Heating & cooling cycles in cool cluster coresprateek/icm16_min.pdfPrateek Sharma (IISc) Collaborators: Deovrat Prasad, Arif Babul COOL CORE CYCLES: COLD GAS AND AGN JET FEEDBACK IN

Heating & cooling cycles in cool cluster cores

Prateek Sharma (IISc) Collaborators: Deovrat Prasad, Arif Babul

COOL CORE CYCLES: COLD GAS AND AGN JET FEEDBACK IN CLUSTER CORES

Deovrat Prasad1, Prateek Sharma1, and Arif Babul21 Joint Astronomy Program and Department of Physics, Indian Institute of Science, Bangalore, 560012, India;

[email protected], [email protected] Department of Physics and Astronomy, University of Victoria, Victoria, BC V8P 1A1, Canada; [email protected]

Received 2015 April 12; accepted 2015 July 28; published 2015 September 28

ABSTRACT

Using high-resolution 3D and 2D (axisymmetric) hydrodynamic simulations in spherical geometry, we study theevolution of cool cluster cores heated by feedback-driven bipolar active galactic nuclei (AGNs) jets. Condensationof cold gas, and the consequent enhanced accretion, is required for AGN feedback to balance radiative coolingwith reasonable efficiencies, and to match the observed cool core properties. A feedback efficiency (mechanicalluminosity M c ;acc

2˙�» where Macc˙ is the mass accretion rate at 1 kpc) as small as 6 × 10−5 is sufficient to reducethe cooling/accretion rate by ∼10 compared to a pure cooling flow in clusters (with M 7 10200

141 ´ M:). Thisvalue is much smaller compared to the ones considered earlier, and is consistent with the jet efficiency and the factthat only a small fraction of gas at 1 kpc is accreted onto the supermassive black hole (SMBH). The feedbackefficiency in earlier works was so high that the cluster core reached equilibrium in a hot state without muchprecipitation, unlike what is observed in cool-core clusters. We find hysteresis cycles in all our simulations withcold mode feedback: condensation of cold gas when the ratio of the cooling-time to the free-fall time (t tcool ff) is10 leads to a sudden enhancement in the accretion rate; a large accretion rate causes strong jets and overheatingof the hot intracluster medium such that t t 10;cool ff > further condensation of cold gas is suppressed and theaccretion rate falls, leading to slow cooling of the core and condensation of cold gas, restarting the cycle.Therefore, there is a spread in core properties, such as the jet power, accretion rate, for the same value of coreentropy or t tcool ff . A smaller number of cycles is observed for higher efficiencies and for lower mass halos becausethe core is overheated to a longer cooling time. The 3D simulations show the formation of a few-kpc scale,rotationally supported, massive ( M1011~ :) cold gas torus. Since the torus gas is not accreted onto the SMBH, it islargely decoupled from the feedback cycle. The radially dominant cold gas (T < 5 × 104 K; v vr∣ ∣ ∣ ∣> f ) consists offast cold gas uplifted by AGN jets and freely infalling cold gas condensing out of the core. The radially dominantcold gas extends out to 25 kpc for the fiducial run (halo mass M7 1014´ : and feedback efficiency 6 × 10−5), withthe average mass inflow rate dominating the outflow rate by a factor of ≈2. We compare our simulation resultswith recent observations.

Key words: galaxies: clusters: intracluster medium – galaxies: halos – galaxies: jets

1. INTRODUCTION

The majority of baryons in galaxy clusters are in the form ofa hot plasma known as the intracluster medium (ICM). In theabsence of cooling and heating, the ICM is expected to followself-similar profiles for density, temperature, etc., irrespectiveof the halo mass (Kaiser 1986, 1991; see also the review byVoit 2005). However, self-similarity is not observed in eithergroups or clusters (e.g., Balogh et al. 1999; Ponman et al. 1999;Babul et al. 2002). Moreover, the core cooling times in about athird of clusters are shorter than 1 Gyr, much shorter than theirage (∼Hubble time; e.g., Cavagnolo et al. 2009; Prattet al. 2009). Thus, we expect cooling to shape the distributionof baryons in these cool-core clusters.

The existence of cool cores with short cooling times in agood fraction of galaxy clusters is a long-standing puzzle.According to the classical cooling flow model, cluster coreswith such short cooling times were expected to coolcatastrophically and to fuel star formation at a rate of100–1000 M: yr−1 (e.g., Fabian 1994; Lewis et al. 2000).However, cooling, dropout, and star formation at these highrates are never seen in cluster cores (e.g., Edge 2001; Petersonet al. 2003; O’Dea et al. 2008). This means that some source(s)of heating is(are) able to replenish the core cooling losses,thereby preventing runaway cooling and star formation.

While there are potential heat sources, such as the kineticenergy of infalling galaxies and sub-halos (e.g., Dekel &Birnboim 2008), thermal conduction from the hotter outskirts(e.g., Voigt & Fabian 2004; Voit 2011), a globally stablemechanism, which increases rapidly with an increasing hot gasdensity in the core, is required to prevent catastrophic cooling.Observations of several cool-core clusters by Chandra andXMM-Newton have uncovered active galactic nucleus (AGN)-jet-driven X-ray cavities, whose mechanical power is enough tobalance radiative cooling in the core (e.g., Böhringeret al. 2002; Bîrzan et al. 2004; McNamara & Nulsen 2007).The AGN jets are powered by the accretion of the cooling ICMonto the supermassive black hole (SMBH) at the center of thedominant cluster galaxy. Thus, more cooling/accretion leads toan enhanced jet power and ICM heating, closing a feedbackloop that prevents runaway cooling in the core.AGN feedback has been long-suspected to play a role in self-

regulating the ICM (e.g., Binney & Tabor 1995; Ciotti &Ostriker 2001; Soker et al. 2001; Babul et al. 2002; McCarthyet al. 2008), but a clear picture has emerged only recently.While AGN feedback should provide feedback heating incluster cores (as it is enhanced with ICM cooling), it is notobvious if, for reasonable parameters, AGN heating can keeppace with cooling that increases rapidly with an increasing coredensity. Moreover, the dense core gas is expected to be highly

The Astrophysical Journal, 811:108 (21pp), 2015 October 1 doi:10.1088/0004-637X/811/2/108© 2015. The American Astronomical Society. All rights reserved.

1

COOL CORE CYCLES: COLD GAS AND AGN JET FEEDBACK IN CLUSTER CORES

Deovrat Prasad1, Prateek Sharma1, and Arif Babul21 Joint Astronomy Program and Department of Physics, Indian Institute of Science, Bangalore, 560012, India;

[email protected], [email protected] Department of Physics and Astronomy, University of Victoria, Victoria, BC V8P 1A1, Canada; [email protected]

Received 2015 April 12; accepted 2015 July 28; published 2015 September 28

ABSTRACT

Using high-resolution 3D and 2D (axisymmetric) hydrodynamic simulations in spherical geometry, we study theevolution of cool cluster cores heated by feedback-driven bipolar active galactic nuclei (AGNs) jets. Condensationof cold gas, and the consequent enhanced accretion, is required for AGN feedback to balance radiative coolingwith reasonable efficiencies, and to match the observed cool core properties. A feedback efficiency (mechanicalluminosity M c ;acc

2˙�» where Macc˙ is the mass accretion rate at 1 kpc) as small as 6 × 10−5 is sufficient to reducethe cooling/accretion rate by ∼10 compared to a pure cooling flow in clusters (with M 7 10200

141 ´ M:). Thisvalue is much smaller compared to the ones considered earlier, and is consistent with the jet efficiency and the factthat only a small fraction of gas at 1 kpc is accreted onto the supermassive black hole (SMBH). The feedbackefficiency in earlier works was so high that the cluster core reached equilibrium in a hot state without muchprecipitation, unlike what is observed in cool-core clusters. We find hysteresis cycles in all our simulations withcold mode feedback: condensation of cold gas when the ratio of the cooling-time to the free-fall time (t tcool ff) is10 leads to a sudden enhancement in the accretion rate; a large accretion rate causes strong jets and overheatingof the hot intracluster medium such that t t 10;cool ff > further condensation of cold gas is suppressed and theaccretion rate falls, leading to slow cooling of the core and condensation of cold gas, restarting the cycle.Therefore, there is a spread in core properties, such as the jet power, accretion rate, for the same value of coreentropy or t tcool ff . A smaller number of cycles is observed for higher efficiencies and for lower mass halos becausethe core is overheated to a longer cooling time. The 3D simulations show the formation of a few-kpc scale,rotationally supported, massive ( M1011~ :) cold gas torus. Since the torus gas is not accreted onto the SMBH, it islargely decoupled from the feedback cycle. The radially dominant cold gas (T < 5 × 104 K; v vr∣ ∣ ∣ ∣> f ) consists offast cold gas uplifted by AGN jets and freely infalling cold gas condensing out of the core. The radially dominantcold gas extends out to 25 kpc for the fiducial run (halo mass M7 1014´ : and feedback efficiency 6 × 10−5), withthe average mass inflow rate dominating the outflow rate by a factor of ≈2. We compare our simulation resultswith recent observations.

Key words: galaxies: clusters: intracluster medium – galaxies: halos – galaxies: jets

1. INTRODUCTION

The majority of baryons in galaxy clusters are in the form ofa hot plasma known as the intracluster medium (ICM). In theabsence of cooling and heating, the ICM is expected to followself-similar profiles for density, temperature, etc., irrespectiveof the halo mass (Kaiser 1986, 1991; see also the review byVoit 2005). However, self-similarity is not observed in eithergroups or clusters (e.g., Balogh et al. 1999; Ponman et al. 1999;Babul et al. 2002). Moreover, the core cooling times in about athird of clusters are shorter than 1 Gyr, much shorter than theirage (∼Hubble time; e.g., Cavagnolo et al. 2009; Prattet al. 2009). Thus, we expect cooling to shape the distributionof baryons in these cool-core clusters.

The existence of cool cores with short cooling times in agood fraction of galaxy clusters is a long-standing puzzle.According to the classical cooling flow model, cluster coreswith such short cooling times were expected to coolcatastrophically and to fuel star formation at a rate of100–1000 M: yr−1 (e.g., Fabian 1994; Lewis et al. 2000).However, cooling, dropout, and star formation at these highrates are never seen in cluster cores (e.g., Edge 2001; Petersonet al. 2003; O’Dea et al. 2008). This means that some source(s)of heating is(are) able to replenish the core cooling losses,thereby preventing runaway cooling and star formation.

While there are potential heat sources, such as the kineticenergy of infalling galaxies and sub-halos (e.g., Dekel &Birnboim 2008), thermal conduction from the hotter outskirts(e.g., Voigt & Fabian 2004; Voit 2011), a globally stablemechanism, which increases rapidly with an increasing hot gasdensity in the core, is required to prevent catastrophic cooling.Observations of several cool-core clusters by Chandra andXMM-Newton have uncovered active galactic nucleus (AGN)-jet-driven X-ray cavities, whose mechanical power is enough tobalance radiative cooling in the core (e.g., Böhringeret al. 2002; Bîrzan et al. 2004; McNamara & Nulsen 2007).The AGN jets are powered by the accretion of the cooling ICMonto the supermassive black hole (SMBH) at the center of thedominant cluster galaxy. Thus, more cooling/accretion leads toan enhanced jet power and ICM heating, closing a feedbackloop that prevents runaway cooling in the core.AGN feedback has been long-suspected to play a role in self-

regulating the ICM (e.g., Binney & Tabor 1995; Ciotti &Ostriker 2001; Soker et al. 2001; Babul et al. 2002; McCarthyet al. 2008), but a clear picture has emerged only recently.While AGN feedback should provide feedback heating incluster cores (as it is enhanced with ICM cooling), it is notobvious if, for reasonable parameters, AGN heating can keeppace with cooling that increases rapidly with an increasing coredensity. Moreover, the dense core gas is expected to be highly

The Astrophysical Journal, 811:108 (21pp), 2015 October 1 doi:10.1088/0004-637X/811/2/108© 2015. The American Astronomical Society. All rights reserved.

1

Cold gas condensation• allows feedback to act sufficiently fast, unlike Bondi

• tcool/tff~threshold around 10 seems robust (at least in sims)

• cooling & heating cycles

• push ε to smallest allowed by observations

• cold gas inflows & outflows

• angular momentum: stochastic cold accretion

AGN jet-ICM sims.@⇢

@t+r · ⇢v = S⇢

⇢

✓@v

@t+ v ·rv

◆= �rp� ⇢r�+ S⇢vjetr

p

� � 1

d

dtln(p/⇢�) = �n2⇤

mass

momentum

source terms to mimic injection by feedback AGN jets

AGN jet-ICM sims.@⇢

@t+r · ⇢v = S⇢

⇢

✓@v

@t+ v ·rv

◆= �rp� ⇢r�+ S⇢vjetr

p

� � 1

d

dtln(p/⇢�) = �n2⇤

mass

momentum

source term applied in a small bipolar cone at the center:

opening angle of 300, size 2 kpc

vjet=0.1c, ε=6x10-5, rin,out=1, 200 kpc

robust to variations

M1.8 10 ,15´ : respectively, and adopt c 4.7200 = for allmodels.

We include the source terms Sρ for mass and rS vjet ˆr for theradial momentum to drive AGN jets (vjet is the velocity whichthe jet matter is put in).3 These source terms and the coolingterm (in Equation (3)) are applied in an operator-split fashion.The mass and momentum source terms are approximatedforward in time and centered in space. The cooling term isapplied using a semi-implicit method described in Equations(7) of McCourt et al. (2012).

Our simulations do not include physical processes like starformation and supernova feedback. Star formation may depletesome of the cold gas available in the cores (see Li et al. 2015),but this is unlikely to change our results for a realistic model ofstar formation. Supernova feedback is energetically subdomi-nant compared to AGN feedback, and cannot realisticallysuppress cluster cooling flows (e.g., Saro et al. 2006). We onlyinclude the most relevant physical processes, namely coolingand AGN jet feedback, in our present simulations.

2.1. Jet Implementation

Jets are implemented in the active domain by adding massand momentum source terms as shown in Equations (1) and(2). The source terms are negligible outside a small biconicalregion centered at the origin around 0, ,q p= mimicking massand momentum injection by fast bipolar AGN jets.

The density source term is implemented as

S r M r, , ,jet( ) ˙ ( )&q y q=r

where Mjet˙ is the single-jet mass loading rate,

r

r r

, 2 tanh tanh

1 tanh14

5r

jet jet

jet

( )

( )

⎡⎣⎢

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥

⎡⎣⎢

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥

y qq q

sq q p

s

s

= +-

++ -

´ +-

´

q q

that describes the spatial distribution of the source term whichfalls smoothly to zero outside the small biconical jet region ofradius rjet and half-opening angle .jetq We smooth the jet sourceterms in space because the Kelvin–Helmholtz instability isknown to be suppressed due to numerical diffusion in a fastflow if the shear layer is unresolved (e.g., Robertsonet al. 2010). The normalization factor

r

32 1 cosjet

3jet( )&

p q=

-

ensures that the total mass added due to jets per unit time isM2 .jet˙ All our simulations use the following jet parameters:

0.05 kpc,rs = 6,jetq p= and 0.05.s =q The jet source regionwith an opening angle of 30°may sound large but we getsimilar results with narrower jets. Also, the fast jet extends wellbeyond the source region and is much narrower (c.f. third panel

in Figure 1). The jet radius rjet is scaled with the halo mass; i.e.,

rM

M2 kpc

7 10.jet

20014

1 3⎛⎝⎜

⎞⎠⎟=

´ :

The jet mass-loading rate is calculated from the current massaccretion rate (Macc˙ ) evaluated at the inner radial boundary suchthat the increase in the jet kinetic energy is a fixed fraction ofthe energy released via accretion; i.e.,

M v M c . 6jet jet2

acc2˙ ˙ ( )�=

We choose the jet velocity v 3 10jet4= ´ km s−1 (0.1 c; c is

the speed of light); such fast velocities are seen in X-rayobservations of small-scale outflows in radio galaxies (Tombesiet al. 2010). The jet efficiency (ò; our fiducial value is6 × 10−5) accounts for both the fraction of the infalling mass atthe inner boundary (at 1 kpc for the cluster runs) that is accretedby the SMBH and for the fraction of accretion energy that ischanneled into the jet kinetic energy. Our results are insensitiveto a reasonable variation in jet parameters (v ,jet r ,jet ,jetq ,rs sq),but depend on the jet efficiency (ò).Like Gaspari et al. (2012), the jet energy is injected only in

the form of kinetic energy; we do not add a thermal energysource term corresponding to the jet. We note that Li & Bryan(2014b) have shown that the core evolution does not dependsensitively on the manner in which the feedback energy ispartitioned into kinetic or thermal form. Another differencefrom previous approaches, which use few grid points to injectjet mass/energy, is that our jet injection region is well-resolved.

2.2. Grid, Initial, and Boundary Conditions

Most AGN feedback simulations evolved for cosmologicaltimescales (e.g., Gaspari et al. 2012; Li & Bryan 2014a) useCartesian grids with mesh refinement. However, we usespherical coordinates with a logarithmically spaced grid inradius, and equal spacing in θ and f. The advantage of aspherical coordinate system is that it gives fine resolution atsmaller scales without a complex algorithm. Perhaps moreimportantly, a spherical setup allows for 2D axisymmetricsimulations which are much faster and capture a lot (but not all)of essential physics.We perform our simulations in spherical coordinates with

0 ,- -q p 0 2 ,- -f p and r rmin - - r ,max with

rM

M1, 200 kpc

7 10.min,max

20014

1 3

[ ][ ]⎛⎝⎜

⎞⎠⎟=

´ :

According to self similar scaling, we have scaled all lengthscales in our simulations (inner/outer radii r r ,min max r200, jetradius rjet) as M .200

1 3

We apply outflow boundary conditions (gas is allowed toleave the computational domain but prevented from entering it)at the inner radial boundary. We fix the density and pressure atthe outer radial boundary to the initial value and prevent gasfrom leaving or entering through the outer boundary. Reflectiveboundary conditions are applied in θ (with the sign of vfflipped) and periodic boundary conditions are used in f. Wenoticed that cold gas has a tendency to artificially “stick” at theθ boundaries (mainly in 2D axisymmetric simulations) for our

3 We have also carried out narrow-jet simulations with momentum injectionin the vertical z[ˆ] direction, but do not find much difference from our runs withmomentum injection in the radial [r ; see Equation (2)] direction.

4

The Astrophysical Journal, 811:108 (21pp), 2015 October 1 Prasad, Sharma, & Babul

2 kpc

Dependence on halo mass & efficiency

larger ε suppresses accretion

more massive halos require

larger ε

depends on where Mdot calculated

7x1014 Msun

1.8x1015 Msun

Density movie

BCG+NFW in PLUTO 256x128x32 in (logr,θ,φ)

rmin=0.5 kpc, rmax=0.5 Mpc evolution for ~2.8 Gyr

made by Deovrat Prasad

150 kpc

r-θ slices

Figure 1. Pressure (upper panel), electron number density (middle panel), and temperature (lower panel) contour plots (R–z plane at 0f = ) in the core at differenttimes for the 3D fiducial run. The density is cutoff at the maximum and the minimum contour level shown. The low-density bubbles/cavities are not symmetric andthere are signatures of mixing in the core. The left panel corresponds to a time just before a cooling time in the core. The second panel from the left shows cold gasdredged up by the outgoing jets. The rightmost panel shows infalling extended cold clouds. The pressure maps show the weak outer shock, but the bubbles/cavities soprominent in the density/temperature plot are indiscernible in the pressure map, implying that the bubbles are in pressure equilibrium and buoyant. Also notice theoutward-propagating sound waves in the two middle pressure panels in which the jet is active. The infalling/rotationally supported cold gas has a much lowertemperature and pressure than the hot phase. The arrows in the temperature plots denote the projected gas velocity unit vectors.

5


pressure

density

sound/weak shock waves

bubble mixing with ICM

50 kpc

buoyantbubbles

r-θ slices

Figure 1. Pressure (upper panel), electron number density (middle panel), and temperature (lower panel) contour plots (R–z plane at 0f = ) in the core at differenttimes for the 3D fiducial run. The density is cutoff at the maximum and the minimum contour level shown. The low-density bubbles/cavities are not symmetric andthere are signatures of mixing in the core. The left panel corresponds to a time just before a cooling time in the core. The second panel from the left shows cold gasdredged up by the outgoing jets. The rightmost panel shows infalling extended cold clouds. The pressure maps show the weak outer shock, but the bubbles/cavities soprominent in the density/temperature plot are indiscernible in the pressure map, implying that the bubbles are in pressure equilibrium and buoyant. Also notice theoutward-propagating sound waves in the two middle pressure panels in which the jet is active. The infalling/rotationally supported cold gas has a much lowertemperature and pressure than the hot phase. The arrows in the temperature plots denote the projected gas velocity unit vectors.

5


pressure

density

sound/weak shock waves

bubble mixing with ICM

50 kpc

buoyantbubbles

infalling cold gas condenses when the jets are weak!

temperature reasonable

the core entropy to higher values. These back-flows and mixingare mainly responsible for heating the cluster core.

3.1.2. Radial Profiles

Before discussing the detailed kinematics of cold gas and jetcycles, we show in Figure 2 the 1D profiles of importantthermodynamic quantities (entropy T n ,ekeV

2 3[ ] t t ,cool ff ne,TkeV) as a function of radius for the fiducial 3D run. In additionto the instantaneous profiles (at 1–4 Gyr), the median profileand spread about it are shown. The median is calculated for theentropy measured at 20 kpc (roughly the core size) and all theprofiles with entropy within one standard deviation at the sameradius are shown in gray.

The spread in quantities outside ∼20 kpc is quite small, butincreases toward the center because multiphase cooling(leading to density spikes) and strong jet feedback (leading tooverheating) are most effective within the core. The density at1 Gyr is peaked toward the center, indicating that the clustercore is in a cooling phase. The spikes in density at 3 Gyr havecorresponding spikes in entropy and t tcool ff profiles, but not asprominent in the temperature profile. The temperature fluctua-tions are rather modest compared to fluctuations in otherquantities because of dropout and adiabatic cooling. Tempera-ture profiles show a general increase with radius, as seen inobservations.

There is a large spread in entropy toward lower values aboutthe median at radii 10 kpc< (top left panel in Figure 2). This isbecause there are short-lived cooling events during which theentropy in the core decreases significantly (simultaneously,density increases and t tcool ff decreases). On the other hand, the

increase in the core entropy is smaller but lasts for a coolingtime, which is longer in this state. This behavior is generic,fairly insensitive to parameters such as the feedback efficiencyand the halo mass.

3.1.3. The Cold Torus

While Figure 1 shows that cold gas can be dredged up byAGN jets (second panel; see also Revaz et al. 2008; Popeet al. 2010) and can also condense out of the ICM at largescales (fourth panel), majority of cold gas is at very small scales(<5 kpc) in the form of an angular-momentum supported coldtorus. Figure 3 shows the zoomed-in density snapshots in theequatorial ( 2q p= ) plane at different times; the arrows showthe projection of velocity unit vectors. As the cluster evolvesthe cold gas, condensing out of the hot ICM, gains angularmomentum from jet-driven turbulence. Because of a significantangular velocity, an angular momentum barrier forms and coldgas circularizes at small radii.Unlike Li & Bryan (2014b), our cold torus is dynamic in

nature as AGN jets disrupt it time and again, but it reforms dueto cooling. Figure 3 shows the evolution of the torus at variousstages of the simulation. The top left panel of Figure 3 showsthe cluster center at 0.5 Gyr. Small cold gas clouds areaccumulating in the core after the first active AGN phase. At1.3 Gyr, cold gas accreting through the inner boundary has ananti-clockwise rotational sense. At 1.98 Gyr, cold gas (and thehot gas out of which it condenses) is rotating clockwise. Jetactivity leading up to this phase has reversed the azimuthalvelocity of the cold gas. At all times after this the dynamic coldgas torus rotates in a clockwise sense, essentially because the

Figure 2. X-ray emissivity-weighted (considering only 0.5–8 keV gas) 1D profiles of important thermodynamic variables as a function of radius. Snapshots at1–4 Gyr are shown. Various quantities are obtained by combining 1D profiles of density and pressure. The median and standard deviation (σ) of entropy(K T nekeV

2 3º ) at 20 kpc are calculated. Various profiles corresponding to the median entropy at 20 kpc (14 keV cm2) are shown in different panels (black lines with“+”). Thick gray lines show the profiles for which the entropy at 20 kpc is within 1 s- of its median value.

7














7


density reasonable













7














7


Cold rotating torus6 Deovrat Prasad & Prateek Sharma

Fig. 3.— The 2-D (z = 0) contour plots of density in the very inner region at different times for the fiducial 3-D run, with the projectionof the velocity unit-vector represented by arrows. The top-left panel shows the beginning of the infall of cold gas with random angularmomentum. The top-middle panel shows an anti-clockwise transient torus. All times after this show a clockwise torus which waxes andwanes because of cooling and AGN heating cycles. Even at late times the cold torus is not stable and gets disrupted by jets.

it reforms over a few cooling times. Figure 3 shows theevolution of the torus at various stages of the simulation.The top-left panel of Figure 3 shows the cluster center at0.5 Gyr. Small cold gas clouds are accumulating in thecore after the first active AGN phase. At 1.3 Gyr, coldgas accreting through the inner boundary has an anti-clockwise rotational sense. At 1.98 Gyr, cold gas (andthe hot gas out of which it condenses) is rotating clock-wise. Jet activity leading up to this phase has reversedthe azimuthal velocity of the cold gas. At all times af-ter this the dynamic cold gas torus rotates in a clockwisesense, essentially because the mass (and angular momen-tum) in the rotating torus is much larger than the newlycondensing cold gas.The middle panels of Figure 3 show the dynamic na-

ture of the rotationally supported torus. The torus getsdisrupted due to jet activity as seen in the middle panelof Figure3, but forms again quickly. The snapshots at 2.4and 2.4 Gyr show that the inner region is covered by thevery hot/dilute jet material. This unphysical behavioris mainly because of our feedback prescription; we scalethe jet power with the instantaneous mass inflow ratethrough the inner boundary (see Eq. 6). Even small os-cillations of the cold torus can sometimes lead to a largeinstantaneous mass inflow through the inner boundaryand hence an explosive jet feedback in which the jet ma-terial encompasses the inner core. The reassuring fact is

that these explosive ‘events’ are rare and the jet mate-rial is quickly mixed with the ICM, and the core settlesback to a quiescent state (see the top panel of Fig. 9which shows a large peak in jet energy at 2.4 Gyr). Inreality, the cold gas in the torus is mainly consumed bystar-formation and only a part of it reaches the SMBH,and that too at the slow viscous timescale. In addition,the rapidly reorienting AGN jets can disrupt the massivecold torus (e.g., see Babul et al. 2012).Li & Bryan (2014b) show that after 3 Gyr the cold

gas settles down in form of a stable torus, with no furthercondensation of extended cold gas. This is inconsistentwith observations. The bottom panels in Figure 3 fromour fiducial run shows that the torus is unsteady even atlate times. Moreover, unlike them, we see extended coldgas condensing out till the end. We compare our resultsin detail with Li & Bryan (2014b) in section 4.1.To test the role of cooling in maintaining the cold ro-

tating torus, we restarted the 3-D fiducial run after amassive cold torus had formed (3 Gyr), and re-ran itwithout radiative cooling or feedback heating. Whilethe cold torus is long-lived even without cooling (Kelvin-Helmholtz instability does not grow for at least the nextGyr), it is heated (by numerical dissipation) to 105 K,and is no longer maintained at the temperature of thestable phase (104 K). Thus, radiative cooling function iswhat dictates the temperature of the cold phase. The

few kpc scale molecular torus

Cold torus in Hydra A6 Hamer et al.

Figure 2. This figure shows the IFU maps of the Hα emission as taken from fits to the Hα/[NII] triplet observed in the VIMOS cubes.Panel (A) shows a continuum image made by collapsing the cube, the contours show the Hα emission clearly centred on the BCG. Panel(B) is a Hα Flux map which shows a disc of bright emission running across the BCG. In panel (C) we show the relative velocity ofthe Hα line to the galaxy redshift, a strong velocity gradient of ∼ 600 km s−1 can clearly be seen. Contoured on this plot are lines ofconstant velocity created by fitting a disc model to the velocity map. The final panel (D) shows the measured Full Width Half Maximum(FWHM) of the line which can be seen to broaden at the centre of the velocity gradient.

is likely to be due to the lower signal–to-noise as the lines arepresent within the total spectrum of this region (extracted1×1 arcsec2 centred on the offset Paα peak) though the lineis weak compared to Paα.

[FeII] emission was the only line detected in the H-bandobservations. The maps presented in Figure 5 show that the[FeII] emission is compact and located at the centre of the

BCG. The luminosity of [FeII] emission has a high depen-dence on the gas density (Bautista et al. 1994) so we wouldexpect it to be brightest in the central regions where thegas density is higher. Despite being compact the line doesappear to be extended to the east on scales slightly greaterthan the seeing. Within this small extent there appears to bea velocity change of ∼ 200 km s−1 across the emission. This

6 Hamer et al.

Figure 2. This figure shows the IFU maps of the Hα emission as taken from fits to the Hα/[NII] triplet observed in the VIMOS cubes.Panel (A) shows a continuum image made by collapsing the cube, the contours show the Hα emission clearly centred on the BCG. Panel(B) is a Hα Flux map which shows a disc of bright emission running across the BCG. In panel (C) we show the relative velocity ofthe Hα line to the galaxy redshift, a strong velocity gradient of ∼ 600 km s−1 can clearly be seen. Contoured on this plot are lines ofconstant velocity created by fitting a disc model to the velocity map. The final panel (D) shows the measured Full Width Half Maximum(FWHM) of the line which can be seen to broaden at the centre of the velocity gradient.

is likely to be due to the lower signal–to-noise as the lines arepresent within the total spectrum of this region (extracted1×1 arcsec2 centred on the offset Paα peak) though the lineis weak compared to Paα.

[FeII] emission was the only line detected in the H-bandobservations. The maps presented in Figure 5 show that the[FeII] emission is compact and located at the centre of the

BCG. The luminosity of [FeII] emission has a high depen-dence on the gas density (Bautista et al. 1994) so we wouldexpect it to be brightest in the central regions where thegas density is higher. Despite being compact the line doesappear to be extended to the east on scales slightly greaterthan the seeing. Within this small extent there appears to bea velocity change of ∼ 200 km s−1 across the emission. This

[Hamer et al. 2014]

~5 kpc cold torus

more examples from ALMA, Hershel? may be SF doesn’t let a massive torus form

Jets & fast outflowsAGN Jets as source of fast outGows

Jet power (1041 erg s-1)

time (Gyr)

N

orm

alized q

uanti

ties

jet power highly time variable

is there any relation between jets and

cold gas kinematics?


Jet power (1041 erg s-1)

Norm

alized

quanti

ties

time (Gyr)

OutGow, 5 kpc (Mʘ yr-1 )

cold outflows generally coincide with sudden rise in jet power


Norm

alized q

uanti

ties

time (Gyr)

Jet power (1041 erg s-1)OutGow, 5 kpc (Mʘ yr-1 )

InGow, 5 kpc (Mʘ yr-1 )

cold inflows when jet power wanes

2.2 Gyr

2.4 Gyr

Snapshots of inflow/outflow phases

radially-dominant component

fast outflowsduring jet rise

slow infallat most times

Cold gas observations

1010 Msun of molecular gas

low (200 km/s) and high (600 km/s) velocity components

A1664 [Russell et al. 2014]

5

Figure 4. Position-velocity diagrams for the BCG’s systemic component at CO(1-0) (left) and CO(3-2) (right) each taken through a slice with position angle77◦. The molecular gas in this structure extends from NE, at velocities of −250 km s−1 , to SW, at velocities of +250 km s−1 . The contours are -2σ, 2σ, 3σ, 4σand 5σ. Negative contours are shown by a dashed line. The dotted straight line marks the continuum point source position. The dashed straight line illustratessolid body rotation with v∝r.

Figure 5. Abell 1664 CO(3-2) position-velocity diagram for the HVS takenthrough a slice with position angle 120◦ . The slice runs from SE to NWand is centred on the point where the HVS intersects the BCG’s systemiccomponent (see Fig. 3). The contours are -2σ, 2σ, 3σ, 4σ and 5σ. Negativecontours are shown by a dashed line.

Figure 6. Left: HST WFPC2 F606W optical image of the BCG in Abell1664. Right: Zoom in of the HST image with ALMA CO(3-2) contoursrepresenting the BCG’s systemic component (−285 to 285 km s−1 , yellow)and high velocity system (−705 to −405 km s−1 , cyan). The ALMA beamsize for CO(3-2) is shown to the lower left.

velocity gradients with larger blueshifted velocities at smallerradii (Salomé et al. 2006; Lim et al. 2008). The molecular gaskinematics are consistent with free fall in the gravitational po-tential of NGC1275, as expected if they originated in coolingfrom the X-ray atmosphere.For radial inflow, we expect velocity gradients increasing

towards the nucleus with the largest velocities towards theBCG center. This is more or less what is seen. The extentand velocity gradients across the HVS gas clumps and theBCG’s systemic component can therefore constrain their dy-namics and origin (Fig. 3). The velocity shear across thegas clumps in the HVS is ∼ 250− 300 km s−1 along the lineof sight (Fig. 5). A similar shear in the transverse directioncould have separated the clouds on the observed scale in only∼ 107 yr. Therefore, the clumps are of order that age or theclouds are moving nearly along the line of sight. In the lattercase, the broad velocity shear could signify a velocity gradientwith high velocity infall onto the nucleus.The BCG’s systemic component has a clear and smooth ve-

locity gradient with a velocity increase of ∼ 500 km s−1 overits ∼ 11 kpc length. The velocity profile of this componentis suggestive of rotation about the BCG center, however themass and velocity structure are strongly asymmetric (section3.1). For a putative rotating disk, we estimate the Toomre Q-criterion for disk stability (Toomre 1964), Q = vcvT/πGrΣ,where the circular velocity vc ∼ 200 km s−1 , the turbulent ve-locity vT ∼ 50−100 km s−1 , the disk radius r ∼ 3 kpc and thedisk surface density Σ∼ 200M⊙ pc−2 . The Q parameter is oforder one suggesting that it could be unstable and potentiallystar forming. However, Fig. 6 does not show strong star for-mation associated with the BCG’s systemic component. Starformation could be obscured by dust but the U-band star for-mation rate, SFRU ∼ 20M⊙ yr−1 (Kirkpatrick et al. 2009),and the infrared star formation rate, SFRIR = 15M⊙ yr−1(O’Dea et al. 2008), are comparable, which is inconsistentwith buried star formation. This could be a recent infall ofmaterial that is in the process of settling into a disk around thenucleus. Its orbital time is ∼ 9× 107 yr so a relaxed disk willtake at least several 108 yr to form.An X-ray cooling origin for the gas inflow must ex-

5

Figure 4. Position-velocity diagrams for the BCG’s systemic component at CO(1-0) (left) and CO(3-2) (right) each taken through a slice with position angle77◦. The molecular gas in this structure extends from NE, at velocities of −250 km s−1 , to SW, at velocities of +250 km s−1 . The contours are -2σ, 2σ, 3σ, 4σand 5σ. Negative contours are shown by a dashed line. The dotted straight line marks the continuum point source position. The dashed straight line illustratessolid body rotation with v∝r.

Figure 5. Abell 1664 CO(3-2) position-velocity diagram for the HVS takenthrough a slice with position angle 120◦ . The slice runs from SE to NWand is centred on the point where the HVS intersects the BCG’s systemiccomponent (see Fig. 3). The contours are -2σ, 2σ, 3σ, 4σ and 5σ. Negativecontours are shown by a dashed line.

Figure 6. Left: HST WFPC2 F606W optical image of the BCG in Abell1664. Right: Zoom in of the HST image with ALMA CO(3-2) contoursrepresenting the BCG’s systemic component (−285 to 285 km s−1 , yellow)and high velocity system (−705 to −405 km s−1 , cyan). The ALMA beamsize for CO(3-2) is shown to the lower left.

velocity gradients with larger blueshifted velocities at smallerradii (Salomé et al. 2006; Lim et al. 2008). The molecular gaskinematics are consistent with free fall in the gravitational po-tential of NGC1275, as expected if they originated in coolingfrom the X-ray atmosphere.For radial inflow, we expect velocity gradients increasing

towards the nucleus with the largest velocities towards theBCG center. This is more or less what is seen. The extentand velocity gradients across the HVS gas clumps and theBCG’s systemic component can therefore constrain their dy-namics and origin (Fig. 3). The velocity shear across thegas clumps in the HVS is ∼ 250− 300 km s−1 along the lineof sight (Fig. 5). A similar shear in the transverse directioncould have separated the clouds on the observed scale in only∼ 107 yr. Therefore, the clumps are of order that age or theclouds are moving nearly along the line of sight. In the lattercase, the broad velocity shear could signify a velocity gradientwith high velocity infall onto the nucleus.The BCG’s systemic component has a clear and smooth ve-

locity gradient with a velocity increase of ∼ 500 km s−1 overits ∼ 11 kpc length. The velocity profile of this componentis suggestive of rotation about the BCG center, however themass and velocity structure are strongly asymmetric (section3.1). For a putative rotating disk, we estimate the Toomre Q-criterion for disk stability (Toomre 1964), Q = vcvT/πGrΣ,where the circular velocity vc ∼ 200 km s−1 , the turbulent ve-locity vT ∼ 50−100 km s−1 , the disk radius r ∼ 3 kpc and thedisk surface density Σ∼ 200M⊙ pc−2 . The Q parameter is oforder one suggesting that it could be unstable and potentiallystar forming. However, Fig. 6 does not show strong star for-mation associated with the BCG’s systemic component. Starformation could be obscured by dust but the U-band star for-mation rate, SFRU ∼ 20M⊙ yr−1 (Kirkpatrick et al. 2009),and the infrared star formation rate, SFRIR = 15M⊙ yr−1(O’Dea et al. 2008), are comparable, which is inconsistentwith buried star formation. This could be a recent infall ofmaterial that is in the process of settling into a disk around thenucleus. Its orbital time is ∼ 9× 107 yr so a relaxed disk willtake at least several 108 yr to form.An X-ray cooling origin for the gas inflow must ex-

AGN feedback cyclescore cooling

large cold accretion onto SMBH

negative FB, heating wins over cooling, energy pumped back in ICM

after few cooling times avg. thermal balance in core

cold, multiphase gas condenses if tcool/tff≲10

cooling & AGN jet heating cycles in cool-core clusters

Cycles in sims.

1001041

1042

1043

1044

1045

min (tcool/tff)

jetpow

er(erg

s−1)

100109

1010

1011

min (tcool/tff)

mass

incold

phase

(M⊙)

100 101108

109

1010

min (tcool/tff)mass

incold

phase

(M⊙;|v

r|>

|vφ|)

0

0.5

1

1.5

2

2.5

3

3.5

4

time (Gyr)

1001041

1042

1043

1044

1045

min (tcool/tff)

jetpow

er(erg

s−1)

100109

1010

1011

min (tcool/tff)

mass

incold

phase

(M⊙)

100 101108

109

1010

min (tcool/tff)

mass

incold

phase

(M⊙;|v

r|>

|vφ|)

0

0.5

1

1.5

2

2.5

3

3.5

4

time (Gyr)

“phase space” of jet power

cold gas mass vs. hot gas properties

Huge scatter in sims.Figure 13. Various important quantities measured at the same time (jet energy, cold gas mass, core entropy, and min[t tcool ff ]) plotted against each other from our 2Dcluster runs with different efficiencies. The data is sampled every 10 Myr. There is a strong correlation between the core entropy and min(t tcool ff ), especially at largervalues of min(t tcool ff ). There is also a positive correlation between K0-jet energy and min(t tcool ff )-jet power. Larger efficiency runs lead to a larger value of min(t tcool ff ) and K0. Notice that cold gas is absent if min(t tcool ff) 30.

Figure 14. Important quantities measured at the same time (jet energy, cold gas mass, core entropy, and min[t tcool ff ]) plotted against each other in our fiducial 3Dcluster run. As in 2D runs (see Figure 13), there is a strong correlation between K0-min(t tcool ff ), K0−jet power, and min(t tcool ff)-jet energy. The cold gas mass is highand becomes almost constant at later times, as seen in the top panel of Figure 9. The color-coding corresponds to time.

17


cold accretion does not show tight correlations!

consequence of chaotic cycles!

Observations of cycles

observations of “phase space”

18

Fig. 9.— 1.4 GHz radio luminosity versus integrated soft X-ray luminosity within the cooling radius. Color refers to the system mass,with blue, green and red referring to systems with M2500 ⇤ 1013 M⇤, 1014 M⇤, and 1014.5 M⇤, respectively. Stars, closed circles andopen circles are systems with filamentary, nuclear or no H� emission. Grey points are groups and clusters from Sun (2009b) and the redellipses describe the two loci identified by Sun. The grey arrows show the proposed evolution of systems from cool, feedback-regulated cores(right ellipse) to X-ray faint corona (left ellipse). If the radio luminosity exceeds a certain threshold, depicted by horizontal dotted lines,the amount of feedback exceeds the required pdV work needed to disrupt the cool core. This simple picture seems to have some merit, asthe three clusters in our sample with extremely disrupted cores (Hydra A, Abell 2052, Abell 4059) all have radio luminosities exceedingthe allowable threshold for their mass and are significantly o�set to the left of the cool core locus. This plot provides an explanation forthe fact that groups with cool cores tend to have low-luminosity AGN when compared to their high-mass counterparts.

[McDonald et al. 2011]

coldhot

hot accretion inadequate MBH . 0.01MBondi

only a small fraction makes it to SMBH

because of outflows

Bondi resolved in Sgr A*, M 87,

NGC 3115: all show suppression

41 41.5 42 42.5 43 43.5 44 44.5 4542

42.5

43

43.5

44

44.5

45

45.5

46

log10(Pcav; [erg s−1])

log10(P

Bon

di;[erg

s−1])

Russell et al., 13

Power Law; Bondi

Isothermal beta profile; Bondi

innner radii flux power; 1 kpc

Allen et al., 06 Pcav= PBondi

Fujita et al., 14

100

Angular momentum problem

tvisc ⇠1

↵(H/R)2⌦K

too long if H/R~10-3, of standard AGN thin disks

moreover, star formation where Md/MBH exceeds H/R

tvisc ⇠ 4.7 Gyr

✓R

1pc

◆3/2 ✓H/R

0.001

◆�2 ⇣↵

0.01

⌘�1 must avoid a large thin disk tvisc < core cooling time

Key issues• microscopic dissipation: turbulent mixing/

heating, shocks, CRs

• conduction, hot accretion secondary

• from 1 kpc to << 1 pc (BH sphere of influence): core to BH accretion

• stochastic cold gas, angular momentum barrier, most cold gas consumed by SF

• relation to radio mini-halos

• spiral structures, cold fronts, sloshingThanks!

turbulent velocities

structure of hot gas vs halo mass

LX–TX relation and missing baryons 1223

Figure 1. The electron number density (ne) as a function of radius (scaled byr200) for different halo masses; the asymptotic gas density slope s = −2.25for these models. The profiles for an entropy core with tTI/tff ≥ 10 are shownby the solid lines and the profiles for a fixed tTI/tff = 10 ‘core’ are shown bythe dotted lines. The halo masses, in the order of decreasing core density,are 3 × 1014, 6 × 1013, 1013, 6 × 1012, 3 × 1012 and 1012 M⊙.

likened to mini cooling flows which feed the central SMBHs andpower radio jets. Instead of flat density cores, these coronae havedensity profiles steeply rising towards the centre. We can explain thecoronae in the context of our models if we include the gravitationalpotential of the central brightest cluster galaxy (BCG), in additionto the NFW potential. We model the gravitational acceleration dueto the BCG as given by (in cgs units)

gBCG =!"

(r/1 kpc)0.5975

3.206 × 10−7

# s

+"

(r/1 kpc)1.849

1.861 × 10−6

# s$−1/s

, (2)

with s = 0.9, and as shown in fig. 1 of Mathews, Faltenbacher& Brighenti (2006). We use the same BCG potential for all ourhaloes. While this assumption is not correct in detail, it captures theessential feature that gravity at the smallest radii is dominated bythe BCG and not by the NFW potential.

Fig. 2 shows a comparison of our models (which include theBCG potential) with observations. The observations agree with ourmodels in that the smaller haloes have lower densities comparedto self-similar models. While we make the simplifying assumptionthat the gas density profile outside the ‘core’ is the same for allhaloes, observations show that smaller haloes have shallower den-sity profiles. This is because realistic feedback can affect the gaseven beyond the core, especially for the lower mass haloes wherethe required feedback efficiency to balance cooling is quite small(see Section 3.2 and Fig. 4). A comparison of Figs 1 and 2 showsthat the core density for tTI/tff = 10 models is much larger whenthe BCG potential is included. The effect is much more pronouncedfor smaller haloes in which the BCG gravity dominates the NFWgravity even at relatively large radii. Thus, by including the BCGpotential we are able to reproduce the observed steep rise in densitytowards the centre in our low-mass halo models.

Figure 2. Electron number density as a function of radius for cool coreArchive of Chandra Cluster Entropy Profile Tables (ACCEPT) groups andclusters (core entropy !30 keV cm2; Cavagnolo et al. 2009), and our modelsincluding the BCG potential. ACCEPT data are averaged in five temperaturebins: < 1 keV (< 3.5 × 1013 M⊙; grey filled circles); 1–2 keV (3.5 × 1013–1.1 × 1014 M⊙; red stars); 2–4 keV (1.1–3.6 × 1014; blue triangles); 4–6 keV (3.6–7 × 1014 M⊙; green squares) and 6–8 keV (7–11 × 1014 M⊙;violet hexagons). The temperature range is converted into mass range usingthe best-fitting M200–TX relation for our core entropy models in Table 1;M200 ≈ 3 × 1014 M⊙ (TX/3.6 keV)5/3. The theoretical profiles are shownfor halo masses of 1013, 6 × 1013, 3 × 1014, 6 × 1014 and 1015 M⊙, in orderof increasing density.

Most of our results stem from the fact that the smaller haloeshave lower core densities; in Section 3.1 we study its implicationsfor the LX–TX relation, and in Section 3.2 we apply it to the missingbaryons problem.

3.1 LX–TX relation

Fig. 1 illustrates that the physics of thermal instability in haloesresults in bigger but lower density cores for smaller haloes (cf.fig. 9 in Paper II). This reduces the X-ray luminosity of low-masshaloes below the predictions of gravitational self-similar models.Moreover, Table 1 shows that the core entropy is nearly independentof the halo mass above !3 × 1013 M⊙, also in contrast with self-similar models. Thus, our models explain the observed steepeningof the LX–TX relation (Evrard & Henry 1991; Bryan 2000 andreferences therein) and excess entropy (e.g. Ponman, Cannon &Navarro 1999) in lower mass haloes.

We can understand this result intuitively as follows. For self-similar evolution of hot gas in haloes, we expect the gas den-sity to be the same for all halo masses. This assumption leadsto LX ∝ n2!(T )r3

200 ∝ T 3/2!(T ), which goes like T2 for free–free cooling (! ∝ T1/2). On the other hand, holding tTI ∝ T/n!(T)constant for all haloes (assuming a similar tff for different haloes)gives n ∝ T/!(T), which is ∝ T 1/2 or M

1/3200 for free–free cool-

ing. Thus, our models predict lower densities for smaller haloes,and hence LX ∝ n2!(T )r3

200 ∝ T 3 for massive haloes, in linewith observations. Above arguments assume that most of the X-rayluminosity is contributed by the dense core and that the scaled core

C⃝ 2012 The Authors, MNRAS 427, 1219–1228Monthly Notices of the Royal Astronomical Society C⃝ 2012 RAS

at University of C

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ay 28, 2013http://m

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Heating & cooling cycles in cool cluster coresprateek/icm16_min.pdfPrateek Sharma (IISc) Collaborators: Deovrat Prasad, Arif Babul COOL CORE CYCLES: COLD GAS AND AGN JET FEEDBACK IN