The Double Pulsar - A unique gravity lab

Michael Kramer, The University of Manchester michael.kramer-at-manchester.ac.uk

Almost a hundred years after Einstein formulated his theory of general relativity (GR), efforts in testing GR and its concepts are still being made by many colleagues around the world, using many different approaches. To date GR has passed all experimental and observational tests with flying colours, but in light of recent progress in observational cosmology in particular, the question of whether alternative theories of gravity need to be considered is as topical as ever.

Many experiments are designed to achieve ever more stringent tests by either increasing the precision of the tests or by testing different, new aspects. Some of the most stringent tests are obtained by satellite experiments in the solar system, providing exciting limits on the validity of GR and alternative theories of gravity like tensor-scalar theories. However, solar-system experiments are made in the gravitational weak-field regime, while deviations from GR may appear only in strong gravitational fields. It happens that nature provides us with an almost perfect laboratory to test the strong-field regime using binary radio pulsars.

While, strictly speaking, the binary pulsars move in the weak gravitational field of a companion, they do provide precision tests of the strong-field regime. This becomes clear when considering strong self-field effects which are predicted by the majority of alternative theories. Such effects would, for instance, clearly affect the pulsars' orbital motion, allowing us to search for these effects and hence providing us with a unique precision strong-field test of gravity.

Pulsars are highly magnetized rotating neutron stars and are unique and versatile objects which can be used to study an extremely wide range of physical and astrophysical problems. Besides testing theories of gravity one can study the Galaxy and the interstellar medium, stars, binary systems and their evolution, plasma physics and solid state physics under extreme conditions. This wide range of applications is exemplified by the first ever discovered double pulsar [1,2]. This unique system allows us to test many aspects of gravitational theories at the same time, representing a truly unique laboratory for relativistic gravity. The experiment is conceptually simple: Nature has provided us with two clocks attached to point masses which fall in the gravitational potential of their companion. Measuring the ticks of these clocks while they move through space-time allows us to compare our observations with the predictions of various theories of gravity.

The double pulsar is a system of two visible radio pulsars with periods of 22.8 ms (PSR J0737$-$3039A, simply called ``A'' hereafter) and 2.8 s (PSR J0737$-$3039B, simply called ``B'' hereafter), respectively. It was discovered and is studied by a large collaboration involving colleagues from Australia, Canada, India, Italy and USA. The double pulsar's short and compact (orbital period of $P_b = 144$ min), slightly eccentric ($e=0.09$) orbit makes the double pulsar the most extreme relativistic binary system ever discovered, demonstrated by the system's remarkably high value of periastron advance ( $\dot{\omega}=16.8995\pm0.0007\deg$ yr$^{-1}$, i.e. four times larger than for the Hulse-Taylor pulsar!). Only four years after the discovery of the system, most of its timing parameters are determined with a precision that took several decades to achieve in the previously known best relativistic binary pulsars [3]. For instance, we measure that the orbit is shrinking every day by $7.42\pm0.09$ mm, which agrees with GR's prediction of an orbital decay due to the emission of gravitational quadrupole waves within an uncertainty of 1%. Ultimately, the shrinkage leads to a coalescence of the two pulsars in only $\sim 85$ Myr. This boosts the hopes for detecting a merger of two neutron stars with first-generation ground-based gravitational wave detectors by a factor of several compared to previous estimates [1,4]. Moreover, the detection of a young companion B around an old millisecond pulsar A confirms the evolution scenario proposed for the creation of recycled millisecond pulsars.

The measured precession of the orbit and the decrease in orbital period of $\dot P_{\rm b}= (1.25\pm0.2)\times 10^{-12}$ seconds per second are both observed deviations from a pure Keplerian description of the orbit. It is important to note that we do not have to assume a particular theory of gravity when measuring such relativistic corrections, called ``post-Keplerian'' (PK) parameters. Instead, we can take the observational values and compare them with predictions made by a theory of gravity to be tested. In the double pulsar, as A has the faster pulse period, we can time A much more accurately than B, allowing us to measure a total of five very precise PK corrections for A's orbit.

The PK parameter, $\dot{\omega}$, is the easiest to measure. When interpreting this advance of periastron in the framework of GR, it provides an immediate measurement of the total mass of the system. The PK parameter $\gamma$ denotes the amplitude of delays in arrival times caused by the varying effects of the gravitational redshift and time dilation (second order Doppler) as the pulsars move in an elliptical orbit at varying distances with varying speeds. As a result of the gravitational redshift, the pulsar clocks slow down when they 'feel' the deeper gravitational potential of the companion and speed up when they are further away.

As mentioned, the decay of the orbit due to gravitational wave damping is observed as a change in orbital period, $\dot{P}_{\rm b}$. Two further PK parameters, $r$ and $s$, are related to a Shapiro delay caused by the curvature of space time near the companion. Their measurement is possible, since - quite amazingly! - we observe the system almost completely edge-on. Hence, at superior conjunction the pulses of A pass the surface of B in only 30,000 km distance, needing to travel an extra length of curved space-time and adding about 100 microseconds to the travel time to Earth. Within GR, we can interprete $s$ as the sine of the orbital inclination angle. With a measurement of $\sin i \equiv s = 0.99974(-0.00039,+0.00016)$ , this is indeed very close to an edge-on geometry of $i=90$deg.

When trying to see whether these PK parameter measurements are in agreement with the predictions of GR or any other theory of gravity, we use that for point masses with negligible spin contributions the PK parameters in each theory should only be functions of the a priori unknown neutron star masses and the well measurable Keplerian parameters. With the two masses as the only free parameters, the measurement of three or more PK parameters over-constrains the system, and thereby provides a test ground for theories of gravity. These tests can be illustrated in a very elegant way [5]: The unique relationship between the two masses of the system predicted by any theory for each PK parameter can be drawn in a diagram showing the mass of A on one axis and that of B on the other. We expect all curves to intersect in a single point if the chosen theory is a valid description of the nature of this system (see figure).

Figure 1: `Mass-mass' diagram showing the observational constraints on the masses of the neutron stars in the double pulsar system J0737-3039. The shaded regions are those that are excluded by the Keplerian mass functions of the two pulsars. Further constraints are shown as pairs of lines enclosing permitted regions as given by the observed mass ratio, $R$, and the PK parameters shown here as predicted by general relativity (see text). Inset is an enlarged view of the small square encompassing the intersection of these constraints. See Kramer, Stairs, Manchester et al. (2006) for details.

Most importantly, the possibility to measure the orbit of both A and B provides a new, qualitatively different constraint in such an analysis. Indeed, with a measurement of the projected semi-major axes of the orbits of both A and B, we obtain a precise measurement of the mass ratio simply from Kepler's third law, via $R \equiv M_A/M_B = x_B/x_A$ where $M_A$ and $M_B$ are the masses and $x_A$ and $x_B$ are the (projected) semi-major axes of the orbits of both pulsars, respectively. We can expect the mass ratio, $R$, to follow this simple relationship to at least 1PN order. In particular, the $R$ value is not only theory-independent, but also independent of strong-field (self-field) effects which is not the case for PK-parameters. Therefore, any combination of masses derived from the PK-parameters must be consistent with the mass ratio derived from Kepler's 3rd law. With five PK parameters already available, this additional constraint makes the double pulsar the most overdetermined system to date where the most relativistic effects can be studied in the strong-field limit. The theory of GR passes this new test at the record-breaking level of 0.05% [3].

The precision of the measured timing system parameters increases continuously with time as further and better observations are made. Soon, we expect the measurement of additional PK parameters, allowing more and new tests of theories of gravity. Some of these parameters arise from a relativistic deformation of the pulsar orbit and those which find their origin in aberration effects and their interplay with geodetic precession. In a few years, we will measure the decay of the orbit so accurately, that we can put limits on alternative theories of gravity which should even surpass the precision achieved in the solar system. On somewhat longer time scales, we will even achieve a precision that will require us to consider post-Newtonian terms that go beyond the currently used description of the PK parameters. Indeed, we already achieve a level of precision in the $\dot \omega$ measurement where we expect corrections and contributions at the 2PN level. One such effect involves the prediction by GR that, in contrast to Newtonian physics, the neutron stars' spins affect their orbital motion via spin-orbit coupling. This effect modifies the observed $\dot{\omega}$ by an amount that depends on the pulsars' moment of inertia, so that a potential measurement of this effect would allow the moment of inertia of a neutron star to be determined for the very first time [6,2]. We do not expect this measurement to be easy, but we will certainly try!

With the measurement of already five PK parameters and the unique information about the mass ratio, the double pulsar indeed provides a truly unique test-bed for relativistic theories of gravity. Again, GR has passed these new tests with flying colours. The precision of these tests and the nature of the resulting constraints go beyond what has been possible with other systems in the past. However, we only just started to study and exploit the relativistic phenomena that can be investigated in great detail in this wonderful cosmic laboratory.