A Statistical Study of Pulsar Proper Motions

This thesis is about a possible statistical bias in the measurement of pulsar proper motion. This bias is similar to the Lutz & Kelker bias in parallax measurements. To investigate this bias, a likelihood analysis was conducted concerning the pulsar proper motion. The likelihood distribution was constraint using the measured parallax, upper and lower distance limits and radio flux of a pulsar as well as the distribution of pulsar three-dimensional velocity, obtained by Hobbs et al. [2005]. The resulting likelihood distribution was analysed, using self-written python methods. For this two different samples of pulsars were used. In summary the results were, that for a single pulsar the bias is insignificant for all pulsars out of the samples, since either the measurement precision of the pulsar proper motion is to high for the bias to occur or the measurement was insignificant to make a statement on the bias. Alternatively, for a larger sample of proper motion measurements, the measured proper motion tend to be underestimated. This is rather surprising, since a distance measurements of a pulsar tend to be underestimated as well. Another result from the analysis is, that for a large value with a significance of two to four σ, there is the possibility, that the measured proper motion is inconsistent with the corrected biased value obtained by this analysis. Then again we find no evidence in the data that such in a case exists in the data available.