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Astron. Astrophys. 329, 725-734 (1998)

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4. Discussion

Wave excitation. The high peak in the second G panel of Fig. 5 confirms the indication in Fig. 5 of Paper I that dark intergranular lanes tend to show excess waves in the photospheric 2-4 min regime. The large temporal width of the peak, about 20 min, corresponds to the relatively long dark-lane persistence in Fig. 1. In contrast, bright granules do not show alignment with high photospheric wave amplitudes, except for the minor peak at [FORMULA]  mHz (lower-right panel of Fig. 5). Thus, local wave excitation does not come from the granules that were taken as pistons in the classical wave generation studies of Evans & Michard 1962, Meyer & Schmidt 1967and Stix 1970but rather from persistent intergranular lanes.

The local contribution seems limited to waves in the propagating regime ([FORMULA]  mHz); in particular, there are no significant 5-min co-alignment peaks in the G panels of Fig. 5 that might have been expected on the basis of the "acoustical event" studies of Goode et al. 1992, Restaino et al. 1993, Espagnet 1994, Rimmele et al. 1995 and Espagnet et al. 1996. The absence of such 5-min amplitude enhancements at intergranular lanes in Fig. 5 confirms the indication in Paper I that these events are statistically insignificant or that the p -mode pistons should rather be sought below the observable surface as proposed by Brown 1991and Kumar 1994.

The preferential alignment between 2-4 min waves and dark lanes in the G data does not survive to the chromospheric heights sampled by the K data. This absence of correspondence was interpreted in Paper I as indication of diffraction. Such loss of vertical alignment for propagating waves may also explain the cutoffs near [FORMULA]  mHz in various high-correspondence features at large time delay [FORMULA], such as the one at the bottom of the middle (K,K) chart of Fig. 4, near the top of the upper righthand chart in Fig. 5 and near the top in the second K panel of Fig. 6.

Mesoscale migration. There are various features with significant correspondence at large values of [FORMULA], for example the striking peak at [FORMULA]  min in the upper-right panel of Fig. 5. As mentioned above, we suspect that migration of the mesoscale patterning observed in horizontal surface flows plays an important role in these time-delayed alignments. The flows possess pattern difference between divergent areas with a surplus of large bright long-lived granules and convergent areas harboring fewer of these but more dark lanes. Excess sound emission is expected from the mesoscale convergence areas because these are rich in sound-emitting dark lanes (second G panel of Fig. 5) and may also mark the subsurface presence of high-speed downflows ("convective fingers") that may be the principal acoustic sources just below the surface. Since mesoscale patterns evolve and migrate at one-hour time scales (cf. Fig. 3 of Brandt et al. 1994), alignment of high wave amplitude and mesoscale convergence may get replaced at half an hour time delay by alignment to a divergent area containing an overload of bright granules.

In this view, the striking peak in the upper-right panel of Fig. 5 may mark time-lapse co-location between high wave amplitudes and bright granules where the latter have replaced sound-emitting dark lanes or subsurface fingers. The peak value is then high because pixels are averaged over only a few meso cells; averaging over a larger field of view with more variation in mesoscale patterns, flow directions and evolutionary changes would diminish its amplitude. The white blobs near the top and bottom of the fourth G panel in Fig. 5, near the bottom of the 3-min and 2-min (K,K) panels of Fig. 4 and near the top of the fourth G panel of Fig. 6 may be similarly explained. A further speculation along the lines of Paper I is that the 4-5 min location of these delayed features betrays subsurface sources since there is no corresponding 4-5 min non-delayed patch of correspondence in the G panels of Fig. 5.

K [FORMULA] grain formation. The broad-band ridge of high correspondence in the upper-right panel of Fig. 6 represents a Fourier decomposition of the K [FORMULA] grain phenomenon and illustrates empirically that grain formation requires a multi-frequency wave mix. It so confirms the split-piston simulations in Fig. 8 of Carlsson & Stein 1997 and the earlier piston experiments of Fleck & Schmitz 1991 and Sutmann & Ulmschneider (1995a, 1995b). Carlsson & Stein employ the observed wave mix at [FORMULA]  km to define the piston in their one-dimensional simulations, so that their detailed reproduction of observed H [FORMULA] grains implies vertical alignment to within the characteristic grain size of 1-2 arcsec over the [FORMULA]  km height difference. The absence of a similar broad-band ridge in the lower-right G panel indicates that such alignment does not extend to below [FORMULA]  km. There is no clear indication of photospheric wave excess that might trigger enhanced K brightness, as proposed for 5-min pistoning by Fleck & Schmitz 1991 and for 3-min pistoning by Cheng & Yi 1996 and Theurer et al. 1997. On the other hand, the correspondence peak between excess K brightness and intergranular lanes at [FORMULA]  min in the upper panel of Fig. 3 suggests preferential alignment between sites of excess 3-min wave excitation (the dark-lane peak in the second G panel of Fig. 5) and K [FORMULA] grain sites in which the waves need about 2.5 min to propagate up to the Ca II K intensity response height of about 1 Mm where they contribute to bright K [FORMULA] grain formation in the weak-shock manner computed by Carlsson & Stein. The peak of correspondence with bright granules up to and at [FORMULA] then implies that such sound-emitting dark sites are followed preferentially by bright granules which persist for some minutes, the reverse of the downflow-driven exploding granules of Rast (1995).

The abruptness of such dark-to-bright transitions may also explain the rather sudden onset of the broadband ridge in the upper-right panel of Fig. 6.

Finally, the most significant feature in the G panels of Fig. 6 is the slanted ridge in the lower-right panel for [FORMULA]  min. It indicates that K is preferentially bright above locations that had excess 4-7 min amplitudes 20-40 min earlier in the photosphere. The piston-repeat experiment of Carlsson & Stein (their Fig. 15) shows a delay of about 17 min between photospheric wave behavior and chromospheric H [FORMULA] response, much longer than the 2-3 min travel time for propagating waves. This delay describes the fact that the state of the overlying chromosphere, in particular its back-fall after preceding shocks, is an important ingredient in K [FORMULA] grain formation; it takes the piston this length of time to generate the particular shock sequences that produce particular grain behavior. The delay in the fourth G panel of Fig. 6 may portray such response. This may even be the case while mesoscale migration has caused a switch between convergence and divergence (or reversely) over this duration, because the chromospheric response follows the local piston history. Since Carlsson & Stein derived their piston excursions from observations at a fixed location, their simulations sense the actual mesoscale migration across that location in a fashion similar to what we have done here.

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© European Southern Observatory (ESO) 1998

Online publication: December 8, 1997