Neutron stars in Einstein-aether theory

As current and future experiments probe strong gravitational regimes around neutron stars and black holes, it is desirable to have theoretically sound alternatives to general relativity against which to test observations. Here we study the consequences of one such generalization, Einstein-aether theory, for the properties of nonrotating neutron stars. This theory has a parameter range that satisfies all current weak-field tests. We find that within this range it leads to lower maximum neutron star masses, as well as larger surface redshifts at a particular mass, for a given nuclear equation of state. For nonrotating black holes and neutron stars, the innermost stable circular orbit is only slightly modified in this theory.

Figure 1

Graphical representation of (11) (solid line) and (12) (dashed lines). The allowed region of the parameter space is below the solid curve, above $c_{-}=0$ and to the left of $c_{+}=1$. The radiation damping constraint will restrict to a nearly one-dimensional subset of this region.

Figure 2

Total mass versus $R$ for the Hm equation of state for $P_0$ up to 100 and $c_{14}=0$, 0.05, 0.2, 0.5, 1 beginning with the upper (GR) curve. The vertical axis is units of solar masses and the horizontal in km. The GR curve reaches its maximum mass of $2.20M_{\odot }$ at slightly more than 10 km. As $c_{14}$ increases to 1 the maximum mass decreases and the value of the radius at the maximum falls to about 9.5 km.

Figure 3

Maximum mass vs $c_{14}$ for the six equations of state. The hadronic models are plotted with solid lines, while the quark models are dashed lines. The thick solid horizontal lines represent the bare minimum constraint of $1.44M_{\odot }$ and a possible constraint value of $2M_{\odot }$.

Figure 4

Surface redshift factor $z$ versus $c_{14}$ for $1.8M_{\odot }$ neutron stars using the hardest equations of state. Hm (solid line) is on top, Qh (dashed line) is in the middle, and Hh (solid line) is on the bottom. Note that the GR value of $z=0.35$ for the hardest EOS, Hh, is consistent with the proposed surface redshift of 0.35 for EXO 0748-676 [48]. The Hm and Qh lines begin to curve up near $c_{14}=1.1–1.2$ because the maximum mass for these equations of state is approaching $1.8M_{\odot }$.