Spin dynamics of a millisecond pulsar orbiting closely around a massive black hole

Abstract

We investigate the spin dynamics of a millisecond pulsar (MSP) in a tightly bounded orbit around a massive black hole. These binaries are progenitors of the extrememass-ratio-inspirals (EMRIs) and intermediate-mass-ratio-inspirals (IMRIs) gravitational wave events. The Mathisson-Papapetrou-Dixon (MPD) formulation is used to determine the orbital motion and spin modulation and evolution. We show that the MSP will not be confined in a planar Keplerian orbit and its spin will exhibit precession and nutation induced by spin-orbit coupling and spin-curvature interaction. These spin and orbital behaviours will manifest observationally in the temporal variations in the MSP's pulsed emission and, with certain geometries, in the self-occultation of the pulsar's emitting poles. Radio pulsar timing observations will be able to detect such signatures. These extreme-mass-ratio binaries (EMRBs) and intermediate-mass-ratio binaries (IMRBs) are also strong gravitational wave sources. Combining radio pulsar timing and gravitational wave observations will allow us to determine the dynamics of these systems in high precision and hence the subtle behaviours of spinning masses in strong gravity.

Covariant version of the Pauli Hamiltonian, spin-induced noncommutativity, Thomas precession, and the precession of spin

“…To obtain equations of motion, the Hamiltonian (17) should be accompanied with some brackets. The spin supplementary condition (16) should be consistent with the resulting equations of motion. This leads us to the observation that will be crucial for our explanation of 1/2 -factor: manifestly-covariant formalism inevitably leads to relativistic corrections of order 1/c 2 to the canonical brackets (4).…”

“…One obscure point of this approach, which has been raised for discussion already in the pioneer works [1][2][3][4] and remains under debates up to date, is the so-called problem of covariant formalism. Clarification of this issue could be of interest in various areas, including muon and electron g − 2 -experiments [5][6][7][8], influence of spin on the trajectory of a rotating body in general relativity [9][10][11][12][13][14], and black hole physics near horizon [9,[15][16][17][18]. In the textbooks and reviews, it has become almost a tradition to discuss the problem without formulating it in an exact form 1 .…”

Radio timing in a millisecond pulsar – extreme/intermediate mass ratio binary system

“…Singh et al 2014) and also a contribution to the precession of periastron (e.g. Li et al 2019) (which is itself a PK parameter). We consider the same eccentric systems and observer orientation as used previously (a * = 825r g , i = 76 • etc.).…”

“…Pulsar timing delays given by the PK approximation in strong-field regimes was partly addressed in Hackmann & Dhani (2018) who investigate the propagation delays (Roemer and Shapiro) from circular orbits in a Schwarzschild spacetime. The influence of the central black hole spin on the measurement of pulsar orbital parameters was investigated in Zhang & Saha (2017), whilst Li et al (2019) explored the impact of relativistic spin dynamics on the PSR emission. In this work, we further develop these previous studies by deploying a consistent, relativistic framework (Kimpson et al 2019b,a) to accurately calculate the pulse ToA from a spinning pulsar orbiting a Kerr BH.…”

“…The influence of the central black hole spin on the measurement of pulsar orbital parameters was investigated in Zhang & Saha (2017), whilst Li et al (2019) explored the impact of relativistic spin dynamics on the PSR emission. In this work, we further develop these previous studies by deploying a consistent, relativistic framework (Kimpson et al 2019b,a) to accurately calculate the pulse ToA from a spinning pulsar orbiting a Kerr BH.…”