CERN Accelerating science

Spectral energy distributions of the four extreme blazars detected with the MAGIC telescopes and for the hint-of-signal source in E$^{2}$ dN/dE representation: observed data (open {gray} markers) and EBL-corrected data (filled black markers) using the \citet{2008AA...487..837F} model. The dashed lines represent the power-law fit to the EBL-corrected data.

\textit{Left panels:} X-ray light curve (2-10\,keV), corrected for Galactic extinction of the sample. The red {squares} show the data point which are used in broadband SED modeling. Shadowed areas illustrate MAGIC observation windows. \textit{Right panels:} Scatter plot of the power-law photon index ($\Gamma$) versus X-ray flux (2-10\,keV) measured with {\it Swift}-XRT for each source of the sample. Dashed lines are the best-fitted linear models fitted to the data of each source.

Broadband SED and modeled spectrum for 1ES~ 0229+200 (archetipal EHBL) and the {four VHE gamma-ray sources detected with MAGIC presented in the study. The broadband SED of RGB J2042+244, for which a hint of signal was detected at VHE gamma-rays is also shown}. Red points represent contemporaneous UVOT, XRT, {\it NuSTAR}, {\it Fermi}-LAT and MAGIC data considered in the fit. Gray markers are archival data from ASDC website. Blue, dashed line is the result of the conical-jet SSC model. Black continuous line represents the outcome of the spine-layer model. Dashed-dotted magenta line is the outcome of the proton-synchrotron model. The third bump in the proton-synchrotron model is the expected neutrino flux resulting from the best fit solution proposed. Details in the text.

Broadband SED and modeled spectra for four sources with no MAGIC detection or hints (but {\it Fermi}-LAT detection) presented in the study. Red points represent contemporaneous UVOT, XRT, NuSTAR, {\it Fermi}-LAT and MAGIC data considered in the fit. Gray markers are archival data from SSDC website. Blue, dashed line is the result of the conical-jet SSC model. Details in the text.

U$_B$/U$e$ distribution as a function of R/R$_0$ for the sources considered in this study in the SSC model (see Tab.~\ref{param_tab}).

1ES~1426+428 multi-year MAGIC VHE gamma-ray light curve above 200 GeV between 2011 and 2013. Black downward-pointing arrows correspond to 95 per cent confidence upper limits, which were computed for the observations where the interval of the measured flux (black points) $\pm$ twice the error contains zero.

Correlation study between the spectral index describing the average spectrum in the HE gamma-ray band and the integral HE gamma-ray flux between 1 and 100 GeV, both reported in Table~\ref{tab:src_lat}. Filled and open circles refer to sources detected and not detected at VHE gamma rays, respectively. The hint-of-signal source is considered here among the detected sources.

\textit{Left}: X-ray power law index versus integral flux (2-10\,keV) from the analysis of the average {\it Swift}-XRT spectra during MAGIC data taking, as reported in Table~\ref{tab:spectra_xrt}. Filled red markers are sources detected at VHE, while open markers represent sources still undetected at VHE. {The hint-of-signal source is considered here among the detected sources.} \textit{Right}: power law index in the X-ray band, from Table\,\ref{tab:spectra_xrt}, and the power law index of the the EBL-corrected (intrinsic) spectrum measured in the VHE gamma-ray band, reported in Table~\ref{tab:spectr_table_magic}.

Left: {\it NuSTAR} (black, FPMA, and red, FPMB, points) and {\it Swift}-XRT (green points) spectra and residuals for TXS~0210+515 collected on 2016 January 30 simultaneously fitted with a log parabola model. Right: {\it NuSTAR} (red and black points) and {\it Swift}-XRT (green points) spectra and residuals of RGB~2313+147 collected on 2015 May 30 simultaneously fitted with a power law model.

SED of RBS~0921, the unique source of the sample still undetected at gamma rays.

The maximum neutrino flux expected from the proton-synchrotron model applied to six EHBLs. The IceCube sensitivity \citep{Aartsen2019} for three different declinations is also represented.