Neutron star cooling with dUrca processes

The gist: The study incorporates neutrino emissivities of relevant Delta direct Urca processes into neutron star cooling simulations, revealing that these processes can act as an efficient neutrino-cooling mechanism and significantly accelerate thermal evolution, potentially explaining unusually low surface temperatures in massive neutron stars.

Introduction to Neutron Star Cooling Challenges

Neutron star (NS) cooling remains a significant open problem because the composition and equation of state (EOS) of matter at supranuclear densities are not well constrained <ref:2610.11435#pg3>. The early stage of NS cooling is dominated by neutrino emission from the core, which rapidly cools the star <ref:2610.11435#pg3>. Nucleonic and hyperonic direct Urca processes are known rapid cooling mechanisms <ref:2610.11435#pg3>. The appearance of ∆ baryons in dense matter introduces additional weak-interaction channels, including ∆ direct Urca processes <ref:2610.11435#pg3>. Although such processes have been discussed in the context of ∆-admixed NS matter, their neutrino emissivities and impact on NS cooling have not been systematically investigated <ref:2610.11435#pg3>.

Incorporating Delta Baryons into the EOS and Cooling Model

The investigation employs the relativistic mean-field (RMF) theory with the DD-ME2 parametrization to investigate the effects of ∆ baryons on NS properties <ref:2610.11435#pg4>. The matter is assumed to consist of neutrons (n), protons (p), electrons (e−), Λ hyperons, and ∆ baryons <ref:2610.11435#pg4>. The threshold densities for the appearance of particles and the onset of ∆ direct Urca processes are detailed in Table 1 <ref:2610.11435#pg5>. The neutrino emissivity associated with the ∆ direct Urca processes was derived in a previous work <ref:2610.11435#pg5>. The relevant weak interaction is described by an effective interaction Hamiltonian <ref:2610.11435#pg6>.

Implementation and Results of NS Cooling Simulations

The thermal evolution of neutron stars is investigated using the publicly available onedimensional NSCool code <ref:2610.11435#pg6>. The total neutrino emissivity entering the energy balance equation is augmented by the ∆ direct Urca contribution, defined as Qν = Q standard ν + Q ∆ ν <ref:2610.11435#pg9>. This modification allows for a consistent assessment of the impact of the process on thermal evolution over a range of stellar masses and model parameters <ref:2610.11435#pg9>. The results show that the inclusion of the N∆ dUrca process substantially enhances neutrino luminosity and leads to faster thermal evolution compared to models without a dUrca process <ref:2610.11435#pg10>.

Impact of Stellar Mass and Other Parameters

The effect is particularly relevant for the higher-mass stars, for which the central density is sufficiently high for the ∆ direct Urca process to operate <ref:2610.11435#pg10>. The M ≃ 1.8–1.9 M⊙ sequences provide the closest correspondence to young and relatively cold objects like PSR J0205+6449 (4) and PSR B2334+61 (14) <ref:2610.11435#pg8>. The mass dependence of the cooling curves is important, as increasing the stellar mass enhances the role of the ∆ direct Urca process once its threshold is reached <ref:2610.11435#pg9>. The comparison with observations indicates that these high-mass sequences can approach locations occupied by several relatively cold sources <ref:2610.11435#pg10>.

Sensitivity to Model Uncertainties

The sensitivity of the cooling predictions to variations in the meson–∆ coupling parameters is examined <ref:2610.11435#pg10>. The variation in the meson–∆ couplings further demonstrates the enhanced cooling associated with the ∆ direct Urca process across a broad range of coupling strengths <ref:2610.11435#pg10>. Furthermore, the effect of ∆ superfluidity is illustrated, showing that including ∆ pairing changes the cooling evolution relative to models without it <ref:2610.11435#pg10>. The main qualitative result is not strongly dependent on the assumed envelope composition <ref:2610.11435#pg10>.

Conclusion and Future Directions

The results demonstrate that the ∆ direct Urca process can provide an efficient neutrino-cooling channel capable of producing substantially colder stars than models without the corresponding process <ref:2610.11435#pg10>. The ability of the ∆ direct Urca process to generate cooling curves reaching the relatively cold region occupied by young NSs provides a new possibility for interpreting the observed diversity of NS thermal evolution <ref:2610.11435#pg10>. A more quantitative assessment will require improved constraints on the ∆ weak couplings, microscopic calculations of the ∆ pairing gap, and a systematic exploration of the density dependence of ∆ superfluidity <ref:2610.11435#pg10>. The inclusion of ∆ direct Urca emission can represent an important additional fast neutrino-cooling mechanism in NSs containing ∆ baryons <ref:2610.11435#pg10>.

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The cooling of neutron stars (NSs) provides insight into their composition and equation of state <ref:2610.11435#pg3>. The early stage of NS cooling is dominated by neutrino emission from the core, which rapidly cools the star <ref:2610.11435#pg3>. Urca processes are one such mechanism where neutrinos escape from the core, carrying away most of the heat <ref:2610.11435#pg3>. Nucleonic and hyperonic direct Urca processes are known rapid cooling mechanisms <ref:2610.11435#pg3>. The possible appearance of ∆ baryons in dense matter introduces additional weak-interaction channels, including ∆ direct Urca processes <ref:2610.11435#pg3>. Although such processes have been discussed in the context of ∆-admixed NS matter, their neutrino emissivities and impact on NS cooling have not been systematically investigated <ref:2610.11435#pg3>. In this work, for the first time we incorporate the neutrino emissivities of the relevant ∆ direct Urca processes into NS cooling simulations <ref:2610.11435#pg3>. We investigate the thermal evolution of ∆-admixed NSs and assess the impact of these additional neutrino emission channels on their cooling behavior <ref:2610.11435#pg3>. We find that ∆ direct Urca processes can provide an efficient neutrino-cooling mechanism and significantly accelerate the thermal evolution of NSs <ref:2610.11435#pg3>. Our results demonstrate that ∆ baryons and their associated weak-interaction processes can play an important role in explaining NSs with unusually low surface temperatures and provide a new connection between the composition of dense matter and NS cooling observations <ref:2610.11435#pg3>.

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The mURCA operates throughout the star while dURCA operates in inner core of massive stars only <ref:2610.11435#pg3>. Consequently, the contribution of mURCA to the overall cooling rate can be subdominant when dURCA is kinematically allowed <ref:2610.11435#pg3>. However, in massive neutron stars, the appearance of exotic degrees of freedom in the inner core can open additional dUrca-like neutrino-emission channels <ref:2610.11435#pg3>. These processes can provide efficient pathways for neutrino cooling and thereby make significant contributions to the overall cooling rate of the star <ref:2610.11435#pg3>. For example, the appearance of hyperons, antikaon condensates, or deconfined strange quark matter can give rise to additional dUrca-like reactions <ref:2610.11435#pg3>.

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The ∆ baryons constitute the lowest lying baryonic resonances and may appear in the core of NSs at densities several times the nuclear saturation density (ρ0) <ref:2610.11435#pg3>. The presence of ∆ baryons can modify the composition of NS matter, the particle fractions, the EOS, and consequently the macroscopic properties of NSs such as their mass–radius relation and maximum mass [8] <ref:2610.11435#pg3>. The inclusion of ∆ baryons can also have a significant impact on the conventional nucleonic dUrca (NdUrca) processes <ref:2610.

1. Incorporation of Exotic Neutrino Channels The improved AI system can now incorporate the neutrino emissivities of the relevant ∆ direct Urca processes into NS cooling simulations, allowing it to assess the impact of these additional neutrino emission channels on their cooling behavior.

2. Composition-Dependent Cooling Prediction The system can now perform comparative analysis between different dense matter compositions, as demonstrated by comparing cooling curves obtained with and without the ∆ dUrca contributions against conventional N dUrca processes to assess the extent to which these additional weak-interaction channels modify the thermal evolution.

3. Exotic Physics Parameter Sensitivity Analysis The AI can now systematically investigate parameter dependencies, such as examining the sensitivity of the cooling predictions to variations in the meson–∆ coupling parameters, allowing it to determine how the appearance and abundance of ∆ baryons in the stellar core influence the density range over which the ∆ dUrca process can operate.

4. Observational Constraint Matching The improved system can match theoretical predictions to astrophysical data by assessing how the M ≃ 1.8–1.9 M⊙ sequences provide the closest correspondence to PSR B2334+61 (14) and other cold sources, enabling it to provide a possible explanation for the relatively low surface temperatures of young NSs.

5. Envelope Composition Robustness Check The system can perform a qualitative assessment of model robustness by comparing Fe- and H-envelope models to ensure that the enhanced cooling associated with the ∆ dUrca process persists for both envelope prescriptions, confirming the main result is not strongly dependent on the assumed envelope composition.

The cooling of neutron stars (NSs) provides insight into their composition and equation of state. However, a complete understanding of this phenomenon is still an open question. The early stage of NS cooling is dominated by neutrino emission from the core, which rapidly cools the star. Urca processes are one such mechanism where neutrinos escape from the core, carrying away most of the heat. Nucleonic and hyperonic direct Urca processes are known rapid cooling mechanisms. The possible appearance of Δ baryons in dense matter introduces additional weak-interaction channels, including Δ direct Urca processes. Although such processes have been discussed in the context of Δ-admixed NS matter, their neutrino emissivities and impact on NS cooling have not been systematically investigated. In this work, for the first time we incorporate the neutrino emissivities of the relevant Δ direct Urca processes into NS cooling simulations. We investigate the thermal evolution of Δ-admixed NSs and assess the impact of these additional neutrino emission channels on their cooling behavior. We find that Δ direct Urca processes can provide an efficient neutrino-cooling mechanism and significantly accelerate the thermal evolution of NSs. Our results demonstrate that Δ baryons and their associated weak-interaction processes can play an important role in explaining NSs with unusually low surface temperatures and provide a new connection between the composition of dense matter and NS cooling observations.