Annu. Rev. Astron. Astrophys. 1994. 32: 277-318
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2.1 X-Ray Imaging Evidence for Cooling Flows

A sharply peaked X-ray surface brightness distribution is indicative of a cooling flow, because it shows that the gas density is rising steeply towards the center of the cluster or group. Since the observed surface brightness depends upon the square of the gas density and only weakly on the temperature, this result is not model dependent. The high central density indicates a short cooling time.

Most of the images have been obtained with the Einstein Observatory, EXOSAT, and ROSAT, although the peaked X-ray surface brightness was anticipated with data from the Copernicus satellite (Fabian et al 1974, Mitchell et al 1975), from rocket-borne telescopes (Gorenstein et al 1977), and from the modulation collimators on SAS 3 (Helmken et al 1978).

The fraction of clusters with high central surface brightness is large, which means that cooling flows must be both common and long-lived. More than 30 to 50% of the clusters well-detected with the Einstein Observatory (Stewart et al 1984b, Arnaud 1988) have surface brightnesses that imply tcool < H0-1 within the central 100 kpc or so. This fraction is certainly an underestimate, because the ~ 1' angular resolution of the images dilutes the central surface brightness. Additional data from EXOSAT (Edge & Stewart 1991a, b) show that more than two thirds of the 50 X-ray brightest clusters in the sky (see list in Lahav et al 1989) have cooling flows (Edge et al 1992). Since this last sample (Table 1) is based on the total flux, to which the cooling, flow makes only a minor contribution, the high fraction is not a selection effect. This fraction is also an underestimate, since many of the remaining clusters in the sample have not been imaged; thus their status is undefined. Whether H0-1 should be used for ta is debatable, but inspection of the results shows that reducing ta by 2, say, does not much change the fraction of clusters containing cooling flows. The overall picture is that the prime criterion for a cooling flow, tcool < 1010 yr, is satisfied in a large fraction (~ 70-80%) of clusters. It is also satisfied in a number of poor clusters and groups (Schwartz et al 1980, Canizares et al 1983, Singh et al 1986, 1988, Schwartz et al 1991, Mulchaey et al 1993, Ponman & Bertram 1993). Cooling flow conditions also occur in large, isolated elliptical galaxies (Nulsen et al 1984, Canizares et al 1987). The largest catalogue of cooling flows to date is by White (1992) who has analyzed the images of most clusters observed with the Einstein Observatory (the selection criteria used for such observations means that this sample is not complete in the statistical sense).

Table 1. Cooling flow properties of the 55 X-ray brightest clusters a

Central Bin Mass Flow
Cooling Time Size Rate
Cluster Redshift O R Fluxb LXc (109 yr) (kpc) (Msun yr-1)

A426 0.0183 check check 75.0 110 0.48±0.02 31 I 183
Ophiuchus 0.028 - - 44.5 152 3.1±7.4 29 L 75
Coma 0.0232 x 0 32.0 75 95±239 47 I 0*
Virgo 18 Mpc check check 30.0 1 0.03±0.01 3 L 10
A2319 0.0564 x x 12.1 170 13.1±2.2 73 I 66
A3571 0.0391 - - 11.5 77 7.8±12.9 35 L 79
Centaurus 0.0109 check check 11.2 6 0.49±0.10 10 L 18
Tri. Aust. 0.051 check check 11.0 126 65±254 160 L 0
3C129 0.022 - check 9.59 20 5.1±4.5 44 L 61
AWM7 0.0172 x - 9.14 12 3.9±1.2 65 I 42
A754 0.0542 x x 8.53 105 9.5±12.5 48 L 24
A2029 0.0767 x check 7.52 197 3.8±0.7 99 I 402
A2142 0.0899 x - 7.50 272 3.0±0.8 48 H 188
A2199 0.0300 check check 7.12 30 2.4±1.8 42 L 150
A3667 0.0530 x - 6.68 83 165±236 112 I 0*
A478 0.0882 check check 6.63 241 2.3±0.5 70 L 570
A85 0.0521 check check 6.37 75 3.8±0.6 69 I 236
A3266 0.0594 x check 5.90 92 21.5±17.3 70 H 10
A401 0.0748 x x 5.88 147 20.1±5.9 92 I 12
0745-191 0.1028 check check 5.87 280 2.1±0.5 32 L 702
A496 0.0330 check check 5.67 25 2.1±0.3 43 I 112
A1795 0.0627 check check 5.30 89 2.5±0.4 81 I 478
A2256 0.0581 x 0 5.20 83 175±38 153 I 0*
Cygnus-A 0.057 check check 4.78 69 4.2±0.5 92 I 187
2A0335+096 0.0349 check check 4.67 25 0.90±0.11 35 L 142
A1060 0.0124 check x 4.36 2 2.2±3.3 16 L 9
A3558 0.0478 x - 4.21 42 - - 50
A644 0.0704 x x 4.15 92 8.7±1.1 146 I 326
A1651 0.0846 x - 3.67 112 - - -
A3562 0.0499 x - 3.52 39 4.5±4.8 25 L 45
A1367 0.0215 x 0 3.45 7 21.5±3.7 92 I 0
A399 0.0715 x x 3.41 78 25.4±5.0 139 I 0
A2147 0.0356 - check 3.28 18 15.2±24.5 83 L 54
A119 0.0440 x - 3.03 26 14.6±9.3 86 L 23
A3158 0.0590 x - 2.99 46 23.2±3.8 197 I 0
Hydra-A 0.0522 check check 2.90 35 1.8±0.7 50 L 315
A2052 0.0348 check check 2.66 14 1.1±0.2 40 L 90
A2063 0.0350 x check 2.64 13 4.1±1.0 68 I 45
A1644 0.0474 x - 2.60 24 13.5±4.6 59 I 19
A2065 0.0721 - - 2.79 65 33.3±8.2 136 I 0
Klemola44 0.0283 - - 2.55 9 - - -
A262 0.0164 check check 2.35 3 0.87±0.40 23 I 47
A2204 0.1523 - - 2.20 235 - - -
A2597 0.0824 check check 2.90 64 11.1±2.0 185 I 480
A1650 0.0845 - x 2.07 66 54±103 160 I 0
A3112 0.0746 x - 1.95 48 2.1±1.0 82 L 430
A3532 0.0585 - - 1.95 30 44.1±14.9 141 I 0
A4059 0.0478 check - 1.88 19 3.5±8.5 35 L 124
A3391 0.0545 x - 1.79 23 31.8±5.7 140 I 0
MKW3s 0.0449 check check 1.79 15 4.0±0.9 77 I 151
A1689 0.181 x - 1.75 268 13.8±2.3 190 I 164
A576 0.0381 x check 1.72 11 15.1±3.3 77 I 6
A2244 0.1024 - x 1.71 81 12.2±2.0 120 I 82
A2255 0.0809 x - 1.71 49 143±268 97 I 0*
A1736 0.046 x - 1.70 16 32.9±7.5 115 I 0

a From Edge et al (1992). A dash in any column means that the information is not available. The statistical uncertainty in the estimate of M is typically about 20%; the systematic uncertainty, given errors on the gravitational potential in the core of a cluster, may be up to a factor of 2. Whether a (focused) cooling flow exists or not can be judged from the estimates of the central cooling time, which should be less than about 1010 yr for a flow. The cooling time depends on the size of the innermost bin used in analyzing the cluster image, which in turn depends on the signal-to-noise of the data, the distance to the cluster, and the resolution of the instrument (I for IPC, H for HRI, L for CMA). As discussed by Edge et al, an estimate of the cooling time of the gas within art image bin depends directly on the size of that bin (strongly if a cooling flow is present). Those clusters where the bin size is larger than about 100 kpc and Mdot is listed as zero may still therefore contain a modest cooling flow. Further observations are needed there, A small Mdot occurring in a gravitationally-unfocused way could occur in even the Coma-like clusters.

b 2-10 keV flux in units of 10-11 erg cm-2 s-1.

c 2-10 keV luminosity in units of 1043 h50-2 erg s-1.

Asterisks in the final column indicate those clusters where there is no focused cooling flow taking place. A tick in the O column means optical line emission is detected, a tick in the R column means radio emission is detected from the central galaxy (Ball et al 1993 and references therein).

The mass deposition rate, Mdot, due to cooling (i.e. the accretion rate, although this is a poor term since most of the gas does not flow in far from rcool) can be estimated from the X-ray images by using the luminosity associated with the cooling region (i.e. Lcool within rcool) and assuming that it is all due to the radiation of the thermal energy of the gas, plus the PdV work done on the gas as it enters rcool:

Equation 2 (2)

where T is the temperature of the gas at rcool. Lcool is similar (but not identical) to the central excess luminosity defined by Jones & Forman (1984); it ranges from ~ 1042 to > 1044 erg s-1 and generally represents ~ 10% of the total cluster luminosity. Values of Mdot = 50-100 Msun yr-1 are fairly typical for cluster cooling flows. Some clusters show Mdot gtapprox 500 Msun yr-1 (e.g. A478, PKS0745, A1795, A2597, A2029, and Hydra A). The main uncertainties in the determination of Mdot lie in the gravitational contribution to Lcool and the appropriate choice for ta. Assuming ta ~ 1010 yr, the estimates of Mdot are probably accurate to within a factor of 2 (Arnaud 1988). Empirically, we find that the deduced Mdot is roughly proportional to ta1/3 (see Figure 2), which means that reducing ta to 109 yr introduces only a factor ~ 2 reduction in Mdot.

Figure 2

Figure 2. Properties of the ICM in A478 obtained by deprojecting the ROSAT HRI and PSPC images (small and larger bins, respectively) and solving for the density and temperature (White et al 1994, Allen et al 1994). The dotted line on the temperature plot indicates the mean temperature determined from the Ginga broad-beam spectrum (Johnstone et al 1992). Note that the cooling time of the gas is less than 1010 yr at 200 kpc. Mdot rises with radius to about 600-800 Msun yr-1.

Since we often measure an X-ray surface brightness profile for the cluster core (where the X-ray emission is well-resolved), we have Lcool(r) which can be turned into Mdot(r), the integral mass deposition rate within radius r. Generally, the surface brightness profiles are less peaked than they would be if all the gas were to flow to the center, giving roughly

Equation 3 (3)

This means that the gas must be inhomogeneous, so that some of the gas cools out of the hot flow at large radii and some continues to flow inward.

The actual computation of Mdot(r) is complicated, since we need to take into account how the gas cools and any gravitational work done on it. The thermal energy of the gas is generally more important than gravitational energy release in clusters (Tgas is several times greater than the virial temperature of the central galaxy), so a simple analysis gives a fair approximation to the profile (see Fabian et al 1986; Thomas et al 1987; White & Sarazin 1987a, b, c, 1988). Even if clusters have small core radii (say < 100 kpc), thereby significantly reducing Lcool, then the fraction with cooling flows would not be more than halved. In the case of A478, a comparison of the temperature decrease observed in the ROSAT Position Sensitive Proportional Counter (PSPC) spectrum with that inferred from the image shows that the core radius in that rich cluster is not small, and must exceed 200 kpc (Allen et al 1993).

The ROSAT High Resolution Imager (HRI) shows that the X-ray surface brightness profile in most clusters continues to rise inward (Figure 1) to within the inner 10 kpc. In A478, the cooling time is seen to drop below 4 x 108 yr at that radius and the total mass deposition rate Mdot approx 800 Msun yr-1 (Figure 2 taken from White et al 1994).

Figure 1

Figure 1. 3-dimensional representation of the X-ray surface brightness of the A478 cluster as seen by the ROSAT HRI (White et al 1994). The pixel size is 24 arcsec which corresponds to about 60 kpc. The cooling flow extends so at least 200 kpc radius, incorporating most of the prominent peak in the figure. Much of the cluster emission lies beyond the 1.3 x 1.3 Mpc area shown here.

In the case of the Perseus cluster, the cooling flow peaks away from the nucleus of the central galaxy NGC 1275, in an arc about 15 kpc away (Figure 3 from Böhringer et al 1993). The radio source in the galaxy appears to be holding off the flow and creating two regions of low X-ray surface brightness either side of the nucleus, coincident with the radio lobes. A similar effect is seen in the tails of the radio lobes of Cygnus A (Harris et al 1994). Sarazin et al (1992a, b) have claimed the detection of X-ray filaments in HRI observations of the flows in A2029 and 2A0335+096. Although the central structure in 2A0335+096 is convincing, the filamentary structures in A2029 were not found to be significant in a re-analysis of the same image by White et al (1994). They may be artifacts of the small ellipticity of the emission since spurious features can appear significant if it is assumed that the underlying emission has circular symmetry. A linear structure identified as a cooling wake is seen in a PSPC image of the NGC 5044 group (David et al 1994).

Figure 3

Figure 3. ROSAT HRI image of the central 130 x 130 kpc region of the Perseus cluster around NGC 1275 (Böhringer et al 1993). The radio image from Pedlar et al (1990) is shown at the right (to the same scale): the nuclei in both pictures superpose directly to show that the outer radio lobes fit in the X-ray dips N and S of the nucleus. The brightest X-ray patch lies about 15-20 kpc SE from the nucleus and does not correspond to features seen at other wavelengths, except that it may be the cause of the bend in the S radio lobe (note the radio contours) and lies just beyond the optical "blue loop" (see the figure in Sandage 1971).

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