Thermal-timescale accretion does not always yield critical rotation in mass gainers

¹ School of Astronomy and Space Science, Nanjing University Nanjing 210023, PR China
² Key Laboratory of Modern Astronomy and Astrophysics, Nanjing University, Ministry of Education Nanjing 210023, PR China
³ Max Planck Institute for Astrophysics Karl-Schwarzschild-Strasse 1 85748 Garching, Germany
⁴ Zentrum für Astronomie der Universität Heidelberg, Astronomisches Rechen-Institut Mönchhofstr. 12-14 69120 Heidelberg, Germany
⁵ Heidelberger Institut für Theoretische Studien Schloss-Wolfsbrunnenweg 35 69118 Heidelberg, Germany
⁶ Argelander-Institut für Astronomie, Universität Bonn Auf dem Hügel 71 53121 Bonn, Germany
⁷ Tsung-Dao Lee Institute, Shanghai Jiao-Tong University Shanghai 201210, China
⁸ JILA, University of Colorado and National Institute of Standards and Technology, 440 UCB Boulder 80308 CO, USA
⁹ Department of Astrophysical and Planetary Sciences, 391 UCB Boulder 80309 CO, USA

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

Received: 13 November 2025
Accepted: 13 January 2026

Abstract

Binary evolution plays a central role in producing rapidly rotating stars. Previous studies have shown that mass gainers in binaries can reach critical rotation after accreting only modest amounts of material, particularly during thermal-timescale Case B mass transfer, in which tidal spin-down is ineffective due to wide orbits. However, such rapid accretion often drives the mass gainer out of thermal equilibrium, and its subsequent spin evolution during thermal relaxation has not been analyzed in depth. In this study, we construct a suite of accreting detailed single-star models with different accretion prescriptions, which inflate and spin up to critical rotation during the accretion. After the accretion has ended, the models relax thermally and deflate. We find that the ratio of surface to critical angular velocity decreases to subcritical values during thermal contraction, with the magnitude of this decrease correlating with the degree of thermal disequilibrium at the end of accretion. This reduction in fractional critical rotation is even stronger when internal angular momentum transport is inefficient. Detailed binary models show the same trend, indicating that the results from our toy single-star models also apply to real binary evolution. Our results highlight that binary mass transfer does not always produce critically rotating stars, but instead may yield a wide range of spin rates depending on the mass transfer and accretion history. Our findings offer new insights into the rotational properties of mass gainers in binaries, stellar merger products, and newly formed massive stars following accretion.