The origin of cutoff frequencies for torsional tube waves propagating in the solar atmosphere

Abstract

Torsional waves supported by magnetic flux tubes have long been thought to bear a high potential for supplying energy and momentum to the upper solar atmosphere, thereby contributing to its heating and to the driving of dynamic events like spicules. This hope rested on the belief that their propagation is not impeded by cutoff restrictions, unlike longitudinal and kink waves. We point out that this applies only to thin, isothermal tubes. When they widen in the chromosphere, and as a result of temperature gradients, cutoff restrictions arise. We compare them to recent observational reports of such waves and of vortex motions and find that their long period components are already affected by cutoff restrictions. An observational strategy is proposed that should permit the derivation of better information on vortex flows from off-center observations with next generation telescopes.

Height variation of the cutoff frequency in a sunspot umbra

“…The situation described above does not take into account magnetic fields, which modify not only the existing temperature and pressure stratification, but also introduce new types of waves. The cutoffs of magnetohy-drodynamic (MHD) waves in isothermal atmospheres with uniform magnetic field (e.g., Thomas 1982Thomas , 1983Campos 1986;Stark & Musielak 1993;Roberts 2006) and magnetic fluxtubes (e.g., Rae & Roberts 1982;Roberts 1983;Hammer et al 2010;Murawski & Musielak 2010;Routh et al 2013;Perera et al 2015) have been thoroughly explored. Using the Solar Optical Telescope aboard Hinode spacecraft, Fujimura & Tsuneta (2009) measured the phase differences between line-of-sight (LOS) velocity and magnetic flux in pores and intergranular magnetic structures, and concluded that the observations are consistent with standing sausage and/or kink MHD waves.…”

New Cutoff Frequency for Torsional Alfv'en Waves Propagating along Wide Solar Magnetic flux Tubes

“…We determined the conditions for propagation of linear (fully incompressible) torsional Alfvén waves along an isolated and isothermal magnetic flux tube embedded in the solar chromosphere and corona. The main difference between the results of this paper and those considered previously (e.g., Hollweg (1981Hollweg ( , 1982; Musielak et al (2007); Routh et al (2007Routh et al ( , 2010; Hammer et al (2010)) is the fact that in the previous work thin magnetic flux tubes were studies but this paper investigates the effects caused by wide magnetic flux tubes on the torsional Alfvén wave propagation. It must be noted that in wide magnetic flux tubes the horizontal magnetic field is non uniform, and that the Alfvén velocity varies with height along the tubes.…”

“…by Perera et al (2015), whose cutoff frequency ranges from 0.022 Hz to 0.005 Hz for propagating linear Alfvén waves in an isothermal solar atmosphere with a uniform magnetic field. In our previous work on cutoff frequencies for transverse Alfvén waves in a thin non-isothermal magnetic flux tube (e.g., Routh et al 2010;Hammer et al 2010), the ranges of cutoff periods for different regions of the solar chromosphere are: 0.003-0.008 Hz for the lower chromosphere, 0.003-0.008 Hz for the middle chromosphere, and 0.003-0.005 Hz for the upper chromosphere. Again, these results are consistent with those obtained in this paper, and some discrepancies between the results reflect the differences in the models of considered flux tubes, thin (previous work) and wide (this paper).…”

“…In general, our results predict low frequency waves to be present in the solar corona while higher frequency waves are propagating in solar chromosphere, which may have implications on the energy and momentum transfer by linear torsional Alfv'en waves in the solar chromosphere and corona. Another important aspect of our results is that they can be used to determine whether the observed waves are propagating or evanescent (e.g., Hammer, Musielak and Routh 2010).…”

Global and Local Cutoff Frequencies for Transverse Waves Propagating Along Solar Magnetic Flux Tubes

“…Such a method was originally developed by Musielak et al (2006) for acoustic waves propagating in non-isothermal media. Routh et al (2007Routh et al ( , 2010 and Hammer et al (2010) used the method to determine cutoff frequencies for the propagation of torsional waves in thick (isothermal) and thin (non-isothermal) magnetic flux tubes. Here, this method will be used to derive local cutoff frequencies for transverse waves propagating along a thin flux tube with different temperature profiles.…”