AGN-stimulated Cooling of Hot Gas in Elliptical Galaxies

5.5 MB·English

by  Milena Valentini

Mon.Not.R.Astron.Soc.000,1–23(2002) Printed6May2015 (MNLATEXstylefilev2.2)
AGN-stimulated Cooling of Hot Gas in Elliptical Galaxies
Milena Valentini1,2(cid:63) and Fabrizio Brighenti2†
1SISSA, via Bonomea 265, I-34136 Trieste, Italy
2Dipartimento di Fisica e Astronomia, Universita` di Bologna, via Ranzani 1, 40126 Bologna, Italy
5
1
0 Accepted2015January13.Received2015January13;inoriginalform2014November25
2

y
ABSTRACT
a
M
WestudytheimpactofrelativelyweakAGNfeedbackontheinterstellarmedium
5 of intermediate and massive elliptical galaxies. We find that the AGN activity, while
globally heating the ISM, naturally stimulates some degree of hot gas cooling on

] scales of several kpc. This process generates the persistent presence of a cold ISM
A phase, with mass ranging between 104 and (cid:38) 5×107 M , where the latter value is
(cid:12)
G appropriateforgroupcentered,massivegalaxies.Widespreadcoolingoccurswherethe
ratio of cooling to free-fall time before the activation of the AGN feedback satisfies
.
h t /t (cid:46)70, that is we find a less restrictive threshold than commonly quoted in the
cool ff
p
literature. This process helps explaining the body of observations of cold gas (both
-
o ionizedandneutral/molecular)inEllipticalsand,perhaps,theresidualstarformation
r detected in many early-type galaxies. The amount and distribution of the off-center
st cold gas vary irregularly with time.
a ThecoldISMvelocityfieldisirregular,initiallysharingthe(outflowing)turbulent
[ hot gas motion. Typical velocity dispersions of the cold gas lie in the range 100−

200 km s−1. Freshly generated cold gas often forms a cold outflow and can appear
2
v kinematically misaligned with respect to the stars.
2 We also follow the dust evolution in the hot and cold gas. We find that the
0 internally generated cold ISM has a very low dust content, with representative values
5 of the dust-to-gas ratio of 10−4−10−5. Therefore, this cold gas can escape detection
3 in the traditional dust-absorption maps.
0
. Key words:
1
galaxies: elliptical and lenticular, cD; galaxies: evolution; galaxies: ISM; galaxies:
0
groups: general.
5
1
:
v
i
X
1 INTRODUCTION gas ratio can be used to track down the origin of the cold
r gas (see below).
a Elliptical galaxies generally have a complex multiphase in-
A multiphase ISM is expected to keep the galaxy
terstellar medium (ISM), which is a key component of the
“alive”, allowing for (perhaps tiny) episodes of star forma-
galacticecosystem.Themixtureofthevariousgasphasesis
tion (SF). Indeed, a sizeable fraction of ETGs shows evi-
usuallydifferentinearly-typegalaxies(ETGs)withrespect
denceofrecentSF(Trageretal.2000;Kavirajetal.2007).
tolate-typesystemsandthis,inturn,reflectsonthediffer-
Therefore,agraspontheoriginandevolutionofthemulti-
ent evolutionary pattern of morphological diverse galaxies.
phase ISM would reveal vital information on the evolution
Reviews of hot, warm and cold gas in ETGs can be found
of ETGs, such as star formation history, quenching mecha-
in e.g. Caon et al. (2000); Mathews & Brighenti (2003a);
nism(s), the role of active galactic nuclei (AGN) feedback,
Sarzi et al. (2006, 2013); Mulchaey & Jeltema (2010); El-
black hole growth, accretion of baryons from the environ-
lis & O’Sullivan (2006); Young et al. (2011); Davis et al.
ment and more.
(2011); Serra et al. (2012). The cold ISM is often spatially
In most ETGs a significant fraction of cold gas is
extended, with irregular distribution and kinematics (Caon
thoughttohaveanexternalorigin,asindicatedbythemis-
etal.2000).DustisalsopresentinallthephasesoftheISM
alignedkinematicsofthecoldgas(bothionizedandneutral)
(Temietal.2004,2009;Smithetal.2012),andthedust-to-
with respect to the stars (e.g. Davis et al. 2011, and refer-
ences therein). Cold gas is indeed commonly found around
(cid:63) E-mail:[email protected] and bound to ETGs (Thom et al. 2012). The fate of this
† E-mail:[email protected] cold gas reservoir is still unclear, but it is likely that some
(cid:13)c 2002RAS
2 M. Valentini & F. Brighenti
ofthislowentropygasisfallingontothegalaxyandreaches demonstratethephysicalexistenceandthebasicproperties
thecorein≈1Gyr.However,ΛCDMhydrodynamicalsim- of widespread gas cooling in ETGs.
ulations on the kinematics of accreted HI in ETGs indicate The thermal stability of gas in galactic or cluster cool-
significant disagreement with respect to the observations, ingflowshasbeeninvestigatedsincethediscoveryofthehot
makingthesourceofmisalignedcoldgasstillanopenques- ISMandICM,throughbothlinearstabilityanalysisandnu-
tion (Serra et al. 2014). merical simulations (see, for instance Mathews & Bregman
1978; Cowie et al. 1980; Bodo et al. 1987; Malagoli et al.
SomeofthecoldISMcertainlycomesfrominternalpro-
1987a; Balbus 1988a; Loewenstein 1989a; Balbus & Soker
cesses, such as stellar mass loss or hot gas cooling (Davis
1989a; Malagoli et al. 1990a; Hattori & Habe 1990; Reale
etal.2011;Werneretal.2014;Davidetal.2014).Theoret-
et al. 1991; Binney et al. 2009; McCourt et al. 2012; Joung
ical investigations about the formation of a cold ISM phase
etal.2012;Gasparietal.2012b;Li&Bryan2014).However,
in ETGs include Brighenti & Mathews (2002); Mathews &
linearstabilityanalysisprovidesanincompleteunderstand-
Brighenti (2003b); Temi et al. (2007); Parriott & Bregman
ingwhenstrongdensityperturbationsarepresent.Itisquite
(2008);McCourtetal.(2012);Gasparietal.(2012a,b);Li&
obviousthatanoverdenseclumpofgascancoolfastandsep-
Bryan(2014);Brighenti,Mathews&Temi(2015).Formas-
aratefromthehotphase.Thedensitycontrastthresholdfor
sive galaxies, especially when located in high density envi-
thislocalizedcoolingdependsonthepropertiesoftheback-
ronments, the internally produced cold gas may well domi-
groundmediumandtheperturbation(seeJoungetal.2012,
nateovertheaccretedone.Cavagnoloetal.(2008)andVoit
forarecentnumericalinvestigation).Therefore,thekeyas-
et al. (2008) found that central galaxies in clusters host a
trophysical problem is to understand if such strong pertur-
multiphasegasonlywhenthecentralICM(ISM)entropyis
belowathresholdkT/n2/3 ∼30keVcm2,providingaclear bationsarenaturallygeneratedinsideellipticalgalaxies.As
we discuss below, the answer delivered by our simulations
link between the presence of cold gas and the properties
is yes. We prefer to keep the assumptions of our models to
of the surrounding hot gas. In a recent theoretical investi-
a minimum. We do not use an ad hoc distributed heating
gation Lagos et al. (2014) argue that cooling from twisted
to ensure global thermal equilibrium, nor we superimpose
hot gas halos results in a large fraction (∼ 46 %) of ETGs
anartificialturbulentvelocityfieldtogeneratedensityper-
withinternallygeneratedmisalignedcoldgas,explainingthe
ATLAS3D observations (Davis et al. 2011). turbations. Adopting low-power, collimated outflows as the
onlyperturbingmeansoftheISM,weaimtoprobetheim-
In this paper we study the generation of a spatially
portance of AGN-stimulated cooling in ETGs in a simple
extended cold gas phase in ETGs by radiative cooling of
yet solid way.
the hot halo gas. The key question is therefore if, and un-
der which circumstances, the hot ISM can cool at large
distance from the galaxy center. Multiwavelength observa-
2 NUMERICAL PROCEDURE
tions often show a strong spatial correlation between X-ray
and Hα images (e.g. Trinchieri et al. 1997; Goudfrooij & The simulations have been carried out with a modified ver-
Trinchieri 1998; Trinchieri & Goudfrooij 2002; Temi et al. sionoftheeuleriancodeZEUS-2D(Stone&Norman1992),
2007; Gastaldello et al. 2009; Werner et al. 2014), implying developedtoincludeinthesetofhydrodynamicalequations
rapid local cooling. Furthermore, the connection between sourceandsinktermsdescribinggalacticscalecoolingflows.
coldgas,radioemissionandAGN-drivenX-raydisturbances Thesetermsincludemassandenergyinjectionbythestellar
(seereferencesabove,alsoBlantonetal.2011)suggeststhe population, as described in Mathews & Brighenti (2003a).
keypointthatspatiallyextendedcoolinghasbeentriggered ThepresenttimetypeIasupernovarateadoptedhereis0.02
by the AGN activity. Evidently, while AGN feedback sup- SNu1. The code has been further enhanced to deal with a
pressesthetotalcoolingratewithrespecttostandardcool- secondfluidrepresentingthedust.Dustdensityρ obeysto
d
ing flow models (e.g. McNamara & Nulsen 2007), it also the equation:
stimulates some gas condensation on scales of several kpc.
∂ρ
d + ∇·(ρ u) = α ρ δ − ρ˙ +ρ˙ , (1)
Guided by these observational results, we present here ∂t d ∗ ∗ ∗ sputt growth
adetailedinvestigationofspatiallyextendedgascoolingre-
where u is the velocity of the gas, α the specific rate of
∗
sultingfromAGNfeedback.Wedonotaddressthelongterm
stellarmassloss,ρ thestellardensityandauniformstellar
∗
fateofthecooledgas—itcanbeinpartaccretedontothe
dust to gas mass ratio δ =0.01 has been assumed. On the
∗
centralblackhole(Gasparietal.2012b),itcansettleinaro-
righthandsideofequation1,besidesthestellarsourceterm
tatingdisk(Brighenti&Mathews1996,1997a)oritmaybe
fordust,therearethesinktermduetograinsputteringand
re-heatedtothehotgastemperaturebythermalconduction
the source term due to grain growth, ρ˙ and ρ˙ ,
sputt growth
or other processes.
respectively.
For the reasons outlined in Gaspari et al. (2012a) we Thermal sputtering (Draine & Salpeter 1979; Tsai &
consider collimated, non-relativistic outflows as the domi- Mathews 1995) rate is estimated as:
nantfeedbackmechanisminlocalETGs.TheAGNfeedback ρ
ρ˙ = d = n (cid:104)m˙ (cid:105), (2)
processisfarmorecomplicatedthanweconsiderhereandis sputt τ d gr
sputt
notappropriatelyunderstood(see,e.g.Gasparietal.2012a,
where n = ρ /(cid:104)m (cid:105) is the number density of dust grains,
for a discussion on the numerical limitations in simulating d d gr
AGNheatingingalaxiesandclusters).However,fortheob-
jectivesofthispaperitisnotnecessarytoaccuratelymodel 1 Thesetermshavenosignificantimpactonourresultsandhave
the whole feedback cycle. An idealized feedback scheme as beenincludedjustforconsistencywithpreviouscoolingflowcal-
theonedescribedinthenextsectionisadequateenoughto culations.
(cid:13)c 2002RAS,MNRAS000,1–23
AGN-stimulated Cooling of Hot Gas in Ellipticals 3
(cid:104)m˙ (cid:105) is the average mass sputtering rate per grain, m˙ = bright group, the isolated galaxy (IG), an isolated, fairly
gr gr
4πa2ρ a˙ beingthemasssputteringrateforagrainofgiven massive elliptical, and the low mass galaxy (LM), an inter-
gr
radius a. Here, ρ = 3.3 g cm−3 is the density of silicate mediateelliptical,whichrepresentsamorecommonmember
gr
grains(Temietal.2003),a˙ istherateatwhichthegrainra- of the early-type galaxy family. The key difference between
diusdecreases(Tsai&Mathews1995;Mathews&Brighenti the first and the two latter models is the amount of hot
2003b) and the resulting average sputtering time is: gaswithinthegalaxy,whichinturnreflectsonasignificant
τsputt = (cid:104)(cid:104)mm˙ggrr(cid:105)(cid:105) = 3|a(cid:82)˙|aa(cid:82)mmaaiamnmxianax3a−2s−dsada = 3|a(cid:104)˙a|(cid:104)3a(cid:105)2(cid:105) (3) dCtriGaffgermroeounspctemoifnedtthihueemhcoo(tIoGgliaMnsg)wt(iiemt.hgei.npB1rro0ifigkhlepecn(stieise&exFpMigeaucttrheede4wt)so. I1bn9e9t9ihn)e-,
0.03(cid:34) (cid:18)2×106(cid:19)2.5(cid:35) whilefortheIGandLMallthehotgasoriginatesfromstel-
= 1+ Myr. lar mass loss (Mathews & Loewenstein 1986; Loewenstein
n T
p & Mathews 1987; Ciotti et al. 1991; Mathews & Brighenti
2003a).
Inequation3,s=3.5(Mathisetal.1977),a =0.01µm
min
and a =1 µm 2. Finally, (cid:104)a3(cid:105)=(cid:82) a3−sda/(cid:82) a−sda and
max
similarly (cid:104)a2(cid:105).
The grain growth rate in cold and dense gas (Dwek 2.1.1 Central Galaxy
1988; Hirashita & Kuo 2011; Hirashita 2012; Zhukovska
We model the CG to agree with NGC 5044, the bright-
et al. 2008) is estimated as:
est galaxy in the homonymous group (see Gaspari et al.
ρ˙ = n (cid:104)m˙ (cid:105), (4) 2011b,2012a,forfurtherdetails).Thegravitatingmasscon-
growth d gr,growth
sists of a NFW (Navarro et al. 1996) halo with virial mass
wherethegrowthrateofeachgrainofmassmandradiusais M = 4×1013 M and concentration c = 8.5, plus a de
vir (cid:12)
m˙ gr,growth =πa2fnmmmvm, f =0.3 being the probability Vaucouleurs profile (Mellier & Mathez 1987) with effective
that a colli√ding atom/metal sticks on the grain surface, nm radius and stellar mass re = 10 kpc and M∗ = 3.5×1011
and vm ∝ T (Dwek 1998) the metal number density and M(cid:12). Although inconsequential here, we also include a cen-
thermalvelocity(assuminganatomicweightmm/mp =20). tralblackholewithmassMBH =4×108M(cid:12).Regardingthe
The averaged dust density growth rate is therefore: hotgas,weadopttheobservedtemperatureprofileforNGC
(cid:104)m˙ (cid:105) 3ρρ (cid:104)a2(cid:105) 5044 (Buote et al. 2003, 2004; David et al. 2009) as initial
ρ˙growth =ρd g(cid:104)rm,grow(cid:105)th = 4 ρ dfvm(0.01−δ)(cid:104)a3(cid:105) , (5) temperature distribution, then we calculate the gas density
gr gr
profile assuming hydrostatic equilibrium, choosing the cen-
whereρisthegasdensityandithasbeentakenintoaccount tral density to approximately agree with observations. Be-
thatwhenthedusttogasmassratioδapproachesthevalue foretoactivatetheAGNoutflow,weletthesystemdevelop
0.01 all the relevant metals are locked in dust grains. a classical cooling flow, by evolving the flow for 100 Myr3.
Radiative cooling describing the loss of energy for X- During this time, the initially present gas mixes with gas
ray emission has been included with the term −nineΛ(T) shedbythe(old)stellarpopulationofthegalaxy4.Thegas
in the thermal energy equation, where the cooling function density and temperature profiles just before the activation
Λ is calculated according to Sutherland & Dopita (1993), of the AGN outflow are shown in Figure 1. The hot gas
assuming solar metallicity. The cooling has been extended mass within r = 10 kpc is ∼ 2.6×109 M , and the bolo-
(cid:12)
to temperatures lower than T = 104 K following Dalgarno metric X-ray luminosity within the virial radius (r ∼900
vir
& McCray (1972) and assuming a value x = 10−2 of the kpc) is L ∼1.5×1043 erg s−1. In Figure 2 it can be seen
X
fractionalionization.ThecoolingistruncatedatT =50K. wherethisgalaxymodelislocatedintheB-bandluminosity
Dust-induced cooling, important for T (cid:38)106 K for a dust- versus the bolometric X-ray luminosity plane for early type
to-gas ratio ∼10−2, has been taken into account according galaxies. As expected, it resides in the high luminosity tip
toMathews&Brighenti(2003b).Wearewellawarethatthe oftheobservedL −L relation(Ellis&O’Sullivan2006),
B X
cooling and chemistry of cold gas is extremely complicated populated by massive galaxies at the center of groups or
and our treatment for the T <104 K gas is approximate. sub-clusters.
The two-dimensional z ×R computational domain is
madeupof1100×700zones.Theresolutionis∆z=∆R=5
pc up to z×R = 5×3 kpc. The outer 100 points in both
2.1.2 Isolated Galaxy
dimensions are separated by increasing distances which are
the terms of a geometric progression whose common ratio For this model, representative of massive but non central
is 1.095. This peculiarity of the grid allows to study the ellipticals, the stellar profile follows a de Vaucouleurs dis-
central region of the computational domain, where most of tribution, with total mass M =5×1011 M and effective
∗ (cid:12)
thecoolingprocessisexpectedtooccur,inanaccurateway. radius r = 6 kpc. The dark halo has a NFW profile with
e
virial mass M =1013 M and concentration 10.0.
vir (cid:12)
2.1 Models
We consider three models of elliptical galaxies: the central 3 Thishasanegligibleeffectontheresultspresentedinthefol-
galaxy (thereafter CG), located at the center of an X-ray lowing. We decided to kick off the AGN feedback from a pure
coolingflowjusttobeconsistentwiththeIGandLMmodels.
4 We refer the reader to Mathews & Brighenti (2003a) for the
2 Wecheckedthatthesevaluesofminimumandmaximumgrain hydrodynamical equations solved here and the relevant source
sizedonotaffectourresults. termsformassandenergy.
(cid:13)c 2002RAS,MNRAS000,1–23
4 M. Valentini & F. Brighenti
Figure 2. LB −LX diagram for the elliptical galaxies sample
ofEllis&O’Sullivan(2006).Filledcirclerepresentgalaxieswith
detected X-ray emission; open circles are used for upper limits.
The location of our models, just before the AGN activation, is
marked with the red squares when only the X-ray luminosity of
the hot gas is considered. Big blue dots individuate the models
when the contribution of the low mass X-ray binaries is added
(Kim&Fabbiano2004).
Figure 1. Upper panel: Density profile just before the outflow
activation for the central galaxy (solid line), the isolated galaxy
(dashed line) and the low mass galaxy (dotted line). The points
representdataforNGC5044takenfromBuoteetal.(2003,2004); 2.1.3 Low Mass Galaxy
Davidetal.(2009).Bottom panel:initial(3D)temperaturepro-
This model is a scaled down version of the IG described
filesforthecentralgalaxy(solidline),theisolatedgalaxy(dashed
line)andthelowmassgalaxy(dottedline).DatapointsforNGC above.ThestellarmassisnowM∗ =1.5×1011 M(cid:12) andthe
5044aretakenfromBuoteetal.(2003,2004);Davidetal.(2009). effectiveradiusre =3.16kpc,avaluewhichagreeswiththe
magnitude-r relation (Faber et al. 1997). The NFW dark
e
halo has a virial mass M = 1.5×1012 M and concen-
vir (cid:12)
tration 11.9. The mass of hot gas within r<10 kpc is only
∼3.4×107 M (∼1.15×107 M within r ), with a X-ray
(cid:12) (cid:12) e
(bolometric)luminosityL ∼1040ergs−1,whichplacesthis
x
model within the lower envelope of the L −L relation.
B X
The initial ISM is generated by evolving a classic cool- As common in intermediate and low mass ellipticals,
ing flow for 1 Gyr (the choice of this time is arbitrary and only the gas in the inner region is inflowing, while the ISM
has no consequence on the results, since the flow reaches at larger radii forms a subsonic outflow, powered by the
a quasi-steady state after ∼ 100 Myr). The ISM entirely SNIa (e.g. Mathews & Baker 1971; Mathews & Brighenti
builds from the mass loss from the stellar population (e.g. 2003a).FortheassumedSNIarate(0.02SNu),thetransition
Loewenstein&Mathews1987;Mathews&Brighenti2003a). betweeninflowandoutflowislocatedatr∼2kpc.Wenote
JustbeforetheAGNoutburst,thehotISMmasswithin10 thatforthisrelativelysmallgalaxythepropertiesoftheISM
kpc is ∼ 1.9×108 M , the X-ray bolometric luminosity arequitesensitivetotheSNheating.DoublingtheSNIarate
(cid:12)
being L ∼ 1.2×1041 erg s−1. Figure 2 shows that this results in a global outflow (but the inner ∼ 200 pc), with
x
model occupies an intermediate and uninteresting place in velocity increasing almost linearly from ∼ 0 at 200 pc to
the L −L diagram. The initial gas density and temper- ∼60 km s−1 at 3 kpc. The hot gas mass (within 10 kpc) is
B X
ature profiles are shown in Figure 1 as dashed lines. Notice reduced to 1.9×107 M , while the X-ray luminosity drops
(cid:12)
as pure cooling flows in elliptical galaxies show an overall to a very small value of 1.8×1039 erg s−1 (see Mathews &
negative temperature gradient, because of the central steep Brighenti (2003a) for more details on the effect of the SNIa
potential well and the resulting compressional heating. rate on the gas flow in elliptical galaxies).
(cid:13)c 2002RAS,MNRAS000,1–23
AGN-stimulated Cooling of Hot Gas in Ellipticals 5
stance, model IG4000 refers to the conical outflow with
R(cid:1)
v =4000 km s−1 activated in the isolated galaxy.
jet
active region(cid:1)
2.2.2 AGN feedback: recurrent outbursts
(cid:6)(cid:5)(cid:5)(cid:1)(cid:3)(cid:2)(cid:1)
InthesemodelsweconsiderthewholeAGNfeedbackcycle,
where the gas cools and accretes on the central black hole,
triggering an AGN outburst which heats the ISM. When
the gas cools in the central region, the cycle is assumed to
(cid:7)(cid:5)(cid:4)(cid:1) startagain.Needlesstosay,thephysicsofAGNfeedbackis
z(cid:1) very complex and poorly known. We have no pretension to
(cid:5)(cid:1) (cid:6)(cid:5)(cid:5)(cid:1)(cid:3)(cid:2)(cid:1)
provide a self-consistent model here, we just need a simple
scheme to set off outflows intermittently, in order to mimic
Figure 3.Schemeshowingthemethodwechosetoimplementa
the dynamical — sometime violent — evolution of the ISM
conicaloutflow(seetext).Theinnercornerofthe2Dcylindrical
inellipticalgalaxies.Wethusemployasimplifiedversionof
grid, with the 100×100 pc2 active region highlighted, is repre-
thefeedbackschemeusedelsewhere(e.g.Brighenti&Math-
sented.Wenotethatinthecodethez andRcomponentsofthe
velocity are located on different positions (see Stone & Norman ews 2006; Gaspari et al. 2012a). Although this feedback is
1992).Hereweshowthevelocityvectorsoriginatingfromthegrid notfullyself-regulated,themodeledoutflowsreproducerea-
centerjustforillustrativepurposes. sonable energies and powers (see Section 8).
The adopted recipe has two main ingredients: the way
ofnumericallydescribingtheoutflowanditsactivationtim-
2.2 Modeling the outflow ing. We adopted a simple method in which the mechanical
feedback activation is triggered by the presence of cooling
2.2.1 Single event
gas in the innermost region (r (cid:54) 100 pc) of the simulated
Asubrelativisticandmassiveoutflow(Brighenti&Mathews galaxy.Thisassumptionmimicstheso-calledcoldaccretion
2006; Gaspari et al. 2012a) which lasts 2 Myr (e.g. Fabian idea(e.g.Gasparietal.2012b,andreferencestherein):AGN
2012)isoursingleeventAGNmechanicaloutburst.Theout- outflows are fed by accretion of gas cooled out of the hot
flowenergyinjectionissimulateddispensingvelocitytothe ISM, which accretes onto the central black hole.
gaslocatedinaboxof(R×z)=(100×100)pc.Thisactive After several numerical experiments, we decided
regionistheinnercornerofthecomputationaldomain,near to adopt a dropout term −q(T)ρ/t , with q(T) =
cool
the origin of the R and z-axis5. q exp[−(T/T )2],(Brighenti&Mathews2002)intheconti-
0 c
The number of cells by which resolve the interior of nuityequationtoindividuateandremovefromthegridgas
the jet has been chosen arbitrarily, the reasonable assump- currently cooling to low temperatures. When gas dropout
tion is that the physics of the outflow does not influence within r (cid:54) 100 pc occurs (at least 1 M in one timestep),
(cid:12)
the AGN feedback effects on kpc scale-length and the IGM the outflow is set off. We choose q = 2 and T = 5×105
0 c
global properties. K to describe q(T), although the results are insensitive to
The outflow velocity is given to the cells of the active the exact values of these parameters. This dropout method
regionwhiletheAGNisswitchedon,thisenergyinputrep- mightresultunpalatableandcontrived,buthasbeenshown
resenting a spatially localized source term in the hydrody- toproviderealisticestimatesforcooledgasmasses,limiting
namicalequationofmomentum.Thevelocityisgivensetting the effect of numerical overcooling over the traditional ap-
itsmoduleanddefiningawayfordescribingthecomponents proach (see Brighenti & Mathews (2002), Brighenti, Math-
along R and z axes. We simulate both cylindrical and con- ews&Temi(2015)andtheAppendix).Besiderectifyingthe
ical outflows, although we will focus mainly on the latter numericalovercoolingproblem,thereisanevenmorecrucial
case. Cylindrical outflows have been simulated by equating reasontopreferthedropouttechnique.Inordertocalculate
the z-component of the velocity to the velocity module and the genuine cooling rate at large distances from the center,
setting the R-component equal to zero in all the aforemen- it is preferable to avoid the presence of cold gas in the in-
tioned zones. On the other hand, for conical outflows we nerregion,whichwouldbeejectedthroughanAGNoutflow
set the velocity vectors as illustrated in Figure 3. At any possibly reaching the off-center region and mixing with the
given grid point the velocity is radially directed, with the freshly cooled hot gas.
centerlocatedat(z,R)=(0,−100pc/tg(30◦)).Theresults Wenotethatweusethedropouttermonlynearthecen-
arequiteinsensitivetotheexactmethodofimplementinga terofthesystem(forr<500pc),sothattheoff-centergas
conical outflow. cooling(seebelow)iscalculatedinthestandardway,thatis
All the models have been evolved for 50 Myr, in or- lettingthegascoolingtolowtemperaturesandkeepingiton
der to investigate the short term evolution of a single AGN the numerical grid, although this is know to cause spurious
outburst.Eachperformedsimulationwasgivenaname:the overcooling (see Appendix).
identifyingconventionencodesthemodelofgalaxyandboth Once the outburst has been activated, the gas which
the shape and the velocity in km/s of the outflow. For in- resides in the inner region defined by R < 100, z < 100 pc
is given a constant velocity as long as the condition on the
presence of dropping out gas in r(cid:54)100 pc is met.
5 Numerical experiments show that injecting the kinetic energy All the models consider a sequence of conical outflows,
fromanozzlealongtheinnerboundaryconditionsatz=0does theiropeninganglebeingθ=30◦,andevolveupto50Myr.
notchangetheresults. Modelsofrecurrentfeedback(FB)weregivenanamewhich
(cid:13)c 2002RAS,MNRAS000,1–23
6 M. Valentini & F. Brighenti
shows the model of galaxy and the velocity in km/s of the 4 SPATIALLY EXTENDED COOLING: SINGLE
outflows, for instance CG-FB2000. AGN OUTFLOW
Below we analize the dynamics and the off-center cooling
process triggered by a single AGN outburst. We focus here
3 COOLING AND TIMESCALES on the conical outflows, the cylindrical ones giving quali-
tatively similar results. This idealized case will be used to
Here we briefly discuss the relevant timescales for thermal
betterunderstandthephysicalnatureofthenon-linearden-
instabilityforourthreemodels.Itiswellknownthatlinear
sityperturbationswhichleadtowidespreadcooling.Weex-
(infinitesimal)perturbationsinthecentralregionsofETGs
pectthatinamorechaoticandrealisticISM,perturbedby
and galaxy clusters are generally stable in the pure hydro-
the intermittent action of AGN feedback, extended cooling
dynamical case (e.g. Malagoli et al. 1987b; Balbus 1988b;
wouldbefacilitated.ThisisthesubjectofSection5.Inthe
Loewenstein 1989b; Balbus & Soker 1989b; Malagoli et al.
following we focus on the gas that cools in the “off-center
1990b; Binney et al. 2009). In fact, slightly overdense fluid
region”definedas:z>500pc,R>150pc.Weexcludethe
elements oscillates at the Brunt-Va¨sa¨ila¨ frequency ω =
BV regionnearthesymmetryz-axisbecausethe2Dcylindrical
2π/τ , where usually the oscillation period τ (cid:28) t .
BV BV cool gridusedinoursimulationsmightleadinspuriousenhanced
The oscillation center of the perturbation slowly sinks to-
cooling along the axis. Indeed, the formation of cold gas
wardthecenterofthesystem,inatimeonlyslightlyshorter
alongthejetaxisisacommonresultofoursimulations.This
than the flow time of unperturbed gas.
isphysicallyreasonablebecausewhenthecavitiesgenerated
However, the linear stability analysis is of limited use,
by the AGN jets move buoyantly toward larger distances,
as in realistic galactic environments violent dynamical pro-
they trigger a vortex flow around them, which compresses
cessesareexpectedtogenerateperturbationsoffiniteampli-
thehotgastowardthez-axis,significantlyloweringthelocal
tude. Indeed, X-ray images of cool cores clearly show large
cooling time (see also Mathews & Brighenti (2008); Revaz
variationsofgasdensityonallscalesprobedbycurrenttele-
et al. (2008); Brighenti, Mathews & Temi(2015)). Prelimi-
scopes.
nary3Dcalculationsverifytheformationofthez−axiscold
Brighenti&Mathews(2002)haveshownthatspatially
filament (C. Melioli, in preparation), but we still prefer to
extended gas cooling in a cool core can happen when the
beconservativeinthisworkandfocusontheregionfarfrom
hot gas is perturbed by the action of AGN feedback heat-
the symmetry axis for most of our analysis.
ing. Brighenti & Mathews (2002) found that localized non-
We also neglect the gas which cools at the very cen-
linear perturbations form in regions of converging flow and
ter.Thesuppressionofthetotalcoolingrateingalaxiesand
are able to cool without undergoing oscillations. Recently,
clusters relates to the so-called cooling flow problem (Mc-
McCourt et al. (2012); Sharma et al. (2012); Gaspari et al.
Namara&Nulsen2007)andwillnotbediscussedhere.For
(2012b); Singh & Sharma (2015) have studied in detail the
calculations about AGN heating in ellipticals see Gaspari
cooling process in galaxy cluster cores perturbed by AGN
et al. (e.g. 2012a), which use a similar feedback scheme.
feedback (see also Gaspari et al. 2011a). They provide a
heuristic criterion for the onset of off-center thermal insta-
bility: the ICM undergoes widespread cooling when stirred
4.1 AGN-cooling in the Central Galaxy
by AGN feedback if t /t (cid:46) 10, with the free fall time
cool ff
t ∼ t = (2r/g)1/2, g being the local gravitational ac- Inthetoppanel,centralcolumnofFigure5weshowthetime
ff dyn
celeration. Joung et al. (2012) investigated the evolution of evolutionofthecoldgasmasslocatedoff-center(z>500pc,
nonlinearperturbationsintheGalactichaloandfoundthat R > 150 pc), for the single conical outflow models. Times
for t /t (cid:46) 1 the “cloud” cools before being disrupted are measured since the activation of the outflow. For the
cool acc
by hydrodynamical instabilities. Here t = c /g, which is CG, the three models with v = 2000, 4000, 8000 km
acc s jet
similar to t . s−1 are able to cool a substantial amount of gas, 104−107
ff
InFigure4weshowtheratiost /t andt /t for M , at large distances from the center. A weak trend with
cool acc cool ff (cid:12)
our three systems, at the time just before the AGN activa- v is evident from Figure 5: the larger is v , the larger
jet jet
tion.FortheCGmodeltheinstabilitycriteriont /t (cid:46)10 is the mass cooled off-center. As already found in Brighenti
cool ff
is met for r (cid:46) 6 kpc, while for IG and LM no unstable re- &Mathews(2002),theAGNfeedbackgeneratesnon-linear,
gion exists outside the galactic core r (cid:46) 100 pc, according almost isobaric perturbations in regions of sustained com-
to Sharma et al. (2012). pression,whichtriggerintermittentandwidespreadcooling
However, in the following we show that the commonly throughout the region with t /t (cid:46) 10. Because of the
cool ff
adopted instability criterion is too restrictive. We find large overdensities formed in converging flows, it seems im-
that extended cooling within elliptical galaxies occurs for proper to describe this cooling process as a thermal insta-
t /t (cid:46)70 for realistic, recurrent, gentle AGN outbursts. bility. This agrees with recent studies of cooling in galaxy
cool ff
We note that the empirical entropy criterion for star for- clusters by McCourt et al. (2012); Gaspari et al. (2012b).
mation and multiphase gas in galaxy clusters cool cores, Contrary to these latter works, however, we do not include
K = kT/n2/3 (cid:46) 30 keV cm2 (Voit et al. 2008; Cavagnolo anartificialsourceofturbulencenoradistributedsourceof
et al. 2008) describes more accurately the spatial extent of heating. Generally, the region over which cooling occurs is
theregionwherecoolinghappens.Fortheprofilesshownin more extended when the power of the outflow is larger.
Figure 1 we find that the radius where K = 30 keV cm2 Interestingly,coolingcanoccurlongaftertheAGNout-
is 17, 5.4, 3.6 kpc for model CG, IG and LM, respectively. flowceases(seealsoBrighenti,Mathews&Temi,2015).For
Thesenumberscomparewellwiththemaximumsizeofthe instance,formodelsCG4000andCG8000off-centercooling
region where cooling occurs. episodeshappenatt∼35Myrandt∼50Myr,respectively,
(cid:13)c 2002RAS,MNRAS000,1–23
AGN-stimulated Cooling of Hot Gas in Ellipticals 7
Figure 4. Upper panels: Cooling time, acceleration time and free fall time (see definitions in the text) just before the AGN outburst,
fortheCG(left),theIG(middle)andLM(right).Bottom panels:ratiosofrelevanttimescales.
while the outflow terminated at t=2 Myr. At these times, everyresolutionadoptedinournumericalexperiments.Cal-
usuallynosignoftheAGNfeedback(cavities,shocks)would culations using coarse resolution might be grossly in error.
bedetectedwithX-rayobservations.Nevertheless,subsonic Usingatracerpassivelyadvectedwiththeflow,weare
motionwithvelocityupto∼1/2ofthesoundspeedisstill able to track down the original location of the cooling gas.
present in localized regions, especially in form of relatively We find that most of the cold gas found off-center comes
largeeddieswithtypicalsize∼0.5kpc.Wenotethatthese fromtheinnerregion(r(cid:46)1kpc),wheretheentropyislower.
featuresarewellresolvedinoursimulationswith∼50−100 ThisconfirmstheresultsbyLi&Bryan(2014).Becausethe
grid points. When exceptionally large eddies are present in ISM(iron)abundancepeaksinthecenter,italsofollowsthat
the inner region of the galaxy, they appear as weak X-ray the metallicity of the cold gas is somewhat higher than the
cavities.Thishappensinfrequentlyinoursimulations,with one of the surrounding hot gas.
large outflow velocities and earlier times making this event InFigure5wealsoshow,inthecentralrow,theevolu-
√
more likely. tion of the cold gas mass in the region r= R2+z2 >500
pc (that is, we include here the cold filament along the
Thespatialdistributionofthecoldgasintheoff-center z−axis) and the total cold gas (bottom panels). The mass
region at several times, for models CG4000 and CG8000, in the filament forming in the wake of the outflow lies in
is displayed in Figure 6. The cold blobs generally arise in therangeM ∼104−106 M 6,althoughthesevaluesmust
fil (cid:12)
a region close to the outflow symmetry axis (R (cid:46) 1 kpc) be confirmed by high resolution 3D simulations. The time
and for z (cid:46) 10 kpc. The cold gas is arranged in a large evolution of the total cold gas mass shows that the single
number of small clouds (actually, toroidal structures, given AGN outburst is unable to significantly suppress the cool-
theimposed2Dcylindricalsymmetry),generallyfew10spc ing rate with respect to the pure coling flow scenario. Only
in size. As expected (see Koyama & Inutsuka 2004) this is fortheCG8000modeltheAGNoutflowtemporarilyreduces
close to our numerical resolution (∆R = ∆z = 5 pc), with the cooling rate by a factor of ∼ 2.5 for a time ∼ 15 Myr,
the unfortunate implication that the evolution of the cold after which the system recovers the standard cooling rate,
clouds may be subject to serious numerical errors. We ad- M˙ ∼10 M yr−1.
(cid:12)
dress some of the numerical problems, such as overcooling,
in the Appendix. The off-center cooling process starts in a
verylocalizedfashion,usuallyinjustoneorfewzones(see, 6 Notethathereandinthefollowingweconsideronlythez>0
forexample,thetop-leftpanelinFigure6).Thisistruefor volume.
(cid:13)c 2002RAS,MNRAS000,1–23
8 M. Valentini & F. Brighenti
Figure 5. Upper left panel: Time evolution of the cold gas mass in the off-center region (R > 150 pc, z > 500 pc), for CG models
withcylindricaljetsCGcyl2000,CGcyl4000andCGcyl8000.Hereandinthefollowing,timesaremeasuredsincethestartoftheAGN
aoutflow.Middle left panel:asaboveforthetotalcoldgasmassintheregionr>500pc,whichincludesthefilamentalongthez−axis.
Lowerleftpanel:sameforthetotalcoldgasmass,mostofwhichislocatedattheverycenterofthegalaxy(r<300pc).Centralpanels:
same as left panels but for the CG galaxy with conical jets (30 degrees) models CG2000, CG4000 and CG8000. Right panels: same as
centralpanelsbutfortheisolatedgalaxy.
4.1.1 Cylindrical outflows thegalaxy,thereforealargervolumeofthesystemhostsan
almostunperturbedcoolingflow.Also,itiswellknownthat
conicalAGNoutflowsgetcollimatedbythehotgaspressure
Wehavealsocalculatedseveralmodelswithcylindricalout-
as they propagate outward, becoming effectively cylindrical
flows,inwhichthevelocityisdirectedalongthez−axis.The
at some distance from the center (cfr. Brighenti & Math-
time evolution of the cold gas mass for the models with jet
velocity2000,4000and8000kms−1isshowninthefirstcol- ews 2006). Given the similarity of models with conical and
cylindrical outflows (and the uncertainties about real AGN
umnofFigure5.Theresultsarequalitativelysimilartothe
outflows),inthefollowingwelimitthediscussiontoconical
conicaloutflows,withatendencytogeneratemoreoff-center
jets.
coldgas.Thereasonisthatcylindricaloutflowsarelesseffi-
cienttodistributetheirkineticenergyintheinnerregionof
(cid:13)c 2002RAS,MNRAS000,1–23
AGN-stimulated Cooling of Hot Gas in Ellipticals 9
CG 4000 km/s 14 Myr CG 8000 km/s 18 Myr
32 Myr 20 Myr
36 Myr 22 Myr
Figure6.Leftcolumn:temperaturemapformodelCG4000atthreedifferenttimes:t=14,32,36Myr,fromtoptobottom.Thez-axis
ishorizontal,theR-axisisvertical.Unitsarekpc.TimeismeasuredsincetheswitchonoftheAGNoutflow(whichlasts2Myr).Right
column: same for model CG8000. The temperature is shown at t=18,20,22 Myr, to follow a strong cooling episode. Notice that the
colorscalediffersforeverypanel.
4.2 AGN cooling in the Isolated Galaxy justbeforetheAGNactivation7.Astimegoesby,moregas
cools and moves away from the original formation location.
At later times, as shown in Figure 7, a multitude of cold
clumps can be found for (R,z) (cid:46) (0.7,2.5) kpc. As for the
CG simulation, the emergence of the off-center cooling de-
As pointed out in Section 3, the fundamental difference be-
pends on two effects. First, the outflow transports (low en-
tween the IG and the CG models is that in the former the
tropy)gasinitiallyatthecentertolargerradii(seealsoLi&
whole hot ISM is generated by the stellar mass loss of the
Bryan 2014). Second, the dynamical evolution of the AGN
galactic (old) stellar population. Therefore, the mass and
outflow generates regions of sustained compression (where
theaveragedensityofthehotgasismuchlowerthaninthe
∇·v<0),whichgivesrisetohighcontrastdensityinhomo-
CGcase.Asaresult,theratiot /t fortheIGisevery-
cool acc geneities.
wherelargerbyafactorof(cid:38)10thanfortheCG(seeFigure
AsinthemodelCG,amassivecoldfilamentiscreated
4). According to the criterion by Sharma et al. (2012) and along the axis of the jet, with mass ∼ 104 M , for models
(cid:12)
McCourt et al. (2012) we should not expect spatially ex-
IG2000 and IG4000. No gas cools instead for r>500 pc in
tendedcoolingforthismodel.Thisconjecturedoesnotpass
the case of the more powerful model IG8000 (middle-right
the test of our simulations. In fact the model IG2000 gives
panel of Figure 5). Evidently, the AGN heating is strong
rise a substantial mass of cold gas at t ∼ 5−25 Myr (top-
enough to completely suppress off-center cooling, at least
right panel of Figure 5). We will see below that in case of
for the timespan probed by our simulation.
repeated AGN outbursts, even moderate outflows with ve-
locity of 1000 km s−1 trigger significant off-center cooling.
ThespatialmapofthecoldgasforIG2000isshowninFig- 7 Justbeforethetimeofthefirstoff-centercoolingepisode,the
ure 7. The off-center cooling process initiates at t∼5 Myr, ratio tcool/tacc near the cooling region has values in the range
with small cold blobs forming at (R,z) ∼ (0.2,2) kpc and [20-50].Thisisduetotheadvectionoflowentropymaterialfrom
(R,z)∼(0.4,2.1) kpc, where the time ratio tcool/tacc ∼60, thecenterbytheAGNoutflow.
(cid:13)c 2002RAS,MNRAS000,1–23
10 M. Valentini & F. Brighenti
filament also forms along the z−axis, with mass ∼ 3×103
M .
(cid:12)
IG 2000 km/s 12 Myr
5 SPATIALLY EXTENDED COOLING: AGN
FEEDBACK
The models presented in Section 4 showed that the dy-
namical interaction of a single AGN-driven outflow with a
smooth and regular ISM generates density (entropy) per-
turbations which lead to (sometime recurrent) widespread
gas cooling. Understanding these idealized calculations has
beenpreparatorytothestudyofthemorerealisticproblem
of repeated AGN outbursts, the subject of this Section.
16 Myr TheintuitiveexpectationisthatinanISMcontinuosly
stirredbytheAGNfeedbackactivitythegenerationofnon-
linear perturbations is facilitated, with the result of more
intensecoolingepisodes.Thisisindeedwhatthesimulations
presented below show.
5.1 Feedback in Central Galaxies
InFigure9weshowtheoff-centertemperaturemapsforthe
feedbackmodelsoftheCGgalaxy,withoutflowvelocitiesof
20 Myr 2000,4000and8000kms−1.Thedarkspotsineverypanel
indicate gas cooled to T < 104 K. In Figure 8 the mass of
coldgasinthevariousregions,asdefinedintheprevioussec-
tions,isshownformostmodels.Thefirstresultrevealedby
theseimagesisthatapersistentcoldISMphaseisnaturally
present,regardlessonthefeedbackdetails.Ofparticularin-
terest is model CG-FB16000 — with the fastest outflows
among our simulations — shown in Figure 8 with the ma-
genta dot-dashed line. In this system the AGN heating is
strongenoughtosuppressalmostcompletelythecoolingat
Figure 7. Temperature maps for the isolated galaxy “single
event” and vjet = 2000 km s−1. Top panel: t = 12 Myr; mid- thecenterofthegalaxy(whereallthecoolingintheclassic
dle panel: t=16 Myr; bottom panel: t=20 Myr. The z-axis is coolingflowpicturewouldoccur).Despitethat,astrongoff-
horizontal, the R-axis is vertical. Units are kpc. Notice that the centercoolingepisodehappensatt∼24Myrandgenerates
colorscalediffersforeverypanel. a total cold gas mass M ∼1.5×108 M .
blob (cid:12)
The network of blobs and filaments occupies a region
typically few kpc in size and has mass M ∼ 106 −107
blob
We notice that the average total cooling rate in the M(cid:12). We are not in the position to calculate the fraction
50 Myr following the AGN outflow, for models IG1000, of this gas in molecular, neutral or photoionized state. It
IG2000,IG4000andIG8000,is0.5,0.45,0.32,0.24M yr−1 is likely, however, that all these components are simultane-
(cid:12)
(see bottom-right panel of Figure 5 - model IG1000 is not ously present (see our Discussion below), as supported by
shown). These values reflect the (temporarily) suppression observations (e.g. Werner et al. 2014; David et al. 2014).
ofcoolingduetoAGNactivity,beingthecoolingrateofthe The spatial distribution of the cold gas generally correlates
pure cooling flow model M˙ ∼0.8 M yr−1 . withthedirectionoftheoutflowsandwiththedisturbances
cool (cid:12)
induced in the hot gas. It is worth noting that the bright-
ness of warm gas clumps is expected to decrease with the
distance from the center, in pace with the decrease of the
4.3 AGN cooling in the Low Mass Galaxy
pressure.TheaspectandamountoftheAGN-triggeredcold
We describe only very briefly the single outflow models for phase are in broad agreement with warm/cold gas observa-
the low mass galaxy. Because of the lower hot ISM density, tionsinmassiveellipticals/galaxygroups(Caonetal.2000;
widespreadcoolingislessefficientforthissystem.However, Werneretal.2014).Webelievethatthisisthemostrobust
we shall see below (Section 5.3) that when repeated AGN andrelevantresultofoursimulations.Thevelocitystructure
events are considerated, even the LM model undergoes sig- of the spatially extended cold phase is discussed in Section
nificant off-center cooling. 7.1.
For the single outflow experiments, we find that only Thefilamentofcoldgasformingalongthez−axisisal-
LM2000showsextendedcooling,fort∼10−25Myr,when wayspresentintheCGsimulations,withmasswhichvaries
∼103−3×103 M arepresentintheoff-centerregion.Few between few 105 to few 107 M . The filament has often a
(cid:12) (cid:12)
small blobs develop at z∼4, R∼0.5 kpc. As usual, a cold clumpy appearance, with density variations within it of 2
(cid:13)c 2002RAS,MNRAS000,1–23