  We seek to clarify the nature of running penumbral (RP) waves: are they
chromospheric trans-sunspot waves or a visual pattern of upward-propagating
waves? Full Stokes spectropolarimetric time series of the photospheric Si I
10827 \AA line and the chromospheric He I 10830 \AA multiplet were inverted
using a Milne-Eddington atmosphere. Spatial pixels were paired between the
outer umbral/inner penumbral photosphere and the penumbral chromosphere using
inclinations retrieved by the inversion and the dual-height pairings of
line-of-sight velocity time series were studied for signatures of wave
propagation using a Fourier phase difference analysis. The dispersion relation
for radiatively cooling acoustic waves, modified to incorporate an inclined
propagation direction, fits well the observed phase differences between the
pairs of photospheric and chromospheric pixels. We have thus demonstrated that
RP waves are in effect low-beta slow-mode waves propagating along the magnetic
field.
