Efficient computation of structure functions for astronomical data with errors.

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:

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:

Computing the error on the structure function is difficult. 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.

The documentation is available here.

To get the latest version from this repo

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

Or, install from PyPi

pip install structurefunction

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

If you use this software in your research, please cite the associated CSIRO software collection:

Thomson, Alec (2024): StructureFunction. v1. CSIRO. Software Collection. https://doi.org/10.25919/dkwn-mg50

MIT.