Fermi Bubbles in the Milky Way: the closest AGN feedback laboratory courtesy of Sgr A*?

18 Pages·2012·1.29 MB·English

Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed15March2012 (MNLATEXstylefilev2.2)
Fermi Bubbles in the Milky Way: the closest AGN feedback
∗
laboratory courtesy of Sgr A ?
∗
2 Kastytis Zubovas and Sergei Nayakshin
1
0
Dept. of Physics & Astronomy, Universityof Leicester, Leicester,LE1 7RH, UK
2

r
a
M 15March2012

4
ABSTRACT
1 Deposition of a massive (104 to 105M⊙) giant molecular cloud (GMC) into the inner
parsecoftheGalaxyiswidelybelievedtoexplaintheoriginofoverahundredunusually
]
A massive young stars born there ∼6 Myr ago. An unknown fraction of that gas could
havebeenaccretedbySgrA∗,thesupermassiveblackhole(SMBH)oftheMilkyWay.
G
It has been recently suggested that two observed γ-ray-emitting bubbles emanating
h. from the very center of our Galaxy were inflated by this putative activity of Sgr A∗.
p We run a suite of numerical simulations to test whether the observed morphology
- of the bubbles could be due to the collimation of a wide angle outflow from Sgr A∗
o
by the disc-like Central Molecular Zone (CMZ), a well known massive repository of
r
t molecular gas in the central ∼ 200 pc. We find that an Eddington-limited outburst
as of Sgr A∗ lasting ≃ 1 Myr is required to reproduce the morphology of the Fermi
[ bubbles, suggesting that the GMC mass was ∼105M⊙ and it was mainly accreted by
Sgr A∗ rather than used to make stars. We also find that the outflow from Sgr A∗
1
enforcesstrongangularmomentummixinginthe CMZdisc,robustlysculptingitinto
v
a much narrowerstructure – a ring – perhaps synonymous with the recently reported
0
“Herschel ring”. In addition, we find that Sgr A∗ outflow is likely to have induced
6
0 formation of massive star-forming GMCs in the CMZ. In this scenario, the Arches
3 and Quintuplet clusters, the two observed young star clusters in the central tens of
. parsecsoftheGalaxy,andalsoGMCssuchasSgrB2,owetheirexistencetotherecent
3 Sgr A∗ activity.
0
2 Key words: galaxies:evolution - galaxies:individual:Milky Way - quasars:general -
1
black hole physics - accretion
:
v
i
X
r
a 1 INTRODUCTION few 1039 erg s−1 in X-rays (e.g. Revnivtsevet al. 2004;
×
Ponti et al.2010).Thisvariabilitymayreflectfeedingevents
The Galactic centre (GC) is a particularly interesting as-
from a few pc-scale molecular gas reservoirs (Morris et al.
trophysical location, primarily due to the presence of the
1999) or variability in the wind capture rate from the
closest supermassive black hole (SMBH) - Sgr A∗, whose young massive stars near Sgr A∗ that feed it presently
mass is Mbh ≃4×106M⊙ (Sch¨odelet al. 2002; Ghez et al. (Cuadra et al. 2008).
2005,2008).AlthoughtheSoltanrelation (Soltan1982)im-
pliesthatSgrA∗ gained most ofitsmassthroughluminous A recent observation may shed a rather unexpected
accretion, it is currently very dim in comparison with ac- light on a much earlier but still rather recent activity of
tivegalactic nuclei(AGN):its X-rayluminosity isless than Sgr A∗. Fermi-LAT data has been recently analysed to re-
10−11LEdd (where LEdd a few 1044 erg s−1 is its Ed- veal two giant γ-ray emitting bubbles, disposed symmetri-
∼dington luminosity; Bagan∼off et al.×2003). Sgr A∗ dimness callyoneithersideoftheGalactic plane(Su et al.2010;al-
has stimulated development of radiatively inneficient ac- thoughseeDobler et al.2011foradifferentinterpretation).
cretionandaccretion/outflowsolutions(e.g.,Narayan et al. Theyareroughlyteardrop-shapedandextend 8 10kpc
1995; Blandford & Begelman 1999). However, X-ray reflec- aboveand below theplane, butare centred on∼Sgr−A∗ with
tion nebulae suggest that Sgr A∗ might have been much a narrow (d 100 pc) waist along the plane. The limbs
brighter about a hundred years ago, with luminosity of a of the lobes c∼oincide with the extended structure seen in
medium-energy X-rays by ROSAT (Snowden et al. 1997).
Thelobes haveγ-rayluminosity L 4 1037 ergs−1.Ob-
γ
≃ ×
⋆ E-mail:[email protected] servational constraints (Suet al. 2010) and emission mod-
(cid:13)c 0000RAS
2 Kastytis Zubovas, Sergei Nayakshin
elling (Crocker & Aharonian 2011) allows one to estimate blescanbereproducedwiththismodel.Inaddition,weare
the total kinetic and thermal energy content of the Fermi interestedinconstraintsthatthesimulationscouldplaceon
bubblesas E 1054−55 erg. akeyunknownof theproblem – theduration of Sgr A∗ ac-
bub
∼
There has been a number of suggestions as to what tivity.Wefindthatalongerquasaroutburstisneededthan
the origin of the Fermi bubbles might be. Su et al. (2010) found in Paper I, most likely because the energy produced
discuss several physical processes and provide a constraint bySgrA∗ outflowisspreadmorewidelyinthesimulations,
that if the bubbles are older than a few 106 yr, the γ- e.g., outside thebubblesthemselves, than assumed analyti-
×
rayemission mustbepowered byionsratherthanelectrons cally.
due to a short cooling time of the latter (see their section The Paper is structured as follows. In Section 2, we
7.1andFigure28),unlesselectronsarecontinuouslyacceler- reviewouranalyticalmodelandthemainresultsofPaperI.
atedwithinthebubbles(whichmaynotbeunreasonable;see InSection3,wedescribethenumericalmodelandtheinitial
5.4below).Crocker et al.(2011)andCrocker & Aharonian conditions of the simulations. We follow this by presenting
§
(2011) detailed these argumentsfurther and suggested that the results in Section 4 and discussing their implications in
the emission is powered by cosmic ray (CR) protons rather Section 5. Webriefly summarize and conclude in Section 6.
than electrons. They further consider a quasi-steady state
model in which the CR protons are continuously injected
by supernova explosions. CR protons and heavier ions are 2 A PHYSICAL MODEL FOR THE FERMI
then trapped inside the bubbles for the lifetime of the lat- BUBBLES
ter (which the authors require to be about 10 Gyrs). On
2.1 Sgr A∗ as the power source
the other hand, Mertsch & Sarkar (2011) argued that the
emission spectrum of the bubbles is inconsistent with CR AsexplainedinPaperI,ourSgrA∗feedbackmodelisbased
protons and therefore thebubblesmust bea recent,cosmic on the analytical models of fast wind outflows from super-
ray electron-powered, feature. massive black holes by King (2003, 2005, 2010b,a), tailored
The scenario with a more recent origin of the bubbles tothepresentdayinnerMilkyWay.Herewesummarisethe
has been investigated by several authors. Guo & Mathews keyassumptions behind thismodel.
(2011) suggest that a jet launched by Sgr A∗ 1 2 Myr Fast (v 0.1c) wide–angle outflows from AGN have
− ∼
agocouldcreatethemorphologyandemissionstructureob- beenrevealedbyobservationsofblue–shiftedX-rayabsorp-
served. Cheng et al. (2011) argue that the bubbles are in- tionlines;theyappeartobeaubiquitousfeature,detectedin
flatedbyepisodicSgrA∗activitycausedbytidaldisruptions 40% of AGN (Tombesi et al. 2010a,b). Recent XMM ob-
of stars passing too close to Sgr A∗. Zubovaset al. (2011, ∼servations(Pounds& Vaughan2011)ofX-rayemissionfrom
hereafter Paper I) argue that an almost spherical outflow alimb-brightenedshellofpost-shock gasbuildingupahead
from Sgr A∗ caused by a short burst of AGN activity coin- of the contact discontinuity corroborate these results and
cidentwiththewell-knownstarformation(SF)event6Myr themodelofKing(2003)further.Theoutflowsareprobably
ago(Paumard et al.2006),canbetheoriginofthebubbles. driven by radiation pressure of photons emitted by Sgr A∗
In the model, the outflow from Sgr A∗ is suggested to be on the gas in the innermost regions of black hole accretion
quasi-spherical at launch as is required to explain the ob- flows.Whilesomeanisotropyintheoutflowmaybepresent
served Mbh σ relations for classical bulges and elliptical ingeneral,hereweconsiderasphericaloutflowforsimplicity
−
galaxies(King2003,2005,2010a).Theoutflowbecomescol- anddemonstratethatitisthepropertiesofthehost galaxy
limatedbyinteractionwithadisc-likestructure,theCentral that may mold the outflows into theteardrop-like shape.
MolecularZone-adensering(aspectratioH/R 0.2 0.3) We assume that Sgr A∗ accretion rate is mildly super-
∼ −
of predominantly molecular gas extending from the Galaxy Eddington, and that its luminosity is limited by the Ed-
centre to 200 pc. This collimation explains the large dingtonlimit. Wedonot modelthesub-parsecscale disc(s)
∼
width of the bubbles and their symmetry with respect to from which Sgr A∗ would be accreting gas here. As shown
the Galactic plane, which is not at all guaranteed by a jet byNayakshin & Cuadra(2005)andAlexanderet al.(2012),
model, since jet directions are known to be completely un- viscousdisctimescalesarelongenoughtomaintainSgrA∗
correlatedwiththelarge-scalestructureofthehostgalaxies feedingviaanaccretiondiscforatleastamillionyears.Fur-
(Kinneyet al. 2000; Nagar & Wilson 1999). Zubovaset al. thermore,Nayakshinetal(2012,ApJsubmitted)showthat
(2011) estimated the duration of the quasar phase to be at AGNfeedbackisunabletoremovegasdiscswithintheblack
the minimum tq =5 104 yr and the mass of gas accreted hole’ssphereofinfluence.Physically,thisresultiseasilyun-
bySgrA∗,∆M >4 ×103M⊙,comparabletothemassinthe derstood: escape velocities for gas in the sub-parsec scale
×
youngstarsinthecentralparsec,M∗ fewtoten 103 M⊙ disc are much larger than that for gas in the bulge of the
∼ ×
(Paumard et al. 2006). host, so much more energy needs to be expended to eject
In this paper, we test the analytical results of Paper I gas from very near the black hole than from the bulge of
byperformingnumericalsimulations.Webroadlyfollowthe theGalaxy.Thisiswhyarelativelylowmasssub-resolution
methodology of simulating spherical outflows from accret- reservoir of gas (an accretion disc) could power Sgr A∗ for
ing SMBHs of Nayakshin& Power (2010). These SPH sim- the duration of the quasar outburst envisioned here, while
ulations involve a prescription for passing momentum and inthemeantimeSgrA∗ drivesmuchmoremassiveoutflows
energy of the outflow to the ambient gas (Nayakshin et al. on scales of theGalaxy’s bulge.
2009). The method has been shown (Nayakshin& Power The outflow is believed to be self-regulating to have
2010) to reproduce the analytical results of the wind feed- a scattering optical depth 1 (King 2010a), so that the
∼
backmodel weusehere(King2003). Weaim toinvestigate photons transfer their momentum to the outflowing wind
whetherthemorphology,sizeandenergycontentofthebub- which carries momentum
(cid:13)c 0000RAS,MNRAS000,000–000
Fermi Bubbles: Sgr A∗ AGN feedback? 3
M˙outv≃ LEcdd, (1) E˙out = 21M˙outv2 = η22c2M˙out = η2LEdd, (4)
wherev ηc,andη 0.1istheaccretionefficiency.Wenote ispassedtotheambientgas,heatingandpushingitoutward.
thatthe∼massoutflow≃ratefromSgrA∗,M˙out,isboundtobe Theshockedshell rapidly (in t < 105 yr)attains aconstant
of the order of M˙Edd, which is negligible on the Galactic velocity, which for a spherically∼symmetric outflow is given
∼
scales, implying that we can neglect injection of the mass by
into the Galaxy (but not the outflow’s momentum or the
energy,as we discuss now). v = 2ησ2c0.16MBHl 1/3 1920σ2/3f−1/3l1/3 km s−1 ,(5)
e (cid:20) 3 fg Mσ (cid:21) ≃ 100 −3
whereM isthevalueoftheSMBHmassexpectedfromthe
σ
2.2 The effects of the outflow on the diffuse gas in M σ relation (Kinget al. 2011),MBH 0.2Mσ and l 1
− ≃ ∼
the Galaxy is theEddington ratio.
Oncethequasar switches off, theshell continuesto ex-
Since the outflow velocity is very much larger than the es-
pand, but stalls and eventually stops (assuming that the
cape velocity from theGalaxy,theoutflow propagates with
isothermal potential of the bulge extends to infinity). The
an approximately constant velocity until it shocks against
maximum radius which theshell reaches is
the ambient gas. For a sufficiently powerful outflow, the
v v2
shockedwindcontinuestodriveanoutflowoutward,clearing R eR et , (6)
theinnerregions of thebulgeof gas. TheM σ relation stall ≃ σ 0 ≃ σ q
BH
−
forelliptical galaxiesandclassical bulgesmayhavebeenes- where tq is theduration of thequasar outburst.
tablishedbysuchoutflowsthatterminatedbothhostgalaxy Using the size of the observed Fermi bubbles
and SMBH growth (King 2005). (Rstall > 10 kpc) we can constrain the free parameters of
The point that we want to emphasize now is that even our mo∼del, f−3 and tq. We estimate the gas fraction from
SMBHs lying well below this relation can drive the gas out equation (5), requiring that the bubbles must have reached
of their host bulges, provided that the gas density is lower thepresent radius in 6 Myr. This is equivalent to assuming
than thatexpected in thegas rich era when thebulgeitself thattheshell’smeanvelocityis v &1600km/s(seePaper
h i
forms (King 2003, 2005). In our model, gas density in the I for details), and yields
bulge is parametrised through thegas fraction f :
g 1920 3
ρg = 2πfgGσR22 =2.5×10−26f−3Rk−p2cgcm−3, (2) f−3 .(cid:18)1600(cid:19) l≃2l. (7)
We see that the gas fraction in the Milky Way halo must
where σ is thevelocity dispersion in thebulge and R is the havebeen similar to10−3 in orderfor thebubblesto bein-
radial coordinate. The R−2 scaling of the density is nat- flated within our model. Numerical simulations below con-
∝
ural as this is the same as that for the background stellar firm this.
density that dominates the potential in the bulge. We fur- Requiring that the bubble stalling radius should be
ther parametrize fg 10−3f−3, R = Rkpc kpc and we use greaterthantheircurrentradius,equations(6)and(5)give
≡
the value σ = 100 km/s, appropriate for the Milky Way.
For reference, the model of King (2003, 2005) assumes that tq>2.5×105f−2/33 yr. (8)
fg = 0.16, the cosmological value, during the bulge forma- Asthebubblesarelikelytobestillexpandingatthepresent
tion epoch. time(seePaperI),thisresult isalowerlimit. Wenotethat
The dynamics of the outflow depends crucially on theestimategivenbyequation 8isafactorof5larger than
whethertheshockedwindcoolsefficientlyornot.Theshock the estimate obtained in Paper I. As both estimates are
temperature is of the order of 1011 K, so the only ef- lowerlimitsontheoutburstduration,onlythelargeroneof
fective form of cooling is the inverse Compton effect of thetwo is relevant.
the shocked outflow’s electrons on the Sgr A∗ radiation In 0.25 Myr, Sgr A∗ accreting at its Eddington limit
field (which would dominate over the whole Galaxy’s light; consumes ∆M 2 104M⊙ of gas. Within our feedback
Ciotti & Ostriker1997).Outsideacertainradius,Rcool,the model, 2 10≃56 e×rg is ejected in the outflow’s mechani-
radiation field is unable to cool the shock and the out- cal ener∼gy. T×his is more than an order of magnitude larger
flow transitions from momentum-driven to energy-driven than the bubbles energy content estimated by Su et al.
(Zubovas& King 2012). This radius can be estimated by (2010). However, we find that a large fraction of the out-
comparing thecooling and theflowtimescales (King2003). flow’s energy goes into mechanical work expended to drive
Fortheparameters of theMilky Way(MBH =4 106M⊙), the ambient cooler medium away from the Galaxy’s cen-
×
Rcool is tre.Zubovas& King(2012)showthatevenwhilethequasar
R 12f1/2 pc. (3) drivingison,only1/3oftheenergyinputisretainedinthe
cool ≃ −3 shocked wind while the quasar is active. When the quasar
Even for the cosmological gas fraction (f−3 = 160), Rcool turns off, the bubble expands adiabatically, converting its
is very small compared with the size of the bulge. For the thermalenergyintokineticenergyofthebubbleandthesur-
problemathand,wherethegasdensityinthebulgeislikely roundingshell.Therefore itislikelythattheactualamount
to be much smaller than this, this implies that for all the of energy retained by the bubbles is much lower than the
relevant parameter space any outflow from Sgr A∗ quickly original energy input by Sgr A∗ into the outflow, bringing
becomesenergy-driven.Inthistypeofoutflow,almostallof thevalueinlinewiththeobservations.Oursimulationscon-
thekinetic power of the outflow, firm this prediction; cf. 5.3.
§
(cid:13)c 0000RAS,MNRAS000,000–000
4 Kastytis Zubovas, Sergei Nayakshin
2.3 The role of the Central Molecular Zone in itstimestepsandmoveradially with aset constantvelocity
focusing the outflow (v =0.1c). Each particle carries linear momentum
w
Theshellexpansionvelocity,v ,dependsonthegasdensity
e L t
inthedirectionofexpansion.Clearly,iftheambientgasdis- pγ = EcdNd BH (11)
tributionisnotsphericallysymmetricthentheoutflowmust γ
lose its spherical symmetry too. As a minimum effect, the
and kinetic energy E = p v /2, where t is the SMBH
velocity of the contact discontinuity must be smaller in the γ γ w BH
timestep, and divided equally among N virtual particles
directionsofdensergas.Themostsalientfeatureinthedis- γ
ejected in that timestep. The scheme is designed to eject
tribution of gas in the inner Galaxy is that a good fraction
the correct momentum flux from the SMBH, L /c, and
ofit–mainlythecoldmoleculargas–liesclosetotheplane Edd
thenumberofparticlesejectedinatimestep,N ,isselected
of the Galaxy. For what follows it is the Central Molecu- γ
so that the interactions with SPH particles are sufficiently
larZone(CMZ;Morris & Serabyn1996),amassivedisc-like
frequenttoreducethe(random-number-generated)noiseto
molecular gas feature in the inner 200 pc, that matters
∼ acceptable levels (see Nayakshinet al. 2009).
the most. As we argued in Paper I, the CMZ presents an
Each virtual particle has a search radius (a multiple
almost impassable barrier to the Sgr A∗ outflow. This can
of the smoothing length of an SPH particle), within which
beseen from thefact that theweight of theCMZ,
search for potential SPH neighbors is performed “on the
GM M 2M σ2 fly”. Whenever an SPH particle kernel contains a virtual
W enc CMZ = CMZ 6.5 1034 dyn, (9)
CMZ ∼ RC2MZ RCMZ ∼ × particle, the two are considered interacting, and a fraction
ofthevirtualparticle’smomentumandenergyistransferred
where R is the mean radius of the CMZ and M is
CMZ enc tothegas.Whenthevirtualparticleenergydropsbelow1%
the mass enclosed within this radius, is greater than the
of its original energy,the particle is destroyed.
momentumfluximpactingontheCMZfromSgrA∗ outflow
The kinetic energy of the virtual particles is passed to
(which is theoutward force on the CMZ):
the SPH particles if the shocked wind does not cool, i.e.
L H if R > R (eq. 3). We have implemented a step function
F Edd CMZ 2 1033 dyn. (10) cool
CMZ ∼ c RCMZ ∼ × transitionbetweenthepuremomentumfeedbackregimeand
the energy feedback one for this. However, testing showed
ThereforeweexpecttheCMZtobeaveryeffectiveobstacle
that since R is very small in the case considered here,
totheoutflow(thisestimatedoes nottakeintoaccount en- cool
there is no significant difference in results between simula-
ergy deposition by the outflow into the CMZ, which makes
tions utilising the switch and those employing the energy
the latter somewhat more prone to the feedback; see 5.6).
Physically,weexpectSgrA∗ outflowimpactingtheCM§Zto feedback scheme throughout the simulation, so we use the
latter below.
shock and thermalise. As the CMZ weight is so large, the
While we do not model hydrodynamically the reverse
outflowiseithercompletely stoppedornearlystalled inthe
wind shock,which thermalizes thewind andcreates apres-
planeoftheGalaxy.Theshockedoutflowgascannotsimply
surized bubble that can expand adiabatically, we find that
pileupthere,however.Indeed,ifthatwerethecasethenthe
thisprocessissomewhatmimickedinthesimulationsbylow
pressure(thermalenergydensity)wouldincreaseinthatlo-
density gas that is present in the otherwise evacuated bub-
cation without limit. The thermal pressure of the shocked
ble.Theseparticlespredominantlyoriginateonthesurfaces
gas in the directions perpendicular to the Galactic plane is
oftheCentralMolecularZone(seeSections3.2and4.1.3be-
muchlowerbecausetheoutflowproceedsinthosedirections
low), where they are heated to very high temperatures and
easily.Thusthereisastrongpressuregradientintheshocked
rise to fill the voids; subsequently quasar wind heats these
outflow gas pointing towards theGalactic plane. This pres-
particles even further. The bubbles are found to be signifi-
sure gradient clearly must launch a “secondary” thermally
cantly overpressurized with respect to the surrounding gas.
drivenoutflowaway fromtheGalactic plane,efficientlycol-
limating Sgr A∗ outflow intothese directions. This allows the bubble to expand thermally as expected if
the reverse shock were modelled by SPH (see Section 4.1
below).
In all the simulations presented below, we use an ideal
3 SIMULATION SETUP equation of state for the gas. The gas pressure is given by
P =ρkT/µ,wheremeanmolecularweight,µ=0.63m (as-
3.1 Numerical method p
sumingionisedgasofSolarabundance),kistheBoltzmann’s
Our workhorse code for solving gas dynamics in the fixed constant,andρandT arethegasdensityandtemperature,
potentialofthebulgeandtheblackholeisGADGET-3,an respectively. In all simulations except for one, we employ
updated version of the code presented in Springel (2005). the standard GADGET optically thin cooling prescription
Feedback from the SMBH is implemented with the ’vir- basedontheSutherland & Dopita(1993)coolingcurves,in
tualparticle’methodexplainedindetailinNayakshin et al. additiontoheatingfromthevirtualparticlesonthecontact
(2009). Rather than hydrodynamically modelling the low- discontinuity of the bubble. In the only exception to this,
densityfast windflowing from theSMBH,itseffectson the simulation ‘Cool’ (see Table 1), we check the sensitivity of
gas distribution at large are simulated via a distinct popu- our results to theassumed cooling function by utilising the
lation of particles, called ‘virtual particles’ since they exist optically thin radiative cooling rates for gas ionised (and
only during their propagation from the source, Sgr A∗, to also heated) by the quasar radiation field as calculated by
the point of interaction with the ambient gas. These par- Sazonov et al.(2005),whoalsoprovidedananalyticalfitto
ticles are ejected isotropically from the SMBH at each of therespective rates that we usehere.
(cid:13)c 0000RAS,MNRAS000,000–000
Fermi Bubbles: Sgr A∗ AGN feedback? 5
Test fg Np,halo tq/Myr (cid:16)HR(cid:17)cmz Mcmz/M⊙ Np,cmz Rb/kpc db/kpc hb/kpc vv/kms−1 vh/kms−1
Base 10−3 7.5×105 1 0.25 108 106 11.5 9 ∼1 1090 670
HR-low 10−3 7.5×105 1 0.125 108 106 11.5 9 ∼1 1110 680
Cool∗ 10−3 7.5×105 1 0.25 108 106 9.5 10 ∼1 820 650
Fg-low 4×10−4 3.0×105 1 0.25 108 106 ∼15 ∼10 2.5 2560 610
Fg-high 4×10−3 3.0×106 1 0.25 108 106 6 6 ∼1 220 400
Tq-low 10−3 7.5×105 0.3 0.25 108 106 7 4 2 300 360
Both-low 4×10−4 3.0×105 0.3 0.25 108 106 ∼7 ∼4 4 960 270
Mc-low 10−3 7.5×105 1 0.25 107 105 7 8 2 330 470
Table1.Simulationparametersandmainresults.Fromlefttoright,theparametersare:TestID,gasfraction,numberofSPHparticles
in the halo, quasar outburst duration, CMZ mass, CMZ scale height, number of particles in the CMZ. The results are: bubble height,
widthanddistancebetween itsloweredgeandtheSMBH;velocityoftheswept-upISMinthez directionatx=y=0andvelocityof
theswept-upISMinthexy planeatthemid-heightofthebubble;allfiveat6Myr.
∗ -Simulation‘Cool’isidenticalto‘Base’,butincludesaSazonov etal.(2005)heating-coolingprescription.
Simulationsnapshotsshowingdensityandtemperature As mentioned above, we position a massive disc of
areplottedusingananglesliceprojectionmethodpresented gas –theCentral Molecular Zone(CMZ; Morris & Serabyn
in Nayakshin& Power (2010). Specifically, the gas column 1996) – in the plane of the Galaxy at a distance between
density projected over they coordinate is calculated by R =5pcandR =200pcfromSgrA∗.Theinner
in,cmz out,cmz
radius is chosen so that the whole CMZ would be comfort-
y(x,z)
Σ(x,z)= ρ(x,y,z)dy, (12) ablyoutsidethesphereofinfluenceofSgrA∗(Rinfl 2pc),
Z ∼
−y(x,z) but still account for the yet smaller circumnuclear disc of
where the limits of the integration are given by y(x,z) = gas, which is observed tolie between 2 and 10pcfrom
∼ ∼
rtanζ and r = √x2+z2. The angle ζ is chosen so that the centre (Guesten et al. 1987; Morris & Serabyn 1996).
tanζ =1/4 throughout this paper. This projection method OurmodelCMZhasuniformtemperaturethroughout,cho-
conveniently allows us to get an unobscured look into the sentogivetheappropriateconstantscaleheightaspectratio
inner parts of the simulation and yet haveenough particles (H/R=0.25or0.125,withacorrespondingdifferenceinthe
attheouteredgesforastatistically meaningfulfiguretobe adopted temperature floor for the simulations). It is rota-
derivedwhenplotting.Inaddition,sincemostoftheresults tionally supported in theradial direction, with vrot =√2σ.
presented in this paper are symmetrical around the z axis, Theradialdensitydistributionfollowsaρ R−2powerlaw,
∝
the snapshot plots, where applicable, are divided vertically and the mass of the disc is set to Mcmz = 108M⊙ (approx-
and show the surface density in blue-white on the left and imately theupper limit from observational constraints), al-
temperature in red-orange on theright. thoughweranonesimulationwithamuchlowerCMZmass.
DespitethehighmassoftheCMZ,itismarginallystableto
self-gravity,since theToomre (1964) parameterQ 3.4 for
3.2 Galaxy model and initial conditions H/R = 0.25, and 1.7 even for H/R = 0.125. We n∼ote that
we do not fine-tune the CMZ to be only marginally sta-
The initial setup for the Galaxy consists of three compo-
ble in the simulations; it is a natural outcome of using the
nents, described below and summarized in Table 1. The
observationally constrained CMZ parameters. This result is
‘Base’ model is themodel which best reproduces theFermi
probablynotacoincidence:massivecolddiscsarewidelybe-
bubbleobservations (Su et al. 2010).Weanalyze thissimu-
lieved to be self-regulating to have Q 1 (Goodman 2003;
lationindetailbelow,andstudytherobustnessofourresults ∼
Thompson et al. 2005; Nayakshinet al. 2012). In principle,
by varyingthefree parameters of themodel.
such alow Q parameter might lead tofragmentation. How-
The whole computational domain is embedded in a
ever,sincewesetthetemperaturefloorinthesimulationsto
static isothermal background potential with σ =100 km/s.
beequaltotheinitialCMZtemperature,wedonotexpecta
Inthecentreofthecoordinatesystem,fixedinspace,isthe
SMBH.WhilewedonotmodelaccretionontoSgrA∗ inde- significantfragmentationtooccur(Gammie2001;Rice et al.
2005).Thisassumptionisconsistentwithsimulationresults
tail (cf. 2.1), ocasionally SPH particles may get very close
§ (seeSections4.1.3and5.6below).TheSPHparticlemassof
totheSMBH,especiallyclosertotheendofthesimulations
whenfeedbackfromSgrA∗isturnedoff.Toavoidverysmall thesimulations is Mpart =100M⊙, giving a minimum mass
time steps, and thus very high numerical costs, associated resolution of ∼4000M⊙.
with these “uninteresting” particles, we remove them using Finally,thereisadiffusesphericallysymmetricgaseous
the sink particle formalism if the SPH particles are closer “halo”extendingbetweenr =1pcandr =15kpcwith
in out
than r = 0.1 pc to Sgr A∗. As explained above, Sgr A∗ densityfollowing theisothermalprofilegivenbyequation2.
sink
is “turned on” at the start of each simulation, radiating at The gas fraction f is a free parameter of our model and is
g
itsEddingtonlimitforadurationt ,whichisafreeparam- variedbetween4 10−4 and4 10−3 indifferenttests,with
q
eter of the model. Most of the models presented here use the fiducial value×of 10−3 for×the ‘Base’ model (this corre-
t = 1 Myr (since this was found to give the best results), spondstoaparticledensity6 10−4 cm−3atR=5kpc;see
q
×
although we explore shorter outburstsas well. the Discussion section for the validity of this choice for gas
(cid:13)c 0000RAS,MNRAS000,000–000
6 Kastytis Zubovas, Sergei Nayakshin
220000 440000
220000 440000
110000 220000
110000 220000
pc] 00 pc] 00
y [ 00 z [ 00
--110000 --220000
--110000 --220000
--220000 --440000
--220000 --440000
--2200--22000000 --1100--11000000 0000 110011000000 220022000000 --4400--44000000 --2200--22000000 0000 220022000000 440044000000
x [ pc] x [ pc]
-3-3 -2-2 -1-1 00 11 -5-5 -4-4 -3-3 -2-2
log Σ [g cm-2] log Σ [g cm-2]
44 55 66 77 88 99 1100
log T [K]
Figure 1. Left: The face-on column density of the CMZ disc at time t=0.1 Myr for the ‘Base’ simulation. Note that the innermost
regionhas beenpartiallyevacuated bySgrA∗ feedback. Right:Cross-sectionalplotofgassurfacedensity(lefthalfof thepanel,blue-
white)andtemperature(right,red-orange)forthesamesnapshot.TheCMZ(colddensewedgeintheGalacticplane)stronglycollimates
theoutflow; eventhoughitssurfacesareablated, teardrop-shapedcavitiesformreadily.
density).Thenumberof particles in thehalois set bytheir 4.1 Base simulation
mass (we use same SPH particle masses for the CMZ disc
4.1.1 Small and intermediate scales
andthehalo).Thegastemperatureinthebulgehaloisini-
tiallysettoThalo=Tvir =2.5 105 K,whichcorrespondsto Overall,thedynamicsofgasinthesimulationcloselyfollows
×
the virial temperature of the bulge. The initial gas velocity ouranalytical expectations. As soon as thequasar switches
in thebulge is set to zero. on, the spherically symmetric outflow hits both the CMZ
This halo setup we use is probably oversimplified. For andthehalogas.TheleftpanelofFigure1showstheface-on
example, we do not account for the likely anisotropy of the viewoftheCMZdiscattimet=0.1Myr.Notethatonlythe
initial gas distribution of the “halo” dueto overall rotation central 25 pc of the disc were evacuated by outflow from
of the Galaxy. We address this point qualitatively in the Sgr A∗.∼The right panel of the same figure shows the edge-
Discussion section. on projections of bothgas column density andtemperature
(whichwepresentinasinglepanelbecauseoftheazimuthal
symmetry of the gas flow). The arrows show gas velocity
vectors projected on theplane of the figure.
Asexpected,thespherical “halo” (thediffusegas com-
ponent)isaffectedbytheoutflowmuchmorethantheCMZ,
with the contact discontinuity between the wind and the
shockedambientmediumatadistanceofabout300pc.We
alsonotethatthebubblesdocontainsomegasmainlycloser
4 RESULTS
totheinterfacewiththeupperlayersoftheCMZ.Thatgas
Table1showsthelist,parametersandmainresultsofallof is heated to temperatures above 108 K. There is a transi-
thesimulationsthatwepresentinthispaper.Resultsofthe tionregionbetweenthealmost-sphericaloutflowperpendic-
threesimulationsinthetopoftheTable,separatedfromthe ular to the Galactic plane and the stalled outflow against
rest by a horizontal line, appear to be a reasonable match the CMZ, completing the figure-8 morphology of the whole
to the Fermi Bubble observations by Su et al. (2010). The flow.
rest of the simulations produce bubbles that are unlike the AstimeproceedstheinnerholeintheCMZ discgrows
observed ones. in size, engulfing most of the disc by theend of the simula-
We first describe the evolution and properties of the tion (see 4.1.3 for a fuller discussion of this). The cavities
‘Base’ model (f =10−3,t =1 Myr). openedby§theoutflowinthedirectionsperpendiculartothe
g q
(cid:13)c 0000RAS,MNRAS000,000–000
Fermi Bubbles: Sgr A∗ AGN feedback? 7
2200000022000000
440000
440000
11000000
11000000
220000
220000
pc] 00 pc] 00
z [ 00 z [ 00
--220000
--220000
--11000000
--11000000
--440000
--440000
--22000000
--2200--2200--0022000000000000 --1100--110000000000 0000 11001100000000 00 22002200000000 00 --4400--44000000 --2200--22000000 0000 220022000000 440044000000
x [ pc] x [ pc]
-6-6 -5-5 -4-4 -3-3 -5-5 -4-4 -3-3 -2-2
log Σ [g cm-2] log Σ [g cm-2]
44 55 66 77 88 99 1100 44 55 66 77 88 99 1100
log T [K] log T [K]
Figure 2. Left:Sideview of gas surfacedensity (left half ofthe panel, blue-white) and temperature (right, red-orange) inthe central
2 kpc of the ‘Base’ simulation at t = 1 Myr. The CMZ has been enveloped by the external ISM shock fronts, but it still maintains
the strong collimation of the diffuse cavities. The cavities are alsofilled with hot 108−109 K gas, which allows them to expand in all
directions once the feedback from Sgr A∗ has switched off. Right: Central 500 pc of the ‘Base’ simulation at t = 6 Myr. The CMZ
remains,althoughitsdensitystructureisperturbed.Thereisalsoa“backflow”ofwarm(T ≃Tvir)gasintothecentralregions,evacuated
bythebuoyant riseofthebubbles.
Galactic plane grow even more. The left panel of Figure 2 4.1.2 Large scales
shows the edge-on view of the inner 2 kpc of the Galaxy
at time t = 1 Myr. One notes the hour-glass shape of the We now discuss the larger scales of the “Base” simulation.
cavitiesopenedbytheoutflow,andastronggradientinthe Figure 3 shows theedge-on views of the simulation domain
outflowvelocitywithangleθ(tanθ= z/x)meausuredfrom at times t = 1,3 and 6 Myr (left, middle and right panels,
the z-axis. In particular, the maximu|m v|elocity is reached respectively).Theleft panelinparticularshowsthatbythe
atθ=0,suchthatvelocitythereisconsistentwiththeana- timeSgrA∗ switchesoffthecavitiesarestillrathersmallon
lyticalpredictionofv 2000km/s,andtheminimumisat Galacticscales:theirheightisR 3kpcandthemaximum
θ=90◦.Thereisalsoea∼“failed”outflowaroundθ 65◦;gas width is d 2.5 kpc. ∼
≈ ∼
flowingalongthesedirectionseventuallyfallsontheGalactic Furtherevolutionofthehotbubblesisdrivenbythein-
plane,shadowedbytheCMZfromfurtherSgrA∗ feedback. ertiaoftheoutflow,thebuoyancyofthebubblesandthefact
Some material is ablated from the surfaces of the CMZ. It that they are significantly over-pressurized with respect to
expandsand contributes to thetenuousgas filling the cavi- theambientmedium(cf.theleft panelofFigure4).Bubble
ties. expansionproceedsinan almost self-similar fashion, except
for a ripple at roughly the middle of the bubbleheight (see
Fig. 3, middle panel). It is most likely a Kelvin-Helmholtz
The right panel of Figure 2 presents the edge-on view
unstable mode which arises due to the material inside the
of the central 500 pc at the end of the simulation, at t =
bubblemovingparallel tothesurfaceof thecontactdiscon-
6 Myr. Due to the relative buoyancy of the hot gas in the
tinuity. The ripple rolls over and disappears by t = 6 Myr
cavitieswithrespecttothecooler“ambient”gas,theformer
(Fig. 3, right).
leavestheregion bythattime,beingreplacedbythelatter.
This “back flow” of warm (T T ) gas returning to the Bytheendofthesimulation,thecavitieshaveexpanded
vir
centralregionafterSgrA∗ swit≃chedoffisclearlyseeninthe toreach aheightof 11.5 kpc(Fig. 3,right panel),consis-
∼
patternofvelocityvectorsontheleftsideoftherightpanel tent with theobserved vertical extent of theFermi bubbles
ofFigure2.WealsopointoutthatwhiletheCMZhasbeen (Su et al. 2010). The width, at 9 kpc, is slightly larger
significantly affectedbytheoutflowfrom SgrA∗,most ofit than observed (d 6 kpc); w∼e return to this point in
obs
∼
remainsintheregionintheform ofaringdiscussedfurther the Discussion section. The cavities are filled with very hot
in 4.1.3. (T 2 108 K 17keV)anddiffuse(f 2 10−5;
bub g,bub
§ ∼ × ∼ ∼ ×
(cid:13)c 0000RAS,MNRAS000,000–000
8 Kastytis Zubovas, Sergei Nayakshin
22..00••11004422..00••110044 22..00••11004422..00••110044 22..00••11004422..00••110044
11..55••11004411..55••110044 11..55••11004411..55••110044 11..55••11004411..55••110044
z [ pc]11..00••11004411..00••110044 z [ pc]11..00••11004411..00••110044 z [ pc]11..00••11004411..00••110044
55..00••11003355..00••110033 55..00••11003355..00••110033 55..00••11003355..00••110033
00 00 00
--110000--1100000000000000 --5500--550000000000 0000 5500550000000000 11000011000000000000 --110000--1100000000000000 --5500--550000000000 0000 5500550000000000 11000011000000000000 --110000--1100000000000000 --5500--550000000000 0000 5500550000000000 11000011000000000000
x [ pc] x [ pc] x [ pc]
-7-7.0.0 -6-6.5.5 -6-6.0.0 -5-5.5.5 -5-5.0.0 -4-4.5.5 -4-4.0.0 -7-7.0.0 -6-6.5.5 -6-6.0.0 -5-5.5.5 -5-5.0.0 -4-4.5.5 -4-4.0.0 -7-7.0.0 -6-6.5.5 -6-6.0.0 -5-5.5.5 -5-5.0.0 -4-4.5.5 -4-4.0.0
log Σ [g cm-2] log Σ [g cm-2] log Σ [g cm-2]
44 55 66 77 88 99 1100 44 55 66 77 88 99 1100 44 55 66 77 88 99 1100
log T [K] log T [K] log T [K]
Figure 3.Gas evolution onlargescales inthe ‘Base’simulation;the three panels correspondto t=1,3and6Myr,fromleftto right.
Onlythepositive-zsideofthecomputationaldomainisshown,duetosymmetryaroundtheGalacticplane.TheCMZstronglycollimates
theoutflowandallowstheformationofateardrop-shapedcavitywithamorphologyverysimilartothatoftheobservedFermibubbles.
Thebubblescontinuetoexpandandriseduetohighpressureandlowdensity,evenoncethefeedbackhasswitchedoff.
110077 10000 109 100
110066 108 10-1
1000
-2m] 110055 -2m] K]
Pressure [dyn c 111100003434 Pressure [dyn c 10100 Temperature [ 110067 1100--32Gas fraction
110022 105 10-4
110011 1 104 10-5
11 1100 0 2 4 6 8 10 12 0 2 4 6 8 10 12
Radius [kpc] Radius [kpc] Radius [kpc]
Figure 4. Left: Gas pressureas a function of cylindrical radius (r2 =x2+y2) for a selection of SPH particles at 1<|z|<2.5 kpc
cyl
(middle of the bubble) for the ‘Base’ simulation at t = 1 Myr; the solid line is the mean value at each radius. The central cavity is
significantly overpressurised in comparison to the ambient medium, leading to lateral expansion of the bubbles. Middle: Same but at
timet=6Myrwhenthebubbleismuchlarger.Theverticalcutchosenisnow4.5<|z|<6kpc.Notethatthegaspressurehasdropped
significantly and is slowly varying accross the bubble and the shocked region. Right:Temperature (green curve and dark blue points,
left scale) and gas fraction (red curve and light blue points, right scale) against cylindrical radius for the same time and particle cut
as the middle panel. The hot diffuse inner cavity and dense surrounding medium are obvious and have rather sharp edges (thickness
∼1kpc). Solidlinesshowmeanvaluesofgasfractionandtemperatureateachradius.
see Fig. 4, right) gas. For completeness, Figure 5 shows the visible in Figure 3, and also in the right panel of figure 2.
timeevolution of thebubble’sheight, R,and width,d.The This detachment is caused by the bubbles rising buoyantly
lateral expansion is initially somewhat faster than the ver- outoftheGalaxypotential.Byt=6Myr,thegapbetween
tical, possibly because some of the material expandingout- the centre and the lower edges of the bubbles is h 1 kpc,
∼
wardalongthediscplanewasblownoffthetopoftheCMZ inagreementwithobservationsthatpermitanyvalueofthe
disc (rotating gas is easier to blow away due to centrifugal gap size below 2 kpc(Su et al. 2010).
∼
force). As is seen in the figure, in the next few Myr, the
bubbles are as wide as they are tall at t 2 Myr. Subse- Theleft panelofFigure4showstheSPHparticlepres-
∼
quently,vertical expansion becomes faster than lateral one. sureversustheircylindricalradiusdefinedasr2 =x2+y2
cyl
Thismaybedrivenbybuoyancy:asthebubblescontinueto selectedataslabofgaswith1< z <2.5kpcatt=1Myr,
rise up, their lower edges “lift off” from the plane, and the roughly corresponding to the mid|p|lane (i.e. half-height) of
cooler gas can start flowing back along theplane. the bubbles at that age. We observe that the difference in
The bubblesare slightly detached from thevery centre pressure within the bubble and outside is greater than two
of the Galaxy; the gradual increase in this detachment is ordersofmagnitude.Thisexcesspressurecontinuestodrive
(cid:13)c 0000RAS,MNRAS000,000–000
Fermi Bubbles: Sgr A∗ AGN feedback? 9
ward force and pressure of quasar wind cause a significant
1122
radial mixing in the CMZ. For example, some of the CMZ
gasontheinnerfaceofthediscissentoutwardbythewind
1100
just above the surface of the outer regions of the disc, but
stalls later on and falls back on the CMZ in the outer re-
88 gions. This failed outflow has a small angular momentum
c] incomparisontogasintheouterdisc.Theangularmomen-
p
e [k 66 tumoftheCMZgasisthenwellmixedup.Thisestablishesa
z narrow distribution of specific angular momentum – aring.
Si
We note that this mechanism of ring formation is similar
44
in spirit to that found by Hobbs et al. (2011) in their sim-
ulation S30, although there shocks between material with
22
different angular momentum were due to initial conditions
in the collapsing gas shell rather than quasar feedback.
00
Subsequently,the ring slowly relaxes and spreads back
00 11 22 33 44 55 66
somewhat into a disc configuration due to viscous stresses;
Time [Myr]
however, the viscous timescale for this to happen at R =
Figure5.Height(solidline)andwidth(dashedline)ofthebub- 100 pc is tvisc 108(0.1/α) yr for H/R=0.25, where α is
∼
blesasfunctionoftimeinthe‘Base’simulation. the standard Shakura& Sunyaev (1973) viscosity parame-
ter.Thisismuchlongerthanthetimescalesweareinterested
in, and thus unsurprisingly the ring persists to the end of
theexpansion in directions both parallel and perpendicular
thesimulation (Figure 6, right).
totheGalacticplanelongafterthequasarhasswitchedoff.
Since the disc is only marginally gravitationally sta-
The middle panel of figure 4 presents the same as the
ble at the start of the simulation, it comes as no real sur-
left figure but at the end of the simulation and for a slab
prise that the ring becomes more unstable than the origi-
of material at a larger z (4.5< z <6 kpc,corresponding
nal disc. As a result, some spiral density waves are visible
| | | |
roughly tothemiddleof thebubblethat has nowrisen fur-
in the middle panel of Fig. 6. Furthermore, a very mas-
ther from the Galactic plane at t = 6 Myr). Note that by
sive dense clump forms at t 3.5 Myr and there are hints
t = 6 Myr, the gas pressure inside the bubble has dropped ∼
of another forming by the end of the simulation at a po-
bytwoordersofmagnitude;thepressureofthesurrounding
sition x,y 80, 20 pc. The radius of the clump is
ISMisalsolower,butonlybyaboutafactor10,sothepres- rcl 5{pc}an∼d i{ts m−ass}mcl 107M⊙. Its density is then
sure difference between the bubble and its surroundings is n ∼7 105cm−3, 500time∼sgreaterthanthebackground
cl
much smaller. Consequently, the bubble expansion is much pote∼nti×al densityat∼theclump’s radial distance R 100 pc
slower, as seen in Fig. 5 and the right panel of Fig. 3. The ≃
and similar to that of dense star forming molecular cloud
vertical expansion of the bubbles persists for longer due to
cores.Duetotheadoptedtemperaturefloorandlackofres-
residual momentum in the gas and buoyancy (see the last olution in the simulations, the cloud cannot fragment into
two columns in Table 1).
smaller globules, butweobviously expect suchan object to
beunstableto gravitational collapse. Theresult would pre-
sumably be a massive star cluster. The orbit of the clump
4.1.3 Feedback effects on the CMZ around Sgr A∗ is mildly eccentric (e 0.2). This may be
∼
Inthesimulation,wefindthattheCMZisnotdispersedby interesting as a potential route to formation of the Arches
the outflow, a result consistent with the prediction of the cluster which has a rather non-circular orbit (Stolte et al.
analytical argument (cf. Section 2.3). However, the quasar 2008)inparticular,butitmaybealsorelevanttotheorigin
wind is powerful enough to displace the inner 120 pc of ofotheryoungGalactic Centrestarclusters andGMCs (cf.
the CMZ to larger radii, resulting in formation∼of a dense furtherdiscussion in 5.6.3).
§
thin ring (Figure 6, left).
Theaverageradialexpansionvelocityoftheinnerparts
4.2 Dependence on the ambient gas density
of the CMZ, v 100 km/s, is larger than the sound
r,cmz
∼
speed in its gas (cs 20 40 km/s, for H/R = 0.125 and TheambientgasdensitybeforeSgrA∗ quasaroutburstisa
∼ −
0.25 respectively) and comparable toitsrotational velocity. free parameter of the model. Therefore, we varied f to see
g
Therefore some of the CMZ gas is shock-heated to T how our conclusions depend on this paerameter. A fourfold
∼
106 K and expands vertically. This allows the quasar wind increase in f (Simulation ‘Fg-high’, Fig. 7, left) results in
g
to ablate the outer surfaces of the CMZ further. Gas from a reduction of the bubble height by 40% for the same
theseregionsfillsthevoidsinthehalo(cf.Sections4.1.1and t . This is consistent with the analyt∼ical prediction from
q
4.1.2, above). This process, however, removes only a small equation(6)andcanbeunderstoodintermsofthelargergas
amount of mass: by the end of the simulation, the CMZ weight, which for an isothermal distribution is independent
mass(definedasthegasmass within aradius250 pcin the of radius and is
Galactic planeandwithin z 100 pc)hasdecreased byless
± 4f σ4
than 5%. W = g (13)
g G
Wewould liketonoteanothermoresignificant dynam-
ical effectof theSgrA∗ outflowontheCMZ thatre-shapes (King 2003, 2010a). Denser gas weighs more, therefore re-
the initial disc configuration into a ring-like one. The out- quiring more energy to be lifted to the same height. Since
(cid:13)c 0000RAS,MNRAS000,000–000
10 Kastytis Zubovas, Sergei Nayakshin
220000220000 220000220000 220000220000
110000110000 110000110000 110000110000
y [ pc] 0000 y [ pc] 0000 y [ pc] 0000
--110000--110000 --110000--110000 --110000--110000
--220000--220000 --220000--220000 --220000--220000
--2200--22000000 --1100--11000000 0000 110011000000 220022000000 --2200--22000000 --1100--11000000 0000 110011000000 220022000000 --2200--22000000 --1100--11000000 0000 110011000000 220022000000
x [ pc] x [ pc] x [ pc]
-3-3 -2-2 -1-1 00 11 -3-3 -2-2 -1-1 00 11 -3-3 -2-2 -1-1 00 11
log Σ [g cm-2] log Σ [g cm-2] log Σ [g cm-2]
Figure6.Densityofgasinthecentral250pcofthe‘Base’simulationatt=1,3and6Myr(left,middleandrightpanels,respectively),
as seen from above the Galactic plane. The inner regions of the CMZ are strongly affected by the quasar activity, forming a ring (left
panel)whichpersistsforseveralMyr(middlepanel)whileslowlyspreadingradiallyanddevelopingunstablespiralfilaments(rightpanel).
A self-gravitating clump forms at t= 3.5 Myr, with another about to form by the end of the simulation. The total mass of the CMZ
remainsalmostconstantthroughout thesimulation.
the energy input is the same in both cases, higher values 4.3 Dependence on the outburst duration
of f result in lower height reached by the bubbles. In fact,
g
in simulation ‘Fg-high’, formally, the stalling radius of the We now explore how simulation results depend on the out-
bubbleisR 10kpc,similartothesizeoftheobserved burstduration.Simulation‘Tq-low’(seeTable1)isidentical
stall
bubbles.Howeve∼r,thestallingtimeiststall 50Myr,which to the ‘Base’ simulation except tq =0.3 Myr. As expected,
ismuchgreaterthanthetimesincethehyp∼othesizedSgrA∗ lower tq results in physically smaller bubbles (see Fig. 7,
outburst.Thisshowsthatrelativelyhighvaluesoff aredef- right panel). Due to a smaller amount of energy injected
g
initelydisfavoredwithinourmodelofarecentoutburstori- and a longer duration of adiabatic expansion phase after
gin fortheFermibubbles(unlessperhapst ismuchlonger quasarswitchoff,thecontrastbetweenthetemperatureand
q
than a 1 Myr; but see Section 4.3). density in the bubble interior and the surrounding shell is
also smaller. The bubbles do have lower densities (effective
f 4 10−4, compared with the ambient f 10−3) and
Conversely, a simulation with a lower gas density ini- g ∼ × g ∼
somewhathighertemperatures(T 107K)thanthesur-
tial condition (‘Fg-low’, Fig. 7, middle) produces a bubble bub∼
roundings,andthusdorisebuoyantlyawayfromthecentre,
that is 40% taller, but its interior temperature is rather
∼ resulting in large (& 3 kpc by 6 Myr) separations of the
low, blurring the distinction between the bubble and its
bubbles from the centre. Vertical expansion of the bubble,
surroundings. Furthermore, the lower density bubble rises
however, is slower than in the ‘Base’ simulation; the outer
further from the Galactic centre, producing a detachment
edges of the bubbles reach only 5 6 kpc by the end of
hb > 2 kpc, inconsistent with the data (Su et al. 2010). ∼ −
thesimulation.Inaddition,thebubblewidthissignificantly
Thesedisagreementsallow ustoexcludethepossibility ofa
smaller than in the ‘Base’ simulation, since a lower energy
significantly lower gas fraction in thehalo as well.
inputresultsinalowerpressureinsidethebubble,therefore
lateral expansion is also slower.
Our simulations show that the width of the bubbles,
on the other hand, is almost independent of the ambient This result provides a rough lower limit to the quasar
gas density. This is probably because the lateral expansion outburst duration required to inflate the bubbles: tq >
of the bubble is governed not only by the thrust from the 0.3 Myr, and quite likely tq 1 Myr. This is compatible
∼
outflow, but also by the pressure balance on both sides of withtheanalyticalresults,wherewefoundtq>2.5 105 yr
×
the bubble (Fig. 4, left and middle panels). The ambient frommorphologicalarguments.Wediscussthispointfurther
gas pressure increases with higher f , but so does the pres- in the Discussion section.
g
sure insidethe cavity duetolower bubblevolume.The two Giventhatalowervalueoft producessmallerbubbles,
q
changes compensate for each other, and the pressure in- whilealowervalueoff increasestheirsize(cf.Section4.2),
g
sidethebubblesremainsseveralordersofmagnitudegreater isitpossiblethatreducingbotht andf mayyieldasgood
q g
than in the external medium, leading to lateral expansion. or better morphological fit to the observed bubbles as the
Additionally, this expansion happens on an approximately “Base”simulation?Werunasimulationtotestthisidea(see
dynamicaltimescale,whichisgivenbythepropertiesofthe simulation “Both-low” in Table 1), but find results incom-
background potential and is also independentof f . patiblewithobservations.Figure9showsthesurfacedensity
g
(cid:13)c 0000RAS,MNRAS000,000–000