gcfit.probabilities.likelihood_pm_ratio

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

Compute the loglikelihood of the cluster proper motion dispersion ratio.

Computes the log likelihood component of a cluster’s proper motion dispersion anisotropy profile as the ratio of the tangential to radial dispersions, 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 proper motion ratio, or anisotropy measure, is given by the fraction:

\[PM_{ratio} = \sqrt{\frac{PM_{T}^2}{PM_{R}^2}}\]