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Using data from the Helioseismic Magnetic Imager, we report on the amplitudesand phase relations of oscillations in quiet-Sun, plage, umbra and the polarityinversion line (PIL) of an active region NOAA$\#$11158. We employ Fourier,wavelet and cross correlation spectra analysis. Waves with 5-minute periods areobserved in umbra, PIL and plage with common phase values of${\phi}(v,I)=\frac{\pi}{2}$, ${\phi}(v,B_{los})=-\frac{\pi}{2}$. In addition,${\phi}(I,B_{los})=\pi$ in plage are observed. These phase values areconsistent with slow standing or fast standing surface sausage wave modes. Theline width variations, and their phase relations with intensity and magneticoscillations, show different values within the plage and PIL regions, which mayoffer a way to further differentiate wave mode mechanics. Significant Dopplervelocity oscillations are present along the PIL, meaning that plasma motion isperpendicular to the magnetic field lines, a signature of Alv\`enic waves. Atime-distance diagram along a section of the PIL shows Eastward propagatingDoppler oscillations converting into magnetic oscillations; the propagationspeeds range between 2$-$6 km s$^{-1}$. Lastly, a 3-minute wave is observed inselect regions of the umbra in the magnetogram data.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

Oscillations observed in Umbra, Plage, Quiet-Sun and the Polarity Inversion Line of Active Region 11158 using HMI/SDO Data