  Context: Resistive Ohmic dissipation has been suggested as a mechanism for
heating the solar chromosphere, but few studies have established this
association. Aim: We aim to determine how Ohmic dissipation by electric
currents can heat the solar chromosphere. Methods: We combine high-resolution
spectroscopic Ca II data from the Dunn Solar Telescope and vector magnetic
field observations from the Helioseismic and Magnetic Imager (HMI) to
investigate thermal enhancements in a sunspot light bridge. The photospheric
magnetic field from HMI was extrapolated to the corona using a non-force-free
field technique that provided the three-dimensional distribution of electric
currents, while an inversion of the chromospheric Ca II line with a local
thermodynamic equilibrium and a nonlocal thermodynamic equilibrium spectral
archive delivered the temperature stratifications from the photosphere to the
chromosphere. Results: We find that the light bridge is a site of strong
electric currents, of about 0.3 A/m^2 at the bottom boundary, which extend to
about 0.7 Mm while decreasing monotonically with height. These currents produce
a chromospheric temperature excess of about 600-800 K relative to the umbra.
Only the light bridge, where relatively weak and highly inclined magnetic
fields emerge over a duration of 13 hr, shows a spatial coincidence of thermal
enhancements and electric currents. The temperature enhancements and the
Cowling heating are primarily confined to a height range of 0.4-0.7 Mm above
the light bridge. The corresponding increase in internal energy of 200 J/m^3
can be supplied by the heating in about 10 min. Conclusions: Our results
provide direct evidence for currents heating the lower solar chromosphere
through Ohmic dissipation.
