Solar p-modes in a vertical magnetic field - Trapped and damped pi-modes

Simulation of [CLC][ITAL]f[/ITAL][/CLC]- and [CLC][ITAL]p[/ITAL][/CLC]-Mode Interactions with a Stratified Magnetic Field Concentration

“…Indeed, it would be a great advance if we could settle on the basic physical mechanism. One possibility is that when the f-or p-modes encounter magnetic field concentrations such as sunspots, there is a partial conversion to magnetoacoustic slow modes, or s-modes, and torsional Alfvén waves, which are channeled along the field lines into the solar interior (Roberts & Soward 1983;Spruit 1991;Spruit & Bogdan 1992;Cally & Bogdan 1993;Cally, Bogdan, & Zweibel 1994, hereafter CBZ;Cally 1995;Hindman, Zweibel, & Cally 1996). At large depths, the s-modes are essentially Alfvénic in character.…”

Oscillations on the Sun in regions with a vertical magnetic field

“…3) that energy can leak from the sunspot umbra to the corona and deep layers of a sunspot in the form of slow MHD waves. The radiation of the waves to the corona and deep layers of a sunspot implies that the eigenfrequencies of the umbral oscillations must be complex (ω = ω r + iω i ) (see Zhukov & Efremov 1988;Cally & Bogdan 1993;Bogdan & Cally 1997), and therefore the results obtained in the present paper are reliable provided that ω i /ω r 1, i.e. the leakage of the wave energy from the umbral resonator is sufficiently small.…”

“…In fact, however, (see Zhukov & Efremov 1988;Cally & Bogdan 1993;Cally et al 1994;Bogdan & Cally 1997;Lites et al 1998;Settele at al. 1999), in order to correctly carry out the numerical integration of the set of Eqs.…”

“…Starting from the study of Uchida & Sakurai (1975), the spectrum of eigenmodes of umbral oscillations has been calculated (Scheuer & Thomas 1981;Thomas & Scheuer 1982;Zhukov et al 1987;Wood 1990Wood , 1997Hasan 1991;Cally & Bogdan 1993;Cally et al 1994;Bogdan & Cally 1997;Gore 1997Gore , 1998Lites et al 1998). In the second approach, Zugzda et al (1983Zugzda et al ( , 1984Zugzda et al ( , 1987; Settele et al (1999) (see also Gurman & Leibacher 1984) calculated the coefficient of the transmission for a longitudinal wave mode excited by broad-band noise from the deep layers of the convective zone.…”

“…In the weak field approximation (v A /c 1), the full set of equations of magnetohydrodynamics proved to be divided into two independent subsystems whose asymptotes can be easily obtained (Sect. 3, see also Hasan & Christensen-Dalsgaard 1992 (for the isothermal atmosphere) and Cally & Bogdan 1993;Cally et al 1994;Bogdan & Cally 1997 (for the polytropic atmosphere)) and, hence, the problem of calculation of the eigenmodes of the umbral oscillations can be completely defined.…”