High-resolution helioseismology observations with the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) provide a unique three-dimensional view of the solar interior structure and dynamics, revealing a tremendous complexity of the physical processes inside the Sun. We present an overview of the results of the HMI helioseismology program and discuss their implications for modern theoretical models and simulations of the solar interior.

We present evidence supporting wave reflection in the lower solar chromosphere based on helioseismic analysis of multi-height Doppler data from the Solar Dynamics Observatory/Helioseismic and Magnetic Imager and the Magneto-Optical filters at Two Heights II instrument. This evidence is derived through a wave propagation model that incorporates both upward- and downward-traveling (reflected) waves. Moreover, we find that the height of the reflecting region varies with magnetic field strengths in a way that suggests a connection with the plasma β ∼ 1 region. We measure an effective reflection coefficient of 13% in a magnetically quiet region of the Sun.

Solar pores are intense concentrations of magnetic flux that emerge through the solar photosphere. When compared to sunspots, they are much smaller in diameter and can therefore be affected and buffeted by neighbouring granular activity to generate significant magnetohydrodynamic (MHD) wave energy flux within their confines. However, observations of solar pores from ground-based telescope facilities may struggle to capture subtle motions that are synonymous with higher-order MHD wave signatures because of the seeing effects that are produced in the Earth's atmosphere. Hence, we exploited timely seeing-free and high-quality observations of four small magnetic pores from the High Resolution Telescope (HRT) of the Polarimetric and Helioseismic Imager (PHI) on board the Solar Orbiter spacecraft during its first close perihelion passage in March 2022 (at a distance of 0.5 au from the Sun). Through acquisition of data under stable observing conditions, we were able to measure the area fluctuations and horizontal displacements of the solar pores. Cross correlations between perturbations in intensity, area, line-of-sight velocity, and magnetic fields, coupled with the first-time application of novel proper orthogonal decomposition techniques on the boundary oscillations, provided a comprehensive diagnosis of the embedded MHD waves as sausage and kink modes. Additionally, the previously elusive $m=2$ fluting mode is identified in the most magnetically isolated of the four pores. An important consideration lies in how the identified wave modes contribute to the transfer of energy into the upper solar atmosphere. Approximately 56, 72, 52, and 34 of the total wave energy of the four pores we examined is associated with the identified sausage modes and about 23, 17, 39, and 49 with their kink modes, while the first pore also receives a contribution of about 11 linked to the fluting mode. This study reports the first-time identification of concurrent sausage, kink, and fluting MHD wave modes in solar magnetic pores.

Context. Joint observations of the Atacama Large Millimeter/Submillimeter Array (ALMA) with other solar observatories can provide a wealth of opportunities for understanding the coupling between different layers of the solar atmosphere. Aims. We present a statistical analysis of the power distribution of oscillations in a plage region in active region NOAA AR12651, which was observed jointly with ALMA, the Interface Region Imaging Spectrograph (IRIS), and the Solar Dynamics Observatory (SDO). Methods. We employ coordinated ALMA Band 6 (1.25 mm) brightness temperature maps, IRIS slit-jaw images in the 2796 Å passband, and observations in six passbands (1600 Å, 304 Å, 131 Å, 171 Å, 193 Å, and 211 Å) from the Atmospheric Imaging Assembly (AIA) on board SDO. We perform Lomb-Scargle transforms to study the distribution of oscillation power by means of dominant period maps and power maps. We study the spatial association of oscillations through the atmosphere, with a focus on the correlation of the power distribution of ALMA oscillations with others. Results. We do not observe any significant association of ALMA oscillations with IRIS and AIA oscillations. While the global behavior of the dominant ALMA oscillations shows a similarity with that of the transition region and coronal passbands of AIA, the ALMA dominant period maps and power maps do not show any correlation with those from the other passbands. The spatial distribution of dominant periods and power in different period intervals of ALMA oscillations is uncorrelated with those of any other passbands. Conclusions. We speculate that the non-association of ALMA oscillations with those of IRIS and AIA is due to significant variations in the height of formation of the millimeter continuum observed by ALMA. Additionally, the fact that ALMA directly maps the brightness temperature, in contrast to the intensity observations by IRIS and AIA, can result in the very different intrinsic nature of the ALMA oscillations compared to the IRIS and AIA oscillations.

Although theoretically predicted, the simultaneous excitation of several resonant modes in sunspots has not been observed. Like any harmonic oscillator, a solar magnetic flux tube can support a variety of resonances, which constitute the natural response of the system to external forcing. Apart from a few single low order eigenmodes in small scale magnetic structures, several simultaneous resonant modes were not found in extremely large sunspots. Here we report the detection of the largest-scale coherent oscillations observed in a sunspot, with a spectrum significantly different from the Sun's global acoustic oscillations, incorporating a superposition of many resonant wave modes. Magnetohydrodynamic numerical modeling agrees with the observations. Our findings not only demonstrate the possible excitation of coherent oscillations over spatial scales as large as 30-40 Mm in extreme magnetic flux regions in the solar atmosphere, but also paves the way for their diagnostic applications in other astrophysical contexts.

The umbral regions of sunspots and pores in the solar photosphere are generally dominated by $3$~mHz oscillations, which are due to $p$-modes penetrating the magnetic region. In these locations, wave power is also significantly reduced with respect to the quiet Sun. However, here we study a pore where the power of the oscillations in the umbra is not only comparable, or even larger than that of the quiet Sun, but the main dominant frequency is not $3$~mHz as expected, but instead $5$~mHz. By combining Doppler velocities and spectropolarimetry and analysing the relationship between magnetic field strength and frequency, the resultant $B-\omega$ diagram reveals distinct ridges which are remarkably clear signatures of resonant MHD oscillations confined within the pore umbra. In addition to velocity oscillations, we demonstrate that these modes are also accompanied by magnetic oscillations, as predicted from MHD theory. The novel technique of $B-\omega$ analysis, proposed in this Letter, opens an exciting new avenue for identifying MHD wave modes in the umbral regions of both pores and sunspots.

Sunspots host a large variety of oscillatory phenomena, whose properties depend on the nature of the wave modes and the magnetic and thermodynamic structure of the spot. Umbral chromospheric oscillations exhibit significant differences compared to their photospheric counterparts. They show an enhanced power and a shorter dominant period, from waves with an amplitude of a few hundred meters per second in the five-minute band at the photosphere, to amplitudes of several kilometers per second in the three-minute band at the chromosphere. Various models have been proposed to explain this behaviour, including the presence of a chromospheric resonance cavity between the photosphere and the transition region. Jess et al. (2020, Nature Astronomy, 4, 220) claimed the detection of observational evidence supporting this model, obtained from the comparison of spectropolarimetric observations and numerical simulations. Here, it is shown that the observational insight reported by Jess et al. is not a common property of sunspots. More importantly, numerical modelling also shows that it is not an unequivocal signature of an acoustic resonator.

By direct measurements of the gas temperature, the Atacama Large Millimeter/submillimeter Array (ALMA) has yielded a new diagnostic tool to study the solar chromosphere. Here, we present an overview of the brightness-temperature fluctuations from several high-quality and high-temporal-resolution (i.e. 1 and 2 s cadence) time series of images obtained during the first 2 years of solar observations with ALMA, in Band 3 and Band 6, centred at around 3 mm (100 GHz) and 1.25 mm (239 GHz), respectively. The various datasets represent solar regions with different levels of magnetic flux. We perform fast Fourier and Lomb–Scargle transforms to measure both the spatial structuring of dominant frequencies and the average global frequency distributions of the oscillations (i.e. averaged over the entire field of view). We find that the observed frequencies significantly vary from one dataset to another, which is discussed in terms of the solar regions captured by the observations (i.e. linked to their underlying magnetic topology). While the presence of enhanced power within the frequency range 3–5 mHz is found for the most magnetically quiescent datasets, lower frequencies dominate when there is significant influence from strong underlying magnetic field concentrations (present inside and/or in the immediate vicinity of the observed field of view). We discuss here a number of reasons which could possibly contribute to the power suppression at around 5.5 mHz in the ALMA observations. However, it remains unclear how other chromospheric diagnostics (with an exception of H α line-core intensity) are unaffected by similar effects, i.e. they show very pronounced 3-min oscillations dominating the dynamics of the chromosphere, whereas only a very small fraction of all the pixels in the 10 ALMA datasets analysed here show peak power near 5.5 mHz. This article is part of the Theo Murphy meeting issue ‘High-resolution wave dynamics in the lower solar atmosphere’.

Internal gravity waves have been observed in the Earth's atmosphere and oceans, on Mars and Jupiter, and in the Sun's atmosphere. Despite ample evidence for the existence of propagating gravity waves in the Sun's atmosphere, we still do not have a full understanding of their characteristics and overall role for the dynamics and energetics of the solar atmosphere. Here, we present a new approach to study the propagation of gravity waves in the solar atmosphere. It is based on calculating the three-dimensional cross-correlation function between the vertical velocities measured at different heights. We apply this new method to a time series of co-spatial and co-temporal Doppler images obtained by SOHO/MDI and Hinode/SOT as well as to simulations of upward propagating gravity wave-packets. We show some preliminary results and outline future developments. This article is part of the Theo Murphy meeting issue 'High-resolution wave dynamics in the lower solar atmosphere'.

We use localized measurements of the dispersion relation for acoustic-gravity waves to generate the first maps of the spatial structure of the sound speed, acoustic cut-off frequency, and radiative damping time in the Sun’s lower atmosphere. These maps offer a new diagnostic for the solar atmosphere.

There are strong scientific cases and practical reasons for building ground-based solar synoptic telescopes. Some issues, like the study of solar dynamics and the forecasting of solar flares, benefit from the 3D reconstruction of the Sun’s atmosphere and magnetic field. Others, like the monitoring and prediction of space weather, require full disk observations, at the proper sampling rate, combining H-alpha images and Doppler velocity and magnetic field. The synoptic telescopes based on Magneto Optical Filters (MOF) using different lines are capable of measuring the line-of-sight Doppler velocity and magnetic field over the full solar disk at different ranges of height in the Sun’s photosphere and low chromosphere. Instruments like the MOTH (Magneto-Optical filters at Two Heights), using a dual-channel based on MOFs operating at 589.0 nm (Na D2 line) and 769.9 nm (K D1 line), the VAMOS instrument (Velocity And Magnetic Observations of the Sun), operating at 769.9 nm (K D1 line), and the future TSST (Tor Vergata Synoptic Solar Telescope), using a dual-channel telescope operating at 656.28 nm (H-alpha line) and at 769.9 nm (K D1 line), allow to face both aspects, the scientific and the operative related to Space Weather applications. The MOTH, VAMOS and TSST data enable a wide variety of studies of the Sun, from seismic probing of the solar interior (sound speed, rotation, details of the tachocline, sub-surface structure of active regions), to the dynamics and magnetic evolution of the lower part of the solar atmosphere (heating of the solar atmosphere, identification of the signatures of solar eruptive events, atmospheric gravity waves, etc.), to the 3D reconstruction of the solar atmosphere and flare locations. However, the use of MOF filters requires special care in calibrating the data for scientific or operational use. This work presents a systematic pipeline that derives from the decennial use of MOF’s technology. More in detail, the pipeline is based on data reduction procedures tested and validated on MOTH data acquired at Mees Solar Observatory of the University of Hawaii Haleakala Observatories and at South Pole Solar Observatory (SPSO), at the Amundsen-Scott South Pole Station in Antarctica, during Antarctica Summer Campaign 2016/17.

There has been tremendous progress in the degree of realism of three-dimensional radiation magneto-hydrodynamic simulations of the solar atmosphere in the past decades. Four of the most frequently used numerical codes are Bifrost, CO5BOLD, MANCHA3D and MURaM. Here we test and compare the wave propagation characteristics in model runs from these four codes by measuring the dispersion relation of acoustic-gravity waves at various heights. We find considerable differences between the various models. The height dependence of wave power, in particular of high-frequency waves, varies by up to two orders of magnitude between the models, and the phase difference spectra of several models show unexpected features, including ±180° phase jumps. This article is part of the Theo Murphy meeting issue ‘High-resolution wave dynamics in the lower solar atmosphere’.

The solar surface is a continuous source of internal gravity waves (IGWs). IGWs are believed to supply the bulk of the wave energy for the lower solar atmosphere, but their existence and role for the energy balance of the upper layers is still unclear, largely due to the lack of knowledge about the influence of the Sun’s magnetic fields on their propagation. In this work, we look at naturally excited IGWs in realistic models of the solar atmosphere and study the effect of different magnetic field topographies on their propagation. We carry out radiation-magnetohydrodynamic simulations of a magnetic field free and two magnetic models—one with an initial, homogeneous, vertical field of 100 G magnetic flux density and one with an initial horizontal field of 100 G flux density. The propagation properties of IGWs are studied by examining the phase-difference and coherence spectra in the k h − ω diagnostic diagram. We find that IGWs in the upper solar atmosphere show upward propagation in the model with predominantly horizontal field similar to the model without magnetic field. In contrast to that the model with predominantly vertical fields show downward propagation. This crucial difference in the propagation direction is also revealed in the difference in energy transported by waves for heights below 0.8 Mm. Higher up, the propagation properties show a peculiar behaviour, which require further study. Our analysis suggests that IGWs may play a significant role in the heating of the chromospheric layers of the internetwork region where horizontal fields are thought to be prevalent. This article is part of the Theo Murphy meeting issue ‘High-resolution wave dynamics in the lower solar atmosphere’.

We present an initial study of one of the first ALMA Band 3 observations of the Sun with the aim to characterise the diagnostic potential of brightness temperatures measured with ALMA on the Sun. The observation covers 48min at a cadence of 2s targeting a Quiet Sun region at disk-centre. Corresponding time series of brightness temperature maps are constructed with the first version of the Solar ALMA Pipeline (SoAP) and compared to simultaneous SDO observations. The angular resolution of the observations is set by the synthesized beam (1.4x2.1as). The ALMA maps exhibit network patches, internetwork regions and also elongated thin features that are connected to large-scale magnetic loops as confirmed by a comparison with SDO maps. The ALMA Band 3 maps correlate best with the SDO/AIA 171, 131 and 304 channels in that they exhibit network features and, although very weak in the ALMA maps, imprints of large-scale loops. A group of compact magnetic loops is very clearly visible in ALMA Band 3. The brightness temperatures in the loop tops reach values of about 8000-9000K and in extreme moments up to 10 000K. ALMA Band 3 interferometric observations from early observing cycles already reveal temperature differences in the solar chromosphere. The weak imprint of magnetic loops and the correlation with the 171, 131, and 304 SDO channels suggests though that the radiation mapped in ALMA Band 3 might have contributions from a larger range of atmospheric heights than previously assumed but the exact formation height of Band 3 needs to be investigated in more detail. The absolute brightness temperature scale as set by Total Power measurements remains less certain and must be improved in the future. Despite these complications and the limited angular resolution, ALMA Band 3 observations have large potential for quantitative studies of the small-scale structure and dynamics of the solar chromosphere.

Solar Orbiter is the first space mission observing the solar plasma both in situ and remotely, from a close distance, in and out of the ecliptic. The ultimate goal is to understand how the Sun produces and controls the heliosphere, filling the Solar System and driving the planetary environments. With six remote-sensing and four in-situ instrument suites, the coordination and planning of the operations are essential to address the following four top-level science questions: (1) What drives the solar wind and where does the coronal magnetic field originate?; (2) How do solar transients drive heliospheric variability?; (3) How do solar eruptions produce energetic particle radiation that fills the heliosphere?; (4) How does the solar dynamo work and drive connections between the Sun and the heliosphere? Maximising the mission's science return requires considering the characteristics of each orbit, including the relative position of the spacecraft to Earth (affecting downlink rates), trajectory events (such as gravitational assist manoeuvres), and the phase of the solar activity cycle. Furthermore, since each orbit's science telemetry will be downloaded over the course of the following orbit, science operations must be planned at mission level, rather than at the level of individual orbits. It is important to explore the way in which those science questions are translated into an actual plan of observations that fits into the mission, thus ensuring that no opportunities are missed. First, the overarching goals are broken down into specific, answerable questions along with the required observations and the so-called Science Activity Plan (SAP) is developed to achieve this. The SAP groups objectives that require similar observations into Solar Orbiter Observing Plans, resulting in a strategic, top-level view of the optimal opportunities for science observations during the mission lifetime. This allows for all four mission goals to be addressed. In this paper, we introduce Solar Orbiter's SAP through a series of examples and the strategy being followed.

We report detection of oscillations in brightness temperature, size and horizontal velocity of three small bright features in the chromosphere of a plage/enhanced-network region. The observations, which were taken with high temporal resolution (i.e. 2 s cadence) with the Atacama large millimetre/ submillimetre array (ALMA) in Band 3 (centred at 3 mm; 100 GHz), exhibit three small-scale features with oscillatory behaviour with different, but overlapping, distributions of period on the order of, on average, 90 ± 22 s, 110 ± 12 s and 66 ± 23 s, respectively. We find anti-correlations between perturbations in brightness, temperature and size of the three features, which suggest the presence of fast sausage-mode waves in these small structures. In addition, the detection of transverse oscillations (although with a larger uncertainty) may also suggest the presence of Alfvénic oscillations which are likely representative of kink waves. This work demonstrates the diagnostic potential of high-cadence observations with ALMA for detecting high-frequency magnetohydrodynamic waves in the solar chromosphere. Such waves can potentially channel a vast amount of energy into the outer atmosphere of the Sun. This article is part of the Theo Murphy meeting issue 'High-resolution wave dynamics in the lower solar atmosphere'.

Solar Orbiter is the first space mission observing the solar plasma both in situ and remotely, from a close distance, in and out of the ecliptic. The ultimate goal is to understand how the Sun produces and controls the heliosphere, filling the Solar System and driving the planetary environments. With six remote-sensing and four in-situ instrument suites, the coordination and planning of the operations are essential to address the following four top-level science questions: (1) What drives the solar wind and where does the coronal magnetic field originate?; (2) How do solar transients drive heliospheric variability?; (3) How do solar eruptions produce energetic particle radiation that fills the heliosphere?; (4) How does the solar dynamo work and drive connections between the Sun and the heliosphere? Maximising the mission’s science return requires considering the characteristics of each orbit, including the relative position of the spacecraft to Earth (affecting downlink rates), trajectory events (such as gravitational assist manoeuvres), and the phase of the solar activity cycle. Furthermore, since each orbit’s science telemetry will be downloaded over the course of the following orbit, science operations must be planned at mission level, rather than at the level of individual orbits. It is important to explore the way in which those science questions are translated into an actual plan of observations that fits into the mission, thus ensuring that no opportunities are missed. First, the overarching goals are broken down into specific, answerable questions along with the required observations and the so-called Science Activity Plan (SAP) is developed to achieve this. The SAP groups objectives that require similar observations into Solar Orbiter Observing Plans, resulting in a strategic, top-level view of the optimal opportunities for science observations during the mission lifetime. This allows for all four mission goals to be addressed. In this paper, we introduce Solar Orbiter’s SAP through a series of examples and the strategy being followed.

Sunspots are intense collections of magnetic fields that pierce through the Sun’s photosphere, with their signatures extending upwards into the outermost extremities of the solar corona1. Cutting-edge observations and simulations are providing insights into the underlying wave generation2, configuration3,4 and damping5 mechanisms found in sunspot atmospheres. However, the in situ amplification of magnetohydrodynamic waves6, rising from a few hundreds of metres per second in the photosphere to several kilometres per second in the chromosphere7, has, until now, proved difficult to explain. Theory predicts that the enhanced umbral wave power found at chromospheric heights may come from the existence of an acoustic resonator8–10, which is created due to the substantial temperature gradients experienced at photospheric and transition region heights11. Here, we provide strong observational evidence of a resonance cavity existing above a highly magnetic sunspot. Through a combination of spectropolarimetric inversions and comparisons with high-resolution numerical simulations, we provide a new seismological approach to mapping the geometry of the inherent temperature stratifications across the diameter of the underlying sunspot, with the upper boundaries of the chromosphere ranging between 1,300 ± 200 km and 2,300 ± 250 km. Our findings will allow the three-dimensional structure of solar active regions to be conclusively determined from relatively commonplace two-dimensional Fourier power spectra. The techniques presented are also readily suitable for investigating temperature-dependent resonance effects in other areas of astrophysics, including the examination of Earth–ionosphere wave cavities12. Spectropolarimetric data combined with high-resolution numerical simulations reveal a resonance cavity above a highly magnetic sunspot. This technique conclusively determines the three-dimensional structure of solar active regions from relatively commonplace two-dimensional data.

We present the observed local dispersion relations for magnetoacoustic-gravity waves in the Sun's atmosphere for different levels of magnetic field strength. We model these data with a theoretical local dispersion relation to produce spatial maps of the acoustic cutoff frequency in the Sun's photosphere. These maps have implications for the mechanical heating of the Sun's upper atmosphere, by magnetoacoustic-gravity waves, at different phases of the solar magnetic activity cycle.