Draft version February 13, 2019Preprint typeset using LATEX style emulateapj v. 12/16/11

THE SOURCES OF EXTREME ULTRAVIOLET AND SOFT X-RAY BACKGROUNDS

Phoebe R. Upton Sanderbeck1, Matthew McQuinn 1, Anson D’Aloisio1,2, Jessica K. Werk1

Draft version February 13, 2019

ABSTRACT

Radiation in the extreme ultraviolet (EUV) and soft X-ray holds clues to the location of the missingbaryons, the energetics in stellar feedback processes, and the cosmic enrichment history. Additionally,EUV and soft X-ray photons help determine the ionization state of most intergalactic and circumgalac-tic metals, shaping the rate at which cosmic gas cools. Unfortunately, this band is extremely difficultto probe observationally due to absorption from the Galaxy. In this paper, we model the contributionsof various sources to the cosmic EUV and soft X-ray backgrounds. We bracket the contribution from(1) quasars, (2) X-ray binaries, (3) hot interstellar gas, (4) circumgalactic gas, (5) virialized gas, and(6) super-soft sources, developing models that extrapolate into these bands using both empirical andtheoretical inputs. While quasars are traditionally assumed to dominate these backgrounds, we dis-cuss the substantial uncertainty in their contribution. Furthermore, we find that hot intrahalo gaseslikely emit an O(1) fraction of this radiation at low redshifts, and that interstellar and circumgalacticemission potentially contribute tens of percent to these backgrounds at all redshifts. We estimatethat uncertainties in the angular-averaged background intensity impact the ionization corrections forcommon circumgalactic and intergalactic metal absorption lines by ≈ 0.3− 1 dex, and we show thatlocal emissions are comparable to the cosmic background only at rprox = 10 − 100 kpc from MilkyWay-like galaxies.

1. INTRODUCTION

The extreme ultraviolet (EUV) through soft X-ray rep-resent a slice of the electromagnetic spectrum that is dif-ficult to observe in astronomical spectra. Not only mustit be observed from above Earth’s atmosphere, but forextragalactic sources much of this slice is absorbed bythe Galaxy. Yet, because most transitions to groundRydberg states of ions fall in this band and, hence,most cooling emissions, the EUV/soft X-ray extragalac-tic background holds clues into the location of the miss-ing baryons, the energetics in stellar feedback processes,and the cosmic enrichment history. The lack of observa-tions in this band complicates inferences from observableionic transitions because these backgrounds often shapethe ionic ratios of diffuse astrophysical gases.

AGN, or more specifically the brightest of these,quasars, are thought to be the dominate extragalacticsource for radiation in the EUV and soft X-ray, especiallyat z . 3 (Meiksin & Madau 1993; Madau et al. 1999;Faucher-Giguere et al. 2008; Haardt & Madau 2012).3

However, quasars’ spectral energy distributions (SEDs)have only been measured at frequencies redward of ∼ 25eV (e.g. Telfer et al. 2002), and current theoretical mod-els are likely not successful enough to motivate extrapola-tions to the soft X-ray. Thus, models for quasar spectraextrapolate with a single power-law between the EUVand soft X-ray, even though the quasar SED is certainlymore complex (Bechtold et al. 1987; Laor et al. 1997;

1 Department of Astronomy, University of Washington

2 Department of Physics and Astronomy, University ofCalifornia, Riverside

3 Starlight is an important contribution at 1−4Ry in some mod-els (and dominant at lower energies), with its relative importancedepending on how efficiently these photons can escape from galax-ies.

Done et al. 2012).Quasars are not the only source that may contribute

substantially to this critical waveband: X-ray bina-ries (XRBs), cooling gases (104-107 K) in the interstel-lar medium of galaxies (ISM) and the circumgalacticmedium (CGM) that surrounds them, and virialized halogas may also substantially contribute. Indeed, XRBstend to dominate galactic X-ray emissions at & 1 keV,while at lower energies radiative cooling from the hotISM in galaxies is thought to become important (Grimeset al. 2005; Tullmann et al. 2006; Owen & Warwick 2009;Mineo et al. 2012b; Lehmer et al. 2015). This hot gasis the result of feedback from supernovae, massive starwinds, and radiation pressure (McKee & Ostriker 1977;Chevalier & Clegg 1985; Strickland et al. 2000). A signif-icant fraction of this feedback could also be radiated inthe surrounding CGM in addition to the hot ISM (e.g.,McQuinn & Werk 2017). Similarly, intrahalo gas thathas been shocked by virialization can also be important,especially with decreasing redshift as more massive and,hence, hotter systems form.

Many fields of study are reliant on models for the meta-galactic ionizing background. Such models are used inessentially all calculations of the ionization state of pho-toionized gas in the intergalactic medium (IGM) andCGM (for a recent review see McQuinn 2016; Tumlinsonet al. 2017), and they are used to set the ionization stateof gas in cosmological simulations (and, hence, shape therate at which simulated gas cools). However, previousionizing background models only considered the contri-bution of quasars in the EUV and soft X-ray, making thetypical simplifying assumptions to extrapolate from ob-served bands (Haardt & Madau 1996; Faucher-Giguereet al. 2009; Haardt & Madau 2012). Even if the back-ground is dominated by quasars, these models may notapply near galaxies (where they are most used), sincemany UV and X-ray sources are (circum)galactic in na-

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ture (Cantalupo 2010; Gnedin & Hollon 2012).This paper estimates the contribution of all source

classes that we are aware of that may emit substantiallyin the EUV and soft X-ray, in the process estimating theplausible range of z ∼ 0 and z ∼ 2 ultraviolet backgroundangular-averaged specific intensities, Jν . Section 2 esti-mates the emissivities of various EUV and soft X-raysources. Using these estimates, we model the relativecontribution of these sources to the ionizing backgroundin Section 3. Section 4 discusses the impact of the un-certainties in the background on the ionization of highlyionized metals. Finally, for galactic sources, we estimatethe size of the local enhancement expected around eachgalaxy in Section 5.

2. MODELING THE SOURCES

This section describes all the known sources that emitsubstantially in the UV and soft X-ray, developing mod-els for their specific emissivity across redshift. These cal-culations are then fed into calculations of the backgroundJν in Section 3.

2.1. Active galactic nuclei (AGN)

Quasars – highly luminous AGN – are likely the mostemissive sources in the EUV and soft X-ray. Yet, theiremissivity in this band is highly uncertain. Ultravioletobservations of quasar emissions can only be used to re-liably estimate the mean SED to wavelengths as shortas several hundred Angstroms (e.g. Telfer et al. 2002).A break is observed in the mean SED at λ ∼ 1000 A,with the spectrum softening blueward of this break. Thisbreak is commonly attributed to the innermost tempera-ture of the quasar’s accretion disk (‘the Big Blue Bump’;Shakura & Sunyaev 1973) and the transition of quasarspectra to Compton up-scattered radiation from a coro-nae (e.g. Czerny & Elvis 1987). However, thin accretiondisk plus corona models have limited success at describ-ing quasar spectra in the UV (Laor et al. 1997; Daviset al. 2007), which may be partly cured by invoking in-homogeneous temperatures (Dexter & Agol 2011) andopacity effects (Czerny & Elvis 1987). Additional tuningmust be added to achieve power law-like emission intothe soft X-ray as is observed (Bechtold et al. 1987; Laoret al. 1997): The disk emission almost certainly needs tobe Compton up-scattered by material distinct from thetraditional coronae. This could be accomplished by anoptically thick region around the disk interior at temper-atures of ∼ 0.2 keV (Done et al. 2012).

Because of these open issues, UV background mod-els have used, rather than theoretically-motivated tem-plates, simple power-laws estimated from quasar stacksto extrapolate to shorter wavelengths. These power-lawsfit stacked spectra blueward of the break at ∼ 1000 Aand redward of the highest energy where the SED canbe reliably estimated (∼ 500A). There is limited dynamicrange over which the power-law is fit. The Lusso et al.(2015) stacked SED is the solid turquoise curve in Fig-ure 1, with the cyan region highlighting the estimated1-σ errors. We have normalized the SED to the z = 0specific emissivity at 1 Ry as described below.

The effective power-law index of the quasar stacks,αQSO (see Equation 1), that analyses estimate variessignificantly, with Telfer et al. (2002) finding αQSO =

1.57±0.17 for their radio quiet sample, Shull et al. (2012)and Stevans et al. (2014) finding αQSO = 1.4 ± 0.2, andLusso et al. (2015) finding αQSO = 1.7 ± 0.6, with theirlarger error owing to analysis differences described below.These observations show rough consistency (althoughthey are discrepant with the lower luminosity sample ofScott et al. (2004), which finds αQSO = −0.6 ± 0.4).Lastly, photoionization calculations for the broad UVlines in these spectra favor somewhat softer spectra withαQSO ≈ 2 (Baskin et al. 2014; Lusso et al. 2015).

Lusso et al. (2015) pointed to several factors that re-sult in differences in the estimated αQSO from stack-ing. Especially for quasars at z ≥ 1, estimates for thestacked SED must correct for H i absorption from theIGM (with the Lyman series affecting λ < 1216 A andLyman-continuum λ < 912 A). The differences in howthis correction is done lead to some of the discrepanciesin the reported values and their uncertainties. In ad-dition, where the ∼ 1000A break wavelength is placedaffects the final slope, and many samples do not havemuch spectral coverage of this break. Finally, broad linefeatures are present in the stacks and so different choicesare made for how to fit the continuum underneath thelines.

A justification often given for extrapolating with a sin-gle power-law into the soft X-ray is that the spectral in-dices of Type 1 AGN required in the EUV is similar tothe spectral index needed to extrapolate to soft X-rayband, as well as the power-law index found in the soft X-ray (Laor et al. 1997). However, both in the UV and softX-ray, individual systems show broad dispersion in theirallowed index (although individual system inferences aredifficult in the UV owing to IGM absorption). In addi-tion, within the range of allowed mean spectral indices,there is no reason why there cannot be a softening fol-lowed by a hardening (indeed a soft spectrum followedby a hotter coronae spectra is seen in models such asDone et al. 2012) or vice versa (in the stacked SED, somequasars should harder and, hence, become more domi-nant at bluer wavelengths, hardening the spectrum).

Figure 1 shows the empirical estimates and extrapola-tion of quasar emissivity at z ∼ 0. For our calculation, weuse quasar emissivities reported at 1 Ry from Khaire &Srianand (2015) that is consistent with the mean Lyα for-est transmission (Fumagalli et al. 2017). These emissiv-ities are extrapolated from the g-band luminosity func-tion with the relation log εg = log ε912 + 0.487 (Khaire& Srianand 2015; Haardt & Madau 2012; Boyle et al.2000; Croom et al. 2004), and since the mean SED ismuch better known between these wavelengths – and thenormalization is essentially calibrated to match robustconstraints at 1 Ry from the Lyα forest – this extrapo-lation should not contribute significantly uncertainty.

We extrapolate from this emissivity at 1Ry with apower-law spectrum parametrized as

J(ν) = J0

(ν

ν1Ry

)−αQSO

. (1)

We vary αQSO between 1.1 and 2.3, the 1σ error bar ofLusso et al. (2015), a range shown by the dashed curvesin Figure 1. However, one cannot extrapolate all the wayto ≈ 1 keV with this spectrum unless it has αQSO ≈ 1.7(Laor et al. 1997) to be compatible with soft X-ray back-

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Quasar stack

Fig. 1.— Observations and stacks of the quasar specific emissiv-ities. The jagged turquoise solid curve shows the stacked quasarSED of Lusso et al. (2015), normalized to match the Khaire & Sri-anand (2015) specific emissivity at 1 Ry. Filled regions representthe range of allowed values. The solid line at 13.6− 800 eV is thefiducial power-law model with αQSO = 1.7. The Lusso et al. (2015)1σ upper and lower limits on αQSO are shown by the blue and reddashed lines. The inner pink shaded region represents the rangeof viable specific, which are tapered to 800eV to match soft X-rayobservations. The harder component above 800eV owes to coronalemission.

ground measurements discussed in § 3. We taper ourspectrum starting at 100 eV so that it converges to thesame point at 800 eV as if αQSO = 1.7. While our choiceshere are somewhat arbitrary, we believe it provides areasonable guess for the allowed range of quasar specificemissivities (motivated both by the error on UV extrapo-lations and the large theoretical uncertainty in the spec-tral form).

Above 800 eV, we assume the spectrum scales witha spectral index of α = 0.5. While 800 eV is on thelower side of the observations for where the harder coro-nal emission dominates, finding 1 − 2 keV (Laor et al.1997), this spectral index is characteristic of the coro-nae of radio loud quasars, and somewhat harder thanthat found for radio quiet ones (although H i absorptionadditionally acts to harden their spectrum; Laor et al.1997). The selected slope of α = 0.5 is a good fit to theslope found in the more detailed models for this com-ponent in Haardt & Madau (2012) and also to z = 0soft X-ray background measurements. However, our ta-pering to a single curve at > 800 eV, which is done tomatch the background intensity measurements in the softX-ray, should underestimate the uncertainty in εν(z) atthese energies. We justify not attempting to quantify theuncertainty > 800 eV because these higher energies areless important for this study.

2.2. X-ray binaries (XRBs)

The X-ray emission from galaxies is thought to be dom-inated by XRBs at > 1 keV. The galactic XRB emissionfrom high mass XRBs should trace the star formationrate – as their formation lags star formation episodes by

just tens of megayears – and low mass XRBs should tracestellar mass – as theirs can lag star formation by manygigayears. These correlations have been confirmed obser-vationally (Ranalli et al. 2003; Grimm et al. 2003; Gil-fanov et al. 2004; Hornschemeier et al. 2005; Lehmer et al.2010; Boroson et al. 2011; Mineo et al. 2012a; Zhang et al.2012). We use these correlations to relate the cosmicXRB emissivity with redshift to the observed star forma-tion rate density and stellar mass density. We approachthe XRB contribution to the EUV/soft X-ray from botha theoretical and an empirical standpoint, consideringtwo models:

Empirical Model— In this model, all X-ray emissiontraces either the star formation rate or the stellar mass(Lehmer et al. 2010). Low-mass XRBs are likely as im-portant as their high-mass counterpart in the averagegalaxy at z ∼ 0, though at z & 1 and in star forminggalaxies, high-mass XRBs dominate the X-ray emissionfrom XRBs. We allow the relationship between star for-mation rate and X-ray emission to account for temporaltrends that result from such things as increasing cos-mic metallicity.4 For high-mass XRBs (HMXBs), weuse the redshift-dependent relation constrained in Di-jkstra et al. (2012), parametrized as LX,0.5−8/SFR =[LX,0.5−8/SFR]z=0(1 + z)b, where LX,0.5−8 is the 0.5 −8 keV X-ray luminosity. Dijkstra et al. (2012) finds0 ≤ b ≤ 1.3, anchoring to the Mineo et al. (2012a)best fit of [LX,0.5−8/SFR]z=0 = 2.6 × 1039 erg s−1 (M�yr−1)−1. For the cosmic star formation rate density,we use the fit in Haardt & Madau (2012) derived fromrest-frame optical and UV observations.5 For low-massXRBs (LMXBs), we use a correlation between total stel-lar mass and X-ray luminosity, LX,0.5−8/M? ∼ 9 × 1028

erg s−1 (Gilfanov et al. 2004; Lehmer et al. 2010). We useWilkins et al. (2008) for the cosmic stellar mass densityas a function of redshift.

This model’s second ingredient is the XRB SED. Above300 eV the SED of galactic X-ray emission has been con-strained observationally. For the SED, we stack the spec-trum of four star-forming galaxy SEDs observed from0.3− 3 keV with Chandra/XMM-Newton (Lehmer et al.2015; Wik et al. 2014; Yukita et al. 2016). The stack iscomputed by averaging the specific luminosity per unitstar formation rate (SFR) of each galaxy, LX(ν)/SFR.However, the spectrum of XRBs is not constrained be-low 300 eV. To extrapolate, we model the XRB spec-trum as a simple power law in specific luminosity withαempirical = 0.7 (using the same conventions as withαQSO in eqn. 1). This slope is based on the scaling ofstacked X-ray emission – not just the four we use for ourempirical spectrum (Rephaeli et al. 1995; Swartz et al.2004).

The thick solid curves in Figure 2 (and later Fig. 3)show the resulting specific emissivity at z = 0 for the

4 Increasing metallicity is expected to decrease the number ofXRBs because metallicity increases mass loss from stellar winds,affecting binary separations, and because higher metallicity starshave larger radii, which increases Roche lobe overflow (Linden et al.2010). There is also observational evidence for X-ray flux scalinginversely with metallicity (Brorby et al. 2016).

5 The total SFR density that is often estimated is likely less ap-propriate because star formation enshrouded behind gas and dustis unlikely to produce EUV and soft X-ray photons that can escape.

4

stacked SED and αempirical = 0.7 models. Even amongthe four stacked galaxy spectra there is ∼ 1 dex scatterin LX(ν)/SFR, owing largely to scatter in the numberof ultra-luminous X-ray sources. An extremely crude es-timate of the error on the mean stack is shown by thehighlighted regions in Figure 2, which is the standarddeviation of the four spectra divided by

√Ngal − 1.

We note that much of the emission below 1 keV islikely from hot gas in the ISM and not XRBs. MostXRB’s emission is found to decline below 1 keV ratherthan have a flat power-law as our extrapolation assumes(because of their intrinsic spectrum and H i absorption),and the < 1 keV appears to owe to more diffuse sourcesas discussed in Section 2.4. Thus, our αempirical = 0.7model may be better conceived as an amalgam of XRBand hot ISM emission, where hot ISM takes over at lowerenergies and has a power law-like spectrum. We discussthe realism of this power-law extrapolation for ISM emis-sion in Section 2.4. In addition, the bounds we place onsuper soft sources in § 2.3 also are relevant to potentialsoft emissions from LMXBs.

Fragos++(2013) Model — We use the XRB populationsynthesis model of Fragos et al. (2013). It uses the XRBpopulation synthesis simulations StarTrack (Belczynskiet al. 2008), which are calibrated to observations ofXRBs at low redshift, and the semi-analytic galaxycatalog of Guo et al. (2011), which models the starformation and stellar metallicity histories. The assumedSED is based on samples of observations of both neutronstar and black hole XRBs. The overall shape of theirXRB SED does not change significantly with redshift,despite accounting for trends in metallicity and thefraction of LMXBs to HMXBs. Emissivities at high red-shift will be slightly enhanced relative to star formationrate density due to the lower metallicity of the stars inbinary systems. This reduces stellar winds and increasesRoche lobe overflow, increasing the number of XRBs,especially HMXBs. The spectrum falls off rapidly atenergies lower than a few hundred electron volts, dueboth to the XRB SED and interstellar/circumstellarabsorption associated with most XRBs. The dashedblue curve in Figure 2 shows this model, with the fainterblue band signifying their estimated uncertainties.

2.3. Super soft X-ray sources

Super soft X-ray sources (SSSs) are observed systemswith blackbody spectra that peak in the soft X-ray andthat are theorized to be compact binary systems with awhite dwarf accreting from either a main sequence star ora red giant and this accretion igniting on the surface (Ka-habka & van den Heuvel 1997; Greiner 2000). Accretiononto white dwarfs should be generic and such accretion isnecessary in a major progenitor scenario of Type 1a su-pernovae. Models find that the accretion should be ther-mally stable with rates of M ∼ 10−7M� yr−1 (Nomoto

et al. 2007). With such M , accreting white dwafs shouldemit substantially in the 0.1− 0.7 keV band. SSS couldincrease ISM photoheating rates enough to explain thehigher temperatures inferred from photoionized ISM ob-servations compared to models (Woods & Gilfanov 2013).

However, the number of SSSs that have been detectedis 1-2 orders of magnitude below expectations from pop-

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SSSs, T= 3× 105 K

SSSs, T= 5× 105 K

Fig. 2.— EUV and soft X-ray models and bounds for the z = 0specific emissivities of XRBs and SSSs. The solid purple andred curves represent respectively the empirical models describedin the text assuming the power-law SED and the stacked four star-forming galaxies. The blue dashed curve represents the theoreticalmodel of Fragos et al. (2013). The highlighted bands around thered solid and blue dashed curves are, respectively, the standarddeviation estimated from the four stacked galaxies and the quoteduncertainties in Fragos et al. (2013). The teal and pink shadedareas represent the allowed emissivity for SSSs with blackbodytemperatures of 3 × 105 K and 5 × 105 K respectively, using theluminosity bounds from Chen et al. (2015). The respective dashedcurves represent this emission with attenuation from a 1020 cm−2

and 3× 1020 cm−2 column.

ulation synthesis models (Chen et al. 2014, 2015). Thelack of sources could be because of obscuring H i columnsaround these sources (although see Nielsen & Gilfanov2015; Woods & Gilfanov 2016), if dynamically unstablemass loss for giant stars occurs differently from in cur-rent models (Chen et al. 2015), or if the nature of accre-tion onto these systems is different (Cassisi et al. 1998).Observations are sensitive to SSSs with a more massivewhite dwarf primary, so the smaller primaries (which aremore important at lower energies) could still be presentat forecast abundances.

Here we assume that stable accretion onto undetected(i.e. less massive) white dwarfs is occurring, and we at-tempt to place an upper bound on the total ionizingemissions. We assume that the spectrum of these ob-jects follows a blackbody with an effective temperatureranging between 3 × 105 and 5 × 105 K, characteristicof the lower mass primaries that would go undetected inprevious soft X-ray searches (Greiner 2000).

For long-term thermally stable accretion onto a whitedwarf in the stable hydrogen-burning regime, the idealdonor star is a 2M� main sequence star (Chen et al.2014). It follows that the luminosity of SSSs is expectedto peak at stellar ages of approximately 1Gyr (the life-time of a 2M� main sequence star) and drop off steeplyat ages > 1Gyr in the soft X-ray6 (Chen et al. 2015),thus, globally, their emissions should peak at roughlyz ∼ 1.8, approximately 1Gyr following peak cosmic starformation rate.

6 4 Ry emission drops off less steeply, but still peaks at 1Gyr

5

To estimate the contribution of SSSs, we constructedthe shape of the emissivity function from the shape ofcosmic star formation rate density and shifted this evo-lution by 1Gyr.7 We normalize the upper bound to theemission from SSSs by setting the integrated ≥ 4Ry lu-minosity from SSSs to equal the HeII-ionizing luminosityof the a025qc15 model in Chen et al. (2015) (which usedbinary Population synthesis models to predict the stellarage-specific luminosity). In this model, the criterion forstable mass loss for binaries with giant donors (a criti-cal mass ratio) is adjusted to better agree with late-timesoft X-ray flux of elliptical galaxies, which is over pre-dicted with the more standard prescription. Their othertwo models that adjust the critical mass criterion to sat-isfy the X-ray limits increase this critical mass ratio, andthus show lower luminosities. However, their model with-out this prescription overpredicts the observational con-straints in the X-ray. We normalize to the He-ionizingmodel rather than normalizing to the soft X-ray predic-tions because the soft X-ray energies fall in the tail of theblackbody and thus the normalization would be sensitiveto the assumed spectrum.

Figure 2 shows the allowed emissivity of SSSs, whereteal and pink shaded areas represent the allowed emis-sivity for SSSs with blackbody temperatures of 3 × 105

K and 5 × 105 K respectively. Although unlike Chenet al. (2015), we use a single temperature for our spec-tral model, the limited range of temperatures consistentwith stably accreting white dwarfs and allowed by ob-servational constraints in the soft X-ray justifies this ap-proximation. The dashed curves show the attenuation ofthis emission from a column of 1020 cm−2 and 3 × 1020

cm−2. These models show upper bounds skimming thelower bounds of quasars at ∼ 100 eV. Our bound onSSSs allows a potential contribution that is as much asan order of magnitude above our empirical XRB model,barring any absorption.

Accreting white dwarfs seem to be a natural conse-quence of stellar evolution – it should then follow thatSSSs contribute substantially to the ionizing background.However, there is limited observational evidence to sup-port their ubiquity. If SSSs are numerous, their observa-tional elusiveness requires a limited mass range of accret-ing WDs and gas-poor environment (Woods & Gilfanov2016) to respectively explain the lack of detections in thesoft X-ray and the lack of ionized nebulae associated withthese objects (although the lack of ionized nebulae maysuggest that the bulk of their ionizing photons escapetheir host galaxy).

2.4. Warm–Hot gas in the ISM and CGM

The ISM is a mix of different gas phases, with this mul-tiphase structure driven largely by stellar wind bubblesand supernovae blastwaves (McKee & Ostriker 1977).The spectrum of radiation emitted by these bubbles andblastwaves depends on the resulting temperatures andionization states of associated gases. Some of this emis-sion escapes into intergalactic space, with the amount de-pending on the H i columns out of the host galaxy. Fur-thermore, some of the gas driven by these feedback pro-

7 Describing this evolution with the more complex lightcurve inChen et al. (2015) should not change results over this 1Gyr-delayedmodel.

cesses vents from galaxies, potentially heating the CGMand leading to additional cooling emission that has lessdifficulty escaping from the galactic environs.

Radiation from warm-hot gas in the ISM can in prin-ciple be observed directly at > 300 eV. However, there isno robust determination of this ISM X-ray emissivity be-cause no straightforward method exists for disentanglingthe ISM contribution from the XRB one. Mineo et al.(2012b) attempted to disentangle the ISM contributionby subtracting off flux from X-ray point sources, whichare likely XRBs, finding that most of the observed fluxremains at the lowest energies observed, with little above1 keV. Using the remaining flux as an estimate for theISM contribution, they measured the relation betweenISM emission and SFR:

LX,0.5−2/SFR ≈ 8.3× 1038 erg s−1 (M� yr−1)−1, (2)

where LX,0.5−2 is the 0.5− 2 keV ISM luminosity.Observationally the shape of the average ISM SED is

essentially unconstrained at < 300eV, and the more dif-fuse emission from the CGM is unconstrained at all wave-lengths. To model the spectral shape, we use the spec-trum of gas cooling from some maximum temperature toa much lower temperature. The specific emissivity of apopulation of objects with this spectrum is then givenby

εν(Tmax) = ρSFR × [Lbol/SFR]×∫ Tmax

Tmin

dT ε−1T,bol εT (ν),

(3)where εT,bol =

∫dνεT (ν), ρSFR is the UV star formation

rate, and [Lbol/SFR] sets the normalization (which wedevelop models for shortly). We compute εT (ν) usingCloudy (Ferland et al. 2013) and assuming collisionalionization equilibrium8. We choose Tmin = 104K, al-though our calculations are not sensitive to this choice.In addition, our calculations assume a single metallic-ity of Z = 0.3Z� for Tmax = 106K and Z = Z� forTmax = 3 × 106K. However, since metal emission linesdominate the bolometric emission – what we normalizeto – metallicity has little effect on the resulting spectrum.

We choose Tmax to have values of 1 × 106 K or3× 106 K. The motivation for this spectral form is thatgas tends to be shock heated to these temperatures by102 − 103 km s−1 flows before cooling. At these tem-peratures, cooling times tend to be short and so there isnot often a heating process to halt cooling from runningaway. (Since we assume a single maximum temperature,our calculation misses that decelerating blastwaves tendto shock gases to a range of temperatures.) In the CGM,our simple model has the additional motivation that gasmay be cooling from the ∼ 106K virialized phase char-acteristic of star forming galaxies.

This model assumes CIE cooling, which is likely not agood approximation for ISM cooling. McQuinn (2012)used Allen et al. (2008) models for unmagnetized super-novae shocks to compute the spectrum of a supernovae

8 To understand the effect of ionizing backgrounds on our predic-tions, we have computed the ionization state with the Haardt andMadau 1996 model and nT = 10K cm−3 and nT = 100K cm−3,thermal pressures justified in McQuinn & Werk (2017). We findthere is a negligible difference in the spectra and thus the pho-toionization background does not have a significant effect on theresulting SED of the hot gas.

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Tmax = 106 K, fescfrad = 0. 1− 0. 5

Empirical Galactic (stack)

Fig. 3.— Estimates for the z = 0 ISM and CGM emissivities us-ing the models discussed in § 2.4. The turquoise band is our fidu-cial, theoretically-calculated ISM emissivity that uses equation (4)with Tmax = 3× 106 K and fescfrad = 0.01− 0.1. The green bandis our CGM/ISM emissivity that also uses Equation 4, but withTmax = 106 K and fescfrad = 0.1 − 0.5. The red curve repre-sents the stack of four star-forming galaxies (the empirical modelin § 2.2). The various blue dashed curves represent the amountof H i + He i absorption for hydrogen column densities increasingfrom 1018cm−2 to 1022cm−2.

blastwave as it decelerates in a constant density mediumof density 1 cm−3. This calculation includes the non-equilibrium ion abundances and consistently models theself-ionization of the shock They found a spectrum thaton average scales as α = 1.7, between 10 eV before a cut-off at ∼ 1 keV. Such a spectral index between 102−103eVfalls in between the effective scaling of our two consideredTmax models.

Our normalization of the ISM and CGM emissivitiesuses that the radiated energy is likely a significant frac-tion of the total feedback energy. We consider supernovafeedback, although stellar winds can be comparable ener-getically (Leitherer et al. 1999). The bolometric luminos-ity per unit SFR – what sets the emissivity normalizationin our models (eqn. 3) – is

[Lbol/SFR] = fescfradfSNESN, (4)

where fSN is the approximate fraction of stars expectedto go supernova that we take to be 10−2, ESN is the ap-proximate energy output per supernova that we take tobe 1051erg s−1, frad is the fraction of the feedback energythat is radiated, and fesc is the fraction that escapes thegalaxy. Calculations find that frad ≈ 0.9 in the local ISMsurrounding supernovae if they are unclustered (Thorn-ton et al. 1998), and that for clustered supernovae thisfraction can go down to frad ≈ 0.5 (Sharma et al. 2014).Much of the energy which is not radiated in the ISM(or, if radiated, that is re-absorbed) is likely radiated inthe CGM where fesc ≈ 1: McQuinn & Werk (2017) ar-gued that the large OVI columns require frad > 0.1 inthe CGM, and large frad appear to be born out in nu-merical simulations of the CGM (Fielding et al. 2017;

van de Voort & Schaye 2013). Observations further sug-gest that the characteristic scale for the CGM emissionextends many tens of kiloparsecs outside of the galaxy(Werk et al. 2014), and so this diffuse emission wouldlikely go undetected in soft X-ray images even if the gasreached sufficiently high temperatures to be seen in thesoft X-ray. We note that this energetics-motivated modelfor CGM emission is similar to that of Miniati et al.(2004, except they assume emission at Tvir), as are ourconclusions for the potential impact on Jν .

In our model of the CGM emission (though it can alsobe colder, less obscured ISM emission), we take the pos-sible range for escaping emission to be fescfrad = 0.1−0.5and Tmax = 106K. This ‘CGM/ISM’ model is shown bythe green band in Figure 3. This spectrum peaks at hun-dreds of eV, and falls off below the X-ray measurementsat > 300eV. However, we again note that falling belowthe X-ray measurements is not required as this emissioncould be too diffuse to detect.

For hotter ISM gas with Tmax ≈ 3 × 106 K, wetune the normalization to meet the observations, find-ing fescfrad = 0.01 − 1. This ‘ISM’ model is shownby the turquoise band in Figure 3. Much of the ISMradiation is likely absorbed in the galaxy to producesuch low fescfrad: the blue dotted lines represent theH i + He i transmissions for H i column densities rang-ing from 1018cm−2 to 1022cm−2. Large H i columns of∼ 1022cm−2 are necessary to obscure the X-ray emission.Additionally, lower columns would obscure ISM modelswith smaller Tmax.

For both the ISM and CGM models, we assume thesame range of fescfrad holds with redshift to computeJν in § 3. As the properties of galaxies change, and itis thought that the escape of ionizing photons goes upwith redshift, this might underestimate temporal trends,especially for Jν at higher redshifts.

2.5. Virialized hot halo gas

This section considers the emission from virialized gasin massive halos. We distinguish this scenario from thediffuse CGM gas previously considered in that, as cool-ing times get longer in larger systems, a roughly singletemperature hydrostatic virialized region forms, whereasthe CGM emission owes to cooling gas and likely a rangeof temperatures. A second distinctions is that the CGMemission is sourced by halos where most star formationoccurs in the Universe, ∼ 1012M� halos, whereas we willsee that hot halo emission owes to systems at least an or-der of magnitude larger (and is powered by virializationand quasar feedback).

The hot gas scenario should be thought of as beingessentially the same as warm hot intergalactic mediumemission that has been discussed extensively by priorstudies as a source of the soft X-ray background (Cen &Ostriker 1999; Dave et al. 2001; Croft et al. 2001). Whilesome of the diffuse emission likely comes from filamen-tary gas, most is likely to come from gas associated withhalos as modeled in Pen (1999). There is 25% (15%) ofdark matter in > 1013M� halos at z = 0 (0.5), and 10%(5%) of dark matter in > 1014M� halos. Filamentarygas is too diffuse (and, possibly, too unenriched) to com-pete with virialized regions even though it constitutes asomewhat larger mass fraction. The amplitude of this

7

emission is more sensitive to how the associated gas isdistributed around halos, which we discuss below.

Group and cluster virialized gas emits in the EUV andsoft X-ray of massive halos via free-free and atomic lineemissions, with the latter becoming more prominent inlower temperature halos. The X-ray emission from viri-alized gas that has been measured for & 1013M� haloscan be directly observed (Jeltema et al. 2008; Holdenet al. 2002; Markevitch 1998; Helsdon & Ponman 2000;Mulchaey et al. 2003; Della Ceca et al. 2000; Arnaud& Evrard 1999; Borgani et al. 2001; Pratt et al. 2009),and we design our models to latch onto these observa-tions. In particular, we use the models of Sharma et al.(2012) based on timescale considerations, which are ableto fit the observed X-ray luminosity – temperature re-lation (LX -TX). In particular, McCourt et al. (2012)and Sharma et al. (2012) find (using simulations of agravitationally stratified atmosphere in which cooling isinitially in balance with heating) that in order for a haloto not be locally thermally unstable, leading to conden-sation and driving star formation rates larger than ob-served, the cooling time must be at least ten times thedynamical time. This bound on the density of gas in ha-los has been confirmed in simulations with more realisticfeedback prescriptions (Gaspari et al. 2013). It also isconsistent with observations (Sharma et al. 2012; Voit &Donahue 2015; Voit et al. 2017).

We use the Sharma et al. (2012) fiducial model whichuses a cooling time to dynamical time ratio of 10 (an up-per limit on the core density and therefore on LX) as anupper limit to our calculation and their lowest luminositymodel with a cooling time to dynamical time ratio of 100as a lower limit. These models, which produce LSharma

X ,generously bracket the spread in LX -TX values seen inobservations (see Figure 3 of Sharma et al. 2012). Indeed,a more detailed analysis likely could shave off factors oftwo in the uncertainty at both sides. Both of these mod-els use an asymptotic gas density slope of -2.25 to solvea differential equation for the gas density profile (seeSharma et al. 2012). We identify TX with Tvir(Mhalo),the virial temperature of a halo of mass Mhalo, calculatedassuming an isothermal sphere (Barkana & Loeb 2001).9

For the spectral form of this emission, `(ν) ≡Lν/

∫dνLν , we use a composite Cloudy spectrum that

is made up of a series of Cloudy “coronal equilib-rium” models with several discrete temperatures. TheseCloudy models assume collisional ionization equilib-rium (Ferland et al. 2013) and a hydrogen density of 10−4

cm−3 – the virial density of halos in spherical collapse atz = 0.2. We use Solar abundance ratios of Grevesseet al. (2010) with an overall metallicity of Z = 0.3Z�, inaccord with the typical metallicity in intracluster and cir-cumgalactic media measurements (Prochaska et al. 2017;Mantz et al. 2017). Changing to Z = 0 (or, to a lesserextent, turning on an ionizing background or decreasingthe density we assume) results in the emission lines dis-appearing in the spectra, but do not significantly changeour results.

The temperatures of these models are computed over

9 We note that the Sharma models are computed for just free-freecooling, which could lead to differences at the lowest temperatureswe consider where atomic cooling becomes important. However,the CGM models become more applicable in this limit.

a large range of virial temperatures. The models in thecomposite spectrum are then weighted in accordance tothe Sheth-Tormen halo mass function (Sheth & Tormen1999), dn

dM , at a given redshift such that

εν =

∫ ∞Mmin

dMdn

dMLM (ν), (5)

where LM (ν) is the frequency-dependent luminosity ofthe halo gas of a given halo mass, set equal to LSharma

X ×`cloudy(ν). We set Mmin = 1013M� here, but smallervalues would not change our results for εν and Jν (asdiscussed below) at z = 0.

Our fiducial model, shown as the red band in Figure 4,is this calculation for the z = 0 emissivity of halo gas,with the band bracketing the two TX − LX models ofSharma et al. (2012) described above. The cyan bandand gold band show this calculation above higher min-imum masses as discussed in the following paragraph.If we treat the observed spread as an indication of mea-surement error (or, e.g., biases owing to missing the mostdiffuse components), then the band indicates the level ofuncertainty. Interestingly, these estimates for virializedgas emission exceed our lower bounds for quasar emissionbetween several tens and a few hundred eV. In contrastto the z = 0 emissivity, the observed background comesfrom a range of redshifts, and when this is considered wefind in Section 3 that quasars are still likely the dominantsource due to the declining abundance of massive halosat increasing redshift.

Most of the z = 0 emission from virialized gas comesfrom small clusters. Figure 4 also shows calculationsthat only allow for emission above halos with masses of1014M� (cyan band) and 1015M� (gold band), respec-tively. We find that the EUV and soft X-ray emissionfrom this gas is dominated by M & 1013M� at z = 0.10

Lower mass halos cool very efficiently and so have lowergas densities. In the Sharma et al. (2012) models, thegas in the most massive halos essentially traces the darkmatter, but becomes cored at lower masses with a largefraction does not fitting within in the virial radius forM . 1013M�. We caution that at M . 1013M�, repre-senting the cooling emission with a virialized atmospheremay be fraught and the CGM calculations described pre-viously likely hold more bearing.

3. THE CONTRIBUTION OF DIFFERENT SOURCES TO Jν

The summary of the emissivity calculations describedin Section 2 is shown in Figure 5. We plot each of thesources’ specific emissivities at z = 0.1, 2.0, and 4.0. Weuse the quasar calculations described in Section 2.1, theXRB calculation of Section 2.2, the SSS calculation ofSection 2.3, the ISM and CGM calculations as describedin Section 2.4, the empirical galactic model with a power-law SED discussed in Section 2.2, and virialized halo gascalculation as described in Section 2.5. The band encap-sulating each model reflects the range of possible valuesthat we motivated.

Both the peak of the quasar emissivity and cosmic starformation rate (to which the XRB and CGM emissivity

10 Because the virial scale is an arc-minute for a M = 1013M�halo at z = 0.5, these sources of emission would not be included inX-ray point source catalogues. Nearly every sightline on the skyintersects a 1013M� halo (McQuinn 2014).

8

102 103

E (eV)

1037

1038

1039

νεν [

erg

s−

1 M

pc−

3]

Mmin = 1013M¯

Mmin = 1014M¯

Mmin = 1015M¯

Fig. 4.— Specific emissivity of z = 0 virialized halo gas followingthe calculation described in § 2.5. The lower (upper) limit uses themodels in Sharma et al. (2012) to relate the halo virial temper-ature and luminosity, assuming a cooling timescale to dynamicaltimescale ratio of 100 (10). These values are chosen to bracketobservations. The red band is our fiducial model and represents aminimum halo mass of 1013M�. The cyan and gold bands corre-spond to minimum masses of 1014M� and 1015M� respectively.

are tied) occur at z = 2− 3, prompting a similar peak ineach sources’ emissivity near these redshifts. In contrast,the amount of free-free emission from virialized halo gasdrops off rapidly with increasing redshift due to the abun-dance of & 1013M� halos decreasing quickly with red-shift. While virialized gas likely is the most importantsource at most of the considered wavelengths at z = 0,quasars become the most important at z = 2 − 4. Athigher redshifts than shown, models suggest that XRBsand perhaps hot ISM gas become the dominant source at100 − 1000 eV (Mirabel et al. 2011; Pacucci et al. 2014;Madau & Fragos 2017).

The solution to the cosmological radiative transferequation gives the background angular-averaged specificintensity at a particular energy as observed at z0,

Jν(z0) =c

4π

∫ ∞z0

dz

∣∣∣∣ dtdz∣∣∣∣ (1 + z0)3

(1 + z)3εν(z)e−τ(z0,z,ν), (6)

where εν is the proper volume emissivity – what wemodeled in Section 2 for various sources –, |dt/dz| =

[H(z)(1 + z)]−1

, and τ is the effective optical depth be-tween z0 and z in a nonuniform IGM, and given by

τ(E0, z0, z) =

∫ z

z0

dz′∫ ∞

0

dNHIf(NHI, z′)(

1− e−τν(NHI))),

(7)for randomly distributed absorbers, where f(NHI, z

′) isthe H i column density distribution and τν(NHI) is theoptical depth at a particular energy through an absorber,

τν = NHIσHI(ν) +NHeIIσHeII(ν), (8)

where σX is the photoionization cross section of speciesX, and the He ii column of a system NHeII must be

modeled in terms of NHI. We use Equation A10 in Fardalet al. (1998) for the relationship between NHeII, NHI, ΓHI

for a single temperature and density slab. We assume104K and a density set by the model in Schaye (2001)in which absorbers column and density are related byassuming the size of absorbers is the Jeans length andphotoionization equilibrium. The Schaye (2001) modelagrees well with simulations (McQuinn et al. 2011; Altayet al. 2011). Our calculations neglect He i continuum ab-sorption and resonant lines, which contribute relativelysmall features in Jν compared the the H i and He iicontinuum absorption that we include.11

For f(NHI, z), our calculations use the piecewise-in-NHI fits of Prochaska et al. (2014), which use a

parametrization of the form f(NHI, z) = AN−βHI (1 + z)γ .While the error bars over the range of columns probedare generally quoted at the tens of percent level, thereare some factor of two discrepancies around 1016cm−2

(Prochaska et al. 2014). However, for the z ∼ 0 back-ground, the dilution from expansion and redshifting(which is perfectly captured) is more important than thecontinuum absorption of hydrogen. At� 1Ry, where wefocus, this is true not just at z ∼ 0 but also at higherredshifts. Therefore, discrepancies in the column den-sity distributions may indicate there is room for as muchas a factor of two difference from mean free path effects,but then likely only at the lowest energies considered andmoderate redshifts. Even a factor of two is smaller thanthe possible amplitude ranges in all of our source models.Thus, our modeling of absorption is not the dominantsource of uncertainty.

Figure 6 shows Jν at z = 0 for each of the sourcesshown in Figure 5. We also include two observationalconstraints from ROSAT: The constraint of Warwick &Roberts (1998) using the lowest energies where the extra-galactic background can be estimated is represented bythe error bar at 250 eV, and the ROSAT PSPC data con-straint of Georgantopoulos et al. (1996) is shown as thered bowtie starting at ∼500 eV. By construction, bothof these observational bounds are reasonably matched bythe full range of quasar emissivity models.

Our calculations show that, even accounting for ourestimated range of specific emissivities, quasars are thedominant contributor to the EUV/soft X-ray backgroundat energies .100 eV. If the value of αQSO is on the softerside as observations may suggest, then the emission of hothalo gas in massive halos could be the more importantcontributor to the EUV background at energies upwardsof a couple hundred electron volts. Figure 6 suggests thatgalactic sources may be of secondary importance to thesetwo sources where E ≥ 100 eV, but the ISM and CGMmay be second only to quasars at lower energies. Eventhough they are not the dominant sources of emission ofthe extragalactic background, they can dominate withinthe halos of galaxies (§ 5) and their contribution.

Potential background sources can be isolated using un-resolved X-ray background measurements. In particular,the 1 − 2 keV, resolved fraction of X-ray background is80% of the total in the Chandra deep fields (a total of

11 Because the mapping of NHI to NHeII depends on Jν , wemust solve for Jν iteratively. Additionally, we use the rates for ourfiducial quasar model when calculating the generally subdominantcontribution to Jν from other sources models.

9

102 103

E [eV]

1035

1036

1037

1038

1039

1040

1041

νεν [e

rg s−

1 M

pc−

3]

z= 0.1

Galaxy stack

XRBs

SSSs

Hot halo gas

Empirical galaxy

CGM+ISM

ISM

QSOs

102 103

E [eV]

z= 2.0

102 103

E [eV]

z= 4.0

Fig. 5.— Estimated specific emissivities of the sources using the models described in Section 2. The purple shaded region shows quasaremissivity estimates from extrapolating into the EUV/soft X-ray with the range of mean power-law slopes that are estimated. TheISM/CGM are represented in the green and yellow bands, with Tmax = 3× 106 K and Tmax = 1× 106 respectively, with their spectra setto a resolution of 15 to smooth out lines. The cyan band represents the virialized hot halo gas described in Section 2.5. The dark blueSED represents the Fragos et al. (2013) XRB model. The red spectrum represents the empirical XRB model from stacked spectra, and thelight pink band the power-law extrapolation of galactic soft X-ray emission (whose width increases with redshift according to the allowedrange of evolution in XRB emissions), and the teal shaded area represents our upper bound on the emissivity of super soft X-ray sourceswith an effective temperature of 5× 105 K.

0.06 sq. deg.), and similar constraints have been foundin larger fields (Hickox & Markevitch 2006). Thus, only≈ 20% of the X-ray background owes to diffuse sourceslike virialized halo gas. This bound suggests that themaximum virialized halo gas emission is a factor of ∼ 2below our maximum estimates. However, at 1 − 2 keV,the signal is dominated by rare > 1014M� halos (Fig. 4),which may not fall in the Chandra field of view. Amore detailed analysis is necessary to understand thisconstraint.

Figure 7 shows Jν for the same sources at z = 2. Herequasars are undisputedly the dominating source of theEUV/soft X-ray background. No other source is likelyto produce enough > 54eV photons to doubly ionize theHe ii if it is ionized at z ∼ 3 as observations suggest(McQuinn 2016). The number of M > 1013M� halossteeply declines with increasing redshift, and thus thecontribution of virialized hot halo gas at z = 2 is negli-gible in comparison to the contribution of both quasarsand galactic sources. The overall increase in the back-ground intensity from z = 0 to z = 2 follows from therise of both the cosmic star formation rate and quasarluminosity function.

4. THE EFFECT OF THE EXTRAGALACTICBACKGROUND ON IGM AND CGM ABSORPTION LINE

INFERENCES

Photoionization models are used to infer the densityand metallicities of intergalactic and circumgalactic ab-sorption systems (e.g. McQuinn 2016; Tumlinson et al.2017). As ions have electronic binding energies in theEUV and soft X-ray, their abundances are shaped bythese radiation backgrounds. We have shown that theuncertainty in the spectrum of the background at theseenergies is considerable, suggesting commensurate uncer-tainties in the density and metallicity inferences. In this

101 102 103

E [eV]

10-12

10-11

10-10

10-9

10-8

10-7

10-6

νJν [

erg

s−

1 c

m−

2]

XRBs

SSSs, Teff = 5× 105 K

SSSs, Teff = 3× 105 K

QSOs

CGM+ISM

Hot halo gas

Empirical galaxy model

ISM

Fig. 6.— Angle-averaged z = 0 specific intensity, Jν , of sourcesdescribed in Section 2 and shown in Figure 5. The errorbarat E = 250 eV is the soft X-ray background intensity ROSATmeasurement by Warwick & Roberts (1998). The red bowtie isROSAT PSPC observations from Georgantopoulos et al. (1996).Despite observations suggesting that αQSO may be on the softerend, quasars likely dominate the background at energies . 100 eV.Between one and several hundred electron volts, virialized hot halogas may can become as important as quasars. Galactic sources suchas XRBs, SSSs, the ISM, and especially the CGM, can contributeat the tens of percent level.

section, we apply our models to quantify the sensitiv-ity of the most observable ions to the assumed ionizingbackground.

Previous attempts to make metallicity and density in-

10

101 102 103

E [eV]

10-12

10-11

10-10

10-9

10-8

10-7

10-6

νJν [

erg

s−

1 c

m−

2]

z= 2

XRBs

SSSs, Teff = 5× 105 K

SSSs, Teff = 3× 105 K

QSOsCGM+ISMHot halo gasEmpirical galaxy modelISM

Fig. 7.— Angle-averaged z = 2 specific intensity, Jν , of sourcesdescribed in Section 2 and shown in Figure 5. At this redshift,quasars dominate the background at throughout the EUV and softX-ray. Virialized hot halo gas is much less important than at z = 0due to the declining abundance of M > 1013M� halos.

ferences from ionic absorption measurements use a meta-galactic ionizing background model, such as Haardt &Madau (2012). When errors are quoted pertaining tothe ionizing background choice, they are computed asthe differences between historical models for these back-grounds, such as comparing how a calculation changesif it uses the Haardt & Madau (1996) rather than theHaardt & Madau (2012). The major differences betweenvarious historical models for the ionizing background isin improved constraints on IGM absorption and for the1Ry emissivity of quasars, and not improved modeling ofthe spectrum of the sources. In contrast, our models al-low for us to quantify the principle source of uncertainty.

We use Cloudy to compute the equilibrium columndensities of several common metal ions in the UV, withour Jν models as the input ionizing spectrum and as-suming temperature equilibrium. We only consider therange of Jν in our quasar models, using the lower and up-per envelopes of the quasar intensity. We then comparethe resulting columns to the columns with the Haardt &Madau (2012) Jν . These models implicitly assume thatphotoionization is dominant for all ionic species as theequilibrium temperature is ∼ 104K. (Collisional ioniza-tion is included, but since our calculations use the equi-librium temperature these effects are generally small.)We vary the dimensionless ionization parameter, U , theratio between the ionizing photon flux and the volumedensity of the gas. We choose log10 U = −1,−2, and−3, which approximately bracket the mean of valuesof U allowed by the data in Werk et al. (2014). ForHaardt & Madau (2012), these correspond to densitiesof 8 × 10−6 − 8 × 10−4cm−3, with larger log10 U corre-sponding to lower densities. However the precise densitydepends on the background model.

The dispersion from the range of models in selections’ column densities is shown in Figure 8. Here we

1.0

0.5

0.0

0.5

1.0

∆lo

gNX

logU= − 1

SiIV

CIV NV OV OVI NeVII NeVIII

1.0

0.5

0.0

0.5

∆lo

gNX

logU= − 2

SiIV CIVNV OV OVI

NeVIINeVIII

102

Ionization energy [eV]

1.0

0.5

0.0

0.5

∆lo

gNX

logU= − 3

SiIV CIVNV OV OVI

NeVIINeVIII

Fig. 8.— Error bars show estimates of column densities of severalobservationally relevant ions for the upper and lower limits of theJν range allowed, normalized to estimates using Haardt & Madau(2012) background model and ordered by ionization energy of theleast bound electron. The top panel shows an ionization param-eter, U , of 10−1, the middle 10−2, and the bottom panel showsU = 10−3, which approximately correspond to n = 10−5cm−3,10−4cm−3 and 10−3cm−3 for the Haardt & Madau (2012) model.The green dashed errors compare the differences at fixed U , andthe cyan errors normalize the larger of our background models toa different U in a manner that matches at the H i photoionizationrate of the smaller background model.

show the difference between the Cloudy column den-sities computed with the lower and upper limits of ourquasar Jν band and those of our Cloudy calculationsusing the Haardt & Madau (2012) background model.(By only using the lower and upper parts of our band,we may underestimate range of expected columns ifthere are complex trends with Jν in the ionic column.)The green bars represent the range of JνQSO

in rela-tion to the Haardt & Madau (2012) background model,logNX,QSO − logNX,HM12. The reason the midpoint ofour errors is not centered at zero, the Haardt & Madau(2012) values, likely owes to our soft X-ray normaliza-tion being slightly lower than theirs. The larger logU aremore applicable for the higher ionization state metal lines(e.g. NeVIII), and the smaller logU are more applicablefor the low ionization state metal lines (e.g. SiIV). We

11

set NHI = 1015 cm−2 and the metallicity to Z = 0.3Z� inthese calculations, but note that these are easily rescaledat fixed U to higher column or more metal-rich systems.For the model with the Haardt & Madau (2012) ionizingbackground, we find that with LogU = −1, the loga-rithmic column densities are {10.0, 13.8, 14.0, 14.9, 15.1,14.4, 14.0} for [SiIV, CIV, NV, OV, OVI, NeVII, NeVIII],for Log U = −3 they are {12.1, 13.7, 13.1, 14.0, 13.3,11.5, 10.4}, and for Log U = −3, the column densitiesare {11.7, 11.9, 10.2, 11.2, 9.5, 6.7, 4.9}. The dispersionin possible Jν results in up to an order of magnitude inthe uncertainty in the calculated column densities for thehighest ions (Fig. 8).

While normalizing to a fixed U is standard practice inthis field, normalizing to a fixed H i photoionization ratewould better encapsulate the uncertainty in the ioniza-tion correction, as this fixes the background to the mostconstrained location, as Lyα forest measurements naildown the H i photoionization rate. While the green er-rors in Figure 8 compare the differences at fixed U , thecyan errors normalize the model that traces our upperenvelope for the quasar Jν to a different U such that itmatches the H i photoionization rate of the lower enve-lope of Jν model. Because this normalization fixes thebackground at a lower energy (near 13.6eV) compared tonormalizing in U , this more physical normalization cansometimes result in more uncertainty, especially for thelow ions. Indeed, most of the low ions show ≈ 0.3 dexvariation. When fixing the H i photoionization rate, wefind factors of 3 − 10 errors in the ionization correctionfor all considered ions, which in turn reflects factor of∼ 3 − 10 uncertainties in density and metallicity infer-ences from IGM and CGM absorbers.

5. PROXIMITY EFFECTS

The uncertainties in derived metal ion column densi-ties in the previous section neglect the possibility thatthe ionization state of circumgalactic gas could be af-fected by the ionizing flux of the host galaxy. Withinsome radius, local galactic sources will dominate the cos-mic EUV/soft X-ray background in ionizing photon flux.The low to mid ionization states of metals tend to arise in104K gas, with their ionization states set predominantlyby the photoionizing radiation background. Thus, knowl-edge of the UV background is critical for estimating thedensities and metallicities of the clouds that these lowerions trace. For example, the inferred densities for theseclouds using standard ionizing background models is anorder of magnitude smaller than predicted by pressureequilibrium with the virialized phase (Werk et al. 2014,2016; McQuinn & Werk 2017). Modifications to the UVbackground have been hypothesized as a potential solu-tion, likely requiring a 1−2 order of magnitude enhance-ment from unknown sources at ∼ 100eV (Werk et al.2016). In addition, because highly-ionized metals aremajor coolants of gas in the CGM, order unity changesin their ionization fractions from local emissions trans-late to order unity changes in their cooling rates whenthe major coolants are predominantly photoionized, po-tentially impacting the rate at which galaxies are fed gas.

We compare the angular-averaged intensity from localgalactic sources ( i.e. ISM, XRBs, and SSSs) to thatfrom the global background to determine the “proxim-ity radius:” the distance from a galaxy where local and

102

E [eV]

101

102

r ν,p

rox/√ S

FR

[kp

c (M

¯/y

r)−

0.5

]

Galaxy stackSSSsEmpirical galaxy modelISMCGM/ISM

Fig. 9.— The proximity region radius for a galaxy with a SFRof 1 M� yr−1 at z = 0.2 for our galactic and circumgalactic sourcemodels, defined as the radius where the background Jν is equal tothe local contribution from galactic EUV and X-ray sources. Thefainter ISM band and the lower SSS curve represent the these mod-els attenuated by a column of 1020 cm−2. Because the luminosityof SSSs is expected to peak at stellar ages of about 1Gyr, the SSSmodels show the expected luminosity at z = 0.2 from a galaxy witha SFR of 1.27 M� yr−1 at z = 0.3 (1Gyr prior to z = 0.2). Thisassumes that this toy galaxy’s star formation history follows theshape of the cosmic SFR density.

background sources contribute equally to the radiation.The proximity radius for a galaxy is given by

rν,prox = 103 kpc

[([νLν ]/[1039erg s−1])

([νJν ]/[10−8erg s−1cm2])

]1/2

(9)

where Lν is the local galactic specific luminosity. Wehave evaluated the equation at a Jν characteristic of ourionizing background calculations, and for an Lν at themaximum of what we find in our galactic source models.Thus, we conclude that the proximity region is unlikelyto extend beyond ∼ 100 kpc, a smaller extent then in-ferred for many absorbers in the CGM and especiallythe O vi (Tumlinson et al. 2011; Prochaska et al. 2011;Johnson et al. 2015; Werk et al. 2016).12 We note thatthis expression treats sources as if they are residing atr < rν,prox; this will generally overestimate the proxim-ity radius in the case of emission extending beyond thisradius (which may happen in the CGM).

Figure 9 shows our full calculations for the proxim-ity radii in our models for z = 0.2, a redshift chosen tomatch COS-Halos L* galaxy CGM survey (Tumlinsonet al. 2013). We show the galactic emission models de-scribed in Sections 2.2, 2.3, and 2.4 for the specific lumi-nosities, Lν,local/SFR. For the extragalactic background,we use our fiducial quasar model with a power-law indexof α = 1.7. In our source models, the proximity radiusfor a star-forming galaxy with a SFR of ∼ 1M� yr−1

varies between 10 and 100 kpc. Taking the median of

12 See the appendix in McQuinn & Werk (2017) for genericarguments that the proximity region must have extent less than. 100 kpc.

12

our bands or the observed X-ray luminosities would sug-gest ∼ 10−30 kpc, a small fraction of the total CGM, butscaling as (SFR)1/2. Thus, proximity radiation changesthe nature of cooling gas that resides fairly close to galax-ies but does not affect the bulk of the halo gas withextent ∼ 100 kpc. Thus, local sources are unlikely tobe dominant for the vast majority of absorbers in manyCGM samples, such as in Tumlinson et al. (2011) andStocke et al. (2013), whose absorbers mainly reside at30 − 150 kpc. That being said, assuming the radiationescapes, proximity emission can substantially affect gasionization near galaxies and, therefore, it can change theCGM gas cooling rate for the ions that are sensitive tothe radiation with energies in the range shown in Figure 9.

This conclusion is consistent with the geometric ar-guments of McQuinn & Werk (2017) that showed thatrprox . 100 kpc, assuming that the proximity regionsources are also the dominant source of the background.Our calculations add the likely-dominant backgroundfrom quasar emissions, which reduces this radius furtherbeyond the McQuinn & Werk (2017) estimates.

6. CONCLUSIONS

We have modeled the sources of the extragalactic back-ground in the EUV and soft X-ray. In addition to thecontribution from quasars, we included emissions thathave so far been neglected in widely-used backgroundmodels: X-ray binaries, the warm-hot interstellar andcircumgalactic gas of star-forming galaxies, and virial-ized halo gas from groups and clusters. Our models arecalibrated against the latest observational measurementsto bracket the possible range of contribution from each ofthese sources. Note that these estimated ranges shouldbe thought of as rough guidelines rather than rigorousbounds.

In agreement with previous studies, we find thatquasars are likely the most important contributor to theionizing background13. However, we also show that theircontribution to the observationally elusive 20 − 500 eVband can vary by up to a factor of 10 for plausible ex-trapolations into this band using power-laws derived inthe far UV and soft X-ray. Furthermore, the evidencethat the quasar SED is a single power-law, as assumedin previous background studies, is weak.

If quasars contribute at the lower envelope of our esti-mated Jν range, we find that emissions from the galacticISM/CGM, from virialized halo gas in groups/clusters,and possibly from super soft sources may contribute sig-nificantly to the background.

• The ISM contribution originates from cooling gaswithin stellar wind bubbles and supernovae blast-waves. While a large fraction of the ISM emis-sion is absorbed by H i within the galaxy, a sig-nificant amount of stellar feedback energy is likelydumped as lower temperature gas and further awayfrom obscuring H i in the ISM, venting into theCGM, where it is more easily radiated away. Ifmost of the energy in stellar feedback is converted

13 With the caveat that stellar emissions – which we do notmodel here – are likely to be important at < 50eV, with manymodels suggesting that they contribute up to a the factor of 2 leveland are possibly dominant at z & 4 (e.g., Haardt & Madau 2012).

into background radiation, we find that the com-bined ISM/CGM contribution is roughly equal tothe lower bound on quasars in the energy range20− 50 eV.

• We also find that, at z = 0, emissions from hot,virialized gas in groups/clusters can be as impor-tant as quasars at energies of ∼ 100−1000 eV. Thiscontribution falls off in importance at higher red-shifts owing to the decreasing abundance of groupsand clusters, and to the increasing number densityof quasars.

• Super soft sources have are often invoked as a hugeunknown contribution at ∼ 100 eV, although thereis little empirical evidence for such a population.By deriving a stringent bound from luminosity pre-dictions of SSSs from previous models, we showthat unseen super soft sources could maximallycontribute tens of percent to the background at∼ 100 eV.

Disentangling the physics of circumgalactic gas withabsorption line spectra requires accurate modeling of theEUV and soft X-ray backgrounds. Previous studies haveestimated the effect of uncertainties in these backgroundsby comparing inferences obtained from different histor-ical background models – for example, the Haardt &Madau (1996) and Haardt & Madau (2012) models. Asan application of our work, we have used our range ofJν models to quantify this uncertainty more rigorously.We bracketed the effect of the ionizing background onthe inferred column densities of ions commonly identifiedin UV absorption line studies of the CGM. We showedthat uncertainties in the average quasar spectrum aloneare sizable, enough to introduce a few tenths of dex dif-ferences in the abundances of the most observationallyimportant ions and up to 1 dex in the inferred columndensities for the highest observationally-relevant ioniza-tion states. These differenes likely translate into com-parable uncertainties in the densities and metallicitiesconstrained by these ions.

The uncertainties in metal ionization corrections areeven larger if local sources – e.g. XRBs and warm-hotISM/CGM gases– contribute significantly. We estimatedthe EUV/soft X-ray proximity radius of a star-forminggalaxy – the radius at which local emissions become equalto the extragalactic background. We found that thisproximity radius is between rprox ≈ 10 kpc and 100 kpc,assuming a star formation rate of 1 M� yr−1, withrprox ≈ 100 kpc for choices that maximize the poten-tial galactic luminosity (and only at E < 100 eV). Thus,local emission is unlikely to be the dominant source ofionization for the absorbers in most extragalactic CGMsamples.

Future observations and theoretical work has the po-tential to further constrain emission process that con-tribute sizably to the EUV and soft X-ray backgrounds.With a factor of 2−3 improved sensitivity, diffuse soft X-ray background measurements would reach most of ourmodel space for hot halo emission. In analogy to the γ-ray, where angular anisotropy analyses have constrainedthe blazar, millisecond pulsar, and galactic contributions(Ackermann et al. 2012), a future soft X-ray space tele-scope could measure the angular anisotropy to constrain

13

source models: Low redshift clusters and groups are rareand have large arc-minute extents, whereas (abundant)galactic sources will contribute a smoother signal in an-gle. Finally, future CGM observations and modeling hasthe potential to better constrain the density and thermalstructure of this medium and, hence, its cooling emis-sions.

This work was supported by NSF award AST 1614439,

by NASA through the Space Telescope Science Instituteawards HST-AR-14307 and HST-AR-14575, and by theAlfred P. Sloan foundation. We thank the referee for use-ful comments and suggestions. PRUS thanks Nell Bylerfor helpful discussion and MM thanks the Institute forAdvanced Study visiting faculty program and the JohnBahcall fellowship for support.

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