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We report on an imaging survey with the Spitzer Space Telescope of 62 brightest cluster galaxies with optical line emission. These galaxies are located in the cores of X-ray luminous clusters selected from the ROSAT All-Sky Survey. We find that about half of these sources have a sign of excess infrared emission; 22 objects out of 62 are detected at 70 microns, 18 have 8 to 5.8 micron flux ratios above 1.0 and 28 have 24 to 8 micron flux ratios above 1.0. Altogether 35 of 62 objects in our survey exhibit at least one of these signs of infrared excess. Four galaxies with infrared excesses have a 4.5/3.6 micron flux ratio indicating the presence of hot dust, and/or an unresolved nucleus at 8 microns. Three of these have high measured [OIII](5007A)/Hbeta flux ratios suggesting that these four, Abell 1068, Abell 2146, and Zwicky 2089, and R0821+07, host dusty active galactic nuclei (AGNs). 9 objects (including the four hosting dusty AGNs) have infrared luminosities greater than 10^11 L_sol and so can be classified as luminous infrared galaxies (LIRGs). Excluding the four systems hosting dusty AGNs, the excess mid-infrared emission in the remaining brightest cluster galaxies is likely related to star formation.

We present first results from an imaging survey with the Spitzer Space Telescope of 62 brightest cluster galaxies with optical line emission located in the cores of X-ray luminous clusters selected from the ROSAT All-Sky Survey. We find that 1/3 of these sources have signs of excess infrared emission; 22 objects of 62 are detected at 70 μm and 19 have 8 to 5.8 μm flux ratios above 0.98. The strength of the excess emission correlates with the luminosity of the optical emission lines. Excluding the four systems dominated by an AGN, the excess mid-infrared emission in the remaining brightest cluster galaxies is likely powered by star formation. We find a correlation between mass deposition rate from a cooling flow model for the X-ray emission and the star formation rate estimated from the infrared luminosity. The star formation rates are 1/10 to 1/100 of the mass deposition rates expected in the absence of heating suggesting that the re-heating of the ICM is generally very effective in reducing the amount of mass cooling from the hot phase.

In this paper, we use Heegaard Floer homology to study reducible surgeries. In particular, suppose K is a non-cable knot in the three-sphere with an L-space surgery. If p-surgery on K is reducible, we show that p equals 2g(K)-1. This implies that any knot with an L-space surgery has at most one reducible surgery, a fact that we show additionally for any knot of genus at most two., 15 pages, 2 figures; added an additional author and a new section (3.2) which improves Theorem 1.3

We summarize the results of Spitzer IRAC and MIPS observations of 62 brightest cluster galaxies (BCGs) with optical line emission located in the cores of X‐ray luminous clusters. We find that at least half of these sources have signs of excess infrared emission. The strength of the mid‐IR excess emission correlates with the luminosity of the optical emission lines. Excluding several systems dominated by an AGN, the excess mid‐infrared emission in the remaining brightest cluster galaxies is likely powered by star formation. The IR luminosity (and thus star formation) is higher in BCGs with shorter cooling times in the central hot ICM suggesting that the gas which cools from the ICM ultimately forms stars. We find a correlation between mass deposition rates estimated from the X‐ray emission and the star formation rate estimated from the infrared luminosity. The star formation rates are 1/10 to 1/100 of the mass deposition rates suggesting that the re‐heating of the ICM is generally very effective in reducing the amount of mass cooling from the hot phase but does not eliminate it completely.

Quillen et al.(2007) presented an imaging survey with the {\it Spitzer Space Telescope} of 62 brightest cluster galaxies with optical line emission located in the cores of X-ray luminous clusters. They found that at least half of these sources have signs of excess infrared emission. Here we discuss the nature of the IR emission and its implications for cool core clusters. The strength of the mid-IR excess emission correlates with the luminosity of the optical emission lines. Excluding the four systems dominated by an AGN, the excess mid-infrared emission in the remaining brightest cluster galaxies is likely related to star formation. The mass of molecular gas (estimated from CO observations) is correlated with the IR luminosity as found for normal star forming galaxies. The gas depletion time scale is about 1 Gyr. The physical extent of the infrared excess is consistent with that of the optical emission line nebulae. This supports the hypothesis that the star formation occurs in molecular gas associated with the emission line nebulae and with evidence that the emission line nebulae are mainly powered by ongoing star formation. We find a correlation between mass deposition rates (${\dot M}_X$) estimated from the X-ray emission and the star formation rate estimated from the infrared luminosity. The star formation rates are 1/10 to 1/100 of the mass deposition rates suggesting that the re-heating of the ICM is generally very effective in reducing the amount of mass cooling from the hot phase but not eliminating it completely.