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 . Goldman  writes45 g cm2, and is the (conserved) total number of baryons in the star. By assuming that this represents the only contribution to the observed of PSR B0655+64, in a manner reminiscent of the test of described above, Goldman then derives an upper limit of , depending on the stiffness of the neutron star equation of state. Arzoumanian  applies similar reasoning to PSR J2019+2425 , which has a characteristic age of 27 Gyr once the “Shklovskii” correction is applied . Again, depending on the equation of state, the upper limits from this pulsar are . These values are similar to those obtained by solar-system experiments such as laser ranging to the Viking Lander on Mars (see, e.g., [113, 62]). Several other millisecond pulsars, once “Shklovskii” and Galactic-acceleration corrections are taken into account, have similarly large characteristic ages (see, e.g., [29, 137]).
The effects on the orbital period of a binary system of a varying were first considered by Damour, Gibbons, and Taylor , who expected 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 . Using Equation (29), this leads to a bound of , which Arzoumanian  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 , 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 . 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 : . 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  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  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 , but as this is one of the youngest systems, this will not change the results appreciably. The recently discovered PSR J1811–1736 , 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.
© Max Planck Society and the author(s)