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Umbral flashes are periodic brightness increases routinely observed in thecore of chromospheric lines within sunspot umbrae and are attributed topropagating shock fronts. In this work we quantify the shock heating energy ofthese umbral flashes using observations in the near infrared He I tripletobtained on 2014 December 7 with the SpectroPolarimetric Imager for theEnergetic Sun (SPIES), which is a novel integral field unit spectrograph at theDunn Solar Telescope. We determine the shock properties (the Mach number andthe propagation speed) by fitting the measured He I spectral profiles with atheoretical radiative transfer model consisting of two constant propertyatmospheric slabs whose temperatures and macroscopic velocities are constrainedby the Rankine-Hugoniot relations. From the Mach number, the shock heatingenergy per unit mass of plasma is derived to be 2 x 10^{10} erg g^{-1}, whichis insufficient to maintain the umbral chromosphere. In addition, we find thatthe shocks propagate upward with the sound speed and the Mach number does notdepend on the temperature upstream of the shocks. The latter may implysuppression of the amplification of the Mach number due to energy loss of theshocks.

Shock Heating Energy of Umbral Flashes Measured with Integral Field Unit Spectroscopy