  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.
