Constraining a possible time variation of the gravitational constant $G$ with terrestrial nuclear laboratory data

Testing the constancy of the gravitational constant $G$ is a longstanding fundamental question in natural science. As first suggested by Jofré, Reisenegger, and Fernández (2006, Phys. Rev. Lett. 97, 131102), Dirac's hypothesis of a decreasing gravitational constant $G$ with time caused by the expansion of the Universe would induce changes in the composition of neutron stars, causing dissipation and internal heating. Eventually, neutron stars reach their quasistationary states where cooling, as a result of neutrino and photon emissions, balances the internal heating. The correlation of surface temperatures and radii of some old neutron stars may thus carry useful information about the rate of change of $G$. Using the density dependence of the nuclear symmetry energy, constrained by recent terrestrial laboratory data on isospin diffusion in heavy-ion reactions at intermediate energies, and the size of neutron skin in ${}^{208}\mathrm{Pb}$, within the gravitochemical heating formalism developed by Jofré et al. (2006, Phys. Rev. Lett. 97, 131102), we obtain an upper limit for the relative time variation $|\stackrel{·}{G}/G|$ in the range ($4.5\text{−}21)\times {10}^{-12}$ yr${}^{-1}$.

Figure 1

Equation of state of stellar matter in β-equilibrium. The upper panel shows the total energy density and lower panel the pressure as functions of the baryon number density (in units of ${\rho }_0$).

Figure 2

Neutron star mass, proton fraction $Y_p$, and symmetry energy $e_{\mathrm{sym}}$. The upper frame displays the neutron star mass as a function of baryon number density. The middle frame shows the proton fraction and the lower frame the nuclear symmetry energy as functions of density. (Symmetry energy is shown for the nucleonic EOSs only.) The proton fraction curve of the Hyb EOS is terminated at the beginning of the quark phase. The termination point is denoted by a “cross” character.

Figure 3

Mass-radius relation. The shaded region corresponds to the mass constraint from Hotan et al. [59].

Figure 4

Stationary photon luminosity (upper frame) and neutron star surface temperature (lower frame) as functions of stellar mass, assuming $|\stackrel{·}{G}/G|=4.5\times {10}^{-12}$ yr${}^{-1}$. The shaded region corresponds to the mass constraint from Hotan et al. [59]. The open (black) square character denotes the maximum possible mass attained by the neutron star models constructed from the hyperonic EOS (Hyp). (The $x=-1$, Hyp and Hyb EOSs allow for fast cooling in the considered mass range. For the Hyb EOS, stellar cooling proceeds via a quark direct Urca process; see Sec. 5.)

Figure 5

Neutron star stationary surface temperature for stellar models satisfying the mass constraint of Hotan et al. [59]. The solid lines are the predictions versus the stellar radius for the considered neutron star sequences. Dashed lines correspond to the 68% and 90% confidence contours of the black-body fit of Kargaltsev et al. [32]. The value of $|\stackrel{·}{G}/G|=4.5\times {10}^{-12}$ yr${}^{-1}$ is chosen so that predictions from the $x=0$ EOS are just above the observational constraints.

Figure 6

Same as Fig. 4 but now the value of $|\stackrel{·}{G}/G|=2.1\times {10}^{-11}$ yr${}^{-1}$ is chosen so that predictions from the $x=-1$ EOS are just above the observational constraints. (The $x=-1$ EOS allows direct Urca reactions in the considered mass range.)

Figure 7

Same as Fig. 5 but with $|\stackrel{·}{G}/G|=2.1\times {10}^{-11}$ yr${}^{-1}$.

Figure 8

Same as Fig. 5 but with $|\stackrel{·}{G}/G|=4\times {10}^{-13}$ yr${}^{-1}$ after Copi et al. [23].

Figure 9

Same as Fig. 5 but with $|\stackrel{·}{G}/G|=3.6\times {10}^{-11}$ yr${}^{-1}$. The value of $\stackrel{·}{G}$ is chosen so that predictions from the hyperonic EOS (Hyp) are just above the empirical constraints.

Figure 10

Models of hybrid stars (upper frame) and triangle inequality (lower frame).

Figure 11

Same as Fig. 5 but with $|\stackrel{·}{G}/G|=1.6\times {10}^{-10}$ yr${}^{-1}$. The value of $\stackrel{·}{G}$ is chosen so that predictions from the hybrid EOS (Hyb) are just above the empirical constraints.