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 GRs 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 GRs. 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.

Prospects for Probing the Spacetime of Sgr A* with Pulsars

The discovery of radio pulsars in compact orbits around Sgr A* would allow an unprecedented and detailed investigation of the spacetime of the supermassive black hole. This paper shows that pulsar timing, including that of a single pulsar, has the potential to provide novel tests of general relativity, in particular its cosmic censorship conjecture and no-hair theorem for rotating black holes. These experiments can be performed by timing observations with 100 micro-second precision, achievable with the Square Kilometre Array for a normal pulsar at frequency above 15 GHz. Based on the standard pulsar timing technique, we develop a method that allows the determination of the mass, spin, and quadrupole moment of Sgr A*, and provides a consistent covariance analysis of the measurement errors. Furthermore, we test this method in detailed mock data simulations. It seems likely that only for orbital periods below ~0.3 yr is there the possibility of having negligible external perturbations. For such orbits we expect a ~10^-3 test of the frame dragging and a ~10^-2 test of the no-hair theorem within 5 years, if Sgr A* is spinning rapidly. Our method is also capable of identifying perturbations caused by distributed mass around Sgr A*, thus providing high confidence in these gravity tests. Our analysis is not affected by uncertainties in our knowledge of the distance to the Galactic center, R0. A combination of pulsar timing with the astrometric results of stellar orbits would greatly improve the measurement precision of R0.

Gravitational wave astronomy of single sources with a pulsar timing array

Abbreviated: We investigate the potential of detecting the gravitational wave from individual binary black hole systems using pulsar timing arrays (PTAs) and calculate the accuracy for determining the GW properties. This is done in a consistent analysis, which at the same time accounts for the measurement of the pulsar distances via the timing parallax. We find that, at low redshift, a PTA is able to detect the nano-Hertz GW from super massive black hole binary systems with masses of $sim10^8 - 10^{10},M_{sun}$ less than $sim10^5$,years before the final merger, and those with less than $sim10^3 - 10^4$ years before merger may allow us to detect the evolution of binaries. We derive an analytical expression to describe the accuracy of a pulsar distance measurement via timing parallax. We consider five years of bi-weekly observations at a precision of 15,ns for close-by ($sim 0.5 - 1$,kpc) pulsars. Timing twenty pulsars would allow us to detect a GW source with an amplitude larger than $5times 10^{-17}$. We calculate the corresponding GW and binary orbital parameters and their measurement precision. The accuracy of measuring the binary orbital inclination angle, the sky position, and the GW frequency are calculated as functions of the GW amplitude. We note that the pulsar term, which is commonly regarded as noise, is essential for obtaining an accurate measurement for the GW source location. We also show that utilizing the information encoded in the GW signal passing the Earth also increases the accuracy of pulsar distance measurements. If the gravitational wave is strong enough, one can achieve sub-parsec distance measurements for nearby pulsars with distance less than $sim 0.5 - 1$,kpc.

Prospects for accurate distance measurements of pulsars with the SKA: enabling fundamental physics

Parallax measurements of pulsars allow for accurate measurements of the interstellar electron density and contribute to accurate tests of general relativity using binary systems. The Square Kilometre Array (SKA) will be an ideal instrument for measuring the parallax of pulsars, because it has a very high sensitivity, as well as baselines extending up to several thousands of kilometres. We performed simulations to estimate the number of pulsars for which the parallax can be measured with the SKA and the distance to which a parallax can be measured. We compare two different methods. The first method measures the parallax directly by utilising the long baselines of the SKA to form high angular resolution images. The second method uses the arrival times of the radio signals of pulsars to fit a transformation between time coordinates in the terrestrial frame and the comoving pulsar frame directly yielding the parallax. We find that with the first method a parallax with an accuracy of 20% or less can be measured up to a maximum distance of 13 kpc, which would include 9,000 pulsars. By timing pulsars with the most stable arrival times for the radio emission, parallaxes can be measured for about 3,600 millisecond pulsars up to a distance of 9 kpc with an accuracy of 20%.

Generic tests of the existence of the gravitational dipole radiation and the variation of the gravitational constant

We present results from the high precision timing analysis of the pulsar-white dwarf (WD) binary PSR J1012+5307 using 15 years of multi-telescope data. Observations were performed regularly by the European Pulsar Timing Array (EPTA) network, consisting of Effelsberg, Jodrell Bank, Westerbork and Nanc{c}ay. All the timing parameters have been improved from the previously published values, most by an order of magnitude. In addition, a parallax measurement of $pi = 1.2(3)$ mas is obtained for the first time for PSR J1012+5307, being consistent with the optical estimation from the WD companion. Combining improved 3D velocity information and models for the Galactic potential the complete evolutionary Galactic path of the system is obtained. A new intrinsic eccentricity upper limit of $e<8.4times 10^{-7}$ is acquired, one of the smallest calculated for a binary system and a measurement of the variation of the projected semi-major axis also constrains the systems orbital orientation for the first time. It is shown that PSR J1012+5307 is an ideal laboratory for testing alternative theories of gravity. The measurement of the change of the orbital period of the system of $dot{P}_{b} = 5(1)times 10^{-14}$ is used to set an upper limit on the dipole gravitational wave emission that is valid for a wide class of alternative theories of gravity. Moreover, it is shown that in combination with other binary pulsars PSR J1012+5307 is an ideal system to provide self-consistent, generic limits, based only on millisecond pulsar data, for the dipole radiation and the variation of the gravitational constant $dot{G}$.

A new technique for timing the double pulsar system

In 2004, McLaughlin et al. discovered a phenomenon in the radio emission of PSR J0737-3039B (B) that resembles drifting sub-pulses. The repeat rate of the sub-pulses is equal to the spin frequency of PSR J0737-3039A (A); this led to the suggestion that they are caused by incidence upon Bs magnetosphere of electromagnetic radiation from A. Here we describe a geometrical model which predicts the delay of Bs sub-pulses relative to As radio pulses. We show that measuring these delays is equivalent to tracking As rotation from the point of view of an hypothetical observer located near B. This has three main astrophysical applications: (a) to determine the sense of rotation of A relative to its orbital plane; (b) to estimate where in Bs magnetosphere the radio sub-pulses are modulated and (c) to provide an independent estimate of the mass ratio of A and B. The latter might improve existing tests of gravitational theories using this system.