Contrasting neutron star heating mechanisms with Hubble Space Telescope observations

¹ Instituto de Astrofísica, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna, 4860, Macul, Santiago, Chile
² Departamento de Física, Facultad de Ciencias Básicas, Universidad Metropolitana de Ciencias de la Educación, Av. José Pedro Alessandri 774, Ñuñoa, Santiago, Chile
³ Centro de Desarrollo de Investigación UMCE, Universidad Metropolitana de Ciencias de la Educación, Santiago, Chile
⁴ Institut de Recherche en Astrophysique et Planétologie (IRAP), UPS-OMP, CNRS, CNES, 9 avenue du Colonel Roche, BP 44346, F-31028, Toulouse Cedex 4, France
⁵ Department of Astronomy, Indiana University, Bloomington, IN, 47405, USA
⁶ Department of Astronomy & Astrophysics, Pennsylvania State University, 525 Davey Lab., University Park, PA, 16802, USA
⁷ Department of Physics, The George Washington University, 725 21st Street NW, Washington, DC, 20052, USA
⁸ Department of Physics, Texas State University, 601 University Drive, San Marcos, TX, 78666, USA

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

Received: 19 November 2025
Accepted: 18 January 2026

Abstract

Passively cooling neutron stars (NSs) are expected to reach undetectably low surface temperatures, T_s < 10⁴ K, within less than 10⁷ yr. However, Hubble Space Telescope (HST) observations have revealed likely thermal ultraviolet emission from the gigayear-old millisecond pulsars PSR J0437−4715 and PSR J2124−3358 and the ∼10^7 − 8 year-old classical pulsars PSR B0950+08 and PSR J0108−1431, implying temperatures of T_s ∼ 10⁵ K and thus suggesting the presence of some heating mechanism. In this work, the thermal evolution for each of these NSs was computed considering rotochemical heating in the NS core with normal or Cooper-paired matter, vortex creep in the inner crust, and crustal heating through nuclear processes. The results were contrasted with the observations while also including the stringent upper limit on the temperature of PSR J2144−3933. No single heating mechanism alone was found to account for all the observations. The high temperature of PSR J0437−4715 can be explained by rotochemical heating in the presence of a large Cooper pairing gap, Δ_i ∼ 1.5 MeV, for either neutrons or protons (or an equivalent combination of both), but this mechanism would require an unrealistically short initial rotation period, P₀ ≲ 1.8 ms, to account for the high temperature of the classical pulsar PSR B0950+08. Conversely, the latter can be explained by rotochemical heating with modified Urca reactions in normal matter or by vortex creep with an excess angular momentum parameter, J ∼ 3 × 10⁴³ erg s, but these models are insufficient to account for the former. However, a model that includes rotochemical heating with a large Cooper pairing gap together with vortex creep is consistent with the temperature measurements of these two pulsars as well as the upper limits for the other three. Moreover, this scenario predicts that the temperatures of the other three pulsars should be close to these upper limits, suggesting that deeper observations and/or a wider wavelength coverage for these and other old nearby pulsars should yield a strong probe of this model.