Seismological determination of the Alfv\'{e}n speed and plasma-beta in solar photospheric bright points

The Alfv\'{e}n speed and plasma beta in photospheric bright points observed by the Broadband Filter Imager (BFI) of the Solar Optical Telescope (SOT) on board the \textit{Hinode} satellite, are estimated seismologically. The diagnostics is based on the theory of slow magnetoacoustic waves in a non-isothermally stratified photosphere with a uniform vertical magnetic field. We identify and track bright points in a G-band movie by using the 3D region growing method, and align them with blue continuum images to derive their brightness temperatures. From the Fourier power spectra of 118 continuum light curves made in the bright points, we find that light curves of 91 bright points have oscillations with properties which are significantly different from oscillation in quiet regions, with the periods ranging 2.2--16.2~min. We find that the model gives a moderate value of the plasma beta when $\gamma$ lies at around 5/3. The calculated Alfv\'{e}n speed is 9.68$\pm$2.02~km~s$^{-1}$, ranging in 6.3--17.4~km~s$^{-1}$. The plasma beta is estimated to be of 0.93$\pm$0.36, ranging in 0.2--1.9.