An Evolving Synoptic Magnetic Flux map and Implications for the Distribution of Photospheric Magnetic Flux

We describe a procedure intended to produce accurate daily estimates of the magnetic flux distribution on the entire solar surface. Models of differential rotation, meridional flow, supergranulation, and the random emergence of background flux elements are used to regularly update unobserved or poorly observed portions of an initial traditional magnetic synoptic map that acts as a seed. Fresh observations replace model estimates when available. Application of these surface magnetic transport models gives us new insight into the distribution and evolution of magnetic flux on the Sun, especially at the poles where canopy effects, limited spatial resolution, and foreshortening result in poor measurements. We find that meridional circulation has a considerable effect on the distribution of polar magnetic fields. We present a modeled polar field distribution as well as time series of the difference between the northern and southern polar magnetic flux; this flux imbalance is related to the heliospheric current sheet tilt. We also estimate that the amount of new background magnetic flux needed to sustain the `quiet-Sun' magnetic field is about 1.1×10²³ Mx d^–1 (equivalent to several large active regions) at the spatial resolution and epoch of our maps. We comment on the diffusive properties of supergranules, ephemeral regions, and intranetwork flux. The maps are available on the NSO World Wide Web page.     

Mid-Term Periodicities in the Solar Magnetic Flux

In this paper we report an analysis of the solar magnetic fluxes estimated in the period 1971–1998. We applied the wavelet technique to find the significant periodicities of these series. We concentrate particularly in the mid-term quasi-periodicities (1–2 years). The mid-term periodicity of 1.7 year is the dominant fluctuation for all the types of fluxes analyzed (total, closed, open, low and high latitude open fluxes) and has a strong tendency to appear during the descending phase of solar activity. The mid-term fluctuation of 1 year is significantly present in total and closed fluxes, but it is less important in open fluxes. It is recognizable in the high latitude open flux, but it is absent in the low latitude open flux. Due to the uncertainties involved in estimating the exact period of the quasi-annual peak, this component may not be different from the previously-reported 1.3 year periodicity. The high frequency fluctuations of all the fluxes but the high latitude open flux are in phase with the 11 years solar cycle. The high latitude flux tends to be present all the time, showing that along the cycle both the low latitude bipolar active regions and the polar coronal holes regulate this flux. These findings rule out the possibility of a more basic periodicity different from the 11 years cycle.     

Solar Intranetwork Magnetic Elements: Flux Distributions

The current study aims at quantifying the flux distributions of solar intranetwork (IN) magnetic field based on the data taken in four quiet and two enhanced network areas with the Narrow-band Filter Imager of the Solar Optical Telescope on board the Hinode satellite. More than 14000 IN elements and 3000 NT elements were visually identified. They exhibit a flux distribution function with a peak at 1?–?3×10¹⁶ Mx (maxwell) and 2?–?3×10¹⁷ Mx, respectively. We found that the IN elements contribute approximately to 52 % of the total flux and an average flux density of 12.4 gauss of the quiet region at any given time. By taking the lifetime of IN elements of about 3 min (Zhou et al., Solar Phys. 267, 63, 2010) into account, the IN fields are estimated to have total contributions to the solar magnetic flux up to 3.8×10²⁶ Mx per day. No fundamental distinction can be identified in IN fields between the quiet and enhanced network areas.     

Magnetic Flux Imbalance of the Solar and Heliospheric Magnetic Fields

A comparative analysis of solar and heliospheric magnetic fields in terms of their cumulative sums reveals cyclic and long-term changes that appear as a magnetic flux imbalance and alternations of dominant magnetic polarities. The global magnetic flux imbalance of the Sun manifests itself in the solar mean magnetic field (SMMF) signal. The north – south asymmetry of solar activity and the quadrupole mode of the solar magnetic field contribute the most to the observed magnetic flux imbalance. The polarity asymmetry exhibits the Hale magnetic cycle in both the radial and azimuthal components of the interplanetary magnetic field (IMF). Analysis of the cumulative sums of the IMF components clearly reveals cyclic changes in the IMF geometry. The accumulated deviations in the IMF spiral angle from its nominal value also demonstrate long-term changes resulting from a slow increase of the solar wind speed over 1965 – 2006. A predominance of the positive IMF B _z with a significant linear trend in its cumulative signal is interpreted as a manifestation of the relic magnetic field of the Sun. Long-term changes in the IMF B _z are revealed. They demonstrate decadal changes owing to the 11/22-year solar cycle. Long-duration time intervals with a dominant negative B _z component were found in temporal patterns of the cumulative sum of the IMF B _z .     

Solar Intranetwork Magnetic Elements: Bipolar Flux Appearance

This study aims to quantify characteristic features of the bipolar flux appearance of solar intranetwork (IN) magnetic elements. To attack this problem, we use the Narrowband Filter Imager (NFI) magnetograms from the Solar Optical Telescope (SOT) on board Hinode; these data are from quiet and enhanced network areas. Cluster emergence of mixed polarities and IN ephemeral regions (ERs) are the most conspicuous forms of bipolar flux appearance within the network. Each of the clusters is characterized by a few well-developed ERs that are partially or fully coaligned in magnetic axis orientation. On average, the sampled IN ERs have a total maximum unsigned flux of several 10¹⁷ Mx, a separation of 3 – 4 arcsec, and a lifetime of 10 – 15 minutes. The smallest IN ERs have a maximum unsigned flux of several 10¹⁶ Mx, separations of less than 1 arcsec, and lifetimes as short as 5 minutes. Most IN ERs exhibit a rotation of their magnetic axis of more than 10 degrees during flux emergence. Peculiar flux appearance, e.g., bipole shrinkage followed by growth or the reverse, is not unusual. A few examples show repeated shrinkage–growth or growth–shrinkage, like magnetic floats in the dynamic photosphere. The observed bipolar behavior seems to carry rich information on magnetoconvection in the subphotospheric layer.     

太阳光球磁通量南北不对称性研究

运用统计方法系统研究了1978-2002年太阳光球磁通量南北不对称性变化特征，发现其与太阳活动周有关．不对称值在太阳活动极小年要明显高于太阳活动极大年，并且磁通量变化总是由上升段的北半球占优逐渐过渡到下降段的南半球占优．另外运用小波变换方法详细讨论了这种不对称性变化可能存在的周期信息．     

Conditions for Propagation of Torsional Waves in Solar Magnetic Flux Tubes

Propagation of torsional waves along isothermal and initially-untwisted magnetic-flux tubes embedded in the solar atmosphere is studied analytically. Conditions for wave propagation along thin and wide magnetic-flux tubes are determined, and it is shown that the propagation along thin tubes is cutoff free; however, for wide tubes the propagation is affected by a cutoff frequency. A method to determine the cutoff frequency is presented and applied to a specific model of solar magnetic flux tubes. An interesting result is that the cutoff frequency is a local quantity in the model and that its value at a given height determines the frequency that torsional tube waves must have to propagate at this height.     

Non-ideal MHD Properties of Magnetic Flux Tubes in the Solar Photosphere

Magnetic flux tubes reaching from the solar convectivezone into the chromosphere have to pass through the relatively cool, and therefore non-ideal (i.e. resistive) photospheric region enclosed between the highly ideal sub-photospheric and chromospheric plasma. It is shown that stationary MHD equilibria of magnetic flux tubes which pass through this region require an inflow of photospheric material into the flux tube and a deviation from iso-rotation along the tube axis. This means that there is a difference in angular velocity of the plasma flow inside the tube below and above the non-ideal region. Both effects increase with decreasing cross section of the tube. Although for characteristic parameters of thick flux tubes the effect is negligible, a scaling law indicates its importance for small-scale structures. The relevance of this `inflow effect' for the expansion of flux tubes above the photosphere is discussed.     

How to Reach Superequipartition Field Strengths in Solar Magnetic Flux Tubes

A number of independent arguments indicate that the toroidal flux system responsible for the sunspot cycle is stored at the base of the convection zone in the form of flux tubes with field strength close to 10⁵ G. Although the evidence for such strong fields is quite compelling, how such field strength can be reached is still a topic of debate. Flux expulsion by convection should lead to about the equipartition field strength, but the magnetic energy density of a 10⁵-G field is two orders of magnitude larger than the mean kinetic energy density of convective motions. Line stretching by differential rotation (i.e., the “Ω effect” in the classical mean-field dynamo approach) probably plays an important role, but arguments based on energy considerations show that it does not seem feasible that a 10⁵-G field can be produced in this way. An alternative scenario for the intensification of the toroidal flux system in the overshoot layer is related to the explosion of rising, buoyantly unstable magnetic flux tubes, which opens a complementary mechanism for magnetic-field intensification. A parallelism is pointed out with the mechanism of “convective collapse” for the intensification of photospheric magnetic flux tubes up to field strengths well above equipartition; both mechanisms, which are fundamentally thermal processes, are reviewed.     

Magnetic Flux Transport Simulations of Solar Surface Magnetic Distributions During a Grand Minimum

It is well known that magnetic activity on the Sun modulates from one cycle to the next. The most striking occurrence of this is called a grand minimum where magnetic activity all but disappears. The latest grand minimum occurred between the years 1645 and 1715 and is called the Maunder minimum. In this paper magnetic flux transport simulations are used to consider what type of surface magnetic field configurations may be produced both during and after a grand minimum depending on how the grand minimum occurs. It is shown that the surface configurations during and after a grand minimum strongly depend on the phase of the cycle in which the grand minimum starts and whether it lasts for an odd or even number of cycles. If the grand minimum starts around cycle minimum then a significant amount of large-scale magnetic flux may persist on the Sun at high latitudes during the grand minimum. In contrast, if it starts at cycle maximum during the grand minimum it is possible for there to be essentially zero large-scale magnetic flux over the entire surface of the Sun. It is shown that for a single grand minimum event the reversal of the polar fields at the presently observed time in the solar cycle is only reproduced if the event starts at cycle minimum and extends over an even number of cycles. In contrast, if the grand minimum runs for an odd number of cycles it is possible for there to be no reversal of the polar fields or for the reversals to occur at times inconsistent with our present understanding of the solar cycle. Consequences of the assumptions made in the modelling are discussed and the significance of the simulations for direct modelling of events such as the Maunder minimum are considered.     

Soft X-ray Solar Activities Associated with Interplanetary Magnetic Flux Ropes

We studied the soft X-ray solar events that could be associated with the interplanetary magnetic flux ropes observed by the WIND satellite during 1995 through 1998. The timings of the launches of the magnetic flux ropes from the Sun were estimated using flux rope speeds derived by the fitting of a cylindrical model. In the reasonable time window, soft X-ray solar signatures were found in approximately 70% of the flux ropes. Parameters (e.g., axis direction, strength of magnetic field, radius, and helicity) of the magnetic flux ropes obtained by the model fitting were compared with the characteristics of the corresponding soft X-ray events observed by Yohkoh. According to the result of the comparison, the magnetic flux ropes with strong magnetic fields or high speeds were observed in association with higher soft X-ray solar activities.     

Non-equilibrium of Magnetic Flux Tubes emerging into the Solar Corona

A lack of equilibrium of twisted magnetic flux tubes emerging from the photosphere into the corona is considered. Assuming mass and flux conservation in the tube and an isothermal tube that is in thermal equilibrium with the surrounding plasma, it is shown that a sufficently rapid temperature increase through the transition zone may lead to the loss of magnetohydrostatic equilibrium of the emerging flux tube due to the enhancement of the plasma pressure inside the tube. The non-equilibrium leads to a rapid expansion of the tube to reach a new equilibrium state. The rise and expansion of the tube before and after the non-equilibrium are accompanied by an increase in the twist of the magnetic field. This may lead to the field exceeding the threshold for the onset of the kink instability and a subsequent explosive release of magnetic energy.     

Reconstruction of Open Solar Magnetic Flux and Interplanetary Magnetic Field in the 20Th Century

We reconstruct mean magnitudes of the open solar magnetic field since 1915 using α magnetic synoptic charts of the Sun. The obtained series allows estimation of the interplanetary magnetic field. They also confirm the known conclusion about the secular increase of the solar open magnetic flux in the first half of the 20th century.     

Magnetic Null Points due to Multiple Sources of Solar Photospheric Flux

How common are magnetic null points in the highly complex magnetic field of the solar atmosphere? In this work we seek to model the magnetic structure of quiet regions by placing magnetic sources and sinks on a hexagonal network of supergranule cells to represent the intense magnetic fields that occur at the boundaries of these cells. The resulting potential coronal magnetic field is then computed analytically and searched numerically for magnetic null points, which are classified according to their types and spine directions. Two relations from the theory of vector fields relate the numbers of null points to the numbers of sources and sinks and these are used to check the numerical results. Previous results relating these quantities for monopolar and dipolar magnetic fields are described and a new one for a particular class of quadrupolar fields arising in this study is derived. We model a three-cell configuration and study the effects of increasing the strength of a central sink and of moving the central sink. A twelve-cell configuration is studied in lesser detail.

     

Modeling Solar Spectral Irradiance and Total Magnetic Flux Using Sunspot Areas

We show that daily sunspot areas can be used in a simple, single parameter model to reconstruct daily variations in several other solar parameters, including solar spectral irradiance and total magnetic flux. The model assumes that changes in any given parameter can be treated mathematically as the response of the system to the emergence of a sunspot. Using cotemporal observational data, we compute the finite impulse response (FIR) function that describes that response in detail, and show that the response function has been approximately stationary over the time period for which data exist. For each parameter, the impulse response function describes the physical evolution of that part of a solar active region that is the source of the measured variability. We show that the impulse response functions are relatively narrow functions, no more than 3 years wide overall. Each exhibits a pre-active, active, and post-active region component; the active region component dominates the variability of most of the parameters studied.     

Interplanetary Magnetic Flux Ropes as Agents Connecting Solar Eruptions and Geomagnetic Activities

We investigate the solar wind structure for 11 cases that were selected for the campaign study promoted by the International Study of Earth-affecting Solar Transients (ISEST) MiniMax24 Working Group 4. We can identify clear flux rope signatures in nine cases. The geometries of the nine interplanetary magnetic flux ropes (IFRs) are examined with a model-fitting analysis with cylindrical and toroidal force-free flux rope models. For seven cases in which magnetic fields in the solar source regions were observed, we compare the IFR geometries with magnetic structures in their solar source regions. As a result, we can confirm the coincidence between the IFR orientation and the orientation of the magnetic polarity inversion line (PIL) for six cases, as well as the so-called helicity rule as regards the handedness of the magnetic chirality of the IFR, depending on which hemisphere of the Sun the IFR originated from, the northern or southern hemisphere; namely, the IFR has right-handed (left-handed) magnetic chirality when it is formed in the southern (northern) hemisphere of the Sun. The relationship between the orientation of IFRs and PILs can be taken as evidence that the flux rope structure created in the corona is in most cases carried through interplanetary space with its orientation maintained. In order to predict magnetic field variations on Earth from observations of solar eruptions, further studies are needed about the propagation of IFRs because magnetic fields observed at Earth significantly change depending on which part of the IFR hits the Earth.     

Modeling and Interpreting the Effects of Spatial Resolution on Solar Magnetic Field Maps

Different methods for simulating the effects of spatial resolution on magnetic field maps are compared, including those commonly used for inter-instrument comparisons. The investigation first uses synthetic data, and the results are confirmed with Hinode/SpectroPolarimeter data. Four methods are examined, one which manipulates the Stokes spectra to simulate spatial-resolution degradation, and three “post-facto” methods where the magnetic field maps are manipulated directly. Throughout, statistical comparisons of the degraded maps with the originals serve to quantify the outcomes. Overall, we find that areas with inferred magnetic fill fractions close to unity may be insensitive to optical spatial resolution; areas of sub-unity fill fractions are very sensitive. Trends with worsening spatial resolution can include increased average field strength, lower total flux, and a field vector oriented closer to the line of sight. Further-derived quantities such as vertical current density show variations even in areas of high average magnetic fill fraction. In short, unresolved maps fail to represent the distribution of the underlying unresolved fields, and the “post-facto” methods generally do not reproduce the effects of a smaller telescope aperture. It is argued that selecting a method in order to reconcile disparate spatial resolution effects should depend on the goal, as one method may better preserve the field distribution, while another can reproduce spatial resolution degradation. The results presented should help direct future inter-instrument comparisons.     

Automated Identification of Coronal Holes from Synoptic EUV Maps

Coronal holes (CHs) are regions of open magnetic field lines in the solar corona and the source of the fast solar wind. Understanding the evolution of coronal holes is critical for solar magnetism as well as for accurate space weather forecasts. We study the extreme ultraviolet (EUV) synoptic maps at three wavelengths (195 Å/193 Å, 171 Å and 304 Å) measured by the Solar and Heliospheric Observatory/Extreme Ultraviolet Imaging Telescope (SOHO/EIT) and the Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA) instruments. The two datasets are first homogenized by scaling the SDO/AIA data to the SOHO/EIT level by means of histogram equalization. We then develop a novel automated method to identify CHs from these homogenized maps by determining the intensity threshold of CH regions separately for each synoptic map. This is done by identifying the best location and size of an image segment, which optimally contains portions of coronal holes and the surrounding quiet Sun allowing us to detect the momentary intensity threshold. Our method is thus able to adjust itself to the changing scale size of coronal holes and to temporally varying intensities. To make full use of the information in the three wavelengths we construct a composite CH distribution, which is more robust than distributions based on one wavelength. Using the composite CH dataset we discuss the temporal evolution of CHs during the Solar Cycles 23 and 24.     

Solar Flux Emergence Simulations

We simulate the rise through the upper convection zone and emergence through the solar surface of initially uniform, untwisted, horizontal magnetic flux, with the same entropy as the nonmagnetic plasma, that is advected into a domain 48 Mm wide by 20 Mm deep. The magnetic field is advected upward by the diverging upflows and pulled down in the downdrafts, which produces a hierarchy of loop-like structures of increasingly smaller scale as the surface is approached. There are significant differences between the behavior of fields of 10 kG and 20 or 40 kG strength at 20 Mm depth. The 10 kG fields have little effect on the convective flows and show small magnetic-buoyancy effects, reaching the surface in the typical fluid rise time from 20 Mm depth of 32 hours. 20 and 40 kG fields significantly modify the convective flows, leading to long, thin cells of ascending fluid aligned with the magnetic field and their magnetic buoyancy makes them rise to the surface faster than the fluid rise time. The 20 kG field produces a large-scale magnetic loop that as it emerges through the surface leads to the formation of a bipolar, pore-like structure.     

Carrington Coordinates and Solar Maps

Solar synoptic charts are normally displayed using Carrington Coordinates with each Carrington rotation being centered at a Carrington longitude of 180^° and with a full 360^° of solar surface properties included. For the case of reproducing solar magnetic fields in the corona and heliosphere, these maps are wrapped onto the solar surface to provide the boundary conditions for a solution to a set of modeling equations such as the potential field theory equations. Due to differential rotation, the full solar surface cannot be reproduced in this fashion since different parts of the solar surface are observed at different times. We describe here the proper technique for combining observations of the solar magnetic or velocity fields made at different times into a representation of the whole solar surface at a particular specified time that we refer to as a “snapshot heliographic map“.