Standing Kink Waves with Longitudinal Flow in Fine Threaded Coronal Loops: A New Method for the Coronal Seismology through Beat and Damped Waves

Stimulated by the first weakly attenuated standing kink oscillations of coronal fine threads filled with cool flowing plasma, seen in a recent Ca II H-line observed by Solar Optical Telescope (SOT) aboard Hinode, in this study we present the effects of longitudinal flow on the standing wave. We have found that flow generates two important consequences: first, it produces a frequency shift, which leads to the phenomenon of wave beating; second, it splits the damping time of the forward and backward waves of the attenuated standing wave (considered here only the resonance absorption) into two different values. A comparative analysis of the beat waves, within the “quarter-beat period approximation” together with attenuated waves, seems to be very appealing for coronal seisomology. We refer a new parameter, modulating time ($\tau_{\rm m}$), which is defined as the time when the amplitude of the beat wave becomes zero for a wave train that lies within a quarter period of the beat envelope, the so-called “quarter beat period approximation”. We can compare this $\tau_{\rm m}$ with the attenuating time ($\tau_{\rm D}$) to discriminate the behaviour of the signal, as follows: if $\tau_{\rm m}~>~\tau_{\rm D}$, the envelope of the signal is dominated by attenuation due to resonance absorption, while if $\tau_{\rm m}~<~\tau_{\rm D}$, the envelope of the signal is dominated by modulation due to beating. Since observation corresponds to first inequality, the amplitude of the signal seems to be dominated by attenuation due to resonance absorption. Hence, the inequality $\tau_{\rm m}~\geq~\tau_{\rm D}$ imposes an upper bounds for the density contrast and magnetic field for a given value of the observed flow. Besides these, we also find that the flow-generated splitting of the damping time also leads to an $\sim\ $8%–10% uncertainty in our estimation of the radial inhomogeneity across the loop boundary, as compared to the static case, i.e., when the flow is zero.