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Statistical Topology and the Random Interstellar Medium

Lookup NU author(s): Professor Robin Henderson, Dr Irina Makarenko, Professor Paul BushbyORCiD, Dr Andrew Fletcher, Professor Anvar ShukurovORCiD



This is the authors' accepted manuscript of an article that has been published in its final definitive form by Taylor and Francis, 2020.

For re-use rights please refer to the publisher's terms and conditions.


We use topological methods to investigate the small-scale variation and local spatial characteristics of the interstellar medium in three regions of the southern sky. We demonstrate that there are circumstances where topological methods can identify differences in distributions when conventional marginal or correlation analyses may not. We propose a non-parametric method for comparing two fields based on the counts of topological features and the geometry of the associated persistence diagrams. We investigate the expected distribution of topological structures quantified through Betti numbers under Gaussian random field assumptions, which underlie many astrophysical models of the interstellar medium. When we apply the methods to the astrophysical data, we find strong evidence that one of the three regions is both topologically dissimilar to the other two and not consistent with an underlying Gaussian random field model. This region is proximal to a region of recent star formation whereas the others are more distant.

Publication metadata

Author(s): Henderson R, Makarenko I, Bushby P, Fletcher A, Shukurov A

Publication type: Article

Publication status: Published

Journal: Journal of the American Statistical Association

Year: 2020

Volume: 115

Issue: 530

Pages: 625-635

Print publication date: 29/08/2019

Online publication date: 25/07/2019

Acceptance date: 22/07/2019

Date deposited: 30/08/2019

ISSN (print): 0162-1459

ISSN (electronic): 1537-274X

Publisher: Taylor and Francis


DOI: 10.1080/01621459.2019.1647841


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Funder referenceFunder name
RPG-2014-427Leverhulme Trust, The