We investigate the relationship between X-ray cooling and star formation in brightest cluster galaxies (BCGs). We present an X-ray spectral analysis of the inner regions, 10-40 kpc, of six nearby cool core clusters (z<0.35) observed with Chandra ACIS. This sample is selected on the basis of the high star formation rate (SFR) observed in the BCGs. We restrict our search for cooling gas to regions that are roughly cospatial with the starburst. We fit single- and multi-temperature mkcflow models to constrain the amount of isobarically cooling intracluster medium (ICM). We find that in all clusters, below a threshold temperature ranging between 0.9 and 3 keV, only upper limits can be obtained. In four out of six objects, the upper limits are significantly below the SFR and in two, namely A1835 and A1068, they are less than a tenth of the SFR. Our results suggests that a number of mechanisms conspire to hide the cooling signature in our spectra. In a few systems the lack of a cooling signature may be attributed to a relatively long delay time between the X-ray cooling and the star burst. However, for A1835 and A1068, where the X-ray cooling time is shorter than the timescale of the starburst, a possible explanation is that the region where gas cools out of the X-ray phase extends to very large radii, likely beyond the core of these systems.
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