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From Empirical to Physical Model: Direct Fits of Optically Thin Inverse Compton Scattering to Prompt GRB Spectra

Pragyan Pratim Bordoloi, Shubh Mittal, Shabnam Iyyani

TL;DR

This study tests optically thin inverse Compton scattering as a physically self-consistent mechanism for GRB prompt emission by directly fitting a Naima-based ICS model to four bright, carefully selected GRBs. The fits reveal mildly heated, Maxwell–Jüttner-like electron distributions with a small non-thermal tail, seed photons dominated by photospheric radiation, and outflow parameters ($\Gamma \approx 170$–$550$, $R_d obreak\approx 8\times10^{12}$–$10^{14}$ cm) that place the dissipation just above the photosphere. The resulting Compton parameters ($y \sim 1$–$3$, $\tau \sim 0.2$–$0.6$) and modest Compton amplification reproduce curved spectral peaks and high-energy tails without requiring extreme magnetic fields or electron energies, supporting ICS as a viable emission channel for at least a subset of bright GRBs. The work provides a physically grounded framework for interpreting GRB spectra, constraining sub-dominant thermal components, and motivating broader application of ICS models in future GRB analyses.

Abstract

Gamma-ray burst (GRB) prompt emission is commonly attributed to non-thermal radiation processes operating in the optically thin regions of a relativistic outflow. Among these, optically thin inverse-Compton (IC) scattering remains an important yet under-tested mechanism. From an initial set of 41 bursts selected using empirical Band-function criteria that highlight quasi-thermal low-energy slopes ($α> -0.5$) and constrained high-energy indices ($-1.7 > β> -3.3$), only four events satisfy these conditions consistently in both time-integrated and time-resolved spectra. The IC fits yield self-consistent constraints on the seed-photon field and the electron population at the dissipation site. For bulk Lorentz factors $Γ\sim 170$-$550$, we infer seed thermal peaks of $\sim 0.05$-$0.2$ keV and electron thermal energies of $\sim 20$-$300$ keV in the co-moving frame. A fraction of only $0.1\%$-$20\%$ of electrons are accelerated into a non-thermal tail with an average index value of $δ\sim 1.8$. The derived Comptonisation parameters indicate moderate $y$ values ($\sim 1$-$3$), optical depths $τ\sim 0.2$-$0.6$, and dissipation radii just above the photosphere, consistent with mildly relativistic ($γ_{\min} \sim 1.2$-$2.6$), photon-dominated, low-magnetic-field dissipation environments. Furthermore, the framework allows us to constrain even sub-dominant thermal components that lie below the detector's low-energy threshold. Taken together, our results show that optically thin IC scattering offers a physically consistent and observationally viable explanation for the prompt emission in a subset of bright GRBs, motivating the application of IC models in future GRB studies.

From Empirical to Physical Model: Direct Fits of Optically Thin Inverse Compton Scattering to Prompt GRB Spectra

TL;DR

This study tests optically thin inverse Compton scattering as a physically self-consistent mechanism for GRB prompt emission by directly fitting a Naima-based ICS model to four bright, carefully selected GRBs. The fits reveal mildly heated, Maxwell–Jüttner-like electron distributions with a small non-thermal tail, seed photons dominated by photospheric radiation, and outflow parameters (–, – cm) that place the dissipation just above the photosphere. The resulting Compton parameters (–, –) and modest Compton amplification reproduce curved spectral peaks and high-energy tails without requiring extreme magnetic fields or electron energies, supporting ICS as a viable emission channel for at least a subset of bright GRBs. The work provides a physically grounded framework for interpreting GRB spectra, constraining sub-dominant thermal components, and motivating broader application of ICS models in future GRB analyses.

Abstract

Gamma-ray burst (GRB) prompt emission is commonly attributed to non-thermal radiation processes operating in the optically thin regions of a relativistic outflow. Among these, optically thin inverse-Compton (IC) scattering remains an important yet under-tested mechanism. From an initial set of 41 bursts selected using empirical Band-function criteria that highlight quasi-thermal low-energy slopes () and constrained high-energy indices (), only four events satisfy these conditions consistently in both time-integrated and time-resolved spectra. The IC fits yield self-consistent constraints on the seed-photon field and the electron population at the dissipation site. For bulk Lorentz factors -, we infer seed thermal peaks of - keV and electron thermal energies of - keV in the co-moving frame. A fraction of only - of electrons are accelerated into a non-thermal tail with an average index value of . The derived Comptonisation parameters indicate moderate values (-), optical depths -, and dissipation radii just above the photosphere, consistent with mildly relativistic (-), photon-dominated, low-magnetic-field dissipation environments. Furthermore, the framework allows us to constrain even sub-dominant thermal components that lie below the detector's low-energy threshold. Taken together, our results show that optically thin IC scattering offers a physically consistent and observationally viable explanation for the prompt emission in a subset of bright GRBs, motivating the application of IC models in future GRB studies.

Paper Structure

This paper contains 16 sections, 23 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. Criteria & Sample selection
  3. Motivation for the Criteria
  4. Optically thin inverse Compton scattering model
  5. Naima ICS Model Setup
  6. Fit Parameter Space
  7. Spectral Analysis
  8. Inverse Compton Characteristics and Jet Outflow Parameters
  9. Discussion
  10. Parameter Degeneracies and Fitting Uncertainties
  11. Synchrotron vs. IC Electron Distributions - Comparison
  12. Physical Implications: Spectral Fit $\&$ Derived Parameters
  13. Thermal Emission Constraints from IC Modelling
  14. Summary and Conclusions
  15. Summary of the catalog of 41 GRBs
  16. ...and 1 more sections

Figures (9)

  • Figure 1: The temporal evolution of the Band $\alpha$ (red triangles) and $\beta$ (black diamonds) within the $T_{70}$ interval (light-green vertical band) for the selected GRBs are shown. The red and grey horizontal shaded regions indicate the allowed ranges of $\alpha$ and $\beta$ used in the sample selection.
  • Figure 2: The multipanel figures show the counts per bin light curves for $0.5$ second binning, resolved into three energy ranges: 8-100 keV, 100-250 keV, and 250 keV-30 MeV for (a) GRB 131014A, (b) GRB 200829A, (c) GRB 200412A, and (d) GRB 230614C. For GRB 131014A, the light curves from LAT-LLE (30-100 MeV) and LAT ($>100$ MeV) are also included. The vertical dashed lines indicate the time resolved intervals determined using Bayesian Block binning applied to the time integrated segment of the burst, while the shaded grey region represents the $T_{70}$ interval of the burst.
  • Figure 3: The left panel shows the observed count spectra (top) together with the best-fit model counts (solid curves) and their corresponding residuals (bottom), while the right panel presents the associated $\nu F_{\nu}$ representation of the IC-model fit for the peak time interval of (a) GRB 131014A, (b) GRB 200412B, (c) GRB 200829A, and (d) GRB 230614C.
  • Figure 4: The temporal evolution of the best-fit parameters of the IC model for GRB 131014A is shown for: (a) the spectral index (grey circles), (b) $E_{\mathrm{th}}$ (orange squares) and $E_{c,\mathrm{seed}}$ (green hexagons), (c) $\delta$ (green triangles), and (d) $\Gamma$ (red hexagons). The temporal evolution of the derived physical parameters of the GRB131014A: (e) $\gamma_{th}$ (purple hexagon) and $\gamma_{min}$ (green square), (f) $A$ (red squares) and $\tau$ (black triangles), (g) $R_d$ (blue square), $R_{ph}$ (green circle), $R_s$ (red hexagon) and $R_0$ (grey diamond), (h) $N_e$ (red triangle) and $f_{N,pl}$ (grey hexagon), and (i) $F_{tot,ob}$ (red solid line) and $F_{comp,co}/F_{seed,co}$ (black squares).
  • Figure 5: The temporal evolution of the best-fit parameters of the IC model and physical parameters derived for GRB 200412B is presented in a format analogous to that of Figure \ref{['131014A_param']}.
  • ...and 4 more figures