The 100—year periodic modulation of solar rotation

A periodic long-term modulation of the solar surface rotation with a time scale on the order of 100 years is found in the sunspot data from 1874 to 1992 obtained by combinig the Greenwich Photoheliographic Results from cycle 11 to cycle 20 analysed by Balthasar, Vázquez, and Wöhl and the Mitaka sunspot sketch data from cycle 18 to 22 of the National Astronomical Observatory of Japan which was the Tokyo Astronomical Observatory of the University of Tokyo until 1988. A new index of the solar rotation M defined by integrating the angular momentum density over the whole surface, which we call the angular momentum surface layer density, reached a maximum at solar cycle 14, decreased to a minimum at cycle 17, and then increased to reach another maximum at cycle 21. The increase of M means acceleration of the surface layer as a whole by transport of angular momentum from the deeper layer. This implies an decrease (increase) of the radial gradient of the differential rotation if the basic radial gradient of the differential rotation increases (decreaes) inward. The decrease of M means deceleration of the surface layer and implies an increase (decrease) of the radial gradient. The degree of the equatorial acceleration of the surface differential rotation is also found to have undergone the same 100 year periodic modulation during the same interval, reaching a minimum at cycle 14, a maximum at cycle 17, and a minimum at cycle 21 in antiphase with the modulation of M. Thus both radial and latitudinal gradients of the differential rotation increased and decreased in phase (in anti-phase) if the basic radial gradient increases (decreases) inward.     

The secular modulation of solar rotation from 1943 to 1992 and its time-delayed correlation with the 55-year grand cycle of the 11-year solar cycle

We devised a new method, which we call the running-segment method, to achieve high-resolution time series of indices of solar rotation for determining the latitude dependence of the differential rotation by a least-squares fitting of the daily translation of positions of sunspot groups during a fixed time segment of 11 years. The segment is moved by an amount of one year to determine the differential profile of the next point of time. Time of the determined rotation data is defined by an arithmetic mean of the beginning and ending years of the segment. The rotation underwent an acceleration from 1948 to 1974 and a deceleration from 1974 to 1987. We found that the time profile of the indexM, the angular momentum surface layer density defined by integration of the angular momentum volume density over the whole surface, follows almost exactly the time profile of the 11-year running mean of the yearly mean of the sunspot relative number with a delay time of about 20 years. The acceleration (deceleration) phase corresponds to the ascending (descending) phase of amplitude of the 11-year solar cycle of cycle 16 (19) to cycle 19 (20) with a delay time of about 20 years. The cycles 15–20 correspond to the 55-year grand cycle V of the 11-year cycle. The delay time of about 20 years agrees well with the delay time predicted by a nonlinear dynamo theory of the solar cycle for driving the 55-year modulation of the 11-year solar cycle. The agreement suggests that the Lorentz force of the magnetic field of the solar cycle during grand cycle V drives the solar rotation modulation from 1948 to 1987 and that the force needed about 20 years to modify the rotation during 1943–1992.     

Hydrodynamic processes of angular momentum transport in the interior of a rotating massive hydrogen-burning star

The evolution of a rotating star with a mass of 16M _⊙ at the hydrogen burning phase is considered together with the hydrodynamic processes of angular momentum transport in its interior. Shear turbulence is shown to limit the amplitude of the latitudinal variations in mean molecular weight on a surface of constant pressure in a layer with variable chemical composition. The resulting nonuniformity in the mean molecular weight distribution and the turbulent energy transport along the surface of constant pressure reduce the absolute value of the meridional circulation velocity. Nevertheless, meridional circulation remains the main mechanism of angular momentum transport in the radial direction in a layer with variable chemical composition. The intensity of the processes of angular momentum transport by meridional circulation and shear turbulence is determined by the angular momentum of the star. At a fairly high angular momentum, more specifically, at J = 3.69 × 10⁵² g cm² s^?1, the star during the second half of the hydrogen-burning phase in its convective core has characteristics typical of classical early Be stars.     

The angular momentum transport in rotating turbulent convection

The angular momentum transport in rotating turbulent convection is simulated with the NIRVANA code for Taylor numbers up to 10⁶. The box consists of an unstable layer embedded in two stable overshoot layers. We find the expected anisotropies in the rotating anisotropic turbulence field: 〈u^′2_r〉 exceeds 〈u^′2_ϕ〉, and 〈u^′2_ϕ〉 exceeds 〈u^′2_θ〉. The resulting radial angular momentum transport is directed inwards and peaks in the middle of the convective layer. The resulting latitudinal angular momentum transport is equatorwards, peaks at the surface and is highly concentrated to the equatorial region. Apart from a factor of 2–3 the total amplitudes of the cross‐correlations are of the same order of magnitude. In the lower overshoot region (‘tachocline’) the cross‐correlations are negative. It is argued that the concentration of the latitudinal angular momentum transport towards the surface and towards the equator does not too strongly reduce its potential to produce rotation laws with accelerated equators. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rotation Profiles of Solar-like Stars with Magnetic Fields

We investigate the rotation profile of solar-like stars with magnetic fields. A diffu-sion coefficient of magnetic angular momentum transport is deduced. Rotating stellar models with different mass incorporating the coefficient are computed to give the rotation profiles. The total angular momentum of a solar model with only hydrodynamic instabilities is about 13 times larger than that of the Sun at the age of the Sun, and this model can not reproduce quasi-solid rotation in the radiative region. However, the solar model with magnetic fields not only can reproduce an almost uniform rotation in the radiative region, but also a total angular momentum that is consistent with the helioseismic result at the 3 σ level at the age of the Sun. The rotation of solar-like stars with magnetic fields is almost uniform in the radiative region, but for models of 1.2-1.5 M⊙, there is an obvious transition region between the convective core and the radiative region, where angular velocity has a sharp radial gradient, which is different from the rotation profile of the Sun and of massive stars with magnetic fields. The change of angular velocity in the transition region increases with increasing age and mass.     

160-min pulsation of the Sun: New observational results

The 1974–1988 Crimean measurements of the solar line-of-sight velocity continue to show the presence of a statistically significant periodicity P ₁ = 160.009 (±) min with an average harmonic amplitude of about 21 cm s^–1. The period is supposed to be that of the global pulsation of the Sun but with a little-known physical mechanism of excitation.The new observations give some evidence for the existence of a second periodicity, P ₁ = 160.014 (±) min. It is hypothesized that the appearance of P ₁ might be a sidelobe mode (of the P ₀-oscillation) induced by rapid rotation of the central solar core.It is also noted that the spacing, in frequency, between P ₀ and P ₁, corresponds to a beat period of 10 ± 3 yr, which happens to be in good agreement with the average duration of the 11 yr cycle of the magnetic activity of the Sun. Accordingly, we suppose that the phase shift of the P ₀-mode between the 1974–1982 and 1986–1988 time intervals reflects a remarkable change of the general magnetic field of the Sun in the course of the 22 yr solar cycle.     

Differential rotation and meridional circulation in global models of solar convection

In the outer envelope of the Sun and in other stars, differential rotation and meridional circulation are maintained via the redistribution of momentum and energy by convective motions. In order to properly capture such processes in a numerical model, the correct spherical geometry is essential. In this paper I review recent insights into the maintenance of mean flows in the solar interior obtained from high-resolution simulations of solar convection in rotating spherical shells. The Coriolis force induces a Reynolds stress which transports angular momentum equatorward and also yields latitudinal variations in the convective heat flux. Meridional circulations induced by baroclinicity and rotational shear further redistribute angular momentum and alter the mean stratification. This gives rise to a complex nonlinear interplay between turbulent convection, differential rotation, meridional circulation, and the mean specific entropy profile. I will describe how this drama plays out in our simulations as well as in solar and stellar convection zones. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Celestial n-Body Coupling in the Lunar Orbit Theory

Making use of the fact that, in the solar system, the angular momentum is carried predominantly by the planets while the mass is beared almost entirely by the Sun, an iterative scheme is devised to solve approximately the n-body contributions of the lunar orbit problem. The scheme envisages the Moon-Earth-Sun three-body subsystem as being nested in the grand Earth-Jupiter-Sun system. In the planetocentric representation, the orbital motion of the Sun about the solar system center of mass is transmitted to the third body via the second primary body in both the grand and nested three-body systems. This revised version was published online in July 2006 with corrections to the Cover Date.     

The impact of aging on the rotation rate of calcium plages in the years 1967–1977

An analysis of Ca ii spectroheliograms obtained at Catania Astrophysical Observatory throughout the years 1967–1977 has been carried out, to throw light on the complex relationship linking (Ternullo, 1986) the angular rotation rate of Ca plages with their age, as well as with solar cycle phase, and with latitude. Given the rotation law w =, a + b sin² I, solar-cycle-related oscillatory properties both of a and b coefficients are described, both for young and old Ca plages.The aging-dependent rate-increments vary, for each epoch, both in module and sign with latitude; that results in deep distortions of the differential rotation latitudinal profile, which exhibits, when old plages are taken into account, a fine structure (Ternullo, 1987). Such a fine structure is absent in the young plage differential rotation profile.Throughout the time interval under examination, the torsional waves observed by Howard and LaBonte (1980) have appeared to be in close spatial relationship with the latitude bands where aging-dependent rate increments occur.

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Disk luminosity and angular momentum for accreting,weak field neutron stars in the ‘Slow’ rotation approximation

For accretion on to neutron stars possessing weak surface magnetic fields and substantial rotation rates (corresponding to the secular instability limit), we calculate the disk and surface layer luminosities general relativistically using the Hartle & Thorne formalism, and illustrate these quantities for a set of representative neutron star equations of state. We also discuss the related problem of the angular momentum evolution of such neutron stars and give a quantitative estimate for this accretion driven change in angular momentum. Rotation always increases the disk luminosity and reduces the rate of angular momentum evolution. These effects have relevance for observations of low-mass X-ray binaries.     

Analytical theory of tachocline transport at mid latitudes

We provide a theory of magnetic diffusion, momentum transport, and mixing in the solar tachocline by considering magnetohydrodynamics (MHD) turbulence on a β plane subject to a large scale shear (provided by the latitudinal differential rotation). In the strong magnetic field regime, we find that the turbulent viscosity and diffusivity are reduced by magnetic fields only, similarly to the two-dimensional MHD case (without Rossby waves). In the weak magnetic field regime, we find a crossover scale (L_R) from a Alfvén dominated regime (on small scales) to a Rossby dominated regime (on large scales). For parameter values typical of the tachocline, L_R is larger than the solar radius so that Rossby waves are unlikely to play an important role in the transport of magnetic field and angular momentum. This is mainly due to the enhancement of magnetic back-reaction by shearing which efficiently generates small scales, thus strong currents. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Angular momentum transport in pre-main-sequence stars of intermediate mass

Pre-Main-Sequence stars with masses between 2 and 5 M (Herbig Ae/Be stars) have radiative subphotospheric envelopes. However, they possess strong stellar winds and show definite signs of activity which could be linked to surface magnetic field. Therefore, they must lose angular momentum at a significant rate.We investigate the effect of such angular momentum losses on the internal structure of these stars, and on the distribution of angular velocity inside them. This paper presents a preliminary analysis guided by an analogy with laboratory and geophysical fluids. We propose that the friction exerted at the stellar surface by the angular momentum losses produces a mixed layer below the surface, separated from the unperturbed interior by an interface. Using scaling laws established by experimental studies of sheared stratified fluids, we discuss a simplified model for the evolution of the mixed layer.Although this model is still too preliminary to allow quantitative predictions, we show that for a reasonable choice of parameters, the mixed layer penetrates into the stellar interior on a time-scale of 10⁶ years, comparable to the Kelvin time-scale for the Herbig Ae/Be stars.     

Solar differential rotation derived from sunspot observations

Sunspot drawings obtained at National Astronomical Observatory of Japan during the years 1954–1986 were used to determine the differential rotation of the Sun. From the limited data set of three solar cycles it was found that three factors (the level of cycle activity, the cycle phase, and sunspot type) affect the solar rotation rate. The differential rotation varies from cycle to cycle in such a way that the rotation velocity in the low activity cycle (cycle 20) is higher than in the high-activity cycle (cycle 19). The equatorial rotation rate shows a systematic variation within each cycle. The rate is higher at the beginning of the cycle and decreases subsequently. Although quite small, the variation of solar differential rotation with respect to Zürich sunspot type was found. The H and J types show the slowest rotation among all the sunspot types.     

Possible dark matter in spiral galaxies of the coma cluster

The relationship between the rotation curves for the galaxies and the distribution of mass and angular momentum within the galaxies is examined. The theory of angular momentum transfer is applied to the observed properties of the galaxies. The coupling between the dynamical mass of a spiral galaxy and its luminosity is studied. Most of the spiral galaxies in subclusters surrounding NGC 4889, NGC 4874, and NGC 4839 in the Coma cluster are galaxies that have lower luminosities, with M_B fainter than −21^m.5. These galaxies are characterized by a higher mass-to-luminosity ratio than that of the galaxies with higher luminosities M_B brighter than −21^m.5, which suggests the presence of a large fraction of dark matter in the spiral galaxies of the subclusters. Translated from Astrofizika, Vol. 52, No. 1, pp. 75–84 (February 2009).     

Magnetic convection

In this paper the process of magnetic convection is studied. It is shown that outside of a radius of about 2 × 10⁵ km, magnetic fields in the Sun may be buoyant. Outside this limit strong field regions tend to rise at the expense of weak field regions which tend to sink. Magnetic convection may be important in magnetic stars and even in the solar interior. A recent calculation of the angular velocity of the Sun provides a period of rotation for the solar core of from 0.5 to 5 days. This calculation requires that the magnetic field extract angular momentum from the solar interior. Magnetic convection thus seems to be required, if this calculation is correct. Furthermore, magnetic convection may transfer heat and thereby possibly change the internal temperature structure of the Sun from what would be expected solely by radiation transfer.     

Angular momentum drain: A mechanism for despinning asteroids

It is proposed that a new mechanism—angular momentum drain—helps account for the relatively slow rotation rates of intermediate-sized asteroids. Impact ejecta on a spinning body preferentially escape in the direction of rotation. This material systematically drains away spin angular momentum, leading to the counterintuitive result that collisions can reduce the spin of midsized objects. For an asteroid of mass M spinning at frequency ω, a mass loss δM correspond to an average decrease in rotation rate $\text{δω ≈}\text{ωδM}\text{M}$. A. W. Harris' (1979), Icarus40, 145–153) theory for the collisional evolution of asteroidal spins is significantly altered by inlusion of this effect. While the modified theory is still somewhat artificial, comparison of its predictions with the data of S. F. Dermott, A. W. Harris, and C. D. Murray (1984, Icarus57, 14–34) suggests that angular momentum drain is essential for understanding the statistics of asteroidal rotations.     

Solar polar spin-down

An explanation for the solar differential rotation is proposed that makes use of angular momentum transfer in the solar wind and corona. Evidence suggests that for most of the solar cycle, the solar wind is connected by magnetic field lines to high heliographic latitudes on the Sun.Thus the angular momentum lost to the solar wind would present a preferential drag to the photospheric material at high heliographic latitudes. It is shown that this drag is sufficient to offset the restoring forces of the Sun's subsurface magnetic field. In fact, the subsurface magnetic field and differential rotation are thought to grow until the stresses are sufficient to balance the torque induced by the solar wind. The present level of differential rotation and solar activity may be maintained by an intricate feedback mechanism involving the whole solar activity cycle.A power calculation based upon this model suggests the Sun's core rotates with a period of between 0.5 and 5 days. Furthermore, this view requires a major change in present theory of solar magnetic field generation.     

Latitudinal shear instability in the solar tachocline

In an attempt to explain the observed rotation profile in the solar radiative zone and the tachocline, Spiegel & Zahn proposed a model based on anisotropic turbulent angular momentum transport. Although very successful in reproducing some of the features of the solar tachocline, their model assumes without verification that the origin of the turbulence could be caused by latitudinal shear instability. This paper studies the weakly non-linear evolution of two-dimensional shear instability, in which the interaction between the global rotation profile and the Reynolds stresses can be described self-consistently. Provided that the initial rotation profile is sufficiently close to marginal stability (which is the case of the solar tachocline), the instability is shown to saturate and to relax to a marginally stable state, which differs very little from the observed rotation profile. It is therefore likely that the tachocline is in a state of marginal stability with respect to latitudinal shear instability, and shows that angular momentum transport in the tachocline is unlikely to be caused by shear-induced turbulence.     

Surface Reynolds stresses determined from the analysis of facular motions and the maintenance of the Sun's differential rotation

From the analysis of the motions of faculae for a four year period from 1967 to 1970, the latitudinal angular momentum transport by Reynolds stresses at the Sun's surface is calculated. The result agrees fairly well with the one obtained by Ward analyzing spot motions. A comparison with theory suggests that the Sun's differential rotation could be maintained only by Reynolds stresses at the surface. The implications of this result are discussed.     

A large-eddy simulation of turbulent compressible convection: differential rotation in the solar convection zone

We present the results of two simulations of the convection zone, obtained by solving the full hydrodynamic equations in a section of a spherical shell. The first simulation has cylindrical rotation contours (parallel to the rotation axis) and a strong meridional circulation, which traverses the entire depth. The second simulation has isorotation contours about mid-way between cylinders and cones, and a weak meridional circulation, concentrated in the uppermost part of the shell.
We show that the solar differential rotation is directly related to a latitudinal entropy gradient, which pervades into the deep layers of the convection zone. We also offer an explanation of the angular velocity shear found at low latitudes near the top. A non-zero correlation between radial and zonal velocity fluctuations produces a significant Reynolds stress in that region. This constitutes a net transport of angular momentum inwards, which causes a slight modification of the overall structure of the differential rotation near the top. In essence, the thermodynamics controls the dynamics through the Taylor–Proudman momentum balance . The Reynolds stresses only become significant in the surface layers, where they generate a weak meridional circulation and an angular velocity 'bump'.