Comparison of Exact and Approximate MHD Slow Body Mode Solutions in Photospheric Waveguides

Abstract In this study, we explore the possibility of simplifying modeling magnetohydrodynamic slow body modes observed in photospheric magnetic structures such as umbrae sunspots and pores. The approach assumes that variation eigenvalues waves can be derived by imposing longitudinal component velocity with respect to tube axis is zero at boundary flux tube, which good agreement observations. To justify our approach, compare results simplified model for cylindrical tubes prediction obtained continuity radial total pressure tube. Our show that, a high accuracy (less than 1% considered model), conditions transversal neglected when under conditions.