Multi-messenger characterization of Mrk 501 during historically low X-ray and γ\gamma-ray activity

We study the broadband emission of the TeV blazar Mrk501 using multi-wavelength (MWL) observations from 2017 to 2020 performed with a multitude of instruments, involving, among others, MAGIC, Fermi-LAT, NuSTAR, Swift, GASP-WEBT, and OVRO. During this period, Mrk501 showed an extremely low broadband activity, which may help to unravel its baseline emission. Despite the low activity, significant flux variations are detected at all wavebands, with the highest variations occurring at X-rays and VHE $\gamma$-rays. A significant correlation (>3$\sigma$) between X-rays and VHE $\gamma$-rays is measured, supporting leptonic scenarios to explain the variable parts of the spectral energy distribution (SED), also during low activity states. Extending our data set to 12-years (from 2008 to 2020), we find significant correlations between X-rays and HE $\gamma$-rays, indicating, for the first time, a common physical origin driving the variability between these two bands. We additionally find a correlation between HE $\gamma$-rays and radio, with the radio emission lagging the HE $\gamma$-ray emission by more than 100 days. This is consistent with the $\gamma$-ray emission zone being located upstream of the radio-bright regions of the Mrk501 jet. Furthermore, Mrk501 showed a historically low activity in both X-rays and VHE $\gamma$-rays from mid-2017 to mid-2019 with a stable VHE flux (>2TeV) of 5% the emission of the Crab Nebula. The broadband SED of this 2-year long low-state, the potential baseline emission of Mrk501, can be adequately characterized with a one-zone leptonic model, and with (lepto)-hadronic models that fulfill the neutrino flux constraints from IceCube. We explore the time evolution of the SED towards the historically low-state, revealing that the stable baseline emission may be ascribed to a standing shock, and the variable emission to an additional expanding or traveling shock