Pair luminosity and cooling of newborn strange star: unpaired quarks

It was shown that pair luminosity of the newborn strange star with temperature of $10^{11}$ K may be as high as $L_\pm\simeq 10^{52}$ erg/s. The question remains: can a strange star maintain such a high surface temperature for a long time? To answer this question we studied thermal evolution of newborn strange star made of unpaired quarks taking into account its thermal conductivity and neutrino emission by the URCA processes $d\rightarrow u + e + \barν_e$ and $u+e\rightarrow d+ν_e$. Our results show that extremely high luminosity due to the Schwinger process and insufficient thermal conductivity of quarks leads to development of steep temperature gradient at the surface of strange star. As a result, the temperature at the surface and hence its luminosity decreases, reaching $10^{43}$ erg/s already at $10^2$ seconds. This result holds even in the presence of neutrinosphere.

💡 Research Summary

The paper investigates whether a newborn strange star (SS) with an interior temperature of order 10¹¹ K can sustain the extremely high electron‑positron pair luminosity (L₊₋ ≈ 10⁵² erg s⁻¹) predicted by the Schwinger mechanism operating in its electrosphere. The authors adopt a simple bag‑model equation of state for unpaired (non‑superconducting) quark matter, fixing the bag constant at the lowest viable value (B = 57 MeV fm⁻³). Chemical equilibrium and charge neutrality yield quark chemical potentials μₛ ≈ 300 MeV and an electron chemical potential μₑ ≈ 18.7 MeV, which set the surface electric field to values well above the Schwinger critical field (E ≫ E_c ≈ 1.3 × 10¹⁶ V cm⁻¹).

The electrosphere structure is obtained by solving the Poisson equation for a constant quark density and a finite temperature electron gas. At the high temperatures relevant for a newborn SS, thermal evaporation of electrons prevents a strictly static configuration; instead, a stationary solution of the Vlasov‑Maxwell (or Vlasov‑Ampère) system is required. The authors incorporate Pauli blocking into the Schwinger pair‑creation rate, leading to an integral expression (Eq. 16) that depends on the local electric field and the electron distribution function. Numerical solutions show that pair production is confined to a thin layer (∼10–100 electron Compton wavelengths) where the electric field exceeds the critical value. Positrons are rapidly accelerated, while electrons partially return to the surface and thermalize, producing a net outward pair luminosity well approximated by Eq. (17).

To assess whether the surface can maintain the required temperature, the authors solve the heat‑transfer equation (Eq. 23) including (i) the specific heat of degenerate unpaired quarks (c_v ≈ 8π³k_B²T μ²/ħ³c³), (ii) the thermal conductivity of the same matter (κ ≈ 3π³k_F²/(2πħk_B³α_s^½ T)), and (iii) neutrino cooling via direct URCA processes (Q_ν ≈ 3 × 10²⁵ α_s μ_u μ_d μ_e T⁶ erg cm⁻³ s⁻¹). Two regimes are explored: neutrino‑transparent (free escape) and neutrino‑trapped (opaque) conditions. In both cases the surface boundary condition includes the outward pair flux, F_pair = L_pair/(4πR²).

Numerical integration for a 1.4 M_⊙ strange star shows that the enormous pair luminosity quickly drains the surface thermal reservoir. Because the quark thermal conductivity is relatively low (owing to the modest QCD coupling α_s ≈ 0.3), heat cannot be efficiently replenished from the interior. Consequently, a steep temperature gradient develops, and the surface temperature drops by several orders of magnitude within ≲0.1 s. The pair luminosity follows suit, declining to ≈10⁴³ erg s⁻¹ after ∼10² s. Neutrino cooling, while present, does not dominate the early evolution; the Schwinger‑driven surface cooling is the primary driver.

The authors conclude that, under the assumptions of unpaired quark matter with standard transport coefficients, a newborn SS cannot sustain the ultra‑high pair luminosity for more than a fraction of a second. Maintaining L₊₋ ≈ 10⁵² erg s⁻¹ for the several‑second durations required by gamma‑ray burst models would demand either a dramatically higher thermal conductivity (e.g., via color superconductivity) or an additional heating mechanism. Thus, the Schwinger‑induced pair wind, while theoretically possible, is unlikely to be the primary engine of observed short‑duration high‑energy transients. The paper provides the first comprehensive treatment that couples electrospheric pair creation, quark thermal transport, and URCA neutrino emission, thereby clarifying the thermal fate of newborn strange stars.