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 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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