pint.derived_quantities.gamma
- pint.derived_quantities.gamma(mp: Unit('solMass'), mc: Unit('solMass'), pb: Unit('d'), e: Unit(dimensionless))[source]
Post-Keplerian time dilation and gravitational redshift gamma, assuming general relativity.
gamma (\(\gamma\)) is the amplitude of the modification in arrival times caused by the varying gravitational redshift of the companion and time dilation in an elliptical orbit. The time delay is \(\gamma \sin E\), where \(E\) is the eccentric anomaly. Can handle scalar or array inputs.
- Parameters:
mp (astropy.units.Quantity) – pulsar mass
mc (astropy.units.Quantity) – companion mass
pb (astropy.units.Quantity) – Binary orbital period
e (astropy.units.Quantity or float) – orbital eccentricity
- Returns:
gamma – in
u.s- Return type:
- Raises:
astropy.units.UnitsError – If the input data are not appropriate quantities
TypeError – If the input data are not quantities
Notes
Calculates
\[\gamma = T_{\odot}^{2/3} \left(\frac{P_b}{2\pi}\right)^{1/3} e \frac{m_c(m_p+2m_c)}{(m_p+m_c)^{4/3}}\]with \(T_\odot = GM_\odot c^{-3}\).
More details in Timing Models. Also see [6]