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.     

On the origin and structure of stellar magnetic fields

Newly formed stars have magnetic fields provided by the compression of the interstellar field, and contrary to a widely accepted idea these fields are not destroyed by convective motions. For the same reason, the fallacy of ‘turbulent diffusion’, turbulent dynamo action is not possible in any star. Thus all stellar magnetic fields have a common origin, and persist throughout the lifetime of each star, including degenerate phases. This common origin, and a general similarity in stellar evolutionary processes, suggest that the fields may develop similar structural characteristics and MHD effects. This would open new possibilities of coordinating the studies of different types of stars and relating them to solar physics which has tended to become isolated from general stellar physics. As an initial step we consider three features of solar magnetic fields and their MHD effects. First, the solar magnetic field comprises two separate components: a poloidal field and a toroidal field. The former is a dipole field, permeating the entire Sun and closely aligned with the rotational axis; at the surface it is always concealed by much stronger elements of the toroidal field. The latter is probably wound from the former by differential rotation at latitudes below about 35°, where sections emerge through the solar surface and are then carried polewards. The second feature of solar magnetic fields is that all flux is concentrated into flux tubes of strength some kG, isolated within a much larger volume of non-magnetic plasma. The third feature is that the flux tubes are helically twisted into flux ropes (up to ?10²²Mx) and smaller elements ranging down to flux fibres (? 10¹⁸Mx). Some implications of similar features in other stars are discussed.     

Solar Magnetic Carpet I: Simulation of Synthetic Magnetograms

This paper describes a new 2D model for the photospheric evolution of the magnetic carpet. It is the first in a series of papers working towards constructing a realistic 3D non-potential model for the interaction of small-scale solar magnetic fields. In the model, the basic evolution of the magnetic elements is governed by a supergranular flow profile. In addition, magnetic elements may evolve through the processes of emergence, cancellation, coalescence and fragmentation. Model parameters for the emergence of bipoles are based upon the results of observational studies. Using this model, several simulations are considered, where the range of flux with which bipoles may emerge is varied. In all cases the model quickly reaches a steady state where the rates of emergence and cancellation balance. Analysis of the resulting magnetic field shows that we reproduce observed quantities such as the flux distribution, mean field, cancellation rates, photospheric recycle time and a magnetic network. As expected, the simulation matches observations more closely when a larger, and consequently more realistic, range of emerging flux values is allowed (4×10¹⁶ – 10¹⁹ Mx). The model best reproduces the current observed properties of the magnetic carpet when we take the minimum absolute flux for emerging bipoles to be 4×10¹⁶ Mx. In future, this 2D model will be used as an evolving photospheric boundary condition for 3D non-potential modeling.     

Multiwavelength Study of a Solar Eruption from AR NOAA 11112 I. Flux Emergence, Sunspot Rotation and Triggering of a Solar Flare

We analyze the multiwavelength observations of an M2.9/1N flare that occurred in the active region (AR) NOAA 11112 in the vicinity of a huge filament system on 16 October 2010. SDO/HMI magnetograms reveal the emergence of a bipole (within the existing AR) 50 hours prior to the flare event. During the emergence, both the positive and negative sunspots in the bipole show translational as well as rotational motion. The positive-polarity sunspot shows significant motion/rotation in the south-westward/clockwise direction, and we see continuously pushing/sliding of the surrounding opposite-polarity field region. On the other hand, the negative-polarity sunspot moves/rotates in the westward/anticlockwise direction. The positive-polarity sunspot rotates ≈?70^° within 30 hours, whereas the one with negative polarity rotates ≈?20^° within 10 hours. SDO/AIA 94 Å EUV images show the emergence of a flux tube in the corona, consistent with the emergence of the bipole in HMI. The footpoints of the flux tube were anchored in the emerging bipole. The initial brightening starts at one of the footpoints (western) of the emerging loop system, where the positive-polarity sunspot pushes/slides towards a nearby negative-polarity field region. A high speed plasmoid ejection (speed ≈?1197 km?s^?1) was observed during the impulsive phase of the flare, which suggests magnetic reconnection of the emerging positive-polarity sunspot with the surrounding opposite-polarity field region. The entire AR shows positive-helicity injection before the flare event. Moreover, the newly emerging bipole reveals the signature of a negative (left-handed) helicity. These observations provide unique evidence of the emergence of twisted flux tubes from below the photosphere to coronal heights, triggering a flare mainly due to the interaction between the emerging positive-polarity sunspot and a nearby negative-polarity sunspot by the shearing motion of the emerging positive sunspot towards the negative one. Our observations also strongly support the idea that the rotation can most likely be attributed to the emergence of twisted magnetic fields, as proposed by recent models.     

Recovering Joy’s Law as a Function of Solar Cycle, Hemisphere, and Longitude

Bipolar active regions in both hemispheres tend to be tilted with respect to the East–West Equator of the Sun in accordance with Joy’s law, which describes the average tilt angle as a function of latitude. Mt. Wilson Observatory data from 1917?–?1985 are used to analyze the active-region tilt angle as a function of solar cycle, hemisphere, and longitude, in addition to the more common dependence on latitude. Our main results are as follows: i) We recommend a revision of Joy’s law towards a weaker dependence on latitude (slope of 0.13?–?0.26) and without forcing the tilt to zero at the Equator. ii) We determine that the hemispheric mean tilt value of active regions varies with each solar cycle, although the noise from a stochastic process dominates and does not allow for a determination of the slope of Joy’s law on an 11-year time scale. iii) The hemispheric difference in mean tilt angles, 1.1^°±0.27, over Cycles 16 to 21 was significant to a three-σ level, with average tilt angles in the Northern and Southern hemispheres of 4.7^°±0.26 and 3.6^°±0.27, respectively. iv) Area-weighted mean tilt angles normalized by latitude for Cycles 15 to 21 anticorrelate with cycle strength for the southern hemisphere and whole-Sun data, confirming previous results by Dasi-Espuig et al. (Astron. Astrophys. 518, A7, 2010). The Northern Hemispheric mean tilt angles do not show a dependence on cycle strength. v) Mean tilt angles do not show a dependence on longitude for any hemisphere or cycle. In addition, the standard deviation of the mean tilt is 29?–?31^° for all cycles and hemispheres, indicating that the scatter is due to the same consistent process even if the mean tilt angles vary.     

Observations of Unresolved Photospheric Magnetic Fields in Solar Flares Using Fe i and Cr i Lines

The structure of the photospheric magnetic field during solar flares is examined using echelle spectropolarimetric observations. The study is based on several Fe i and Cr i lines observed at locations corresponding to brightest Hα emission during thermal phase of flares. The analysis is performed by comparing magnetic-field values deduced from lines with different magnetic sensitivities, as well as by examining the fine structure of I±V Stokes-profiles’ splitting. It is shown that the field has at least two components, with stronger unresolved flux tubes embedded in weaker ambient field. Based on a two-component magnetic-field model, we compare observed and synthetic line profiles and show that the field strength in small-scale flux tubes is about 2?–?3 kG. Furthermore, we find that the small-scale flux tubes are associated with flare emission, which may have implications for flare phenomenology.     

Solar transients disturbing the terrestrial magnetic environment at higher latitudes

Geomagnetic field variations during five major Solar Energetic Particle (SEP) events of solar cycle 23 have been investigated in the present study. The SEP events of 1 October 2001, 4 November 2001, 22 November 2001, 21 April 2002 and 14 May 2005 have been selected to study the geomagnetic field variations at two high-latitude stations, Thule (77.5^° N, 69.2^° W) and Resolute Bay (74.4^° E, 94.5^° W) of the northern polar cap. We have used the GOES proton flux in seven different energy channels (0.8–4 MeV, 4–9 MeV, 9–15 MeV, 15–40 MeV, 40–80 MeV, 80–165 MeV, 165–500 MeV). All the proton events were associated with geoeffective or Earth directed CMEs that caused intense geomagnetic storms in response to geospace. We have taken high-latitude indices, AE and PC, under consideration and found fairly good correlation of these with the ground magnetic field records during the five proton events. The departures of the H component during the events were calculated from the quietest day of the month for each event and have been represented as ΔH _THL and ΔH _RES for Thule and Resolute Bay, respectively. The correspondence of spectral index, inferred from event integrated spectra, with ground magnetic signatures ΔH _THL and ΔH _RES along with Dst and PC indices have been brought out. From the correlation analysis we found a very strong correlation to exist between the geomagnetic field variation (ΔHs) and high-latitude indices AE and PC. To find the association of geomagnetic storm intensity with proton flux characteristics we derived the correspondence between the spectral indices and geomagnetic field variations (ΔHs) along with the Dst and AE index. We found a strong correlation (0.88) to exist between the spectral indices and ΔHs and also between spectral indices and AE and PC.     

Contribution to the Solar Mean Magnetic Field from Different Solar Regions

Seven-year-long seeing-free observations of solar magnetic fields with the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) were used to study the sources of the solar mean magnetic field, SMMF, defined as the net line-of-sight magnetic flux divided over the solar disk area. To evaluate the contribution of different regions to the SMMF, we separated all the pixels of each SDO/HMI magnetogram into three subsets: weak (\(B^{\mathrm{W}}\)), intermediate (\(B^{\mathrm{I}}\)), and strong (\(B^{\mathrm{S}}\)) fields. The \(B^{\mathrm{W}}\) component represents areas with magnetic flux densities below the chosen threshold; the \(B^{\mathrm{I}}\) component is mainly represented by network fields, remains of decayed active regions (ARs), and ephemeral regions. The \(B^{\mathrm{S}}\) component consists of magnetic elements in ARs. To derive the contribution of a subset to the total SMMF, the linear regression coefficients between the corresponding component and the SMMF were calculated. We found that i) when the threshold level of 30 Mx?cm^?2 is applied, the \(B^{\mathrm{I}}\) and \(B^{\mathrm{S}}\) components together contribute from 65% to 95% of the SMMF, while the fraction of the occupied area varies in a range of 2?–?6% of the disk area; ii) as the threshold magnitude is lowered to 6 Mx?cm^?2, the contribution from \(B^{\mathrm{I}}+B^{\mathrm{S}}\) grows to 98%, and the fraction of the occupied area reaches a value of about 40% of the solar disk. In summary, we found that regardless of the threshold level, only a small part of the solar disk area contributes to the SMMF. This means that the photospheric magnetic structure is an intermittent inherently porous medium, resembling a percolation cluster. These findings suggest that the long-standing concept that continuous vast unipolar areas on the solar surface are the source of the SMMF may need to be reconsidered.     

Modeling and Measuring the Flux Reconnected and Ejected by the Two-Ribbon Flare/CME Event on 7 November 2004

Observations of the large two-ribbon flare on 7 November 2004 made using SOHO and TRACE data are interpreted in terms of a three-dimensional magnetic field model. Photospheric flux evolution indicates that ?1.4×10⁴³ Mx² of magnetic helicity was injected into the active region during the 40-hour buildup prior to the flare. The magnetic model places a lower bound of 8×10³¹ ergs on the energy stored by this motion. It predicts that 5×10²¹ Mx of flux would need to be reconnected during the flare to release the stored energy. This total reconnection compares favorably with the flux swept up by the flare ribbons, which we measure using high-time-cadence TRACE images in 1?600 Å. Reconnection in the model must occur in a specific sequence that would produce a twisted flux rope containing significantly less flux and helicity (10²¹ Mx and ?3×10⁴² Mx², respectively) than the active region as a whole. The predicted flux compares favorably with values inferred from the magnetic cloud observed by Wind. This combined analysis yields the first quantitative picture of the flux processed through a two-ribbon flare and coronal mass ejection.     

The Relationship Between Plasma Flow Doppler Velocities and Magnetic Field Parameters During the Emergence of Active Regions at the Solar Photospheric Level

A statistical study has been carried out of the relationship between plasma flow Doppler velocities and magnetic field parameters during the emergence of active regions at the solar photospheric level with data acquired by the Michelson Doppler Imager (MDI) onboard the Solar and Heliospheric Observatory (SOHO). We have investigated 224 emerging active regions with different spatial scales and positions on the solar disc. The following relationships for the first hours of the emergence of active regions have been analysed: i) of peak negative Doppler velocities with the position of the emerging active regions on the solar disc; ii) of peak plasma upflow and downflow Doppler velocities with the magnetic flux growth rate and magnetic field strength for the active regions emerging near the solar disc centre (the vertical component of plasma flows); iii) of peak positive and negative Doppler velocities with the magnetic flux growth rate and magnetic field strength for the active regions emerging near the limb (the horizontal component of plasma flows); iv) of the magnetic flux growth rate with the density of emerging magnetic flux; v) of the Doppler velocities and magnetic field parameters for the first hours of the appearance of active regions with the total unsigned magnetic flux at the maximum of their development.     

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.     

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.     

Forecasting the Maxima of Solar Cycle 24 with Coronal Fe xiv Emission

The onset of the “Rush to the Poles” of polar-crown prominences and their associated coronal emission is a harbinger of solar maximum. Altrock (Solar Phys. 216, 343, 2003) showed that the “Rush” was well observed at 1.15 R _o in the Fe xiv corona at the Sacramento Peak site of the National Solar Observatory prior to the maxima of Cycles 21 to 23. The data show that solar maximum in those cycles occurred when the center line of the Rush reached a critical latitude of 76^°±2^°. Furthermore, in the previous three cycles solar maximum occurred when the highest number of Fe xiv emission features per day (averaged over 365 days and both hemispheres) first reached latitudes 20^°±1.7^°. Applying the above conclusions to Cycle 24 is difficult due to the unusual nature of this cycle. Cycle 24 displays an intermittent Rush that is only well-defined in the northern hemisphere. In 2009 an initial slope of 4.6^°?year^?1 was found in the north, compared to an average of 9.4±1.7^°?year^?1 in the previous cycles. An early fit to the Rush would have reached 76^° at 2014.6. However, in 2010 the slope increased to 7.5^°?year^?1 (an increase did not occur in the previous three cycles). Extending that rate to 76^°±2^° indicates that the solar maximum in the northern hemisphere already occurred at 2011.6±0.3. In the southern hemisphere the Rush to the Poles, if it exists, is very poorly defined. A linear fit to several maxima would reach 76^° in the south at 2014.2. In 1999, persistent Fe xiv coronal emission known as the “extended solar cycle” appeared near 70^° in the North and began migrating towards the equator at a rate 40 % slower than the previous two solar cycles. However, in 2009 and 2010 an acceleration occurred. Currently the greatest number of emission features is at 21^° in the North and 24^° in the South. This indicates that solar maximum is occurring now in the North but not yet in the South.     

The Association of Solar Flares with Coronal Mass Ejections During the Extended Solar Minimum

We study the association of solar flares with coronal mass ejections (CMEs) during the deep, extended solar minimum of 2007?–?2009, using extreme-ultraviolet (EUV) and white-light (coronagraph) images from the Solar Terrestrial Relations Observatory (STEREO). Although all of the fast (v>900 km?s^?1), wide (θ>100^°) CMEs are associated with a flare that is at least identified in GOES soft X-ray light curves, a majority of flares with relatively high X-ray intensity for the deep solar minimum (e.g. ?1×10^?6 W?m^?2 or C1) are not associated with CMEs. Intense flares tend to occur in active regions with a strong and complex photospheric magnetic field, but the active regions that produce CME-associated flares tend to be small, including those that have no sunspots and therefore no NOAA active-region numbers. Other factors on scales similar to and larger than active regions seem to exist that contribute to the association of flares with CMEs. We find the possible low coronal signatures of CMEs, namely eruptions, dimmings, EUV waves, and Type III bursts, in 91 %, 74 %, 57 %, and 74 %, respectively, of the 35 flares that we associate with CMEs. None of these observables can fully replace direct observations of CMEs by coronagraphs.     

Solar activity during first six years of solar cycle 24 and 23: a comparative study

Attempt to look into the nature of solar activity and variability have increased importance in recent days because of their terrestrial relationships. In the present work we have attempted to compare the solar activity events during first six years (2008–2013) of the ongoing solar cycle 24 with first six years (1996–2001) of solar cycle 23. To that end, we have considered sunspot numbers, F10.7 cm solar flux, halo CMEs and geomagnetic storms as comparison parameters. Sunspot number during the year 2008–2013 varied from 0 to 96.7 while during the year 1996 to 2001 it was observed from 0.9 to 170.1. Solar radio flux (F10.7 cm index) varied from 65 to 190 during the years 2008–2013 while it was observed from 65 to 283 during the years 1996–2001. 197 cases of halo CMEs (width=360^°) in solar cycle 23 (1996–2001) and 177 cases of halo CMEs (width=360^°) in solar cycle 24 (2008–2013) are investigated. 287 and 104 geomagnetic storm cases (Dst varies between ?50 and ?350 nT) are analysed during the half period of solar cycle 23 and 24 respectively. Comparative results indicate that solar cycle 23 was more pronounced in comparison of solar cycle 24.     

A coupled model of magnetic flux generation and transport in stars

We present a combined model for magnetic field generation and transport in cool stars with outer convection zones. The mean toroidal magnetic field, which is generated by a cyclic thin-layer α Ω dynamo at the bottom of the convection zone is taken to determine the emergence probability of magnetic flux tubes in the photosphere. Following the nonlinear rise of the unstable thin flux tubes, emergence latitudes and tilt angles of bipolar magnetic regions are determined. These quantities are put into a surface flux transport model, which simulates the surface evolution of magnetic flux under the effects of large-scale flows and turbulent diffusion. First results are discussed for the case of the Sun and for more rapidly rotating solar-type stars. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The flux-rope-fibre theory of solar magnetic fields

The flux-rope theory of solar magnetic fields is reviewed briefly and, together with the dynamo theory, compared with various observational results. Dynamo and related theories are based on fields controlled by the plasma, and it is shown that such fields cannot account for the strong surface fields or even emerge without becoming tangled. Observations which appear uniquely explicable in terms of powerful (4000 G), helically twisted flux ropes and their many twisted flux fibres (3×10¹⁸ Mx) are listed as follows. (i) Emerging magnetic flux is seen first as pairs of small, closely spaced flux concentrations whose motions suggest magnetic control to provide bipolar regions of extent10⁵ km. The associated system of arch filaments rotates on the disk as would a series of emerging flux fibres twisted into a rope. (ii) Sunspots form by the accretion of pores and magnetic knots of like polarity, sometimes moving along curved paths between stationary elements of opposite polarity. (iii) Fluxes of10²² Mx in large sunspots must have been concentrated to strengths of4000 G before emerging, and also strongly helically twisted to avoid the flute instability. (iv) The trumpet-shaped flux-rope-fibre sunspot model (Figure 6) accounts readily for the phenomena of the moat convection, the sunspot energy deficit, the complex Evershed flow, penumbral filaments (flux 3×10¹⁸ Mx) and temporary light bridges. (v) Asymmetries in sunspot groups (in spot size, lifetime and proper motion) show that the spot fields are extensions of two submerged magnetic structures comprising strong fields. (vi) Sunspots decay by the loss of magnetic knots with strong fields and flux 5×10¹⁸ Mx. These must be isolated flux tubes, twisted to account for their stability. (vii) Flux fibres leaving a spot are prone to the kink instability, thus accounting for their sudden appearance in pairs, the transport of total flux several times that of the spot and net flux equal to that of the spot. (viii) Ephemeral active regions and X-ray bright points are explained similarly without invoking improbably huge quantities of new flux. (ix) Atmospheric structures show a high prevalence of helical twists (force-free fields) and rotary motions on all scales from spicules to large prominences. It is difficult to account for these twists unless they are present in emerging flux. (x) In and above the photosphere the flux fibres (3×10¹⁸ Mx) fray into loose associations of flux threads (3×10¹⁷ Mx) to provide a simple, selfconsistent model of the solar filigree and the chromospheric rosette (bush) with its group of mottles (spicules). (xi) Global patterns of surface and coronal magnetic fields reveal puzzling features such as the migration of large unipolar regions and the freedom from differential rotation of some structures. Submerged flux ropes peeling out of the Sun provide a starting point for explaining these effects. These results provide a strong case for the flux-rope theory against the entrenched dynamo theory, and suggest that more observations should be made of the above ten phenomena. Where possible, simultaneous observations should be made of Zeeman effects and of plasma distributions and velocity field seen in white light and spectral lines.     

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.