A Common Synchrotron Origin for Prompt Gamma-Ray and Soft X-Ray Emission in GRBs: Evidence from Joint Spectral Analysis

Abstract

The recent launches of the Einstein Probe (EP) and the Space Variable Objects Monitor (SVOM) mission have led to the detection of a growing number of long GRBs with significant, early soft X-ray flux during their gamma-ray emission, prompting the question of whether their multi-band prompt emission shares a common origin in region and mechanism. To address this, we utilize the 20-year Swift archival data, which provides a substantial sample of joint soft X-ray and gamma-ray observations, enabling a systematic joint spectral study. We resolve 110 temporal pulses from 46 GRBs and find that a single power-law model with a low-energy break or cutoff adequately describes the prompt spectra from 150 keV down to 0.5 keV. More than half of the sample pulses require a break around a few keV, with average spectral indices $\langle \alpha_1 \rangle = -0.88$ and $\langle \alpha_2 \rangle = -1.46$ consistent with synchrotron radiation in a marginally fast-cooling regime. The observed spectral evolution and the distribution of indices support a single-emission-region origin, where the varying spectral shapes are largely governed by the evolution of the synchrotron cooling frequency $\nu_c$ and the effect of finite emission width. The observed differences in the temporal behavior between X-ray and gamma-ray light curves can be naturally explained by this spectral evolution across the broad band.