Published January 26, 2026 | Version v1
Model Open

Thermal evolution models for old pulsars from neutron star reheating mechanisms

  • 1. EDMO icon Pontificia Universidad Católica de Chile

Description

This dataset contains the numerical thermal evolution models shown in Fig. A1
and summarized in Table 3 of the associated Astronomy & Astrophysics article
“Contrasting neutron star heating mechanisms with Hubble Space Telescope observations”.

The models correspond to surface temperature evolution curves for the following pulsars:
PSR J0437−4715, PSR J2124−3358, PSR B0950+08, PSR J0108−1431, and PSR J2144−3933.

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DATA FORMAT
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The file j0437_ZENODOmodels.csv contains one table with paired columns for each model.
For each model label (I, II, III, …, XI), two columns are provided:

  <LABEL>_t      : log10(t / yr)
  <LABEL>_Tinf   : log10(T_s^∞ / K)

Different models may have different time sampling. Missing values are represented as NaN.

The initial time point is explicitly set to t = 0 (i.e. log10(t) = 0).
In the original simulations, arrays were preallocated and padded with zeros beyond the
physical end of the evolution. When taking logarithms, these padded zeros produced
−Inf values. During post-processing for this dataset, such non-physical values were
removed and replaced by NaN, so that no ±Inf values appear in the released data.

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PHYSICAL ASSUMPTIONS
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All curves were computed assuming magnetic dipole spin-down with a constant dipole
moment inferred from the observed spin period P and spin-down rate Ṗ of each pulsar.

For the millisecond pulsars (MSPs: J0437−4715 and J2124−3358), the initial conditions are:
  P0 = 1 ms
  T0^∞ = 10^9 K

For the classical pulsars (CPs: B0950+08, J0108−1431, and J2144−3933), the initial conditions are:
  P0 = 5 ms
  T0^∞ = 10^11 K

PSRs B0950+08 and J0108−1431 are plotted together and share the same inferred dipole
magnetic field (that of B0950+08).

Observed temperatures, 1σ error bars, and upper limits are shown in the figures at the
times when the present-day spin parameters are reached.

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MODEL LABELS
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The column labels correspond to the following physical models (see Tables 2 and 3 of the paper):

I   Passive cooling with Murca reactions in normal (non-superfluid, non-superconducting) matter.

II  Passive cooling with Durca reactions in normal matter.

III Rotochemical heating with Murca reactions in normal matter.

IV  Rotochemical heating with Durca reactions in normal matter.

V   Vortex creep with Murca reactions, assuming normal particles in the core and
    an excess angular momentum parameter J = 3 × 10^43 erg s.

VI  Same as V, but with Durca reactions.

VII Crustal heating (present only in MSPs) with Murca reactions and normal particles
     in the core.

VIII Same as VII, but with Durca reactions.

IX  Rotochemical heating with Murca reactions, assuming normal protons and superfluid
    neutrons with a uniform energy gap Δ_n = 1.5 MeV, and reaction rates reduced by
    a factor f = 10^−2.

X   Same as IX, but with Durca reactions and reaction rates reduced by a factor f = 10^−8.

XI  Rotochemical heating with Murca reactions assuming normal protons and superfluid
    neutrons with Δ_n = 1.5 MeV and reaction rates reduced by a factor f = 10^−2,
    combined with vortex creep with J = 3 × 10^43 erg s.

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REFERENCE
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If you use these data, please cite the associated A&A article.

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Additional details

Dates

Accepted
2026-01-26