Probing the physical properties of the intergalactic medium using gamma-ray bursts
MMNRAS , 1–17 (2015) Preprint 5 February 2021 Compiled using MNRAS L A TEX style file v3.0
Probing the physical properties of the intergalactic medium usinggamma-ray bursts
Tony Dalton, (cid:63) Simon L. Morris, and Michele Fumagalli Centre for Extragalactic Astronomy, Durham University, South Road, Durham DH1 3LE, UK Dipartimento di Fisica ‘G. Occhialini’, Universit`a degli Studi di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy
Accepted 2021 February 02. Received 2021 January 29; in original form 2020 December 14
ABSTRACT
We use Gamma-ray burst (GRB) spectra total continuum absorption to estimate the key intergalactic medium(IGM) properties of hydrogen column density ( N hxigm ), metallicity, temperature and ionisation parameter over aredshift range of . ≤ z ≤ . , using photo-ionisation (PIE) and collisional ionisation equilibrium (CIE) models forthe ionised plasma. We use more realistic host metallicity, dust corrected where available, in generating the hostabsorption model, assuming that the host intrinsic hydrogen column density is equal to the measured ionisationcorrected intrinsic neutral column from UV spectra ( N h i,ic ). We find that the IGM property results are similar,regardless of whether the model assumes all PIE or CIE. The N hxigm scales as (1 + z ) . − . , with equivalent hydrogenmean density at z = of n = . + . − . × − cm − . The metallicity ranges from ∼ . Z (cid:12) at z ∼ to ∼ . Z (cid:12) atredshift z > . The PIE model implies a less rapid decline in average metallicity with redshift compared to CIE.Under CIE, the temperature ranges between . < log ( T / K ) < . . For PIE the ionisation parameter ranges between . < log ( ξ ) < . . Using our model, we conclude that the IGM contributes substantially to the total absorption seenin GRB spectra and that this contribution rises with redshift, explaining why the hydrogen column density inferredfrom X-rays is substantially in excess of the intrinsic host contribution measured in UV. Key words: gamma-ray burst: general–intergalactic medium–X-rays: general–galaxies: high-redshift
The main objective of this paper is to estimate the key IGMparameters of column density, metallicity, temperature andionisation, using the latest models for ionised absorbers on theline of sight (LOS) to GRBs. We examine past observationsand simulations to set the parameters ranges and priors forour models. Our hypothesis is that the bulk of the excess inobserved hydrogen column density in GRB spectra, inferredfrom X-rays over the intrinsic host contribution measured inthe UV, is due to absorption in the IGM, and that this IGMcolumn density increases with redshift.Most baryonic matter resides in the IGM and in particu-lar, the regions between galaxies. In the early universe, thefraction of baryons in the IGM was even higher, as less ma-terial had coalesced gravitationally from it (McQuinn 2016,hereafter M16). IGM temperature varies widely over redshiftand phase. Recent simulations predict that up to 50% of thebaryons by mass have been shock-heated into a warm-hotphase (WHIM) at low redshift z < with T = − K and n b = − − − cm − where n b is the baryon density (e.g Cen& Ostriker 1999, 2006; Dav´e & Oppenheimer 2007; Schayeet al. 2015). Martizzi et al. (2019, hereafter M19), using the Il- (cid:63) E-mail:[email protected] lustrisTNG simulations (Piattella 2018), estimated that thecool diffuse IGM constitutes ∼ and the WHIM ∼ ofthe baryons at redshift z = . Observations of the cool diffuseIGM and WHIM are essential for effective tracing of matteracross time and to validate the simulations (Danforth et al.2016). We adopt the common temperature naming conven-tion for IGM plasma: cool is log( T /K) < and Warm-Hot,log( T /K ) ∼ α forestsystems (SLFSs): 15 < log N H i < ; partial Lyman LimitSystems (pLLSs) 16.2 < log N H i < < log N H i <
19 ; super-LLSs (sLLSs) : 19.0 < log N H i < α Systems (DLAs) log N H i > α absorption in the spectra of quasars has provided ahighly sensitive probe of the cool IGM (e.g. Morris et al. 1991;York et al. 2000; Harris et al. 2016; Fumagalli et al. 2020). Inthe cool phases of the IGM including voids, − of theuniverse by mass has [ O/H ] > − while, by volume, only Throughout this paper, logarithmic column densities are ex-pressed in units of cm − © a r X i v : . [ a s t r o - ph . C O ] F e b T. Dalton et al of the overdense universe has a metallicity [ C/H ] > − (F14and references therein). Both Schaye et al. (2003, hereafterS03) and Aguirre et al. (2008, hereafter A08) found virtuallyno evidence for metallicity evolution in the cool IGM in therange z = . − . , but metallicity did have a strong depen-dency on density. S03 confirmed that collisional ionisation didnot apply to the phases they studied.A significant fraction of the cool gas probed by SLFSs,pLLSs, and LLSs has been associated with galaxy haloes andthe circum-galactic medium (CGM) (Pieri et al. 2014; Fu-magalli et al. 2013, 2016, hereafter F16). As we move fromthe diffuse IGM to virialised luminous matter, the metallic-ity rises from the very low values of [X/H] ∼ − to − , toapproximate values of − . for SLFS, − . for pLLSs, ≤ − for LLSs and > − . for DLAs (Wotta et al. 2019, L19, F16).F16 noted considerable evolution in LLS metallicity. How-ever, these systems contribute only ∼ to the cosmic metaldensity budget (L19). The intracluster medium (ICM) meanmetallicity in the range ≤ z ≤ . is Z = . ± . Z (cid:12) (S12; McDonald et al. 2016). At the outer ICM, the metal-licity falls to < . Z (cid:12) (Mernier et al. 2017), which is thestart of the true IGM. Temperature in the ICM are typicallylog ( T /K) > . However, the ICM only contains ∼ of cosmicmetals (Shull et al. 2012, M16).At higher temperatures, for some time since the first pre-diction of substantial baryons at low redshift, the expectedbaryons were not observed in the WHIM, giving rise to the”missing”baryon problem (Danforth & Shull 2005, 2008; Shullet al. 2012, 2014). Recent literature points to the CGM asreservoir for at least a fraction of this missing matter (Tum-linson et al. 2011, 2013; Werk et al. 2013; Lehner et al. 2016).Other claims to have detected the WHIM include possibledetection of O vii lines, excess dispersion measure over ourGalaxy and the host galaxy in Fast Rasio Bursts (FRB), andstacked X-ray emission from cosmic web filaments using thethermal Sunyaev Zelodovich effect (e.g. Nicastro et al. 2018;Macquart et al. 2020; Tanimura et al. 2020).Detection of the WHIM is extremely challenging, as itsemission is very weak, it lacks sufficient neutral hydrogen tobe seen via Ly α absorption in spectra of distant quasars, andthe X-ray absorption signal expected from the WHIM is ex-tremely weak (Nicastro et al. 2018; Khabibullin & Churazov2019). There appears to be a consensus that, at least for z < ,the predicted mean metallicity of the WHIM from simulationsand O vi absorption studies is ∼ . Z (cid:12) (e.g. Wiersma et al.2011; Danforth et al. 2016; Pratt et al. 2018, S12).Post reionisation, the vast majority of hydrogen and heliumis ionized in the IGM. Therefore, the observation of metalsis essential for parameterising the IGM properties includingdensity, temperature and metallicity. Huge work has beencompleted on individual systems from absorption-line stud-ies that use the ionization states of abundant heavy elements(e.g. Shull et al. 2014; Raghunathan et al. 2016; Selsing et al.2016; Lusso et al. 2015). While these surveys have been verysuccessful, most very highly ionised metals are not observedin optical to UV. High resolution X-ray observations are re-quired as they are sensitive to a broad range of cross-sectionsover the full integrated LOS. However, tracing individual fea-tures of the IGM metals in X-ray with current instruments isvery limited. Athena, the proposed European Space AgencyX-ray observatory, aims to study the IGM through detailed observations of O vii (E = 573 eV) and O viii (E = 674 eV)absorption features (Walsh et al. 2020).While we await this future mission, GRBs are currentlyone of the most effective observational methods to study theIGM as their X-ray absorption yields information on the to-tal absorbing column density of the matter between the ob-server and the source (e.g. Galama & Wijers 2001; Watsonet al. 2007; Watson 2011; Wang 2013; Schady 2017). GRBsare among the most powerful explosions known in the uni-verse. GRBs exist over an extensive range of redshifts anddistances, and have high luminosities combined with a broadenergy range of observed emissions. Any element that is notfully ionized contributes to the absorption of X-rays. ThoughThomson scattering is essentially energy independent, scat-tering by electrons only becomes important at energies above10keV (Wilms et al. 2000, hereafter W00).Although the X-ray absorption cross-section is mostly dom-inated by metals, with hydrogen and helium contribution be-ing minimal but not nil (Fig.1 W00), it is typically reportedas an equivalent hydrogen column density (hereafter N hx ). N hx consists of contributions from the local GRB environ-ment, the IGM, and our own Galactic medium. With currentinstruments, GRB X-ray absorption cannot generally revealthe redshift of the matter in the column due to a lack of signalto noise and spectral resolution.The two main results of earlier studies of the IGM usingGRBs are the apparent increase in N hx with redshift, andthat N hx exceeds the host intrinsic neutral hydrogen columndensity ( N h i ) in GRB, often by over an order of magnitude(e.g. Behar et al. 2011; Watson 2011; Campana et al. 2012). N h i is generally obtained from observations of strong indi-vidual absorbers in the GRB host system. The cause of an N hxigm excess over N h i , and the N hxigm rise with redshiftseen in GRBs has been the source of much debate over the lasttwo decades. One school of thought argues that the GRB hostaccounts for all the excess and evolution e.g. dense Helium(He ii ) regions close to the GRB (Watson et al. 2013), ultra-ionised gas in the environment of the GRB (Schady et al.2011), a dense environment near the burst location (Cam-pana et al. 2012), dust extinction bias (Watson & Jakobsson2012), and/or a host galaxy mass N hxigm relation (Buch-ner et al. 2017). The other school of thought argues that theIGM is the cause of excess absorption and redshift relatione.g. (Starling et al. 2013; Arcodia et al. 2016; Rahin & Be-har 2019). While we acknowledge that the GRB host maycontribute to the excess absorption, it is the IGM that is thefocus of this paper.The convention in prior work using GRB was to use so-lar metallicity as a device used to place all of the absorbingcolumn density measurements on a comparable scale. Theseworks all noted that the resulting column densities were,therefore, lower limits as GRB typically have much lowermetallicities. Dalton & Morris (2020, hereafter D20) used re-alistic GRB host metallicities to generate improved estimatesof N hx . They confirmed the N hx redshift relation and thatthe revised N hx showed an even greater excess over N h i .As the bulk of matter in the IGM is ionised and existsoutside of gravitationally bound structures, in this paper weuse a homogeneity assumption. We will use tracer objectsthat have LOS orders of magnitude greater than the largescale structure.The sections that follow are: Section 2 describes the data MNRAS , 1–17 (2015) robing IGM properties using GRB selection and methodology; Section 3 covers the models forthe IGM LOS including key assumptions and plausible valueranges for key parameters; Section 4 gives the results ofGRB spectra fitting using collisional and photoionisationIGM models with free IGM key parameters; we discuss theresults and compare with other studies in Section 5; and Sec-tion 6 gives our conclusions. Appendix A covers model com-parisons and investigating the robustness of the IGM modelfits. We suggest for readers interested in the key findings onIGM parameters from fittings only, read Sections 4, 5 and6. Readers interested in detailed spectra fitting methodologyand model assumptions should also read Sections 2 and 3. Fi-nally, for readers interested in more detailed examination ofkey IGM parameters, plus software model comparisons, readAppendix A. We used the D20 data for N hx which consisted of all ob-served GRBs with spectroscopic redshift available up to 31July 2019 from the UK Swift
Science Data Centre repository(hereafter Swift ; Burrows et al. 2005). Spectra from the
Swift repository were taken from the Photon Counting Late Timemode. D20 investigated the plausibility of assuming that thehost intrinsic hydrogen column density is equal to the mea-sured ionisation corrected intrinsic neutral column from UVspectra. D20 used ionisation corrections from F16 who reporton the values of the neutral fraction as a function of NHI. Wefollow their method for GRB host hydrogen column density.The GRB N h i sample is taken from Tanvir et al. (2019). Oursample criteria was that the GRB has detections with quan-tified uncertainties for N hx , N h i , and spectroscopic redshift.The selection criteria resulted in a total GRB sample of 61.We selected the best S/N sample representative of the rangefrom . < z < . . D20 examined if a S/N limited samplewould cause a bias by plotting log( N hx ) versus both log oftotal error in N hx and total error/ N hx for all detections. Thescatter appeared random so any selection by total error/ N hx should not result in a bias in N hx . The total final data sam-ple consists therefore of 32 GRB, details are available in theonline supplementary material.We refitted the GRB spectra using xspec v12.10.1 (Arnaud1996, hereafter A96), assuming an underlying power law inthe X-ray band from 0.3 - 10.0 keV, which is suitable for thevast majority of GRB and again is consistent with the Swift repository (Starling et al. 2013, hereafter S13). The Galac-tic component is fixed to
Swift values based on (Willingaleet al. 2013, hereafter W13). Asplund et al. (2009) is generallyregarded as providing the most accurate solar abundances.However, we used the solar abundances from W00 which takeinto account dust and H in the interstellar medium in galax-ies.Most works on the WHIM use absorption line observationsfocusing on oxygen, carbon, nitrogen and neon because oftheir relatively high abundance, and because the strongestresonance lines in He and H-like ions are in a relatively ‘clean’wavelength band, compared to typical X-ray spectra resolu-tions. Due to the small Doppler broadening, ignoring tur- bulence, the lines rapidly saturate. The challenge for X-rayspectroscopy in the IGM is to detect small equivalent widths(Richter et al. 2008, hereafter R08), which is only possiblecurrently in the UV. Accordingly, we chose to base our workon total absorption by the ionised IGM as opposed to fittingindividual line absorption, avoiding misidentifation of absorp-tion features (Gatuzz & Churazov 2018, hereafter G15).When fitting models to spectra, chi-squared ( χ ) is thegenerally used statistical method. However, deep field X-raysources such as our sample from Swift , only have a smallnumber of photon counts, well into the Poisson regime. The χ regression approach is inappropriate in this circumstance(Buchner et al. 2014). The common practice of rebinning datato use a χ statistic results in loss of energy resolution. Themaximum likelihood C-statistic (Cash 1979), based on thePoisson likelihood, does not suffer from these issues. For aspectrum with many counts per bin the C-statistic → χ ,but where the number of counts per bin is small, the valuefor C-statistic can be substantially smaller than the χ value(Kaastra 2017). Accordingly, we use the C-statistic (Cstat in xspec ) with no rebinning.Typically, when using xspec to fit models to spectra, localoptimisation algorithms like the Levenberg- Marquardt algo-rithm are employed to iteratively explore the space from astarting point. However, given we are studying the IGM withX-ray spectra, we can expect some degeneracies between theparameters. Therefore, there may be multiple, separate, ad-equate solutions, i.e. local probability maxima. In these cir-cumstances, these algorithms cannot identify them or jumpfrom one local maximum to the other. The steppar functionin xspec allows the forcing of parameters to specific ranges.This can overcome the local maximum problem to some de-gree. Markov chain Monte Carlo (MCMC) is a commonlyemployed integration method for Bayesian parameter estima-tion. However, MCMC also has difficulty finding and jump-ing between well-separated maxima (Buchner et al. 2014).Given the issues of goodness of fit and getting out of localprobability maxima, we use a combination of the steppar function and confirmation with MCMC to validate our fit-ting and to provide confidence intervals on Cstat. We preferthis approach over alternatives such as the Akaike Informa-tion Criterion (AIC). The AIC, popular in astrophysics is AIC = χ + k where k is the number of parameters of themodel. However, as it is based on χ , it suffers from the sameproblems i.e. based on a Gaussian assumption for errors andrequirung a high bin count.We follow a similar MCMC methodology as Foreman-Mackey et al. (2013) for the number of walkers ( ×
10 freeparameters), chain length and burn-in period. We use Good-man Weare MCMC (Goodman & Weare 2010).
In this section we describe the motivation and expected phys-ical conditions in the IGM that lead to our choice of CIE andPIE models, the priors and parameter ranges.In our models, we use different xspec (A96) absorptionsub-routines for the absorbers on the LOS. For Galaxy ab-sorption ( N hxGal ) , we use tbabs (W00) fixed to the valuesmeasured by W13. tbabs calculates the cross-section for X-ray absorption by the ISM as the sum of the cross sections for MNRAS , 1–17 (2015)
T. Dalton et al the gas, grain and molecules in the ISM. For the GRB hostgalaxy absorption, we use tbvarabs which is the same as tbabs but with metallicity, dust and redshift as free variables.We follow D20 for the metallicity of the GRB host galaxy i.e.using dust corrected actual metallicity where available, andotherwise their average GRB host value of Z = . Z (cid:12) . The N hx for the GRB host is fixed to the N h i,ic values, fol-lowing the D20 method. By fixing N hx for both our Galaxyand the GRB host, the excess absorption in the models isregarded as being produced by the IGM. W00 noted thatthe tbabs model does not include the effects of the warmphase or of the ionized phase of the ISM. We review thephotoionisation (PIE) and collisional ionisation equilibrium(CIE) models available in xspec to determine which is bestfor our purposes of modelling the IGM. These are warmabs (Kallman et al. 2009, hereafter K09) for PIE, hotabs (K09), ioneq (G15) and absori (Done et al. 1992) for CIE. In ear-lier works on using tracers such as GRB and quasars for IGMabsorption, absori was generally used (e.g. Behar et al. 2011;Starling et al. 2013). While absori was the best model avail-able when it was developed in 1992, it is not self-consistentas it allows one to have both ionisation parameter and tem-perature as free parameters which would not occur in eitherPIE or CIE (Done et al. 1992). Other issues with absori arethat it only uses ionisation edges with no line absorption. Themetals included are limited to H, He, C, N, O Ne, Mg, Si, Sand Fe, and only Fe is allowed as a free parameter. Accord-ingly, we do not use it for PIE, but do for CIE to comparewith earlier studies in Appendix A.We chose to use warmabs as a more sophisticated PIEmodel which is designed to determine the physical conditionsin partially ionized gases. It calculates the absorption dueto neutral and all ionized species of elements with atomicnumber Z ≤
30. While warmabs does not account for self-shielding, this effect is negligible at high ionization parame-ters (K09). For CIE, we chose hotabs , a sophisticated code,similar to warmabs except that it has temperature as thefree parameter as opposed to ionisation. An alternative CIEmodel is ioneq . It is similar to hotabs except that it allowsmetallicity to vary for O, Ne and Fe only (G15). warmabs , hotsabs and ioneq have turbulent velocity (vturb) as a freeparameter. We examined varying vturb to assess impact onfittings. The broad range trialled ( − km s − ) showedminimal variation in column densities or other parameters.Thus, we set vturb = 0.We model the IGM assuming a thin uniform plane par-allel slab geometry in thermal and ionization equilibrium.This simplistic approximation is generally used to representa LOS through a homogenous medium and is appropriatefor our model (e.g. Savage et al. 2014; Nicastro et al. 2017;Khabibullin & Churazov 2019; Lehner et al. 2019). This slabis placed at half the GRB redshift as an approximation of thefull LOS medium. We examined placing the slab at half theredshift equivalent distance integral as an approximation ofdistance, but it did not change our results.Any LOS to a GRB is likely to encounter many differ-ent intervening phases of matter, density, temperature andphotoionisation levels. Given the current quality of the GRBspectra, the most pragmatic approach is to define the pa-rameters ranges and priors from the past measurements andobservations. The slab fit results will then characterise ’typi-cal’ conditions integrated along the LOS. We now review the physical processes and key conditions to pin down the rangeof parameters and models that are best suited for our analy-sis. Generally, there are two processes that determine the ionisa-tion state of plasma in the IGM i.e. photoionisation and col-lisional ionisation. Different physical processes are thereforeinvolved and any assumptions regarding whether collisional,photoionisation or a combination dominates will impact anyattempts to model the IGM.The photoionisation rate, Γ H i depends on the ionising radi-ation field in the IGM provided by the cosmic ionising back-ground (CIB). For photoionisation IGM modelling, the ion-isation parameter ξ (the ratio of ionising photon density toelectron density) is a key variable. We set the parameter rangeas ≤ log( ξ ) ≤ for an ionised IGM (Starling et al. 2013).For IGM modelling with the collisional assumption for ionisa-tion, temperature is a key variable. Collisions by thermal elec-trons ionise hydrogen to a high degree for gas temperatures > . × K. Metals require higher temperatures or ionisa-tion. Therefore, we set the parameter range as ≤ log ( T /K) ≤ .We chose to use equilibrium based models. The relationbetween ionisation state or fraction and gas temperature andionisation parameter explicitly assumes that the gas is in anionisation equilibrium (R08). Opinions on the IGM equilib-rium state differ greatly (e.g. Branchini et al. 2009; Nicastroet al. 2018). In non-equilibrium, the plasma remains over-ionised compared to CIE at any temperature, as recombi-nation lags behind cooling (Gnat & Sternberg 2007). Whilethere is still debate on the equilibrium state of the WHIM,it is likely that a substantial part of the baryons in the uni-verse are in regions where extremely low densities and ioni-sation equilibrium conditions persist (M16). Importantly forIGM modelling, well outside the influence of galaxies andclusters, the radiation background becomes more important.Oppenheimer & Schaye (2013a) noted that non-equilibriumeffects are smaller in the presence of the CIB, and are over-estimated in CIE. However, they also showed that in thepresence of AGN, a large fraction of the metal-enriched in-tergalactic medium may consist of non-equilibrium regions(Oppenheimer & Schaye 2013b).In summary, for our IGM models we assume ionisationequilibrium, with the caveat that the equilibrium assumptioncould result in an underestimation of column density wherethe IGM plasma remains over ionised in non-equilibrium con-ditions. As we are using ionised metal absorption, we have to allowfor a large range in the metallicity parameter as the LOSto the GRBs trace the various IGM phases. In our analysis,we include the highly ionised metals that dominate X-rayabsorption given that H and He are relatively unimportant.Below 1 keV, C, N, O, and Ne are the main absorbers, whileabove 1keV, Si, S, and Fe dominate (W00). O vii & O viii are the most abundant and Neon species also very important( Ne vii , Ne viii , Ne ix , Ne x ). Metallicity currently constitutes MNRAS , 1–17 (2015) robing IGM properties using GRB Figure 1. N hx and redshift relation for different CIB indices using absori for GRB120909A. A power law of 2 produces the high-est estimated column densities at all redshift, but only marginallygreater than a photon index of 1.4 the main uncertainty of the IGM models (Branchini et al.2009).In Section 1, we noted that in the cool IGM phases, typ-ical metallicity is observed to be at the very low range − < [ X / H ] < − (e.g. Simcoe et al. 2004, S03,A04). In thehotter phases including the WHIM, the metallicity has beenobserved to be [ X / H ] ∼ − (e.g. Danforth et al. 2016; Prattet al. 2018, S12). As we are modelling the LOS through thecool, warm and hot diffuse IGM, but noting that some con-tribution will come from overdense phases, we will set the xspec metallicity parameter range as − < [ X / H ] < − . ( . < Z / Z (cid:12) < . . The abundance of ionic species is partially dependent on theCIB. Many studies have been completed on the sources ofthe background radiation such as star forming galaxies andAGN with power laws in the range . − (e.g. Haardt &Madau 1996, 2012; De Luca & Molendi 2004; Luo et al. 2011;Moretti et al. 2012). To explore uncertainties in the UV back-ground, Crighton et al. (2015) and Fumagalli et al. (2016)introduced a free parameter α UV to account for the AGN-dominated (hard) to galaxy-dominated (soft) spectrum. Acommon practice is to adopt a fixed power law for the back-ground radiation. This is a reasonable approach in calculatingthe ionisation balance. absori is the only xspec model which allows the back-ground CIB as a free parameter. In warmabs , hotabs and ioneq , the CIB photon index is set to 2 which is consistentwith the work by Moretti et al. (2012). In many prior workson the IGM using absori , general practice has been to setCIB photon index to 1.4 following (De Luca & Molendi 2004).We examined the impact of different CIB indices on columndensity using absori on GRB120909A in Fig. 1.A photon index of 2 results in the highest estimated columndensity at all redshift. The lowest column densities resultedfrom a CIB photon index of 0.5 at logarithmic difference ∼ Table 1.
Upper and lower limits for the free parameters in the IGMmodels. Power law slope and normalisation for the GRB spectrumwere also free parameters. The fixed parameters are Galactic andhost log( N hx ), GRB redshift, the IGM slab at half the GRB red-shift, and host metallicity at the observed dust corrected value, or Z = . Z (cid:12) .IGM parameter equilibrium model range in xspec modelscolumn density PIE & CIE ≤ log( N hx ) ≤ temperature CIE ≤ log( T /K) ≤ ionisation PIE 0 ≤ log( ξ ) ≤ metallicity PIE & CIE − ≤ [ X / H ] ≤ − . . lower than when the index is 2. However, the differencein the commonly observed CIB range of . − is minimal.Accordingly, we set the photon index at 2 for absori to allowcomparison with the other models where it is fixed at 2. Based on the extensive observations and simulations of theIGM to date, a combined CIE and PIE model for the IGMwould be required for optimum fitting of the GRB spectra.However, given the quality of the spectra, we chose insteadto examine the two extreme scenarios where all the IGM ab-sorption is either in the CIE or PIE phase. As warmabs and hotabs are the most sophisticated PIE and CIE models,these are used for generating the final results of the IGM pa-rameters of density, metallicity, temperature and ionisationparameter in Section 4. We then investigated robustness andvalidity of models and assumptions, together with a compar-ison of the various ionisation model results (Appendix A).The parameters ranges that were applied to the PIE andCIE models are summarised in Table 1. The full multi-plicative models (*) which we trialled for the absorbers onthe LOS and including the GRB spectra power law (po) in xspec terminology are:PIE: tbabs*warmabs*tbvarabs*po
CIE: tbabs*hotabs*tbvarabs*po
CIE: tbabs*ioneq*tbvarabs*po
CIE: tbabs*absori*tbvarabs*po
Fig. 2 shows an example of the model components for thefull LOS absorption using hotabs for IGM CIE absorption.The model example is for a GRB at redshift z = , with [ X / H ] = . for the IGM. For our Galaxy and the GRB host,log( N hx ) = , and log( N hxigm ) = (to represent the col-umn density of the IGM LOS cumulatively to z = ). The ab-sorption by the GRB host is minimal compared to the ISM ofour Galaxy and the IGM. This is because of the redshift z = and low metallicity Z = . Z (cid:12) of the GRB host. The sam-ple transmission plots using hotabs and warmabs show theimpact of different key parameters and redshift for both PIEand CIE models are available in the online supplementarymaterial. MNRAS , 1–17 (2015)
T. Dalton et al
Figure 2.
Model components for the LOS absorption using hotabs for IGM CIE absorption in the energy range 0.3 - 2.0keV (
Swift
GRB spectra extend to 10keV). The model example is for a GRBat redshift z = , with [ X / H ] = . for the IGM, log( N hx ) = forour Galaxy and the GRB host. The IGM log( N hxigm ) = approx-imates the total column density of the IGM LOS to z = . Mostabsorbtion is due to the IGM (grey) and our Galaxy (red). TheGRB host has little contribution due to its redshift and low metal-licity (magenta). The total absorption from all three componentsis the blue line. In Section 4, we firstly discuss the impact of using additionalmodel components on a sub-sample in Section 4.1, then givethe results for the full sample using the CIE IGM absorptionmodel in Section 4.2 and using the PIE IGM model in Section4.3.
We started by fitting a sub-sample of GRB from our full sam-ple, to examine the impact of adding additional model com-ponents leading to the full model including the ionised IGM.We show the fitting results in Fig. 3 for GRB150403A at red-shift z = . as an example of typical results. We initiallyfitted with a simple model of power law and absorption onlyfrom our Galaxy. The top-left panel in Fig. 3 shows residualsat low energy with a Cstat of 737.6 for 684 degrees of freedom(dof). We then add a fixed GRB host absorber equal to themeasured ionised corrected intrinsic neutral column from UVspectra as detailed in Section 2 plus a variable IGM compo-nent. The IGM component is either the CIE or PIE model.The top-right panel of Fig. 3 shows the result for the modelwith the CIE IGM component. The spectral fit is visuallyimproved compared with the Galaxy only model, with muchless low energy residual. The Cstat for the full model withthe CIE IGM component is 655.0 (680 dof), and for the PIEmodel 652.8 (680 dof). The Fig. 3 bottom-left and right pan-els show the MCMC integrated probability results for N hxigm with temperature and metallicity respectively. The red, greenand blue contours represent , and ranges for the two parameters respectively. On the y-axis bottom-left panel,log(T4/K) means that 0 is log ( T / K ) = .All the fittings in the sub-sample for both CIE and PIEmodel components showed Ctat results as good as or betterthan the simple models where all the absorption in excessof our Galaxy was assumed to be at the GRB host redshift.Accordingly, we proceeded to fit the full GRB sample withour CIE and PIE models and give the results for the IGMparameters in Sections 4.2 and 4.3. In these scenarios, we use hotabs for CIE and warmabs for PIE with N hx , metallicityand temperature or ionisation parameters all free. The errorbars for all fits are reported with a confidence interval.In the plots of N hx and redshift, the green line is the meanhydrogen density of the IGM based on the simple model usedin D20 and references therein. N hxigm = n cH (cid:90) z (1 + z ) dz [ Ω M (1 + z ) + Ω Λ ] (1)where n is the hydrogen density at redshift zero, taken as . × − cm − (Behar et al. 2011). This value is based on of the baryons being in the IGM. Values for this IGMfraction in the literature vary e.g. . − . (S12) and . (Zhang et al. 2020). We give the key detailed results for the IGM parameters fromfitting our model CIE model to the GRB spectra in our sam-ple.Modelling the IGM using hotabs for CIE with parameters N hx , Z and T free, results in N hxigm showing similar valuesand correlation with redshift as the mean IGM density modelin Fig. 4 (top left). A power law fit to the N hxigm versusredshift trend scales as (1 + z ) . ± . . The reduced χ = . indicates a good fit. The mean hydrogen density at z = from the sample is n = . + . − . × − cm − , providing a goodconstraint on this important IGM parameter. Nearly all GRBfits are proximate to both the χ fit and mean IGM densitycurve. However, there are a few notable outliers, especiallythe lowest redshift GRB140430A with z = . . This fit hasmuch higher N hxigm than both the mean density curve andthe χ fit. This could be due to a strong absorber on theLOS. To test this, we removed the cap of Z = . Z (cid:12) as thethere is covariance between column density and metallicityparameters i.e. a higher metallicity results in a lower columndensity. The best fit then for GRB140430A was with Z ≈ . Z (cid:12) with a much lower column density similar to the meanIGM model density at z = . . At the highest redshift z > ,the two GRB fits are well below the cosmic mean density and χ fit. There is some dispersion in the GRB data points at z ≤ . This could indicate that at these redshifts, the GRBhost contribution is dominant over the IGM absorption, whileat higher redshifts, the host contribution becomes diluted bythe IGM, therefore showing a smaller dispersion of results.It is notable that most of the GRB fits sit at the high endof the confidence interval error bars. xspec failed to fittwo GRB from sample of 32. This was either because thebest fit was at the limit of the parameters or the error barswere at one or both parameter limits. This could be due topoor spectra resolution or that the parameter range was toonarrow. MNRAS , 1–17 (2015) robing IGM properties using GRB Figure 3.
Impact of adding additional model components to a simple power law in fitting GRB150403A. Top-left panel is with N hxGal only.Top-right panel is with the addition of a fixed host component and CIE IGM absorption component. The spectrum fit shows improvementin low energy absorption over the simple power law fit with N hxGal . The bottom-left and right panels show the MCMC integratedprobability results for N hxigm with temperature and metallicity respectively. The red, green and blue contours represent , and ranges for the two parameters respectively, with grey-scale showing increasing integrated probability from dark to light. On the y-axis inthe bottom-left panel T4 means the log of the temperature is in units of 10 K. The top-right panel of Fig. 4 shows the dependence of [ X / H ] with redshift. A power law fit to the [ X / H ] versus red-shift trend scales as (1 + z ) − . ± . . The reduced χ = . in-dicates a plausible linear fit. Metallicity ranges from [X/H] ∼ − . Z (cid:12) ) at z = to [X/H] ∼ − . Z (cid:12) ) at highredshift ( z > ).There is a large range in the fitted temperature . < log( T /K) < . , with substantial error bars in the Fig. 4bottom-left panel. The mean temperature over the full red-shift range is log( T /K) = . + . − . . These values are consistentwith the generally accepted WHIM range. It is interesting tonote that even at the highest redshifts z > , temperaturesof log ( T / K) > steppar results. In conclusion, with the caveats of low GRB X-rayresolution, small data sample and the slab model to representto full LOS, there are reasonable grounds for arguing thatthe CIE model using hotabs is plausible for modelling the warm/hot component of the IGM at all redshifts. The resultsare consistent with a mean hydrogen density of n = . × − cm − , providing constraints on this IGM parameter of n = . + . − . × − cm − . However, cosmological simulations suggestthat the fraction of mass contained in the warm-hot IGMphase is a strong function of redshift being ∼ at z = ,dropping by a factor of 20 by z = , while the diffuse coolerIGM becomes dominant (Martizzi et al. 2019). Our modelindicates a decline in the average metallicity on the LOS,with a significant drop in metallicity at the highest redshifts.The temperature range of log( T /K) ∼ − and mean of . + . − . are consistent with the expected values from simulations for awarm/hot phase. We discuss the results further and comparewith other studies in Section 6. Modelling the IGM using warmabs for PIE with N hxigm , Zand ξ as free parameters results in values for N hxigm and cor-relation with redshift comparable to the mean IGM densitymodel (the top-left panel of Fig. 5). The data points appear toshow less dispersion and are marginally below the mean IGMdensity model at higher redshift z > , though with large er-ror bars. A power law fit to the N hxigm versus redshift trendscales as (1 + z ) . ± . , flatter than for CIE. The reduced χ MNRAS , 1–17 (2015)
T. Dalton et al
Figure 4.
Results of the IGM parameters using the CIE ( hotabs ) model . The error bars are reported with a confidence interval. Thegreen line is the simple IGM model using a mean IGM density. Top-left panel is N hx and redshift. Top-right panel is [X/H] and redshift.Bottom-left panel is temperature and redshift. Bottom-right panel is [ X / H ] and N hx . The orange line is the 1 sigma χ fit. We do notinclude a χ curve in the temperature-redshift plot, or the [ X / H] and N hx plot as the fit was poor due to a large scatter and error bars. of 0.67 indicates a reasonable fit. Only 2 GRB failed to befit in xspec out of our sample of 32. The mean hydrogendensity at z = from the sample is n = . + . − . × − cm − ,providing a similar constraint on the IGM density parame-ter to our CIE model. It is notable that the lowest redshiftGRB140430A z = . in our sample has a best fit N hxigm again considerably higher than the mean density curve, sim-ilar to the CIE model. Again, this could indicate a highermetallicity absorber along the LOS.Fig. 5 top-right panel is a plot of [ X / H ] versus redshiftwith a trend scaling as (1 + z ) − . ± . . The reduced χ of 1.84indicates a reasonable linear fit. The metallicity is approx-imately [ X / H ] ∼ − . . Z (cid:12) ) at z ∼ falling to [ X / H ] ∼− . . Z (cid:12) ) at z > . At higher redshift, the average LOSmetallicity value appears to decline more rapidly, but withlarge error bars. This could suggest that there was very lit-tle higher metallicity aborption at those redshifts. However,there are very few high redshift GRB in the sample.There is a large range in the fitted ionisation parameter . < log( ξ ) < . , with substantial error bars in Fig. 5(bottom left). The mean ionisation parameter over the fullredshift range is log( ξ ) = . + . − . . We note that these valuesare the LOS average and not representative of any individualabsorber or redshift. As discussed in Section 2, we use Cstat minimization due tosmall number of photon counts, well into the Poisson regime.Thus, χ and AIC are inappropriate. If the model improve-ment criteria is any improvement in Cstat when comparedwith the model with all excess absorption over Galactic as-sumed at the host redshift, then 26/30 CIE, 23/30 PIE, 27/30combined show improvements. Approximating a χ criterion,some authors consider fits to be significantly improved by theaddition of a component if Cstat > . for each extra freeparameter e.g. (Ricci et al. 2017). Our IGM inclusive xspec models have 2 extra free parameters, so the test would beCstat > . . Using this criterion, 12/30 for CIE and 9/30are significantly improved, combined 15/30.In conclusion, with the same caveats as for CIE, there arereasonable grounds for arguing that the PIE model using warmabs is plausible for modelling the cool diffuse IGM.The results are similar to the mean hydrogen density of n = . × − cm − . The PIE model results show a declinewith redshift in the average metallicty values along the in-tegrated LOS. The ionisation range and mean are consistentwith the expected values from simulations. It is not possibleto conclude whether PIE or CIE is the better single model forthe IGM at all redshift. From the outset, it was noted thata combined model is likely but this requires better data. The MNRAS , 1–17 (2015) robing IGM properties using GRB Figure 5.
Results for the PIE IGM parameters using PIE ( warmabs ) models. The error bars are reported with a confidence interval.The green line in the top-left panel is the simple IGM model using a mean IGM density. Top-left panel is N hx and redshift. Top-rightpanel is [ X / H] and redshift. Bottom-left panel is ionisation parameter and redshift. Bottom-right panel is [ X / H and N hx . The orange lineis the χ fit. We do not include a χ curve in the ionisation-redshift plot , or the [ X / H] and N hx plot as the fit was poor due to a largescatter. results may indicate that we are seeing different IGM phasesalong the LOS, though we are examining the extremes of CIEan PIE models separately. In both CIE and PIE IGM scenarios, the IGM is highlyionised with either high temperatures or high ionisation pa-rameters. We find that under both scenarios for the IGM, theaverage metallicity along the LOS declines with redshift, withthe caveat that we are using a cumulative LOS absorption.The decline in average metallicity is less in the PIE model.It may be that at lower redshift regions of higher metallicitysuch as the WHIM may be dominant, while at higher red-shift, the diffuse cool IGM becomes dominant, diluting theaverage metallicity, but we would require a combined CIE/PIE model to establish this. Fixing metallicity to any valuegave poor and unreliable results (see Appendix A). Most prior studies were based on simplistic assumptions of solar metal-licity, and all absorption in excess of our Galaxy being atthe host redshift(e.g. Behar et al. 2011; Campana et al. 2010,2012). Further, the absorber was assumed to be neutral. Laterstudies used absori which has only 10 metals, and only Fevariable (Starling et al. 2013; Campana et al. 2015). The useof solar metalicity leads to underestimate of column density,while the assumption of all excess absorption at the host red-shift leads to overestimation of the column density.Our analysis, using the more sophisticated models for PIEand CIE, shows that substantially higher metallicity is in-dicated at lower redshifts compared to higher redshifts. Asnoted in more detail in Sections 1 and 3, there is some consen-sus for the diffuse cool IGM metallicity with redshifts z = − at Z = . Z (cid:12) ( [ X / H ] = − , but with little or no observedevolution. However, these are either in Ly α forest regions ormore dense systems such as LLSs or DLAs (e.g. S03, A08,F14, F16). At lower redshift z = − , in the WHIM and theICM, there is some consensus that the predicted mean metal- MNRAS , 1–17 (2015) T. Dalton et al licity is Z ∼ . Z (cid:12) (e.g. Wiersma et al. 2011; Danforth et al.2016, S12), though it is unlikely that many GRB LOS piercethe ICM. Our CIE and PIE models in Section 4 show thatregardless of the IGM model, both CIE and PIE are pickingup substantial absorption by highly ionised absorbers. Thisuse of sophisticated ionised absorber models for GRB has notbeen completed previously.Campana et al. (2015) completed simulations of IGM ab-sorption using GRBs and quasars. For GRBs, their simula-tions indicated that the LOS does not contain any absorberswith over-density ∆ > , log ( T / K) ∼ − and mean metal-licity Z = . Z (cid:12) . As we are tracing the full LOS and not anyindividual absorber, we cannot compare our results directlywith Campana et al. (2015) in terms of overdensities. Theirresult for temperature range is consistent with ours for theCIE model. However, we find that a decline in metallicityis observed in both CIE and PIE scenarios for the IGM. Incontrast, using AGNs, their simulations showed prevalenceof absorption systems with large over-densities ( ∆ > at z ∼ . − . , temperature of ∼ (3 − × K and mean metal-licity in these regions of Z = . ± . Z (cid:12) . We would agree withtheir speculation that it is unlikely that GRB trace differentLOS to AGN through the diffuse IGM and that therefore,these large overdensities and high metallicity may be proxi-mate to the AGNs, e.g. in their CGM.Behar et al. (2011) noted that in their GRB sample theobserved opacity at low energies, while high at low redshift,tended toward an asymptotic value at z ∼ . They interpretedthis as possible evidence for the detection of absorption bya diffuse, highly ionized intergalactic medium. This interpre-tation would solve the problems of the lack of correlationobserved between the N hx and N h i in GRB afterglows, andthe very low apparent dust-to-metals ratios. Rahin & Behar(2019) extended this earlier work to include all GRB up to2019 and found very similar results.There have been some claims in recent years to have foundthe missing baryons in the WHIM using different tracers. Wenow compare our work with some of these studies. Arcodiaet al. (2018) used blazars as potential IGM absorption tracers.They modelled IGM absorption using igmabs in xspec . Thisis based on absori , with solar abundance and limited numberof metals. Only 4 blazars were fitted. Their resulting average n = . + . − . cm − is lower than our result. Their temperaturelog( T /K) = . + . − . and ionisation log ( ξ ) = . ± . (notelog ( ξ ) was tied to n ) are consistent with our results. Theyderived a value of Z IGM = . + . − . Z (cid:12) based on an average IGMdensity from their fittings, as compared to n = . × − cm − which is substantially higher than our results but they notedthis should only be viewed as a consistency check.Macquart et al. (2020) used FRB dispersion measure (DM)to measure the total electron column density on the LOS tothe FRB host. Their sample is limited to 5 FRB in the red-shift range 0.12 to 0.52. To isolate the possible IGM compo-nent, they fix the Galactic DM to values measured by Cordes& Lazio (2002) with an additional fixed component to rep-resent the Galactic halo of 50 pc cm − . They also assumed afixed FRB host at DM host = / (1 + z ) pc cm − . They add thatfurther analysis of their sample mildly favors a median hostgalaxy contribution of ∼ pc cm − with a factor of two dis-persion around this value. This is the conventional approachin FRB i.e. to fix the FRB host DM with the assumption thatall excess DM is then due to the IGM. This is very different to the traditional GRB approach of assuming all absorptionin excess of our Galaxy is at the host redshift. Their result-ing baryon fraction is a median value of Ω b h = . and a confidence interval spanning [0 . , . . Based on thisresult they claim that their FRB DM measurements confirmthe presence of baryons with the density estimated from theCMB and Big Bang Nucleosynthesis, and are consistent withall the missing baryons being present in the ionized inter-galactic medium. Our median value for the baryon fractionfor both CIE and PIE models is Ω b h = . and a confi-dence interval spanning [0 . , . (CIE) and [0 . , . (PIE) which is consistent with their results. Their approachto fixing the host DM component is also analogous to ourapproach with GRB.Nicastro et al. (2018) claim to have observed the WHIMin absorption. Only 1 to 2 strong O vii absorbers are pre-dicted to exist per unit redshift. Nicastro et al. (2018) re-ported observations of two O vii systems. System 1 ( z = . )had T = . + . − . × K, N hxigm = . + . − . / ( Z / Z (cid:12) ) × cm − .System 2 ( z = . ) had T = . + . − . × K, N hxigm = . + . − . / ( Z / Z (cid:12) ) × cm − . With Z = . Z (cid:12) , and with an av-erage of 1.5 systems per unit redshift, this gives N hxigm ∼ . × cm − for z ∼ . While the temperatures are con-sistent with our results, the column densities are an orderof magnitude lower than our results and that of (Arcodiaet al. 2018) and (Macquart et al. 2020) for blazars and FRBrespectively. This could be interpreted as supporting the con-tribution of the IGM to absorption over and above individualstrong WHIM absorbers.It is not possible at present to detect the individual fila-ments using the thermal Sunyaev–Zeldovich (tSZ) effect asthe signal is much smaller than both the noise in the lat-est CMB experiments, and compared to the sensitivity ofPlanck. Tanimura et al. (2020, hereafter T20) used gas fila-ments between the Luminous Red Galaxy (LRG) pairs rely-ing on stacking the individual frequency maps for 88000 pairsin the low redshift range z < . . The stacking removes theCMB component while the dust foreground becomes homo-geneous. Their stacked tSQZ signal, with an assumed tem-perature of × K for the filaments, gives an electron over-density of ∼ , based on electron number density today tobe n e = . × − cm − . This is consistent with (Cen & Os-triker 2006) and M19 simulations for the WHIM. Our resultsfor the mean density and temperature ranges in the CIE sce-nario are consistent with these results, with the caveat thatthe IGM slab in our model is placed at half the GRB redshifti.e. at much higher redshifts than the T20 sample.While there are GRB at low redshift with high N hx , thebulk of low redshift GRB are consistent with our work. Themean NHX (revised for Z = . Z (cid:12) or actual metallicity, dust-corrected if available) for z < taken from D20 is . × cm − . GRB N h i do not show any relation with redshift. Themean for a sample again from D20 with z < is . × cm − . Following our method of approximating the GRB hostcolumn density as equal to N h i , this leaves only a smallabsorption difference . × cm − . At z ∼ . , the meanIGM from our work is ∼ . × cm − .Some GRB at low redshift have very high X-ray absorptione.g. GRB190114C. The host-galaxy system of GRB190114Cis composed of two galaxies, a close pair merger system(Postigo et al. 2020). Drawing from their observations, thereare several possible factors which may explain the very high MNRAS , 1–17 (2015) robing IGM properties using GRB intrinsic N hx in this low redshift GRB. The GRB explodedwithin the central cluster of the host galaxy, where the densityis higher, at a projected distance of ∼ pc from the core.The GRB location is indicative of a denser environment thantypically observed for GRBs.The host system stellar mass isan order of magnitude higher than the median value of GRBhosts at < z < as measured for the BAT6 host sample.Finally,the GRB host has a much higher metallicity at 0.43than the average GRB host at 0.07 from D20.Our results show that substantial absorption probably oc-curs in the IGM in both the PIE and CIE scenarios. Most fitshave consistently, if marginally better Cstat results comparedto the simple model with all excess absorption occurring atthe GRB host redshift. We would argue that while some ex-cess absorption is attributable to the GRB host, and that bet-ter host models may identify this host excess absorption, theIGM contributes substantially to the total absorption seen inGRB spectra, and that it indeed rises with redshift. This IGMabsorption at least partly explains why N hxigm seen in GRBfull LOS afterglow spectra is substantially in excess of the in-trinsic N h i in GRB hosts. However, the CGM in the GRBhost may also contribute to the N hxigm , and future mod-els incorporating more advanced modelling for a warm/hotCGM component in GRB hosts are needed to explore therelative contribution of the IGM and the host CGM to theobserved absorption. The main aim of this paper is to probe the key parametersof density, metallicity, temperature and photo-ionisation ofthe IGM using sophisticated software models for the ionisedplasma. We use spectra from
Swift for GRBs as our tracerswith a redshift range of . ≤ z ≤ . . We isolated the IGMLOS contribution to the total absorption for the GRBs byassuming that the GRB host absorption is equal to ionisedcorrected intrinsic neutral column N h i,ic estimated from theLy α host absorption. We use more realistic host metallic-ity, dust corrected where available in generating the host ab-sorption model. We model the IGM assuming a thin uniformplane parallel slab geometry in thermal and ionization equi-librium to represent a LOS through a homogeneous isother-mal medium. We use xspec fitting with steppar and MCMCto generate best fits to the GRB spectra. Our work uses thecontinuum total absorption to model plasma as opposed tofitting individual line absorption as the required resolution isnot available currently in X-ray. We set the xspec metallicityparameter range as − < [ X / H ] < − . ( . < Z / Z (cid:12) < . ,with temperature for CIE at < log ( T / K) < and ionisationparameter between ≤ log( ξ ) ≤ . The CIB photon index isfixed at 2.Our main findings and conclusions are:(i) Modelling the IGM using hotabs for CIE with parame-ters N hx , Z and T free appears to present plausible results for N hxigm with an equivalent mean hydrogen density at z = of n = . + . − . × − cm − . It shows similar values and corre-lation with redshift as the mean IGM density model, Fig. 4top-left panel. A power law fit to the N hxigm versus redshifttrend scales as (1 + z ) . ± . .(ii) A power law fit to the [ X / H ] and redshift trend forCIE scales as (1 + z ) − . ± . , Fig. 4 top-right panel. Metallicity ranges from [ X / H] = − Z = . Z (cid:12) ) at z ∼ to [ X / H] ∼− Z = . Z (cid:12) ) at high redshift z > . This could suggestthat at low redshift, the higher metallicity warm-hot phaseis dominant with Z ∼ . Z (cid:12) , while at higher redshift the lowmetallicity IGM away from knots and filaments is dominant.(iii) The CIE temperature range is . < log ( T / K ) < . ,Fig. 4 bottom-left panel indicating that very highly ionisedmetals are prominent absorbers over the LOS. The mean tem-perature over the full redshift range is log ( T / K ) = . + . − . .These values are consistent with the generally acceptedWHIM range and with the latest simulations.(iv) Modelling the IGM using warmabs for PIE with N hxigm , Z and ξ as free parameters appears to present plau-sible results though with more scatter at lower redshift com-pared to our CIE model . The PIE N hxigm shows valuesand rise with redshift comparable to the mean IGM hydro-gen density model in Fig. 5 top-left panel. A power law fit tothe N hxigm versus redshift trend scales as (1 + z ) . ± . , a muchflatter power law than for CIE. The mean hydrogen densityequivalent from this model at z = is n = . + . − . × − cm − ,very similar to the CIE result.(v) In the PIE scenario, there is a power law fit to the [ X / H ] and redshift trend scaling as (1 + z ) − . ± . , a slowerdecline than under the CIE IGM model. The metallicity isapproximately [ X / H ] = − . Z = . Z (cid:12) ) at z ∼ falling to [ X / H] = − . Z = . Z (cid:12) ) at z > .(vi) The PIE ionisation parameter range from fits is . < log ( ξ ) < . , Fig. 5 bottom-left panel. The mean ionisationparameter over the full redshift range is log ( ξ ) = . + . − . .(vii) Regardless of the assumed ionisation state of theIGM, both models pick up considerable highly ionised ab-sorption.(viii) We compared our CIE model with absori in Ap-pendix A which was generally used in prior studies usingGRBs as IGM tracers. absori is limited with only 10 metals,all fixed to solar metallicity except Fe. Our CIE and PIE IGMmodels use software which include all metals and ionisationspecies up to Z ≤ , with variable metallicity. In conclusion, absori is no longer a preferred model for IGM absorptionand the results of earlier studies using it for IGM modellingmay not be reliable.(ix) All our GRB spectra have fits as good as or betterthan the model with all excess absorption assumed to occur atthe GRB host redshift. While some excess absorption may beattributable to the GRB host and its CGM, in our models theIGM contributes substantially to the total absorption seen inGRB spectra, and it rises with redshift. We provide clearevidence that a complete model should also account for a(possibly dominant) fraction of intervening IGM material.This study is based on observations of GRB X-ray spectra,and provides results on the IGM parameters. The constraintswill only be validated when observations are available frominstruments with large effective area, high energy resolution,and a low energy threshold in the soft X-ray energy band e.g.Athena which will study the IGM through detailed observa-tions of O vii and O viii absorption features with equivalentwidth > . eV and > . eV respectively. MNRAS , 1–17 (2015) T. Dalton et al
ACKNOWLEDGEMENTS
We thank the reviewer, Darach Watson for his valuable andconstructive feedback, which contributed to improving thequality of this paper. We thank T. Kallman and K. Arnaudfor assistance with warmabs , hotabs and xspec , and E.Gatuzz with ioneq . S.L. Morris also acknowledges supportfrom STFC (ST/P000541/1). This project has received fund-ing from the European Research Council (ERC) under theEuropean Union’s Horizon 2020 research and innovation pro-gramme (grant agreement No 757535) and by FondazioneCariplo (grant No 2018-2329). DATA AVAILABILITY
Supplementary data containing the results for the IGM prop-erties from fitting the GRB spectra with the PIE and CIEmodel components, and the transmission plots for the CIEand PIE models with different IGM parameter examples areavailable in the online supplementary material. For access toother data in this work, please contact Tony Dalton.
REFERENCES
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SUPPORTING INFORMATION
Supplementary data containing the results for the IGM prop-erties from fitting the GRB spectra with the PIE and CIEmodel components, and the transmission plots for the CIEand PIE models with different IGM parameter examples areavailable at MNRAS online.
MNRAS , 1–17 (2015) T. Dalton et al
APPENDIX A: MODEL COMPARISONS ANDINVESTIGATING ROBUSTNESS OF CIE AND PIE FREEPARAMETER FITSA1 Metallicity fixed to Z = . Z (cid:12) To test the selected PIE and CIE models, we conducted trialsfreezing one key parameter at a time. We limited the sampledata size to 15 covering the full redshift range . − . . Forthe first trial we froze the metallicity of the IGM to Z = . Z (cid:12) as representative of the diffuse IGM. Most studiesof the cooler PIE IGM in Ly α regions found virtually noevidence for metallicity evolution in the range z ∼ − (e.g.S03, A08) so it is reasonable to test this scenario. The greenline for all models is the mean density of the IGM based onthe simple model from eq. 1. A1.1 warmabs (PIE)
In Fig. A1 left, the expected increase of N hxigm with redshiftdoes not arise with warmabs when the metallicity is frozen to Z = . Z (cid:12) . The low redshift N hxigm is substantially higherthan the expected mean IGM density, while at higher red-shifts it is below the IGM mean density. This could indicatethat a fixed metallicity assumption is unrealistic, or the PIEmodel is not appropriate for the LOS to the GRB. In Fig. A1middle panel, we see a wide range of ionisation parameterswith substantial error bars at lower redshift. There appearsto be a negative trend with redshift, though this may be dueto the metallicity being fixed.Fig. A1 right panel shows an example of the a MCMCintegrated probability plot for the warmabs PIE N hxigm and ξ . Most MCMC integrated probability plots are reasonablyconsistent with steppar , indicating a good fit with low Cstat,but some are not. In this example, there are a few islands ofhigh probability. As for several of the GRB, its shows thatthe best fit could have occurred at the low or high end of theconfidence range. In conclusion, primarily due to the result forcolumn density, it is likely, that a fixed metallicity warmabsbased PIE model for the IGM is not realistic. A1.2 hotabs (CIE)
Similar to the warmabs
PIE model, the expected increaseof N hxigm with redshift in Fig. A2 left panel does not arisewith hotabs when the metallicity is frozen to Z = . Z (cid:12) .This could indicate that a fixed metallicity assumption is un-realistic, or that the CIE model is not appropriate. Again,at low redshift, the N hxigm is much greater than the meandensity model, while at high redshift it is much lower. Theerror bars are very large. In Fig. A2 middle panel, we see awide range of temperatures with substantial error bars. Thebest fit data points appear to favour either the high or lowend of the confidence range. Finally, Fig. A2 right panelshows an example of the MCMC integrated probability plotfor the hotabs CIE N hxigm and T. In this example, thereis a characteristic S shape where, at high column density, arange of temperatures at a similar column density could fit,while at low temperature, there is a different range of columndensities that could fit. There is a single high maximum butthere are a couple of islands of 1 sigma probability. In conclusion, it is likely, that a fixed metallicity hotabs based CIE model for the IGM is not realistic. A1.3 ioneq (CIE)
Modelling the IGM using ioneq with a fixed metallicity ap-pears to present plausible results for N hxigm in Fig. A3 leftpanel, showing a similar rise with redshift as the mean IGMdensity model, except at very high redshift. A power law fitto the N hxigm versus redshift trend scales as (1 + z ) . ± . . Wenote that all metals included in the ioneq model, except O,Ne and Fe, are fixed to the solar abundance, an unrealisticvalue for the diffuse IGM. ioneq is currently being updatedto allow all metals as free parameters but was not availablefor this paper (Gatuzz, E., private communication). As with hotabs , the error bars on temperature with redshift in Fig.A3 middle panel are substantial, but the best fits do notfavour the high or low end of the confidence interval.Most MCMC integrated probability plots for ioneq fit-tings show large degeneracy as seen in the example in Fig.A3 right panel, with many local maxima. The Cstat fits tothe GRB spectra are as good as for warmabs and hotabs .In conclusion, the plots suggest that a CIE IGM model withfixed metallicity of Z = Z . (cid:12) may be plausible. However,due to the MCMC showing substantial degeneracies, and theunrealistic solar metallicities, we have not used this model. A1.4 absori
Fig. A4 left panel shows the results for N hxigm using ab-sori for the IGM absorption with metallicity fixed again at Z = . Z (cid:12) . In absori , only Fe is affected as the other 9metals in the model are fixed to solar. The ionisation param-eter was fixed at ξ = , so only temperature was allowed tovary as a CIE model. The fits were very poor, errors couldnot be generated in xspec , and the MCMC runs failed togenerate plausible results. No apparent redshift correlationcan be seen, similar to warmabs and hotabs . Due to thepoor fits, it cannot be said whether this is due to the absori model being limited to 10 metals, having all metals, exceptFe at solar, edge absorption only or the model not being self-consistent. Fig A4 right panel shows the IGM temperaturesfrom the fittings. As with all models, it shows a large scatter.In conclusion, absori is no longer an ideal model for IGMabsorption.In summary, warmabs and hotabs are the most sophis-ticated models, and the MCMC integrated probability plotswere the most consistent with the steppar results and haveplausible integrated probability plots. Most show a singledeep maximun, but there is degeneracy with several possibleparameter fit solutions. Accordingly, we decided to proceedonly with warmabs and hotabs , and not ioneq nor absori for the remaining tests. However, the fixing of metallicity forboth PIE and CIE IGM models with redshift is not appro-priate for any model. MNRAS , 1–17 (2015) robing IGM properties using GRB Figure A1.
Results for the IGM parameters using the PIE warmabs model with Z = . Z (cid:12) . The error bars are reported with a confidence interval. Left panel is N hx and redshift. The green line is the simple IGM model using the mean IGM density. Middle panel isionisation parameter versus redshift. Right panel is an example of an integrated MCMC plot. The red, green and blue contours represent , and ranges for the two parameters respectively, with grey-scale showing increasing integrated probability from dark to light.On the y-axis rlogxi = log ( ξ ) . Figure A2.
Results for the IGM parameters using the CIE hotabs model with Z = . (cid:12) CIE Z=0.01. The error bars are reported with a confidence interval. Left panel is N hx and redshift. The green line is the simple IGM model using the mean IGM density. Middlepanel is temperature versus redshift. Right panel is an example of an integrated MCMC plot. The red, green and blue contours represent , and ranges for the two parameters respectively, with grey-scale showing increasing integrated probability from dark to light.On the y-axis in the bottom-left panel T4 means the log of the temperature is in units of 10 K. Figure A3.
Results for the IGM parameters using the ioneq
CIE model with IGM Z = . (cid:12) . The error bars are reported with a confidence interval. Left panel is N hx and redshift. The green line is the simple IGM model using the mean IGM density. Middle panel istemperature versus redshift. Right panel is an example of an integrated MCMC plot. The red, green and blue contours represent , and ranges for the two parameters respectively, with grey-scale showing increasing integrated probability from dark to light. A2 Forcing N HXIGM to equal the mean IGM density
The next approach investigated was to freeze the N hxigm parameter at the value for mean IGM density integrated tothe GRB redshift using eq.1 . Metallicity and ionisation pa-rameters (PIE) or temperature (CIE) were free.For both PIE and CIE, nearly all fits were consistent with steppar and showed good integrated probability plots. Thereis a requirement for strong metallicity evolution in both sce-narios with power law fits to the [ X / H ] versus redshift trendscaling as (1 + z ) − . ± . and (1 + z ) − . ± . for PIE (Fig. A5 top-left panel) and CIE (Fig. A5 bottom-left panel) respectively.The confidence range was much improved for the [ X / H ] fits as compared with the fixed metallicity scenario fits for N hxigm . The ionisation parameter for the PIE fits variedwidely between < log ( ξ ) < without any simple trend withredshift. The temperature parameter for the CIE fits also var-ied widely between < log ( T / K) < . without any simpletrend with redshift.Fig. A6 shows two examples of MCMC integrated probabil-ity plots for the CIE scenario. Both show the patterns thatmost GRB showed in this scenario of N hxigm fixed to themean density where at high temperature, a range of metal-licity could fit, while at low metallicity, there is a range oftemperature that could fit.In conclusion, if the scenario where the average densitymodel of the IGM is valid for the GRB sight lines, it re- MNRAS , 1–17 (2015) T. Dalton et al
Figure A4.
Results for the IGM parameters using the absori
CIE model with the IGM Z = . (cid:12) . Left panel is N hx and redshift. The greenline is the simple IGM model using the mean IGM density. Right panel is temperature and redshift. No error bars could be generated by xpec . Figure A5.
Results for the IGM parameters with N hxigm fixed at the mean IGM density. The error bars are reported with a confidenceinterval. Top-left panel is [ X / H ] versus redshift for the PIE model. Top-right panel is ionisation versus redshift for PIE. Bottom-left panelis the CIE model [ X / H ] versus redshift. Bottom-right panel is log ( T / K) versus redshift for CIE. The orange line is the χ fit. We do notinclude a χ curve in the temperature-redshift plot (bottom-right) as the fit had very large uncertainties. Figure A6.
Sample MCMC integrated probability plots with hotabs CIE IGM for two GRB with N hxigm equal to the mean density. Thered, green and blue contours represent , and ranges for the two parameters respectively, with grey-scale showing increasingintegrated probability from dark to light. On the x-axis T4 means the log of the temperature is in units of 10 K. On the y-axis all metalsare tied to the Z / Z (cid:12) for Carbon.MNRAS , 1–17 (2015) robing IGM properties using GRB quires strong metallicity evolution for both CIE and PIE. Itis not possible to determine which scenario (CIE versus PIE)is more plausible from the fits apart from the fact that thehigh redshift z = . GRB140505 was well fitted with CIEbut not with PIE. The results support the Section 4 free pa-rameter fit model scenarios for both PIE snd CIE IGM andcould be interpreted as validity check.
A3 Freezing temperature for CIE and ionisation parameterfor PIE
The next test was to freeze temperature for CIE and ioni-sation parameter for PIE and leave N hxigm and metallicityfree. For temperature in the CIE hotabs model, we frozetemperature at log ( T /K) = 5 and 6 as representative of thecooler and hotter CIE phases.The fits for N hxgm with temperature fixed at log ( T / K ) = ,are much lower than the mean IGM model in Fig. A7 top-leftpanel, with considerable scatter. In Fig. A7 top-right panelwith log ( T / K ) = , some fits are similar to the mean IGMmodel and show a suggestion of a rise with redshift withsome outliers. However, several are well below the mean den-sity. The metallicity plots for both fixed temperatures showno apparent relation with redshift. The higher temperaturelog ( T / K ) = CIE model appears more realistic if the IGMmean density model is appropriate for the IGM. However,it is unlikely that a fixed average temperature approach isappropriate for our CIE IGM modelling.For PIE, the ionisation parameter was frozen at log( ξ ) = 1and 2. At both log( ξ ) = 1 and 2, there is a possible N hxigm rise with redshift in Fig. A8 top-left and right panels. Further,the fits for both are similar to the mean density model, withlog( ξ ) = 2 being closer. There is a suggestion of metallicityevolution at log( ξ ) = 2. It is not possible to say whetherfreezing ionisation parameter is a reasonable approach butthe fits and overall results for log( ξ ) = are better, withlower Cstat.In summary, freezing the ionisation parameter gives some-what more plausible results in the PIE scenarios than theCIE scenarios with fixed temperatures. However, overall, thescenarios with such fixed parameters are not preferred andtherefore, we suggest that our free parameter IGM scenariosare more realistic in Section 4.The warmabs and hotabs models are more sophisticatedthan the current version of ioneq and absori , again sup-porting our model choices in Section 4. This paper has been typeset from a TEX/L A TEX file prepared bythe author. MNRAS , 1–17 (2015) T. Dalton et al
Figure A7.
Results for the IGM parameters using the hotabs
CIE model with fixed temperatures. The green curve is the simple IGMmodel using the mean IGM density. Top-left panel is N hxigm versus redshift and bottom-left panel is [ X / H ] versus redshift for the CIEmodel with log ( T / K ) = . Top-right panel is N hxigm versus redshift and bottom-right panel is [ X / H ] versus redshift for the CIE modelwith log ( T / K ) = . We do not include error bars as the plots are not plausible models. Figure A8.
Results for the IGM parameters using the warmabs
PIE model with fixed ionisation parameters. The green curve is the simpleIGM model using the mean IGM density. Top-left panel is N hxigm and redshift and bottom-left panel is [ X / H ] and redshift for the PIEmodel with log ( ξ ) = . Top-right panel is N hxigm and redshift and bottom-right panel is [ X / H ] and redshift for the PIE model withlog ( ξ ) = . We do not include error bars as the plots are not meant to be representative of plausible models.MNRAS000