Modelling the Coupling Role of Magnetic Fields in Helioseismology

Helioseismic global modes change in time, in particular on time scales of the solar cycle. These changes show, in fact, strong correlation with the magnetic activity cycle of the Sun, indicating that a most likely cause of the variation of the mode characteristics, such as frequency, is the magnetic field. In the present paper I attempt to find out in what ways and to what degree the magnetic atmosphere of the Sun can influence the f and p modes of helioseismology. Frequency shifts of the order of a microhertz, line widths of the order of a nanohertz, and penetration depths of the order of a megameter are obtained.     

Solar p and g modes in a model with a convection layer above a sub-adiabatic interior

We study high-order acoustic modes which reside in the outer layers of the solar interior. Magnetic field effects are not taken into account in this paper as we wish first to filter out how the modal frequencies depend on physical characteristics of a particular model structure of the Sun. In particular, we are interested in how the modal frequencies of solar global oscillations depend on the thickness of the convection layer and on the temperature gradient of the solar interior below. The model we use consists of three planar layers: an isothermal atmosphere, while the convection layer and the interior have temperature gradients that are adiabatic and sub-adiabatic, respectively. The presence of a convection layer with a finite thickness brings in additional modes while the variations in temperature gradient of the interior cause shifts in eigenfrequencies that are more pronounced for the p modes than for the g modes. These shifts can easily be of the order of several hundreds of Hz, which is much larger than the observational accuracy.     

First order latitude effects in the solar wind

The Weber-Davis model of the solar wind is generalized to include the effects of latitude. The principal assumptions of perfect electrical conductivity, rotational symmetry, a polytropic relation between pressure and density, and a flow aligned magnetic field in a system rotating with the Sun, are retained. A flow aligned magnetic field in the rotating system may be expressed in terms of the flow velocity and density. Rotational symmetry fixes the longitudinal flow velocity V_φ in terms of the flow in the r?θ plane. Thus, the original three dimensional magnetohydrodynamic flow problem is reduced to a two dimensional hydrodynamic flow problem in the r?θ plane.There are three critical surfaces associated with the equations which supply conditions to determine three of six required boundary conditions. The specified boundary conditions at the base of the corona are the temperature, density, and magnitude of the magnetic field. The equations are then expanded about the radial, nonrotating Parker solution and an analytic solution is obtained for the resulting first order equations. The results show that for constant coronal boundary conditions there is a latitudinal flow toward the solar poles, as a result of magnetic stresses, which persists out to large distances for the Sun. Associated with this flow is a latitudinal component of the magnetic field. The radial flow parameters are, to within small first order differences, in agreement with those of the Parker and the Weber-Davis models of the solar wind.The equations are further generalized to permit first order latitudinal variations in the specified coronal boundary conditions. Results at 1 a.u. are presented for 5 per cent latitudinal differences between the equatorial and polar values. These results show that the solution at 1 a.u. is most sensitive to a latitudinal dependence in the boundary temperature and least sensitive to a latitudinal dependence in the magnetic field magnitude.A solution is then obtained for an approximate dipolar variation in the coronal magnetic field magnitude. This solution predicts that the latitudinal flow is initially toward the Equator due to magnetic channeling; however, this effect is rapidly overcome and the latitudinal flow at 1 a.u. is toward the pole and not significantly different from the solution for constant boundary conditions.     

Acoustic Mode Frequencies of the Sun During the Minimum Phase Between Solar Cycles 23 and 24

We investigate the spatial and temporal variations of the high-degree mode frequencies calculated over localized regions of the Sun during the extended minimum phase between solar cycles 23 and 24. The frequency shifts measured relative to the spatial average over the solar disk indicate that the correlation between the frequency shift and magnetic field strength during the low-activity phase is weak. The disk-averaged frequency shifts computed relative to a minimal activity period also reveal a moderate correlation with different activity indices, with a maximum linear correlation of about 72?%. From the investigation of the frequency shifts at different latitudinal bands, we do not find a consensus period for the onset of solar cycle 24. The frequency shifts corresponding to most of the latitudes in the northern hemisphere and 30° south of the equator indicate the minimum epoch to be February 2008, which is earlier than inferred from solar activity indices.     

Distribution of magnetic flux on the solar surface and low-degree p-modes

The frequencies of solar p-modes are known to change over the solar cycle. There is also recent evidence that the relation between frequency shift of low-degree modes and magnetic flux or other activity indicators differs between the rising and falling phases of the solar cycle, leading to a hysteresis in such diagrams. We consider the influence of the changing large-scale surface distribution of the magnetic flux on low-degree ( l ≤3) p-mode frequencies. To that end, we use time-dependent models of the magnetic flux distribution and study the ensuing frequency shifts of modes with different order and degree as a function of time. The resulting curves are periodic functions (in simple cases just sine curves) shifted in time by different amounts for the different modes. We show how this may easily lead to hysteresis cycles comparable to those observed. Our models suggest that high-latitude fields are necessary to produce a significant difference in hysteresis between odd- and even-degree modes. Only magnetic field distributions within a small parameter range are consistent with the observations by Jiménez-Reyes et al. Observations of p-mode frequency shifts are therefore capable of providing an additional diagnostic of the magnetic field near the solar poles. The magnetic distribution that is consistent with the p-mode observations also appears reasonable compared with direct measurements of the magnetic field.     

Mapping Solar Wind Streams from the Sun to 1 AU: A Comparison of Techniques

A variety of techniques exist for mapping solar wind plasma and magnetic field measurements from one location to another in the heliosphere. Such methods are either applied to extrapolate solar data or coronal model results from near the Sun to 1 AU (or elsewhere), or to map in-situ observations back to the Sun. In this study, we estimate the sensitivity of four models for evolving solar wind streams from the Sun to 1 AU. In order of increasing complexity, these are: i) ballistic extrapolation; ii) ad hoc kinematic mapping; iii) 1-D upwinding propagation; and iv) global heliospheric MHD modeling. We also consider the effects of the interplanetary magnetic field on the evolution of the stream structure. The upwinding technique is a new, simplified method that bridges the extremes of ballistic extrapolation and global heliospheric MHD modeling. It can match the dynamical evolution captured by global models, but is almost as simple to implement and as fast to run as the ballistic approximation.     

The pulses as a diagnostic technique in the Sun

In this paper we discuss a method of finding physical parameters by studying the pulses in the Sun. For the sake of a mathematical approach, we consider an ideal,highly relevant model which could exist in the Sun with the effects of ionization, due to which there will be a continuous formation of ionized particles. It is observed that the pulse originated at the centre of a dipole field propagates along the magnetic field. We derive a dispersion relation for these types of pulses, propagating from the centre to the solar surface. The time taken by the pulse from its source to the solar surface is also estimated, with due account of the ionization effects on the pulse. Without proper account of these effects, the technique employed in determing the physical parameters may lead to error. Temporal and spatial damping of the pulses lead to estimates of the velocity distribution of the ionized particles and of the amplitude of the magnetic field of the wave in pulse.     

DeepSun:machine-learning-as-a-service for solar flare prediction

Solar flare prediction plays an important role in understanding and forecasting space weather.The main goal of the Helioseismic and Magnetic Imager(HMI), one of the instruments on NASA's Solar Dynamics Observatory, is to study the origin of solar variability and characterize the Sun's magnetic activity.HMI provides continuous full-disk observations of the solar vector magnetic field with high cadence data that lead to reliable predictive capability; yet, solar flare prediction effort utilizing these data is still limited. In this paper, we present a machine-learning-as-a-service(MLaa S) framework, called Deep Sun,for predicting solar flares on the web based on HMI's data products. Specifically, we construct training data by utilizing the physical parameters provided by the Space-weather HMI Active Region Patch(SHARP)and categorize solar flares into four classes, namely B, C, M and X, according to the X-ray flare catalogs available at the National Centers for Environmental Information(NCEI). Thus, the solar flare prediction problem at hand is essentially a multi-class(i.e., four-class) classification problem. The Deep Sun system employs several machine learning algorithms to tackle this multi-class prediction problem and provides an application programming interface(API) for remote programming users. To our knowledge, Deep Sun is the first MLaa S tool capable of predicting solar flares through the internet.     

Simulation of the Unusual Solar Minimum with 3D SIP-CESE MHD Model by Comparison with Multi-Satellite Observations

The observations both near the Sun and in the heliosphere during the activity minimum between solar cycles 23 and 24 exhibit different phenomena from those typical of the previous solar minima. In this paper, we have chosen Carrington rotation 2070 in 2008 to investigate the properties of the background solar wind by using the three-dimensional (3D) Solar?CInterPlanetary Conservation Element/Solution Element Magnetohydrodynamic (MHD) model. We also study the effects of polar magnetic fields on the characteristics of the solar corona and the solar wind by conducting simulations with an axisymmetric polar flux added to the observed magnetic field. The numerical results are compared with the observations from multiple satellites, such as the Solar and Heliospheric Observatory (SOHO), Ulysses, Solar Terrestrial Relations Observatory (STEREO), Wind and the Advanced Composition Explorer (ACE). The comparison demonstrates that the first simulation with the observed magnetic fields reproduces some observed peculiarities near the Sun, such as relatively small polar coronal holes, the presence of mid- and low-latitude holes, a tilted and warped current sheet, and the broad multiple streamers. The numerical results also capture the inconsistency between the locus of the minimum wind speed and the location of the heliospheric current sheet, and predict slightly slower and cooler polar streams with a relatively smaller latitudinal width, broad low-latitude intermediate-speed streams, and globally weak magnetic field and low density in the heliosphere. The second simulation with strengthened polar fields indicates that the weak polar fields in the current minimum play a crucial role in determining the states of the corona and the solar wind.     

On Absorption and Scattering of P Modes by Small-Scale Magnetic Elements

The solar surface is characterised everywhere by the presence of small-scale magnetic structures. Their collective behaviour in the form of active regions is known to have strong influence on p-mode power. For example, sunspots and plages are strong absorbers of acoustic waves. This paper studies the effects of individual small-scale magnetic elements to understand the details of absorption of p-mode power. For this, we consider a thin magnetic flux tube and calculate the phase shifts and the absorption coefficients by numerically solving the linearised MHD equations. The phase shifts calculated from the Born Approximation are then compared for the same range of degrees. The results are discussed with a view to understanding the physical mechanism.     

Variations of Magnetic Bright Point Properties with Longitude and Latitude as Observed by Hinode/SOT G-band Data

Small-scale magnetic fields can be observed on the Sun in high-resolution G-band filtergrams as magnetic bright points (MBPs). We study Hinode/Solar Optical Telescope (SOT) longitude and latitude scans of the quiet solar surface taken in the G-band in order to characterise the centre-to-limb dependence of MBP properties (size and intensity). We find that the MBP’s sizes increase and their intensities decrease from the solar centre towards the limb. The size distribution can be fitted using a log–normal function. The natural logarithm of the mean (μ parameter) of this function follows a second-order polynomial and the generalised standard deviation (σ parameter) follows a fourth-order polynomial or equally well (within statistical errors) a sine function. The brightness decrease of the features is smaller than one would expect from the normal solar centre-to-limb variation; that is to say, the ratio of a MBP’s brightness to the mean intensity of the image increases towards the limb. The centre-to-limb variations of the intensities of the MBPs and the quiet-Sun field can be fitted by a second-order polynomial. The detailed physical process that results in an increase of a MBP’s brightness and size from Sun centre to the limb is not yet understood and has to be studied in more detail in the future.     

Multiparameter Computations of Solar Wind Characteristics in the Near-Earth Space from the Data on the Solar Magnetic Field

The solar wind parameters were analyzed using the concept which is being developed by the authors and assumes the existence of several systems of magnetic fields of different scales on the Sun. It was demonstrated that the simplest model with one source surface and a radial expansion does not describe the characteristics of the quiet solar wind adequately. Different magnetic field subsystems on the Sun affect the characteristics of the solar wind plasma in a different way, even changing the sign of correlation. New multiparameter schemes were developed to compute the velocity and the magnetic field components of the solar wind. The radial component of the magnetic field in the solar corona and the tilt of the heliospheric current sheet, which determines the degree of divergence of field lines in the heliosphere, were taken into account when calculating the magnetic field in the solar wind. Both the divergence of field lines in the corona and the strength of the solar magnetic field are allowed for in calculating the solar wind speed. The suggested schemes provide a considerably higher computation accuracy than that given by commonly used one-parameter models.     

Imbalance of magnetic fields on the Sun

Differences of magnetic field flows of “+” and “?” polarities, i.e. the imbalance of magnetic fields for 26 years—from January 1, 1977, to September 30, 2003—are investigated,. The synoptic maps of the longitudinal vector of Sun’s magnetic field strength obtained at the Kitt Peak National Observatory (United States) and kindly given to us by Dr. J. Harvey have served as the initial material. The imbalance of magnetic fields’ cyclicity features and the deviations from the dipole structure of Sun’s magnetic field are determined. The contribution of latitude zones and fields of various strength into the general magnetic flux from the Sun is found. The latter characteristic was compared with the Sun’s mean magnetic field (MMF) obtained from the observations of the Sun as a star (Kotov et al., 2002; Kotov, 2008). The obtained results testify that the imbalance is one of physical characteristics of the Sun. The confirmations of this conclusion are the strict regularities of the Sun’s dipole structure changing; the complicated character of the imbalance cyclicity, i.e., the multiplicity of cycles; the solar nature of MMF changing; and the distinction between two classes of magnetic fields in the imbalance characteristics.     

Gamma-ray lines and neutrons from solar flares

An analysis, with a representative (canonical) example of solar-flare-generated equatorial disturbances, is presented for the temporal and spatial changes in the solar wind plasma and magnetic field environment between the Sun and one astronomical unit (AU). Our objective is to search for first order global consequences rather than to make a parametric study. The analysis - an extension of earlier planar studies - considers all three plasma velocity and magnetic field components (V _r, V_φ, V₀, and B _r, B₀, B_φ) in any convenient heliospheric plane of symmetry such as the ecliptic plane, the solar equatorial plane, or the heliospheric equatorial plane chosen for its ability (in a tilted coordinate system) to order northern and southern hemispheric magnetic topology and latitudinal solar wind flows. Latitudinal velocity and magnetic field gradients in and near the plane of symmetry are considered to provide higher-order corrections of a specialized nature and, accordingly, are neglected, as is dissipation, except at shock waves. The representative disturbance is examined for the canonical case in which one describes the temporal and spatial changes in a homogeneous solar wind caused by a solar-flare-generated shock wave. The ‘canonical’ solar flare is assumed to produce a shock wave that has a velocity of 1000 km s^#X2212;1 at 0.08 AU. We have examined all plasma and field parameters at three radial locations: central meridian and 33° W and 90° W of the flare's central meridian. A higher shock velocity (3000 km s^#X2212;1) was also used to demonstrate the model's ability to simulate a strongly-kinked interplanetary field. Among the global (first-order) results are the following: (i) incorporation of a small meridional magnetic field in the ambient magnetic spiral field has negligible effect on the results; (ii) the magnetic field demonstrates strong kinking within the interplanetary shocked flow, even reversed polarity that - coupled with low temperature and low density - suggests a viable explanation for observed ‘magnetic clouds’ with accompanying double-streaming of electrons at directions ～ 90° to the heliocentric radius.     

A paradox in measuring the magnetic field of the Sun

Significant discrepancies are often observed among the values of the mean magnetic field (MMF) of the Sun as a star observed by various instruments using various spectral lines. This is conventionally attributed to the measurement errors and “saturation” of a solar magnetograph in fine-structure photospheric elements with a strong magnetic field. Measurements of the longitudinal MMF performed in 1968–2006 at six observatories are compared in this paper. It is shown that the degree of discrepancy (slopes b of linear regression lines) varies significantly over the phase of the 11-year cycle. This gives rise to a paradox: the magnetograph calibration is affected by the state of the Sun itself. The proposed explanation is based on quantum properties of light, namely, nonlocality and “coupling” of photons whose polarization at the telescope-spectrograph output is determined by spacious parts of the solar disk. In this case, the degree of coupling, or “identity,” of photons depends on the field distribution in the photosphere and the instrument design (as Bohr said, “the instrument inevitably affects the result”). The “puzzling” values of slope b are readily explained by the dependence of the coupling on the solar-cycle phase. The very statistical nature of light makes discrepancies unavoidable and requires the simple averaging of data to obtain the best approximation of the actual MMF. A 39-year time series of the MMF absolute value is presented, which is indicative of significant variations in the magnitude of the solar magnetic field with a cycle period of 10.5(7) yr.     

The Global Context of Solar Activity During the Whole Heliosphere Interval Campaign

The Whole Heliosphere Interval (WHI) was an international observing and modeling effort to characterize the 3-D interconnected ??heliophysical?? system during this solar minimum, centered on Carrington Rotation 2068, March 20??C?April 16, 2008. During the latter half of the WHI period, the Sun presented a sunspot-free, deep solar minimum type face. But during the first half of CR 2068 three solar active regions flanked by two opposite-polarity, low-latitude coronal holes were present. These departures from the quiet Sun led to both eruptive activity and solar wind structure. Most of the eruptive activity, i.e., flares, filament eruptions and coronal mass ejections (CMEs), occurred during this first, active half of the interval. We determined the source locations of the CMEs and the type of associated region, such as active region, or quiet sun or active region prominence. To analyze the evolution of the events in the context of the global solar magnetic field and its evolution during the three rotations centered on CR 2068, we plotted the CME source locations onto synoptic maps of the photospheric magnetic field, of the magnetic and chromospheric structure, of the white light corona, and of helioseismological subsurface flows. Most of the CME sources were associated with the three dominant active regions on CR 2068, particularly AR 10989. Most of the other sources on all three CRs appear to have been associated with either isolated filaments or filaments in the north polar crown filament channel. Although calculations of the flux balance and helicity of the surface magnetic features did not clearly identify a dominance of one region over the others, helioseismological subsurface flows beneath these active regions did reveal a pronounced difference among them. These preliminary results suggest that the ??twistedness?? (i.e., vorticity and helicity) of subsurface flows and its temporal variation might be related to the CME productivity of active regions, similar to the relationship between flares and subsurface flows.     

Large-Scale Magnetic Field of the Sun and Evolution of Sunspot Activity

The evolution of the large-scale magnetic field of the Sun has been studied using an algorithm of tomographic inversion. By analyzing line-of-sight magnetograms, we mapped the radial and toroidal components of the Sun??s large-scale magnetic field. The evolution of the radial and toroidal magnetic field components in the 11-year solar cycle has been studied in a time?Clatitude aspect. It is shown that the toroidal magnetic field of the Sun is causally related to sunspot activity; i.e., the sunspot formation zones drift in latitude and follow the toroidal magnetic fields. The results of our analysis support the idea that the high-latitude toroidal magnetic fields can serve as precursors of sunspot activity. The toroidal fields in the current cycle are anomalously weak and also show a barely noticeable equatorward drift. This behavior of the toroidal magnetic field suggests low activity levels in the current cycle and in the foreseeable future.     

On Hoyle's theory of the origin of the solar system

A quantitative re-formulation of Hoyle's theory on the formation of the solar system is attempted, according to a three-dimensional scheme based on the assumption that the original magnetic field of the star is a dipole field. This allows us to obtain analytic expressions for the main paraeters describing the different phases of the process. The protostar is assumed to evolve in gravitational contraction along the Hayashi track, along which, for a given value of the radiusR ₀ depending on the total angular momentum, matter begins to be shed at the equator as a consequence of centrifugal instability. However, owing to the geometry of the dipole field and to Hoyle's assumption that, for a star with a convective envelope, the sign of the inward magnetic pressure determines whether the magnetic lines do wind up or not, it turns out that the magnetic coupling between the star and the disk formed at the equator starts only when the radius of the contracting star has reached the value ofR _s=4/5R ₀; and that the shedding of matter stops for a radius valueR d, depending on the strength of the magnetic field. One is thus able to calculate the total quantity of matter emitted at the solar equator and the distance reached by the rings thus formed as functions of the radius of the star, of the initial values of the magnetic field, of the total angular momentum and of the structural factors of the star. The quantitative results are discussed in order to see whether it is possible to deduce the main characteristics of the disk, from which the solar system should have originated, for reasonable values of these main parameters.     

Evolution of the Fine Structure of Magnetic Fields in the Quiet Sun: Observations from Sunrise/IMaX and Extrapolations

Observations with the balloon-borne Sunrise/Imaging Magnetograph eXperiment (IMaX) provide high spatial resolution (roughly 100 km at disk center) measurements of the magnetic field in the photosphere of the quiet Sun. To investigate the magnetic structure of the chromosphere and corona, we extrapolate these photospheric measurements into the upper solar atmosphere and analyze a 22-minute long time series with a cadence of 33 seconds. Using the extrapolated magnetic-field lines as tracer, we investigate temporal evolution of the magnetic connectivity in the quiet Sun’s atmosphere. The majority of magnetic loops are asymmetric in the sense that the photospheric field strength at the loop foot points is very different. We find that the magnetic connectivity of the loops changes rapidly with a typical connection recycling time of about 3±1 minutes in the upper solar atmosphere and 12±4 minutes in the photosphere. This is considerably shorter than previously found. Nonetheless, our estimate of the energy released by the associated magnetic-reconnection processes is not likely to be the sole source for heating the chromosphere and corona in the quiet Sun.