Dependence of sunspot photospheric waves on the depth of the source of solar $p-$modes

Abstract

Photospheric waves in sunspots moving radially outwards at speeds faster than the characteristic wave velocities have been recently detected. It has been suggested that they are the visual pattern of $p-$modes excited around 5 Mm beneath the sunspot. Using numerical simulations, we have performed a parametric study of the waves observed at the photosphere and higher layers produced by sources located at different depths. The observational measurements are consistent with waves driven between approximately 1 Mm and 5 Mm below the sunspot surface.

Accepted for publication in A&A