Standing sausage modes in nonuniform magnetic tubes: An inversion scheme for inferring flare loop parameters

Standing sausage modes in flare loops are important for interpreting quasi-periodic pulsations (QPPs) in solar flare light curves. We propose an inversion scheme that consistently uses their periods P and damping times τ 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 τ depend on the combination of $[R/v_{Ai},L/R,l/R,{\rho }_i/{\rho }_e],$ where R is the loop radius, L is the looplength, v_Ai is the internal Alfvén speed, and ρ_i/ρ_e is the density contrast. For all the density profiles examined, P and τ experience saturation when L/R ≫ 1, yielding an inversion curve in the $[R/v_{Ai},l/R,{\rho }_i/{\rho }_e]$ 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_Ai is the best constrained, whereas l/R corresponds to the other extreme. For spatially resolved QPPs, while L/R ≫ 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 $[v_{Ai},l,{\rho }_i/{\rho }_e]$ can be inferred. We conclude that the proposed scheme provides a useful tool for magneto-seismologically exploiting QPPs.