Numerical Simulation of the Hydrodynamical Combustion to Strange Quark Matter

We present results from a numerical solution to the burning of neutron matter inside a cold neutron star into stable (u,d,s) quark matter. Our method solves hydrodynamical flow equations in 1D with neutrino emission from weak equilibrating reactions, and strange quark diffusion across the burning front. We also include entropy change due to heat released in forming the stable quark phase. Our numerical results suggest burning front laminar speeds of 0.002-0.04 times the speed of light, much faster than previous estimates derived using only a reactive-diffusive description. Analytic solutions to hydrodynamical jump conditions with a temperature dependent equation of state agree very well with our numerical findings for fluid velocities. The most important effect of neutrino cooling is that the conversion front stalls at lower density (below approximately 2 times saturation density). In a 2-dimensional setting, such rapid speeds and neutrino cooling may allow for a flame wrinkle instability to develop, possibly leading to detonation.

💡 Research Summary

The paper presents a comprehensive numerical study of the conversion of cold neutron‑star matter into stable three‑flavor (u, d, s) quark matter, often referred to as strange quark matter. The authors go beyond the traditional reactive‑diffusive (RD) framework by solving the full set of one‑dimensional hydrodynamic equations coupled to weak‑interaction processes, strange‑quark diffusion, and the thermodynamic consequences of the phase transition. The model includes four essential physical ingredients: (1) mass, momentum, and energy conservation for a compressible fluid; (2) a temperature‑dependent equation of state (EOS) that distinguishes between nuclear and quark phases; (3) a source term for neutrino emission arising from β‑decay, electron capture, and related weak processes, which acts as an efficient cooling mechanism; and (4) a diffusion term for strange quarks that supplies the unburned side of the front with the necessary reactant.

The numerical scheme employs high‑resolution finite‑difference methods with appropriate symmetry and outflow boundary conditions. By extracting the post‑ and pre‑front states (density, pressure, temperature, velocity) the authors verify the analytic jump conditions derived from the same EOS. The agreement is within a few percent, confirming that the hydrodynamic treatment is self‑consistent.

The most striking result is the laminar front speed, which the simulations find to lie in the range 0.002–0.04 c. This is one to two orders of magnitude larger than the speeds predicted by pure RD models (∼10⁻⁴ c). The acceleration originates from two coupled effects. First, the conversion releases a substantial amount of binding energy, raising the temperature and pressure behind the front. The resulting pressure gradient provides a strong mechanical push that drives the front forward. Second, the diffusion of strange quarks ahead of the front ensures a steady supply of reactants, preventing the reaction from becoming diffusion‑limited. Together, these mechanisms produce a fast, pressure‑driven combustion wave.

Neutrino cooling, however, plays a decisive counter‑role. The emitted neutrinos carry away a large fraction of the liberated heat, reducing the post‑front pressure rise. The simulations show that when the ambient density drops below roughly twice nuclear saturation density (≈2 n₀), the cooling is sufficient to stall the front entirely. Thus, the critical density for front propagation is set by the balance between pressure‑driven acceleration and neutrino‑driven cooling. This finding implies that, in realistic neutron‑star profiles, the conversion may halt at a finite radius, leaving an inner core of strange quark matter surrounded by unconverted nuclear material.

The authors also discuss the implications of extending the problem to two dimensions. Because the laminar speed is relatively high and the front thickness becomes small, the interface is susceptible to a flame‑wrinkle (or Darrieus–Landau) instability. Such an instability would increase the effective surface area of the front, further accelerating the conversion and potentially leading to a transition from a deflagration to a detonation. A detonation would release the conversion energy on a timescale comparable to the sound crossing time of the star, producing a burst of neutrinos, a possible gravitational‑wave signal, and a dramatic electromagnetic transient.

In summary, the study demonstrates that a full hydrodynamic treatment, including weak‑interaction cooling and strange‑quark diffusion, dramatically revises our expectations for the speed and fate of the nuclear‑to‑quark conversion in neutron stars. The laminar front can travel at a few percent of the speed of light, but neutrino cooling can halt the process at densities below ∼2 n₀. The combination of rapid propagation and strong cooling opens the door to flame‑wrinkle instabilities and possible detonation in multi‑dimensional settings. These results provide a solid theoretical foundation for future 2‑D and 3‑D simulations and for interpreting potential observational signatures—such as sudden neutrino bursts, gravitational‑wave chirps, or fast radio transients—associated with a quark‑matter phase transition inside neutron stars.