Magnetic and thermal phase shifts in the local helioseismology of sunspots

Phase perturbations due to inclined surface magnetic field of active region strength are calculated numerically in quiet Sun and simple sunspot models in order to estimate and compare the direct and indirect (thermal) effects of the fields on helioseismic waves. It is found that the largest direct effects occur in highly inclined field characteristic of penumbrae, and scale roughly linearly with magnetic field strength. The combined effects of sunspot magnetic and thermal anomalies typically yield negative travel-time perturbations in penumbrae. Travel-time shifts in umbrae depend on details of how the thermal and density structure differs from the quiet Sun. The combined shifts are generally not well approximated by the sum of the thermal and magnetic effects applied separately, except at low field strengths of around 1 kG or less, or if the thermal shift is small. A useful rule-of-thumb appears to be that travel-time perturbations in umbrae are predominantly thermal, whereas in penumbrae they are mostly magnetic.     

Imaging optically-thin hotspots near the black hole horizon of Sgr A* at radio and near-infrared wavelengths

Submilliarcsecond astrometry and imaging of the black hole Sgr A* at the Galactic Centre may become possible in the near future at infrared and submillimetre wavelengths. Motivated by the observations of short-term infrared and X-ray variability of Sgr A*, in a previous paper, we computed the expected images and light curves, including polarization, associated with a compact emission region orbiting the central black hole. We extend this work, using a more realistic hotspot model and including the effects of opacity in the underlying accretion flow. We find that at infrared wavelengths, the qualitative features identified by our earlier work are present, namely it is possible to extract the black hole mass and spin from spot images and light curves of the observed flux and polarization. At radio wavelengths, disc opacity produces significant departures from the infrared behaviour, but there are still generic signatures of the black hole properties. Detailed comparison of these results with future data can be used to test general relativity and to improve existing models for the accretion flow in the immediate vicinity of the black hole.     

Probing sunspot magnetic fields with p-mode absorption and phase shift data

Long-standing observations of incoming and outgoing f- and p-modes in annuli around sunspots reveal that the spots partially absorb and substantially shift the phase of waves incident upon them. The commonly favoured absorption mechanism is partial conversion to slow magneto-acoustic waves that disappear into the solar interior channelled by the magnetic field of the sunspot. However, up until now, only f-mode absorption could be accounted for quantitatively by this means. Based on vertical magnetic field models, the absorption of p-modes was insufficient. In this paper, we use the new calculations of Crouch & Cally for inclined fields, and a simplified model of the interaction between spot interior and exterior. We find excellent agreement with phase shift data assuming field angles from the vertical in excess of 30° and Alfvén/acoustic equipartition depths of around 600–800 km. The absorption of f-modes produced by such models is considerably larger than is observed, but consistent with numerical simulations. On the other hand, p-mode absorption is generally consistent with observed values, up to some moderate frequency dependent on radial order. Thereafter, it is too large, assuming absorbing regions comparable in size to the inferred phase-shifting region. The excess absorption produced by the models is in stark contrast with previous calculations based on a vertical magnetic field, and is probably due to finite mode lifetimes and excess emission in acoustic glories. The excellent agreement of phase shift predictions with observational data allows some degree of probing of subsurface field strengths, and opens up the possibility of more accurate inversions using improved models. Most importantly, though, we have confirmed that slow mode conversion is a viable, and indeed the likely, cause of the observed absorption and phase shifts.     

Magnetic field inclination and atmospheric oscillations above solar active regions

Recent observational evidence for magnetic field direction effects on helioseismic signals in sunspot penumbrae is suggestive of magnetohydrodynamic (MHD) mode conversion occurring at lower levels. This possibility is explored using wave mechanical and ray theory in a model of the Sun's surface layers permeated by uniform inclined magnetic field. It is found that fast-to-slow conversion near the equipartition depth at which the sound and Alfvén speeds coincide can indeed greatly enhance the atmospheric acoustic signal at heights observed by Solar and Heliospheric Observatory/Michelson Doppler Imager and other helioseismic instruments, but that this effect depends crucially on the wave attack angle , i.e. the angle between the wavevector and the magnetic field at the conversion/transmission depth. A major consequence of this insight is that the magnetic field acts as a filter, preferentially allowing through acoustic signal from a narrow range of incident directions. This is potentially testable by observation.     

Calibration of Vector Magnetogram with the Nonlinear Least-squares Fitting Technique

To acquire Stokes profiles from observations of a simple sunspot with the Video Vector Magnetograph at Huairou Solar Observing Station (HSOS), we scanned the FeI λ5324.19A line over the wavelength interval from 150mA redward of the line center to 150 mA blueward, in steps of 10 mA. With the technique of analytic inversion of Stokes profiles via nonlinear least-squares, we present the calibration coefficients for the HSOS vector magnetic magnetogram. We obtained the theoretical calibration error with linear expressions derived from the Unno-Becker equation under weak-field approximation.     

Modeling helioseismic modes in the magnetic atmosphere of the Sun

The pulsation of the solar surface is caused by acoustic waves traveling in the solar interior. Thorough analyses of observational data indicate that these f and p helioseismic oscillation modes are not bounced back completely at the surface but they partially penetrate into the atmosphere. Atmospheric effects and their possible observational application are investigated in one‐dimensional magnetohydrodynamic models. It is found that f and p mode frequencies are shifted of the order of μHz due to the presence of an atmospheric magnetic field. This shift varies with the direction of the wave propagation.Resonant coupling of global helioseismic modes to local Alfvén and slow waves reduce the life time of the global modes. The resulting line width of the frequency line is of the order of nHz, and it also varies with propagation angle. These features enable us to use helioseismic observations in magnetic diagnostics of the lower atmosphere. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Search for relationship between duration of the extended solar cycles and amplitude of sunspot cycle

Duration of the extended solar cycles is taken into the consideration. The beginning of cycles is counted from the moment of polarity reversal of large-scale magnetic field in high latitudes, occurring in the sunspot cycle n till the minimum of the cycle n + 2. The connection between cycle duration and its amplitude is established. Duration of the “latent” period of evolution of extended cycle between reversals and a minimum of the current sunspot cycle is entered. It is shown, that the latent period of cycles evolution is connected with the next sunspot cycle amplitude and can be used for the prognosis of a level and time of a sunspot maximum. The 24th activity cycle prognosis is made. The found dependences correspond to transport dynamo model of generation of solar cyclicity, it is possible with various speed of meridional circulation. Long-term behavior of extended cycle's lengths and connection with change of a climate of the Earth is considered. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Looking inside the butterfly diagram

The suitability of Maunder's butterfly diagram to give a realistic picture of the photospheric magnetic flux large scale distribution is discussed. The evolution of the sunspot zone in cycle 20 through 23 is described. To reduce the noise which covers any structure in the diagram, a smoothing algorithm has been applied to the sunspot data. This operation has eliminated any short period fluctuation, and given visibility to long duration phenomena. One of these phenomena is the fact that the equatorward drift of the spot zone center of mass results from the alternation of several prograde (namely, equatorward) segments with other stationary or poleward segments. The long duration of the stationary/retrograde phases as well as the similarities among the spot zone alternating paths in the cycles under examination prevent us from considering these features as meaningless fluctuations, randomly superimposed on the continuous equatorward migration. On the contrary, these features should be considered physically meaningful phenomena, requiring adequate explanations. Moreover, even the smoothed spotted area markedly oscillates. The compared examination of area and spot zone evolution allows us to infer details about the spotted area distribution inside the butterfly diagram. Links between the changing structure of the spot zone and the tachocline rotation rate oscillations are proposed. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The solar dynamo in the light of the distribution of various sunspot magnetic classes over butterfly diagram

We present the data concerning the distribution of various sunspot magnetic classes over the solar butterfly diagram and discuss how this data can inform solar dynamo models. We use the statistics of sunspots that violate the Hale polarity law to estimate the ratio of the fluctuating and mean components of the toroidal magnetic field inside the solar convective zone. An analysis of the spatial distribution of bipolar, unipolar and complex sunspot groups in the context of simple dynamo models results in the conclusion that the mean toroidal field is relatively simple and maintains its shape during the course of the solar cycle (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cluster analysis for pattern recognition in solar butterfly diagrams

We investigate to what extent the wings of solar butterfly diagrams can be separated without an explicit usage of Hale's polarity law as well as the location of the solar equator. We apply two algorithms of cluster analysis for this purpose, namely DBSCAN and C‐means, and demonstrate their ability to separate the wings of contemporary butterfly diagrams based on the sunspot group density in the diagram only. Then we apply the method to historical data concerning the solar activity in the 18th century (Staudacher data). The method separates the two wings for Cycle 2, but fails to separate them for Cycle 1. In our opinion, this finding supports the interpretation of the Staudacher data as an indication of the unusual nature of the solar cycle in the 18th century (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The role of emerging bipoles in the formation of a sunspot penumbra

The generation of magnetic flux in the solar interior and its transport from the convection zone into the photosphere, the chromosphere, and the corona will be in the focus of solar physics research for the next decades. With 4 m class telescopes, one plans to measure essential processes of radiative magneto‐hydrodynamics that are needed to understand the nature of solar magnetic fields. One key‐ingredient to understand the behavior of solar magnetic field is the process of flux emergence into the solar photosphere, and how the magnetic flux reorganizes to form the magnetic phenomena of active regions like sunspots and pores. Here, we present a spectropolarimetric and imaging data set from a region of emerging magnetic flux, in which a proto‐spot without penumbra forms a penumbra. During the formation of the penumbra the area and the magnetic flux of the spot increases. First results of our data analysis demonstrate that the additional magnetic flux, which contributes to the increasing area of the penumbra, is supplied by the region of emerging magnetic flux. We observe emerging bipoles that are aligned such that the spot polarity is closer to the spot. As an emerging bipole separates, the pole of the spot polarity migrates towards the spot, and finally merges with it. We speculate that this is a fundamental process, which makes the sunspot accumulate magnetic flux. As more and more flux is accumulated a penumbra forms and transforms the proto‐spot into a full‐fledged sunspot (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Center to limb variation of penumbral Stokes V profiles

We investigated the horizontal and the vertical component of the Evershed flow (EF). To this end, we computed average Stokes V profiles for various velocity classes in penumbrae at different heliocentric angles. Our results show that for blueshifted profiles an additional lobe with the same polarity as the spot is present in the blue side of the average Stokes V profile. The amplitude of the additional lobe grows with increasing blueshift and with increasing heliocentric angle. For small redshifts, the profiles show an additional lobe with the opposite polarity as the spot on the red side of the average Stokes V profile. Even at disk center, the original polarity of the average Stokes V profile is reversed for strong redshifts. The transition between the different types of Stokes V profiles is continuous and indicates that not only the vertical, but also the horizontal EF is a magnetized stream of plasma in a magnetic background field (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamics of the solar magnetic field from SOHO/MDI

The investigation of the dynamics of magnetic fields from small scales to the large scales is very important for the understanding of the nature of solar activity. It is also the base for producing adequate models of the solar cycle with the purpose to predict the level of solar activity. Since December 1995 the Michelson Doppler Imager (MDI) on board of the Solar and Heliospheric Observatory (SOHO) provides full disk magnetograms and synoptic maps which cover the period of solar cycle 23 and the current minimum. In this paper, I review the following important topics with a focus on the dynamics of the solar magnetic field. The synoptic structure of the solar cycle; the birth of the solar cycle (overlapping cycles 23 and 24); the relationship of the photospheric magnetic activity and the EUV solar corona, polar magnetic fields and dynamo theory (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)