Internal rotation of the Sun as inferred from GONG observations

Helioseismology is a direct and most informative method of studying the structure and dynamics of the Sun. Determining the internal differential rotation of the Sun requires that the frequencies of its eigentones be estimated with a high accuracy, which is possible only on the basis of continuous long-term observations. The longest quasi-continuous series of data have been obtained by the Global Oscillation Network Group (GONG). The parameters of each individual mode of solar acoustic oscillations with low spherical degrees l=0, 1, 2, 3, 4, 5, 6 are determined by using 1260-day-long series of GONG observations. The mean frequency splitting by rotation for the modes of each radial order n is calculated by using all possible combinations between the eigenfrequencies in multiplets. As a result, it has become possible to statistically estimate the splitting and its measurement errors for the modes of each radial order. The mean splitting for each given degree l=1–6 is presented under the assumption of its independence of oscillation frequency, which holds for the achieved accuracy. The frequencies and splittings for the modes with low spherical degrees l, together with the MDI group results for higher degrees l, are used to invert the radial profile of solar angular velocity. Using the SOLA method to solve the inverse problem of restoring the rotation profile has yielded solutions sensitive to the deepest stellar interiors. Our results indicate that the solar core rotates faster than the surface, and there may be a local minimum in angular velocity at its boundary.     

Active longitudes of the sun: The rotation period and statistical significance

Using data from the Greenwich catalog, we determined the nonuniformity of the longitudinal distribution of sunspot groups as a function of the rotation period taken for the longitude determination. We estimated the statistical significance of the active longitudes found. A fairly high significance was achieved only for sunspot groups of the Northern Hemisphere and odd activity cycles and only for a synodic rotation period close to 28 days. In this case, one interval of active longitudes was found. The active longitudes are assumed to be associated with the fossil magnetic field frozen in the uniformly rotating radiative zone of the Sun.     

22-Year periodicity in the solar differential rotation

Using the data on sunspot groups compiled during 1879–1975, we determined variations in the differential rotation coefficientsA andB during the solar cycle. The variation in the equatorial rotation rateA is found to be significant only in the odd numbered cycles, with an amplitude ∼ 0.01 μ rads^-1. There exists a good anticorrelation between the variations of the differential rotation rateB derived from the odd and even numbered cycles, suggesting existence of a ‘22-year’ periodicity inB. The amplitude of the variation ofB is ∼ 0.05 μ rad s^-1.     

Physics of the sun’s hot atmosphere

This article briefly overviews the physics of the Sun’s hot atmosphere, using observations from recent solar spacecrafts: Yohkoh, SOHO, TRACE and RHESSI.     

1米太阳望远镜光谱仪像旋转及消旋控制

光谱仪是1 m太阳望远镜的主要终端设备之一,该望远镜采用地平式的机架结构和修正的格里高利光学系统。在望远镜跟踪太阳时,由于地平式望远镜的自身运动特点和光学系统中平面反射镜的存在,其光谱仪狭缝所在平面上的太阳像随时间绕主光轴旋转,因此光谱仪必须进行消旋才能正常工作。首先深入研究了光谱仪狭缝平面上像的旋转变化,分析其旋转范围、速度和加速度随时角变化的特性,然后根据光谱仪消旋精度并结合像的旋转特性提出伺服系统位置检测和驱动电机的主要性能指标,最后给出光谱仪消旋伺服控制方案。     

A synthesized method for determining the azimuth of solar transverse magnetic field

The analyses have been made with the emphasis on four existing criteria for calibrating the azimuth of the photospheric transverse magnetic field measured with a heliomagnetograph. The results indicate that the potential criterion, Krall's criterion, i.e. B_t · B_z < 0 and Wu-Ai's criterion, i.e.

Full-size image (1K)

, are applicable to different cases, and the criterion based on the assumption about azimuth continuity of the transverse field is unreliable for the magnetograms with discrete data. On the basis of these analyses, a synthesized method for determining the azimuth of the transverse magnetic field on solar photosphere has been suggested in this paper. The main points of the method are as follows:

The transverse magnetic field observed with a heliomagnetograph could be calibrated, respectively, by means of potential criterion and Krall's criterion, and two different results could be obtained. By comparing the both results with one another, we can find that the azimuth distributions of transverse field are the same in some areas, which are named as areas with certain transverse field (CA), and different in other areas, which are named as areas with uncertain transverse field(UA). In order to determine the transverse field in UA, we introduce an assumption that the values of (the factor of force-free magnetic field) at neighbouring points are close. According to this assumption, the distribution of in UA could be determined through extrapolating from the CA, and hence the azimuth distribution of the transverse field in UA could be determined as well.

An observational example shown in this paper preliminarily demonstrates the availability of the synthesized method.     

A kinematic study of the Galaxy

Using the proper motion and parallax data for 1011 O-B stars in the Hipparcos Catalogue we have derived the Oort constants, A = 17.60 ± 0.21 (km/s)/kpc, B = −14.62 ± 0.20 (km/s)/kpc, and a solar velocity V = 16.7 ± 0.10 km/s in the direction l = 45.3° ± 2.8°, b = 21.0° ± 2.3°. For a galactocentric distance of the sun of R₀ = 8.5 kpc, we then get a galactic rotational velocity of the solar neighbourhood of V_lsr = 273.9 km/s, obviously much higher than the IAU published value of 220 km/s. We have investigated the cause for this difference.     

A method of astronomical autonomous orbit and attitude determinations for satellites

A method of realtime autonomous orbit determination for earth satellites using the extended Kalman filtering is proposed. The observed quantities are: the satellite-sun direction vector measured by a sun sensor, the satellite-earth and satellite-moon direction vectors measured by an ultraviolet sensor, and the geocentric distance measured by a radar altimeter. At the same time the satellite attitude to the earth is also determined. Results of our simulation of the autonomous orbit determination show that the precision of the orbit determinations is better than 200 m. The effects of the sampling period, orbital inclination, orbital eccentricity and orbital altitude on the precision of orbit determination are analyzed and compared, and certain principles helpful for improving the precision of orbit determination are suggested.     

Does sunspot activity originate in slow global oscillations of the sun?

We present preliminary results of a spherical-harmonic-Fourier analysis of sunspot activity during the twenty-two years 1933–1954. The results indicate that the sunspot activity might be originating in global solar oscillations with periods of years and decades. However, except for the axisymmetric mode of degree 6, the set of other axisymmetric modes showing ∼ 11 yr periodicities are different from one sunspot cycle to another. A more detailed analysis, preferably with larger data series, will be needed to arrive at a more definite conclusion.     

On the rotation of rigid Venus

According to A.A. Khentov Venus' rotation is in the quasi-stationary state as a result of the balance interaction of the solar tidal torque with the aerodynamical torque of the rotating Venus' atmosphere. In case of the nonconservative forces are negligible and the solar attraction is the stabilizing factor, the rotation of the rigid Venus may be assumed as the first approximation. The theory of the rotation of the rigid Venus in the coordinates,, had been constructed. It have been found that Venus rotates almost uniformly and the libration harmonics are negligible.     

Spin vectors in the Koronis family: II. Additional clustered spins, and one stray

We recorded 101 new rotation lightcurves of five Koronis family members, and then combined the new observations with previous data to determine the objects' sidereal rotation periods, spin vector orientations, and model shape solutions. The observing program was tailored specifically for spin vector analyses by determining single-apparition Lumme–Bowell solar phase coefficients, and by measuring synodic rotation periods precisely enough to unambiguously count the rotations between two consecutive oppositions, which is a prerequisite for identifying the correct sidereal period. The new data make possible first pole and shape determinations for (263) Dresda, (462) Eriphyla, and (1289) Kutaïssi, and they improve the models for (277) Elvira and (534) Nassovia, two objects previously studied by Slivan et al. [Slivan, S.M., Binzel, R.P., Crespo da Silva, L.D., Kaasalainen, M., Lyndaker, M.M., Kr?o, M., 2003. Icarus 162, 285–307]. Our results increase the number of Koronis family spin vectors reported in the literature to fourteen, a sample which now includes the seven largest family members. The spin properties of Eriphyla (rotation period , spin vector obliquity ε=51°) and Kutaïssi (P=3.62 h, ε=165°) are consistent with the markedly nonrandom distribution reported by Slivan [Slivan, S.M., 2002. Nature 419, 49–51], and explained by Vokrouhlický et al. [Vokrouhlický, D., Nesvorný, D., Bottke, W.F., 2003. Nature 425, 147–151] as the result of the effects of thermal “YORP” torques combined with solar and planetary gravitational torques. Dresda (P=16.81 h, ε=16°) is the first prograde Koronis member whose spin obliquity and spin rate significantly differ from the clustered spin properties previously found for other prograde Koronis members; nevertheless, its spin vector is consistent with several of the spin evolution possibilities that were identified in the YORP modeling.     

太阳风扰动传输模式研究进展

随着观测手段、理论模型和数值方法的发展,人们对各种太阳风扰动如日冕物质抛射,以及相关的空间天气效应的认识和理解越来越深入。为获取行星际背景磁场、背景太阳风参数和日冕物质抛射、激波等太阳风扰动的传播参数,人们建立发展了各种模式;在这些获取的参数基础上,建立了各种太阳风扰动的传播模式,从而为空间天气预报提供了必要的经验和理论模型支持。根据这些模式所研究和描述物理量的不同,将这些参数获取模式和传播预报模式分为背景磁场获取模式、背景太阳风参数获取模式、日冕物质抛射传播参数获取模式、日冕物质抛射偏转模式、日冕物质抛射(激波)传播模式以及基于三维磁流体力学的数值模拟方法,并分别概述性地总结了各种模式的特点及其用途。     

The theory of canonical perturbations applied to attitude dynamics and to the Earth rotation. Osculating and nonosculating Andoyer variables

In the method of variation of parameters we express the Cartesian coordinates or the Euler angles as functions of the time and six constants. If, under disturbance, we endow the “constants” with time dependence, the perturbed orbital or angular velocity will consist of a partial time derivative and a convective term that includes time derivatives of the “constants”. The Lagrange constraint, often imposed for convenience, nullifies the convective term and thereby guarantees that the functional dependence of the velocity on the time and “constants” stays unaltered under disturbance. “Constants” satisfying this constraint are called osculating elements. Otherwise, they are simply termed orbital or rotational elements. When the equations for the elements are required to be canonical, it is normally the Delaunay variables that are chosen to be the orbital elements, and it is the Andoyer variables that are typically chosen to play the role of rotational elements. (Since some of the Andoyer elements are time-dependent even in the unperturbed setting, the role of “constants” is actually played by their initial values.) The Delaunay and Andoyer sets of variables share a subtle peculiarity: under certain circumstances the standard equations render the elements nonosculating. In the theory of orbits, the planetary equations yield nonosculating elements when perturbations depend on velocities. To keep the elements osculating, the equations must be amended with extra terms that are not parts of the disturbing function [Efroimsky, M., Goldreich, P.: J. Math. Phys. 44, 5958–5977 (2003); Astron. Astrophys. 415, 1187–1199 (2004); Efroimsky, M.: Celest. Mech. Dyn. Astron. 91, 75–108 (2005); Ann. New York Acad. Sci. 1065, 346–374 (2006)]. It complicates both the Lagrange- and Delaunay-type planetary equations and makes the Delaunay equations noncanonical. In attitude dynamics, whenever a perturbation depends upon the angular velocity (like a switch to a noninertial frame), a mere amendment of the Hamiltonian makes the equations yield nonosculating Andoyer elements. To make them osculating, extra terms should be added to the equations (but then the equations will no longer be canonical). Calculations in nonosculating variables are mathematically valid, but their physical interpretation is not easy. Nonosculating orbital elements parameterise instantaneous conics not tangent to the orbit. (A nonosculating i may differ much from the real inclination of the orbit, given by the osculating i.) Nonosculating Andoyer elements correctly describe perturbed attitude, but their interconnection with the angular velocity is a nontrivial issue. The Kinoshita–Souchay theory tacitly employs nonosculating Andoyer elements. For this reason, even though the elements are introduced in a precessing frame, they nevertheless return the inertial velocity, not the velocity relative to the precessing frame. To amend the Kinoshita–Souchay theory, we derive the precessing-frame-related directional angles of the angular velocity relative to the precessing frame. The loss of osculation should not necessarily be considered a flaw of the Kinoshita–Souchay theory, because in some situations it is the inertial, not the relative, angular velocity that is measurable [Schreiber, K. U. et al.: J. Geophys. Res. 109, B06405 (2004); Petrov, L.: Astron. Astrophys. 467, 359–369 (2007)]. Under these circumstances, the Kinoshita–Souchay formulae for the angular velocity should be employed (as long as they are rightly identified as the formulae for the inertial angular velocity).     

On the onset of thermal metastabilities in the solar core

For infinitesimal, homologous perturbations, stability analysis has found the solar radiative interior thermally stable. It is considered for the first time here whether stability is preserved when finite amplitude nonhomologous perturbations are present. We argue that local heated regions may develop in the solar core due to magnetic instabilities. Simple numerical estimations are derived for the timescales of the decay of these events and, when heated bubbles are generated that rise towards the surface, of their rising motion. These estimations suggest that the solar core is in a metastable state. For more detailed analysis, we developed a numerical code to solve the differential equation system. Our calculations determined the conditions of metastability and the evolution of timescales. We obtained two principal results. One of them shows that small amplitude heating events (with energy surplus Q_o < 10²⁶ ergs) contribute to subtle but long-lifetime heat waves and give the solar interior a persistently oscillating character. Interestingly, the slow decay of heat waves may make their accumulation possible and so their overlapping may contribute to the development of an intermittent, individual, local process of bubble generation, which may also be generated directly by stronger (Q_o > 10²⁶ ergs) heating events. Our second principal result is that for heated regions with ΔT/T ≥ 10⁻⁴ and radius 10⁵–10⁶cm, the generated bubbles may travel distances larger than their linear size. We point out to some possible observable consequences of the obtained results.     

On the solar rotation and activity

The interaction between differential rotation and magnetic fields in the solar convection zone was recently modelled by Brun (2004). One consequence of that model is that the Maxwell stresses can oppose the Reynolds stresses, and thus contribute to the transport of the angular momentum towards the solar poles, leading to a reduced differential rotation. So, when magnetic fields are weaker, a more pronounced differential rotation can be expected, yielding a higher rotation velocity at low latitudes taken on the average. This hypothesis is consistent with the behaviour of the solar rotation during the Maunder minimum. In this work we search for similar signatures of the relationship between the solar activity and rotation determined tracing sunspot groups and coronal bright points. We use the extended Greenwich data set (1878–1981) and a series of full-disc solar images taken at 28.4 nm with the EIT instrument on the SOHO spacecraft (1998–2000). We investigate the dependence of the solar rotation on the solar activity (described by the relative sunspot number) and the interplanetary magnetic field (calculated from the interdiurnal variability index). Possible rotational signatures of two weak solar activity cycles at the beginning of the 20th century (Gleissberg minimum) are discussed. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the attitude dynamics of perturbed triaxial rigid bodies

Attitude dynamics of perturbed triaxial rigid bodies is a rather involved problem, due to the presence of elliptic functions even in the Euler equations for the free rotation of a triaxial rigid body. With the solution of the Euler–Poinsot problem, that will be taken as the unperturbed part, we expand the perturbation in Fourier series, which coefficients are rational functions of the Jacobian nome. These series converge very fast, and thus, with only few terms a good approximation is obtained. Once the expansion is performed, it is possible to apply to it a Lie-transformation. An application to a tri-axial rigid body moving in a Keplerian orbit is made.     

On the stationary configuration of the heliospheric sheet

The expansion of solar coronal plasma is considered for the model described in Koutchmy et al. (1999). In addition to a spherical solar surface, the initial configuration represents a heliospheric sheet of dense plasma in the dipole equatorial plane. The heliospheric-sheet current decreases with distance as 1/r ², with its sign being opposite to the sign of the initial-dipole current. The latter follows from the fact that the plasma sheet is denser than the surrounding corona and that the equilibrium condition for the sheet in the gravitational and magnetic fields is satisfied. The field lines of this configuration are nearly straight. We have obtained a general solution of the steady-state MHD equations, which depends not only on distance r but also on latitude θ. Applicability of the solution to interpreting observational data, in particular, those obtained from the Ulysses spacecraft, is discussed.     

On the Asynchronous Rotation of Accretors in Interacting Binaries

We show that the gaining component in interacting binaries can rotate faster than its orbital revolution as a consequence of the accretion process. We derive an approximative analytical formula for the Roche lobe radius of asynchronously rotating accretors. We present the case of the semi-detached interacting binary TX UMa, for which we measured directly asynchronous rotation of its accretor. We suggest a method to detect indirectly a fast spinning of accretors in symbiotic binaries based on the the X-ray luminosity of the boundary layer. We demonstrate this possibility for the case of EG And.