Dirac stars supported by nonlinear spinor fields

We study configurations consisting of a gravitating spinor field $\psi$ with a nonlinearity of the type $\lambda {(\overline{\psi }\psi )}^2$. To ensure spherical symmetry of the configurations, we use two spin-$\frac{1}{2}$ fields forming a spin singlet. For such systems, we find regular stationary asymptotically flat solutions describing compact objects. For negative values of the coupling constant $\lambda$, it is shown that, by choosing physically reasonable values of this constant, it is possible to obtain configurations with masses comparable to the Chandrasekhar mass. It enables us to speak of an astrophysical interpretation of the obtained systems, regarding them as Dirac stars.

Figure 1

Dimensionless Dirac-star total mass $\overline{M}$ as a function of the parameter $\overline{E}$ for $\overline{\lambda }=-100,-50,-20$, 0, and 20. The bold dots mark the positions of the configurations for which the graphs of Fig. 3 are plotted.

Figure 2

Maximum Dirac-star masses as a function of $|\overline{\lambda }|$. The solid curve corresponds to the asymptotic relation (17).

Figure 3

Spinor fields $\overline{g}$ and $\overline{f}$ as functions of dimensionless radius $x$ for $\overline{\lambda }=-100$ and $\overline{\lambda }=0$. The dashed line shows the solution to Eqs. (18)–(20) with $\overline{E}/{\sigma }_c$ from the exact ${\overline{g}}_c=0.0275$, $\overline{\lambda }=-100$ model, scaled to $\overline{\lambda }=-100$.

Figure 4

Dimensionless Dirac-star total mass ${\overline{M}}_{*}$ as a function of $\overline{E}/{\sigma }_c$ for the limiting configurations described by Eqs. (18)–(20). The graph is plotted only for the values of $\overline{E}$ for which the binding energy is positive.