Companion Limits

This module is designed for computing mass upper-limits on potential unseen companions of singly-transiting planets.

Module for computing upper limits on the mass of any unseen companions to an observed singly-transiting planet.

ttv2fast2furious.companion_limits.PerturberPeriodPhaseToBestSigmaChiSquared(Ppert, phi, TransitObservations, PlanetData=None, full_output=False)[source]

Convert a hypothetical perturber period and phase to a mean and std. deviation of a gaussian distribution describing the perturber mass conditional posterior.

Parameters:
  • Ppert (real) – Period of the pertuber
  • phi (real) – Orbital phase of perturber
  • TransitData (PlanetTransitObservations) – Observation data on transiting planet.
  • PlanetData (list of reals (optional)) – List containing transiting planet’s T0 and Period.
  • full_output (bool (optional)) –
    Include a dictionary in the function output that contains
    the full best fit, covariance matrix, design matrix, and weighted observations vector.
Returns:

results – Returns the best-fit mass, mass distribution ‘sigma’ and the chi-squared of the timing residuals.
Return type:

tuple
ttv2fast2furious.companion_limits.UnseenPerturberMassUpperLimit(Ppert, confidence_levels, TransitObservations, Nphi=50, Mmax0=0.003, PlanetData=None)[source]

Compute mass upper limit(s) on a potential perturber at a given orbital period using transit data. Marginalizes over possible orbital phases of the perturber.

Parameters:
  • Ppert (real) – The orbital period of the hypothetical perturbing planet
  • confidence_levels (array-like) – The confidence level(s) for which to return mass upper limits.
  • TransitObservations (PlanetTransitObservations) – Observation data on transiting planet
  • Nphi (int (optional)) – Number of perturber phase points used to compute integrals for marginalizing over phase. Default value is Nphi=50.
  • Mmax0 (real (optional)) – Initial guess of mass upper limit for root-finding purposes. All mass upper-limits are guessed to fall between 0 and Mmax0.
  • PlanetData (list (optional)) –
    List containing [T0,P] where T0 is the initial transit time and P is period
    of the traniting planet. If these values are not supplied they are computed from the transit data.
Returns:

limits – List of mass upper limits and the given confidence levels.
Return type:

array-like
ttv2fast2furious.companion_limits.q_integrand(mup, mbest, sigma)[source]

Compute the value of the integrand in the integral over phase that determines q(m).

Parameters:
  • mup (real) – The mass upper limit for which q is being computed
  • mbest (real) – The best-fit mass (mhat) which sets the mean of the gaussian mass distribution. Depends on phase phi.
  • sigma (real) – The std. deviation parameter of the gaussian mass distribution. Depends on phase phi.
Returns:

The value of the integrand
Return type:

real