| Wavelengths | Frequency | Notes | |
| λ1 | λ2 | (mHz) | |
| NBP7 | |||
|---|---|---|---|
| Hα | Mg I b2 | 1.8 - 2.0 | MCT |
| Hα | Mg I b1-0.4 Å | 1.8 - 2.0 | MCT |
| Mg I b2 | Mg I b1-0.4 Å | 1.8 - 2.0 | MCT |
| Mg I b2 | Mg I b1-0.4 Å | 3.3 - 3.5 | MCL |
| Hα | Mg I b2 | 3.55 - 3.75 | MCL |
| Ca II K3 | Mg I b1-0.4 Å | 1.3 - 1.5 | U |
| Ca II K3 | Mg I b2 | 1.5 -1.7 | U |
| Hα | Mg I b2 | 2.8 - 3.0 | D |
| NBP2 | |||
| Ca II K3 | Mg I b2 | 1.25 - 1.45 | MCT |
| Ca II K3 | Mg I b1-0.4 Å | 1.2 - 1.4 | MCT |
| Mg I b2 | Mg I b1-0.4 Å | 1.3 - 1.5 | MCT |
| Ca II K3 | Hα | 2.4 - 2.6 | MCL |
| Ca II K3 | Mg I b2 | 1.75 - 1.95 | U |
| Ca II K3 | Mg I b1-0.4 Å | 1.7 - 1.9 | U |
| Mg I b2 | Mg I b1-0.4 Å | 1.6 - 1.8 | U |
| Hα | Mg I b2 | 3.85 - 4.05 | U |
| Mg I b2 | Mg I b1-0.4 Å | 4.2 - 4.4 | D |
| NBP5 | |||
| Ca II K3 | Mg I b2 | 1.05 - 1.25 | MCT |
| Hα | Mg I b2 | 1.2 - 1.4 | MCT |
| Mg I b2 | Mg I b1-0.4 Å | 1.5 - 1.7 | MCT |
| Hα | Mg I b1-0.4 Å | 4.15 - 4.35 | U |
| Ca II K3 | Hα | 3.3 - 3.5 | U |
| Ca II K3 | Mg I b2 | 0.9 - 1.1 | D |
| Ca II K3 | Hα | 3.65 - 3.85 | D |
| Ca II K3 | Mg I b1-0.4 Å | 4.55 - 4.75 | D |
| NBP1 | |||
| Ca II K3 | Mg I b2 | 1.9 - 2.1 | MCT |
| Ca II K3 | Mg I b1-0.4 Å | 1.7 - 1.9 | MCT |
| Mg I b2 | Mg I b1-0.4 Å | 1.5 - 1.7 | MCT |
| Hα | Mg I b1-0.4 Å | 4.1 - 4.3 | MCL |
| Ca II K3 | Hα | 1.2 - 1.4 | D |
| Hα | Mg I b2 | 1.2 - 1.4 | D |
A summary of all the propagating waves in each NBP is provided in Table 5.6. The ordering of the waves in this table, and notes as to whether each wave may be a possible mode-coupling candidate, or simply an upward- or downward- moving wave reflects the discussion in Sections 5.3.1 to 5.3.4. Correlations which do not correspond to wave packets are omitted.
In each NBP, there is at least one frequency which satisfies the five tests described in Section 5.1. However, a few points must be addressed concerning this. Firstly, Kalkofen (1997) suggests that transverse waves should not normally be viewable at disk centre. If they are viewable it will be due to a flux tube which, being slightly slanted, will make a small angle with the line-of-sight. In this case the resulting light curve will have two maxima for each complete oscillation of the wave and hence the frequency detected will be twice that of the wave. However, this will only be true for completely symmetrical profiles. If the line profile is asymmetric, or if the filter is in the wing of the line, the Doppler shift from the transverse wave will result in a light curve which will still contain a signal at the original transverse wave frequency.
Secondly, the main area of disagreement with theory is in the values of the cut-off frequencies determined from Kalkofen (1997). As stated in Section 5.1 it should be noted that the cut-offs calculated have not been derived specifically for the network. In the network several parameters may vary, due to the highly magnetised structure and local depression, or non-adiabatic effects, which may alter νk. A complete understanding of the structure within the network is necessary, which may introduce other factors into the equations given by Kalkofen (1997) for the cut-off frequencies. It is also apparent that the thin flux tube approximation will not be appropriate in the high chromosphere. Further modelling using thick flux tubes will be necessary. The results here suggest transverse cut-offs of ~1.3 mHz, and ~1.9 mHz, with longitudinal cut-offs at around twice these frequencies. Hasan & Kalkofen (1999) suggest cut-off periods of 534 s and 227 s for the transverse and longitudinal mode respectively, which agree with the higher frequency (1.9 mHz) cut-off suggested here.
Thirdly, results such as those presented here have never before been so clearly demonstrated. There are several reasons for this. It is important to note that our method uses 2-dimensional images, making it easier to spatially isolate the NBP throughout the entire time series (as first pointed out by Cauzzi et al. 2000). The contour method also ensures only pixels inside the NBP are included, ignoring any other bright pixels in the FOV. In addition, some oscillatory components can be missed if each NBP is not followed completely from the outer reaches to the bright centre. In Chapter 4 I demonstrated how spatially averaging over many NBPs can lead to overlooking power at several frequencies. The contrast light curve and digital high-pass filtering techniques used here also remove all very low frequency power which can dominate the power spectrum (Figures 4.5 and 4.4). It is of course important to remove this low-frequency component without unduly affecting the higher frequencies. It is also of note that the time series used here (150 minutes) is longer than most previous studies. Most importantly, the use of wavelet analysis to create the power curves gives temporal information associated with any wave-packets. A Fourier phase analysis, which will average over time, may result in any correlation across wave-packets being `washed out' by the longer non-periodic component. This may explain the lack of correlation found in previous work (e.g., Lites et al. 1993). It is also important to note the multi-wavelength nature of the data used in this study. Although a few papers have previously performed correlations across wavelet power diagrams (Bocchialini & Baudin 1995; Baudin, Bocchialini, & Koutchmy 1996), they have used only two wavelengths in a limited frequency range. Using four wavelengths across all observable frequencies gives a much higher chance of detecting correlated oscillations, and makes the findings more significant.
Finally, the results reported here suggest longitudinal waves shock in the mid- to high- chromosphere, hence heating the surrounding plasma, and the oscillations subsequently disappear. However simulations by Carlsson & Stein (1992) of K2V grains suggest that these shocks may be coherent which will lead to further oscillations at 5.5 mHz. This lack of agreement suggests that either the magnetic network differs from the internetwork bright points, or the coherence area must be well less than the areas integrated over in this paper.
In this chapter I have used a novel combination of wavelet analysis and cross-correlation to study propagating waves in the chromosphere. For each NBP studied I have found the possibility of transverse wave propagation in the lower chromosphere. There is also evidence of these transverse waves coupling to longitudinal waves in the upper chromosphere, which can then shock. Thus mode-coupling provides a means of energy transport to heat the upper chromosphere. In the next chapter I will present another novel wavelet analysis technique to study oscillatory signals in TRACE ultraviolet datasets.