Neutrino and antineutrino energy loss rates in massive stars due to isotopes of titanium

Weak interaction rates on titanium isotopes are important during the late phases of evolution of massive stars. A search was made for key titanium isotopes from available literature and a microscopic calculation of weak rates of these nuclei were performed using the proton-neutron quasiparticle random phase approximation (pn-QRPA) theory. Earlier the author presented the stellar electron capture rates on titanium isotopes. In this paper I present the neutrino and antineutrino energy loss rates due to capture and decay rates on isotopes of titanium in stellar environment. Accurate estimate of neutrino energy loss rates are needed for the study of the late stages of the stellar evolution, in particular for cooling of neutron stars and white dwarfs. The results are also compared against previous calculations. At high stellar temperatures the calculated neutrino and antineutrino energy loss rates are bigger by more than two orders of magnitude as compared to the large scale shell model results and favor stellar cores with lower entropies. This study can prove useful for core-collapse simulators.

💡 Research Summary

The paper presents a comprehensive calculation of neutrino and antineutrino energy loss rates for seven titanium isotopes (⁴⁹Ti, ⁵¹Ti, ⁵²Ti, ⁵³Ti, ⁵⁴Ti, ⁵⁵Ti, and ⁵⁶Ti) under stellar conditions relevant to the late evolutionary stages of massive stars. The motivation is that weak interaction processes, especially electron captures and β‑decays, dominate the cooling of the stellar core during silicon burning, core contraction, and the pre‑supernova phase. Accurate neutrino energy loss rates are crucial for determining the entropy, temperature, and density evolution of the core, which in turn affect the dynamics of core‑collapse supernovae, neutron‑star cooling, and white‑dwarf evolution.

The author employs the proton‑neutron quasiparticle random phase approximation (pn‑QRPA) to compute the weak transition strengths. Unlike large‑scale shell‑model (LSSM) calculations that are limited by model‑space size, pn‑QRPA can treat up to seven major oscillator shells (7 ℏω) and thus includes a far richer set of particle‑hole configurations. Both Fermi (B(F)) and Gamow‑Teller (B(GT)) transition matrix elements are evaluated for each possible initial and final nuclear state. The calculation explicitly incorporates thermal population of excited parent states by weighting each state with a Boltzmann factor, thereby accounting for the significant contribution of excited states at the high temperatures (T₉ = 0.01–30, where T₉ = 10⁹ K) encountered in massive‑star interiors.

The neutrino (λ_ν) and antineutrino (λ_{\barν}) energy loss rates are obtained from the standard expression

λ_{ν(\barν)} = (ln 2 / D) ∑{i,j} f{ν(\barν)}(T, ρ, E_F)