Magnetohydrostatic equilibrium. I: Three-dimensional open magnetic flux tube in the stratified solar atmosphere

A single open magnetic flux tube spanning the solar photosphere (solar radius R) and the lower corona (R + 10 Mm) is modelled in magnetohydrostatic equilibrium within a realistic stratified atmosphere subject to solar gravity. Such flux tubes are observed to remain relatively stable for up to a day or more, and it is our aim to apply the model as the background condition for numerical studies of energy transport mechanisms from the surface to the corona. We solve analytically an axially symmetric 3D structure for the model, with magnetic field strength, plasma density, pressure and temperature all consistent with observational and theoretical estimates. The self similar construction ensures the magnetic field is divergence free. The equation of pressure balance for this particular set of flux tubes can be integrated analytically to find the pressure and density corrections required to preserve the magnetohydrostatic equilibrium. The model includes a number of free parameters, which makes the solution applicable to a variety of other physical problems and it may therefore be of more general interest.Comment: 9 pages, 8 figure

The NonLinear Evolution of a Twist in a Magnetic Shocktube

The interaction between a small twist and a horizontal chromospheric shocktube is investigated. The magnetic flux tube is modeled using 1.5-D magnetohydrodynamics. The presence of a supersonic yet sub-Alfvénic flow along the flux tube allows the Alfvénic pulse driven at the photospheric boundary to become trapped and amplified between the stationary shock front and photosphere. The amplification of the twist leads to the formation of slow and fast shocks. The pre-existing stationary shock is destabilized and pushed forward as it merges with the slow shock. The propagating fast shock extracts the kinetic energy of the flow and launches rapid twists of 10–15 km s−1 upon each reflection. A cavity is formed between the slow and fast shocks where the flux tube becomes globally twisted within less than an hour. The resultant highly twisted magnetic flux tube is similar to those prone to kink instabilities, which may be responsible for solar eruptions. The generated torsional flux is calculated

New approach for analysing dynamical processes on the surface of photospheric vortex tubes

The majority of studies on multi-scale vortex motions employ a two-dimensional geometry by using a variety of observational and numerical data. This approach limits the understanding the nature of physical processes responsible for vortex dynamics. Here we develop a new methodology to extract essential information from the boundary surface of vortex tubes. 3D high-resolution magnetoconvection MURaM numerical data has been used to analyse photospheric intergranular velocity vortices. The Lagrangian Averaged Vorticity Deviation (LAVD) technique was applied to define the centers of vortex structures and their boundary surfaces based on the advection of fluid elements. These surfaces were mapped onto a constructed envelope grid that allows the study of the key plasma parameters as functions of space and time. Quantities that help in understanding the dynamics of the plasma, e.g. Lorentz force, pressure force, plasma-$\beta$ were also determined. Our results suggest that, while density and pressure have a rather global behaviour, the other physical quantities undergo local changes, with their magnitude and orientation changing in space and time. At the surface, the mixing in the horizontal direction is not efficient, leading to appearance of localized regions with higher/colder temperatures. In addition, the analysis of the MHD Poynting flux confirms that the majority of the energy is directed in the horizontal direction. Our findings also indicate that the pressure and magnetic forces that drive the dynamics of the plasma on vortex surfaces are unbalanced and therefore the vortices do not rotate as a rigid body

Transient effects in atmosphere and ionosphere preceding the 2015 M7.8 and M7.3 Gorkha–Nepal earthquakes

We analyze retrospectively/prospectively the transient variations of six different physical parameters in the atmosphere/ionosphere during the M7.8 and M7.3 earthquakes in Nepal, namely: 1) outgoing longwave radiation (OLR) at the top of the atmosphere (TOA); 2) GPS/TEC; 3) the very-low-frequency (VLF/LF) signals at the receiving stations in Bishkek (Kyrgyzstan) and Varanasi (India); 4) Radon observations; 5) Atmospheric chemical potential from assimilation models; and; 6) Air Temperature from NOAA ground stations. We found that in mid-March 2015, there was a rapid increase in the radiation from the atmosphere observed by satellites. This anomaly was located close to the future M7.8 epicenter and reached a maximum on April 21–22. The GPS/TEC data analysis indicated an increase and variation in electron density, reaching a maximum value during April 22–24. A strong negative TEC anomaly in the crest of EIA (Equatorial Ionospheric Anomaly) occurred on April 21, and a strong positive anomaly was recorded on April 24, 2015. The behavior of VLF-LF waves along NWC-Bishkek and JJY-Varanasi paths has shown abnormal behavior during April 21–23, several days before the first, stronger earthquake. Our continuous satellite OLR analysis revealed this new strong anomaly on May 3, which was why we anticipated another major event in the area. On May 12, 2015, an M7.3 earthquake occurred. Our results show coherence between the appearance of these pre-earthquake transient’s effects in the atmosphere and ionosphere (with a short time-lag, from hours up to a few days) and the occurrence of the 2015 M7.8 and M7.3 events. The spatial characteristics of the pre-earthquake anomalies were associated with a large area but inside the preparation region estimated by Dobrovolsky-Bowman. The pre-earthquake nature of the signals in the atmosphere and ionosphere was revealed by simultaneous analysis of satellite, GPS/TEC, and VLF/LF and suggest that they follow a general temporal-spatial evolution pattern that has been seen in other large earthquakes worldwide

An Inside Look at Sunspot Oscillations with Higher Azimuthal Wavenumbers

Solar chromospheric observations of sunspot umbrae offer an exceptional view of magneto-hydrodynamic wave phenomena. In recent years, a wealth of wave signatures related to propagating magneto-acoustic modes have been presented, which demonstrate complex spatial and temporal structuring of the wave components. Theoretical modelling has demonstrated how these ubiquitous waves are consistent with an m=0 slow magneto-acoustic mode, which are excited by trapped sub-photospheric acoustic (p-mode) waves. However, the spectrum of umbral waves is broad, suggesting that the observed signatures represent the superposition of numerous frequencies and/or modes. We apply Fourier filtering, in both spatial and temporal domains, to extract chromospheric umbral wave characteristics consistent with an m=1 slow magneto-acoustic mode. This identification has not been described before. Angular frequencies of 0.037 +/- 0.007 rad/s (2.1 +/- 0.4 deg/s), corresponding to a period approximately 170 s for the m=1 mode are uncovered for spatial wavenumbers in the range of 0.45<k<0.90 arcsec^-1 (5000-9000 km). Theoretical dispersion relations are solved, with corresponding eigenfunctions computed, which allows the density perturbations to be investigated and compared with our observations. Such magnetohydrodynamic modelling confirms our interpretation that the identified wave signatures are the first direct observations of an m=1 slow magneto-acoustic mode in the chromospheric umbra of a sunspot

Oscillatory response of the 3D solar atmosphere to the leakage of photospheric motion

The direct propagation of acoustic waves, driven harmonically at the solar photosphere, into the three-dimensional solar atmosphere is examined numerically in the framework of ideal magnetohydrodynamics. It is of particular interest to study the leakage of 5-minute global solar acoustic oscillations into the upper, gravitationally stratified and magnetised atmosphere, where the modelled solar atmosphere possesses realistic temperature and density stratification. This work aims to complement and bring further into the 3D domain our previous efforts (by Erdélyi et al., 2007, Astron. Astrophys. 467, 1299) on the leakage of photospheric motions and running magnetic-field-aligned waves excited by these global oscillations. The constructed model atmosphere, most suitable perhaps for quiet Sun regions, is a VAL IIIC derivative in which a uniform magnetic field is embedded. The response of the atmosphere to a range of periodic velocity drivers is numerically investigated in the hydrodynamic and magnetohydrodynamic approximations. Among others the following results are discussed in detail: i) High-frequency waves are shown to propagate from the lower atmosphere across the transition region, experiencing relatively low reflection, and transmitting most of their energy into the corona; ii) the thin transition region becomes a wave guide for horizontally propagating surface waves for a wide range of driver periods, and particularly at those periods that support chromospheric standing waves; iii) the magnetic field acts as a waveguide for both high- and low-frequency waves originating from the photosphere and propagating through the transition region into the solar corona

Numerical modeling of footpoint-driven magneto-acoustic wave propogation in a localized solar flux tube

In this paper, we present and discuss results of two-dimensional simulations of linear and nonlinear magneto-acoustic wave propagation through an open magnetic flux tube embedded in the solar atmosphere expanding from the photosphere through to the transition region and into the low corona. Our aim is to model and analyze the response of such a magnetic structure to vertical and horizontal periodic motions originating in the photosphere. To carry out the simulations, we employed our MHD code SAC (Sheffield Advanced Code). A combination of the VALIIIC and McWhirter solar atmospheres and coronal density profiles were used as the background equilibrium model in the simulations. Vertical and horizontal harmonic sources, located at the footpoint region of the open magnetic flux tube, are incorporated in the calculations, to excite oscillations in the domain of interest. To perform the analysis we have constructed a series of time-distance diagrams of the vertical and perpendicular components of the velocity with respect to the magnetic field lines at each height of the computational domain. These time-distance diagrams are subject to spatio-temporal Fourier transforms allowing us to build ω-k dispersion diagrams for all of the simulated regions in the solar atmosphere. This approach makes it possible to compute the phase speeds of waves propagating throughout the various regions of the solar atmosphere model. We demonstrate the transformation of linear slow and fast magneto-acoustic wave modes into nonlinear ones, i.e., shock waves, and also show that magneto-acoustic waves with a range of frequencies efficiently leak through the transition region into the solar corona. It is found that the waves interact with the transition region and excite horizontally propagating surface waves along the transition region for both types of drivers. Finally, we estimate the phase speed of the oscillations in the solar corona and compare it with the phase speed derived from observations

The response of a three-dimensional solar atmosphere to wave-driven jets

Global oscillations from the solar interior are, mainly, pressure-driven (p-modes) oscillations with a peak power of a five-minute period. These oscillations are considered to manifest in many phenomena in the lower solar atmosphere, most notably, in spicules. These small-scale jets may provide the key to understanding the powering mechanisms of the transition region (TR) and lower corona. Here, we simulate the formation of wave-driven (type-I) spicule phenomena in three dimensions and the transmission of acoustic waves from the lower chromosphere and into the corona. The outer atmosphere oscillates in response to the jet formation, and in turn, we reveal the formation of a circular seismic surface wave, which we name as a Transition Region Quake (TRQ). The TRQ forms as a consequence of an upward propelling spicular wave train that repeatedly punctures and energizes the TR. The steep density gradient enables the TRQ to develop and radially fan outward from the location where the spicular plasma column impinges the TR. We suggest the TRQ formation as a formidable mechanism in continuously sustaining part of the energy budget of the TR. We present a supporting numerical model which allow us to determine the level of energy dumping at the TR by upward-propagating p-modes. Upon applying a wavelet analysis on our simulations we identify the presence of a chromospheric cavity which resonates with the jet propagation and leaves behind an oscillatory wake with a distinctive periodicity. Through our numerical analysis we also discover type-I spicule turbulence leading to a convection-based motion in the low corona