Features

The library contains functions for computing properties of spherical neutron stars. It solves the TOV ODE as well as the ODE for tidal deformability. Models are specified by central density and the EOS (via the barotropic EOS interface). Basic support for finding models by mass or the maximum mass model is also implemented.

Any barotropic EOS can be used, including ones which are not adiabatic (for example, density-dependent arbitrary electron fraction or non-zero temperature). One can also employ EOS with phase transitions where the pressure remains constant over a density range and the soundspeed drops to zero. The TOV solver employs a formulation of the TOV equations suitable also for those cases.

The following global properties are computed:

  • Gravitational (ADM) mass \(M_g\)

  • Baryonic mass \(M_b\)

  • Circumferential surface radius \(R_c\)

  • Proper volume \(V_p\)

  • Moment of inertia \(I\)

  • Central internal energy \(\epsilon_c\), pressure \(P_c\), and sound speed \(c_{sc}\)

  • Dimensionless tidal deformability \(\Lambda\) and love number \(k_2\)

  • Properties of the “bulk” (optional, see below)

The metric can also be obtained. It is expressed as follows

\[\mathrm{d} s^2 = - e^{2\nu(r_c)} \mathrm{d} t^2 + e^{2\lambda(r_c)} \mathrm{d} r^2 + r_c^2 \mathrm{d} \Omega^2\]

The metric potentials \(\nu(r_c)\) and \(\lambda(r_c)\) and the matter state are provided as functions of circumferential radius \(r_c\).

The tidal deformability formalism is described in 12. Since the formalism assumes adiabatic perturbations, the tidal deformability is only computed for isentropic EOS, for example zero-temperature stars. The library uses a reformulation of the ODE in 2 that is well-behaved across phase transitions (currently undocumented).

The moment of inertia is defined in the slow-rotation approximation following 3. Finally, the library can also compute a relatively new definition of “bulk” properties from 4. This definition uses a sort of maximum compactness iso-density surface and can also be applied to systems without symmetry or surface, such as early merger remnants.

Warning

Strong phase transitions are allowed by design but they have not been considered during the calibration of the error bars.

References

1

Tanja Hinderer. Tidal Love Numbers of Neutron Stars. Astrophys. J., 677(2):1216–1220, April 2008. arXiv:0711.2420, doi:10.1086/533487.

2(1,2)

Sophia Han and Andrew W. Steiner. Tidal deformability with sharp phase transitions in binary neutron stars. Phys. Rev. D, 99(8):083014, April 2019. arXiv:1810.10967, doi:10.1103/PhysRevD.99.083014.

3

James B. Hartle. Slowly Rotating Relativistic Stars. I. Equations of Structure. Astrophys. J., 150:1005, December 1967. doi:10.1086/149400.

4

W. Kastaun, R. Ciolfi, and B. Giacomazzo. Structure of stable binary neutron star merger remnants: a case study. Phys. Rev. D, 94:044060, August 2016. arXiv:1607.02186, doi:10.1103/PhysRevD.94.044060.