gcfit.probabilities.likelihood_pm_tot

gcfit.probabilities.likelihood_pm_tot(model, pm, *, mass_bin=None, hyperparams=False)

Compute the loglikelihood of the cluster total proper motion dispersion.

Computes the log likelihood component of a cluster’s proper motion dispersion profile for the total proper motion, that is, the combined radial and tangential components, assuming a gaussian likelihood.

Parameters:

modelgcfit.FittableModel

Cluster model used to compute probability distribution.

pmgcfit.core.data.Dataset

Proper motion dispersions profile dataset used to compute probability distribution and evaluate log likelihood.

mass_binint, optional

Index of model.mj mass bin to use in all calculations. If None (default), attempts to read ‘m’ from pulsars.mdata, else uses largest of the main sequence bins, given by model.nms.

hyperparamsbool, optional

Whether to include bayesian hyperparameters.

Returns:

float

Log likelihood value.

Notes

The “total” combined proper motion is given by the averaged vector:

\[PM_{tot} = \sqrt{\frac{(PM_{T}^2 + PM_{R}^2)}{2}}\]