By affecting the gravitational binding of neutron stars, a non-zero would reasonably be expected to alter the moment of inertia of the star and hence change its spin on the same timescale [34]. Goldman [56] writes

where is the moment of inertia of the neutron star, about 10

The effects on the orbital period of a binary system of a varying were first considered by Damour, Gibbons, and Taylor [41], who expected

Applying this equation to the limit on the deviation from GR of the for PSR 1913+16, they found a value of . Nordtvedt [102] took into account the effects of on neutron-star structure, realizing that the total mass and angular momentum of the binary system would also change. The corrected expression for incorporates the compactness parameter and is (Note that there is a difference of a factor of in Nordtvedt’s definition of versus the Damour definition used throughout this article.) Nordtvedt’s corrected limit for PSR B1913+16 is therefore slightly weaker. A better limit actually comes from the neutron-star–white-dwarf system PSR B1855+09, with a measured limit on of [74]. Using Equation (29), this leads to a bound of , which Arzoumanian [7] corrects using Equation (30) and an estimate of NS compactness to . Prospects for improvement come directly from improvements to the limit on . Even though PSR J1012+5307 has a tighter limit on [85], its shorter orbital period means that the limit it sets is a factor of 2 weaker than obtained with PSR B1855+09.

The Chandrasekhar mass, , is the maximum mass possible for a white dwarf supported against gravitational collapse by electron degeneracy pressure [30]. Its value – about – comes directly from Newton’s constant: , where is Planck’s constant and is the neutron mass. All measured and constrained pulsar masses are consistent with a narrow distribution centred very close to : [136]. Thus, it is reasonable to assume that sets the typical neutron star mass, and to check for any changes in the average neutron star mass over the lifetime of the Universe. Thorsett [135] compiles a list of measured and average masses from 5 double-neutron-star binaries with ages ranging from 0.1 Gyr to 12 or 13 Gyr in the case of the globular-cluster binary B2127+11C. Using a Bayesian analysis, he finds a limit of at the 95% confidence level, the strongest limit on record. Figure 5 illustrates the logic applied.

While some cancellation of “observed” mass changes might be expected from the changes in neutron-star
binding energy (cf. Section 3.4.2 above), these will be smaller than the changes by a factor of order
the compactness and can be neglected. Also, the claimed variations of the fine structure constant
of order [140] over the redshift range could
introduce a maximum derivative of of about 5 × 10^{–16} yr^{–1} and hence
cannot influence the Chandrasekhar mass at the same level as the hypothesized changes in
.

One of the five systems used by Thorsett has since been shown to have a white-dwarf companion [138], but as this is one of the youngest systems, this will not change the results appreciably. The recently discovered PSR J1811–1736 [90], a double-neutron-star binary, has a characteristic age of only and, therefore, will also not significantly strengthen the limit. Ongoing searches for pulsars in globular clusters stand the best chance of discovering old double-neutron-star binaries for which the component masses can eventually be measured.

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