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

## TL;DR

This study measures the shock heating energy of umbral flashes in sunspot umbrae using novel integral field spectroscopy, revealing that shock energy is insufficient to sustain the chromosphere and that shocks propagate at sound speed.

## Contribution

It introduces a new integral field spectrograph for detailed shock analysis in sunspot umbrae and quantifies shock properties and energies using radiative transfer modeling.

## Key findings

- Shock heating energy per unit mass is 2 x 10^{10} erg g^{-1}.
- Shocks propagate upward at the sound speed.
- Mach number does not depend on upstream temperature.

## Abstract

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. 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 x 10^{10} 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 upstream of the shocks. The latter may imply suppression of the amplification of the Mach number due to energy loss of the shocks.