root , ∆ root =(117 , − , , h − kpc for [this paper, Smith et al. (2011), Oppenheimer et al. (2012),Tepper-Garc´ıa et al. (2011)]. We note that a region of overdensity δ is approximately resolvedat a resolution of C∆ root δ − / (up to a pre-specified highest resolution), where the pre-factor C is about unity for AMR simulations and ∼ δ ≥ ∼ . − ∼
10 should test thisprediction definitively. The outline of this paper is as follows. In § § § §
3. In § § § §
4. 5 –
2. Simulations2.1. Hydrocode and Simulation Parameters
We perform cosmological simulations with the AMR Eulerian hydro code, Enzo (Bryan1999; Bryan & Norman 1999; O’Shea et al. 2005; Joung et al. 2009). First we ran a lowresolution simulation with a periodic box of 120 h − Mpc on a side. We identified two regionsseparately, one centered on a cluster of mass of ∼ × M (cid:12) and the other centered ona void region at z = 0. We then resimulate each of the two regions separately with highresolution, but embedded in the outer 120 h − Mpc box to properly take into account large-scale tidal field and appropriate boundary conditions at the surface of the refined region. Wename the simulation centered on the cluster “C” run and the one centered on the void “V”run. The refined region for “C” run has a size of 21 × × h − Mpc and that for “V” run is31 × × h − Mpc . At their respective volumes, they represent 1 . σ and − . σ fluctuations. The root grid has a size of with dark matter particles. The initial staticgrids in the two refined boxes correspond to a grid on the outer box. Theinitial number of dark matter particles in the two refined boxes correspond to particles on the outer box. This translates to initial condition in the refinedregion having a mean interparticle-separation of h − kpc comoving and darkmatter particle mass of . × h − M (cid:12) . The refined region is surrounded by twolayers (each of ∼ h − Mpc) of buffer zones with particle masses successively larger by afactor of 8 for each layer, which then connects with the outer root grid that has a darkmatter particle mass 8 times that in the refined region. The initial density fluctuations areincluded up to the Nyquist frequency in the refined region. The surrounding volume outsidethe refined region is aso followed hydrodynamically, which is important in order to properlycapture matter and energy exchanges at the boundaries of the refined region. Because westill can not run a very large volume simulation with adequate resolution and physics, wechoose these two runs of moderate volumes to represent two opposite environments thatpossibly bracket the average.We choose the mesh refinement criterion such that the resolution is always better than460 h − pc physical, corresponding to a maximum mesh refinement level of 11 at z = 0. Thesimulations include a metagalactic UV background (Haardt & Madau 2012), and a modelfor shielding of UV radiation by neutral hydrogen (Cen et al. 2005). The simulations alsoinclude metallicity-dependent radiative cooling and heating (Cen et al. 1995). We clarifythat our group has included metal cooling and metal heating (due to photoionization ofmetals) in all our studies since Cen et al. (1995), contrary to some claims (e.g., Wiersmaet al. 2009; Tepper-Garc´ıa et al. 2011). Star particles are created in cells that satisfy a set ofcriteria for star formation proposed by Cen & Ostriker (1992). Each star particle is taggedwith its initial mass, creation time, and metallicity; star particles typically have masses of ∼ M (cid:12) . 6 –Supernova feedback from star formation is modeled following Cen et al. (2005). Feedbackenergy and ejected metal-enriched mass are distributed into 27 local gas cells centered atthe star particle in question, weighted by the specific volume of each cell (i.e., weightingis equal to the inverse of density), which is to mimic the physical process of supernovablastwave propagation that tends to channel energy, momentum and mass into the leastdense regions (with the least resistance and cooling). We allow the whole feedback processesto be hydrodynamically coupled to surroundings and subject to relevant physical processes,such as cooling and heating, as in nature. The extremely inhomogeneous metal enrichmentprocess demands that both metals and energy (and momentum) are correctly modeled sothat they are transported into right directions in a physically sound (albeit still approximateat the current resolution) way, at least in a statistical sense.The primary advantages of this supernova energy based feedback mechanism are three-fold. First, nature does drive winds in this way and energy input is realistic. Second,it has only one free parameter e SN , namely, the fraction of the rest mass energy of starsformed that is deposited as thermal energy on the cell scale at the location of supernovae.Third, the processes are treated physically, obeying their respective conservation laws (wherethey apply), allowing transport of metals, mass, energy and momentum to be treated self-consistently and taking into account relevant heating/cooling processes at all times. We use e SN = 1 × − in these simulations. The total amount of explosion kinetic energy from TypeII supernovae with a Chabrier IMF translates to e SN = 6 . × − . Observations of localstarburst galaxies indicate that nearly all of the star formation produced kinetic energy (dueto Type II supernovae) is used to power galactic superwinds (e.g., Heckman 2001). Giventhe uncertainties on the evolution of IMF with redshift (i.e., possibly more top heavy athigher redshift) and the fact that newly discovered prompt Type I supernovae contribute acomparable amount of energy compared to Type II supernovae, it seems that our adoptedvalue for e SN is consistent with observations and within physical plausibility. Test of thesuccess of this feedback approach comes empirically. As we show in Cen (2012), the metaldistribution in and around galaxies over a wide range of redshift is in good agreement withrespect to the properties of observed damped Ly α systems; this is a non-trivial success andprovides strong validation of the simulations. We will provide additional validation of thesimulations in § h − Mpc) .Top-right and bottom-right panels show the gas density and density-weighted temperatureprojection of a portion of the refinement box of the V run of size (30 h − Mpc) .that are motivated by some subgrid turbulence model as a remedy parameterized to roughlymatch results from hydrodynamic simulations (e.g., Shen et al. 2010), most SPH simulationsof WHIM obtain gas metallicities based on kernel-smoothed metal masses of feedback SPHparticles that are assigned at birth and un-evolved (e.g., Tepper-Garc´ıa et al. 2011; Oppen-heimer & Dav´e 2009; Oppenheimer et al. 2012). In the simulations of Oppenheimer et al.(2012) “feedback” SPH particles with initially given metal masses are launched (in randomdirections) to be transported ballistically to sufficiently large distance ( ∼ ∼ − M = 0 .
28, Ω b = 0 . Λ = 0 . σ = 0 . H = 100 h kms − Mpc − = 70km s − Mpc − and n = 0 . The photoionization code CLOUDY (Ferland et al. 1998) is used post-simulation tocompute the abundance of O VI and O VII, adopting the shape of the UV backgroundcalculated by Haardt & Madau (2012) normalized by the intensity at 1 Ryd determined byShull et al. (1999) and assuming ionization equilibrium.We generate synthetic absorption spectra using a code similar to that used in our earlierpapers (e.g., Cen et al. 1994, 2001; Cen & Fang 2006), given the density, temperature, metal-licity and velocity fields from simulations. Each absorption line is identified by the intervalbetween one downward and the next upward crossing in the synthetic flux spectrum withoutnoise at a flux equal to 0 .
99 (flux equal to unity corresponds to an unabsorbed continuum).Since the absorption lines in question are sparsely distributed in velocity space, their iden-tifications have no significant ambiguity. Column density, equivalent width, Doppler width,mean column density weighted velocity and physical space locations, mean column densityweighted temperature, density and metallicity are computed for each line. We sample theC and V run, respectively, with 72 ,
000 and 168 ,
000 random lines of sight at z = 0, witha total pathlength of ∆ z ∼
200 400 60000.20.40.60.81 v (km/s) f l u x
200 400 600 − l og o v e r den s i t y
200 400 600 − − − − v p ( k m / s )
200 400 60034567 v (km/s) l og T ( K ) − − −
10 v (km/s) [ Z / H ]
200 400 60000.20.40.60.81 v (km/s) f l u x
200 400 600 − v (km/s) l og o v e r den s i t y
200 400 600 − − − v (km/s) v p ( k m / s )
200 400 60034567 v (km/s) l og T ( K ) − − − v (km/s) [ Z / H ] Fig. 2.— shows flux spectra of two separate O VI lines and physical conditions. The left andright cases have column densities of log N(OVI)cm = 14 .
48 and 14 .
30, respectively. The fivepanels from top to bottom are: flux, gas overdensity, proper peculiar velocity, temperatureand metallicity in solar units. While the x-axis for the top panel is the Hubble velocity,the x-axis for the bottom four panels is physical distance that is multiplied by the Hubbleconstant.the absorber properties, because bulk velocities are very important (see Figure 6 below) andvelocity substructures within an absorber do not necessarily correspond to separate physicalentities.A small number of simulated spectra may not serve to illustrate the extreme rich andcomplex physics involved. It may even be misleading in the sense that any statistical conclu-sions drawn based on anecdotal evidence could be substantially wrong. Thus, we will presenttwo absorption spectrum segments merely only for the purpose of illustration. Figure 2 showstwo O VI lines and their associated physical environment.
The C and V runs at z = 0 are used to obtain an “average” of the universe. Thiscannot be done precisely without much larger simulation volumes, which is presently notfeasible. Nevertheless, it is still possible to obtain an approximate average. Since the WHIMis mostly closely associated with groups and clusters of galaxies, we will use X-ray clusters 10 – CD F ( > T ) All IGM at z=0Only WHIM with log T=5 − Fig. 3.— shows the cumulative probability distribution function (CDF) of the IGM at z = 0as a function of gas temperature (black dashed curve) and that of the WHIM only in thetemperature range T = 10 − K (red solid curve); stars are not included.as an appropriate “normalization” anchor point. We normalize averaging weightings of theC and V runs by requiring that the fraction of hot gas with temperature T ≥ K isconsistent with the observed value of ∼
15% of baryons at z = 0 (Bahcall 2011). Note thatsmall variations on the adopted X-ray gas fraction do not cause large changes in most of theresults. For comparative measures such as the coincidence rates between O VI and O VIIabsorbers, the dependence on the normalization procedure is still weaker. The results areshown in Figure 3, which shows the temperature distribution of entire IGM and WHIM at z = 0. In agreement with previous simulations (e.g., Cen & Ostriker 1999; Dav´e et al. 2001;Cen & Ostriker 2006), we find that ∼
40% of the IGM at z = 0 is in WHIM. This is comparedto 35-40% in Smith et al. (2011), 24% in Dav´e et al. (2010) (limited to overdensities outsidehalos), 40% in Shen et al. (2010) and 40% and 50% in Tornatore et al. (2010) in their windand black hole feedback models, respectievely. In simulations of Cen et al. (1995); Cen &Ostriker (1999); Cen et al. (2001); Cen & Ostriker (2006); Cen & Chisari (2011), Wiersmaet al. (2009); Tepper-Garc´ıa et al. (2011), Shen et al. (2010) and Shull et al. (2011), inadditional to radiative processes of a primordial gas, both metal cooling (due to collisionalexcitation and recombination) and metal heating (due to photo-ionization heating of metalspecies) in the presence of UV-X-ray background are included, whereas in Oppenheimer& Dav´e (2009), Oppenheimer et al. (2012) and Tornatore et al. (2010) only metal coolingis included. Tepper-Garc´ıa et al. (2011) suggest that the relatively overall low fraction of 11 –WHIM in the latter (25%) versus higher fraction in the former (35-50%) may be accounted bythe difference in the treatment of metal heating; we concur with their explanation for at leastpart of the difference. All these simulations have a box size of ∼ h − Mpc, which still suffersfrom significant cosmic variance: Dav´e et al. (2001) show that WHIM fraction increases from37% to 42% from a box size of 50 h − Mpc to 100 h − Mpc in two Eulerian simulations. Theamplitude of power spectrum has a similar effect and may be able to, at least in part, accountfor some of the differences among the simulations; σ = (0 . , . , . , . , . , .
82) in[this work, Shull et al. (2011), Tepper-Garc´ıa et al. (2011), Shen et al. (2010), Tornatore et al.(2010), Oppenheimer et al. (2012)]. Gravitational collapse of longer waves powers heating ofthe IGM at later times. We suggest that the peak of WHIM fraction at z ∼ . h − Mpc simulation boxes in Smith et al. (2011) is because of the small box size; in otherwords, available, reduced gravitational heat input in the absence of breaking density wavesof lengths longer than 25 h − Mpc at z ≤ . − Mpc at low redshift ( z ≤ . T = 10 − Kand T = 10 − K.
3. Results3.1. Simulation Validation with Properties of O VI Absorbers
The present simulations have been shown to produce the metal distribution in andaround galaxies over a wide range of redshift ( z = 0 −
4) that is in good agreement withrespect to the properties of observed damped Ly α systems (Cen 2012). Here we provide addi-tional, more pertinent validation with respect to O VI absorbers in the IGM at z = 0. The toppanel of Figure 4 shows a scatter plot of simulated O VI absorbers (red pluses) in the Dopplerwidth ( b )-O VI column density [N(OVI)] plane, compared to observations. The agreement isexcellent in that the observed O VI absorbers occupy a region that overlaps with the simu-lated one. It is intriguing to note that the simulations predict a large number of large b , lowN(OVI) (i.e., broad and shallow) absorbers in the region b > / cm − ) . km/s,corresponding to the upper left corner to the green dashed line, where there is no observedO VI absorber. This green dashed line, however, has no physical meaning to the best of ourknowledge. The blue solid line of unity logarithmic slope has a clear physical origin, whichis a requirement for the decrement at the flux trough of the weaker of the O VI doublet tobe 4%: b = 25(N(OVI) / cm − ) km / s. Current observational data are heterogeneous withvarying qualities. Thus, the blue solid line is a much simplified characterization of the com-plex situation. Nevertheless, one could understand the desert of observed O VI absorbersin the upper left corner to the blue solid line, thanks to the difficulty of identifying broad 12 –and shallow lines in existing observations. We attribute the “missing” observed O VI linesin the upper right corner between the blue solid line and the green dashed line, in part, tothe observational procedure of Voigt profile fitting that may break up some large b lines intoseparate, narrower components, whereas no such procedure is performed in the presentedsimulation results.Ongoing and upcoming observations by the Cosmic Origins Spectrograph (COS) (e.g.,Froning & Green 2009; Shull 2009; Green et al. 2012) will be able to substantially improvein sensitivity and thus likely be able to detect a sizeable number of O VI lines in the upperleft corner to the blue solid line. Quantitative distribution functions of b parameter will beshown in Figure 10 later, for which COS may provide a strong test. The bottom panel ofFigure 4 shows a scatter plot of simulated O VII absorbers (red pluses); because there isno data to compare to, we only note that the positive correlation between b and N(OVI) isstronger for O VII lines than for O VI lines, in part due to less important contribution tothe O VII lines from photoionization and in part due to positive correlation between densityand velocity dispersion.Figure 5 shows O VI line density as a function of column density. The agreementbetween simulations and observations of Danforth & Shull (2008) is excellent over the entirecolumn density, N(OVI) ∼ − cm − , where comparison can be made. The simulationresults are up to a factor of ∼ ∼ . − . cm − . Some of the disagrement isdue to different treatments in defining lines in that we do not perform Voigt profile fittingthus deblending of non-gaussian profiles into multiple components, where the observationalgroups do and different groups often impose different, subjective criteria of choosing the“goodness” of the fit. The down turn of line density towards lower column densities fromN(OVI) ∼ . cm − from Tripp et al. (2008) as well as the lower values in the columndensity range N(OVI) ∼ . − . cm − of Danforth & Shull (2008) may be related tothe “missing” broad and shallow lines, as indicated in the top panel of Figure 4. It is notedthat the observed line density at N(OVI) ∼ cm − of the Danforth & Shull (2008) datadisplays an upturn and lies on top of the simulated curve. Closer examination reveals thatthis is due to the presence of two relatively broad absorbers at N(OVI) ∼ cm − and b ∼
30 km / s. We expect that the upcoming COS observations will substantially raise theline density at N(OVI) ≤ . cm − . 13 –
12 13 14 150.511.52 log N(OVI) (cm − ) l og b ( k m / s ) simulationobs: Danforth et al 2008obs: Tripp et al 2008
13 14 15 160.511.52 log N(OVII) (cm − ) l og b ( k m / s ) Fig. 4.— Top panel shows a scatter plot of simulated O VI absorbers (red pluses) in the b -N(OVI) plane. Also shown as black dots and blue triangles are the observations fromDanforth & Shull (2008) and Tripp et al. (2008), respectively. The green dashed line ofslope 4 /
10 is only intended to guide the eye to suggest that there appears to be a desert ofobserved O VI absorbers in the upper left corner. The blue solid line of unity logarithmicslope is a requirement for the decrement at the flux trough of the weaker of the O VI doubletto be 4%: b = 25(N(OVI) / cm − ) km / s. Bottom panel shows the same for the O VIIabsorbers. 14 – − N(OVI) (cm − ) dn / d z / pe r un i t l og N ( O V I ) totalT>10 KT<10 Kobs: Danforth & Shull 2008obs: Tripp et al. 2008
Fig. 5.— shows the O VI line density as a function of column density, defined to bethe number of lines per unit redshift per unit logarithmic interval of the column density.The red solid dots, green squares and blue triangles are the total, collisionally ionized andphotoionized absorbers, respectively. Also shown as black open circles and stars are theobservations from Danforth & Shull (2008) and Tripp et al. (2008), respectively.These results show that our simulation results are realistic with respect to the abundanceof O VI lines in the CGM and IGM. This is a substantial validation of the simulations, whenconsidered in conjunction with the success of the simulations with respect to the damped Ly α systems (Cen 2012). The damped Ly α systems primarily originate in gas within the virialradii of galaxies, whereas the O VI absorbers examined here extend well into the IGM, somereaching as far as the mean density of the universe (see Figure 7 below). In combination,they require the simulations to have substantially correctly modeled the propagation of initialmetal-enriched blastwaves from sub-kpc scales to hundreds of kiloparsecs as well as othercomplex thermodynamics, at least in a statistical sense. Since O VII absorbers arise inregions in-between, this gives us confidence that O VII lines are also modeled correctly andthe comparisons that we will make between O VI and O VII lines are meaningful. 15 – b ( k m / s ) EW(1032)>100mAEW(1032)=30 − b ( k m / s ) EW(OVII)>2mAEW(OVII)=0.5 − Fig. 6.— shows absorbers in the b − T plane for O VI line (top panel) and O VII line (bottompanel). Within each panel, we have broken up the absorbers into strong ones (blue squares)and weak ones (red circles). Only thermally broadened lines should follow the indicated solidgreen curve (Eq. 1). Also shown as right-pointing triangles are observed data of Tripp et al.(2008) based on a joint analysis of Ly α and O VI lines; the location of each triangle is thebest estimate of the temperature and the rightmost tip of the attached line to each trianglerepresents a 3 σ upper limit. 16 – (cid:98) l og T ( K ) log N(O VI)>14log N(O VI)=13 − (cid:98) l og T ( K ) log N(O VII)>15log N(O VII)=14 − Fig. 7.— shows absorbers in the temperature-density plane for O VI line (top panel) andO VII line (bottom panel). Within each panel, we have broken up the absorbers into strongones (blue squares) and weak ones (red circles). 17 –
In this subsection we will present physical properties of both O VI and O VII absorbersand relationships between them. For most of the figures below we will show results in pairs,one for O VI and the other for O VII, to facilitate comparisons.Figure 6 shows absorbers in the b − T plane for O VI (top panel) and O VII absorbers(bottom panel). For thermal broadening only absorbers the b − T relation would follow thesolid green curve obeying this formula:b(O) = 10 . / K) / km / s . (1)It is abundantly clear from Figure 6 that b is a poor indicator of absorber gas temperature.Bulk velocity structures within each absorbing line are important. For O VI lines of equiv-alent width greater than 100mA, it appears that bulk velocity structures are dominant overthermal broadening at all temperatures. No line is seen to lie below the green curve, as ex-pected. All of the observationally derived temperature limits shown, based on a joint analysisof line profiles of well-matched coincidental Ly α and O VI lines by Tripp et al. (2008), areseen to be fully consistent with our simulation results. It is noted that velocity structuresin unvirialized regions typically do not have gaussian distributions (in 1-d). Caustic-likevelocity structures are frequently seen that are reminiscent of structure collapse along onedimension (e.g., Zeldovich pancake or filaments); for anecdotal evidence see Figure 2. Thus,we caution that temperatures derived on the grounds of gaussian velocity profile (e.g., Trippet al. 2008) may be uncertain. A more detailed analysis will be performed elsewhere. Thesituations with respect to O VII absorbers are similar to O VI absorbers.Figure 7 shows absorbers in the temperature-density plane for O VI (top panel) andO VII absorbers (bottom panel). In the top panel we see that strong O VI absorberswith N(OVI) ≥ cm − have a large concentration at ( δ , T)= (10 − , ∼ . K) thatcorresponds to collisional ionization dominated O VI population, consistent with Figure 5.For weaker absorbers with N(OVI)= 10 − cm − we see that those with temperature aboveand those below 10 K are roughly equal, consistent with Figure 5; the density distributionsfor the two subsets are rather different: for the lower-temperature (T < K) subset the gasdensity is concentrated around δ ∼
10 that is photoionization dominated, whereas for thehigher-temperature (T > K) subset the gas density is substantially spread out over δ ∼ − < cm − , not shown here, are mostly photoionization dominated, asindicated in Figure 5. In the bottom panel we see that strong O VII absorbers with N(OVI) ≥ cm − are predominantly collisionally ionized at T ∼ . − . K and δ ∼ − ∼ −
20 and temperaturesbelow 10 . K. For weaker absorbers with N(OVII)= 10 − cm − collisionally ionized ones attemperatures greater than 10 . K and those photoionized at lower temperatures are roughly 18 – CD F ( > T ) log N(OVI)=12.5 − − CD F ( > T ) log N(OVII)=13 − − Fig. 8.— shows the cumulative probability distribution functions as a function of absorbertemperature for three subsets of O VI line with column densities of log N(OVI)cm = (12 . − , − , >
14) (top panel) and O VII line of log N(OVI)cm = (13 − , − , > δ , T)=( ∼
10, 10 . K) and the other at ( δ , T)=( ∼ . K) (see their Figures 4,5).Figure 8 shows the cumulative probability distribution functions as a function of ab-sorber temperature for three subsets of O VI lines with column densities of log N(OVI)cm =(12 . − , − , >
14) (top panel) and O VII line of log N(OVI)cm = (13 − , − , > , , = (12 . − , − , >
14) have temperature greater than 10 K,(25% , , =(13 − , − , >
15) have temperature greater than 10 K. Our findings are in broadagreement with previous results obtained by our group (e.g., Cen et al. 2001; Cen & Os-triker 2006; Cen & Chisari 2011) and some other groups (e.g., Tepper-Garc´ıa et al. 2011;Shull et al. 2011), but in substantial disaccord with results of Oppenheimer & Dav´e (2009)and Oppenheimer et al. (2012) who find that photo-ionized O VI lines with temperaturelower than 10 K make up the vast majority of O VI lines across the column density rangelog N(OVI)cm = 12 . −
15. Given the differences in simulation codes and in treatment offeedback processes, we cannot completely ascertain the exact cause for the different results.Nevertheless, the explanation given by Oppenheimer et al. (2012) that the lack of metalmixing in their SPH simulations plays an important role in contributing to the difference isfurther elaborated here.Oppenheimer et al. (2012) find a large fraction of metal-carrying feedback SPH par-ticles wound up in low density regions that have relatively high metallicity ( ∼ (cid:12) ) andlow temperature (T ∼ K). As a result, they find low-density, high-metallicity and low-temperature photo-ionized O VI absorbers to dominate the overall O VI absorber populationin their SPH simulations. According to Tepper-Garc´ıa et al. (2011), they repeat simulationswith the same feedback model used in Oppenheimer & Dav´e (2009) and Oppenheimer et al.(2012) but with metal heating included, and are unable to reproduce the dominance of low-temperature photoionized O VI absorbers seen in the latter. This leads them to concludethat lack of metal heating, in the presence of high-metallicity feedback SPH particles, is thecause of the dominance of low-density, high-metallicity and low-temperature photo-ionizedO VI absorbers found in Oppenheimer & Dav´e (2009) and Oppenheimer et al. (2012). Wesuggest that this overcooling problem may have been exacerbated by lack of metal mix-ing. Consistent with this conjecture, while Tepper-Garc´ıa et al. (2011) suffer less severelyfrom the metal overcooling problem (because of metal heating), the median metallicity oftheir O VI absorbers is still ∼ . (cid:12) , substantially higher than that of our O VI absorbers, Z ∼ . − . (cid:12) , even though their overall abundance of O VI absorbers is lower thanobserved by a factor of ∼
2. This noticeable difference in metallicity may be rooted in lackof metal mixing in theirs. 20 –As we will show later (see Figure 13 below), the metallicity of simulated O VI in our simula-tions appears to better match observations. Despite that, it is desirable to directly probe thephysical nature of O VI absorbers to test models by different simulation groups. One ma-jor difference between SPH simulations (e.g., Tepper-Garc´ıa et al. 2011; Oppenheimer et al.2012) and AMR simulations (e.g., Smith et al. 2011, and this work) is that the former predictmetallicity distributions that are peaked at (0 . −
1) Z (cid:12) compared to peaks of ∼ (0 . − .
2) Z (cid:12) in the latter. In addition, in the latter positive correlations between metallicity and O VIcolumn density and between metallicity and temperature are expected, whereas in the formerthe opposite or little correlation seems to be true. Therefore, direct measurements of O VImetallicity and correlations between metallicity and other physical quantities would providea good discriminator. Putting differences between SPH simulations of WHIM by differentgroups aside, what is in common among them is the dominance of low-density ( δ ≤ δ ∼ ≥ cm − population. Given thesesignificant differences between SPH and AMR simulations, we suggest a new test, namely,the cross-correlation function between galaxies and strong [N(O VI) ≥ cm − ] O VI ab-sorbers. Available observations appear to point to strong correlations at relatively smallscales ≤ − ≥ . L ∗ ) and N(OV) ≥ . − . cm − O VI absorbers at z = 0 − . z > .
47 to shift into the HST (COS or STIS)observable band, for which current galaxy surveys will only be able to probe most luminousgalaxies (
L > L ∗ ). Detailed calculations and comparisons to observations will be needed toascertain these expectations to nail down their physical nature and to constrain feedbackmodels.The rapid rise in the cummulative fraction in the temperature range log T = 5 . ± . >
14 (green dashed curve), simplystating the fact that collisional ionization is dominant in high column density O VI lines. 21 –For O VII there is a similar feature except that it is substantially broader at log T = 6 . ± . = 12 . − . − .
4, a regimewhere neither collisional ionization nor photoionization is effective due to structured multi-phase medium (i.e., positive correlation between density and temperature in this regime, seeFigure 17 below); at still lower temperature log T < . b is not a good indicator of the temperature of absorbinggas. It is thus useful to quantify the fraction of absorbers at a given b whose temperature isin the WHIM regime. Figure 9 shows the fraction of O VI (top panel) and O VII (bottompanel) absorbers that is in WHIM temperature range of 10 − K as a function of b . Broadlyspeaking, above the threshold (thermally broadened Doppler width of 10 . K), the WHIM fraction is dominant at ≥
50% for both O VI and O VIIlines, but only close to 100% when b is well in excess of 100km/s. This again indicates theorigin of the O VI absorbing gas whose random motions are far from completely thermalized,consistent with its (mostly) intergalactic nature. The approximate fitting curve (blue curve)for the column density weighted hisotogram for O VI shown in Figure 9 can be formulatedas the following equation:f(OVI) = 0 .
20 for b <
10 km / s= 0 . b −
10) + 0 . b = 10 −
160 km / s= 1 for b >
160 km / s (2)As already indicated in Figure 4 that a substantial fraction of broad but shallow absorbersmay be missing in current observational data, here we quantify it further. Figure 10 showsfour cumulative probability distribution functions as a function of b for four subsets of O VI(top panel) and O VII (bottom panel) lines of differing column densities. To give somequantitative numbers, (15%, 20%, 26%, 39%) of O VI absorbers with log N(O VI) = (12 . − , − . , . − , >
14) have b >
40 km / s; the fractions drop to (1%, 2%, 4%, 7%) for b >
80 km / s. Similarly, (17%, 46%, 77%, 88%) of O VII absorbers with log N(O VI) = (13 − , − , − , >
16) have b >
40 km / s, with (2%, 9%, 29%, 30%) having b >
80 km / s.With COS observations of substantially higher sensitivities, broad O VI lines are begun tobe detected (Savage et al. 2010). A direct, statistical comparison between simulation 22 – f r a c t i on o f O V I li ne s i n W H I M K f r a c t i on o f O V II li ne s i n W H I M Fig. 9.— shows the fraction of O VI (top panel) and O VII (bottom panel) absorbersthat is in WHIM temperature range of 10 − K as a function of b . The red and greenhistograms are number and column density weighted, respectively, including only lines withcolumn density above 10 cm − in the case of O VI and 10 cm − for O VII. The verticalblack line indicates b for a purely thermally broadened line at a temperature of 10 K. Theapproximate fitting curve indicated by blue dashed line is given in Equation (2). 23 – CD F ( > b ) log N(OVI)=12.5 − − − CD F ( > b ) log N(OVII)=13 − − − Fig. 10.— Top panel shows four cumulative probability distribution functions as a functionof b for four subsets of O VI lines in the four column density ranges: log N(OVI)cm =12 . −
13 (black dotted curve), log N(OVI)cm = 13 − . =13 . −
14 (green dashed curve) and log N(OVI)cm >
14 (blue dot-dashed curve). Bottompanel shows four cumulative probability distribution functions as a function of b for foursubsets of O VII lines in the four column density ranges: log N(OVI)cm = 13 −
14 (blackdotted curve), log N(OVI)cm = 14 −
15 (red solid curve), log N(OVI)cm = 15 −
16 (greendashed curve) and log N(OVI)cm >
16 (blue dot-dashed curve). 24 –results found here and observations will be possible in the near future. It will be extremelyinteresting to see if there is indeed a large population of broad but shallow O VI lines stillmissing. That is also important, because, if that is verified, one will have more confidence onthe results for O VII lines, which suggest that the O VII lines may be substantially broaderthan a typical thermally broadened width of 40 −
50 km / s. Additional useful informationis properties of other lines, including Ly α , which we will present in a subsequent paper.Since the expected b of O VII lines is still substantially smaller than spectral resolutionof Chandra and XMM-Newton X-ray instruments, it does not make much difference forextant observations. However, it should be taken into consideration in designing futureX-ray telescopes to probe WHIM in absorption or emission (e.g., Yao et al. 2012).Figure 11 shows absorbers in the metallicity-overdensity plane. The apparent anti-correlation between metallicity and overdensity with a log slope of approximately − − b plane. Because of complex behaviors seen in Figure 11 and the additional roleplayed by complex temperature and velocity distributions, one may not be surprised to seethe large dispersions in metallicity at a given b . The metallicity distribution is seen to be, tozero-order within the large dispersions, nearly independent of b . When metallicity of O VIand O VII absorbers can be measured directly in the future, this prediction may be tested.No further detailed information on this shall be given here due to its still more futuristicnature in terms of observability, except noting that the weak trends can be understood andthese trends are dependent upon the column density cuts.Figure 13 shows the mean metallicity as a function of column density for O VI (redcircles) and O VII absorbers (blue squares). We see that a substantial dispersion of about 0.5-1 dex is present for all column density bins. The mean metallicity for O VI lines increases by0.9 dex from [Z / H] ∼ − . cm − to [Z / H] ∼ − . cm − .For O VII lines the mean metallicity increases by 0.4 dex from [Z / H] ∼ − . cm − to [Z / H] ∼ − . cm − . The trend of increasing metallicity with increasing columndensity is consistent with the overall trend that higher density regions, on average, havehigher metallicity, at least in the density range of interest here (see Figure 11 below). Itis noted that the mean metallicity for O VII absorbers is, on average, lower than that forO VI lines at a fixed column density for the respective ions. This and some other relativebehaviors between O VI and O VII seen in Figure 13 merely reflect the facts (1) that the 25 –product of oscillator strength and restframe wavelength of O VII line is about a factor of 10lower than that of O VI, (2) the peak collisional ionization fraction for O VII is about a factorof 5 higher than that of O VI, and (3) the peak width for collisional ionization temperaturefor O VII is larger by a factor of ∼ ∼ − . ∼ . OVI from 10 cm − to 10 cm − , which should becompared to an increase of metallicity from ∼ − . ∼ − .
5. Thus, our results are ingood agreement with Smith et al. (2011) except that their metallicity is uniformly higher bya factor of ∼ . − (cid:12) encompasses them. Given that, some quantitative physical considerations are useful here.The cooling time for gas of δ = 100, T = 10 . K and Z = 0 . (cid:12) at z = 0 is ∼ . t H ( t H is the Hubble time at z = 0) (this already takes into account metal heating by the X-raybackground; it should be noted that the X-ray background at z ∼ T ∼ . K and δ ≥ δ ≥ × ( Z/ . (cid:12) ) − is transient in natureand their appearance requires either constant heating of colder gas or higher temperature gascooling through. Which process is more responsible for O VI production will be investigatedin a future study. Second, the metal cooling that is linearly proportional to gas metallicitymay give rise to an interesting “selection effect”, where high metallicity O VI gas in denseregions, having shorter cooling time than lower metallicity O VI gas of the same density,would preferentially remove itself from being O VI productive by cooling, leaving behind onlylower metallicity gas at O VI-bearing temperatures. We suggest that this selection effectmay have contributed to a much reduced proportion of collisionally ionized O VI lines inSPH simulations that lack adequate metal mixing; in other words, dense metal “bullets” ofSPH particles either cools very quickly to ∼ K or they have reached regions of sufficientlylow density before that happens. The results of Oppenheimer et al. (2012) appear to suggest,in the context of this scenario, that the feedback metal-bearing SPH particles have cooledto ∼ K, before they can reach low density regions to avoid severe cooling, thus resultingin high-metallicity, low-density, photoionized O VI lines when they eventually wind up inlow density regions. An analogous situation occurs in Tepper-Garc´ıa et al. (2011) SPHsimulations but with two significant differences from those of Oppenheimer et al. (2012): (1)in the former the inclusion of metal heating (due to photoionization of metal species) keepsthe corresponding SPH particles at a higher temperature floor ( ∼ . − K barring adiabaticcooling) than in the latter, and (2) “smoothed” metallicity used in the former to compute 26 –metal cooling/heating rates has reduced the metal cooling effects (which still dominate overmetal heating at T ≥ K) compared to the case without such smoothing in the latter. − − − [ Z / H ] ( O V I ) N(OVI)=10 − cm − & T>10 KN(OVI)=10 − cm − & T<10 K − − − N(OVI)>10 cm − & T>10 KN(OVI)>10 cm − & T<10 K − − −
10 log (cid:98) [ Z / H ] ( O V II ) N(OVII)=10 − cm − & T>10 KN(OVII)=10 − cm − & T<10 K − − −
10 log (cid:98)
N(OVII)>10 cm − & T>10 KN(OVII)>10 cm − & T<10 K Fig. 11.— shows absorbers in the metallicity-overdensity plane for O VI line with N(OVI) =10 − cm − (top left panel) and N(OVI) > cm − (top right panel. The bottom twopanels show O OVII line with N(OVII) = 10 − cm − (bottom left panel) and N(OVII) > cm − (bottom right panel). Within each panel, we have broken up the absorbers intotwo subsets using temperature: T > K (red circles) and
T < K (blue squares). In § § − − − < [ Z / H ] > N(OVI) − weighted mean metallicity of lines w/ T>10 K and log N(OVI)>13N(OVI) − weighted mean metallicity of lines w/ T<10 K and log N(OVI)>13 − − − < [ Z / H ] > N(OVII) − weighted mean metallicity of lines w/ T>10 K and log N(OVII)>14N(OVII) − weighted mean metallicity of lines w/ T<10 K and log N(OVII)>14
Fig. 12.— shows the mean absorber metallicity as a function of b for O VI line with columndensity above 10 cm − (top panel) and O VII line with column density above 10 cm − (bottom panel). Within each panel, we have broken up the absorbers into two subsets usingtemperature: T > K (blue squares) and
T < K (red circles).
12 13 14 15 16 17 − − − − − ) < [ Z / H ] > X=O VIX=O VIIO VI: obs of Danforth & Shull (2008)O VI: obs of Lacki & Charlton (2010)
Fig. 13.— shows the mean metallicity as a function of column density for O VI (red opencircles) and O VII (blue open squares) lines. Also shown as solid symbols are observationaldata. It is likely that the observational errorbars are underestimated. 28 – − N(OVII) (cm − ) dn / d z [ > N ( O V II ) ] O VII: totalO VII: T>10 KO VII: T<10 KNicastro et al (2005)
Fig. 14.— shows the cumulative O VII line density as a function of column density, definedto be the number of lines per unit redshift at the column density greater than the value at thex-axis. The red solid dots, green squares and blue triangles are the total, collisionally ionizedand photo-ionized lines, respectively. Also shown as a black open circle is the observationof Nicastro et al. (2005a) with 1 σ errorbar. Note that the quantify shown in the y-axis ofFigure 5 is differential, not cumulative density.the O VII line incidence rate to assess the self-consistency of our simulations with extantobservations. Figure 14 shows the cumulative O VII line density as a function of columndensity. We also show the implied observed line density, under the assumption that thedetection reported by Nicastro et al. (2005a) is true. We see that the claimed observationaldetection is about 2 σ above or a factor of ∼ ≥ × cm − . Our model is clearly in a more comfortable situation, if theclaimed observational detection turns out to be negative. As discussed in the introductionthe detection reported by Nicastro et al. (2005a) is presently controversial. This highlightsthe urgent need of higher sensitivity X-ray observations of this or other viable targets thatcould potentially place strong constraints on the model.We now turn to the coincidences between O VI and O VII lines. The top panel of 29 –Figure 15 shows the cumulative probability distribution functions as a function of velocitydisplacement of having a coincidental O VII line above the indicated equivalent width foran O VI line of a given equivalent width. We see that O VI lines of equivalent widthin the range 50 − , , . , . , / s.The vast majority of coincidental O VII lines for O VI lines for those equivalent widths inquestion are concentrated within a velocity displacement of ≤
50 km / s and more than 50%at ≤
25 km / s.The bottom panel of Figure 15 shows the cumulative probability distribution functionsas a function of velocity displacement of having a coincidental O VI line above the indicatedequivalent width for an O VII line of a given equivalent width. It is seen that for O VII linesof equivalent width in the range 2 − −
27% probability of finding an O VI linewith equivalent width in the range 5 − / s.Likewise, the vast majority of coincidental O VI lines for O VII lines for those equivalentwidths in question are concentrated within a velocity displacement of ≤
50 km / s and morethan 80% at ≤
25 km / s.The results shown in Figure 15 presently can not be compared to observations, becausethere is no definitive detection of O VII absorbers, although there are many detected O VIabsorbers. Thus, we use the stacking method of Yao et al. (2009) to enable a direct com-parison with available observations. The top panel of Figure 16 shows the expected meanO VII column density at the location of detected O VI lines of column density indicated bythe x-axis, compared to the 3 σ upper limits from observations of Yao et al. (2009) shown asblack triangles. We see that the non-detection of O VII lines, or more precisely, a 3 σ upperlimit on the mean column of O VII lines for detected O VI lines of column density in therange log N(OVI)cm = 13 . − .
1, is fully consistent with our simulations. The reported3 σ upper limit is above the expected value by a factor of 2 . −
4. This suggests that afactor of ∼
10 increase in sample size or sensitivity will be able to yield a definitive detectionof O VII column density using the stacking technique even without detection of individualO VII absorbers. The bottom panel of Figure 16 shows the expected mean O VI columndensity at the location of detected O VII lines of column density indicated by the x-axis.It is evident from Figures 15,16 that O VI and O VII lines are coincidental only in alimited sense. We attribute the limited coincidence of O VII lines for O VI lines primarily totwo situations for O VI producing regions. A line of sight that intersects an O VI producingregion does not necessarily intersect a strong O VII producing region along the same line ofsight, either because the temperature of the overall region does not reach a high enough valueto be strong O VII bearing, or because the intersected O VI region is laterally an outskirt ofan onion-like structure where the more central, higher temperature, O VII region makes upa smaller cross section. The former case should be ubiquitous, because weaker gravitational 30 –shocks that produce regions of temperature, say, 10 . K are more volume filling than strongergravitational shocks giving rise to regions of temperature, say, 10 . K. In addition, feedbackshocks from star formation tend to be weaker than required to collisionally produce O VIIat the spatial scales of interest here. In other words, one expects to see many O VI-bearingregions that have no associated O VII-bearing sub-regions. The latter case where hotterbut smaller regions are surrounded by cooler regions is expected to arise naturally aroundlarge virialized systems such as groups and clusters of galaxies. A more quantitative but stillintuitive physical check of the obtained results is not straight-forward, without performinga much more detailed study of individual physical regions that produce O VI and O VIIabsorbers. We shall reserve such a study for the future.The situation of coincidental O VI lines for given O VII lines might appear to beless ambiguous at first sight in the sense that the hotter central, O VII-producing regionsshould be surrounded by cooler regions and thus one might expect that the line of sight thatintersects a strongly O VII-producing region should automatically intersect cooler regionsthat would show up as O VI absorbers. While it is true that a hot region is in generalsurrounded by cooler regions, it is not necessarily true that a hot 10 K, O VII-bearing gas issurrounded by significant 10 . K, O VI-bearing gas. For example, one may have a post-shockregion of temperature 10 K that is surrounded only by pre-shocked gas that is much colderthan 10 . K. We note that for a gas of δ = 100, T = 10 K and Z = 0 . (cid:12) at z = 0, its coolingtime is t cool ∼ . t H ( t H is the Hubble time at z = 0). This means that O VII-bearing WHIMgas at δ ≤ T ≥ K, is unlikely to cool to T ∼ . K to become O VI rich gas. On the other hand, the cooling time for gas of δ = 100,T = 10 . K and Z = 0 . (cid:12) at z = 0 is ∼ . t H , as noted earlier. Thus, it is physicallypossible that sharp interfaces between hot (T ≥ K) and cold T ≤ K gas develop. Thesimulations do not include thermal conduction, which can be shown to be unimportant here.The electron mean free path (mfp) is 0 . / K) ( δ/ − kpc, adopting the standardSpitzer value. The likely presence of magnetic fields (not treated here) would further reducethe mfp by an order of magnitude (e.g., Cowie & McKee 1977). Thus, thermal conductionis insignificant and multi-phase media is expected to exist. 31 – (cid:54) v (km/s) CD F ( O | O , > (cid:54) v ) P[finding EW>2mA O7 line given EW=50 − − − (cid:54) v (km/s) CD F ( O | O , > (cid:54) v ) P[finding EW>100mA O6 line given EW=2 − − − Fig. 15.— Top panel shows the cumulative probability distribution functions as a function ofvelocity displacement of having a coincidental O VII line above the indicated equivalent widthfor an O VI line of a given equivalent width. Bottom panel shows the cumulative probabilitydistribution functions as a function of velocity displacement of having a coincidental O VIline above the indicated equivalent width for an O VII line of a given equivalent width. 32 –
12 13 14 151313.51414.515 log N(OVI) (cm − ) l og < N ( O V II ) > ( c m − ) sim3 (cid:31) upper limit (Yao et al 2009)
14 15 1612.51313.514 log N(OVII) (cm − ) l og < N ( O V I ) > ( c m − ) simlimit case: assuming polytropic gaslimit case: assuming only hot gas at T>=10 K Fig. 16.— The top panel shows the expected mean O VII column density at the location ofdetected O VI lines of column density indicated by the x-axis. Also shown as black trianglesare 3 σ upper limits from observations of Yao et al. (2009). The bottom panel shows theexpected mean O VI column density at the location of detected O VII lines of columndensity indicated by the x-axis. The solid and dashed straight lines are possible limit casesbased on simple physical considerations. 33 –Equipped with this information and adopting the simpler implied geometry allows fora simple physical check of the results in the bottom panel of Figure 16, as follows. We willtake two separate approaches to estimate this. The first approach assumes a polytropic gasin the temperature range relevant for O VI and O VII collisional ionization. In the toppanel of Figure 17 we show the entire temperature-overdensity phase diagram for the refinedregion in the C run. Note that the gas density reaches about 1 billion times the mean gasdensity, corresponding to ∼ − , i.e., star formation regions. For the regions of presentrelevance, the density range is about 10 −
300 times the mean density, illustrated by theupper part of the red tornado-like region near the middle of the plot. It is useful to notethat for this density range, the gas mass is dominated by gas in the temperature range of10 − K, i.e., WHIM. Because of this reason, it is a valid exercise to compute the meanpressure as a function of overdensity, at least for the density range relevant for WHIM, shownin the bottom panel of Figure 17. We see that for the WHIM overdensity range of 10 − /
3, shown as the dashed line, provides an excellent approximation forthe polytropic index of the gas. It is also necessary to have a relation between gas metallicityas a function of gas overdensity, shown in Figure 18. We only note that the metallicity isgenerally an increasing function with density above one tenth of the mean density, that thesharp rise of metallicity below one tenth of the mean density is due to metal-enrich galacticwinds escaping into the low density regions, and that for our present purpose concerning theWHIM overdensity range of 10 −
300 the metallicity roughly goes as Z ∝ δ .
4, as indicatedby the dashed line.Given the information in Figures 17, 18 we can now proceed to estimate the expectedO VI column at a given O VII column density, i.e., < N(OVI) > / <
N(OVII) > , assumingboth are dominated by collisional ionization. The O VI column density may be roughly ap-proximated as < N(OVI) > ∝ f(OVI)∆ log T(OVI) ρ (OVI)Z(OVI)L(OVI), where f(OVI) = 0 . / K = 5 .
5, ∆ log T(OVI) = 0 . ρ (OVI), Z(OVI) and L(OVI) are the peak col-lisional ionization fraction for O VI, the FWHM of the logarithmic temperature of thecollisional ionization peak (see the blue curve in the top panel of Figures 8), the density ofthe O VI absorbing gas, the metallicity of the O VI absorbing gas and the physical thicknessof the O VI absorbing gas, respectively. We have an exactly analagous relation for O VII,with f(OVII) = 1, log T(OVII) = 6, ∆ log T(OVII) = 0 .
7. With an additional assumptionthat the characteristic thickness at a given density goes as L(OVI) ∝ ρ (OVI) / (i.e., massdistribution across log density is roughly uniform), we can now evaluate the column densityratio < N(OVI) >< N(OVII) > = f(OVI)f(OVII) ∆ log T(OVI)∆ log T(OVII) ρ (OVI) ρ (OVII) Z(OVI)Z(OVII) L(OVI)L(OVII)= f(OVI)f(OVII) ∆ log T(OVI)∆ log T(OVII) (cid:18) T(OVI)T(OVII) (cid:19) (2 / α ) / ( γ − = 0 . , (3) 34 – − − − − − − − − − (cid:98) p r e ss u r e ( e r g / c m ) simulationp=n Fig. 17.— Top panel shows mass weighted phase diagram in the temperature-overdensityplane for the refined region in the C run. The bottom panel shows the mean pressure as afunction of overdensity averaged over all cells in the regions in the C run. The black dashedline indicates the slope for polytropic gas of index 5 / −
300 that ismost pertinent to the absorbing WHIM in O VI and O VII. 35 –where α = 0 . γ = 5 / − − − − (cid:98) [ Z / H ] <[Z/H]>log(dispersion in linear Z)[Z/H]=0.4log( (cid:98) ) Fig. 18.— shows the mean gas metallicity (red solid curve) as a function of overdensityaveraged over all cells in the refined region of the C run. Also shown as the green dotted curveis the logarithm of the dispersion in Z (linear metallicity). The black dashed line indicatesthe logarithmic slope of 0 .
4, which provides a good approximation to the simulation in theoverdensity range 10 − < N(OVI) > / <
N(OVII) > .We assume that the O VII-bearing gas is at the peak temperature of 10 K and is surroundedby gas that has a temperature that is much lower than 10 . K (neglecting photoionization forthe moment), in which case the coincidental O VI line is produced by the same temperaturegas that produces the O VII line, giving < N(OVI) >< N(OVII) > = f(OVI)(T = 10 K)f(OVII)(T = 10 K)= 0 . , (4)which is shown as the dashed line in the bottom panel of Figure 16. Admittedly, ourapproaches to estimate the column density ratios are quite simplistic. Nevertheless, we think 36 –they capture some of the essential underlying relationships between O VI-bearing gas andO VII-bearing gas in the collisional ionization dominated regime and it is reassuring that theyare consistent with detailed calculations. Note that at N(OVII) < cm − photoionizationbecomes important, especially for related O VI lines, hence our simple physical illustrationbreaks down in that regime.
4. Conclusions
Utilizing high resolution (0 . h − kpc), adaptive mesh-refinement Eulerian cosmologicalhydrodynamic simulations we examine properties of O VI and O VII absorbers in the warm-hot intergalactic medium (WHIM) at z = 0, along with a physical examination. We findthat our new high resolution simulations are in broad agreement with all other simulationswith respect to the thermal distribution of baryons in the present universe. In particular,we find that about 40% of the intergalactic medium is in the WHIM. We find that oursimulations are in excellent agreement with observed properties of O VI absorbers, includingline incidence rate, Doppler width-column density relation, and consistent with observedDoppler width-temperature relation. Physical properties of O VI and O VII absorbers aregiven, including inter-relations between metallicity, temperature, density, Doppler width, tofacilitate a coherent understanding. We highlight some of the important or new findings.(1) We find that strong O VI absorbers are predominantly collisionally ionized, whereasfor weaker absorbers the contributions from photoionization become progressively more im-portant. We find that (39% , , = (12 . − , − , >
14) have temperature greater than 10 K. Thismay be contrasted with the results of Oppenheimer & Dav´e (2009) where low temperature( ∼ K), high metallicity, photoionized O VI absorbers dominate even at high columndensities (log N(OVI)cm > ≥ cm − ] O VI absorbers and galaxies on ∼ σ upper limit on themean column density of coincidental O VII lines at the location of detected O VI lines byYao et al. (2009) is above the predicted value by a factor of 2 . −
4, implying that a factorof ∼
10 increase in sample size or sensitivity will be able to yield a definitive detectionof O VII column density using the stacking technique even without detection of individualO VII absorbers.(5) We show that, if the previously claimed observational detection of O VII lines byNicastro et al. (2005a) is true, our predicted O VII line density is 2 σ below that. This showsthat higher sensitivity X-ray observations of this or other viable targets will be very usefulto potentially place strong constraints on the model.I would like to thank Dr. M.K.R. Joung for help on generating initial conditions for thesimulations and running a portion of the simulations and Greg Bryan for help with Enzocode. I would like to thank the referee Mike Shull for critical and constructive reports. Iwould like to thank Dr. Edward Jenkins for a careful reading of the manuscript and helpfuldiscussion, Dr. Charles Danforth for kindly providing the observational data and usefuldiscussion, Dr. Jeremiah P. Ostriker for useful discussion and Drs. John Wise, MatthewTurk and Cameron Hummels for help with visualization program yt (Turk et al. 2011).Computing resources were in part provided by the NASA High- End Computing (HEC)Program through the NASA Advanced Supercomputing (NAS) Division at Ames ResearchCenter. This work is supported in part by grants NNX08AH31G and NAS8-03060. Thesimulation data are available from the author upon request. REFERENCES
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