Towards Skyrmion stars: Large baryon configurations in the Einstein-Skyrme model

We investigate the large baryon number sector of the Einstein-Skyrme model as a possible model for baryon stars. Gravitating hedgehog skyrmions have been investigated previously and the existence of stable solitonic stars excluded due to energy considerations [P. Bizon and T. Chmaj, Phys. Lett. B 297, 55 (1992).]. However, in this paper we demonstrate that by generating gravitating Skyrmions using rational maps, we can achieve multibaryon bound states while recovering spherical symmetry in the limit where $B$ becomes large.

Figure 1

Plot of the two branches of solutions found for $B=2$ configurations generated with the rational map ansatz.

Figure 2

Plot of the decrease in ${\alpha }_{\mathrm{crit}}$ with increasing baryon number, for configurations generated with the rational map ansatz. $+$: ${\alpha }_{c}r$ for the minimum value of $I$; curve: ${\alpha }_{c}r=0.0404{\mathcal{B}}^{-1/2}$.

Figure 3

Numerical solutions for the profiles $F(x)$, $\mu (x)$, and $A(x)$ when $B=2\times {10}^6$ and $\alpha =1\times {10}^{-6}$.

Figure 4

Numerical solutions for the profiles $F(x)$, $\mu (x)$, and $A(x)$ when $\mathcal{B}=2\times {10}^6$ and $\alpha =1\times {10}^{-6}$.