The Regulation of Cooling and Star Formation in Luminous Galaxies by AGN Feedback and the Cooling-Time/Entropy Threshold for the Onset of Star Formation
AAccepted for publication in The Astrophysical Journal
Preprint typeset using L A TEX style emulateapj v. 03/07/07
THE REGULATION OF COOLING AND STAR FORMATION IN LUMINOUS GALAXIES BY AGNFEEDBACK AND THE COOLING-TIME/ENTROPY THRESHOLD FOR THE ONSET OF STAR FORMATION
D. A. Rafferty
Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, PA 16802 andDepartment of Physics and Astronomy, Ohio University, Athens, OH 45701
B. R. McNamara
Department of Physics and Astronomy, University of Waterloo, Waterloo, ON N2L 2G1, Canada,Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, N2L 2Y5 Ontario, Canada, andHarvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138 andP. E. J. Nulsen
Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138
Accepted for publication in The Astrophysical Journal
ABSTRACTUsing broadband optical imaging and
Chandra
X-ray data for a sample of 46 cluster central domi-nant galaxies (CDGs), we investigate the connection between star formation, the intracluster medium(ICM), and the central active galactic nucleus (AGN). We report the discovery of a remarkably sharpthreshold for the onset of star formation that occurs when the central cooling time of the hot atmo-sphere falls below ∼ × yr, or equivalently when the central entropy falls below ∼
30 keV cm . Inaddition to this criterion, star formation in cooling flows also appears to require that the X-ray andgalaxy centroids lie within ∼
20 kpc of each other, and that the jet (cavity) power is smaller than theX-ray cooling luminosity. These three criteria, together with the high ratio of cooling time to AGNoutburst (cavity) age across our sample, directly link the presence of star formation and AGN activityin CDGs to cooling instabilities in the intracluster plasma. Our results provide compelling evidencethat AGN feedback into the hot ICM is largely responsible for regulating cooling and star formationin the cores of clusters, leading to the significant growth of supermassive black holes in CDGs at latetimes.
Subject headings: galaxies: clusters: general — galaxies: elliptical and lenticular, cD — X-rays:galaxies: clusters — cooling flows INTRODUCTION
X-ray observations of the intracluster medium (ICM)in a majority of clusters show stongly peaked centralemission from gas with short cooling times (Peres et al.1998). Such clusters were thought to harbor cooling flows(Fabian 1994), in which gas cooling out of the ICM at thecore of the cluster is replaced by gas at larger radii in aslow inward flow. Low-spectral-resolution X-ray observa-tions predicted deposition rates of 100 − (cid:12) yr − (e.g., Peres et al. 1998). These rates and the implied coldgas masses exceeded the inferred star formation rates(McNamara 1997) and the observed gas masses (Edge2001) in the central galaxy by an order of magnitude.This apparent disagreement between the amount of gasseen cooling and the amount seen in traditional sinkspersisted for more than two decades.Recently, however, high-spectral resolution observa-tions by the Chandra and XMM-
Newton
X-ray Obser-vatories have shown that the cooling rates predicted byROSAT are too large by a factor of ten (e.g., Davidet al. 2001; Blanton et al. 2003; Peterson et al. 2003;Kaastra et al. 2004). These new telescopes have shownthat cooling-flow spectra lack the emission signatures ex-pected from gas cooling below ∼ a r X i v : . [ a s t r o - ph ] J un Rafferty et al.the cooling ICM (Crawford et al. 1999; Edwards et al.2007).However, only recently, with the advent of
Chandra ,has it become possible to derive the X-ray properties onthe same scales as the optical properties to determinemore precisely the relationship between cooling and starformation. In this paper, we use optical and X-ray dataof similar spatial resolution for 46 CDGs to examine theconnection between the ICM properties, such as the cen-tral cooling time and the AGN’s feedback power, andthe presence of star formation in the central galaxy. Weadopt H = 70 km s − Mpc − , Ω Λ = 0 .
7, and Ω M = 0 . THE SAMPLE
The sample comprises 39 CDGs for which we have ob-tained broadband optical data, plus an additional 7 sys-tems for which we have taken optical data from the lit-erature. The sample was constructed to test whetherthe presence of active star formation in the CDG is re-lated to the properties of the cooling flow. To that end,the objects in the sample were chosen from the
Chandra
Data Archive to include both cooling flows and noncool-ing flows, with a wide range of central cooling times, from t cool (cid:46) yr to t cool (cid:38) yr. Additional constraintson the sample were that the available X-ray images havesufficient counts to derive density and temperature pro-files and that the systems be visible to the optical ob-servatory during the alloted observing windows. Table 1lists the general properties of the objects in the sample. OBSERVATIONS AND DATA REDUCTION
Optical Data
The primary signatures of star formation are due tothe presence of hot, massive stars in the star-formingpopulation. This population is mixed with the generallyold stellar population of the underlying CDG, as well aswith cold gas and dust. These massive stars emit mostof their energy in the ultraviolet and blue parts of thespectrum, unlike the less massive but much longer-livedstars that account for most of the CDG’s emission atlonger wavelengths. The ultraviolet emission in turn canionize nearby cool gas, resulting in optical line emissionsuch as H α emission (e.g., Heckman et al. 1989; Voit &Donahue 1997; Hatch et al. 2007). Additionally, the en-ergetic photons from the massive stars heat surroundingdust, which re-emits the light at far infrared wavelengths(O’Dea et al. 2008). In this study, we use the excess blueemission (above that expected from the old backgroundpopulation) as an indicator of recent star formation.We use broadband imaging at short and long wave-lengths to search for the excess blue emission in thecores of the CDGs. By comparing the short-wavelengthsurface-brightness profile, which is sensitive to young, hotstars, with the long-wavelength profile, which traces theold background population, we can detect the presenceof star formation. Elliptical galaxies generally show nosigns of recent star formation, and have color profiles thatbecome bluer with increasing radius (e.g., Vader et al.1988; Franx et al. 1989; Peletier et al. 1990; Goudfrooijet al. 1994). This effect is thought to be generally dueto a decreasing stellar metalicity with increasing radius(e.g., Carollo et al. 1993; Kobayashi & Arimoto 1999;Tamura & Ohta 2000; Ferreras et al. 2005). Therefore, a color profile that becomes increasingly blue towards thecenter is unusual (i.e. the CDG has excess blue emission),and is indicative of recent star formation in that region.We use this property to identify star formation in oursample.The excess blue emission, while generally indicative ofstar formation, can be the result of other sources, suchas the scattered light from an AGN or a low-metalicitystellar population. However, because AGNs are pointsources, their emission should not be spatially extendedon scales of tens of kpc, as the excess blue emission isoften observed to be in CDGs. Scattered light can makethe AGN emission appear more extended, but studies ofthe nearby cooling flows A1795 and A2597 have ruled outsignificant polarization in the excess blue light (e.g., Mc-Namara et al. 1996a, 1999). As to metalicity effects, mostmodeling of spectra and broadband colors of CDGs hasfound that systems with large color excesses are bettermodeled by emission from massive O and B stars, ratherthan old, low-metalicity stellar populations (e.g., Allen1995; Cardiel et al. 1995; Smith et al. 1997; Cardiel et al.1998; Crawford et al. 1999). Additionally, Hubble SpaceTelescope studies of two CDGs with prominent blue ex-cesses, A1795 and A2597, have resolved the blue emissioninto knots and demonstrated that it is most likely dueto recent star formation (Koekemoer et al. 1999, 2002;O’Dea et al. 2004).Since our goal is to search for connections between starformation and the cooling flow, we used data that aresensitive to the presence of active star formation. Suchstar formation is best detected at short wavelengths dueto the rising spectral energy distribution (SED) of hotstars in the ultraviolet and the falling SED of the back-ground galaxy population. Therefore, we chose to ob-serve in the U band (with a central wavelength of 3582˚A). This choice minimizes contamination from redshifted[OII] λ α and H β lines can bea problem; therefore, we chose to observe in both R and I filters (with central wavelengths of 6513 ˚A and 8204 ˚A,respectively). Colors obtained from both filters give usa means of verifying that any anomalous blue emissionis due to star formation. If the U − R and U − I colorsare both anomalously blue, it is likely to be due to starformation, and not due to contamination from emissionlines (at least in the red images).Optical data were obtained during five separate runs.Three runs, totaling 11 nights, were done using the 2.4-m telescope at the MDM observatory on Kitt Peak, Ari-zona between the dates of March 9-12, 2005, September26-29, 2005, and May 22-24, 2006. An additional runof four nights was performed at the KPNO Mayall 4-mtelescope between October 5-8, 2005. Lastly, a 2-nightrun was performed at the WIYN 3.5-m telescope overJanuary 22-23, 2006. See Table 2 for details of the opti-cal observations. Broadband imaging was done at MDMusing the Echelle CCD with a 9 . × . − . At the KPNO4-m telescope, imaging was done using the Mosaic CCDarray of eight CCDs with a 36 ×
36 arcmin field of viewand a scale of 0.26 arcsec pixel − . At the WIYN 3.5-mhe Regulation of Cooling and Star Formation by AGN Feedback 3 TABLE 1Sample Properties.
X-ray Core (J2000) CDG Core (J2000) ∆ r b System z α ( ◦ ) δ ( ◦ ) CDG Name M K a α ( ◦ ) δ ( ◦ ) (kpc)A85 0.055 10.4593 -9.3022 PGC 002501 − . ± .
04 10.4603 -9.3031 5.23C 28 0.195 13.9599 26.4098 PGC 138263 − . ± .
18 13.9609 26.4105 12.9A133 0.057 15.6744 -21.8804 ESO 541-013 − . ± .
06 15.6739 -21.8820 6.5A223 0.207 24.4828 -12.8198 2MASX J01375602-1249106 − . ± .
16 24.4833 -12.8195 < . − . ± .
03 28.1936 36.1520 1.7A383 0.187 42.0139 -3.5291 PGC 145057 − . ± .
12 42.0141 -3.5291 < . − . ± .
03 43.6139 41.5796 < . − . ± .
04 49.9510 41.5116 < .
72A 0335+096 0.035 54.6700 9.9660 PGC 013424 − . ± .
05 54.6691 9.9701 10.6A478 0.088 63.3551 10.4653 PGC 014685 − . ± .
07 63.3553 10.4652 < . − . ± .
04 68.4077 -13.2619 < . − . ± .
27 73.5160 2.8923 494.4MS 0735.6+7421 0.216 115.4351 74.2440 PGC 2760958 − . ± .
17 115.4361 74.2438 < . − . ± . · · · · · · · · · Hydra A 0.055 139.5238 -12.0953 PGC 026269 − . ± . · · · · · · · · · Zw 3146 0.290 155.9152 4.1863 2MASX J10233960+0411116 − . ± . · · · · · · · · · A1068 0.138 160.1853 39.9532 PGC 093944 − . ± . · · · · · · · · · A1361 0.117 175.9150 46.3562 PGC 093947 − . ± .
09 175.9150 46.3556 4.6A1413 0.143 178.8249 23.4052 PGC 037477 − . ± .
08 178.8250 23.4049 < . − . ± .
02 187.7059 12.3912 < . − . ± .
03 193.2738 -9.2040 < . − . ± .
10 194.6730 -1.7614 < . − . ± .
03 194.8988 27.9593 85.8A1795 0.063 207.2196 26.5913 PGC 049005 − . ± .
08 207.2188 26.5929 7.5A1835 0.253 210.2581 2.8789 2MASX J14010204+0252423 − . ± . · · · · · · · · · A1991 0.059 223.6314 18.6445 NGC 5778 − . ± .
08 223.6313 18.6424 8.8MS 1455.0+2232 0.258 224.3128 22.3424 PGC 1668167 − . ± .
14 224.3130 22.3429 < . − . ± .
18 226.0313 -2.8045 < . − . ± . · · · · · · · · · A2052 0.035 229.1851 7.0215 UGC 09799 − . ± . · · · · · · · · · A2065 0.073 230.6224 27.7052 PGC 054888 · · · · · · < . · · · − . ± .
11 252.7840 4.9927 < . − . ± .
09 255.6772 34.0604 < . − . ± .
03 258.8456 57.4114 < . − . ± .
11 260.0419 26.6256 8.5MACS J1720.2+3536 0.391 260.0699 35.6075 · · · · · · < . − . ± .
09 260.6133 32.1326 < . − . ± .
06 290.2918 43.9456 50.1A2390 0.228 328.4034 17.6955 PGC 140982 − . ± .
17 328.4035 17.6957 < . − . ± .
10 330.2191 20.9693 46.6A2597 0.085 351.3322 -12.1239 PGC 071390 − . ± .
11 351.3322 -12.1242 < . − . ± .
06 354.1270 21.1464 2.6A2657 0.040 356.2393 9.1919 PGC 072297 − . ± .
07 356.2393 9.1932 3.5A2670 0.076 358.5571 -10.4189 PGC 072804 − . ± .
09 358.5570 -10.4190 < . Note . — The X-ray and CDG core positions are from this work; see Sections 4.1 and 4.2.1. Systems that lack optical CDG positionswere not observed in this study; optical data for these systems was taken from the literature (see references given in Table 5). Uncertaincore positions (due to the lack of a cooling core or to the presence of confusing substructure) are marked with an asterisk. a Total K -band magnitudes from the 2MASS catalog. b Projected radius from the X-ray core to the CDG’s core. Separations of less than 2 arcsec are treated as upper limits. telescope, imaging was done using the Mini-Mosaic CCDarray of two CCDs, with a 9 . × . − .Harris U, R, and I filters were used during all runs. Allobjects were imaged in the U band and in either R or I band (most objects were imaged in both R and I bands).Exposure times were typically 2 ×
600 s in U, ×
150 sin I, and 2 ×
225 s in R ; however, in some cases (e.g.,for distant systems), longer total exposure times wererequired to achieve sufficient signal to noise. Multiple frames were taken to allow for easy removal of cosmic-ray events. The frames were dithered by ∼ −
60 arcsecbetween exposures to allow for the removal of artifactssuch as bad columns and CCD gaps and to improve flatfielding. Conditions varied during the runs, with pho-tometric conditions for approximately two-thirds of thetotal time.Optical reduction and analysis was performed using Rafferty et al.
TABLE 2X-ray and Optical Observations.
X-ray Observations Optical ObservationsExp. Time a Total Exp. Time (s)System OBSID (ks) Telescope
U R I
A85 904 37.5 2.4 m 1200 300 4503C28 3233 48.2 2.4 m 1800 300 450A133 2203 30.9 4 m 2000 200 800A223 4967 42.2 4 m 2200 1600 300A262 2215 26.7 4 m 1200 · · · · · · · · · · · ·
A496 4976 58.0 2.4 m 1200 300 450A520 4215 54.2 4 m 3200 300 1200MS 0735.6+7421 4197 39.9 3.5 m 2100 3600 2400PKS 0745-191 2427 17.4 · · · · · · · · · · · ·
Hydra A 4970 98.8 · · · · · · · · · · · ·
Zw 3146 909 41.5 · · · · · · · · · · · ·
A1068 1652 25.6 · · · · · · · · · · · ·
A1361 3369 3.0 2.4 m 1800 450 225A1413 5003 65.8 2.4 m 2700 900 450M87 3717 15.1 2.4 m 600 200 345HCG 62 921 47.5 2.4 m 300 150 150A1650 4178 26.6 2.4 m 300 150 150Coma 1086 9.3 2.4 m 900 300 · · ·
A1795 3666 14.2 2.4 m 1800 450 225A1835 496 10.3 · · · · · · · · · · · ·
A1991 3193 35.8 2.4 m 1800 450 225MS 1455.0+2232 4192 83.2 2.4 m 1800 450 225RXC J1504.1-0248 5793 33.2 2.4 m 1800 600 900A2029 4977 77.3 · · · · · · · · · · · ·
A2052 890 36.1 · · · · · · · · · · · ·
A2065 3182 26.0 2.4 m 1800 450 225RX J1532.8+3021 1649 8.8 2.4 m 3600 1200 900A2218 1666 34.2 2.4 m 1800 400 600Hercules A 1625 12.5 4 m 2400 1200 · · ·
A2244 4179 55.7 2.4 m 1500 450 600NGC 6338 4194 44.0 2.4 m 1800 450 225RX J1720.2+2637 4361 22.0 2.4 m 1200 300 3004 m 2400 · · · · · · · · · a Exposure time after cleaning for background flares.
IRAF (the Image Reduction and Analysis Facility ), ver-sion 12.2.1, and custom procedures written in IDL. Standard Reductions
The bias level and its row-to-row variation were mod-eled and subtracted in all frames by fitting a high-orderfunction to the overscan region of each chip. The re-maining bias structure was removed with a bias frame See http://iraf.noao.edu/ . See . constructed by averaging 30-40 individual frames takeneach night in the evening and morning. Twilight flatswere then used to remove differences in pixel sensitiv-ities across the chip. Flats were made for each nightby averaging together at least 3 dithered frames takenduring the evening and morning twilight with exposurelevels of ∼ / ∼ . − . − ) during theMarch and September 2005 runs (the dark current dur-he Regulation of Cooling and Star Formation by AGN Feedback 5ing the May 2006 run was much lower), which resulted inlarge sky gradients in the long-exposure U -band frames.Additionally, a small but significant light contamination(probably due to light from the red light-emitting diodeson the instrument mounting) was present in the R - and I -band dark frames. We corrected for the dark currentand light leak by creating a master dark frame in eachband by averaging 4-5 individual frames together andsubtracting a scaled version of this master frame fromeach object frame. Each individual dark frame had adark time typical of the longest exposure time used dur-ing observation (e.g., 900 s for U ). Unfortunately, thedark current was found to vary both in magnitude (by afactor of two) and in spatial structure over the course ofa single night. This variation made it impossible to usea simple scaling by dark time. Instead, the best scalingwas determined using a χ minimization routine.The best dark scaling for each object frame was deter-mined by minimizing the residuals between the modesof the pixel values in multiple regions of the CCD af-ter dark subtraction. This method effectively scales thedark frame to produce the flattest sky across the CCD.However, for this method to be effective, sky variationsdue to pixel-to-pixel differences in sensitivity must firstbe removed by flat fielding. Therefore, the dark imageswere also flat fielded before fitting and subtraction. Thefitting was done in IDL using the MPFIT package. Typ-ically 9 object-free sub-regions of the chip in which thedark structure was most pronounced were used for fit-ting. If the fitted scaling in any given region differedby more than 3 sigma from the adopted mean it was re-jected. The mean scaling across all the remaining regionswas then used for dark subtraction. Remaining sky gra-dients were typically on the order of 2-3% of sky acrossthe CCD, but they are generally much smaller ( ∼ . I -band images. Therefore, a fringe framefor each night was constructed and subtracted from the I -band object frames. The fringe frame was made by av-eraging together all the I -band object frames of a givennight, after masking of all objects (using the objmasks task in IRAF). The sky level and any large-scale gradi-ent were removed from the fringe frame using a medianfilter over large blocks of pixels to filter out small-scalevariations. The final fringe frame was then scaled andsubtracted from all the I -band object frames using the rmfringe tool in IRAF.In the KPNO data, an additional additive feature waspresent in I - and U -band images due to scattered light offof the prime-focus corrector (this feature is not presentin the R -band images due to the anti-reflective coatingapplied to the corrector). A template image of this “pupilghost” was made using the mscpupil task in IRAF. Thistask isolates the pupil contribution to an image by fittinga spline function to the background of a master imageand subtracting it off. The master image was made byaveraging all flat-corrected images in a given filter overthe entire run, after the masking of all objects using the objmask task in IRAF, and scaling by the mode of pixelvalues in object-free regions of the image. The resultingpupil template image was then scaled and subtracted off See http://cow.physics.wisc.edu/~craigm/idl/fitting/ . of each image interactively.Once the additive features were subtracted from eachframe, a dark-sky flat was made by again averaging allframes in a given filter over each night. Generally, 10-20 frames were required to produce good dark-sky flats.When an insufficient number of frames existed for a givennight (due, e.g., to poor weather), a dark-sky flat from aneighboring night was used. Once again, all objects weremasked before averaging. The sky flats were then mediansmoothed with a 129 × ± Sky subtraction
Accurate determination of the sky surface brightness isessential for tracing galaxy profiles to large radius, wherethe galaxy’s surface brightness is often just a few per-cent of the sky. Our study is concerned mainly with theprofiles in the centers of the galaxies, where their emis-sion dominates over the sky. However, we have nonethe-less attempted to determine the sky level as accuratelyas possible. To this end, we have adopted the methodof sky determination used in McNamara & O’Connell(1992), in which counts in source-free regions of the skyare assumed to be dominated by Poisson noise. The dis-tribution of counts in each region should then be wellrepresented by a gaussian whose width is an estimate ofthe statistical error in the sky level. Therefore, to deter-mine the sky level, we extract the counts in a number ofsource-free regions, construct a histogram of sky values,and fit a gaussian to the histogram. This method of fit-ting the distribution of sky values, in contrast to usinga simple mode or mean, allows one to use the distribu-tion’s deviation from a normal distribution to identifythe presence of contaminating sources.We use the mean of the best-fit gaussian as the modalsky value for a given region. We used 7-9 sky regionswith areas of at least 1000 pixels each, distributed overthe chip in the region of the CDG (but far enough away tominimize contamination), and eliminated regions whosesky modes were more than 2 σ from the adopted mean.Comparison with sky values determined by fitting a planeto the entire CCD (median filtered over large blocks)showed typical differences in sky values between the twomethods of (cid:46) − S max = S max − S min ) to define the systematic errorin sky levels as ∆ S sys = ∆ S max /
2. When computingtotal errors in colors, systematic errors were added inquadrature with the statistical errors. Rafferty et al.
Image stacking
After sky subtraction and before stacking, the pixelvalues were changed to units of electrons per second bymultiplying by the gain and dividing by the exposuretime. Next, the individual frames in each band werescaled to remove differences in intensity due to changes inairmass between exposures. The IRAF task mscimatch was used to perform this scaling.
Mscimatch uses themeasured intensities of unsaturated stars to determinethe scalings; typically, 50-200 stars per frame were used.Since the frames for a given object were always takenwithin a short time of one another, scalings were typi-cally (cid:46) mscimatch was not used todetermine zero-point offsets, as this step was done duringsky subtraction.In order to stack the frames into a final master im-age, the frames must be tangent-plane projected ontothe same pixel grid. To minimize artifacts due to projec-tion, cosmic rays were identified and removed using the craverage and fixpix tasks in IRAF.
Mscimage was usedto perform the projection using a sinc interpolant. Next,in the rare cases where there were large point spreadfunction (PSF) variations between frames, PSF match-ing was done to remove these variations. Finally, theframes were stacked using a median filter (or an averagewhen only 2 frames were used) and a σ -clipping routinewith the mscstack task in IRAF. Calibration
For the purposes of this paper, in which we com-pare colors measured between different radii of the samesource, photometric calibration is unnecessary and wasnot done. While it is possible that we may miss signif-icant active star formation if it is distributed smoothlyacross the galaxy (resulting in possibly negative colorgradients), calibrated colors for similar systems (e.g., Mc-Namara & O’Connell 1992) are consistent with there be-ing little or no active star formation. Therefore, we con-sider it unlikely that significant star formation is presentin any of the systems in our sample with negative colorgradients.Usually, because our sources are scattered across thesky, corrections must be made to remove extinction dueto dust in our own galaxy, which varies as a function ofposition on the sky. However, we are measuring radialgradients and hence comparing colors between two radiiin the same source. Since the Galactic extinction doesnot vary significantly over the typical angular scale ofour galaxies ( r (cid:46) X-ray Data
All systems were observed with the
Chandra
ACIS de-tector in imaging mode and the data were obtained fromthe
Chandra
Data Archive. Details of the observationsare given in Table 2.The Chandra data were reprocessed with CIAO 3.3using CALDB 3.2.0 and were corrected for known time-dependent gain and charge transfer inefficiency problems.Blank-sky background files, normalized to the count rateof the source image in the 10 −
12 keV band, were usedfor background subtraction. See http://asc.harvard.edu/contrib/maxim/acisbg/ . DATA ANALYSIS AND RESULTS
Derivation of ICM Properties
X-ray spectra were extracted in elliptical annuli with ∼ dmextract in CIAO, andweighted response files were made using the CIAO tools mkwarf and mkacisrmf or mkrmf ( mkacisrmf was usedfor all observations taken at the −
120 C focal plane tem-perature; mkrmf was used for all other observations).Gas temperatures and densities were found by depro-jecting the spectra with a single-temperature plasmamodel (MEKAL) with a foreground absorption model(WABS) using the PROJCT mixing model in XSPEC11.3.2, between the energies of 0.5 keV and 7.0 keV.The redshift was fixed to the value given in Table 1, andthe foreground hydrogen column density was fixed to theGalactic value of Dickey & Lockman (1990), except in thecases of 2A 0335+096 and A478, when a significantly dif-ferent value was preferred by the fit. In these two cases,the column density in each annulus was allowed to vary.The density was then calculated from the normalizationof the MEKAL component, assuming n e = 1 . n H (for afully ionized gas with hydrogen and helium mass frac-tions of X = 0 . Y = 0 . n e = (cid:115) . × (4 πD L ) × norm(1 + z ) V , (1)where n e has units of cm − , the luminosity distance ( D L )has units of cm, and the volume of the shell ( V ) has unitsof cm .We derived the cooling times using the deprojecteddensities and temperatures found above and the coolingcurves of Smith et al. (2001), calculated using APEC (the results do not change significantly if we use thecurves of B¨ohringer & Hensler 1989). The pressure ineach annulus was calculated as p = nkT, where we haveassumed an ideal gas and n ≈ n e . Lastly, the entropyis defined as in Lloyd-Davies et al. (2000): S = kT n − / , (2)and has units of keV cm .A primary objective of this study is to determine howthe ICM properties relate to the optical colors. In par-ticular, we are interested in properties at the core of thecluster, where the cooling times are the shortest. How-ever, the systems in our sample span a wide range ofredshift and core surface brightness, resulting in a wide See http://cxc.harvard.edu/atomdb/ . he Regulation of Cooling and Star Formation by AGN Feedback 7range in the physical size of the innermost region (whichwe required to contain ∼ (cid:15) ∼ n e ) to extrapolate the density closer to the core thanis generally possible using spectral deprojection. We usedthis method for 15 of the 46 objects with optical data;for the remaining objects, this method did not resultin a significant decrease in the central region over thatused in spectral deprojection (due either to reaching theresolution limit of r ≈ ≈ σ er-rors), derived as close as possible to the core (after theexclusion of any non-thermal point sources).Lastly, to make comparisons of the ICM properties be-tween objects at a single physical radius, we used linearinterpolation of the profiles in log − log space, using themean radius of each annulus. We chose a radius of 12 kpc,as this radius was the smallest physical radius that couldbe achieved across most of our sample (excluding onlyA520; the mean radius of A1835 lies at 12.7 kpc, but theproperties at this radius should differ only slightly fromthose at 12 kpc). We also interpolated the cooling-timeprofiles in the same way to find the cooling time at theradius corresponding to the distance between the X-raycore and the CDG’s core (denoted ∆ r and listed in Table1). Table 4 lists the interpolated ICM properties. Analysis of Optical Data
We identified the CDG as the most extended galaxywithin the field, which generally lies near the X-ray core. However, when the cluster contains more than one verylarge galaxy and it is unclear which is the dominantgalaxy, we chose as the CDG the galaxy with the largestintegrated K -band magnitude from the 2MASS catalog.Below we note any unusual characteristics of the CDGor image. A85:
The CDG has extended optical line emission (Huet al. 1985; Fisher et al. 1995).
3C 28:
An excess of UV flux has been detected in theCDG by Wills et al. (2002) and was ascribed bythem to active star formation.
A262:
The CDG has a large, central dust lane and abright star nearby which were masked.
Perseus:
The Perseus CDG (NGC 1275) is well knownfor its blue, emission-line filaments, dust lanes, andthe foreground high-velocity system, all of whichwere masked before analysis. Significant star for-mation was detected by McNamara & O’Connell(1989); Romanishin (1987); Smith et al. (1992).
2A 0335+096:
There is a nearby bright star in the im-age that results in large areas of the galaxy beingmasked. Significant star formation was detected byRomanishin & Hintzen (1988).
A478:
Cardiel et al. (1998) found spectral evidence forsignificant star formation in the CDG.
A520:
The cluster appears to have no well-defined opti-cal core (Dahle et al. 2002), and instead has severalconcentrations of galaxies, none of which coincidewith the X-ray core. Crawford et al. (1999) notethat there are three dominant galaxies and chosethe SW one as the CDG, as did we.
M87:
The optical jet and central region, associated withthe AGN, were masked before analysis.
HCG 62:
The dominant galaxy of this compact grouphas a large, nearby companion galaxy which wasmasked before analysis.
A1795:
The CDG is well known to harbor a tail of blueemission that is thought to be due to star forma-tion triggered by compression of the gas by theradio source (McNamara et al. 1996a,b; Pinkneyet al. 1996; O’Dea et al. 2004). The R - and I -bandimages were affected by scattered light, which wasmasked as thoroughly as possible. A1991:
As with A1795, the long-wavelength imageswere affected by scattered light, requiring masking,and the seeing was poor. McNamara & O’Connell(1989) report spectral evidence for a small SFR,and McNamara & O’Connell (1992) report a posi-tive U − I color gradient in the core. RXC J1504.1-0248:
The U -band image shows an elon-gated blue region in the core, extending 6 arcsec inlength. A2065:
This cluster has two dominant galaxies. Wehave analyzed the southern galaxy, which appearsto be associated with the X-ray core (Chatzikoset al. 2006).
RX J1532.5+3021:
The CDG is known to be very blue(Dahle et al. 2002). The U − I colormap shows avery blue region offset slightly to the south of thecore and extending 4–8 arcsec in radius. Hercules A:
The CDG has extended optical line emis-sion (Tadhunter et al. 1993). The CDG core is thesoutheastern of the two surface-brightness peaks. Rafferty et al.
TABLE 3Central ICM Properties. r a n e kT Entropy t cool System (arcsec) (kpc) (cm − ) (keV) (keV cm ) (10 yr)A85 2.4 2.6 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − .
3C 28 2.2 7.2 0 . +0 . − . . +0 . − . . +2 . − . . +1 . − . A133 3.0 3.3 0 . +0 . − . . +0 . − . . +1 . − . . +0 . − . A223 2.0 6.7 0 . +0 . − . . +0 . − . . +13 . − . . +5 . − . A262 2.0 0.7 0 . +0 . − . . +0 . − . . +1 . − . . +0 . − . A383 1.5 4.6 0 . +0 . − . . +0 . − . . +1 . − . . +0 . − . AWM 7 2.2 0.8 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . Perseus 11.8 4.2 0 . +0 . − . . +0 . − . . +1 . − . . +0 . − .
2A 0335+096 3.4 2.4 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . A478 1.5 2.6 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . A496 1.0 0.6 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . A520 7.7 25.2 0 . +0 . − . . +3 . − . . +120 . − . . +66 . − . MS 0735.6+7421 2.9 10.1 0 . +0 . − . . +0 . − . . +1 . − . . +0 . − . PKS 0745-191 2.5 4.8 0 . +0 . − . . +0 . − . . +1 . − . . +0 . − . Hydra A 2.2 2.4 0 . +0 . − . . +0 . − . . +2 . − . . +1 . − . Zw 3146 1.6 6.8 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . A1068 2.0 4.9 0 . +0 . − . . +0 . − . . +1 . − . . +0 . − . A1361 2.0 4.2 0 . +0 . − . . +0 . − . . +3 . − . . +1 . − . A1413 3.8 9.5 0 . +0 . − . . +1 . − . . +11 . − . . +2 . − . M87 5.9 0.5 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . HCG 62 2.0 0.6 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . A1650 3.0 4.7 0 . +0 . − . . +1 . − . . +12 . − . . +2 . − . Coma 9.8 4.6 0 . +0 . − . . +3 . − . . +85 . − . . +73 . − . A1795 2.0 2.4 0 . +0 . − . . +0 . − . . +4 . − . . +1 . − . A1835 3.2 12.7 0 . +0 . − . . +0 . − . . +1 . − . . +0 . − . A1991 2.2 2.5 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . MS 1455.0+2232 1.3 5.3 0 . +0 . − . . +1 . − . . +7 . − . . +2 . − . RXC J1504.1-0248 1.1 3.8 0 . +0 . − . . +3 . − . . +12 . − . . +1 . − . A2029 0.6 0.9 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . A2052 3.9 2.7 0 . +0 . − . . +0 . − . . +1 . − . . +7 . − . A2065 2.0 2.7 0 . +0 . − . . +0 . − . . +4 . − . . +3 . − . RX J1532.8+3021 2.0 9.6 0 . +0 . − . . +0 . − . . +1 . − . . +0 . − . A2218 3.9 11.7 0 . +0 . − . . +0 . − . . +32 . − . . +22 . − . Hercules A 2.0 5.3 0 . +0 . − . . +0 . − . . +1 . − . . +0 . − . A2244 2.0 3.5 0 . +0 . − . . +0 . − . . +8 . − . . +3 . − . NGC 6338 1.5 0.8 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . RX J1720.2+2637 1.7 4.8 0 . +0 . − . . +0 . − . . +4 . − . . +2 . − . MACS J1720.2+3536 2.2 11.7 0 . +0 . − . . +0 . − . . +2 . − . . +1 . − . A2261 2.0 7.1 0 . +0 . − . . +1 . − . . +13 . − . . +4 . − . A2319 4.4 4.8 0 . +0 . − . . +7 . − . . +90 . − . . +17 . − . A2390 0.6 2.3 0 . +0 . − . . +1 . − . . +4 . − . . +0 . − . A2409 3.0 7.6 0 . +0 . − . . +0 . − . . +42 . − . . +18 . − . A2597 3.4 5.5 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . A2626 2.0 2.1 0 . +0 . − . . +0 . − . . +5 . − . . +2 . − . A2657 3.0 2.3 0 . +0 . − . . +1 . − . . +29 . − . . +18 . − . A2670 3.0 4.3 0 . +0 . − . . +0 . − . . +17 . − . . +8 . − . Mean radius of the inner-most region; when elliptical regions were used, the equivalent redius( r = [ ab ] / , where a and b are the semi-axes) is given. A2244:
A nearby bright star required large areas ofmasking.
RX J1720.2+2637:
The CDG has a blue central re-gion some 13 arcsec in radius.
MACS J1720.2+3536:
The U − I colormap showsblue emission extending to a radius of 2.5 arcsec. A2390:
The U -band image shows a very blue, elongatedregion in the core, extending SE to NW some 4–5arcsec in length. A2597:
The CDG possesses knots of star formation(Koekemoer et al. 2002; O’Dea et al. 2004).
Surface Brightness Profiles
The master frames, created by stacking the individualframes for each object (see Section 3.1.3), were first reg-istered to a common coordinate grid using wregister inIRAF. Next, the master frames were PSF-matched usingthe psfmatch task to the lowest-resolution frame of theset (typically the U -band frame). This step is necessarybefore spatial comparisons between frames taken in dif-ferent bands can be made. However, since the bands arefairly broad ( F W HM ∼ TABLE 4Interpolated ICM Properties. r = 12 kpc r = ∆ r a n e kT Entropy t cool t cool System (cm − ) (keV) (keV cm ) (10 yr) (10 yr)A85 0 . +0 . − . . +0 . − . . +1 . − . . +0 . − . . +0 . − .
3C 28 0 . +0 . − . . +0 . − . . +1 . − . . +1 . − . . +1 . − . A133 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . A223 0 . +0 . − . . +0 . − . . +12 . − . . +5 . − . . +21 . − . A262 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . A383 0 . +0 . − . . +0 . − . . +1 . − . . +0 . − . . +0 . − . AWM 7 0 . +0 . − . . +0 . − . . +2 . − . . +2 . − . . +0 . − . Perseus 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − .
2A 0335+096 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . A478 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . A496 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . A520 · · · · · · · · · · · · . +17 . − . MS 0735.6+7421 0 . +0 . − . . +0 . − . . +1 . − . . +0 . − . . +0 . − . PKS 0745-191 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . · · · Hydra A 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . · · · Zw 3146 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . · · · A1068 0 . +0 . − . . +0 . − . . +1 . − . . +0 . − . · · · A1361 0 . +0 . − . . +0 . − . . +2 . − . . +1 . − . . +1 . − . A1413 0 . +0 . − . . +1 . − . . +11 . − . . +2 . − . . +2 . − . M87 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . HCG 62 0 . +0 . − . . +0 . − . . +0 . − . . +1 . − . . +0 . − . A1650 0 . +0 . − . . +1 . − . . +9 . − . . +2 . − . . +2 . − . Coma 0 . +0 . − . . +2 . − . . +68 . − . . +52 . − . · · · b A1795 0 . +0 . − . . +0 . − . . +2 . − . . +0 . − . . +2 . − . A1835 0 . +0 . − . . +0 . − . . +1 . − . . +0 . − . · · · A1991 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . MS 1455.0+2232 0 . +0 . − . . +0 . − . . +4 . − . . +1 . − . . +2 . − . RXC J1504.1-0248 0 . +0 . − . . +1 . − . . +4 . − . . +0 . − . . +1 . − . A2029 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . · · · A2052 0 . +0 . − . . +0 . − . . +0 . − . . +2 . − . · · · A2065 0 . +0 . − . . +0 . − . . +3 . − . . +3 . − . . +7 . − . RX J1532.8+3021 0 . +0 . − . . +0 . − . . +1 . − . . +0 . − . . +0 . − . A2218 0 . +0 . − . . +0 . − . . +31 . − . . +22 . − . . +22 . − . Hercules A 0 . +0 . − . . +0 . − . . +1 . − . . +1 . − . . +1 . − . A2244 0 . +0 . − . . +0 . − . . +7 . − . . +3 . − . . +4 . − . NGC 6338 0 . +0 . − . . +0 . − . . +1 . − . . +1 . − . . +0 . − . RX J1720.2+2637 0 . +0 . − . . +0 . − . . +2 . − . . +1 . − . . +1 . − . MACS J1720.2+3536 0 . +0 . − . . +0 . − . . +2 . − . . +1 . − . . +1 . − . A2261 0 . +0 . − . . +1 . − . . +12 . − . . +4 . − . . +5 . − . A2319 0 . +0 . − . . +7 . − . . +67 . − . . +12 . − . . +26 . − . A2390 0 . +0 . − . . +0 . − . . +2 . − . . +0 . − . . +0 . − . A2409 0 . +0 . − . . +0 . − . . +33 . − . . +14 . − . . +18 . − . A2597 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . A2626 0 . +0 . − . . +0 . − . . +3 . − . . +1 . − . . +2 . − . A2657 0 . +0 . − . . +1 . − . . +36 . − . . +21 . − . . +21 . − . A2670 0 . +0 . − . . +0 . − . . +23 . − . . +21 . − . . +23 . − . The ∆ r radius is the projected distance between the X-ray core and the CDG core (seeTable 1). b The Coma data lack sufficient counts to derive a cooling time at the CDG’s radius. some effect due to PSF mismatches will remain in thedata.Surface brightness profiles were constructed from thePSF-matched, registered master frames using the el-lipse task in IRAF. This task works by fitting ellipsesto isophotes of the surface brightness distribution of agalaxy and calculating the mean surface brightness alongthe ellipse (see Jedrzejewski 1987). Clipping routinesare used to reject stars, superimposed galaxies, or othersource of contamination. Additionally, such contaminat- ing objects as were visible were masked out by eye beforefitting. The ellipticities and position angles were allowedto vary from ellipse to ellipse to reflect changes in theunderlying galaxy. Typically, the surface brightness dis-tributions of CDGs become more elliptical at larger radii(e.g., Patel et al. 2006). The ellipse centroids were notallowed to vary, to make comparisons between profilesin different bands possible. The centroids were deter-mined from the long-wavelength images ( R or I ), whichare generally smooth and relaxed (reflecting the old stel-0 Rafferty et al. U - R A2390RX J1532.8+3021RXC J1504.1-0248MACS J1720.2+3536A4783C 28A2597A1795Hercules ARX J1720.2+2637A3832A 0335+096A85
MS 1455.0+2232A2626A1650A2657A1361A496MS 0735.6+7421A2244 M87A1413HCG 62A223A2409A1991A2065A2218A2261 U -I RX J1532.8+3021PerseusMACS J1720.2+3536RXC J1504.1-0248A2390A25973C 28A1795RX J1720.2+26372A 0335+096A383 A85MS 1455.0+2232A2244
A2626A1650A1361A2657MS 0735.6+7421A496 NGC 6338A2319A2409 AWM 7A520 M87A133A1413A1991HCG 62A2670A2065A262A2261A2218
Fig. 1.— U − R ( left ) and U − I ( right ) color versus the equivalent radius ( r = [ ab ] / , where a and b are the semiaxes), ordered bydecreasing gradient. The colors for each object have been shifted by arbitrary values. The error bars shown for each point are the statisticalerrors; the dashed lines show the total (statistical plus systematical) errors. The best-fit gradients (see Section 4.3) are overplotted as solidlines between the inner and outer radii used in the fit. lar populations of the galaxy). Centroid positions werecalculated using imexamine in IRAF, which finds thecentroid using Gaussian fits to the radial surface bright-ness profile.The ellipse centers, ellipticities, and position angleswere fixed to those resulting from a fit to the R - or I -band image, whichever was of higher signal-to-noise, tomake it possible to compare profiles in different bands.We note that fixing the U -band ellipse properties to thoseof a longer-wavelength band will tend to reduce the U -band surface brightness along the ellipse if the U -bandemission has significantly different preferred ellipticitiesor position angles. An example of such a case is A2390,which has a bar of very blue emission near its center thatis clearly different in shape from the I -band emission inthe same region. The net effect of our procedure is todilute somewhat the signatures of star formation in ourprofiles; however, we estimate that the effect is generallysmall. The resulting color profiles for the optical sampleare shown in Figure 1. Comparison with Other Studies and betweenObserving Runs
As a check for systematic errors in our reduction andanalysis, we can compare our color profiles both to pro-files from the literature and between different observingruns. In Figure 2, we compare our U − I profiles with Fig. 2.—
Comparison of our U − I color profiles ( triangles ) tothose of McNamara & O’Connell (1992) ( circles ) for the objectscommon to both samples. those from Figure 5 of McNamara & O’Connell (1992).In general, the profiles agree well within the errors overthe inner 10-20 arcsec. At the extreme inner radii thereis often some discrepancy, probably due to seeing effectshe Regulation of Cooling and Star Formation by AGN Feedback 11 U - R A2390A2261RX J1720.2+2637 U -I A2390A2261A2244
Fig. 3.—
Comparison of U − R color profiles ( left ) and U − I color profiles ( right ) from different observing runs: A2390 and RXJ1720.2+2637 – MDM ( triangles ) and KPNO ( circles ), A2261 andA2244 – MDM September 2005 ( triangles ) and MDM May 2006( circles ). at a (cid:46) a (cid:38) −
20 arcsec)our profiles do not match well, as those of McNamara& O’Connell (1992) often show a steep positive gradientthat ours do not (particularly apparent in the profiles ofA1991 and A262). This effect may be due to misesti-mation of the sky by McNamara & O’Connell (1992), asthey used a much smaller CCD (FOV ∼ . × . . × . < a < U -band image shows a linear bluefeature in this region, the color of which would be dilutedif fairly circular annuli are used (as we have done).As a further check of consistency, we also compare pro-files taken from observations made during different runsand at different telescopes. In Figure 3 we show profilesfor three objects that we observed twice. A2390 was ob-served with the MDM 2.4-m telescope and the KPNO 4-m telescope; A2261 and A2244 were observed twice withMDM. The profiles agree well, with the exception of theinner 2 arcsec of the A2390 profiles, which is probablydue to seeing differences between the two observations. Color Gradients and ∆ Colors
Color gradients were derived for the U − I and U − R color profiles using a least-squares fitting routine in theMPFIT package. The color gradient is defined as thechange in color (in magnitudes) over the corresponding -0.5 0.0 0.5 1.0 1.5 2.0 2.5G(U-R) (mag/dex)-0.50.00.51.01.52.02.5 G ( U -I) ( m a g / d e x ) Fig. 4.—
The U − I color gradient versus the U − R color gradient.The dotted line shows equality between the two gradients, whilethe solid line shows the best-fit straight line. change in log( r ) (in dex); e.g., for U − I : G ( U − I ) = d ( U − I ) d log( r ) . (3)The following function was fit to the data in color-log( r )space: U − I = G ( U − I ) log( r ) + b, (4)where G ( U − I ) is the color gradient and b is the inter-cept. The data were weighted by their total (systematicplus statistical) error, and errors on the gradient werereturned by the covariance matrix of the best fit. Toeliminate possible effects from the PSF on the fitted gra-dient, the fits were restricted to radii greater than twicethe radius of the FWHM of the PSF.The outer radius used in the fit was set differentlyfor objects with blue cores and for those without. Forblue objects, the outer radius was set to the approxi-mate point at which the excess blue emission ends, sothat the resulting gradient would trace the star-formingregion only. The edge of the blue emission was deter-mined by examining the U − I or U − R colormaps ofthe galaxy, made by dividing the U -band image by eitherthe R - or I -band image. For red objects, the outer ra-dius was set to the radius at which the total errors reach0.5 mag to avoid regions where sky-subtraction errorssignificantly affect the profile (however, since the datawere weighted by their errors, this choice has little effecton the measured gradients). See Figure 1 for plots of thecolor profiles with the best-fit gradients overlaid. Table 5lists the color gradients and the radial range over whichthey were derived.The U − R and U − I color gradients are very similar,with the U − I color gradients being on average slightlymore positive (due to a lower contribution from the starformation to the flux in the I band). To illustrate this,we plot in Figure 4 the two gradients against one an-other. Since the errors in the two gradients are correlatedthrough the errors in the U -band surface-brightness pro-files, we perform a linear regression using the BCES least-squares method of Akritas & Bershady (1996), which2 Rafferty et al. TABLE 5CDG Color Gradients and ∆ Colors.
Color Gradients ∆ Colors G ( U − R ) G ( U − I ) Range ∆( U − R ) ∆( U − I ) RangeSystem (mag dex −
1) (mag dex −
1) (arcsec) (mag) (mag) (kpc)A85 0 . ± .
04 0 . ± .
05 1.6-9.5 − . ± .
05 0 . ± .
05 5-10 − . ± . − . ± .
10 5-203C 28 0 . ± .
26 0 . ± .
30 1.3-5.1 0 . ± .
14 0 . ± .
15 5-10A133 · · · − . ± .
04 1.8-39.6 · · · − . ± .
05 5-10 · · · − . ± .
10 5-20A223 − . ± . · · · − . ± . · · · − . ± . · · · · · · − . ± .
03 2.0-176.4 · · · − . ± .
10 5-10 · · · − . ± .
25 5-20A383 0 . ± .
28 0 . ± .
25 1.8-5.3 · · · · · · · · ·
AWM 7 · · · − . ± .
03 1.1-84.8 · · · − . ± .
18 5-10 · · · − . ± .
45 5-20Perseus · · · . ± .
07 6.5-47.0 · · · . ± .
05 5-10 · · · . ± .
17 5-202A 0335+096 0 . ± .
08 0 . ± .
09 1.5-4.2 − . ± . − . ± .
08 5-10A478 0 . ± . · · · . ± . · · · − . ± . − . ± .
06 1.7-18.7 − . ± . − . ± .
09 5-10 − . ± . − . ± .
24 5-20A520 · · · − . ± .
28 1.2-9.0 · · · − . ± .
16 5-10 · · · − . ± .
48 5-20MS 0735.6+7421 − . ± . − . ± .
28 1.0-4.9 − . ± .
24 0 . ± .
24 5-10PKS 0745-191a · · · . ± .
13 2.0-6.0 · · · · · · · · ·
Hydra Ab · · · . ± .
16 1.0-5.0 · · · · · · · · ·
Zw 3146c 3 . ± . · · · · · · · · · · · · A1068d 1 . ± . · · · · · · · · · · · · A1361 − . ± . − . ± .
06 2.0-13.1 − . ± . − . ± .
03 5-10 − . ± . − . ± .
07 5-20A1413 − . ± . − . ± .
21 1.7-9.6 − . ± . − . ± .
10 5-10 − . ± . − . ± .
21 5-20M87 − . ± . − . ± .
07 11.5-96.6 − . ± . − . ± .
42 5-10HCG 62 − . ± . − . ± .
05 2.3-42.1 − . ± . − . ± .
13 5-10A1650 − . ± . − . ± .
14 2.1-19.7 − . ± . − . ± .
11 5-10 − . ± . − . ± .
20 5-20Coma − . ± . · · · − . ± . · · · − . ± . · · · . ± .
10 0 . ± .
11 2.1-9.1 0 . ± .
08 0 . ± .
08 5-100 . ± .
18 0 . ± .
20 5-20A1835e 4 . ± . · · · · · · · · · · · · A1991 − . ± . − . ± .
08 2.6-16.9 − . ± . − . ± .
06 5-10 − . ± . − . ± .
12 5-20MS 1455.0+2232 − . ± .
23 0 . ± .
25 1.5-5.8 · · · · · · · · ·
RXC J1504.1-0248 0 . ± .
17 1 . ± .
16 1.7-5.8 · · · · · · · · · − . ± .
014 3.0-10.0 · · · · · · · · ·
A2052a · · · − . ± .
021 5.0-35.0 · · · · · · · · ·
A2065 − . ± . − . ± .
08 1.4-29.2 0 . ± .
10 0 . ± .
10 5-10 − . ± . − . ± .
18 5-20RX J1532.8+3021 1 . ± .
40 1 . ± .
53 2.0-5.4 · · · · · · · · ·
A2218 − . ± . − . ± .
12 1.4-8.7 0 . ± .
10 0 . ± .
10 5-10 − . ± . − . ± .
11 5-20Hercules A 0 . ± . · · · . ± . · · · . ± . · · · − . ± . − . ± .
13 1.9-18.1 − . ± . − . ± .
10 5-10 − . ± . − . ± .
17 5-20NGC 6338 · · · − . ± .
01 1.6-102.2 · · · − . ± .
03 5-10 · · · − . ± .
09 5-20RX J1720.2+2637 0 . ± .
14 0 . ± .
17 1.5-11.7 0 . ± .
10 0 . ± .
11 5-100 . ± .
18 0 . ± .
19 5-20MACS J1720.2+3536 0 . ± .
85 1 . ± .
88 1.6-2.2 · · · · · · · · ·
A2261 − . ± . − . ± .
19 1.4-7.4 − . ± . − . ± .
10 5-10 − . ± . − . ± .
17 5-20A2319 · · · − . ± .
05 1.3-18.0 · · · − . ± .
07 5-10 · · · − . ± .
13 5-20A2390 1 . ± .
67 1 . ± .
76 1.9-4.0 0 . ± .
17 0 . ± .
17 5-101 . ± .
54 1 . ± .
56 5-20A2409 − . ± . − . ± .
28 1.5-6.3 − . ± . − . ± .
17 5-10A2597 0 . ± .
14 0 . ± .
14 2.1-8.6 0 . ± .
10 0 . ± .
10 5-100 . ± .
32 0 . ± .
32 5-20A2626 − . ± . − . ± .
04 1.1-18.8 − . ± . − . ± .
07 5-10 − . ± .
13 0 . ± .
13 5-20A2657 − . ± . − . ± .
07 1.4-9.5 − . ± .
15 0 . ± .
15 5-10 − . ± .
39 0 . ± .
39 5-20A2670 · · · − . ± .
03 1.4-32.2 · · · − . ± .
03 5-10 · · · − . ± .
06 5-20a Gradient taken from McNamara & O’Connell (1992)b Gradient taken from McNamara (1995). We have adopted the average G ( U − I ) error for our sample.c Gradient taken from unpublished data (B. R. McNamara, private communication). We have adopted the average G ( U − R ) error for our sample.d Gradient taken from McNamara & O’Connell (1992). We have adopted the average G ( U − R ) error for our sample.e Gradient taken from McNamara et al. (2006). We have adopted the average G ( U − R ) error for our sample. properly accounts for correlated errors. The resulting fit(with 1- σ errors) is: G ( U − I ) = (0 . ± . . ± . G ( U − R ) . (5)The U − I color gradients are therefore consistent witha simple offset from the U − R color gradients. We notethat there are no objects for which the difference betweenthe two gradients is large enough ( (cid:38) σ ) to indicate sig-nificant contamination from emission lines in the R or I images. The gradients discussed above do not by themselvesgive an indication of the radial extent of the star forma-tion. For two objects with the same gradient, one mayhave star formation over a much larger physical radius.Therefore, it is useful to derive the change in color be-tween two physical radii. Objects with star-forming re-gions that are physically smaller will tend to have smallercolor changes than those objects with more extendedstar formation. To derive the color changes, denoted∆( U − R ) and ∆( U − I ), we use simple linear interpo-he Regulation of Cooling and Star Formation by AGN Feedback 13lation to estimate the colors at 5, 10, and 20 kpc. The∆( U − R ) color changes are then:∆( U − R ) = ( U − R ) outer − ( U − R ) inner (6)Table 5 lists the ∆ colors for the optical sample.The detectability of blue emission depends on sev-eral factors, such as the signal-to-noise ratio of the im-ages, the seeing or PSF size (as we exclude unresolvedemission), and the redshift of the source. Since thisPSF size limits our spatial resolution, an obvious biasis that we are sensitive to blue emission that extendsover smaller physical radii in lower-redshift systems thanin higher-redshift systems. This bias could be impor-tant if the red systems are at systematically higher red-shift than the blue systems, such that extended blueemission could be missed preferentially in the red sys-tems. However, the mean redshift of the blue systems( < z > = 0 . < z > = 0 . DISCUSSION
The Relation between Star Formation and CoolingTime
The cooling time of the ICM is a critical measure ofits thermal state. If the cooling time is sufficiently short(on the order of the age of the system or less), signif-icant condensation of gas should occur unless heatingbalances the cooling entirely. In this section, we investi-gate whether the cooling times we derived from
Chandra data are related to the presence of excess blue emissionin the CDG.To this end, in Figure 5 we plot the optical color gra-dients of the CDG against the central cooling times ofthe cluster’s ICM. We plot the U − I color gradient whenavailable; otherwise, we plot the U − R gradient, as theyare almost equivalent (see Section 4.3). The left panelshows the emission-weighted central cooling time derivedas close to the core as our data allow us to achieve (seeTable 3). Since the systems in our sample vary greatlyin redshift, we plot in the middle panel the cooling timeat a single physical radius of 12 kpc (see Table 4). At 12kpc, the very short cooling times (those below ∼ × yr) measured at the center disappear, demonstrating thattheir short cooling times relative to the rest of the sampleare due to resolution effects.For comparison, we also plot the ∆ colors against thecooling times in Figure 6. In this figure, the overall re-lationship between cooling time and the presence of starformation is unchanged from that shown in Figure 5. Ifthe star formation rate is governed by the local value ofthe cooling time at each point throughout the ICM, thenwe should expect the ∆ colors to increase smoothly asthe cooling time at 12 kpc decreases. The abrupt turnon of star formation at t cool (cid:39) × yr in Figure 6does not support such behavior.It is apparent from Figure 5 that positive gradients,which are indicative of active star formation, occur onlyin objects with central ( r (cid:46)
12 kpc) cooling times be-low ∼ × yr. Such a direct relationship between star formation and the local state of the intracluster gasstrongly implicates the gas as the cause of the star for-mation. The simplest possibility is that cooling gas fu-els the star formation directly. Alternatively, dense gasmight have fueled an AGN outburst that triggered thestar formation. However, it is also apparent that thepresence of a short central cooling time does not guar-antee the presence of a positive color gradient, as severalof the objects with cooling times below ∼ × yr donot have blue cores (although the majority do).To emphasize that the systems with blue central col-ors are different on average from those with red colors,we show in Figure 7 histograms of the cooling times at12 kpc for the objects in our optical sample with cool-ing times below 4 × yr. We have divided the sampleinto those systems with positive color gradients (blue sys-tems) and those with negative gradients (red systems).We include MS 1455.0+2232, which has a positive U − I gradient and a negative U − R gradient, in the bluesample. Compared with the red systems, the blue sys-tems clearly prefer shorter cooling times. A Kolmogorov-Smirnov (K-S) test gives a probability of just 1 . × − that the red and blue samples are drawn randomly fromthe same parent distribution of cooling times. This re-sult is a strong indicator that the cooling flow and starformation in the CDG are connected.The large disparity between the mass of gas within thecooling regions of the cluster and the mass of cold gasand new stars, coupled with the sharply declining coolingtimes with decreasing radius, precludes the possibilitythat the central cooling time is significantly affected bythe cold gas. Thus, the tight relationship between coolingtimes and color gradients make it implausible that thestars are formed from infalling cold gas.One possibility is that thermal instabilities in the hot,cooling gas are driving the star formation. Under theright conditions, the motion of a cooling blob of gas willbecome unstable, leading eventually to catastrophic cool-ing. These conditions are met roughly when the growthrate of the instabilities due to cooling exceeds the coun-teracting rate of any damping, such as that from viscousdamping (which acts to slow the blob’s radial oscilla-tions) or thermal conduction (which acts to reduce theblob’s temperature contrast with its surroundings). Thestability condition in any region can be determined fromthe X-ray data, and a detailed treatment of this scenariowill be presented in a forthcoming paper. Star Formation and Other ICM and GalaxyProperties
We also investigated the dependence of the presence ofexcess central blue emission on the temperature, density,and entropy of the ICM. We plot the CDG color gradi-ents against each of these properties, derived at a singlephysical radius of 12 kpc, in Figure 8. The temperatureshows no clear relation to the color gradient. However, itappears that high densities ( (cid:38) .
03 cm − ) are requiredfor blue colors, in agreement with the cooling time find-ings discussed earlier (since t cool ∝ n − e ).Additionally, we find that positive gradients occur onlyin objects in our sample whose entropies at 12 kpc are (cid:46)
30 keV cm (see the right-hand panel of Figure 8).The range in entropy levels seen in this plot for the blueobjects is consistent with that found by Donahue et al.4 Rafferty et al. cool (10 yr)012345 G ( U -I) , G ( U - R ) ( m a g / d e x ) cool at 12 kpc (10 yr) 1 10 100t cool at CDG (10 yr) Fig. 5.—
Color gradient versus the central cooling time ( left panel ), the cooling time at a radius of 12 kpc ( middle panel ), and thecooling time at the location of the CDG ( right panel ). U − I gradients ( empty symbols ) are used when available; U − R gradients ( filledsymbols ) are used when U − I gradients are unavailable. The horizontal, dashed line marks the division between systems with positivecolor gradients (blue, star-forming systems) and those with negative color gradients (red systems). The vertical line in the middle panelmarks t cool (12 kpc) = 8 × yr. cool at 12 kpc (10 yr)-0.50.00.51.01.52.0 ∆ ( U -I) , ∆ ( U - R ) b e t w ee n - kp c ( m a g ) Fig. 6.— ∆( U − R ) and ∆( U − I ) between 5-20 kpc versus thecooling time at 12 kpc. Symbols are the same as those in Figure 5. (2006) for a sample of 9 cooling-flow clusters (all of whichare shared with our sample). Voit & Donahue (2005)show that such entropy levels of ∼ areconsistent with those expected from the effects of AGNheating on a simple cooling entropy profile, implying anindirect connection between feedback and star formation.The great majority of CDGs host a radio source ( ? ).Therefore, it is useful to examine whether the presenceof a radio source (and hence an AGN) is related to thepresence of star formation. To identify AGNs, we havesearched available radio catalogs (e.g., the NVSS andFIRST catalogs) for radio sources associated with theCDGs in our sample. We find detections at 1400 MHz for42 of our 46 CDGs. The four sources that lack detectionsare A1413, A2218, AWM 7, and A2261, all of which havenegative central color gradients (and consequently no ev-idence of recent star formation) and long central coolingtimes. However, the remaining 21 systems with negative
10 20 30 40t cool at 12 kpc (10 yr)024681012 N
10 20 30 40 10 20 30 40
Fig. 7.—
Histogram of the cooling times at 12 kpc for objectswith positive color gradients (blue systems, gray region ) and neg-ative gradients (red systems, hatched region ). Three red systemswith cooling times greater than 4 × yr are not shown. gradients have radio sources and, therefore, the presenceof an AGN does not appear to depend stongly on thepresence of star formation in the CDG (and vice versa).A detailed study of the relation between the radio-sourceand star-formation properties is beyond the scope of thispaper and will presented in a future paper.Lastly, we investigated whether the color gradient hassome dependence on the total luminosity of the galaxy.We plot in Figure 9 the color gradient versus the total K -band luminosity of the CDG. Apparent, total K -bandmagnitudes were taken from the Two Micron All SkySurvey (2MASS) catalog. The apparent magnitudeswere corrected for Galactic extinction with the valuesof Schlegel et al. (1998) and corrected for redshift ( K - See . he Regulation of Cooling and Star Formation by AGN Feedback 15 G ( U -I) , G ( U - R ) ( m a g / d e x ) e (cm -3 ) 10 100Entropy (keV cm ) Fig. 8.—
Color gradient versus the temperature, density, and entropy at 12 kpc. Symbols and the dashed line are the same as those inFigure 5. -25.0 -25.5 -26.0 -26.5 -27.0 -27.5 -28.0MK (mag)012345 G ( U -I) , G ( U - R ) ( m a g / d e x ) Fig. 9.—
Color gradient versus the total K -band absolute mag-nitude of the galaxy. Symbols and the dashed line are the same asthose in Figure 5. corrected) and evolution using the corrections of Pog-gianti (1997). Lastly, the magnitudes were converted toabsolute magnitudes using our assumed cosmology andthe redshifts listed in Table 1 (which also gives the re-sulting absolute magnitudes). It is clear from Figure 9that the color gradient shows no clear relation to the to-tal luminosity of the galaxy; positive gradients are foundacross almost the full range of luminosities. Addition-ally, a clear dichotomy between quiescent red galaxiesand blue star-forming galaxies with steep gradients isevident. Cooling, Star-Formation, and AGN-HeatingTimescales
In the simple AGN feedback model, the timescales overwhich cooling, star formation, and heating occur shouldbe related. The presence of shocks, in particular, sug-gest that AGN heating is intermittent (e.g., Nulsen et al. 2005a,b; Wilson et al. 2006; Fabian et al. 2006; Formanet al. 2007). In such a model, the AGN must create cav-ities frequently enough to prevent large amounts of netcooling and to maintain the gas at the observed temper-atures. This condition can only be met when the averagetime between outbursts is less than the average centralcooling time. Additionally, cooling must occur over along enough period for significant cool gas to accumu-late and star formation to occur, after which the signa-tures of star formation may persist even though coolinghas ceased. The probable interrelation of the varioustimescales will lead to temporally induced scatter when-ever quantities that depend on these timescales are com-pared.We plot in Figure 10 the current central cooling timeagainst the average cavity age calculated as the averageof three standard age estimates: the sound speed age,the buoyancy age, and refill age (for details, see Raffertyet al. 2006). For systems with two cavities, an averageis taken across both cavities. For systems with multiplegenerations of cavities (Perseus and Hydra A), the av-erage age is the average difference in ages between theinner and outer sets of cavities (i.e. the time betweenoutbursts). We adopt the range in age from the three es-timates as the error. For systems unique to the Raffertyet al. (2006) sample, cooling times were derived followingthe procedure described in Section 4.1.We note that cavities are rarely seen with ages greaterthan ∼ yr (McNamara & Nulsen 2007), perhaps be-cause they disrupt on that timescale or fade into thebackground as they rise. Therefore, systems without vis-ible cavities would likely lie at inter-outburst times (cav-ity ages) above 10 yr in Figure 10. In keeping with thisconclusion, such systems are shown in Fig 10 as lower lim-its. For three systems in our sample (A496, A1991, andNGC 6338), this limit exceeds the central cooling timeby a significant factor, implying that feedback cannot op-erate effectively and significant cooling should occur. InA1991, McNamara & O’Connell (1989, 1992) found ev-idence for recent star formation (while we do not find apositive color gradient in A1991, our images of this sys-tem were affected by poor seeing and scattered light, andhence the excess blue emission was likely missed). The6 Rafferty et al. cav (10 yr)110 t c oo l ( y r) Fig. 10.—
The central cooling time versus the average cavityage from Rafferty et al. (2006). The errors in age reflect the rangein the three age estimates (see text for details). Lower limits areshown for systems without visible cavities under the assumptionthat any cavities must have disrupted (or faded below detectionlimits) and are therefore likely older than 10 yr. The line denotesequality between the two times. two remaining systems do not show evidence of recentstar formation. It is possible that these systems do havecavities, but that they are below our detection limit (in-deed, the existing Chandra image of A496 shows someevidence of faint cavities).Figure 10 demonstrates that the average cavity age inall systems with detected cavities is less than the currentcooling time, a result that is consistent with feedback.We note that there is evidence of a trend between the twotimes, as expected if systems with shorter cooling timesneed more frequent outbursts to prevent the cooling oflarge amounts of gas. However, the trend is very weak,as systems with similar cavity ages have cooling timesthat differ by up to a factor of ∼ , possibly becausethe true average time between outbursts is not knownfor the majority of systems in our sample (for systemswithout multiple generations of cavities, the current cav-ity age is only a lower limit on the average time betweenoutbursts). The central cooling time may also vary overtime as the ICM is heated and cools, inducing additionalscatter in Figure 10.The timescales relevant for star formation are the timefor cool gas to form stars and the time for star formationto fade below detection limits. The former timescale isnot well known, but is believed to be on the order of10 yr (e.g., Mouschovias et al. 2006). The timescalefor star formation to fade may be roughly estimatedfor our sample using the ∆ colors given in Table 5 andthe approximately power-law relation between the colorand age of a young stellar population. For a burst ofstar formation with a metallicity one-half solar, the stel-lar population synthesis models of Bruzual & Charlot(2003) predict that the U − I color fades at a rate of∆( U − I ) / ∆ log t ≈ . − . If we assume that theaverage age for the star forming regions in our sample is ∼ yr, a ∆( U − I ) color of 0.3 mag (typical of the blue G ( U -I) , G ( U - R ) ( m a g / d e x ) Fig. 11.—
Color gradient versus the cooling time at the projectedradius of the CDG’s core. Symbols and the dashed line are the sameas those in Figure 5. objects in our sample) would fade to ∆( U − I ) ∼ − . yr. Alterna-tively, the mean change across the sample in U − I or U − R color calculated between the inner and outer radiiof star formation (instead of between 5-10 kpc or 5-20kpc as was done for the ∆ colors) is ≈ . , resulting inthe same fading time. Consequently, detectable emissionfrom star formation should typically persist for a few 10 yr after cooling ceases.The total process of gas condensation, star formation,and the fading of the UV emission should therefore re-quire ∼ × –10 yr. This timescale is longer thanthe typical time between outbursts or the typical cen-tral cooling time of the systems in our sample, thusthe colors that we observe could represent the propertiesof star-forming populations averaged over several heat-ing events. Additionally, the cooling time at 12 kpc,which is comparable to this total timescale, could roughlytrace the state of the ICM averaged over timescales longenough to be typical of the conditions under which thestars we see now were accumulated. This scenario mightexplain the strong dependence of star formation on thecooling time at 12 kpc seen in Figure 5. Star Formation and the CDG’s Location
It is quite common to find the CDG offset 100 kpcor more in projection from the X-ray core (e.g., Patelet al. 2006; Edwards et al. 2007). If the CDG does notlie at the core of the cooling flow where cooling timesare short, but instead resides at larger radii where thecooling times are relatively long, we should expect littleactive star formation if it is fueled by the cooling ICM.To investigate this possibility, we plot in Figure 11 thecolor gradient against the projected physical separationbetween the CDG’s core and the cluster’s core. In theright panel of Figure 5 we plot the color gradient againstthe cooling time of the ICM at the projected locationof the CDG’s core. In neither plot do the red objectssegregate to large separations or long cooling times (al-he Regulation of Cooling and Star Formation by AGN Feedback 17though those objects with large separations tend to havelong cooling times). However, the blue objects all havesmall ( (cid:46)
20 kpc) projected separations. We note thatprojection could result in measured separations that aremuch smaller than the true ones. However, on average,such effects should be relatively small.In summary, although a small (projected) separationbetween the X-ray cusp and the galaxy does not guar-antee a blue core, it appears to be a necessary condi-tion. This result agrees with the findings of Edwardset al. (2007), who find that all the CDGs in their samplewith strong optical line emission (indicative of an ion-izing source, such as young stars or an AGN, near coolgas) lie within 50 kpc of the cluster’s X-ray core (see alsoCrawford et al. 1999). Therefore, the CDG’s location rel-ative to the cluster’s core is critical to the presence of starformation, a finding which supports the hypothesis thatthe cooling ICM, which preferentially cools in the core,fuels the star formation.
The Suppression of Star Formation by AGNFeedback
The lack of excess blue emission in some objects withshort cooling times may be due to several factors. Ingeneral, two situations could apply: either active starformation is present, but the excess blue emission is ob-scured, or no active star formation is present. In theformer case, dust obscuration is the most likely cause;however, as we argue below, dust is unlikely to obscureall signs of significant star formation. In the latter case,where no active star formation is occurring, some mech-anism for suppressing star formation must be present,since cooling times are short and significant condensa-tion from the ICM onto the CDG should be occurring.An obvious (but perhaps not the only) mechanism forthe suppression of cooling and star formation in thesesystems is AGN feedback. In this section, we examinethe red systems with short cooling times and discuss thepossibility that dust obscuration or suppression by AGNfeedback could explain their properties.Dust is often associated with cold gas and star forma-tion and is common in the cores of CDGs (e.g., Laineet al. 2003). Dust will preferentially scatter and absorbshort-wavelength emission, resulting in observed colorsthat are redder than the intrinsic ones. However, dustin CDGs is generally observed to be patchy or filamen-tary (e.g., Laine et al. 2003), not spread smoothly acrossthe galaxy in significant quantities (see however Silva &Wise 1996). Therefore, it is unlikely that dust wouldobscure the entire star forming region if star formationin all of the objects with short cooling times is similar.New far-infrared measurements of star formation in cool-ing flows obtained with the
Spitzer observatory roughlyagree with optical and near-UV rates (O’Dea et al. 2008).Furthermore, for the 17 systems in our sample that areincluded in recent infrared studies (Egami et al. 2006;O’Dea et al. 2008; Quillen et al. 2008), the 8 systemsthat show infrared evidence of star formation also haveblue cores, implying that star formation in these systemsis not heavily obscured. Of the remaining 9 systems with-out infrared-detected star formation, most (7) have redcores. The remaining two, A1991 and MS 1455.0+2232,have only weakly blue cores. Therefore, near-UV andinfrared data appear to have similar sensitivity to the cav / L X G ( U -I) , G ( U - R ) ( m a g / d e x ) Fig. 12.—
Color gradient versus the ratio of cavity power tocooling luminosity. The vertical, dotted line divides systems withcavity power in excess of that needed to balance the cooling lu-minosity ( P cav /L X (cid:38)
1) from those with insufficient cavity power( P cav /L X (cid:46)
1) to do so. The dashed line and symbols are the sameas those in Figure 5. presence of star formation in these systems, and we areunlikely to have missed significant star formation in thered systems.If instead star formation is suppressed in some systemswith short cooling times, AGN feedback may be the pri-mary cause. As noted in Section 5.2, 42 of the 46 sys-tems in our sample have detections at 1400 MHz, and allof the systems with short cooling times have detections.Therefore, AGNs appear to be almost ubiquitous in thecores of cooling flows. Additionally, AGN feedback atthe cores of clusters has been shown to be energeticallycapable of completely quenching cooling from the ICMin many systems (Bˆırzan et al. 2004; Rafferty et al. 2006;Dunn & Fabian 2006). Some systems with recent AGNoutbursts seem to be in a heating stage, in which AGNfeedback is supplying excess heat above that requiredto balance cooling losses from the ICM, whereas othersystems appear to be in a cooling stage, in which AGNfeedback cannot balance the entire cooling luminosity ofthe cluster. Simulations suggest that these systems maycycle between the two stages (Omma & Binney 2004;Ciotti & Ostriker 2007). An intriguing possibility is thatthe blue systems occupy different temporal locations onthe cycle of cooling and heating than the red systems.The blue systems could reside in clusters in which thecentral AGN is not currently supplying sufficient heat tooffset cooling, whereas in the red systems, the AGN pre-vents large amounts of cooling from occurring, despitethe sometimes short cooling times. In this scenario, onemight expect that those objects with large amounts ofheating relative to cooling would be redder than thosewith insufficient heating.To test this prediction, we plot in Figure 12 the colorgradient versus the ratio of cavity power to ICM lumi-nosity within the cooling radius, P cav /L X , where P cav and L X were taken from Rafferty et al. (2006). P cav wascalculated as 4 pV /t cav , and L X is the bolometric lumi-nosity of the X-ray–emitting gas within the radius inside8 Rafferty et al.which t cool < . × yr. While our sample lacks a largenumber of systems with a high ratio of cavity power tocooling luminosity (the X-ray–cavity sample of Raffertyet al. 2006, however, consists of roughly equal numbersof systems above and below a ratio of unity), it appearsthat systems with excess blue emission are more likely tohave a low ratio of P cav /L X (i.e. insufficient heating tobalance cooling). The average (median) ratio of P cav /L X for objects with detected X-ray cavities and positive gra-dients is 0.65 (0.28); for objects with negative gradients,it is 3.78 (1.51). However, a K-S test does not rule outthe possibility that the positive- and negative-gradientcavity samples share the same parent distribution of theratio of cavity power to ICM luminosity (the resultingprobability that they do is 0.17). A larger sample ofsystems with high ratios of P cav /L X will be critical totest the hypothesis that AGN feedback is quenching starformation.For comparative purposes, we estimated P cav for theremaining systems (that lack evidence of X-ray cavi-ties) with short cooling times (those with t cool [12 kpc] (cid:46) × yr) from the monochromatic 1400 MHz radio lu-minosities using the jet-power scaling relation of Bˆırzanet al. (2008):log P cav = (0 . ± .
07) log P + (1 . ± . , (7)where P cav has units of 10 erg s − and P has units of10 W Hz − . The radio fluxes for all systems were takenfrom the VLA FIRST (Becker et al. 1995) or NVSS (Con-don et al. 1998) catalogs, with the exception of A2390,the flux of which was taken from Owen et al. (1982). Thisscaling relation was calibrated using a large sample of X-ray–cavity systems in clusters (many of which are also inour sample) and should therefore be generally applicableto our sample. It should be noted that the scatter aboutthis relation is large ( σ ≈ . U − I gradient in A1991 ( G [ U − I ] = 0 . ± . (cid:104) P cav /L X (cid:105) = 0 .
1. The remaining 2 sys-tems (A1361 and A496), with negative gradients, have (cid:104) P cav /L X (cid:105) = 0 . P cav /L X > P cav /L X < Chandra
Data Archive, may be biasedtowards systems with easily detected cavities (see e.g.,Diehl et al. 2008), such biases should not be related tothe detectability of star formation. Therefore, the ten-dency for systems with low ratios of P cav /L X to host recent star formation and those with high ratios to lacksuch star formation does not appear to be due to the biasin our sample towards systems with low ratios.The tendency for blue systems to have low ratios of P cav /L X and red systems to have high ratios lends sup-port to the feedback scenario outlined above, and canexplain 5 of the 7 red systems in Figure 5 with a coolingtime at 12 kpc less than ∼ × yr: A1361, A133,HCG 62, A2052, MS 0735.6+7421, all of which have P cav /L X (cid:38)
1. The two remaining systems are A496( t cool [12 kpc] ≈ × yr and P cav /L X ≈ .
3) and A2029( t cool [12 kpc] ≈ × yr and P cav /L X ≈ . P cav using equation (7). Additionally, Clarkeet al. (2004) found a spiral excess structure in Chandra data at the core of A2029 that most likely indicates arecent infall or merger, which may have disrupted cool-ing and star formation in the core without increasing thecooling time at 12 kpc greatly. Lastly, we may have sim-ply caught the two systems just before star formation willoccur (i.e., they are transitioning to a cooling phase).We note that the dividing point between blue and redsystems appears to be roughly at P cav /L X ≈
1, implyingthat, if the above scenario is correct, the cavity poweris a good tracer of the heat input of the AGN. Cavitiesmay trace the total heat input well because their powersscale with those of associated heating mechanisms, suchas shocks (e.g., Nulsen et al. 2005a; McNamara et al.2005) and sound waves (Sanders & Fabian 2007). Itis also possible that cavities are the dominant heatingmechanism in these systems. Nevertheless, it appearsfrom Figure 12 that the assumptions that go into thecalculation of the cavity power and cooling luminosityare approximately correct, or the dividing line would beshifted far from unity. The division between blue andred systems is not perfectly clean, however, as some bluesystems fall somewhat above unity and some red systemsfall below unity. Uncertainties in the cavity timescalesthat go into the calculation of the cavity power and thetime required for the fading of star formation after cool-ing has been quenched would blur the division betweenred and blue systems. CONCLUSIONS
We have measured broadband optical colors and de-rived X-ray properties for a sample of CDGs in bothcooling-flow and non-cooling-flow clusters to investigatepossible connections between the presence of star forma-tion and the properties of the cooling flow and the AGN.We show that, on similar spatial scales, the presence ofcentral blue colors, indicative of active star formation,depends critically upon the presence of cooling gas withshort cooling times. Blue cores are found to occur onlyin the clusters in our sample with central ICM coolingtimes below a threshold of ∼ × yr, with central en-tropies below ∼
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