MAGIC observations of the February 2014 flare of 1ES 1011+496 and ensuing constraint of the EBL density

Context. During February-March 2014, the MAGIC telescopes observed the high-frequency peaked BL Lac 1ES 1011 + 496 (z = 0.212) in flaring state at very-high energy (VHE, E > 100 GeV). The flux reached a level of more than ten times higher than any previously recorded flaring state of the source. Aims. To describe the characteristics of the flare presenting the light curve and the spectral parameters of the night-wise spectra and the average spectrum of the whole period. From these data we aim to detect the imprint of the extragalactic background light (EBL) in the VHE spectrum of the source, to constrain its intensity in the optical band. Methods. We analyzed the gamma-ray data from the MAGIC telescopes using the standard MAGIC software for the production of the light curve and the spectra. To constrain the EBL, we implement the method developed by the H.E.S.S. collaboration, in which the intrinsic energy spectrum of the source is modeled with a simple function (<= 4 parameters), and the EBL-induced optical depth is calculated using a template EBL model. The likelihood of the observed spectrum is then maximized, including a normalization factor for the EBL opacity among the free parameters. Results. The collected data allowed us to describe the night-wise flux changes and also to produce differential energy spectra for all nights in the observed period. The estimated intrinsic spectra of all the nights could be fitted by power-law functions. Evaluating the changes in the fit parameters, we conclude that the spectral shape for most of the nights were compatible, regardless of the flux level, which enabled us to produce an average spectrum from which the EBL imprint could be constrained. The likelihood ratio test shows that the model with an EBL density 1.07 (-0.20, + 0.24)(stat+sys), relative to the one in the tested EBL template, is preferred at the 4.6 sigma level to the no-EBL hypothesis, with the assumption that the intrinsic source spectrum can be modeled as a log-parabola. This would translate into a constraint of the EBL density in the wavelength range [0.24 mu m, 4.25 mu m], with a peak value at 1.4 mu m of lambda F-lambda = 12. 27(-2.29)(+2.75) nWm(-2) sr(-1), including systematics.