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

On 2014 December 7 we used new integral field spectroscopy techniques to observe umbral flashes, which 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 HeI triplet obtained with the SpectroPolarimetric Imager for the Energetic Sun (SPIES), which is novel integral field unit spectrograph at the Dunn Solar Telescope. We determine the shock properties (the Mach number and the propagation speed) by fitting the measured HeI spectral profiles with a theoretical radiative transfer model using 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 as 2 x 10¹⁰ erg/g. We conclude that the estimated shock heating energy rate is less than the amount required to maintain the umbral chromosphere.