Mathematical Model for Measuring Pulsar Parameters by Pulsar Timing Observations and Precision Estimation

Abstract

Pulsar rotational and astrometric parameters can be measured with a very high precision by pulsar timing observations. The pulsar timing model, the methods to measure the pulsar parameters by least squares fitting and to estimate their covariances are briefly described. The mathematical relations between the timing residuals of a pulsar and the errors of its different parameters are derived in the ecliptic coordinate system. The relationships of the measuring precisions of pulsar's ecliptic longitude, latitude, and annual parallax with the absolute value of pulsar's ecliptic latitude are shown by curves. And the relations of the measuring precisions of pulsar's astrometric parameters with the pulsar's latitudinal parameter itself are discussed as well.