  Acoustic modes of oscillation are affected by stellar activity, however it is
unclear how starspots contribute to these changes. Here we investigate the
nonmagnetic effects of starspots on global modes with angular degree $\ell \leq
2$ in highly active stars, and characterize the spot seismic signature on
synthetic light curves. We perform 3D time-domain simulations of linear
acoustic waves to study their interaction with a model starspot. We model the
spot as a 3D change in the sound speed stratification with respect to a
convectively stable stellar background, built from solar Model S. We perform a
parametric study by considering different depths and perturbation amplitudes.
Exact numerical simulations allow the investigation of the wavefield-spot
interaction beyond first order perturbation theory. The interaction of the
axisymmetric modes with the starspot is strongly nonlinear. As mode frequency
increases, the frequency shifts for radial modes exceed the value predicted by
linear theory, while the shifts for the $\ell=2, m=0$ modes are smaller than
predicted by linear theory, with avoided-crossing-like patterns forming between
the $m=0$ and $m=1$ mode frequencies. The nonlinear behavior increases with
increasing spot amplitude and/or decreasing depth. Linear theory still
reproduces the correct shifts for nonaxisymmetric modes. In the nonlinear
regime the mode eigenfunctions are not pure spherical harmonics, but rather a
mixture of different spherical harmonics. This mode mixing, together with the
frequency changes, may lead to misidentification of the modes in the observed
acoustic power spectra.
