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The weak lensing radial acceleration relation: Constraining modified gravity and cold dark matter theories with KiDS-1000

Brouwer, Margot M.; Oman, Kyle A.; Valentijn, Edwin A.; Bilicki, Maciej; Heymans, Catherine; Hoekstra, Henk; Napolitano, Nicola R.; Roy, Nivya; Tortora, Crescenzo; Wright, Angus H.; Asgari, Marika; van den Busch, Jan Luca; Dvornik, Andrej; Erben, Thomas; Giblin, Benjamin; Graham, Alister W.; Hildebrandt, Hendrik; Hopkins, Andrew M.; Kannawadi, Arun; Kuijken, Konrad; Liske, Jochen; Shan, HuanYuan; Tröster, Tilman; Verlinde, Erik; Visser, Manus

The weak lensing radial acceleration relation: Constraining modified gravity and cold dark matter theories with KiDS-1000 Thumbnail


Margot M. Brouwer

Edwin A. Valentijn

Maciej Bilicki

Catherine Heymans

Henk Hoekstra

Nicola R. Napolitano

Nivya Roy

Crescenzo Tortora

Angus H. Wright

Marika Asgari

Jan Luca van den Busch

Andrej Dvornik

Thomas Erben

Benjamin Giblin

Alister W. Graham

Hendrik Hildebrandt

Andrew M. Hopkins

Arun Kannawadi

Konrad Kuijken

Jochen Liske

HuanYuan Shan

Tilman Tröster

Erik Verlinde

Manus Visser


We present measurements of the radial gravitational acceleration around isolated galaxies, comparing the expected gravitational acceleration given the baryonic matter (gbar) with the observed gravitational acceleration (gobs), using weak lensing measurements from the fourth data release of the Kilo-Degree Survey (KiDS-1000). These measurements extend the radial acceleration relation (RAR), traditionally measured using galaxy rotation curves, by 2 decades in gobs into the low-acceleration regime beyond the outskirts of the observable galaxy. We compare our RAR measurements to the predictions of two modified gravity (MG) theories: modified Newtonian dynamics and Verlinde’s emergent gravity (EG). We find that the measured relation between gobs and gbar agrees well with the MG predictions. In addition, we find a difference of at least 6σ between the RARs of early- and late-type galaxies (split by Sérsic index and u − r colour) with the same stellar mass. Current MG theories involve a gravity modification that is independent of other galaxy properties, which would be unable to explain this behaviour, although the EG theory is still limited to spherically symmetric static mass models. The difference might be explained if only the early-type galaxies have significant (Mgas ≈ M⋆) circumgalactic gaseous haloes. The observed behaviour is also expected in Λ-cold dark matter (ΛCDM) models where the galaxy-to-halo mass relation depends on the galaxy formation history. We find that MICE, a ΛCDM simulation with hybrid halo occupation distribution modelling and abundance matching, reproduces the observed RAR but significantly differs from BAHAMAS, a hydrodynamical cosmological galaxy formation simulation. Our results are sensitive to the amount of circumgalactic gas; current observational constraints indicate that the resulting corrections are likely moderate. Measurements of the lensing RAR with future cosmological surveys (such as Euclid) will be able to further distinguish between MG and ΛCDM models if systematic uncertainties in the baryonic mass distribution around galaxies are reduced.


Brouwer, M. M., Oman, K. A., Valentijn, E. A., Bilicki, M., Heymans, C., Hoekstra, H., …Visser, M. (2021). The weak lensing radial acceleration relation: Constraining modified gravity and cold dark matter theories with KiDS-1000. Astronomy & Astrophysics, 650, Article A113.

Journal Article Type Article
Acceptance Date Apr 12, 2021
Online Publication Date Jun 22, 2021
Publication Date 2021-06
Deposit Date Aug 19, 2021
Publicly Available Date Aug 19, 2021
Journal Astronomy and astrophysics.
Print ISSN 0004-6361
Electronic ISSN 1432-0746
Publisher EDP Sciences
Peer Reviewed Peer Reviewed
Volume 650
Article Number A113


Published Journal Article (4.4 Mb)

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Copyright Statement
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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