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Astron. Astrophys. 335, L97-L100 (1998)

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4. Simulation

We now test whether the oscillations seen in the magnetogram signal are due to oscillations of the magnetic field vector (field strength or inclination to the vertical) or has an instrumental source (cross-talk from the velocity oscillations). If they are produced by cross-talk, we would expect them to show the same frequency as the velocity oscillations. At least in the main umbra of the following spot the magnetic oscillation frequency is distinctly different from that of the velocity (or from its second harmonic).

In order to strengthen the case against a cross-talk origin of the magnetogram signal oscillations, we have modelled the influence of the velocity oscillations on the magnetogram signal with spectral line calculations. Here we discuss the results for the leading spot's umbra. Tests for the other umbrae give similar results.

We have computed a spectral line profile to simulate the magnetogram signal at the locations showing magnetogram oscillations. We use the non-grey radiative equilibrium model of Kurucz with effective temperature 4000 K (representative of the continuum contrast of the biggest spot). We then create a time series by shifting the synthetic line profile by the Doppler shift time series (lower panel of Fig. 2). Finally, using the filter functions of MDI, we compute the fluctuations in the magnetogram signal that are due to cross-talk. The results of these computations are presented in Fig. 5. The solid line corresponds to the observed magnetogram signal (same as upper panel of Fig. 2), while the dotted line is the result of the computations. The computed signal does show oscillations, but with a very small amplitude. The rms fluctuations of the magnetogram signal in the 5 min band corresponds to 6.4 G for the observed data, but only to 1.2 G for the simulated data. In addition, the observed and computed magnetogram signals differ in phase by [FORMULA]. We have also considered other possibilities, such as errors in the spot effective temperature or oscillations of the temperature. None of these could reproduce the observed magnetogram oscillations. Hence these oscillations cannot be of instrumental origin, but must be solar. It is not possible to tell if they are due to oscillations of the magnetic field strength (magnetoacoustic gravity waves) or of the inclination angle of the magnetic field vector (Alfvén waves) directly from the data.

[FIGURE] Fig. 5. The solid line is the same as in Fig. 2a. The dotted line represents the magnetogram signal that would be expected from cross-talk from the velocity oscillations.

An oscillation amplitude of less than [FORMULA] for the inclination angle would produce oscillations of the observed amplitude. Such an oscillation of the field direction is small and entirely possible. However, in the case of Alfvén waves, which cause fluctuations of the magnetic field orientation, the magnetic and velocity signals are expected to oscillate in phase, which doesn't correspond to our measurements. In the absence of radiative damping, the magnetic and velocity signal of a magnetoacoustic gravity wave are expected to be [FORMULA] out of phase. Radiative damping could lower this value to the observed range ([FORMULA]). Our observations are therefore better explainable in terms of magnetoacoustic gravity waves.

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© European Southern Observatory (ESO) 1998

Online publication: June 26, 1998
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