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

## TL;DR

This study uses numerical simulations to explore how the depth of the wave source beneath sunspots affects the observed photospheric waves, revealing that observed waves are consistent with sources located 1 to 5 Mm below the surface.

## Contribution

It provides a parametric analysis linking wave observations to their subsurface source depths, enhancing understanding of sunspot wave dynamics.

## Key findings

- Waves are consistent with sources between 1 and 5 Mm deep.
- Numerical simulations match observational data.
- Wave speeds exceed characteristic velocities in sunspots.

## 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.