The Scattering Polarization of the Sr I 4607 \AA Line at the Diffraction Limit Resolution of a 1-m Telescope

One of the greatest challenges in solar and stellar physics in coming years will be to observe the Second Solar Spectrum with a spatial resolution significantly better than 1 arcsec. This type of scattering polarization observations would probably allow us to discover hitherto unknown aspects of the Sun's hidden magnetism. Here we report on some theoretical predictions for the photospheric line of Sr I at 4607 \AA, which we have obtained by solving the three-dimensional (3D) radiative transfer problem of scattering line polarization in a realistic hydrodynamical model of the solar photosphere. We have taken into account not only the anisotropy of the radiation field in the 3D medium and the Hanle effect of a tangled magnetic field, but also the symmetry breaking effects caused by the horizontal atmospheric inhomogeneities produced by the solar surface convection. Interestingly, the Q/I and U/I linear polarization signals of the emergent spectral line radiation have sizable values and fluctuations, even at the very center of the solar disk where we meet the forward scattering case. The ensuing small-scale patterns in Q/I and U/I turn out to be sensitive to the assumed magnetic field model, and are of great diagnostic value. We argue that it should be possible to observe them with the help of a 1-m telescope equipped with adaptive optics and a suitable polarimeter.Comment: Accepted for publication in The Astrophysical Journal Letters (12 pages and 2 color figures

Nature of the solar dynamo at small scales

It is often claimed that there is not only one, but two different types of solar dynamos: the one that is responsible for the appearance of sunspots and the 11-yr cycle, frequently referred to as the "global dynamo", and a statistically time-invariant dynamo, generally referred to as the "local dynamo", which is supposed to be responsible for the ubiquitous magnetic structuring observed at small scales. Here we examine the relative contributions of these two qualitatively different dynamos to the small-scale magnetic flux, with the following conclusion: The local dynamo does not play a significant role at any of the spatially resolved scales, nearly all the small-scale flux, including the flux revealed by Hinode, is supplied by the global dynamo. This conclusion is reached by careful determination of the Sun's noise-corrected basal magnetic flux density while making use of a flux cancellation function determined from Hinode data. The only allowed range where there may be substantial or even dominating contributions from a local dynamo seems to be the scales below about 10 km, as suggested by observations of the Hanle depolarization effect in atomic spectral lines. To determine the fraction of the Hanle depolarization that may be due to the action of a local dynamo, a synoptic program is being initiated at IRSOL (Istituto Ricerche Solari Locarno)

Transition of the Sunspot Number from Zurich to Brussels in 1980: A Personal Perspective

The Swiss Federal Observatory, which had been founded in 1863 by Rudolf Wolf, was dissolved in connection with the retirement of Max Waldmeier in 1979. The determination of the Zurich sunpot number, which had been a cornerstone activity of the observatory, was then discontinued by ETH Zurich. A smooth transition of the responsibility for the sunspot number from Zurich to Brussels could however be achieved in 1980, through which it was possible to avoid a discontinuity in this important time series. Here we describe the circumstances that led to the termination in Zurich, how Brussels was chosen for the succession, and how the transfer was accomplished

The Magnetic Sensitivity of the Ba II D1 and D2 Lines of the Fraunhofer Spectrum

The physical interpretation of the spectral line polarization produced by the joint action of the Hanle and Zeeman effects offers a unique opportunity to obtain empirical information about hidden aspects of solar and stellar magnetism. To this end, it is important to achieve a complete understanding of the sensitivity of the emergent spectral line polarization to the presence of a magnetic field. Here we present a detailed theoretical investigation on the role of resonance scattering and magnetic fields on the polarization signals of the Ba II D1 and D2 lines of the Fraunhofer spectrum, respectively at 4934 \AA\ and 4554 \AA. We adopt a three-level model of Ba II, and we take into account the hyperfine structure that is shown by the $^{135}$Ba and $^{137}$Ba isotopes. Despite of their relatively small abundance (18%), the contribution coming from these two isotopes is indeed fundamental for the interpretation of the polarization signals observed in these lines. We consider an optically thin slab model, through which we can investigate in a rigorous way the essential physical mechanisms involved (resonance polarization, Zeeman, Paschen-Back and Hanle effects), avoiding complications due to radiative transfer effects. We assume the slab to be illuminated from below by the photospheric solar continuum radiation field, and we investigate the radiation scattered at 90 degrees, both in the absence and in the presence of magnetic fields, deterministic and microturbulent. We show in particular the existence of a differential magnetic sensitivity of the three-peak Q/I profile that is observed in the D2 line in quiet regions close to the solar limb, which is of great interest for magnetic field diagnostics.Comment: 40 pages, 1 table and 19 figures. Accepted for publication in The Astrophysical Journal (ApJ

Iterated function systems with a given continuous stationary distribution

For any continuous probability measure $\mu$ on ${\mathbb R}$ we construct an IFS with probabilities having $\mu$ as its unique measure-attractor.Comment: 7 pages, 3 figure

The electromagnetic structure of interplanetary space

A method to calculate the three-dimensional structure of the interplanetary magnetic field is presented. The integrations are based on magnetograph recordings of longitudinal magnetic fields in the solar photosphere. The program by Altschuler and Newkirk is used to calculate the radial component of the magnetic field on the source surface, situated at r = 2.6r. This determines the inner boundary conditions for the integration outwards of the interplanetary field equations by means of the method that is described. Computer-drawn plots of the interplanetary field lines out to the earth's orbit are presented for the periods around the total solar eclipses of November 12, 1966, and March 7, 1970. During the former period the interplanetary field exhibited a clean, dipole-type structure, while during the latter period the field was more complicated and had four sectors in the equatorial plane. A movie was presented, showing how the interplanetary field structure rotates as seen by a magnetometer in the sun's equatorial plane

Hanle effect in the CN violet system with LTE modeling

Weak entangled magnetic fields with mixed polarity occupy the main part of the quiet Sun. The Zeeman effect diagnostics fails to measure such fields because of cancellation in circular polarization. However, the Hanle effect diagnostics, accessible through the second solar spectrum, provides us with a very sensitive tool for studying the distribution of weak magnetic fields on the Sun. Molecular lines are very strong and even dominate in some regions of the second solar spectrum. The CN $B {}^{2} \Sigma - X {}^{2} \Sigma$ system is one of the richest and most promising systems for molecular diagnostics and well suited for the application of the differential Hanle effect method. The aim is to interpret observations of the CN $B {}^{2} \Sigma - X {}^{2} \Sigma$ system using the Hanle effect and to obtain an estimation of the magnetic field strength. We assume that the CN molecular layer is situated above the region where the continuum radiation is formed and employ the single-scattering approximation. Together with the Hanle effect theory this provides us with a model that can diagnose turbulent magnetic fields. We have succeeded in fitting modeled CN lines in several regions of the second solar spectrum to observations and obtained a magnetic field strength in the range from 10--30 G in the upper solar photosphere depending on the considered lines.Comment: Accepted for publication in Astronomy and Astrophysic

Scaling laws for magnetic fields on the quiet Sun

The Sun's magnetic field is structured over a range of scales that span approximately seven orders of magnitudes, four of which lie beyond the resolving power of current telescopes. Here we have used a Hinode SOT/SP deep mode data set for the quiet-sun disk center in combination with constraints from the Hanle effect to derive scaling laws that describe how the magnetic structuring varies from the resolved scales down to the magnetic diffusion limit, where the field ceases to be frozen-in. The focus of the analysis is a derivation of the magnetic energy spectrum, but we also discuss the scale dependence of the probability density function (PDF) for the flux densities and the role of the cancellation function for the average unsigned flux density. Analysis of the Hinode data set with the line-ratio method reveals a collapsed flux population in the form of flux tubes with a size distribution that is peaked in the 10-100 km range. Magnetic energy is injected into this scale range by the instability mechanism of flux tube collapse, which is driven by the external gas pressure in the superadiabatic region at the top of the convection zone. This elevates the magnetic energy spectrum just beyond the telescope resolution limit. Flux tube decay feeds an inertial range that cascades down the scale spectrum to the magnetic diffusion limit, and which contains the tangled, "hidden" flux that is known to exist from observations of the Hanle effect. The observational constraints demand that the total magnetic energy in the hidden flux must be of the same order as the total energy in the kG flux tubes. Both the flux tubes and the hidden flux are found to be preferentially located in the intergranular lanes, which is to be expected since they are physically related.Comment: accepted for publication in Astronomy & Astrophysic

Measuring the Hidden Aspects of Solar Magnetism

2008 marks the 100th anniversary of the discovery of astrophysical magnetic fields, when George Ellery Hale recorded the Zeeman splitting of spectral lines in sunspots. With the introduction of Babcock's photoelectric magnetograph it soon became clear that the Sun's magnetic field outside sunspots is extremely structured. The field strengths that were measured were found to get larger when the spatial resolution was improved. It was therefore necessary to come up with methods to go beyond the spatial resolution limit and diagnose the intrinsic magnetic-field properties without dependence on the quality of the telescope used. The line-ratio technique that was developed in the early 1970s revealed a picture where most flux that we see in magnetograms originates in highly bundled, kG fields with a tiny volume filling factor. This led to interpretations in terms of discrete, strong-field magnetic flux tubes embedded in a rather field-free medium, and a whole industry of flux tube models at increasing levels of sophistication. This magnetic-field paradigm has now been shattered with the advent of high-precision imaging polarimeters that allow us to apply the so-called "Second Solar Spectrum" to diagnose aspects of solar magnetism that have been hidden to Zeeman diagnostics. It is found that the bulk of the photospheric volume is seething with intermediately strong, tangled fields. In the new paradigm the field behaves like a fractal with a high degree of self-similarity, spanning about 8 orders of magnitude in scale size, down to scales of order 10 m.Comment: To appear in "Magnetic Coupling between the Interior and the Atmosphere of the Sun", eds. S.S. Hasan and R.J. Rutten, Astrophysics and Space Science Proceedings, Springer-Verlag, Heidelberg, Berlin, 200