ell1_truncation_error

ell1fit.phase_utils.ell1_truncation_error(EPS1, EPS2, A1, F0)[source]

Phase error, in cycles, from ELL1 truncating the orbit at O(e**2).

ELL1 expands the Roemer delay in eccentricity; this package carries the O(e**2) terms, so what remains scales as \(e^3\). The residual lives almost entirely in the 3 Phi harmonics, which are orthogonal to every direction the model can move in – so exceeding this costs sensitivity, through unmodelled structure smearing the profile, rather than biasing the recovered eccentricity. At e = 0.01 the recovered e is biased by only 2.7e-5 relative, some three orders of magnitude below its statistical error.

Parameters:
EPS1, EPS2float

Laplace-Lagrange parameters; only their quadrature sum matters.

A1float

Projected semi-major axis, light-seconds.

F0float

Spin frequency, Hz.

Returns:
float

RMS phase error in cycles. Compare it against the precision the data support; ell1fit.pipeline._warn_on_eccentric_orbit() does.

Examples

>>> round(ell1_truncation_error(1.2e-3, -1.6e-3, 22.215, 7.5), 10)
3.15e-07