Fast-Cooling Synchrotron in Decaying Magnetic Fields: Implications for the GRB Spectral Distribution

TL;DR

This study evaluates a fast-cooling synchrotron model with decaying magnetic fields to explain GRB spectra, finding it partially addresses spectral softness but cannot fully match observations, indicating more physics is needed.

Contribution

It systematically tests a decaying magnetic field synchrotron model against GRB spectral data, revealing its limitations in reproducing observed spectral indices.

Findings

Magnetic field decay can harden the low-energy spectral index but is not robust.

Spectral curvature and $E_p$ position influence the recovered spectral index.

The model yields $ ext{alpha}$ mostly between -1.5 and -0.8, centered around -1.5.

Abstract

The prompt-emission spectra of gamma-ray bursts (GRBs) are commonly described by the empirical Band function. The typical low-energy spectral index is $\sim -1$, which poses a challenge to standard synchrotron radiation models. We systematically investigate a fast-cooling synchrotron model with a decaying magnetic field and test, within an observation-consistent pipeline, whether it reproduces the Band-fit parameter distributions in the GBM catalog, in a statistical sense. We solve the electron continuity equation with synchrotron, adiabatic, and synchrotron self-Compton cooling to obtain the time-dependent electron distribution and synthetic spectra; we then forward-fold through the GBM response matrices and recover $(\alpha, \beta, E_p)$ with Band fits. We find that magnetic-field decay can harden the recovered $\alpha$ relative to the fast-cooling limit in part of parameter space, but the effect is not robust and is sensitive to the location of $E_p$ within the finite band and to spectral curvature; varying key physical scales reshapes the recovered $\alpha$ distribution, indicating that catalog $\alpha$ often represents an effective in-band slope rather than the asymptotic index. SSC cooling provides modest additional hardening and, in our setups, does not stabilize $\alpha$ near the observed peak. Using Monte Carlo samples designed to mimic the observations, the model yields $\alpha$ mostly between $-1.5$ and $-0.8$, but remains centered around $\alpha \approx -1.5$. Overall, while decaying-field fast-cooling synchrotron can partially alleviate overly soft spectra expected from standard fast-cooling synchrotron emission, it still falls short of reproducing the GBM $\alpha$ distribution at the population level, implying that additional physical processes are required.