Spectral Energy Distribution Modeling of Markarian 501 through a non-linear least square minimization

So far the Spectral Energy Distribution (SED) of Active Galactic Nuclei (AGN), in particular blazars, have been obtained in a heuristics way. This is mainly due to both the many free parameters of the emission model and the severe lack of simultaneous multi-frequency data. This leads to non-rigorous and possibly biased analyses, and makes it difficult to compare results coming from different analyses. However, recent simultaneous multi-frequency campaigns are providing long-term broad-band coverages of source activity, and large multi-frequency data sets are becoming available. So emission model fitting may be attempted with better profit now. The main aim of this thesis is to develop a statistical approach that fits AGN SEDs in a rigorous way. Such an approach consists in a Chi squared -minimization, based on the Levenberg-Marquardt algorithm, that returns the most likely values of the SED parameters, plus a method devised to obtain the related uncertaintes. The whole minimization process is implemented in a C++ code. However, this approach may reveal unexpected features of the Chi squared-manifold that might affect convergence, due to spurious correlations between model parameters and/or inadequacy of the currently available datasets. For these reasons, a statistical analysis will be carried out on the solutions obtained from several minimizations, each starting from different points of the parameter space. This approach is applied to different activity states of the blazar Markarian 501, in a Synchrotron Self Compton (SSC) framework. In particular, starting from available observations of this source taken with the ground-based Major Atmospheric Gamma-ray Imaging Cherenkov telescopes (MAGIC) in 2011, 7 multi-frequency datasets were obtained. Based on multi-frequency and simultaneity requirements, all datasets include also data provided by the Swift UVOT, Swift XRT, and Fermi LAT orbiting telescopes. The SED modelling of each dataset will be performed through a non-linear Chi squared-minimization in order to obtain the most likely values of the parameters describing the SSC model. Finally, it is worth remarking that this approach is not only a rigorous statistical method to find the most likely source parameters for different scenarios, but it also represents a powerful tool to efficiently discriminate between different emission models.