Which AGN Jets Quench Star Formation in Massive Galaxies?
Kung-Yi Su, Philip F. Hopkins, Greg L. Bryan, Rachel S. Somerville, Christopher C. Hayward, Daniel Anglés-Alcázar, Claude-André Faucher-Giguère, Sarah Wellons, Jonathan Stern, Bryan A. Terrazas, T. K. Chan, Matthew E. Orr, Cameron Hummels, Robert Feldmann, Dušan Kereš
MMNRAS , 1–27 (2021) Preprint 5 February 2021 Compiled using MNRAS L A TEX style file v3.0
Which AGN Jets Quench Star Formation in Massive Galaxies?
Kung-Yi Su , , (cid:63) , Philip F. Hopkins , Greg L. Bryan , Rachel S. Somerville , Christo-pher C. Hayward , Daniel Angl´es-Alc´azar , , Claude-Andr´e Faucher-Gigu`ere , SarahWellons , Jonathan Stern , Bryan A. Terrazas , T. K. Chan , , Matthew E. Orr , ,Cameron Hummels , Robert Feldmann , Duˇsan Kereˇs Department of Astronomy, Columbia University, 550 West 120th Street, New York, NY 10027, USA Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA TAPIR 350-17, California Institute of Technology, 1200 E. California Boulevard, Pasadena, CA 91125, USA Department of Physics, University of Connecticut, 196 Auditorium Road, U-3046, Storrs, CT 06269-3046, USA Department of Physics & Astronomy and CIERA, Northwestern University, 1800 Sherman Ave, Evanston, IL 60201, USA Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA Institute for Computational Cosmology, Durham University, South Road, Durham DH1 3LE, UK Department of Physics and Center for Astrophysics and Space Science, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA Department of Physics and Astronomy, Rutgers, The State University of New Jersey, 136 Frelinghuysen Rd, Piscataway, NJ 08854, USA Institute for Computational Science, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
Submitted to MNRAS
ABSTRACT
In the absence of additional heating, radiative cooling of gas in the halos of massive galaxies(Milky Way and above) produces cold gas or stars in excess of that observed. Previous workhas suggested that a contribution to this heating from AGN jets is likely required, howeverthe form of jet energy required to quench remains unclear. This is particularly challengingfor galaxy simulations, in which the resolution is orders of magnitude coarser than necessaryto form and evolve the jet. On such scales, the uncertain parameter space includes: jet en-ergy form (kinetic, thermal, and cosmic ray energy), energy flux, momentum flux, mass flux,magnetic field strength and geometry, jet precession angle and period, jet opening-angle, andduty cycle. We investigate all of these parameters in a M (cid:12) halo using high-resolutionnon-cosmological MHD simulations with the FIRE-2 (Feedback In Realistic Environments)stellar feedback model, conduction, and viscosity. We explore which scenarios match obser-vational constraints and show that cosmic ray-dominated jets can most efficiently quench thecentral galaxy through a combination of cosmic ray pressure support and a modification of thethermal instability. Jets with most of their energy in mildly relativistic ( ∼ MeV or ∼ K)thermal plasma can also work, but require a factor ∼ larger energy input. For a fixed energyflux, jets with lower mass loading (higher specific energy, hence longer cooling times) quenchmore effectively. For this halo size, kinetic jets are less efficient in quenching unless they havewide opening or precession angles; however, if the jet becomes too wide, it produces a large,low-density core, in tension with observations. Magnetic fields, while they may be critical forjet acceleration near the black hole horizon, also play a relatively minor role except when themagnetic flux reaches (cid:38) erg s − in a kinetic jet model, which causes the jet cocoon tosignificantly widen, and the quenching to become explosive. We conclude that the criteria fora jet model to be successful are an optimal energy flux and a sufficiently wide jet cocoon withlong enough cooling time at the cooling radius. Key words: methods: numerical — galaxies: clusters: intracluster medium — cosmic rays— turbulence — galaxies: jets — galaxies: magnetic fields (cid:63)
E-mail: [email protected]
A major outstanding problem in galaxy formation for decades hasbeen how to “quench” massive galaxies (stellar masses (cid:38) M (cid:12) or above ∼ L ∗ in the galaxy luminosity function) and keep them © 2021 The Authors a r X i v : . [ a s t r o - ph . GA ] F e b “red and dead” over a large fraction of cosmic time (see e.g., Bellet al. 2003; Kauffmann et al. 2003; Madgwick et al. 2003; Baldryet al. 2004; Kereˇs et al. 2005; Blanton et al. 2005; Dekel & Birn-boim 2006; Kereˇs et al. 2009; Pozzetti et al. 2010; Wetzel et al.2012; Feldmann & Mayer 2015; Voit et al. 2015). The difficultylies in the classic “cooling flow” problem — X-ray observationshave found significant radiative cooling in the hot gas of ellipticalgalaxies and clusters, indicating cooling times shorter than a Hub-ble time (Fabian et al. 1994; Peterson & Fabian 2006; Stern et al.2019). However, compared to the inferred cooling flow (reachingup to ∼ (cid:12) yr − in clusters), neither sufficient cold gas fromH I and CO observations (McDonald et al. 2011; Werner et al. 2013)nor sufficient star formation (Tamura et al. 2001; O’Dea et al. 2008;Rafferty et al. 2008) has been observed in galaxies. Simulations andsemi-analytic models which do not suppress the cooling flows, andsimply allow gas to cool into the galactic core, typically predictover an order of magnitude higher star formation rates (SFRs) thanobserved (for recent examples see, e.g., the weak/no feedback runsin Sijacki et al. 2007; Somerville et al. 2008; Booth & Schaye 2009;Choi et al. 2015; Li et al. 2015; Angl´es-Alc´azar et al. 2017).Some heat source or pressure support must be present to com-pensate for the observed cooling. Moreover, the heating must stillpreserve the cool core structure (e.g., density and entropy profiles)observed in the majority of galaxies (Peres et al. 1998; Mittal et al.2009). One way to achieve this is to suppress the cooling flowand maintain a very-low-SFR, stable cool-core (CC) cluster. An-other possibility is that clusters undergo cool-core—non-cool-core(NCC) cycles: a stronger episode of feedback overturns the coolingflows, resulting in a non-cool-core cluster, which gradually recov-ers to a cool-core cluster and starts another episode of feedback.The various non-AGN solutions to the cooling flow problemproposed in the literature generally belong to the former case, in-cluding: stellar feedback from shock-heated AGB winds (Conroyet al. 2015), Type Ia supernovae (SNe) (e.g. Sharma et al. 2012, andreferences therein), SNe-injected cosmic rays (CRs) (Ruszkowskiet al. 2017a; Pfrommer et al. 2017; Butsky & Quinn 2018; Farberet al. 2018; Jacob et al. 2018), magnetic fields (Soker & Sarazin1990; Beck et al. 1996, 2012) and thermal conduction (Binney &Cowie 1981; Tucker & Rosner 1983; Voigt et al. 2002; Fabian et al.2002; Zakamska & Narayan 2003) in the circum-galactic medium(CGM) or intra-cluster medium (ICM), or “morphological quench-ing” via altering the galaxy morphology and gravitational stabilityproperties (Martig et al. 2009; Dekel et al. 2009). Although theseprocesses can slightly suppress star formation, or help suppress thecooling flows, most previous studies, including our own exhaustivesurvey studying each of these in simulations similar to those pre-sented here (Su et al. 2019, hereafter Paper I ), have shown that theydo not fundamentally alter the classic cooling flow picture. In theend, the star formation is still regulated by cooling flows, and thestar formation rate is orders of magnitude too high.Consequently, AGN feedback seems to be the most promis-ing candidate to solve the cooling flow problem, and there has beena tremendous amount of theoretical work on the topic (for recentstudies, see the reference in later paragraphs for the AGN jet ande.g., Gaspari & Sa¸dowski 2017; Eisenreich et al. 2017; Weinbergeret al. 2018; Li et al. 2018; Pellegrini et al. 2018; Yoon et al. 2018for other type of AGN feedback; also see e.g., Silk & Rees 1998;Fabian 1999; Ciotti & Ostriker 2001; Hopkins et al. 2005, 2006a;Croton et al. 2006; Ciotti et al. 2009; Choi et al. 2012 for earlierworks). Observational studies also infer that the available energybudget from AGN can match the cooling rate (Bˆırzan et al. 2004).There are also observations of un-ambiguous cases of AGN ex- pelling gas from galaxies, injecting thermal energy via shocks orsound waves, or via photo-ionization and Compton heating, or via“stirring” the CGM and ICM, and creating “bubbles” of hot plasmawith non-negligible relativistic components which are ubiquitousaround massive galaxies (see, e.g., Fabian 2012; Hickox & Alexan-der 2018, for a detailed review).However, despite its plausibility and the extensive work above,the detailed physics of AGN feedback remain uncertain, as do therelevant “input parameters.” Several studies also suggested certaincategories of AGN feedback models struggle to stably quench thestar formation, self-regulate themselves, or meet some of the obser-vational constraints (e.g., Bˆırzan et al. 2004; Vernaleo & Reynolds2006; Glines et al. 2020; Su et al. 2020). Therefore, a broad system-atic exploration of AGN feedback models can be useful to under-stand which, if any, are more plausible for solving the cooling flowproblem. In Su et al. (2020) (here after Paper II ), we explored vari-ous idealized AGN “toy models” with energy injection in differentforms (e.g., direct isotropic momentum injection, turbulent stirring,thermal heating, cosmic-ray injection). We found that turbulent stir-ring within a radius of order the halo scale radius, or cosmic ray in-jection (with appropriate energetics) were able to maintain a stable,cool-core, low-SFR halo for extended periods, across halos withmass − M (cid:12) , without obviously violating observationalconstraints on halo gas properties or exceeding plausible energybudgets for low luminosity AGN in massive galaxies. But in thatstudy, we did not attempt to model realistic jets or AGN outflows;instead, we intentionally considered energy input or “stirring” ratesdistributed according to an arbitrary spatial kernel, without consid-ering how that energy would actually propagate from a collimatedgeometry, or how turbulence would actually be produced. Giventhat AGN jets can be a dominant source of cosmic rays and an im-portant mechanism to stir turbulence in the CGM, we move a stepforward in this work to study the effects of a wide range of morerealistic jet models in cooling flows.Extensive studies have shown that various AGN jet modelsare, in principle, capable of quenching a galaxy and stopping thecooling flows in galaxy-scale simulations (e.g., Dubois et al. 2010;Gaspari et al. 2012a; Yang et al. 2012; Li & Bryan 2014a; Li et al.2015; Prasad et al. 2015; Yang & Reynolds 2016a; Ruszkowskiet al. 2017a; Bourne & Sijacki 2017). However, in such simula-tions, AGN jets are launched from the smallest resolved scale, act-ing as a sort of inner boundary condition, instead of being gener-ated self-consistently. Due to the uncertainties of the jet propertiesat these scales, the details of how the jet is launched are highlymodel-dependent, spanning a vast parameter space.AGN jets most likely physically consist of relativistic parti-cles at the black hole horizon scale, powered by magnetic fieldsthrough the Blandford-Znajek process (Blandford & Znajek 1977;Tchekhovskoy et al. 2011; Blandford et al. 2019), where the mag-netic energy is supplied by the black hole spin. Recent devel-opments in GRMHD simulations have made it possible to self-consistently follow the formation and evolution of the jet in sim-ulations resolving the black hole horizon scale and accretion disc(e.g., Hawley & Villiers 2004; Tchekhovskoy et al. 2011; McK-inney et al. 2012; White et al. 2019), and the fields carried withthe jet can reach ∼ Gauss at scales (cid:28) (Guan et al. 2014).However, at the finest resolvable scale ( (cid:38) pc) in galaxy simula-tions, the jet velocity and magnetic field strength evolve radicallythrough interactions with the surrounding gas. Depending on themodel and the sub-resolution environment around the black hole,part of the kinetic energy can be transformed into thermal or cos-mic ray energy. The balance between thermal, kinetic, magnetic, MNRAS , 1–27 (2021) hat Types of Jet Quench? and cosmic ray energy at the scales where jets begin to interact withresolvable galaxy scales (the key for quenching models) thereforeremains highly uncertain.Momentum and kinetic energy can be directly transferred tothe gas, suppressing inflows. The fast-moving jets can also shockheat the surrounding gas. Many models have invoked kinetic jetsto suppress cooling flows and SFRs in massive halos (e.g., Duboiset al. 2010; Gaspari et al. 2012a; Li & Bryan 2014a; Prasad et al.2015; Yang & Reynolds 2016a). Many models in the literature alsoinvoke the idea that AGN can effectively drive strong pressure-driven outflows and offset cooling if a large fraction of the accre-tion energy is thermalized (Begelman 2004; Springel et al. 2005; DiMatteo et al. 2005; Hopkins et al. 2006b,c, 2007, 2008; Hopkins &Elvis 2010; Johansson et al. 2009; Ostriker et al. 2010; Faucher-Gigu`ere & Quataert 2012; Dubois et al. 2013; Barai et al. 2014;Weinberger et al. 2017a; Pillepich et al. 2018; Richings & Faucher-Gigu`ere 2018a,b; Torrey et al. 2020). Physically, as the jet prop-agates, part of the kinetic energy can thermalize through shocks.Some studies have argued that the heat from those weak shockscan suppress cooling flows and SFRs in massive halos (Yang &Reynolds 2016b; Li et al. 2017; Martizzi et al. 2019). The mag-netic fields carried by the jet at its launch might also help suppresscooling flows by providing additional pressure support (Soker &Sarazin 1990; Beck et al. 1996, 2012), although our studies findthat they have limited effects on global star formation propertiesof sub- L ∗ galaxies (Su et al. 2017) . Finally, CRs arise generi-cally from processes that occur in fast shocks, so could come fromshocked winds or outflows, but are particularly associated with rel-ativistic jets from AGN (where they can make up the bulk of thejet energy; Berezinsky et al. 2006; Ruszkowski et al. 2017b) andhot, relativistic plasma-filled “bubbles” or “cavities” (perhaps in-flated by jets in the first place) around AGN. Different authors haveargued that they could help suppress cooling flows by providingadditional pressure support to the gas, driving pressurized outflowsin the galaxy or CGM, or via heating the CGM/ICM directly viacollisional (hadronic & Coulomb) and streaming-instability losses(Guo & Oh 2008; Sharma et al. 2010; Enßlin et al. 2011; Fujita& Ohira 2011; Wiener et al. 2013; Fujita et al. 2013; Pfrommer2013; Pfrommer et al. 2017; Ruszkowski et al. 2017a,b; Jacob &Pfrommer 2017a,b; Jacob et al. 2018).The direction and geometry of the jet at these scales are alsouncertain. The width of the jet can change substantially with timeor distance. Although there is still a debate as to whether jets pre-cess or not, several proposed mechanisms including self-inducedwarping of an irradiated accretion disc (Pringle 1996, 1997), tornaccretion discs (Nixon et al. 2012a,b) due to the Lense-Thirring ef-fect (Lense & Thirring 1918), massive black hole binaries (Begel-man et al. 1980), or simply the widely varying angular momentumdirection of gas accreting from larger scales on short time scales( < . Myr) (Hopkins et al. 2012; Angles-Alcazar et al. 2020),can plausibly alter the angular momentum direction of the accre-tion disc, causing jet precession. Multiple observations also sug-gest jet precession occurs (e.g., Dunn et al. 2006; Mart´ı-Vidal et al.2011; Babul et al. 2013; Aalto et al. 2016). Reflecting such uncer-tainties, AGN feedback models have adopted energy injection withopening-angles ranging from small or negligible (e.g. Li & Bryan2014a,b; Weinberger et al. 2017b; Martizzi et al. 2019), to muchwider opening-angles (e.g., Prasad et al. 2015; Hillel & Soker 2017, Even if magnetic fields are dynamically important on large scales, theycan still be critical on scales near the black hole that we do not resolve. II , we showed that an explicit externally driven turbulence couldvery effectively quench the galaxy. Here we further test whether aprecessing jet can drive such turbulence and thereby quench thegalaxy.Finally, AGN feedback is generally episodic. A period ofstrong feedback can shut down the cooling flow and the black holeaccretion, which subsequently turns off feedback. During the timewithout feedback, the cooling flows and accretion can be reestab-lished, starting another episode of feedback, as may have occurredin the Phoenix cluster (Stern et al. 2019). However, the duty cy-cle and the duration of each episode are highly dependent on boththe accretion and feedback models. Most of the literature aboveonly studied a limited part of this large parameter space. In orderto narrow down the parameter space of jet launching, in this studywe conduct the most extensive set of simulations to date surveyingAGN jet launching parameters including energy form (kinetic, ther-mal, and cosmic ray energy), energy flux, mass flux, magnetic fieldstrength and geometry, jet precession angle and period, jet opening-angle, and jet duty cycles. We will test for what part of the param-eter space jets can quench galaxies without violating observationalconstraints on the CGM density and entropy profiles. For viablemodels, we will also study how and why those models work andwhat is the required energy.All of these questions have been studied to a varying ex-tent in the literature already (see references above). However, thiswork expands on these previous studies in at least four importantways. (a) We attempt a broader and more comprehensive survey,across a wide variety of parameters characterizing jet injection, us-ing an otherwise identical set of physics and numerics, to enablefair comparisons. (b)
We implement all of these in global simu-lations that self-consistently (and simultaneously) treat the entirehalo and star-forming galactic disk. We also reach higher resolutionthan most previous work, which allows us to resolve more detailedsub-structure in the CGM and galactic disk. (c)
We include explicit,detailed treatments of radiative cooling, the multi-phase ISM andCGM, star formation, and stellar feedback following the FIRE-2 simulation physics (Hopkins et al. 2014, 2018b), in order to morerobustly model both the gas dynamics and the response of galacticstar formation rates to cooling flows. (d) We test our jet model insimulations with MHD, conduction, viscosity, and explicit cosmic- FIRE project website: http://fire.northwestern.edu
MNRAS000
MNRAS000 , 1–27 (2021) ray transport and dynamics (from AGN) to capture any interactionbetween the jet and fluid microphysics.In § 2, we summarize our initial conditions (ICs) and the AGNjet parameters we survey and describe our numerical simulations.We present our results and describe the observational propertiesof the more successful runs in § 3. We discuss the effects of eachmodel in turn, and explain why it works or does not, in § 4 - § 4.8.We summarize in § 6. We include some observational properties ofall the successful and unsuccessful runs in Appendix A.
We perform simulations of isolated galaxies with a halo mass of ∼ M (cid:12) . We set up the initial conditions according to the ob-served profiles of cool-core clusters at low redshift, as detailed in§ 2.1. Without any AGN feedback, although the galaxies have ini-tial properties consistent with observations, their cooling flow rates,and SFRs quickly run away, exceeding the observational values byorders of magnitude (Paper I and Paper II ). We evolve the simula-tions with various AGN jet models and test to what extent (if any)they suppress the cooling flow and whether they can maintain sta-bly quenched galaxies.We note that while there are more constraints from X-ray ob-servations for rich clusters of mass ∼ M (cid:12) , we focus on agalaxy with a halo mass of M (cid:12) . The reason is that a halo ofthis mass already has most of the cooling flow properties of themore massive clusters, and will experience a major cooling catas-trophe unless properly quenched, but requires less computationalexpense. We will consider how jet models scale with halo mass infuture work.Our simulations use GIZMO (Hopkins 2015), in its meshlessfinite mass (MFM) mode, which is a Lagrangian mesh-free Go-dunov method, capturing advantages of grid-based and smoothed-particle hydrodynamics (SPH) methods. Numerical implementa-tion details and extensive tests are presented in a series of meth-ods papers for, e.g., the hydrodynamics and self-gravity (Hopkins2015), magnetohydrodynamics (MHD; Hopkins & Raives 2016;Hopkins 2016), anisotropic conduction and viscosity (Hopkins2017; Su et al. 2017), and cosmic rays (Chan et al. 2019).All of our simulations have the FIRE-2 implementation of theFeedback In Realistic Environments (FIRE) physical treatments ofthe ISM, star formation, and stellar feedback, the details of whichare given in Hopkins et al. (2018a,b) along with extensive numeri-cal tests. Cooling is followed from − K, including the effectsof photo-electric and photo-ionization heating, collisional, Comp-ton, fine structure, recombination, atomic, and molecular cooling.Star formation is treated via a sink particle method, allowedonly in molecular, self-shielding, locally self-gravitating gas, abovea density n >
100 cm − (Hopkins et al. 2013). Star particles,once formed, are treated as a single stellar population with metal-licity inherited from their parent gas particle at formation. All feed-back rates (SNe and mass-loss rates, spectra, etc.) and strengthsare IMF-averaged values calculated from STARBURST99 (Leithereret al. 1999) with a Kroupa (2002) IMF. The stellar feedback modelincludes: (1) Radiative feedback including photo-ionization andphoto-electric heating, as well as single and multiple-scattering ra-diation pressure tracked in five bands (ionizing, FUV, NUV, optical-NIR, IR), (2) OB and AGB winds, resulting in continuous stellar A public version of this code is available at ∼ phopkins/Site/GIZMO.html mass loss and injection of mass, metals, energy, and momentum(3) Type II and Ia SNe (including both prompt and delayed pop-ulations) occuring according to tabulated rates, and injecting theappropriate mass, metals, momentum, and energy to the surround-ing gas. All the simulations except the ‘B0’ run also include MHD,and fully anisotropic conduction, and viscosity with the Spitzer-Braginski coefficients. The initial conditions studied here are presented and described indetail in Paper I . The ICs are designed to be similar to observedcool-core systems of similar mass wherever possible at z ∼ (seee.g., Humphrey et al. 2012; Humphrey & Buote 2013; Su et al.2013, 2015; Mernier et al. 2017). Their properties are summarizedin Table 1. In this paper, we focus on the m14 halo from Paper I ,which has the most dramatic (massive) cooling flow. The dark mat-ter (DM) halo, bulge, black hole, and gas+stellar disk are initializedfollowing Springel & White (1999) and Springel (2000). We as-sume a spherical, isotropic, Navarro et al. (1996) profile DM halo;a Hernquist (1990) profile stellar bulge ( × M (cid:12) ); an exponen-tial, rotation-supported disk of gas and stars ( and × M (cid:12) ,respectively) initialized with Toomre Q ≈ ; a BH with mass / of the bulge mass (e.g., H¨aring & Rix 2004); and an ex-tended spherical, hydrostatic gas halo with a β -profile ( β = 1 / )and rotation at twice the net DM spin (so ∼ − of the sup-port against gravity comes from rotation, and most of the supportfrom thermal pressure as expected in a massive halo). All the com-ponents of the initial conditions are ‘live’. The initial metallicityof the CGM/ICM drops from solar ( Z = 0 . ) to Z = 0 . with radius as Z ( r ) = 0 .
02 (0 .
05 + 0 . / (1 + ( r/
20 kpc) . )) .Initial magnetic fields are azimuthal with a seed vlue of | B | =0 . µ G / (1 + ( r/
20 kpc) . ) (which will later be amplified) ex-tending throughout the ICM, and the initial CR energy density isin equipartition with the local initial magnetic energy density. TheICs are run adiabatically (no cooling or star formation) to relax anyinitial transients.Our m14 halo has an initial cooling rate of ∼ × erg s − ,with ∼ × erg s − radiated in the X-ray band (0.5-7 kev).A resolution study is included in the appendix of Paper I . Toachieve better convergence, we use a hierarchical super-Lagrangianrefinement scheme (Paper I and Paper II ) to reach ∼ × M (cid:12) mass resolution in the core region and around the z-axis where thejet is launched, much higher than many previous global studies.The mass resolution decreases as a function of both radius ( r )and distance from the z-axis ( r ), roughly proportional to r and r / , whichever is smaller, down to × M (cid:12) . The highestresolution region is where either r or r is smaller than 10 kpc. In this paper, we focus on the effects of a given AGN jet. All the jetmodels are run with a preset mass, energy, and momentum flux:we do not attempt to simultaneously model BH accretion from ∼ − pc to the event horizon. We systematically vary thejet velocity, energy composition (kinetic, thermal, magnetic, andcosmic ray energy), mass flux, opening-angle, procession, and dutycycle. We note that such variations reflect the uncertainties from thenature of AGN jets and the sub-resolution ( <
10 pc) physics aroundthe black hole, which affects the balance of different energy formsand other jet parameters. A full list of simulations can be found in
MNRAS , 1–27 (2021) hat Types of Jet Quench? Table 1.
Properties of Initial Conditions for the Simulations/Halos Studied In This PaperResolution DM halo Stellar Bulge Stellar Disc Gas Disc Gas HaloModel (cid:15) g m g M halo r dh V Max M baryon M b a M d r d M gd r gd M gh r gh (pc) (M (cid:12) ) (M (cid:12) ) (kpc) (km/s) (M (cid:12) ) (M (cid:12) ) (kpc) (M (cid:12) ) (kpc) (M (cid:12) ) (kpc) (M (cid:12) ) (kpc) m14 1 3e4 8.5e13 220 600 1.5e13 2.0e11 3.9 2.0e10 3.9 1e10 3.9 1.5e13 22 Parameters of the galaxy/halo model studied in this paper (§ 2.1): (1) Model name. The number following ‘m’ labels the approximate logarithmic halo mass.(2) (cid:15) g : Minimum gravitational force softening for gas (the softening for gas in all simulations is adaptive, and matched to the hydrodynamic resolution; here,we quote the minimum Plummer equivalent softening). (3) m g : Gas mass (resolution element). There is a resolution gradient for m14, so its m g is the massof the highest resolution elements. (4) M halo : Halo mass. (5) r dh : NFW halo scale radius (the corresponding concentration of m14 is c = 5 . ). (6) V max :Halo maximum circular velocity. (7) M baryon : Total baryonic mass. (8) M b : Bulge mass. (9) a : Bulge Hernquist-profile scale-length. (10) M d : Stellar discmass. (11) r d : Stellar disc exponential scale-length. (12) M gd : Gas disc mass. (13) r gd : Gas disc exponential scale-length. (14) M gh : Hydrostatic gas halomass. (15) r gh : Hydrostatic gas halo β = 1 / profile scale-length. Table 2. We emphasize that the parameters in the table reflect the jetparameters at our launch scale. The jet properties will continuouslyevolve as it interacts with the surrounding gas.We launch the jet with a particle spawning method, which cre-ates new gas cells (resolution elements) from the central black hole.With this method, we have better control of the jet properties as thelaunching is less dependent on the neighbor-finding results. We canalso enforce a higher resolution for the jet elements. The numericalmethod in this paper is similar to Torrey et al. (2020), which stud-ied the effects of BAL wind feedback on disk galaxies.The spawnedgas particles have a mass resolution of 5000 M (cid:12) and are forbiddento de-refine (merge into a regular gas element) before they decel-erate to 10% of the launch velocity. Two particles are spawned inopposite z-directions at the same time when the accumulated jetmass flux reaches twice the target spawned particle mass, so lin-ear momentum is always exactly conserved. Initially, the spawnedparticle is randomly placed on a sphere with a radius of r , whichis either 10 pc or half the distance between the black hole and theclosest gas particle, whichever is smaller. If the particle is initial-ized at a position ( r , θ , φ ) and the jet opening-angle of a specificmodel is θ op , the initial velocity direction of the jet will be set at θ op θ /π for θ < π/ and at π − θ op ( π − θ ) /π for θ > π/ .With this, the projected paths of any two particles will not intersect.The naming of each model starts from the primary form ofenergy at our injection scale (‘Kin’, ‘Th’, and ‘CR’ for kinetic,thermal and CR energy, respectively) and the corresponding en-ergy flux in erg s − . The run with ‘B4’ in the name means that theinitial jet magnetic field is toroidal with a maximum field strengthof − G. The number after the ‘m’ label provides the mass fluxin units of M (cid:12) yr − . The number after ‘w’ and ‘pr’ gives the initialopening-angle and precession angle in degrees. The number after‘ t p ’ and ‘ t d ’ denotes the precession period and the duty cycle inMyr. If a specific quantity is not labeled in the name, the jet modelhas fiducial values of a constant mass flux of 2 M (cid:12) yr − , an initialtoroidal magnetic field with a maximum field strength of − , ◦ opening-angle, no precession, and 100% duty cycle (i.e., we onlylabel runs with parameters that differ from these default values). Each spawned jet element carries mass, velocity, thermal energy,magnetic field, and cosmic ray energy, so the energy flux of eachkind is well controlled. In the initial conditions, we set the black-hole mass at M (cid:12) , corresponding to an Eddington luminosity L Edd ∼ erg s − . We systemically test the jet model with en-ergy input in each form ranging from ∼ × up to × erg s − , which corresponds to roughly × − − × − L Edd , around the total X-ray luminosity of the whole system and the plau-sible energy flux according to Paper II .Each energy form is briefly described below: • Kinetic component : Despite the relativistic nature of jets atthe black hole scale, such scales are orders of magnitude smallerthan the finest scale we can resolve. Instead, we have to initiate thespawned element at ∼ pc, at which point the jet has alreadybeen decelerated significantly. Moreover, we are also constrainedby the Newtonian nature of our MHD solver, which cannot accu-rately treat relativistic velocities. Accordingly, we leave the jet el-ement’s initial spawning velocity as a free parameter varied within3000-30000 km s − . This roughly spans the range from the min-imum velocity required to sustain a clear bi-polar jet shape to themaximum feasible velocity, as limited by the numerical methodsand computational time. • Thermal component : At the scale where we initiate the jet,a significant amount of energy has probably already been thermal-ized, but the fraction is uncertain. Therefore, we also leave the in-ternal temperature of the jet plasma as a free parameter rangingfrom − × K , corresponding to roughly the same rangeof specific energy as the kinetic jet models we studied. We empha-size that due to the injection in jet form, this is very different from“traditional” thermal feedback, which we will discuss later. • Magnetic component : Given the uncertainties of the mag-netic field strength and geometry at the scale where we launchour jet, we parameterize the initial magnetic fields as either purelytoroidal or purely poloidal with different strengths. The toroidalmagnetic fields follow: B tor ,φ ∝ r sin θ exp (cid:18) − r r (cid:19) , (1)where r inj is set to 10 pc. The poloidal magnetic fields follow: B pol ,r ∝ r sin θr cos θr exp (cid:18) − r r (cid:19) ,B pol ,z ∝ (cid:18) − r sin θr (cid:19) exp (cid:18) − r r (cid:19) . (2)(e.g., Guan et al. 2014) We study models with a maximum initial magnetic field strength Given that the spawned particle is launched at a radius of 10 pc (most ofthe time, since the closest neighborhood gas cell rarely goes closer to theblack hole), we always set the exponential part in the poloidal expression(except for B pol r timesexponential part in the toroidal expression to a constant. This only deviatesfrom the above expressions during the time in a run when there is a veryMNRAS000
Properties of Initial Conditions for the Simulations/Halos Studied In This PaperResolution DM halo Stellar Bulge Stellar Disc Gas Disc Gas HaloModel (cid:15) g m g M halo r dh V Max M baryon M b a M d r d M gd r gd M gh r gh (pc) (M (cid:12) ) (M (cid:12) ) (kpc) (km/s) (M (cid:12) ) (M (cid:12) ) (kpc) (M (cid:12) ) (kpc) (M (cid:12) ) (kpc) (M (cid:12) ) (kpc) m14 1 3e4 8.5e13 220 600 1.5e13 2.0e11 3.9 2.0e10 3.9 1e10 3.9 1.5e13 22 Parameters of the galaxy/halo model studied in this paper (§ 2.1): (1) Model name. The number following ‘m’ labels the approximate logarithmic halo mass.(2) (cid:15) g : Minimum gravitational force softening for gas (the softening for gas in all simulations is adaptive, and matched to the hydrodynamic resolution; here,we quote the minimum Plummer equivalent softening). (3) m g : Gas mass (resolution element). There is a resolution gradient for m14, so its m g is the massof the highest resolution elements. (4) M halo : Halo mass. (5) r dh : NFW halo scale radius (the corresponding concentration of m14 is c = 5 . ). (6) V max :Halo maximum circular velocity. (7) M baryon : Total baryonic mass. (8) M b : Bulge mass. (9) a : Bulge Hernquist-profile scale-length. (10) M d : Stellar discmass. (11) r d : Stellar disc exponential scale-length. (12) M gd : Gas disc mass. (13) r gd : Gas disc exponential scale-length. (14) M gh : Hydrostatic gas halomass. (15) r gh : Hydrostatic gas halo β = 1 / profile scale-length. Table 2. We emphasize that the parameters in the table reflect the jetparameters at our launch scale. The jet properties will continuouslyevolve as it interacts with the surrounding gas.We launch the jet with a particle spawning method, which cre-ates new gas cells (resolution elements) from the central black hole.With this method, we have better control of the jet properties as thelaunching is less dependent on the neighbor-finding results. We canalso enforce a higher resolution for the jet elements. The numericalmethod in this paper is similar to Torrey et al. (2020), which stud-ied the effects of BAL wind feedback on disk galaxies.The spawnedgas particles have a mass resolution of 5000 M (cid:12) and are forbiddento de-refine (merge into a regular gas element) before they decel-erate to 10% of the launch velocity. Two particles are spawned inopposite z-directions at the same time when the accumulated jetmass flux reaches twice the target spawned particle mass, so lin-ear momentum is always exactly conserved. Initially, the spawnedparticle is randomly placed on a sphere with a radius of r , whichis either 10 pc or half the distance between the black hole and theclosest gas particle, whichever is smaller. If the particle is initial-ized at a position ( r , θ , φ ) and the jet opening-angle of a specificmodel is θ op , the initial velocity direction of the jet will be set at θ op θ /π for θ < π/ and at π − θ op ( π − θ ) /π for θ > π/ .With this, the projected paths of any two particles will not intersect.The naming of each model starts from the primary form ofenergy at our injection scale (‘Kin’, ‘Th’, and ‘CR’ for kinetic,thermal and CR energy, respectively) and the corresponding en-ergy flux in erg s − . The run with ‘B4’ in the name means that theinitial jet magnetic field is toroidal with a maximum field strengthof − G. The number after the ‘m’ label provides the mass fluxin units of M (cid:12) yr − . The number after ‘w’ and ‘pr’ gives the initialopening-angle and precession angle in degrees. The number after‘ t p ’ and ‘ t d ’ denotes the precession period and the duty cycle inMyr. If a specific quantity is not labeled in the name, the jet modelhas fiducial values of a constant mass flux of 2 M (cid:12) yr − , an initialtoroidal magnetic field with a maximum field strength of − , ◦ opening-angle, no precession, and 100% duty cycle (i.e., we onlylabel runs with parameters that differ from these default values). Each spawned jet element carries mass, velocity, thermal energy,magnetic field, and cosmic ray energy, so the energy flux of eachkind is well controlled. In the initial conditions, we set the black-hole mass at M (cid:12) , corresponding to an Eddington luminosity L Edd ∼ erg s − . We systemically test the jet model with en-ergy input in each form ranging from ∼ × up to × erg s − , which corresponds to roughly × − − × − L Edd , around the total X-ray luminosity of the whole system and the plau-sible energy flux according to Paper II .Each energy form is briefly described below: • Kinetic component : Despite the relativistic nature of jets atthe black hole scale, such scales are orders of magnitude smallerthan the finest scale we can resolve. Instead, we have to initiate thespawned element at ∼ pc, at which point the jet has alreadybeen decelerated significantly. Moreover, we are also constrainedby the Newtonian nature of our MHD solver, which cannot accu-rately treat relativistic velocities. Accordingly, we leave the jet el-ement’s initial spawning velocity as a free parameter varied within3000-30000 km s − . This roughly spans the range from the min-imum velocity required to sustain a clear bi-polar jet shape to themaximum feasible velocity, as limited by the numerical methodsand computational time. • Thermal component : At the scale where we initiate the jet,a significant amount of energy has probably already been thermal-ized, but the fraction is uncertain. Therefore, we also leave the in-ternal temperature of the jet plasma as a free parameter rangingfrom − × K , corresponding to roughly the same rangeof specific energy as the kinetic jet models we studied. We empha-size that due to the injection in jet form, this is very different from“traditional” thermal feedback, which we will discuss later. • Magnetic component : Given the uncertainties of the mag-netic field strength and geometry at the scale where we launchour jet, we parameterize the initial magnetic fields as either purelytoroidal or purely poloidal with different strengths. The toroidalmagnetic fields follow: B tor ,φ ∝ r sin θ exp (cid:18) − r r (cid:19) , (1)where r inj is set to 10 pc. The poloidal magnetic fields follow: B pol ,r ∝ r sin θr cos θr exp (cid:18) − r r (cid:19) ,B pol ,z ∝ (cid:18) − r sin θr (cid:19) exp (cid:18) − r r (cid:19) . (2)(e.g., Guan et al. 2014) We study models with a maximum initial magnetic field strength Given that the spawned particle is launched at a radius of 10 pc (most ofthe time, since the closest neighborhood gas cell rarely goes closer to theblack hole), we always set the exponential part in the poloidal expression(except for B pol r timesexponential part in the toroidal expression to a constant. This only deviatesfrom the above expressions during the time in a run when there is a veryMNRAS000 , 1–27 (2021) in the jet plasma ranging from − µG to × − µG (roughly themaximum feasible magnetic field strength limited by the numericalmethod and computational time). We use a toroidal magnetic fieldconfiguration with the maximum field strength at − µG as thefiducial parameters since it is roughly the minimum value able toclearly affect the global magnetic field configurations. • Cosmic Rays : We treat this component analogously to our‘thermal jet’ runs – simply injecting a fixed specific cosmic ray en-ergy with the spawned jet elements, i.e., assuming a constant frac-tion of the jet plasma energy is in CRs. The CR physics and numer-ical implementation are described in detail in Chan et al. (2019).Briefly, this treats CRs including streaming (at the local Alfv´enspeed, with the appropriate streaming loss term, which thermalizes,following Uhlig et al. 2012, but with v st = v A ), diffusion with afixed diffusivity κ CR , adiabatic energy exchange with the gas andcosmic ray pressure, and hadronic and Coulomb losses (followingGuo & Oh 2008). We follow a single energy bin (i.e., GeV protonCRs, which dominate the pressure), treated in the ultra-relativisticlimit. Streaming and diffusion are fully-anisotropic along magneticfield lines. In Chan et al. (2019); Hopkins et al. (2019, 2021c),we showed that matching observed γ -ray luminosities in simula-tions with the physics above, requires κ CR ∼ cm s − , ingood agreement with detailed CR transport models that includean extended gaseous halo around the Galaxy (see e.g. Strong &Moskalenko 1998; Strong et al. 2010; Trotta et al. 2011), so weadopt this as our fiducial value. , We study models with CR energy fluxes ranging from × − × erg s − , roughly the values suggested to be capable of sta-bly quenching a M (cid:12) halo in our previous study with isotropicenergy injection (Paper II ). All of the tested runs have a constant mass flux, unless we specifya duty cycle below unity. We explicitly test the jet models with thesame energy flux in each form but with a different mass flux and,therefore, specific energy. The tested mass fluxes range from 0.02-2 M (cid:12) yr − (0.01-1 L Edd /c ), roughly comparable to the valuesobtained in the AGN feedback models considered in the literature(e.g., Yang et al. 2012; Li et al. 2015; Prasad et al. 2015). Cor-respondingly, the kinetic, thermal, or cosmic ray energy per unitmass we tested ranged from ∼ × − × erg g − , sothat the total energy flux is comparable to the halo cooling rate andthe required energy flux suggested in Paper II . Due to our jet spawning method, we are able to strictly control theinitial opening-angle of the jet. We emphasize that this is the initial strong cooling flow (SFR (cid:38) (cid:12) yr − ). During those times, the closestparticle to the black hole is smaller than 10 pc and therefore the jet particlesare spawned at a smaller radius. However, magnetic fields do very little inthose cases anyway, and none of the conclusions should change. We alsochecked the B pol We caution that we do not account for the possibility of different diffusioncoefficients in different environments (see e.g., Hopkins et al. 2021b,c). We also note that in runs with CR jets, CRs from SNe are not included,so we have a clean test of the impact of AGN CR jets. We showed in Pa-per I that CRs from stars have little effect on the cooling flows in massivegalaxies. opening-angle, which may change as the jet expands or collimatesdue to external interactions. We perform most of our runs with adefault initial jet opening-angle of ◦ ; however, we explicitly testeddifferent jet opening-angles ranging from ◦ (a very narrow jet) tocompletely isotropic (resembling a BAL wind model; e.g., Hopkinset al. 2016; Torrey et al. 2020). We tested jet precession with different precession angles and pe-riods. The angles ranged from ◦ − ◦ , and the periods rangedfrom 10-100 Myr, a broader range than the values usually quotedin the literature ( ∼ − ◦ , 5-10 Myr) (e.g., Li & Bryan 2014b;Yang & Reynolds 2016a; Bourne & Sijacki 2017). Cycles of AGN jets are observed and can naturally occur in sim-ulations with a self-consistently coupled AGN accretion and feed-back model. Given that we do not intend to model accretion ex-plicitly in this study, we test models with preset fixed duty cyclesand episodic life times. In ‘Th6e44-B4-t d
10’ the mass flux fol-lows ˙ M ∝ sin ( πt/ “on” for 2 Myr and is then turned off( ˙ M = 0 ) for 8 Myr, before repeating. In ‘Th6e44-B4-t d ˙ M = 2M (cid:12) yr − for 10 Myrand then off for 90 Myr. When the jet is on, both models have aspecific thermal energy of ∼ × erg g − ; the label ‘6e44’ inthe model name refers to its energy flux at the peak, in erg s − . Inboth runs, the averaged energy flux is × erg s − , and theduty cycle (percentage of time that a jet is on) is − and therecurrence time of the jet ( − Myr) is broadly within the ob-servational range (e.g., McNamara & Nulsen 2007, and referencestherein) and the range of values seen in self-regulating AGN jetsimulations in the literature (e.g., Prasad et al. 2015; Li et al. 2015;Yang & Reynolds 2016a).
In this section, we summarize the results of all our simulations be-fore turning to a more detailed analysis of individual mechanisms.§ 3.1 describes the star formation and cooling-flow properties ofall the runs. In § 3.2, we further show the key X-ray observa-tional properties of the quenched runs labeled as ‘strong ↓ ’ (SFR ∼ − (cid:12) yr − ) or ‘quenched’ (SFR < (cid:12) yr − ) in Table 2,which do not “overheat” the halo (high entropy and low densitywithin the cooling radius inconsistent with X-ray observations). Fig. 1 and Fig. 2 show the star formation rate and baryonic masswithin 30 kpc of all the runs. Each panel shows a subset of sim-ulations, selected to explore one parameter. The runs which areboth “not-overheated” (consistent with X-ray observations) and“quenched” (labeled ‘strong ↓ ’ or ‘quenched’ in Table 1, definedas those with SFR (cid:46) (cid:12) yr − or sSFR (cid:46) × − yr − ) arehighlighted with thicker lines. The averaged SFRs of the last 50Myr of the simulations are also summarized in Table 2.Jets with most of their energy in a thermalized component(“thermal jets”, for the sake of brevity) can stably quench thegalaxies with energy injection rates ˙ E (cid:38) × erg s − ∼ × − L Edd and ˙ M = 2M (cid:12) yr − . If the energy input is higher MNRAS , 1–27 (2021) hat Types of Jet Quench? Table 2.
Physics variations (run at highest resolution) in our halo- m14 survey
Model ∆ T SFR Summary ˙ E Kin ˙ E Th ˙ E Mag ˙ E CR ˙ M v ˙ P T B θ op θ p T on p / T allp T p Gyr M (cid:12) yr − erg s − M (cid:12) yr − km s − cgs K G deg MyrNoJet 1.5 65 strong CF N/A N/A N/A N/A N/A Kinetic Energy Flux
Kin6e42 1.0 44 strong CF 5.8e42 1.9e41 8e37-8e41 0 2.0 3e3 3.9e34 1e7 1e-3 (t) 1 N/A N/A N/AKin6e43 1.5 16 slight ↓ Thermal Energy Flux
Th6e42 1.0 27 strong CF 5.8e42 5.8e42 1e39-8e41 0 2.0 3e3 3.9e34 3e8 1e-3 (t) 1 N/A N/A N/A
Th6e43 1.5 quenched 5.8e42 5.8e43 2e42 0 2.0 3e3 3.9e34 3e9 1e-3 (t) 1 N/A N/A N/A
Th6e44 0.5 0 overheated 5.8e42 5.8e44 2e43 0 2.0 3e3 3.9e34 3e10 1e-3 (t) 1 N/A N/A N/A
CR Energy FluxCR6e42 1.5 strong ↓ quenched 5.8e42 1.9e41 1e42 5.8e43 2.0 3e3 3.9e34 1e7 1e-3 (t) 1 N/A N/A N/A CR6e44-B4 1.0 0 overheated 5.8e42 1.9e41 1e40 5.8e44 2.0 3e3 3.9e34 1e7 1e-3 (t) 1 N/A N/A N/A
Magnetic fields
B0 1.0 64 strong CF 5.8e42 1.9e41 0 0 2.0 3e3 3.9e34 1e7 0 1 N/A N/A N/AB tor tor tor pol pol pol
Jet width
Kin6e43-w15 1.5 19 slight ↓ ↓ ↓ Kin6e43-wiso 1.5 quenched 5.8e43 1.9e41 2e43 0 2.0 9.5e3 3.9e34 1e7 1e-3 (t) iso N/A N/A N/AJet Precession Kin6e43-pr15-t p
10 1.5 17 slight ↓ p
10 1.5 12 slight ↓ Kin6e43-pr45-t p
10 1.5 strong ↓ p
100 1.5 3.0 strong ↓ p
100 1.5 1.0 quenched 5.8e43 1.9e41 1e43-3e43 0 2.0 9.5e3 3.9e34 1e7 1e-3 (t) 1 45 N/A 100Kinetic Specific Energy
Kin6e42-B4-m2e-2 1.02 43 strong CF 5.8e42 1.9e39 4e34-1e41 0 0.02 3e4 3.9e32 1e7 1e-4 (t) 1 N/A N/A N/AKin6e43-B4-m2e-1 1.5 17 slight ↓ ↓ Thermal Specific Energy
Th6e42-B4-m2e-2 1.5 29 slight ↓ Th6e43-B4 1.5 strong ↓ Th6e44-B4 0.5 0 overheated 5.8e42 5.8e44 2e41 0 2.0 3e3 3.9e34 3e10 1e-4 (t) 1 N/A N/A N/A
CR Specific EnergyCR6e43-B4-m2e-1 1.5 0 quenched 5.8e41 1.9e40 1e42-6e42 5.8e43 0.2 3e3 3.9e33 1e7 1e-4 (t) 1 N/A N/A N/ACR6e43-B4 1.5 0.12 quenched 5.8e42 1.9e41 1e40 5.8e43 2.0 3e3 3.9e34 1e7 1e-4 (t) 1 N/A N/A N/ADuty Cycle
Th6e44-B4-t d
10 0.6 0 overheated 5.8e42 5.8e44 8e41-2e43 0 2.0 3e3 3.9e34 3e10 1e-4 (t) 1 N/A 1/10 N/A
Th6e44-B4-t d
100 1.5 quenched 5.8e42 5.8e44 2e41-6e41 0 2.0 3e3 3.9e34 3e10 1e-4 (t) 1 N/A 10/100 N/A
This is a partial list of simulations studied here: each was run using halo m14 , systematically varying the jet parameters. Columns list: (1) Model name: Thenaming of each model starts with the primary form of energy flux and the energy flux value in erg s − used. A run with ‘B4’ in the name means the initial jetmagnetic field has a toroidal geometry with a maximum field strength of − µ G . The number after the ‘m’ label is the mass flux in M (cid:12) yr − . Thenumbers after the ‘w’ and ‘pr’ labels are the initial opening-angle and precession angle, respectively. The numbers after the ‘ t p ’ and ‘ t d ’ label the precessionperiod and duty cycle period. If a specific quantity is not labeled in the name, the jet model is launched with a constant mass flux of 2 M (cid:12) yr − , toroidalmagnetic field, with a maximum field strength of − µ G , ◦ opening-angle, no precession, and 100% duty cycle. (2) ∆ T : Simulation duration. Allsimulations are run to . Gyr, unless either the halo is completely “blown out” or completely unaffected. (3) The SFR averaged over the last 50 Myr. (4)Summary of the results. ‘strong CF’, ‘slight ↓ ’, ‘significant ↓ ’ , and ‘quenched’ correspond respectively to a SFR of (cid:38) , ∼ − , ∼ − and (cid:46) (cid:12) yr − . ‘Overheated’ means the jet explosively destroys the cooling flow in < Myr, leaving a core with much lower density and high entropy andtemperature (e.g. (cid:29) K), violating observational constraints. (5) ˙ E Kin , ˙ E Th , ˙ E Mag , and ˙ E CR tabulate the total energy input of the corresponding form.The dominant energy form is highlighted in blue. (6) ˙ M , v, and ˙ P tabulate the mass flux, jet velocity and momentum flux. (7) T: The initial temperature ofthe jet. (8) B: The maximum initial magnetic field strength of the jet; (t) and (p) mean toroidal and poloidal respectively. (9) θ op : The opening angle of the jet.(10) θ p : The precession angle of the jet. (11) T on p and T all p : The time that the jet is on in each duty cycle and the period of the duty cycle. (12) T p : Precessionperiod. than ∼ × erg s − , the results become explosive – the gas isstrongly expelled, and the cores are overheated, inconsistent withthe X-ray observations (see Appendix A). The balance betweenmass flux and thermal energy loading also changes the results.With the same thermal energy flux, the lower the mass flux (the higher the specific thermal energy), the more efficiently the galaxyis quenched.With the same averaged thermal energy and mass fluxes, the“thermal jet” run with a duty cycle reaching 100 Myr, ‘Th6e44-B4-t d MNRAS000
This is a partial list of simulations studied here: each was run using halo m14 , systematically varying the jet parameters. Columns list: (1) Model name: Thenaming of each model starts with the primary form of energy flux and the energy flux value in erg s − used. A run with ‘B4’ in the name means the initial jetmagnetic field has a toroidal geometry with a maximum field strength of − µ G . The number after the ‘m’ label is the mass flux in M (cid:12) yr − . Thenumbers after the ‘w’ and ‘pr’ labels are the initial opening-angle and precession angle, respectively. The numbers after the ‘ t p ’ and ‘ t d ’ label the precessionperiod and duty cycle period. If a specific quantity is not labeled in the name, the jet model is launched with a constant mass flux of 2 M (cid:12) yr − , toroidalmagnetic field, with a maximum field strength of − µ G , ◦ opening-angle, no precession, and 100% duty cycle. (2) ∆ T : Simulation duration. Allsimulations are run to . Gyr, unless either the halo is completely “blown out” or completely unaffected. (3) The SFR averaged over the last 50 Myr. (4)Summary of the results. ‘strong CF’, ‘slight ↓ ’, ‘significant ↓ ’ , and ‘quenched’ correspond respectively to a SFR of (cid:38) , ∼ − , ∼ − and (cid:46) (cid:12) yr − . ‘Overheated’ means the jet explosively destroys the cooling flow in < Myr, leaving a core with much lower density and high entropy andtemperature (e.g. (cid:29) K), violating observational constraints. (5) ˙ E Kin , ˙ E Th , ˙ E Mag , and ˙ E CR tabulate the total energy input of the corresponding form.The dominant energy form is highlighted in blue. (6) ˙ M , v, and ˙ P tabulate the mass flux, jet velocity and momentum flux. (7) T: The initial temperature ofthe jet. (8) B: The maximum initial magnetic field strength of the jet; (t) and (p) mean toroidal and poloidal respectively. (9) θ op : The opening angle of the jet.(10) θ p : The precession angle of the jet. (11) T on p and T all p : The time that the jet is on in each duty cycle and the period of the duty cycle. (12) T p : Precessionperiod. than ∼ × erg s − , the results become explosive – the gas isstrongly expelled, and the cores are overheated, inconsistent withthe X-ray observations (see Appendix A). The balance betweenmass flux and thermal energy loading also changes the results.With the same thermal energy flux, the lower the mass flux (the higher the specific thermal energy), the more efficiently the galaxyis quenched.With the same averaged thermal energy and mass fluxes, the“thermal jet” run with a duty cycle reaching 100 Myr, ‘Th6e44-B4-t d MNRAS000 , 1–27 (2021) duty cycle (10 Myr) or with continuous jets with the same averageenergy and mass flux. The latter two cases essentially produce thesame results.Cosmic ray dominated jets (“CR jets”), on the other hand,quench much more efficiently. With an order of magnitude lowerenergy input than is required for thermal jets, ˙ E (cid:38) × erg s − ∼ × − L Edd , the SFR is significantly suppressed to (cid:46) (cid:12) yr − . With ˙ E (cid:38) × erg s − , the CR jets also quenchmore efficiently than thermal jets.Narrow jets with most of their energy in kinetic form (“ki-netic jets”) quench much less efficiently than CR or thermal jets.With an energy input of ˙ E (cid:46) × erg s − , the star forma-tion rate is only marginally suppressed. With an even higher energyinput ˙ E (cid:46) × erg s − , kinetic jets also do very little tothe SFR (‘Kin6e44-B4’) unless they are significantly widened bystrong magnetic fields (‘Kin6e44), where the result becomes ex-plosive. This will be discussed in § 4.3.Making the kinetic jet wider by construction (at injection)or precessing with a wider angle can potentially help kinetic jetsquench more efficiently. However, these effects only matter whenthe angles are wider than the solid angle affected by an initiallynarrower jet (30-45 ◦ in the case of ‘Kin6e43’) as we can see in‘Kin6e43-wiso’, ‘Kin6e43-pr45-t p p p (cid:46) ) effect on the SFR. The only exception is forthe very fast kinetic jets, ‘Kin6e44’, and ‘Kin6e44-B4’, where themagnetic fields can non-linearly alter the jet propagation and makea difference between having minor effects and causing explosivequenching. The reason for this will be discussed in § 4.5.Out of all the investigated runs, ‘Th6e43’, ‘CR6e42’,‘CR6e43’, ‘CR6e43-B4’, ‘Kin6e43-wiso’, ‘Kin6e43-pr45-t p p d ˙ E CR = 6 × erg s − (‘CR6e42’) is theonly run with a significantly suppressed SFR which also maintainsa steady cooling flow (i.e., growth of the core baryonic mass). Therest of the runs all have roughly constant core baryonic mass, indi-cating an explicit suppression of the cooling flow and some switch-ing between “cool core” and “non cool core” halos. The reason forthis will be discussed in § 4.4. The resulting X-ray luminosity of the halo gas is an important con-straint for AGN feedback models (e.g. Choi et al. 2015; McCarthyet al. 2010). Fig. 3 shows the predicted X-ray cooling luminosityat the end of all the “non-overheated” quiescent runs, which areruns with a strong suppression of cooling flows but which do notgenerate overheated entropy or density profiles (labeled ‘strong ↓ ’or ‘quenched’ in Table 2), integrated over all gas in the halo, from . − keV. The luminosity is calculated using the same methodsas in Schure et al. (2009); Ressler et al. (2018), in which the cool- ing curve is calculated for photospheric solar abundances (Lodders2003), using the spectral analysis code SPEX (Kaastra et al. 1996)and scaled according to the local hydrogen, helium, and metal massfractions.None of the non-overheated quiescent runs show a significantdrop in the X-ray luminosity, indicating that they do not expel asignificant amount of the virialized gas. The X-ray luminosity of allruns is above ∼ × erg s − , within the observational range(Reiprich & B¨ohringer 2002; Stanek et al. 2006; Balogh et al. 2006;Kim & Fabbiano 2013; Anderson et al. 2015). Among the runs,the ‘CR6e42’ run has the highest X-ray luminosity (still within theconstraint), consistent with the build up of a large core baryonicmass, as previously noted. Fig. 4 shows the average density, luminosity-weighted density, tem-perature, and entropy as a function of radius, averaged over the last Myr for each simulations. We excluded the jet cells themselvesfrom the calculation. The shaded regions in the top and second rowindicate the observational density profiles (scaled) for cool-core(blue) and non-cool-core (red) clusters (McDonald et al. 2013). Toaccount for the difference in halo mass between the observationsand our simulations, we use the panel for z < . in Fig. 9 of Mc-Donald et al. (2013) and assume ρ crit ∼ . × g cm − and r = 650 kpc (our m14 initial condition). The lightened curvesin the bottom row indicate the observational entropy profiles forcool-core (blue) and non-cool-core (red) clusters (McDonald et al.2013). We note that the halos in McDonald et al. (2013) have amass range of ∼ × < M < × M (cid:12) /h . We usetheir Fig. 2 and scale the average entropy at r = 700 kpc to 500kev cm given that our halo is lower mass (cooler). Most of the runs with a significantly suppressed SFR also havea lower gas density, and show the presence of heated gas in thecore region of the galaxy (r <
10 kpc). ‘CR6e42’ is, again, the onlyexception in that neither the temperature nor the density is signifi-cantly altered. For the run with a 100 Myr duty cycle, ‘Th6e44-B4-t d d We also note that the luminosity-weighted density, temperature, and en-tropy are not precisely the same as the observed quantities, so the compari-son should be viewed qualitatively. MNRAS , 1–27 (2021) hat Types of Jet Quench? − − ˙ M ? [ M (cid:12) y r − ] Kinetic
NoJetKin6e42Kin6e43Kin6e4410 − − ˙ M ? [ M (cid:12) y r − ] B for ˙ E kin =6e42 B0B tor tor tor pol pol pol − − ˙ M ? [ M (cid:12) y r − ] Mass loading (kinetic)
Kin6e42Kin6e42-B4-m2e-2Kin6e43Kin6e43-B4-m2e-1Kin6e44-B40 .
00 0 .
25 0 .
50 0 .
75 1 .
00 1 .
25 1 . Time [Gyr] − − ˙ M ? [ M (cid:12) y r − ] Duty cycle (thermal)
Th6e43-B4-m2e-1Th6e44-B4-t d d Thermal
NoJetKin6e42Th6e42Th6e43Th6e44 B for ˙ E =6e43 Th6e43-B4Th6e43CR6e43-B4CR6e43
Mass loading (thermal)
Th6e43-B4Th6e43-B4-m2e-1Th6e42Th6e42-B4-m2e-1Th6e42-B4-m2e-20 .
00 0 .
25 0 .
50 0 .
75 1 .
00 1 .
25 1 . Time [Gyr]Jet width (kinetic)
Kin6e43Kin6e43-w15Kin6e43-w30Kin6e43-w45Kin6e43-wiso CR NoJetCR6e42CR6e43CR6e44-B4 B for ˙ E =6e44 Kin6e44-B4Kin6e44Th6e44-B4Th6e44
Mass loading (CR)
CR6e43-B4CR6e43-B4-m2e-10 .
00 0 .
25 0 .
50 0 .
75 1 .
00 1 .
25 1 . Time [Gyr]Jet precession (kinetic)
Kin6e43Kin6e43-pr15-t p p p p p p p p p Figure 1.
The SFR as a function of time for all runs. Each panel labels the corresponding parameters we vary, and we also show the NoJet (no jet feedback)case in the top three panels. The thick lines indicate the quiescent and “non-overheated” cases. The gray areas at the bottom indicates an SFR below ∼ (cid:12) yr − and (darker grey) ∼ (cid:12) yr − , which we defined as ‘strong ↓ ’ and ‘quenched’ respectively in Table 2. Kinetic jets are the least effective in suppressingthe SFR unless the opening-angle or precession angle is set to be wider than 30-45 ◦ , or is significantly widened by magnetic fields. Thermal jets can moreeffectively quench the galaxy when the energy input reaches ∼ × erg s − . CR jets quench the most efficiently, requiring an energy input of only ∼ × erg s − . In the sampled parameter space, magnetic fields cause less than a factor ∼ effect in most cases. For the same thermal or cosmic rayinput, lower mass flux and the higher specific energy produces more effective quenching. With the same averaged mass flux and thermal energy flux, dutycycles with periods (cid:28)
100 Myr are effectively the same as “continuous” jets at these (cid:29) kpc scales, while models with ∼ duty cycles spread over (cid:38) Myr periods are less effective than continuous or short period jets.MNRAS000
100 Myr are effectively the same as “continuous” jets at these (cid:29) kpc scales, while models with ∼ duty cycles spread over (cid:38) Myr periods are less effective than continuous or short period jets.MNRAS000 , 1–27 (2021) − − ∆ M ba r y on [ M (cid:12) ] Kinetic
NoJetKin6e42Kin6e43Kin6e44
Thermal
NoJetKin6e42Th6e42Th6e43Th6e44 CR NoJetCR6e42CR6e43CR6e44-B4 − − ∆ M ba r y on [ M (cid:12) ] B for ˙ E kin =6e42 B0B tor tor tor pol pol pol B for ˙ E =6e43 Th6e43-B4Th6e43CR6e43-B4CR6e43 B for ˙ E =6e44 Kin6e44-B4Kin6e44Th6e44-B4Th6e44 − − ∆ M ba r y on [ M (cid:12) ] Mass loading (kinetic)
Kin6e42Kin6e42-B4-m2e-2Kin6e43Kin6e43-B4-m2e-1Kin6e44-B4
Mass loading (thermal)
Th6e43-B4Th6e43-B4-m2e-1Th6e42Th6e42-B4-m2e-1Th6e42-B4-m2e-2
Mass loading (CR)
CR6e43-B4CR6e43-B4-m2e-1 .
00 0 .
25 0 .
50 0 .
75 1 .
00 1 .
25 1 . Time [Gyr] − − ∆ M ba r y on [ M (cid:12) ] Duty cycle (thermal)
Th6e43-B4-m2e-1Th6e44-B4-t d d .
00 0 .
25 0 .
50 0 .
75 1 .
00 1 .
25 1 . Time [Gyr]
Jet width (kinetic)
Kin6e43Kin6e43-w15Kin6e43-w30Kin6e43-w45Kin6e43-wiso .
00 0 .
25 0 .
50 0 .
75 1 .
00 1 .
25 1 . Time [Gyr]
Jet precession (kinetic)
Kin6e43Kin6e43-pr15-t p p p p p Figure 2.
The evolution of the core baryonic mass (total star + gas mass within 30 kpc) as a function of time. The panels and runs follow the same grid andstyle as in Fig. 1. Most of the quiescent non-overheated runs (indicated with thick lines) have a core baryonic mass that remains almost constant over theduration of the run, indicating an explicit suppression of the cooling flow. The only exception is the lower flux cosmic ray jet run (‘CR6e42’), where there isstill a non-negligible increase of core baryonic mass even while the SFR is significantly suppressed. reasonably well with the observed cool-core clusters, while the ki-netic jet runs with a shorter precession period (10 Myr) have aslightly more extended heated core region and fall in between thecool-core and non-cool-core populations. Isotropic kinetic inputcauses a very dramatic density suppression and a sharp tempera-ture increase in the core region, resulting in the most significanttension with the observations.
Fig. 5 shows the rms 1D turbulent velocity, defined as v turb ≡ (( v θ + v φ ) / / , and the 1D Mach number ( v turb /v thermal ) forgas hotter than K as a function of radius, averaged over the last50 Myr of the runs. We exclude the radial velocity in the calculationdue to the contamination of radial outflows and inflows. We excludethe spawned jet cells as well since they, by construction, can havevelocities in excess of km s − .All thermal jets with × erg s − result in a similar boostin velocity for radii larger than ∼ kpc, despite the different dutycycle, energy loading, and mass flux. Beyond this radius, the dy- MNRAS , 1–27 (2021) hat Types of Jet Quench? Halo Mass [M (cid:12) ] L . − e V [ e r g s − ] ICReiprich & B¨ohringer (2002)Stanek et al. (2006) CR6e42CR6e43CR6e43-B4CR6e43-B4-m2e-1Kin6e43-wisoKin6e43-pr45-t p p p d d Figure 3.
The X-ray luminosity in the 0.5 - 7 keV band at the end of allthe non-overheated quiescent runs. We use M as the halo mass forour simulations. The lighter markers and the error bars denote the observedvalues from (Reiprich & B¨ohringer 2002; Stanek et al. 2006). We observevery little evolution of the total X-ray luminosity in these runs (comparedto the values for the initial conditions). All of the listed runs have X-rayluminosity within the observational range. Note that unless a run is veryoverheated, its cooling luminosity does not deviate from the initial conditionby much. This is true even in the ‘NoJet’ run, and other ‘strong CF’ runs.‘Overheated’ runs generally have slightly lower X-ray luminosity due to alower core gas mass, ranging from 1-1.5 erg s − except for ’Th6e44-B4-t d ∼ erg s − . namical time is long enough that the duty cycle’s effect can beaveraged out. We see a very small boost of the turbulent veloc-ity for gas at small radii in the thermal jet run with a duty cycleof 100 Myr. The maximum velocity reaches roughly 200 km s − ,broadly consistent with observations of the Perseus cluster (HitomiCollaboration et al. 2016, 2018). On the other hand, the continuousthermal jet with the same average energy flux boosts the turbulentvelocity in the core region of the galaxy to (cid:46) km s − , slightlyhigher than the observations.The cosmic ray jet with × erg s − results in a very sim-ilar turbulent velocity boost as the corresponding thermal jet run,and the maximum velocity reaches (cid:46) km s − . The run withlower CR input, ‘CR6e42’, has a much lower turbulent velocity( (cid:46) km s − ) at all radii, consistent with the Perseus observa-tion. Kinetic jets with a wide opening-angle or with precession alsoboost the turbulent velocity to (cid:46) km s − , again, slightly higherthan the observations. Comparing with the thermal or CR jet runswith a similar energy input, the velocity boosts of kinetic jets ex-tend to larger radii. Long-precession-period jets (100 Myr) furtherboost the turbulent velocity around 10-70 kpc when the opening-angle reaches 30-40 ◦ , but only by a factor of (cid:46) . As shown in the first three panels of Fig. 1, a cosmic ray jetquenches more efficiently than a thermal jet with the same energy flux — i.e., CR jets require only about one-tenth of the energy fluxas a thermal jet to quench the same galaxy. Kinetic jets are the leastefficient at stopping the cooling flow, and only marginally suppressthe SFR unless the opening-angles or procession angles are quitewide. In this section, we discuss how different jet parameters affectjet propagation and galaxy quenching. We first provide a simplemodel in § 4.1 for the jet propagation and cocoon expansion, whichhelps us to interpret the results of our numerical experiments. Thenwe discuss how it applies to each of the cases in the following sec-tions.
Despite the different energy forms, the propagation of a jet buildsup a pressurized region (cocoon) with the thermal, CR, or magneticenergy it carries at launch or gains through converting its kinetic en-ergy through shocks. This both heats up gas within the cocoon, re-versing the cooling and suppressing cooling instabilities (Voit et al.2015), as well as building up a pressure gradient, slowing down thegas inflow. We found three criteria to successfully quench a halo,which are summarized in Fig. 6. First, the input energy of any formshould, at a minimum, offset the gravitational collapse of the cool-ing gas: ˙ E min ∼ ˙ M cool v ff [ R cool ] ∼ erg s − (cid:18) ˙ M cool
100 M (cid:12) yr − (cid:19) (cid:18) v ff [ R cool ]300 km s − (cid:19) , (3)where ˙ M cool is the cooling rate and v ff [ R cool ] is the free fall veloc-ity at the cooling radius ( R cool ). However, if the energy flux is too high, the result will be ex-plosive. This happens at an energy flux of ˙ E max , in which casethe jet bubble expands quasi-isotropically at the escape velocity( v esc [ R cool ] ) at the cooling radius. It may expand until it has sweptout most of the ICM gas. Supposing the energy is purely advective,and the energy loss is negligible, then, the injected energy ( ˙ E tot , J )is related to the outer shell velocity ( v exp ) as ˙ E tot , J ∼ πR v exp × ρ R v ∝ ρ R R v , (4)where ρ R is the density around the cooling radius. Therefore, ˙ E max ˙ E min ∝ (cid:18) v esc [ R cool ] v ff [ R cool ] (cid:19) ∼ − , (5)given that ˙ M cool ∝ πR ρ R /t ff ∝ R ρ R v ff [ R cool ] . Thisgives a roughly one-order-of-magnitude range for the allowed en-ergy flux.Another important criterion is that the cooling time within thejet cocoon/bubble has to be long enough such that the energy willnot be lost before the cocoon reaches the cooling radius, other-wise, the bulk of the gas within the cooling radius will not be af-fected and the cooling flows persist. The cooling time is roughly t cool ∼ kT / ¯ n Λ( T ) , where T is the temperature within the jet co-coon/bubble, ¯ n is the average number density within the coolingradius, and Λ is the cooling function. From Eq. (4), the expansion Here we define the cooling radius ( R cool ∼ − kpc) as the radiuswithin which the cooling time is shorter than our simulation time ( ∼ − Gyr).MNRAS000
100 M (cid:12) yr − (cid:19) (cid:18) v ff [ R cool ]300 km s − (cid:19) , (3)where ˙ M cool is the cooling rate and v ff [ R cool ] is the free fall veloc-ity at the cooling radius ( R cool ). However, if the energy flux is too high, the result will be ex-plosive. This happens at an energy flux of ˙ E max , in which casethe jet bubble expands quasi-isotropically at the escape velocity( v esc [ R cool ] ) at the cooling radius. It may expand until it has sweptout most of the ICM gas. Supposing the energy is purely advective,and the energy loss is negligible, then, the injected energy ( ˙ E tot , J )is related to the outer shell velocity ( v exp ) as ˙ E tot , J ∼ πR v exp × ρ R v ∝ ρ R R v , (4)where ρ R is the density around the cooling radius. Therefore, ˙ E max ˙ E min ∝ (cid:18) v esc [ R cool ] v ff [ R cool ] (cid:19) ∼ − , (5)given that ˙ M cool ∝ πR ρ R /t ff ∝ R ρ R v ff [ R cool ] . Thisgives a roughly one-order-of-magnitude range for the allowed en-ergy flux.Another important criterion is that the cooling time within thejet cocoon/bubble has to be long enough such that the energy willnot be lost before the cocoon reaches the cooling radius, other-wise, the bulk of the gas within the cooling radius will not be af-fected and the cooling flows persist. The cooling time is roughly t cool ∼ kT / ¯ n Λ( T ) , where T is the temperature within the jet co-coon/bubble, ¯ n is the average number density within the coolingradius, and Λ is the cooling function. From Eq. (4), the expansion Here we define the cooling radius ( R cool ∼ − kpc) as the radiuswithin which the cooling time is shorter than our simulation time ( ∼ − Gyr).MNRAS000 , 1–27 (2021) Figure 4.
Mean gas density ( top row ), X-ray cooling luminosity-weighted density ( second row ), luminosity-weighted temperature ( third row ), and luminosity-weighted entropy ( bottom row ) versus radius averaged over the last ∼ Myr in the non-overheated quiescent runs from Fig. 1. The shaded regions in thefirst and second row and the light curves in the bottom row indicate the observational density and entropy profiles (scaled) for cool-core (blue) and non-cool-core (red) clusters (McDonald et al. 2013) (scaled to account for the halo mass differences). Almost all of the plotted runs with an energy input of × erg s − have a heated core but are mostly within the observational range. The isotropic kinetic input run (‘Kin6e43-wiso’) has a larger heated region,possibly in tension with the observations. The density and entropy profiles of the run with low-energy cosmic ray jets (‘CR6e42’) and the runs with a long-precession-period kinetic jet (‘Kin6e43-pr30-t p p d × erg s − (‘Th6e43’, ‘Th6e43-B4’, ‘CR6e43’, and ‘CR6e43-B4’) fall between the cool-core and non-cool-core populations.MNRAS , 1–27 (2021) hat Types of Jet Quench? − M ac h N u m b e r (T > K) Thermal
NoJetTh6e43-B4Th6e43Th6e44-B4-t d Radius [kpc] V e l o c it y [ k m s − ] (T > K) CR NoJetCR6e42CR6e43CR6e43-B4CR6e43-B4-m2e-1 Radius [kpc]
Kinetic
NoJetKin6e43-wisoKin6e43-pr45-t p p p Radius [kpc]
Figure 5.
Top row:
1D rms Mach number in gas with
T > K (averaged over the last 50 Myr of the runs) as a function of radius for the non-overheatedquiescent runs.
Bottom row:
1D rms velocity dispersion for the same gas. All thermal and CR jets with × erg s − result in a similar boost of theturbulent velocity, reaching (cid:46) km s − in the core region, which is slightly higher than the (limited) observational constraints. Kinetic jets with wideopening-angle or precession also boost the turbulent velocities to a similar value, and the velocity boosts extend to larger radii. Long-precession-period jets(100 Myr) further boost the turbulent velocity around 10-70 kpc when the opening-angle reaches 30-40 ◦ , but only by a factor of (cid:46) . The ‘CR6e42’ run hasslightly lower turbulent velocities, roughly 100 km s − , which is broadly consistent with observations of the Perseus cluster (Hitomi Collaboration et al. 2016,2018). Coolingflow GalaxyAGN jetcocoonAGNjet R
Cocoon Z C o c oon Active galactic nucleus (AGN) jets can suppress cooling flows (and therefore quench star formation) in massive galaxies if the following three criteria are met.
1. Moderate jet energy flux
Enough energy for cocoon expansion to balance gas cooling, but not so much energy as to exceed escape velocity at Rcool.
2. Long cooling time within jet cocoon
Longer than time to reach Rcool.Can be achieved by thermal or kinetic jetswith high specific energy or CR jets.
3. Wide jet cocoon
Width of cocoon at Rcool is enough to suppressthe cooling flow over a wide solid angle.Can be achieved by jets with a high non-kinetic component, very light kinetic jets, or jets with initially wide angles. t cool [ R cool ] > t expansion [ R cool ] ~ R cocoon z cocoon R cool > ½ R R cool v exp > E tot , J > M cool v ® [ R cool ] ~ ~ C o o l i n g f l o w s u p p r e s s e d C o o l i n g r a d i u s ( R c o o l ) Figure 6.
A cartoon picture of the criteria for successful jet models.MNRAS000
A cartoon picture of the criteria for successful jet models.MNRAS000 , 1–27 (2021) time is roughly t exp ∼ R cool /v exp ∝ ρ / R ˙ E − / , J R / . The cool-ing time is long enough when t cool (cid:29) t exp or T (cid:29) ¯ n Λ( T ) ρ / R R / ˙ E − / , J k ∼ K (cid:16) ¯ n . − (cid:17) / (cid:18) R cool (cid:19) / (cid:18) ˙ E tot , J erg s − (cid:19) − / . (6)The third criterion is that the solid angle affected by the jetcocoon should be wide enough that cooling can be suppressedover a significant fraction of the volume. The propagation of thejet cocoon qualitatively follows momentum conservation in the z-direction (e.g., Begelman & Cioffi 1989), A c v z ¯ ρv z = ¯ ρπR v z = 12 ˙ M J v J , (7)and the balance of energy flux in the perpendicular directions, A tot v R (cid:18)
12 ¯ ρv R (cid:19) = (2 πR cocoon z cocoon ) v R ¯ ρv R β = γ M J v ) , (8)where A c is the cross section of the whole pressurized region, A tot is the total surface area of the same region, R cocoon is the radiusof A c , z is the height to which the jet reaches, v R ≡ dR cocoon /dt and v z ≡ dz cocoon /dt are the expansion velocities of the pressur-ized region in the mid-plane and polar directions, ¯ ρ is the averageddensity within the radius out to which the jet reaches, ˙ M J is the jetinitial mass flux, v J is the initial jet velocity, β is an order-of-unitygeometric factor for the surface area of the pressured region, and γ ≡ ˙ E expansion / ˙ E kin ∝ ˙ E tot , J / ˙ E kin ≡ f − is the ratio of theenergy flux in the perpendicular direction (proportional to the totalinjected energy ˙ E tot , J ) to the injected kinetic energy flux.From the equations above, we can solve for the time depen-dence of R cocoon and z cocoon . In particular, for a fixed ¯ ρ , ˙ M J , ˙ E tot , J and time, the opening-angle of the resulting cocoon scalesas R cocoon z cocoon ∝ (cid:18) ˙ E tot , J ˙ E kin (cid:19) / . (9)On the other hand, for a fixed propagation height z cocoon = z , theopening-angle scales as R cocoon z cocoon = γz β (cid:18) π ¯ ρv J ˙ M J (cid:19) / ∝ (cid:16) ˙ E tot , J ˙ E kin (cid:17) / for a fixed ¯ ρ , ˙ M J , ˙ E tot , J (cid:16) ˙ E tot , J ˙ M J (cid:17) / for a fixed ¯ ρ , v J , ˙ E tot , J (cid:16) v J ˙ M J (cid:17) / for a fixed ¯ ρ , ˙ E kin , ˙ E tot , J (10)Therefore, to have a wider cocoon, the jet needs to have either a) asmaller kinetic component for fixed total energy and mass flux, b)a higher non-kinetic specific energy for fixed jet velocity and totalenergy flux, or c) a lighter but faster jet with fixed total and kineticenergy flux.At the cooling radius, R cool ∼
30 kpc , the opening-anglefor the jet cocoon is wide enough to be considered quasi-isotropicwhen R cocoon /z cocoon (cid:38) . As the jet cocoon evolves, it gradu-ally widens and becomes quasi-isotropic (if ever) at a certain height R cocoon /z cocoon = 1 corresponds to a polar angle of ◦ . z cocoon = z iso . If z iso (cid:29) R cool , the jet can only suppress the in-flows within a small solid angle and will not quench the coolingflow, no matter how high the injected energy is. On the contrary, if z iso (cid:28) R cool , the cooling flow can be suppressed if the energy fluxis sufficiently high.For a purely kinetic jet launched with a very high Mach num-ber, which is always the case, γ ∼ ρ after − shocked v − shocked ρ pre − shocked v − shocked ∼ / . (11)The scaling of z iso generally follows z iso = (cid:18) ˙ M J πρv J (cid:19) / (cid:18) βγ (cid:19) ∼
23 kpc f kin × (cid:18) ˙ M J (cid:12) yr − (cid:19) / (cid:16) ¯ n .
01 cm − (cid:17) − / (cid:16) v J km s − (cid:17) − / . (12)Therefore, z iso < R cool when v J (cid:38) × km s − f × (cid:18) ˙ M J (cid:12) yr − (cid:19) (cid:16) v ff
300 km s − (cid:17) (cid:18) ˙ M cool
100 M (cid:12) yr − (cid:19) − , (13)which corresponds to a purely kinetic jet with a very high velocity,or with f kin (cid:46) . (cid:16) v J − (cid:17) / (cid:18) ˙ M J (cid:12) yr − (cid:19) − / × (cid:16) v ff
300 km s − (cid:17) − / (cid:18) ˙ M cool
100 M (cid:12) yr − (cid:19) / , (14)which corresponds to the jet models with more than half of theenergy in a non-kinetic form. In the following sub-sections, we dis-cuss how the above scaling relations help explain which jet modelsquench most efficiently. Kinetic jets quench galaxies mostly through heating and reversingthe inflow in the affected region. By shock heating the gas withina specific solid angle Ω (and also transferring momentum/kineticenergy to the gas), they halt the inflows in that cone and suppresscooling flows roughly proportional to Ω / π .In fact, many properties of the outflows in both thermal andkinetic jet runs are very similar despite the very different initial jettemperature and jet velocity. The bottom row of Fig. 7 shows en-tropy vs. radial velocity plots of the thermal and kinetic runs withidentical energy fluxes (‘Kin6e43’ and ‘Th6e43’). In both runs, theuppermost disconnected part (at high entropy) consists entirely ofspawned jet elements. The kinetic jet elements are shock-heatedto a similar entropy and temperature as the thermal jet elements,which are initialized with these values. As expected, the post-shockvelocity of the kinetic jet cells is slightly higher than that of the ther-mal jet cells, but it is important to note that even the “thermal jets”are moving with very large bulk velocity > − on kpcscales. Because the energetics and ram+thermal pressure of the jetsare similar in both cases, the bulk outflow velocity of the affectedICM is similar in both runs. MNRAS , 1–27 (2021) hat Types of Jet Quench? Although the properties of entrained, out-flowing gas aroundthe polar direction are similar in these runs, the distribution of in-flow vs. outflow is quite different away from the poles. Injectingenergy in a predominantly kinetic form generally transfers energyout to a large distance from the BH, in a narrower solid angle. Asshown in the entropy slices (the top row of Fig. 7), the kinetic jet(‘Kin6e43’) is narrower, especially at smaller radius, while a ther-mal jet with the same energy flux (‘Th6e43’) more effectively heatsthe core region. This is consistent with Eq. (13) and Eq. (14): aninitially narrow kinetic jet ( v J = 10 km s − ), has an effectiveopening-angle less than ◦ at the cooling radius ( ∼ kpc), whilethe thermal jet with a small f kin widens very quickly. ‘Kin6e43’also generates a more continuous chimney, indicating a more effi-cient propagation to large radius. This is expected since the kineticjets initially have a much higher velocity. Accordingly, kinetic jetsmostly invert the inflow within a confined solid angle and only re-duce the cooling flow proportionally. On the other hand, thermaljets more uniformly heat up the core region r (cid:46) and moreeffectively quench. Whether the substantially less-collimated ther-mal jets are theoretically and observationally realistic remains to bedetermined. Given that the effects of the kinetic jets are limited to a relativelysmall solid angle, the value of the solid angle can determine howeffective the jet is at quenching. Keeping a similar solid angle butincreasing the energy (or momentum) flux, on the other hand, hasmuch smaller effects. To produce a kinetic-jet-inflated cocoon witha wide enough solid angle to suppress the cooling flows, we eitherneed a jet with v J (cid:29) × km s − (following Eq. (13)), or a jetthat is initialized with a wide opening-angle. Exploring the formerpossibility is limited by the maximum jet velocity we can adopt inour MHD simulations.As we can see in the “Mass loading (kinetic)” panel of Fig. 1and Fig. 2, despite very different jet velocities, specific energiesand initial jet opening-angles, ‘Kin6e43’, ‘Kin6e44-B4’, ‘Kin6e43-w15’, ‘Kin6e43-w30’, and ‘Kin6e43-w45’ share very similar corebaryonic mass growth and SFRs. ‘Kin6e44-B4’ and ‘Kin6e43-wiso’, on the other hand, are quenched and have lower core bary-onic mass due to the larger opening-angle of the jet-inflated cocoon.Fig. 8 shows the distributions of the entropy (1st and 3rd row)and the radial velocity (2nd and 4th row) of these seven runs andthe ‘NoJet’ run. Inflowing and outflowing velocities are indicatedby red and gray color scales, respectively. Fig. 9 shows the in-flow/outflow rates along different angles as a function of polar an-gle. It is clear that although the entropy distribution differs from runto run, the velocity structures of the runs with similar baryonic in-flows (‘Kin6e43’, ‘Kin6e44-B4’, ‘Kin6e43-w15’, ‘Kin6e43-w30’,and ‘Kin6e43-w45’) look quite similar. In the ‘NoJet’ case, gasis inflowing in all directions. In the five aforementioned runs, onthe other hand, the velocity is all outflowing at small polar angle(closer to the jet), while at large polar angle (closer to the mid-plane), the velocity is all inflowing. This transition happens at 30 ◦ -40 ◦ for all of the four cases. As labeled on the plot, the angle isroughly consistent with the angle derived from (10) at r = 30 kpc assuming n ∼ .
01 cm − . Even the ‘Kin6e43-wiso’ run, despitethe isotropic injection, is still collimated by the surrounding over-density in the midplane of the galaxy. However, the inflow at thecore region of this run is shut down isotropically, consistent withthe zero SFR at a later time. In contrast, ‘Kin6e44’ has a much wider region that is dramatically outflowing. The reason for this isthat the jet has a non-thermal component (in this case, magnetic)with comparable energy to the kinetic component, producing rapidbroadening of the cocoon.In Fig. 9, the inflows and outflows are calculated in a shell of25-35 kpc, somewhat inside the cooling radius. We clearly seethat runs which produce a wider opening-angle outflow “cocoon”or bubble in Fig. 8, and thus have outflow along a broader range ofangles, have lower integrated inflow rates, which is consistent withtheir accreted baryonic mass and SFRs in Fig. 1 and Fig. 2.In brief, the jet drives shocks which inflate a cocoon, directlyimpacting gas within an opening angle that depends on the form ofthe jet. Beyond this effective opening-angle, the cooling flows aremuch less affected. As a result, increasing the kinetic energy inputdoes not necessarily mean more effective quenching if the affectedsolid angle is not enlarged because the maximum effect is expellingall the gas in that cone. Consistent with this, the ‘Kin6e44-B4’run has very similar inflow and outflow structures as ‘Kin6e43’ inFig. 9 despite having an order of magnitude higher kinetic energyflux. However, enlarging the initial kinetic jet opening-angle whilekeeping the total energy flux the same can potentially make the jetquench the galaxy more efficiently.Remarkably, if we use Eq. (12) to estimate the scaling of thecocoon opening-angle with the jet ˙ M and ˙ E or v J , we obtain thesame scaling for opening-angle as seen in Fig. 9 for the initially“narrow” jets (vertical dashed lines). We find that cosmic ray (CR)-dominated jets quench more effi-ciently, and potentially more stably, than thermal, kinetic, and mag-netic jets. We argue that this is due to three factors: (i) CR pres-sure support, (ii) modification of the thermal instability, and (iii)CR propagation. Injected CRs provide pressure support to the gasand have long cooling times, which leads to the formation of aCR pressure-dominated cocoon. Because the CR energy density ismuch larger than kinetic energy density, the CR jet cocoon cov-ers a wider angle (as expected), and can therefore more efficientlysuppress inflow. If the CR losses are negligible and CRs becomequasi-isotropic, with an effective isotropically-averaged diffusivity ˜ κ (which includes streaming+advection), then as shown in variousstudies (Butsky & Quinn 2018; Hopkins et al. 2019; Ji et al. 2020;Hopkins et al. 2021a,b,c) the CR pressure for steady-state injectionis P CR ( r ) ∼ ˙ E CR / π ˜ κ r . Comparing the outward acceleration ρ − ∇ P to gravity ( ∼ v c /r ), where v c is the circular velocity, CRpressure alone can support the gas if ˙ E CR (cid:38) erg s − (cid:18) ˜ κ (cid:19) (cid:16) n gas .
01 cm − (cid:17) (cid:18) r
30 kpc (cid:19) (cid:16) v c
500 km s − (cid:17) (15)(where we recall the cooling radius is ∼ kpc here and the dif-fusivity used here is cm s − ; see Chan et al. 2019; Hopkinset al. 2019, 2021c). This roughly explains the required CR energet-ics we find in our simulations, as well as the radii/densities whereCR pressure dominates for a given ˙ E CR . This is also consistentwith the comparison of the total centrifugal acceleration and the We note that the plotted values will vary if we choose a different radius,but the conclusions remain the same.MNRAS000
500 km s − (cid:17) (15)(where we recall the cooling radius is ∼ kpc here and the dif-fusivity used here is cm s − ; see Chan et al. 2019; Hopkinset al. 2019, 2021c). This roughly explains the required CR energet-ics we find in our simulations, as well as the radii/densities whereCR pressure dominates for a given ˙ E CR . This is also consistentwith the comparison of the total centrifugal acceleration and the We note that the plotted values will vary if we choose a different radius,but the conclusions remain the same.MNRAS000 , 1–27 (2021) Figure 7. Top row:
Entropy distribution of the kinetic jet and thermal jet runs with an equal energy flux of × erg s − (a δy = 10 kpc slice). Bottomrow:
Entropy and radial velocity distribution. The thermal jet causes a wider heated region in the core ( (cid:46) kpc), while the kinetic jet propagates moreefficiently to a larger radius. Despite the difference in jet velocity and jet temperature, both thermal and kinetic jets show a similar positive correlation betweenentropy and radial velocity in outflowing gas. acceleration due to CR and thermal pressure gradient as shown inFig. 10. CR-dominated jets can also help quench by modifying thenon-linear behavior of the thermal instability, as suggested in Jiet al. (2020) and shown rigorously in Butsky et al. (2020). In brief: if CR pressure balances gravity and dominates over thermal pres-sure in a thermally-unstable medium, then cooling gas follows to-tal pressure equilibrium (not just thermal pressure equilibrium) andcooling gas can remain diffuse (rather than being compressed tohigh densities; i.e., the cooling changes from isobaric to isochoric),as shown in Fig. 11. This, in turn, slows the “precipitation” ofdense, cold gas from the cooling flow that would otherwise ac-crete (Voit et al. 2017), allowing it to instead remain diffuse andsupported by CR pressure. We see indirect evidence for this (inFig. 11) in our CR runs as more warm thermally-unstable gas re-sides at intermediate densities (and at ∼ − kpc radii) withoutaccreting (e.g., our ‘CR6e42’ run) and formation of the dense, coldphase appears somewhat delayed. There is also a slight thermal in-stability difference in the cosmic ray jet runs with different fluxes.We discuss this further in Appendix B.Heating from cosmic rays plays a smaller role in quenching.For all of our CR jet runs, CR collisional heating and streamingheating contribute at most / and / of our CR injection rate,respectively. This amount of heating should not have a major effect We used the median pressure (weighted by mass) in each radial bin tocalculate the pressure gradient in Fig. 10 to better show the difference. on quenching, as we can see in the thermal jet runs with such acorresponding energy flux.The ability of CRs to stream or diffuse (i.e., large ˜ κ above)relative to the gas is crucial to these behaviors. If CRs were purelyadvected with the gas, they would simply represent slowly-coolinginternal energy. But because CRs can stream through gas, theirpressure profile operates akin to a fixed background, which meansthat if we increase ˙ E CR further, the behavior is not “explosive.”Specifically, as shown in Hopkins et al. (2021a), even if |∇ P CR | (cid:29) ρ | a grav | , then although CR pressure is sufficient to drive gas out-flows, these outflows are weak. Independent of P CR or ˙ E CR , theyrapidly accelerate gas up to a terminal velocity ∼ V c , i.e., trans-sonic with respect to the hot halo gas, which then “coasts” in theouter halo and beyond. In comparison, a conventional continuous-injection pressure-driven blastwave generally produces hypersonicoutflows (and accelerates more rapidly in a declining density pro-file as is typical of outer halos). CR diffusion is more effectivethan thermal conduction (except at high temperature), making both‘CR6e44’ and ‘CR6e43-B4-m2e-1’ less overheated than the corre-sponding ‘Th6e44’ and ‘Th6e43-B4-m2e-1’, as shown in Fig. A1and Fig. A2. Magnetic fields usually only have limited effects (factor (cid:46) ) inquenching the galaxy or suppressing cooling flows. The exceptionis ‘Kin6e44’, where the galaxy is quenched while an otherwiseidentical simulation with an order of magnitude lower magnetic MNRAS , 1–27 (2021) hat Types of Jet Quench? Figure 8.
Entropy and radial velocity of some representative kinetic jet runs shown in a δy = 10 kpc slice. The radial velocity is indicated separately forinflowing gas (red color scale) and outflowing gas (gray color scale). Despite the different opening-angles, and kinetic energy fluxes, ‘Kin6e43’, ‘Kin6e44-B4’, ‘Kin6e43-w15’, and ‘Kin6e43-w30’ all have outflowing gas confined within a very similar solid angle. The entropy distribution shows larger differences.‘Kin6e44’ has a significantly wider opening-angle due to the magnetic fields, which is explained in § 4.5. field strength (‘Kin6e44-B4’) has strong cooling flows and highSFRs.In ‘Kin6e44’, the magnetic energy input is ∼ − × erg s − , similar to the kinetic energy input. We therefore expectthe non-kinetic pressure to broaden the jet cocoon (Eq. (14)) andindeed, we see a much wider jet cocoon which produces a wide-angle outflow. In other runs, the highest magnetic energy input rateis ∼ erg s − , insufficient to strongly broaden the cocoon.The direct effect of gas acceleration by magnetic pressureis weak. Magnetic pressure is only high in the core region anddense structures, as shown in Fig. 12. The magnetic pressure can behigher than the thermal pressure within ∼ kpc if mass-weightedbut is always subdominant to thermal pressure if volume-weighted. This indicates that magnetic field strengths are only high in thedense cooler gas, and in that gas the B-fields appear saturated (inde-pendent of injected field strengths). Moreover, in those dense struc-tures, the cooling is already effective, and the extra magnetic pres-sure cannot do much. In the regions where the density is relativelylow, the magnetic pressure support is less important.Outside of these dense regions, we do see slightly broader co-coons (hence more efficient quenching) for jets with toroidal (vs.poloidal) fields, at the same initial strength (compare e.g., ‘B tor pol MNRAS000
Entropy and radial velocity of some representative kinetic jet runs shown in a δy = 10 kpc slice. The radial velocity is indicated separately forinflowing gas (red color scale) and outflowing gas (gray color scale). Despite the different opening-angles, and kinetic energy fluxes, ‘Kin6e43’, ‘Kin6e44-B4’, ‘Kin6e43-w15’, and ‘Kin6e43-w30’ all have outflowing gas confined within a very similar solid angle. The entropy distribution shows larger differences.‘Kin6e44’ has a significantly wider opening-angle due to the magnetic fields, which is explained in § 4.5. field strength (‘Kin6e44-B4’) has strong cooling flows and highSFRs.In ‘Kin6e44’, the magnetic energy input is ∼ − × erg s − , similar to the kinetic energy input. We therefore expectthe non-kinetic pressure to broaden the jet cocoon (Eq. (14)) andindeed, we see a much wider jet cocoon which produces a wide-angle outflow. In other runs, the highest magnetic energy input rateis ∼ erg s − , insufficient to strongly broaden the cocoon.The direct effect of gas acceleration by magnetic pressureis weak. Magnetic pressure is only high in the core region anddense structures, as shown in Fig. 12. The magnetic pressure can behigher than the thermal pressure within ∼ kpc if mass-weightedbut is always subdominant to thermal pressure if volume-weighted. This indicates that magnetic field strengths are only high in thedense cooler gas, and in that gas the B-fields appear saturated (inde-pendent of injected field strengths). Moreover, in those dense struc-tures, the cooling is already effective, and the extra magnetic pres-sure cannot do much. In the regions where the density is relativelylow, the magnetic pressure support is less important.Outside of these dense regions, we do see slightly broader co-coons (hence more efficient quenching) for jets with toroidal (vs.poloidal) fields, at the same initial strength (compare e.g., ‘B tor pol MNRAS000 , 1–27 (2021) − − − d ˙ M / d | c o s θ p o l | [ M (cid:12) y r − ] ↑ outflow ↓ inflow cos θ cos θ Kin6e43-w15Kin6e43-w30Kin6e43-w45Kin6e43-wiso0.0 0.2 0.4 0.6 0.8 1.0 | cos θ pol | [degree] − − − − − ˙ M ( < | c o s θ p o l | ) [ M (cid:12) y r − ] ↑ outflow ↓ inflow ← mid plane → polarNoJetKin6e43Kin6e44-B4Kin6e44 Figure 9.
Top:
The distribution of radial gas inflow ( ˙ M < ) and out-flow ( ˙ M > ) as a function of the cosine of the polar angle ( | cos θ pol | )calculated in a shell of 25-35 kpc averaged over the last 50 Myr of eachrun. Bottom:
The integrated value of the mass flux from | cos θ pol | = 0 to | cos θ pol | . The vertical lines label the corresponding cocoon opening-angle at 30 kpc for the ‘Kin6e43’ and ‘Kin6e44-B4’ runs according toEq. (10). Without jets, there is net inflow in all directions. With kineticjets, we generically see outflow along the polar directions and inflow in themid-plane, with net (angle-integrated) inflow. The outflow opening-angleincreases as we increase the effective jet opening-angle, but even isotropicjets (‘Kin6e43-wiso’) are collimated by the inflowing halo gas and featureinflows within ∼ ◦ of the mid-plane (only the most violent jet here pro-duces isotropic outflows). plification, as the galactic field is also toroidal near the injectionsite. We also tested how the cooling flows and SFRs differ when usingthe same total energy in a given form but with different mass fluxand energy loading. Given a fixed total energy, the lower the massflux (i.e., the higher the specific energy of the jet), the more effec-tive the quenching is, as expected from simple analytic predictionsof how rapidly the cocoon can inflate (Eq. (10) and Eq. (14)).As we can see in Fig. 1 ,‘Th6e43-B4-m2e-1’ quenches moreeffectively than ‘Th6e43-B4’. The former jet has an order of mag-nitude lower mass flux than the latter despite having the same ther-mal energy flux. ‘Th6e42-B4-m2e-2’ also quenches slightly moreefficiently than ‘Th6e42-B4-m2e-1’ and ‘Th6e42’. The major dif-ference between jets with different specific thermal energies andmass fluxes is the cocoon width, as shown in Fig. 14, especially inthe 6 × erg s − runs. ‘Th6e43-B4-m2e-1’ has a wider solidangle for which the gas is outflowing than for the ‘Th6e43-B4’run. We see the same comparing CR runs (‘CR6e43-B4-m2e-1’ and‘CR6e43-B4’ ). In all of these cases, the width of the low-densityevacuated cocoon scales roughly ∝ ( ˙ E tot , J / ˙ M J ) / , as expected − − − − A cce l e r a ti on [ c m s − ] Th6e42
ThermalCRGravityCentrifugal Radius [kpc] − − − − A cce l e r a ti on [ c m s − ] CR6e42 Th6e43 Radius [kpc]
CR6e43
Figure 10.
Comparison of gravitational, rotational, thermal pressure andCR pressure gradient acceleration. The centrifugal acceleration is definedas GM enc /r − v /r . In the core region, where cooling is rapid, thethermal pressure gradient is not outward and support is lost. In our CR runs,the CR pressure gradient predominantly balances gravity in the core region. from Eq. (10). The effects in the low-energy thermal jet runs orpure kinetic runs are weaker, as the cooling flows are not stronglysuppressed (the cocoon has insufficient energy to grow). As shownin Eq. (13), a purely kinetic jet with ˙ M = 2 M (cid:12) yr − needs a ve-locity > × km s − to have a sufficient width at the coolingradius. We also tested the difference between a jet with constant mass andenergy flux and jets with various duty cycles but the same aver-aged mass and energy flux. We found that the run with a ∼ Myr episodic period and a ∼ duty cycle (‘Th6e44-B4-t d d d d ∼ kpc) is roughly 10 Myrand the cooling time for the hot gas at the same radius is (cid:38) Myr, so the cooling flow has time to recover when the jet is off. Onthe contrary, in the run with a 10 Myr period, both the cooling timeand dynamical time of the gas around the same region are largerthan or equal to the period, so the effect is approximately the sameas a continuous jet.The jet with visible duty cycles (‘Th6e44-B4-t d MNRAS , 1–27 (2021) hat Types of Jet Quench? Figure 11.
Ratio of the cooling time to dynamical time ( t cool /t dyn ) (toprow) and the phase structure for 15-30 kpc in the temperature-density plane(middle row) and entropy-pressure (thermal + CR) plane (bottom row) forthe thermal and CR jet runs. The plots are averaged over 0.95-1 Gyr of eachrun. In the CR runs (‘CR6e42’), there is more warm, thermally-unstable gasresiding at intermediate densities (and at ∼ − kpc) without accreting(e.g., our ‘CR6e42’ run) and the formation of the dense, cold phase appearssomewhat delayed. The cosmic ray jet run also has gas following a con-stant total pressure path with narrow density variation while cooling. In thethermal jet run, there is generally a wider density distribution. the perpendicular expansion of the cocoon is sub-linear in time and ˙ E . Additionally, since cooling times are not much longer than 100Myr, some of the injected energy is lost in each “off” cycle. We experimented with different precession angles and precessionperiods and find that the dominant effect of the precessing kineticjet is still shock heating the surrounding gas and suppressing theinflows or pushing the gas outward within a specific solid angle.Thus, making an otherwise narrow cocoon “efficient” requires pre-cession angles (cid:38) − ◦ so that the cocoon can become effec-tively quasi-isotropic.Specifically, we see that when the precession period is around10 Myr, the jet becomes more effective only after the precessionangle reaches (cid:38) ◦ (’Kin6e43-pr45-t p ◦ precession (’Kin6e43-pr30-t p ◦ . Consistently, as shown in Fig. 16, ’Kin6e43- P [ K c m − ] B for ˙ E kin =6e42 MassMagneticThermalCR Radius [kpc] P [ K c m − ] B for ˙ E CR =6e43 Mass Vol B tor tor tor pol pol pol Radius [kpc]
Vol
CR6e43-B4CR6e43
Figure 12.
The volume and mass-weighted thermal (thin dashed), magnetic(thick solid) and CR (thin dotted if applicable) pressure profiles for runswith different jet magnetic field variations. The magnetic pressure can onlybe comparable to the thermal pressure in the 10-30 kpc range and then, onlyin dense cool gas, given that the volume-weighted values are much lowerthan the mass-weighted ones. At radius (cid:38) kpc (where jet effects areweak), or wherever the B-fields are a large fraction of the total pressure(i.e., appear to have saturated), | ¯ B | is weakly sensitive to the injected fields. pr30-t p p
10’ in the core region.A non-precessing wide jet (‘Kin6e43-w15’, ‘Kin6e43-w30’,and ‘Kin6e43-w45’) can be viewed as a high-speed precessing jet,since the spawned cells are sampling the opening-angle, with aneffective period (cid:28)
Myr. Consistent with the cocoon behaviour dis-cussed above, although the SFR starts to drop when the opening-angle reaches 45 ◦ , ‘Kin6e43-w45’ has a higher SFR and strongercooling flows than the precessing jet with ◦ precession angle.Therefore, an opening-angle between ◦ and isotropic should berequired to reach a similar level of quenching effect.We also see a factor of (cid:46) boost in the turbulent velocity at ∼ ◦ . So precessing jets can stir someturbulence, but this, by itself is nowhere near the level of turbulencerequired to quench (see Paper II ).The reason for these “second order” trends is that, all elseequal, a more slowly precessing jet can more efficiently expand to asufficiently large radius. Since it stays in each direction for a longertime, it ‘clears out’ a path before moving to another direction. II In Paper II (Su et al. 2020), we considered the same ICs, with AGNtoy models using 4 different mechanisms: CR injection, thermalheating, radial momentum injection, and turbulent stirring with var-ied ˙ E and radial distribution of the injection (i.e., these did not fol-low any physical propagation model). The CR-dominated jets hereproduce broadly similar results to the simpler CR-injection runs MNRAS000
Myr. Consistent with the cocoon behaviour dis-cussed above, although the SFR starts to drop when the opening-angle reaches 45 ◦ , ‘Kin6e43-w45’ has a higher SFR and strongercooling flows than the precessing jet with ◦ precession angle.Therefore, an opening-angle between ◦ and isotropic should berequired to reach a similar level of quenching effect.We also see a factor of (cid:46) boost in the turbulent velocity at ∼ ◦ . So precessing jets can stir someturbulence, but this, by itself is nowhere near the level of turbulencerequired to quench (see Paper II ).The reason for these “second order” trends is that, all elseequal, a more slowly precessing jet can more efficiently expand to asufficiently large radius. Since it stays in each direction for a longertime, it ‘clears out’ a path before moving to another direction. II In Paper II (Su et al. 2020), we considered the same ICs, with AGNtoy models using 4 different mechanisms: CR injection, thermalheating, radial momentum injection, and turbulent stirring with var-ied ˙ E and radial distribution of the injection (i.e., these did not fol-low any physical propagation model). The CR-dominated jets hereproduce broadly similar results to the simpler CR-injection runs MNRAS000 , 1–27 (2021) Figure 13.
The magnetic pressure morphology shown in a δy = 10 kpc slice of the runs with the same kinetic jet, × erg s − , but with different jetmagnetic fields. Beyond ∼ kpc, the magnetic pressure is high only close to the z-axis, where the gas is directly affected by the jet. With similar initialmagnetic field strengths, a jet with initially toroidal magnetic fields is able to maintain larger magnetic field strengths further along the jet axis, compared to ajet with poloidal magnetic fields. in Paper II , as the CR-dominated cocoon becomes quasi-isotropicand dominates the dynamics. The thermal jets here are qualitativelydifferent from the thermal heating runs in Paper II : here, extremelyhot, low-density, slow-cooling plasma is injected, which inflates aquasi-isotropic cocoon providing pressure and bouyancy supportto halt/reverse inflows inside R cool . In Paper II , the “thermal heat-ing” was applied as a direct heating term to the pre-existing gas inthe galaxy or halo: this requires far more energy to offset cooling“directly” (since it requires re-heating dense cool-phase gas wherecooling is rapid) and is far more unstable, as either the appliedheating is less than cooling (in which case the gas still cools) oris greater than cooling (in which case a Sedov-Taylor-type explo-sion immediately results in “overheating”). The kinetic jet modelshere are also distinct from, although in some ways in-between, themomentum-injection and turbulent-stirring runs from Paper II . Ourwidest-angle kinetic jets are somewhat akin to the isotropic radialmomentum injection runs in Paper II , but less explosive owing tothe cocoon dynamics that occur here (and not in Paper II owingto the isotropy and effectively large mass-loading of the coupling).None of our models here produces turbulent power approachingthe level identified in Paper II as required for quenching from “pureturbulence” effects. We place our results in context through several comparisons as fol-lows (although there is too much previous work to make the com-parison comprehensive):The fiducial model in Li & Bryan (2014b,a) has the energyflux equally distributed between thermal and kinetic energy. Theyalso tested various jet models with a varied balance between kinetic and thermal energy and different efficiencies. They found, like us,that feedback stronger than the favored value causes overheatingin the core region. They also found that with a pure kinetic model,the cocoons are narrower and less pressurized. However, they sug-gested that the exact kinetic fraction versus thermal fraction doesnot significantly alter galaxy evolution, while we found that ther-mal jets are more effective in quenching. This likely owes to thefact that they do not fix the jet energies: in their runs, when a spe-cific jet model is not as efficient in quenching at the same energyflux, the accretion rate and energy flux rise to compensate. Kineticjets are also shown to be able to quench the galaxy, reach self-regulation, and maintain the cool-core properties across a range ofhalo mass in Gaspari et al. (2011a,b, 2012a,b). This probably oc-curs for the same reason discussed above, and also the frequentlyhigher jet velocity in their model.In Bourne & Sijacki (2017), the authors discussed the CGMturbulence caused by kinetic jets and compared with the CGM tur-bulence caused by substructures. The authors found that the jetis mostly responsible for the smaller scale turbulence around itsedges, but not as effective in inducing larger-scale turbulence. Wefind a qualitatively similar result that even our most widely precess-ing jets boost the turbulence at a large radius at most by a factor of2, insufficient to quench on its own (Paper II ).Cosmic ray jets have been studied by Wang et al. (2020) (in a × M (cid:12) halo) and Ruszkowski et al. (2017b) and Yang et al.(2019) in a more massive Perseus-mass cluster. The cosmic ray en-ergy flux we find to stably quench a M (cid:12) halo ( ∼ × - ∼ × ergs − ) in this work is roughly consistent with theenergy range suggested in Wang et al. (2020), given their slightlyless massive system. Also consistent with Yang et al. (2019), wefind that a cosmic ray dominated jet is generally more efficient at MNRAS , 1–27 (2021) hat Types of Jet Quench? Figure 14.
Entropy and radial velocity morphology for runs with different mass fluxes while keeping the same energy flux, shown in a δy = 10 kpc slice.With the same thermal or CR energy flux of × erg s − , a run with lower mass flux but higher energy per unit mass results in a wider jet cocoon. Thesituation is not as evident in the cases with lower energy thermal jets or kinetic jets. quenching and results in a wider bubble compared to a kinetic jet.Like Ruszkowski et al. (2017b), we find that CR pressure plays akey role regulating the cooling flows, and that including CR mo-tion relative to the gas is the key. Otherwise, if CRs were purelyadvected, they would behave explosively like thermal energy. Notethat we parametrized the CR motion relative to the gas as diffusion,but within our approximations, this is mathematically identical totheir super-Alfv´en streaming. To further constrain the models here, a more detailed analysis of X-ray properties and further comparisons with the multi-phase obser-vations will be required. We leave this for future work, but brieflycomment on directions we think would be fruitful. Although var-ious models in this work are broadly consistent with the X-rayinferred radially averaged density, temperature, and entropy pro-files, the detailed spatial distribution of these properties may vary,especially between the region closer to and further from the jetaxis. These can be further constrained by more extensive X-raymap comparisons. Likewise mapping the kinetic properties (in-
MNRAS000
MNRAS000 , 1–27 (2021) Figure 15.
The radial velocity field for thermal jet runs with the same time-averaged energy flux × erg s − within a δy = 10 kpc slice, but withdifferent duty cycles (continuous, versus “on” for ∼ of the time with a period of 10 Myr or 100 Myr, as labeled). The results are shown at the end of eachsimulation. The run with a 10 Myr period looks effectively similar to the continuous run. Both of them eventually shut down the inflows at the core regionof the galaxy completely. The run with a 100 Myr period has concentric shells of inflows and outflows, showing the previous cycles. The inflows at the coreregion rebuild again when the jet is off. Figure 16.
The entropy and radial velocity morphology for runs with different jet opening-angles, precession periods, and precession angles, shown in a δy = 10 kpc slice. The runs with a wider opening-angle and/or more extended precession (‘Kin6e43-pr30-t p ’, ‘Kin6e43-pr45-t p ’, ‘Kin6e43-pr45-t p ’, and ‘Kin6e43-w45’) have a slightly wider solid angle for outflowing material at the core region of the galaxy, consistent with their lower cooling flowsand SFR. MNRAS , 1–27 (2021) hat Types of Jet Quench? − M ac h N u m b e r (T > K)10 Radius [kpc] V e l o c it y [ k m s − ] (T > K) Kin6e43Kin6e43-w15Kin6e43-w30Kin6e43-w45
Kin6e43Kin6e43-pr15-t p p p Radius [kpc]
Kin6e43-pr30-t p p Figure 17.
As Fig. 5, 1D rms Mach number ( v θ,φ turb / √ v thermal ; top), anddispersion ( v θ,φ turb / √ ; below) in gas with T > K, averaged over thelast 50 Myr of the runs, as a function of radius for the runs with differentwidths, precession periods and precession angles from Fig. 16. Jet mod-els with a long precession period and a sufficiently wide precession anglecan slightly boost the turbulent velocity at 10-70 kpc by a factor of (cid:46) ,indicating more efficient turbulent “stirring”. flow/outflow and turbulent velocities vs. polar angle) near the jetcan further constrain the models. Given that the gas properties atvery large radii are dominated by the initial conditions in isolatedgalaxy simulations, thermal and kinetic Sunyaev–Zeldovich (Sun-yaev & Zeldovich 1970) properties might not be as sensitive to thejet model. As shown in Fig. 11, the thermal properties of lower tem-perature gas can differ within ∼ kpc between runs with cosmic-ray and thermal jets of different energy flux. These will predict dif-ferent column densities of various ions in different phases.We have verified that, in our CR jets, the predicted ∼ GeVgamma-ray luminosity from hadronic interactions is below the cur-rent observational upper limits (Ackermann et al. 2016; Wiener& Zweibel 2019). ‘CR6e43’ and ‘CR6e43-B4-m2e-1’ have L γ ∼ − × erg s − . In ‘CR6e42’ L γ grows from ∼ erg s − to ∼ − × erg s − , roughly at the upper limit. The values inthe latter case are higher due to the denser core that develops. Like-wise, the estimated ∼ GHz radio luminosity from secondary CRelectrons is well within the observational constraint from the radioflux assuming all the secondary CR electrons decay via synchrotronemission (e.g., Giacintucci et al. 2014; Bravi et al. 2016). Tomake more detailed predictions for radio emission, explicitly mod-eling the cosmic ray electrons will be required. The gamma-ray energy flux per volume is roughly ˙ e γ ∼ / ∗ Λ had e CR n , where Λ had ∼ . × − s − is the hadronic couplingcoefficient, e CR is the CR energy density, and n is the number density.The radio flux per volume in GHz from secondary electrons is roughly ˙ e radio ∼ f GHz (2 / / / had e CR n , where f GHz ∼ . is thefraction of energy flux in the GHz band. We emphasize that we are, by design, testing jet models with con-stant flux in a fixed initial cluster configuration. Our model doesnot include dynamically-variable black hole accretion, so is not“self-regulating”. Although we explore the effect of duty cycles,we expect a self-consistently fueled jet will have a more compli-cated duty cycle. With these limitations in mind, the less dramatic“overheated” models we considered (like ‘Th6e43-B4-m2e-1’ or‘Kin-6e43-iso’) may be allowed if the jet only lasts for a shorterduration. The most overheated models like ‘Kin6e44’ or ‘Th6e44’,on the other hand, may still result in tension with observations evenif the jet is on only for a short time episodically, like what we seein our duty cycle test ‘Th6e44-B4-t d In this paper, we have attempted a systematic exploration of differ-ent AGN jet models that inject energy into massive halos, quench-ing galaxies and suppressing cooling flows. We specifically con-sidered models with pure kinetic jets, thermal energy dominatedjets, and cosmic ray jets. We also systematically varied the massloading, jet width, jet magnetic field strength and field geometry,precession angle and period, and jet duty cycle. These were stud-ied in full-halo-scale but non-cosmological simulations includingradiative heating and cooling, self-gravity, star formation, and stel-lar feedback from supernovae, stellar mass-loss, and radiation, en-abling a truly “live” response of star formation and the multi-phaseISM to cooling flows. We used a hierarchical super-Lagrangian re-finement scheme to reach ∼ M (cid:12) mass resolution, much higherthan many previous global studies.We summarize our key results in the following points and inTable 3: • All our successful models quench via the (initially narrow) jetinflating a quasi-isotropic (large solid-angle at r (cid:46) R cool ) cocoonin which pressure (ram or thermal or CR) is able to balance gravityand “loft” and heat gas within most of the solid angle inside R cool .Narrow-angle cocoons fail to quench regardless of energetics, asinflow continues near the midplane. We stress that the mode withwhich the jet delivers energy is important and it is not enough tosimply directly dump in thermal energy or induce turbulent dissi-pation to offset cooling. The qualitative behaviors of these cocoonsin our kinetic+thermal+magnetic+CR runs are well-described bysimple similarity solutions (§ 4 & § 4.4). • This implies three necessary criteria for jet quenching, whichwe find are sufficient to identify all our quenched runs. (1)
Amean energy input rate sufficient to reverse the cooling flowdynamics (sustain pressure that balances gravity), (cid:104) ˙ E tot , J (cid:105) (cid:38) × erg s − ( ˙ M cool /
100 M (cid:12) yr − ) ( v c [ R cool ] /
500 km s − ) . (2) A specific energy of jet material large enough that the direct
MNRAS000
MNRAS000 , 1–27 (2021) Table 3.
Executive summary of our experiments with different jet models in a M (cid:12) haloForm Variations ˙ E q at (cid:12) yr − Other Criteria Higher ˙ E/ ˙ m ProblemKinetic non-precessing, narrow none needs broader cocoon wider cocoon inefficientnon-precessing wide ∼ θ op (cid:29) ◦ not tested extended heated coreprecessing narrow ∼ θ p (cid:38) ◦ if t p ∼
10 Myr not tested extremely large precession θ p (cid:38) ◦ if t p ∼
100 MyrThermal constant ˙ E ∼ T jet material (cid:38) K wider cocoon narrow ˙ E range10% duty cycle (cid:104) ˙ E ( t ) (cid:105) = t d (cid:38) Myr not tested dT/dr < when “on”Cosmic ray constant ˙ E ∼ B ini none none quenches wider cocoon inefficient by itselfThis is a summary of all the parameter space we explore. Each column is as follow: (1) “Form”: The dominant energy form in the jet at launch. (2)“Variations”: Qualitative model variations we considered. (3) ˙ E q at (cid:12) yr − : The required energy flux to stably quench the galaxy (for our default IC)when the mass flux is (cid:12) yr − . (4) “Other criteria”: Additional requirements for this model group to stably quench. θ op : opening-angle. θ p : precessingangle. (5) Higher ˙ E/ ˙ m : Effect of increased specific energy in the jet. (6) “Problems”: Physical problems or major inconsistencies with observations commonto all runs in a given “group”. (for thermal/CR) or post-shock (for kinetic) cocoon coolingtime is always much longer than the cocoon expansion time, ˙ E tot , J / ˙ M J (cid:38) erg g − (e.g. T > K, for thermal jets, or v (cid:38) − for kinetic). (3) A means to ensure the cocooncan expand to fill broad solid angles (so effectively suppressinflows) before the jet breaks through ∼ R cool . This can beaccomplished by either (a) the jet having a dominant fraction ofits injection energy in non-kinetic (thermal, CR, or magnetic) form(with the relevant solid angle scaling as ( ˙ E tot , jet / ˙ E kin , J ) / ); (b) an extremely “light” kinetic jet having a high specific-energy at ∼ pc (our coupling radius), with jet velocity at this radius (cid:38) ( ˙ M J / M (cid:12) yr − )( v ff /
300 km s − )( ˙ M cool /
100 M (cid:12) yr − ) − ;or (c) a large kinetic jet opening or precession angle. • For thermal+kinetic+magnetic jets (provided the above con-ditions are met), the criterion for this quenching to become “ex-plosive” is a larger mean (cid:104) ˙ E tot (cid:105) by only a factor ∼ or so. Be-yond this energy flux, the jet violently expels the inner halo gas,leaving a remnant which is too hot and has an inverted tempera-ture/entropy gradient compared to observations. Modifying preces-sion or opening-angles or duty cycles can shift the “preferred” ener-gies slightly but does not appreciably widen this range. Thus thereis a rather narrow range of energetics where such jets quench with-out violating observations. But it remains possible that jets “self-regulate” to this range in models where accretion and jet powerscale self-consistently with nuclear gas properties. • For CR-dominated jets, the fact that CRs can diffuse or streamthrough the gas provides a sort of “pressure valve,” making the in-duced outflows less “overheated” at high energies. At lower ener-gies, the combination of efficient CR diffusion isotropizing the CRcocoon, efficient CR pressure support of cool gas, and the modifiednature of thermal instability in a CR-pressure dominated mediumallows CR jets to quench at order-of-magnitude lower energetics.Together this means the allowed dynamic range of energetics forCR-dominated jets is much larger (factor ∼ ). Moreover, thelower-energy CR jets are the only successfully quenched modelshere which do not strongly alter the core density and thereforeretain observed cool-core features and lower turbulent velocities (cid:46)
100 km s − .In summary, our study supports the idea that quenching – atleast of observed z ∼ massive halos – can be accomplishedwithin the viable parameter space of AGN jets. But with this studyand Paper II , we show the viable parameter space which producessuccessful quenching and does not violate observational constraints is rather narrow, and points to specific jet/cocoon processes andquite possibly a role for CRs. Many caveats remain (see § 5.4) toexplore in future work, alongside more detailed comparisons withobservations (§ 5.3). ACKNOWLEDGEMENTS
We thank Eliot Quataert for useful discussion. KS acknowl-edges financial support from the Simons Foundation. Support forPFH and co-authors was provided by an Alfred P. Sloan ResearchFellowship, NSF Collaborative Research Grant
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APPENDIX A: DENSITY AND ENTROPY PROFILES FORALL RUNS
In Fig. A1 and Fig. A2 we provide the density and luminosity-weighted entropy profiles of all our runs averaged over the last ∼ Myr. The runs labeled ‘overheated’ in Table 2 generally havevery low density, high entropy core regions within ∼ Myr. Theruns labeled ‘strong CF’ or ‘slight ↓ ’ in Table 2 generally have anover-dense core region. The other runs agree more reasonably withthe observations. APPENDIX B: THERMAL STABILITY FOR CR JETSWITH DIFFERENT FLUX
CRs stabilize the gas more effectively in the runs with lower CR en-ergy injection. The reason is due to the balance between CR energy
MNRAS , 1–27 (2021) hat Types of Jet Quench? − − − D e n s it y [ c m − ] (CC)(non-CC) Kinetic
NoJetKin6e42Kin6e43Kin6e4410 − − − D e n s it y [ c m − ] B for ˙ E kin =6e42 B0B tor tor tor pol pol pol − − − D e n s it y [ c m − ] Mass loading (kinetic)
Kin6e42Kin6e42-B4-m2e-2Kin6e43Kin6e43-B4-m2e-1Kin6e44-B4 Radius [kpc] − − − D e n s it y [ c m − ] Duty cycle (thermal)
Th6e43-B4-m2e-1Th6e44-B4-t d d Thermal
NoJetKin6e42Th6e42Th6e43Th6e44 B for ˙ E =6e43 Th6e43-B4Th6e43CR6e43-B4CR6e43
Mass loading (thermal)
Th6e43-B4Th6e43-B4-m2e-1Th6e42Th6e42-B4-m2e-1Th6e42-B4-m2e-2 Radius [kpc]
Jet width (Kinetic)
Kin6e43Kin6e43-w15Kin6e43-w30Kin6e43-w45Kin6e43-wiso CR NoJetCR6e42CR6e43CR6e44-B4 B for ˙ E =6e44 Kin6e44-B4Kin6e44Th6e44-B4Th6e44
Mass loading (CR)
CR6e43-B4CR6e43-B4-m2e-110 Radius [kpc]
Jet precession (Kinetic)
Kin6e43Kin6e43-pr15-t p p p p p Figure A1.
Density versus radius averaged over the last ∼ Myr in the all runs from Fig. 1. The shaded regions indicate the observational density profiles(scaled) for cool-core (blue) and non-cool-core (red) clusters (McDonald et al. 2013), scaled according to the halo mass differences. Runs labeled ‘overheated’in Table 2 generally have very low density core regions. Runs labeled ‘strong CF’ or ‘slight ↓ ’ in Table 2 generally have an over-dense core region. The otherruns agree reasonably well with the observations. and thermal energy, f CR = P CR /P thermal . The gas will only fol-low an isochoric and constant thermal+CR pressure process whenCRs are the dominant energy form (high f CR ).The first row of Fig. B1 shows such a ratio of the two cosmicray injection runs at the beginning (100 Myr) and end (1.5Gyr) ofthe simulations. In ‘CR6e42’, initially, the ratio, f CR , for the gasthat is cooling (the blue square region in Fig. B1) is not sufficientlyhigh, so the density in that phase shows a broader distribution re-sembling that in the ‘Th6e42’ run. After the CR energy builds up asthe energy injection continues and f CR increases, the density dis-tribution becomes narrow. On the other hand, in the higher CR flux run, ‘CR6e43’, initially, the ratio f CR is slightly higher than the‘CR6e42’ run. However, at a later time, the CR energy of the gaswith density n > − cm − does not increase much due to gasexpansion (because of the suppressed density) and the advectionof CR rich gas. Instead, the CR energy goes into the lower densityphase at larger radii (the red square region in Fig. B1). MNRAS000
Density versus radius averaged over the last ∼ Myr in the all runs from Fig. 1. The shaded regions indicate the observational density profiles(scaled) for cool-core (blue) and non-cool-core (red) clusters (McDonald et al. 2013), scaled according to the halo mass differences. Runs labeled ‘overheated’in Table 2 generally have very low density core regions. Runs labeled ‘strong CF’ or ‘slight ↓ ’ in Table 2 generally have an over-dense core region. The otherruns agree reasonably well with the observations. and thermal energy, f CR = P CR /P thermal . The gas will only fol-low an isochoric and constant thermal+CR pressure process whenCRs are the dominant energy form (high f CR ).The first row of Fig. B1 shows such a ratio of the two cosmicray injection runs at the beginning (100 Myr) and end (1.5Gyr) ofthe simulations. In ‘CR6e42’, initially, the ratio, f CR , for the gasthat is cooling (the blue square region in Fig. B1) is not sufficientlyhigh, so the density in that phase shows a broader distribution re-sembling that in the ‘Th6e42’ run. After the CR energy builds up asthe energy injection continues and f CR increases, the density dis-tribution becomes narrow. On the other hand, in the higher CR flux run, ‘CR6e43’, initially, the ratio f CR is slightly higher than the‘CR6e42’ run. However, at a later time, the CR energy of the gaswith density n > − cm − does not increase much due to gasexpansion (because of the suppressed density) and the advectionof CR rich gas. Instead, the CR energy goes into the lower densityphase at larger radii (the red square region in Fig. B1). MNRAS000 , 1–27 (2021) Figure A2.
Luminosity-weighted entropy versus radius averaged over the last ∼ Myr in the non-overheated quiescent runs from Fig. 1. The light curvesin the bottom row indicate the observational entropy profiles (scaled) for cool-core (blue) and non-cool-core (red) clusters (McDonald et al. 2013) (scaledaccording to the halo mass differences). Runs labeled ‘overheated’ in Table 2 generally have very high entropy in the core regions. The other runs have entropyprofiles resembling the observed cool-core populations. MNRAS , 1–27 (2021) hat Types of Jet Quench? Figure B1.
The distribution of P CR /P thermal as a function of gas density (top), and the phase distribution in the temperature-density plane (bottom) for the‘CR6e42’ and ‘CR6e43’ runs at 100 Myr and 1.5 Gyr, for the gas above K and from 10-30 kpc. At 1.5 Gyr, the run with a lower CR flux jet (‘CR6e42’)reaches a higher P CR /P thermal than the run with higher CR flux (‘CR6e43’) for the gas that is cooling (the region outlined with a blue dotted line in theplot). The latter run has more cosmic rays distributed to the lower density phase at a larger radius (the red region in the plot). Only when P CR /P thermal builds up to a sufficiently high value does the density distribution tighten.MNRAS000