pycbc.neutron_stars package¶

pycbc.neutron_stars.eos_utils module¶

Utility functions for handling NS equations of state

pycbc.neutron_stars.eos_utils.foucart18(eta, ns_compactness, ns_b_mass, bh_spin_mag, bh_spin_pol)[source]

Function that determines the remnant disk mass of an NS-BH system using the fit to numerical-relativity results discussed in Foucart, Hinderer & Nissanke, PRD 98, 081501(R) (2018).

Parameters
• eta ({float, array}) – The symmetric mass ratio of the system (note: primary is assumed to be the BH).

• ns_compactness ({float, array}) – NS compactness parameter.

• ns_b_mass ({float, array}) – Baryonic mass of the NS.

• bh_spin_mag ({float, array}) – Dimensionless spin magnitude of the BH.

• bh_spin_pol ({float, array}) – The tilt angle of the BH spin.

pycbc.neutron_stars.eos_utils.initialize_eos(ns_mass, eos)[source]

Load an equation of state and return the compactness and baryonic mass for a given neutron star mass

Parameters
• ns_mass ({float, array}) – The mass of the neutron star, in solar masses.

• eos (str) – Name of the equation of state.

Returns

• ns_compactness (float) – Compactness parameter of the neutron star.

• ns_b_mass (float) – Baryonic mass of the neutron star.

pycbc.neutron_stars.eos_utils.interp_grav_mass_to_baryon_mass(ns_g_mass, ns_sequence)[source]

Determines the baryonic mass of an NS given its gravitational mass and an NS equilibrium sequence (in solar masses).

Parameters
• ns_g_mass (float) – NS gravitational mass (in solar masses)

• ns_sequence (numpy.array) – contains the sequence data in the form NS gravitational mass (in solar masses), NS baryonic mass (in solar masses), NS compactness (dimensionless)

Return type

float

pycbc.neutron_stars.eos_utils.interp_grav_mass_to_compactness(ns_g_mass, ns_sequence)[source]

Determines the dimensionless compactness parameter of an NS given its gravitational mass and an NS equilibrium sequence.

Parameters
• ns_g_mass (float) – NS gravitational mass (in solar masses)

• ns_sequence (numpy.array) – contains the sequence data in the form NS gravitational mass (in solar masses), NS baryonic mass (in solar masses), NS compactness (dimensionless)

Return type

float

Load the data of an NS non-rotating equilibrium sequence generated using the equation of state (EOS) chosen by the user. File format is: grav mass (Msun), baryonic mass (Msun), compactness

Parameters

eos_name (string) – NS equation of state label (‘2H’ is the only supported choice at the moment)

Returns

• ns_sequence (numpy.array) – contains the sequence data in the form NS gravitational mass (in solar masses), NS baryonic mass (in solar masses), NS compactness (dimensionless)

• max_ns_g_mass (float) – the maximum NS gravitational mass (in solar masses) in the sequence (this is the mass of the most massive stable NS)

pycbc.neutron_stars.pg_isso_solver module¶

Innermost Stable Spherical Orbit (ISSO) solver in the Perez-Giz (PG) formalism. See Stone, Loeb, Berger, PRD 87, 084053 (2013).

pycbc.neutron_stars.pg_isso_solver.ISCO_solution(chi, incl)[source]

Analytic solution of the innermost stable circular orbit (ISCO) for the Kerr metric.

..See eq. (2.21) of Bardeen, J. M., Press, W. H., Teukolsky, S. A. (1972) https://articles.adsabs.harvard.edu/pdf/1972ApJ…178..347B

Parameters
• chi (float) – the BH dimensionless spin parameter

• incl (float) – inclination angle between the BH spin and the orbital angular momentum in radians

Return type

float

pycbc.neutron_stars.pg_isso_solver.ISSO_eq_at_pole(r, chi)[source]

Polynomial that enables the calculation of the Kerr polar ($$\iota = \pm \pi / 2$$) innermost stable spherical orbit (ISSO) radius via the roots of

$\begin{split}P(r) &= r^3 [r^2 (r - 6) + \chi^2 (3 r + 4)] \\ &\quad + \chi^4 [3 r (r - 2) + \chi^2] \, ,\end{split}$

where $$\chi$$ is the BH dimensionless spin parameter. Physical solutions are between 6 and $$1 + \sqrt{3} + \sqrt{3 + 2 \sqrt{3}}$$.

Parameters
• r (float) – the radial coordinate in BH mass units

• chi (float) – the BH dimensionless spin parameter

Return type

float

pycbc.neutron_stars.pg_isso_solver.ISSO_eq_at_pole_dr(r, chi)[source]

Partial derivative of ISSO_eq_at_pole() with respect to r.

Parameters
• r (float) – the radial coordinate in BH mass units

• chi (float) – the BH dimensionless spin parameter

Return type

float

pycbc.neutron_stars.pg_isso_solver.ISSO_eq_at_pole_dr2(r, chi)[source]

Double partial derivative of ISSO_eq_at_pole() with respect to r.

Parameters
• r (float) – the radial coordinate in BH mass units

• chi (float) – the BH dimensionless spin parameter

Return type

float

pycbc.neutron_stars.pg_isso_solver.PG_ISSO_eq(r, chi, incl)[source]

Polynomial that enables the calculation of a generic innermost stable spherical orbit (ISSO) radius via the roots in $$r$$ of

$\begin{split}S(r) &= r^8 Z(r) + \chi^2 (1 - \cos(\iota)^2) \\ &\quad * [\chi^2 (1 - \cos(\iota)^2) Y(r) - 2 r^4 X(r)]\,,\end{split}$

where

$\begin{split}X(r) &= \chi^2 (\chi^2 (3 \chi^2 + 4 r (2 r - 3)) \\ &\quad + r^2 (15 r (r - 4) + 28)) - 6 r^4 (r^2 - 4) \, ,\end{split}$
$\begin{split}Y(r) &= \chi^4 (\chi^4 + r^2 [7 r (3 r - 4) + 36]) \\ &\quad + 6 r (r - 2) \\ &\qquad * (\chi^6 + 2 r^3 [\chi^2 (3 r + 2) + 3 r^2 (r - 2)]) \, ,\end{split}$

and $$Z(r) =$$ ISCO_eq(). Physical solutions are between the equatorial ISSO (i.e. the ISCO) radius (ISCO_eq()) and the polar ISSO radius (ISSO_eq_at_pole()). See Stone, Loeb, Berger, PRD 87, 084053 (2013).

Parameters
• r (float) – the radial coordinate in BH mass units

• chi (float) – the BH dimensionless spin parameter

• incl (float) – inclination angle between the BH spin and the orbital angular momentum in radians

Return type

float

pycbc.neutron_stars.pg_isso_solver.PG_ISSO_eq_dr(r, chi, incl)[source]

Partial derivative of PG_ISSO_eq() with respect to r.

Parameters
• r (float) – the radial coordinate in BH mass units

• chi (float) – the BH dimensionless spin parameter

• incl (float) – inclination angle between the BH spin and the orbital angular momentum in radians

Return type

float

pycbc.neutron_stars.pg_isso_solver.PG_ISSO_eq_dr2(r, chi, incl)[source]

Second partial derivative of PG_ISSO_eq() with respect to r.

Parameters
• r (float) – the radial coordinate in BH mass units

• chi (float) – the BH dimensionless spin parameter

• incl (float) – inclination angle between the BH spin and the orbital angular momentum in radians

Return type

float

pycbc.neutron_stars.pg_isso_solver.PG_ISSO_solver(chi, incl)[source]

Function that determines the radius of the innermost stable spherical orbit (ISSO) for a Kerr BH and a generic inclination angle between the BH spin and the orbital angular momentum. This function finds the appropriate root of PG_ISSO_eq()`.

Parameters
• chi ({float, array}) – the BH dimensionless spin parameter

• incl ({float, array}) – the inclination angle between the BH spin and the orbital angular momentum in radians

Returns

solution – the radius of the orbit in BH mass units

Return type

array