Long-term multi-wavelength study of 1ES 0647+250

Context. The BL Lac object 1ES 0647+250 is one of the few distant γ-ray emitting blazars detected at very high energies (VHEs; ≳100 GeV) during a non-flaring state. It was detected with the MAGIC telescopes during a period of low activity in the years 2009−2011 as well as during three flaring activities in the years 2014, 2019, and 2020, with the highest VHE flux in the last epoch. An extensive multi-instrument data set was collected as part of several coordinated observing campaigns over these years. Aims. We aim to characterise the long-term multi-band flux variability of 1ES 0647+250, as well as its broadband spectral energy distribution (SED) during four distinct activity states selected in four different epochs, in order to constrain the physical parameters of the blazar emission region under certain assumptions. Methods. We evaluated the variability and correlation of the emission in the different energy bands with the fractional variability and the Z-transformed discrete correlation function, as well as its spectral evolution in X-rays and γ rays. Owing to the controversy in the redshift measurements of 1ES 0647+250 reported in the literature, we also estimated its distance in an indirect manner through a comparison of the GeV and TeV spectra from simultaneous observations with Fermi-LAT and MAGIC during the strongest flaring activity detected to date. Moreover, we interpret the SEDs from the four distinct activity states within the framework of one-component and two-component leptonic models, proposing specific scenarios that are able to reproduce the available multi-instrument data. Results. We find significant long-term variability, especially in X-rays and VHE γ rays. Furthermore, significant (3−4σ) correlations were found between the radio, optical, and high-energy (HE) γ-ray fluxes, with the radio emission delayed by about ∼400 days with respect to the optical and γ-ray bands. The spectral analysis reveals a harder-when-brighter trend during the non-flaring state in the X-ray domain. However, no clear patterns were observed for either the enhanced states or the HE (30 MeV < E < 100 GeV) and VHE γ-ray emission of the source. The indirect estimation of the redshift yielded a value of z = 0.45 ± 0.05, which is compatible with some of the values reported in the literature. The SEDs related to the low-activity state and the three flaring states of 1ES 0647+250 can be described reasonably well with the both one-component and two-component leptonic scenarios. However, the long-term correlations indicate the need for an additional radio-producing region located about 3.6 pc downstream from the gamma-ray producing region