Highprecision pulsar timing and spin frequency second derivatives
Abstract
We investigate the impact of intrinsic, kinematic, and gravitational effects on highprecision pulsar timing. We present an analytical derivation and a numerical computation of the impact of these effects on the first and second derivative of the pulsar spin frequency. In addition, in the presence of white noise, we derive an expression to determine the expected measurement uncertainty of a second derivative of the spin frequency for a given timing precision, observing cadence and timing baseline and find that it strongly depends on the latter (∝t^{7/2}). We show that for pulsars with significant proper motion, the spin frequency second derivative is dominated by a term dependent on the radial velocity of the pulsar. Considering the data sets from three Pulsar Timing Arrays, we find that for PSR J04374715 a detectable spin frequency second derivative will be present if the absolute value of the radial velocity exceeds 33 km s^{1}. Similarly, at the current timing precision and cadence, continued timing observations of PSR J19093744 for about another 11 yr , will allow the measurement of its frequency second derivative and determine the radial velocity with an accuracy better than 14 km s^{1}. With the ever increasing timing precision and observing baselines, the impact of the, largely unknown, radial velocities of pulsars on highprecision pulsar timing cannot be neglected.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 August 2018
 DOI:
 10.1093/mnras/sty1202
 arXiv:
 arXiv:1805.02892
 Bibcode:
 2018MNRAS.478.2359L
 Keywords:

 methods: data analysis;
 time;
 pulsars: general;
 pulsars: individual: PSR J04374715;
 PSR J10240719;
 PSR J19093744;
 PSR B1937+21;
 Astrophysics  High Energy Astrophysical Phenomena
 EPrint:
 10 pages, 1 figure, accepted by MNRAS