Modelling the differential rotation of F stars

We model stellar differential rotation based on the mean-field theory of fluid dynamics. DR is mainly driven by Reynolds stress, which is anisotropic and has a non-diffusive component because the Coriolis force affects the convection pattern. Likewise, the convective heat transport is not strictly radial but slightly tilted towards the rotation axis, causing the polar caps to be slightly warmer than the equator. This drives a flow opposite to that caused by differential rotation and so allows the system to avoid the Taylor-Proudman state. Our model reproduces the rotation pattern in the solar convection zone and allows predictions for other stars with outer convection zones. The surface shear turns out to depend mainly on the spectral type and only weakly on the rotation rate. We present results for stars of spectral type F which show signs of very strong differential rotation in some cases. Stars just below the mass limit for outer convection zones have shallow convection zones with short convective turnover times. We find solar-type rotation and meridional flow patterns at much shorter rotation periods and horizontal shear much larger than on the solar surface, in agreement with recent observations. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new look at the relationship between activity, dynamo number and Rossby number in late-type stars

The correlation between stellar activity, as measured by the indicator Δ R _HK, and the Rossby number Ro in late-type stars is revisited in light of recent developments in solar dynamo theory. Different stellar interior models, based on both mixing-length theory and the full spectrum of turbulence, are used in order to see to what extent the correlation of activity with Rossby number is model dependent, or otherwise can be considered universal. Although we find some modest model dependence, we find that the correlation of activity with Rossby number is significantly better than with rotation period alone for all the models we consider. Dynamo theory suggests that activity should scale with the dynamo number. A current model of the solar dynamo, the so-called interface dynamo, proposes that the amplification of the toroidal magnetic field by differential rotation (the ω -effect) and the production of the poloidal magnetic field from toroidal by helical turbulence (the α -effect) take place in different, adjacent layers near the base of the convection zone. A new scale analysis based on the interface dynamo shows that the appropriate dynamo number does not depend on the Rossby number alone, but also depends on an additional dimensionless factor related to the differential rotation. This leads to a new interpretation of the correlation between activity and Rossby number, which in turn leads to some conclusions about the magnitude of differential rotation in the dynamo layers of late-type main-sequence stars.     

Differential rotation of giant stars

From a set of high-resolution spectral observations of late type giant stars we used Doppler imaging to derive time-series temperature maps of the stellar surfaces. Using these temperature maps, it is possible to track the temporal changes of the spot features and derive estimates of the strength and sign of the differential surface rotation of these stars. Looking into the latitudinal changes of the surface maps, it is also possible to derive meridional flows on these stars. But due to the lower accuracy of the latitudes of the reconstructed spot features, the data requirements are higher than for the detection of differential rotation. Nevertheless, a correlation between the differential rotation and meridional flow estimates is suggested. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On global and local magnetic fields of flare stars with YZ CMi and OT Ser as examples

Global magnetic fields of flare stars evolve very fast—at times of tens–hundreds of days. In our opinion, this is due to mutual addition of local magnetic fields generated by the differential rotation of these objects.With the example of two flare stars,OT Ser and YZCMi, we consider possiblemechanisms of generation and disspation of local and global magnetic fields and the mechanism of “magnetic deceleration” of these stars according to the scheme “differential rotation–generation of local magnetic fields–fluorescence of energy accumulated by local magnetic fields during flares.” We also estimated the rotation energy and global magnetic field for OT Ser and YZCMi. It is shown that even strong dissipation of the accumulated local magnetic energy in the flare on February 9, 2008 (UT 20:22:00) in YZCMi has not had any impact on the global magnetic field.     

Change in the activity character of the coronae of low-mass stars of various spectral types

We study the dependence of the coronal activity index on the stellar rotation velocity. This question has been considered previously for 824 late-type stars on the basis of a consolidated catalogue of soft X-ray fluxes. We carry out a more refined analysis separately for G, K, and M dwarfs. Two modes of activity are clearly identified in them. The first is the saturation mode, is characteristic of young stars, and is virtually independent of their rotation. The second refers to the solar-type activity whose level strongly depends on the rotation period. We show that the transition from one mode to the other occurs at rotation periods of 1.1, 3.3, and 7.2 days for stars of spectral types G2, K4, and M3, respectively. In light of the discovery of superflares on G and K stars from the Kepler spacecraft, the question arises as to what distinguishes these objects from the remaining active late-type stars. We analyze the positions of superflare stars relative to the remaining stars observed by Kepler on the “amplitude of rotational brightness modulation (ARM)—rotation period” diagram. The ARM reflects the relative spots area on a star and characterizes the activity level in the entire atmosphere. G and K superflare stars are shown to be basically rapidly rotating young objects, but some of them belong to the stars with the solar type of activity.     

Differential rotation on rapidly rotating stars

Theories of meridional circulation and differential rotation in stellar convective zones predict trends in surface flow patterns on main-sequence stars that are amenable to direct observational testing. Here I summarise progress made in the last few years in determining surface differential rotation patterns on rapidly-rotating young main-sequence stars of spectral types F, G, K and M. Differential rotation increases strongly with increasing effective temperature along the main sequence. The shear rate appears to increase with depth in the sub-photospheric layers. Tidal locking in close binaries appears to suppress differential rotation, but better statistics are needed before this conclusion can be trusted. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Aurora on Uranus: A Faraday disc dynamo mechanism

We propose a mechanism whereby the solar wind flowing past the magnetosphere of Uranus causes a Faraday disc dynamo topology to be established and power to be extracted from the kinetic energy of rotation of Uranus. An immediate consequence of this dynamo is the generation of Birkeland currents that flow in and out of the sunlit polar cap with the accompanying production of polar aurora. We calculate the power extracted from planetary rotation as a function of planetary dipole magnetic moment and the ionospheric conductivity of Uranus. For plausible values of ionospheric conductivity, the observed auroral power requires a magnetic moment corresponding to a surface equatorial field of the order of 4 Gauss, slightly larger than the value 1.8 Gauss given by the empirical “magnetic Bodes law”.     

Meridional Motions and Reynolds Stress Determined by Using Kanzelhöhe Drawings and White Light Solar Images from 1964 to 2016

Sunspot position data obtained from Kanzelhöhe Observatory for Solar and Environmental Research (KSO) sunspot drawings and white light images in the period 1964 to 2016 were used to calculate the rotational and meridional velocities of the solar plasma. Velocities were calculated from daily shifts of sunspot groups and an iterative process of calculation of the differential rotation profiles was used to discard outliers. We found a differential rotation profile and meridional motions in agreement with previous studies using sunspots as tracers and conclude that the quality of the KSO data is appropriate for analysis of solar velocity patterns. By analyzing the correlation and covariance of meridional velocities and rotation rate residuals we found that the angular momentum is transported towards the solar equator. The magnitude and latitudinal dependence of the horizontal component of the Reynolds stress tensor calculated is sufficient to maintain the observed solar differential rotation profile. Therefore, our results confirm that the Reynolds stress is the dominant mechanism responsible for transport of angular momentum towards the solar equator.     

Determination of the rotation curve for stars of the Gould Belt using bottlinger's formulas

Based on the Hipparcos catalog and the radial velocities of stars published to date, we perform a kinematic analysis of OB stars. Parameters of the general Galactic rotation were determined from distant OB stars. We used the residual velocities of stars corrected for the general Galactic rotation to study the proper rotation of nearby OB stars. Geometrical characteristics of the Gould Belt were estimated by analyzing its kinematic parameters. We obtained parameters of peculiar solar motion as well as parameters of the proper rotation, expansion, and contraction for rotation around both the Galactic z axis and an axis perpendicular to the plane of symmetry of the disk. Kinematic parameters of the proper differential rotation were found for two age groups of nearby OB stars. Almost all of the nearby OB stars were shown to rotate in the same direction as the Galactic rotation. We constructed rotation curves.     

Differential rotation in F stars

Differential rotation can be detected in single line profiles of stars rotating more rapidly than about v sin i = 10km s-1 with the Fourier transform technique. This allows to search for differential rotation in large samples to look for correlations between differential rotation and other stellar parameters. I analyze the fraction of differentially rotating stars as a function of color, rotation, and activity in a large sample of F-type stars. Color and rotation exhibit a correlation with differential rotation in the sense that more stars are rotating differentially in the cooler, less rapidly rotating stars. Effects of rotation and color, however, cannot be disentangled in the underlying sample. No trend with activity is found. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Differential rotation of cool active stars: the case of intermediate rotators

In this paper, we present a new method for measuring the surface differential rotation of cool stars with rotation periods of a few days, for which the sparse phase coverage achievable from single-site observations generally prevents the use of more conventional techniques. The basic idea underlying this new analysis is to obtain the surface differential rotation pattern that minimizes the information content of the reconstructed Doppler image through a simultaneous fit of all available data.
Simulations demonstrate that the performance of this new method in the case of cool stars is satisfactory for a variety of observing strategies. Differential rotation parameters can be recovered reliably as long as the total data set spans at least 4 per cent of the time for the equator to lap the pole by approximately one complete cycle. We find in particular that these results hold for potentially complex spot distributions (as long as they include a mixture of low- and high-latitude features), and for various stellar inclination angles and rotation velocities. Such measurements can be obtained from either unpolarized or polarized data sets, provided their signal-to-noise ratio is larger than approximately 500 and 5000 per 2 km s⁻¹ spectral bin, respectively.
This method should therefore be very useful for investigating differential rotation in a much larger sample of objects than what has been possible up to now, and should hence give us the opportunity of studying how differential rotation reacts to various phenomena operating in stellar convective zones, such as tidal effects or dynamo magnetic field generation.     

Solar Rotation And Cycle Length

A positive correlation is suggested between solar rotation rate and solar cycle length for cycles 12 to 20. This result seems to be opposite to recent observations in solar-type stars and the Sun and yields inverse correlations between cycle lengths and chromospheric activity, but it agrees with previous work with solar-type stars and the Sun suggesting a positive correlation between cycle length and rotation rate. Estimates of solar cycle length for the Maunder minimum suggest a length 17 yr.     

Carrington Coordinates and Solar Maps

Solar synoptic charts are normally displayed using Carrington Coordinates with each Carrington rotation being centered at a Carrington longitude of 180^° and with a full 360^° of solar surface properties included. For the case of reproducing solar magnetic fields in the corona and heliosphere, these maps are wrapped onto the solar surface to provide the boundary conditions for a solution to a set of modeling equations such as the potential field theory equations. Due to differential rotation, the full solar surface cannot be reproduced in this fashion since different parts of the solar surface are observed at different times. We describe here the proper technique for combining observations of the solar magnetic or velocity fields made at different times into a representation of the whole solar surface at a particular specified time that we refer to as a “snapshot heliographic map“.     

Differential rotation of cool active stars

The surface differential rotation of active solar‐type stars can be investigated by means of Doppler and Zeeman‐Doppler Imaging, both techniques enabling one to estimate the short‐term temporal evolution of photospheric structures (cools spots or magnetic regions). After describing the main modeling tools recently developed to guarantee a precise analysis of differential rotation in this framework, we detail the main results obtained for a small number of active G and K fast rotating stars. We evoke in particular some preliminary trends that can be derived from this sample, bearing the promise that major advances in this field will be achieved with the new generation of spectropolarimeters (ESPaDOnS/CFHT, NARVAL/TBL). (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Night‐time science with large solar telescopes: The magnetic Sun through time

Today the Sun has a regular magnetic cycle driven by a dynamo action. But how did this regular cycle develop? How do basic parameters such as rotation rate, age, and differential rotation affect the generation of magnetic fields? Zeeman Doppler imaging (ZDI) is a technique that uses high‐resolution observations in circularly polarised light to map the surface magnetic topology on stars. Utilising the spectropolarimetric capabilities of future large solar telescopes it will be possible to study the evolution and morphology of the magnetic fields on a range of Sun‐like stars from solar twins through to rapidly‐rotating active young Suns and thus study the solar magnetic dynamo through time. In this article I discuss recent results from ZDI of Sun‐like stars and how we can use night‐time observations from future solar telescopes to solve unanswered questions about the origin and evolution of the Sun's magnetic dynamo (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The solar surface differential rotation from disk-integrated chromospheric fluxes

Disk-integrated solar chromospheric Caii K-line (3933.68 ) fluxes have been measured almost daily at Sacramento Peak Observatory since 1977. Using observing windows selected to mimic seasonal windows for chromospheric measurements of lower Main-Sequence stars such as those observed by Mount Wilson Observatory's HK Project, we have measured the solar rotation from the modulation of the Caii K-line flux. We track the change of rotation period from the decline of cycle 21 through the maximum of cycle 22. This variation in rotation period is shown to behave as expected from the migration of active regions in latitude according to Maunder's butterfly diagram, including an abrupt change in rotation period at the transition from cycle 21 to cycle 22. These results indicate the successful detection of solar surface differential rotation from disk-integrated observations. We argue that the success of our study compared to previous investigations of the solar surface differential rotation from disk-integrated fluxes lies primarily with the choice of the length of the time-series window. Our selection of 200 days is shorter than in previous studies whose windows are typically on the order of one year. The 200-day window is long enough to permit an accurate determination of the rotation period, yet short enough to avoid complications arising from active region evolution. Thus, measurements of the variation of rotation period in lower Main-Sequence stars, especially those that appear to be correlated with long-term changes in chromospheric activity (i.e., cycles), are probably evidence for stellar surface differential rotation.     

Starspots, Activity Cycles, and Differential Rotation on Cool Stars

We present the first results of searching for stellar cycles by analysis of stellar spottedness using an algorithm developed at the Crimean Astrophysical Observatory. For more than 35 red spotted stars, we find ten targets which demonstrate cyclic variations of average latitudes and total areas of starspots. Activity cycles detected by this method have a typical cycle length about 4–15 years which are analogous to the 11-year solar Schwabe cycle. Most of the program stars demonstrate a rough analogue with the solar butterfly diagram. They show a tendency for the average starspot latitude lowering when the total spot area grows. At the same time these stars show variations of stellar photometric period (which is traced by starspots) with the starspot latitudinal drift analogously to the solar differential rotation effect. We suspect that the starspot latitudinal drift rate and the differential rotation gradient depend on the stellar spectral type.     

Stellar irradiance variations due to surface temperature inhomogeneities

Observations of rotational modulation of continuum brightness and photospheric and chromospheric spectral-line profiles of late-type stars indicate the presence of very inhomogeneous surface temperature distributions. We present three stellar examples (VY Ari, HR 7275, HU Vir) where time-series photometry is used to trace the evolution of spotted regions. Simultaneous spectroscopy and Doppler imaging for one of the three stars (HU Virgo, Fig. 1) makes it possible to compute the temperature distribution of the photosphere and the relative intensity distribution of parts of the chromosphere (from CaII K and H line profiles). The combination of time-series spot modeling and Doppler imaging enabled us to determine thesign and amount of differential surface rotation on HU Vir. We found a big, cool polar spot (see figure below) and a differential (surface) rotation law where higher-latitude regions rotate faster than lower-latitude regions (opposite to what we see on the Sun). Currently, this ensemble of techniques - time-series photometry and photospheric and chromospheric Doppler imaging - is only applicable to stars overactive by approximately a factor of 100 as compared to the active Sun, e.g. the evolved components in RS CVn-type binaries and some rapidly-rotating, single, pre-main sequence stars or giant stars. Stellar rotation is a fundamental parameter for (magnetic) activity. Starspots, or any other surface inhomogeneities, allow one to derive very precise stellar rotation rates and, if coupled with seismological observations of solar-type stars, could provide information on the internal angular momentum distribution in overactive late-type stars.To be published in Astronomy & Astrophysics.     

Simulating the generation of the solar toroidal magnetic field by differential rotation

Within the kinematic dynamo theory, we construct a mathematical model for the evolution of the solar toroidal magnetic field, excited by the differential rotation of the convective zone in the presence of a poloidal field of a relic origin. We use a velocity profile obtained by decoding the data of helioseismological experiments. For the model of ideal magnetic hydrodynamics, we calculate the latitudinal profiles of the increasing-with-time toroidal field at different depths in the solar convection zone. It is found that, in the region of differential rotation, the excited toroidal field shows substantial fluctuations in magnitude with depth. Based on the simulations results, we propose an explanation for the “incorrect polarity” of magnetic bipolar sunspot groups in solar cycles.     

Extrasolar planetary systems

The article deals with the occurrence of planetary systems in the Universe. In Section I, the terms “planet” and “planet-like objects” are defined. Two definitions proposed for the term “planetary system” are examined from the point of view (1) of the relation between planetary systems and binary and multiple star systems and (2) of planetary systems as abodes of intelligent beings. In Section II, the observational search for extrasolar planetary systems is described, as performable by earthbound optical telescopes, by space probes, by long baseline radio interferometry, and finally by inference from the reception of signals sent by intelligent beings in other worlds.In Section III we show that any planetary system must be preceded by a rotating disk of gas and dust around a central mass. Both observational evidence and theoretical reasons indicate the ease of formation of such disk structures in the cosmos. The time scale of collapse of a gaseous medium into a disk and that of the latter's dissipation are examined. This provides us with a new empirical approach and leads us to consider the problem of the frequency of occurrence of planetary systems to be ripe for scientific study. In Section IV, a brief review of theories of the formation of the solar system is given along with a proposed scheme for classification of these theories. In Section V, the evidence for magnetic activity in the early stages of stellar evolution is presented, as developed from six independent clues: the nuclear abundance of light elements, the behavior of flare stars, the intensities of H and K emission in stars, the nonthermal radiation of premain sequence stars, the properties of meteorites, and finally the existence of contact binaries. The magnetic braking theories of solar and stellar rotation are discussed in Section VI, thereby introducing the idea of formation of a rotating disk of gas and dust around stars in Section VII. From this disk a planetary system emerges.Section VIII gives an estimate for the frequency of occurrence of planetary systems in the Universe. It is based on the rotational behavior of main-sequence stars, and concludes that planetary systems have a far greater chance to appear around single main-sequence stars of spectral types later than F5 than around any other kind of star. The combined probability distribution of sizes and masses could be obtained. From physical considerations, it appears that sizes of planetary systems around stars of any given spectral type may not vary greatly from one to another.