Last stable orbit around rapidly rotating neutron stars

We compute the binding energy and angular momentum of a test particle at the last stable circular orbit (LSO) on the equatorial plane around a general relativistic, rotating neutron star (NS). We present simple, analytic, but accurate formulas for these quantities that fit the numerical results and which can be used in several astrophysical applications. We demonstrate the accuracy of these formulas for three different equations of state (EOS) based on nuclear relativistic mean-field theory models and argue that they should remain still valid for any NS EOS that satisfy current astrophysical constraints. We compare and contrast our numerical results with the corresponding ones for the Kerr metric characterized by the same mass and angular momentum.

Figure 1

Mass-radius relation for nonrotating NSs for the three EOS NL3 (green solid curve), TM1 (red dashed curve) and GM1 (blue dotted-dashed curve) used in this work. The gray dashed horizontal line shows the mass of the heaviest NS observed, PSR $\mathrm{J}0348+0432$, $M=2.01\pm 0.04M_{\odot }$ [28].

Figure 2

Mass versus central density of uniformly rotating NSs with the GM1 EOS. The region of stability is bounded by the nonrotating sequence (solid red curve), the maximally rotating models (solid green curve), namely the mass-shedding limit or Keplerian sequence, and the secular axisymmetric stability limit (solid black curve). The dashed curve corresponds to configurations for which the LSO of corotating particles equals the NS equatorial radius: configurations on the right side of it possess an LSO exterior to their surface while configurations on the left side of the curve, have stable circular orbits down to the NS surface. Analogously, the dashed-dotted curve corresponds to configurations for which the LSO of counter-rotating particles equals the NS equatorial radius: configurations above it possess an LSO exterior to their surface while, configurations below it, have stable circular orbits down to the NS surface.

Figure 3

Binding energy ($E_{\mathrm{bind}}/\mu \equiv 1-\tilde{E}$) of corotating test particles in the LSO for constant mass sequences of NS configurations versus the dimensionless angular momentum $a/M=cJ/(G{M}^2)$. We compare and contrast our results with the values given by the Schwarzschild and Kerr solutions. In this example the NSs obey the GM1 EOS.

Figure 4

Dimensionless angular momentum ($|L|/(\mu M)$) of corotating test particles in the LSO for constant mass sequences of NS configurations versus the dimensionless angular momentum $a/M=cJ/(G{M}^2)$. We compare and contrast our results with the values given by the Schwarzschild and Kerr solutions. In this example the NSs obey the GM1 EOS.

Figure 5

Same as Fig. 3 but for counter-rotating orbits.

Figure 6

Same as Fig. 6 but for counter-rotating orbits.

Figure 7

Maximum error (in percentage) of Eqs. (19) and (20) with respect to the numerical value of $\tilde{E}$ and $\tilde{L}$ for the sequences of constant gravitational mass in the range $2–3.4M_{\odot }$. The results for corotating orbits are shown in the left upper and lower panels and for counter-rotating ones in the right upper and lower ones.