A timing formula for main-sequence star binary pulsars

In binary radio pulsars with a main-sequence star companion, the spin-induced quadrupole moment of the companion gives rise to a precession of the binary orbit. As a first approximation one can model the secular evolution caused by this classical spin-orbit coupling by linear-in-time changes of the longitude of periastron and the projected semi-major axis of the pulsar orbit. This simple representation of the precession of the orbit neglects two important aspects of the orbital dynamics of a binary pulsar with an oblate companion. First, the quasiperiodic effects along the orbit, due to the anisotropic $1/r^3$ nature of the quadrupole potential. Secondly, the long-term secular evolution of the binary orbit which leads to an evolution of the longitude of periastron and the projected semi-major axis which is non-linear in time. In this paper a simple timing formula for binary radio pulsars with a main-sequence star companion is presented which models the short-term secular and most of the short-term periodic effects caused by the classical spin-orbit coupling. I also give extensions of the timing formula which account for long-term secular changes in the binary pulsar motion. It is shown that the short-term periodic effects are important for the timing observations of the binary pulsar PSR B1259--63. The long-term secular effects are likely to become important in the next few years of timing observations of the binary pulsar PSR J0045--7319. They could help to restrict or even determine the moments of inertia of the companion star and thus probe its internal structure. Finally, I reinvestigate the spin-orbit precession of the binary pulsar PSR J0045--7319 since the analysis given in the literature is based on an incorrect expression for the precession of the longitude of periastron.Comment: 12 pages (LaTeX), 20 Postscript figures; replaced by accepted versio

Small-eccentricity binary pulsars and relativistic gravity

Small-eccentricity binary pulsars with white dwarf companions provide excellent test laboratories for various effects predicted by alternative theories of gravity, in particular tests for the emission of gravitational dipole radiation and the existence of gravitational Stark effects. We will present new limits to these effects. The statistical analysis presented here, for the first time, takes appropriately care of selection effects.Comment: 4 pages, to be published in Proc. of IAU Colloq. 177, "Pulsar Astronomy - 2000 and Beyond", eds. M. Kramer, N. Wex & R. Wielebinsk

Pulsar-black hole binaries: prospects for new gravity tests with future radio telescopes

The anticipated discovery of a pulsar in orbit with a black hole is expected to provide a unique laboratory for black hole physics and gravity. In this context, the next generation of radio telescopes, like the Five-hundred-metre Aperture Spherical radio Telescope (FAST) and the Square Kilometre Array (SKA), with their unprecedented sensitivity, will play a key role. In this paper, we investigate the capability of future radio telescopes to probe the spacetime of a black hole and test gravity theories, by timing a pulsar orbiting a stellar-mass-black-hole (SBH). Based on mock data simulations, we show that a few years of timing observations of a sufficiently compact pulsar-SBH (PSR-SBH) system with future radio telescopes would allow precise measurements of the black hole mass and spin. A measurement precision of one per cent can be expected for the spin. Measuring the quadrupole moment of the black hole, needed to test GR's no-hair theorem, requires extreme system configurations with compact orbits and a large SBH mass. Additionally, we show that a PSR-SBH system can lead to greatly improved constraints on alternative gravity theories even if they predict black holes (practically) identical to GR's. This is demonstrated for a specific class of scalar-tensor theories. Finally, we investigate the requirements for searching for PSR-SBH systems. It is shown that the high sensitivity of the next generation of radio telescopes is key for discovering compact PSR-SBH systems, as it will allow for sufficiently short survey integration times.Comment: 20 pages, 11 figures, 1 table, accepted for publication in MNRA

A new test of conservation laws and Lorentz invariance in relativistic gravity

General relativity predicts that energy and momentum conservation laws hold and that preferred frames do not exist. The parametrised post-Newtonian formalism (PPN) phenomenologically quantifies possible deviations from general relativity. The PPN parameter alpha_3 (which identically vanishes in general relativity) plays a dual role in that it is associated both with a violation of the momentum conservation law, and with the existence of a preferred frame. By considering the effects of alpha_3 neq 0 in certain binary pulsar systems, it is shown that alpha_3 < 2.2 x 10^-20 (90% CL). This limit improves on previous results by several orders of magnitude, and shows that pulsar tests of alpha_3 rank (together with Hughes-Drever-type tests of local Lorentz invariance) among the most precise null experiments of physics.Comment: Submitted to Classical Quantum Gravity, LaTeX, requires ioplppt.sty, no figure

Gravitational waveforms from unequal-mass binaries with arbitrary spins under leading order spin-orbit coupling

The paper generalizes the structure of gravitational waves from orbiting spinning binaries under leading order spin-orbit coupling, as given in the work by K\"onigsd\"orffer and Gopakumar [PRD 71, 024039 (2005)] for single-spin and equal-mass binaries, to unequal-mass binaries and arbitrary spin configurations. The orbital motion is taken to be quasi-circular and the fractional mass difference is assumed to be small against one. The emitted gravitational waveforms are given in analytic form.Comment: 13 pages, 2 figures, submitted to PRD on 11 Sep. 200

Prospects for probing strong gravity with a pulsar-black hole system

The discovery of a pulsar (PSR) in orbit around a black hole (BH) is expected to provide a superb new probe of relativistic gravity and BH properties. Apart from a precise mass measurement for the BH, one could expect a clean verification of the dragging of space-time caused by the BH spin. In order to measure the quadrupole moment of the BH for testing the no-hair theorem of general relativity (GR), one has to hope for a sufficiently massive BH. In this respect, a PSR orbiting the super-massive BH in the center of our Galaxy would be the ultimate laboratory for gravity tests with PSRs. But even for gravity theories that predict the same properties for BHs as GR, a PSR-BH system would constitute an excellent test system, due to the high grade of asymmetry in the strong field properties of these two components. Here we highlight some of the potential gravity tests that one could expect from different PSR-BH systems, utilizing present and future radio telescopes, like FAST and SKA.Comment: Proceedings of IAUS 291 "Neutron Stars and Pulsars: Challenges and Opportunities after 80 years", J. van Leeuwen (ed.); 6 pages, 3 figure

Timing models for the long-orbital period binary pulsar PSR B1259-63

The pulsar PSR B1259-63 is in a highly eccentric 3.4-yr orbit with the Be star SS 2883. Timing observations of this pulsar, made over a 7-yr period using the Parkes 64-m radio telescope, cover two periastron passages, in 1990 August and 1994 January. The timing data cannot be fitted by the normal pulsar and Keplerian binary parameters. A timing solution including a (non-precessing) Keplerian orbit and timing noise (represented as a polynomial of fifth order in time) provide a satisfactory fit to the data. However, because the Be star probably has a significant quadrupole moment, we prefer to interpret the data by a combination of timing noise, dominated by a cubic phase term, and $\dot\omega$ and $\dot x$ terms. We show that the $\dot\omega$ and $\dot x$ are likely to be a result of a precessing orbit caused by the quadrupole moment of the tilted companion star. We further rule out a number of possible physical effects which could contribute to the timing data of PSR B1259-63 on a measurable level.Comment: LaTeX, 9 pages, 8 figures, accepted for publication in MNRA

13 Years of Timing of PSR B1259-63

This paper summarizes the results of 13 years of timing observations of a unique binary pulsar, PSR B1259$-$63, which has a massive B2e star companion. The data span encompasses four complete orbits and includes the periastron passages in 1990, 1994, 1997 and 2000. Changes in dispersion measure occurring around the 1994, 1997 and 2000 periastrons are measured and accounted for in the timing analysis. There is good evidence for a small glitch in the pulsar period in 1997 August, not long after the 1997 periastron, and a significant frequency second derivative indicating timing noise. We find that spin-orbit coupling with secular changes in periastron longitude and projected semi-major axis ($x$) cannot account for the observed period variations over the whole data set. While fitting the data fairly well, changes in pulsar period parameters at each periastron seem ruled out both by X-ray observations and by the large apparent changes in pulsar frequency derivative. Essentially all of the systematic period variations are accounted for by a model consisting of the 1997 August glitch and step changes in $x$ at each periastron. These changes must be due to changes in the orbit inclination, but we can find no plausible mechanism to account for them. It is possible that timing noise may mask the actual changes in orbital parameters at each periastron, but the good fit to the data of the $x$ step-change model suggests that short-term timing noise is not significant.Comment: 9 pages, 7 figures, accepted by MNRA