Parameter Estimation Limits in Blazars

TL;DR

This paper applies Fisher Information analysis to quantify the fundamental limits of parameter estimation in blazar spectral models, revealing significant differences between SSC and EC models and emphasizing the importance of time-resolved data.

Contribution

It introduces a Fisher Information framework to assess the theoretical bounds of parameter inference in blazar SED models, highlighting the constraints on key parameters like the Doppler factor.

Findings

Fisher information in EC models is over 10,000 times less than in SSC models.

Doppler factor $$ carries 100-1000 times more Fisher information than other parameters.

Time-resolved SED modeling is crucial for constraining physical parameters in EC-dominated blazars.

Abstract

Parameter degeneracy in blazar spectral energy distributions (SEDs) is known but rarely quantified. This paper introduces a Fisher Information approach to determine theoretical limits to information extraction in the context of one-zone models. By evaluating the total Fisher Information by varying $\delta$, $B$, $p$, $\gamma_{\rm min}$ and $\gamma_{\rm max}$, we find that EC models encode Fisher information $\gtrsim10^4$ times less than that in SSC models, establishing differences in limits of physical information extraction even in the case of perfect sampling. Moreover, the Fisher information in both SSC and EC models exhibit strong fluctuations across the parameter space, but since the magnitudes are orders of magnitude lower in EC, limits of parameter inference are expected to be worse in FSRQ SEDs than BL Lacs. We also find that the Doppler factor $\delta$ carries at least $10^{2-3}$ more Fisher information than that for $p$ and $B$ in both EC and SSC, making $\delta$ the most constrained SED parameter. Applying our Fisher Information motivated framework to real flaring SEDs of Flat Spectrum Radio Quasars (FSRQs) CTA 102 and 3C 279, we show that mild variations in $\delta$ and $p$ can appreciably produce the flaring SEDs starting from the quiescent model, while two other flares in 3C 279 simple geometric and spectral considerations cannot reproduce the flares, reducing the efficacy of one-zone models. We propose that time-resolved SED models are indispensable to constraining physical parameters in EC-dominated blazars.