1 Introduction

This paper addresses oscillations of the quiet solar atmosphere from image sequences taken with the Transition Region and Coronal Explorer (TRACE). TRACE images the Sun from a Sun-synchronous orbit at characteristic temperatures between 10⁴K and 10⁷K by sequentially selecting different spectral passbands to feed a $1024 \times 1024$ px² CCD camera with 0.5 arcsec pixels (366 km/px on the Sun) that covers nearly 10% of the solar disk. Details are given by Handy et al. (1999). First results from the spectacular coronal movies taken through the TRACE far-ultraviolet passbands were presented by Schrijver et al. (1999).

In this paper we use image sequences taken through the ultraviolet TRACE passbands centered at $\lambda = 1700$, 1600, and 1550Å to study quiet-Sun oscillations in the upper photosphere and low chromosphere. We so return to the domain of the pioneering rocket studies of 1600Å "cell grains'' by Brueckner (1980) and Cook et al. (1983) using the HRTS rocket spectrograph, and by Bonnet et al. (1982), Foing & Bonnet (1984a,b), Foing et al. (1986), and Damé et al. (1986) using the TRC rocket filtergraph. The obvious improvement that TRACE brings over the TRC flights is enormous sequence duration increase and digital data registration per CCD instead of emulsion. TRACE has no spectrograph so that emulation of the HRTS flights requires multi-spacecraft campaigns as in the recent TRACE-plus-SUMER (and MDI) analysis of Judge et al. (2001). The strength of the present analysis is the large statistical significance offered by TRACE image sequences and the use of comprehensive and complementary Fourier diagnostics to provide a complete inventory.

In standard models of the solar atmosphere such as VAL-C of Vernazza et al. (1973, 1976, 1981) and FAL-C of Fontenla et al. (1993), the disk-center intensity at 1700Å emerges from the "upper photosphere'', 1550Å radiation from the "lower chromosphere'', and 1600Å radiation from the "temperature minimum region'', where the temperature minimum at h = 500km above continuum optical depth $\tau_5 = 1$ at $\lambda = 5000$Å defines the transition from photosphere to chromosphere (see the formation panels in Fig. 36 of Vernazza et al. 1981). The ubiquitous existence of a chromospheric temperature rise in shell-like ("plane-parallel'') stratification over h = 500 - 1000km is presently in debate on the basis of the very oscillations discussed here and reviewed below, but we maintain this nomenclature for clarity. Also, we prefer to use "chromospheric dynamics'' even for the upper-photosphere diagnostics since the TRACE UV passbands essentially sample the onset of chromospheric oscillations and the chromospheric network.

The same atmospheric regime is accessible to ground-based observation and has been studied extensively using the cores of strong absorption lines and the Ca II K_2V and H_2V inner-wing reversals. Although TRACE does not reach the angular resolution of ground-based telescopes at good seeing, TRACE image sequences offer the important advantage of distortion-free sampling over relatively long duration. Compared with oscillation studies employing Fraunhofer line spectrometry in the visible to probe these and lower heights in the solar atmosphere or ultraviolet line spectrometry to probe greater heights, the lack of Dopplershift information is a disadvantage, but TRACE imaging yields data from a far larger area than is sampled by a spectrograph slit and so permits a much more complete view of solar variations as well as much better statistical reliability in their diagnosis. In addition, the wide-band continua sampled by the TRACE 1700 and 1600Å passbands do not suffer Dopplershift contamination as is the case for the apparent brightness modulation of optically thick lines (including the inner wings of Ca IIH & K, see Sect. 4.3). These outstanding TRACE capabilities are exploited here to wrap up much previous work.

The extensive older literature on oscillations in the upper photosphere and lower chromosphere has been reviewed by Rutten & Uitenbroek (1991a); more recent work is reviewed by Rutten (1994, 1995, 1999, 2001). Stein & Carlsson (1997), Carlsson & Stein (1998), Carlsson (1999), Deubner (1998), and Deubner & Steffens (1999). Even in quiet-Sun areas strict distinction must be made between network and internetwork. The first term denotes those parts of the supergranular cell boundaries that contain kiloGauss magnetic elements at sufficient spatial density to show up on photospheric magnetograms and on chromospheric images taken in the core of Ca IIK or the ultraviolet TRACE passbands. On such filtergrams the chromospheric network appears as chains of bright patches, each corresponding to a cluster of thin magnetic elements in the underlying photosphere. The latter, commonly identified with the modeller's fluxtubes, make up the magnetic network and may appear as individual bright grains in high-resolution (better than 0.5 arcsec) movies made in the Fraunhofer G band around $\lambda=430.5$ Å (e.g., Muller et al. 1989; Title & Berger 1996; Berger et al. 1998; movies on the Dutch Open Telescope website (URL http://dot.astro.uu.nl).

The bright patches on chromospheric filtergrams map the supergranular cell boundaries too sparsely to make the network identifiable as cellular patterning on snapshot images (cf. Hagenaar et al. 1997), but they stand out in longer-duration image sequences by being generally brighter and much more stably present than the transient, often briefly repetitive and often fast-moving, grainy brightness features seen in the intervening "internetwork'' areas corresponding to supergranular cell interiors.

The high degree of cospatiality of the brightness features seen in Ca IIK and the TRACE ultraviolet channels has been demonstrated by Rutten et al. (1999a). The correspondence between network grains in Ca IIK and clusters of smaller G-band magnetic elements located in underlying intergranular lanes is illustrated in Fig. 2 of Lites et al. (1999). The dynamical behaviour of the Ca IIK internetwork brightness patterning is illustrated in Fig. 3 of the same paper. Figure 5 of Rutten et al. (1999b) illustrates similar behaviour in a TRACE 1550Å image sequence. Figure 5 below shows a comparable 1700Å sequence.

The internetwork "three-minute'' oscillations (often in their "internetwork grain'' disguise and often called "K_2V grains'', see Rutten & Uitenbroek 1991a) are intensely discussed in the recent literature after their identification as weak acoustic shocks by Carlsson & Stein (1992, 1994, 1995, 1997, 1998). Major issues that are presently in debate are, respectively: (i) - the degree of correlation between internetwork grain occurrence and enhanced internetwork field (Lites et al. 1999 and references therein; Worden et al. 1999), (ii) - the presence of identifiable pistons at or below the surface that cause enhanced acoustic flux higher up in the atmosphere (Hoekzema & Rutten 1998; Hoekzema et al. 1998; Hoekzema & Brandt 2000; Kiefer & Balthasar 1998; Goode et al. 1998; Skartlien 1998; Rast 1999; Skartlien et al. 2000), (iii) - the relation between such pistons and observed velocity-intensity (V-I) phase-difference patterns in photospheric ($k,\omega$) diagrams (Straus et al. 1999; Oliviero et al. 1999; Skartlien & Rast 2000) with additional interest concerning p-mode asymmetries (Nigam & Kosovichev 1999a, 1999b; Georgobiani et al. 2000), (iv) - the amount of wave reflection in the upper chromosphere (Deubner et al. 1992, 1996; Kneer & von Uexküll 1993; von Uexküll & Kneer 1995; Jefferies et al. 1997; Schmitz & Steffens 1999; Carlsson & Stein 1999), (v) - the penetration height of the shocks into the higher chromosphere as evidenced by ultraviolet spectrometry with HRTS (Hoekzema et al. 1997) and SUMER (Steffens et al. 1997; Carlsson et al. 1997, 1999; (Curdt & Heinzel 1998); Gouttebroze et al. 1999; Doyle et al. 1999; Curdt et al. 1999; Carlsson 1999; Wikstøl et al. 2000; Judge et al. 2001), (vi) - the shock contribution to chromospheric heating (Theurer et al. 1997a, 1997b; Kalkofen et al. 1999), (vii) - the shock contribution to the basal flux observed from cool stars (Cuntz et al. 1999; cf. Ulmschneider 1999), and (viii) - the shock contribution to the FIP split affecting solar wind abundances (Rutten 1997; Judge & Peter 1998). Our TRACE results displayed below bear, directly or indirectly, on all these internetwork debates.

Network oscillations are often invoked to supply chromospheric or coronal heating, but there is no firm identification yet nor have they so far benefited from detailed observation modelling comparable to the Carlsson-Stein internetwork shock simulation. No high-frequency modes have been identified. Well-established (and often rediscovered) dichotomies are that the chromospheric network brightness modulation differs distinctly from the internetwork in showing primarily periodicities of $P \approx 5$ min and longer, and that these modulations are much clearer in Dopplershift than in brightness (e.g., Jensen & Orrall 1963; Liu & Sheeley 1971; Cram 1978; Lites et al. 1993). Kneer & Von Uexküll (1985, 1986) have suggested that the observed slow periodicities represent erratic fluxtube footpoint motions whereas Kalkofen (1997, 1999) argues that they are magnetoacoustic modes that are generated impulsively as transverse waves in the photosphere and become longitudinal higher up, and Goodman (2000) proposes that linear fluxtube waves drive transverse charged-particle currents which provide heating by resistive dissipation. An additional network issue is posed by the three-minute "power aureoles'' around dense network and plage (Braun et al. 1992; Brown et al. 1992; Toner & LaBonte 1991; Hindman & Brown 1998; Braun & Lindsey 1999), and the reversed-sign "power shadows'' found by Judge et al. (2001). We address the network issues below as well.

This paper is an initial TRACE study of oscillations in the quiet-Sun temperature-minimum domain. Our goal is to provide a comprehensive inventory and to place that in the context summarised above, combining standard oscillation analysis techniques with a variety of display formats: (i) - space-time displays plotting spatial development patterns; (ii) - power-map displays plotting Fourier amplitude per spatial element and per temporal frequency bin; (iii) - one-dimensional Fourier spectra of oscillatory power, phase difference and phase coherence, with separation of the network and internetwork contributions, and (iv) - two-dimensional (k_h,f) phase-difference spectra. These displays represent a space-based counterpart to the similar ones from ground-based filtergram sequences in Kneer & von Uexküll (1993). It is worthwhile to combine these different formats in a single paper to enable interpretative comparisons, but the disadvantage is that the interpretation ranges widely, from acoustic to gravity to canopy waves.

We also add pertinent comparison displays of the Ca IIH spectrogram sequences that were used by Lites et al. (1993, henceforth Paper I) to describe chromospheric network oscillations in the first paper of this series. The internetwork part of these sequences provided both the photospheric input and the chromospheric testing ground for the numerical simulations of Carlsson & Stein (1997, henceforth CS1997). These data merit a revisit here in order to link our TRACE results to this numerical modelling and to the properties of the same oscillations when sampled by the Ca IIH core and wings.

The organization of the paper is as follows. The observations are presented in the next section. Section 3 defines our Fourier methods. In Sect. 4 we display TRACE results from May 12, 1998 together with Ca IIH comparisons in the various graphical forms listed above. We add an extensive error analysis in Sect. 5, including comparison with an independent TRACE data set from October 14, 1998. Some results are discussed in the context of other work in Sect. 6. The conclusions follow in Sect. 7.