Fundamental (f) oscillations in a magnetically coupled solar interior-atmosphere system – An analytical approach

Solar fundamental (f) acoustic mode oscillations are investigated analytically in a magnetohydrodynamic (MHD) model. The model consists of three layers in planar geometry, representing the solar interior, the magnetic atmosphere, and a transitional layer sandwiched between them. Since we focus on the fundamental mode here, we assume the plasma is incompressible. A horizontal, canopy-like, magnetic field is introduced to the atmosphere, in which degenerated slow MHD waves can exist. The global (f-mode) oscillations can couple to local atmospheric Alfvén waves, resulting, e.g., in a frequency shift of the oscillations. The dispersion relation of the global oscillation mode is derived, and is solved analytically for the thin-transitional layer approximation and for the weak-field approximation. Analytical formulae are also provided for the frequency shifts due to the presence of a thin transitional layer and a weak atmospheric magnetic field. The analytical results generally indicate that, compared to the fundamental value ($\omega =\sqrt{\mathit{gk}}$), the mode frequency is reduced by the presence of an atmosphere by a few per cent. A thin transitional layer reduces the eigen-frequencies further by about an additional hundred microhertz. Finally, a weak atmospheric magnetic field can slightly, by a few percent, increase the frequency of the eigen-mode. Stronger magnetic fields, however, can increase the f-mode frequency by even up to ten per cent, which cannot be seen in observed data. The presence of a magnetic atmosphere in the three-layer model also introduces non-permitted propagation windows in the frequency spectrum; here, f-mode oscillations cannot exist with certain values of the harmonic degree. The eigen-frequencies can be sensitive to the background physical parameters, such as an atmospheric density scale-height or the rate of the plasma density drop at the photosphere. Such information, if ever observed with high-resolution instrumentation and inverted, could help to gain further insight into solar magnetic structures by means of solar magneto-seismology, and could provide further insight into the role of magnetism in solar oscillations.     

Spectral analysis of 3D MHD models of coronal structures

We study extreme-ultraviolet emission line spectra derived from three-dimensional magnetohydrodynamic models of structures in the corona. In order to investigate the effects of increased magnetic activity at photospheric levels in a numerical experiment, a much higher magnetic flux density is applied at the photosphere as compared to the Sun. Thus, we can expect our results to highlight the differences between the Sun and more active, but still solar-like stars. We discuss signatures seen in extreme-ultraviolet emission lines synthesized from these models and compare them to observed signatures in the spatial distribution and temporal evolution of Doppler shifts in lines formed in the transition region and corona. This is of major interest to test the quality of the underlying magnetohydrodynamic model to heat the corona, i.e. currents in the corona driven by photospheric motions (flux braiding).     

A MHD-turbulence model for solar corona

The disposition of energy in the solar corona has always been a problem of great interest. It remains an open question how the low temperature photosphere supports the occurence of solar extreme phenomena. In this work, a turbulent heating mechanism for the solar corona through the framework of reduced magnetohydrodynamics (RMHD) is proposed. Two-dimensional incompressible long time simulations of the average energy disposition have been carried out with the aim to reveal the characteristics of the long time statistical behavior of a two-dimensional cross-section of a coronal loop and the importance of the photospheric time scales in the understanding of the underlying mechanisms. It was found that for a slow, shear type photospheric driving the magnetic field in the loop self-organizes at large scales via an inverse MHD cascade. The system undergoes three distinct evolutionary phases. The initial forcing conditions are quickly “forgotten” giving way to an inverse cascade accompanied with and ending up to electric current dissipation. Scaling laws are being proposed in order to quantify the nonlinearity of the system response which seems to become more impulsive for decreasing resistivity. It is also shown that few, if any, qualitative changes in the above results occur by increasing spatial resolution.     

太阳色球层-日冕中扰动的传播(Ⅱ)

首先讨论了磁流波传播的线性特征，然后构造了球坐标中-自治的非等温，非均匀等离子体初态，应用二维时变可压缩磁流体动力学模拟，数值研究了色球层底部压力脉冲所引起扰动的全球传播过程，结果表明，在极区，压力脉冲导致的扰动传播可以区分成两类不同模式的波动，快磁声波与慢磁声波，而在赤道附近，传播扰动是快模磁声波，在源区附近还存在一非传播的扰动，模拟结果的特征有助于解释SOHO/EIT观测到的波动事件。     

The creation of fine structure by magnetic fields

The solar plasma is strongly structured by the presence of magnetic field. This structuring is manifest in the photosphere in the form of flux tubes, from the readily visible sunspots to the sub-telescopic intense tubes, so that the atmosphere is divided into strong-field media or field-free media. In the corona, by contrast, the magnetic field permeates the whole of the atmosphere and structuring consists principally of density and temperature inhomogeneities. We discuss some of the causes of magnetic structuring, including kinematic concentration, convective collapse and magnetoconvection for photospheric tubes, spicules in the chromosphere, and thermal instability for coronal loops.     

Modeling the (upper) solar atmosphere including the magnetic field

The atmosphere of the Sun is highly structured and dynamic in nature. From the photosphere and chromosphere into the transition region and the corona plasma-β changes from above to below one, i.e., while in the lower atmosphere the energy density of the plasma dominates, in the upper atmosphere the magnetic field plays the governing role – one might speak of a “magnetic transition”. Therefore the dynamics of the overshooting convection in the photosphere, the granulation, is shuffling the magnetic field around in the photosphere. This leads not only to a (re-)structuring of the magnetic field in the upper atmosphere, but induces also the dynamic reaction of the coronal plasma, e.g., due to reconnection events. Therefore the (complex) structure and the interaction of various magnetic patches is crucial to understand the structure, dynamics and heating of coronal plasma as well as its acceleration into the solar wind.

The present article will emphasize the need for three-dimensional modeling accounting for the complexity of the solar atmosphere to understand these processes. Some advances on 3D modeling of the upper solar atmosphere in magnetically closed as well as open regions will be presented together with diagnostic tools to compare these models to observations. This highlights the recent success of these models which in many respects closely match the observations.     

Coronal index as a solar activity index applied to space weather

All possible changes of the solar activity can be expressed by the coronal index of solar activity that represents the averaged daily power of the green corona emitted from the Sun’s visible hemisphere. The representative character of this index allows us to study long-term, intermediate and short-term variations of the Sun as a star. This index can be expressed well as a function of other solar indices. As green line reflects the distribution of the photospheric magnetic fields in the solar corona, the dependence of this index on the solar magnetic field is confirmed by means of statistical analysis of these two parameters. Daily values of the coronal index, as well as of the magnetic field data obtained from the Wilcox Solar Observatory, has been analysed by Fast Fourier analysis and Wavelet Transform analysis for the time period 1966–1998 covering more than three solar cycles. Periodicities of 11.4, 3.2, 2.3, 1.7, 1, 0.29, 0.07 and 0.04 years have been found in both parameters that means once again that the coronal index is probably related to the underlying photospheric magnetic fields and can be used as a global index of solar activity useful for Space Weather studies.     

太阳色球层-日冕中扰动的传播

为了模拟太阳色球层、过渡层和日冕中扰动的传播特征,本文在一自洽的非等温、非均匀等离子体初态下,应用二维时变可压缩磁流体动力学模拟,数值研究了过渡层附近局地加热引起的扰动传播过程.结果表明,扰动分别以局地快磁流波速度向四周传播,数值模拟结果与局地快磁流波推算结果符合得很好,其特征可以解释SOHO/EIT观测到的波动事件.      

Excitation of flare-induced waves in coronal loops and the effects of radiative cooling

EUV imaging observations from several space missions (SOHO/EIT, TRACE, and SDO/AIA) have revealed a presence of propagating intensity disturbances in solar coronal loops. These disturbances are typically interpreted as slow magnetoacoustic waves. However, recent spectroscopic observations with Hinode/EIS of active region loops revealed that the propagating intensity disturbances are associated with intermittent plasma upflows (or jets) at the footpoints which are presumably generated by magnetic reconnection. For this reason, whether these disturbances are waves or periodic flows is still being studied. This study is aimed at understanding the physical properties of observed disturbances by investigating the excitation of waves by hot plasma injections from below and the evolution of flows and wave propagation along the loop. We expand our previous studies based on isothermal 3D MHD models of an active region to a more realistic model that includes full energy equation accounting for the effects of radiative losses. Computations are initialized with an equilibrium state of a model active region using potential (dipole) magnetic field, gravitationally stratified density and temperature obtained from the polytropic equation of state. We model an impulsive injection of hot plasma into the steady plasma outflow along the loops of different temperatures, warm (～1 MK) and hot (～6 MK). The simulations show that hot jets launched at the coronal base excite slow magnetoacoustic waves that propagate to high altitudes along the loops, while the injected hot flows decelerate rapidly with heights. Our results support that propagating disturbances observed in EUV are mainly the wave features. We also find that the effect of radiative cooling on the damping of slow-mode waves in 1–6 MK coronal loops is small, in agreement with the previous conclusion based on 1D MHD models.     

Numerical modeling of inhomogeneous orographic wave influence on planetary waves in the middle atmosphere

Parameterization of dynamical and thermal effects of stationary orographic gravity waves (OGWs) generated by the Earth’s surface topography is incorporated into a numerical model of general circulation of the middle and upper atmosphere. Responses of atmospheric general circulation and characteristics of planetary waves at altitudes from the troposphere up to the thermosphere to the effects of OGWs propagating from the earth surface are studied. Changes in atmospheric circulation and amplitudes of planetary waves due to variations of OGW generation and propagation in different seasons are considered. It is shown that during solstices the main OGW dynamical and heat effects occur in the middle atmosphere of winter hemispheres, where changes in planetary wave amplitudes due to OGWs may reach up to 50%. During equinoxes OGW effects are distributed more homogeneously between northern and southern hemispheres.     

Model of a fluxtube with a twisted magnetic field in the stratified solar atmosphere

We build a single vertical straight magnetic fluxtube spanning the solar photosphere and the transition region which does not expand with height. We assume that the fluxtube containing twisted magnetic fields is in magnetohydrostatic equilibrium within a realistic stratified atmosphere subject to solar gravity. Incorporating specific forms of current density and gas pressure in the Grad–Shafranov equation, we solve the magnetic flux function, and find it to be separable with a Coulomb wave function in radial direction while the vertical part of the solution decreases exponentially. We employ improved fluxtube boundary conditions and take a realistic ambient external pressure for the photosphere to transition region, to derive a family of solutions for reasonable values of the fluxtube radius and magnetic field strength at the base of the axis that are the free parameters in our model. We find that our model estimates are consistent with the magnetic field strength and the radii of Magnetic bright points (MBPs) as estimated from observations. We also derive thermodynamic quantities inside the fluxtube.     

Study of backward propagating Langmuir waves with PIC simulation

The conversion of Langmuir waves into electromagnetic radiations is an important mechanism of solar type III bursts. Langmuir waves can be easily excited by electron beam instability, and they can be converted into backward propagating Langmuir waves by wave–wave interaction. Generally, the backward propagating Langmuir waves are very important for the second harmonic emission of solar type III bursts. In this work, we pay particular attention to the mechanism of the backward propagating Langmuir waves by particle in cell (PIC) simulations. It is confirmed that the ions play a key role in exiting the backward propagating Langmuir waves. Moreover, the electron beam can hardly generated the backward propagating Langmuir waves directly, but may directly amplify the second harmonic Langmuir waves.     

Numerical modeling of propagation of breaking nonlinear acoustic-gravity waves from the lower to the upper atmosphere

Acoustic-gravity waves (AGWs) observed in the upper atmosphere may be generated near the Earth’s surface due to a variety of meteorological sources. Two-dimensional simulations of vertical propagation and breaking of nonlinear AGWs in the atmosphere are performed. Forcing near the Earth’s surface is used as the AGW source in the model. We use a numerical method based on finite-difference analogues of fundamental conservation laws for solving atmospheric hydrodynamic equations. This approach selects physically correct generalized solutions of the wave hydrodynamic equations. Numerical simulations are performed in a representative region of the Earth’s atmosphere up to altitude 500 km. Vertical profiles of temperature, density, molecular viscosity and heat conductivity were taken from the standard atmosphere model MSIS-90 for January. Calculations were made for different amplitudes and frequencies of lower boundary wave forcing. It is shown that after activating the tropospheric wave forcing, the initial pulse of AGWs may very quickly propagate to altitudes of 100 km and above and relatively slowly dissipate due to molecular viscosity and heat conduction. This may increase the role of transient nonstationary waves in effective energy transport and variations of atmospheric parameters and gas admixtures in a broad altitude range.     

Particle acceleration and gamma rays in solar flares: Recent observations and new modeling

Experiments on SMM, GAMMA, Yohkoh, GRANAT, Compton GRO, INTEGRAL, RHESSI and CORONAS-F satellites over the past three decades have provided copious data for fundamental research relating to particle acceleration, transport and energetics of flares and to the ambient abundance of the solar corona, chromosphere and photosphere. We summarize main results of solar gamma-astronomy (including some results of several joint Russian–Chinese projects) and try to appraise critically a real contribution of those results into modern understanding of solar flares, particle acceleration at the Sun and some properties of the solar atmosphere. Recent findings based on the RHESSI, INTEGRAL and CORONAS-F measurements (source locations, spectrum peculiarities, ³He abundance etc.) are especially discussed. Some unusual features of extreme solar events (e.g., 28 October 2003 and 20 January 2005) have been found in gamma-ray production and generation of relativistic particles (solar cosmic rays, or SCR). A number of different plausible assumptions are considered concerning the details of underlying physical processes during large flares: (1) existence of a steeper distribution of surrounding medium density as compared to a standard astrophysical model (HSRA) for the solar atmosphere; (2) enhanced content of the ³He isotope; (3) formation of magnetic trap with specific properties; (4) prevailing non-uniform (e.g., fan-like) velocity (angular) distributions of secondary neutrons, etc. It is emphasized that real progress in this field may be achieved only by combination of gamma-ray data in different energy ranges with multi-wave and energetic particle observations during the same event. We especially note several promising lines for the further studies: (1) resonant acceleration of the ³He ions in the corona; (2) timing of the flare evolution by gamma-ray fluxes in energy range above 90 MeV; (3) separation of gamma-ray fluxes from different sources at/near the Sun (e.g., different acceleration sources/episodes during the same flare, contribution of energetic particles accelerated by the CME-driven shocks etc.); (4) asymmetric magnetic geometry and new magnetic topology models of the near-limb flares; (5) modeling of self-consistent time scenario of the event.     

MHD oscillations in solar and stellar coronae: Current results and perspectives

Wave and oscillatory activity is observed with modern imaging and spectral instruments in the visible light, EUV, X-ray and radio bands in all parts of the solar corona. Magnetohydrodynamic (MHD) wave theory gives satisfactory interpretation of these phenomena in terms of MHD modes of coronal structures. The paper reviews the current trends in the observational study of coronal oscillations, recent development of theoretical modelling of MHD wave interaction with plasma structures, and implementation of the theoretical results for the mode identification. Also the use of MHD waves for remote diagnostics of coronal plasmas is discussed. In particular, the applicability of this method to the estimation of the coronal magnetic field is demonstrated.     

Quiet sun XUV and EUV spectroscopy

The two XUV–EUV spectrometers on SOHO have collected a large amount of data in the 6000–10⁶ K solar plasma temperature range. These data have allowed us to greatly enhance our knowledge of the processes acting in the solar atmosphere, from the chromosphere to the corona. Some results on the quiet Sun structure (network, quiet Sun versus coronal hole), on the dynamics (velocities, waves, transient events), and the main characteristics of the quiet Sun atmosphere are presented and discussed.     

太阳宁静区色球磁场观测

利用中国科学院北京天文台怀柔太阳磁场望远镜,对日面中心宁静区光球和色球磁场进行了长时间的积分观测。通过对光球、色球以及色球不同层次的长时间积分的观测发现,网络磁元从光球到色球扩展不大,并且部分内网络磁元升到了色球。这些结果对描述太阳磁场的两大模型提出了挑战。      

Inferring plasma flow velocities from photospheric vector magnetic field observations for the investigation of flare onsets

The amount of emergence and submergence of magnetized plasma and the horizontal motion of the footpoints of flux tubes might be crucial for the dynamics of the solar atmosphere. Although the rate of flux emergence and submergence can be observationally determined near the polarity inversion line (Chae et al., 2004), the same is not true for regions away from the PIL. Also, the horizontal motions cannot be directly measured in the solar photosphere. In this sense, the evolution of the photospheric magnetic field provides valuable information which can be used to estimate photospheric plasma flows since magnetic field and plasma are closely associated (frozen-in-condition). We used three methods to estimate the photospheric plasma motion from magnetic field observations. The methods were applied to photospheric vector magnetic field data of active region NOAA 9077, observed by the Huairou Solar Observing Station (HSOS) of the National Astronomical Observatories of China before and after the ‘Bastille Day’ flare on July 13th and 14th, 2000.     

Numerical MHD modeling of the solar driver for the destabilization of a coronal helmet streamer

We investigate the forms of the solar driver which cause the destabilization of helmet streamers. Two forms of solar drivers are considered; (i) emergence of a flux-rope from sub-photospheric levels and (ii) application of a photospheric shear motion to a streamer-flux rope system. Numerical results showed that both cases exhibit the characteristics of commonly observed coronal mass ejections (CMEs), but the propagation speed of the CME is higher than the background solar wind speed when the solar driver is the emerging magnetic flux and is the same as the solar wind speed when the photospheric shear is used as the solar driver. The energy constraint allowing the magnetic field transition from a closed to an open configuration is also addressed.     

Turbulence,complexity, and solar flares

The issue of predicting solar flares is one of the most fundamental in physics, addressing issues of plasma physics, high-energy physics, and modelling of complex systems. It also poses societal consequences, with our ever-increasing need for accurate space weather forecasts. Solar flares arise naturally as a competition between an input (flux emergence and rearrangement) in the photosphere and an output (electrical current build up and resistive dissipation) in the corona. Although initially localised, this redistribution affects neighbouring regions and an avalanche occurs resulting in large scale eruptions of plasma, particles, and magnetic field. As flares are powered from the stressed field rooted in the photosphere, a study of the photospheric magnetic complexity can be used to both predict activity and understand the physics of the magnetic field. The magnetic energy spectrum and multifractal spectrum are highlighted as two possible approaches to this.