A novel approach to identify resonant MHD wave modes in solar pores and sunspot umbrae: $B-\omega$ analysis

The umbral regions of sunspots and pores in the solar photosphere are generally dominated by $3$~mHz oscillations, which are due to $p$-modes penetrating the magnetic region. In these locations, wave power is also significantly reduced with respect to the quiet Sun. However, here we study a pore where the power of the oscillations in the umbra is not only comparable, or even larger than that of the quiet Sun, but the main dominant frequency is not $3$~mHz as expected, but instead $5$~mHz. By combining Doppler velocities and spectropolarimetry and analysing the relationship between magnetic field strength and frequency, the resultant $B-\omega$ diagram reveals distinct ridges which are remarkably clear signatures of resonant MHD oscillations confined within the pore umbra. In addition to velocity oscillations, we demonstrate that these modes are also accompanied by magnetic oscillations, as predicted from MHD theory. The novel technique of $B-\omega$ analysis, proposed in this Letter, opens an exciting new avenue for identifying MHD wave modes in the umbral regions of both pores and sunspots.