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): $R_L=log(L_{5GHz}/L_B)$, $q_{24}=log(L_{24mu m}/L_{1.4GHz})$, $R_{uv}=log(L_{5GHz}/L_{2500AA})$, $R_{i}=log(L_{1.4GHz}/L_i)$, $R_X=log( u L_{ u}(5GHz)/L_X)$, $P_{5GHz}=log(P_{5GHz}(W/Hz/Sr))$, $R_{L,obs}=log(f_{1.4GHz}/f_B)$ (observed frame), $R_{i,obs}=log(f_{1.4GHz}/f_i)$ (observed frame), and $q_{24, obs}=log(f_{24mu m}/f_{1.4GHz})$ (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.