Figure 1: Artist’s impression of a neutron star.
The oblate or prolate shape of a neutron star is characterised by the deformation parameter “γ”, where γ = 1 denotes a perfect sphere. An oblate neutron star has γ < 1 and a prolate neutron star has γ > 1. Basically, the maximum mass of a neutron star is how massive a neutron star can get before it becomes too massive and collapses into a black hole. The ability to deform results in a range of maximum masses a neutron star can have.
The maximum mass of a neutron star increases with increasing oblateness, but decreases with increasing prolateness. Assuming a perfectly spherical neutron star has a maximum mass of 2.3 times the Sun’s mass. If instead the neutron star has oblateness γ = 0.8, its maximum mass increases to 3.02 times the Sun’s mass. On the contrary, if the neutron star has prolateness γ = 1.2, its maximum mass decreases to 1.81 times the Sun’s mass.
Figure 2: An oblate neutron star with γ = 0.8 and a maximum mass of 3.02 times the Sun’s mass. Weber et al. (2015).
Figure 3: A prolate neutron star with γ = 1.2 and a maximum mass of 1.81 times the Sun’s mass. Weber et al. (2015).
Weber et al. (2015), “Non-Spherical Models of Neutron Stars”, arXiv:1504.03006 [astro-ph.SR]