Minute Oscillations Research Articles

Statistical Investigation of Wave Propagation in the Quiet-Sun Using IRIS Spectroscopic Observations

In this analysis, we use spectroscopic observations of the quiet Sun made by the IRIS instrument and investigate wave propagation. We analyze various spectral lines formed in different atmospheric layers, such as the photosphere, chromosphere, and transition region. We examine the Doppler velocity time series at various locations in the quiet Sun to determine the dominant oscillation periods. Our results executing statistical analysis resemble those of the classical physical scenario, indicating that the photosphere is mainly characterized by the dominant 5 minute period, while the chromosphere is primarily associated with the 3 minute oscillation period. In the transition region, we observe a variety of oscillation periods, with dominant periods of 3, 8, and 12 minutes. We estimate the cutoff frequency by deducing the phase difference between two Doppler velocity time series obtained from spectral line pairs in different atmospheric layers formed at different temperatures. This reveals a significant correlation between 3 minute periods in the transition region and photospheric oscillations, suggesting that these oscillations in the transition region might propagate from the photosphere. Additionally, we analyze the phase difference between chromospheric oscillations and photospheric oscillations, demonstrating that only the 3 minute oscillations propagate upward. Based on the statistical analyses, we suggest the presence of magnetoacoustic waves in the solar atmosphere, some of which are propagating from the lower solar atmosphere upward, while some others are propagating downward. The transition region carries both long-period oscillations generated in situ and some photospheric oscillations that are also able to reach there from below.

Long-period oscillations in the lower solar atmosphere prior to flare events

Multiple studies have identified a range of oscillation periods in active regions, from 3-5 minutes to long-period oscillations that last from tens of minutes to several hours. Recently, it was also suggested that these periods are connected with eruptive activity in the active regions. Thus, it is essential to understand the relation between oscillations in solar active regions and their solar eruption activity. We investigate the long-period oscillations of NOAA12353 prior to a series of C-class flares and correlate the findings with the 3- to 5-minute oscillations that were previously studied in the same active region. The objective of this work is to elucidate the presence of various oscillations with long periods in the lower solar atmosphere both before and after the flare events. To detect long-period oscillations, we assessed the emergence, shearing, and total magnetic helicity flux components from the photosphere to the top of the chromosphere. To analyze the magnetic helicity flux in the lower solar atmosphere, we used linear force-free field extrapolation to construct a model of the magnetic field structure of the active region. Subsequently, the location of long-period oscillations in the active region was probed by examining the spectral energy density of the measured intensity signal in the 1700\,AA , 1600\,AA , and 304\,AA channels of the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO). Significant oscillation periods were determined by means of a wavelet analysis. Based on the evolution of the three magnetic helicity flux components, 3- to 8-hour periods were found both before and after the flare events, spanning from the photosphere to the chromosphere. These 3- to 8-hour periods were also evident throughout the active region in the photosphere in the 1700\,AA channel. Observations of AIA 1600\,AA and 304\,AA channels, which cover the chromosphere to the transition region, revealed oscillations of 3-8 hours near the region in which the flare occurred. The spatial distribution of the measured long-period oscillations mirror the previously reported distribution of 3- to 5-minute oscillations in NOAA12353 that were seen both before and after the flares. This case study suggest that the varying oscillation properties in a solar active region could be indicative of future flaring activity.

Non-perturbative wavefunction of the universe in inflation with (resonant) features

We study the statistics of scalar perturbations in models of inflation with small and rapid oscillations in the inflaton potential (resonant non-Gaussianity). We do so by deriving the wavefunction Ψ[ζ(x)] non-perturbatively in ζ, but at first order in the amplitude of the oscillations. The expression of the wavefunction of the universe (WFU) is explicit and does not require solving partial differential equations. One finds qualitative deviations from perturbation theory for |ζ| ≳ α−2, where α ≫ 1 is the number of oscillations per Hubble time. Notably, the WFU exhibits distinct behaviours for negative and positive values of ζ (troughs and peaks respectively). While corrections for ζ < 0 remain relatively small, of the order of the oscillation amplitude, positive ζ yields substantial effects, growing exponentially as eπα/2 in the limit of large ζ. This indicates that even minute oscillations give large effects on the tail of the distribution.

Intensity and velocity oscillations in a flaring active region

ABSTRACT Chromospheric oscillations can give us insight into the physical environment in the solar atmosphere, both in quiet Sun and flaring conditions. Many authors have reported increases in the prevalence of 3-minute oscillations which are thought to be excited by events which impact the chromosphere such as flares. In this study, we utilized the Ca ii 8542 Å line to study the oscillatory behaviour of the chromosphere in an active region which underwent two B-class flares. We analysed oscillations in both intensity and velocity, and found different behaviours in both. Intensity oscillations were most prevalent over the umbrae of sunspots and magnetic pores in the active region, and the extent of the area which contained significant oscillations was found to decrease when comparing times after the flares to before. By measuring the evolution of the magnetic field, we found that this could be because the areas surrounding the umbrae were becoming more ‘penumbral’ with an increase to the magnetic field inclination. Velocity oscillations were found across the active region both before and after the flares but were observed clearly in areas which were brightened by the second flare. By comparing to EUV imaging, it was seen that strong chromospheric velocity oscillations with 3–4-minute periods occurred at the same time and location as a flare loop cooling 30 min after the second flare peak. This could be evidence of disturbances in the loop exciting a response from the chromosphere at its acoustic cut-off frequency.

Investigation of the Oscillations in a Flare-productive Active Region

We investigate the oscillations in active region (AR) NOAA 12891, which produces a C2.0 three-ribbon flare accompanying a jet on 2021 November 2. Using the data from the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory, the 5 minutes decayless kink oscillations of coronal loops were detected and they are independent of the solar flare. Based on the observed oscillations and seismological diagnostics, we estimate that the Alfvén speed and magnetic field in these coronal loops are around 466 km s−1 and 7.6 G, respectively. Additionally, the flare-related jet shows its plasmoids with 1 minute periodicity same as the intensity fluctuation of nearby flare ribbon. The correlation between the intensity fluctuation of jet and that of flare ribbon indicates that their 1 minute oscillations should originate from the same reconnection process.

Coronal Quasi-periodic Fast-mode Propagating Wave Trains

QFP wave trains in the corona have been studied intensively in the past decade, thanks to the full-disk, high spatiotemporal resolution, and wide-temperature coverage observations taken by the SDO/AIA. In AIA observations, QFP wave trains are seen to consist of multiple coherent and concentric wavefronts emanating successively near the epicenter of the accompanying flares; they propagate outwardly either along or across coronal loops at fast-mode magnetosonic speeds from several hundred to more than 2000 km/s, and their periods are in the range of tens of seconds to several minutes. Based on the distinct different properties of QFP wave trains, they might be divided into two distinct categories including narrow and broad ones. For most QFP wave trains, some of their periods are similar to those of quasi-periodic pulsations (QPPs) in the accompanying flares, indicating that they are probably different manifestations of the same physical process. Currently, candidate generation mechanisms for QFP wave trains include two main categories: pulsed energy excitation mechanism in association with magnetic reconnection and dispersion evolution mechanism related to the dispersive evolution of impulsively generated broadband perturbations. In addition, the generation of some QFP wave trains might be driven by the leakage of three and five minute oscillations from the lower atmosphere. As one of the new discoveries of SDO, QFP wave trains provide a new tool for coronal seismology to probe the corona parameters, and they are also useful for diagnosing the generation of QPPs, flare processes including energy release and particle accelerations. This review aims to summarize the main observational and theoretical results of the spatially-resolved QFP wave trains in extreme ultraviolet observations, and states briefly a number of questions that deserve further investigations.

A Study of Sunspot 3 Minute Oscillations Using ALMA and GST

Abstract Waves and oscillations are important solar phenomena, not only because they can propagate and dissipate energy in the chromosphere, but also because they carry information about the structure of the atmosphere in which they propagate. The nature of the 3 minute oscillations observed in the umbral region of sunspots is considered to be an effect of propagation of magnetohydrodynamic waves upward from below the photosphere. We present a study of sunspot oscillations and wave propagation in NOAA Active Region 12470 using an approximately 1 hr long data set acquired on 2015 December 17 by the Atacama Large Millimeter/submillimeter Array (ALMA), the Goode Solar Telescope (GST) operating at the Big Bear Solar Observatory, the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory, and the Interface Region Imaging Spectrograph. The ALMA data are unique in providing a time series of direct temperature measurements in the sunspot chromosphere. The 2 s cadence of ALMA images allows us to well resolve the 3 minute periods typical of sunspot oscillations in the chromosphere. Fourier analysis is applied to ALMA Band 3 (∼100 GHz, ∼3 mm) and GST Hα data sets to obtain power spectra as well as oscillation phase information. We analyzed properties of the wave propagation by combining multiple wavelengths that probe physical parameters of solar atmosphere at different heights. We find that the ALMA temperature fluctuations are consistent with that expected for a propagating acoustic wave, with a slight asymmetry indicating nonlinear steepening.

Spatial and Temporal Analysis of 3 minute Oscillations in the Chromosphere Associated with the X2.2 Solar Flare on 2011 February 15

Abstract Three minute oscillations in the chromosphere are attributed to both slow magnetoacoustic waves propagating from the photosphere and to oscillations generated within the chromosphere itself at its natural frequency as a response to a disturbance. Here we present an investigation of the spatial and temporal behavior of the chromospheric 3 minute oscillations before, during, and after the SOL2011-02-15T01:56 X2.2 flare. Observations in ultraviolet emission centered on 1600 and 1700 Å obtained at 24 s cadence from the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory are used to create power maps as functions of both space and time. We observe higher 3 minute power during the flare, spatially concentrated in small areas ∼10 pixels ( ) across. This implies that the chromospheric plasma is not oscillating globally as a single body. The locations of increased 3 minute power are consistent with observations of HXR flare emission from previous studies, suggesting that these small areas are manifestations of the chromosphere responding to injection of energy by nonthermal particles. This supports the theory that the chromosphere oscillates at the acoustic cutoff frequency in response to a disturbance.

Estimating Parameters in Mathematical Model for Societal Booms through Bayesian Inference Approach

In this study, based on our previous study in which the proposed model is derived based on the SIR model and E. M. Rogers’s Diffusion of Innovation Theory, including the aspects of contact and time delay, we examined the mathematical properties, especially the stability of the equilibrium for our proposed mathematical model. By means of the results of the stability in this study, we also used actual data representing transient and resurgent booms, and conducted parameter estimation for our proposed model using Bayesian inference. In addition, we conducted a model fitting to five actual data. By this study, we reconfirmed that we can express the resurgences or minute oscillations of actual data by means of our proposed model.

Magnetic Connectivity between the Light Bridge and Penumbra in a Sunspot

Abstract A light bridge is a prominent structure commonly observed within a sunspot. Its presence usually triggers a wealth of dynamics in a sunspot and has a lasting impact on sunspot evolution. However, the fundamental structure of light bridges is still not well understood. In this study, we used the high-resolution spectropolarimetry data obtained by the Solar Optical Telescope on board the Hinode satellite to analyze the magnetic and thermal structure of a light bridge at AR 12838. We also combined the high-cadence channel data provided by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory to study the dynamics on this bridge. We found a pair of blue and red Doppler shift patches at two ends of this bridge; this pattern appears to be the convective motion directed by the horizontal component of the magnetic field aligned with the spine of the bridge. Paired upward and downward motions imply that the light bridge could have a two-legged or undulating magnetic field. Significant 4 minute oscillations in the emission intensity of the bandpass were detected at two ends, which overlapped the paired blue- and redshift patches. The oscillatory signals at the light bridge and the penumbra were highly correlated with each other. Although they are separated in space at the photosphere, the periodicity seems to have a common origin from underneath the sunspot. Therefore, we infer that the light bridge and penumbra could share a common magnetic source and become fragmented at the photosphere by magnetoconvection.

A New Type of Jet in a Polar Limb of the Solar Coronal Hole

Abstract A new type of chromospheric jet in a polar limb of a coronal hole is discovered in the Ca ii filtergram of the Solar Optical Telescope on board the Hinode. We identify 30 jets in a filtered Ca ii movie with a duration of 53 minutes. The average speed at their maximum heights is found to be 132 ± 44 km s−1 ranging from 57 to 264 km s−1 along the propagation direction. The average lifetime is 20 ± 6 ranging from 11 to 36 s. The speed and lifetime of the jets are located at end-tails of those parameters determined for type II spicules, hence implying a new type of jets. To confirm whether these jets are different from conventional spicules, we construct a time–height image averaged over a horizontal region of 1″, and calculate lagged cross-correlations of intensity profiles at each height with the intensity at 2 Mm. From this, we obtain a cross-correlation map as a function of lag and height. We find that the correlation curve as a function of lag time is well fitted into three different Gaussian functions whose standard deviations of the lag time are 193, 42, and 17 s. The corresponding propagation speeds are calculated to be 9 km s−1, 67 km s−1, and 121 km s−1, respectively. The kinematic properties of the former two components seem to correspond to the 3-minute oscillations and type II spicules, while the latter component to the jets is addressed in this study.

Linear Acoustic Waves in a Nonisothermal Atmosphere. II. Photospheric Resonator Model of Three-minute Umbral Oscillations

Abstract The velocity oscillations observed in the chromosphere of sunspot umbrae resemble a resonance in that their power spectra are sharply peaked around a period of about three minutes. In order to describe the resonance that leads to the observed 3-minute oscillations, we propose the photospheric resonator model of acoustic waves in the solar atmosphere. The acoustic waves are driven by the motion of a piston at the lower boundary, and propagate in a nonisothermal atmosphere that consists of the lower layer (photosphere), where temperature rapidly decreases with height, and the upper layer (chromosphere), where temperature slowly increases with height. We have obtained the following results: (1) The lower layer (photosphere) acts as a leaky resonator of acoustic waves. The bottom end is established by the piston, and the top end by the reflection at the interface between the two layers. (2) The temperature minimum region partially reflects and partially transmits acoustic waves of frequencies around the acoustic cutoff frequency at the temperature minimum. (3) The resonance occurs in the photospheric layer at one frequency around this cutoff frequency. (4) The waves escaping the photospheric layer appear as upward-propagating waves in the chromosphere. The power spectrum of the velocity oscillation observed in the chromosphere can be fairly well reproduced by this model. The photospheric resonator model was compared with the chromospheric resonator model and the propagating wave model.

The Physical Nature of Spiral Wave Patterns in Sunspots

Abstract Recently, spiral wave patterns (SWPs) have been detected in 3 minute oscillations of sunspot umbrae, but the nature of this phenomenon has remained elusive. We present a theoretical model that interprets the observed SWPs as the superposition of two different azimuthal modes of slow magnetoacoustic waves driven below the surface in an untwisted and non-rotating magnetic cylinder. We apply this model to SWPs of the line-of-sight (LOS) velocity in a pore observed by the Fast Imaging Solar Spectrograph installed at the 1.6 m Goode Solar Telescope. One- and two-armed SWPs were identified in instantaneous amplitudes of LOS Doppler velocity maps of 3 minute oscillations. The associated oscillation periods are about 160 s, and the durations are about 5 minutes. In our theoretical model, the observed spiral structures are explained by the superposition of non-zero azimuthal modes driven 1600 km below the photosphere in the pore. The one-armed SWP is produced by the slow-body sausage (m = 0) and kink (m = 1) modes, and the two-armed SWP is formed by the slow-body sausage (m = 0) and fluting (m = 2) modes of the magnetic flux tube forming the pore.

Oscillations Accompanying a He I 10830 Å Negative Flare in a Solar Facula II. Response of the Transition Region and Corona

We studied oscillations related to flare SOL2012-09-21T02:19 in the transition region and chromosphere based on Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) and Solar Dynamics Observatory (SDO) data, as well as data from a ground-based observatory. We found that 2-minute oscillations triggered by the flare first appeared in the RHESSI channels then subsequently showed up in the SDO 171 {\AA} and 304 {\AA} channels and after that in the chromospheric He I 10830 {\AA} line. The delay of the chromospheric signal compared to the RHESSI signal is 7 minutes, which indicates that the wave perturbation propagated from the corona to the chromosphere. We used the sharp increase in 3- and 5-minute oscillations during the flare in the lower atmosphere to trace the propagation of the oscillation trains to the transition region and corona. The results show that the 171 {\AA} channel signals lagged behind the photospheric and chromospheric signals by 200 s on average. We suggest that we observed slow magnetoacoustic waves both in the case of 2-minute oscillations propagating downwards from the corona and in the case of 3- and 5-minute oscillations leaking to the corona from beneath.

Local sunspot oscillations and umbral dots

Data analysis of sunspot oscillations based on a 6-hr SDO run of an observation showed that low frequency () oscillations are locally similar to three and five minute oscillations. The oscillations in the sunspot are concentrated in cells of a few arcsec, each of which has its own oscillation spectrum. The analysis of two scenarios for sunspot oscillations leads to a conclusion that local sunspot oscillations occur due to a subphotospheric resonator for slow MHD waves. Empirical models of a sunspot atmosphere and the theory of slow waves in thin magnetic flux tubes are applied to modeling the subphotospheric resonator. The spectrum of local oscillations consists of a great number of lines. This kind of spectrum can occur only if the subphotospheric resonator is a magnetic tube with a rather weak magnetic field. Magnetic tubes of this sort are umbral dots that appear due to the convective tongues in monolithic sunspots. The interrelation of local oscillations with umbral dots and wavefronts of traveling waves in sunspots is discussed.

Vertical propagation of acoustic waves in the solar internetworkas observed by IRIS

We investigate the Interface Region Imaging Spectrograph (IRIS) observations of the quiet-Sun (QS) to understand the propagation of acoustic waves in transition region (TR) from photosphere. We selected a few IRIS spectral lines, which include the photospheric (Mn~{\sc i} 2801.25~{\AA}), chromospheric (Mg~{\sc ii} k 2796.35~{\AA}) and TR (C~{\sc ii} 1334.53~{\AA}), to investigate the acoustic wave propagation.The wavelet cross-spectrum reveals significant coherence (about 70\% locations) between photosphere and chromosphere. Few minutes oscillations (i.e., period range from 1.6 to 4.0 minutes) successfully propagate into chromosphere from photosphere, which is confirmed by dominance of positive phase lags. However, in higher period regime (i.e., greater than $\approx$ 4.5 minutes), the downward propagation dominates is evident by negative phase lags. The broad spectrum of waves (i.e., 2.5-6.0 minutes) propagates freely upwards from chromosphere to TR. We find that only about 45\% locations (out of 70\%) show correlation between chromosphere and TR. Our results indicate that roots of 3 minutes oscillations observed within chromosphere/TR are located in photosphere. Observations also demonstrate that 5 minute oscillations propagate downward from chromosphere. \textbf{However, some locations within QS also show successful propagation of 5 minute oscillations as revealed by positive phase lags, which might be the result of magnetic field}. In addition, our results clearly show that a significant power, within period ranging from 2.5 to 6.0 minutes, of solar chromosphere is freely transmitted into TR triggering atmospheric oscillations. Theoretical implications of our observational results are discussed.

Sausage oscillations in a plasma cylinder with a surface current

Linear sausage oscillations of a cylinder embedded in a plasma with an azimuthal magnetic field, created by a current on the surface of the cylinder, are studied. Such a plasma configuration could be applied to modelling flaring loops, and magnetic ropes in coronal mass ejections. The plasma is assumed to be cold everywhere. Dispersion relations demonstrate that the lowest radial harmonic of the sausage mode is in the trapped regime for all values of the parallel wave number. In the long-wavelength limit, phase and group speeds of this mode are equal to the Alfvén speed in the external medium. It makes the oscillation period to be determined by the ratio of the parallel wavelength, e.g. double the length of an oscillating loop, to the external Alfvén speed, allowing for its seismological estimations. The application of the results obtained to the interpretation of long-period (longer than a minute) oscillations of emission intensity detected in solar coronal structures, gives reasonable estimations of the external Alfvén speed. Cutoff values of the parallel wavenumber for higher radial harmonics are determined analytically. Implications of this finding to the observational signatures of fast magnetoacoustic wave trains guided by cylindrical plasma non-uniformities are discussed.

Observations of Upward Propagating Waves in the Transition Region and Corona above Sunspots

Abstract We present observations of persistent oscillations of some bright features in the upper-chromosphere/transition region above sunspots taken by IRIS SJ 1400 Å and upward propagating quasi-periodic disturbances along coronal loops rooted in the same region taken by the AIA 171 Å passband. The oscillations of the features are cyclic oscillatory motions without any obvious damping. The amplitudes of the spatial displacements of the oscillations are about 1″. The apparent velocities of the oscillations are comparable to the sound speed in the chromosphere, but the upward motions are slightly larger than that of the downward. The intensity variations can take 24%–53% of the background, suggesting nonlinearity of the oscillations. The FFT power spectra of the oscillations show a dominant peak at a period of about 3 minutes, which is consistent with the omnipresent 3 minute oscillations in sunspots. The amplitudes of the intensity variations of the upward propagating coronal disturbances are 10%–15% of the background. The coronal disturbances have a period of about 3 minutes, and propagate upward along the coronal loops with apparent velocities in a range of 30 ∼ 80 km s−1. We propose a scenario in which the observed transition region oscillations are powered continuously by upward propagating shocks, and the upward propagating coronal disturbances can be the recurrent plasma flows driven by shocks or responses of degenerated shocks that become slow magnetic-acoustic waves after heating the plasma in the coronal loops at their transition-region bases.

Detection of Three-minute Oscillations in Full-disk Lyα Emission during a Solar Flare

Abstract In this Letter we report the detection of chromospheric 3-minute oscillations in disk-integrated EUV irradiance observations during a solar flare. A wavelet analysis of detrended Lyα (from GOES/EUVS) and Lyman continuum (from Solar Dynamics Observatory (SDO)/EVE) emission from the 2011 February 15 X-class flare (SOL2011-02-15T01:56) revealed a ∼3 minute period present during the flare’s main phase. The formation temperature of this emission locates this radiation at the flare’s chromospheric footpoints, and similar behavior is found in the SDO/Atmospheric Imaging Assembly 1600 and 1700 Å channels, which are dominated by chromospheric continuum. The implication is that the chromosphere responds dynamically at its acoustic cutoff frequency to an impulsive injection of energy. Since the 3-minute period was not found at hard X-ray (HXR) energies (50–100 keV) in Reuven Ramaty High Energy Solar Spectroscopic Imager data we can state that this 3-minute oscillation does not depend on the rate of energization of non-thermal electrons. However, a second period of 120 s found in both HXR and chromospheric lightcurves is consistent with episodic electron energization on 2-minute timescales. Our finding on the 3-minute oscillation suggests that chromospheric mechanical energy should be included in the flare energy budget, and the fluctuations in the Lyα line may influence the composition and dynamics of planetary atmospheres during periods of high activity.

The Frequency-dependent Damping of Slow Magnetoacoustic Waves in a Sunspot Umbral Atmosphere

Abstract High spatial and temporal resolution images of a sunspot, obtained simultaneously in multiple optical and UV wavelengths, are employed to study the propagation and damping characteristics of slow magnetoacoustic waves up to transition region heights. Power spectra are generated from intensity oscillations in sunspot umbra, across multiple atmospheric heights, for frequencies up to a few hundred mHz. It is observed that the power spectra display a power-law dependence over the entire frequency range, with a significant enhancement around 5.5 mHz found for the chromospheric channels. The phase difference spectra reveal a cutoff frequency near 3 mHz, up to which the oscillations are evanescent, while those with higher frequencies propagate upward. The power-law index appears to increase with atmospheric height. Also, shorter damping lengths are observed for oscillations with higher frequencies suggesting frequency-dependent damping. Using the relative amplitudes of the 5.5 mHz (3 minute) oscillations, we estimate the energy flux at different heights, which seems to decay gradually from the photosphere, in agreement with recent numerical simulations. Furthermore, a comparison of power spectra across the umbral radius highlights an enhancement of high-frequency waves near the umbral center, which does not seem to be related to magnetic field inclination angle effects.