gcfit.probabilities.pulsars.cluster_component#
- gcfit.probabilities.pulsars.cluster_component(model, R, mass_bin, DM=None, ΔDM=None, DM_mdata=None, *, eps=0.001)#
Compute the “cluster” component over LOS accelerations at a radius R.
Given a model, computes the probability distribution of (line-of-sight) accelerations in the cluster at a projected distance R from the cluster centre (representing a pulsar’s position), which provides the key component in computing the pulsar likelihoods.
The cluster acceleration component is complicated by the fact that the 3D position of the pulsar cannot be easily determined, and the line-of-sight position of the pulsar within the cluster potential well is unknown, and therefore an entire probability distribution is required, in contrast to the Shklovskii and galactic components.
- Parameters:
- modelgcfit.Model
Cluster model used to compute the acceleration probability distribution.
- Ru.Quantity
The projected radius from the cluster centre of a given pulsar. Cannot be outside of the cluster tidal radius model.rt.
- mass_binint
The mass bin index to use for this given pulsar. Likely to be that of a tracer mass bin.
- DM, ΔDMfloat, optional
If DM measurements are known for a given pulsar, can attempt to discern it’s line-of-sight position in the cluster using them. See los_dm for more details.
- DM_mdatadict, optional
If DM is given, a dictionary of corresponding metadata must also be supplied. See los_dm for more details.
- epsfloat, optional
Optionally change the normalization epsilon stop condition. Defaults to 1e-3.
- Returns:
- PdotP_domainu.Quantity
Array containing the Pdot-P domain of the probability distribution computed.
- P_PdotP_distu.Quantity
Array containing the P-Pdot probability distribution of this model at the given R.
Notes
The probability distribution of the cluster component of acceleration (or Pdot-P) is given by the simple relation:
\[P(a_{\hat{z}}|z) = \frac{dm}{da(z)} = \frac{dm}{dz} \frac{dz}{da(z)} = \frac{\rho(z)}{\left| \frac{da(z)}{dz} \right|}\]