In a recent paper (Straus et al. 2008) we determined the energy flux of internal gravity waves in the lower solar atmosphere using a combination of 3D numerical simulations and observations obtained with the IBIS instrument operated at the Dunn Solar Telescope and the Michelson Doppler Imager (MDI) on SOHO. In this paper we extend these studies using coordinated observations from SOT/NFI and SOT/SP on Hinode and MDI. The new measurements confirm that gravity waves are the dominant phenomenon in the quiet middle/upper photosphere and that they transport more mechanical energy than the high-frequency (> 5mHz) acoustic waves, even though we find an acoustic flux 3-5 times larger than the upper limit estimate of Fossum & Carlsson (2005). It therefore appears justified to reconsider the significance of (non-M)HD waves for the energy balance of the solar chromosphere.
We present the observed local dispersion relations for magneto-acoustic-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 cut-off frequency in the Sun's photosphere. These maps have implications for the mechanical heating of the Sun's upper atmosphere, by magneto-acoustic-gravity waves, at different phases of the solar magnetic activity cycle.
Recently Wiśniewska et al. demonstrated observationally how the acoustic cutoff frequency varies with height in the solar atmosphere including the upper photosphere and the lower and middle chromosphere, and showed that the observational results cannot be accounted for by the existing theoretical formulas for the acoustic cutoff. In order to reproduce the observed variation of the cutoff with atmospheric height, numerical simulations of impulsively generated acoustic waves in the solar atmosphere are performed, and the spectral analysis of temporal wave profiles is used to compute numerically …
We present simulations of magneto-acoustic wave propagation in a magnetic, plane-parallel stratified solar model atmosphere, employing the CO5BOLD-code. The tests are carried out for two models of the solar atmosphere, which are similar to the ones used by Cally (2007) and Schunker & Cally (2006). The two models differ only in the orientation of the magnetic field. A qualitative comparison shows good agreement between the numerical results and the results from ray theory. The tests are done in view of the application of the present numerical code for the computation of energy fluxes of propaga…
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 o…
We use the exact solutions for magnetoacoustic waves in a two dimensional isothermal atmosphere with uniform inclined magnetic field to calculate the wave reflection, transmission, and conversion of slow and fast waves incident from above ($z=\infty$). This is relevant to the question of whether waves excited by flares in the solar atmosphere can penetrate the Alfvén/acoustic equipartition layer (which we identify as the canopy) to reach the photosphere with sufficient energy to create sunquakes. It is found that slow waves above the acoustic cutoff frequency efficiently penetrate (transmit) a…
We study the energy flux carried by acoustic waves excited by convective motions at sub-photospheric levels. The analysis of high-resolution spectropolarimetric data taken with IMaX/Sunrise provides a total energy flux of ~ 6400--7700 Wm$^{-2}$ at a height of ~ 250 km in the 5.2-10 mHz range, i.e. at least twice the largest energy flux found in previous works. Our estimate lies within a factor of 2 of the energy flux needed to balance radiative losses from the chromosphere according to Anderson & Athay (1989) and revives interest in acoustic waves for transporting energy to the chromosphere. T…
Rapidly oscillating Ap stars exhibit an astrophysically interesting combination of strong, dipolar-like magnetic fields and high-overtone p-mode pulsations similar to the Sun. Recent time-resolved spectroscopy of these stars unravelled a complex picture of propagating magneto-acoustic pulsation waves, with amplitude and phase strongly changing as a function of atmospheric height. To interpret these observations and gain a new insight into the atmospheric dynamics of roAp stars we have carried out 2-D time-dependent, non-linear magneto-hydrodynamical simulations of waves for a realistic atmosph…
Gamma-rays and neutrons are the only sources of information on energetic ions present during solar flares and on properties of these ions when they interact in the solar atmosphere. The production of γ-rays and neutrons results from convolution of the nuclear cross-sections with the ion distribution functions in the atmosphere. The observed γ-ray and neutron fluxes thus provide useful diagnostics for the properties of energetic ions, yielding strong constraints on acceleration mechanisms as well as properties of the interaction sites. The problem of ion transport between the accelerating and i…
The excess temperature of the solar corona over the photosphere poses a challenge. Multiple energetic events contribute to maintaining the corona at such high temperatures. The energy released in different events can vary across several orders of magnitude. Large energy events of geomagnetic importance like flares and coronal mass ejections (CMEs) contribute little to the global energetics of the solar corona. Therefore, events with several (9-10) orders of magnitudes of lower energy, with much higher frequency of occurrence, need to be studied in great detail. Observations suggest that these …
Observations carried out with the Magneto-Optical Filter at Two Heights (MOTH) experiment show upward-traveling wave packets in magnetic regions with frequencies below the acoustic cut-off. We demonstrate that the frequency dependence of the observed travel times, i.e. the dispersion relation shows significant differences in magnetic and non-magnetic regions. More importantly, at and above the layer where the Alfven speed equals the sound speed we do not see the dispersion relation of the slow acoustic mode with a lowered cut-off frequency. Our comparisons with theoretical dispersion relations…
Multi--wavelength studies of energetic solar flares with seismic emissions have revealed interesting common features between them. We studied the first GOES X--class flare of the 24th solar cycle, as detected by the Solar Dynamics Observatory (SDO). For context, seismic activity from this flare (SOL2011-02-15T01:55-X2.2, in NOAA AR 11158) has been reported in the literature (Kosovichev, 2011; Zharkov et al., 2011). Based on Dopplergram data from the Helioseismic and Magnetic Imager (HMI), we applied standard methods of local helioseismology in order to identify the seismic sources in this even…
Shear flows are ubiquitous in astrophysical objects including planetary and stellar interiors, where their dynamics can have significant impact on thermo-chemical processes. Investigating the complex dynamics of shear flows requires numerical calculations that provide a long time evolution of the system. To achieve a sufficiently long lifetime in a local numerical model the system has to be forced externally. However, at present, there exist several different forcing methods to sustain large-scale shear flows in local models. In this paper we examine and compare various methods used in the lit…
We present and discuss the strong correspondence between evolution of the emission length scale in the lower transition region and in situ measurements of the fast solar wind composition during this most recent solar minimum. We combine recent analyses demonstrating the variance in the (supergranular) network emission length scale measured by SOHO (and STEREO) with that of the Helium abundance (from WIND) and the degree of Iron fractionation in the solar wind (from the ACE and Ulysses). The net picture developing is one where a decrease in the Helium abundance and the degree of Iron fractionat…
The hard X-ray (HXR) emission in solar flares comes almost exclusively from a very small part of the flaring region, the footpoints of magnetic loops. Using RHESSI observations of solar flare footpoints, we determine the radial positions and sizes of footpoints as a function of energy in six near-limb events to investigate the transport of flare accelerated electrons and the properties of the chromosphere. HXR visibility forward fitting allows to find the positions/heights and the sizes of HXR footpoints along and perpendicular to the magnetic field of the flaring loop at different energies in…
The aim of this work is to determine the multi-thermal characteristics and plasma energetics of an eruptive plasmoid and occulted flare observed by Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA). We study an event from 03-Nov-2010 (peaking at 12:20UT in GOES soft X-rays) of a coronal mass ejection and occulted flare which demonstrates the morphology of a classic erupting flux rope. The high spatial, and time resolution, and six coronal channels, of the SDO/AIA images allows the dynamics of the multi-thermal emission during the initial phases of eruption to be studied in deta…
This paper investigates the onset time of Solar Energetic Particle (SEP) events with numerical simulations, and analyses the accuracy of the Velocity Dispersion Analysis (VDA) method. Using a 3-dimensional focused transport model, we calculate the fluxes of protons observed in the ecliptic at 1 AU in the energy range between 10 MeV and 80 MeV. In particular, three models are used to describe different SEP sources produced by flare or coronal shock, and the effects of particle perpendicular diffusion in the interplanetary space are also studied. We have the following findings: When the observer…
We consider damping and absorption of solar $p$ modes due to their energy loss to magnetic tube waves that can freely carry energy out of the acoustic cavity. The coupling of $p$ modes and sausage tube waves is studied in a model atmosphere composed of a polytropic interior above which lies an isothermal upper atmosphere. The sausage tube waves, excited by $p$ modes, propagate along a magnetic fibril which is assumed to be a vertically aligned, stratified, thin magnetic flux-tube. The deficit of $p$-mode energy is quantified through the damping rate, $Γ$ and absorption coefficient, $α$. The va…
Solar dynamics and turbulence occur at all heights of the solar atmosphere and could be described as stochastic processes. We propose that finite lifetime transients recurring at a certain place could trigger quasi-periodic processes in the associated structures. In this study, we developed a mathematical model for finite lifetime and randomly occurring transients, and found that quasi-periodic processes, with period longer than the time scale of the transients, are detectable intrinsically in form of trains. We simulate their propagation in an empirical solar atmospheric model with chromosphe…
We investigate the effects of interactions between ions and neutrals on the chromosphere and overlying corona using 2.5D radiative MHD simulations with the Bifrost code. We have extended the code capabilities implementing ion-neutral interaction effects using the Generalized Ohm's Law, i.e., we include the Hall term and the ambipolar diffusion (Pedersen dissipation) in the induction equation. Our models span from the upper convection zone to the corona, with the photosphere, chromosphere and transition region partially ionized. Our simulations reveal that the interactions between ionized parti…
Observations of the solar atmosphere show that internal gravity waves are generated by overshooting convection, but are suppressed at locations of magnetic flux, which is thought to be the result of mode conversion into magneto-acoustic waves. Here, we present a study of the acoustic-gravity wave spectrum emerging from a realistic, self-consistent simulation of solar (magneto-)convection. A magnetic field free, hydrodynamic simulation and a magneto-hydrodynamic (MHD) simulation with an initial, vertical, homogeneous field of 50 G flux density were carried out and compared with each other to hi…
We present a study of multi-wavelength observations, of a C 2.3 solar flare in Active Region NOAA 12353, observed on 2015 May 23, which reveal new properties of acoustic waves in the flaring region. The space-, and ground-based data measured by the HELioseismological Large Regions Interferometric Device, operating at the Vacuum Tower Telescope, the Atmospheric Imaging Assembly, and Helioseismic and Magnetic Imager on board the Solar Dynamic Observatory, were used in this paper. First, using power spectra of solar oscillations, we identified the dominant frequencies and their location at seven …
Recent high-resolution observations of sunspot oscillations using simultaneously operated ground- and space-based telescopes reveal the intrinsic connection between different layers of the solar atmosphere. However, it is not clear whether these oscillations are externally driven or generated in-situ. We address this question by using observations of propagating slow magneto-acoustic waves along a coronal fan loop system. In addition to the generally observed decreases in oscillation amplitudes with distance, the observed wave amplitudes are also found to be modulated with time, with similar v…
We report 2D time-dependent non-linear magneto-hydrodynamical simulations of waves in the atmospheres of roAp stars. We explore a grid of simulations in a wide parameter space. The aim of our study is to understand the influence of the atmosphere and the magnetic field on the propagation and reflection properties of magneto-acoustic waves, formation of shocks and node layers.
We present two-dimensional simulations of wave propagation in a realistic, non-stationary model of the solar atmosphere. This model shows a granular velocity field and magnetic flux concentrations in the intergranular lanes similar to observed velocity and magnetic structures on the Sun and takes radiative transfer into account. We present three cases of magneto-acoustic wave propagation through the model atmosphere, where we focus on the interaction of different magneto-acoustic wave at the layer of similar sound and Alfvén speeds, which we call the equipartition layer. At this layer the acou…
Solar energetic particles acceleration by a shock wave accompanying a coronal mass ejection (CME) is studied. The description of the accelerated particle spectrum evolution is based on the numerical calculation of the diffusive transport equation with a set of realistic parameters. The relation between the CME and the shock speeds, which depend on the initial CME radius, is determined. Depending on the initial CME radius, its speed, and the magnetic energy of the scattering Alfven waves, the accelerated particle spectrum is established during 10-60 minutes from the beginning of CME motion. The…
The detection of upward propagating internal gravity waves at the base of the Sun's chromosphere has recently been reported by Straus et al., who postulated that these may efficiently couple to Alfven waves in magnetic regions. This may be important in transporting energy to higher levels. Here we explore the propagation, reflection and mode conversion of linear gravity waves in a VAL C atmosphere, and find that even weak magnetic fields usually reflect gravity waves back downward as slow magnetoacoustic waves well before they reach the Alfven/acoustic equipartition height at which mode conver…
A set of 464-min high-resolution high-cadence observations were acquired for a region near the Sun's disk center using the Interferometric BI-dimensional Spectrometer (IBIS) installed at the Dunn Solar Telescope. Ten sets of Dopplergrams are derived from the bisector of the spectral line corresponding approximately to different atmospheric heights, and two sets of Dopplergrams are derived using MDI-like algorithm and center-of-gravity method. These data are then filtered to keep only acoustic modes, and phase shifts are calculated between Doppler velocities of different atmospheric heights as …
Stellar irradiation and particles forcing strongly affect the immediate environment of extrasolar giant planets orbiting near their parent stars. Here, we use far-ultraviolet emission spectra from HD209458 in the wavelength range (1180-1710)A to bring new insight to the composition and energetic processes in play in the gas nebula around the transiting planetary companion. In that frame, we consider up-to-date atmospheric models of the giant exoplanet where we implement non-thermal line broadening to simulate the impact on the transit absorption of superthermal atoms (HI, OI, and CII) populati…
We consider linear and nonlinear waves in a stratified hydrostatic fluid within a channel of variable area, under the restriction of one-dimensional flow. We derive a modified version of Riemann's invariant that is related to the wave luminosity. This quantity obeys a simple dynamical equation in linear theory, from which the rules of wave reflection are easily discerned; and it is adiabatically conserved in the high-frequency limit. Following a suggestion by Lighthill, we apply the linear adiabatic invariant to predict mildly nonlinear waves. This incurs only moderate error. We find that Ligh…
Planar acoustically dominated magneto\-hydro\-dynamic waves are initiated at the high-$β$ base of a simulated 2D isothermal stratified atmosphere with potential magnetic field exhibiting both open and closed field regions as well as neutral points. They shock on their way upward toward the Alfvén-acoustic equipartition surface $a=c$, where $a$ and $c$ are the Alfvén and sound speeds respectively. Expanding on recent 1.5D findings that such shocks mode-convert to fast shocks and slow smoothed waves on passing through $a=c$, we explore the implications for these more complex magnetic geometries.…
This paper is an attempt to understand the physical processes occurring in different layers of solar atmosphere during a solar flare. For a complete understanding of the flare we must analyze multi-wavelength datasets, as emission at different wavelength originates from different layers of the solar atmosphere. Also, flares are transient and localized events observed to occur at all longitudes. With these considerations, we have carried out multi-wavelength analysis of two representative flare events. One event occurred close to the centre of the solar disk and other occurred close to the limb…
Acoustic and magnetoacoustic waves are among the possible candidate mechanisms that heat the upper layers of solar atmosphere. A weak chromospheric plage near a large solar pore NOAA 11005 was observed on October 15, 2008 in the lines Fe I 617.3 nm and Ca II 853.2 nm with the Interferometric Bidimemsional Spectrometer (IBIS) attached to the Dunn Solar Telescope. Analyzing the Ca II observations with spatial and temporal resolutions of 0.4" and 52 s, the energy deposited by acoustic waves is compared with that released by radiative losses. The deposited acoustic flux is estimated from power spe…
Solar energetic transients occurring in solar atmosphere are associated with catastrophic release of energy in the solar corona. These transients inject a part of their energy by various physical processes to the deeper, denser photospheric layer at which velocity and magnetic fields are measured using suitable spectral lines. Serious questions have been raised about the nature of the observed magnetic (and velocity) field changes associated with energetic transients as their measurements are expected to be affected by flare-induced line profile changes. In this paper, we shall discuss some re…
We describe the presence of wavefront dislocations in magnetohydrodynamic waves in stratified stellar atmospheres. Scalar dislocations such as edges and vortices can appear in Alfvén waves, as well as in general magneto-acoustic waves. We detect those dislocations in observations of magnetohydrodynamic waves in sunspots in the solar chromosphere. Through the measured charge of all the dislocations observed, we can give for the first time estimates of the modal contribution in the waves propagating along magnetic fields in solar sunspots.
Slow waves are commonly observed on the entire solar atmosphere. Assuming a thin flux tube approximation, the cut-off periods of slow-mode magneto-acoustic-gravity waves that travel from the photosphere to the corona were obtained in Costa et al. (2018). In that paper, however, a typo in the specific heat coefficient at constant pressure $c_{\mathrm{p}}$ value led to an inconsistency in the cut-off calculation, which is only significant at the transition region. Due to the abrupt temperature change in the region, a change of the mean atomic weight (by a factor of approximately two) also occurs…
We investigate the properties of acoustic events (AEs), defined as spatially concentrated and short duration energy flux, in the quiet sun using observations of a 2D field of view (FOV) with high spatial and temporal resolution provided by the Solar Optical Telescope (SOT) onboard \textit{Hinode}. Line profiles of Fe \textsc{i} 557.6 nm were recorded by the Narrow band Filter Imager (NFI) on a $82" \times 82"$ FOV during 75 min with a time step of 28.75 s and 0.08$"$ pixel size. Vertical velocities were computed at three atmospheric levels (80, 130 and 180 km) using the bisector technique allo…
The well-observed acoustic halo is an enhancement in time-averaged Doppler velocity and intensity power with respect to quiet-sun values which is prominent for weak and highly inclined field around the penumbra of sunspots and active regions. We perform 3D linear wave modelling with realistic distributed acoustic sources in a MHS sunspot atmosphere and compare the resultant simulation enhancements with multi-height SDO observations of the phenomenon. We find that simulated halos are in good qualitative agreement with observations. We also provide further proof that the underlying process respo…
We study the coupling of magneto-acoustic waves to Alven waves using 2.5D numerical simulations. In our experiment, a fast magnetoacoustic wave of a given frequency and wavenumber is generated below the surface. The magnetic field in the domain is assumed homogeneous and inclined. The efficiency of the conversion to Alfven waves near the layer of equal acoustic and Alfven speeds is measured calculating their energy flux. The particular amplitude and phase relations between the oscillations of magnetic field and velocity help us to demonstrate that the waves produced after the transformation an…
A considerable fraction of the energy in a solar flare is released as suprathermal electrons; such electrons play a major role in energy deposition in the ambient atmosphere and hence the atmospheric response to flare heating. Historically the transport of these particles has been approximated through a deterministic approach in which first-order secular energy loss to electrons in the ambient target is treated as the dominant effect, with second-order diffusive terms (in both energy and angle) being generally either treated as a small correction or neglected. However, it has recently been poi…
The extreme ultraviolet portion of the solar spectrum contains a wealth of diagnostic tools for probing the lower solar atmosphere in response to an injection of energy, particularly during the impulsive phase of solar flares. These include temperature and density sensitive line ratios, Doppler shifted emission lines and nonthermal broadening, abundance measurements, differential emission measure profiles, and continuum temperatures and energetics, among others. In this paper I shall review some of the advances made in recent years using these techniques, focusing primarily on studies that hav…
MHD wave propagation inside the Sun's atmosphere is closely related to the magnetic field topology. For example, magnetic fields are able to lower the cutoff frequency for acoustic waves thus allowing waves which would otherwise be trapped below the photosphere to propagate into the upper atmosphere. Another example is that MHD waves can be transmitted or converted into other forms of waves at altitudes where the sound speed equals the Alfvén speed. We take advantage of the large field-of-view provided by the IBIS experiment to study the wave propagation at two heights in the solar atmosphere,…
Gamma-ray emission during long-duration gamma-ray flare (LDGRF) events is thought to be caused mainly by $>$300 MeV protons interacting with the ambient plasma at or near the photosphere. Prolonged periods of the gamma-ray emission have prompted the suggestion that the source of the energetic protons is acceleration at a coronal mass ejection (CME)-driven shock, followed by particle back-precipitation onto the solar atmosphere over extended times. We study the latter hypothesis using test particle simulations, which allow us to investigate whether scattering associated with turbulence aids par…
From the analysis of Dopplergrams in the K I 7699 A and Na I 5890 A spectral lines observed with the Magneto-Optical filter at Two Heights (MOTH) experiment during the austral summer in 2002-03 we find upward traveling waves in magnetic regions. Our analysis shows that the dispersion relation of these waves strongly depends on whether the wave is detected in the low-beta or high-beta regime. Moreover, the observed dispersion relation does not show the expected decrease of the acoustic cut-off frequency for the field guided slow magnetic wave. Instead, we detected an increase of the travel time…
We present high-cadence observations and simulations of the solar photosphere, obtained using the Rapid Oscillations in the Solar Atmosphere imaging system and the MuRAM magneto-hydrodynamic code, respectively. Each dataset demonstrates a wealth of magneto-acoustic oscillatory behaviour, visible as periodic intensity fluctuations with periods in the range 110-600 s. Almost no propagating waves with periods less than 140s and 110s are detected in the observational and simulated datasets, respectively. High concentrations of power are found in highly magnetised regions, such as magnetic bright p…
During solar flares, a large fraction of the released magnetic energy is carried by energetic electrons that transfer and deposit energy in the Sun's atmosphere. Electron transport is often approximated by a cold thick-target model (CTTM), assuming that electron energy is much larger than the temperature of the ambient plasma, and electron energy evolution is modeled as a systematic loss. Using kinetic modeling of electrons, we re-evaluate the transport and deposition of flare energy. Using a full collisional warm-target model (WTM), we account for electron thermalization and for the propertie…
In this paper, we review observational aspects of three common small-scale energetic events in the solar transition region (TR), namely: TR explosive events, ultraviolet bursts and jets. These events are defined in either (both) spectral or (and) imaging data. The development of multiple instruments capable of observing the TR has allowed researchers to gain numerous insights into these phenomena in recent years. These events have provided a proxy to study how mass and energy are transported between the solar chromosphere and the corona. As the physical mechanisms responsible for these small-s…
University of Oslo（奥斯陆大学）；The Czech Academy of Sciences（捷克科学院）；University of Graz（格拉茨大学）；University of Zagreb（萨格勒布大学）；University of Warwick（华威大学）；Air Force Research Laboratory（美国空军研究实验室）；University of New Mexico（新墨西哥大学）；Lockheed Martin Solar & Astrophysics Laboratory（洛马太阳与天体物理实验室）；National Astronomical Observatory of Japan（日本国立天文台）；National Institute of Nature Science（国立自然科学研究所）；Russian Academy of Sciences（俄罗斯科学院）；Ioffe Institute（约费研究所）；Max Planck Institute for Solar System Research（马克斯·普朗克太阳系研究所）；Special Astrophysical Observatory（特殊天体物理观测站）
Assuming the thin flux tube approximation, we introduce an analytical model that contemplates the presence of: a non-isothermal temperature; a varying magnetic field and a non-uniform stratified medium in hydrostatic equilibrium due to a constant gravity acceleration. This allows the study of slow magnetoacoustic cut-off periods across the solar transition region, from the base of the solar chromosphere to the lower corona. The used temperature profile approaches the VAC solar atmospheric model. The periods obtained are consistent with observations. Similar to the acoustic cut-off periods, the…
The acoustic cut-off frequency -the highest frequency for acoustic solar eigenmodes- is an important parameter of the solar atmosphere as it determines the upper boundary of the p-mode resonant cavities. At frequencies beyond this value, acoustic disturbances are no longer trapped but traveling waves. Interference amongst them give rise to higher-frequency peaks -the pseudomodes- in the solar acoustic spectrum. The pseudomodes are shifted slightly in frequency with respect to p modes making possible the use of pseudomodes to determine the acoustic cut-off frequency. Using data from GOLF and VI…
Context: Solar pores are small sunspots lacking a penumbra that have a prevailing vertical magnetic field component. They can include light bridges at places with locally reduced magnetic field. Like sunspots, they exhibit a wide range of oscillatory phenomena. Aims: A large isolated pore with a light bridge (NOAA 11005) is studied to obtain characteristics of a chromospheric filamentary structure around the pore, to analyse oscillations and waves in and around the pore, and to understand the structure and brightness of the light bridge. Methods: Spectral imaging observations in the line Ca II…
