First Calorimetric Measurement of OI-line in the Electron Capture Spectrum of $^{163}$Ho

The isotope $^{163}$Ho undergoes an electron capture process with a recommended value for the energy available to the decay, $Q_{\rm EC}$, of about 2.5 keV. According to the present knowledge, this is the lowest $Q_{\rm EC}$ value for electron capture processes. Because of that, $^{163}$Ho is the best candidate to perform experiments to investigate the value of the electron neutrino mass based on the analysis of the calorimetrically measured spectrum. We present for the first time the calorimetric measurement of the atomic de-excitation of the $^{163}$Dy daughter atom upon the capture of an electron from the 5s shell in $^{163}$Ho, OI-line. The measured peak energy is 48 eV. This measurement was performed using low temperature metallic magnetic calorimeters with the $^{163}$Ho ion implanted in the absorber. We demonstrate that the calorimetric spectrum of $^{163}$Ho can be measured with high precision and that the parameters describing the spectrum can be learned from the analysis of the data. Finally, we discuss the implications of this result for the Electron Capture $^{163}$Ho experiment, ECHo, aiming to reach sub-eV sensitivity on the electron neutrino mass by a high precision and high statistics calorimetric measurement of the $^{163}$Ho spectrum.