Solar active region scaling laws revisited

¹ Dept. of Astronomy, Institute of Physics and Astronomy, ELTE Eötvös Loránd University, Budapest, Hungary
² Gyula Bay Zoltán Solar Observatory (GSO), Hungarian Solar Physics Foundation (HSPF), Gyula, Hungary
³ Solar Physics and Space Plasma Research Centre, School of Mathematical and Physical Sciences, University of Sheffield, UK
⁴ School of Space and Earth Sciences, Beihang University, Beijing, PR China
⁵ Key Laboratory of Space Environment Monitoring and Information Processing of MIIT, Beijing, PR China

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 21 January 2026
Accepted: 17 April 2026

Abstract

Context. The systematic variation of solar active region (AR) properties with magnetic flux has been the subject of numerous studies but the proposed scaling laws still vary widely.

Aims. A correct representation of these laws and deviations from them is important for modelling the source term in surface flux transport and dynamo models of space climate variation, and may also help constrain the subsurface origin of ARs.

Methods. We determined active region scaling laws based on the recently constructed ARISE AR database that lists bipolar ARs for cycles 23, 24, and 25.

Results. For the area A, pole separation d, and tilt angle γ, we find the following scalings against magnetic flux Φ and heliographic latitude λ: A ∝ Φ^0.84, ⟨d⟩ = 3°.32 log(Φ/Φ0), and ⟨γ⟩ ≃ 28°.62 sin λ, with Φ₀ = 1.6 × 10²⁰ Mx. We also modelled residuals from these relations.

Conclusions. We recommend these scaling relations for use in space climate research to model future data or missing past data, as well as to identify candidate rogue ARs.