p-mode PROPAGATION THROUGH THE TRANSITION REGION INTO THE SOLAR CORONA. I. OBSERVATIONS

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1 The Astrophysical Journal, 643: , 2006 May 20 # The American Astronomical Society. All rights reserved. Printed in U.S.A. A p-mode PROPAGATION THROUGH THE TRANSITION REGION INTO THE SOLAR CORONA. I. OBSERVATIONS M. S. Marsh 1 and R. W. Walsh Centre for Astrophysics, University of Central Lancashire, Preston, PR1 2HE, UK; mmarsh@uclan.ac.uk Received 2005 November 17; accepted 2006 January 18 ABSTRACT Oscillations have long been observed in the sunspot umbral chromosphere and transition region, connected to global p-mode oscillations. These p-modes are thought to undergo mode conversion to slow magnetoacoustic waves in regions of strong magnetic field. More recently, propagating oscillations have also been observed in solar coronal loops. Using new spectroscopic imaging data at transition-region temperatures, combined with coronal imaging, we present direct observations of the propagation of these slow magnetoacoustic p-modes through the transition region and into the solar corona, along the magnetic field. The waves are observed as oscillations in the chromosphere/ transition region and propagations in the corona due to the emission scale height of the different temperature lines combined with the magnetic field geometry. Subject headinggs: MHD Sun: atmosphere Sun: corona Sun: oscillations sunspots waves Online material: color figures 1. INTRODUCTION km s 1, periods of s, and short damping lengths (8:9 4:4 Mm). De Moortel et al. (2002b) suggest a Three minute oscillations have long been associated with sunspot umbrae, using spatially unresolved narrow-slit spectro- relation between 3 minute oscillations found in TRACE coronal graph observations. Beckers & Tallant (1969) observe intensity loops situated above sunspot regions and 5 minute oscillations found in nonsunspot loops. and velocity oscillations with an approximate 3 minute period, Marsh et al. (2003) present the first observation of a 5 minute which are visible in the Ca H and K lines above sunspot umbrae. propagating oscillation in a coronal active-region loop, observed Gurman et al. (1982) observe 3 minute intensity and velocity simultaneously at transition-region temperatures. These results oscillations above sunspots in the C iv ultraviolet line with the suggest wave propagation through the chromosphere and transition region and into the coronal loops. Ultraviolet Spectrometer and Polarimeter ( UVSP) on the Solar Maximum Mission (SMM ). More recently, the 3 minute oscillations above sunspots have been observed in the extreme ultra- In this paper we use new, spatially resolved spectral imaging observations of a sunspot active region to directly observe the violet with the Solar and Heliospheric Observatory (SOHO)using well-known 3 minute chromospheric/transition-region oscillations narrow-slit sit-and-stare observations. Fludra (2001) observes 3 minute intensity oscillations in chromospheric and transitionregion lines associated with sunspot plumes above sunspot re- propagating into the emerging coronal loop system. In Paper II we analyze the observations further, in terms of deriving properties of the atmosphere and prospects for atmospheric seismology. gions, using the Coronal Diagnostic Spectrometer (CDS; Harrison et al.1995). The amplitude of the oscillations is found to reach a 2. OBSERVATIONS peak in the transition-region lines then decrease with increasing temperature. Brynildsen et al. (2002) confirm this result The observations were taken as part of a coordinated loop with observations using CDS and also find indications of oscillations at the footpoints of Transition Region and Coronal Explorer CDS and TRACE observations of quiescent, active-region loop variability study campaign. The campaign utilizes simultaneous (TRACE; Handy et al. 1999) coronal loops. O Shea et al. (2002) structures to study waves/flows. The campaign was designed to suggest that time delays between the oscillations in lines of increasing formation temperature are due to upwardly propagat- the CDS Normal Incidence Spectrometer ( NIS) wide slit, com- make the first coordinated observations of active regions using ing slow magnetoacoustic waves. Brynildsen et al. (2003) also bined with cotemporal TRACE observations. The primary aim of interpret observations of oscillations in the wings of transitionregion lines as upwardly propagating acoustic waves. and directly observe the manifestation of the coronal TRACE these observations was to progress the work of Marsh et al. (2003) Intensity disturbances propagating along active-region loops are propagations at corresponding low- to mid-transitionregion temperatures using CDS. observed by Berghmans & Clette (1999) in Extreme-ultraviolet Imaging Telescope (EIT; Delaboudiniere et al. 1995) data. NOAA active region was observed on 2004 March 13 Nightingale et al. (1999) observe equivalent disturbances with near disk center. While the active region consists of two clear TRACE. These propagations are observed in TRACE and sunspot regions, here we concentrate on the westerly sunspot quantified by De Moortel et al. (2002c, 2002a). They observe propagating oscillations in the footpoints of large, diffuse, coronal active-region loops. These oscillations are interpreted as slow magnetoacoustic waves with propagation speeds in the range region, located at (315 00, ) in solar coordinates. Figure 1 shows the sunspot active region viewed with the Michelson Doppler Imager (MDI; Scherrer et al. 1995) in magnetogram (left panel) and white light (second panel), CDS wide slit (He i [third panel], O v [ fourth panel], and Mg ix/vii [ fifth panel]), and 1 NASA Postdoctoral Fellow, NASA Goddard Space Flight Center, Greenbelt, MD slit is plotted for each instrument. The MDI white-light contours TRACE (171 8; right panel).thefieldofviewofthecdswide 540

2 p-mode PROPAGATION INTO SOLAR CORONA. I. 541 Fig. 1. Western sunspot region of AR observed in MDI: magnetogram (left panel) and white light (second panel), CDS wide slit (negativeimages): He i (third panel), O v ( fourth panel), Mg ix/vii ( fifth panel), and TRACE (negativeimage; right panel): MDI white light contours are overplotted indicating the location of the umbra and penumbra. [See the electronic edition of the Journal for a color version of this figure.] are overplotted, indicating the sunspot umbral and penumbral regions. The magnetogram shows the intense negative magnetic field of the sunspot surrounded by a number of small bipolar magnetic fragments. The CDS NIS wide slit produces large-scale spectral intensity images (without rastering) in He i, Ov and Mg ix at high cadence. Essentially, for the first time we use CDS as a transition region imager of active regions coordinated with TRACE; a summary of the observations is given in Table 1. The wide-slit observations have a duration of 44 minutes (07:08 07:52 UT) and consist of ; intensity images with a pixel size of 1B68 in He i 584 8, Ov 629 8, and Mg ix 368 8, with an exposure of 20 s and cadence of 26 s. The Mg ix line is blended with the Mg vii and lines, which have peak formation temperatures of log T ¼ 5:9, using the CHIANTI version 4.2 atomic database active-region differential emission measure (Dere et al. 1997; Young et al. 2003). Spectroscopic rasters above the sunspot plume region show that the Mg vii contributions are of the same order or in places greater than the Mg ix line profile. For simplicity this blend is hereafter referred to as Mg ix/vii. Inthis data set we find that the signal-to-noise ratio of Mg ix/vii is too low to be included in the analysis of x 3, and use it for context only. The peak line formation temperatures of He i,ov,mgix, and Fe ix (dominant in the TRACE bandpass) are log T ¼ 4:5, log T ¼ 5:4, log T ¼ 6:0, and log T ¼ 6:0, respectively, spanning the lower transition region, mid-transition region, and corona. The TRACE observations analyzed are ; images in the bandpass with a pixel size of 1 00, an exposure of 23 s, and 30 s cadence taken during the hour 07:00 08:00 UT. The spectral lines of neutral helium have complex formation processes, which are not yet fully understood. The observations presented here use the He i line, which is commonly referred to as a chromospheric line. Although the He i lines share similarities with chromospheric lines, the He i line is thought to be formed in the low-transition region (Jordan 1975; Andretta & Jones 1997). Mauas et al. (2005) study the effect of coronal photoionization on He i line formation. They find that incident coronal radiation has little effect on ultraviolet lines such as He i 584 8, while it is an important effect for the D and lines. Considering Figure 1, in the He i lower transition-region line we observe relatively uniform emission above the sunspot with a number of emitting structures in the surroundings. The mid transition-region temperature of O v shows similar emission structures to He i around the sunspot. However, there is a significant difference in structure above the sunspot; here we observe the intense emission of the sunspot plume located above the umbra and southeastern penumbra. Sunspot plumes show enhanced emission at transition-region temperatures above sunspot umbrae, as described by Foukal et al. (1974). The missing data on the left of the O v image (Fig. 1, third from right) occurs because the TABLE 1 Summary of the Analyzed CDS and TRACE Observations on 2004 March 13 Parameter CDS Wide Slit TRACE Lines... He i 584 8, Ov 629 8, Mgix/vii ( bandpass) Observation time... 07:08 07:52 UT 07:00 08:00 UT Pointing (Solar x, Solar y)... (322 00, ) (119 00, ) Field of view ; ; Pixel size... 1B Cadence s 30 s

3 542 MARSH & WALSH Vol ANALYSIS Standard reductions are applied to the CDS and TRACE data as described in Marsh et al. (2003). The data are corrected for cosmic ray spikes, detector bias, flat field, and pointing offsets, and the TRACE background diffraction pattern is removed. Lowfrequency trends within time series are removed using a thirdorder polynomial subtraction Solar Rotation Correction Once the CDS wide-slit and TRACE data are cleaned and calibrated, they must be corrected for spatial solar rotation to perform a time series analysis. Solar rotation is removed by calculating the offset of each image from the first in the time series. The data are then aligned by translating each frame by its negative offset and applying cubic convolution interpolation. The offset values of the CDS wide-slit data are calculated using the solar rotation rate at the coordinates of the center of the first image. The resulting three-dimensional data cube is then co-aligned to subpixel accuracy. TRACE is located in a polar orbit and displays an orbitally affected pointing variation, possibly due to thermal effects ( Handy et al. 1999). We use a two-dimensional cross-correlation method between each TRACE image and the first image in the time series to calculate the offset components produced by the orbital variation and solar rotation in the TRACE data. In this data we find a possible orbital variation with a peak-to-peak amplitude of approximately 1B4 in the solar y direction. Vibrations due to shutter quadrant changes can cause an additional pointing error of the order 0B1 ( Handy et al. 1999). A high-frequency variation present within the y-axis offsets appears to be due to the quadrant shutter changes in this alternating 171/1600 observing sequence. The x-axis has a linear offset as expected, due to solar rotation. Fig. 2. Composite TRACE , CDS O v, and TRACE image of AR on 2004 March 12. The image has been contrast enhanced for clarity. The coincidence of the umbra, sunspot plume, and emerging coronal loop system is clearly apparent, centered around the coordinates (310 00, ). The vertical line is caused by the edge of the O v data. Toward the top of the image from coordinates (275 00, )to(360 00,0 00 ), a plasma flow is visible, originating from just outside the eastern edge of the wide-slit field of view. [See the electronic edition of the Journal for a color version of this figure.] O v image is dispersed onto the right edge of the detector, and SOHO was inverted 180 during the observations. In Mg ix/vii and TRACE 171 8, we observe the coronal loop structures associated with the sunspot region. These loops outline the magnetic field emerging from the sunspot, embedded within plasma emitting at coronal temperatures. In the online edition of the Journal, Figure 2 shows a composite color image of AR on 2004 March 12, with TRACE (red ), CDS O v (green), and TRACE (blue). The three separate images were contrast enhanced by rescaling the color table to exclude the brightest and darkest pixels having a low occurrence frequency within the histogram of pixel intensities. The images were then composed to form the RGB components of the composite color image. This image clearly shows the coincidence of the sunspot umbra, the intense transition-region emission of the sunspot plume, and the emerging coronal loop system CDS Wide Slit To investigate oscillatory behavior within the wide-slit data, we form maps of Fourier power where the fast Fourier transform (FFT) of the time series at each pixel location is calculated. The resulting three-dimensional data cube contains the Fourier power with frequency for each pixel. In this analysis, the Interactive Data Language (IDL) version 5.5 FFT routine is applied, based on the algorithm by Cooley & Tukey (1965). To test the significance of power within the data cube, we use a randomization method (see x 3.4). Here we use a significance level S of 95%, and power at frequencies occurring below this level is set equal to zero. Then maps of significant Fourier power are employed to observe the spatial distribution of oscillations at different frequencies. The time series can then be investigated at locations showing oscillating structures. The frequencies/periods of oscillations within these structures are determined using a Fourier analysis. In x 3.3 we describe the running difference method used to investigate propagating intensity oscillations within the TRACE coronal loops. This method cannot be applied to the CDS wideslit data; at He i and O v temperatures, the signature of the TRACE propagations is observed as an oscillation without a spatial propagation. This is discussed inx 5 in terms of the emission scale height of the different temperature lines, combined with the geometry of the sunspot magnetic field TRACE To investigate any propagating intensity oscillations in the TRACE data, we use a running difference method, as in Marsh et al. (2003). A tube is defined overlying a coronal loop structure. Cross-sections of 2 00 width are formed along the tube. A running difference is formed by using the integrated intensity profile of the tube along its length and subtracting the profile of the tube 90 s earlier. Thus any propagating oscillations appear as diagonal light and dark bands in the difference image. The gradient

4 No. 1, 2006 p-mode PROPAGATION INTO SOLAR CORONA. I. 543 of these bands can then be used as an indication of the propagation velocity of the oscillations. The periodicity of the propagating oscillations is investigated using a Fourier analysis of time series formed from cross-sections along the defined tube Randomization Significance Test To test the significance of power within the Fourier transform, a randomization method is used, following Linnell Nemec & Nemec (1985) and O Shea et al. (2001), in which the technique is applied to solar data. Briefly, the method is applied as follows: the null hypothesis that Fourier power P at a particular frequency is caused by chance is tested. The method is based on the principal that under the null hypothesis, the measured order of the time series data points is one of the possible, equally likely permutations of the order. If there is no periodicity within the time series, then the measured values y 1 ; y 2 ; y 3 ;:::; y n can be randomly rearranged y r(1) ; y r(2) ; y r(3) ;:::; y r(n) without affecting the distribution of Fourier power for large n, where r(1); r(2); r(3); :::; r(n) is a random permutation of the data point subscripts, assuming a white noise distribution of power consistent with the CDS and TRACE detectors. To test the hypothesis that the power P() is due to chance, the maximum power at all frequencies may be calculated for the n! possible permutations of the time series; p is then defined as the fraction of permutations having greater power than the original time series at frequency. Practically, n! permutations is too large to calculate for long or large numbers of time series, and thus the value of p can be estimated by calculating the maximum power for mtn random permutations of the time series. The fraction of permutations having greater maximum power than the original time series P() gives an estimate of the value of p. Then 100(1 p) gives an estimate of the percentage probability that P() is due to a periodic signal within the time series. The significance level S can then be defined as the probability level above which power is assumed to be due to real periodicity. A significance level of S ¼ 95% is used here, with m ¼ 250 random time series permutations. 4. RESULTS 4.1. CDS Wide Slit Figure 3 shows the intensity and Fourier power maps for He i and O v, significant to the 95% level within the 3 minute frequency range mhz ( s). The region above the sunspot appears quite uniform in He i intensity; however, the power map for He i (bottom left) shows statistically significant 3 minute power confined above the sunspot umbral region. This suggests the region above the sunspot umbra is not quiescent but instead supports a dynamic oscillating structure at the temperature of He i. The O v power map (Fig. 3, bottom right) shows greater significant power than He i above the umbral region. The increase in the magnitude of power suggests a greater oscillation amplitude within the mid-transition-region temperature of O v. The 3 minute power is located above the umbra, coincident with the intense emission from the sunspot plume. In the O v intensity map, the sunspot plume also extends over the southeastern penumbral region. However, at this location the intensity becomes so large that the detector becomes saturated. Therefore, in the O v power map we are not able to observe the oscillation in the region of greatest intensity. The Mg ix/vii blend is too weak in this data set to observe any significant oscillation above the noise level and so is not included in this analysis. Fig. 3. Intensity (top panels) and Fourier power maps (bottom panels) for the CDS wide-slit data in He i (left panels)and O v (right panels) overplotted with MDI white light contours. Within the power maps, the shaded regions indicate 95% significant power within the frequency range mhz ( s). [See the electronic edition of the Journal for a color version of this figure.] To investigate the periodicity of oscillations in the intensity time series of He i and O v, we sum all the pixels above the sunspot containing the significant 3 minute oscillations. The FFT is applied to these time series to determine the frequency distribution of power within the 3 minute band. The top row of plots in Figure 4 shows the He i time series with a cadence of 26 s, the relative amplitude of the 3 minute oscillation to the mean intensity of the times series I(t)/Ī 1, and the FFT of the time series. The time series shows a clear oscillation present throughout the

5 544 MARSH & WALSH Vol. 643 Fig. 4. Left: He i (top) and O v (bottom) time series of the binned pixels above the sunspot umbra that show significant 3 minute power. Middle: Amplitude relative to the mean intensity for the He i and O v time series. Right: FFT for the He i and O v time series; the dashed lines indicate the 95% significance level. [See the electronic edition of the Journal for a color version of this figure.] duration of the observations. The relative amplitude indicates that the oscillation has an amplitude of 2% in the He i line. The FFT reveals that the oscillation is not a single frequency but consists of two dominant frequencies within the 3 minute band. These frequencies are centered around 6.1 and 7.1 mhz (164 and 141 s). The bottom row of plots in Figure 4 displays the results for the O v time series. Comparing the two time series, it is clear that the oscillation amplitude is greater in O v; the relative amplitude of the oscillation is 4%. As in He i, the FFT of the O v time series shows that the oscillation is not composed of a single frequency, but consists of two dominant frequencies. In the O v data, these frequencies are centered around 5.9 and 7.3 mhz (169 and 137 s). To isolate the two dominant frequencies, we filter the time series by setting all power outside the 3 minute band equal to zero and take the inverse Fourier transform. Figure 5 shows the results for the filtered He i and O v time series and their filtered FFTs. The filtered time series show the beat oscillation of the two frequencies. If we compare the filtered time series to the original time series we observe the beat oscillation of the two frequencies within the original time series, suggesting that both frequencies are present throughout. Considering the plots of the filtered time series data in Figure 5, the correlation between the time series can be observed more clearly. The plot of the relative amplitudes shows a very good correlation between the time series. The cross-correlation for the whole of the filtered time series has a maximum correlation coefficient of 0.75 with zero time lag. The second half of the time series appear to have a greater correlation, confirmed by a correlation coefficient of 0.9 with zero lag. The cross-correlation of the time series does not show any significant lag between He i and O v. We may expect to observe a lag, assuming that the observed oscillations are caused by upwardly propagating waves and that He i is formed at a lower altitude than O v. However, the cross-correlation coefficients are calculated for lags of integer factors of the data cadence (26 s). If the phase difference between He i and O v produces a lag that is smaller than the time series cadence, then this phase difference will not be observable TRACE The TRACE data display propagating oscillations present in many of the loop structures emerging from the sunspot. The Fig. 5. Left: Filtered He i and O v time series. Middle: Filtered He i FFT. Right: Filtered O v FFT. The dashed lines within the FFT plots indicates the 95% significance level. [See the electronic edition of the Journal for a color version of this figure.]

6 No. 1, 2006 p-mode PROPAGATION INTO SOLAR CORONA. I. 545 Fig. 6. Top: TRACE context image (left) indicating the location of sunspot umbra/penumbra and running difference tube. The running difference image (right) indicates outward intensity propagations along the coronal loops. The dashed lines outline one of the propagations and give an estimated velocity of 80 km s 1. Bottom: TRACE time series formed from the cross-section at the base of the tube (left), amplitude relative to the mean intensity (middle), and time series FFT (right) with the dashed line indicating the 95% significance level. [See the electronic edition of the Journal for a color version of this figure.] majority of the loop structures emerging to the west of the sunspot show periodic propagations in their corresponding running difference image. We select one of the loop structures that appears to be rooted in the umbra where we observe significant oscillations with the CDS wide slit. The top left panel of Figure 6 shows the TRACE context image of the CDS wide-slit field of view. Overplotted are the MDI white light contours of the sunspot umbra and penumbra, along with the tube outlining the loop structures selected to form the running difference image. The running difference image in Figure 6 (top right) clearly shows the light and dark diagonal bands that indicate intensity propagations along the loop structure. The regular spacing of the bands suggests that the propagations have a periodic nature (180 s) over the duration of the observations. The positive gradient of the bands indicates that the propagations originate at the base of the loops and propagate outward along their length. The gradient of the dashed lines in the running difference image gives an estimate of the propagation velocity perpendicular to the line of sight of 80 km s 1. To analyze the periodicity of the TRACE propagations, we select the cross-section at the base of the defined tube above the sunspot umbra. The pixels of this cross-section are summed to form the TRACE time series. The bottom plots in Figure 6 show the time series, the relative amplitude of the propagating oscillations, and the FFT of the time series with the 95% significance level. The time series shows that the oscillation at the base of the loops is caused by the periodic propagations. The amplitude relative to the mean intensity indicates that the propagating oscillations have amplitudes of 3%. The FFT shows that in the 3 minute band, the TRACE propagating oscillations at the base of the loops consist of one dominant frequency, significant above the 95% level. This frequency is centered around 5.9 mhz (169 s), as in O v. We also observe power at 3 mhz(330s) coincident with the 5 minute p-mode oscillation and at 7.3 mhz (137 s), as in O v; however, these frequencies are not significant to the 95% level. 5. SUMMARY AND DISCUSSION A sunspot active region and its associated quiescent coronal loops are observed with spatially resolved, high-cadence observations using CDS and TRACE. The unique CDS wide-slit observations reveal highly dynamic oscillations above the sunspot umbra at transition-region temperatures. The spatially resolved nature of the observations allows the location and geometry of the oscillating region to be observed. It can then be seen that the oscillations are located above the sunspot umbra, the sunspot plume is cospatial with the oscillating region, and the plume is located at the base of the coronal loops that carry the 3 minute propagations. The 3 minute sunspot oscillations in CDS wide-slit data at the low- to mid-transition-region temperatures of He i (log T ¼ 4:5) and O v (log T ¼ 5:4) are observed. Fourier power maps indicate that the oscillations are confined above the umbra in He i and appear to be coincident with the emission from the sunspot plume in O v. In coordinated TRACE observations of the coronal loops emerging from the sunspot, we observe periodic intensity propagations concurrent with the He i and O v oscillations. The propagations have a velocity perpendicular to the

7 546 MARSH & WALSH Vol. 643 line of sight of 80 km s 1 (cf. Robbrecht et al. 2001; De Moortel et al. 2002c). The FFTs of the He i and O v time series formed above the umbra indicate that the 3 minute band contains two distinct frequencies. The TRACE time series shows only one of the frequencies to be significant above the 95% level. In He i we observe the two frequencies around 6.1 and 7.1 mhz (164 and 141 s), with the lower frequency having the greatest peak power. In O v the two frequencies are observed around 5.9 and 7.3 mhz (169 and 137 s), with the higher frequency having the greater peak power. In TRACE we observe the two frequencies around 5.9 and 7.3 mhz (169 and 137 s), as in O v; however, only the power at 5.9 mhz is significant above the 95% level. The relative oscillation amplitudes of the time series are He i 2%, O v 4%, and TRACE 3%. This agrees with the observations of Fludra (2001), Brynildsen et al. (2002), and O Shea et al. (2002), who find that the oscillation amplitude peaks at transition-region temperatures. The TRACE bandpass contains contributions from O v and O vi; therefore, it could be suggested that the TRACE observations are not of coronal origin. However, Brynildsen et al. (2002) examine spectroscopic data above sunspots using CDS; they find that the oxygen lines contribute on the order of 10% to the total intensity within the TRACE bandpass. To produce the amplitude of the oscillations observed with TRACE, theycalculate that the oxygen oscillations would require an amplitude on the order of 30%. This is not observed in the CDS O v data; therefore, the TRACE oscillations must be due to coronal emission. The new spatially resolved data presented here support this further, since TRACE propagations are not observed in the O v data. It was suggested by De Moortel et al. (2002a) that there may be a relation between their observations of 3 minute propagations in TRACE loops and the 3 minute oscillations above sunspots observed by Brynildsen et al. (2002). Here, we present the first observations that the long-observed 3 minute umbral oscillations in the transition region are directly connected to the 3 minute propagations along the TRACE loops. This work shows that the oscillations in the transition region and the propagations along the coronal loops are consistent with the same wave phenomena. Although we do not observe chromospheric lines directly, it is a logical progression to conclude that the chromospheric oscillations are also due to the upward propagation of these waves, as suggested by Fludra (2001), Brynildsen et al. (2002), and O Shea et al. (2002). In the magnetic structure above sunspots, the emission scale heights are relatively small for He i and O v formation temperatures. Thus, emission from these lines is located in regions at low altitudes above the photosphere where the umbral magnetic field is almost vertical (see Mathew et al. 2003). Therefore, we only observe an oscillation rather than a propagation at low- to mid-transition-region temperatures. At the coronal temperatures of the TRACE loops, the emission scale height is much larger, and the emitting region extends a greater distance along the loops magnetic field. At these altitudes the plasma decreases and the magnetic field diverges, becoming inclined to the vertical. Thus, we are then able to observe the wave propagation perpendicular to the line of sight. Figure 7 shows the potential magnetic field above the sunspot, extrapolated with a constant linear forcefree code (courtesy of D. S. Brown; the code is described by Carcedo et al. [2003] and uses the original method of Chiu & Hilton 1977). Considering the emission scale heights of the different regions, combined with the magnetic field geometry of the sunspot, this illustrates the line-of-sight effects involved in Fig. 7. Linear force-free potential magnetic field extrapolated from the MDI magnetogram, courtesy D. S. Brown. [See the electronic edition of the Journal for a color version of this figure.] observing the waves as either oscillations or propagations in the different temperature regions. Figure 8 shows the changing emission structure above the sunspot with increasing temperature. Above the sunspot umbra, the magnetic field is predominantly vertical through the photosphere and low/mid-transition region, viewed with MDI, and He i/o v. The emission structure of the coronal loops outlines the magnetic field, indicating that in the corona, the magnetic field becomes significantly inclined at the temperatures of Mg ix/vii and TRACE Since these waves are present in an ionized plasma and a strong magnetic field, they cannot exist as pure acoustic waves. Their propagation speed and radiative flux oscillation suggest slow magnetoacoustic modes. Observations show that the 5 minute waves in the sunspot photosphere are connected to the 5 minute global p-modes (Penn & Labonte 1993; Balthasar et al. 1987; Braun et al. 1987). Theoretical models predict mode conversion of these waves and the generation of slow magnetoacoustic waves in sunspots (see Bogdan 2000). It is thought that the 3 minute oscillations in the chromosphere and transition region are due to amplitude steepening of the photospheric p-modes above the acoustic cutoff frequency ( Bogdan 2000), excitation at the acoustic cutoff frequency due to the photospheric p-modes (Fleck & Schmitz 1991), or p-modes modified by the strong magnetic field (Zhukov 2002). In the low- umbral atmosphere above the photosphere, these waves may be considered as acoustic waves that propagate parallel to the magnetic field and that can propagate upward into the atmosphere at frequencies above the acoustic

8 No. 1, 2006 p-mode PROPAGATION INTO SOLAR CORONA. I. 547 Fig. 8. Atmospheric structure above the sunspot with increasing temperature. [See the electronic edition of the Journal for a color version of this figure.] cutoff frequency (Bogdan 2000; Lites et al. 1998; Khomenko et al. 2003). There have been many observations of multiple frequencies within the 3 minute band above sunspots, e.g., Beckers & Tallant (1969), Beckers & Schultz (1972), Gurman et al. (1982), and Lites (1984) and more recently by Fludra (2001), O Shea et al. (2002), and Christopoulou et al. (2003). Resonant theory predicts the formation of closely spaced oscillation frequencies within the 3 minute band (see Zhukov 2005; Settele et al. 2001, and references within). However, using sit-and-stare CDS observations, Brynildsen et al. (2002) find only one dominant frequency in the 3 minute band, in contrast to the other observations. Doyle et al. (1998) discuss the qualitative effect of sit-andstare observations on power spectra. They find that the effect of solar rotation on oscillating structures broadens the distribution of power around the frequencies within the power spectra. To limit the spatial drift of the slit, Brynildsen et al. (2002) limit the duration of the analyzed time series to 20 minutes. Limiting the duration of the time series reduces the frequency resolution, restricting the information that can be gained about the beat frequency of possible multiple frequencies. Two frequencies separated by 1 mhz produce a beat oscillation period of 16 minutes, for example; this is of the order of their time series duration. This also broadens the distribution of power around the oscillation frequencies. It is suggested here that the combination of these solar rotation and time series duration effects can explain the single frequency observed by Brynildsen et al. (2002). This work demonstrates the connectivity between the oscillations in the transition region and the propagation along the coronal loops, due to the transmission of slow magnetoacoustic waves. Simultaneous observations of the source of the waves have not yet been made. A complete set of observations at photospheric to coronal temperatures are needed to discover the photospheric signature of these waves. This will allow the propagation along the magnetic field and coupling through the atmosphere to be quantified. An accurate and consistent approach such as this may then allow the study of solar atmospheric seismology across a complete temperature range in active regions. The combination of imaging and spectroscopy provided by the upcoming missions SOLAR-B,theSolar and Terrestrial Relations Observatory (STEREO), and the Solar Dynamics Observatory (SDO) will play a key role in developing this new field. This work demonstrates the need for imaging spectroscopy in future instruments, particularly at transition-region temperatures. Paper II will examine how the observations can be analyzed to derive properties of the atmosphere and discuss the potential for future atmospheric seismology. This work was partly funded by a PPARC research studentship. Data provided courtesy of the TRACE and SOHO consortia. SOHO is a project of international cooperation between ESA and NASA. CHIANTI is a collaborative project involving the NRL (USA), RAL (UK), and the Universities of Florence ( Italy) and Cambridge ( UK). Running difference software provided by J. Ireland. We would like to thank the anonymous referee for comments that improved the manuscript. Facilities: SOHO(CDS), SOHO(MDI), TRACE. Andretta, V., & Jones, H. P. 1997, ApJ, 489, 375 Balthasar, H., Wiehr, E., & Kueveler, G. 1987, Sol. Phys., 112, 37 Beckers, J. M., & Schultz, R. B. 1972, Sol. Phys., 27, 61 Beckers, J. M., & Tallant, P. 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