gcfit.probabilities.likelihood_pulsar_spin

gcfit.probabilities.likelihood_pulsar_spin(model, pulsars, Pdot_kde, cluster_μ, coords, use_DM=False, *, mass_bin=None, hyperparams=False)

Compute the loglikelihood of pulsar spin period derivatives.

Computes the log likelihood component of a cluster’s pulsar’s spin period derivatives, evaluating the observed pulsar timing solutions against the combined probability distributions of the clusters acceleration field, the pulsars intrinsic spin-down, the proper-motion contribution and the galactic potential.

Parameters:

modelgcfit.FittableModel

Cluster model used to compute probability distribution.

pulsarsgcfit.core.data.Dataset

Pulsars dataset used to compute probability distribution and evaluate log likelihood.

Pdot_kdescipy.stats.gaussian_kde

Gaussian KDE of the galactic field pulsars Pdot-P distribution, from field_Pdot_KDE. Should be generated beforehand for speed, but if None, will generate at runtime.

cluster_μfloat

Total cluster proper motion, in mas/yr.

coords2-tuple of float

Cluster Galactic (Latitude, Longitude), in degrees.

use_DMbool, optional

Whether to use dispersion measure data in pulsar likelihoods.

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 -1.

hyperparamsbool, optional

Not implemented.

Returns:

float

Log likelihood value.

See also

likelihood_pulsar_orbital

Binary pulsar orbital period likelihood.

gcfit.probabilities.pulsars

Module containing all pulsar prob. components.

Notes

The combined timing solutions for pulsars embedded in clusters, which is used alongside the model acceleration field to compute this likelihood, is given by the combination of components:

\[\left(\frac{\dot{P}}{P}\right)_{\rm{obs}} = \left(\frac{\dot{P}}{P}\right)_{\rm{int}} + \frac{a_{\rm{clust}}}{c} + \frac{a_{\rm{gal}}}{c} + \frac{\mu^2 D}{c}\]