Impact of model parameter degeneracy on leptonic radiation models

The case of blazar multiwavelength spectra

¹ Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), Universitätsstraße 150, 44801 Bochum, Germany
² Ruhr Astroparticle and Plasma Physics Center (RAPP Center), Germany
³ University of Hamburg, MIN Department, Bundesstraße 55, 20146 Hamburg, Germany

^★ Corresponding authors: apel@astro.rub.de; omeliukh@astro.rub.de

Received: 6 June 2025
Accepted: 10 August 2025

Abstract

Context. Leptonic one-zone radiation models are commonly used to describe multiwavelength data and explore the physical properties of high-energy sources, such as active galactic nuclei. However, these models often require a large number of free parameters.

Aims. In the context of a possible parameter degeneracy and the complex landscape of the parameter space, we study how the choice of the fitting procedure impacts the characterization of the source properties. Furthermore, we examine how the data coverage and the uncertainties associated with the data influence the model parameter degeneracy.

Methods. We generated simulated spectral energy distribution datasets with different properties and fit them with a numerical model, using seven free parameters to describe the relevant radiation processes. We compared different optimization algorithms and studied the parameter degeneracy using t-distributed stochastic neighbor embedding. In addition, we applied the same fitting procedures to the observational data of two sources: Mrk 501 and PKS 0735+178.

Results. We demonstrate significant degeneracies in the seven-dimensional parameter space of the one-zone leptonic models caused by the incomplete wavelength coverage of the data. Given the same goodness-of-fit function, we find that the best-fit result depends on the choice of the minimization algorithm.

Conclusions. Source properties extracted from the best-fit solution and applied to realistic datasets cannot be interpreted as the only solution given the significant degeneracies in the model parameters. We find that adding new energy ranges (e.g., MeV) and regular source monitoring would allow for the gaps in the data to be reduced, significantly decreasing the parameter degeneracy.