Extreme binary pulsar shows no deviation from general relativity

Einstein’s general theory of relativity (GR), the standard theory of gravity, has passed every high-precision test in the solar system, where gravitational fields are relatively weak. In those familiar precincts, the 97-year-old theory correctly predicts the gravitational bending, redshifting, and delaying of light; the precession of planetary orbits; and the strict equivalence of gravitational and inertial mass. But because GR has problems with quantization, spacetime infinities, cosmological inflation, and the unification of the fundamental forces, theorists widely anticipate that the true macroscopic gravity theory must diverge significantly from it in places with much stronger gravitational fields.

The gravitational field exerted by an extended object of mass M is said to be strong, in the sense of GR, when its Schwarzschild radius

R_s(M) ≡ 2GM/c²

is comparable to some physically relevant distance. The closest thing to a strong field in the solar system is at the surface of the Sun, whose radius is more than 10⁵ times its R_s of 3 km.

The situation is dramatically different for neutron stars, ultradense stellar remnants of core-collapse supernovae. A solar-mass (1 M_⊙) neutron star has a radius of order 10 km, only a few times its R_s. And whereas the gravitational binding energy of an ordinary star is a negligible fraction of its mass, the binding energy of a neutron star can reduce the total mass of its unassembled constituents by as much as 20%. Strong-field effects predicted by proposed variations on GR generally have highly nonlinear dependence on gravitational binding energy.

The binding energies of neutron stars grow monotonically with increasing stellar mass. So several attractive variant theories suggest detectable deviations from GR in and around neutron stars above some critical mass. But no such deviations have been seen. And now an international team centered at the Max Planck Institute for Radio Astronomy (MPIR) in Bonn, Germany, has reported one more confirmation of GR, from the discovery and monitoring of a neutron-star system whose extreme properties had made it the most promising candidate to date for the revelation of new gravity physics. ¹

An extraordinary binary

The system is a binary pair, labeled J0348+0432, in which the most massive neutron star yet weighed is closely orbited every 2.46 hours by a much lighter white-dwarf star. Though 7000 light-years away, J0348 is quite observer friendly. The white dwarf’s unusually bright hydrogen spectrum yields high-resolution Doppler-shift data and much information about its intrinsic properties. And the neutron star is a radio pulsar whose lighthouse-like radio beam, sweeping Earth every 39 milliseconds, provides an exquisite long-term timing reference.

That timing capability serves the team’s principal goal: to compare the binary orbit’s decay rate with that predicted by GR. But such measurements have been confirming GR ever since Joseph Taylor and Russell Hulse discovered the first binary pulsar four decades ago (see the Reference Frame by Dan Kleppner, Physics Today, April 1993, page 9 ). So why expect better of J0348?

The orbits of “clean, relativistic” binaries—those with relativistic velocities and negligible losses due to tidal dissipation or mass transfer—lose energy primarily by gravitational radiation. In GR, the lowest-order gravity-wave production by an extended dynamical source is quadrupole radiation. But many variations on GR predict that dipole radiation will, under the right circumstances, sap a binary’s orbital energy much faster than the quadruple radiation. The right circumstances would be very high neutron-star mass and orbital velocity, and a lightweight binary companion to provide the requisite asymmetry for GR-violating dipole radiation. The Taylor–Hulse binary, like many of the early test systems, lacks that asymmetry. It comprises two neutron stars, both with masses close to 1.4 M_⊙.

The new binary pulsar was first spotted by team member Ryan Lynch (McGill University) in accumulated data from a 2007 radio-telescope survey. In follow-up optical observations, MPIR graduate student John Antoniadis studied the periodic Doppler shifting of the white dwarf’s spectrum. “It was quickly evident,” he recalls, “that the pulsar was quite a heavyweight.”

Figure 1 shows the 2.46-hour oscillation of the line-of-sight velocity components of the white dwarf and the pulsar as measured, respectively, by spectral Doppler shifts and pulsar timing. The ratio of their oscillatory amplitudes measures the ratio q ≡ M_p/M_wd of their masses to be 11.7 ± 0.1.

To pin down M_wd, Antoniadis produced a model of the white dwarf from its surface temperature and gravity, determined from the intensities and pressure broadening of spectral lines. The model yields a mass of 0.17 M_⊙. That’s atypically light. But white-dwarf models are surprisingly reliable, because those end-stage stars are rather simple objects. With all its fusion fuels exhausted, a white dwarf is sustained against collapse mainly by the Pauli principle’s electron-degeneracy pressure.

Thus the pulsar mass M_p = qM_wd was determined to be a record (2.01 ± 0.04) M_⊙. The two masses plus the orbit’s period and its line-of-sight velocity components yield a detailed description of the binary orbit: Its plane is inclined 40° from the plane of the sky, and the white dwarf’s orbital velocity is about 0.2% of the speed of light. Its separation from the pulsar is about half the diameter of the Sun.

Figure 2 compares J0348 with other binary pulsar systems, with regard to pulsar mass, orbital velocity, and gravitational binding energy. The figure shows another 2-M_⊙ pulsar orbited by a white dwarf. But that binary’s orbital velocity is much slower (see Physics Today, January 2011, page 12 ). On the other hand, the plot shows a unique double pulsar—two pulsars orbiting their center of mass with a relative velocity slightly faster than that of J0348. But neither pulsar’s mass exceeds the well-trodden regime below 1.4 M_⊙. And besides, the double pulsar lacks the desired asymmetry a white-dwarf companion brings. “We found the new binary sitting all by itself in an intriguing, previously untested gravitational regime,” says Norbert Wex (MPIR).

No deviation yet

Given the new binary’s measured parameters, GR predicts that its present 2.46-hour orbital period P_b should be decreasing by about 8 µs per year as the orbit shrinks due to energy loss by gravitational radiation. To test that prediction, Lynch and Paulo Freire (MPIR) began continual pulsar timing with Puerto Rico’s Arecibo radio telescope in April 2011. Now, based on two years of timing data, the orbital period’s measured time derivative is 1.05 ± 0.18 times the GR prediction. So thus far there’s no evidence of new physics.

Figure 3 illustrates the degree of concordance between the measurements and the theory. The yellow swath is the 1-standard-deviation confinement imposed on the binary’s mass plane by the measurement, assuming that GR is the correct theory. The fact that the intersection of the measured q and M_wd lines, which involve no assumptions about GR, falls nicely in the middle of the calculated swath indicates that GR has thus far passed the team’s radiative test. With increased observing time t over the next few years, the uncertainty on should shrink rather rapidly—like t^−5/2.

Scalar–tensor theories

The MPIR observations have already made significant inroads into alternative theories that expect orbital decay rates to increase steeply—by orders of magnitude—at some critical neutron-star mass. A seminal theory of that kind was introduced in 1993 by Thibault Damour and Gilles Esposito-Farèse in France. ² Their theory, like many others, is an elaboration of the 1961 theory by Carl Brans and Robert Dicke, which posited that gravity is mediated not only by Einstein’s metric-tensor field but also by an additional scalar field. The original Brans–Dicke theory was eventually refuted by precision tests within the solar system. But elaborations that proposed nonlinear couplings of the scalar field to matter held out prospects for observable consequences in strong-gravity regimes. (See the article by Clifford Will in Physics Today, October 1999, page 38 .)

In particular, Damour and Esposito pointed out an unanticipated consequence of such nonlinear scalar elaborations: Within a particular range of coupling parameters, those theories imply that the coupling strength of the scalar field to neutron-star matter increases steeply at some critical binding energy. They call that abrupt transition spontaneous scalarization and compare it to the onset of ferromagnetism. Given a fast enough white-dwarf companion, scalarization would strongly increase a binary’s dipole radiation and manifest itself as an increase of a few orders of magnitude in the orbit’s decay rate.

Having found no such excess in the uniquely auspicious J0348 binary, the MPIR team effectively excludes almost all of the Damour–Esposito parameter space that predicts spontaneous scalarization. “More generally,” says Wex, “we’ve placed an upper limit on the effective coupling strength of long-range extra gravity fields to matter in a previously unexplored strong-gravity regime.”

Most proposed extra gravity fields are “long range” in the sense that, like the GR tensor field, the Brans–Dicke scalar field, and the electromagnetic field, their quanta are massless. The J0348 results would be insensitive to short-range fields with quanta heavier than 10⁻¹⁹ eV—that is, a Compton wavelength shorter than the binary’s 10⁹-km gravitational wavelength, which is given by cP_b/2.

“There are still lots of long-range scalar–tensor theories with strong-field effects that would be consistent with the [MPIR] team’s data,” says theorist Clifford Will (University of Florida). Many of those predict neutron-star effects much less dramatic than scalarization. Continued monitoring of J0348 should serve to test some of those still viable elaborations of GR.