StructureFunction

Efficient computation of structure functions for astronomical data with errors.

Structure functions

I follow the definitions laid out by Haverkorn et al. 2004. Whilst structure functions can be computed for any value on a sparse grid, here I focus on rotation meaures (RM) from astronomical sources. As such, data points are distributed on a spherical surface.

The second-order structure function of RM is given by:

$$SF_{\text{RM},\text{obs}}(\delta\theta) = \langle[\text{RM}{(\theta)} - \text{RM}{(\theta + \delta\theta)}]^2\rangle$$

That is, the ensemble average of the squared-difference in RM for sources with angular seperation $\delta\theta$. We also need to correct for the impact of errors by:

$$SF_{\text{RM}}(\delta\theta) = SF_{\text{RM},\text{obs}}(\delta\theta) - SF_{\sigma_\text{RM}}(\delta\theta)$$

Computing the error on the structure function is diffifcult. Here I use Monte-Carlo error propagation to compute the errors numerically.

I provide the ability to fit a broken power-law to the data using both standard least-squares, and full-blown MCMC fitting powered by bilby.

Documentation

The documentation is available here.

Installation

To get the latest version from this repo

pip install git+https://github.com/AlecThomson/structurefunction

Or, install from PyPi

pip install structurefunction

Usage

See the notebook included in the examples. There I repoduce the results of Mao et al. 2010.