Impulsively Generated Sausage Waves in Coronal Tubes With Transversally Continuous Structuring

Abstract

The frequency dependence of the longitudinal group speeds of trapped sausage waves plays an important role in determining impulsively generated wave trains, which have often been invoked to account for quasi-periodic signals in coronal loops. We examine how the group speeds (v gr ) depend on angular frequency (ω) for sausage modes in pressureless coronal tubes with continuous transverse density distributions by solving the dispersion relation pertinent to the case where the density inhomogeneity of arbitrary form takes place in a transition layer of arbitrary thickness. We find that in addition to the transverse lengthscale l and density contrast ρ i /ρ e , the group speed behavior depends also on the detailed form of the density inhomogeneity. For parabolic profiles, v gr always decreases with ω first before increasing again, as happens for the much studied top-hat profiles. For linear profiles, however, the behavior of the ω − v gr curves is more complex. When ρ i /ρ e 6, the curves become monotonical for large values of l. On the other hand, for higher density contrasts, a local maximum v in particular, is reflected in the temporal evolution and Morlet spectra of impulsively generated wave trains. We conclude that the observed quasi-periodic wave trains not only can be employed to probe such key parameters as density contrasts and profile steepness, but also have the potential to discriminate between the unknown forms of the transverse density distribution.

Dispersive Evolution of Nonlinear Fast Magnetoacoustic Wave Trains

“…Nakariakov et al (2004) used wavelet transforms to analyze quasi-periodic wave trains and demonstrated that their timedependent power spectrum produces a characteristic "crazy tadpole" signature. This signature was shown to be a robust feature of plane fast magnetoacoustic waveguides with different perpendicular profiles of the plasma density (Yu et al 2015(Yu et al , 2016(Yu et al , 2017, and was found to be consistent with analytical estimations (Oliver et al 2015). On the other hand, wavelet signatures of impulsively generated fast wave trains formed in cylindrical waveguides appear "head-first" (Shestov et al 2015).…”

A statistical study of the inferred transverse density profile of coronal loop threads observed with SDO/AIA

“…The specific shape of the transverse non-uniformity is also responsible for the geometrical dispersion of the fast magnetoacoustic waves guided by the loop, which determines the specific shape of the quasi-periodic rapidly propagating wave trains (Nakariakov et al 2004;Mészárosová et al 2014;Yu et al 2016). These wave trains have recently been detected in the corona with the EUV imagers (e.g.…”

Nonlinear Evolution of Short-wavelength Torsional Alfvén Waves

“…Sausage modes are collective perturbations of the flux tube, and fill in the whole flux tube. Their specific properties, such as the radial structure and dispersion, are prescribed by the specific radial profile of the fast speed (e.g., Nakariakov et al 2012;Yu et al 2016). Consideration of this effect is out of scope of this paper.…”

“…The amplitude of this perturbation is approximately five times smaller than the amplitude of parallel motions, and the speed of propagation in the z-direction is higher than the speed of the torsional wave. These perturbations correspond to the third kind of the induced compressive perturbations, the fast magnetoacoustic sausage wave (e.g., Edwin & Roberts 1983;Nakariakov et al 2012;Yu et al 2016). In the low-β plasma considered here, this mode is characterized by compressive, mainly radial flows, and propagates at the speed that lies between the Alfvén speed inside and outside the tube.…”