PS4.2

The Earth’s Ionosphere limits radio measurements on its surface, blocking out any radiation below 10 MHz. Valuable insight into many astrophysical processes could be gained by having a radio interferometer in space to image the low frequency window, which has never been achieved. One application for such a system is observing type II bursts that track solar energetic particle acceleration occurring at Coronal Mass Ejection (CME)-driven shocks. This is one of the primary science targets for SunRISE, a 6 CubeSat interferometer to circle the Earth in a GEO graveyard orbit. SunRISE is a NASA Heliophysics Mission of Opportunity that began Phase B (Formulation) in June 2020, and plans to launch for a 12-month mission in mid-2023. In this work we present an update to the data processing and science analysis pipeline for SunRISE and evaluate its performance in localizing type II bursts around a simulated CME.

To create realistic virtual type II input data, we employ a 2-temperature MHD simulation of the May 13th 2005 CME event, and superimpose realistic radio emission models on the CME-driven shock front, and propagate the signal through the simulated array. Data cuts based on different plasma parameter thresholds (e.g. de Hoffman-Teller velocity and angle between shock normal and the upstream magnetic field) are tested to get the best match to the true recorded emission.  This model type II emission is then fed to the SunRISE data processing pipeline to ensure that the array can localize the emission. We include realistic thermal noise dominated by the galactic background at these low frequencies, as well as new sources of phase noise from positional uncertainty of each spacecraft. We test simulated trajectories of SunRISE and image what the array recovers, comparing it to the virtual input, finding that SunRISE can resolve the source of type II emission to within its prescribed goal of 1/3 the CME width. This shows that SunRISE will significantly advance the scientific community’s understanding of type II burst generation, and consequently, acceleration of solar energetic particles at CMEs.  This unique combination of SunRISE observations and MHD recreations of space weather events will allow an unprecedented look into the plasma parameters important for these processes. 

How to cite: Hegedus, A., Manchester, W., Kasper, J., Lazio, J., and Romero-Wolf, A.: Localizing the Source of Type II Emission Around a CME with the Sun Radio Interferometer Space Experiment (SunRISE) and MHD Simulations, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-6435, https://doi.org/10.5194/egusphere-egu21-6435, 2021.

We present a new insight into the propagation of ion magnetoacoustic and neutral acoustic waves in a magnetic arcade in the lower solar atmosphere. By means of numerical simulations, we aim to: (a) study two-fluid waves propagating in a magnetic arcade embedded in the partially-ionized, lower solar atmosphere; and (b) investigate the impact of the background magneticfield configuration on the observed wave-periods. We consider a 2D approximation of the gravitationally stratified and partially-ionized lower solar atmosphere consisting of ion + electron and neutral fluids that are coupled by ion-neutral collisions. In this model, the convection below the photosphere is responsible for the excitation of ion magnetoacoustic-gravity and neutral acoustic-gravity waves. We find that in the solar photosphere, where ions and neutrals are strongly coupled by collisions, magnetoacoustic-gravity and acoustic-gravity waves have periods ranging from250s to350s. In the chromosphere, where the collisional coupling is weak, the wave characteristics strongly depend on the magnetic field configuration. Above the foot-points of the considered arcade, the plasma is dominated by vertical magnetic field along which ion slow magnetoacoustic-gravity waves are guided. These waves exhibit a broad range of periods with the most prominent periods of 180 s, 220 s, and 300 s. Above the main loop of the solar arcade, where mostly horizontal magnetic field lines guide ion magnetoacoustic waves, the main spectral power reduces to the period of about 180 s and longer wave-periods do not exist. The obtained results demonstrate unprecedented, never reported before level of agreement with the recently reported observational data of Wisniewska et al. (2016) and Kayshap et al. (2018). We demonstrate that the two-fluid approach is indeed crucial for a description of wave-related processes in the lower solar atmosphere, with energy transport and dissipation being of the highest interest among them.

How to cite: Kuźma, B., Murawski, K., Musielak, Z., Poedts, S., and Wójcik, D.: Spatial variation of periods of ion and neutral waves in a solar magnetic arcade., EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-6726, https://doi.org/10.5194/egusphere-egu21-6726, 2021.

The Sun is an active star that often produces numerous bursts of electromagnetic radiation at radio wavelengths. In particular, low frequency (< 150 MHz)  radio bursts have recently been brought back to light with the advancement of novel radio interferometric arrays. However, the polarisation properties of solar radio bursts have not yet been explored in detail, especially with the Low Frequency Array (LOFAR). Here, we explore the circular polarisation of type III radio bursts and a type I noise storm and present the first Stokes V low frequency radio images of the Sun with LOFAR in tied array mode observations. We find that the degree of circular polarisation for each of the selected bursts increases with frequency for fundamental plasma emission, while this trend is either not clear or absent for harmonic plasma emission. In the case of type III bursts, we also find that the sense of circular polarisation varies with each burst, most likely due to their different propagation directions, despite all of these bursts being part of a long-lasting type III storm. Furthermore, we use the degree of circular polarisation of the harmonic emission of type III bursts to estimate the coronal magnetic field at distances of 1.4 to 4 solar radii from the centre of the Sun. We found that the magnetic field has a power law variation with a power index in the range 2.4-3.6, depending on the individual type III burst observed.

How to cite: Morosan, D., Kumari, A., Räsänen, J., Kilpua, E., Zucca, P., Bisi, M., Dabrowski, B., Krankowski, A., Magdalenić, J., Mann, G., Rothkaehl, H., and Vocks, C.: Exploring the circular polarisation of low-frequency solar radio bursts with LOFAR and estimating the coronal magnetic field, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9853, https://doi.org/10.5194/egusphere-egu21-9853, 2021.

On March 15, 2013, an Earth directed halo CME, associated with an SEP event, was observed. This study aims to characterize the interplanetary medium conditions in which the event propagated, in order to make the first steps towards the validation of the modeling of SEPs employing two recently coupled models, EUHFORIA (EUropean Heliosferic FORcasting Information Asset) and PARADISE (PArticle Radiation Asset Directed at Interplanetary Space Exploration).

The Sun in the days prior and after the event was very active, with several strong flares and coronal mass ejections during this period. The main event was associated with the long duration GOES M1.1 X-ray flare originating from the active region (AR) 11692, located at N11E12. Imagers aboard SOHO and STEREO spacecrafts observed the CME launch at 7:12 UT and the projected line of the sight speed was estimated to be about 1060 km/s. A rise in the $>$10 MeV GOES proton count was observed the following day, with flux exceeding the 1000 pfu threshold, and stayed above it for several days. Another strong CME was launched, within the following hours, towards the west but with a good magnetic connection to Earth's position, which could have accelerated even further the particle population seeded by the main event.

We model the solar wind and its transients CMEs with EUHFORIA, in order to obtain the realistic conditions of the ambient plasma through which the associated particles are propagating. Different spatial and temporal resolutions of the model will be explored to run the newly developed model for energetic protons PARADISE in an optimal environment and make a step towards better SEP predictions.

How to cite: Niemela, A., Wijsen, N., Rodriguez, L., Magdalenic, J., and Poedts, S.: The Solar Energetic Particle Event of March 15 2013 - Characterization of the interplanetary medium conditions, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10332, https://doi.org/10.5194/egusphere-egu21-10332, 2021.

The solar atmosphere is fluctuated and highly refractive for low frequency waves (<300MHz), the observed features of solar radio sources have indicated the existence of complex propagation effects. The propagation effect has two major parts: refraction and scattering, these two parts have combined influence on the observed source size and position of radio imaging and temporal-frequency features in the radio spectroscopy.

We present a parametric simulation for the propagation effect of the radio wave from solar radio bursts, with the method of parametric simulation, we can build connections between the solar atmosphere plasma condition and the observed radio source properties. By comparing the simulation results with the observed source size and property we estimated the scattering rate and the degree of anisotropic of the background electron, and from the simulation results we propose a possible explanation for the co-spatial phenomena of the fundamental wave and harmonic wave in single frequency.

How to cite: Zhang, P., Wang, C., and Kontar, E.: Parametric simulation studies on the wave propagation of solar radio emission: the source size, duration, and position, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10620, https://doi.org/10.5194/egusphere-egu21-10620, 2021.

Radio emissions accompanying coronal mass ejections (CMEs) from their flaring sources (type III bursts) to interplanetary shocks (type II bursts) are believed to originate in the electrostatic (ES) wave instabilities, which are excited by the electrons beaming along the intense magnetic fields. Theoretically, radio emissions of fundamental (plasma) frequency $\omega_{p}$ or the second harmonic $2 \omega_{p}$ may result from non-linear three waves interaction of electrostatic Langmuir and ion sound fluctuations. However, it is not clear yet what kind of electron beams and specific CME plasma conditions can determine destabilization of Langmuir waves (ion sound waves may result from non-linear decay). Recent attempts to identify and characterize these unstable regimes suggest very critical and limited conditions for Langmuir instabilities to develop, which may undermine our current understanding of their implication in nonlinear generation of radio waves. Thus, even for a dominance of ES instabilities, conditioned by high beaming velocities, Langmuir waves appear to be in close competition with other ES growing modes (such as electron acoustic instabilities), while for less energetic beams the theory predicts a strong interplay with instabilities of different nature (electromagnetic or hybrid, and propagating obliquely to the magnetic field). 

How to cite: Lazar, M., Lopez, R., Shaaaban, S. M., Poedts, S., and Fichtner, H.: Electron beaming instabilities as sources of CME radio emissions, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-11912, https://doi.org/10.5194/egusphere-egu21-11912, 2021.

Solar type J radio bursts are the signatures of electron beams travelling along closed magnetic loops in the solar corona. Type J bursts provide diagnostics for observing and understanding coronal loops geometry and electron beams dynamics. Due to the observational limitations, large loops around 1 solar radius in height are ill-defined. Whilst J-bursts at meter-wavelengths are well suited for the analysis of coronal loops at these solar altitudes, applying standard empirical solar plasma density distributions have limitations as they are designed for flux tubes extending into the solar wind and do not capture the curvature of such coronal loops.

We analysed over 20 type J bursts observed by the LOw-Frequency ARray (LOFAR) on the 10th of April 2019. Using a reference height, we derived the ambient plasma density models that varied along the ascending leg of coronal loops, and also with solar altitude. By estimating the density scale height, we inferred physical parameters of large coronal magnetic loops, roughly 0.7 to 1.5 solar radii above the photosphere. These coronal loops had temperatures around 2 MK and pressures around  5 dyn cm^-2 . We then inferred the minimum magnetic field strength of these closed loops to be around 0.3 G. These large coronal loops' plasma conditions are significantly different to smaller coronal loops and loops that extend out into the solar wind.

How to cite: Zhang, J. and Reid, H.: Deriving plasma parameters of large coronal magnetic loops using J-burst observation from LOFAR, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-12306, https://doi.org/10.5194/egusphere-egu21-12306, 2021.

Eruptive activity in the solar corona can often lead to the propagation of shockwaves. In the radio domain the primary signature of such shocks are type II radio bursts, observed in dynamic spectra as bands of emission slowly drifting towards lower frequencies over time. These radio bursts can sometimes have inhomogeneous and fragmented fine structure, but the cause of this fine structure is currently unclear. Here we observe several type II radio bursts on 2019-March-20th using the New Extension in Nancay Upgrading LOFAR (NenuFAR), a radio interferometer observing between 10-85 MHz. We show  that the distribution of size-scales of density perturbations associated with the fine structure of one type II follows a power law with a spectral index of -1.71, which closely matches the value of -5/3 expected of fully developed turbulence. We determine this turbulence to be upstream of the shock, in background coronal plasma at a heliocentric distance of ~2 R_sun. The observed inertial size-scales of the turbulent density inhomogeneities range from ~62 Mm to ~209 km. This shows that type II fine structure and fragmentation can be due to shock propagation through an inhomogeneous and turbulent coronal plasma, and we discuss the implications of this on electron acceleration in the coronal shock.

How to cite: Carley, E., Cecconi, B., Reid, H., Briand, C., Raja, K. S., Masson, S., Dorovskyy, V., Tiburzi, C., and Zucca, P.: Observations of shock propagation through turbulent plasma in the solar corona, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-13113, https://doi.org/10.5194/egusphere-egu21-13113, 2021.

Coronal Mass Ejections (CMEs) influence the interplanetary environment over vast distances in the solar system by injecting huge clouds of fast solar plasma and energetic particles (SEPs). A number of fundamental questions remain about how SEPs are produced, but current understanding points to CME-driven shocks and compressions in the solar corona. At the same time, unprecedented remote (AIA, LOFAR, MWA) and in situ (Parker Solar Probe, Solar Orbiter) solar observations are becoming available to constrain existing theories. As part of the MOSAIICS project under the VIHREN programme, we are developing a suite of Python tools to reliably analyze radio and EUV remote imaging observations of CMEs and  shock. We present the method for smart characterization and tracking of solar eruptive features, based on the A-Trous wavelet decomposition technique, intensity rankings and a set of filtering techniques. We showcase its performance on a small set of CME-related phenomena observed with the SDO/AIA telescope. With the data represented hierarchically on different decomposition and intensity levels our method allows to extract certain objects and their masks from the series of initial images, in order to track their evolution in time. The method presented here is general and applicable to detecting and tracking various solar and heliospheric phenomena in imaging observations.

How to cite: Stepanyuk, O., Kozarev, K., and Nedal, M.: Advanced Image Preprocessing and Feature Tracking for Remote CME Characterization, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-13803, https://doi.org/10.5194/egusphere-egu21-13803, 2021.

The presence of Quasi-periodic pulsations (QPPs) is found to be a common feature of flaring energy release processes on the Sun. They are observed all across the EM range from hard X-rays to radio and provide insights into the physical conditions in the coronal plasma and the processes involved in the generation of these waves and oscillations. There have been numerous observations of spatially resolved QPPs at higher energies, though there are fewer examples at radio frequencies. Spatially resolved observations of these phenomena are particularly rare at low radio frequencies and there are none which are associated with the weaker episodes of active emissions which are much more numerous and frequent. The key reason limiting such studies has been the lack of availability of spectroscopic snapshot images of sufficient quality to detect and characterise the low level changes in the morphology of the sources of active emissions. Together, the data from the Murchison Widefield Array (MWA), a SKA precursor, and an imaging pipeline developed to meet the specific needs of solar imaging, now meet this challenge and enable us to explore this rich and interesting science area. Our work has led to the discovery of several previously unknown phenomena - second-scale QPPs in the size and orientation of a type III source, with simultaneous QPPs in intensity; 30 s QPPs in the radio light curve of a type I emission source associated with active region loop hosting a transient brightening; and intermittent presence of an anti-correlation in the size and intensity of a type I noise storm source along with QPPs. In this presentation we will briefly summarise these recent results and discuss their implications.

How to cite: Oberoi, D., Mohan, A., and Mondal, S.: Waves and Quasi-Periodic-Pulsations in Weak Active Solar Emissions, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14817, https://doi.org/10.5194/egusphere-egu21-14817, 2021.

Decametric radio emission provides a unique insight into the physics of solar and heliospheric plasmas. Along with dynamic spectra, the spatial characteristics of the emission sources observed in solar radio bursts yield important information about the behaviour of high-energy non-thermal electrons, and the state of thermal plasma in the upper solar corona. Recently, it has been shown that sizes and locations of radio sources in the 10-100 MHz range can be used as a diagnostic tool for plasma turbulence in the upper corona and inner heliosphere. However, observations in this spectral range can be strongly affected by limited spatial resolution of the instrument, as well as by the effect of the Earth's ionosphere on radio wave propagation.

We describe a new method for correcting radio intensity maps for instrumental and ionospheric effects using observations of a known radio source at an arbitrary location in the sky. Based on this method, we derive sizes and areas of the emission sources in the solar radio bursts observed by the Low-Frequency Array (LOFAR) in 30-45 MHz range. It is shown that the sizes of sources are of the order of ten arcminutes and decrease with increasing frequency. Overall, we find that the sizes and their variation, as well as the shapes of the sources in the considered events are consistent with the theoretical models of turbulent radio-wave scattering in the solar corona  developed by Kontar et al. 2019 (Astrophys.J., 884, 122).

How to cite: Gordovskyy, M., Kontar, E., Clarkson, D., and Browning, P.: Sizes of solar radio sources observed by LOFAR, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-15852, https://doi.org/10.5194/egusphere-egu21-15852, 2021.

Auroral Kilometric Radiation (AKR) emanates from acceleration regions from which escaping particles also excite a number of phenomenon in the terrestrial ionosphere, notably aurorae. As such, AKR emission is a barometer for particle precipitation, indicating activity in the magnetosphere. Observations suggest that the emission is mostly limited to the nightside, relating to bursty tail reconnection events. In this study we investigate the relationship between upstream interplanetary magnetic field and solar wind conditions, and the onset and morphology of corresponding AKR emission. Additionally, we explore the delay time between the arrival of solar wind phenomena at the magnetopause, and the onset of related AKR emission and morphology changes. Connections between AKR and solar wind observations allude to solar wind driving of energetic particle precipitation at different local times. The WAVES instrument on the Wind satellite has provided measurements of radio and plasma phenomenon at a range of locations for over two decades, and in this study a recently developed method is utilised to extract AKR bursts from WAVES data, enabling quantitative examination of AKR emission over statistical timescales.

How to cite: Fogg, A. R., Jackman, C. M., Waters, J. E., Bonnin, X., Lamy, L., Cecconi, B., and Issautier, K.: Solar Wind control of Auroral Kilometric Radiation as measured by the Wind Satellite, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-5896, https://doi.org/10.5194/egusphere-egu21-5896, 2021.

In this study, we use a combination of 3D Particle-in-Cell (PIC) simulations and a laboratory experiment to investigate the dynamics of solar wind - Moon interaction. It is known that the Moon has no global magnetic field, but there exist areas of intense remanent magnetization of the lunar crust which are strongly non-dipolar. Performed simulations indicate that the localized crustal fields are capable of scattering solar wind ions, efficiently heat electrons, and produce magnetic field perturbations in the upstream plasma. Numerical study of reflected ion flux compares well to the laboratory experiment performed at induction discharge theta-pinch "KI-1" facility (Novosibirsk). The plasma flow interacts with a magnetic field source (dipolar or quadrupolar), producing a minimagnetosphere with typical scales comparable to (or less than) a few ion inertial lengths. Our numerical and laboratory study concludes that the magnetic field should drop faster than r^-3 with the distance in order to reproduce the spacecraft observations. In this case, gyroradii of the reflected ions are considerably larger than the scale of the minimagnetosphere density cavity. Reflected ions generate enhancements in the upstream magnetic field, supposedly seen as LEMEs (lunar external magnetic enhancements) in spacecraft data above the Moon crustal fields.

How to cite: Divin, A., Shaikhislamov, I., Rumenskikh, M., Zaitsev, I., Semenov, V., Deca, J., and Korovinskiy, D.: Numerical and laboratory studies of magnetic enhancements produced by solar wind interaction with Lunar crustal magnetic fields, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-16209, https://doi.org/10.5194/egusphere-egu21-16209, 2021.

Five different Jupiter’s magnetic field models (O6, VIP4, VIT4, VIPAL and JRM09) are used to investigate the angular distribution of the Jovian decameter radiation occurrence probability, relatively to the local magnetic field B and its gradient ∇B in the source region. The most recent model JRM09, proposed by Connerney et al. [Geophys. Res. Lett., 45, 2590-2596, 2018], and derived from Juno’s first nine orbits observations, confirms the results obtained several years ago using older models (O6, VIP4, VIT4 and VIPAL): the radio emission is beamed in a hollow cone presenting a flattening in a specific direction. In this study, the same assumptions were made as in the previous ones: the Jovian decameter radiation is supposed to be produced by the cyclotron maser instability (CMI) in a plasma where B and ∇B are not parallel. The main result of our study is that the emission cone does not have any axial symmetry and then presents a flattening in a privileged direction. This flattening appears to be more important for the northern emission (34.8%) than for the southern emission (12.5%) probably due to the fact that the angle between the directions of B and ∇B is greater in the North (~10°) than in the South (~4°).

How to cite: Galopeau, P. and Boudjada, M.: Beaming cone of the Jovian decameter emission derived from different magnetic field models, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7744, https://doi.org/10.5194/egusphere-egu21-7744, 2021.

The interaction between a circularly polarized electromagnetic wave and an energetic gyrating particle is described [1] using a relativistic pseudo-potential that is a function of the frequency mismatch,  a measure of the extent to which ω-k_zv_z=Ω/γ is not true. The description of this wave-particle interaction involves a sequence of relativistic transformations that ultimately demonstrate that the pseudo potential energy of a pseudo particle adds to a pseudo kinetic energy giving a total pseudo energy that is a constant of the motion. The pseudo kinetic energy is proportional to the square of the particle acceleration (compare to normal kinetic energy which is the square of a velocity) and the pseudo potential energy is a function of the mismatch and so effectively a function of the particle velocity parallel to the background magnetic field (compare to normal potential energy which is a function of position). Analysis of the pseudo-potential provides a means for interpreting particle motion in the wave in a manner analogous to the analysis of a normal particle bouncing in a conventional potential well.  The wave-particle  interaction is electromagnetic and so differs from and is more complicated than the well-known Landau damping of electrostatic waves.  The pseudo-potential profile depends on the initial mismatch, the normalized wave amplitude, and the initial angle between the wave magnetic field and the particle perpendicular velocity. For zero initial mismatch, the pseudo-potential consists of only one valley, but for finite mismatch, there can be two valleys separated by a hill. A large pitch angle scattering of the energetic electron can occur in the two-valley situation but fast scattering can also occur in a single valley. Examples relevant to magnetospheric whistler waves are discussed. Extension to the situation of a distribution of relativistic particles is presented in a companion talk [2].

[1] P. M. Bellan, Phys. Plasmas 20, Art. No. 042117 (2013)

[2] Y. D. Yoon and P. M. Bellan, JGR 125, Art. No. e2020JA027796 (2020)

How to cite: Bellan, P. M.: Pitch angle scattering of an energetic magnetized particle by a circularly polarized electromagnetic wave, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1932, https://doi.org/10.5194/egusphere-egu21-1932, 2021.

A recent study and a companion talk [1] showed that an exact rearrangement of the relativistic particle equation of motion under a coherent circularly-polarized electromagnetic wave leads to an equation describing the motion of the “frequency mismatch” parameter ξ under a pseudo-potential ψ(ξ). When the particle undergoes a so-called “two-valley motion” in ξ-space, it experiences large changes in ξ and thus its pitch-angle because ξ is a function of the particle’s velocity parallel to the background magnetic field. This single-particle analysis is extended [2] to a distribution of relativistic particles. First, the condition for two-valley motion is derived with parameters relevant to magnetospheric contexts. Single-particle simulations verify that particles which satisfy this condition indeed undergo large pitch-angle fluctuations. Second, assuming a relativistic Maxwellian particle distribution, the fraction of particles that undergo two-valley motion is analytically derived and is numerically verified by Monte-Carlo simulations. A significant fraction (1% - 5%) of the distribution undergoes two-valley motion for typical magnetospheric parameters. For sufficiently fast interactions where a uniform background magnetic field and a constant wave frequency can be assumed, the widely-used second-order trapping theory [3] is shown to be an erroneous approximation of the present theory.

[1] P. M. Bellan, Phys. Plasmas, 20 (4), Art. No. 042117 (2013)

[2] Y. D. Yoon and P. M. Bellan, JGR Space Physics, 125 (6), Art. No. e2020JA027796 (2020)

[3] D. Nunn, Planet. and Space Sci., 22 (3), 349-378 (1974)

How to cite: Yoon, Y. D. and Bellan, P.: Non-diffusive pitch-angle scattering of a distribution of energetic particles by coherent whistler waves, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3604, https://doi.org/10.5194/egusphere-egu21-3604, 2021.