Inter-comparison of Radio-Loudness Criteria for Type 1 AGNs in the
  XMM-COSMOS Survey
  Limited studies have been performed on the radio-loud fraction in X-ray
selected type 1 AGN samples. The consistency between various radio-loudness
definitions also needs to be checked. We measure the radio-loudness of the 407
type 1 AGNs in the XMM-COSMOS quasar sample using nine criteria from the
literature (six defined in the rest-frame and three defined in the observed
frame): $R_L=\log(L_{5GHz}/L_B)$, $q_{24}=\log(L_{24\mu m}/L_{1.4GHz})$,
$R_{uv}=\log(L_{5GHz}/L_{2500\AA})$, $R_{i}=\log(L_{1.4GHz}/L_i)$,
$R_X=\log(\nu L_{\nu}(5GHz)/L_X)$, $P_{5GHz}=\log(P_{5GHz}(W/Hz/Sr))$,
$R_{L,obs}=\log(f_{1.4GHz}/f_B)$ (observed frame),
$R_{i,obs}=\log(f_{1.4GHz}/f_i)$ (observed frame), and $q_{24,
obs}=\log(f_{24\mu m}/f_{1.4GHz})$ (observed frame). Using any single criterion
defined in the rest-frame, we find a low radio-loud fraction of $\lesssim 5\%$
in the XMM-COSMOS type 1 AGN sample, except for $R_{uv}$. Requiring that any
two criteria agree reduces the radio-loud fraction to $\lesssim 2\%$ for about
3/4 of the cases. The low radio-loud fraction cannot be simply explained by the
contribution of the host galaxy luminosity and reddening. The
$P_{5GHz}=\log(P_{5GHz}(W/Hz/Sr))$ gives the smallest radio-loud fraction. Two
of the three radio-loud fractions from the criteria defined in the observed
frame without k-correction ($R_{L,obs}$ and $R_{i,obs}$) are much larger than
the radio-loud fractions from other criteria.
