arXiv:1111.2337v2 [astro-ph.CO] 24 May 2012 fteatv aatcnces(G)i h eta cD central the output in conduction (AGN) energy nucleus the ( thermal galactic galaxy by active or the by of 2008) buoyancy heat (Quataert by example modified instabilities 2003) Narayan & for (Zakamska suppressed, of (2010). Soker reviews (2006); Fabian (2007); For typically) & Nulsen Peterson few, & see McNamara a center. (CCCs), of cool- clusters the CC (factor observed such towards mild the drop the balance sustain temperature to to order mech- the and in heat of ing, intra- needed distributed age the is smoothly the steady, anism of below Some well time drops cooling cluster. (ICM) radiative medium the cluster which in (CC) tcudfrihsc edaklo n unhthe quench and ( plasma, loop well cooling feedback as AGN instability a accreted, the thermal such If the global furnish core. by could the the regulated it in regulate changes is to to output order a adapt in Moreover, and steadily needed instability. heating transferred is thermal in local mechanism be plasma, the feedback can cooling stem energy to the However, order the throughout 2006). homogeneously if least Fabian hot & and at unclear (Dunn in in is cores found deposited cool it 2002), the be al. of to et 70% (Churazov thought bubbles is AGN energy mechanical 06 adr ta.20;Jhsne l 2010; al. et Johnson suggest al. observations et Blanton These al. 2010; 2011). 2009; et Tanaka al. al. et et a Roediger 2004; Randall 2011; al. in 2010; et al. Sanders et al. quality patterns (Clarke Lagan´a et high available which spiral 2006; for are of CCCs the data presence of fraction the significant revealed have 2008). nreial,cr oln a luil be plausibly can cooling core Energetically, core cool dense, central a show clusters galaxy Most nrcn er,hg eouinXryobservations X-ray resolution high years, recent In rpittpstuigL using 2018 typeset 3, Preprint November version Draft e.g., prlflw u eut a etse ietyi h etfwyear few next the in directly tested be can so headings: results CCs, Subject Our of flow. properties spiral key a several reproduces model component omto ae n xliigsm etrso ube uha th as such re bubbles bubbles, of nucleus features galactic some active explaining by accretion-quenc and regulated rates an outflow, formation for re an model mechanism is feedback quasi-steady-state phase a a that present provided we problem, cooling the eliminate and yasol oaig riig us prl agnildsotniys discontinuity belo tangential propagates spiral, which plasma, two-phase quasi flow, pattern, fast trailing, spiral im a cold, logarithmic rotating, fronts thermal a slowly piecewise-spiral of a the presence by of X in the by observations features and implying that CCs, CC, spiral show of by properties analytically multi-phase gauged We the are by medium, flows intracluster Such galaxies. eageta uksia osaeuiutu nteco oe (CCs cores cool the in ubiquitous are flows spiral bulk that argue We ∼ ˆ ra ta.20) npriua,sufficient particular, In 2004). al. Bˆırzan et hsc eatet e-uinUiest fteNgv Be Negev, the of University Ben-Gurion Department, Physics 0 p ie hrceitco C.B detn etadmxn th mixing and heat advecting By CCs. of characteristic size, kpc 100 1. A INTRODUCTION T E tl mltajv 5/2/11 v. emulateapj style X aais lses eea yrdnmc neglci medium intergalactic — hydrodynamics — general clusters: galaxies: ed -as aais clusters galaxies: X-rays: — fields PRLFOSI OLCR AAYCLUSTERS GALAXY COOL-CORE IN FLOWS SPIRAL e.g., aet tal. et Rafferty rf eso oebr3 2018 3, November version Draft Dtd oebr3 2018) 3, November (Dated: ABSTRACT r Keshet Uri ρ ∼ r − 1 lsicueA24,R 12. 68 2204, A indicate CFs 2638, such + across profiles references J1720.1 and thermal Exam- 2007, The RX Vikhlinin & therein). (Markevitch 2142, on. spi- 496 A with A a edge and cluster, with include observed consistent the ples manifold size, of discontinuity and center found ral distance the often projec- increasing of are various an sides CFs in alternating quasi-concentric di- seen on Multiple, three pattern underlying spiral tions. an (3D) suggesting mensional concentric, nearly pressure or metallicity, expected. flow, are al. tangential gradients the et no on (Birnboim where collisions nor 2010), shock merger (2007)), by created in a Vikhlinin CFs (for & found putative large Markevitch typically CFs see is the jump review, pressure on such the on not where exclusively clusters, and focus mild we fronts, a work and core-type this gradient, In metallicity jump. a pressure 2001), typi- ( al. CFs equilibrium et These hydrostatic Mazzotta (2010). CCs from al. 10 deviations the et show of Ghizzardi cally each of For in sample found cores. the of was redshift in CF half low one least well-observed, and than at the 2003), example, more of al. all et in are in (Markevitch found nearly effects CCs relaxed were projection edge otherwise when CFs X-ray the (CF) Such an front of cold favorable. form a the forms as above in known from observed entropy discontinuity, high and a cluster) the of center h o nrp hs rmblw( below from phase entropy core. low the the beyond extend may structure spiral factor the similar cases, a by (both denser q entropy and low are colder The is which component phases, equilibrium. pressure plasma alternating, entropy at spatially approximately high of and entropy composed low morphology spiral a est (or density oeCsaeotnqaisia,peeiesia,or spiral, piecewise spiral, quasi often are CFs Core h alihTyo R)sal onaybetween boundary stable (RT) Rayleigh-Taylor The fu oafw,adhge nmtliiy nsome In metallicity. in higher and few), a to up of e-hv 40,Ire;[email protected] Israel; 84105, ’er-Sheva e,cmoieflw nwihtefast the which in flow, composite hed, epooeta l uhcrsharbor cores such all that propose we T eir ∼ ,freapeb ASTRO-H. by example for s, rdcn h bevdlwstar low observed the producing rae hslast h nearly the to leads This urface. ryegskona odfronts. cold as known edges -ray oesrn osrit nthe on constraints strong pose o,so no,separated inflow, slow hot, a w r R uae h o.I particular, In flow. the gulates dceia rpriso the of properties chemical nd 0 . b 4 ∝ fcutr n rusof groups and clusters of ) eprtr)rda profile, radial temperature) r ie h ipettwo- simplest The size. a,sc oscan flows such gas, e magnetic — i.e. lsrt the to closer e.g., 2 U. Keshet that they are strongly sheared tangential discontinuities and the interpretation of CFs as tangential bulk flows, (TDs) seen in projection (Keshet et al. 2010). These is supported by anecdotal evidence such as the intricate TDs are thought to be stabilized magnetically, with fast, velocity structure in Perseus (Sanders et al. 2004, figure nearly sonic, narrow shear layers lying beneath them 8), and by the agreement between sloshing simulations (Keshet et al. 2010). and observed spirals. Moreover, we argue that spiral Spiral features and core CFs are typically observed flows may in fact be essential in the formation of a core, in only marginally, at low significance, because a high reso- shaping its (universal) profile, fixing its size, and avoiding lution is needed in order to identify the modest gradients catastrophic cooling. Indeed, this would suggest that and small TD contrasts in projection, and spectral data CCs are synonymous with spiral flows. are needed to resolve the temperature/metallicity struc- Sloshing simulations have demonstrated that a quasi ture. Spirals are rarely unambiguously resolved, but the stable, spiral mode is easily excited in the core, and de- abundance of subtle spiral features in high quality data cays only on a long, >Gyr timescale if cooling is not taken suggests the prevalence of spirals, in particular consider- into account. We analytically study spiral modes in the ing projection effects, supporting evidence (such as CFs ICM in the presence of cooling and AGN activity. We consistent with edge-on spirals) and the complex core constrain the flow only by the observed, nearly spher- morphologies (hot bubbles, jets, minor mergers, etc.). ically symmetric pressure profile, and by the presence Moreover, indirect evidence suggests that CCs have a of fast flows below spiral CFs inferred in Keshet et al. universal, unrelaxed structure, which we argue is closely (2010). The implied features of the core are then shown related to the spiral features. First, although CCs dif- to be strongly constrained, and in good agreement with fer in their parameters, reside in different gravitational observations and simulations, even for the simplest two- potentials which are strongly affected by the cD galax- component toy model we investigate. ies, and are out of equilibrium due to cooling, they The paper is organized as follows. In §2 we intro- broadly adhere to universal thermal and chemical pro- duce the framework and the equations governing the flow. files. Thus, CCs show radial profiles of density, temper- Power-law scalings of the core and flow parameters are ature and metallicity that cluster around ρ ∝ r−1, T ∼ derived in §3. We study the general properties of the r0.4, and Z ∼ r−0.3, respectively (e.g., Voigt & Fabian flow in §4, and explore its two main variants, in which 2004; Sanderson et al. 2006; Vikhlinin et al. 2006; the fast flow beneath CFs is either an inflow or an out- Donahue et al. 2006; Sanderson et al. 2009). Second, ac- flow, in §5. A full solution to one of these variants, which cumulating evidence indicates that the plasma in many combines a hot inflow and a cold, fast outflow, is derived cores, both with and without observed CFs and spiral in §6. Heating and feedback are discussed, qualitatively, features, consists of two (or more) spatially separated in §7. We examine the observational evidence for a mul- phases (e.g., Molendi & Pizzolato 2001; Kaastra et al. tiphase CC plasma in §8. Our results are summarized 2004; Werner et al. 2010). These phases are identified as and discussed in §9. associated with the two distinct components that alter- nate to give rise to the spiral structure in select nearby 2. DEFINITIONS AND GOVERNING EQUATIONS clusters such as Perseus and Virgo, and can be thus in- The flow is governed by the continuity equation terpreted in general, as we discuss in §8 below. Core CFs and spiral features were modelled as associ- ∂tρ + ∇·(ρU)=0, (1) ated with large scale “sloshing” oscillations of the ICM, driven by mergers (Markevitch et al. 2001), possibly in- the momentum equation volving only a dark matter subhalo (Tittley & Henriksen −1 2005; Ascasibar & Markevitch 2006), or by weak (∂t + U · ∇) U = a = −ρ ∇P + g , (2) shocks/acoustic waves displacing cold central plasma (Churazov et al. 2003; Fujita et al. 2004). A subset of and the energy equation spiral CFs may be created as low entropy plasma from a ds ρ subcluster core spirals down the gravitational potential, ρT = (∂t + U · ∇)T + ρT ∇·U (3) following an off-axis merger (Clarke 2004). dt Γ − 1 Sloshing simulations have produced CFs and = ∇·(κ∇T ) − Λ. spiral features that nicely resemble observations (Ascasibar & Markevitch 2006; ZuHone et al. 2010; Here, we denote the mass density ρ, the pressure P , the Roedigeret al. 2011; ZuHoneet al. 2011). How- temperature T , the normalized temperature T ≡ kB T/µ, ever, these features are essentially transients the Boltzmann constant kB, the mean particle mass (Ascasibar & Markevitch 2006; ZuHone et al. 2010), µ ≃ 0.6mp, the proton mass mp, the velocity vector U, which do not survive long once cooling and isolation the inertial acceleration vector a, the entropy s, and the by the TD-sheared magnetic fields (Keshet et al. 2010) thermal conduction coefficient κ. are taken into account (ZuHone et al. 2011). Moreover, For simplicity, the cooling function Λ is approximated these simulations assume a preexisting CC with the as typically observed size and universal thermal profiles, 0 < Λ ∝ ρ2T 1/2 , (4) rather than address the formation of such a core. Finally, sloshing simulations have not yet addressed the independent of metallicity; the effect of a different tem- role of AGN feedback and its coupling to the flow. perature dependence is discussed at the end of §3. We The preceding discussion suggests that spiral flows are approximate the equation of state as that of an ideal gas, ubiquitous in CCs. This is based on the combination of ρk T the common appearance of spiral structure involving CFs P = B = ρT , (5) µ Spiral flows in cool cores 3 with adiabatic index Γ = 5/3. For simplicity, we assume in a simple form: continuity, that the gravitational potential Φ is spherically symmet- ∇ d ln ρ r ric, such that the gravitational acceleration g = − Φ λρ ≡ = − ∇ · U = − 1+ λw + λ˜z ; (7) is radial. In addition, we neglect thermal conduction by d ln r v   taking κ = 0. This is probably justified for conduction momentum conservation along φ, perpendicular to the flow, as the shear amplified mag- 2 2 netic fields quench the perpendicular transport. Parallel d w w aφ + = − 2ωw ; (8) conduction is suppressed by scattering off plasma waves dr  2  r γ (e.g., Pistinner & Eichler 1998); the role of parallel con- duction is discussed in §7. momentum conservation along r, The observation of a spiral pattern in a galaxy cluster 2 2 d v w 2 suggests a symmetry axis, denoted by z, perpendicular − = ar + ω r +2ωw ; (9) to the plane of the spiral. We assume that the spiral flow dr  2  r evolves sufficiently slowly to approach a steady state, in and energy conservation, a (possibly rotating) cluster frame of reference. There- fore, if the spiral pattern is rotating, it must do so uni- vρT 1+ λw + λτ + λ˜z = −Λ . (10) formly, in order to avoid a winding problem. Henceforth, r   we assume that the pattern is rotating with a constant 1/(Γ−1) but arbitrary angular frequency ω about the z axis, and Here, τ ≡ T is the reduced temperature, γ ≡ work in the corresponding rotating frame unless other- sin (α) serves as the pattern parameter, full derivatives wise stated. This requires the addition of fictitious forces are taken along the flow, to the momentum equation, which then becomes d ∂ 1 ∂ = + , (11) − (U · ∇)U = −ρ 1∇P − ∇Φ (6) dr ∂r γr ∂φ −2Ω × U − Ω × (Ω × x), and we defined power-law indices Ω zˆ d ln |A| where ≡ ω is the rotation vector. λA ≡ (12) For simplicity, we assume that an equatorial plane can d ln r be found, perpendicular to the z symmetry axis, in which for the evolution of each quantity A along the flow. These all streamlines are approximately confined to the plane. equations apply along streamlines that are parallel to the We use cylindrical coordinates x ≡{r, φ, z}, with r being TD, both above and below it, everywhere that Eq. (11) the radial distance and φ the azimuth, defined such that holds. Deviations are expected far from the TD, but for a the origin coincides with the center of the cluster, and spiral flow these are significant only in a localized mixing the equatorial plane lies at z = 0. We label the velocity layer interleaved between the TDs. components by U ≡ {v, w, Uz}, and sometimes use the In order to incorporate the 3D structure of the flow in two-dimensional (2D) velocity parallel to the equatorial a simple manner, we assume that U and the TD surface plane, u ≡{v, w}. The TD pattern in such a plane per- are perpendicular when projected onto the z − r plane. pendicular to z is quantified by the angle α(r) it makes Parameterizing the effects of the flow component per- with respect to φˆ. These definitions are illustrated in pendicular to the plane of interest is thus simplified, as Figure 1. it depends only on the TD radius of curvature in the r−z plane, R = −[1 + r′(z)2]3/2/r′′(z), through the relation ` θ r ˜ Uz r u λz ≡ r∂z = . (13) v Α  v  Rθ This assumption is illustrated in Figure 2. w ` Α z` Equivalently, this assumption means that the flow is Φ r= confined to the plane spanned by the local TD normal, const nˆ, and nˆ × zˆ. This generalizes the equatorial analy- sis which follows to any point in the core, both inside and outside the equatorial plane, as long as streamlines TD within the confined plane remain parallel to the TD. Note Ω that a flow of this type is well-defined globally only if r/Rθ . 1, such that the flow planes do not intersect. Fig. 1.— Parameter illustration in a plane parallel to the equa- ˆ Moreover, a pure equatorial spiral pattern is in general tor. The TD (solid curve) forms an angle α with φ, i.e. with the deformed in such confined planes that are not parallel to circle r = constant (dot-dashed). The plasma must flow parallel to the TD. The planar velocity u (thick green arrow; parallel to the equator, as γ(r) may become complicated and even the TD at the point analyzed) is decomposed into radial (v) and non-monotonic. angular (w) components (dashed green arrows). The pattern may ˆ Next, we solve the tangential momentum equation (8), rotate about the z-axis, in the +z sense if ω > 0 (circular arrow). by assuming that the inertial acceleration is approxi- mately radial, |aφ| ≪ |ar|. This is justified by the ap- The flow along a TD must be parallel to it. Thus, proximately spherical distributions of pressure and of to- focusing on the flow along (on either side of) a TD in the tal (including dark matter) gravitating mass in CCs, al- equatorial plane, the steady state equations can be cast though we shall later see that first order corrections in 4 U. Keshet

approximately adiabatic. Equations (5), (7), and (10) then yield for this fast (indices f) component: λ 3 z λ (f) = = λ ≃−0.36, (16) RΘ ρ Γ 5 Γ − 1 2 λ (f) = λ = λ ≃−0.24, (17) T Γ 5

` (f) r Γ+ λ 3 λw + = − = −1 − λ ≃−0.64, (18) i Rθ Γ 5 where we took λ ≡ λP ≃−0.6 (19) on the right hand side (RHS) of these equations as a typical value of the logarithmic pressure gradient. To il- Fig. 2.— Illustration of the flow perpendicular to the equatorial plane, and of CF projection along the line of sight ˆi (black arrow). lustrate the weak dependence upon λ, Table 1 reproduces Three examples of CFs, intersecting the equatorial plane (dotted these and the following relations for a slightly different horizontal line) at the same distance r from the center (black disk), pressure profile, λ = −2/3. are shown in a plane perpendicular to the equator, i.e. “edge on”. Next consider the momentum equation along φ. The The CFs have radii of curvature Rθ = r (solid red), Rθ >r (dashed trivial solution Eq. (14) corotates with the TD pattern, blue), and Rθ

2 2 Γ 1+ γ = CΦ − Φ − Tf . (24) (s) 1+3λ λ 1 2 λw ≃− + = − (31) wf  Γ − 1  5 Γ 5 However, the γ term is a small correction here (γ2 ≃ 0.04; (independent of λ for Γ=5/3). see §6). Therefore, in addition to the reservations men- These relations also fix the pattern of the spiral, tioned above, the resulting pattern would be sensitive (s) (s) Γ − 1 2 to the precise form of Φ, would depend on the ω correc- λγ = λv − λw ≃ λ = λ ≃−0.24. (32) tions, and in general would not produce a pure power-law Γ 5 profile. Instead, we shall compute γ(r) using the slow The pattern in turn may be used to determine the scal- component of the flow. ing of the radial velocity of the fast flow, which was left undetermined above: 3.3. Nearly corotating slow inflow Γ − 1 2 λ (f) ≃ λ − 1= λ − 1 ≃−1.24. (33) Consider the slow flow just above the CF. If this com- v Γ 5 ponent were to follow the non-trivial solution Eq. (15), then there would be fast flows above the CF, at ei- These power-law indices are all fairly weak functions ther small or large radii. Such flows are not observed; of λ, indicating that the model is robust. They are sum- rather, the region above the CF is typically consistent marized in Table 1, evaluated numerically for a slightly with hydrostatic equilibrium (Markevitch et al. 2001; different pressure profile, λ = −2/3. Keshet et al. 2010). We deduce that the velocity of the slow component is approximately given by the trivial so- TABLE 1 lution Eq. (14). If the flow were adiabatic, this would 5 2 Scaling of the two-component model, for Γ= 3 ; λ = − 3 . correspond to stationary, hydrostatic equilibrium plasma Property A Power law index λA = d ln |A|/d ln(r) in the rotating frame, with an arbitrary thermal profile 2 pressure P λ ≡ λP = − 3 and consistent with any spiral pattern. 2 4 However, a slow flow, in particular one with v ≃ 0, spiral slope γ 5 λ = − 15 ≃−0.27 must be modified by cooling. Indeed, a stationary flow Fast phase Slow phase 3 2 −4+3λ 6 with u = 0 does not satisfy the energy equation (10). density ρ 5 λ = − 5 = −0.4 5 = − 5 = −1.2 2 4 4+2λ 8 Therefore, we must consider small deviations from a triv- temperature T 5 λ = − 15 ≃−0.27 5 = 15 ≃ 0.53 2 19 −1+2λ 7 ial flow and from a purely radial acceleration. Linearizing rad. velocity v 5 λ − 1= − 15 ≃−1.27 5 = − 15 ≃−0.47 1 Eq. (8) to first order in {aφ, v, w} yields tan. velocity w −1 − 5 = −0.2 a 1 Note that λ here is taken slightly different numerically than in 2ωv ≃ aφ ≃− ∂φP , (25) the text, in order to show its rather weak effect, in particular on the rρ slow component. The flow equations require r/Rθ = −λ/Γ = 2/5, intermediate between cylindrical and spherical TD geometry. 1 One may alternatively model the gravitating mass distribution, for example using an NFW profile (Navarro et al. 1996) for the dark matter, but the cD galaxy must be included due to its strong The above scaling relations imply that the bracketed influence on the core. term in the energy equation (10) is positive for the slow 6 U. Keshet component, tween the fast, cold flow from below and the slow, hot component from above. This strongly sheared boundary (s) (s) ˜ 1+ λw + λτ + λz ≃ [4Γ + (5 − 3Γ)λ]/[5(Γ − 1)] ≃ 2 . is thought to be stabilized magnetically, isolating the two Therefore, the slow component must be an inflow, components (Keshet et al. 2010). In contrast, the tran- sition layer between slow flow from below and fast flow with vs < 0. Approximating the cooling rate −27 −3 2 1/2 −1 −3 from above is not discontinuous, as such a discontinuity as Λ ≃ 2.1 × 10 n[cm ] T [K] erg s cm would become RT unstable. This layer is likely to involve (Rybicki & Lightman 1986), we find substantial heat conduction, convection, and gas mixing, −1/2 − and may become turbulent. In this region our analysis v ≃−10 n T r km s 1 , (34) s 0.03 4 10 breaks down, as streamlines may no longer be parallel to where n0.03 is the electron number density n = ρ/µ the TD. −3 in 0.03 cm units, T4 ≡ (kB T/4 keV), and r10 ≡ In order for the TD to remain RT stable, the fast flow (r/10 kpc). This velocity is of order 1% of the sound below the discontinuity must remain at least as dense velocity cs, consistent with the slow flows above CFs in- and as cool as the flow above the TD. The temperature ferred from observations. (or equivalently, as we assume an isobaric transition, the Notice that the spiral pattern and fast flow are inde- density) contrast q across the TD increases with r as pendent of, and the slow flow depends weakly on, the T ρ precise temperature dependence of the cooling function 1 < q ≡ s ≃ f ∝ r4/5 , (35) Eq. (4). For example, in the cold, high metallicity re- Tf ρs gions in the centers of small clusters and groups of galax- ies, the temperature dependence weakens to Λ ∝ T 0 so the discontinuity would become RT unstable at very (e.g., Peterson & Fabian 2006). Here, the scaling laws small radii, limiting the extent of the flow or the validity (s) of the scaling derived above. Similarly, the velocity ratio in Eqs. (28)–(31) slightly change, to λρ ≃ −1.07, between the fast and slow components diminishes with (s) (s) (s) λT ≃ 0.47, λv ≃−0.53, and λw ≃−0.29. increasing radius,

u u − 4. GENERAL PROPERTIES OF THE FLOW 1 < f ≃∓ f ∝ r 4/5 , (36) The scaling relations derived in §3 indicate that the us us velocity of the fast, cold component increases at smaller where the minus (plus) sign corresponds to a fast out- radii, while the slow, hot flow becomes denser and some- flow (inflow). Thus, the shear responsible for the stabi- what cooler at small radii. The spiral pattern is found to lizing magnetic fields gradually diminishes at large radii, be nearly logarithmic (for a logarithmic spiral γ = const., again limiting the extent of the flow or the validity of the or equivalently, λγ = 0), with a slight tendency towards power-law scaling. Note that the ±4/5 power-law indices an Archimedes spiral (for which λγ = −1). We may now in Eqs. (35) and (36) are independent of Γ and λ. combine these scaling laws with observations in order to As TD contrasts of order q ∼ 2 and nearly sonic shear test the model and further explore the nature of the flow. ∆u ∼ cs are inferred from CF observations, extrapolat- Observations suggest (Keshet et al. 2010) that the fast ing these scalings to small radii suggests that the two flow inward of a CF is confined to the vicinity of the components have similar temperatures and densities at discontinuity, inducing shear up to distances of order some small radius r0, near the base of the TD, where q ∆r . 0.2r below the CF at radius r. Therefore, in approaches unity and the fast component is nearly sonic, the simple approximation where the core is composed of only the two, fast and slow, components, we expect q(r0) ≃ 1 ; uf (r0) ≃ cs . (37) the thermal properties of the core to be dominated by the slow flow. Hence, the core must approximately fol- More generally, a measured contrast q(r) or shear low ρ ∼ r−1 and T ∼ r1/2. Similarly, the behavior of the ∆u(r) thus places an upper limit on the radial extent −5/4 TD shear is dominated by the fast flow, so approximately of the discontinuity, for example r0 > q(r) r. As an −1 ∆u ≡ us − uf ∼ r . illustration, a TD following the power-law scalings of §3 These properties are broadly consistent with the ther- extends no more than a factor r/r0 ≃ 2.4 (≃ 3.9) below a mal structure of observed cores (e.g., Voigt & Fabian CF observed at radius r, if the inferred TD contrast there 2004; Sanderson et al. 2006; Vikhlinin et al. 2006; is q(r) = 2 (= 3). In practice, the flow may extend some- Donahue et al. 2006; Sanderson et al. 2009), and with what beyond such estimates, because (i) the flow can the (presently weak) constraints on shear (Keshet et al. persist beyond the TD, if the discontinuity evolves into a 2010). We also find that the spiral pattern inferred more gradual transition; (ii) inaccurate deprojection may above is consistent with the observed spiral pattern in cause q and ∆u to appear smaller than they really are, Perseus, which is amongst the clearest spirals observed for example if a very dense or fast flow is confined to the to date, and is presumably seen nearly face-on (approx- very near vicinity of the TD; and (iii) deviations from imately along the z-axis); see Figures 3 and 4. Even our power-law model are expected at small radii, due to better agreement is found with the late-time, quasi- the nearly sonic velocity of the fast component, the pos- stable pattern discovered in the merger simulation of sible breakdown of the assumption us ≡ |us| ≪ ωr, and Ascasibar & Markevitch (2006), where the projection is the active environment near the AGN. controlled; see Figures 5 and 6. In both cases, the spiral The scaling relations derived in §3 are likely to break is approximately logarithmic, with slightly negative λγ . down at some large radius rmax, where the fast flow be- The two components of the flow slide across each other comes sufficiently slow that its cooling can no longer be along the spiral, RT stable, TD surface that separates be- neglected. We may use Eqs. (34), (36), and (37), to Spiral flows in cool cores 7

Fig. 3.— Spiral pattern observed in Perseus. Shown is an XMM image (Churazov et al. 2003, data courtesy: E. Churazov), before (left; 30′ diameter) and after (right; 25′ diameter) smoothing with an adaptive, photon count per-bin conserving, Gaussian filter, cropping edge effects, and applying a gradient filter. Red contours enclose dark regions that correspond to enhanced gradients, tracing CFs. The light regions have small gradients, and show mosaic and other artifacts. The dashed green curve is the best-fit power-law spiral derived in Figure 4. (e.g., Richtmyer–Meshkov) instabilities, turbulence, and the weaker seed magnetic fields anticipated at large radii, this suggests that the two components mix at some radius r & rmax. Both effects may contribute to the absence of observed CFs with large contrasts. The momentum equations for the slow component re- quire that ω 6= 0, i.e. the spiral pattern must rotate, albeit much slower than the fast component. The sense of rotation is related to the tangential force acting on the slow component, by Eq. (25) (with v < 0): if aφ points towards the outspiral (inspiral) direction, then the spiral is trailing (leading). For a spherically symmetric gravita- tional potential, sign(aφ)= −sign(∂φP ), so the sense of rotation is fixed by the minute tangential pressure gra- Fig. 4.— Discontinuity pattern in Perseus. The strong gradient dients observed. regions (enclosed by red contours in Figure 3) are shown in the r–θ In a quasi spherical system, the deviation of the pres- phase space. Although θ is 2π-periodic (pale regions), one may trace it along an extended interval (dark regions) by following the sure map from its azimuthal average may reveal such pattern in Figure 3 and varying the threshold. The best fit (red small gradients. In Perseus, such a procedure shows a curve) power-law spiral, θ[rad] ≃−107.8+78.3(r/arcsec)0.054, cor- slightly elevated thermal pressure significantly outside ′′ ′ responds to λγ = −1 − rθ (r)/θ (r) ≃−0.05: nearly a logarithmic the CFs, at a finite distance above them: compare the spiral. pressure map in figure 10 of Churazov et al. (2003) to crudely estimate that the temperature or entropy maps. This corresponds to a pressure gradient within the slow component point- 1/2 1/2 cs r10T4 ing towards the inspiral direction. It suggests that the rmax ≃ ≃ 100 kpc. (38) spiral pattern is (i) indeed rotating; and (ii) trailing, be- |vs|r  n0.03 r 0 0 cause the force ∼ aφ exerted on the slow component is The spiral flow may persist beyond rmax with a some- directed along the outspiral direction. The above con- what different scaling, or may retain the same scaling if clusions are not sensitive to the presence of a magnetic the cooling of the cold component is compensated, for pressure, because the elevated thermal pressure is found example by heat conduction from the hot component. significantly far above the CF: one does not expect the Note that by rmax, the contrast across the TD becomes magnetic pressure to increase to significant levels as one 4/5 large, of order q ≃ (rmax/r0) ≃ 6. approaches the CF from above. Alternatively, the TD may be disrupted by Kelvin- The projected appearance of a spiral TD depends on Helmholtz (KH) and other instabilities near or somewhat the orientation of the spiral axis with respect to the line above rmax. At small radii, shear magnetic amplification of sight, and on the 3D structure of the TD manifold. As is thought to generate strong magnetic fields that sta- CFs are often nearly concentric, and some spiral CFs are bilize the discontinuity (Keshet et al. 2010). At larger observed, Rθ/r cannot be much larger or much smaller radii, the shear gradually weakens. This implies weaker than unity. Some projection effects are illustrated in Fig- KH instabilities, on one hand, but slower magnetic am- ure 2 (a full analysis of projection is deferred to future plification, on the other. Taking into account additional work). The figure shows how, for Rθ > r (in dashed 8 U. Keshet blue), as the line of sight gradually deviates from face- on viewing (in which the line of sight is parallel to the z axis of symmetry), the spiral pattern is stretched par- allel to the projected z axis. An opposite, perpendicu- lar stretching occurs for Rθ < r (shown in dot-dashed green). Due to the poor statistics, it is difficult to mea- sure this curvature observationally and test Eq. (21) and the corresponding parallel stretching. We have determined the radius of curvature of the flow perpendicular to the equatorial plane, but did not ad- dress the evolution of streamlines far from the equator, nor have we specified the extent of the spiral flow above the plane. The flow must extend a substantial fraction of the way towards the poles, in order to account for the observation of spiral patterns at various projections. In principle, the flow can extend all the way to the pole, where the model streamlines have an approximate heli- cal pattern around the z-axis, with an amplitude that diminishes close to the pole. Fig. 5.— Spiral flow formed as a result of a mass ratio 5 merger 5. TWO TYPES OF COMPOSITE FLOWS with a dark matter subcluster, in the adiabatic SPH simulation of Ascasibar & Markevitch (2006, data courtesy: Y. Ascasibar). Due to the adiabatic nature of the fast component, The slice shown is 560 kpc on the side. Greyscale shows the gas its behavior is symmetric under time-reversal. Hence, in temperature, ranging from 3.3 keV (dark) to 9.8 keV (bright). Ar- contrast to the slow component which must be an inflow2, rows trace the gas flow. Green contours enclose regions in which (∇× U)z is smaller than a negative threshold, i.e. strong local the analysis above does not distinguish whether the fast clockwise circulation. The dark matter peak is shown as a yellow component is an inflow or an outflow. We thus consider triangle. The spiral pattern rotates counterclockwise, i.e. is trail- below both options for the composite spiral flow: (i) a ing. The fast component here is an inflow. The slow component is in part an outflow, although this is obscured by the uniform combination of slow and fast inflows; or (ii) a combina- rotation of the pattern. tion of a fast outflow and a slow inflow. The former type of flow is essentially a transient that accretes mass onto the center, while the latter could in principle be long-lived, and may form a closed circulation loop with quenched accretion. Note that although spi- ral inflow and outflow components carry opposite signs of mass and heat radial fluxes, they carry the same sign of angular momentum flux. Hence, both an inflow and an outflow similarly transfer angular momentum in the trailing (leading) spiral sense inward (outward), across the core, limiting the lifetime of the flow unless an exter- nal torque is involved.

5.1. fast and slow inspiral The first option, in which the fast component is an inflow, is in essence a transient phenomenon (albeit long- Fig. 6.— Discontinuity pattern in the simulation of lasting, of timescale & Gyr in the absence of cooling), as Ascasibar & Markevitch (2006) shown in Figure 5, derived in the the cold, metal-rich inflow must originate deep in the same method as Figure 4, based on regions exceeding a gradient threshold (blue points). The best power-law spiral fit (red curve), core. In order to produce such a flow, the central plasma 0.27 θ = −26.2 + 8.5(r/kpc) , corresponds to λγ ≃ −0.27: nearly a must first be uplifted by some violent process, such as logarithmic (slightly tending towards an Archimedes) spiral. the gravitational kick and angular momentum deposition imparted by a merger event (Markevitch et al. 2001), the 2005; Ascasibar & Markevitch 2006) and of minor merg- impact of weak shocks or acoustic waves (Churazov et al. ers (Roediger et al. 2011), and in simulations that incor- 2003; Fujita et al. 2004), or the uplift of hot (radio) AGN porated cooling (ZuHone et al. 2010, 2011). bubbles that buoyantly rise from the center. However, without additional effects, such sloshing can- In particular, sloshing motions induced by strong not protect CCs from catastrophic cooling. Although perturbations of the core following a merger event shown to somewhat delay cooling by mixing the gas were shown to produce CFs and spiral patterns in (ZuHone et al. 2010), sloshing alone cannot sustain the broad agreement with observations, provided that the core for more than ∼ 1 Gyr, once magnetic shear ampli- merger does not strongly disrupt the original core. fication along the TDs (Keshet et al. 2010) is taken into This was demonstrated in simulations of major merg- account (ZuHone et al. 2011). Nevertheless, it remains ers with a dark matter subhalo (Tittley & Henriksen to be seen if AGN feedback could stem cooling in the presence of such a composite spiral inflow. 2 This is due to cooling. A slow outflow is possible, for example, Strong magnetic fields, which are thought to form in an adiabatic simulation. not only at the TD, but throughout the fast flow layer Spiral flows in cool cores 9

(Keshet et al. 2010), as recently demonstrated numeri- ence frame, although it does transfer angular momentum cally (ZuHone et al. 2011), can divert AGN bubbles and radially, across the flow region. entrain them within the spiral pattern. Such entrain- Such a non-accreting flow essentially constitutes a ment is indeed observed in some cores, as illustrated closed circulation loop, which could explain the low star for Perseus in Figure 7. See also Forman et al. (2007); formation rate observed in cores (e.g., Rafferty et al. Fabian et al. (2011). Projection effects confuse the in- 2008; O’Dea et al. 2008). Here, cold gas from the base terpretation of such images, in particular in regards to of the flow at r0 is rapidly removed from the center out- the interaction of the spiral flow with entrained bubbles, wards, decelerates, and in part slowly accretes back to linear cold filaments, and other localized features. For the center, after being non-adiabatically heated by close example, some bubbles axes or long filaments may in proximity to hotter gas, through gas mixing and heat fact be oriented perpendicular to the equatorial plane, conduction. The flow thus solves the cooling problem, along the z symmetry axis. by advecting heat from the huge heat reservoir outside In addition to enhancing the dissipation of bubble en- the core and removing dense gas from the center before it ergy, such interaction between rising bubbles and a spiral can catastrophically cool, while quenching or maintain- inflow suggests a natural feedback mechanism: accretion- ing a low level of mass accretion, and carrying angular driven AGN activity may disrupt or heat the inflow. An- momentum away from the center. other possibility is that mechanical feedback may stop Such a flow requires some mechanism to rapidly propel the inflow and push it outwards, resulting in an inflow– gas from the central parts of the core outwards. Can- outflow composite spiral of the type studied in §5.2 be- didate mechanisms include gravitational forces, such as low. Feedback is further discussed in §7. the stirring effect of the rotating vector separating be- tween gas and dark matter peaks, and the AGN energy 5.2. fast outspiral and slow inspiral output, coupled for example through the forces exerted The second possible type of composite flow combines a by shocks, jets, and buoyant hot bubbles. Such AGN fast, cold outflow and a slow, hot inflow, spiraling across bubbles, in particular, suggest a natural feedback mech- each other. Such a flow follows the same scaling relations anism, provided that their production is moderated by as the double-inflow model of §5.1, although shear and the accretion rate, as discussed in §7. gas mixing are probably somewhat stronger. High angular momentum in the inner core is another It is interesting to note that adiabatic sloshing simu- requirement, needed both in order to sustain the an- lations sometimes show, at least locally, composite flows gular momentum flux, and to loosen the gravitational of an opposite character, combining a fast inflow and binding of the core. Such angular momentum can build a slow outflow, as seen for example in some regions in up through (possibly alternating) epochs of strong spi- the snapshot of the Ascasibar & Markevitch (2006) sim- ral flows, for example in the form of an inspiral–inspiral ulation depicted in Figure 5. The flow discussed here composite flow, by merger events, and by the sinking is similar, in the adiabatic limit, to the time-reversal of of dark matter substructure towards the center. The such an adiabatic simulation. initial formation of the spiral pattern can be facilitated A novel property of a composite inspiral–outspiral flow by a merger event, by amplified g-modes, or by spiral of the type discussed here is that, unlike the composite instabilities that tend to separate even a non-rotating, inflow model of §5.1, it could constitute a quasi steady- uniformly accreting, cooling gas into spiral motions of state solution, as long as the center can absorb angular opposite orientation, for example in the standing ac- momentum in the trailing spiral sense. This can occur, cretion shock instability (SASI) simulations discussed in for example, if an external force torques the center in the Blondin & Shaw (2007). opposite, leading spiral direction. Feedback-regulated 6. TWO-COMPONENT INFLOW–OUTFLOW TOY MODEL flows that alternate between fast and slow mass accre- tion, or between spirals of an opposite orientation, are Above we derived some of the properties and scaling also possible. relations of a spiral flow of the type expected in a cluster Specifically, consider the mass flux across a given ra- core, constrained by the presence of a spiral TD surface dius in the equatorial plane. The outflow layer is much with strong shear due to a fast flow below the disconti- faster than the inflow, but is also much narrower, so the nuity. We showed that the flows immediately above and relative widths of the two components (defined, say, as immediately below the TD follow different scaling rela- tions, but have not quantified the variation in the flow the ratio ν(r) ≡ ∆φf /∆φs < 1 of their φ extents at a given r) can be chosen to eliminate the radial mass flux. properties with distance from the TD. Here we wish to Due to the curvature of the streamlines both inside and provide the full solution to one type of such a spiral flow, outside the equatorial plane, the planar mass flux ρvr of by introducing a simple two-component toy model. each component is r-dependent. Nevertheless, for both In order to obtain a fully constrained system and re- components it follows the same scaling, produce the low mass accretion rate inferred from obser- vations, we choose the flow variant of §5.2, combining a d ln(ρvr) r fast outflow and a slow inflow, and require that the ra- = λ + = λ . (39) d ln r γ R dial mass flux vanishes. In order to account for the mild, θ q ∼ 2 contrast of typical CFs, and the nearly sonic shear Thus, a fixed ratio ν between inflow and outflow vol- inferred from their profiles, we assume that ρf = ρs, ume fractions would guarantee a choked mass accretion Tf = Ts, and uf ≡ |uf | = cs at some small radius r0, as throughout the flow, if ν is properly tuned. Note that, as discussed in §4; see Eq. (37). These constraints fix all the the streamlines are approximately parallel, such a spiral model parameters except the normalization of γ, which flow carries no angular momentum in the rotating refer- can be approximately measured as demonstrated below. 10 U. Keshet

Fig. 7.— Deep (900 ks ACIS-S) archival Chandra image of Perseus (presented, e.g., by Fabian et al. 2006; Sanders & Fabian 2007), 8′ (∼ 240 kpc) on the side, shown with (right) and without (left) the features discussed in the text. Over-plotted on the right are the best-fit spiral CF pattern (dashed blue) derived in Figure 4, along with apparent (green closed curves) and possible (yellow curves) X-ray cavities, suggesting AGN bubbles interacting, and possibly entrained in the spiral flow. The X-ray cavities were identified by a visual inspection (M. Markevitch, private communications, 2009, 2011); some of them were also pointed out in Fabian et al. (2011).

The requirement of choked mass accretion fixes the ra- function of the normalized radius σ ≡ r/r0 by tio between the widths of the two layers, which we pa- (f) (s) λρ λρ rameterize using the angular extents ∆φ of each phase ρ(σ) ∝ ∆φf σ + ∆φsσ (42) at a given r, − 4/5 − 4 3λ ∝ 1 − ν 1 − σ σ 5 h  i ∆φf ρsvs vs n0.03r10 4/5 −1.16 ν ≡ ≃ ≃ ≃ 0.05 . ≃ 1 − 0.05ν0.05 1 − σ σ , ∆φs ρf vf r0 csγ r0  T4γ0.2 r h  i 0 (40) where ν0.05 ≡ (ν/0.05), and we used a pressure profile Here we defined γ0.2 ≡ γ(r0)/0.2 ≃ 1, based on pre- λ ≃ −0.6 in the last line. This profile is best fit for liminary estimates of γ at the base of the spiral pat- the above typical parameters by ρ ∝ σ−1.1 in the range terns: (i) in Perseus, where γ(10 kpc) ≃ 0.20 (see Figure 1 <σ< 10, as shown in Figure 8 (left panel). 3); and (ii) in the Ascasibar & Markevitch (2006) sim- The emissivity-weighted temperature profile is simi- ulation, where γ(10 kpc) ≃ 0.23 (see Figure 5). Recall larly given by that although ν is evaluated at r0, it remains constant 3 (f) (f) 3 (s) (s) λT +2λρ λT +2λρ along the spiral; cf. Eq. (39). ∆φf σ 2 + ∆φsσ 2 γφ T (σ) ∝ A logarithmic spiral follows r(φ) ∝ e . As the spi- 1 λ (f)+2λ (f) 1 λ (s)+2λ (s) ∆φ σ 2 T ρ + ∆φ σ 2 T ρ ral patterns observed are nearly logarithmic, the radial f s 2/5 separation between consecutive TD spiral arms in the 1 − ν 1 − σ 4+2λ 2πγ ∝ σ 5 (43) equatorial plane is approximately rn+1/rn ≃ e ≃ 1+ ν σ6/5 − 1
2π(γ−0.2) 3.5e . In the toy model, the fast flow is confined
2/5 1 − 0.05ν0.05 1 − σ to a thin layer below the TD, with an approximate radial ≃ σ0.56 . 6/5 thickness of 1+0.05ν0.05 σ − 1

− The logarithmic slope of T (σ) declines with σ. The best ∆r ≃ r 1 − e 2πγν ≃ 0.06r , (41) f fit power law for the above typical parameters is T ∝ σ0.4
in the range 1 <σ < 5, as shown in Figure 8 (right where we used the parameters of Eq. (40). In reality, panel). The figure also shows, for comparison, the uni- the fast layer may be more extended, and the transition versal mean deprojected temperature profile found by between the fast and slow phases must be gradual. Sanderson et al. (2006), scaled with r0 =0.01r500, where Next, we compute the azimuthal averages of the flow r500 is the radius enclosing 500 times the critical density properties within the equatorial plane. Note that al- of the Universe. though these quantities approximately give the projected These density and temperature profiles are in good radial profiles when the streamlines lie on spheres (i.e. agreement with the characteristic structure of cores. In when Rθ ∼ r), a viewing angle-dependent correction is particular, the temperature peak typically observed near needed to account for projection effects when Rθ 6= r, in rmax is reproduced, although the power-law solution may particular when the spiral is not observed face-on. Nev- break down above ∼ rmax due to cooling and the steep- ertheless, as long as Rθ/r is not too far removed from ening of the pressure profile. The azimuthally averaged unity, such corrections are in general small. profiles depend on the volume fraction ν of the fast flow: The azimuthally averaged density profile is given as a smaller (larger) values of ν lead to a steeper (flatter) Spiral flows in cool cores 11

1.00 4 4 0.50 3 3 L

L 2 2 0 0 r

0.20 r H H Ρ

T 1.5 1.5 L L r r H 0.10 H Ρ T 1 1

0.05

0.5 0.5 0.02 1.0 1.5 2.0 3.0 5.0 7.0 10.0 15.0 20.0 30.0 1.0 1.5 2.0 3.0 5.0 7.0 10.0 15.0 20.0 30.0

rr0 rr0 Fig. 8.— Equatorial radial profiles of density (left panel) and temperature (right panel) in the accretion-choked spiral flow model described in §6. Shown are the azimuthally averaged profiles (solid curves), their best-fit power-laws ρ ∝ r−1.1 and T ∝ r0.4 (dot-dashed curves) evaluated near r0, and the profiles of the dominant, slow (short dashed) and subdominant, fast (long dashed) components. The model parameters used here are n0.03r10/T4 = 1 and γ(r0) = 0.2, or equivalently ν = 0.05 and rmax/r0 = 10; see Eqs. (38) and (40). The power-law solution is probably modified beyond ∼ rmax (dotted horizontal line), unless cooling of the fast component is balanced, for example by heat conduction. We assume that Γ = 5/3 and λ = −0.6; in reality the pressure gradient λ steepens above ∼ rmax. The mean deprojected CCC temperature profile found by Sanderson et al. (2006) is shown for r0 = 0.01r500 (dotted curve in the right panel, with a band representing the 1σ confidence level). density decline and temperature rise, approaching (devi- A significant fraction of the angular momentum inflow ating from) the slow phase profiles shown as black short- may be transferred to the uniform rotation of the spiral dashed curves in Figure 8. This may explain the scatter flow region, thus extending tL, as demonstrated in §7 for seen around the universal thermal profiles among differ- the case of torqued bubbles. However, as the uniform ent clusters. rotation must remain slow, the spiral flow must eventu- Various properties of the model can be directly read off ally stop or reverse, unless angular momentum is lost to Eqs. (35)–(37), and (40), in particular within the equa- the cluster’s periphery or an additional source of angular torial plane. For example, the fast outflow contains a momentum torques the center in the opposite, leading small, ν ∼ 5% fraction of the mass at the base of the sense. −1 −4/5 −1 spiral r0, but an increasing, [1 + (ν − 1)(r/r0) ] fraction at larger radii. The kinetic energy of this fast 7. THERMAL AND MECHANICAL FEEDBACK 2 −8/5 outflow is a small, ∼ (Γν/3)(uf /cs) ≃ 0.03(r/r0) , An energy source that offsets cooling in the core, and radially decreasing fraction of the thermal energy. a feedback loop that regulates it, are thought to be es- Eq. (40), which guarantees a vanishing mass accretion, sential in quenching the global thermal instability. AGN similarly implies that the spiral flow carries no angular output and heat conduction can in principle stem cool- momentum in the rotating frame, because the slow and ing, provided that the feedback efficiency is sufficiently fast streamlines are parallel. The angular momentum of high (e.g., Guo et al. 2008), and that the energy is prop- the flow region is therefore L ≃ ωI, where the moment erly distributed in space and time. Here we discuss the of inertia is I ≃ (π/8)r2M(< r) in the ρ ∝ r−1 approxi- nature of feedback in general terms; a quantitative anal- mation. ysis is beyond the scope of the present study. As mentioned above, although spiral flows may carry Heat conduction and convection can be significantly negligible angular momentum, for example in the choked- elevated in the spiral flow region, due to the influence of accretion case with ω → 0, the flow necessarily transfers the bulk flow on the transport processes and the close angular momentum radially, because (i) the angular mo- proximity between hot and cold phases. Magnetic shear mentum fluxes of the two components always add up, amplification leads to strong magnetic fields parallel to rather than cancel; and (ii) here the angular momen- the streamlines, along the TD and within the fast shear tum flux carried by the fast component strongly dom- layer beneath it, thus suppressing transverse transport inates that carried by the slow component, by a factor (Keshet et al. 2010; ZuHone et al. 2011). However, par- −1 −4/5 uf /us ∼ 20(ν/0.05) (r/r0) . allel transport may be enhanced due to the stronger, Thus, angular momentum in the sense of a leading spi- aligned fields, with less plasma wave inhibition. More ral rotation is transferred outwards, within the equatorial importantly, the RT unstable layer is not expected to plane and perpendicular to it, towards the poles. Equiva- undergo coherent shear; it could support substantial ra- lently, angular momentum in the sense of a trailing spiral dial heat conduction and convection. rotation is transported inward. This torques the central In order to close the feedback loop, the AGN output region in the trailing direction, for example slowing it must be regulated by mass accretion through the slow down if it initially rotates in a leading sense. This an- inspiral, as well as by the fast component if it is an gular momentum inflow sets a characteristic timescale inflow (in the composite inflow case discussed in §5.1). during which the equatorial rotation velocity at the base Although the fast flow is denser, it is not sensitive to of the spiral changes by the sound speed, heating (or cooling) due to its fast, near-sonic velocity, in particular at small radii. In contrast, the cooling reg- ulated, slow component is susceptible to heating, but the rcs r10 −1 tL ∼ ∼ 1 ν Gyr . (44) resulting behavior is sensitive to the details of the heat v w ν  T γ  0.05 f f r0 4 0.2 r0 12 U. Keshet deposition. Importantly, both fast and slow components than it would obtain in the absence of a spiral. This is can be significantly modified mechanically, for example clear in the extreme case where bubbles are sufficiently by the forces exerted by shocks, jets, and in particular large to span a substantial fraction of the cross section buoyant AGN bubbles. area of the inflow, such that gas is either forced outwards Consider heating first. Our model remains valid, with or compressed below the bubbles. This would agree with catastrophic cooling being quenched, if heating of the the large bubble size Rb and its tight, linear scaling with slow inflow is both efficient and able to approximately re- distance, Rb ≃ 0.6r, found by Diehl et al. (2008, see fig- (s) ure 1); note that the inflow cross section is indeed similar tain the λv ∼−1/2 scaling derived above. This may be − achieved, for example, if the specific heating rate roughly in size and in radial dependence, ∼ e 2πγr/(1+ν) ∼ 0.7r scales, on average, asǫ ˙(r) ∼ r−2, like the Λ ∝ ρ2T 1/2 (for a logarithmic spiral; see §6). Conversely, confine- cooling profile. These requirements are less strict than ment by the spiral magnetic structure can explain the theǫ ˙(r) ∝ ρ2 scaling sometimes invoked, as they rely on observed size and size–distance relation of bubbles. heat conduction and gas mixing for distributing the heat This confinement, so far ignored in feedback studies, along streamlines and on small scales. is likely to play a major role in the flow. The force that Next, consider a mechanical forcing of the flow. Slow- the spiral structure exerts on the bubbles, and the com- ing the inflow would only have a cooling effect, as it would pression of gas below the bubbles, could explain the en- increase the ratio between the inspiral time and the cool- hanced pressure observed above the TD, and the deduced ing time. In the limit where the forcing is strong enough trailing rotation of the spiral (see §4). It may also ex- to cause the infall to change sign and become an out- plain the high angular momentum of the outflow near flow, but still remain slow and susceptible to cooling, a the base of the spiral: bubbles are pushed in the leading steady flow would imply unrealistic thermal profiles, for direction by the magnetic layer already near or below r0, example λρ > λτ (cf. Eqs. 7 and 10). and throughout the spiral, while the more massive spi- We conclude that mechanical forces can effectively ral structure thus acquires equal angular momentum in stem cooling in a (quasi) steady-state flow of the type the trailing rotation sense. Thus, once the magnetic spi- studied here, only by pushing gas outwards at high ve- ral structure has formed, e.g., by a SASI-like instability, locity. The fast, outgoing flow may then drag some of the flow can in principle be sustained (well beyond tL the inspiraling gas along, causing the remaining inflow in Eq. 44) by mechanical feedback without an additional to expand (thus slightly cooling adiabatically), and the source of angular momentum, and in particular without cooling rate to decline. The ultimate outcome, even for invoking mergers, if the trailing rotation imparted to the an initially pure inflow, is a slow inspiral–fast outspiral, spiral structure is transferred to large radii. Such a sce- composite flow, of the type discussed in §5.2 and §6, with nario, in which there is neither a net angular momentum an outflow-to-inflow volume ratio ν regulated by the me- nor a net angular momentum flux, is beyond the scope of chanical feedback. the present analysis (e.g., it probably breaks the uniform In this scenario, the inflow–outflow spiral composite rotation assumption), and will be examined numerically flow becomes a direct manifestation of cooling and feed- in future work. back, in the presence of angular momentum. The slow 8. OBSERVATIONAL EVIDENCE FOR TWO COMPONENTS inflow, which dominates the core, is in essence a cooling flow, whereas the fast outflow removes dense gas from Observations indicate that CCs typically harbor more the center of the core before it has a chance to catas- than one plasma phase at any given distance from the trophically cool. Both components and the flux ratios center of the cluster. This is seen quite generally, in- between them are regulated by feedback, self-consistently cluding in clusters where no spiral pattern was so far enforced by the spiral-constrained flow. The steady state detected (see, e.g., Kaastra et al. 2004). The charac- here corresponds to a closed circulation with quenched teristic temperature spread at a given radius is a factor accretion, advecting heat inward and angular momen- of ∼ 2 − 4 (Buote et al. 2003; Kaastra et al. 2004), see tum (in the leading spiral sense) outward. The small, Figure 9 (abscissa). An identical spread exists in den- few percent ratio between the kinetic energy of the out- sity, as azimuthal pressure gradients are negligible. A flow and the thermal energy (see §6) indicates that this single phase is typically observed only in the outer parts mechanism is energetically plausible. of the core, although this may be due to poor statistics The rise of AGN bubbles is a natural candidate for me- (Kaastra et al. 2004). diating the necessary mechanical feedback, as the bub- The azimuthally averaged temperature, and the tem- bles preferentially deposit their energy at or just below perature of the hottest phase, were shown to decline the strongly magnetized, cool layer. Preliminary evi- towards the center of the cluster, approximately as a λT dence for this is seen in the suggested entrainment of power law, T ∝ r with λT ≃ 0.4 (Kaastra et al. 2004; bubbles within the spiral pattern; see Figure 7. Piffaretti & Kaastra 2006). The presence of the spiral, with its ordered bulk flow, Molendi & Pizzolato (2001) claim that X-ray observa- shear, and magnetic layer, constrains the motion of bub- tions of CCs are consistent at any given radius with a bles through the flow, and facilitates the transfer of ki- single plasma phase, with azimuthal temperature varia- netic bubble energy to the inflowing gas. In particu- tions. There have been attempts to attribute the multi- lar, the spiral directs the bubbles, by channelling them ple temperature measurements in some clusters to pro- along the magnetic layer and furnishing them with angu- jection effects through an inherently spherical tempera- lar momentum in the leading spiral sense. Thus, the gas ture profile (e.g., in A478, de Plaa et al. 2004). How- encountered by the bubbles acquires more momentum ever, this was shown not to be the case in select cases, for along the outspiral direction, and less random motions, example in 2A 0335+096 (Tanaka et al. 2006). Indeed, in some well-resolved clusters, coherent azimuthal tem- Spiral flows in cool cores 13 perature variations of a factor 2–4 are clearly observed, 4 sometimes taking the form of a spiral, as discussed in §1. The emission measure was found to scale roughly as æ D 3 2 αY Y ≡ ρ dV ∼ T with an average α ∼ 4, in various æ Y keV @ clusters and different radii (Kaastra et al. 2004). The à æ R max à à T 2 à æ æ hotter phase or phases thus strongly dominate the distri- à à à æ æ ç ç bution. For example, for two phases at pressure balance and ç ç ç ç with an average temperature ratio hqi = Tmax/Tmin ∼ 2, min ç T á á this would imply a small volume fraction of the cold 1 á á á á á phase,

αY +2 −6−(αY −4) 0 Tmin hqi 0 2 4 6 8 10 ν ∼ ≃ 0.02 , (45) arcmin Tmax   2  Fig. 10.— Projected radial temperature profiles of the hot (filled where the result strongly depends upon the poorly con- symbols) and cold (empty symbols) phases in Virgo. Shown are the strained hqi and αY . azimuthally averaged temperatures (circles; data from tables 6 and We point out in Figure 9 that the results of multiphase 8 of Kaastra et al. (2004)), and the temperatures measured along the southwestern X-ray arm (squares; from Werner et al. (2010)). modelling (Kaastra et al. 2004) suggest a correlation be- Here, 1′ corresponds to ∼ 4.7 kpc. tween the range Tmin/Tmax of temperatures observed at a given radius, and the spatial variation Tin/Tout of the Note, however, that the significance of the evidence re- temperature of the hottest phase across the core. (How- viewed in this section is in general quite low. ever, the statistical errors are substantial.) Studies of individual clusters also suggest that Tmin ∼ Tin (e.g., in 9. SUMMARY AND DISCUSSION 2A 0335+096, Tanaka et al. 2006). Such a correlation is We argue that spiral flows are ubiquitously present consistent with a model in which the ICM at any radius in cool cores, and show that the properties of the CCs in the core combines hot plasma from outside the core, and of the spiral flows are strongly constrained by the and cool plasma of a nearly constant temperature. very appearance of piecewise spiral cold fronts in high- 0.9 resolution X-ray maps. We interpret such core CFs as çì projected tangential discontinuities that lie above layers 0.8 of fast flowing, cold gas, as inferred from the observed ì CF profiles in Keshet et al. (2010). 0.7 ì In order to obtain a simple, analytic model, we make out

T several simplifying assumptions/approximations: (i) a  ì in 0.6

T ì symmetry axis z, with a preferred (equatorial, spiral) ì çì ì çì perpendicular plane; (ii) a steady state flow in some ro- 0.5 ì ì tating (about zˆ) frame; (iii) an ideal gas of adiabatic in- çìì ì çì dex Γ = 5/3; (iv) a spherically symmetric gravitational 0.4 potential, i.e. in particular, negligible self gravity of the 0.2 0.3 0.4 0.5 0.6 0.7 0.8 spiral pattern; (v) an approximately thermal pressure,

TminTmax nearly (but not exactly) spherically symmetric, scaling λ≃−0.6 Fig. 9.— Ratio between the inner and outer annulus temperature as P ∝ r (our results depend weakly on λ); (vi) a of the hottest phase in CCs (data from tables 6-7 in Kaastra et al. two-component flow approximation; (vii) negligible heat (2004); Perseus data from Sanders & Fabian (2007)), plotted conduction and convection; (viii) flow outside the equa- (green diamonds) against the average ratio Tmin/Tmax between the coldest and hottest phases in the same annulus (average of torial plane is confined to the plane spanned by the TD best fit column in table 8 of Kaastra et al. (2004)). Higher quality normal nˆ and nˆ × zˆ, so the equatorial analysis trivially λ data are highlighted (blue circles with linear fit in red, for clusters generalizes to the entire volume; and (ix) ∂φP ∼ r . with data for ≥ 3 annuli). Statistical errors (not shown) are large; Under these assumptions and approximations, we find we use only data with standard deviation smaller than half the mean. that the TDs and streamlines must follow a bulging cylin- drical spiral manifold: parallel to the equatorial plane, While the hottest, dominant phase usually becomes the manifold is approximately a logarithmic (tending colder towards the center of the cluster, the behavior slightly towards an Archimedes, λγ . 0) spiral, while of the cold, subdominant component/s is less clear. In perpendicular to the equator it is intermediate between some clusters, the data are consistent with a cold phase a concentric semicircle and a line parallel to the z axis; of constant temperature. This is illustrated for Virgo see Figures 1 and 2. Pictorially, one may image such a in Figure 10, using data from Kaastra et al. (2004, we TD surface as a (rather useless) open barrel, in which chose Virgo because its bins are the most numerous, and the metal hoops were replaced by spiral bands. The TD amongst the least noisy) and Werner et al. (2010). parameters (curvature Rθ perpendicular to the equator, The above lines of evidence, combined at face value, and spiral pattern λγ ) are summarized in Table 1. The suggest azimuthal temperature variations by a factor of TD pattern must slowly and uniformly rotate around 2–4, throughout the core, which is on average strongly the z-axis. Subtle pressure gradients (observed at a fi- 0.4 dominated by a hot, Tmax ∼ r phase, with a small (of nite distance above CFs in Perseus) suggest that the spi- order a few percent by volume) contribution from a cold, ral is trailing. The spiral pattern remains apparent in Tmin ∼ const. component. These are indeed the qualita- obliquely projected CFs, although it is increasingly dis- tive features derived in the two-component spiral model. torted and broken to pieces as the viewing axis deviated 14 U. Keshet from zˆ (see Figure 2). An additional assumption of choked mass accretion We examine the spiral pattern observed in Perseus (see may account for the weak cooling flows and the low star Figures 3 and 4), and the pattern found in the slosh- formation rates inferred from observations. This selects ing simulation of Ascasibar & Markevitch (2006, gener- the second, inflow–outflow type of composite spiral flow, ated by a major merger with a dark subcluster; see Fig- strongly constrains the properties of such a flow, and ures 5 and 6). Indeed, in both cases a nearly logarith- produces thermal profiles in good agreement with obser- mic spiral pattern is found. The pattern in the simu- vations (see Figure 8). Such a flow is essentially a closed lations, in particular, is an approximately uniformly ro- circulation, carrying no angular momentum in the rotat- tating, trailing, logarithmic (slightly tending towards an ing frame, advecting heat inward from outside the core, Archimedes) spiral, in agreement with the model. and carrying cold, dense gas outwards at high velocity In order to account for CF observations, the spiral flow before it can catastrophically cool. must combine a dense, cold, and metal-rich component, Both types of spiral flows transfer angular momentum flowing fast and nearly adiabatically in a narrow layer radially, torquing the central core in the sense of a trailing beneath the TD, and a slowly inspiraling, cooling, hotter spiral rotation. This can persist over timescales longer component, which fills most of the volume. These two than tL ∼ 1 Gyr (see Eq. (44)) only if the spiral pattern flow components correspond to the two distinct solutions reverses, additional angular momentum is deposited in of the angular momentum equation (8). Extrapolating the center, or the angular momentum involved in the the properties of observed CFs suggest that at some small trailing rotation of the entire structure is transferred radius r0, the two components have comparable densi- (e.g., magnetically; see §7) outwards. ties and temperatures, and the fast component is nearly Both types of flows may quench the local thermal in- 4/5 −4/5 sonic, such that q ≃ (r/r0) and uf /us ≃ 20(r/r0) , stability, as they efficiently distribute energy spatially independent of Γ and λ; see Eqs. (35)–(37) and (40). A and temporally across the core by bringing cold gas from transition layer that separates between the two compo- small radii and hot gas from outside the core into close nents at their RT unstable side (where the fast, dense contact, strongly mix the gas in the RT unstable layer, flow lies above the slow flow) mixes the gas and may and possibly enhance transport along streamlines. heat the cold component. Moreover, in the presence of AGN feedback, the spiral The scaling properties derived for each component of may stabilize the core also against the global thermal in- the flow are summarized in Table 1. The density and stability, as discussed in §7. One way this could happen is through heating, but this requires an approximately temperature of the fast, adiabatic component change − slowly with radius, and it is increasingly fast near the r 2 heating profile. A more natural and robust feed- center. In contrast, the velocity of the slow component back involves the mechanical energy output of the AGN, changes more gradually, and it becomes much denser and forcing gas outwards at high velocity. This can lead to somewhat colder at small radii. The azimuthally aver- stable flows of the second, inflow–outflow type, with re- aged density and temperature profiles are dominated by alistic core profiles and choked mass accretion. Here, the the slow component, and are found to be in good agree- spiral plays a central role in coupling the AGN output − ment with observations3: ρ ∼ r 1 and T ∼ rλT .0.5. The to the gas, for example by channelling bubbles along the model qualitatively agrees with the multiphase proper- spiral. This efficiently quenches cooling by regulating the ties observed in CCs (see §8), and reproduces the typical inflow, removing dense gas from the base of the spiral, ∼ 100 kpc core size; see Eq. (38). and modulating the spiral in response to perturbations as The equations governing the flow do not break a degen- to maintain a low level of accretion. The observed linear, eracy in the direction in which the fast, adiabatic compo- Rb ∼ 0.6r scaling of bubble sizes (Diehl et al. 2008) may nent is flowing, allowing for two types of composite spi- provide direct evidence for such mechanical feedback and ral flows. In the first type (see §5.1), both fast and slow coupling. components are inflows, such as expected in the slosh- Regardless of the cooling problem and the type of flow, ing oscillations induced after a merger event disrupts the a spiral flow strongly affects/mediates the AGN output, core (in the presence of cooling). This is essentially a for example by diverting hot bubbles, distorting jets, and transient mode, with substantial accretion and little re- deflecting shocks. Indeed, there is evidence that bubbles silience to cooling, unless AGN feedback reverses part of interact with, and appear to be entrained by, the spiral the slow infall and accelerates it outwards to high veloc- pattern (see for example Figure 7; Forman et al. (2007); ity. In such a scenario, the core evolves into a second Fabian et al. (2011)); such rising bubbles do provide di- type of flow: an inspiral–outspiral composite mode. rect evidence that at least some part of the ICM is an This second type of composite flow (see §5.2) involves outflow. AGN bubbles are therefore natural candidates a cold, fast outflow and a hot, slow inflow. While this for mediating the mechanical feedback; this can also ex- requires some mechanism for launching or sustaining the plain the trailing spiral rotation. Interactions with a spi- outflow, it naturally solves the global cooling problem ral flow may explain the rapid growth of bubbles and with a low level of mass accretion, provided that the their linear size–distance relation (Diehl et al. 2008, and outflow is regulated by some accretion-driven feedback see §6), the asymmetric deformation of flow around some mechanism. AGN bubbles, in particular, provide both a bubbles (Lim 2011), and the large sizes some bubbles at- launching mechanism and a plausible feedback loop; see tain (e.g., McNamara et al. 2005). the discussions in §6, §7, and below. Bubbles and cold filamentary nebulae, observed near the centers of some CCs, gauge the flow. In particular, 3 One of the two independent thermal parameters is essentially coherent axes of bubbles (e.g., Fabian et al. 2011) and fixed by the gravitational potential; the second is a prediction of extended linear cold filaments, thought to arise from the the model. Here we choose to externally fix the pressure profile. local thermal instability (e.g., Pizzolato & Soker 2006; Spiral flows in cool cores 15

Sharma et al. 2012), may seem to limit the presence of of) the TD-stabilizing magnetic fields. spiral flows to larger radii. However, (i) most of the vol- The existence of spiral flows in cores can be directly ume is filled with the slow, . 100 km s−1 gas in which tested through the spectroscopic shift and broadening differential rotation is minimal, whereas the fast flow is induced by flows along the line of sight. Evidence confined to a thin layer below the TD; (ii) bubbles appear for an intricate, possibly spiral velocity structure was to be entrained by the flow, possibly driving or stabiliz- thus uncovered in Perseus (Sanders et al. 2004, figure ing it, so extended, albeit slightly bent, axes are to be 8), and evidence for spectral broadening at the level expected; and (iii) some extended linear structures may of the sound velocity was found in a small subset of be parallel to the rotation axis z, for example the long, clusters (Sanders et al. 2011). Upper limits on the en- warped filaments sometimes observed in isolation. The ergy associated with the projected velocity dispersion, presence of filamentary nebulae in some CCs may reflect at the level of 5% to 20% of the thermal energy, were im- enhanced cooling due to the weakening of the spiral out- posed in several other clusters, by Churazov et al. (2008); flow in those clusters. Sanders et al. (2010, 2011); Bulbul et al. (2012). Thus, By focusing on the steady state flow, we have not ad- present spectroscopy is in general unable to probe the dressed the initial formation of the spiral pattern. How- narrow, fast outflows, whose kinetic energy is a small, −8/5 ever, sloshing simulations have demonstrated that such ∼ 0.03(r/r0) fraction of the thermal energy (see patterns easily form in cores in response to strong pertur- §6). In addition, such observations are only sensitive bations, and standing accretion shock instability (SASI) to motions along the line of sight, and typically probe simulations suggest that spiral modes are excited even in scales larger than the base of the spiral, where the flow unperturbed spherical accretion in the presence of cool- is fastest. ing. Note that, if the universal thermal profiles of CCs The spiral bulk flows should be directly observable with are indeed the signature of a spiral flow, and if these are future telescopes, for example using the next interna- composite inflows (of the first type) of a merger origin, tional X-ray satellite, ASTRO-H (Takahashi et al. 2010), then a major merger (of the type invoked to explain the scheduled for launch in 2014. In particular, ASTRO- minority, ∼ 1/3 of non cool-core clusters) would be nec- H should be able to spectroscopically resolve the fast essary in order to generate these spirals. Otherwise, one flows near the centers of nearby, well-resolved clusters, would expect to see clusters with a disrupted core or no in which the spiral is not observed face-on (along zˆ). core at all, with no evidence for a major merger. In conclusion, we show that the universal thermal pro- Groups of galaxies show CCs that resemble those in files of CCs, their size, multiphase properties, common clusters, with similar profiles and occasionally CFs, but spiral thermal and chemical features, and ubiquitous with a higher fraction of gas cooling per unit time (e.g., CFs, can all be explained by the presence of bulk spiral McDonald et al. 2011). Our results suggest that such flows. This suggests that spiral flows may be the funda- groups too carry spiral flows, but the latter are less effi- mental, defining property of CCs. Such flows can glob- cient in mixing the gas due to the scaling of AGN feed- ally stabilize the core against cooling, while quenching back with system mass. mass accretion, by combining a slow, volume-dominant Our analysis bears important implications for inter- inspiral, with a fast, cold, feedback-regulated outflow. preting the structure, composition, and gravitational po- Present observations are just sensitive to the ”tip of the tential of CCs, showing for example that deviations from iceberg” of this prevalent, large scale phenomenon. hydrostatic equilibrium are locally significant. Spiral flows may play an important role in mixing the gas on large scales, possibly facilitating the smooth metallicity It is a pleasure to thank Y. Birnboim, A. Loeb, N. distribution observed (e.g., Sanderson et al. 2009), and Soker, W. Forman, P. Sharma, E. Quataert, C.K. Chan, the homogeneity of cosmic-ray ions inferred from radio and B. Katz, for encouragement and useful discussions. observations (Keshet 2010). Our results emphasize that Special thanks to M. Markevitch for numerous insightful spiral flow studies, such as sloshing simulations, should discussions, and for identifying the X-ray cavities. This incorporate AGN feedback, in particular in the form of work is supported by NASA through Einstein Postdoc- buoyant bubbles. Such simulations can directly test if toral Fellowship grant number PF8-90059 awarded by the a spiral flow naturally produces the characteristic core Chandra X-ray Center, which is operated by the Smith- structure observed, by studying the evolution and long- sonian Astrophysical Observatory for NASA under con- term stability of flows with different initial conditions. tract NAS8-03060, by a Harvard Institute for Theory and Notice that spiral flows cannot be properly simulated Computation (ITC) fellowship, and by a Marie Curie without accounting for (or at least mimicking the effect Reintegration Grant (CIG).

REFERENCES Ascasibar, Y., & Markevitch, M. 2006, ApJ, 650, 102, Bulbul, G. E., Smith, R. K., Foster, A., Cottam, J., Loewenstein, arXiv:astro-ph/0603246 M., Mushotzky, R., & Shafer, R. 2012, ApJ, 747, 32, 1110.4422 Birnboim, Y., Keshet, U., & Hernquist, L. 2010, MNRAS, 408, Buote, D. A., Lewis, A. D., Brighenti, F., & Mathews, W. G. 199, 1006.1892 2003, ApJ, 595, 151, arXiv:astro-ph/0303054 Bˆırzan, L., Rafferty, D. A., McNamara, B. R., Wise, M. W., & Churazov, E., Forman, W., Jones, C., & B¨ohringer, H. 2003, ApJ, Nulsen, P. E. J. 2004, ApJ, 607, 800, arXiv:astro-ph/0402348 590, 225, arXiv:astro-ph/0301482 Blanton, E. L., Randall, S. W., Clarke, T. E., Sarazin, C. L., Churazov, E., Forman, W., Vikhlinin, A., Tremaine, S., Gerhard, McNamara, B. R., Douglass, E. M., & McDonald, M. 2011, O., & Jones, C. 2008, MNRAS, 388, 1062, 0711.4686 ApJ, 737, 99, 1105.4572 Churazov, E., Sunyaev, R., Forman, W., & B¨ohringer, H. 2002, Blondin, J. M., & Shaw, S. 2007, ApJ, 656, 366, MNRAS, 332, 729, arXiv:astro-ph/0201125 arXiv:astro-ph/0611698 16 U. Keshet

Clarke, T. E. 2004, Journal of Korean Astronomical Society, 37, O’Dea, C. P. et al. 2008, ApJ, 681, 1035, 0803.1772 337, arXiv:astro-ph/0412268 Peterson, J. R., & Fabian, A. C. 2006, Phys. Rep., 427, 1, Clarke, T. E., Blanton, E. L., & Sarazin, C. L. 2004, ApJ, 616, arXiv:astro-ph/0512549 178, arXiv:astro-ph/0408068 Piffaretti, R., & Kaastra, J. S. 2006, A&A, 453, 423, de Plaa, J., Kaastra, J. S., Tamura, T., Pointecouteau, E., arXiv:astro-ph/0602376 Mendez, M., & Peterson, J. R. 2004, A&A, 423, 49, Pistinner, S. L., & Eichler, D. 1998, MNRAS, 301, 49, arXiv:astro-ph/0405307 arXiv:astro-ph/9807025 Diehl, S., Li, H., Fryer, C. L., & Rafferty, D. 2008, ApJ, 687, 173, Pizzolato, F., & Soker, N. 2006, MNRAS, 371, 1835, 0801.1825 arXiv:astro-ph/0605534 Donahue, M., Horner, D. J., Cavagnolo, K. W., & Voit, G. M. Quataert, E. 2008, ApJ, 673, 758, 0710.5521 2006, ApJ, 643, 730, arXiv:astro-ph/0511401 Rafferty, D. A., McNamara, B. R., & Nulsen, P. E. J. 2008, ApJ, Dunn, R. J. H., & Fabian, A. C. 2006, MNRAS, 373, 959, 687, 899, 0802.1864 arXiv:astro-ph/0609537 Randall, S. W., Clarke, T. E., Nulsen, P. E. J., Owers, M. S., Fabian, A. C. et al. 2011, ArXiv e-prints, 1105.5025 Sarazin, C. L., Forman, W. R., & Murray, S. S. 2010, ApJ, 722, Fabian, A. C., Sanders, J. S., Taylor, G. B., Allen, S. W., 825, 1008.2921 Crawford, C. S., Johnstone, R. M., & Iwasawa, K. 2006, Roediger, E., Br¨uggen, M., Simionescu, A., B¨ohringer, H., MNRAS, 366, 417, arXiv:astro-ph/0510476 Churazov, E., & Forman, W. R. 2011, MNRAS, 413, 2057, Forman, W. et al. 2007, ApJ, 665, 1057, arXiv:astro-ph/0604583 1007.4209 Fujita, Y., Matsumoto, T., & Wada, K. 2004, ApJ, 612, L9, Rybicki, G. B., & Lightman, A. P. 1986, Radiative Processes in arXiv:astro-ph/0407368 Astrophysics, ed. Rybicki, G. B. & Lightman, A. P. Ghizzardi, S., Rossetti, M., & Molendi, S. 2010, A&A, 516, Sanders, J. S., & Fabian, A. C. 2007, MNRAS, 381, 1381, A32+, 1003.1051 0705.2712 Guo, F., Oh, S. P., & Ruszkowski, M. 2008, ApJ, 688, 859, Sanders, J. S., Fabian, A. C., Allen, S. W., & Schmidt, R. W. 0804.3823 2004, MNRAS, 349, 952, arXiv:astro-ph/0311502 Johnson, R. E., Markevitch, M., Wegner, G. A., Jones, C., & Sanders, J. S., Fabian, A. C., & Smith, R. K. 2011, MNRAS, 410, Forman, W. R. 2010, ApJ, 710, 1776, 1001.2441 1797, 1008.3500 Kaastra, J. S. et al. 2004, A&A, 413, 415, arXiv:astro-ph/0309763 Sanders, J. S., Fabian, A. C., Smith, R. K., & Peterson, J. R. Keshet, U. 2010, ArXiv e-prints, 1011.0729 2010, MNRAS, 402, L11, 0911.0763 Keshet, U., & Loeb, A. 2010, ApJ, 722, 737, 1003.1133 Sanders, J. S., Fabian, A. C., & Taylor, G. B. 2009, MNRAS, 396, Keshet, U., Markevitch, M., Birnboim, Y., & Loeb, A. 2010, ApJ, 1449, 0904.1374 719, L74 Sanderson, A. J. R., O’Sullivan, E., & Ponman, T. J. 2009, Lagan´a, T. F., Andrade-Santos, F., & Lima Neto, G. B. 2010, MNRAS, 395, 764, 0902.1747 A&A, 511, A15+, 0911.3785 Sanderson, A. J. R., Ponman, T. J., & O’Sullivan, E. 2006, Lim, J. 2011, in Structure in Clusters and Groups of Galaxies in MNRAS, 372, 1496, arXiv:astro-ph/0608423 the Chandra Era, 2011 Chandra Science Workshop held July Sharma, P., McCourt, M., Quataert, E., & Parrish, I. J. 2012, 12-14, 2011. Edited by Jan Vrtilek and Paul J. Green. Hosted MNRAS, 420, 3174, 1106.4816 by the Chandra X-ray Center, Published online at: Soker, N. 2010, ArXiv e-prints, 1007.2249 http://cxc.harvard.edu/cdo/xclust11, p.29, ed. J. Vrtilek & Takahashi, T., et al. 2010, in Society of Photo-Optical P. J. Green, 29–+ Instrumentation Engineers (SPIE) Conference Series, Vol. 7732, Markevitch, M., & Vikhlinin, A. 2007, Phys. Rep., 443, 1, Society of Photo-Optical Instrumentation Engineers (SPIE) arXiv:astro-ph/0701821 Conference Series, 1010.4972 Markevitch, M., Vikhlinin, A., & Forman, W. R. 2003, in Tanaka, T., Kunieda, H., Hudaverdi, M., Furuzawa, A., & Astronomical Society of the Pacific Conference Series, Vol. 301, Tawara, Y. 2006, PASJ, 58, 703 Astronomical Society of the Pacific Conference Series, ed. Tittley, E. R., & Henriksen, M. 2005, ApJ, 618, 227, S. Bowyer & C.-Y. Hwang, 37–+ arXiv:astro-ph/0409177 Markevitch, M., Vikhlinin, A., & Mazzotta, P. 2001, ApJ, 562, Vikhlinin, A., Kravtsov, A., Forman, W., Jones, C., Markevitch, L153, arXiv:astro-ph/0108520 M., Murray, S. S., & Van Speybroeck, L. 2006, ApJ, 640, 691, Mazzotta, P., & Giacintucci, S. 2008, ApJ, 675, L9, 0801.1905 arXiv:astro-ph/0507092 Mazzotta, P., Markevitch, M., Vikhlinin, A., Forman, W. R., Voigt, L. M., & Fabian, A. C. 2004, MNRAS, 347, 1130, David, L. P., & VanSpeybroeck, L. 2001, ApJ, 555, 205, arXiv:astro-ph/0308352 arXiv:astro-ph/0102291 Werner, N. et al. 2010, MNRAS, 407, 2063, 1003.5334 McDonald, M., Veilleux, S., & Mushotzky, R. 2011, ApJ, 731, 33, Zakamska, N. L., & Narayan, R. 2003, ApJ, 582, 162, 1102.1972 arXiv:astro-ph/0207127 McNamara, B. R., & Nulsen, P. E. J. 2007, ARA&A, 45, 117, ZuHone, J. A., Markevitch, M., & Johnson, R. E. 2010, ApJ, 717, 0709.2152 908, 0912.0237 McNamara, B. R., Nulsen, P. E. J., Wise, M. W., Rafferty, D. A., ZuHone, J. A., Markevitch, M., & Lee, D. 2011, ApJ, 743, 16, Carilli, C., Sarazin, C. L., & Blanton, E. L. 2005, Nature, 433, 1108.4427 45 Molendi, S., & Pizzolato, F. 2001, ApJ, 560, 194, arXiv:astro-ph/0106552 Navarro, J. F., Frenk, C. S., & White, S. D. M. 1996, ApJ, 462, 563, arXiv:astro-ph/9508025