Efficient solution of the anisotropic spherically aligned axisymmetric Jeans equations of stellar hydrodynamics for galactic dynamics
Open accessAbstract
I present a flexible solution for the axisymmetric Jeans equations of stellar hydrodynamics under the assumption of an anisotropic (three-integral) velocity ellipsoid aligned with the spherical polar coordinate system. I describe and test a robust and efficient algorithm for its numerical computation. I outline the evaluation of the intrinsic velocity moments and the projection of all first and second velocity moments, including both the line-of-sight velocities and the proper motions. This spherically aligned Jeans anisotropic modelling (JAMsph) method can describe in detail the photometry and kinematics of real galaxies. It allows for a spatially varying anisotropy, or stellar mass-to-light ratio gradients, as well as for the inclusion of general dark matter distributions and supermassive black holes. The JAMsph method complements my previously derived cylindrically aligned JAMcyl and spherical Jeans solutions, which I also summarize in this paper. Comparisons between results obtained with either JAMsph or JAMcyl can be used to assess the robustness of inferred dynamical quantities. As an illustration, I modelled the ATLAS3D sample of 260 early-type galaxies with high-quality integral-field spectroscopy, using both methods. I found that they provide statistically indistinguishable total density logarithmic slopes. This may explain the previously reported success of the JAM method in recovering density profiles of real or simulated galaxies. A reference software implementation of JAMsph is included in the publicly available jam software package.
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JAM models with spherical and cylindrical alignment have been found to generally agree.
“As noted in Birrer et al. [65], JAM models with spherical and cylindrical alignment have been found to generally agree [72, 73], and both Shajib et al. [62], Birrer et al. [65] use the spherical alignment in joint models of lensing and dynamics.”
From Constraint on dark matter self-interaction from combined strong lensing and stellar kinematics in MACS J0138-2155 (2026) · cites this paper as [72]
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Python for scientific computing
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O’Donnell, J. H., Jeltema, T. E., Roberts, M. G., Nightingale, J., Flowers, A., & Aldas, D. (2026) · Physical Review D · doi:10.1103/hfgd-245k · Cited by 5 · see citing works
- Authors
- Cappellari, M.
- Affiliations
- University of Oxford (GB)
- Corresponding author
- Cappellari, Michele
- ORCID
- Cappellari, Michele
- Venue
- Monthly Notices of the Royal Astronomical Society
- Publisher
- Oxford University Press (OUP)
- Published
- 2020-04-09
- Volume
- 494
- Issue
- 4
- Pages
- 4819-4837
- ISSN
- 0035-8711 (ISSN-L)
- 1365-2966
- OpenAlex
- W2962960908
- Cited by
- 94
- References
- 1
- Citations by year
- 2026: 15 · 2025: 27 · 2024: 15 · 2023: 16 · 2022: 6 · 2021: 8 · 2020: 6 · 2019: 1
- FWCI
- 3.98
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
- Locations
- Monthly Notices of the Royal Astronomical Society (publishedVersion)
- Oxford University Research Archive (ORA) (University of Oxford) (acceptedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Galaxies: Formation, Evolution, Phenomena
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Stellar, planetary, and galactic studies
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Astrophysical Phenomena and Observations
- Keywords
- stellar hydrodynamics, galaxy dynamics, velocity moments, radial velocity, proper motions, dark matter distribution, supermassive black holes, early-type galaxies, integral field spectroscopy, ATLAS3D, galaxy density profiles
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