The Generation of Coronal Loop Waves below the Photosphere byp‐Mode Forcing

Abstract

Recent observations of coronal-loop waves by TRACE and within the corona as a whole byCoMP clearly indicate that the dominant oscillation period is 5 minutes, thus implicating the solar p modes as a possible source. We investigate the generation of tube waves within the solar convection zone by the buffeting of p modes. The tube waves-in the form of longitudinal sausage waves and transverse kink waves-are generated on the many magnetic fibrils that lace the convection zone and pierce the solar photosphere. Once generated by p-mode forcing, the tube waves freely propagate up and down the tubes, since the tubes act like light fibers and form a waveguide for these magnetosonic waves. Those waves that propagate upward pass through the photosphere and enter the upper atmosphere where they can be measured as loop oscillations and other forms of propagating coronal waves. We treat the magnetic fibrils as vertically aligned, thin flux tubes and compute the energy flux of tube waves that can generated and driven into the upper atmosphere. We find that a flux in excess of 10 5 ergs cm −2 s −1 can be produced, easily supplying enough wave energy to explain the observations. Furthermore, we compute the associated damping rate of the driving p modes and find that the damping is significant compared to observed line widths only for the lowest order p modes.

Damping rates of p-modes by an ensemble of randomly distributed thin magnetic flux tubes

“…The pressure, density and sound speed vary as power laws (see Bogdan et al 1996 for details). Following Bogdan et al (1996), Hindman & Jain (2008) and Jain et al (2009) we set the truncation depth at z = −z 0 352 A. Gascoyne & R. Jain which is our model photosphere where the quantities ρ 0 and P 0 are the values of the mass density and gas pressure at this depth. Above the truncation depth z > −z 0 we assume the existence of a hot vacuum (ρ ext → 0 with temperature T ext → ∞).…”

“…For these thin magnetic flux tubes, the lateral variation of the magnetic field across the tube is ignored and the plasma β is constant with depth (see Bogdan et al 1996 andJain 2008 for details).…”

“…In this paper we will also ignore the kink waves and specifically concentrate on the m = 0 mode (m being the azimuthal order). Using the formulation of Jain et al (2009) (see also Jain 2008 andBogdan et al 1996), the fluid displacement due to the excitation of sausage waves within the tube can be described by the following equation,…”

“…Also, it is found that the absorption is frequency dependent. Thus, the importance of sub-surface field structure in modifying the properties of f-and p-modes has been realised and many theoretical investigations have concentrated on understanding the physical mechanism responsible for this absorption (e.g., Spruit 1991;Bogdan & Cally 1995;Bogdan et al 1996;Crouch & Cally 2005;Hindman & Jain 2008;Jain et al 2009).…”

“…We construct a model consistent with Hindman & Jain (2008) in order to calculate damping rates produced by the excitation of sausage tube waves across the whole Sun. In Hindman & Jain (2008) they used an idealised model where by each tube of the ensemble was identical; this need not be the case. Thus we use a random ensemble of thin, axisymmteric, vertical magnetic flux tubes with varying plasma-β.…”