Universal relations for fast rotating neutron stars without equation of state bias

Abstract

We provide a summary of several parametrisations for the nuclear equation of state that have been proposed over the past decades and list viable ranges for their parameters. Based on these parametrisations, we construct a large database of rotating neutron star models, which are arranged in sequences of constant central energy density. After filtering these sequences with respect to generous astrophysical constraints, we discover tight universal relations for various bulk quantities of uniformly rotating neutron stars of arbitrary rotation rates. These universal relations allow to estimate, at very low computational cost, bulk quantities of rotating neutron stars employing mass, radius, and moment of inertia of associated non-rotating neutron stars. The relations are calibrated to a large, model-agnostic dataset, thereby eliminating a potential bias, and prove to be robust. Such relations are important for future, high-precision measurements coming from electromagnetic and gravitational wave observations and may be used in equation of state inference codes or gravitational wave modeling among others.

Figures (10)

• Figure 1: Scatter plot for the parameters $p_1$ and $\Gamma_2$ in the piecewise polytropic parametrization; the correlation coefficient is $-0.715$.
• Figure 2: Scatter plot for the parameters $K_1$ and $\Gamma_1$ of 320 randomly drawn equations of state in the generalised piecewise polytropic parametrization (after filtering for astrophysically relevant equations of state); the correlation coefficient is $-0.999916$.
• Figure 3: Visualisation of an exemplary sequence of constant central energy density (dashed, green) in a generic mass-radius diagram. Quantities belonging to the non-rotating model at $\Omega_n = 0$ are denoted with "$\star$", while Keplerian values at $\Omega_n = 1$ carry the subscript "$K$". The black line is the usual mass-radius curve of non-rotating neutron stars, the red line is the corresponding curve at the Kepler limit, the blue curve depicts the limit of quasi-radial instability, and the grey dashed line is our lower limit of $1.05\,M_\odot$. We do not show any labels on the axes as such diagrams are qualitatively identical for any equation of state.
• Figure 4: Corner plot of the dataset on which we construct the universal relations. Each black dot in the $M$ vs. $R_e$ diagram represents one of 998639 neutron star models in our dataset. Their density distribution is indicated by the red contour lines. The top and right diagram show the corresponding histograms of radius and mass using 100 bins, respectively.
• Figure 5: Scatter plot of the rescaled equatorial radius $R_{e,n}$ against the fractional angular rotation rate $\Omega_n$ for the 21383 sequences of stars in our dataset. As the graph shows a very large number of data points, we display an inset, in which we enlarge a small region of the graph; it becomes visible that the majority of the data points gather within $5\,\%$ (indicated by dashed grey lines, not shown in the main graph) of the polynomial fit (black solid line) and there are some with a larger deviation from the fit. The relative error for the equatorial radius $R_e$ is bounded by $1.3\,\%$; see the discussion in the main text for details.