The contribution of bulk Comptonization to the soft X-ray excess in AGN

0.6 MB·

by  Jason Kaufman

Mon.Not.R.Astron.Soc.000,1–??(2015) Printed25January2017 (MNLATEXstylefilev2.2)
The contribution of bulk Comptonization to the soft X-ray
excess in AGN
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1 J. Kaufman⋆, O. M. Blaes, and S. Hirose
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Department of Physics, Universityof California, Santa Barbara, CA 93106, USA
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n
a
Accepted —.Received—;inoriginalform—
J

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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.
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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-