This chapter presents an automated wavelet analysis approach to TRACE quiet-Sun UV intensity oscillations for both the network and internetwork. This idea was originally applied to Coronal Diagnostic Spectrometer (CDS, Harrison et al. 1995) data by Ireland et al. 1999. The oscillations in each region are discussed in relation to chromospheric heating via waves discussed in Chapter 2. When studying quiet-Sun data, wavelet analysis has two specific benefits over the Fourier transform. Firstly, the intermittency of the oscillations present (Banerjee et al. 2001; Hansteen, Betta, & Carlsson 2000) means that their Fourier power may be swamped by the much longer non-periodic component, whereas wavelet analysis provides localised temporal information. Secondly, quiet-Sun datasets are difficult to align compared to active region datasets due to a relative lack of features. Again the time-localised nature of wavelet analysis is better suited than Fourier analysis in dealing with frames which may not be perfectly aligned (Ireland et al. 1999). In order to reduce alignment problems, TRACE was used to provide long duration observations of the Sun, free of atmospheric distortions. The large FOV of TRACE makes it very useful for quiet-Sun studies, where it provides a larger spatial sample than slit-based spectrometers (e.g., SUMER, CDS). The large passbands of TRACE also mean that any oscillations present are free from Doppler-shift effects due to plasma motions. Oscillations must therefore be due to changes in temperature and/or density. However, it is noted that the wide passbands make it difficult to estimate their height of formation (HOF), as each passband contains significant contributions from continuum in addition to line emission. The wide passbands may also lead to phase averaging.
As discussed in Chapter 1, the quiet Sun displays a distinct network appearance identical to the supergranular cell structure in Dopplergrams (Leighton, Noyes, & Simon 1962). The nature of supergranular flow results in magnetic flux coalescing at cell vertices, with replenishment of flux occurring on the scale of a few days to a week (Schrijver et al. 1998). This creates a dense collection of flux tubes (Berger et al. 1998; Lites, Rutten, & Berger 1999) at these vertices and is observable as kilogauss fields in magnetograms. In time-integrated UV images of the chromosphere, the network is only partially defined as patches of increased intensity (NBPs), which display a one-to-one spatial correlation with this underlying photospheric magnetic field (similar to optical wavelengths; Figure 5.1). On the other hand, the internetwork is mainly field-free, and appears dark on time-integrated images of the chromosphere.
This spatial dichotomy between the network and internetwork is also apparent in the Fourier spectrum of light curves from these two regions, leading to the suggestion that different heating mechanisms may dominate in each region (Gallagher et al. 1999). The internetwork contains oscillations with periodicities around 180 s (a broad 3-8 mHz peak in the Fourier spectrum: the acoustic band), intermittently present in small grains, and with a good correlation between the photosphere and the chromosphere (Lites et al. 1993). Some work shows the existence of nodal planes and hence standing waves (e.g., Kneer & von Uexküll 1993; Deubner, Waldschik, & Steffens 1996). Other studies show a directly proportional increase of phase lag with frequency between lines formed at different heights in the atmosphere (e.g., Judge et al. 2001; Wikstøl et al. 2000). This suggests the presence of upwardly-propagating acoustic waves, which have been successfully modelled by Carlsson & Stein (1992; 1995; 1997). Brandt et al. (1992) suggest a scenario whereby there are two types of grains: one with a long term memory, termed `persistent flashers', with a magnetic dependence; and a second, 5-10 times more common, with no spatial memory or magnetic dependence. This may explain the difference between the conclusions reached by Worden, Harvey, & Shine (1999) and Lites et al. (1999), who suggest no correlation between the small internetwork magnetic fields and the chromospheric grains, and those of Sivaraman et al. (2000) who found a strong correlation between the internetwork grains and magnetic fields.
Longer-period network oscillations (5-20 mins) have not benefited from such similarly detailed simulations, mainly due to the difficulty of modelling the chromospheric plasma in the presence of the kilogauss magnetic fields (Bogdan et al. 2003). Current theories of network heating suggest that the magnetic field is critical and these fall into three main categories:
(i) in situ resistive dissipation from the stochastic rearrangement of magnetic field lines (Kneer & von Uexküll 1985; 1986);
(ii) upwardly-propagating transverse magnetohydrodynamic (MHD) waves coupling, and hence transferring power, to longitudinal waves, which can then form shocks (Kalkofen 1997; Hasan & Kalkofen 1999; Hasan et al. 2003);
(iii) resistive dissipation of Pedersen currents, driven by longitudinal MHD waves (Goodman 2000).
Observations show a poor temporal correlation between chromospheric network oscillations and those in the underlying photosphere (Lites et al. 1993). However in Chapter 5 I have shown how wavelet-based studies (also Bocchialini & Baudin 1995; Baudin, Bocchialini, & Koutchmy 1996) show the existence of mainly upwardly-propagating (but also some downwardly-propagating) waves in the chromosphere at speeds close to the sound speed. Furthermore, the tendency of oscillations to occur in the very centre of network elements (as shown in Chapter 4), combined with a lack of both intensity and oscillatory power near, but not directly above, photospheric network elements (termed `magnetic shadows'), suggests the existence of mode-conversion of acoustic waves as they interact with the magnetic canopy (Judge et al. 2001; McIntosh & Judge 2001; McIntosh, Fleck, & Judge 2003).
The outline of this chapter is as follows. An overview of the dataset, including a discussion of the HOF of each passband, is presented in Section 6.2. The alignment procedure, creation of the network/internetwork subsets and high-pass filtering are discussed in Section 6.3. This is followed by a detailed description of the wavelet analysis routine designed to search for both periodicity and lifetime of any oscillations in all the pixels in each subset. Section 6.4 compares the differing results from the network and internetwork, while conclusions are given in Section 6.5.