Annu. Rev. Astron. Astrophys. 2003. 41: 191-239
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The cooling paradox refers to the remarkable discovery that the hot gas radiates but does not seem to cool. Many who have been closely involved with so-called "cooling flows" now doubt that they are cooling and some question whether they are flowing. Current attempts to resolve this paradox are generally taking two approaches: (1) the gas is cooling, but for some reason it evades detection and/or (2) the gas is being heated in some way so that very little gas cools. In this section we briefly review the evidence supporting the first approach, and heating is discussed in the following section.

7.1. Spectroscopic and Morphological Cooling Rates

Most of the evidence that cooling is incomplete or absent comes from XMM RGS (Reflection Grating Spectrometer) spectra of cluster scale flows (Abell 1835: Peterson et al. 2001; Abell 1795: Tamura et al. 2001; Abell S1101: Kaastra et al. 2001). In general the older data from ROSAT and ASCA could not easily distinguish between flows with a radially varying single temperature (i.e. single phase) and truly multiphase flows in which a range of temperatures is also present at every radius. For Abell 1835, a massive cluster with Tvir approx 9 keV, Allen et al. (1996) estimated a large mass deposition rate, dot{M} approx 2000 Modot yr-1, using an X-ray image deprojection procedure based on a steady state cooling flow model. This cooling rate has now been adjusted downward to dot{M} < 200 Modot yr-1 as a result of the XMM RGS spectrum of Abell 1835 that shows no emission lines from ions at temperatures T ltapprox Tvir / 3 (Peterson et al. 2001). Similar drastic reductions were made to morphological dot{M} estimates for other clusters, although the RGS only views the central 1' of each cluster, a radius of 30". In these clusters, the gas temperature drops from Tvir at large radii to about ~ Tvir / 3 near the center, similar to Figure 2b, with little or no indication of multiphase (cooling) gas at lower temperatures, k T ltapprox 1 - 2 keV.

At present the XMM and Chandra data for galaxy/group flows are limited, but the spectroscopic dot{M} also seems to be significantly lower than the morphological dot{M}, as in cluster flows. XMM RGS observations of NGC 4636 by Xu et al. (2002) indicate that the gas temperature decreases from 8.1 × 106 K at 3 kpc to 6.4 × 106 K at the center, but there is little or no spectroscopic evidence for gas emitting at temperatures ltapprox 6 × 106 K. The OVII line at 0.574 keV that emits near 2.5 × 106 K is not detected. Xu et al. determine dot{M} < 0.3 Modot yr-1 within r ~ 2.5 kpc. This is less than the total stellar mass loss rate expected in NGC 4636, alpha M*t approx 0.5 Modot yr-1, but most of the gas in NGC 4636 is circumgalactic so the mass cooling rate expected in a traditional cooling flow model would be larger: dot{M} approx 1 - 2 Modot yr-1 at distance d = 17 Mpc (e.g. Bertin & Toniazzo 1995). However, Bregman, Miller & Irwin (2001) have observed NGC 4636 with the Far Ultraviolet Spectroscopic Explorer (FUSE) and detected the OVI 1032,1038Å doublet emitted from gas at T ~ 3 × 105 K. It is generally assumed that this emission arises from gas that is cooling, not from the stellar ejecta as it is being heated to the hot gas phase. The heating process, possibly involving shocks and rapid thermal mixing, is likely to be faster and more efficient than collisional excitation of emission lines during cooling (Fabian, Canizares, & Böhringer 1994). The FUSE observations indicate a cooling rate of only dot{M} approx 0.17 ± 0.02 Modot yr-1 for d = 17 Mpc. Both XMM RGS and FUSE observations are consistent with a cooling rate that is ~ 5 times less than predicted from cooling flow models. However, FUSE has only a 30" (2.5 kpc) square aperture containing ~ 0.083 of the total X-ray luminosity. If the cooling were spatially distributed in proportion to the X-ray surface brightness, as reckoned by Bregman et al., the total cooling rate in NGC 4636 would be ~ 0.17 / 0.083 ~ 2 Modot yr-1, which is consistent with traditional cooling flow models. The OVI line width observed with FUSE is 44 km s-1. However, if the OVI emission shares the same kinematic widths ~ 150 km s-1 as the Halpha + [NII] lines observed in the central 15" of NGC 4636 by Caon et al. (2000), the additional flux in the broad wings might not have been detected by FUSE.

Spectroscopic X-ray and FUSE cooling rates for M87 and NGC 1399, respectively centered in the Virgo and Fornax clusters, are also much less than previously expected morphological rates. XMM-EPIC observations of M87 indicate dot{M} ltapprox 0.5 Modot yr-1 (Molendi & Pizzolato 2001; Matsushita et al. 2002), much less than earlier predictions from X-ray images: ~ 40 Modot yr-1 (Peres et al. 1998) and ~ 10 Modot yr-1 (Stewart et al. 1984; Fabian et al. 1984b). In NGC 1399 Buote (2002) found that the XMM spectrum within ~ 20 kpc is best fit with a two temperature emission model; spectral models with a single temperature or a continuum of temperatures (as in a cooling flow) give less satisfactory fits. Buote identifies the hotter phase (1.5 - 1.8 keV) with gas from the Fornax cluster and the colder phase (1.0 - 1.3 keV) with gas ejected from stars in NGC 1399, but there is no evidence that the cool phase cools to even lower temperatures. This is supported by FUSE observations of NGC 1399 by Brown et al. (2002) who find dot{M} < 0.2 Modot yr-1 within a 3 × 3 kpc region at the center of NGC 1399 - this is much less than the total cooling rate of ~ 2 Modot yr-1 inferred from the X-ray image using cooling flow models (Bertin & Toniazzo 1995; Rangarajan et al. 1995). Perhaps the cooling is intermittent.

7.2. Warm and Cold Gas at T < 105 K

In view of the failure to detect significant cooling at X-ray temperatures, it is remarkable that faint, diffuse, warm gas at T ~ 104 K (Halpha + [NII]) is almost universally observed near the centers of groups and clusters formerly identified as cooling flows. Although the mass of warm gas (104 - 105 Modot) is very much less than the mass that would have cooled in the cooling flow scenario, it could represent an important short-lived phase in the cooling process. The density of this warm gas, estimated from the [S II] 6716/6731 ratio, is ~ 100 cm-3 (Heckman et al 1989; Donahue & Voit 1997) compatible with pressure equilibrium with the hot gas within ~ 1 kpc of the galactic centers. The warm gas can be ionized by galactic starlight from old, hot post-AGB stars (Binette et al 1994) or by UV from locally cooling gas and thermal conduction (Donahue & Voit 1991; 1997). The total luminosity in Halpha + [NII] emission is ~ 1 - 10 × 1039 erg s-1. In E galaxies that are strong radio sources most of the line emission is concentrated within ~ 1 arcsecond of the center (Kleijn et al. 2002), but it is unclear if this is true in general.

Recent surveys of Halpha + [NII] images and kinematics in elliptical galaxies (Shields 1991; Buson et al. 1993; Goudfrooij et al. 1994; Macchetto et al. 1996; Caon, Macchetto & Pastoriza 2001) reveal that the images are rarely as smooth and regular as the stellar isophotes. The spatial irregularities in the Halpha + [NII] images appear to be compatible with the random Halpha + [NII] velocities ~ ± 150 km s-1 observed (Zeilinger et al. 1996; Caon et al. 2000). The warm gas clearly does not track the smooth rotation or dispersion kinematics of the stars but instead may approximately follow the motion of the hot gas. If so, the hot gas would be subsonically turbulent with energy on spatial scales (~ 0.5 kpc) too large to be produced by Type Ia supernovae.

A small number of elliptical galaxies have detectable neutral or molecular gas. Surveys (Knapp, Turner & Cunniffe 1985; Huchtmeier 1994; Huchtmeier, Sage & Henkel 1995) detect HI emission in ltapprox 15 percent of E galaxies, but in some cases this may include emission from nearby late type galaxies within the beam. HI disks are more common in low luminosity E galaxies that do not have observable X-ray emission from hot gas (Sadler, et al. 2000; Oosterloo et al. 2002). Some of the more spectacular examples, in which the HI gas probably results from a recent merger, have blue colors like spiral galaxies. Similarly, Wiklind, Combes & Henkel (1995), Knapp & Rupen (1996) and Young (2002) detect CO emission from a relatively small number of E galaxies selected because of their large far infrared fluxes. The molecular gas is often rotating in large (1 - 10 kpc) disks of mass 107 - 109 Modot. In some cases the high specific angular momentum of the molecular gas (or its sign) requires an external origin. Using spectroscopic stellar ages, Georgakakis et al. (2001) have shown that the mass of neutral and molecular gas decreases with time (by star formation?) since the last merger event.

7.3. Dust in Elliptical Galaxies

About 80 percent of elliptical galaxies have dust clouds, lanes or disks within ~ 1 kpc of the center (van Dokkum & Franx 1995; Martel et al. 2000; Colbert, Mulchaey & Zabludoff 2001; Tran et al. 2001; Kleijn et al. 2002) with associated gas masses 104 - 107 Modot. Some of the Halpha-emitting gas is undoubtedly related to the photoionized boundaries of these dusty clouds (Goudfrooij et al. 1994; Ferrari et al. 1999). One might expect the dusty cores having an irregular (non-disk) appearance to be related to recent AGN outbursts, but the evidence for this is not yet compelling (e.g. Tomita et al. 2000; Krajnovic & Jaffe 2002). If AGN energy outbursts are common in E galaxies, it is remarkable that these rather fragile central dusty regions have survived. IRAS luminosities, detected in ~ 50 percent of ellipticals, indicate that there is much more dust in E galaxies than that responsible for the optical extinction in the central clouds (Goudfrooij & de Jong 1995; Bregman et al. 1998: Merluzzi 1998; Ferrari et al. 2002). The ratio of 100 µm to optical B-band fluxes is noticeably higher for cD galaxies (Bregman, McNamara & O'Connell 1990). Knapp, Gunn and Wynn-Williams (1992) have shown that the mid-infrared ~ 12 µm radiation has an r1/4 distribution like the galactic stars, consistent with circumstellar dust associated with stellar mass loss. Recent midIR ISO spectra show the 9.7 µm feature characteristic of circumstellar silicate grains expected in low mass AGB stars (Athey et al. 2002), this is proof that galactic stars are ejecting alpha-elements. According to Athey et al., the total midIR emission is consistent with typical stellar mass loss rates ~ 1 Modot yr-1 in luminous E galaxies, although dot{M} may not scale with LB.

7.4. Origin of Warm Gas, Cold Gas and Dust

The diffuse warm (~ 104 K) gas that emits optical emission lines gas could have been recently ejected from stars, cooled from the hot phase, acquired in a recent galactic merger, or accreted from local gas clouds similar to the high velocity clouds that fall toward the Milky Way. Interesting morphological similarities between the Halpha + [NII] and X-ray images have been reported in some E galaxies (Trinchieri & di Serego Alighieri 1991; Trinchieri, Noris, & di Serego Alighieri 1997; Trinchieri & Goudfrooij 2002), suggesting a generic relationship. Optical line emission traces (part of) the perimeters of X-ray cavities in 3C317/Abell 2052 (Blanton et al. 2001b) and Perseus/NGC 1275 (McNamara, O'Connell & Sarazin 1996), but apparently does not fill in the cavities. This may be significant. Since the cavity rims show little heating due to strong shocks, the pressure inside the cavity must be similar to that in the rims. If so, recent stellar ejecta or warm gas introduced by a merger should be just as luminous inside the cavities, but evidently this is not observed. Either the evaporation-heating time is shorter inside the cavities or the Halpha-emitting gas may have cooled from the hot phase.

The total Halpha luminosity among luminous E galaxies, LHalpha approx 1039.5±1.0 ergs s-1 (Goudfrooij et al. 1994), holds for E galaxies for which Lx varies by ~ 103. This uniformity and upper bound (LHalpha ltapprox 1040.5 ergs s-1) on the line emission may reflect the similarity of central hot gas pressure among massive E galaxies, again suggesting (but not proving) an internal origin for the warm gas. Mergers with gas-rich dwarfs might produce a wider spread in LHalpha. Evidently all nearby X-ray bright E galaxies contain diffuse Halpha + [NII] emission. It seems unlikely that mergers with gas-rich galaxies would be equally common for E galaxies in small groups and those in richer clusters. The tendency for some of the diffuse Halpha + [NII] images to approximately follow the stellar isophotes (Caon et al. 2000) also suggests an internal source for the warm gas, but the exceptions (e.g. NGC 5044) could arise from a merger or from recent AGN energy release.

The strange velocity patterns in the Halpha + [NII] emission (e.g. Caon et al. 2001) may also constrain the origin of this warm gas. The total stellar mass loss rate and hot gas cooling rate in classical "cooling flows" are both ~ 1 Modot yr-1 in large E galaxies. If this warm gas has a stellar origin, its lifetime must be short, twarm ltapprox 105 yrs, to keep LHalpha within observed limits (Mathews & Brighenti 1999a). The velocity distribution of the warm gas is very different from that of the stars. But the warm gas clouds are Thot / Twarm ~ 1000 times denser than the hot gas, so they cannot be be drag-accelerated to the local hot gas velocity in time twarm. Therefore the Halpha + [NII] emitting gas cannot be swept to the rims of the X-ray cavities by the motion of the hot gas. The chaotic velocity structure of the warm gas could be understood either as the undissipated motions of a very recent merger, or (more likely ?) as turbulent motions in the hot gas from which it cooled. The obvious difficulty with this second possibility is that XMM observations so far provide little or no evidence for cooling.

It is often claimed that most or all of the cold gas and dust in E galaxies is a result of mergers with gas-rich galaxies (e.g. Sparks et al. 1989; Sparks 1992; de Jong et al. 1990; Zeilinger et al. 1996; Caon et al. 2000; Trinchieri & Goudfrooij 2002). If the warm gas has a finite lifetime, an ongoing supply of new gas is required. However, there are relatively few reported cases of gas-rich dwarf galaxies currently merging with giant E galaxies although the optical line emission would make such merging galaxies easy to find. Moreover, most of the gas in merging galaxies could be lost by ram pressure stripping during the 108 - 109 yrs as they orbit toward the center of the giant E galaxy. Undoubtedly, however, mergers do occur. A sure signature for mergers are the counter-rotating warm gas clouds found in some E galaxies by Zeilinger et al. (1996) and Caon et al. (2000). Further detailed observations of warm gas distributions and kinematics in normal E galaxies are needed to better constrain its origin.

7.5. Hiding the Cooling Gas

The spectral contributions of cooling gas can be reduced if X-ray emission from the cooling gas is absorbed or if the cooling is more rapid than normal radiative cooling (Peterson et al. 2001; Fabian et al. 2001).

Intrinsic X-ray absorption has been invoked to interpret ROSAT and ASCA observations of cluster cooling flows (e.g. Allen 2000; Allen & Fabian 1997; Allen et al. 2001). Column densities N of a few 1021 cm2 are sufficient to absorb 1 keV X-rays provided the absorbing gas is reasonably cold, T ltapprox 106 K. Because X-ray absorption varies rapidly with energy, sigma(E) propto E-3, it can reduce the low temperature contributions to the ~ 1 keV FeL iron line complex, simulating the absence of cooler gas (Böhringer et al. 2002). At ASCA resolution spectral models with conventional cooling flows are possible if the low temperature gas is largely hidden by intrinsic X-ray absorption. Buote (2000b, d; 2001) and Allen et al. (2001) reported evidence for an absorbing oxygen edge (at ~ 0.5 keV) and intrinsic absorbing columns N ~ 1021 cm2 within ~ 5 - 10 kpc in several bright E galaxies such as NGC 5044 and NGC 1399. But the mass of absorbing gas required to occult the central regions of these galactic flows is large, Mabs approx (4/3) pi r3 n mp ~ 3 × 107 rkpc2 N21 Modot with unit filling factor. It is unclear how this (necessarily colder) gas would be supported in the galactic gravity field and how it would escape detection at other frequencies (Voit & Donahue 1995). Absorbing gas with N gtapprox 1020 cm2 would produce observable reddening of the background stars and large far-infrared luminosities unless the gas is dust-free. Resonant X-ray lines emitted from ions expected at low-temperatures can in principle be scattered and then absorbed by the continuous X-ray opacity (Gil'fanov et al. 1987), but the line-center optical depths are small and not all of the missing lines in XMM spectra are resonance transitions (Peterson et al. 2001). XMM and Chandra spectra of the non-thermal nucleus and jet of M87 and the nucleus of NGC 1275 fail to show intrinsic X-ray absorption at the level required to mask cooling in the thermal gas (Böhringer et al. 2001). Perhaps the ideal X-ray absorption model would be one in which the cooling regions are themselves optically thick at ltapprox 1 keV, but our attempts to achieve this have been unsuccessful. Overall, the prospects for intrinsic X-ray absorption are not particularly encouraging.

If the cooling rate at kT ltapprox 1 keV were somehow accelerated, the X-ray emission from cooling gas would be reduced. Begelman & Fabian (1990) and Fabian et al. (2001) propose that hot gas (Thot) may rapidly mix with cold gas (Tcold) and thermalize to Tmix ~ (Thot Tcold)1/2 with little emission from temperatures Thot > T > Tmix. Assuming Thot ~ 107 K and Tcold ~ 104 K, then Tmix ~ 3 × 105. One potential difficulty with this process is that the ~ 104 K gas in E galaxies has a filling factor of only ~ 10-6 (e.g. Mathews 1990) so it is not clear that the hot gas can find enough cold gas to mix with. (Neutral and molecular gas at T < 104 K are also in short supply.) In any case, when the gas at Tmix ~ 3 × 105 K cools further, it should radiate strongly in the OVI UV doublet which, at least for NGC 1399, is not observed. Finally, the soft X-ray emission missing from cooling regions may appear somewhere else in the spectrum (Fabian et al. 2002b).

Fujita, Fukumoto & Okoshi (1997), Fabian et al. (2001) and Morris & Fabian (2003) describe cooling flows in which the metal (iron) abundance is very inhomogeneous. Regions of enhanced iron abundance, possibly enriched by individual Type Ia supernovae, cool rapidly, reducing the X-ray line emission from intermediate temperatures, as required by XMM. The remaining gas of lower metallicity can also cool with less line emission. This is an attractive idea that could help solve the cooling paradox, but it needs to be tested with detailed flow models. In the presence of strong abundance inhomogeneities, the observed abundance and inferred Type Ia supernova rate will need to be appropriately adjusted. This type of inhomogeneity would differ from successful models of Milky Way enrichment where it is usually assumed that Type Ia enrichment products are widely distributed in the interstellar gas, enriching subsequent stellar generations.

Incomplete mixing of stellar ejecta can also have beneficial results. Mathews & Brighenti have recently modeled the thermal evolution of dusty gas ejected from red giant (AGB) stars in E galaxies in which the gas is first rapidly heated to the ambient temperature, ~ 1 keV, then cools by thermal electron collisions with the grains. The electron-grain cooling time (Dwek & Arendt 1992) is faster than normal plasma cooling time, the local galactic dynamical time and the grain sputtering time. Some grains survive in the cooled gas and may account for the central clouds of dusty gas observed in E galaxies. Rapid electron-grain cooling may also be consistent with the weakness of X-ray lines at subvirial temperatures in NGC 4636.

In view of the small mass of gas with T ltapprox 105 K in E galaxies, any gas that cools must rapidly convert to dense objects that are difficult to observe, like low mass stars. Star formation is aided by the high pressure and low temperature of the cold gas in E galaxy cores (Ferland, Fabian & Johnstone 1994; 2002; Mathews & Brighenti 1999a). In cluster cooling flows there is considerable evidence of ongoing star formation (Allen 1995; McNamara 1997; Cardiel et al. 1998: Crawford et al. 1999; Martel et al. 2002). For the much smaller cooling dot{M} in E galaxies and their groups the evidence for star formation is less obvious such as the features in optical spectra from a "frosting" of young stars (Mathews & Brighenti 1999a; Trager et al. 2000).

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