Standing sausage modes in coronal loops with plasma flow

Magnetohydrodynamic waves are important for diagnosing the physical parameters of coronal plasmas. Field-aligned flows appear frequently in coronal loops.We examine the effects of transverse density and plasma flow structuring on standing sausage modes trapped in coronal loops, and examine their observational implications. We model coronal loops as straight cold cylinders with plasma flow embedded in a static corona. An eigen-value problem governing propagating sausage waves is formulated, its solutions used to construct standing modes. Two transverse profiles are distinguished, one being the generalized Epstein distribution (profile E) and the other (N) proposed recently in Nakariakov et al.(2012). A parameter study is performed on the dependence of the maximum period $P_\mathrm{max}$ and cutoff length-to-radius ratio $(L/a)_{\mathrm{cutoff}}$ in the trapped regime on the density parameters ($\rho_0/\rho_\infty$ and profile steepness $p$) and flow parameters (magnitude $U_0$ and profile steepness $u$). For either profile, introducing a flow reduces $P_\mathrm{max}$ relative to the static case. $P_\mathrm{max}$ depends sensitively on $p$ for profile N but is insensitive to $p$ for profile E. By far the most important effect a flow introduces is to reduce the capability for loops to trap standing sausage modes: $(L/a)_{\mathrm{cutoff}}$ may be substantially reduced in the case with flow relative to the static one. If the density distribution can be described by profile N, then measuring the sausage mode period can help deduce the density profile steepness. However, this practice is not feasible if profile E better describes the density distribution. Furthermore, even field-aligned flows with magnitudes substantially smaller than the ambient Alfv\'en speed can make coronal loops considerably less likely to support trapped standing sausage modes.Comment: 11 pages, 9 figures, to appear in Astronomy & Astrophysic

Spatial damping of propagating sausage waves in coronal cylinders

Sausage modes are important in coronal seismology. Spatially damped propagating sausage waves were recently observed in the solar atmosphere. We examine how wave leakage influences the spatial damping of sausage waves propagating along coronal structures modeled by a cylindrical density enhancement embedded in a uniform magnetic field. Working in the framework of cold magnetohydrodynamics, we solve the dispersion relation (DR) governing sausage waves for complex-valued longitudinal wavenumber $k$ at given real angular frequencies $\omega$. For validation purposes, we also provide analytical approximations to the DR in the low-frequency limit and in the vicinity of $\omega_{\rm c}$, the critical angular frequency separating trapped from leaky waves. In contrast to the standing case, propagating sausage waves are allowed for $\omega$ much lower than $\omega_{\rm c}$. However, while able to direct their energy upwards, these low-frequency waves are subject to substantial spatial attenuation. The spatial damping length shows little dependence on the density contrast between the cylinder and its surroundings, and depends only weakly on frequency. This spatial damping length is of the order of the cylinder radius for $\omega \lesssim 1.5 v_{\rm Ai}/a$, where $a$ and $v_{\rm Ai}$ are the cylinder radius and the Alfv\'en speed in the cylinder, respectively. We conclude that if a coronal cylinder is perturbed by symmetric boundary drivers (e.g., granular motions) with a broadband spectrum, wave leakage efficiently filters out the low-frequency components.Comment: 6 pages, 2 figures, to appear in Astronomy & Astrophysic

B→SB\to S Transition Form Factors in the PQCD approach

Under two different scenarios for the light scalar mesons, we investigate the transition form factors of $B(B_s)$ mesons decay into a scalar meson in the perturbative QCD approach. In the large recoiling region, the form factors are dominated by the short-distance dynamics and can be calculated using perturbation theory. We adopt the dipole parametrization to recast the $q^2$ dependence of the form factors. Since the decay constants defined by the scalar current are large, our predictions on the $B\to S$ form factors are much larger than the $B\to P$ transitions, especially in the second scenario. Contributions from various light-cone distribution amplitudes (LCDAs) are elaborated and we find that the twist-3 LCDAs provide more than a half contributions to the form factors. The two terms of the twist-2 LCDAs give destructive contributions in the first scenario while they give constructive contributions in the second scenario. With the form factors, we also predict the decay width and branching ratios of the semileptonic $B\to Sl\bar\nu$ and $B\to Sl^+l^-$ decays. The branching ratios of $B\to Sl\bar\nu$ channels are found to have the order of $10^{-4}$ while those of $B\to Sl^+l^-$ have the order of $10^{-7}$. These predictions can be tested by the future experiments.Comment: 20 pages, 31 figure