5.2 Second standing harmonics

Recently, Nakariakov et al. (2004b

) modelled the evolution of a coronal loop in response to an impulsive energy release and demonstrated that the second standing acoustic harmonics appears as a natural response of the loop to an impulsive energy deposition. Modelling the loop as a 1D hydrodynamic system with nonlinearity, radiative damping, thermal conduction and accounting for possible chromospheric up and down flows, it was demonstrated that the second harmonics is a common feature of the loop evolution. Figure 15

shows typical time curves of the density and temperature at the loop apex. The quasi-periodic behaviour is clearly seen in the apex density curve, which is consistent with the mode structure

( ) ( ) 2pCs- 2p- Vx(s,t) = A cos L t sin L s , (50) Ar0 (2pCs ) (2p ) r(s, t) = - ---- sin -----t cos ---s , (51) Cs L L

where $A$ is the wave amplitude. (The paper of Nakariakov et al., 2004b

, contains a misprint, the factor of two is missing from Equations (3) and (4)). The density perturbations have a maximum near the loop apex, while longitudinal velocity perturbations have there a node.

Figure 15:

A typical response of a 1D loop to the flaring heat deposition near the apex. The density curve demonstrates pronounced quasi-periodic pulsations associated with the second standing acoustic harmonics.

The second standing acoustic mode may be responsible for quasi-periodic pulsation with periods in the range $10 -300 s$ which are often observed in flare light curves in radio and X-ray bands. The SUMER oscillations mentioned above are likely to be associated with some other excitation mechanism, as only a small fraction of SUMER oscillations are observed in association with solar flares (Wang et al., 2003a ). Traditionally, the acoustic wave interpretation has been excluded as the waves of these periodicities were supposed to be highly dissipative in the hot plasma of flaring loops. However, the numerical simulations performed by Nakariakov et al. (2004b ), as well as the recently gained abundant observational evidence of the presence of acoustic waves in the solar corona, suggest that the observed periodicities can be associated with this mode. The decayless character of these oscillations may be explained in terms of auto-oscillations: By the competition of the oscillation energy losing by dissipation and the energy deposition to the oscillation, e.g., through thermal over-stability.