  We study a sample of 69 X-ray detected Early Type Galaxies (ETGs), selected
from the Chandra COSMOS survey, to explore the relation between the X-ray
luminosity of hot gaseous halos (L_X, gas) and the integrated stellar
luminosity (L_K) of the galaxies, in a range of redshift extending out to
z=1.5. In the local universe a tight steep relationship has been stablished
between these two quantities (L_X,gas~ L_K^4.5) suggesting the presence of
largely virialized halos in X-ray luminous systems. We use well established
relations from the study of local universe ETGs, together with the expected
evolution of the X-ray emission, to subtract the contribution of low mass X-ray
binary populations (LMXBs) from the X-ray luminosity of our sample. Our
selection minimizes the presence of active galactic nuclei (AGN), yielding a
sample representative of normal passive COSMOS ETGs; therefore the resulting
luminosity should be representative of gaseous halos, although we cannot
exclude other sources such as obscured AGN, or enhanced X-ray emission
connected with embedded star formation in the higher z galaxies. We find that
most of the galaxies with estimated L_X<10^42 erg/s and z<0.55 follow the
L_X,gas- L_K relation of local universe ETGs. For these galaxies, the
gravitational mass can be estimated with a certain degree of confidence from
the local virial relation. However, the more luminous (10^42<L_X<10^43.5 erg/s)
and distant galaxies present significantly larger scatter; these galaxies also
tend to have younger stellar ages. The divergence from the local L_X,gas - L_K
relation in these galaxies implies significantly enhanced X-ray emission, up to
a factor of 100 larger than predicted from the local relation. We discuss the
implications of this result for the presence of hidden AGN, and the evolution
of hot halos, in the presence of nuclear and star formation feedback.
