Lutz-Kelker Bias

Lutz and Kelker (1973) first described how parallax measurements are biased because the volume of space per unit of parallax is not constant. This website provides an online interface and source code to allow correction of that effect for neutron star parallax measurements, as described in Verbiest, Lorimer & McLaughlin, 2010, MNRAS.

Not only parallax measurements are affected by this bias, but any distance measurement. This means that bias-correction is also pertinent for HI-based distance limits. This correction (along with a completely analytic treatment of the Verbiest et al. (2010) work), is described by Verbiest, Weisberg, Chael, Lee & Lorimer, 2012, ApJ.

On-line functionality

Under RUN LK, we allow on-line determination of the distance, corrected for Lutz-Kelker bias, based on parallax, HI and/or luminosity information. For added flexibility, more detailed analysis and to allow the user to scrutinise our implementation, we provide the source code under DOWNLOAD.

Explanation of results

The bias-correction result is provided in two separate ways: numerically and graphically. The numeric result is the peak of the probability density function for the parallax measurement and the 68% probability interval as described in Verbiest et al., ApJ 2012. The graphical result shows the final probability density function for both distance and parallax, as well as the breakdown of this probability, as described in the paper.