3.3. TF Parameters Obtained from VELMOD

The mock catalogs also enable us to test the accuracy of the TF parameters determined from the likelihood maximization procedure. The comparison of input and output values is given in Table 1. The results for the TF slope and scatter are consistent with the statement that VELMOD returns unbiased values of these TF parameters for each of the two samples. The fact that the TF scatters and _v are unbiased means that VELMOD correctly measures the overall variance in peculiar velocity predictions.

The TF zero points returned by VELMOD are systematically in error by 2-3 standard deviations. This can be traced to a bias in the IRAS-predicted peculiar velocities; the mean value of the quantity f in Section 3.2 over 20 realizations was 0.018 ± 0.007. This bias makes the IRAS-predicted distances d_IRAS cz - u_IRAS too large by a factor of 1.018, or ~ 0.04 mag, as in fact we see in Table 1. Thus, VELMOD determines the TF zero points in such a way as to compensate for a small systematic error in the IRAS predictions. We expect such an error to be present in the real data as well, but it will be completely absorbed into the TF zero points, and our derived value of _I will be unaffected.