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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., Comment: 35 pages, 15 figures, accepted for publication in ApJ

While standing fast sausage modes in flare loops are often invoked to interpret quasi-periodic pulsations (QPPs) in solar flares, it is unclear as to how they are influenced by the combined effects of a continuous transverse structuring and a finite internal plasma beta ($\beta_{\rm i}$). We derive a generic dispersion relation (DR) governing linear sausage waves in straight magnetic tubes for which plasma pressure is not negligible and the density and temperature inhomogeneities of essentially arbitrary form take place in a layer of arbitrary width. Focusing on fast modes, we find that $\beta_{\rm i}$ only weakly influences $k_{\rm c}$, the critical longitudinal wavenumber separating the leaky from trapped modes. Likewise, for both trapped and leaky modes, the periods $P$ in units of the transverse fast time depend only weakly on $\beta_{\rm i}$, which is compatible with the fact that the effective wavevectors of fast sausage modes are largely perpendicular to the background magnetic field. However, a weak $\beta_{\rm i}$ dependence of the damping times $\tau$ is seen only when the length-to-radius ratio $L/R$ is $\sim 50\%$ larger than some critical value $\pi/(k_{\rm c} R)$, which itself rather sensitively depends on the density contrast, profile steepness as well as on how the transverse structuring is described. In the context of QPPs, we conclude that the much simpler zero-beta theory can be employed for trapped modes, as long as one sees the deduced internal Alfv\'en speed as actually being the fast speed. In contrast, effects due to a finite beta in flare loops should be considered when leaky modes are exploited., Comment: 43 pages, 10 figures, accepted for publication in ApJ

Standing sausage modes in flare loops are important for interpreting quasi-periodic pulsations (QPPs) in solar flare lightcurves. We propose an inversion scheme that consistently uses their periods $P$ and damping times $\tau$ to diagnose flare loop parameters. We derive a generic dispersion relation governing linear sausage waves in pressure-less straight tubes, for which the transverse density inhomogeneity takes place in a layer of arbitrary width $l$ and is of arbitrary form. We find that $P$ and $\tau$ depend on the combination of $[R/v_{\rm Ai}, L/R, l/R, \rho_{\rm i}/\rho_{\rm e}]$, where $R$ is the loop radius, $L$ is the looplength, $v_{\rm Ai}$ is the internal Alfv\'en speed, and $\rho_{\rm i}/\rho_{\rm e}$ is the density contrast. For all the density profiles examined, $P$ and $\tau$ experience saturation when $L/R \gg 1$, yielding an inversion curve in the $[R/v_{\rm Ai}, l/R, \rho_{\rm i}/\rho_{\rm e}]$ space with a specific density profile when $L/R$ is sufficiently large. When applied to a spatially unresolved QPP event, the scheme yields that $R/v_{\rm Ai}$ is the best constrained, whereas $l/R$ corresponds to the other extreme. For spatially resolved QPPs, while $L/R \gg 1$ cannot be assumed beforehand, an inversion curve remains possible due to additional geometrical constraints. When a spatially resolved QPP event involves another mode, as is the case for a recent event, the full set of $[v_{\rm Ai}, l, \rho_{\rm i}/\rho_{\rm e}]$ can be inferred. We conclude that the proposed scheme provides a useful tool for magneto-seismologically exploiting QPPs., Comment: 26 pages, 5 figures, accepted for publication in ApJ

Coronal mass ejections (CMEs) can be continuously tracked through a large portion of the inner heliosphere by direct imaging in visible and radio wavebands. White-light (WL) signatures of solar wind transients, such as CMEs, result from Thomson scattering of sunlight by free electrons, and therefore depend on both the viewing geometry and the electron density. The Faraday rotation (FR) of radio waves from extragalactic pulsars and quasars, which arises due to the presence of such solar wind features, depends on the line-of-sight magnetic field component $B_\parallel$, and the electron density. To understand coordinated WL and FR observations of CMEs, we perform forward magnetohydrodynamic modelling of an Earth-directed shock and synthesise the signatures that would be remotely sensed at a number of widely distributed vantage points in the inner heliosphere. Removal of the background solar wind contribution reveals the shock-associated enhancements in WL and FR. While the efficiency of Thomson scattering depends on scattering angle, WL radiance $I$ decreases with heliocentric distance $r$ roughly according to the expression $I \propto r^{-3}$. The sheath region downstream of the Earth-directed shock is well viewed from the L4 and L5 Lagrangian points, demonstrating the benefits of these points in terms of space weather forecasting. The spatial position of the main scattering site $\mathbf{r}_{\rm sheath}$ and the mass of plasma at that position $M_{\rm sheath}$ can be inferred from the polarisation of the shock-associated enhancement in WL radiance. From the FR measurements, the local $B_{\parallel {\rm sheath}}$ at $\mathbf{r}_{\rm sheath}$ can then be estimated. Simultaneous observations in polarised WL and FR can not only be used to detect CMEs, but also to diagnose their plasma and magnetic field properties., Comment: 20 pages, 11 figures, 1 table. To be published by Astrophys. J., 2013