Testing General Relativity with Pulsar Timing

Abstract

Pulsars of very different types, including isolated objects and binaries (with short- and long-period orbits, and white-dwarf and neutron-star companions) provide the means to test both the predictions of general relativity and the viability of alternate theories of gravity. This article presents an overview of pulsars, then discusses the current status of and future prospects for tests of equivalence-principle violations and strong-field gravitational experiments.

Figure 1

Top: 100 single pulses from the 253-ms pulsar B0950+08, demonstrating pulse-to-pulse variability in shape and intensity. Bottom: Cumulative profile for this pulsar over 5 minutes (about 1200 pulses); this approaches the reproducible standard profile. Observations taken with the Green Bank Telescope [ 98 ]. (Stairs, unpublished.)

Figure 2

Pulse profile shapes for PSR J1740-3052 at multiple frequencies, aligned by pulse timing. The full pulse period is displayed at each frequency. The growth of an exponential scattering tail at low frequencies is evident. All observations taken with the Green Bank Telescope [98] (Stairs, unpublished), except for the 660-MHz profile which was acquired at the Parkes telescope [9, 122].

Figure 3

Pulse profile of the fastest rotating pulsar, PSR B1937+21, observed with the 76-m Lovell telescope at Jodrell Bank Observatory [67]. The top panel shows the total-intensity profile derived from a filterbank observation (see text); the true profile shape is convolved with the response of the channel filters. The lower panel shows the full-Stokes observation with a coherent dedispersion instrument [126, 123]. Total intensity is indicated by black lines, and linear and circular power by red and blue lines, respectively. The position angle of the linear polarization is plotted twice. The coherent dedispersion observation results in a much sharper and more detailed pulse profile, less contaminated by instrumental effects and more closely resembling the pulse emitted by the rotating neutron star. Much better timing precision can be obtained with these sharper pulses.

Figure 4

“Polarization” of a nearly circular binary orbit under the influence of a forcing vector g, showing the relation between the forced eccentricity e_F, the eccentricity evolving under the general-relativistic advance of periastron e_R(t), and the angle θ. (After [145].)

Figure 5

Measured neutron star masses as a function of age. The solid lines show predicted changes in the average neutron star mass corresponding to hypothetical variations in G, where ζ_-12=10 implies . (From [135], used by permission.)

Figure 6

The parabola indicates the predicted accumulated shift in the time of periastron for PSR B1913+16, caused by the decay of the orbit. The measured values of the epoch of periastron are indicated by the data points. (From [ 144 ], courtesy Joel Weisberg.)

Figure 7

Mass-mass diagram for the PSR B1913+16 system, using the ω̇ and γ parameters listed in Table 2. The uncertainties are smaller than the widths of the lines. The lines intersect at the point given by the masses derived under the DDGR formalism. (From [144], courtesy Joel Weisberg.)

Figure 8

Mass-mass diagram for the PSR B1534+12 system. Labeled curves illustrate 68% confidence ranges of the DD parameters listed in Table 3. The filled circle indicates the component masses according to the DDGR solution. The kinematic correction for assumed distance has been subtracted from the observed value of Ṗ_b; the uncertainty on this kinematic correction dominates the uncertainty of this curve. A slightly larger distance removes the small apparent discrepancy between the observed and predicted values of this parameter. (After [125].)

Figure 9

Portions of the tensor-biscalar β′-β″ plane permitted by timing observations of PSRs B1913+16, B1534+12, and B1855+09 up to 1992. Values lying above the curve labeled “a” are incompatible with the measured ω̇ and γ parameters for PSR B1913+16. The curves labeled “b” and “d” give the allowed ranges of β′ and β″ for PSRs B1913+16 and B1534+12, respectively, fitting for the two neutron-star masses as well as β′ and β″, using data available up to 1992. The vertical lines labeled “c” represent limits on β′ from the SEP-violation test using PSR B1855+09 [41]. The dot at (0,0) corresponds to GR. (Reprinted by permission from Nature [134], © 1992, Macmillan Publishers Ltd.)

Figure 10

The parameter space in the non-linear α₀, β₀ gravitational theory, for neutron stars described by a polytrope equation of state. The regions below the various curves are allowed by various pulsar timing limits, by solar-system tests (“1PN”), and by projected LIGO/VIRGO observations of NS-NS and NS-BH inspiral events. The shaded region is allowed by all tests. The plane and limits are symmetric about α₀=0. (From [37]; used by permission.)

Figure 11

Solid line: predicted value of the Shapiro delay in PSR J0437-4715 as a function of orbital phase, based on the observed inclination angle of 42°±9°. For such low-eccentricity binaries, much of the Shapiro delay can be absorbed into the orbital Roemer delay; what remains is the ∼ P_b/3 periodicity shown. The points represent the timing residuals for the pulsar, binned in orbital phase, and in clear agreement with the shape predicted from the inclination angle. (Reprinted by permission from Nature [139], ©2001, Macmillan Publishers Ltd.)

Figure 12

Changes in the observed pulse profile of PSR B1913+16 throughout the 1980s, due to a changing line-of-sight cut through the emission region of the pulsar. (Taken from [ 133 ]; used by permission.)

Figure 13

Top: change in peak separation of the relativistic double-neutron-star binary PSR B1913+16, as observed with the Arecibo (solid points, [ 141 ]) and Effelsberg (open circles, [ 80 ]) telescopes. Bottom: projected disappearance of PSR B1913+16 in approximately 2025. (Taken from [ 80 ]; used by permission.)

Figure 14

Hourglass-shaped beam for PSR B1913+16 derived from the symmetric-component analysis of [ 143 ]. (Taken from [ 143 ]; used by permission.)

Figure 15

Alternate proposed beam shape for PSR B1913+16, consisting of a symmetric cone plus an offset core. The red lines indicate an example cut through the emission region, as well as the predicted pulse peak ratio and separation as functions of time. (After [ 81 ], courtesy Michael Kramer.)

Figure 16

Evolution of the low-level emission surrounding the main pulse of PSR B1534+12, over a period of nearly 10 years, as measured with the Arecibo telescope [ 96 ]. (Stairs et al., unpublished.)