We are starting a discussion group on cool cores, tentatively on Mondays at 2 in the Tower Room, but let us know if you'd like it shifted. Add your favorite topics below:

Mark Voit, Peng Oh

-- How is AGN feedback triggered?
-- What is the origin of optical filaments and what energizes them?
-- What regulates the star formation rate in brightest cluster galaxies?
-- Galactic Coronae---what is their origin and how are they stabilized?
-- Is the cluster population bimodal (cool-core/non cool-core), and if so, what is the origin of bimodality?
-- What can we learn from metallicity profiles in cluster cores?
-- How does thermal conduction influence the structure of cluster cores?
-- What astrophysical ingredients are necessary to accurately simulate cluster cores?
-- How does the incidence of cool cores evolve with time?

Discussion 1, Feb 14 (Notes from Mark Voit)

This discussion focused mainly on galactic coronae, their relationship to classic cool cores, and how they might be used to investigate the AGN feedback loop thought to prevent overcooling and star formation in large elliptical galaxies. Ming Sun outlined the general properties of galactic coronae in cluster and group galaxies. A galactic corona consists of gas at ~0.5-1 keV extending over a few-kiloparsec region at the center of a galaxy. In a cluster or group it is surrounded by hotter gas at a similar pressure. The temperature contrast with that hotter gas can be up to a factor of 5-10, depending on the mass of the parent halo. The total amount of gas in a galactic corona found in a group or cluster galaxy is ~ 10^7-10^8 solar masses. Not much is known about the structure of galactic coronae or the boundary that separates a corona from the surrounding hot gas because the angular sizes of coronae, even in relatively nearby clusters, are only a few arcseconds. Understanding what happens at the boundary is important, though, because it somehow preserves the coronae from evaporation, stripping, and turbulent mixing with the hotter gas. (From Ming, it is also interesting to ask the question in this context, whether cool cores are self-similar? It the primary heating mechanism the same in cool cores with different sizes? )

One of the most interesting features of galactic coronae in the central galaxies of groups and clusters is their association with a strong central radio source. Much of the discussion centered around the plot from Sun (2009, ApJ, 704, 1586) comparing the X-ray luminosity of gas having a short central cooling time (< 4Gyr) at the center of a group or cluster with the radio luminosity of the central AGN. On the right side of the plot one finds classic cool cores in which the gas with a short cooling time has an X-ray luminosity ~ 10^42 - 10^44 erg/s. Among this set of objects there is a correlation between the radio luminosity of the central AGN and the X-ray luminosity of the cool core, suggesting that AGN feedback come into balance with the cooling rate of the core.
(from Ming: the work by Rafferty et al. shows a correlation between the kinetic power measured from cavities and the cool core luminosities. The right side of the plot uses the 1.4 GHz luminosities for a larger sample. ) On the left side of the plot are galactic coronae in which gas with a short central cooling time typically has an X-ray luminosity ~ 10^41 erg/s. Among the galactic coronae there is no correlation between X-ray and radio luminosity and radio power, and the range of radio luminosity is equivalent to that in cool cores.

If the classic cool cores represent a set of objects in which AGN feedback has come into balance with radiative cooling, then the coronae appear to be objects in which the feedback loop has broken down (from Ming: or never established as the embryonic large cool cores have been destroyed by radio heating from coronae) . The AGNs in some of these systems appear to produce far more power than necessary to replace the energy lost by radiative cooling in the corona. In fact, one of the mysteries of coronae is how they manage to persist in the presence of a strong AGN. Energy from the AGN manages to pass through a corona without coupling very strongly to it. Several people suggested that the coupling of AGN power to the environment of the central galaxy might depend on the pressure of the gas at ~30-100 kpc and therefore the mass of the parent halo. In larger systems, AGN outflows might be halted and thermalized at smaller radii, allowing more efficient coupling with the gas surrounding the central halo galaxies. This seems to be a potentially fruitful area to explore with simulations. (From Ming: on the other hand, small radio outbursts can help the energy balance in coronae, as those small cavities and weak shocks observed in nearby galaxies. Such kind of small outbursts, if frequent, can help to suppress cooling close to the nucleus, while heating energy from rarer, stronger heating events will be more likely to channel out and avoid the central several kpc.)

We also discussed whether there were any known strong radio sources in central cluster or group galaxies that do not have classical cool core or galactic corona around them. If there are any, they are quite uncommon. Steve mentioned the recent paper by Dunn (from Ming: the Dunn sample only has nearby galaxies and most of them are not radio luminous. In fact, only M87 is above the 10^24 W/Hz threshold at 1.4 GHz by Sun 2009. Even at above 10^23 W/Hz, there are only M87, NGC 4696 - the BCG of Centaurus and IC 310. Sun et al. (2007) studied IC 310 and it has a small corona and a gaseous tail. The galaxy Steve mentioned may be NGC 4203, which is not a BCG and it is 500x fainter than the 10^23 W/Hz threshold at 1.4 GHz. ) It would appear that gas with a short cooling time is necessary to fuel a strong radio source in a central cluster or group galaxy.

Since AGN power in central galaxies seems so closely associated with the properties of the hot-gas environment, the discussion concluded with the topic of Bondi accretion. All those present seemed to think that Bondi accretion is too simplistic to describe the accretion rates onto the supermassive black holes in central cluster galaxies. Yet, observations continue to suggest a close link between the accretion rates needed to explain the observed AGN power and extrapolations of the hot-gas environment to radii below the X-ray resolution limits. In addition to the work of Allen et al. (2006, MNRAS, 372, 21) people also cited Balmaverde et al. (2008, A&A, 486, 119) in this context.

Ming emphasized that such kind of effort to derive Bondi accretion rate requires very careful work. This is discussed in this paper. As Bondi radius is only resolved in 3-4 galaxies, the Balmaverde et al. work
relied on extrapolation of the density profile. However, they did not check whether the model density profile
is consistent with the observed luminosity of the central bin. In fact, many of their fits imply an infinite central surface brightness. A better method was suggested in this work and Ming concluded that Balmaverde et al.
largely over-estimated Bondi accretion rate in many systems.

Discussion 2, 02/28/11

Megan: I led off the discussion with an overview of star formation rate estimates in BCGs in cool cores, with the caveats that most estimates are based on assumptions of constant star formation and a standard IMF. The unobscured star formation is measured in the UV, but with these large galaxies one has to subtract off the UV-upturn component from the evolved population. That correction has significant scatter, although the ratio of UV to K-band light in these most massive BCGs is better behaved than in the general population of elliptical galaxies, where it shows considerably larger scatter (probably due to contributions from tiny amounts of star formation, unaccounted for by usual diagnostics of emission lines.) H-alpha traces star formation, but only the most recent star formation, since after the hottest O stars die, H-alpha goes away. (So a galaxy can have relatively recent star formation, and exhibit UV emission but very little H-alpha.) Finally, the cold gas and dust surrounding the newly formed stars re-emit in the mid-infrared. I discussed some of the infrared work we just recently had accepted to ApJ, including detections of PAHs, continuum dust emission, forbidden lines, and extremely strong rotational H2 lines.
Some relevant papers are:
UV and optical: Johnstone, R. et al. 1987; McNamara & O'Connell 1989, Hicks & Mushotzky 2005 (but don't use their SFR numbers, an error makes them about x10 too high); Hicks et al. 2010; Donahue et al. 2010.)
H-alpha: Heckman et al. 1989; Crawford et al. 1999
CO-masses: Edge, A. C. 2001
Dust: Egami et al 2006; Donahue et al. 2007; O'Dea et al. 2008, including recent Herschel: Edge et al. 2010ab.
IR-lines: Egami et al. 2006; Kaneda et al. 2008; Donahue et al. 2011.
These signatures of star formation are strongly correlated, as in a threshold, with the presence of low-entropy ICM below about 30 keV cm^2 (Cavagnolo et al. 2009).

There was considerable discussion about the radio-IR correlation (these things likely are bright in radio, the radio in these sources is not associated with star formation.)

There was discussion of the dusty gas and the mass loss from the evolved stars.

There was discussion of variation in the IMF.

There was discussion of why the stellar distribution in BCGs is so much more puffy (Sersic n=5-10) than in elliptical galaxies (Sersic n=4).

Please edit as you recall!

Andrey: the paper on mass loss that I mentioned during the discussion: Leitner & Kravtsov 2011, ApJ submitted [arXiv/1011.1252] Fig. 4 shows mass loss for an average galaxy of a given z=0 stellar mass. For M*(z=0)=1e11 Msun, the stellar mass loss is ~3 Msun/yr. For a massive BCG of 1e12 Msun, this would be several times larger.

The above paper also compiles and discusses various IMFs used in the literature.

The papers modeling IR-radio correlation: Lacki, Thompson & Quataert (2010) and Lacki & Thompson (2010)

Discussion 3, Mar 7 (Notes from Mark Voit)
Today's cool-core discussion covered two topics: (1) the fate of stellar mass loss in central cluster galaxies, and (2) the problem of quantifying cool-core-ness in clusters, so that we can determine how successful simulations are a reproducing it.

The Fate of Stellar Mass Loss in Central Cluster Galaxies
The central galaxies of clusters have lots of stars, which shed lots of mass. For example, the R-band luminosities of the central ~17 kpc of REXCESS clusters are ~10^11 L_Sun, corresponding to a current stellar mass of ~10^12 M_Sun for a Salpeter-ish IMF at an age of ~10 Gyr. Normal stellar mass loss from such a population should now be shedding several solar masses per year, depending on the IMF (as noted above, one can use the results from Leitner & Kravtsov 2011, ApJ, submitted, arXiv/1011.1252). This mass loss rate is generally greater than the observed star-formation rates in the central galaxies of the REXCESS clusters, which are typically ~1 solar mass per year for cool-core clusters and zero for clusters without cool cores (see Donahue et al. 2010, ApJ, 715, 881). In only one case does the star-formation rate at the center of a cool-core cluster exceed the stellar mass-loss rate of the central galaxy. This implies that that the flow of gas mass at the centers of galaxy clusters generally removes gas from the central galaxy, even in cool-core clusters. Only in rare cases (e.g., Abell 1068) does the star-formation rate in a central cluster galaxy vastly exceed the stellar mass-loss rate.

If normal stellar mass loss from the central galaxy is indeed the primary source of the cool star-forming gas in these systems, then the fact that this gas is dusty is not such a mystery. The presence of dust would be harder to explain if most of the cool gas seen in these galaxies had condensed from the ICM. In fact, from a Spitzer Space Telescope point of view, the dust emission and star-formation properties of these systems look like those of other normal star-forming galaxies (see, for example, Donahue et al. 2011, ApJ, in press, should be posted on astro-ph real soon). The primary unusual features of the cool gas are the abnormally strong rotational lines of H2, the unusually strong forbidden-line to H-alpha ratios, and the incidence of H-alpha emission filaments in regions without any obvious star formation. A population of suprathermal electrons in the cool gas can plausibly account for these peculiarities (e.g., Ferland et al. 2009, MNRAS, 392, 1475).

In light of all this, one question that received a lot of discussion was what happens to the gas shed by a dying star in an elliptical galaxy. Does it all get heated to the virial temperature, or can some of it remain "cold" at ~10^4 K? The fate of mass loss by an individual star has been considered in detail by Parriott & Bregman (2008, ApJ, 681, 1215; 2009, ApJ, 699, 923). They find that a significant fraction of the mass lost can remain cool as it mixes with the ambient medium, depending on the efficiency of radiative cooling. It therefore seems likely that the rate at which normal stellar mass loss adds cool gas to a central cluster galaxy will depend on the ambient pressure, since greater pressure increases the efficiency of cooling. Simulating the transfer of stellar mass to the ICM is clearly very difficult, and it's not clear how the sub-grid model for that mass source should be designed. Andrey pointed out a clue: the distribution of PAH, dust, and hot gas in the elliptical NGC 4125 suggests that the cool gas in this system is evaporating/mixing into the ambient medium, since the PAHs are confined to a dust lane rich in molecular gas, while the non-PAH dust emission is more extended, with structures similar to the distribution of the X-ray plasma (see Kaneda et al. 2011).

Exactly how the gas mass introduced by stars leaves the vicinity of the central galaxy is not clear. Markus pointed out that there are simulations in which SN Ia explosions drive winds from galactic bulges (Tang et al. 2009, MNRAS, 398, 1468), but this mechanism is unlikely to provide enough energy to drive winds from central cluster galaxies, which are much more massive and are surrounded by higher-pressure gas. Transport processes such as thermal conduction or turbulent mixing seem the like most likely culprits, since AGN feedback does not appear to be active in non-cool-core clusters, whose central galaxies are shedding comparable mass and yet do not experience star formation.

Quantifying Cool-Core-ness
We all would like simulated clusters to have cores that look like those of cool-core clusters and for the ratio of cool-core clusters to non-cool-core clusters in simulations to be like the observed ratio. We're obviously not there yet, but as simulations improve we will need to quantitatively define the property of cool-core-ness in order to profitably compare simulations with observations. Classically, back when cool-core-ness was quantified in terms of cooling-flow rates, clusters were divided into cooling and non-cooling categories on the basis of central cooling time. Categorizing clusters by central cooling time (or almost equivalently, central entropy) still seems useful, since phenomena associated with cool cores (i.e., X-ray cavities, strong central radio source, emission-line nebulae, central star formation) appear only when the central cooling time is less than about ~ 1 Gyr and/or the central entropy is < 30 keV cm^2.

However, as Dick Bond emphasized, both these quantities are resolution-dependent. If we really want to measure how the incidence of cool cores evolves with redshift, we need measures of cool-core-ness that are less resolution dependent. To complicate matters further, Hans Bohringer pointed out that the surface-brightness contrast between a cool core and the surrounding cluster may be less pronounced at higher redshifts (see Santos et al. 2010, A&A, 521, 64).

We ran out of time on this topic but would like to discuss it further at a future meeting.

Discussion 4, March 21 (Notes from Mark Voit)
The emission-line filaments at the centers of cool-core clusters were the subject of today's discussion. It has long been known that the central galaxies of some clusters have extended emission-line nebulae, and that they are present only in systems whose minimum cooling time is less than a Hubble time (e.g. Hu et al. 1985). More recently, it has become apparent that the conditions under which these nebulae appear are more restrictive. They are found only in systems with a cooling time less than ~1 Gyr, or equivalently, a central entropy less than ~30 keV cm^2 (Cavagnolo et al. 2008, Donahue et al. 2010). However, we are not yet sure where the nebular gas comes from, what energizes it, or why it appears in some clusters but not in others.

Origin of the Filaments
The most recent contribution to the topic of filament origin was Eliot Quataert's very stimulating talk at last week's Monsters Inc. conference. He presented simulation results showing that thermal instability can lead to multiphase structure in a spherical environment if the cooling time (strictly speaking, the thermal instability timescale) is less than about 10 times the freefall time (in a Cartesian environment the critical ratio is closer to unity). The freefall time is defined locally as (2r/g)^0.5 and tcool = (3/2) nkT / n_e n_p \Lambda(T). Their analysis of the data on about a dozen clusters shows that those with extended H-alpha emission indeed have t_c/t_ff < 10 and those with larger values of this ratio do not.

At the meeting, Andy Fabian strenuously objected to the suggestion that thermal instability was producing the filaments on the grounds that the ratio of t_c/t_ff in the ICM was simply too large to matter, particularly at the farthest radii at which H-alpha emission is detected: ~ 50-100 kpc. However, Ian Parish showed a plot (also in Quataert's talk) illustrating that the ratio t_c/t_ff remains less than about 20 from 1-100 kpc, with a shallow minimum at ~10 kpc in systems with nebulosity (note: tff and tcool are defined locally). But since Andy wasn't present at our discussion to make his case more quantitatively, we don't know how much of the disagreement boiled down to differences in definitions.

Another objection lodged against the thermal instability origin for the nebulosity concerned the presence of dust. Several different kinds of observations indicate that the filaments are dusty (). Among the most constraining are the upper limits on Ca II line emission (Donahue & Voit 1993), which imply that a large majority of the calcium in the nebular gas is in solid form. However, sputtering should destroy dust grains in the core ICM of a cool-core cluster within about ~ 1 Myr. If the nebular gas does indeed condense out of the ICM, then it needs to form dust quite readily after condensing, but it's not at all clear how that would happen. Furthermore, as mentioned in our earlier discussions, the dust emission properties of star-forming BCGs are similar to those of other star-forming galaxies, suggesting that the dust-grain population is also similar.

The most obvious source of dust grains in the BCG is the population of evolved stars that is currently shedding mass into the ICM. Again, as mentioned in a previous discussion, normal stellar mass loss in a BCG currently releases of order several solar masses per year. This is roughly an order of magnitude greater than what thermal instability contributes according to the Berkeley model outlined here, which predicts a condensation rate ~(t_c / t_ff)^2 times the naive cooling-flow rate. If the BCG's stars are the primary source of the dust, then they also seem to be a source of nebular gas that is potentially more copious than thermal instability alone.

A more general point raised in favor of thermal instability involved the spatial correspondence between filamentary gas and the presumed trails of buoyant, radio-emitting bubbles. Entrainment and lifting of low-entropy gas to larger radii can promote thermal instability by increasing the density contrast between the low-entropy gas and its surroundings (see, for example, the simulations of Revaz et al. 2008). This kind of stirring was not included in the Berkeley work and could increase the condensation rate.

While we were discussing the origin of filaments, we also considered the limits that the straightness of filaments may place on turbulence in cluster cores. Eugene Churazov sketched out a calculation linking the ability of turbulence to affect filament geometry to the correlation length of the turbulence. If this correlation length is greater than the product of the filament density contrast and the filament diameter, then it should be able to bend the filaments. However, this way of looking at the problem did not lead directly to limits on turbulent velocities.

Energy Source of the Filaments
We only scratched the surface of the rich topic of filament energy sources. Churazov suggested that the stretching of field lines as buoyant bubbles uplift the filamentary gas could be an interesting energy source, although the energetic arguments were not worked out quantitatively. As Fabian mentioned at the meeting (see also Voit & Donahue 1997, Ferland et al. 2009), the energy flux needed to produce the observed line emission is of order the pressure times the sound speed in the surrounding hot gas. We could revisit the energetics of filaments (including the suitability of H-alpha emission as a measure of star formation) in a future discussion if people desire.

Incidence of the Filaments
The question of why some clusters contain nebular filaments while others do not (a global stability issue) can be considered separately from the question of filament origin (a local stability issue). Most central cluster galaxies lack star formation, H-alpha nebulosity, and appreciable amounts of cooler gas. Therefore, the mass shed by their stars must somehow be heated and transported out of the central galaxy. Whatever this process is, it appears to be less effective in galaxies with cool cores, in which multiphase gas persists.

One currently popular idea about cluster cores is that AGN feedback turns on when thermal conduction, perhaps assisted by turbulence, fails to keep the central entropy above some critical threshold (e.g., Donahue et al. 2005, Voit et al. 2008, Guo et al. 2008, Parrish et al. 2010, Ruszkowski et al. 2010). Within this interpretation, conduction+turbulence would eradicate multiphase gas from systems in which it is competitive with cooling. And multiphase structure and H-alpha nebulosity would appear in systems in which conduction is faltering.

The recent Berkeley work adds another wrinkle. According to the models presented in Quataert's talk, the mass condensation rate depends critically on the cooling-to-freefall ratio, with Mdot \propto (t_c/t_ff)^2. As the amount of condensed gas rises, so does the overall radiative cooling rate and the compensating heating rate, implying that AGN feedback might maintain the inner ~10 kpc of the core at the threshold of thermal instability in cases where conduction+turbulence has failed.

Discussion 5, Mar 28 (Notes from Megan Donahue)

First I'm going to apologize for the lameness and the lateness of these notes! I will attempt to bolster them by editing for paper links, but of course anyone is welcome to augment!

The discussion today was cast as a dialogue between theorists and observers: what would the theorists like from the observers and what do the simulations require to model cool cores and their incidence in clusters of galaxies with redshift. Since the presence of a cool core can change its visibility in an X-ray survey and its influence can affect the inferred mean emission-weighted temperature of the ICM of a distant cluster of galaxies, such a question has both cosmological and astrophysical relevance.

The primary culprit in stablizing the cool core is likely to be AGN-related feedback, although see possible alternative proposed by Ian Parrish, who suggests that perhaps stabilization could be managed through magnetic field-mediated mechanisms. (I may be butchering this characterization because Ian was not there today, but I think I'm not far off. However, today we talked mostly of stabilization through AGN feedback. The theoretical challenge for this mechanism, as described in the discussion by Stefano Borgani, to stabilize a cool core with AGN feedback is twofold: (1) how to distribute the energy, and (2) how to close the feedback loop. Much of this boils down to describing the relevant physics coupling the (kinetic) output of the AGN to a relatively large volume of surrounding gas. The event horizon of a billion solar mass black hole is ~ 3e14 cm, while the cool core radius is some ~ 3e23 cm. It is unlikely that simulations in the near future will ever be able to model the physics at the event horizon simultaneously with the cosmological scales required to track realistic merger environments.

Therefore "sub-grid" physics will be required for the foreseeable future. See Scannapieco & Bruggen (ADS) for simulations of an AGN using subgrid models for turbulence and heating; but these features are not yet incorporated into cosmological-scale simulations. In those simulations the AGN feedback is "AGN" feedback by name. It is extremely phenomenological; it is not regulated by feedback. In current simulations, "AGN" feedback is inserted by hand at z~3-4 to regulate and minimize star formation at those epochs, to prevent overproduction of stars.

Observers: Definition of a Cool Core
As far as data, there is almost too much data! (Although I suspect the more accurate statement is that there is almost too much marginal data.)
It would be useful for observers to make a clear definition of what they mean by a "cool core". It would be useful to know the incidence of such cool cores in populations of clusters and groups of clusters selected in different ways. Alternatively, it would be useful to know the distribution of quantities like central (excess) entropy, central cooling times, central densities & core radii, as a function of cluster mass and redshift.
Papers by Hudson were mentioned (ADS).

Observers: Quantify Mg(T)
The multiphase nature of cluster cores is difficult to simulate currently, but simulators would find it useful to have a quantify distribution of gas mass by temperature, particularly for the X-ray emitting gas. (I would also like to include even cooler gas, since there are large repositories of molecular gas in some of these systems.)

Observers: A great sample of groups
It's very difficult to characterize groups in the X-ray because of their low surface brightness and low fluxes. (On the other hand, group temperatures ~1 keV require fewer photons to measure.) But X-ray observations of groups with z>0.1-0.2 must be long. Groups of galaxies, however, are of great interest to theorists: groups are natural testing grounds for the feedback process. Cool cores exist in groups but their entropy profiles are not as steep as in groups (Ming Sun et al. 2009). Since only a small number of mainly X-ray selected groups have been characterized in the X-ray we only have some idea of the break between cool cores and non-cool cores in groups. The strength of the radio source in the central galaxies of groups is correlated with the thermodynamic state of the ICM (Sun et al) , unlike in clusters where the incidence of a strong radio source is much higher in clusters with low central excess entropy, but the radio luminosity is not otherwise correlated. Churazov mentioned that cool core groups they have studied have deeper potential wells (@ 400 km/s) and that the dynamic state of a group appears to be critical. A single CD galaxy is a signature of a CC group, while binary or double brightest central galaxies indicate non-cool core. These are only indicative: groups are understudied as a class because they are difficult to study.

Peng Oh pointed out that the group environment, there is no conduction; conduction can't be important in groups.

For your group proposals: X-ray observations of groups critically test predictions of models of feedback. Editorial note from MD: the better - the more concretely -- this type of claim can be described in the context of what data will test what set of models, the more likely the TAC awards the proposal. Also for some reason, TACs often lose track the scientific notion that data falsify models, rather than prove models! So they sometimes push away a project that has one or more favored models in its crosshairs.

Observers: Don't forget the AGN
Low-frequency, high-resolution observations of AGN will reveal aspects of AGN particle acceleration currently invisible to us.

Turbulence with ASTRO-H
High resolution X-ray spectroscopy with the calorimeter on board ASTRO-H hopefully will provide us with insights about line widths (turbulence), line centroid shifts (bulk flows), and weak emission lines (multiphase gas, cooling). The official resolution is 7 eV but rumors abound of possible 4 eV lab measurements. The spatial resolution will be quite poor, 1.5-2' cells at best. See talks by Zhuravleva in this workshop.

Stellar Mass
The discussion then centered on the updated mass profile for M87 from the IFS measurements published by Gebhardt et al, doubling the mass of the central black hole from 3 to 6 million solar masses. Since their measurements differ from previous data, this result is controversial.

Mass measurements of several sorts were discussed: isolated ellipticals, stellar luminosity profiles (with M/L assumed starting from Salpeter IMFs) compared to X-ray based masses. Some discussion of lack of evidence for a non-universal IMF, despite theoretical intuitions based on, for example, the Jeans mass concept, that suggest the IMF is not universal (Bastian, Covey, & Meyer, 2010, Annual Reviews.)

Discussion 6, April 4 (Notes from Megan Donahue)

Suggested overall topic: how does the cool core phenomenon scale with redshift and mass?
(I was hoping simulators might also express how the incidence of cool cores change with mass of the cluster and with time, but we are yet limited by the physical prescriptions (subgrid), range of physical scales accessed, and do not yet have robust predictions of what the incidence rate ought to be because current simulations do not yet produce a mix of cool core and non-cool core clusters in current simulations -- is this a fair statement?)

A brief summary of the observations:
Working definition of a cool core cluster at z=0: central entropy < about 30 keV cm^2, central cooling time shorter than few billion years.
Suggested hypothesis for conditions under which optical filaments / multi-phase gas survives/develops: t_c < 10 t_ff.

Cool cores exist at high redshift (Joanna Santos's result, discussed in a talk in the conference) and they exist in groups (see Ming Sun's work). In a controversial proceedings, Alexei Vikhlinin suggest very few exist at z>0.5 (Vikhlinin 2007). However, at least some of the high redshift MACS clusters are also cool core clusters. The MACS clusters are generally quite massive, because they were found in the ROSAT All Sky Survey, which has enough sky coverage to pick up the rarest, most luminous X-ray sources. There was debate during the conference about the lack of cool cores in the 160SD (160 Square Degree) survey (Samuele et al. 2011), which is a subset of the ROSAT serendipitous cluster 400SD survey. This survey has a smaller area coverage, is deeper than the RASS, and therefore includes clusters of lower X-ray luminosities than those in the MACS sample. Roughly a third of the 32 REXCESS clusters turned out to be cool core clusters, of which 70% hosted BCGs with optical emission lines (Donahue et al. 2010.) These samples do not have sufficient sample sizes to show whether the cool core phenomenon has a mass dependence. I think it is fair to say that so far there is no evidence for a mass dependence yet.

We do not have enough X-ray information on groups at moderate to high redshift to speculate on the evolution of the cool core phenomenon at that mass scale. The compact (r~100 kpc) cool core can produce up to 50% of a cluster's X-ray luminosity, so the presence of a cool core makes it easier for X-ray surveys to find it. So X-ray surveys are naturally biased to find cool cores. The incidence of cool cores in the brightest 55 clusters (the "B55" sample) is fairly high (at least ~1/2 ); 35% of the B55 clusters have BCGs with optical emission lines (Crawford et al. 1999; Donahue et al. 2010 completed the sample coverage.) Interesting to note that the B55 sample (e.g. Piccinotti et al. 1982; Edge et al. 1992) was originally based on collimator (non-imaging) X-ray samples from HEAO-1. Samples of somewhat more distant, optically selected clusters exhibit emission-line BCG fractions ~15% (e.g. von der Linden et al 2007; Edwards et al. 2007). These samples (more numerous) do include clusters of lower mass than the typical X-ray survey.

Cool cores seem to prefer clusters in which there has not been recent merger activity (based on dynamical properties, lack of radio halos, X-ray morphology.) Silvano Molendi discussed a new result, currently a Nice conference proceedings but about to be submitted, of GMRT observations of 40 clusters. No clusters with radio halos have a cool core.

Irina Zhuravleva and Eugene Churazov discussed the difference in the circular velocity^2 vs. radius (scaled radius) for cool core clusters compared to non-cool core clusters. She used hydrostatic masses to estimate the mass.

From Ian Parrish, Michael McCourt, Prateek Sharma's work: If the ratio free-fall time / cooling time is the most relevant criterion in determining whether a cluster has multiphase gas, the filament phenomenon presumably may scale (somehow) with system gravitating mass.

How do mergers affect cool cores?
Simulations (see Ian McCarthy) suggest that cool cores are difficult to disrupt in cosmologically realistic merger scenarios; but in these simulations the cool cores may be a little extreme (over cooled?)
Eugene asked: what would happen if clusters were set up to look like realistic clusters (with typical density, entropy profiles) and allowed to merge.

What is the effect of conduction?
Isotropic conduction alone is not physically realistic, anisotropic conduction on its own switches off cooling. However subsonic turbulence and mergers could modify this behavior. Groups are seen to have flatter profiles. Mateusz stated that turbulence is more important in groups (and as we heard last week, conduction is not very effective.)