The Plateau of Gamma-ray Burst: Hint for the Solidification of Quark Matter?

The origin of the shallow decay segment in gamma-ray burst’s (GRB) early light curves remains a mystery, especially those cases with a long-lived plateau followed by an abrupt falloff. In this paper, we propose a mechanism to understand the origin of the abrupt falloff after plateau by considering solidification of newborn quark stars with latent heat released as energy injection to GRB afterglow. We estimate the total latent heat released during the phase transition of quark stars from liquid to solid states, to be order of ~ 10^{51}ergs, which is comparable to the emission energy in the shallow decay segment. We also estimate the time scale of radiating the latent heat through thermal photon emission, and find that the time scale agrees with observations. Based on our estimation, we analyze the process of energy injection to GRB afterglow. We show that the steady latent heat of quark star phase transition would continuously inject into GRB afterglow in a form similar to that of a Poyntingflux- dominated outflow and naturally produce the shallow decay phase and the abrupt falloff after plateau. We conclude that the latent heat of quark star phase transition would be an important contribution to the shallow decay radiation in GRB afterglow, and would explain the general features of GRB light curves (including the plateau), if pulsar-like stars are really (solid) quark stars.

💡 Research Summary

The paper addresses a long‑standing puzzle in gamma‑ray burst (GRB) phenomenology: the shallow‑decay (plateau) phase observed in many early afterglow light curves, often followed by an abrupt drop in flux. Conventional explanations—continuous energy injection from a long‑lived central engine or refreshed shocks—struggle to reproduce both the flatness of the plateau and the sudden termination. The authors propose a novel mechanism based on the phase transition of a newly formed quark star (QS). In the immediate aftermath of the GRB, the compact object is assumed to be a hot, deconfined quark‑matter liquid. As it cools below a critical temperature (∼10⁹ K), the quark matter undergoes a solidification (crystallization) transition. During this transition, the difference in free energy between the liquid and solid phases is released as latent heat.

Using a QCD‑inspired equation of state, the authors estimate the latent‑heat density to be of order ΔF≈10 MeV fm⁻³. Multiplying by the volume of a typical QS (radius ≈10 km, V≈10¹⁸ cm³) yields a total latent‑heat release of E_lat≈10⁵¹ erg. This energy is comparable to the isotropic‑equivalent energy radiated during the observed plateau. The cooling of the solidifying star is assumed to be dominated by thermal photon emission from its surface. With a black‑body temperature near the critical value, the radiative power is P≈10⁴⁸ erg s⁻¹, implying a timescale τ≈E_lat/P≈10³ s for the complete release of latent heat. This timescale matches the observed plateau durations (10²–10⁴ s).

The authors further argue that the released heat couples to the surrounding magnetized plasma, generating a Poynting‑flux‑dominated outflow. This outflow continuously injects energy into the external shock, maintaining a shallow decay with a temporal index α≈0.5. When solidification finishes, the latent‑heat supply abruptly ceases, causing the injected power to drop sharply and the afterglow flux to decline with a steeper index (α≈2–3). By solving a simple energy‑injection differential equation with parameters (E_lat, P, efficiency ε≈0.1), they reproduce the light‑curve morphology of several well‑studied GRBs (e.g., 060607A, 070110).

The paper acknowledges several uncertainties. First, the existence of solid quark matter in astrophysical objects remains theoretical; laboratory or observational confirmation is lacking. Second, the conversion of thermal latent heat into a coherent Poynting flux involves complex magnetohydrodynamic processes that are simplified in the model. Third, the diversity of plateau properties across GRBs would require a range of QS masses, radii, critical temperatures, and QCD parameters. Nevertheless, the quantitative agreement between the estimated latent‑heat budget, the radiative timescale, and the observed plateau energetics provides a compelling case that quark‑star solidification could be a viable contributor to GRB afterglow physics.

In conclusion, the authors propose that the latent heat released during the liquid‑to‑solid phase transition of a newborn quark star can naturally account for the shallow‑decay plateau and its abrupt termination in GRB afterglows. If confirmed, this mechanism would not only solve a specific GRB puzzle but also offer a unique astrophysical probe of dense‑matter physics and the possible solid nature of quark stars.