Role of the symmetry energy on the neutron-drip transition in accreting and nonaccreting neutron stars

In this paper, we study the role of the symmetry energy on the neutron-drip transition in both nonaccreting and accreting neutron stars, allowing for the presence of a strong magnetic field as in magnetars. The density, pressure, and composition at the neutron-drip threshold are determined using the recent set of the Brussels-Montreal microscopic nuclear mass models, which mainly differ in their predictions for the value of the symmetry energy $J$ and its slope $L$ in infinite homogeneous nuclear matter at saturation. Although some correlations between on the one hand the neutron-drip density, the pressure, the proton fraction, and on the other hand $J$ (or equivalently $L$) are found, these correlations are radically different in nonaccreting and accreting neutron stars. In particular, the neutron-drip density is found to increase with $L$ in the former case, but decreases in the latter case depending on the composition of ashes from x-ray bursts and superbursts. We have qualitatively explained these different behaviors using a simple mass formula. We have also shown that the details of the nuclear structure may play a more important role than the symmetry energy in accreting neutron-star crusts.

Figure 1

Experimental constraints on the symmetry energy parameters, taken from Ref. [31]; the dashed line represents the constraint obtained from fitting experimental nuclear masses using the Brussels-Montreal Hartree-Fock-Bogoliubov models (including unpublished ones) with a root-mean-square deviation below $0.84$ MeV; star symbols correspond to the series of models from Ref. [43] that we consider in this work. See text for details.

Figure 2

Symmetry energy of infinite homogeneous nuclear matter $S_1\left(n\right)$ versus density, for the Brussels-Montreal energy density functionals BSk22 to BSk25 [43].

Figure 3

Neutron-drip density in nonaccreting neutron-star crusts as a function of the slope $L$ of the symmetry energy of infinite homogeneous nuclear matter at saturation and for different magnetic field strengths, as obtained using the HFB-22 to HFB-25 Brussels-Montreal nuclear mass models [43].

Figure 4

(a) Mass number $A$ and (b) proton fraction $Z/A$ at the neutron-drip transition for nonaccreting neutron-star crusts as a function of the slope $L$ of the symmetry energy of infinite homogeneous nuclear matter at saturation, as obtained using the HFB-22 to HFB-25 Brussels-Montreal nuclear mass models [43]. Squares (circles) correspond to $B_{☆}=0,500$ and 1500 ($B_{☆}=1000$ and 2000).

Figure 5

Difference in mass predictions for two pairs of Brussels-Montreal nuclear mass models along the two isotopic chains $Z=36$ and $Z=38$ relevant at the neutron-drip transition.

Figure 6

Electron density $n_e$ (solid line) at the neutron-drip transition in nonaccreting neutron-star crusts as a function of the magnetic field strength, using the Brussels-Montreal nuclear mass model HFB-22 and assuming that the neutron-drip nucleus is ${}^{122}\mathrm{Kr}$, as in the absence of magnetic field. The horizontal dotted line represents $n_e^0$, as given by Eq. (35). See text for details.

Figure 7

Neutron-drip density as a function of the slope $L$ of the symmetry energy of infinite homogeneous nuclear matter at saturation, as obtained using the HFB-22 to HFB-25 Brussels-Montreal nuclear mass models, for accreting neutron-star crusts with different initial composition of ashes (see text for details).

Figure 8

Mass difference $\mathrm{\Delta }{M}^{\prime }$ (in units of $\mathrm{MeV}/c^2$) as a function of the slope $L$ of the symmetry energy of infinite homogeneous nuclear matter at saturation, as obtained using the HFB-22 to HFB-25 Brussels-Montreal nuclear mass models, for accreting neutron-star crusts with different initial composition of ashes (see text for details).

Figure 9

$\mathrm{\Delta }N$-neutron separation energy $S_{\mathrm{\Delta }Nn}$ (in units of MeV) as a function of the slope $L$ of the symmetry energy of infinite homogeneous nuclear matter at saturation, as obtained using the HFB-22 to HFB-25 Brussels-Montreal nuclear mass models, for accreting neutron-star crusts with different initial composition of ashes (see text for details).