J. O. Stenflo

Magnetic-field structure of the photospheric network

A method is developed to determine the physical parameters of the spatially unresolved photospheric network. The apparent magnetic fluxes are recorded simultaneously in the two FeI lines 5250 and 5247 Å, which belong to the same multiplet and have practically the same oscillator strength and excitation potential of the lower level, but differ in the effective Lande factor. By analysing magnetograph recordings in this pair of lines together with simultaneous recordings in the two FeI lines 5250 and 5233 Å, it is possible to separate the effects on the line profiles due to Zeeman splitting and temperature enhancement in the network.From an analysis of the observations the following properties of the photospheric network are obtained: Field strengths of about 2000 G are present in the network in quiet regions. The characteristic size of the magnetic-field structures in the network appears to be in the range 100–300 km. The 5250 Å line is weakened by roughly 50% in the network. If the line had been non-magnetic, the weakening would have been about 20%. The rest of the weakening is caused by the strong Zeeman splitting. The downward velocity at the supergranular cell boundaries is estimated to be of the order of 0.5 km s-1.

Solar Magnetic Fields: Polarized Radiation Diagnostics

Preface. 1. Solar Magnetism -- an Overview. 2. Theory of Polarized Radiation. 3. Interaction of Matter with Radiation. 4. Radiative Transfer without Scattering. 5. Classical Scattering and the Hanle Effect. 6. Non-LTE Radiative Transfer: Phenomenological Treatment. 7. Introduction to Quantum Field Theory of Polarized Radiative Transfer. 8. Multi-Level Radiative Transfer with Coherence Effects. 9. Rayleigh and Raman Scattering. 10. Collisions, Partial Redistribution, and Turbulent Magnetic Fields. 11. Solutions of the Polarized Transfer Equation. 12. Diagnostics of Small-Scale Magnetic Fields. 13. Instrumentation for Solar Polarimetry. References. Symbol Index. Subject Index.

On the filamentary nature of solar magnetic fields

A method is presented for obtaining information about the unresolved filamentary structure of solar magnetic fields. A comparison is made of pairs of Mount Wilson magnetograph recordings made in the two spectral lines Fei 5250 Å and Fei 5233 Å obtained on 26 different days. Due to line weakenings and saturation in the magnetic filaments, the apparent field strengths measured in the 5250 Å line are too low, while the 5233 Å line is expected to give essentially correct results. From a comparison between the apparent field strengths and fluxes and their center to limb variations, we draw the following tentative conclusions: (a) More than 90 % of the total flux seen with a 17 by 17 arc sec magnetograph aperture is channeled through narrow filaments with very high field strengths in plages and at the boundaries of supergranular cells. (b) An upper limit for the interfilamentary field strength integrated over the same aperture seems to be about 3 G. (c) The field lines in a filament are confined in a very small region in the photosphere but spread out very rapidly higher up in the atmosphere. (d) All earlier Mount Wilson magnetograph data should be multiplied by a factor that is about 1.8 at the center of the disk and decreased toward the limb in order to give the correct value of the longitudinal magnetic field averaged over the scanning aperture.

Small-Scale Solar Magnetic Fields

As we resolve ever smaller structures in the solar atmosphere, it has become clear that magnetism is an important component of those small structures. Small-scale magnetism holds the key to many poorly understood facets of solar magnetism on all scales, such as the existence of a local dynamo, chromospheric heating, and flux emergence, to name a few. Here, we review our knowledge of small-scale photospheric fields, with particular emphasis on quiet-sun field, and discuss the implications of several results obtained recently using new instruments, as well as future prospects in this field of research.

On the small-scale structure of solar magnetic fields

The small-scale structure of solar magnetic fields has been studied using simultaneous recordings in the spectral lines Fe i 5250 Å and Fe i 5233 Å, obtained with the Kitt Peak multi-channel magnetograph. We find that more than 90% of the magnetic flux in active regions (excluding the sunspots), observed with a 2.4 by 2.4″ aperture, is channelled through narrow filaments. This percentage is even higher in quiet areas. The field lines in a magnetic filament diverge rapidly with height, and part of the flux returns back to the neighbouring photosphere. Therefore the strong fields within a magnetic filament are surrounded by weak fields of the order of a few gauss of the opposite polarity. The field-strength distribution within a filament, including the surrounding opposite-polarity fields, seems to be almost the same for all filaments within a given active or quiet region.The analysis of a scan made during an imp. 2 flare showed that observations during and after the flare would give a fictitious decrease of the magnetic energy in the region by a factor of 2–3 due to line-profile changes during the flare.

Small-scale magnetic structures on the Sun

SummaryThe Sun provides us with a unique astrophysics laboratory for exploring the fundamental processes of interaction between a turbulent, gravitationally stratified plasma and magnetic fields. Although the magnetic structures and their evolution can be observed in considerable detail through the use of the Zeeman effect in photospheric spectral lines, a major obstacle has been that all magnetic structures on the Sun, excluding sunspots, are smaller than what can be resolved by present-day instruments. This has led to the development of indirect, spectral techniques (combinations of two or more polarized spectral lines), which overcome the resolution obstacle and have revealed unexpected properties of the small-scale magnetic structures. Indirect empirical and theoretical estimates of the sizes of the flux elements indicate that they may be within reach of planned new telescopes, and that we are on the verge of a unified understanding of the diverse phenomena of solar and stellar activity.In the present review we describe the observational properties of the smallscale field structures (while indicating the diagnostic methods used), and relate these properties to the theoretical concepts of formation, equilibrium structure, and origin of the surface magnetic flux.

Evolution and rotation of large-scale photospheric magnetic fields of the sun during cycles 21-23 : Periodicities, north-south asymmetries and r-mode signatures

We present the results of an extensive time series analysis of longitudinally-averaged synoptic maps, recorded at the National Solar Observatory (NSO/Kitt Peak) from 1975 to 2003, and provide evidence for a multitude of quasi-periodic oscillations in the photospheric magnetic field of the Sun. In the low frequency range, we have located the sources of the 3.6 yr, 1.8 yr, and 1.5 yr periodicities that were previously detected in the north-south asymmetry of the unsigned photospheric flux (Knaack et al. 2004, A&A, 418, L17). In addition, quasi-periodicities around 2.6 yr and 1.3 yr have been found. The 1.3 yr period is most likely related to large-scale magnetic surges toward the poles and appeared in both hemispheres at intermediate latitudes ∼30°-55° during the maxima of all three cycles 21-23, being particularly pronounced during cycle 22. Periods near 1.3 yr have recently been reported in the rotation rate at the base of the convection zone (Howe et al. 2000, Science, 287, 2456), in the interplanetary magnetic field and geomagnetic activity (Lockwood 2001, J. Geophys. Res., 106, 16021) and in sunspot data (Krivova & Solanki 2002, A&A, 394, 701). In the intermediate frequency range, we have found a series of quasi-periodicities of 349-307 d, 282 ± 4 d, 249-232 d, 222-209 d, 177 ± 2 d, 158-151 d, 129-124 d and 103-100 d, which are in good agreement with period estimates for Rossby-type waves and occurred predominantly in the southern hemisphere. We provide evidence that the best known of these periodicities, the Rieger period around 155 d, appeared in the magnetic flux not only during cycle 21 but also during cycle 22, likely even during cycle 23. The high frequency range, which covers the solar rotation periods, shows a dominant (synodic) 28.1 ± 0.1 d periodicity in the southern hemisphere during cycles 21 and 22. A periodicity around 25.0-25.5 d occurred in the south during all three cycles. The large-scale magnetic field of the northern hemisphere showed dominant rotation periods at 26.9 ± 0.1 d during cycle 21, at 28.3-29.0 d during cycle 22 and at 26.4 ± 0.1 d during cycle 23.

Periodic oscillations in the north-south asymmetry of the solar magnetic field

. We report on significant periodic variations of the magnetic activity between the north and south hemisphere of the Sun. For this purpose, we have investigated the north-south asymmetry of two solar data sets, namely the Kitt Peak synoptic Carrington rotation maps of the photospheric magnetic field (1975-2003) and monthly averaged sunspot areas (1874-2003). Using Fourier and wavelet analysis, we have found a regular pattern of pronounced oscillations with periods of 1.50 ± 0.04 yr, 1.79 ± 0.06 yr and 3.6 ± 0.3 yr in the magnetic flux asymmetry. The former two periods are related to a process which leads to a gradual shift in the excess magnetic flux from north to south or vice versa. Additional periods of 43.4 ± 7.1 yr (twice the magnetic cycle) and 320-329 days were detected in the sunspot asymmetry.

BIPOLAR MAGNETIC REGIONS ON THE SUN: GLOBAL ANALYSIS OF THE SOHO/MDI DATA SET

The magnetic flux that is generated by dynamo processes inside the Sun emerges in the form of bipolar magnetic regions. The properties of these directly observable signatures of the dynamo can be extracted from full-disk solar magnetograms. The most homogeneous, high-quality synoptic data set of solar magnetograms has been obtained with the Michelson Doppler Imager (MDI) instrument on the Solar and Heliospheric Observatory spacecraft during 1995-2011. We have developed an IDL program that has, when applied to the 73,838 magnetograms of the MDI data set, automatically identified 160,079 bipolar magnetic regions that span a range of scale sizes across nearly four orders of magnitude. The properties of each region have been extracted and statistically analyzed, in particular with respect to the polarity orientations of the bipolar regions, including their tilt-angle distributions and their violations of Hales polarity law. The latitude variation of the average tilt angles (with respect to the E-W direction), which is known as Joys law, is found to closely follow the relation 321 ? sin (latitude). There is no indication of a dependence on region size that one may expect if the tilts were produced by the Coriolis force during the buoyant rise of flux loops from the tachocline region. A few percent of all regions have orientations that violate Hales polarity law. We show explicit examples, from different phases of the solar cycle, where well-defined medium-size bipolar regions with opposite polarity orientations occur side by side in the same latitude zone in the same magnetogram. Such oppositely oriented large bipolar regions cannot be part of the same toroidal flux system, but different flux systems must coexist at any given time in the same latitude zones. These examples are incompatible with the paradigm of coherent, subsurface toroidal flux ropes as the source of sunspots, and instead show that fluctuations must play a major role at all scales for the turbulent dynamo. To confirm the profound role of fluctuations at large scales, we show explicit examples in which large bipolar regions differ from the average Joys law orientation by an amount between 90? and 100?. We see no observational support for a separation of scales or a division between a global and a local dynamo, since also the smallest scales in our sample retain a non-random component that significantly contributes to the accumulated emergence of a north-south dipole moment that will lead to the replacement of the old global poloidal field with a new one that has the opposite orientation.

Distribution functions for magnetic fields on the quiet Sun

The statistical properties of the highly structured magnetic field of the quiet Sun are best described in terms of distribution functions, in particular the probability density functions (PDF) for the flux densities and the angular distribution for the orientations of the field vector. They are needed to test the validity of various MHD simulations, but past determinations have led to contradictory results. A main reason for these difficulties lies in the circumstance that the magnetic structuring continues on scales that are much smaller than the telescope resolution, and that this structuring strongly affects the quantities averaged over each pixel due to the non-linear relation between polarization and magnetic field. Here we use a Hinode SOT/SP data set for the disk center of the quiet Sun to explore the complex behavior of the polarized 6301-6302 A line system and identify the observables that allow the most robust determinations of inclination angles and flux densities. These observables are then used to derive the empirical distribution functions. Our Stokes V line ratio analysis leads us to an unexpected discovery: a magnetic dichotomy with two distinct populations, representing strong (kG) and weak fields. This can be understood in terms of the convective collapse mechanism, which makes the Suns magnetic flux end up in two states: collapsed and uncollapsed. With the linear-to-circular polarization ratio as a robust observable for the inclination angles, we find that the angular distribution is extremely peaked around the vertical direction for the largest flux densities, but gradually broadens as we go to smaller flux densities, to become asymptotically isotropic at zero flux density. The PDF for the vertical flux density, after accounting for the smearing effect of measurement noise, is found to have an extremely narrow core peak centered at zero flux density, which can be analytically represented by a stretched exponential. The PDF wings are extended and decline quadratically. The PDFs for the horizontal and total flux densities have a similar behavior. In particular we demonstrate that earlier claims that the PDF for the total flux density increases from small values at zero flux density to have a maximum significantly shifted from zero is an artefact of measurement noise.