The Impact of Errors in the Shape Function of Rotating Neutron Stars in the Oblate Schwarzschild Approximation

[2608.27744] The Impact of Errors in the Shape Function of Rotating Neutron Stars in the Oblate Schwarzschild Approximation Skip to main content Search Submit Donate Log in Astrophysics > High Energy Astrophysical Phenomena arXiv:2608.27744 (astro-ph) [Submitted on 27 Aug 2026 ( v1 ), last revised 16 Oct 2026 (this version, v2)] Title: The Impact of Errors in the Shape Function of Rotating Neutron Stars in the Oblate Schwarzschild Approximation Authors: John Ming Ngo , Charlee Amason , Sharon M. Morsink View PDF HTML (experimental) Abstract: Measurements of thermal X-ray flux emitted by neutron stars can constrain their radii and the equation of state of cold dense matter. Accurate flux modeling of rapidly rotating neutron stars requires an approximation for their oblate surface shape, usually given by a shape function. We examine the accuracy of five shape functions by comparing them against numerical relativistic stellar surfaces for seven representative equations of state over a broad range of compactness and spin. We characterize their errors in the surface radius and their derivative with respect to colatitude, test the extent of quasi-universality, and propagate these errors into the differential solid angle d{\Omega}, a geometric factor underlying the observed flux, under the oblate Schwarzschild approximation. We find that the shape functions produce distinct error patterns associated with their forms and parameter ranges. These errors remain structured in compactness, spin, and colatitude. Simple polynomial corrections substantially reduce the radius errors of several shape functions, with most corrected errors within approximately 0.5%. We show that errors in d{\Omega} may be understood as coming from an area contribution, which scales with twice the relative radius error, and a projection contribution controlled primarily by the error in the surface derivative. The projection contribution grows towards the limb, where small surface errors can produce much larger local errors in d{\Omega}. We provide a set of guidelines for the construction of improved quasi-universal shape functions that can be used in future radius estimation efforts. Our recommendations include that both the shape and its derivative be modeled accurately, that more accurate predictions of the polar radius be developed, and that the shape function be calibrated over the same compactness-spin range that is to be tested. Comments: Accepted by Physical Review D. This revision matches the accepted version Subjects: High Energy Astrophysical Phenomena (astro-ph.HE) Cite as: arXiv:2608.27744 [astro-ph.HE] (or arXiv:2608.27744v2 [astro-ph.HE] for this version) https://doi.org/10.48550/arXiv.2608.27744 Focus to learn more arXiv-issued DOI via DataCite Submission history From: John Ngo [ view email ] [v1] Thu, 27 Aug 2026 22:11:42 UTC (5,791 KB) [v2] Fri, 16 Oct 2026 21:25:45 UTC (5,767 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: astro-ph.HE < prev | next > new | recent | 2026-08 Change to browse by: astro-ph References & Citations INSPIRE HEP SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. 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