Spatial dependence of high energy electrons and their radiations in pulsar wind nebulae

We investigate the spatial dependence of high energy electrons and their radiations in pulsar wind nebulae(PWNe).By assuming a time-dependent broken power-law injection and spatial dependence of convection velocity,magnetic field strength and diffusion coefficient on the radial distance of an expanding system,we numerically solve the Fokker-Planck transport equation including convection,diffusion,adiabatic loss and radiative loss in spherical coordinates,and investigate the effects of magnetic field,PWN age,maximum energy of electrons,and diffusion coefficient on electron spectra and non-thermal photon emissions.Our results indicate that(1) electron spectra and the corresponding photon spectra are a function of radial distance r of the expanding system;(2) for a given expansion velocity,the increase of the PWN age causes a slower decrease of the convection velocity(V ∝ r~(-β)) and a more rapid decrease of the magnetic field strength(B ∝ r~(-1+β)),but a more rapid increase of the diffusion coefficient(κ∝ r~(1-β)) because the index β decreases with the PWN age;and(3) the lower energy part of the electron spectra is dominated by convection and adiabatic loss,but the higher energy part is dominated by the competition between synchrotron loss and diffusion,and such a competition is a function of radial distance.Therefore the diffusion effect has an important role in the evolution of electron spectra as well as non-thermal photon spectra in a PWN.     

Structure and evolution of magnetic fields associated with solar eruptions

This paper reviews the studies of solar photospheric magnetic field evolution in active regions and its relationship to solar flares. It is divided into two topics, the magnetic structure and evolution leading to solar eruptions and rapid changes in the photospheric magnetic field associated with eruptions. For the first topic, we describe the magnetic complexity, new flux emergence, flux cancelation, shear motions, sunspot rotation and magnetic helicity injection, which may all contribute to the storage and buildup of energy that trigger solar eruptions. For the second topic, we concentrate on the observations of rapid and irreversible changes of the photospheric magnetic field associated with flares, and the implication on the restructuring of the three-dimensional magnetic field. In particular, we emphasize the recent advances in observations of the photospheric magnetic field, as state-of-the-art observing facilities(such as Hinode and Solar Dynamics Observatory) have become available. The linkages between observations, theories and future prospectives in this research area are also discussed.     

Analysis of sudden variations in photospheric magnetic fields during a large flare and their influences in the solar atmosphere

The solar active region NOAA 11719 produced a large two-ribbon flare on 2013 April 11. We have investigated sudden variations in the photospheric magnetic fields in this active region during the flare by employing magnetograms obtained in the spectral line Fe I 6173 A? acquired by the Helioseismic and Magnetic Imager(HMI) onboard the Solar Dynamics Observatory(SDO) spacecraft. The analysis of the line-of-sight magnetograms from HMI show sudden and persistent magnetic field changes at different locations of the active region before the onset of the flare and during the flare. The vector magnetic field observations available from HMI also show coincident variations in the total magnetic field strength and its inclination angle at these locations. Using the simultaneous Dopplergrams obtained from HMI, we observe perturbations in the photospheric Doppler signals following the sudden changes in the magnetic fields in the aforementioned locations. The power spectrum analysis of these velocity signals shows enhanced acoustic power in these affected locations during the flare as compared to the pre-flare condition. Accompanying these observations, we have also used nearly simultaneous chromospheric observations obtained in the spectral line Hα 6562.8 A? by the Global Oscillation Network Group(GONG) to study the evolution of flareribbons and intensity oscillations in this active region. The Hα intensity oscillations also show enhanced oscillatory power during the flare in the aforementioned locations. These results indicate that the transient Lorentz force associated with sudden changes in the magnetic fields could drive localized photospheric and chromospheric oscillations, like the flare-induced oscillations in the solar atmosphere.     

A new parametrization of dark energy equation of state leading to double exponential potential

We show that a phenomenological form of energy density for the scalar field can provide the required transition from decelerated(q 0) to accelerated expansion(q 0) phase of the universe.We have used the latest type Ia supernova(SNIa) and Hubble parameter datasets to constrain the model parameters. The best fit values obtained from those datasets are then applied to reconstruct ωφ(z), the equation of state parameter for the scalar field. The results show that the reconstructed forms of q(z) and ω_φ(z) do not differ much from the standard ΛCDM value at the current epoch. Finally, the functional form of the relevant potential V(φ) is derived by a parametric reconstruction. The corresponding V(φ)comes out to be a double exponential potential, which has a number of cosmological implications.Additionally, we have also studied the effect of this particular scalar field dark energy sector on the evolution of matter overdensities.     

Formation of Solar Delta Active Regions： Twist and Writhe of Magnetic Ropes

We analyze the process of formation of delta configuration in some well-known super active regions based on photospheric vector magnetogram observations. It is found that the magnetic field in the initial developing stage of some delta active regions shows a potential-like configuration in the solar atmosphere, the magnetic shear develops mainly near the magnetic neutral line with magnetic islands of opposite polarities, and the large-scale photospheric twisted field forming gradually later. Some results are obtained: (1) The analysis of magnetic writhe of whole active regions cannot be limited in the strong field of sunspots, because the contribution of the fraction of decayed magnetic field is non-negligible. (2) The magnetic model of kink magnetic ropes, supposed to be generated in the subatmosphere, is not consistent with the evolution of large-scale twisted photospheric transverse magnetic field and not entirely consistent with the relationship with magnetic shear in some delta active regions. (3) T     

Coherent structures and spectral shapes of kinetic Alfvén wave turbulence in solar wind at 1 AU

This paper presents the generation of kinetic Alfv én wave(KAW) coherent structures of magnetic filaments applicable to solar wind at 1 AU, when the background plasma density is modified by parallel ponderomotive force and Joule heating. The inhomogeneity in the magnetic field, which was included as a perturbation in the transverse direction of the magnetic field, takes energy from the main pump KAWs and generates the filamentary structures. When the intensity is high enough, the filaments are broken down and the energy initially confined to low wavenumbers is redistributed to higher wavenumbers, leading to cascades of energy at small scales less than the ion acoustic gyroradius or comparable to electron gyroradius.The magnetic field spectral profile is generated from the numerical simulation results, and its dependence on different directions of the wavevector and initial conditions of the simulation representing the transverse magnetic field inhomogeneity is studied. The relevance of these results with other spacecraft observations and measurements is also pointed out.     

Magnetic Field Strengths and Structures from Radio Observations of Solar Active Regions

Radio observations of some active regions (ARs) obtained with the Nobeyama radioheliograph at λ=1.76cm are used for estimating the magnetic field strength in the upper chromosphere, based on thermal bremsstrahlung. The results are compared with the magnetic field strength in the photosphere from observations with the Solar Magnetic Field Telescope (SMFT) at Huairou Solar Observing Station of Beijing Astronomical Observatory. The difference in the magnetic field strength between the two layers seems reasonable. The solar radio maps of active regions obtained with the Nobeyama radioheliograph, both in total intensity (I-map) and in circular polarizations (V-map), are compared with the optical magnetograms obtained with the SMFT. The comparison between the radio map in circular polarization and the longitudinal photospheric magnetogram of a plage region suggest that the radio map in circular polarization is a kind of magnetogram of the upper chromosphere. The comparison of the radio map in total intensity with the photospheric vector magnetogram of an AR shows that the radio map in total intensity gives indications of magnetic loops in the corona, thus we have a method of defining the coronal magnetic structure from the radio I-maps at λ=1.76 cm. Analysing the I-maps, we identified three components: (a) a compact bright source; (b) a narrow elongated structure connecting two main magnetic islands of opposite polarities (observed in both the optical and radio magnetograms); (c) a wide, diffuse, weak component that corresponds to a wide structure in the solar active region which shows in most cases an S or a reversed S contour, which is probably due to the differential rotation of the Sun. The last two components suggest coronal loops on different spatial scales above the neutral line of the longitudinal photospheric magnetic field.     

A Fluid Dynamics Approach for the Computation of Non—linear Force—Free Magnetic Field

Inspired by the analogy between the magnetic field and velocity field of incompressible fluid flow, we propose a fluid dynamics approach for computing nonlinear force-free magnetic fields. This method has the advantage that the divergence-free condition is automatically satisfied, which is a sticky issue for many other algorithms, and we can take advantage of modern high resolution algorithms to process the force-free magnetic field. Several tests have been made based on the well-known analytic solution proposed by Low & Lou. The numerical results are in satisfactory agreement with the analytic ones. It is suggested that the newly proposed method is promising in extrapolating the active region or the whole sun magnetic fields in the solar atmosphere based on the observed vector magnetic field on the photosphere.     

Estimations of cosmological parameters from the observational variation of the fine structure constant

We present constraints on the quintessence scalar field model from observational data of the variation of the fine structure constant obtained from the Keck telescope and VLT. Within the theoretical frame proposed by Bekenstein, the constraints on the parameters of the quintessence scalar field model are obtained. Considering the prior of Ωm0 as WMAP 7 suggests, we obtain various results from different sam- ples. Based on these results, we also calculate the probability density function of the coupling constant ζ. The best-fit values show a consistent relationship between ζ and the different experimental results. In our work, we test two different potential models, namely, the inverse power law potential and the exponential potential. The results show that both the large value of the parameters in the potential and the strong coupling can cause a variation in the fine structure constant.     

An explanation for 13 consecutive day activities of Mrk 421

It is surprising to find an instance of migration in the peak positions of synchrotron spectral energy distribution components during the activity epochs of Markarian 421(Mrk 421),accompanying an orphan flare at the X-ray and GeV-TeVγ-ray bands.A geometric interpretation and standard shock or stochastic acceleration models of blazar emission have difficulty reproducing these observed behaviors.The present paper introduces a linear acceleration by integrating the reconnection electric field into the particle transport model for the observed behaviors of Mrk 421.We note that strong evidence for evolution in characteristic of multi-wavelength spectral energy distribution including shifting the peak frequency,accompanying an orphan flare at the X-ray and GeV-TeVγ-ray bands provides an important electrostatic acceleration diagnostic in a blazar jet.Assuming suitable model parameters,we apply the results of the simulation to the 13-day flaring event in March 2010 of Mrk 421,concentrating on the evolution of multiwavelength spectral energy distribution characteristic by shifting the peak frequency.It is clear that the ratio of the electric field and magnetic field strength plays an important role in temporal evolution of the peak frequency of synchrotron spectral energy distribution component.We suggest it is reasonable that the electrostatic acceleration is responsible for the evolution of multi-wavelength spectral energy distribution characteristic by shifting the peak frequency.Based on the model results,we assert that the peak frequency of the synchrotron spectral energy distribution component may signify a temporary characteristic of blazars,rather than a permanent one.     

Vector Magnetic Field Measurement of NOAA AR 10197

A set of two-dimensional Stokes spectral data of NOAA AR 10197 obtained by the Solar Stokes Spectral Telescope (S3T) at the Yunnan Observatory are qualitatively analyzed. The three components of the vector magnetic field, the strength H, inclinationγand azimuth X, are derived. Based on the three components, we contour the distributions of the longitudinal magnetic field and transverse magnetic field. The active region (AR) has two different magnetic polarities apparent in the longitudinal magnetic map due to projection effect. There is a basic agreement on the longitudinal magnetic fields between the S3T and SOHO/MDI magnetograms, with a correlation coefficientρBl = 0.911. The transverse magnetic field of the AR has a radial distribution from a center located in the southwest of the AR. It is also found that the transverse magnetic fields obtained by Huairou Solar Observing Station (HRSOS) have a similar radial distribution. The distributions of transverse magnetic field obtained by S3T and HRSOS have correlation coefficients,ρAzimu = 0.86 andρBt = 0.883, in regard to the azimuthal angle and intensity.     

Location of energy source for coronal heating on the photosphere

It is reported that ultra-fine dynamic ejections along magnetic loops of an active region originate from intergranular lanes and they are associated with subsequent heating in the corona. As continuing work, we analyze the same set of data but focus on a quiet region and the overlying EUV/UV emission as observed by the Atmospheric Imaging Assembly(AIA) on board Solar Dynamics Observatory(SDO). We find that there appear to be dark patches scattered across the quiet region and the dark patches always stay along intergranular lanes. Over the dark patches, the average UV/EUV emission at 131, 171, 304 and 1600 (middle temperature) is more intense than that of other regions and EUV brightness is negatively correlated with 10830  intensity, though, such a trend does not exist for high temperature lines at 94, 193, 211 and 335 . For the same quiet region, where both Ti O 7057  broad band images and 10830  filtergrams are available, contours for the darkest lane areas on Ti O images and dark patches on 10830  filtergrams frequently differ in space. The results suggest that the dark patches do not simply reflect the areas with the darkest lanes but are associated with a kind of enhanced absorption(EA) at 10830 . A strict definition for EA with narrow band 10830  filtergrams is found to be difficult. In this paper, we define enhanced absorption patches(EAPs) of a quiet region as the areas where emission is less than ~90% of the mean intensity of the region. The value is equivalent to the average intensity along thin dark loops connecting two moss regions of the active region. A more strict definition for EAPs, say 88%, gives even more intense UV/EUV emission over those in the middle temperature range. The results provide further observational evidence that energy for heating the upper solar atmosphere comes from the intergranular lane area where the magnetic field is constantly brought in by convection motion in granules.     

Comparison between the eruptive X2.2 flare on 2011 February15 and confined X3.1 flare on 2014 October 24

We compare two contrasting X-class flares in terms of magnetic free energy, relative magnetic helicity and decay index of the active regions(ARs) in which they occurred. The events in question are the eruptive X2.2 flare from AR 11158 accompanied by a halo coronal mass ejection(CME) and the confined X3.1 flare from AR 12192 with no associated CME. These two flares exhibit similar behavior of free magnetic energy and helicity buildup for a few days preceding them. A major difference between the two flares is found to lie in the time-dependent change of magnetic helicity of the ARs that hosted them. AR 11158 shows a significant decrease in magnetic helicity starting ～4 hours prior to the flare, but no apparent decrease in helicity is observed in AR 12192. By examining the magnetic helicity injection rates in terms of sign, we confirmed that the drastic decrease in magnetic helicity before the eruptive X2.2 flare was not caused by the injection of reversed helicity through the photosphere but rather the CME-related change in the coronal magnetic field. Another major difference we find is that AR 11158 had a significantly larger decay index and therefore weaker overlying field than AR 12192. These results suggest that the coronal magnetic helicity and the decay index of the overlying field can provide a clue about the occurrence of CMEs.     

Energetics and Propagation of Coronal Mass Ejections in Different Plasma Environments

Based on previous work, we investigate the propagation of CMEs in a more realistic plasma environment than the isothermal atmosphere, and find that it is a slightly faster reconnection for flux ropes to break free. The average Alfven Mach number MA for the inflow into the reconnection site has to be at least 0.013 in order to give a plausible eruption (compared to MA = 0.005 for the isothermal atmosphere). Taking MA = 0.1, we find that the energy output and the electric field induced inside the current sheet match the temporal behavior inferred from the energetic, long duration, CME-associated X-ray events. The results indicate that catastrophic loss of equilibrium in the coronal magnetic field provides the most promising mechanism for major solar eruptions, and that the more energetic the eruption is, the earlier the associated flare peaks. The variation of the output power with the background field strength revealed by our calculations implies the poor correlation between slow CMEs and solar flares. Th     

Modeling the 2017 September 10 solar energetic particle event using the iPATH model

On 2017 September 10, a fast coronal mass ejection(CME) erupted from the active region(AR)12673, leading to a ground level enhancement(GLE) event at Earth. Using the 2D improved Particle Acceleration and Transport in the Heliosphere(iPATH) model, we model the large solar energetic particle(SEP) event of 2017 September 10 observed at Earth, Mars and STEREO-A. Based on observational evidence, we assume that the CME-driven shock experienced a large lateral expansion shortly after the eruption, which is modeled by a double Gaussian velocity profile in this simulation. We apply the in-situ shock arrival times and the observed CME speeds at multiple spacecraft near Earth and Mars as constraints to adjust the input model parameters. The modeled time intensity profiles and fluence for energetic protons are then compared with observations. Reasonable agreements with observations at Mars and STEREO-A are found. The simulated results at Earth differ from observations of GOES-15. However, the simulated results at a heliocentric longitude 20° west to Earth fit reasonably well with the GOES observation. This can be explained if the pre-event solar wind magnetic field at Earth is not described by a nominal Parker field.Our results suggest that a large lateral expansion of the CME-driven shock and a distorted interplanetary magnetic field due to previous events can be important in understanding this GLE event.     

Cosmological constraints on ultra-light axion fields

Ultra-light axions(ULAs) with mass less than 10-20 eV have interesting behaviors that may contribute to either dark energy or dark matter at different epochs of the Universe. Their properties can be explored by cosmological observations, such as expansion history of the Universe, cosmic large-scale structure, cosmic microwave background, etc. In this work, we study the ULAs with mass around 10~(-33) eV,which means that the ULA field still rolls slowly at present with the equation of state w =-1 as dark energy. To investigate the mass and other properties of this kind of ULA field, we adopt the measurements of Type Ia supernova(SN Ia), baryon acoustic oscillation(BAO), and Hubble parameter H(z). The Markov Chain Monte Carlo(MCMC) technique is employed to perform the constraints on the parameters. Finally,by exploring four cases of the model, we find that the mass of this ULA field is about 3 × 10-33 eV if assuming the initial axion field φ_i = M_(pl). We also investigate a general case by assuming φ_i ≤ M_(pl), and find that the fitting results of φ_i/M_(pl) are consistent with or close to 1 for the datasets that we use.     

A Better Reconciliation of Hubble Tension in the Dark Energy Scalar Field

Hubble tension between the local measurement and global observation has been a key problem in cosmology. In this paper, we consider the quintessence scalar field, phantom field and quintom field as the dark energy to reconcile this problem. Different from most previous work, we start from the dimensionless equation of state(w) of dark energy, not a parameterization of potential. The combined analysis shows that observational data sets favor Hubble constant H₀ =71.3_-0.917     

Energy Buildup,Flux Confinement and Helicity Accumulation in the Solar Corona

Starting from a dipole field and a given distribution of footpoint displace- ment of field lines on the photosphere,we find axisymmetric,force-free field solutions in spherical coordinates that have the same distribution of normal field on the photo- sphere and magnetic topology as the dipole field.A photospheric shear is introduced in the azimuthal direction in a region that strides across the equator and ends at latitude γ_s.The footpoint displacement has a sine distribution in latitude and a peak amplitude of (?)_m.The magnetic energy E,azimuthal flux F_(?),and magnetic helicity H_T in the solar corona are then calculated for each force-free field solution.It is found that for a given shear region range γ_s,all of the three quantities increase monotoni- cally with increasing (?)_m.In particular,both F_(?) and H_T have a linear dependence on (?)m.When (?)_m reaches a certain critical value (?)_(mc),the force-free field loses equilib- rium,leading to a partial opening of the field and the appearance of a current sheet in the equatorial plane.At this point,E,F_(?)and H_T reach their maximum values, E_c,F_((?)c) and H_(Tc).E_c increases,and F_((?)c) and H_(Tc)decrease with decreasing λ_s.It is found that E_c is always smaller than the open field energy,in agreement with the Aly conjecture.Of the three critical parameters,E_c has the weakest dependence on λ_s.Therefore,if one is interested in the transition of a magnetic configuration from a stable state to a dynamic one,the magnetic energy is probably the most appropriate marker of the transition.     

Magnetic Energy of Force-Free Fields with Detached Field Lines

Using an axisymmetrical ideal MHD model in spherical coordinates, we present a numerical study of magnetic configurations characterized by a levitating flux rope embedded in a bipolar background field whose normal field at the solar surface is the same or very close to that of a central dipole. The characteristic plasma β (the ratio between gas pressure and magnetic pressure) is taken to be sosmall (β= 10^-4) that the magnetic field is close to being force-free. The system as a whole is then let evolve quasi-statically with a slow increase of either the annular magnetic flux or the axial magnetic flux of the rope, and the total magneticenergy of the system grows accordingly. It is found that there exists an energy threshold: the flux rope sticks to the solar surface in equilibrium if the magneticenergy of the system is below the threshold, whereas it loses equilibrium if the threshold is exceeded. The energy threshold is found to be larger than that of thecorresponding fully-open magnetic field by a factor of nearly 1.08 irrespective as towhether the background field is completely closed or partly open, or whether the magnetic energy is enhanced by an increase of annular or axial flux of the rope.This gives an example showing that a force-free magnetic field may have an energy larger than the corresponding open field energy if part of the field lines is allowed tobe detached from the solar surface. The implication of such a conclusion in coronal mass ejections is briefly discussed and some comments are made on the maximum energy of force-free magnetic fields.     

Projection Effects on Physical Parameters Obtained from Solar Vector Magnetograms

1 INTRODUCTION Magnetic field plays an important role in solar activity. The stressing and subsequent partialrelaxation of magnetic fields in the active regions are generally accepted to be the energy sourceof solar flares. To quantitatively study the extent of stressed magnetic field as distinct from itspotential field, Hagyard et al. (1984) defined a magnetic shear angle膖he azimuth differencebetween the observed transverse magnetic field vector and the computed potential field vectorth…