Effects of Field-Aligned Flows on Standing Kink and Sausage Modes Supported by Coronal Loops

Fundamental standing modes and their overtones play an important role in coronal seismology. We examine the effects of a significant field-aligned flow on standing modes that are supported by coronal loops, which are modeled here as cold magnetic slabs. Of particular interest are the period ratios of the fundamental to its (n?1)th overtone [P ₁/nP _n ] for kink and sausage modes, and the threshold half-width-to-length ratio for sausage modes. For standing kink modes, the flow significantly reduces P ₁/nP _n in general, the effect being particularly strong for higher n and weaker density contrast [ $rho_{0}/rho_{rm e}$ ] between loops and their surroundings. That said, even when $rho_{0}/rho_{rm e}$ approaches infinity, this effect is still substantial, reducing the minimal P ₁/nP _n by up to 13.7?% (24.5?%) for n=2 (n=4) relative to the static case, when the Alfvén Mach number [M _A] reaches 0.8, where M _A measures the loop flow speed in units of the internal Alfvén speed. Although it is not negligible for standing sausage modes, the flow effect in reducing P ₁/nP _n is not as strong. However, the threshold half-width-to-length ratio is considerably higher in the flowing case than in its static counterpart. For $rho_{0}/rho_{rm e}$ in the range [9,1024] and M _A in the range [0,0.5], an exhaustive parameter study yields that this threshold is well fitted by $(d/L)_{rm cutoff, fit} = frac{1}{2}sqrt{frac{1}{rho_{0}/rho_{rm e}-1}} exp (3.7 M_{mathrm{A}}^{2} )$ , which involves the two parameters in a simple way. This allows one to analytically constrain the combination $(rho_{0}/rho_{rm e}, M_{mathrm {A}})$ for a loop with a known width-to-length ratio when a standing sausage oscillation is identified. It also allows one to examine the idea of partial sausage modes in more detail, and the flow is found to significantly reduce the spatial extent where partial modes are allowed.