Mathematical Model for Measuring Pulsar Parameters and Precision Estimation with Pulsar Timing Observations
Abstract
Pulsar rotational and astrometric parameters can be measured with a very high precision by pulsar timing observations. The pulsar timing model, the estimation method of pulsar parameters and their covariances by least square solution are briefly described. The relationship between the timing residuals of a pulsar and errors of its rotational parameters is denoted with the polynomial of time. The relationship between the timing residuals of a pulsar and errors of its astrometric parameters can be derived from the Roemer delay due to the Earth motion around the solar system barycenter. The mathematical expressions for the relationship between timing residuals and errors of pulsar astrometric parameters adopted for timing solution are derived within the ecliptic coordinate reference system using the transformation from analytical vector expression of the Roemer delay to the corresponding spherical coordinate expression. The precision of pulsar astrometric parameters determined by timing observation is dependent on the absolute ecliptic latitude of pulsar. For the pulsar located close to the ecliptic plane, it is difficult to precisely measure the pulsar latitude parameter by timing observations. For the pulsar located close to the ecliptic pole, it is difficult to precisely measure the pulsar longitude and annual parallax parameters by timing observations. The precision of pulsar ecliptic coordinate and annual parallax parameters determined by timing observations versus pulsar absolute ecliptic latitude is shown. The relationship between the precision of proper motion parameters of pulsar measured by timing observations and pulsar absolute latitude is also discussed.
- Publication:
-
Acta Astronomica Sinica
- Pub Date:
- July 2015
- Bibcode:
- 2015AcASn..56..370Y
- Keywords:
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- astrometry;
- reference system;
- pulsar;
- methods: analytical