6 Discussion

Acoustic oscillations.

A major supplier of dynamics in the internetwork atmosphere at the heights sampled by TRACE's ultraviolet passbands is, obviously, the so-called chromospheric three-minute oscillation, i.e. the broad peak for 2-5 min periodicity in the spatially-averaged power spectra in Figs. 12, 13 and 23. The fast-changing "sea of motion'' sampled by the cutouts in Fig. 5, the dappled appearance of the internetwork parts of the timeslices in Fig. 7, the tight concentration of the three-minute $\Delta \phi$ spread in Figs. 18, 19, and the amount of three-minute power in Fig. 12 all attest to this ubiquitous oscillation gaining dynamical dominance already in the upper photosphere. There is not much else happening at these heights for frequencies around f=5 mHz or the coherences wouldn't be so high and the $\Delta \phi$ spreads wouldn't be so small.

Our extensive comparisons with comparable displays from the Ca IIH data of Lites et al. (1993) in Figs. 9-11 and Figs. 20-22 show that the ultraviolet continua sample the upper photosphere and low chromosphere rather like the inner wings of Ca IIH, but without the higher-up Dopplershift effects of H₃ that produce the spectral asymmetry and intricate time-dependent spectral variations of the H & K emission reversals. Since the spectral Ca IIH behaviour in these very data was convincingly reproduced by the simulations of CS1997, we deem it beyond doubt that the highly similar internetwork behaviour in the ultraviolet timeslices and Fourier spectra is set by acoustic waves that are steepening into weak shocks on their way up. As discussed in Sect. 4.3, we suspect that the mean $\Delta \phi$ decline in Figs. 18, 19 from $f \approx 7$ mHz to $f \approx 15$ mHz (where $\Delta \phi$ becomes unreliable) results at least partially from wave steepening. We suspect also that similar phase-difference declines in older ground-based data were also partially due to wave steepening rather than atmospheric seeing.

Many of our results, in particular the phase differences in Figs. 18-19, are amenable to radiation-hydrodynamics simulations as those of Skartlien et al. (1994). Compared to their Ca IIH modelling, the lower heights of formation of the ultraviolet continua (implying smaller sensivity to canopy geometry) and the more straightforward computation (no sensitivity to unidentified microturbulence or to coherency in resonance and Raman scattering) warrant the expectation that such numerical modelling should reproduce our observations in considerable detail. The major obstacle might be the one-dimensionality of the Carlsson-Stein approach, but it should be noted that the spatial extent of the time-compressed internetwork features in the lower panel of Fig. 11 is appreciably larger than the pixel size; column shifts of 1-2 arcsec (700-1500 km) sample scene differences primarily in the form of phase shifts, whereas the radial stratification varies much more rapidly.

The ongoing debate on the presence or absence, both in the Carlsson-Stein Ca IIH simulation and in the real Sun, of a sizable heating contribution by high-frequency waves (e.g., Kalkofen et al. 1999) is not decided by our data. Our initial expectations were that phase differences should provide the clearest signature of high-frequency oscillations in the presence of much larger power at lower frequencies, and that the ultraviolet continua, which are formed at heights where wave amplitudes grow and steepen but are not yet disturbed by magnetic canopies, should provide the best diagnostic. Our hope was that TRACE's seeing-free and large-sample data gathering would unequivocally settle this issue - but we did not anticipate that the sequentiality of TRACE's imaging in different passbands upsets phase difference measurements as far below the Nykvist frequency as shown in Sect. 5. Of course, the wide contribution functions of the ultraviolet continua (sampled by TRACE with very wide passbands), the reduced sensitivity to thermal modulation caused by resonance-like bound-free scattering in these continua, and slowness of the pertinent recombination rates may together cause low modulation sensitivity and so limit the detectability of high-frequency phases. Numerical simulations can assess which waves may leave what signature in TRACE-like data and indicate up to what frequency waves are at all observable with future (or ideal) instruments.

Excess sound emission from collapsing granules (Skartlien 1998; Rast 1999; Skartlien et al. 2000), in intergranular lanes within mesoscale convergence areas (Hoekzema & Brandt 2000) and in acoustic flux events (Goode et al. 1998) as well as wave refraction (Hoekzema et al. 1998b; Stix 2000) are likely to contribute some mapping of granular dynamics into the acoustic modulation pattern. For oscillations with long-duration persistence as the global p-modes, the signatures of local excitations are largely - if not fully - lost in the many-wave and multi-pass interference that produces the wavy-curtain five-minute timeslice patterns (e.g., Fig. 9), but above the cutoff frequency the pseudo-mode ridges are mostly due to single-bounce enhancement so that more of the excitation pattern may remain. However, the rapid apparent motions of the brightness modulation along the background-mesh strands and the timeslice patterns in Figs. 9-11 strongly suggest wave interference as the major acoustic patterning agent. The acoustic piston studies listed above indeed rely on extensive spatial averaging to identify collapsing granules and mesoscale convergence as sites of enhanced acoustic wave excitation. Apparently, direct one-to-one mapping of individual pistons to resulting wave trains is made impossible by the ubiquitous wave spreading and interference.

Low-frequency modulation.

The three-minute acoustic oscillation appears as modulation of the background mesh pattern seen in the reversed-greyscale panels in Fig. 5 and as columnar structures in the compressed timeslices in Fig. 11. This background pattern corresponds to the pronounced low-frequency modulation peak in the spatially-averaged power spectra in Fig. 12 and Fig. 23. It is likely to be a complex mixture of granular overshoot dynamics, internal gravity waves, and the low-frequency tail of acoustic interference patterns as those evident in the photospheric five-minute Doppler timeslice in Fig. 10. However, on the basis of the well-defined negative-phase signatures in Figs. 18 and 24, we believe that internal gravity waves are the principal constituent and that the mesh pattern primarily portrays their spatio-temporal interference. Further analysis adding the October 14 white light sequence confirms this view and will be reported in a future paper.

Internetwork grains.

The physics of spectral K_2V grain formation has been explained by CS1997 but the spatial patterns in which grains appear are not directly amenable to such one-dimensional simulation. The latter ascertained that acoustic three-minute waves are the principal grain-causing ingredient, but our results suggest that an important additional contribution comes from the slowly-varying background mesh which we attribute to internal gravity waves. The dominance of the two corresponding power peaks in Figs. 12, 13, the well-defined phase relations in Fig. 18, and the consistent grain-to-mesh superposition observed in movies and shown by Fig. 11 suggest that these two constituents together dominate internetwork grain occurrence. Thus, we conclude once again that internetwork grain patterns are set primarily by wave interference with the brightest grains resulting from constructive additions (e.g., Rutten & Uitenbroek 1991a; von Uexküll & Kneer 1995; Judge et al. 2001), but we now add the gravity-wave background as extra occurrence agent.

Neither the acoustic-wave nor the gravity-wave interference patterns should be regarded as pistons, but rather as modulations that combine to define grain appearance. The combining explains the grain-mesh correlation, the apparent travel along mesh strands seen in the TRACE movies, and the frequent appearance of grains in close pairs and clusters outlining the mesh pattern. Note that the combining is nonsinusoidal through the nonlinear temperature sensitivity of the Planck function in the ultraviolet and the onset of wave steepening at these heights.

The actual pistons are to be sought in collapsing, exploding, and/or overshooting granules, or other convective generators of acoustic events and gravity-wave emission. As noted above, such searches are effectively hampered by the ubiquitous interference of the resulting waves. Acoustic waves preferentially propagate straight up but gravity waves propagate downward and spread under large angles with the vertical (Mihalas & Toomre 1981, 1982).

As shown in Sect. 4.3, the internetwork grains also sense higher-up Dopplershifts when observed in optically thick lines such as H & K (Figs. 21, 22). The ultraviolet continua provide a cleaner picture, but we should note that the time-dependent spectral asymmetry introduced by H₃ Dopplershifts to H_2V grain evolution did provide a suitable yardstick to gauge CS1997 simulation success.

Network waves.

The modulation spectra in Fig. 12 and the modulation maps in Fig. 14 once again confirm that network harbours low-frequency rather than high-frequency motions. The lower panels of Figs. 18, 19 show no distinctive network properties as those seen higher up (Fig. 21). Note that observed wave amplitudes may also be reduced by phase mixing between different fluxtubes within a cluster making up a network patch; Fourier studies of single-element flashers may provide a tactic to isolate fluxtube wave modes.

At low frequencies there is no sign of distinctive peaks in the network power spectra in Figs. 18, 19 as the one at 2.5 mHz in the H₃ Dopplershift spectrum in Fig. 6 of Paper I, which was taken as significant and attributed to kink-wave cutoff by Hasan & Kalkofen (1999). Such peaks are absent in the fourth panel of Fig. 21 which is produced from the same data with somewhat different averaging and smoothing choices. Our TRACE data provide far better statistics, so that we conclude that specific network modulation peaks that might suggest specific fluxtube wave modes have not really been detected so far.

On the other hand, the ubiquitous presence of internal gravity waves indicated by the low-frequency power and phase-difference behaviour in Figs. 18, 23, 24 and the coupling to fluxtube modes suggested by the low-frequency peak equality in Fig. 21 may signify the importance of fluxtube interaction with internal gravity waves. The lack of coherence between H₃ and Ca I 4226.7 Å Dopplershifts in network led to the conclusion in Paper I that the slow network modulation is not correlated with underlying photospheric disturbances. A similar lack of V-V coherence is seen in the fourth panel of Fig. 21. However, the I-I comparison in the second panel has low-frequency network peaks for both signals, with larger coherence between them. The absence of a comparable Dopplershift connection may be due to the smallness of gravity-wave velocity perturbations compared to brightness perturbations.

Alternative explanations of the large low-frequency modulation in network are (i) - slow footpoint motions as suggested by Kneer & von Uexküll (1985, 1986), and (ii) - that the canopies spreading out from fluxtubes funnel gravity waves down as suggested by Deubner & Fleck (1990), but their interpretation of phase differences between the Ca II infrared lines suffers from non-trivial response characteristics of these lines (Shine & Linsky 1974; Rutten & Uitenbroek 1991a; Skartlien et al. 1994). As noted above, alternative explanations for the slow Ca II H₃ Doppler modulation in network are also such slow footpoint motions, or mottle flow changes as observed in C IV. The latter ones would have to also affect deeper fluxtube parts to cause the low-frequency brightness modulation enhancements in Fig. 12.

Intermediate zones.

Two unexpected findings are the wide zones of intermediate-brightness pixels between network and "true'' internetwork in Fig. 4 and the appearance of mottle-like structures surrounding network in low-frequency C IV modulation maps (Fig. 14). In older Ca IIK filtergram sequences we have also noted wide zones of somewhat enhanced emission around network, but at the time suspected atmospheric seeing and telescopic straylight as main cause. The C IV modulation maps indicate that these zones are low-lying magnetic canopies rather like the fibrils that fan out from network on H$\alpha$ movies, as discussed in Sect. 4.2. These zones may be brighter in ultraviolet continua due to smaller opacity. There may also be a time-averaged brightness enhancement from a larger density of single-fluxtube magnetic flashers, or there may be more wave dissipation in the network neighbourhood.

Network modulation aureoles.

The same zones appear as enhanced three-minute modulation aureoles in the fourth column of Fig. 14. Hindman & Brown (1998) proposed that the absence of brightness modulation aureoles in their photospheric MDI data implies incompressible waves, and that the Ca IIK brightness on the image sequences of Braun et al. (1992) was contaminated by Dopplershifts. Such contamination is indeed illustrated by Figs. 21, 22, but the aureoles in our TRACE continuum brightness data sample intrinsic brightness modulation resulting from temperature and/or opacity variations, not Dopplershifts. However, even the decidedly acoustic waves that make up Ca II K_2V grains quickly loose their brightness signature with height, whereas their Doppler signature persists (e.g., Cram 1978; Carlsson et al. 1997; Doyle et al. 1999). Intensity is formed with much more complexity than Dopplershift (in which the last particle-photon interaction does the coding) in any non-LTE situation; we note once more that the ultraviolet continua are affected by scattering similar to two-level-atom resonance scattering. Thus, non-existence of brightness aureoles would not prove wave incompressibility. The slight but definitely present brightness-modulation aureoles in (Figs. 14-16) point to some compressibility. We suspect that they are basically acoustic.