Binary and ternary ionic compounds in the outer crust of a cold nonaccreting neutron star

The outer crust of a cold nonaccreting neutron star has been generally assumed to be stratified into different layers, each of which consists of a pure body-centered cubic ionic crystal in a charge compensating background of highly degenerate electrons. The validity of this assumption is examined by analyzing the stability of multinary ionic compounds in dense stellar matter. It is thus shown that their stability against phase separation is uniquely determined by their structure and their composition irrespective of the stellar conditions. However, equilibrium with respect to weak and strong nuclear processes imposes very stringent constraints on the composition of multinary compounds, and thereby on their formation. By examining different cubic and noncubic lattices, it is found that substitutional compounds having the same structure as cesium chloride are the most likely to exist in the outer crust of a nonaccreting neutron star. The presence of ternary compounds is also investigated. Very accurate analytical expressions are obtained for the threshold pressure, as well as for the densities of the different phases irrespective of the degree of relativity of the electron gas. Finally, numerical calculations of the ground-state structure and of the equation of state of the outer crust of a cold nonaccreting neutron star are carried out using recent experimental and microscopic nuclear mass tables.

Figure 1

Schematic representation of the pressure $P$ versus mean baryon number density $\overline{n}$ for a transition between two pure body-centered cubic lattice solid phases of nuclei $(A_1,Z_1)$ and $(A_2,Z_2)$. The two phases coexist at pressure $P_{1\to 2}$ irrespective of their proportion.

Figure 2

Schematic representation of the pressure $P$ versus mean baryon number density $\overline{n}$ for a transition between two pure body-centered cubic solid phases of nuclei $(A_1,Z_1)$ and $(A_2,Z_2)$ accompanied by the formation of a binary compound (with cesium chloride structure in this case). For comparison, the transition leading to the coexistence of pure phases is indicated by the dotted line. The figure is not to scale. In reality, the range of pressures for which the compound is present (from $P_{1\to 1+2}$ to $P_{1+2\to 2}$) is very small, $(P_{1+2\to 2}-P_{1\to 1+2})/P_{1\to 2}\ll 1$, as shown in Eq. (86).

Figure 3

Binary compounds made of two nuclear species $(A_1,Z_1)$ (black circles) and $(A_2,Z_2)$ (white circles) with face-centered cubic (fcc) and simple cubic (sc) crystal structures.

Figure 4

Binary compounds made of two nuclear species $(A_1,Z_1)$ (black circles) and $(A_2,Z_2)$ (white circles) based on the cubic perovskite structure shown in Fig. 8.

Figure 5

Binary compound made of two nuclear species $(A_1,Z_1)$ (black circles) and $(A_2,Z_2)$ (white circles) with an hexagonal close-packed (hcp) structure.

Figure 6

Values of the dimensionless ratio $\mathcal{R}\left(q\right)$ as a function of the charge ratio $q=Z_2/Z_1$ for the binary compounds shown in Figure 3. The thin horizontal line delimits the region of stability against phase separation; a compound is stable if $\mathcal{R}\left(q\right)>1$. The right panel shows a close-up view near $q=1$. See text for details.

Figure 7

Same as Fig. 6 for the binary compounds shown in Figs. 4 and 5.

Figure 8

Ternary compound with cubic perovskite structure made of three nuclear species $(A_1,Z_1)$ (black circles), $(A_2,Z_2)$ (grey circle), and $(A_3,Z_3)$ (white circles).

Figure 9

Stability of cubic perovskite compounds shown in Fig. 8 against phase separation, as a function of the charge ratios $q=Z_2/Z_1$ and $p=Z_3/Z_1$. Stable compounds only exist in black regions, where the dimensionless ratio $\mathcal{R}(q,p)$ exceeds unity. See text for details.

Figure 10

Pressure versus mean baryon number density in the outer crust of a cold nonaccreting neutron star. Results were obtained using experimental masses from the 2012 Atomic Mass Evaluation [32] supplemented with the Brussels-Montreal nuclear mass model HFB-24 [33]. Two regions of the crust are highlighted corresponding to the change of composition from ${}^{56}\mathrm{Fe}$ to ${}^{62}\mathrm{Ni}$ (left panel) and from ${}^{80}\mathrm{Ni}$ to ${}^{124}\mathrm{Mo}$ (right panel). In both cases, a binary compound with the sc1 structure shown in Fig. 3 is present in the intermediate layers. The dashed lines represent the transition considering pure crystalline phases only.