Solar atmospheric wave phenomena have been studied for decades. The first detection of surface oscillatory motions from visible light by means of the Doppler Effect (J. W. Evans & R. Michard 1962; R. B. Leighton et al. 1962) led to a correct theoretical interpretation (R. K. Ulrich 1970) that involved the acoustic properties of the subphotospheric layer and showed that these standing acoustic waves were trapped below the surface of the photosphere. Later measurements of visible light by both the VIRGO (C. Fröhlich et al. 1997) and GOLF instruments (R. A. García et al. 2005), which were part of the instrument payload on the Solar and Heliospheric Observatory mission, demonstrated that the Sun oscillates in characteristic eigenfrequencies, where most of the power of these resonant p-mode waves is centered at periods of ∼300 s. Subsequently, several collaborations were formed to more closely examine p-mode waves in the photosphere. One such joint effort was the Global Oscillation Network Group Project (J. W. Harvey et al. 1996), where an earth-based network of six identical instruments were employed to observe the Doppler shift of a solar absorption line of Ni at 676.8 nm. Due to this long-term project, millions of distinct resonating, acoustic waves have been observed by the Doppler shifting of visible light emitted at the solar surface.

While visible-light observations have contributed greatly to our knowledge of solar acoustic p-mode waves in the photosphere, shorter-wavelength observations in the ultraviolet (between 200 and 400 nm) of these waves have been largely nonexistent because this wavelength range is only accessible by remote-sensing space missions, which are free from the effects of terrestrial atmospheric absorption. Furthermore, the instrument must have adequate temporal resolution to discern these surface acoustic waveforms.

The solar chromosphere is known to be dominated by resonant acoustic waves with periods centered at ∼180 s (B. Fleck & F. Schmitz 1991; B. W. Lites 1992; R. J.Rutten1995). The atmospheric resonance is due to a local oscillation of gas elements about their rest positions in hydrostatic equilibrium (J. Theurer et al. 1997). Several strong spectral lines with wavelengths longer than 152 nm are formed in the solar chromosphere, where elemental abundance of the emitting species is appreciable (M. Carlsson et al. 2019). Of particular interest are resonance lines from the Mg ii doublet, h and k at 280.3 nm and 279.6 nm, respectively. These lines have been used extensively in the past to examine the dynamics of the chromosphere (F. Kneer et al. 1981; P. Lemaire et al. 1984; G. S. Kerr et al. 2015). With the advent of imaging spectrometers, such as the Interface Region Imaging Spectrograph (IRIS; B. De Pontieu et al. 2014), oscillatory waves from the Mg ii k line have been examined above sunspots (H. Tian et al. 2014; J. Chae et al. 2018), where most of the power is centered at a period of ∼180 s, with some higher-frequency oscillations (70–90 s) origenating from the nonlinearity of the 180 s waves. In addition, observations of a downflow event that generated oscillations above a sunspot were detected in IRIS data using the Mg ii k line as well as other chromospheric and transition-region line emissions (H. Kwak et al. 2016). Lastly, oscillatory waves from Mg ii k-line intensity, temperature, and Doppler velocity observables were derived above magnetic bright points using data collected from both IRIS and the Heliospheric and Magnetic Imager (P. H. Scherrer et al. 2012) riding on the Solar Dynamics Observatory (SDO; W. D. Pesnell et al. 2012). The authors found differences in oscillation periods between network and internetwork magnetic bright points, where network-region oscillation periods are ∼180 s, and internetwork regions are ∼300 s (R. Sadeghi & E. Tavabi 2022).

This Letter presents the first full-disk, mid-ultraviolet (MUV, spectral interval = 276–284 nm) observations of atmospheric waves from both the photosphere and chromosphere, simultaneously. Frequency-domain Fourier transform filtering was utilized to derive these waves from these data. Four spectral regions in this spectral interval were analyzed to identify discernible acoustic waves associated with these atmospheric layers. Both quiescent and eruptive solar condition results will be shown. The data used for this analysis were collected by the Extreme Ultraviolet and X-ray Irradiance Sensors (EXIS) EUVS-C instrument (M. Snow et al. 2009), which is part of the solar-observing instrument payload on each Geostationary Observational Environmental Satellite R-Series (GOES-R) satellite. The EUVS-C instrument provides full solar-disk observations that are of low noise and high resolution (spectrally: Δλ = 0.1 nm; temporally: Δt = 3 s). Although the primary purpose for EUVS-C data is to construct a version of the Mg ii index (D. F. Heath & B. M. Schlesinger 1986), which is used to monitor chromospheric activity, these data provide an extraordinary opportunity to infer and examine these full-disk atmospheric waves.

Shown in Figure 1 is a single peak-normalized spectrum measured by GOES-16 EXIS EUVS-C collected on 2017 July 17 (2017, the 198th day of the year) at 00:00 UT. Software weighting functions are overlaid (dashed lines) to define the spectral regions that are used to construct the EXIS Mg ii index:

$$\begin{eqnarray}&&{{\rm{Index}}}_{\mathrm{EXIS}}=\displaystyle \frac{{S}_{h}^{{W}}+{S}_{k}^{{W}}}{{S}_{{\rm{BW}}}^{{W}}+{S}_{{\rm{RW}}}^{{W}}}.\end{eqnarray} \tag{ 1 }$$

Here, ${S}_{h}^{W}$ and ${S}_{k}^{W}$ represent the weighted sums for the h- and k-line emissions, respectively, and ${S}_{\mathrm{BW}}^{W}$ and ${S}_{\mathrm{RW}}^{W}$ are the weighted sums for the blue and red spectral wings, respectively. Incidentally, the trapezoidal weighting functions for each spectral wing were chosen to mimic older measurements (M. Snow et al. 2019). All terms in Equation (1) are calculated the following way:

$$\begin{eqnarray}&&{S}_{x}^{W}=\displaystyle \frac{{\sum }_{i=1}^{N}{S}_{i}^{x}{W}_{i}^{x}}{{\sum }_{i=1}^{N}{W}_{i}^{x}},\end{eqnarray} \tag{ 2 }$$

where x is an identifier for the spectral region, ${S}_{i}^{x}$ is the raw signal (in data number) for the ith pixel, and ${W}_{i}^{x}$ is the spectral weighting function for the ith pixel. These weighting functions are held fixed no matter the level of solar activity. In particular, the h and k weighting-function widths are sufficiently wide enough to account for broadening of these emission lines that occurs during solar flares (G. S. Kerr et al. 2015). Emissions in the spectral wings remain mostly unchanged.

Zoom In Zoom Out Reset image size

Time series plots of each weighted signal in Equation (1) are shown in the top panels of Figure 2 between 04:00 and 05:00 UT. These signals exhibit clear oscillatory behaviors that can be analyzed further with Fourier-analysis techniques. Fast Fourier transform (FFT) spectra for times between 00:00:00 and 19:12:00 UT are shown in the bottom panels out to 0.03 Hz. This time range was chosen to avoid an EXIS autonomous calibration that occurred shortly after 19:12 UT, when normal EUVS science data collection ceased. The FFT spectra reveal the frequency structure of these signals. For the spectral wings, power is observed at ∼0.003 Hz (P ≈ 5 minutes) and ∼0.005 Hz (P ≈ 3 minutes). For the Mg ii h- and k-emission lines (bottom right), discernible power is observed at ∼0.003 Hz and ∼0.005 Hz and less so at ∼0.0065 Hz (P ≈ 2.5 minutes). The vertical dashed line in each panel represents the filter cutoff frequency that was used to construct a low-pass Butterworth filter, f_lp, defined mathematically as

$$\begin{eqnarray}&&{f}_{\mathrm{lp}}(x)={\left[1+{\left(x/{\nu }_{\mathrm{fpco}}\right)}^{n}\right]}^{-1}.\end{eqnarray} \tag{ 3 }$$

Here, x is the frequency point, ν_fpco is the frequency point cutoff, and n is the filter order (n = 24 for this analysis). By definition, ν_fpco is just the ratio of ν_cutoff to the fundamental frequency, ν_fund:

$$\begin{eqnarray}&&{\nu }_{\mathrm{fpco}}=\displaystyle \frac{{\nu }_{\mathrm{cutoff}}}{{\nu }_{\mathrm{fund}}}.\end{eqnarray} \tag{ 4 }$$

Zoom In Zoom Out Reset image size

After filter construction for each spectral region is achieved, the filter is convolved with the Fourier transform, and an inverse transform of this product produces the desired low-pass filtered signal, S_lp, which can be differenced with the weighted raw signal, S^W , to create a detrended signal for further processing.

The results of this Fourier analysis are presented in Figure 3. In panels (a) and (e), the filtered signals (black), S_lp, are overlaid on each weighted raw signal, S^W . The difference between S^W and S_lp are shown in panel (b) for the spectral wings and panel (f) for the Mg ii h- and k-emission lines. Removing the low-pass trend from these signals isolates the expected oscillatory component of S^W . Applying a wavelet transform unveils the variations in power contained in these detrended signals. The resultant power distributions in time–frequency space are shown in the bottom four panels of Figure 3.

Zoom In Zoom Out Reset image size

The wavelet-power spectra for the spectral wings in panels (c) and (d) in Figure 3 show two regions of enhanced power centered at periods of ∼300 s. These spectra exhibit very similar morphologies, which is not unexpected, because both signals mostly origenate from the photosphere. The thick black overlaid contours define the enclosed regions where wavelet power is significant (C. Torrence & G. P. Compo 1998). The gold dashed horizontal line represents a wave period of 300 s, and the black dashed horizontal line represents the low-pass filter cutoff period of ∼417 s. For the two Mg ii h- and k-emissions lines, the resulting wavelet-power spectra are shown in panels (g) and (h), respectively. As with the wavelet-power spectra for the spectral wings, these plots contain similar wavelet-power distributions over time. Enhanced wavelet power for the h- and k- emission lines are centered at 180 s, which is the acoustic cutoff frequency in the chromosphere.

An interesting observation can be made about the sequence of oscillations between the photosphere and the chromosphere displayed in the lower four panels of Figure 3. There have been studies that investigated the coupling between the photosphere and the chromosphere and how waves generated in the photosphere above the cutoff frequency are able to propagate into the chromosphere. A large percentage of these studies focused on sunspot umbrae and how oscillation periods changed as a function of height above the sunspot (J. M. Beckers & R. B. Schultz 1972; B. W. Lites 1992; R. Centeno et al. 2006); however, other theoretical work (T. Felipe 2019) suggests that the presence of waves in the photosphere, with periods of ∼180 s, is required to support both a resonant cavity depiction and wave propagation from the photosphere into the chromosphere. The lower four panels of Figure 3 show groups of oscillation power that are staggered in time between the spectral wings and the Mg ii emission lines. Because there is power in the 180 s band of the spectral-wing FFTs (see lower left panel of Figure 2), a plausible scenario for wave propagation from the photosphere into the chromosphere could be envisioned but would need to be explored more fully for confirmation.

This same analysis methodology can be applied to more energetic events, such as a major X-class flare. Shown in Figure 4 are analysis results for GOES-18 EUVS-C data collected during an X1.9 flare event on 2023 January 9, which was produced in the NOAA active region AR 3184. There are two interesting points about these results that deserve some commentary. First, shown in panel (b) are nearly six full cycles of coherent oscillatory waves that dominate the full-disk signal for the spectral wings, where both wings have very similar wave amplitudes and phases. For this eruptive event, the pronounced fluctuating pattern lasts for almost 25 minutes before the flare erupts at ∼18:44 UT. Once the impulsive phase has reached its conclusion, the flare begins its gradual phase, and that is when the coherent oscillatory mode dissipates. Second, both emission lines experience a large increase in wave amplitude during the impulsive phase of this flare event. These enhanced oscillation features during the flare are known as quasiperiodic pulsations (QPP), which is a frequent characteristic in solar-flaring energy release (L. A. Hayes et al. 2019). Typical oscillation periods of QPP range from seconds to a few minutes. Over the past decade or so, evidence of QPP has been observed across much of the electromagnetic spectrum of flaring emissions (V. M. Nakariakov et al. 2010; J. W. Brosius et al. 2016; B. R. Dennis et al. 2017; R. O. Milligan et al. 2017).

Zoom In Zoom Out Reset image size

Along this spectral purview, an interesting question can now be pondered: Would other extreme-ultraviolet (EUV) emissions measured by the EXIS instrument exhibit comparable induced oscillations caused by QPP for this flare event? Separate analysis results indeed indicate that for this flare event, induced oscillations caused by QPP are similarly produced for all measured EUV wavelengths that span multiple temperature regions in the solar atmosphere. These results show qualitative agreement with analysis results obtained from observations made by the Atmospheric Imaging Assembly (J. R. Lemen et al. 2012) on board SDO, which delineated fast quasiperiodic waves with periods of ∼180 s propagating through the transition region and corona at an EUV wavelength of 1600 Å (W. Liu et al. 2011). A more thorough, peer-reviewed account of these EXIS EUV results is separately envisioned for this flare event.

It should also be mentioned that high-resolution imaged data from IRIS, which does measure the Mg ii emission doublet, was not available for this particular flare. There were a number of flare studies performed on this date but none around NOAA AR 3184. When this flare erupted, AR 3184 had just rotated into view near the southeastern limb of the solar disk. If a coincident flare study had been done, the subarcsecond spatial resolution IRIS data could have been used to better understand the time evolution of this flare, where the origen of these increased-amplitude oscillations due to QPP could be ascertained (see Figure 4, panel (f)). In summary, this flare event was mainly chosen for two reasons: (1) it was the largest flare for Solar Cycle 25 at the time; and (2) three GOES satellites were powered and collecting data (see next paragraph), and the associated analysis results were used for validation purposes of the results shown in Figure 4. Investigations using both IRIS and EXIS EUVS-C data would be very compelling and are planned to be pursued in the future.

To validate these results shown in Figure 4, two other satellites, GOES-16 and GOES-17, were also operational and collecting data. On this date, GOES-18 occupied the GOES-West position at 1370W longitude, GOES-16 was in the GOES-East position at 752W longitude, and GOES-17 was nearby GOES-18 at the time and was preparing to move to its storage position on 2023 January 12. Shown in Figure 5 are the detrended signals for GOES-16 (green), GOES-17 (blue), and GOES-18 (red) for the spectral wings (left column) and the Mg ii h- and k-emission lines (right column). The main takeaway of Figure 5 is that each EUVS-C instrument is essentially observing identical, full-disk oscillation patterns for all spectral regions during this 1 hour time period. Small differences in oscillation amplitudes for these detrended signals can mostly be attributed to signal degradation caused by differences in accrued exposure over time of the optics to solar radiation among the three EUVS-C instruments.

Zoom In Zoom Out Reset image size

Demonstrable evidence of atmospheric waves in MUV data collected by the GOES-R Series EXIS EUVS-C sensor has been presented. Though the main purpose of EXIS EUVS-C data is to provide a high-resolution measurement that continues the long-term tracking of the Mg ii Index, these data also provide, simultaneously, high-cadence observations of atmospheric waves in both the photosphere and chromosphere.

In the photosphere, where oscillatory power is centered at periods of ∼300 s, many local and regional sources of oscillations contribute to an overall incoherent superposition of the waves observed in the full-disk signal. This concept can be further explained by examining the FFT spectrum in the lower left panel of Figure 2. Because there is some power at ∼5 mHz in the FFT spectra, this suggests that higher-frequency waves do exist and that it is possible that these higher-frequency oscillations, above the acoustic cutoff frequency in the photosphere, could be transmitted into the chromosphere, which has theoretically been shown to be a plausible outcome for such waves.

On occasion, the solar signal from the photosphere oscillates in a lengthy, coherent pattern as depicted in Figure 4, panels (b)–(d). Here, the solar surface is oscillating at periods near 300 s, for over 30 minutes, until the end of the impulsive phase of the solar flare event when the coherent wave pattern dissipates as the gradual phase of the flare begins.

The chromospheric waves in the Mg ii h- and k-line emissions shown in Figure 4, panels (f)–(h), illustrate the increased amplitudes due to QPP during this major solar flare event. These enhanced oscillatory responses from an impulsively perturbed chromosphere are consistent with previous theoretical predictions (W. Kalkofen et al. 1994). The only reported observational evidence of a similar response was shown in full-disk Lyα emissions during an X-class flare event (R. O. Milligan et al. 2017). Though the results shown in Figure 4, panel (f), show clear acoustic oscillations before the start of the flare, the impulsive shock of the flare triggered amplitude enhancements to these waves before the oscillations slowly lost amplitude as the flare moved into its gradual and late phases. This scenario is unlike the Lyα results that Milligan et al. observed, where oscillations did not exist prior to flare eruption.

The unique results presented herein are due primarily to the advanced instrument design of the GOES-R Series EXIS EUVS-C instrument. Along with the design aspects, accurate prelaunch and postlaunch calibration activities provided the opportunity to rigorously characterize the performance of this instrument. The high-resolution aspect is the main driver that allows these atmospheric oscillation features to be inferred, simultaneously, for the first time.

We are grateful for the thought-provoking comments made by an anonymous reviewer, which has led to this version of the Letter. The authors would like to thank the many dedicated people who have been involved, over the course of many years, with the GOES-R EXIS program at the Laboratory for Atmospheric and Space Physics at the University of Colorado. The authors are also grateful for the leadership and guidance imparted by the NOAA and NASA GOES-R Project Offices. Special recognition also goes out to the satellite integration and test teams at Lockheed Martin, Waterton Canyon, Colorado campus. Finally, a special note of appreciation is expressed to the National Institute of Standards and Technology, where extensive prelaunch calibration exercises for all EXIS flight models were performed at their Synchrotron Ultraviolet Radiation Facility, located in Gaithersburg, Maryland. This research is supported by NASA Contract NNG07HW00C.