Marco Velli

Alfvén Waves and Turbulence in the Solar Atmosphere and Solar Wind

We solve the problem of propagation and dissipation of Alfvenic turbulence in a model solar atmosphere consisting of a static photosphere and chromosphere, transition region, and open corona and solar wind using a phenomenological model for the turbulent dissipation based on wave reflection. We show that most of the dissipation for a given wave-frequency spectrum occurs in the lower corona, and the overall rms amplitude of the fluctuations evolves in a way consistent with observations. The frequency spectrum for a Kolmogorov-like slope is not found to change dramatically from the photosphere to the solar wind; however, it does preserve signatures of transmission throughout the lower atmospheric layers, namely, oscillations in the spectrum at high frequencies reminiscent of the resonances found in the linear case. These may disappear once more realistic couplings for the nonlinear terms are introduced or if time-dependent variability of the lower atmospheric layer is introduced.

A Semiempirical Magnetohydrodynamical Model of the Solar Wind

We present a new MHD model for simulating the large-scale structure of the solar corona and solar wind under “steady state” conditions stemming from the Wang-Sheeley-Arge empirical model. The processes of turbulent heating in the solar wind are parameterized using a phenomenological, thermodynamical model with a varied polytropic index. We employ the Bernoulli integral to bridge the asymptotic solar wind speed with the assumed distribution of the polytropic index on the solar surface. We successfully reproduce the mass flux from Sun to Earth, the temperature structure, and the large-scale structure of the magnetic field. We reproduce the solar wind speed bimodal structure in the inner heliosphere. However, the solar wind speed is in a quantitative agreement with observations at 1 AU for solar maximum conditions only. The magnetic field comparison demonstrates that the input magnetogram needs to be multiplied by a scaling factor in order to obtain the correct magnitude at 1 AU.

Parametric decay of circularly polarized Alfvén waves: Multidimensional simulations in periodic and open domains

The nonlinear evolution of monochromatic large-amplitude circularly polarized Alfven waves subject to the decay instability is studied via numerical simulations in one, two, and three spatial dimensions. The asymptotic value of the cross helicity depends strongly on the plasma beta: in the low beta case multiple decays are observed, with about half of the energy being transferred to waves propagating in the opposite direction at lower wave numbers, for each saturation step. Correspondingly, the other half of the total transverse energy (kinetic and magnetic) goes into energy carried by the daughter compressive waves and to the associated shock heating. In higher beta conditions we find instead that the cross helicity decreases monotonically with time towards zero, implying an asymptotic balance between inward and outward Alfvenic modes, a feature similar to the observed decrease with distance in the solar wind. Although the instability mainly takes place along the propagation direction, in the two and three-dimensional case a turbulent cascade occurs also transverse to the field. The asymptotic state of density fluctuations appears to be rather isotropic, whereas a slight preferential cascade in the transverse direction is seen in magnetic field spectra. Finally, parametric decay is shown to occur also in a non-periodic domain with open boundaries, when the mother wave is continuously injected from one side. In two and three dimensions a strong transverse filamentation is found at long times, reminiscent of density ray-like features observed in the extended solar corona and pressure-balanced structures found in solar wind data.

Alfvén wave propagation and ion cyclotron interactions in the expanding solar wind: One‐dimensional hybrid simulations

We carry out one-dimensional hybrid simulations of Alfven waves propagating along the magnetic field in the presence of a mean radial spherically expanding plasma outflow, representing fast solar wind streams. The equations for particle ions of multiple species and fluid electrons are solved using the Expanding Box Model, a locally Cartesian representation of motion in spherical coordinates, in a frame moving with the local average wind speed. The model gives a minimally consistent description of the effects associated with such motion on particle dynamics, e.g., the flux-conserving decrease of magnetic field intensity and consequent decrease of cyclotron frequency with increasing distance from the Sun. The cyclotron frequency decreases faster than Alfven wave frequency, allowing fluctuations below the cyclotron frequency at smaller distance from the Sun to come into cyclotron resonance at greater distances. The hybrid treatment yields a fully self-consistent description of the consequent cyclotron wave-particle interaction in a multi-ion plasma. We present results for cases of monochromatic circularly polarized Alfven waves propagating radially outward and for initially well developed Alfvenic spectra with and without alpha particles. When both alpha particles and protons are present, the alpha particles, which come into resonance first as the wind expands, are observed to be preferentially heated and accelerated. For high beta (equal to ratio of ion pressure to magnetic field pressure) the amount of alpha particles acceleration and heating is limited by the available wave power. For low beta cases the amount of heating and acceleration is limited, not by the wave power, but by the depletion of the distribution function in the resonance region by pitch-angle scattering. The implication of these results for solar wind models is discussed.

Energy Release in a Turbulent Corona

Numerical simulations of a two-dimensional section of a coronal loop subject to random magnetic forcing are presented. The forcing models the link between photospheric motions and energy injection in the corona. The results show the highly intermittent spatial distribution of current concentrations generated by the coupling between internal dynamics and external forcing. The total power dissipation is a rapidly varying function of time, with sizable jumps even at low Reynolds numbers, and is caused by the superposition of magnetic dissipation in a number of localized current sheets. Both spatial and temporal intermittency increase with the Reynolds number, suggesting that the turbulent nature of the corona can physically motivate statistical theories of solar activity.

A TURBULENCE-DRIVEN MODEL FOR HEATING AND ACCELERATION OF THE FAST WIND IN CORONAL HOLES

A model is presented for generation of fast solar wind in coronal holes, relying on heating that is dominated by turbulent dissipation of MHD fluctuations transported upward in the solar atmosphere. Scale-separated transport equations include large-scale fields, transverse Alfvenic fluctuations, and a small compressive dissipation due to parallel shears near the transition region. The model accounts for proton temperature, density, wind speed, and fluctuation amplitude as observed in remote sensing and in situ satellite data.

A MODEL FOR MAGNETICALLY COUPLED SYMPATHETIC ERUPTIONS

Sympathetic eruptions on the Sun have been observed for several decades, but the mechanisms by which one eruption can trigger another remain poorly understood. We present a three-dimensional MHD simulation that suggests two possible magnetic trigger mechanisms for sympathetic eruptions. We consider a configuration that contains two coronal flux ropes located within a pseudo-streamer and one rope located next to it. A sequence of eruptions is initiated by triggering the eruption of the flux rope next to the streamer. The expansion of the rope leads to two consecutive reconnection events, each of which triggers the eruption of a flux rope by removing a sufficient amount of overlying flux. The simulation qualitatively reproduces important aspects of the global sympathetic event on 2010 August 1 and provides a scenario for the so-called twin filament eruptions. The suggested mechanisms are also applicable for sympathetic eruptions occurring in other magnetic configurations.

Waves and streams in the expanding solar wind

The expanding box model (EBM) allows the simulation of the evolution of compressible MHD turbulence within the expanding solar wind, taking into account the basic properties of expansion. Using the EBM we follow the evolution of waves within a compressive stream shear and magnetic sector structure in the range of 0.1 to 1 AU from the Sun. We analyze the physical processes which lead in these simulations to the modulation and erosion of the wave component, combined with WKB and non-WKB processes due to expansion. A strong erosion by stream shear corresponds indeed to one of the observed regimes in the solar wind ; however, we are unable to reproduce the regime which holds during solar minimum, in which the correlation between large-scale stream structure and turbulence remains high independently from distance to the Sun. The main point of disagreement with observations concerns the energy spectrum (it is difficult to generate and sustain small-scale turbulence with an Alfvenic wave band present, and even more so in an expanding medium) ; the main point of agreement concerns the statistics of density fluctuations, which are independent of distance, and matches the observed amplitudes both within slow and fast wind. At the same time, small scales appear to be dominated in the simulations by compressible effects, which contradicts popular ideas on solar wind turbulence.

Coronal Heating, Weak MHD Turbulence, and Scaling Laws

Long-time high-resolution simulations of the dynamics of a coronal loop in Cartesian geometry are carried out, within the framework of reduced magnetohydrodynamics (RMHD), to understand coronal heating driven by the motion of field lines anchored in the photosphere. We unambiguously identify MHD anisotropic turbulence as the physical mechanism responsible for the transport of energy from the large scales, where energy is injected by photospheric motions, to the small scales, where it is dissipated. As the loop parameters vary, different regimes of turbulence develop: strong turbulence is found for weak axial magnetic fields and long loops, leading to Kolmogorov-like spectra in the perpendicular direction, while weaker and weaker regimes (steeper spectral slopes of total energy) are found for strong axial magnetic fields and short loops. As a consequence we predict that the scaling of the heating rate with axial magnetic field intensity B0, which depends on the spectral index of total energy for given loop parameters, must vary from B for weak fields to B for strong fields at a given aspect ratio. The predicted heating rate is within the lower range of observed active region and quiet-Sun coronal energy losses.

Statistical Properties of Magnetic Activity in the Solar Corona

The long-time statistical behavior of a two-dimensional section of a coronal loop subject to random magnetic forcing is presented. The highly intermittent nature of dissipation is revealed by means of magnetohydrodynamic (MHD) turbulence numerical simulations. Even with a moderate magnetic Reynolds number, intermittency is clearly present in both space and time. The response of the loop to the random forcing, as described either by the time series of the average and maximum energy dissipation or by its spatial distribution at a given time, displays a Gaussian noise component that may be subtracted to define discrete dissipative events. Distribution functions of both maximum and average current dissipation, for the total energy content, the peak activity, and the duration of such events are all shown to display robust scaling laws, with scaling indices δ that vary from δ -1.3 to δ -2.8 for the temporal distribution functions, while δ -2.6 for the overall spatial distribution of dissipative events.