Table Of Content**VolumeTitle**
ASPConferenceSeries,Vol.**VolumeNumber**
**Author**
(cid:13)c**CopyrightYear**AstronomicalSocietyofthePacific
GasAccretion onto a SupermassiveBlack Hole: a stepto model
AGNfeedback
2
1
0 KentaroNagamine,1 ParamitaBarai,1,2 andDanielProga1,3
2
1University ofNevada,LasVegas,DepartmentofPhysicsandAstronomy,4505
n
S.MarylandPkwy,LasVegas,NV89154-4002, USA
a
J
2INAF-AstronomicalObservatory ofTrieste,ViaG.B.Tiepolo11,I-34143
1
Trieste,Italy
1
3Princeton UniversityObservatory, PeytonHall,Princeton, NJ08540, USA
]
O
C Abstract. Westudythegasaccretionontoasupermassiveblackhole(SMBH)using
the 3D SPH code GADGET-3 on scales of 0.1−200pc. First we test our code with
.
h sphericallysymmetric,adiabaticBondiaccretionproblem.Wefindthatoursimulation
p
canreproducetheexpectedBondiaccretionflowverywellforalimitedamountoftime
-
o untiltheeffectofouterboundarystartstobevisible. We alsofindartificialheatingof
r gas near the inner accretion boundary due to the artificial viscosity of SPH. Second,
t weimplementradiativecoolingandheatingduetoX-rays,andexaminetheimpactof
s
a thermalfeedbackbythecentralX-raysource. Theaccretionflowroughlyfollowsthe
[ Bondi solution for low central X-ray luminosities, however, the flow starts to exhibit
non-sphericalfragmentationduetothermalinstabilityforacertainrangeofcentralL ,
2 X
andastrongoveralloutflowdevelopsforgreaterL . Thecoldgasdevelopsfilamentary
v X
5 structuresthatfallintothecentralSMBH,whereasthehotgastriestoescapethrough
2 the channels in-between the cold filaments. Such fragmentationof accreting gas can
5 assistintheformationofcloudsaroundAGN,inducestar-formation,andcontributeto
3 theobservedvariabilityofnarrow-lineregions.
.
2
1
1
1
: 1. Introduction
v
i
X
Feedback from active galactic nuclei (AGN) is considered to be one of the important
r processes inregulating galaxy growth overcosmic time. Severalresearch groups have
a
implementedAGNfeedbackincosmologicalhydrodynamicsimulations(e.g.DiMatteoetal.
2005;Booth&Schaye2009),howevertheyallhavetoassumeasubgridmodelforthe
accretionontoSMBHandfeedbackwithuncertainparametersduetolimitedresolution
incosmological simulations.
Herewetake adifferent approach and perform small-scale simulations of gasac-
cretion ontoSMBHusingtheGADGET-3SPHcode(originally described bySpringel
2005)onsmall-scalesofr < 200pc. Ourlong-termgoalistodevelopabettermodelof
AGNfeedback for large-scale cosmological simulations based on the results of small-
scaleBHaccretion simulations. Inthisarticle, wereport ourinitial results ofadiabatic
Bondi accretion simulations, aswellasthose withradiative cooling and heating byX-
rays from the central SMBH (Baraietal. 2011b). We run a large set of simulations
ofspherically symmetric Bondi accretion withdifferent resolution, volume, and initial
1
2 Nagamine,Barai,&Proga
0 10-18
s) -500 3m) 10-19
m/ -1000 c 10-20
k g/
v (r --21050000 v vZEUS ρ ( 1100--2221 ρZEUS ρff
ff
-2500 10-23
0.1 1.0 10.0 100.0 0.1 1.0 10.0 100.0
r (pc) r (pc)
100.0
108
oT (K) 111000567 TZEUS Tff,ar Mach = |v| / cs 110..00 Machff,ar
104 Tff,a 0.1
0.1 1.0 10.0 100.0 0.1 1.0 10.0 100.0
r (pc) r (pc)
Figure1. RadialprofilesnapshotofgasparticlesinarunwithX-rayheatingand
cooling,showingradialvelocity,density,temperatureandMachnumber. Thesolid
lineisthemedianvalue,thedashedlinesarethe95percentile,andthedottedlines
arethemin/maxvalues. Theredcurveineachpanelshowsthefree-fallscaling,and
thebluecurveshowsthecorrespondingZEUSsimulationresults: v andv are
ZEUS ff
indistinguishable,ρ isataconstantoffsetfromρ becauseofdifferentnormal-
ZEUS ff
ization. Thegreencurveinthebottom-leftpanelindicatesthefree-falltemperature
withonlyadiabaticprocesses. FiguretakenfromBaraietal.(2011b).
conditions. TheBondiproblemisidealfortestinganyhydrodynamic code,sinceithas
asemi-analytic solution.
2. SimulationsofBondiAccretion ontoaSMBH
The central SMBH has a mass of M = 108M , and the initial conditions are gener-
BH ⊙
ated using γ = 1.01, ρ = 10−19g/cm3, and T = T = 107K. The corresponding
∞ init ∞
BondiradiusisR =GM /c2 = 3.0pc,theBonditimeist = R /c = 7.9×103yrs,
B BH s,∞ B B s
and the sonic radius is R = 1.5pc. The total initial mass of the gas sphere is in the
s
range of105 −107M depending on thesetup, and the particle counts werevaried be-
⊙
tween 643 − 2563 for resolution test. The inner boundary radius is r = 0.1pc from
in
thecentral SMBH,andweregardthattheparticle isaccreted toSMBHonceitcrosses
r . Theouterboundaryradiuswasvariedbetweenr = 5−200pc. Forthefulllistof
in out
runsandparameters, seeTable1ofBaraietal.(2011b).
Firstwefindthattheadiabatic simulationsreproduce theexpectedBondisolution
verywellforalimitedtime. Sincethegasparticlesneartheouterboundaryescapedue
toadiabaticexpansion,afteracertaintimethemassaccretionratestarttodecreasefrom
theBondirate. Thisisaproblemowingtothedifficultyofsettingaboundarycondition
GasAccretionontoaSupermassiveBlackHole 3
intheSPHmethod,anditdoesnotarisewiththemeshcodes,asonecansimplyfixthe
outerboundary withρ andT .
∞ ∞
Inthe second set ofruns with radiative cooling and heating by X-rays, wefollow
the approximate treatment of Blondin (1994) and Proga (2007), assuming that the 10
keVbremsstrahlung radiation fromthecentralSMBHisilluminating theoptically thin
gas. InFigure1,weshowtheparticle radial profileforvarious quantities inarunwith
L = 0.01L , where L is the Eddington luminosity. We find that the simulation
X Edd Edd
roughlyfollowstheBondiflowsolutionevenwiththeX-rayheatingandcooling,except
at r < 0.5pc where we see a spurious heating due to artificial viscosity (AV) of SPH
particles. WehaveconfirmedthatthiseffectisduetoAVbyturningitonandoff. With
no AV,the overheating does not occur, and the gas particles overshoot the SMBH due
tolackofviscosity andmanyarenotaccreted. Themassinflowrateatr inthisrunis
in
enhanced overtheBondiaccretion ratebyafactorofafewduetocooling.
3. Non-sphericalFragmentationduetoThermalInstability,andOutflowsdueto
X-rayThermalFeedback
To study the effect of X-ray thermal feedback, we gradually increase L /L from
X Edd
5×10−5 to5×10−2. Intheseruns, theinitial condition contains 12.7millionparticles
for a gas sphere of 9.77×106M , each gas particle mass of 0.791M , adiabatic index
⊙ ⊙
γ = 5/3,r = 200pc,ρ = 10−23g/cm3,andT = 105K.TheBondiradiusforthese
out ∞ ∞
parametersis183.9pc,thereforemostofourcomputationalvolumeiswithintheBondi
radius and we fully resolve below the Bondi radius with minimum smoothing length
of ∼ 0.1pc. In general we find that, with increasing L , the mass accretion rate at r
X in
decreases, andtheoutflowrateatr increases.
out
WhenL becomes≥ 0.01L ,westarttoseeaninterestingtransitionfrominflow
X Edd
tooutflow,andnon-spherical fragmentation ofgasintomultiphasemediumtakesplace
due to thermal instability. The filamentary cold gas continues to flow in, and the hot
gas tries to escape through the channels between cold filaments. Examination of the
flowmotionshowsthat thefilaments getstretched, fragments, andthe ‘clouds’ merge.
SuchfragmentationofaccretinggascanassistintheformationofcloudsaroundAGN,
inducestar-formation,andcontributetotheobservedvariabilityofnarrow-lineregions.
Figure 2 shows an example of such multiphase structure in a run with L =
X
0.01L , when the outflow is still not very prominent and the hot gas is still being
Edd
accreted to SMBH. Studies with 1D & 2D ZEUS simulation shows that this fragmen-
tation does not occur in a spherically symmetric Bondi flow, unless some perturbation
is introduced by hand. The SPH simulations inherently have tiny fluctuations in the
density field due to its algorithmic nature, which can be amplified through thermal in-
stability.
As L is increased to >0.01L , the outflow starts to dominate over the inflow,
X Edd
and the hot gas escapes through the channels between cold filaments, as shown in the
left panel of Figure 3. We find that the transition from inflow to outflow occurs in-
between L /L = 0.01−0.02, but note that this transition luminosity would depend
X Edd
on the value of ρ . In other words, the more relevant parameter for the transition is
∞
the range of photoionization parameter ξ ∝ L /ρ for the unstable branch of the T −ξ
X
equilibrium curve.
With a high enough L (= 0.05L ), a strong outflow is produced due to strong
X Edd
thermal feedback, and the mass outflow rate at r = r increases dramatically. A jet-
out
4 Nagamine,Barai,&Proga
Figure2. Densityandtemperaturecross-sectionsin a runwith L /L = 0.01.
X Edd
Thetoptwopanelsshowtheinner±30pc,andthebottomtwotheinner±4pcofthe
[x−y]planethroughz = 0. Cold,densefilamentarystructurehasdevelopeddueto
thermalinstability,whichisfallingintotheSMBHrapidly. Thehotgasistryingto
escape,butastrongoutflowhasnotdevelopedyetduetolowL .
X
likeplumeofhotandbuoyantgasescapesfromthecentralregiontotheouterboundary,
asshownintherightpanelofFigure3.
Theseresultsonthenon-spherical flowhavebeenreportedinoursecondpaperin
series(Baraietal.2011a),whereweexaminedtheT−ξequilibriumcurveindetailand
determinetheunstable ξ-range.
4. Conclusions
We find that GADGET-3 SPH code can reproduce the spherically symmetric Bondi
accretion flow properly with mainly two limitations: 1) the gas particles escape from
theouterboundaryduetoadiabaticexpansion; 2)spuriousheatingisobservednearthe
innerboundary aroundSMBHduetotheartificialviscosity ofSPH.
Wealsoexamined theimpactofradiative cooling andheating duetoX-rays. The
accretion flow roughly follows the Bondi solution when the central X-ray luminosity
is relatively low, but the mass accretion rate at r is enhanced by a factor of a few
in
over the Bondi accretion rate due to cooling. The simulation starts to exhibit non-
spherical fragmentation due to thermal instability once L exceeds ≃ 0.01L . At
X Edd
L = 0.02L , thehot gas escapes in-between thecold filaments. When L is further
X Edd X
increased to 0.05L , the outflow completely dominates over the inflow, and most
Edd
of the gas escapes from the computational volume. A jet-like outflow feature is also
GasAccretionontoaSupermassiveBlackHole 5
Figure3. Temperaturecross-sectioninrunswith L /L = 0.02(left)and0.05
X Edd
(right). Theleftpanelshowstheinner±100pc,andtherightpanelshowstheentire
computational volume of ±200pc. In the left panel, the cold, dense, filamentary
structurehasdevelopedduetothermalinstability,whichis fallingintotheSMBH.
The hotgastries to escape throughthe channelsin-betweenthe cold filaments. In
therightpanel,theoutflowdominatesovertheentirecomputationalvolume,andthe
hotplumeofgasisescapingfromthecentertotheouterboundary.
observed atthis L ,whichselectsapreferential direction forhotgastoescape rapidly.
X
Suchnon-sphericalfeaturesofaccretinggascanassistintheformationofcloudsaround
AGN, induce star-formation, and contribute to the observed variability of narrow-line
regions.
Inthefuture,weplantoimplementrotation,radiationpressure,anddifferentinitial
geometryofgasdistribution. Wewillmeasuretheefficienciesofthermal,radiative,and
kineticfeedback,andcomparethemwiththosemeasuredbyKurosawaetal.(2009)and
thoseusedinthecosmological simulations.
Acknowledgments. WearegratefultoV.SpringelforallowingustousetheGADGET-
3code. ThisworkissupportedinpartbytheNSFgrantAST-0807491,NationalAero-
nauticsandSpaceAdministrationunderGrant/CooperativeAgreementNo. NNX08AE57A
issuedbytheNevadaNASAEPSCoRprogram,andthePresident’sInfrastructureAward
from UNLV. DP also acknowledges the UNLV sabbatical assistance. This research is
also supported by the NSF through the TeraGrid resources provided by the Texas Ad-
vanced Computing Center. Some numerical simulations and analyses have been per-
formedontheUNLVCosmologyCluster.
References
Barai,P.,Proga,D.,&Nagamine,K.2011a,ArXive-prints.1112.5483
—2011b,MNRAS,418,591.1102.3925
Blondin,J.M.1994,ApJ,435,756
Booth,C.M.,&Schaye,J.2009,MNRAS,398,53.0904.2572
DiMatteo,T.,Springel,V.,&Hernquist,L.2005,Nature,433,604
Kurosawa,R.,Proga,D.,&Nagamine,K.2009,ApJ,707,823.0906.3739
Proga,D.2007,ApJ,661,693.arXiv:astro-ph/0702582
Springel,V.2005,MNRAS,364,1105.arXiv:astro-ph/0505010
