Shock-induced chiral magnetic effect

Abstract: Weak-interaction-mediated chiral imbalance generation in idealized massless electrons during core-collapse supernovae was once proposed to be the source of strong magnetic fields found in neutron stars. The effect goes by the name of chiral plasma instability (CPI). However, it was found that a finite electron mass damps out this process, inactivating the instability and preventing magnetic field growth. In this work we show that the instability can survive in the presence of abrupt density and temperature perturbation that drives the system sufficiently far out of weak equilibrium. As an example, we work with such perturbations generated by shockwaves which are common during both core collapse as well as neutron star mergers. We find that the chiral imbalance resulting from shock waves, under the right conditions of density and temperature, can sustain the chiral plasma instability despite the damping from the electron mass. Additionally, in an already magnetized medium, the chiral magnetic effect resulting from shock wave density and temperature perturbation can generate substantial ohmic heating. Our results imply that shockwaves during core-collapse supernovae and merging neutron stars can act as a source of strong heating in a magnetized medium as well as CPI.

• The paper shows that shock-driven departures from beta equilibrium can sustain an electron chiral chemical potential despite mass-induced damping, enabling chiral plasma instability when ΓCPI tweak exceeds one.
• Strong shocks can amplify magnetic fields by roughly 275-fold in an illustrative case, while CME-driven Joule heating may exceed shock heating by about four times for fields near 10¹⁸ G.
• Interacting nuclear equations of state reduce the available chiral imbalance, requiring temperature jumps near 60 MeV and magnetic fields above a few 10¹⁷ G, while uncertainties in neutrino transport, reaction rates, and unresolved field structure remain decisive.

Overview

The paper "Shock-induced chiral magnetic effect" (2602.21294) addresses a long-standing obstacle in the application of chiral transport to dense astrophysical matter: the finite electron mass. It has been established that although weak interactions generate a chiral imbalance among electrons during core collapse, chirality-flipping processes induced by the electron mass equilibrate left- and right-handed populations faster than the chiral plasma instability (CPI) can amplify magnetic fields, rendering the mechanism ineffective (2602.21294). Harris and Sen revisit this conclusion and demonstrate that abrupt density and temperature perturbations—specifically those produced by shock waves in core-collapse supernovae and neutron star mergers—can drive matter sufficiently far out of beta equilibrium that a sustained chiral chemical potential $\mu_5$ survives despite mass-induced damping. Under favorable conditions this sustained imbalance can power CPI growth or produce Joule heating comparable to or exceeding the thermal energy deposited by the shock itself.

Chiral transport framework

The authors work with degenerate $npe$ matter characterized by vector chemical potential $\mu_e$ and chiral chemical potential $\mu_5 = \mu_{e,R} - \mu_{e,L}$. A nonzero $\mu_5$ sources the chiral magnetic effect current ${\bf J}_{\rm CME} = \xi {\bf B}$ with $\xi = \alpha_{\rm EM}\mu_5/\pi$, which modifies Maxwell's equations. Two consequences follow. First, helical gauge-field modes grow exponentially with rate $$\Gamma_{\rm CPI} \approx \alpha_{\rm EM}^3 \mu_5^2 \log(\alpha_{\rm EM}^{-1})/(\pi^2 \mu_e)$$ for modes near $k = \xi/2$. Second, in a pre-existing uniform field ${\bf B}_0$, the CME current induces an electric field $npe$0, dissipating energy at a rate $npe$1.

The central theoretical device is the notion of a sustained background chiral chemical potential. The axial charge evolves as $npe$2, where $npe$3 is the weak-interaction source (the Urca rate) and $npe$4 is the chirality-flip rate from electron-proton scattering. Equilibrium yields $npe$5, i.e., a constant $npe$6 maintained for the duration $npe$7 over which beta equilibration proceeds. The criterion for significant magnetic field amplification is then $npe$8.

Shock waves as chiral-imbalance generators

The paper constructs shock solutions using relativistic Rankine–Hugoniot conditions for cold upstream $npe$9 matter in beta equilibrium, first with a non-interacting equation of state (EoS) and later with two relativistic mean-field (RMF) EoSs, NL3 (stiff) and IUFII (soft), chosen to bracket realistic behavior. Because weak equilibration is too slow across the femtometer-scale shock front, particle composition is frozen across the jump while the density rises abruptly, pushing the downstream region out of equilibrium. The Urca process then restores equilibrium over a time $\mu_e$0, generating an excess population of left-handed electrons throughout a co-moving sliver of width $\mu_e$1 behind the front.

Two illustrative cases are analyzed in detail:

Quantity	Case I	Case II
Upstream $\mu_e$2	180 MeV	200 MeV
Downstream temperature	~13 MeV	70 MeV
Density jump	1.53	2.5
Shock speed $\mu_e$3	0.41	0.58
$\mu_e$4	$\mu_e$5 s	$\mu_e$6 s
Sustained $\mu_e$7	~0.08 keV	~0.5 MeV
$\mu_e$8	$\mu_e$9	~5.6

The contrast is stark: the weaker shock (Case I) fails to sustain CPI, while the stronger shock (Case II) yields $\mu_5 = \mu_{e,R} - \mu_{e,L}$0, corresponding to magnetic field amplification by a factor $\mu_5 = \mu_{e,R} - \mu_{e,L}$1. In both cases the non-equilibrium sliver width ($\mu_5 = \mu_{e,R} - \mu_{e,L}$2 of order meters down to millimeters) vastly exceeds the hydrodynamic shock thickness, validating the abrupt-jump approximation.

The authors also verify that including electromagnetic stress-energy in the Rankine–Hugoniot equations leaves the downstream conditions essentially unchanged even for fields as strong as $\mu_5 = \mu_{e,R} - \mu_{e,L}$3 G, so the heating estimates are robust against magnetohydrodynamic corrections to the jump conditions.

Joule heating

In a magnetized medium, the CME current driven by the shock-sustained $\mu_5 = \mu_{e,R} - \mu_{e,L}$4 produces ohmic dissipation over the time $\mu_5 = \mu_{e,R} - \mu_{e,L}$5. For Case I, $\mu_5 = \mu_{e,R} - \mu_{e,L}$6, only about 0.2% of the shock's thermal energy $\mu_5 = \mu_{e,R} - \mu_{e,L}$7. For Case II, however, $\mu_5 = \mu_{e,R} - \mu_{e,L}$8 exceeds the shock thermal energy $\mu_5 = \mu_{e,R} - \mu_{e,L}$9 by roughly a factor of four—a notable claim, since it implies that chiral transport can dominate local energy deposition in strongly shocked, highly magnetized matter. This result assumes the maximal QCD-scale background field $\mu_5$0 G; the paper notes explicitly that at $\mu_5$1 G the ratio falls by $\mu_5$2, making the heating difficult to distinguish from ordinary shock heating except under extreme conditions.

Results with interacting equations of state

Extending to RMF EoSs, the authors find that interactions increase the beta-equilibrium proton fraction at fixed density and predict larger shock heating for a given density jump, but smaller departures from beta equilibrium ($\mu_5$3) than the free gas—reducing, though not eliminating, the parameter space for chiral effects. They derive compact general expressions showing that $\mu_5$4, the CPI exponent $\mu_5$5, and the Joule heating all scale linearly with the beta-equilibration rate and with powers of $\mu_5$6 and $\mu_5$7. Quantitatively, interacting EoSs require temperature jumps of roughly 60 MeV or more for CPI to develop, and Joule heating reaches 10% of shock heating only if the field exceeds a few times $\mu_5$8 G and the upstream density lies below about $\mu_5$9. These thresholds sit at the upper end of what merger simulations predict: spatially averaged fields of a few ${\bf J}_{\rm CME} = \xi {\bf B}$0 G with pockets up to perhaps a few ${\bf J}_{\rm CME} = \xi {\bf B}$1 G, unresolved below tens-of-meters grid scales.

Limitations and open questions

The paper is candid that its quantitative conclusions rest on approximations whose validity is uncertain precisely in the regime of interest. The Urca rate is evaluated in the degenerate limit even though shocked protons and neutrons become semi-degenerate or non-degenerate at tens of MeV, so the true temperature dependence—and hence the equilibration dynamics—may differ substantially; whether equilibration is subthermal or suprathermal is left open. Neutrino trapping downstream, neglected here, could modify the beta-equilibrium condition if the neutrino mean free path becomes comparable to ${\bf J}_{\rm CME} = \xi {\bf B}$2. The nuclear EoS itself is poorly constrained at the high densities, high temperatures, and large ${\bf J}_{\rm CME} = \xi {\bf B}$3 where the chiral effects are largest, and additional degrees of freedom (pions, hyperons, deconfined quark matter) or phase transitions across the shock front are unaddressed. The analysis also assumes the shock thickness is much smaller than the equilibration length, freezing composition across the front; shocks at low densities well below neutron drip, common in supernovae, fall outside the applicable Urca treatment entirely. Finally, the small-scale structure of magnetic fields within the meter-scale sliver is unknown given current simulation resolution, leaving the effective value of ${\bf J}_{\rm CME} = \xi {\bf B}$4—and therefore the magnitude of the Joule heating—uncertain.

Conclusion

This work establishes a concrete theoretical link between shock-wave physics, weak equilibration, and chiral transport in dense matter, showing that sufficiently strong shocks can sustain a chiral imbalance against electron-mass damping long enough to seed CPI growth (with exponents of order unity to ten) or to generate ohmic heating that can rival the shock's own thermal output. The effects are confined to sub-meter to meter-scale regions traveling with the shock front, below current numerical resolution, and their quantitative significance depends on EoS uncertainties, neutrino physics, and unresolved small-scale magnetization. Whether these mechanisms materially affect neutron star merger remnants or magnetar field evolution requires embedding the framework developed here into full simulations—an explicit program the paper sets out to enable.