5.1 Global acoustic mode

The SOHO/SUMER spectral instrument has recently discovered quasi-periodic oscillations of intensity and a Doppler shift in the coronal emission lines Fe XIX and Fe XXI (Kliem et al., 2002 ; Wang et al., 2002 , 2003b ,a

, and references therein). Figure 14

gives an illustration of such oscillations. These spectral lines are associated with a temperature of about $6 MK$ , corresponding to the sound speed of about $370 km s-1$ . The observed periods are in the range $7 -31 min$ , with decay times $5.7 -36.8 min$ , and show an initial large Doppler shift pulse with peak velocities up to $-1 200 km s$ . The intensity fluctuation lags the Doppler shifts by $1/4$ period. In a statistical study of $54$ oscillation cases, Wang et al. (2003a

) found that except for a few cases, the presence of definite periodicity in intensity fluctuations is not certain. Moreover, oscillations are not seen in other emission lines observed simultaneously with the oscillating lines. In the initial stage of all $54$ cases analysed by Wang et al. (2003a

), there is a rapid increase in the line intensity and a large Doppler shift, indicating that the oscillations are excited impulsively.

Figure 14:

Doppler oscillation events in the Fe XIX line observed with the SUMER instrument on 9 March 2001. a) Doppler shift time series. The redshift is represented with the bright colour, and the blueshift with the dark colour. b) Average time profiles of Doppler shifts along cuts AC and BD. The thick solid curves are the best fit functions of the form $V (t) = V0 + VD sin(wt + f) exp(- gt)$ . c) Line-integrated intensity time series. d) Average time profiles of line-integrated intensities along cuts AC and BD. For a clear comparison, the intensity profile for BD has been stretched by a factor of $10$ . e) Line width (measured Gaussian width) time series. f) Average time profiles of line width along cuts AC and BD (from Wang et al., 2003a

Ofman and Wang (2002 ) suggested that these oscillations are produced by the global standing acoustic mode,

(pCs ) (p ) Vz(s,t) oc cos ----t cos --s , (48) ( L ) (L ) r(s,t) oc sin pCs-t sin -ps , (49) L L

where $V z$ is the longitudinal velocity, $C s$ is the speed of sound, $L$ is the loop length, and $s$ is a distance along the loop with the zero at the loop top. More strictly, the phase speed of the longitudinal mode of a coronal loop should, in the long wave length limit, be equal to the tube speed $CT0$ inside the tube, however in the low plasma- $b$ plasma of the solar corona this value is very close to the sound speed $Cs$ . From Equation (48

), the oscillation period is given by the expression $2L/C s$ . According to the thermally conductive, viscous, nonlinear one-dimensional MHD simulations, the short decay time is connected with the dissipation because of high thermal conductivity of the hot plasma filling the loop. Mendoza-Briceño et al. (2004 ) has recently developed this study, taking into account effects of stratification. It was found that stratification would lead to insignificant changes in the decay times (maximum $15 -20%$ ).

There are still several open questions in both the theory and the observations: how are the oscillations triggered and excited; why are intensity oscillations not always seen, whether the occurrence rate of oscillations is temperature dependent (in major cases in Fe XIX, i.e., in hot plasma), what is the role of non-adiabatic effects (e.g., thermal instability)?

Also, it is not clear how the SUMER oscillations are related with other coronal oscillations, observed in the radio (e.g., Aschwanden, 2003 ) and X-ray bands.