The scattering of f-modes by magnetic tubes is analyzed using
three-dimensional numerical simulations. An f-mode wave packet is propagated
through a solar atmosphere embedded with three different flux tube models which
differ in radius and total magnetic flux. A quiet Sun simulation without a tube
present is also performed as a reference. Waves are excited inside the flux
tube and propagate along the field lines, and jacket modes are generated in the
surroundings of the flux tube, carrying 40% as much energy as the tube modes.
The resulting scattered wave is mainly an f-mode composed of a mixture of m=0
and m=+/-1 modes. The amplitude of the scattered wave approximately scales with
the magnetic flux. A small amount of power is scattered into the p_1-mode. We
have evaluated the absorption and phase shift from a Fourier-Hankel
decomposition of the photospheric vertical velocities. They are compared with
the results obtained from the emsemble average of 3400 small magnetic elements
observed in high-resolution MDI Doppler datacubes. The comparison shows that
the observed dependence of the phase shift with wavenumber can be matched
reasonably well with the simulated flux tube model. The observed variation of
the phase-shifts with the azimuthal order m appears to depend on details of
the ensemble averaging, including possible motions of the magnetic elements and
asymmetrically shaped elements.Comment: Accepted for publication in The Astrophysical Journa
