Shock heating energy in an umbra of a sunspot with integral field unit spectroscopy

Umbral flashes are periodic brightness increases routinely observed in the core of chromospheric lines within sunspot umbrae and are attributed to propagating shock fronts. In this work we quantify the shock heating energy of these umbral flashes using observations in the near infrared He I triplet obtained on 2014 December 7 with the SpectroPolarimetric Imager for the Energetic Sun (SPIES), which is a novel integral field unit spectrograph at the Dunn Solar Telescope. The SPIES is a prototype instrument of a facility instrument of the Daniel K. Inouye Solar Telescope. We determine the shock properties (the Mach number and the propagation speed) by fitting the measured He I spectral profiles with a theoretical radiative transfer model consisting of two constant property atmospheric slabs whose temperatures and macroscopic velocities are constrained by the Rankine-Hugoniot relations. From the Mach number, the shock heating energy per unit mass of plasma is derived to be 2 × 1010 erg g−1, which is insufficient to maintain the umbral chromosphere. In addition, we find that the shocks propagate upward with the sound speed and the Mach number does not depend on the temperature in the upstream of the shocks. The latter may imply suppression of the amplification of the Mach number due to strong viscosity and/or energy loss of the shocks.