Universal I-Q relations for rapidly rotating neutron and strange stars in scalar-tensor theories

We study how rapid rotation influences the relation between the normalized moment of inertia $\overline{I}$ and quadrupole moment $\overline{Q}$ for scalarized neutron stars. The questions one has to answer are whether the equation of state universality is preserved in this regime and what are the deviations from general relativity. Our results show that the $\overline{I}-\overline{Q}$ relation is nearly equation of state independent for scalarized rapidly rotating stars, but the differences with pure Einstein’s theory increase compared to the slowly rotating case. In general, smaller negative values of the scalar field coupling parameters $\beta$ lead to larger deviations, but these deviations are below the expected accuracy of the future astrophysical observations if one considers values of $\beta$ in agreement with the current observational constraints. An important remark is that although the normalized $\overline{I}-\overline{Q}$ relation is quite similar for scalar-tensor theories and general relativity, the unnormalized moment of inertia and quadrupole moment can be very different in the two theories. This demonstrates that although the $\overline{I}-\overline{Q}$ relations are potentially very useful for some purposes, they might not serve us well when trying to distinguish between different theories of gravity.

Figure 1

$\overline{I}-\overline{Q}$ relations for GR (continuous black lines) and for STT (red lines) for all hadronic EOSs and for several values of the parameter $\alpha$. The case of $\alpha =0.32$ is given as dashed black line as representative for slow rotation (GR and STT solutions in this case are almost indistinguishable). In the middle panel the relative deviation of the STT solutions from the GR polynomial fits is presented. In the bottom panel the relative deviations of STT solutions from the fits to the STT data are plotted.

Figure 2

Comparison between $\overline{I}-\overline{Q}$ relations for GR and for STT, for several values of $\beta =-4.5,-5,-6$. The presented data are for EOS APR.

Figure 3

The unnormalized moment of inertia (left panel) and quadrupole moment (right panel) as functions of the neutron star mass for several sequences with fixed rotational frequency. The presented results are for EOS APR.