Network - Internetwork Comparison

Table 6.4: Centres and one sigma widths (both in log₁₀ seconds) of the Gaussian fits to the occurrence rate and Fourier power curves for the first half (block A) and second half (block B) in each bandpass.

Wavelength	Network				Internetwork
Dataset	Wavelet		Fourier		Wavelet		Fourier
	Centre	Width	Centre	Width	Centre	Width	Centre	Width
1550 A	2.441	0.080	2.460	0.141	2.391	0.089	2.408	0.143
1216 A	2.457	0.084	2.462	0.127	2.413	0.093	2.421	0.136
1600 A	2.440	0.081	2.452	0.135	2.391	0.084	2.407	0.136
1700 A	2.443	0.077	2.453	0.136	2.393	0.082	2.408	0.131
1550 B	2.455	0.089	2.479	0.166	2.401	0.088	2.435	0.166
1216 B	2.464	0.090	2.473	0.136	2.414	0.092	2.421	0.137
1600 B	2.453	0.098	2.470	0.140	2.406	0.096	2.422	0.143
1700 B	2.457	0.100	2.563	0.141	2.409	0.093	2.419	0.137
Average	2.451±0.087		2.464±0.140		2.402±0.090		2.418±0.141

From a comparison of the network and internetwork results in all passbands, a few common themes are apparent. As often confirmed before, the network tends to oscillate with a period close to 5 min. The internetwork, whilst exhibiting many more oscillations around 3 min, contains a peak close to 4 min. Table 6.4 contains a list of the centre of the Gaussian fits and one sigma widths for the Fourier and wavelet approaches. The calculated averages of the COGs for the Fourier and wavelet approaches agree within the one sigma widths and both regions contain a wide range of periodicities. The widths are typically larger in the Fourier than the wavelet approach, but in both cases a range of ~ log₁₀(P) = 2.1-2.6 is fitted (2.5-7.9 mHz; other work (e.g., Lites et al. 1999; McIntosh et al. 2003) sums over 3-8 mHz). This periodicity range is important to remember when using the 3- and 5- min oscillations in modelling.

Table 6.5: Frequency of occurrence of the most common oscillation (lifetime-period plots), and peak of the Gaussian fit for occurrence rate and Fourier Power of oscillations in the network (NWK) and the internetwork (INWK) for the first half (block A) and second half (block B) in each bandpass. Columns are numbered (2-7) for ease of reference to the text in Section 6.4.5

	Most Common Osc.		Peak of Gaussian Fit
Wavelength	Occurrence Rate		Occurrence Rate		Fourier Power
Dataset	NWK(2)	INWK(3)	NWK(4)	INWK(5)	NWK(6)	INWK(7)
1550 A	0.212	0.229	0.081	0.073	4.80	4.89
1216 A	0.217	0.257	0.086	0.098	4.61	5.12
1600 A	0.206	0.246	0.079	0.085	4.82	5.15
1700 A	0.188	0.260	0.070	0.090	4.47	5.30
1550 B	0.120	0.138	0.043	0.041	4.33	4.24
1216 B	0.197	0.254	0.079	0.099	4.55	5.13
1600 B	0.179	0.241	0.071	0.088	4.48	4.86
1700 B	0.161	0.259	0.058	0.092	3.96	5.02

The power of the dominant oscillations in each region was studied using several different methods. Table 6.5 contains a summary of the occurrence rate of the peak periodicity in both the lifetime-period diagrams (e.g., Figures 6.4 and 6.6) and the centre of the Gaussian fits to the average occurrence rate and Fourier power diagrams (e.g., Figures 6.5 and 6.7) in all passbands. It is immediately apparent that the results from the second half of the 1550 Å dataset (1550 B) display very low values in both the network and internetwork. These low values may be due to the larger number of saturated pixels, dropped data and streaks in this part of the dataset. Hence for the following interpretation, the 1550 B dataset is ignored.

For the network, the lifetime-period approach (column 2) shows an increasing occurrence rate with increasing HOF from 1700 Å through 1600 Å to 1216 Å. It then decreases in 1550 Å. This trend is also prevalent in the values of the peak of the COG fit for the occurrence rate (column 4) and the peak of the COG fit for the Fourier power of data block B (bottom of column 6). This suggests oscillations occurring more frequently, leading to an increase in oscillatory power, as waves move up through the atmosphere to the HOF of the 1216 Å passband. As the number, as well as the total oscillatory power, increases, this suggests that waves are exciting oscillations in neighbouring regions as they propagate through the atmosphere. Before the waves reach the 1550 Å passband HOF several of these oscillations are no longer observed. There are a number of possible explanations for this decrease in both occurrence and power of oscillations:
(i) waves may either shock or damp between the HOF of 1216 Å and 1550 Å;
(ii) at the height where the canopy closes over completely, the magnetic field lines may be almost horizontal, and hence may channel oscillations away from areas defined as network;
(iii) upwardly-propagating acoustic waves near network areas may undergo mode-conversion when interacting with the closing magnetic canopy in the upper chromosphere (Judge et al. 2001), hence oscillations will change in frequency.
It is difficult to determine which one, or combination of two or more, of these explanations is correct.

From a comparison of the Fourier and wavelet approaches in Table 6.5 it is clear that the internetwork normally has a higher value of oscillatory power (Fourier) and occurrence rate (wavelet) than the network. For the lifetime-period approach (column 3), the occurrence rate decreases from the 1700 Å HOF to the 1600 Å HOF, then increases at the 1216 Å HOF, and decreases again at the 1550 Å HOF. This trend is repeated in the COG fitting approach (column 5, column 7 bottom). Therefore some waves at the 1700 Å HOF must disappear before the 1600 Å HOF. This agrees with the low-lying shocks in internetwork grain simulations of Carlsson & Stein (1992; 1995; 1997). Above the 1600 Å HOF both long- and short-period waves will produce shocks separated by the acoustic cut-off period (Carlsson & Stein 1992), which may explain the increase at 1216 Å. The subsequent decrease at the 1550 Å HOF may then be due to a decreased number of these oscillations propagating to this height.