Cyclic and Long-term Variation of Sunspot Magnetic Fields

Measurements from the Mount Wilson Observatory (MWO) are used to study the long-term variations of sunspot field strengths from 1920 to 1958. Following a modified approach similar to that in Pevtsov et al. (2011), for each observing week we select a single sunspot with the strongest field strength measured that week and then compute monthly averages of these weekly maximum field strengths. The data show the solar cycle variation of the peak field strengths with an amplitude of about 500-700 gauss (G), but no statistically significant long-term trends. Next, we use the sunspot observations from the Royal Greenwich Observatory (RGO) to establish a relationship between the sunspot areas and the sunspot field strengths for Cycles 15-19. This relationship is then used to create a proxy of peak magnetic field strength based on sunspot areas from the RGO and the USAF/NOAA network for the period from 1874 to early 2012. Over this interval, the magnetic field proxy shows a clear solar cycle variation with an amplitude of 500-700 G and a weaker long-term trend. From 1874 to around 1920, the mean value of magnetic field proxy increases by about 300-350 G, and, following a broad maximum in 1920-1960, it decreases by about 300 G. Using the proxy for the magnetic field strength as the reference, we scale the MWO field measurements to the measurements of the magnetic fields in Pevtsov et al. (2011) to construct a combined data set of maximum sunspot field strengths extending from 1920 to early 2012. This combined data set shows strong solar cycle variations and no significant long-term trend (linear fit to the data yields a slope of $-0.2\pm$0.8 G year$^{-1}$). On the other hand, the peak sunspot field strengths observed at the minimum of the solar cycle show a gradual decline over the last three minima (corresponding to cycles 21-23) with a mean downward trend of $\approx$ 15 G year$^{-1}$

Structural Invariance of Sunspot Umbrae Over the Solar Cycle: 1993-2004

Measurements of maximum magnetic flux, minimum intensity, and size are presented for 12 967 sunspot umbrae detected on the NASA/NSO spectromagnetograms between 1993 and 2004 to study umbral structure and strength during the solar cycle. The umbrae are selected using an automated thresholding technique. Measured umbral intensities are first corrected for a confirming observation of umbral limb-darkening. Log-normal fits to the observed size distribution confirm that the size spectrum shape does not vary with time. The intensity-magnetic flux relationship is found to be steady over the solar cycle. The dependence of umbral size on the magnetic flux and minimum intensity are also independent of cycle phase and give linear and quadratic relations, respectively. While the large sample size does show a low amplitude oscillation in the mean minimum intensity and maximum magnetic flux correlated with the solar cycle, this can be explained in terms of variations in the mean umbral size. These size variations, however, are small and do not substantiate a meaningful change in the size spectrum of the umbrae generated by the Sun. Thus, in contrast to previous reports, the observations suggest the equilibrium structure, as testified by the invariant size-magnetic field relationship, as well as the mean size (i.e. strength) of sunspot umbrae do not significantly depend on solar cycle phase.Comment: 17 pages, 6 figures. Published in Solar Physic

Crop supply dynamics and the illusion of partial adjustment

We use field-level data to estimate the response of corn and soybean acreage to price shocks. Our sample contains more than eight million observations derived from satellite imagery and includes every field in Iowa, Illinois, and Indiana. We estimate that aggregate crop acreage responds more to price shocks in the short run than in the long run, and we show theoretically how the benefits of crop rotation generate this response pattern. In essence, farmers who change crops due to a price shock have an incentive to switch back to the previous crop to capture the benefits of crop rotation. Our result contradicts the long-held belief that agricultural supply responds gradually to price shocks through partial adjustment. We would not have obtained this result had we used county-level panel data. Standard econometric methods applied to county-level data produce estimates consistent with partial adjustment. We show that this apparent partial adjustment is illusory, and we demonstrate how it arises from the fact that fields in the same county are more similar to each other than to fields in other counties. This result underscores the importance of using models with appropriate micro-foundations and cautions against inferring micro-level rigidities from inertia in aggregate panel data. Our preferred estimate of the own-price long-run elasticity of corn acreage is 0.29 and the cross-price elasticity is -0.22. The corresponding elasticities for soybean acreage are 0.26 and -0.33. Our estimated short-run elasticities are 37 percent larger than their long-run counterparts

Finite covers of random 3-manifolds

A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture posits that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. In this paper, we study random 3-manifolds and their finite covers in an attempt to shed light on this difficult question. In particular, we consider random Heegaard splittings by gluing two handlebodies by the result of a random walk in the mapping class group of a surface. For this model of random 3-manifold, we are able to compute the probabilities that the resulting manifolds have finite covers of particular kinds. Our results contrast with the analogous probabilities for groups coming from random balanced presentations, giving quantitative theorems to the effect that 3-manifold groups have many more finite quotients than random groups. The next natural question is whether these covers have positive betti number. For abelian covers of a fixed type over 3-manifolds of Heegaard genus 2, we show that the probability of positive betti number is 0. In fact, many of these questions boil down to questions about the mapping class group. We are lead to consider the action of mapping class group of a surface S on the set of quotients pi_1(S) -> Q. If Q is a simple group, we show that if the genus of S is large, then this action is very mixing. In particular, the action factors through the alternating group of each orbit. This is analogous to Goldman's theorem that the action of the mapping class group on the SU(2) character variety is ergodic.Comment: 60 pages; v2: minor changes. v3: minor changes; final versio

Evolution of active and polar photospheric magnetic fields during the rise of Cycle 24 compared to previous cycles

The evolution of the photospheric magnetic field during the declining phase and minimum of Cycle 23 and the recent rise of Cycle 24 are compared with the behavior during previous cycles. We used longitudinal full-disk magnetograms from the NSO's three magnetographs at Kitt Peak, the Synoptic Optical Long-term Investigations of the Sun (SOLIS) Vector Spectro-Magnetograph (VSM), the Spectromagnetograph and the 512-Channel Magnetograph instruments, and longitudinal full-disk magnetograms from the Mt. Wilson 150-foot tower. We analyzed 37 years of observations from these two observatories that have been observing daily, weather permitting, since 1974, offering an opportunity to study the evolving relationship between the active region and polar fields in some detail over several solar cycles. It is found that the annual averages of a proxy for the active region poloidal magnetic field strength, the magnetic field strength of the high-latitude poleward streams, and the time derivative of the polar field strength are all well correlated in each hemisphere. These results are based on statistically significant cyclical patterns in the active region fields and are consistent with the Babcock-Leighton phenomenological model for the solar activity cycle. There was more hemispheric asymmetry in the activity level, as measured by total and maximum active region flux, during late Cycle 23 (after around 2004), when the southern hemisphere was more active, and Cycle 24 up to the present, when the northern hemisphere has been more active, than at any other time since 1974. The active region net proxy poloidal fields effectively disappeared in both hemispheres around 2004, and the polar fields did not become significantly stronger after this time. We see evidence that the process of Cycle 24 field reversal has begun at both poles.Comment: Accepted for publication in Solar Physic

Solar Intranetwork Magnetic Elements: bipolar flux appearance

The current study aims to quantify characteristic features of bipolar flux appearance of solar intranetwork (IN) magnetic elements. To attack such a problem, we use the Narrow-band Filter Imager (NFI) magnetograms from the Solar Optical Telescope (SOT) on board \emph{Hinode}; these data are from quiet and an 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 co-aligned in magnetic axis orientation. On average, the sampled IN ERs have total maximum unsigned flux of several 10^{17} Mx, separation of 3-4 arcsec, and a lifetime of 10-15 minutes. The smallest IN ERs have a maximum unsigned flux of several 10^{16} Mx, separations 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 magneto-convection in the sub-photospheric layer.Comment: 26 pages, 14 figure

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.Comment: 43 pages, 18 figure

Modeling the Subsurface Structure of Sunspots

While sunspots are easily observed at the solar surface, determining their subsurface structure is not trivial. There are two main hypotheses for the subsurface structure of sunspots: the monolithic model and the cluster model. Local helioseismology is the only means by which we can investigate subphotospheric structure. However, as current linear inversion techniques do not yet allow helioseismology to probe the internal structure with sufficient confidence to distinguish between the monolith and cluster models, the development of physically realistic sunspot models are a priority for helioseismologists. This is because they are not only important indicators of the variety of physical effects that may influence helioseismic inferences in active regions, but they also enable detailed assessments of the validity of helioseismic interpretations through numerical forward modeling. In this paper, we provide a critical review of the existing sunspot models and an overview of numerical methods employed to model wave propagation through model sunspots. We then carry out an helioseismic analysis of the sunspot in Active Region 9787 and address the serious inconsistencies uncovered by \citeauthor{gizonetal2009}~(\citeyear{gizonetal2009,gizonetal2009a}). We find that this sunspot is most probably associated with a shallow, positive wave-speed perturbation (unlike the traditional two-layer model) and that travel-time measurements are consistent with a horizontal outflow in the surrounding moat.Comment: 73 pages, 19 figures, accepted by Solar Physic

Polyfuran Conducting Polymers: Synthesis, Properties, and Applications.

In this review, polyfuran (PFu) synthesis methods and the nucleation mechanism; the electrochemical, structural, morphological, and magnetic properties of PFu; thermal behavior; theoretical calculations on PFu, as well as its applications reported to date, have been compiled. Not only PFu homopolymers have been reviewed, but also PFu co-polymers, PFu bipolymers, and PFu composites. The results are listed, discussed, and compared. It is hoped that this assembly of all the relevant data might enhance knowledge about this conducting polymer and lead to new research fields

Measurement of the Nucleon Structure Function F2 in the Nuclear Medium and Evaluation of its Moments

We report on the measurement of inclusive electron scattering off a carbon target performed with CLAS at Jefferson Laboratory. A combination of three different beam energies 1.161, 2.261 and 4.461 GeV allowed us to reach an invariant mass of the final-state hadronic system W~2.4 GeV with four-momentum transfers Q2 ranging from 0.2 to 5 GeV2. These data, together with previous measurements of the inclusive electron scattering off proton and deuteron, which cover a similar continuous two-dimensional region of Q2 and Bjorken variable x, permit the study of nuclear modifications of the nucleon structure. By using these, as well as other world data, we evaluated the F2 structure function and its moments. Using an OPE-based twist expansion, we studied the Q2-evolution of the moments, obtaining a separation of the leading-twist and the total higher-twist terms. The carbon-to-deuteron ratio of the leading-twist contributions to the F2 moments exhibits the well known EMC effect, compatible with that discovered previously in x-space. The total higher-twist term in the carbon nucleus appears, although with large systematic uncertainites, to be smaller with respect to the deuteron case for n<7, suggesting partial parton deconfinement in nuclear matter. We speculate that the spatial extension of the nucleon is changed when it is immersed in the nuclear medium.Comment: 37 pages, 15 figure