  Only three of the dozen central compact objects (CCOs) in supernova remnants (SNRs) show thermal X-ray pulsations due to non-uniform surface temperature (hot-spots). The absence of X-ray pulsations from several unpulsed CCOs has motivated suggestions that they have uniform-temperature carbon atmospheres (UTCAs), which adequately fit their spectra with appropriate neutron star (NS) surface areas. This is in contrast to the two-temperature blackbody or hydrogen atmospheres that also fit well. Here we investigate the applicability of UTCAs to CCOs. We show the following: (i) The phase-averaged spectra of the three pulsed CCOs can also be fitted with a UTCA of the appropriate NS area, despite pulsed CCOs manifestly having non-uniform surface temperature. A good spectral fit is therefore not strong support for the UTCA model of unpulsed CCOs. (ii) An improved spectrum of one unpulsed CCO, previously analyzed with a UTCA, does not allow an acceptable fit. (iii) For two unpulsed CCOs, the UTCA does not allow a distance compatible with the SNR distance. These results imply that, in general, CCOs must have hot, localized regions on the NS surface. We derive new X-ray pulse modulation upper limits on the unpulsed CCOs, and constrain their hot spot sizes and locations. We develop an alternative model that accounts for both the pulsed and unpulsed CCOs: a range of angles between hot spot and rotation axes consistent with an exponential distribution with scale factor $\lambda \sim 20^{\circ}$. We discuss physical mechanisms that could produce such small angles and small hot-spots. 
Do Central Compact Objects have Carbon Atmospheres?