{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T18:33:34Z","timestamp":1772476414746,"version":"3.50.1"},"reference-count":36,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2019,9,16]],"date-time":"2019-09-16T00:00:00Z","timestamp":1568592000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001732","name":"Danish National Research Foundation","doi-asserted-by":"publisher","award":["DNRF106"],"award-info":[{"award-number":["DNRF106"]}],"id":[{"id":"10.13039\/501100001732","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["267864"],"award-info":[{"award-number":["267864"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"publisher","award":["FT1400147"],"award-info":[{"award-number":["FT1400147"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,11,21]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n               <jats:p>The characterization of stellar cores may be accomplished through the modelling of asteroseismic data from stars exhibiting either gravity-mode or mixed-mode pulsations, potentially shedding light on the physical processes responsible for the production, mixing, and segregation of chemical elements. In this work, we validate against model data an analytical expression for the period spacing that will facilitate the inference of the properties of stellar cores, including the detection and characterization of buoyancy glitches (strong chemical gradients). This asymptotically based analytical expression is tested both in models with and without buoyancy glitches. It does not assume that glitches are small and, consequently, predicts non-sinusoidal glitch-induced period-spacing variations, as often seen in model and real data. We show that the glitch position and width inferred from the fitting of the analytical expression to model data consisting of pure gravity modes are in close agreement (typically better than 7\u00a0${{\\ \\rm per\\ cent}}$ relative difference) with the properties measured directly from the stellar models. In the case of fitting mixed-mode model data, the same expression is shown to reproduce well the numerical results, when the glitch properties are known a priori. In addition, the fits performed to mixed-mode model data reveal a frequency dependence of the coupling coefficient, q, for a moderate-luminosity red-giant-branch model star. Finally, we find that fitting the analytical expression to the mixed-mode period spacings may provide a way to infer the frequencies of the pure acoustic dipole modes that would exist if no coupling took place between acoustic and gravity waves.<\/jats:p>","DOI":"10.1093\/mnras\/stz2582","type":"journal-article","created":{"date-parts":[[2019,9,13]],"date-time":"2019-09-13T15:30:29Z","timestamp":1568388629000},"page":"909-926","source":"Crossref","is-referenced-by-count":36,"title":["Analytical modelling of period spacings across the HR diagram"],"prefix":"10.1093","volume":"490","author":[{"given":"M S","family":"Cunha","sequence":"first","affiliation":[{"name":"Instituto de Astrof\u00edsica e Ci\u00eancias do Espa\u00e7o, Universidade do Porto, CAUP, Rua das Estrelas, PT4150-762 Porto, Portugal"},{"name":"School of Physics and Astronomy, University of Birmingham, Edgbaston Park Rd, Birmingham B15 2TT, UK"}]},{"given":"P P","family":"Avelino","sequence":"additional","affiliation":[{"name":"Instituto de Astrof\u00edsica e Ci\u00eancias do Espa\u00e7o, Universidade do Porto, CAUP, Rua das Estrelas, PT4150-762 Porto, Portugal"},{"name":"School of Physics and Astronomy, University of Birmingham, Edgbaston Park Rd, Birmingham B15 2TT, UK"},{"name":"Departamento de F\u00edsica e Astronomia, Faculdade de Ci\u00eancias, Universidade do Porto, Rua do Campo Alegre 687, PT4169-007 Porto, Portugal"}]},{"given":"J","family":"Christensen-Dalsgaard","sequence":"additional","affiliation":[{"name":"Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark"}]},{"given":"D","family":"Stello","sequence":"additional","affiliation":[{"name":"Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark"},{"name":"School of Physics, The University of New South Wales, Sydney, NSW 2052, Australia"},{"name":"Sydney Institute for Astronomy (SIfA), School of Physics, University of Sydney, Sydney, NSW 2006, Australia"}]},{"given":"M","family":"Vrard","sequence":"additional","affiliation":[{"name":"Instituto de Astrof\u00edsica e Ci\u00eancias do Espa\u00e7o, Universidade do Porto, CAUP, Rua das Estrelas, PT4150-762 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7614-1665","authenticated-orcid":false,"given":"C","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Physics and Astronomy, Sun Yat-Sen University, Haizhu, Guangzhou 510275, China"}]},{"given":"B","family":"Mosser","sequence":"additional","affiliation":[{"name":"LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universit\u00e9, Universit\u00e9 Paris Diderot, F-92195 Meudon, France"}]}],"member":"286","published-online":{"date-parts":[[2019,9,16]]},"reference":[{"key":"2019101007484172600_bib1","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4020-5803-5","volume-title":"Asteroseismology","author":"Aerts","year":"2010"},{"key":"2019101007484172600_bib2","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1146\/annurev-astro-091918-104359","volume":"57","author":"Aerts","year":"2019","journal-title":"ARA&A"},{"key":"2019101007484172600_bib3","first-page":"33","volume-title":"ESA SP-1306: The CoRoT Mission Pre-Launch Status - Stellar Seismology and Planet Finding","author":"Baglin","year":"2006"},{"key":"2019101007484172600_bib4","doi-asserted-by":"publisher","first-page":"2290","DOI":"10.1093\/mnras\/stv1738","volume":"453","author":"Bossini","year":"2015","journal-title":"MNRAS"},{"key":"2019101007484172600_bib5","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1086\/191668","volume":"80","author":"Brassard","year":"1992","journal-title":"ApJS"},{"key":"2019101007484172600_bib6","doi-asserted-by":"publisher","first-page":"1828","DOI":"10.1093\/mnras\/stu393","volume":"440","author":"Broomhall","year":"2014","journal-title":"MNRAS"},{"key":"2019101007484172600_bib7","doi-asserted-by":"publisher","first-page":"396","DOI":"10.1086\/169900","volume":"371","author":"Brown","year":"1991","journal-title":"ApJ"},{"key":"2019101007484172600_bib8","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1007\/s10509-007-9675-5","volume":"316","author":"Christensen-Dalsgaard","year":"2008","journal-title":"Ap&SS"},{"key":"2019101007484172600_bib9","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1007\/s10509-007-9689-z","volume":"316","author":"Christensen-Dalsgaard","year":"2008","journal-title":"Ap&SS"},{"key":"2019101007484172600_bib10","first-page":"503","volume-title":"ASP Conf. 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