Determination of the Coronal and Interplanetary Magnetic Field Strength and Radial Profiles from Large-Scale Photospheric Magnetic Fields

We propose a new model for the magnetic field at different distances from the Sun during different phases of the solar cycle. The model depends on the observed large-scale non-polar (\({\pm}\, 55^{\circ }\)) photospheric magnetic field and on the magnetic field measured at polar regions from \(55^{\circ }\) N to \(90^{\circ }\) N and from \(55^{\circ }\) S to \(90^{\circ }\) S, which are the visible manifestations of cyclic changes in the toroidal and poloidal components of the global magnetic field of the Sun. The modeled magnetic field is determined as the superposition of the non-polar and polar photospheric magnetic field and considers cycle variations. The agreement between the model predictions and magnetic fields derived from direct in situ measurements at different distances from the Sun, obtained with different methods and at different solar activity phases, is quite satisfactory. From a comparison of the magnetic fields as observed and calculated from the model at 1 AU, we conclude that the model magnetic field variations adequately explain the main features of the interplanetary magnetic field (IMF) radial, \(B_{\mathrm{x}}\), component cycle evolution at Earth’s orbit. The modeled magnetic field averaged over a Carrington rotation (CR) correlates with the IMF \(B_{\mathrm{x}}\) component also averaged over a CR at Earth’s orbit with a coefficient of 0.691, while for seven CR-averaged data, the correlation reaches 0.81. The radial profiles of the modeled magnetic field are compared with those of already existing models. In contrast to existing models, ours provides realistic magnetic-field radial distributions over a wide range of heliospheric distances at different cycle phases, taking into account the cycle variations of the solar toroidal and poloidal magnetic fields. The model is a good approximation of the cycle behavior of the magnetic field in the heliosphere. In addition, the decrease in the non-polar and polar photospheric magnetic fields is shown. Furthermore, the magnetic field during solar cycle maxima and minima decreased from Cycle 21 to Cycle 24. This implies that both the toroidal and poloidal components, and therefore the solar global magnetic field, decreased from Cycle 21 to Cycle 24.     

Modeling the Global Coronal Field with Simulated Synoptic Magnetograms from Earth and the Lagrange Points $L_{3}$, L4$L_{4}$, and L5$L_{5}$

The solar photospheric magnetic flux distribution is key to structuring the global solar corona and heliosphere. Regular full-disk photospheric magnetogram data are therefore essential to our ability to model and forecast heliospheric phenomena such as space weather. However, our spatio-temporal coverage of the photospheric field is currently limited by our single vantage point at/near Earth. In particular, the polar fields play a leading role in structuring the large-scale corona and heliosphere, but each pole is unobservable for \({>}\,6\) months per year. Here we model the possible effect of full-disk magnetogram data from the Lagrange points \(L_{4}\) and \(L_{5}\), each extending longitude coverage by \(60^{\circ}\). Adding data also from the more distant point \(L_{3}\) extends the longitudinal coverage much further. The additional vantage points also improve the visibility of the globally influential polar fields. Using a flux-transport model for the solar photospheric field, we model full-disk observations from Earth/\(L_{1}\), \(L_{3}\), \(L_{4}\), and \(L_{5}\) over a solar cycle, construct synoptic maps using a novel weighting scheme adapted for merging magnetogram data from multiple viewpoints, and compute potential-field models for the global coronal field. Each additional viewpoint brings the maps and models into closer agreement with the reference field from the flux-transport simulation, with particular improvement at polar latitudes, the main source of the fast solar wind.     

Variability of the quiet photospheric network

High-resolution photographs of the photospheric network taken in the Caii K 3933 Å line and at 4308 Å are analysed in order to study the variation, in latitude and over the sunspot cycle, of its density (the density is defined as the number of network elements - also called facular points - per surface unity). It appears that the density of the photospheric network is not distributed uniformly at the surface of the Sun: on September 1983, during the declining phase of the current activity cycle, it was weakened at both the low (equatorial) and high (polar) active latitudes, while it was tremendously enhanced toward the pole. The density at the equator is varying in antiphase to the sunspot number: it increases by a factor 3 or more from maximum to minimum of activity. As a quantum of magnetic flux is associated to each network element, density variations of the photospheric network express in fact variations of the quiet Sun magnetic flux. It thus results that the quiet Sun magnetic flux is not uniformly distributed in latitude and not constant over the solar cycle: it probably varies in antiphase to the flux in active regions.The variation over the solar cycle and the latitude distribution of photospheric network density are compared to those of X-ray bright points and ephemeral active regions: there are no clear correlations between these three kinds of magnetic features.     

Ca ii Transient Brightenings Associated with Canceling Magnetic Features

We analyzed transient Ca ii H brightening associated with small-scale canceling magnetic features (CMFs) in the quiet Sun near disk center using Ca ii H filter images and Na D₁ magnetograms of Hinode/SOT. We found that in most Ca ii brightening events related to CMFs the Ca ii H intensity peaks after the magnetic flux cancellation. Moreover, the brightening tends to appear as a pair of bright points of similar size and brightness overlying a magnetic bipole. Then a new opposite polarity fragment moves to them and cancels out. These results imply that magnetic reconnection takes place there and is responsible for CMFs.     

Does the solar magnetic field increase?

We consider measurements of the general magnetic field (GMF) of the Sun as a star at four world observatories from 1968 until 1999. We show that, within the error limits, the mean strength of the photospheric magnetic field H (of its longitudinal component, in magnitude) has not changed over the last 32 years. This is in conflict with the recent conclusion by Lockwood et al. (1999) that the solar coronal magnetic field increased by 40% from 1964 until 1996 and has almost doubled in the last 100 years. The causes of discrepancies in the results are discussed. At the same time, the GMF exhibits a natural 11-year variation associated with the solar cycle. The strength of the photospheric longitudinal magnetic field (in absolute value) averaged over 32 years is 0.46 G (at an rms GMF strength of 0.57 G). The mean GMF for all years of measurements had a south polarity: $\bar H = - 0.030 \pm 0.018 G$ . The difference from zero is statistically significant at 1.7σ (90%) and may be directly related to the outstanding problem of the solar magnetic “monopole.”     

Probing the Quiet Solar Atmosphere from the Photosphere to the Corona

We investigate the morphology and temporal variability of a quiet-Sun network region in different solar layers. The emission in several extreme ultraviolet (EUV) spectral lines through both raster and slot time-series, recorded by the EUV Imaging Spectrometer (EIS) on board the Hinode spacecraft is studied along with \(\mbox{H}\upalpha\) observations and high-resolution spectropolarimetric observations of the photospheric magnetic field. The photospheric magnetic field is extrapolated up to the corona, showing a multitude of large- and small-scale structures. We show for the first time that the smallest magnetic structures at both the network and internetwork contribute significantly to the emission in EUV lines, with temperatures ranging from \(8\times 10^{4}~\mbox{K}\) to \(6\times 10^{5}~\mbox{K}\). Two components of transition region emission are present, one associated with small-scale loops that do not reach coronal temperatures, and another component that acts as an interface between coronal and chromospheric plasma. Both components are associated with persistent chromospheric structures. The temporal variability of the EUV intensity at the network region is also associated with chromospheric motions, pointing to a connection between transition region and chromospheric features. Intensity enhancements in the EUV transition region lines are preferentially produced by \(\mbox{H}\upalpha\) upflows. Examination of two individual chromospheric jets shows that their evolution is associated with intensity variations in transition region and coronal temperatures.     

Polarity Reversal Time of the Magnetic Dipole Component of the Sun in Solar Cycle 24

The Sun’s general magnetic field has shown polarity reversal three times during the last three solar cycles. We attempt to estimate the upcoming polarity reversal time of the solar magnetic dipole by using the coronal field model and synoptic data of the photospheric magnetic field. The scalar magnetic potential of the coronal magnetic field is expanded into a spherical harmonic series. The long-term variations of the dipole component ( $g^{0}_{1}$ ) calculated from the data of National Solar Observatory/Kitt Peak and Wilcox Solar Observatory are compared with each other. It is found that the two $g^{0}_{1}$ values show a similar tendency and an approximately linear increase between the Carrington rotation periods CR 2070 and CR 2118. The next polarity reversal is estimated by linear extrapolation to be between CR 2132.2 (December 2012) and CR2134.8 (March 2013).     

Solar Magnetic Carpet III: Coronal Modelling of Synthetic Magnetograms

This article is the third in a series working towards the construction of a realistic, evolving, non-linear force-free coronal-field model for the solar magnetic carpet. Here, we present preliminary results of 3D time-dependent simulations of the small-scale coronal field of the magnetic carpet. Four simulations are considered, each with the same evolving photospheric boundary condition: a 48-hour time series of synthetic magnetograms produced from the model of Meyer et al. (Solar Phys. 272, 29, 2011). Three simulations include a uniform, overlying coronal magnetic field of differing strength, the fourth simulation includes no overlying field. The build-up, storage, and dissipation of magnetic energy within the simulations is studied. In particular, we study their dependence upon the evolution of the photospheric magnetic field and the strength of the overlying coronal field. We also consider where energy is stored and dissipated within the coronal field. The free magnetic energy built up is found to be more than sufficient to power small-scale, transient phenomena such as nanoflares and X-ray bright points, with the bulk of the free energy found to be stored low down, between 0.5?–?0.8 Mm. The energy dissipated is currently found to be too small to account for the heating of the entire quiet-Sun corona. However, the form and location of energy-dissipation regions qualitatively agree with what is observed on small scales on the Sun. Future MHD modelling using the same synthetic magnetograms may lead to a higher energy release.     

The Number of Magnetic Null Points in the Quiet Sun Corona

The coronal magnetic field above a particular photospheric region will vanish at a certain number of points, called null points. These points can be found directly in a potential field extrapolation or their density can be estimated from the Fourier spectrum of the magnetogram. The spectral estimate, in which the extrapolated field is assumed to be random and homogeneous with Gaussian statistics, is found here to be relatively accurate for quiet Sun magnetograms from SOHO’s MDI. The majority of null points occur at low altitudes, and their distribution is dictated by high wavenumbers in the Fourier spectrum. This portion of the spectrum is affected by Poisson noise, and as many as five-sixths of null points identified from a direct extrapolation can be attributed to noise. The null distribution above 1500 km is found to depend on wavelengths that are reliably measured by MDI in either its low-resolution or high-resolution mode. After correcting the spectrum to remove white noise and compensate for the modulation transfer function we find that a potential field extrapolation contains, on average, one magnetic null point, with altitude greater than 1.5 Mm, above every 322 Mm² patch of quiet Sun. Analysis of 562 quiet Sun magnetograms spanning the two latest solar minima shows that the null point density is relatively constant with roughly 10% day-to-day variation. At heights above 1.5 Mm, the null point density decreases approximately as the inverse cube of height. The photospheric field in the quiet Sun is well approximated as that from discrete elements with mean flux 〈|φ|〉=1.0×10¹⁹ Mx distributed randomly with density n=0.007 Mm⁻².     

High-Resolution Vector Magnetograms of the Sun’s Poles from Hinode: Flux Distributions and Global Coronal Modeling

The Sun’s polar fields play a leading role in structuring the large-scale solar atmosphere and in determining the interplanetary magnetic field. They are also believed to supply the seed field for the subsequent solar activity cycle. However, present-day synoptic observations do not have sufficient spatial resolution or sensitivity to diagnose accurately the high-latitude magnetic vector field. The high spatial resolution and sensitivity of the full-Stokes observations from the Hinode Solar Optical Telescope Spectro-Polarimeter, observing the poles long-term, allows us to build up a detailed picture of the Cycle 24 polar field reversal, including the changing latitude distribution of the high-latitude flux, and to study the effect on global coronal field models. The Hinode observations provide detailed information on the dominant facular-scale magnetic structure of the polar fields, and their field inclination and flux distribution. Hybrid synoptic magnetograms are constructed from Hinode polar measurements and full-disk magnetograms from the Synoptic Optical Long-term Investigations of the Sun (SOLIS) Vector Spectro-Magnetograph (VSM), and coronal potential field models are calculated. Loss of effective spatial resolution at the highest latitudes presents complications. Possible improvements to synoptic polar data are discussed.     

Granular-Scale Elementary Flux Emergence Episodes in a Solar Active Region

We analyse data from Hinode spacecraft taken over two 54-minute periods during the emergence of AR 11024. We focus on small-scale portions within the observed solar active region and discover the appearance of very distinctive small-scale and short-lived dark features in Ca ii H chromospheric filtergrams and Stokes I images. The features appear in regions with close-to-zero longitudinal magnetic field, and are observed to increase in length before they eventually disappear. Energy release in the low chromospheric line is detected while the dark features are fading. Three complete series of these events are detected with remarkably similar properties, i.e. lifetime of ≈ 12 min, maximum length and area of 2 – 4 Mm and 1.6 – 4 Mm², respectively, and all with associated brightenings. In time series of magnetograms a diverging bipolar configuration is observed accompanying the appearance of the dark features and the brightenings. The observed phenomena are explained as evidencing elementary flux emergence in the solar atmosphere, i.e. small-scale arch filament systems rising up from the photosphere to the lower chromosphere with a length scale of a few solar granules. Brightenings are explained as being the signatures of chromospheric heating triggered by reconnection of the rising loops (once they have reached chromospheric heights) with pre-existing magnetic fields, as well as being due to reconnection/cancellation events in U-loop segments of emerging serpentine fields. The characteristic length scale, area and lifetime of these elementary flux emergence events agree well with those of the serpentine field observed in emerging active regions. We study the temporal evolution and dynamics of the events and compare them with the emergence of magnetic loops detected in quiet Sun regions and serpentine flux emergence signatures in active regions. The physical processes of the emergence of granular-scale magnetic loops seem to be the same in the quiet Sun and active regions. The difference is the reduced chromospheric emission in the quiet Sun attributed to the fact that loops are emerging in a region of lower ambient magnetic field density, making interactions and reconnection less likely to occur. Incorporating the novel features of granular-scale flux emergence presented in this study, we advance the scenario for serpentine flux emergence.     

Detection of small scale structure in metal lines at the extreme solar limb

We describe a tangential limb spectrum at 5870 Å which geometrically probes the high photosphere through the low chromosphere. Velocity and brightness structures with sizes ranging from 500 to 1500 km are present in the stronger emission lines. Such structure is consistent between the Fe i and Ba ii lines, and emission knots in these lines coincide with continuum bright streaks. But no correlation is evident between structure in the He i D₃ line, emission in the Na i D₂ line, and emission in the Fe i and Ba ii lines as a group. Two classes of near-horizontal velocity structure are seen in the height range from 0 to 500 km above the limb: υ ? 1 km s^?1 for the weaker metals and υ ～ 7–10 km s^?1 for the Na i line. Differences in line opacity are suggested as the cause of the low correlation between the fine structure in the various lines.

     

High resolution spectroscopy of the disk chromosphere

We describe time-series observations of small-scale Ca ii emission features located outside the network in the quiet chromosphere. Simultaneous spectra in K and λ 8542 show unambiguously that the evolutionary behaviour of the K-line profile due to an outwardly propagating velocity pulse. Assuming that this pulse is a progressive acoustic wave, as suggested by the inferred flow parameters, we show that the wave loses mechanical energy in traversing the chromosphere. This implies that the bright Ca ii features (K-grains) are the manifestation of local heating in the chromosphere, possibly by shock waves.

     

Fine structures of chromospheric magnetic field and material flow in a solar active region

In this paper, we analyze the relations between photospheric vector magnetic fields, chromospheric longitudinal magnetic fields and velocity fields in a solar active region. Agreements between the photospheric and chromospheric magnetograms can be found in large-scale structures or in the stronger magnetic structures, but differences also can be found in the fine structures or in other places, which reflect the variation of the magnetic force lines from the photosphere to the chromosphere. The chromospheric superpenumbral magnetic field, measured by the Hline, presents a spoke-like structure. It consists of thick magnetic fibrils which are different from photospheric penumbral magnetic fibrils. The outer superpenumbral magnetic field is almost horizontal. The direction of the chromospheric magnetic fibrils is generally parallel to the transverse components of the photospheric vector magnetic fields. The chromospheric material flow is coupled with the magnetic field structure. The structures of the H chromospheric magnetic fibrils in the network are similar to H dark fibrils, and the feet of the magnetic fibrils are located at the photospheric magnetic elements.     

Sunspots and large-scale magnetic fields at various heights

Height variation of the magnetic field structure over groups of sunspots for heights ranging from the photosphere to the source surface (R = 2.5 Ro, where Ro is the radius of the Sun) is examined. For all heights, starting from the photospheric level, groups of sunspot are shown as being independent of long-lived boundaries of large-scale structures rotating with a period shorter than the Carrington period. At heights of 1–1.5 Ro, there is a clear relation between sunspot groups and boundaries separating the head and tail sunspots in the groups (the Hale boundaries). The rotation periods of these structures are close to the Carrington period, their lifespan being less than three to five rotations. The maximal intensity of the solar magnetic field drops by two orders when height increases from H = 1 to H = 1.1 Ro. Further decrease in intensity proceeds gradually (dropping by one order from H = 1.1 to 2.5 Ro). The results obtained can be considered as evidence that large-scale magnetic field structures and long-lived boundries between them (the lines dividing polarities of the magnetic field or zero lines) all exist irrespective of sunspot fields being generated by other sources than sunspots. At the photospheric level, active regions fields are superimposed on these structures.     

The evolution of the photospheric network

A time-lapse sequence of spectroheliograms in the bandhead of CN at λ3883 reveals the following behavior of the photospheric network with time:

1. There is a steady flow of bright ‘points’ (? 1000 km in diameter) laterally outward from sunspots at speeds on the order of 1 km·sec^?1. After traveling about 10 000 km from a sunspot they either conglomerate to form fragments of the photospheric network or disappear.
2. Spatial changes in the network pattern seem to take place by means of the shifting of network fragments laterally on the solar surface. Although most small-scale details are recognizable after 5–10 minutes, within 30 minutes nearly all the details have changed completely. In contrast to this, the large-scale network pattern seems relatively unchanged after 2 1/2 hours.
3. Occasionally ‘new’ network, not resulting from the lateral motion of bright features from either previously existing network or sunspots, appears on the solar surface. This process consists of the formation in approximately 10 minutes of bright points and a darker-than-average feature between them. The dark feature disappears in another 5–10 minutes and the bright points separate at a relative speed of a few km·sec^?1. If the event is of a sufficiently large magnitude, a sunspot will appear.

These observed changes of the photospheric network with time are interpreted as formation and motions of photospheric magnetic fields. It is suggested that these motions reflect the presence of both short-lived small-scale and long-lived large-scale photospheric currents such as one might expect from the granulation and the supergranulation.     

Relative Velocities and Linewidths in a Coronal Hole and Outside

Relative Doppler velocities and spectral linewidths in a coronal hole and in the quiet Sun region outside have been obtained from Solar and Heliospheric Observatory (SOHO)/Coronal Diagnostic Spectrometer (CDS) observations. Five strong emission lines in the CDS wavelength range (namely, O? iii 599 Å, O?v 630 Å, Ne?vi 562.8 Å, He?ii 304 Å, and Mg?ix 368 Å), whose formation temperatures represent different heights in the solar atmosphere from the lower transition region to the inner corona, have been used in the study. As reported earlier, relative velocities in the coronal hole are generally blueshifted with respect to the quiet Sun, and the magnitude of the blueshifts increases with height. It has been found that the polar coronal hole has larger relative velocities than the equatorial extension in the inner corona. Several localized velocity contours have been found mainly on network brightenings and in the vicinity of the coronal hole boundary. The presence of velocity contours on the network may represent network outflows whereas the latter could be due to localized jets probably arising from magnetic reconnection at the boundary. All spectral lines have larger widths in the coronal hole than in the quiet Sun. In O?v 630 Å an extended low-linewidth region is seen in the coronal hole?–?quiet Sun boundary, which may indicate fresh mass transfer across the boundary. Also polar coronal holes have larger linewidths in comparison with the equatorial extension. Together with larger relative velocities, this suggests that the solar wind emanating from polar hole regions is faster than that from equatorial hole regions.     

Small-Scale Energy Release Driven by Supergranular Flows on the Quiet Sun

We present data and modelling for the quiet Sun that strongly suggest a ubiquitous small-scale atmospheric heating mechanism that is driven solely by converging supergranular flows. A possible energy source for such events is the power transfer to the plasma via the work done on the magnetic field by photospheric convective flows, which exert drag on the footpoints of magnetic structures. We present evidence of small-scale energy release events driven directly by the hydrodynamic forces that act on the magnetic elements in the photosphere, as a result of supergranular-scale flows. We show strong spatial and temporal correlation between quiet-Sun soft X-ray emission (from Yohkoh SXT) and SOHO MDI-derived flux removal events driven by deduced photospheric flows. We also present a simple model of heating generated by flux submergence, based on particle acceleration by converging magnetic mirrors. In the near future, high resolution soft X-ray images from XRT on the Hinode satellite will allow definitive, quantitative verification of our results. Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users.     

A Possible Cause of the Diminished Solar Wind During the Solar Cycle 23 – 24 Minimum

Interplanetary magnetic field and solar wind plasma density observed at 1 AU during Solar Cycle 23?–?24 (SC-23/24) minimum were significantly smaller than those during its previous solar cycle (SC-22/23) minimum. Because the Earth’s orbit is embedded in the slow wind during solar minimum, changes in the geometry and/or content of the slow wind region (SWR) can have a direct influence on the solar wind parameters near the Earth. In this study, we analyze solar wind plasma and magnetic field data of hourly values acquired by Ulysses. It is found that the solar wind, when averaging over the first (1995.6?–?1995.8) and third (2006.9?–?2008.2) Ulysses’ perihelion (\({\sim}\,1.4~\mbox{AU}\)) crossings, was about the same speed, but significantly less dense (\({\sim}\,34~\%\)) and cooler (\({\sim}\,20~\%\)), and the total magnetic field was \({\sim}\,30~\%\) weaker during the third compared to the first crossing. It is also found that the SWR was \({\sim}\,50~\%\) wider in the third (\({\sim}\,68.5^{\circ}\) in heliographic latitude) than in the first (\({\sim}\,44.8^{\circ}\)) solar orbit. The observed latitudinal increase in the SWR is sufficient to explain the excessive decline in the near-Earth solar wind density during the recent solar minimum without speculating that the total solar output may have been decreasing. The observed SWR inflation is also consistent with a cooler solar wind in the SC-23/24 than in the SC-22/23 minimum. Furthermore, the ratio of the high-to-low latitude photospheric magnetic field (or equatorward magnetic pressure force), as observed by the Mountain Wilson Observatory, is smaller during the third than the first Ulysses’ perihelion orbit. These findings suggest that the smaller equatorward magnetic pressure at the Sun may have led to the latitudinally-wider SRW observed by Ulysses in SC-23/24 minimum.     

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.