Analytical Transit Light Curves for Arbitrary Power-Law Limb Darkening: A Unified Framework

Clicks: 1
ID: 314967
2026
Free PDF
Article Quality & Performance Metrics
Overall Quality
Not rated
Combines reader engagement with the AI quality analysis. This article has not been analysed, so there is no overall score — reader engagement is measured and shown alongside.
AI Quality Assessment
Not analyzed
Readership in this journal

Ranked #532 of 897 articles by views in monthly notices of the royal astronomical society

Most read Least read

Bar heights use a square-root scale. Only the 120 most-read articles are drawn; the journal has 897 in total.

Mint this article as an NFT
Not yet minted

Create a permanent, verifiable on-chain record of this article on the Scimatic Network. The NFT is held in your Journament account, and you can withdraw it to your own wallet at any time.

5 SUSD one-off · no wallet required
Sign in to mint
Abstract
Abstract We present a unified analytical framework for computing exoplanet transit light curves under arbitrary real power-law limb darkening I(μ) = I0μα, α > −2, eliminating the two-decade restriction to integer-polynomial forms. Our central result is an exact closed-form expression for the normalised stellar flux in terms of Appell’s bivariate hypergeometric function F1, valid for all real α and all geometric transit configurations. Three mutually equivalent formulations—a geometric kernel representation, a Riemann-Liouville fractional-calculus framework, and a hypergeometric-integrand representation—provide complementary physical insights and independent computational routes, with inter-method agreement at $|\Delta \mathcal {F}|\lesssim 10^{-17}$. The framework encompasses the square-root law (α = 1/2) essential for M-dwarf characterisation, half-integer powers required by Claret’s four-parameter law, and arbitrary real values enabling empirical fitting, while recovering integer-polynomial elliptic-integral expressions as special cases. Validation at 40-digit precision across five geometric regions and seven α values confirms a ∼104 × computational speedup over Monte Carlo integration and thirteen orders of magnitude accuracy advantage. Linear superposition enables exact treatment of arbitrary multi-parameter limb-darkening laws without special-case logic.
Reference Key
openalex_W7162412033 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors F A Chishtie, M I Saeed, S N Goderya
Journal monthly notices of the royal astronomical society
Year 2026
DOI
10.1093/mnras/stag830
URL
https://doi.org/10.1093/mnras/stag830
Keywords Keywords not found

Citations

No citations found. To add a citation, contact the admin at info@scimatic.org

Comments

No comments yet. Be the first to comment on this article.