Mon.Not.R.Astron.Soc.000,1–??(2015) Printed25January2017 (MNLATEXstylefilev2.2) The contribution of bulk Comptonization to the soft X-ray excess in AGN 7 1 J. Kaufman⋆, O. M. Blaes, and S. Hirose 0 Department of Physics, Universityof California, Santa Barbara, CA 93106, USA 2 n a Accepted —.Received—;inoriginalform— J 4 2 ABSTRACT Bulk velocities exceed thermal velocities for sufficiently radiation pressure dominated ] E accretion flows. We model the contribution of bulk Comptonization to the soft X-ray H excess in AGN. Bulk Comptonization is due to both turbulence and the background shear.Wecalculatespectrabothtakingintoaccountandnottakingintoaccountbulk . h velocities using scaled data from radiation magnetohydrodynamic (MHD) shearing p box simulations.We characterizeour results with temperatures and optical depths to - make contact with other warm Comptonization models of the soft excess. We chose o r our fiducial mass, M = 2×106M⊙, and accretion rate, L/LEdd =2.5, to correspond t to those fit to the super-Eddington narrow line Seyfert 1 (NLS1) RE1034+396. The s a temperatures, optical depths, and Compton y parameters we find broadly agree with [ thosefittoRE1034+396.TheeffectofbulkComptonizationistoshifttheWientailto higher energyand lowerthe gastemperature, broadeningthe spectrum. Observations 1 of the soft excess in NLS1s can constrain the properties of disc turbulence if the v 4 bulkComptonizationcontributioncanbeseparatedoutfromcontributionsfromother 0 physical effects, such as reflection and absorption. 7 Key words: accretion, accretion discs — radiation mechanisms: non-thermal — 6 0 turbulence — galaxies: active. . 1 0 7 1 1 INTRODUCTION gies to contribute at all, and so in these sources the entire : soft excess must originate elsewhere. v ThesoftX-rayexcessinAGNspectraisthecomponentbe- Xi low 1keV that lies on top of the extrapolation of the best One class of models for the soft excess invokes warm fitting 2-10keV power law (Singh et al. 1985; Arnaud et al. Comptonization. In this picture, a warm (kTe 0.2 keV) ar 1985; Vasudevanet al. 2014). The dependence of effective medium with moderate optical depth upscatte∼rs photons temperature on mass and accretion rate in optically thick fromacool,opticallythickdisc.Magdziarz et al.(1998),for accretion disc models (Shakura& Sunyaev 1973, hereafter example,fitthesoft excessofthebroadlineSeyfert1NGC SS73) is Teff (m˙/M)1/4, where m˙ =M˙/M˙Edd. We there- 5548 with kTe =0.3keV, τ =30. Inthiscase, theypictured fore expect in∼trinsic disc emission to contribute to the soft themediumasatransitionregionbetweentheaccretiondisc excessmostinnarrowlineSeyfertIs(NLS1),whicharecom- and an inner hot geometrically thick flow. In other studies parativelylowmass( 106M⊙),near-Eddingtonsources.In the medium is a warm layer above the inner regions of the the most luminous re∼gions of NLS1 discs the temperature disc. For example, Janiuk et al. (2001) fit the soft excess is greater than the hydrogen ionization energy, so electron of the quasar PG 1211+143 with kTe = 0.4keV, τ = 10. scattering is the dominant opacity. The color temperature Dewangan et al. (2007) fit two NLS1s, Ark 564 and Mrk is therefore greater than the effective temperature, which 1044, with kTe =0.18keV, τ =45, and kTe =0.14keV, τ = augments the expected contribution to the soft excess in 45, respectively. Jin et al. (2009) fit the super-Eddington these sources. While the soft excess is particularly promi- (L/LEdd =2.7)NLS1RXJ0136.9-3510withkTe=0.28keV, nentinNLS1s,theexpecteddisccontributionisinsufficient τ = 12. Mehdipouret al. (2011) fit the broad line Seyfert toaccountforit(Done et al.2012,hereafterD12).Inbroad 1 Mrk 509 with kTe = 0.2keV, τ = 17. More recently, D12 line Seyferts, which are lower Eddington ratio sources, the constructedtheXSPECmodelOPTXAGNFforthesoftex- intrinsicdiscemission doesnotextendtohighenoughener- cess, which uses the disc spectrum at the outer coronal ra- diusastheseedphotonsourceand,forthepurposeofenergy conservation, models the warm medium as part of the disc ⋆ E-mail: [email protected] (JK); atmosphere. D12 fit the super-Eddington (L/LEdd = 2.4) [email protected](OMB) NLS1 RE 1034+396 with kTe = 0.23keV, τ = 11. Since 2 J. Kaufman, O. M. Blaes, and S. Hirose then, this model has been applied to several sources, such modifications to the intrinsic disc atmosphere physics, be- astheNLS1IIZw177(Pal et al.2016),forwhichtheyfound causethethermalspectrumfallsoffatenergiessignificantly kTe 0.2keV, τ 20. below the soft X-rays. ∼ ∼ Warm comptonization models fit the spectra well, but KB16 outlined the fundamental physical processes un- theminimalvariationofthefittedelectrontemperaturewith derlying bulk Comptonization by turbulence in accretion black hole mass and accretion rate (e.g. Gierlinski & Done disc atmospheres. In this paper we model the effect of bulk 2004)motivatedalternativemodelsbasedondiscreteatomic Comptonization on disc spectra using data from radiation features. In reflection models, photons from the hot ( 100 MHD simulations (Hirose et al. 2009), including both tur- ∼ keV)coronaarereflected andrelativistically blurredbythe bulent Comptonization and Comptonization by the back- innerregionsoftheaccretiondisc(e.g.Crummy et al.2006; groundshear.Weparametrizethiseffectbytemperatureand Ross & Fabian 2005). In ionized absorption models, high opticaldepthinordertomakecontactwithobservationsfit velocity winds originating from the accretion disc absorb by other warm Comptonization models. In particular, we andreemitphotonsfromthehotcorona(Gierlinski & Done compare our results to the temperature and optical depth 2004). While these models naturally predict the mini- fit to RE 1034+396 (D12), a super-Eddington NLS1 with mal variation in the soft excess temperature, they typi- an unusually large soft excess. The structure of this paper cally require extreme parameters to sufficiently smear the isasfollows.Insection2wedescribeourmodelindetail.In discrete atomic features on which they are based. Re- section3wedescribeourresults,andinsection4wediscuss flection models, for example, require near maximal spin them.Finally, we summarize our findingsin section 5. black holes (e.g. Crummy et al. 2006), and the original absorption models require unrealistically large wind ve- locities (Schurch& Done 2007). More complex absorption 2 MODELING BULK COMPTONIZATION models circumvent this difficulty, but they lack predictive 2.1 Overview power (e.g. Middleton et al. 2009). Other proposed expla- nations for the soft excess include magnetic reconnection InordertofacilitatecomparisonswithwarmthermalComp- (Zhong& Wang2013)andComptonizationbyshockheated tonizationmodelsofthesoftX-rayexcess,weseektocharac- electrons (Fukumuraet al. 2016). Because warm Comp- terize thecontribution of bulkComptonization with a tem- tonization, reflection, and absorption all fit the spectra peratureandanopticaldepth.Todothis,weusedatafrom adequately (e.g. Middleton et al. 2009), solving this prob- radiationMHDshearingboxsimulationstocomputespectra lem requires variability and multiwavelength studies (e.g. bothincludingandexcludingbulkvelocities.Sinceoursim- Mehdipour et al. 2011;Vasudevan et al. 2014). ulationdataislimited,weuseaschemetoscaledatafroma Because optically thick disc models predict that disc simulationrunwithaparticularradius,mass,andaccretion emission associated with NLS1s already extends into the rate to different sets of these parameters. We describe this soft X-rays, in these sources warm Comptonization could scheme in section 2.2. In this work we use data from sim- be due to modifications to the vertical structure that oc- ulation 110304a, which is similar to simulations 1112a and cur in this regime. For example, warm Comptonization 1226b (Hirose et al. 2009), but has a lower surface density, may be due to turbulence in the disc (Socrates et al. 2004; Σ=2.5 104gcm−2,which resultsin ahigherradiation to Kaufman & Blaes 2016, hereafter KB16), if bulk electron gas pres×sure ratio. The parameters of interest for 110304a velocities exceed thermal electron velocities. For the alpha are given in Table 1. disk model1 (SS73), We calculate the spectrum at a given timestep using MonteCarlo post processing simulations. Forthiswork, we vt2urb α me Prad , (1) chose the 140 orbit timestep at random. The details of our (cid:10)hvt2hi(cid:11) ∼ (cid:18)mp(cid:19)(cid:18)Pgas(cid:19) MonteCarloimplementationofbulkComptonscatteringare inAppendixA.Toisolatetheeffectoftheturbulencealone, so we expect turbulent Comptonization to be important in wealso calculate spectra without thebackground shear. To theextremeradiationpressuredominatedregime.Sincethe model an entire accretion disc we calculate spectra at mul- ratioofradiationtogaspressureincreaseswithmassandac- tipleradii.Wediscussourchoiceofradiiinsection2.3.The cretionrate,turbulentComptonizationshouldbemostrele- flux obtained at a particular radius corresponds to an Ed- vantforsupermassiveblackholesaccretingnear-Eddington, dington ratio. Ifour scaling schemewere perfect, thecorre- such as NLS1s. In this regime, therefore, turbulent Comp- sponding Eddington ratios at the other radii would be the tonization could provide a physical basis for the construc- same by construction. We correct for minor discrepancies tion of warm Comptonization models. By connecting the by normalizing the other spectra so that their correspond- observedtemperatureandoptical depthtothediscvertical ing Eddington ratios are the same. structure,thiscouldhelpsolvetheproblemofthesoftexcess We transport the spectra computed with bulk veloci- andalsoshedlightonthepropertiesofMHDturbulence.In ties at multiple radii to infinity and superpose the results broad line Seyferts, which have lower Eddington ratios, the to obtain the final, observed spectrum. We choose a view- ratio of radiation to gas pressure is too small for turbulent ingangleof60◦.Atthisanglethegravitational redshift ap- Comptonization to be significant, so if warm Comptoniza- proximatelycancelstheDopplerblueshift(D12,Zhang et al. tionispresentit mustoriginate elsewhere. Inthesesources, 1997), which allows us to use a Newtonian transport code. it is unlikely that warm Comptonization could be due to Wechosethismethodbecauseitiseasytoincludetheprop- agationoferrorbars,butweverifiedthatourresultsareun- changed when a fully relativistic Kerr spacetime transport 1 Themp/me factorinKB16Eq.(1)shouldbeflipped. code (Agol 1997) is used instead. The contribution of bulk Comptonization to the soft X-ray excess in AGN 3 The spectracomputed without bulkvelocities are used as seed photon sources for a warm Comptonizing medium 101 characterized solely by a uniform temperature and optical 110304a depth.WeimplementthisbysolvingtheKompaneetsequa- OPALR20 tionateachradius.Wethentransporttheresultantspectra 100 to infinity to obtain the observed spectrum. We fit the ob- served spectrum Comptonized by the warm medium to the 10-1 observedspectrumcomputedwithbulkvelocitiesbyadjust- ingthetemperatureandopticaldepth.Weexploretheeffect ρ/ρc ofvaryingtheouterradius,rcor,ofthewarmComptonizing 10-2 medium on the goodness of fit parameter, χ2/ν, and select theradius for which this parameter is minimized. ToprovideinsightintothephysicsofbulkComptoniza- 10-3 tion,wealsoperformspectralcalculationsinwhichthesim- ulation data are truncated at theeffective photosphere and 10-4 the emissivity is zero everywhere except in the cells at the 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 z/h base.SinceweexpectbulkComptonizationtobedominated by the contribution from photons emitted at the effective Figure1.Normalizedshearingboxdensityprofilesat140orbits. photosphere, we expect the resulting temperature and op- tical depth to be nearly unchanged. We discuss this point more in section 4.2. 101 110304a 2.2 Scalings for radiation MHD shearing box OPALR20 simulation data 100 In this section we derive a scheme to scale data from a ra- diationMHDsimulationrunwithaparticularradius,mass, 10-1 and accretion rate to a different set of these parameters. ρ/ρc We first observe that the construction of an appropriate 10-2 schemeismadepossiblebythefactthatthedensity,temper- ature,and velocity profilesshowconsiderable self-similarity across a wide range of simulation parameters. For example, 10-3 in Figures 1 and 3 we compare the density and bulk veloc- ity profiles from the 140 orbit timestep of 110304a, which is the basis of this work, with those from a snapshot of 10-40.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 z/h OPALR20 (Jiang et al. 2016), a simulation run in an en- tirely different regime (Table 1). The bulk temperature is Figure2.Normalizedshearingboxdensityprofilesat180orbits. defined by (3/2)kBTbulk = (1/2)mev2. Subscript “c” de- notes midplane values. The variable z is the distance from the midplane and the scale height h is the value of z for which ρ/ρc = 1/e. The profiles nearly coincide, and even 103 the discrepancy between the density profiles at large z/h 110304a is likely just due to a temporary fluctuation at 140 orbits. OPALR20 At 180 orbits, for example, there is no discrepancy (Figure 102 2). This self-similarity is perhaps an even more robust phe- nomenonthanthedifferenceinsimulationparametersalone wimnoauOllsPdtAainbLdiRliict2ya0toeisfsOianPcneAontLh-Rter2iiv0nicadlluepesffieonencdtos.foItnnhepthaierrotiinncucollpuaars,icoittnhyeobftuhtmherips- T/Tbulkbulk,c 101 effect(Jiang et al.2016),whereasitisnowbelievedthatthe thermalstabilityin110304aisaresultofthenarrowboxsize 100 intheradialdirectionandisthereforeartificial(Jiang et al. 2013). Despite this caveat as well as the fact that the mass parameter for OPALR20 is closer to our regime of interest, 10-1 we chose 110304a for this work because the photospheres 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 z/h are better resolved, a decisive advantage for the purpose of computing spectra. Figure3.Normalizedshearingboxbulktemperatureprofilesat Becauseofself-similarity,weprimarilyneedtoscalethe 140orbits. midplane values for the profiles of interest and the scale height. Analogous to the derivation of the standard α-disc scalings intheradiation pressuredominatedregime(SS73), wederivescalings in termsoftheshearing boxsurface den- 4 J. Kaufman, O. M. Blaes, and S. Hirose Table 1.Shearingboxsimulationparameters Table 2. Ratios of variables predicted using 110304a data to variables measured in OPALR20, taking into account α/α0 = Simulation M/M⊙ L/LEdd r/rg 2.38. 110304a 6.62 1.68 30 OPALR20 5×108 0.03 40 Variable Ratio hscaled/h 0.9 sity Σ, the vertical epicyclic frequency Ω , and the shear Tg,c,scaled/Tg,c 1.0 ∂ v .Theintegrated hydrostaticequilibriuzmequationfora Tbulk,c,scaled/Tbulk,c 0.9 x y density profile with scale height h and midplane radiation pressure Pc is To test these scalings, we scale the midplane values and the scale height from 110304a to the simulation parame- 1 Pc = 4Ω2zΣh. (2) ters of OPALR20 and then divide by the actual midplane values and the scale height in OPALR20 (Table 2). We as- The thermal equilibrium equation, given the radiation flux F and themidplane turbulentstress τc is ssutrmesesβr/aβti0o=α1/.αT0a=kin2g.3i8n,towaeccsoeuentthtahtetehmeprieriscualltitnugrbrualteinost F =(∂xvy)τch. (3) are all near unity, and that our scalings therefore capture theessential physics in the shearing box. This is even more The stress prescription is remarkable given that our scalings only take into account τ¯=αP¯, (4) Thomson scattering and radiation diffusion, while the iron which for a profile that decays with scale height h is equiv- opacity bump and vertical advection are non-trivial effects alent to in OPALR20. The density and turbulent velocity profiles follow di- τc=αPc. (5) rectlyfromEqs.(7),(10),and(12),butthepressureprofile, The radiative diffusion equation with the opacity given by whichdeterminesthegastemperatureprofile,isnon-trivial. κ is The density profileis F = 2cPc. (6) Σ h −1 κΣ ρ(z)= ρ0(h0z/h). (13) Eqs. (3), (5), and (6) give thescale height scaling: (cid:18)Σ0(cid:19)(cid:18)h0(cid:19) h α −1 κ −1 ∂ v −1 Σ −1 The turbulentvelocity profile is = x y . (7) (cid:18)h0(cid:19) (cid:18)α0(cid:19) (cid:18)κ0(cid:19) (cid:18)∂xvy,0(cid:19) (cid:18)Σ0(cid:19) v(z)= α −1/2 β 1/2 κ −1 Ωz Sinceweintendtoscaletothelowermass( 106M⊙),high (cid:18)α0(cid:19) (cid:18)β0(cid:19) (cid:18)κ0(cid:19) (cid:18)Ωz,0(cid:19) Eddington ratio regime, the opacity remain∼s dominated by ∂ v −1 Σ −1 electronscatteringsowesetκ/κ0 =1.Eqs.(2)and(7)give (cid:18)∂xxvyy,0(cid:19) (cid:18)Σ0(cid:19) v0(h0z/h). (14) themidplane pressure scaling: But scaling the radiation pressure profile by adjusting only Pc = α −1 κ −1 Ωz 2 ∂xvy −1. (8) thescaleheightandtheoverallnormalizationistoosimplis- (cid:18)Pc,0(cid:19) (cid:18)α0(cid:19) (cid:18)κ0(cid:19) (cid:18)Ωz,0(cid:19) (cid:18)∂xvy,0(cid:19) tic a scheme for the purpose of calculating spectra because Below we will also need thefluxscaling: near the photosphere the flux begins to free stream and is no longer carried by radiative diffusion. In such a scheme, F α −1 κ −2 Ω 2 ∂ v −1 Σ −1 = z x y . therefore,theprofilewillbeleastaccurateintheregionthat (cid:18)F0(cid:19) (cid:18)α0(cid:19) (cid:18)κ0(cid:19) (cid:18)Ωz,0(cid:19) (cid:18)∂xvy,0(cid:19) (cid:18)Σ0(cid:19) itismostimportant.Thisdifficultycanbeaddressedbyim- (9) posinga boundarycondition at thephotosphere.Insidethe For the purpose of calculating spectra, the profiles of inter- photosphere, estarethedensity,thegastemperature,theturbulentveloc- ity,andtheshearvelocity.Themidplanedensityistrivially Pph,in∼Tp4h,in∼(fcorTph,out)4 ∼fc4orF, (15) given by wherefcor isdeterminedbythephysicsatthephotosphere. ρc = Σ h −1. (10) Fteorrinegxaamndplteh,eifbtohuenodpaarycitcyonisdidtioomninisatimedpbosyedcoahtertehnetesffceact-- (cid:18)ρc,0(cid:19) (cid:18)Σ0(cid:19)(cid:18)h0(cid:19) tivephotosphere,thenfcor =fcol,thecolor correction. The Since the gas temperature is coupled to the radiation tem- scaling for P is then ph,in perature, the scaling for the midplane gas temperature fol- lows directly from Eq. (8). To find the turbulent velocity P = fcor 4 F P . (16) scaling, we defineβ as follows: ph,in (cid:18)fcor,0(cid:19) (cid:18)F0(cid:19) ph,in,0 1 ρv2 =βτ. (11) The simplest scheme that imposes this boundary condition 2 is given by The midplane turbulentv(cid:10)eloc(cid:11)ity scaling is then (cid:10)vvc2c2,0(cid:11) =(cid:18)αα0(cid:19)−1(cid:18)ββ0(cid:19)(cid:18)κκ0(cid:19)−2(cid:18)ΩΩzz,0(cid:19)2 P(z)=Pph,in+(cid:18)PPcc,0(cid:19)(P0(h0z/h)−P0(h0zph/h)), (17) which we formally derive in Appendix B. We recall that (cid:10) (cid:11) ∂xvy −2 Σ −2. (12) Pc/Pc,0 isgivenbyEq.(8).Sincethepressureatthephoto- (cid:18)∂xvy,0(cid:19) (cid:18)Σ0(cid:19) sphereis always orders of magnitude smaller than the mid- The contribution of bulk Comptonization to the soft X-ray excess in AGN 5 plane pressure, we find that are given in AppendixE. Weonly use Kerrscalings for our spectralcalculations,buttheNewtonianscalingsarepoten- P(0) Pc P0(0), (18) tially useful for the purpose of comparing with other works ≈(cid:18)Pc,0(cid:19) inwhichNewtonianparametersareusedandalsofordevel- sothatthisschemeisself-consistent.Insidethephotosphere oping physical intuition. thegastemperatureiscoupledtotheradiationtemperature, sointhisregionthegastemperatureprofileisthengivenby 2.3 Dependence of turbulent Comptonization on Tg4,in(z)=Tg4,ph+(cid:18)PPcc,0(cid:19) Tg4,0(h0z/h)−Tg4,0(h0zph/h) , To charraadcituersize the contribution of turbulent Comptoniza- (cid:0) (1(cid:1)9) tion, we must model spectra at multiple radii. Our choice where ofradii isguided bythescaling of theratio of bulktother- P malelectronenergies.Weestimatethiseffectforadiscwith Tg4,ph = Pph,in Tg4,ph,0. (20) nospin andastress-free innerboundarycondition with the (cid:18) ph,in,0(cid:19) NewtonianscalingsinAppendixE.Thebulkvelocityscaling Inorderthatthegastemperatureprofilebecontinuous,the is scaling outside thephotosphere is given by 2 Tg4,out(z)=(cid:18)PPpphh,i,nin,0(cid:19)Tg4,0(zph,0+h0(z−zph)/h). (21) The photosphe(cid:10)revt2tuhrbe(cid:11)rm∼alr−v3el(cid:16)o1ci−typscrailnin/rg(cid:17)is. (23) Fwihniachllyi,swteriavlisaollnyegeidvetnhebsycalingfortheshearvelocityprofile, vt2h,ph ∼r−3/4 1− rin/r 1/4. (24) ∂ v h Thescalingf(cid:10)orthe(cid:11)ratioofbu(cid:16)lkveplocityto(cid:17)thermalvelocity vs(x)=(cid:18)∂xxvyy,0(cid:19)(cid:18)h0(cid:19)vs,0(h0x/h). (22) at thephotosphereis Wτse=de1fin(ewhzeprhetsoubbsecriwphte“res”thdeensoctaetstesrciantgteoripntgic)aalnddepsteht (cid:10)vv2t2urb(cid:11) ∼r−9/4 1− rin/r 7/4. (25) fcor/fcor,0 =1.Nearthephotospheremagneticpressurebe- th,ph (cid:16) p (cid:17) D E gins to play a major role in hydrostatic equilibrium (e.g. Wealsocalculatethescalingfortheratioofbulktothermal Blaes, Hirose & Krolik 2007), and near the effective photo- velocity using the midplane thermal velocity scaling, which spherethegastemperaturebeginstodivergefromtheradi- is ationtemperature,soweacknowledgethattheassumptions v2 r−3/8. (26) underlyingourschemedonotreflectthedetailed physicsin th,c∼ this region. But since our goal is only to calculate spectra, The scaling for the ratio is for opticaldepthsτs 1theaccuracy ofthisschemeis not important. We can a≪ssess the validity of this scheme in the vt2urb r−21/8 1 rin/r 2. (27) lraetgiioonnsτwsit≈h 1thbeyinctoemndpeadrinflguxthgeivflenuxbyfroEmq.s(p9e)c,torar,l ecqaulciuv-- (cid:10)vt2h,c(cid:11) ∼ (cid:16) −p (cid:17) D E alently, by comparing the corresponding Eddington ratios. WeplotEqs.(25)and(27)inFig.4,normalizedto30gravi- Insection3.1,wemakethiscomparison foreachsetofscal- tationalradii.WeexpectthatturbulentComptonizationwill ing parameters we use and find that they generally agree bemostsignificantbetween8and20gravitationalradii.We to within 10%. More importantly, we find that normalizing verifythisassumptioninsection3.Forourmodelwechoose thespectraatdifferentradiisothattheircorrespondingEd- tocomputespectraat30,20,14,11,10,9.5,9.0,8.5,and7.5 dington ratios match hasa neglible impact on theobserved gravitationalradii.Wealsorunsimulationsforspina=0.5, spectrum when contrasted with the discrepances between forwhichrin=4.2.Forthesewecomputespectraat30,20, spectral calculations with and without bulk velocities. In 15, 12, 10, 8, 7, 6, 5.5, and 5 gravitational radii. other words, because thepotential error is significantly less than the effect we are measuring, our scaling scheme is ad- equate. 3 RESULTS Thesearetheappropriateequationsforscaling datato a different set of fundamental shearing box simulation pa- WecomputethecontributionofbulkComptonizationtothe rameters, in particular Ω , ∂ v , and Σ. If we substitutein softX-rayexcessandcharacterizeourresultswithatemper- z x y Eq.(9)forΣ,wecanalternativelyregardF asafundamen- atureandopticaldepth.Ourfiducialmass,M =2 106M⊙, × tal parameter instead of Σ. Shearing box scalings in terms and Eddington ratio, L/L = 2.5, were chosen to corre- Edd of F are given in Appendix C. This substitution is useful spond to those of the NLS1 source RE 1034+396 in D12 in order to scale to a different set of fundamental accretion (Table8).Table4summarizesourmainresults.Theoriginal disc parameters, since it is straightforward to express F in (unscaled) simulation parameters for 110304a are listed in termsofaccretiondiscradius,mass,andaccretionrate.The Table1.Eachsystemismodeledbycalculatingspectrawith scalings for Ω , ∂ v , and F for both Newtonian and Kerr andwithoutthebulkvelocitiesatthesetofradiidiscussedin z x y discs, allowing for a non-zero stress inner boundary condi- section 2.3. The target L/L is the Eddington ratio that Edd tion, are given in Appendix D. The final scalings for ρ, Tg, would correspond to the observed flux at 30 gravitational v,andvs intermsoffundamentalaccretiondiscparameters radii if the scaling scheme were exact. The turbulent stress 6 J. Kaufman, O. M. Blaes, and S. Hirose Table 3.Simulationsetindependent variables Set Type M/M⊙ L/LEdd (target) a α/α0 vturb vshear a Full 2×106 2.5 0 1 Y Y a2 Truncated, emissivityatbase 2×106 2.5 0 1 Y Y b Full 2×106 2.5 0 1 Y N b2 Truncated, emissivityatbase 2×106 2.5 0 1 Y N c Full 2×106 2.5 0 2 Y Y c2 Truncated, emissivityatbase 2×106 2.5 0 2 Y Y d Full 2×106 2.5 0.5 1 Y Y d2 Truncated, emissivityatbase 2×106 2.5 0.5 1 Y Y e Full 2×107 2.5 0 1 Y Y e2 Truncated, emissivityatbase 2×107 2.5 0 1 Y Y Table 4.Resultsforfullatmospherespectralcalculations Set M/M⊙ L/LEdd (target) a α/α0 vturb vshear L/LEdd (observed) kTe (keV) τ rcor(rg) yp χ2/ν a 2×106 2.5 0 1 Y Y 2.5 0.14±0.0067 15±1.4 20 0.26 1 b 2×106 2.5 0 1 Y N 2.5 0.18±0.056 11±4.2 14 0.14 1.7 c 2×106 2.5 0 2 Y Y 2.3 0.17±0.012 17±1.8 20 0.38 2.3 d 2×106 2.5 0.5 1 Y Y 2.3 0.21±0.011 12±0.82 20 0.22 1.9 e 2×107 2.5 0 1 Y Y 2.1 0.081±0.0075 24±4.1 20 0.37 0.87 3.5 1045 Photosphere Midplane 3.0 1044 2.5 22v/vturbth21(cid:1)(cid:0)(cid:1)(cid:0)..05 1L (erg s)−eff,ν1043 ν 1.0 1042 set (a), no BC + Komp 0.5 set (a), no BC 1041 set (a), BC 0.0 5 10 15 20 25 30 102 r/rg hν (eV) Figure 4. Scaling for the relative magnitude of the turbulent Figure5.Observeddiscspectracomputedforset(a).BC(bulk velocityforrin=6rg,normalizedtor=30rg. Comptonization) means bulk velocities were included. Komp means thezerobulkComptonization spectrum fromeach radius for r 6 rcor was passed through a warm Comptonizing medium withtheparametersgiveninTable4. scalingisgivenbyα/α0.Inallcases,∆ǫ=0(AppendixD), whichimposesthestress-freeinnerboundarycondition.The Table7.FluxnormalizationstotheEddingtonratioatr=30rg choicesofwhetherornottoincludeturbulentandshearve- forset(a). locities in the spectral calculations with bulk velocities are indicated by v and v , respectively. The Compton y r/rg Fluxnorm(NoBC) Fluxnorm(BC) turb shear 30 1 1 parameteriscalculatedfromthefittedtemperatureandop- 20 1.04 1.10 tical depth. To calculate χ2/ν, we first correct for uncer- 14 1.04 1.15 tainty in the overall normalization of the data point errors 11 0.99 1.06 by normalizing them to the standard deviation calculated 10 0.95 0.96 from the fit for set (a) (shown in Fig. 5). In section 3.1, we 9.5 0.92 0.94 discuss the results of each set. To provide physical insight 9.0 0.91 0.89 into the physics of bulk Comptonization, we also perform 8.5 0.90 0.87 spectralcalculationsinwhichthesimulationdatawastrun- 7.5 1.03 1.06 catedattheeffectivephotosphereandtheemissivitywasset to zero everywhere except in the cells at the base. Table 5 3.1 Full spectral calculations summarizes these results, which we discuss in section 3.2. For clarity, in Table 3 we list the independent variables for Theobservedspectrumforset(a)computedwithandwith- all simulation sets. out the bulk velocities along with the Kompaneets fit are The contribution of bulk Comptonization to the soft X-ray excess in AGN 7 Table 5.Resultsfortruncatedatmospherespectralcalculations withemissivityonlyatthebase. Set M/M⊙ L/LEdd (target) a α/α0 vturb vshear kTe (keV) τ rcor(rg) yp χ2/ν a2 2×106 2.5 0 1 Y Y 0.14±0.0065 16±1.4 30 0.26 0.67 b2 2×106 2.5 0 1 Y N 0.13±0.013 12±2.5 20 0.15 1.3 c2 2×106 2.5 0 2 Y Y 0.18±0.015 14±1.4 30 0.28 0.93 d2 2×106 2.5 0.5 1 Y Y 0.18±0.011 14±1.2 20 0.28 0.93 e2 2×107 2.5 0 1 Y Y 0.074±0.0040 32±4.5 20 0.57 0.52 Table6.Goodnessoffitofparametersderivedfromtruncatedatmospherespectralcalculationstoobservedspectracalculatedwiththe fullatmosphere. Set kTe (keV) τ rcor(rg) yp χ2/ν a 0.14 16 30 0.26 1.6 b 0.13 12 20 0.15 2.0 c 0.18 14 30 0.28 2.6 d 0.18 14 20 0.28 1.9 e 0.074 32 20 0.57 1.1 1045 1045 1044 1044 1g s)−1043 1g s)−1043 er er L (eff,ν L (eff,ν ν ν 1042 1042 set (a), no BC set (a), no BC set (a), BC set (a), BC set (d), no BC 1041 set (b), BC 1041 set (d), BC 102 102 hν (eV) hν (eV) Figure 7.Observed discspectra computed forsets (a) and (b). Figure 9.Observed discspectra computed forsets (a) and (d). BC (bulk Comptonization) means bulk velocities were included. BC (bulk Comptonization) means bulk velocities were included. Set(a)includesbothturbulenceandshear.Set(b)includesonly Forset(a), thespinparametera=0.Forset(d), a=0.5. turbulence. shown in Figure 5. We see that the fit is excellent, which 1045 means that bulk Comptonization here is well modeled by thermal Comptonization with a fitted temperature and op- ticaldepth.WenotethattheobservedL/L matchesthe Edd 1044 target L/LEdd, which confirms that our scaling scheme is self-consistent. The required flux normalizations given the flux at 30 gravitational radii are given in Table 7. They 1g s)−1043 hardlydeviatefromunity,whichprovidesanothercheckfor L (ereff,ν tshpeecsterlaf-caotnmsiustletinpclye roafdoiuirfosrcasleitng(sa.).InWFeigs.ee6twheatshtohwe slpoceac-l ν 1042 trapassed through thewarm Comptonizing medium fit the spectracalculated withbulkvelocitiesfor 9.5rg 6r620rg, set (a), no BC but overshoot them for r = 7.5rg and r = 30rg. This con- 1041 sseett ((ac)),, BBCC firms that bulk Comptonization is most significant in the region we expected it to be (section 2.3). Furthermore, this 102 hν (eV) isconsistent withthevaluewefindforrcor,sinceweexpect thebestfittobeobtainedwhentheComptonizingmedium Figure 8. Observed discspectra computed for sets (a) and (c). is restricted to the region in which bulk Comptonization is BC (bulk Comptonization) means bulk velocities were included. most significant. For set (a) the turbulent stress scaling α/α0 is 1. For set (c), Forset(b)wecalculatespectrawithoutthebackground α/α0=2. shear to isolate the effect of turbulence. The resulting ob- servedspectrumisplottedinFigure7.Weseethatthespec- 8 J. Kaufman, O. M. Blaes, and S. Hirose 1019 r=7.5rg 1019 r=9.5rg 1018 1018 νFν1017 νFν1017 1016 1016 set(a), no BC + Komp set(a), no BC + Komp set(a), no BC set(a), no BC set(a), BC set(a), BC 1015 102 1015 102 hν (eV) hν (eV) 1019 r=11rg 1019 r=14rg 1018 1018 νFν1017 νFν1017 1016 1016 set(a), no BC + Komp set(a), no BC + Komp set(a), no BC set(a), no BC set(a), BC set(a), BC 1015 102 1015 102 hν (eV) hν (eV) 1019 r=20rg 1019 r=30rg 1018 1018 νFν1017 νFν1017 1016 1016 set(a), no BC + Komp set(a), no BC + Komp set(a), no BC set(a), no BC set(a), BC set(a), BC 1015 102 1015 102 hν (eV) hν (eV) Figure 6. Disc spectra at select radii, labeled at the top of each plot, computed for set (a). BC (bulk Comptonization) means bulk velocitieswereincluded.KompmeansthezerobulkComptonizationspectrumwaspassedthroughawarmComptonizingmediumwith theparameters giveninTable4. trumcomputedwithoutshearliessignificantlyclosertothe example, α/α0 = 2.38. The resulting observed spectrum is spectrum computed with shear than to the spectrum com- plottedinFigure8.Weseethatalthoughtheobservedspec- puted without the bulk velocities. This indicates that bulk trum computed with α/α0 = 2 is Comptonized more than Comptonization is primarily dueto turbulence,not shear. the spectrum computed with α/α0 = 1, the effect is not For set (c) we test the robustness of our results by re- huge.Inparticular,thefittedtemperatureandopticaldepth peatingspectralcalculationswithadifferentturbulentstress areonly21%and13%higher,respectively.Sincetheturbu- scaling ratio, α/α0 = 2. For OPALR20 (section 2.2), for lentvelocitysquaredscalesasα(Eq.C4),onemightexpect The contribution of bulk Comptonization to the soft X-ray excess in AGN 9 1045 1045 1044 1044 1g s)−1043 1g s)−1043 er er L (eff,ν L (eff,ν ν ν 1042 1042 set (a), no BC set (a), no BC + Komp 1041 set (a2), no BC 1041 set (a), no BC + Komp 2 102 102 hν (eV) hν (eV) Figure10.Observeddiscspectracomputedforsets(a)and(a2). Figure11.Observeddiscspectracomputedforset(a).BC(bulk In set (a2), the atmosphere is truncated at the effective photo- Comptonization) means bulk velocities were included. Komp sphereandtheemissivityiszeroeverywhereexceptatinthecells means thezerobulkComptonization spectrum fromeach radius atthebase. for r 6 rcor was passed through a warm Comptonizing medium withtheparametersgiveninTable4.ForKomp2theparameters usedarethosefittoset(a2),giveninTable5. that the fitted temperature would also scale as α, but this neglects the contribution by shear as well as the fact that weare fittingtheoptical depthalong with thetemperature ent,butweexpecttheeffectofbulkComptonization onthe ratherthanholdingtheopticaldepthfixed.Themagnitude observed spectra to be nearly unchanged. For example, the of bulk Comptonization is better indicated by yp. From set spectra computed without velocites for sets (a) and (a2), (b) we see that for α/α0 = 1, yp = 0.14 for turbulence normalized to the total flux of (a), are plotted in Fig. 10. alone. From sets (a) and (b) we infer that for α/α0 = 1, The spectra coincide at high energies and diverge at low yp = 0.26 0.14 = 0.12 for shear alone. We would expect, energies since photons emitted from lower temperature re- − therefore, that for α/α0 = 2, yp = 2 0.14+0.12 = 0.40, gions are omitted in (a2). But the fitted temperatures and × which is very close tothe fittedvalue yp =0.38. opticaldepthsforcorrespondingsetsareverysimilar,which Forset(d)weexploretheeffectofvaryingthespinpa- supportsour pictureof bulk Comptonization. rameterbysettinga=0.5.Theresultingobservedspectrum For sets (a) to (e), we also pass the spectra computed isplottedinFigure9.Asexpected,theoriginalspectracom- without the bulk velocities through a warm Comptonizing putedwithoutbulkvelocitiesarehotterandmoreluminous mediumwiththetemperaturesandopticaldepthsfittosets for the higher spin parameter since the accretion efficiency (a2)to(e2),respectively,andseewhethertheresultsfitthe ishigher.ButtheeffectofbulkComptonizationiscompara- spectra computed with the bulk velocities. For each case ble.Thefittedtemperatureisslightly higher,butthefitted we calculate χ2/ν to assess the goodness of fit and list the optical depth is slightly lower, leading to an effect that is resultsinTable6.InFig.11forset(a)weplottheobserved nearly thesame. spectrum obtained by thisprocedure as well as theoriginal Finally, for set (e) we use a higher mass, M = 2 fit. We see that the two curves nearly coincide and note 107M⊙.Thefittedtemperatureislower,consistentwithth×e that thecorresponding values of χ2/ν differ by 0.6. For the dependence of overall accretion disc temperature on mass. otherpairsofsetsthecorrespondingvaluesofχ2/ν differby But the larger value of yp indicates that the effect of bulk even less, which again confirms our expectation that bulk Comptonization on the spectrum is greater. This is consis- Comptonization is due to the Comptonization of photons tentwithEq.(1),sincetheratioofradiationtogaspressure emitted at the effectivephotosphere. increases with mass (SS73). 4 DISCUSSION 3.2 Truncated atmosphere spectral calculations with emissivity only at the base 4.1 Comparison with RE1034+396 We expect that bulk Comptonization is predominantly ex- In NLS1s the Wien tail of the intrinsic disc spectrum con- plainedbytheComptonizationofphotonsemittedattheef- tributes to the soft excess (D12). Bulk Comptonization in- fectivephotosphere.Wediscussthisin detailin section 4.2. creases the contribution to the soft excess by shifting the Totestthispicture,werepeatspectralcalculationswiththe Wien tail to higher energy. Since bulk Comptonization in- parametersgiveninTable4buttruncatetheatmosphereat creases with accretion rate, we expect this contribution to the effective photosphere and set the emissivity to zero ev- be greatest in near and super-Eddington sources. In broad erywhereexceptinthecellsatthebase.Table5summarizes line Seyferts, the ratio of radiation to gas pressure is too these results. low for bulk Comptonization to be significant. We com- For these calculations the observed spectra are differ- pare our results to the analysis by D12 of RE1034+396, 10 J. Kaufman, O. M. Blaes, and S. Hirose Table 8.FitstoobservedNLS1s Source Model Reference M/M⊙ L/LEdd kTe (keV) τ yp RE1034+396 OPTXAGNF D12 1.9×106 2.4 0.23±0.03 11±1 0.22 a super-Eddington NLS1 with an unusually large soft ex- that second order effects, not first order effects, are domi- cess. This analysis is summarized in Table 8. The compari- nant. This may be because MRI turbulence is incompress- sonisappropriatebecausethemassandEddingtonratiowe ibleandfirstordereffectsvanishforincompressible,butnot choseforourspectralcalculationscorrespondtothosefitto compressible, turbulence (KB16). On the other hand, the RE1034+396, thoughwedonotethatourmodelforComp- photosphere regions are magnetically dominated and show tonization is more detailed than the one in D12.2 We see considerable compressible motions because of the Parker thattheComptony parameter,yp =0.22, whichcharacter- instability (Blaes, Hirose & Krolik 2007), so it seems more izestheoverallimpact of Comptonization on thespectrum, likely that first order effects average out. isremarkablysimilartothevalueswefound.Thefittedtem- Assuming second order effects are dominant, we can peratureandoptical deptharealso similar toourvalues.It gain physical insight into the fitted temperatures and opti- may be, therefore, that the soft excess is unusually large in caldepthsbyconsideringthedependenceoftheshearstress, thissystembecauseofthecontributionofbulkComptoniza- Pij,onthephotonmeanfreepath.Thestressislargestwhen tion. thephoton mean free pathis longrelative tothemaximum A soft excess is also present in less luminous AGN for turbulencewavelength, and isproportional tothesquareof whichbulkComptonizationisunlikelytobesignificant,and thephoton mean free pathwhen it is small (KB16). There- ingeneralitseemsthatnosinglephysicaleffectcanfullyex- fore, Comptonization is only significant in the region near plain the soft excess in all AGN. Until the contribution to enough to the photosphere that the photon mean free path thesoftexcessbyotherproposedmechanismssuchasreflec- iscomparabletothemaximum turbulencewavelength.The tionandabsorptionarebetterunderstood,itwillbedifficult resulting Comptonization temperature and optical depth to tease out the contribution of bulk Comptonization. But should be the same for all photons emitted below this re- ourcalculationsshowthatifthiscanbedonethenobserva- gion.Insidethisregion,ontheotherhand,photonsemitted tions of the soft excess can be used to constrain properties nearer the photosphere should have comparatively larger of the turbulenceas well as other disc parameters. Comptonization temperatures and smaller optical depths. Forrealdiscatmospheres,whicharestratifiedin(gas) tem- perature,photonscontributingtothespectralpeakarepre- dominantly emitted at the effective photosphere, which for 4.2 Physical interpretation of results modest turbulence should be below the region where bulk Comptonizationofphotonsbybulkmotionsisduetoeffects Comptonization is significant. We therefore expect the re- both first and second order in velocity (KB16). The Kom- sulting Comptonization temperature and optical depth to paneetsequation,whichdescribesthermalComptonization, be unchanged when we truncate the atmosphere at the ef- cannot be used to describe first order effects, but KB16 fective photosphere and set theemissivity equal to zero ev- showed that for incompressible motions in a periodic box erywhereexceptatthebase.Ourfindingsconfirmthis.This with an escape probability, it does capture second order is also useful because these spectral calculations run much effects. The Kompaneets temperature for bulk velocities, faster which allows for a more efficient exploration of the which is a function of the photon mean free path, is given disc parameter space. by kBTKomp = −2λEpmec Pij(∂ivj+∂jvi) , (28) 4.3 sSiemlfu-claotnisoinstsency of results with shearing box D E whereEistheradiationenergydensityandPij istheradia- We see that when bulk velocities are included in spectral tionpressuretensor.Notethatonlythetracelesspartofthe calculations, the observed spectrum is shifted to higher en- pressure tensor, which is the shear stress, contributes since ergy.Inparticular,theWientailisshiftedright.Whilethis thisresultassumesincompressiblemotions.Weseethatthe allows us to characterize bulk Comptonization with a tem- Kompaneets temperature for bulk velocities is proportional perature and optical depth as a function of accretion disc to thestress multiplied by thestrain rate, which is just the parameters, to determine the actual impact on disc spec- viscousdissipation ofbulkmotionsbythephotons.Astrat- tra we must consider whether our spectral calculations are ified disc atmosphere is more complex than a periodic box, consistent with the underlying shearing box simulations on buttheKompaneetsequationmaystilladequatelydescribe which they are based. second order effects. Insection4.2weshowedthatbulkComptonizationhere For our spectral calculations bulk Comptonization is is predominantly an effect that is second order in velocity, welldescribedbytheKompaneetsequation,whichsuggests but the underlying shearing box simulations (Hirose et al. 2009)donotincludethiseffectbecausethefluxlimiteddif- fusion approximation is used (KB16). Therefore, according 2 Inparticular,inD12thephotonspectrum passedthroughthe to this picture we expect the spectral calculations without warmComptonizingmediumisgivenbythespectrumatrcorand the bulk velocities to be consistent with the flux found in onlytheoverallnormalizationvarieswithradius.Thischoicewas the underlying shearing box simulation. In order to deter- madetominimizecomputation time. minetheeffectofincludingthebulkvelocitiesontheresult-