get_t_merge_ecc

legwork.evol.get_t_merge_ecc(ecc_i, a_i=None, f_orb_i=None, beta=None, m_1=None, m_2=None, small_e_tol=0.15, large_e_tol=0.9999, exact=True)

Computes the merger time for binaries

This function implements Peters (1964) Eq. 5.10, 5.14 and the two unlabelled equations after 5.14 (using a different one depending on the eccentricity of each binary)

Parameters

ecc_ifloat/array

Initial eccentricity (if ecc_i is known to be 0.0 then use get_t_merge_circ instead)

a_ifloat/array

Initial semi-major axis (if supplied f_orb_i is ignored)

f_orb_ifloat/array

Initial orbital frequency (required if a_i is None)

betafloat/array

Constant defined in Peters and Mathews (1964) Eq. 5.9. See legwork.utils.beta() (if supplied m_1 and m_2 are ignored)

m_1float/array

Primary mass (required if beta is None)

m_2float/array

Secondary mass (required if beta is None)

small_e_tolfloat

Eccentricity below which to apply the small e approximation (see first unlabelled equation following Eq. 5.14 of Peters 1964), defaults to 0.15 to keep relative error below approximately 2%

large_e_tolfloat

Eccentricity above which to apply the large e approximation (see second unlabelled equation following Eq. 5.14 of Peters 1964), defaults to 0.9999 to keep relative error below approximately 2%

exactboolean

Whether to calculate the merger time exactly with numerical integration or to instead use the fit from Mandel 2021 (see legwork.evol.t_merge_mandel_fit())

Returns

t_mergefloat/array

Merger time