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A sparse regression approach to modelling the relation between galaxy stellar masses and their host haloes

Icaza-Lizaola, M; Bower, Richard G; Norberg, Peder; Cole, Shaun; Schaller, Matthieu; Egan, Stefan

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M Icaza-Lizaola

Richard G Bower

Matthieu Schaller

Stefan Egan


Sparse regression algorithms have been proposed as the appropriate framework to model the governing equations of a system from data, without needing prior knowledge of the underlying physics. In this work, we use sparse regression to build an accurate and explainable model of the stellar mass of central galaxies given properties of their host dark matter (DM) halo. Our data set comprises 9521 central galaxies from the EAGLE hydrodynamic simulation. By matching the host haloes to a DM-only simulation, we collect the halo mass and specific angular momentum at present time and for their main progenitors in 10 redshift bins from z = 0 to z = 4. The principal component of our governing equation is a third-order polynomial of the host halo mass, which models the stellar-mass–halo-mass relation. The scatter about this relation is driven by the halo mass evolution and is captured by second- and third-order correlations of the halo mass evolution with the present halo mass. An advantage of sparse regression approaches is that unnecessary terms are removed. Although we include information on halo specific angular momentum, these parameters are discarded by our methodology. This suggests that halo angular momentum has little connection to galaxy formation efficiency. Our model has a root mean square error (RMSE) of 0.167log10(M*/M⊙), and accurately reproduces both the stellar mass function and central galaxy correlation function of EAGLE. The methodology appears to be an encouraging approach for populating the haloes of DM-only simulations with galaxies, and we discuss the next steps that are required.


Icaza-Lizaola, M., Bower, R. G., Norberg, P., Cole, S., Schaller, M., & Egan, S. (2021). A sparse regression approach to modelling the relation between galaxy stellar masses and their host haloes. Monthly Notices of the Royal Astronomical Society, 507(3), 4584-4602.

Journal Article Type Article
Acceptance Date Aug 12, 2021
Online Publication Date Aug 19, 2021
Publication Date 2021-11
Deposit Date Nov 23, 2021
Publicly Available Date Nov 24, 2021
Journal Monthly Notices of the Royal Astronomical Society
Print ISSN 0035-8711
Electronic ISSN 1365-2966
Publisher Royal Astronomical Society
Peer Reviewed Peer Reviewed
Volume 507
Issue 3
Pages 4584-4602


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Copyright Statement
© The Author(s) 2021.<br /> Published by Oxford University Press on behalf of Royal Astronomical Society. This is an Open Access article distributed under the terms of the Creative<br /> Commons Attribution License (, which permits unrestricted reuse, distribution, and reproduction in any medium,<br /> provided the original work is properly cited.

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