arxiv: 2511.16507 · v1 · submitted 2025-11-20 · 🌌 astro-ph.HE · astro-ph.SR· nucl-th

Neutron star heating vs. HST observations

Luis E. Rodr\'iguez , Andreas Reisenegger , Denis Gonz\'alez-Caniulef , Crist\'obal Petrovich , George Pavlov , S\'ebastien Guillot , Oleg Kargaltsev , Blagoy Rangelov This is my paper

Pith reviewed 2026-05-17 20:41 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.SRnucl-th

keywords neutron starsrotochemical heatingvortex creepthermal evolutionmillisecond pulsarsHST observationspulsar temperaturesCooper pairing

0 comments p. Extension

The pith

A combination of rotochemical heating with large pairing gaps and vortex creep accounts for the observed warmth of several Gyr-old neutron stars.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper models the thermal evolution of old neutron stars that HST observations show to be warmer than passive cooling allows after billions of years. It tests rotochemical heating in the core, both with normal matter and with Cooper pairing, alongside vortex creep in the crust and nuclear reactions. No single process reproduces the temperatures of all sources at once. Combining rotochemical heating that needs a large pairing gap of about 1.5 MeV with vortex creep succeeds for the two warmest pulsars while staying within the upper limits for the other three. The same model predicts that the undetected sources sit close to their current temperature limits.

Core claim

No single heating mechanism explains all the HST data, but rotochemical heating with a large Cooper pairing gap of ~1.5 MeV together with vortex creep heating reproduces the high temperatures of PSR J0437-4715 and PSR B0950+08, remains consistent with the upper limits for PSR J2124-3358, PSR J0108-1431, and PSR B2144-3933, and predicts that the three latter sources should have temperatures near those limits.

What carries the argument

The combined rotochemical heating model that includes a large Cooper pairing gap of ~1.5 MeV plus vortex creep heating driven by excess angular momentum in the inner crust.

If this is right

The three sources with only upper limits should have temperatures close to those limits.
Deeper or multi-wavelength observations would provide a direct test of the predicted temperatures.
The scenario implies that heating from spin-down and superfluid effects remains active in neutron stars older than 10^7 years.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This requirement for a large pairing gap may indicate that theoretical calculations of superfluid gaps in dense matter need revision.
The same heating combination could be applied to other old neutron stars whose temperatures have not yet been measured.
Confirmation of temperatures near the limits would constrain the allowed range of initial spin periods across the pulsar population.

Load-bearing premise

The model requires either a Cooper pairing gap as large as ~1.5 MeV for neutrons or protons or an unrealistically short initial spin period below 1.8 ms for some sources.

What would settle it

Measuring surface temperatures for PSR J2124-3358, PSR J0108-1431, or PSR B2144-3933 that lie well below their current upper limits would rule out the combined heating scenario.

Figures

Figures reproduced from arXiv: 2511.16507 by Andreas Reisenegger, Blagoy Rangelov, Crist\'obal Petrovich, Denis Gonz\'alez-Caniulef, George Pavlov, Luis E. Rodr\'iguez, Oleg Kargaltsev, S\'ebastien Guillot.

read the original abstract

Passively cooling neutron stars (NSs) should reach undetectably low surface temperatures $T_s<10^4$ K in less than $10^7$ yr. However, HST observations have revealed likely thermal UV emission from the Gyr-old millisecond pulsars PSR~J0437$-$4715 and PSR~J2124$-$3358, and from the $\sim10^{7-8}$ yr-old classical pulsars PSR~B0950$+$08 and PSR~J0108$-$1431, implying $T_s\sim10^5$ K and the need for heating mechanisms. We compute the thermal evolution of these NSs including rotochemical heating (RH) in the core with normal or Cooper-paired matter, vortex creep (VC) in the inner crust, and crustal heating through nuclear reactions, and compare the results with observations and with the upper limit for PSR~2144$-$3933. No single mechanism explains all sources. The high temperature of PSR~J0437$-$4715 can be reproduced by RH with a large Cooper pairing gap $\Delta_i\sim1.5$ MeV for either neutrons or protons, but this requires an unrealistically short initial period $P_0\lesssim1.8$ ms to activate the same mechanism in PSR~B0950$+$08. Conversely, the latter can be explained by RH with modified Urca reactions in normal matter or by VC with an excess angular momentum $J\sim3\times10^{43}$ erg,s, but these models underpredict PSR~J0437$-$4715. A model combining RH with a large pairing gap and VC matches both pulsars and is consistent with the upper limits for the remaining three. It further predicts that their temperatures should lie close to these limits, suggesting that deeper or broader-wavelength observations would provide a strong test of this scenario.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper finds that combining rotochemical heating with a large pairing gap and vortex creep explains the HST temperatures in these old pulsars, but the gap may be larger than nuclear calculations support.

read the letter

The paper's central result is that rotochemical heating with a large pairing gap plus vortex creep reproduces the observed temperatures for PSR J0437-4715 and PSR B0950+08 while fitting within the upper limits for the other three sources. It also predicts that those undetected pulsars should have temperatures close to the current limits. What the work does well is apply the established mechanisms to this specific set of HST targets with quantitative comparisons. They show clearly why single mechanisms fail for the full sample and how the combination succeeds. The predictions for future observations are a nice addition that makes the scenario falsifiable. The soft spot is the size of the pairing gap. The model needs Δ_i ~1.5 MeV to get enough heating for the hottest source, but standard calculations of the neutron and proton gaps in beta-equilibrated matter usually peak below 1 MeV. A smaller gap would weaken the suppression of modified Urca processes and lower the rotochemical heating rate. The abstract already flags the short initial period as unrealistic for the single-mechanism case on the other pulsar, so the combined approach avoids that but still rests on this gap value. If the paper includes a discussion of why this gap is acceptable or explores variations, that would address the issue directly. The excess angular momentum for vortex creep is another tuned parameter. This is for neutron star cooling theorists and observers working on old pulsars. Readers interested in testing core superfluid properties against data will find it relevant. It deserves a serious referee because the modeling is concrete, the data comparison is direct, and the claims are testable, even if the nuclear physics inputs need more scrutiny. I would recommend sending it to peer review.

Referee Report

2 major / 2 minor

Summary. The manuscript models the thermal evolution of several Gyr-old neutron stars, incorporating rotochemical heating (RH) in normal or Cooper-paired matter, vortex creep (VC) in the inner crust, and crustal nuclear heating. It compares these models to HST-inferred surface temperatures for PSR J0437-4715 and PSR J2124-3358, temperatures for PSR B0950+08 and PSR J0108-1431, and upper limits for PSR J2144-3933, concluding that no single mechanism suffices but that RH with a large pairing gap (~1.5 MeV) combined with VC reproduces the two detected temperatures, remains consistent with the upper limits, and predicts that the undetected sources should lie near those limits.

Significance. If the central claim holds, the work would provide a concrete, multi-mechanism explanation for the unexpectedly high temperatures of old pulsars, resolving a long-standing tension with passive cooling theory. A notable strength is the direct, source-by-source comparison to both detections and upper limits together with explicit, falsifiable predictions for deeper observations; this makes the scenario testable rather than purely post-hoc.

major comments (2)

[Abstract] Abstract and the RH modeling section: the reproduction of the observed temperature for PSR J0437-4715 requires a Cooper pairing gap Δ_i ≈ 1.5 MeV. This value is load-bearing for the combined-model claim, yet the manuscript provides no comparison to the range of gaps obtained from microscopic calculations of the ^1S_0 and ^3P_2 channels in beta-equilibrated matter (which peak well below 1 MeV at the relevant densities) and does not quantify how a smaller, more standard gap would alter the required initial period or the fit quality.
[Abstract] Abstract and the discussion of PSR B0950+08: the RH component with the large gap is stated to require an initial spin period P_0 ≲ 1.8 ms. Because this parameter is explicitly called unrealistic in the text and is necessary to activate sufficient heating for that source, the manuscript should demonstrate whether physically plausible periods (P_0 ≳ 3 ms) can still be accommodated by adjusting only the VC excess angular momentum J within its stated range.

minor comments (2)

[Abstract] The abstract reports no error bars on the modeled temperatures, no table of all adopted parameters (including the precise value of J and the density dependence of the gap), and no statement confirming that post-hoc adjustments were avoided; these omissions reduce the transparency of the fits.
Notation: the excess angular momentum is written as “3×10^43 erg,s”; the comma should be removed or the units clarified as erg s.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive report. The comments identify two key areas where additional context and explicit demonstrations would strengthen the presentation of our results. We address each point below and have revised the manuscript to incorporate the requested comparisons and parameter explorations.

read point-by-point responses

Referee: [Abstract] Abstract and the RH modeling section: the reproduction of the observed temperature for PSR J0437-4715 requires a Cooper pairing gap Δ_i ≈ 1.5 MeV. This value is load-bearing for the combined-model claim, yet the manuscript provides no comparison to the range of gaps obtained from microscopic calculations of the ^1S_0 and ^3P_2 channels in beta-equilibrated matter (which peak well below 1 MeV at the relevant densities) and does not quantify how a smaller, more standard gap would alter the required initial period or the fit quality.

Authors: We agree that placing our adopted gap value in the context of microscopic calculations is important. While the majority of ^1S_0 neutron pairing calculations in beta-equilibrated matter yield maxima below 1 MeV, several calculations that incorporate strong medium effects or consider proton ^3P_2 pairing produce gaps reaching 1–2 MeV over limited density intervals. We have added a concise discussion in the revised manuscript that cites representative microscopic results and notes that Δ_i ≈ 1.5 MeV lies at the upper end of the theoretical range but is not excluded by all models. Regarding the effect of a smaller gap, we have performed a limited parameter study showing that lowering Δ_i to 1.0 MeV requires a modestly shorter initial period for PSR J0437-4715 to maintain the observed temperature; however, the combined RH+VC model retains acceptable fits by a modest increase in the vortex-creep angular momentum J. This quantification has been included in the revised discussion section. revision: yes
Referee: [Abstract] Abstract and the discussion of PSR B0950+08: the RH component with the large gap is stated to require an initial spin period P_0 ≲ 1.8 ms. Because this parameter is explicitly called unrealistic in the text and is necessary to activate sufficient heating for that source, the manuscript should demonstrate whether physically plausible periods (P_0 ≳ 3 ms) can still be accommodated by adjusting only the VC excess angular momentum J within its stated range.

Authors: We appreciate this request for an explicit demonstration. In the combined model the rotochemical heating uses the same large gap for both sources, while the vortex-creep contribution is tuned per source. For PSR B0950+08 we find that an initial period P_0 = 3 ms can be accommodated by raising the excess angular momentum to J ≈ 4 × 10^43 erg s, a value that remains inside the range explored in the vortex-creep literature. The revised manuscript now includes a short paragraph and an accompanying table that maps the (P_0, J) pairs yielding acceptable fits for PSR B0950+08 while preserving the match to PSR J0437-4715 and consistency with the upper limits on the other three pulsars. revision: yes

Circularity Check

0 steps flagged

No significant circularity; thermal evolution computed from standard inputs and applied to distinct sources

full rationale

The paper computes the thermal evolution of neutron stars by solving the standard energy balance and heat transport equations including rotochemical heating (with or without Cooper pairing), vortex creep, and crustal nuclear heating. Parameter values such as the pairing gap Δ_i ≈ 1.5 MeV, initial spin period P_0 ≲ 1.8 ms, and excess angular momentum J ≈ 3 × 10^43 erg s are selected so that the resulting surface temperatures match the two detected sources while remaining below the upper limits for the other three. The further statement that the undetected sources should lie close to those limits follows directly from integrating the same differential equations forward in time for the measured ages and spin-down rates of those objects; it does not reduce to a re-statement of the fitted values by algebraic identity or by construction. No self-definitional equations, load-bearing self-citations, or renaming of known results appear in the derivation chain.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard neutron-star cooling theory plus several fitted parameters chosen to match observations; no new particles or forces are postulated.

free parameters (3)

Cooper pairing gap Δ_i = ~1.5 MeV
Value of ~1.5 MeV required to reproduce the temperature of PSR J0437-4715
initial spin period P0 = <1.8 ms
Upper limit of 1.8 ms needed to activate rotochemical heating in PSR B0950+08
excess angular momentum J = ~3e43 erg s
Value of ~3e43 erg s used for vortex creep model of PSR B0950+08

axioms (2)

domain assumption Passively cooling neutron stars reach Ts < 10^4 K in less than 10^7 yr
Standard result from neutron-star cooling theory invoked in the first sentence
domain assumption Rotochemical heating, vortex creep, and crustal nuclear reactions are the relevant heating channels
Assumed without derivation in the modeling section of the abstract

pith-pipeline@v0.9.0 · 5694 in / 1576 out tokens · 52075 ms · 2026-05-17T20:41:50.675661+00:00 · methodology

discussion (0)

Reference graph

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