A study of dynamical effects in the observed second time-derivative of the spin or orbital frequencies of pulsars. (arXiv:1909.13113v4 [astro-ph.HE] UPDATED)

<a href="http://arxiv.org/find/astro-ph/1/au:+Pathak_D/0/1/0/all/0/1">Dhruv Pathak</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Bagchi_M/0/1/0/all/0/1">Manjari Bagchi</a>

The observed values of the time-derivatives of the spin or orbital frequency

of pulsars are affected by their dynamical properties. We derive thorough

analytical expressions for such dynamical contributions in terms of the

Galactic coordinates, the proper motion, the pulsar distance, and the radial

velocity. We find that the effects of the dynamical terms in the

second-derivative of frequencies or parameters based on such second

derivatives, e.g., braking index, are usually negligible. However, unique

pulsars for which the effects of the dynamical terms are significant can exist.

In particular, dynamical effects can make the magnitude of the observed value

of the braking index to be in the order of thousand while the true value of it

is close to the theoretically expected value three, especially if the pulsars

lie close to the Galactic centre. Dynamics can also affect the value of the

second derivative of the orbital frequency of a binary pulsar at the first

decimal place. We also emphasize the fact that our expressions provide more

accurate results than pre-existing approximate ones that exclude some of the

terms. Comparison with a set of pulsars showed that the median value of the

difference between the results obtained by our method and a pre-existing method

is about 50 percent.

The observed values of the time-derivatives of the spin or orbital frequency

of pulsars are affected by their dynamical properties. We derive thorough

analytical expressions for such dynamical contributions in terms of the

Galactic coordinates, the proper motion, the pulsar distance, and the radial

velocity. We find that the effects of the dynamical terms in the

second-derivative of frequencies or parameters based on such second

derivatives, e.g., braking index, are usually negligible. However, unique

pulsars for which the effects of the dynamical terms are significant can exist.

In particular, dynamical effects can make the magnitude of the observed value

of the braking index to be in the order of thousand while the true value of it

is close to the theoretically expected value three, especially if the pulsars

lie close to the Galactic centre. Dynamics can also affect the value of the

second derivative of the orbital frequency of a binary pulsar at the first

decimal place. We also emphasize the fact that our expressions provide more

accurate results than pre-existing approximate ones that exclude some of the

terms. Comparison with a set of pulsars showed that the median value of the

difference between the results obtained by our method and a pre-existing method

is about 50 percent.

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