dc.contributor.author Lilley, Edward dc.contributor.author Sanders, Jason dc.contributor.author Evans, Wyn dc.date.accessioned 2018-09-08T06:31:00Z dc.date.available 2018-09-08T06:31:00Z dc.date.issued 2018-07 dc.identifier.issn 0035-8711 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/279806 dc.description.abstract Biorthonormal basis function expansions are widely used in galactic dynamics, both to study problems in galactic stability and to provide numerical algorithms to evolve collisionless stellar systems. They also provide a compact and efficient description of the structure of numerical dark matter haloes in cosmological simulations. We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley, Sanders, Evans & Erkal expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the $\gamma$ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding further examples. In the process, we also uncovered a novel integral transform solution to Poisson's equation. dc.publisher Oxford University Press (OUP) dc.rights Publisher's own licence dc.title A two-parameter family of double-power-law biorthonormal potential-density expansions dc.type Article prism.endingPage 1291 prism.issueIdentifier 1 prism.publicationDate 2018 prism.publicationName Monthly Notices of the Royal Astronomical Society prism.startingPage 1281 prism.volume 478 dc.identifier.doi 10.17863/CAM.27176 dcterms.dateAccepted 2018-04-21 rioxxterms.versionofrecord 10.1093/MNRAS/STY1038 rioxxterms.licenseref.uri http://www.rioxx.net/licenses/all-rights-reserved rioxxterms.licenseref.startdate 2018-07-21 dc.contributor.orcid Sanders, Jason [0000-0003-4593-6788] dc.contributor.orcid Evans, Wyn [0000-0002-5981-7360] dc.identifier.eissn 1365-2966 dc.publisher.url http://dx.doi.org/10.1093/mnras/sty1038 rioxxterms.type Journal Article/Review pubs.funder-project-id Science and Technology Facilities Council (ST/N000927/1) pubs.funder-project-id Science and Technology Facilities Council (1788901) cam.issuedOnline 2018-05-11
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