We investigate physical scaling laws for magnetic energy dissipation in solar flares, in the framework of the Sweet-Parker model and the Petschek model. We find that the total dissipated magnetic energy $E_{diss}$ in a flare depends on the mean magnetic field component $B_f$ associated with the free energy $E_f$, the length scale $L$ of the magnetic area, the hydrostatic density scale height $λ$ of the solar corona, the Alfvén Mach number $M_A=v_1/v_A$ (the ratio of the inflow speed $v_1$ to the Alfvénic outflow speed $v_A$), and the flare duration $τ_f$, i.e., $E_{diss} = (1/4π) B_f^2\ L\ λ v_A\ M_A\ τ_f$, where the Alfvén speed depends on the nonpotential field strength $B_{np}$ and the mean electron density $n_e$ in the reconnection outflow. Using MDI/SDO and AIA/SDO observations and 3-D magnetic field solutions obtained with the vertical-current approximation nonlinear force-free field code (VCA-NLFFF) we measure all physical parameters necessary to test scaling laws, which represents a new method to measure Alfvén Mach numbers $M_A$, the reconnection rate, and the total free energy dissipated in solar flares.
The process of fast magnetic reconnection supported by the formation of plasmoid chains in the high Lundquist number ($S$) regime is investigated using a recently developed adaptive finite-element magnetohydrodynamic (MHD) code. We employ a two-dimensional incompressible model with a set of reduced visco-resistive MHD equations. The tilt instability setup is chosen to provide a three-step mechanism, where two curved current sheets initially form on an Alfvénic time scale followed by a second phase of super-Alfvénic growth of plasmoid chains for $S \ge S_c$ (Baty 2020). A third phase is reached…
The Sun regularly produces large-scale eruptive events, such as coronal mass ejections (CMEs) that can drive shock waves through the solar corona. Such shocks can result in electron acceleration and subsequent radio emission in the form of a type II radio burst. However, the early-phase evolution of shock properties and its relationship to type II burst evolution is still subject to investigation. Here we study the evolution of a CME-driven shock by comparing three commonly used methods of calculating the Alfvén Mach number ($M_A$), namely: shock geometry, a comparison of CME speed to a model …
We present a constructive numerical example of fast magnetic reconnection in a three dimensional periodic box. Reconnection is initiated by a strong, localized perturbation to the field lines. The solution is intrinsically three dimensional, and its gross properties do not depend on the details of the simulations. $\sim 50%$ of the magnetic energy is released in an event which lasts about one Alfven time, but only after a delay during which the field lines evolve into a critical configuration. We present a physical picture of the process. The reconnection regions are dynamical and mutually int…
Averaging Effects on the Solar Wind Alfven Mach Number: Implications for Switchbacks and Alfven Transition
University of Delaware（特拉华大学）；Princeton University（普林斯顿大学）；University of California, Berkeley（加州大学伯克利分校）；Mahidol University（玛希隆大学）；University of Orléans（奥尔良大学）；Kasetsart University（泰国农业大学）；NASA Goddard Space Flight Center（美国宇航局戈达德太空飞行中心）
We investigate the generation and evolution of switchbacks (SBs), the nature of the sub-Alfvénic wind observed by Parker Solar Probe (PSP), and the morphology of the Alfvénic transition, all of which are key issues in solar wind research. First we highlight a special structure in the pristine solar wind, termed a low Mach-number boundary layer (LMBL). An increased Alfvén radius and suppressed SBs are observed within an LMBL. A probable source on the Sun for an LMBL is the peripheral region inside a coronal hole with rapidly diverging open fields. The sub-Alfvénic wind detected by PSP is an LMB…
We investigate conditions under which kink magnetohydrodynamic waves propagating along photospheric uniformly twisted flux tubes with axial mass flows become unstable as a consequence of the Kelvin-Helmholtz instability. We employed the dispersion relations of kink waves derived from the linearised magnetohydrodynamic equations. We assumed real wave numbers and complex angular wave frequencies, namely complex wave phase velocities. The dispersion relations were solved numerically at fixed input parameters and several mass flow velocities. We show that the stability of the waves depends upon fo…
To measure the magnetic field strength in the solar corona, we examined 10 fast (> 1000 km/s) limb CMEs which show clear shock structures in SOHO/LASCO images. By applying piston-shock relationship to the observed CME's standoff distance and electron density compression ratio, we estimated the Mach number, Alfven speed, and magnetic field strength in the height range 3 to 15 solar radii (Rs). Main results from this study are: (1) the standoff distance observed in solar corona is consistent with those from a magnetohydrodynamic (MHD) model and near-Earth observations; (2) the Mach number as a s…
We show that it is possible to measure Alfvénic Mach numbers, defined as the shock velocity in the flow divided by the Alfvén velocity, for low-velocity (V$_{shock}$ $\lesssim$ 100 km$\,$s$^{-1}$) radiative shocks. The method combines observations of bright forbidden lines with a measure of the size of the cooling zone, the latter typically obtained from spatial separation between the Balmer emission lines and the forbidden lines. Because magnetic fields become compressed as gas in the postshock region cools, even relatively weak preshock magnetic fields can be detected with this method. We de…
The Type-II solar radio burst recorded on 13 June 2010 by the radio spectrograph of the Hiraiso Solar Observatory was employed to estimate the magnetic-field strength in the solar corona. The burst was characterized by a well pronounced band-splitting, which we used to estimate the density jump at the shock and Alfven Mach number using the Rankine-Hugoniot relations. The plasma frequency of the Type-II bursts is converted into height [R] in solar radii using the appropriate density model, then we estimated the shock speed [Vs], coronal Alfven velocity [Va], and the magnetic-field strength at d…
Hydrodynamic jets are unstable to the kink instability (m=1 mode in cylindrical geometry) owing to the centripetal force, which increases the transverse displacement of the jet. When the jet moves along a magnetic field, then the Lorentz force tries to decrease the displacement and stabilises the instability of sub-Alfvenic flows. The threshold of the instability depends on the Alfven Mach number (the ratio of Alfven and jet speeds). We suggest that the dynamic kink instability may be of importance to explain observed transverse motions of type II spicules in the solar atmosphere. We show that…
Ambipolar diffusion (AD) is believed to be a crucial process for redistributing magnetic flux in the dense molecular gas that occurs in regions of star formation. We carry out numerical simulations of this process in regions of low ionization using the heavy ion approximation. The simulations are for regions of strong field (plasma β=0.1) and mildly supersonic turbulence (M=3, corresponding to an Alfven mach number of 0.67). The velocity power spectrum of the neutral gas changes from an Iroshnikov-Kraichnan spectrum in the case of ideal MHD to a Burgers spectrum in the case of a shock-dominate…
We present a quantitative model of the magnetic energy stored and then released through magnetic reconnection for a flare on 26 Feb 2004. This flare, well observed by RHESSI and TRACE, shows evidence of non-thermal electrons only for a brief, early phase. Throughout the main period of energy release there is a super-hot (T>30 MK) plasma emitting thermal bremsstrahlung atop the flare loops. Our model describes the heating and compression of such a source by localized, transient magnetic reconnection. It is a three-dimensional generalization of the Petschek model whereby Alfven-speed retraction …
By measuring the geometrical properties of the coronal mass ejection (CME) flux rope and the leading shock observed on 2010 June 13 by the Solar Dynamics Observatory (SDO) mission's Atmospheric Imaging Assembly (AIA) we determine the Alfvén speed and the magnetic field strength in the inner corona at a heliocentric distance of ~ 1.4 Rs. The basic measurements are the shock standoff distance (deltaR) ahead of the CME flux rope, the radius of curvature of the flux rope (Rc), and the shock speed. We first derive the Alfvénic Mach number (M) using the relationship, deltaR/Rc = 0.81[(gamma-1) M^2 +…
We examine the effects of self-gravity and magnetic fields on supersonic turbulence in isothermal molecular clouds with high resolution simulations and adaptive mesh refinement. These simulations use large root grids (512^3) to capture turbulence and four levels of refinement to capture high density, for an effective resolution of 8,196^3. Three Mach 9 simulations are performed, two super-Alfvénic and one trans-Alfvénic. We find that gravity splits the clouds into two populations, one low density turbulent state and one high density collapsing state. The low density state exhibits properties s…
A stellar wind passing through the reverse shock is deflected into the astrospheric tail and leaves the stellar system either as a sub-Alfvenic or as a super-Alfvenic tail flow. An example is our own heliosphere and its heliotail. We present an analytical method of calculating stationary, incompressible, and field-aligned plasma flows in the astrotail of a star. We present a recipe for constructing an astrosphere with the help of only a few parameters, like the inner Alfven Mach number and the outer Alfven Mach number, the magnetic field strength within and outside the stellar wind cavity, and…
We determine the coronal magnetic field strength in the heliocentric distance range 6 to 23 solar radii (Rs) by measuring the shock standoff distance and the radius of curvature of the flux rope during the 2008 March 25 coronal mass ejection (CME) imaged by white-light coronagraphs. Assuming the adiabatic index, we determine the Alfven Mach number, and hence the Alfven speed in the ambient medium using the measured shock speed. By measuring the upstream plasma density using polarization brightness images, we finally get the magnetic field strength upstream of the shock. The estimated magnetic …
Vortex motions are frequently observed on the solar photosphere. These motions may play a key role in the transport of energy and momentum from the lower atmosphere into the upper solar atmosphere, contributing to coronal heating. The lower solar atmosphere also consists of complex networks of flux tubes that expand and merge throughout the chromosphere and upper atmosphere. We perform numerical simulations to investigate the behaviour of vortex driven waves propagating in a pair of such flux tubes in a non-force-free equilibrium with a realistically modelled solar atmosphere. The two flux tub…
3D Magnetohydrodynamic (MHD) turbulent flows with initially magnetic and kinetic energies at equipartition spontaneously develop a magnetic excess (or residual energy), as well in numerical simulations and in the solar wind. Closure equations obtained in 1983 describe the residual spectrum as being produced by a dynamo source proportional to the total energy spectrum, balanced by a linear Alfvén damping term. A good agreement was found in 2005 with incompressible simulations; however, recent solar wind measurements disagree with these results. The previous dynamo-Alfvén theory is generalized t…
Stellar Wind Driven Alfvén Wing Dynamics in Planetary and Exoplanetary Magnetospheres
Center of Excellence in Space Sciences India, Indian Institute of Science Education and Research Kolkata（印度空间科学卓越中心，印度科学教育研究所加尔各答分校）；Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata（印度科学教育研究所加尔各答分校物理科学系）；Center for High Energy Systems and Sciences, Defence Research and Development Organization（国防研究与发展组织高能系统与科学中心）；Department of Physics, Fakir Chand College（法基尔昌德学院物理系）
One of the key challenges in solar and heliospheric physics is to understand the acceleration of the solar wind. As a super-sonic, super-Alfvénic plasma flow, the solar wind carries mass, momentum, energy, and angular momentum from the Sun into interplanetary space. We present a framework based on two-fluid magnetohydrodynamics to estimate the flux of these quantities based on spacecraft data independent of the heliocentric distance of the location of measurement. Applying this method to the Ulysses dataset allows us to study the dependence of these fluxes on heliolatitude and solar cycle. The…
It is known that hydrodynamic triangular jets are unstable to antisymmetric kink perturbations. The inclusion of magnetic field may lead to the stabilisation of the jets. Jets and complex magnetic fields are ubiquitous in the solar atmosphere, which suggests the possibility of the kink instability in certain cases. The aim of the paper is to study the kink instability of triangular jets sandwiched between magnetic tubes/slabs and its possible connection to observed properties of the jets in the solar atmosphere. A dispersion equation governing the kink perturbations is obtained through matchin…
Opher et al. (2015), Drake et al. (2015) have shown that the heliospheric magnetic field results in formation of two-jet structure of the solar wind flow in the inner heliosheath, i.e. in the subsonic region between the heliospheric termination shock and the heliopause. In this scenario the heliopause has a tube-like topology as compared with a sheet-like topology in the most models of the global heliosphere (e.g. Izmodenov and Alexashov, 2015). In this paper we explore the two-jet scenario for a simplified astrosphere in which 1) the star is at rest with respect to the circumstellar medium, 2…
We study the magnetic field to density ($B-ρ$) relation in turbulent molecular clouds with dynamically important magnetic fields using nonideal three-dimensional magnetohydrodynamic simulations. Our simulations show that there is a distinguishable break density $ρ_{\rm T}$ between the relatively flat low density regime and a power-law regime at higher densities. We present an analytic theory for $ρ_{\rm T}$ based on the interplay of the magnetic field, turbulence, and gravity. The break density $ρ_{\rm T}$ scales with the strength of the initial Alfvén Mach number $\mathcal{M}_{\rm A0}$ for su…
It is well established now that the solar atmosphere, from photosphere to the corona and the solar wind is a highly structured medium. Satellite observations have confirmed the presence of steady flows. Here, we investigate the parallel propagation of magnetohydrodynamic (MHD) surface waves travelling along an ideal incompressible flowing plasma slab surrounded by flowing plasma environment in the framework of the Hall magnetohydrodynamics. The propagation properties of the waves are studied in a reference frame moving with the mass flow outside the slab. In general, flows change the waves' ph…
Direct Observations of Magnetic Reconnection in the Solar Wind Current Sheets near Mars
Boston University（波士顿大学）；Institute for Advanced Study, Princeton（普林斯顿高等研究院）；University of Iowa（爱荷华大学）；Space Sciences Laboratory, University of California, Berkeley（加州大学伯克利分校空间科学实验室）；University of Toulouse（图卢兹大学）；Kyoto University（京都大学）；Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder（科罗拉多大学博尔德分校大气与空间物理实验室）
Magnetohydrodynamic configurations with strong localized current concentrations and vortices play an important role for the dissipation of energy in space and astrophysical plasma. Within this work we investigate the relation between current sheets and vortex sheets in incompressible, stationary equilibria. For this approach it is helpful that the similar mathematical structure of magnetohydrostatics and stationary incompressible hydrodynamics allows us to transform static equilibria into stationary ones. The main control function for such a transformation is the profile of the Alfven-Mach num…
Motivated by prior remote observations of a transition from striated solar coronal structures to more isotropic ``flocculated'' fluctuations, we propose that the dynamics of the inner solar wind just outside the Alfvén critical zone, and in the vicinity of the first $β=1$ surface, is powered by the relative velocities of adjacent coronal magnetic flux tubes. We suggest that large amplitude flow contrasts are magnetically constrained at lower altitude but shear-driven dynamics are triggered as such constraints are released above the Alfvén critical zone, as suggested by global magnetohydrodynam…
Strong Alfvénic turbulence develops eddy-like motions perpendicular to the local direction of magnetic fields. This local alignment induces velocity gradients perpendicular to the local direction of the magnetic field. We use this fact to propose a new technique of studying the direction of magnetic fields from observations, the Velocity Gradient Technique. We test our idea by employing the synthetic observations obtained via 3D MHD numerical simulations for different sonic and Alfvén Mach numbers. We calculate the velocity gradient, $\mathbfΩ$, using the velocity centroids. We find that $\mat…
One of the striking observations from the Parker Solar Probe (PSP) spacecraft is the prevalence in the inner heliosphere of large amplitude, Alfvénic magnetic field reversals termed 'switchbacks'. These $δB_R/B \sim \mathcal{O}(1$) fluctuations occur on a range of timescales and in {\em patches} separated by intervals of quiet, radial magnetic field. We use measurements from PSP to demonstrate that patches of switchbacks are localized within the extensions of plasma structures originating at the base of the corona. These structures are characterized by an increase in alpha particle abundance, …
We report turbulence effects on magnetic reconnection in relativistic plasmas using 3-dimensional relativistic resistive magnetohydrodynamics simulations. We found reconnection rate became independent of the plasma resistivity due to turbulence effects similarly to non-relativistic cases. We also found compressible turbulence effects modified the turbulent reconnection rate predicted in non-relativistic incompressible plasmas; The reconnection rate saturates and even decays as the injected velocity approaches to the Alfvén velocity. Our results indicate the compressibility cannot be neglected …
We have shown the simultaneous generation of macro-scale fast flows and strong magnetic fields in the 2-temperature relativistic electron-ion plasmas of astrophysical objects due to Unified Reverse Dynamo/Dynamo mechanism. The resulting dynamical magnetic field amplification and/or flow acceleration is directly proportional to the initial turbulent kinetic/magnetic (magnetic) energy; the process is very sensitive to relativistically hot electron-ion fraction temperature and magneto-fluid coupling. It is shown, that for realistic physical parameters of White Dwarfs accreting hot astrophysical f…
We consider a magnetic configuration consisting of an arcade structure and a detached plasmoid, resulting from a magnetic reconnection process, as is typically found in connection with solar flares. We study spontaneous current fragmentation caused by shear and vortex plasma flows. An exact analytical transformation method was applied to calculate self-consistent solutions of the nonlinear stationary MHD equations. The assumption of incompressible field-aligned flows implies that both the Alfven Mach number and the mass density are constant on field lines. We first calculated nonlinear MHS equ…
The properties of collisionless shocks, like the density jump, are usually derived from magnetohydrodynamics (MHD), where isotropic pressures are assumed. Yet, in a collisionless plasma, an external magnetic field can sustain a stable anisotropy. In \cite{BretJPP2018}, we devised a model for the kinetic history of the plasma through the shock front, allowing to self-consistently compute the downstream anisotropy, hence the density jump, in terms of the upstream parameters. This model dealt with the case of a parallel shock, where the magnetic field is normal to the front both in the upstream a…
The first estimation of the energy cascade rate ${|ε_C|}$ of magnetosheath turbulence is obtained using the CLUSTER and THEMIS spacecraft data and an exact law of compressible isothermal magnetohydrodynamics turbulence. ${|ε_C|}$ is found to be of the order of ${10{^{-13}} J.m^{3}.s^{-1}}$, at least two orders of magnitude larger than its value in the solar wind (order of ${10{^{-16}} J.m^{3}.s^{-1}}$ in the fast wind). Two types of turbulence are evidenced and shown to be dominated either by incompressible Alfvénic or magnetosonic-like fluctuations. Density fluctuations are shown to amplify t…
We derive and compare six theoretical models for the star formation rate (SFR) - the Krumholz & McKee (KM), Padoan & Nordlund (PN), and Hennebelle & Chabrier (HC) models, and three multi-freefall versions of these, suggested by HC - all based on integrals over the log-normal distribution of turbulent gas. We extend all theories to include magnetic fields, and show that the SFR depends on four basic parameters: (1) virial parameter alpha_vir; (2) sonic Mach number M; (3) turbulent forcing parameter b, which is a measure for the fraction of energy driven in compressive modes; and (4) plasma beta…
Interplanetary Coronal Mass Ejection (ICME) shocks are known to accelerate particles and contribute significantly to Solar Energetic Particle (SEP) events. We have performed Magnetohydrodynamic-Particle in Cell (MHD-PIC) simulations of ICME shocks to understand the acceleration mechanism. These shocks vary in Alfvénic Mach numbers as well as in magnetic field orientations (parallel \& quasi-perpendicular). We find that Diffusive Shock Acceleration (DSA) plays a significant role in accelerating particles in a parallel ICME shock. In contrast, Shock Drift Acceleration (SDA) plays a pivotal role …
Astrophysical shocks are often studied in the high Mach number limit but weakly compressive fast shocks can occur in magnetic reconnection outflows and are considered to be a site of particle energization in solar flares. Here we study the microphysics of such perpendicular, low Mach number collisionless shocks using two-dimensional particle-in-cell (PIC) simulations with a reduced ion/electron mass ratio and employ a moving wall boundary method for initial generation of the shock. This moving wall method allows for more control of the shock speed, smaller simulation box sizes, and longer simu…
We investigate the validity of Taylor's Hypothesis (TH) in the analysis of Alfvénic fluctuations of velocity and magnetic fields in solar wind streams measured by Parker Solar Probe (PSP)~during the first four encounters. We use PSP velocity and magnetic field measurements from 24 h intervals selected from each of the first four encounters. The applicability of TH is investigated by measuring the parameter $ε=δu_0/\sqrt{2}V_\perp$, which quantifies the ratio between the typical speed of large-scale fluctuations, $δu_0$, and the local perpendicular PSP speed in the solar wind frame, $V_\perp$. …
The rich structure that we observe in molecular clouds is due to the interplay between strong magnetic fields and supersonic (turbulent) velocity fluctuations. The velocity fluctuations interact with the magnetic field, causing it too to fluctuate. Using numerical simulations, we explore the nature of such magnetic field fluctuations, $\vec{δB}$, over a wide range of turbulent Mach numbers, $\mathcal{M} = 2 - 20$ (i.e., from weak to strong compressibility), and Alfvén Mach numbers, $\mathcal{M}_{\text{A}0} = 0.1 - 100$ (i.e., from strong to weak magnetic mean fields, $B_0$). We derive a compre…
