Offset Functions

This doc describes the offset functions that are coded in astropath. A future refactor will allow for user-supplied functions.

In our formalism, the offset function is written as \(p(\omega|O)\) and it describes the true distribution of the transient within its host galaxy.


Here are the key items related to \(p(\omega|O)\):

  • \(\omega\): 3-D true position of the transient

  • \(O\): galaxy properties (e.g. position, angular size)

  • \(\theta\): offset between the transient and the center of a galaxy.

  • \(\phi\): galaxy angular size

  • \(\theta_{max}\): the maximum separation between the transient and the galaxy allowed in units of \(\phi\). \(p(\omega|O) = 0\) for \(\theta > \theta_{max}\)


The code base uses a dict named theta_prior to handle the offset function. It currently holds three items:

  • method – A string defining the method used. core, uniform, exp

  • max – \({\theta_{max}}\) in units of \(\phi\). \(p(\omega|O) = 0\) for \(\theta > \theta_{max}\)

  • ang_size – An array of angular sizes \(\phi\) for all of the candidate galaxies.

Below are the 3 offset functions currently coded. Note that each of these are normalized to unit total probabilty when integrated over the full sphere.


Here, \(p(\omega|O)\) is given equal weighting for all locations with \(\theta < \theta_{max}\).


Here, \(p(\omega|O)\) is proportional to \(\phi / (\theta + \phi)\)


Here, \(p(\omega|O)\) is proportional to \((\theta/\phi) \, \exp [-(\theta/\phi)]\)