Statistical Insights into Flux and Photon Index Distributions of VHE FSRQs from Fermi-LAT Observations

TL;DR

This paper analyzes 16 years of Fermi-LAT data on VHE FSRQs, revealing double lognormal flux and index distributions, and explores their variability patterns, correlations, and spectral behaviors across different timescales.

Contribution

It provides the first detailed statistical analysis of flux and photon index distributions of VHE FSRQs, highlighting the significance of timescale in capturing blazar states and spectral trends.

Findings

Double lognormal profiles in flux and index distributions at short timescales.

Most VHE FSRQs show a harder-when-brighter trend.

Correlation between flux and photon index increases with longer time bins.

Abstract

This study examines the flux and photon index distributions of 11 Very High Energy (VHE) Flat Spectrum Radio Quasars (FSRQs) using over 16 years of Fermi-LAT $\gamma$-ray data. The distributions reveal double lognormal profiles in both flux and index, primarily in the 3-day and 7-day binnings, supporting the ``two-flux-state hypothesis" for blazars. These profiles, which become insignificant at 30-day binning, suggest that shorter timescales are better at capturing distinct states, while longer timescales smooth out shorter variations. Most VHE FSRQs exhibit a ``harder-when-brighter" trend, where the photon index decreases during high-flux states, suggesting efficient particle acceleration and possibly reduced radiative cooling. In contrast, two sources display a ``softer-when-brighter" behavior, likely due to enhanced radiative cooling in high photon density environments. Additionally, we observe that the Spearman rank correlation between flux and photon index strengthens with increasing time bin sizes, indicating more pronounced correlations over longer timescales. This possibly indicates that, on shorter timescales, flux variations are driven by a combination of photon index changes and normalization effects. Averaging flux over longer durations minimizes the effect of normalization variation, thereby enhancing the observed correlation. We also compare the flux and index distributions of VHE and non-VHE FSRQs, emphasizing the differences in their variability and emission patterns.