Draft version February 21, 2017 PreprinttypesetusingLATEXstyleemulateapjv.01/23/15 UNIFYING THE MICRO AND MACRO PROPERTIES OF AGN FEEDING AND FEEDBACK Massimo Gaspari1,∗,† & Aleksander Sądowski2,∗ 1DepartmentofAstrophysicalSciences,PrincetonUniversity,4IvyLane,Princeton,NJ08544-1001USA;mgaspari@astro.princeton.edu 2MITKavliInstituteforAstrophysicsandSpaceResearch,77MassachusettsAve,Cambridge,MA02139,USA;asadowsk@mit.edu Draft version February 21, 2017 ABSTRACT We unify the feeding and feedback of supermassive black holes with the global properties of galaxies, groups,andclusters,bylinkingforthefirsttimethephysicalmechanicalefficiencyatthehorizonand 7 Mpcscale. Themacrohothaloistightlyconstrainedbytheabsenceofoverheatingandovercoolingas 1 0 probedbyX-raydataandhydrodynamicsimulations(εBH (cid:39)10−3Tx,7.4). Themicroflowisshapedby 2 general relativistic effects tracked by state-of-the-artGR-RMHD simulations(ε• (cid:39)0.03). The SMBH b properties are tied to the X-ray halo temperature Tx, or related cosmic scaling relation (as Lx). The modelisminimallybasedonfirstprinciples, asconservationofenergyandmassrecycling. Theinflow e occursviachaoticcoldaccretion(CCA),therainofcoldcloudscondensingoutofthequenchedcooling F flow and recurrently funneled via inelastic collisions. Within 100s gravitational radii, the accretion 0 energy is transformed into ultrafast 104kms−1 outflows (UFOs) ejecting most of the inflowing mass. 2 At larger radii the energy-driven outflow entrains progressively more mass: at roughly kpc scale, the velocitiesofthehot/warm/coldoutflowsareafew103,1000,500kms−1,withmedianmassrates∼10, ] 100, several 100M yr−1, respectively. The unified CCA model is consistent with the observations of E (cid:12) nuclear UFOs, and ionized, neutral, and molecular macro outflows. We provide step-by-step imple- H mentationforsubgridsimulations,(semi)analyticworks,orobservationalinterpretationswhichrequire . self-regulated AGN feedback at coarse scales, avoiding the a-posteriori fine-tuning of efficiencies. h p Keywords: black hole accretion – ISM, IGM, ICM – methods: 3D GR-RMHD simulations, analytics - o r t 1. INTRODUCTION derson et al. 2015 and refs. within). Such plasma radia- s a Last-decade observations and simulations have shown tively cools in the core (< 0.1r100) through a top-down [ that supermassive black holes (SMBHs) and cosmic condensation cascade to dense warm gas (∼ 104-105K; 2 structures are not separate elements of the universe optical/IR-UV) and cold gas (<∼ 100K; radio), subse- v (Heckman & Best 2014 for a review). While cosmic quently raining toward the nuclear region (<10−3r100). 0 structuresarecharacterizedbyvirialradii1r (∼Mpc), Viarecurrentcollisions,thecondensedcloudsarerapidly 100 3 SMBHs have a characteristic Schwarzschild radius rS = funneled toward the inner stable orbit (rISCO ≈ 3rS). 0 2GM /c2 (10−4pc for M = 109 M ), implying a dif- Suchprocessisknownaschaotic cold accretion(Gaspari • • (cid:12) 7 ference of 10 dex in length scale. This magnitude of sep- et al. 2013; §2.1). CCA has been independently probed 0 aration might strike as insurmountable, however, black by several observational works (e.g., Werner et al. 2014; . holes would not exist without matter feeding them, and David et al. 2014; Voit et al. 2015; Tremblay et al. 2016 1 0 cosmicstructureswouldtendtoaquickcolddeathwith- and refs. therein). 7 out feedback from SMBHs (often called active galactic General-relativistic, radiative magneto-hydrodynamic 1 nuclei – AGN – to emphasize such role), thus creating a simulations (GR-RMHD) provide crucial constraints for : symbiotic relation. the last stage of feeding (e.g., Sa¸dowski et al. 2015, v At the present, no simulation is capable of covering si- 2016; Sadowski & Gaspari 2017 – SG17; §2.2). Near Xi multaneouslythe10dexdynamicrangeinvolvingSMBH the ISCO, the final drastic SMBH pull converts a frac- feedingandfeedback(Fig.1), andtotracktheevolution tion of the gravitational energy into mechanical output, ar from 0.1 yr to 10 Gyr. Recent attempts have been made ejectingmostofthemassviaultra-fast outflows(UFOs). in the direction of linking the large-scale multiphase Such outflows re-heat the core, while entraining the am- gaseoushalosofgalaxies(ISM),groups(IGM),andclus- bientgas,inaself-regulatedAGNfeedbackloop(Fig.1). ters (ICM) down to the subpc accretion scale (e.g., Gas- In the paper companion to this work (SG17), we present pari et al. 2015, 2017 – G15, G17). The dark matter ha- anddiscussin-depththeGR-RMHDsimulationsresults, los heat up the diffuse gas during gravitational collapse, including the mechanical and radiative efficiencies. creating stratified hot plasma halos (∼107K) filling cos- In §3, we will quantitatively link the macro and mi- mic structures, which are detected in X-ray (e.g., An- cro properties of cosmic structures and SMBHs by using first principles, as mass and energy conservation, and bypreservingminimalassumptionsbasedonlast-decade * EinsteinFellow. observations. The final equations provide the mass out- † SpitzerFellow. flowratesandvelocitiesatdifferentscales(andfordiffer- 1 The radius r encloses δ times the critical overdensity δ ent phases). In §4, we compare the predictions with re- ρc(z) = 3H2(z)/(8πG) (H is the Hubble parameter; H0 (cid:39) cent ionized, warm, and molecular outflow samples, and 7δ0(cid:39)km10s0−f1oMrtphce−v1i)rigailvriandgiuasnaenndcl5o0se0dfomraosbssMervδa=tio(n4aπl/c3o)nδsρtcr(azi)nrtδ3s.; discuss the limitations. In §5, we discuss how to apply 2 Gaspari & Sądowski ourmodeltootherstudies, assubgridsimulations, semi- numbersquared). Fromlessmassive,lower-temperature, analytic(SAM)studies,orobservationalinterpretations. compact galaxies to more massive, hotter, and larger In §6, we carefully discuss the limitations of the model galaxy clusters (T ≈0.5−10keV), the mechanical effi- x andadditionalimportantfeatures(asthedutycycleand ciency covers a range ε (cid:39) 2×10−4 −4×10−3. The BH the M• −σ∗ relation). In §7, we summarize the main macro efficiency is a function of hot halo temperature points and conclude with future prospects. (∝ T ), thus total mass, decreasing for smaller halos x since the cooling rate is a function ∝ L /T (as seen 2. LARGEANDSMALLSCALESEFFICIENCIES x x later in Eq. 6). Smaller, less bound halos experience a We highlight here 3 key regions which are central to our stronger relative condensation due to the lower specific study (see Fig. 1 for a full diagram). internal energy, and necessitate of less sinked material – (i) The region closest to the SMBH horizon, r <∼ 5rS with slightly more evacuation – in order to avoid over- (a few ISCO radii), where gas is rushing toward the BH heating. Such quasi thermal equilibrium constraint on and there is no outflow. This region is fully resolved X-rayhalosfillingcosmicsystemsiskeytosetthemacro by the horizon scale GR-RMHD simulations. We denote efficiency. properties in this region by a black dot, e.g., M˙ . This picture has been corroborated by self-regulated • (ii)Theultra-fastoutflowlaunchingregion,r <∼100rS, AGNsimulationsofCCAandmassiveoutflowstestedin within which the binding energy of the infalling gas is clusters,groups,andisolatedgalaxies(e.g.,Gasparietal. converted into mechanical outflow, not interacting yet 2011a,b, 2012a,b; Prasad et al. 2015; Yang & Reynolds with the ambient gas. We denote this by M˙ . 2016), which independently retrieve the same range of out (iii) The macro region, r < r ≈ 109r ≈ 0.1r , feedback efficiencies described above in varying systems. core S vir within which the nuclear outflow is entrained (denoted The few available observational estimates, albeit limited byM˙ ),sloweddown,andeventuallythermalized(via by several extrapolations, are also consistent with a me- OUT chanical efficiency of the order of ε ∼ 10−3 (Merloni bubbles, shocks, and turbulent mixing). The CCA rain BH & Heinz 2008). develops in such core, with major collisions increasing within the kpc scale (10-100 Bondi radii2). 2.2. Horizon efficiency: GR-RMHD 2.1. Macro efficiency: chaotic cold accretion [CCA] Gas approaching the SMBH liberates its gravitational We introduce now the two key property of the feeding energy. A test particle falling straight on the BH would and feedback, i.e., the mechanical efficiency which has converttheliberatedamountintokineticenergyofradial dimension of a power divided by the rest mass energy motion and, finally, take it with it below the horizon. rate, ε≡P/(M˙ c2). From the point of view of the observer at infinity, no The best consistent way to solve the cooling flow energyhasbeenextracted. Accretionflowsactinamore problem appears to be mechanical AGN feedback self- complex way. The liberated gravitational energy goes regulated via CCA (§1). Solving the cooling flow prob- mostly into kinetic motion. The turbulent nature of the lem means to avoid at the same time overcooling and flowinducesthisenergytodissipateandheatupthegas. overheating, preserving the inner structure of hot halos At the same time outflows can be generated often via for ∼10Gyr, as tightly constrained over the last decade the magneto-centrifugal mechanism. Only for idealized by Chandra and XMM-Newton data (e.g., McNamara models, like advection dominated accretion flows (e.g., & Nulsen 2012; McDonald et al. 2016). Such hot ha- Narayan & Yi 1995), all the dissipated heat is advected los are continuously perturbed by subsonic turbulence withtheflowontotheBH.Inamoregeneralcase,energy (e.g.,Khatri&Gaspari2016). Inturbulentregionswhere isextractedfromthesystem,andgasinfallingfromlarge the cooling time drops below the local dynamical time, radiiandmarginallybound,crossestheBHhorizonwith nonlinearmultiphasecondensationdevelops(Fig.1,bot- negative energy. tom). Such cold clouds and warm filaments collide in Theamountoftheextractedenergy,i.e.,theefficiency chaotic, inelastic way while raining on the SMBH (G15, ofagivenaccretionflow,dependssolelyontheenergetics G17; see also Pizzolato & Soker 2010), boosting the ofthemagnetizedgascrossingtheBHhorizon. E.g.,ifon accretion rate with rapid intermittency. Massive sub- average gas with energy e=−0.01ρc2 falls into the BH, relativisticoutflowsarethentriggeredwithkineticpower then the luminosity of such a system, as seen from in- P proportionaltothelarge-scaleinflowrate,prevent- finity, is L=0.01M˙ c2. The properties of the accretion OUT • ing a run-away pure cooling flow (§3). flow in the innermost region must be determined by nu- Due to self-regulation, the large-scale mechanical effi- mericalmeans,sincetheflowishighlynonlinear,strongly ciency can be estimated by comparing the AGN energy magnetized, and turbulent. In the companion paper, output with the radiative energy losses, P (cid:39) L , SG17, general relativistic radiative simulations of mag- OUT x yielding (§3.1 for the derivation) netized gas falling on the SMBH are carried out, testing over5ordersofmagnitudeinaccretionrates. SG17show c2 ε (cid:39)10−3 T ∝ s,x, (1) that for a non-rotating BH and standard non-saturated BH x,7.4 c2 configuration of the magnetic field, thick accretion flows (asexpectedinthemaintenancemodeofAGNfeedback) where c is the hot halo adiabatic sound speed and c is s,x haveafairlystableextractionoftherestmassenergyac- the speed of light (the scaling shares analogy to a Mach creted through the horizon, 2 The Bondi radius, rB = GM•/c2s,x (cid:39) (7.5pc)M•,9Tx−,71.4 ≈ ε• (cid:39)0.03±0.01, (2) 105rS,isnotstrictlyrelevantforCCAbutprovidesaknownrefer- enceintermediate(pc)scalebetweenthemacroandmicroregion. Such mechanical efficiency will be the reference horizon Linking the micro to macro properties of AGN feedback 3 Figure 1. Middle – Diagram of the multiphase accretion inflow and outflow covering the entire range of scales, from the inner SMBH horizontothevirialradiusofthegalaxy,group,orcluster. Theself-regulatedAGNfeedbackloopworksasfollows. Theturbulentgaseous halo condenses in localized, large-scale high density peaks (cyan), leading to the drop out of cold clouds and warm filaments (blue). The cloudsraindownandrecurrentlycollideinchaoticandinelasticway(CCA),cancelingangularmomentumandflowingtowardtheSMBH. ThemassinflowrateoriginatesfromthequenchedX-raycoolingratewithinthecoreregion. Within∼100rS,thegravitationalaccretion process releases ultrafast outflows (UFOs), while only a small gas fraction is sinked through the horizon (this is balanced by a net inflow fromtheoutskirts). Theoutflowsslowdownatlargerradii,entrainingthegasofthebackgroundprofile. Theenergyisthermalizedinthe core,balancingtheX-rayluminosity. TheCCArainisthusstopped,andsoaretheoutflows,allowingtheglobalhalotorestorethequasi HSEprofile. Ascoolingresumeswithoutasourceofheating,anothercycleofCCArainandcollisions,massejectionandentrainment,and restorationistriggered,consistentlywithX-raydata. Thesystemconservestotalenergyandmassinagentlerecyclingmultiphaseflow. Top–GR-RMHDsimulationofthemicroflow(§2.2),showingthemagnitudeandstreamlinesofthetotalenergyflux(fromSa¸dowskietal. 2016;codeunits)whichisdominatedbythekineticcomponentwith(cid:15)•(cid:39)0.03(seeSG17formoredetailsonthemechanicalefficiency). Bottom–MultiphasehydrosimulationofthemacroflowtrackingtheCCAevolution(fromGasparietal.2017: §2.1). Themapshowsthe surfacebrightness(ergs−1cm−2sr−1)ofthefilamentarywarmphasecondensedoutoftheturbulenthothaloandchaoticallycolliding. efficiency for our model. We note that chaotic accretion the outflow interacts with the ambient medium, entrain- (ourmacroscalemodel)willnaturallyleadtoanaverage ing gas via shocks and mixing instabilities, finally dissi- null spin configuration (e.g., King & Pringle 2006). An pating its energy within the core region, r ≈ r /5 = c 500 important result from SG17 is that such value is essen- (148kpc)T1/2 (App.A).Ontopofthisenergyfluxthere tially independent of the ion-electron temperature ratio, x,7.4 might be a very thin, relativistic jet forming whenever i.e., the strength of the gas cooling does not affect the the SMBH quickly spins and the magnetic field threads mechanical efficiency value at the micro scale. the horizon. Such a jet may be substantially energetic This energy outflow accelerates within the inner re- and could lead to larger efficiencies (e.g., Tchekhovskoy gion (∼100r ) and is ejected in a quasi-spherical way S et al. 2011). However, relativistic jets are in most cases (Fig. 1, top) in the form of an ultra-fast kinetic outflow very collimated and less likely to interact with the host. of gas. The outflow is both thermally (equatorial) and For such reason and for the null spin expected from magnetically driven (polar region; see also the simula- chaotic accretion, we consider here only the wide, mas- tions by Moller & Sadowski 2015). At larger distances, 4 Gaspari & Sądowski sive sub-relativistic outflows as dominant component of 3.1. Inflow properties the kinetic feedback. Albeit not driving the total ram The large-scale inflow rate is the quenched cooling flow pressure, we note the jet and radio emission can still be rate. The maximal pure cooling flow (CF) rate can be correlated with the presence of massive AGN outflows, calculatedfromtheenthalpyvariationofthehotgaseous thus tracing some of the major AGN bubbles (§6). halo via the first law of thermodynamics (e.g., Gaspari The emergence of ultra-fast outflows and the connec- 2015) in isobaric mode, yielding tion with large-scale warm absorbers has been corroborated by other analytic studies. Fukumura et al. (2010, γ k T c2 2014) show that magnetic torques acting on the inner Lx = γ−1µbmxM˙CF = γ−s,x1M˙CF, (5) rotating gas can efficiently drive an outflow through p the magneto-centrifugal mechanism. The MHD wind is where T and L denote the core X-ray temperature x x stratified, having slower velocity at progressively larger and luminosity of the hot halo (App. A), γ = 5/3 is launching radii, akin to an entrained outflow. In the ra- the adiabatic index, µ (cid:39) 0.62 is the average atomic diativelyefficient,Eddingtonregime,thesphericalmodel weight for a fully ionized plasma with (cid:39) 25% He in by King & Pounds (2014) suggests that radiation pres- mass, and k and m are the usual Boltzmann con- b p sureisabletodriveUFOs;theexpanding,swept-upshell stant and proton mass, respectively. The last equal- is decelerated by the background medium, again corrob- ity converts temperature into adiabatic sound speed, oratingthekeyroleoftheentrainmentactioninunifying c = (γk T /µm )1/2 (cid:39) 1.5×104T1/2. From galaxies s b x p x AGN outflows over a large range of scales. to clusters (T ≈0.5−10keV), c =361−1615kms−1. x s,x AGN feedback preserves the hot halos in quasi ther- 3. LINKINGTHEMACROANDMICROSCALES mal equilibrium throughout the 10 Gyr evolution3. The The two complementary simulations discussed above al- warm filaments drop out of the hot halo just below the low us to link the large-scale to small-scale properties soft X-ray regime (G17) as the cooling curve drastically of the feeding and feedback mechanism in a simple, co- increases due to line cooling. Thereby the actual mass herent model. Fig. 1 illustrates the main features and flux arising out of the condensation process is linked to characteristic scales of the model. thesuppressedsoftX-rayluminosity. X-rayspectroscop- The large-scale outflow power can be modeled as icalobservations(e.g.,Petersonetal.2003;Kaastraetal. 2004) show that the soft X-ray emission is on average POUT =εBHM˙coolc2, (3) suppressedby2dexcomparedwiththepureisobaricCF tied to the core L (cf. Gaspari 2015 for a review of ob- where M˙cool is the quenched cooling flow rate and εBH servationalworksaxndanalysisofthesoftX-rayspectrum is the macro-scale mechanical efficiency (§2.1). The quenching). For such reasons, the effective quenched gaseous halo is losing internal energy via radiative emis- cooling rate is sion (mainly via Bremsstrahlung), while the AGN feeds L heatingback,onaveragebalancingthepurecoolingflow. M˙ (cid:39)10−2M˙ (cid:39)6.7×10−3 x . (6) Such halos perturbed by subsonic turbulence develop lo- cool CF c2 s,x cal multiphase condensation within the core, as long as turbulent Taylor number Tat ≡ σv/vrot <∼ 1 (G15). As BWoenndoitreatseuc(hGaqsupeanrciheetda,lC. 2C0A13r)a,ttehiesltaytpteicrablleyin1g00in×sutffihe- cold clouds and filaments rain down, they experience re- cient to properly boost the AGN heating (see also Soker current chaotic, fractal collisions, which cancel angular et al. 2009; McNamara & Nulsen 2012). Since hot ha- momentum at progressively smaller radii, in particular los are formed via the gravitational collapse of the cos- astheycollapsewithinr <1kpc. Theinflowratecanbe mic structures, the temperature and luminosity are in- thus considered independent of radius. In other words, terchangeable via scaling relations (Sun 2012), such as during CCA rain, the cold gas condensed in the core is quickly funneled to the ISCO region with no long-term Lx (cid:39)6×1043(Tx/2.2keV)3 ergs−1 (includingtheminor accumulation. G17 simulations showed that the CCA corrections due to the core radius instead of R500; see inflow rate is proportional to the effective viscosity of App. A). We can thus rewrite Eq. 6 as the cloud collisions, ν ≈ λ σ . The collisional mean c c v M˙ (cid:39)(1.1 M yr−1)T2 =(1.1 M yr−1)L2/3 , free path λ and the ensemble velocity dispersion σ are cool (cid:12) x,7.4 (cid:12) x,43.8 c v directly inherited from the large-scale turbulence (for a (7) mchaasostiivcepgraolcaexsys,nλoct ≈tied10t0opac,raσdvia≈l d1e5p0enkmdesn−ce1.) – a 3D wanhder2e.6th×e c1o0r7eKLx(2a.2ndkeVTx),arreespinecutniviteloy.f 6F×ro1m04c3oemrgpsa−c1t The inner, tiny SMBH is the actual source of energy galaxies to massive clusters (Tx ≈ 0.5−10keV), the in- injection with power flowratecoversM˙ (cid:39)0.06−23M yr−1. Interestingly, cool (cid:12) all the below scalings can be also expressed in terms of Pout =ε•M˙•c2, (4) total mass or virial radius, e.g., M˙cool ∝ rvir (App. A). It is important to note that if the core cooling time is where ε• is the horizon efficiency (§2.2) and M˙• is the tcool >∼ tH/2, then the system is in a non-cool-core con- inflow rate through the black hole horizon. The major dition and no condensation rain, feeding, and feedback difference between the macro and horizon efficiency shallbeapplied(regardlessofscalingrelations),untilthe implies that the sinked mass rate is the net inflow rate corecoolsdown,ignitingtheself-regulatedloop(see§6). survivingtheultra-fastoutflowgeneratedneartheISCO scale, before falling into the unescaping BH horizon. 3McDonaldetal.(2017)showthatcoolcoresareobservedeven uptoz≈1.5withpropertiesidenticaltolocalones. Linking the micro to macro properties of AGN feedback 5 1 The energy conservation requirement, P = M˙ v2 , (15) OUT 2 OUT OUT P =P , (8) out OUT respectively. As shown in Eq. 12, only a few percent impliesthatthehorizoninflowrateisrelatedtothecool- of the total inflow is actually sinked through the SMBH ing rate as follows: horizon; most of the mass is returned as ultra-fast outflows launched within ∼100r , such as ε S M˙• = εB•H M˙cool, (9) M˙ =M˙ −M˙ =(cid:18)1− εBH(cid:19) M˙ ≈M˙ , out cool • ε cool cool where the horizon mechanical efficiency is directly pro- • (16) vided by the GR-RMHD simulations (§2.2), ε = 0.03. • From the results and observations discussed in §2.1, hot which leads to the inner outflow velocity via Eq. 14 halosmustavoidatthesametimeoverheatingandover- cooling, i.e., the energy lost via radiative emission in the (cid:115)2ε M˙ c2 (cid:115) 2ε √ core must be replaced by the SMBH feedback power, v = • • = BH c(cid:39) 2ε c (17) out M˙out 1−εBH/ε• BH P (cid:39)L . (10) OUT x (cid:39)(1.4×104 kms−1)T1/2 =(1.4×104 kms−1)L1/6 . x,7.4 x,43.8 Thereby εBH = Lx/(M˙coolc2) and by using Eq. 6, the (18) macro efficiency reduces to Wenotev inEq.17canbetiedtoamomentump = out out ε = 102 c2s (cid:39)10−3 T =10−3 L1/3 (11) M˙outvout, which satisfies (1/2)M˙outvo2ut =p2out/(2M˙out). BH γ−1c2 x,7.4 x,43.8 Together with the above outflow rates, these are the typical velocities of ultra-fast outflows (UFOs) observed Notice that the efficiency only mildly varies with the as blue-shifted absorption lines tracingthe inner launch- main variable, the X-ray luminosity. We can now use ingregionneartheSMBHgravitationalradius(Tombesi both efficiencies to retrieve the horizon inflow rate rela- et al. 2012, 2013; Fukumura et al. 2015; more discus- tive to the macro value via Eq. 9 as sions and comparisons in §4). We note the outflow velocity is only weakly dependent on the halo tempera- M˙ (cid:39)(0.03M˙ )T =(0.03M˙ )L1/3 , (12) • cool x,7.4 cool x,43.8 ture/luminosity, varying at best by a factor of 2.5. We i.e., only a few percent of the quenched cooling flow rate thusexpect104kms−1 tobeafairlygeneralattribute5 of isactuallysinkedthroughtheSMBHhorizon. Substitut- innerlaunchingoutflows(Crenshawetal.2003;Tombesi ingM˙ inEq.12,weconsistentlyretrievetheaccretion 2016 for reviews). cool As the inner ultra-fast outflow propagates outward rate directly proportional to the X-ray luminosity, (r (cid:29) 100r ), it will entrain the background gas (em- S M˙ = Lx (cid:39)(0.04 M yr−1) L (13) bedding the low volume-filling CCA rain6) along its way • ε c2 (cid:12) x,43.8 such as • M˙ =ηM˙ , (19) =(0.04 M yr−1) T3 . OUT out (cid:12) x,7.4 where η > 1 is the entrainment factor. We note at kpc For SMBHs in the local universe, such accretion rates scale the mechanical outflow has not yet thermalized, are typically sub-Eddington, as expected for the mainte- conserving most of the kinetic energy, as we see the for- nance, mechanically dominated mode of AGN feedback. mationofX-raycavitiesandhotspotsatlargerdistances. As shown by Russell et al. (2013) and corroborated by At a given radius, the entrained mass outflow rate can SG17, the radiative efficiency and thus power due to ra- be retrieved via the mass flux equation diation is several dex lower than the mechanical input, and it can be neglected in terms of driver of the dy- M˙ =Ωr2ρ(r)v (r)=Ωr2−αρ rα v (r) OUT OUT 0 0 OUT namics (albeit radiation is clearly relevant to detect and (cid:39)Ωρ r rv , (20) trace AGN; §6). Eq. 12-13 imply that SMBHs in lower 0 0 OUT masshaloshavetypicallyalowerabsoluteaccretionrate. where the inner gas density profile is typically a power- Moreover, a relatively smaller fraction of gas reaches the law ρ = ρ (r/r )−α and Ω ≤ 4π is the covering angle of 0 0 horizon as AGN feedback is more effective in halos with the bipolar outflow. As shown in G17 and observational lower binding energy, which are tied to both lower M refs. within,thetypicalnuclearprofilesforallthephases 500 and lower black holes masses (§6). follow a slope α(cid:39)1 (with ≈0.25 scatter), hence the last step in Eq. 20. By using Eq. 15 and 19, the entrained 3.2. Outflow properties outflow velocity can be written as Havingassessedtheinflowproperties,wearenowinapo- (cid:115) 2P sition to retrieve the structure of the outflows, again via v = OUT =η−1/2v , (21) minimalfirstprinciples. Thepowerintermsofcharacter- OUT M˙ out OUT istic mass outflow rates4 and velocities at the launching 5 This is also similar to the characteristic nuclear (100-200rS) and macro scale is escapevelocity,i.e.,asthedrivenoutflowovercomesgravity. 6 Through the feedback cycle, the underlying halo gently ex- 1 P = M˙ v2 , (14) pands during entrainment, and contracts after dissipation, restor- out 2 out out ingquasihydrostaticequilibrium(HSE).X-rayobservationsindeed showthatdensityprofilesincool-coresystemsvaryonlybyasmall 4 Thetermduetovv˙ issubdominantandcanbeneglected. amount,evenafterstrongoutbursts(e.g.,McNamaraetal.2016). 6 Gaspari & Sądowski which inserted in Eq. 20 yields an entrainment factor Abovesuchthermalizationradius,anymodelshouldsim- plyinjectthermalenergyratebalancingthecoreL . Be- x (cid:18) v (cid:19)2/3 r2/3 lowsuchradius(asresolvedbymostofthecurrentMHD η = Ωρ r r out ∝ . (22) 0 0 M˙out Tx amnadsscivoesmooultoflgoiwcaslwsiimthultahteionabs)o,vaenryelmatoiodnesl.shSouuclhdriandjeiucst This implies that, while the macro velocities at a given roughly approaches the core radius, which is where the radius are unchanged over different systems (v ∝ feedback loop is active. OUT Tx1/2/Tx1/2), and are thus more robust probes, the macro In principle the momentum equation, M˙OUTvOUT = outflow rate linearly increases for more massive sys- M˙outvout, might be adopted instead of Eq. 14-15, if the tems M˙ ≈ ηM˙ ∝ T . Note the mass outflow outflow would immediately radiate away most of its en- OUT cool x ratehasmuchstrongerrelativevariationsthanvelocities ergy. However, besides losses being likely subdominant (∝η−1/2), corroborating Eq. 14-15. (see Faucher-Giguère & Quataert 2012), the decelera- tion would result to be dramatic, v = v /η (with Depending on the current thermodynamical back- OUT out ground state of the system, the outflows can entrain dif- η ∝r1/2Tx−3/4 reducedbyafew),whichwouldmakethe ferent phases, including the hot plasma, the warm neu- outflow aborted at the macro scale, inconsistently with tral/ionized gas, and the molecular gas. We use the re- data. Adopting the same procedure as above, the hot, sults of the CCA simulations (G17) to retrieve the mul- warm,andmolecularoutflowwouldmerelypreserve870, tiphase environment and profiles of the 3 phases, taking 280,and90kms−1 at1kpcscale,respectively. Arelated as reference macro scale r = 1kpc. A typical plasma crucialpointtorejectpurelymomentum-drivenoutflows 0 density ρ (cid:39) 10−25gcm−3 at 1 kpc leads to an en- is that self-regulation would be broken, since the macro 0,hot trainment factor (Ω(cid:39)4π) feedback energy could not balance the core L , leading x to a global massive pure CF. η (cid:39)40 T−1 r2/3 . (23) hot x,7.4 1kpc 4. COMPARISONWITHOBSERVATIONS This implies median entrained mass outflow rates and The proposed CCA GR-RMHD unification predicts nu- velocities of 10sM yr−1 and a few 103kms−1, which clear ultra-fast outflows of the order of 104kms−1 and a (cid:12) are typical properties of observed macro ionized out- progressively slower propagation of the outflow at larger flows (e.g., Nesvadba et al. 2010; Tombesi et al. 2013). radii, which are consistent with recent AGN data. If the halo is mainly filled with cooler gas, such as at In a sample of 35 AGN, Tombesi et al. (2013) unify high redshift, the entrainment can also proceed mainly the velocities of UFOs and the slower warm absorbers via the warm (ρ (cid:39) 10−24gcm−3) and cold phase as a function of radial distance (see also Tombesi et al. 0,warm (ρ (cid:39)10−23gcm−3)7,thusleadingtomoreentrained 2014 for analogous radio galaxy sample). Velocity is the 0,cold outflows with most robust indicator (e.g., compared to mass outflow rates) since directly observed through blue-shifted ab- ηwarm (cid:39)183 Tx−,71.4r12/k3pc, (24) sorption lines in AGN X-ray spectra. Fig. 2 shows the comparison of our model prediction (blue; §3) and the η (cid:39)850 T−1 r2/3 . (25) fit to the unified X-ray data. The bands denote 0.5dex cold x,7.4 1kpc scatter,whichisthetypicalmodelvariation(mainlydue to inner density and bipolar angle) and the range in the Mass outflow rates with 102 and several 102M yr−1 (cid:12) observed data points. The prediction of the CCA GR- tied to velocities 1000 and 500kms−1 at the kpc scale RMHD model well reproduces the observed values. If are characteristic properties found throughout observa- theoutflowwouldbepurelydrivenbymomentum(green tions of neutral (e.g., Morganti et al. 2005, 2007; Teng line) and not energy, it would be aborted within the etal.2013;Morganti2015)andmolecularAGNoutflows Bondi radius, remaining clearly below data. In other (Sturmetal.2011;Ciconeetal.2014;Russelletal.2014; words, entrainment must occur in a gentle way, such Combes 2015; Feruglio et al. 2015; Morganti et al. 2015; as v ∝ η−1/2 ∝ r−1/3. In the nuclear region, the Tombesi et al. 2015), respectively (more detailed com- OUT outflow tends to be slightly lower than the data, albeit parisons in §4). within typical uncertainties. The slope of the data, - At large radii, the outflow is halted by the external 0.40, is slightly steeper than the -0.33 model. The two pressure, inflating a bubble and thermalizing its kinetic matches exactly if the density profile has slightly shal- energy mainly via turbulent mixing (e.g., Gaspari et al. lower α=0.8 (instead of 1); we did not attempt to fine- 2012a; Soker 2016; Yang & Reynolds 2016). Such radius tuneit,sincewithinuncertaintiesofthesimulatedradial crudelycorrespondstotheregionwheretheoutflowram profiles and not granting further insight. pressure becomes equal to the hot halo pressure. Since The mass outflow rates have very large observational outflow ram pressure is equal for all the phases, we can estimate the thermalization radius as v2 ∼ c2/γ, uncertainties (due to the unknown geometry and pro- OUT,hot s jection effects) and theoretical scatter (due to the T yielding via Eq. 21-23 x dependance, unlike the macro velocity). In the above r ∼(55kpc)T3/2 =(55kpc)L1/2 . (26) sample, UFOstypicallyshowM˙out ≈0.3M(cid:12)yr−1, while th x,7.4 x,43.8 the warm absorbers have 1.5-2 dex larger magnitude, whichcanbeexplainedviatheentrainmentaction(T ≈ 7Hereweassumethatthecharacteristicphasedensitiesretrieved x 0.6keV).Weareherenotattemptingtofitvaluesofsingle inG17applyoverthewholeinnerregionasabackground; thisis more typical at high redshift, as cold flows can penetrate deep objects;nevertheless,severalX-raystudiesdetectnuclear withinthegrowingproto-galaxy. 104kms−1UFOsandionizedoutflowswith103kms−1at Linking the micro to macro properties of AGN feedback 7 flows in Sturm et al. (2011) show very similar mean Tombesi et al. 2013 properties. From Eq. 25, the average molecular veloc- 5.0 CCA GR-MHD model (EC) CCA GR-MHD model (MC) ity and mass outflow rate at kpc scale is expected to be 480kms−1 and M˙ (cid:39) 425 M yr−1 (T ≈1keV), in 4.5 OUT (cid:12) x agreementwiththedata. Otherworksfocusonsingleob- 1s]−4.0 jects, finding very similar properties at kpc scale as pre- m dictedbyourmodel;e.g.,Phoenix/A1664BCGcoresdis- k [3.5 playv (cid:39)550/590kms−1 andcrudeoutflowrates OUT,mol T U >250M yr−1(Russelletal.2014,2016). Awellstudied O (cid:12) v3.0 multiphaseoutflowinboththehotandcoldphaseisMrk g lo 231 (Feruglio et al. 2010, 2015). IRAM data indicates a 2.5 kpc-scale molecular outflow with v (cid:39)750 kms−1 OUT,mol and M˙ (cid:39)700 M yr−1 (Feruglio et al. 2010); in the 2.0 OUT (cid:12) same system, Chandra and NuSTAR show the presence of a nuclear UFO with v (cid:39) 2 × 104 kms−1 and out,hot 2 3 4 5 6 7 8 9 M˙ (cid:39)1 M yr−1. Both values are in excellent agree- logradius [r ] OUT (cid:12) S ment with our entrainment multiphase model. Notably, Figure 2. Outflowvelocityasafunctionofradialdistance(nor- the same authors remark that energy is conserved dur- malized to the Schwarzschild radius) for the unified X-ray UFO ing the entrainment process, P ≈ P , consistently out OUT plus warm absorber data (red; Tombesi et al. 2013) and the pre- with our Eq. 8. Tombesi et al. (2015) present another dictionofourenergy-conservingCCAGR-RMHDmodel(blue;§3). similar multiphase outflow in IRAS F11119+3257. As Thedashedgreenlineshowsthe(inconsistent)purelymomentum- drivenoutflow. Theregionwithin∼100rS istheUFOgeneration above, the mass outflow rates bear large uncertainties region,wheremostoftheinflowmassisejected. Atlargerradii,the and a large sample linking the small and large radii (as UFOentrainsprogressivelymoremass,slowingdown. Theadopted doneforUFOs)iscurrentlymissing;weencourageobser- profile slope of the warm gas background is α=1. The proposed vational proposals in such unification direction. We are model,basedonlinkingthehorizon/GR-RMHDandmacro/CCA efficiencies,wellreproducesthedatawithinscatter. livinganeweraformultiphaseAGNoutflows,asthefield is rapidly growing via new high-resolution ALMA cycles intermediate scale down to several 100 kms−1 at large able to probe ∼ 500kms−1 CO outflows (as shown by radii8 (seethereviewbyTombesi2016andrefs.within). Morganti et al. 2015). Follow-up observational investigations are required to betterunifytheradialpropertiesofionizedoutflowsover 5. SUBGRID/SAMMODELFORAGNFEEDBACK a large homogeneous sample, in particular adding more Below we describe how to incorporate our model into low-luminosity AGN and central galaxies. large-scale simulations of structure formation. Let us Depending on the dominant nuclear phase, the AGN denote the typical resolution of a given simulation by ejectacanalsodevelopintoaneutralandmolecularout- ∆r (nowadays ∼ 1kpc (cid:29) r in a typical zoom-in run). flow. This is more common in QSOs and ULIRGs with S Assuming the resolution is enough to resolve the ther- abundant cold/warm mass with large volume filling in malization region (∆r r (Eq. 26), injecting massive outflows loses feedingandfeedbackprocessrequires3D(GR)MHDsim- th physicalmeaning,andtheaverageradiativeenergylosses ulations covering the whole dynamical spatial and tem- should be simply balanced via thermal energy injection, poralrange. However,untilwewillbeabletobreaksuch since the outflows are expected to be thermalized. computational barrier, we can rely on key properties of Such prescription is perfectly suited to be used also in theinflowsandoutflowssetbythemultiwavelengthcon- semi-analytic models (SAM), e.g., of galaxy and cluster straints,whichmustbesatisfiedevenintheadvancednu- evolution,aswellasintheinterpretationofobservational mericalruns. WeremarkX-raydatashowthatthefeed- data (limited by the instrumental – instead of numerical back must be gentle and kinetically driven (with large- – resolution). Furthermore, the injected properties, in scalethermalizationupto100skpcformassiveclusters). particular the efficiency, are known a priori, regardless Notice that the details of the energy conserving outflow of numerics, implying that the fine-tuning loop plagu- areinourmacromodelnotrelevant. Ontheotherhand, ing current cosmological runs can be avoided (typically the momentum flux boost of the swept-up material due fitting one mass range, but overheating or overcooling to the hot shocked gas and entrainment via hydro insta- the opposite regime due to keeping a constant macro ef- bilities (e.g., Kelvin-Helmholtz and Rayleigh-Taylor) re- ficiency). In other words, there is no main free param- quires numerical simulations to be robustly understood. eter involved, except for the scatter intrinsic in obser- In addition to direct uplift, an interesting possibility to vations. A sanity check is to retrieve the observed X- formmolecularoutflowsisthein-situcondensationofthe ray properties, e.g., X-ray luminosity and temperature massivegalaxy-scalehotwindviathermalinstability–as profiles of the group or cluster. If not, the implementa- discussedbyZubovas&King(2014)–whichmayfurther tion of AGN feedback is numerically flawed and shall be promote the subsequent precipitation phase. modified accordingly, not retuning the parameters, but In this work, we decided to aim for minimal assump- changing the injection implementation and carefully as- tions and rely on first principles as much as possible. sessing which hydrodynamic solver and discretization to Further sophistications to the model are possible and use. In other words, retuning some parameters to coun- can be easily incorporated to fit more specific objects, teract the numerical flaws must be avoided, and can be at the expense of an increased number of parameters. avoided with the above a-priori prescription, thus pre- For instance, the inner background density profile can serving predictability. be modified with a more complex functional form than asinglepowerlawand/orassigningdifferentvolumefill- 6. DISCUSSION ing profiles to the warm/cold phases. The configuration We now discuss some details of the proposed model, to- of the inner outflows can be modified by reducing Ω, in gether with the limitations and possible improvements. order to accommodate for a thinner bipolar setup. We The approach of this work differs from typical ana- note, in one loop, the cold inflow can occur along one lyticmodelingconsideringaperfectsteadystatesolution direction, while the entrained outflow may occur in the (e.g., Bondi 1952) in which inflow and outflow coexist at perpendicular direction, further corroborating the sepa- exactly the same time (setting ∂/∂t = 0 in the hydro ration of the large-scale CCA inflow and outflow mass equations). AsindicatedbyX-rayobservationsandsim- rate, instead of a perfectly radial steady-state solution. ulations (§1), the detailed self-regulated AGN feedback A time delay in the loop can be introduced by tracking loopistimevarying. Wehaveinsteadconsideredanearly turbulent Taylor number: if Ta > 1, then a rotating t stationarycaseoverafeedbackcycle,whichistypicallyof structure (disc, ring, torus) can momentarily reduce ac- the order of the central cooling time t (cid:39) k T/(nΛ), cretion. We did not aim to fit one particular system or cool b where Λ is the plasma cooling function (Sutherland & AGN outflow in this study, discussing only mean values. Dopita 1993); from isolated galaxies to massive clusters As noted in §4, considering the scatter in cooling system thetypicalcentralcoolingtimeofthehotgasvariesfrom properties, the outflow variations are ∼0.5 dex over a tenstoseveral100Myr(Gasparietal.2014). Withinone large sample. Fitting and interpreting single object data cycle the process is time varying, with energy and mass can be easily refined, e.g., by analyzing the core and nu- changing form and phase. Specifically, the inflow acts clear X-ray spectrum both in terms of cooling rate (soft first via the self-similar CCA rain, then the SMBH re- X-ray)andoutflowlineabsorptionfeatures(hardX-ray). actstothefeedingvianuclearultra-fastoutflows(Fig.1). Consistently with the observational results by Russell The propagating UFOs entrain the diffuse phase and et al. 2013 (Fig. 12), the GR-RMHD simulations (SG17) thermalize in the core, such that POUT (cid:39) Lx, as shown show that for accretion rates below 10−2 the Edding- by X-ray data (e.g., Main et al. 2017). The background ton rate, the nuclear SMBH power is dominated by ki- haloisrecurrentlycontractingandexpandinginagentle netic energy over the SMBH radiative output, P (cid:29) out manner, and is never evacuated; in other words the core L . Themechanical,sub-Eddingtonmodeisthelong- AGN oscillates near HSE. Over the whole core region and one termmaintenancemodeofAGNfeedback(McNamara& loop time the mass and energy are conserved (the small Nulsen 2012 for a review) preserving hot halos and cool- mass loss onto the BH is replenished from the virial hot core systems in quasi thermal equilibrium at least for 9- halo). Note that if central tcool >∼ tH/2, the system is Linking the micro to macro properties of AGN feedback 9 10Gyr (McDonald et al. 2014, 2016, 2017). At high red- Finally, supernova feedback due to star formation (e.g., shift(z >2),theEddingtonratecanbeapproachedtrig- with rate a few precent of the galaxy cooling rate) can gering a brief ‘quasar’ phase (seeding part of the SMBH alsobecomeenergeticallyimportantinlowmassgalaxies mass). The wind may be thus radiatively driven, al- and shall be investigated in the future. though its coupling with the gas is matter of ongoing While here we have investigated the instantaneous debate. Moreover, there is no physical reason to think properties as the SMBH accretion rates, M˙ ∝ L , in • x that the mechanical power from AGN is erased in this a separate work, we will focus on the integrated prop- regime, as corroborated by our GR-RMHD run covering erties of the proposed unified model, as the total black the quasar transition (see SG17). Even in such short- hole masses and related scalings (e.g., the Magorrian re- lived radiative regime, the outflow is still expected to be lation). We anticipate some important considerations. energy conserving9 (Faucher-Giguère & Quataert 2012) As discussed above, the CCA self-regulation has a char- although it may be more appropriate to use a slightly acteristic frequency related to the cooling time, 1/t , cool larger ε• (cid:39) 0.057 (Novikov & Thorne 1973; Merloni & as the hot halo requires such time to promote condensa- Heinz 2008) and rescale Eq. 9. As long as ε• (cid:29) εBH, tion, rain down, and then activate the ultra-fast outflow the outflow properties are however not significantly al- feedback. One loop requires t = t +t ≈ t cyc cool OUT cool tered. A few quasar blasts may evacuate the system, (the outflow active time is always shorter than the con- but these anomalously powerful outbursts – which are densation time). In other words, the duty cycle in- much easier to detect – must be outliers (increasing the creases from clusters to galaxies, as corroborated by high-redshift population scatter) otherwise the majority long-termAGNfeedbacksimulations(e.g.,Gasparietal. ofsystemswouldlaterremainnon-cool-core,whichisnot 2011a,b, 2012a) and X-ray shocks/cavities observations observed(e.g.,Gasparietal.2014). Overall,regardlessof (e.g.,Randalletal.2015). Thenumberofcyclesoverthe the details of the driving mechanism (e.g., magnetic ver- Hubble time is thus n =t /t , with an active time cyc H cool sus radiative), if self-regulation is on average preserved, t =n t . The black hole masses are expected to act cyc OUT the proposed model applies in similar way throughout grow as M (cid:39) M˙ t , hence with a temperature scal- cosmic time. ing given b•y M ∝• aLct/t ∝ T3/(T /Λ) ∝ T2 ∝ σ4, Inthecurrentinterpretation,themicroandmacrome- • x cool x x x ∗ as core temperature is a measure of the (stellar) veloc- chanical driver is a sub-relativistic outflow. Given the ity variance in virialized structures. This is valid in the BHnullspinexpectationfromchaoticaccretion(King& galacticregime(T ≈0.5-2keV)asΛremainsessentially Pringle 2006) and the high piercing collimation, a radio x constantforsolarmetallicity. Forclusters,Λ∝T1/2 due jet is expected to be subdominant, albeit it can coex- to Bremsstrahlung, thus M ∝ T2.5 ∝ σ5. Observations ist and trace the large-scale features, as bubbles. Ob- • x ∗ showaverysimilarscaling,withultramassiveblackholes servationally, radio synchrotron (electron) power is less found predominantly in more massive halos which are thanapercentofthecavityinternalpower(McNamara& consistentwithourself-regulatedCCAmodelinducinga Nulsen 2012), so only relativistic ions are left to inflate steepeningoftheMagorrianrelation(e.g.,Gültekinetal. a bubble; however, this would produce strong Gamma 2009; McConnell & Ma 2013; Kormendy & Ho 2013). emission in all systems, which Fermi does not typically observe. Moreover, several AGN bubbles are ghost cavities devoid of radio emission. Having said that, our 7. SUMMARYANDCONCLUSIONS model is general and the radio jet interpretation can be Welinkedforthefirsttimethephysicalmicroandmacro trivially implemented, e.g., by replacing the related mi- mechanical efficiency of SMBHs, the latter based on key cro efficiency and opening angle. X-ray data and hydrodynamical simulations, the former A current observational limitation which is worth dis- retrieved by state-of-the-art GR-RMHD horizon simula- cussing is the low-mass end regime. While hot, X- tions, such that ε = 10−3T and ε = 0.03, re- BH x,7.4 • ray halos are well detected above stellar masses M∗ >∼ spectively (§2). By using minimally first principles, as 1010.8M , in particular massive galaxies, galaxy groups conservation of energy (P = P (cid:39) L , where the (cid:12) out OUT x and clusters, the precise level of the X-ray luminosity latter is the core luminosity of the hot halo), we unified due to the diffuse component in the opposite regime the macro and micro properties of self-regulated AGN (Tx <∼0.3keV)isstilluncertainduetothecontamination feedback from the galactic to the cluster regime (§3). ofX-raybinaries(e.g.,Andersonetal.2015). TheX-ray Theinflowmechanismoccursviachaoticcoldaccretion luminosityinsuchregimemaybelowerthanouradopted (CCA) – probed during the last years – i.e., the rain of scaling, and the relative cooling rate (Eq. 7) should be cold clouds condensing out of the quenched cooling flow properly rescaled if necessary. While the outflow veloci- (M˙ ), which are recurrently funneled via fractal, in- cool ties are overall unaffected (Eq. 18-21), the mass outflow elastic collisions. Near hundreds gravitational radii, the rate may be lower than the expected value. Conversely, binding energy of accreting gas is strongly transformed whilemoremassivesystemshavebetterconstrainedcore into ultrafast outflows (UFOs) with characteristic veloc- √ X-ray luminosity, the stronger and harder diffuse emis- ity of a few 104kms−1 ( 2ε c) ejecting most of the BH sionsubstantiallyhindersthenuclearX-rayspectralfea- inflowing gas mass as M˙ ≈ M˙ (≈ 1M yr−1 for tures, making UFO detection challenging. If T is not out cool (cid:12) x intermediate systems). available (e.g., for proto-galaxies), we suggest to use a Atlargerradii,theoutflowentrainsprogressivelymore core temperature in lower energy bands, as condensa- mass, such as M˙ = ηM˙ and v = η−1/2v , tionoccursthroughoutthewarmandcoldphaseregime. OUT out OUT out with η ∝ r2/3. At roughly the kpc scale, the charac- 9 Ascoolingactsonelectrons,thisslowsdowninverseCompton teristic velocities of large-scale hot/warm/cold outflows process;free-freecoolingissecondary. are predicted to be a few 103, 1000, and 500kms−1, re- 10 Gaspari & Sądowski spectively(dependingontheinnerdominantgasphase). AndersonM.E.,GaspariM.,WhiteS.D.M.,WangW.,DaiX., The related average mass outflow rates (for 1keV sys- 2015,MNRAS,449,3806 tems) are expected to be of the order of 10, 100, several BondiH.,1952,MNRAS,112,195 CiconeC.,etal.,2014,A&A,562,A21 100M yr−1, respectively. Such properties are in agree- (cid:12) CombesF.,2015,inZieglerB.L.,CombesF.,DannerbauerH., ment with observations of UFOs, and kpc-scale ionized, VerdugoM.,eds,IAUSymposiumVol.309,Galaxiesin3D neutral, and molecular outflows (§4). Velocities are the acrosstheUniverse.pp182–189(arXiv:1408.1591), more robust and stable indicator compared with out- doi:10.1017/S1743921314009636 CrenshawD.M.,KraemerS.B.,GeorgeI.M.,2003,ARA&A, flow rates, both observationally and in the model. Ul- 41,117 timately, the outflows thermalize within the system core DavidL.P.,etal.,2014,ApJ,792,94 (<∼ 0.1rvir), balancing the cooling losses, and allowing EttoriS.,FabianA.C.,2000,MNRAS,317,L57 another self-regulated loop to reload via CCA rain and Faucher-GiguèreC.-A.,QuataertE.,2012,MNRAS,425,605 outflow feedback – with frequency ∝t−1 . FeruglioC.,MaiolinoR.,PiconcelliE.,MenciN.,AusselH., cool LamastraA.,FioreF.,2010,A&A,518,L155 A key aspect of the newly presented model is that the FeruglioC.,etal.,2015,A&A,583,A99 irradiatedcool-coreenergyrate(Lx)reflectsthegasflow FukumuraK.,KazanasD.,ContopoulosI.,BeharE.,2010,ApJ, onto the tiny SMBH, creating a symbiotic link over a 10 715,636 dex dynamical range. The tiny SMBHs are not isolated FukumuraK.,TombesiF.,KazanasD.,ShraderC.,BeharE., ContopoulosI.,2014,ApJ,780,120 point objects where space-time diverges, but appear to FukumuraK.,TombesiF.,KazanasD.,ShraderC.,BeharE., be central actors in the evolution of both the micro and ContopoulosI.,2015,ApJ,805,17 cosmic structures. In particular, the SMBH growth rate GaspariM.,2015,MNRAS,451,L60 is linked to the large-scale T halo and thus any other GaspariM.,MelioliC.,BrighentiF.,D’ErcoleA.,2011a, x cosmic scaling (e.g., L ,M ), in addition to inducing a MNRAS,411,349 x vir GaspariM.,BrighentiF.,D’ErcoleA.,MelioliC.,2011b, consistentM −σ relation. Despitethenecessarylimita- • ∗ MNRAS,415,1549 tions (§6), the CCA+UFO model captures the essential GaspariM.,BrighentiF.,TemiP.,2012a,MNRAS,424,190 ingredients than any more sophisticated self-regulation GaspariM.,RuszkowskiM.,SharmaP.,2012b,ApJ,746,94 modelandsimulationshouldhaveatitscore,inparticu- GaspariM.,RuszkowskiM.,OhS.P.,2013,MNRAS,432,3401 larthegentlequasi-thermalequilibriumofplasmahalos. GaspariM.,BrighentiF.,TemiP.,EttoriS.,2014,ApJ,783,L10 GaspariM.,BrighentiF.,TemiP.,2015,A&A,579,A62 The pursued minimalism of the CCA+UFO model GaspariM.,TemiP.,BrighentiF.,2017,MNRAS,466,677 makes it suited to be trivially implemented in subgrid GültekinK.,etal.,2009,ApJ,698,198 modules and semi-analytic works (§5), as well as in es- HeckmanT.M.,BestP.N.,2014,ARA&A,52,589 timates for the interpretation of observational studies, KaastraJ.S.,etal.,2004,A&A,413,415 e.g., related to nuclear and entrained outflow velocities KhatriR.,GaspariM.,2016,MNRAS,463,655 KingA.,NixonC.,2015,MNRAS,453,L46 and mass rates. 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Unifying the micro and macro properties of AGN feeding and feedback

Similar Unifying the micro and macro properties of AGN feeding and feedback