Impulsively generated sausage waves in coronal tubes with transversally continuous structuring

TL;DR

This study investigates how the group speeds of sausage waves in coronal tubes depend on frequency and density profiles, revealing complex behaviors that can help diagnose plasma parameters and density distributions in the solar corona.

Contribution

It provides a detailed analysis of group speed behaviors for different density profiles and demonstrates their impact on impulsively generated wave trains in coronal loops.

Findings

Group speed behavior varies with density profile shape and contrast.

Complex wave train spectra can distinguish between density distribution types.

Impulsive wave signals can diagnose coronal plasma parameters.

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 ($v_{\rm gr}$) depend on angular frequency ($\omega$) 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 $\rho_{\rm i}/\rho_{\rm e}$, the group speed behavior depends also on the detailed form of the density inhomogeneity. For parabolic profiles, $v_{\rm gr}$ always decreases with $\omega$ first before increasing again, as happens for the much studied top-hat profiles. For linear profiles, however, the behavior of the $\omega-v_{\rm gr}$ curves is more complex. When $\rho_{\rm i}/\rho_{\rm e} \lesssim 6$, the curves become monotonical for large values of $l$. On the other hand, for higher density contrasts, a local maximum $v_{\rm gr}^{\rm max}$ exists in addition to a local minimum $v_{\rm gr}^{\rm min}$ when coronal tubes are diffuse. With time-dependent computations, we show that the different behavior of group speed curves, the characteristic speeds $v_{\rm gr}^{\rm min}$ and $v_{\rm gr}^{\rm max}$ 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.