pint.derived_quantities.pulsar_mass

pint.derived_quantities.pulsar_mass(pb: Unit('d'), x: Unit('cm'), mc: Unit('solMass'), i: Unit('deg'))[source]

Compute pulsar mass from orbital parameters

Return the pulsar mass (in solar mass units) for a binary. Can handle scalar or array inputs.

Parameters:

pb (astropy.units.Quantity) – Binary orbital period
x (astropy.units.Quantity) – Projected pulsar semi-major axis (aka ASINI) in pint.ls
mc (astropy.units.Quantity) – Companion mass in u.solMass
i (astropy.coordinates.Angle or astropy.units.Quantity) – Inclination angle, in u.deg or u.rad

Returns:

mass – In u.solMass

Return type:

astropy.units.Quantity

Raises:

astropy.units.UnitsError – If the input data are not appropriate quantities
TypeError – If the input data are not quantities

Example

>>> import pint
>>> import pint.derived_quantities
>>> from astropy import units as u
>>> print(pint.derived_quantities.pulsar_mass(2*u.hr, .2*pint.ls, 0.5*u.Msun, 60*u.deg))
7.6018341985817885 solMass

Notes

This forms a quadratic equation of the form: \(a M_p^2 + b M_p + c = 0`\)

with:

\(a = f(P_b,x)\) (the mass function)
\(b = 2 f(P_b,x) M_c\)
\(c = f(P_b,x) M_c^2 - M_c\sin^3 i\)

except the discriminant simplifies to: \(4f(P_b,x) M_c^3 \sin^3 i\)

solve it directly this has to be the positive branch of the quadratic because the vertex is at \(-M_c\), so the negative branch will always be < 0