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)     

Perspectives on the interior of the Sun

The interior of the Sun is not directly accessible to observations. Nonetheless, it is possible to infer the physical conditions inside the Sun with the help of structure equations governing its equilibrium and with the powerful observational tools provided by the neutrino fluxes and oscillation frequencies. The helioseismic data show that the internal constitution of the Sun can be adequately represented by a standard solar model. It turns out that a cooler solar core is not a viable solution for the measured deficit of neutrino fluxes, and the resolution of the solar neutrino puzzle should be sought in the realm of particle physics.     

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)     

Solar p modes of high degree l: coupling by differential rotation

Accurate measurements of solar p-mode frequencies and frequency splittings at high degree l require an adequate theoretical knowledge of the effects of mode coupling, induced by the variation with latitude of the angular velocity of the solar internal rotation. Earlier results for expansion coefficients of composite solutions (coupling coefficients) are due to Woodard. In this paper, the analysis is extended to allow for the dependence of the differential rotation on depth, and the result is expressed in terms of measurable quantities (the rotational splitting coefficients), which makes it convenient for diagnostic purposes. The analysis is based on the approach of quasi-degenerate perturbation theory, and is extended further to address possible effects of mode coupling in the observational line profiles. It is shown, using approximations applicable at high degree l , that the expected line profiles of composite modes in the observational power spectra are not distorted by mode coupling.     

New aspects of Doppler imaging in Sun-as-a-star observations

Birmingham Solar Oscillations Network (BiSON) instruments use resonant scattering spectrometers to make unresolved Doppler velocity observations of the Sun. Unresolved measurements are not homogenous across the solar disc and so the observed data do not represent a uniform average over the entire surface. The influence on the inhomogeneity of the solar rotation and limb darkening has been considered previously and is well understood. Here, we consider a further effect that originates from the instrumentation itself. The intensity of light observed from a particular region on the solar disc is dependent on the distance between that region on the image of the solar disc formed in the instrument and the detector. The majority of BiSON instruments have two detectors positioned on opposite sides of the image of the solar disc and the observations made by each detector are weighted towards differing regions of the disc. Therefore, the visibility and amplitudes of the solar oscillations and the realization of the solar noise observed by each detector will differ. We find that the modelled bias is sensitive to many different parameters such as the width of solar absorption lines, the strength of the magnetic field in the resonant scattering spectrometer, the orientation of the Sun's rotation axis, the size of the image observed by the instrument and the optical depth in the vapour cell. We find that the modelled results best match the observations when the optical depth at the centre of the vapour cell is 0.55. The inhomogeneous weighting means that a 'velocity offset' is introduced into unresolved Doppler velocity observations of the Sun, which varies with time, and so has an impact on the long-term stability of the observations.     

Another view of synodic solar rotation

Adding the angular velocity of sidereal solar rotation and the apparent rotational effect of the Earth's revolution vectorially, a new synodic solar rotation vector has been obtained. The sidereal and synodic solar rotation axes (and equators) are separated. Using the known parameters of the Earth's orbital motion, the synodic rotation angular velocity and the inclination of the synodic equator, the corresponding sidereal rotation parameters have been calculated (ω₁ = 2.915 × 10^#X2212;6 rad s^#X2212;1 and i ₁ = 6.076). Various linear rotational velocities at the solar globe are briefly described.     

Modulation and symmetry changes in stellar dynamos

Stellar dynamos are governed by non-linear partial differential equations (PDEs) which admit solutions with dipole, quadrupole or mixed symmetry (i.e. with different parities). These PDEs possess periodic solutions that describe magnetic cycles, and numerical studies reveal two different types of modulation. For modulations of Type 1 there are parity changes without significant changes of amplitude, while for Type 2 there are amplitude changes without significant changes in parity. In stars like the Sun, cyclic magnetic activity is interrupted by grand minima that correspond to Type 2 modulation. Although the Sun's magnetic field has maintained dipole symmetry for almost 300 yr, there was a significant parity change at the end of the Maunder Minimum. We infer that the solar field may have flipped from dipole to quadrupole polarity (and back) after deep minima in the past and may do so again in the future. Other stars, with different masses or rotation rates, may exhibit cyclic activity with dipole, quadrupole or mixed parity. The origins of such behaviour can be understood by relating the PDE results to solutions of appropriate low-order systems of ordinary differential equations (ODEs). Type 1 modulation is reproduced in a fourth-order system while Type 2 modulation occurs in a third-order system. Here we construct a new sixth-order system that describes both types of modulation and clarifies the interactions between symmetry-breaking and modulation of activity. Solutions of these non-linear ODEs reproduce the qualitative behaviour found for the PDEs, including flipping of polarity after a prolonged grand minimum. Thus we can be confident that these patterns of behaviour are robust, and will apply to stars that are similar to the Sun.     

90年代太阳模型和太阳震荡研究进展(I):太阳模型研究进展(英)

太阳模型的研究是了解太阳整体结构和性质的极为重要的手段。90年代以来太阳模型研究取得了进展。随着MHD及OPAL物态方程的引入,理论上的太阳振荡频率与观测值的差别已大为减小,而考虑湍流频谱分布的局域对流理论和三维流体动力学模拟结果可对太阳内部对流能量传输过程有更深刻的理解．以前所发现的理论模型与反演结果得到的初始氦丰度的差别已能由扩散过程加以解释,而太阳表面锂丰度亏损问题也可以由扩散过程或早期演化星风来加以解决,太阳中微子问题则似应由粒子物理而不是天体物理来解决。     

Relationship between Rotating Sunspots and Flares

Active Region (AR) NOAA 10486 was a super AR in the declining phase of solar cycle 23. Dominated by the rapidly rotating positive polarity of an extensive δ sunspot, it produced several powerful flare-CMEs. We study the evolution and properties of the rotational motion of the major poles of positive polarities and estimate the accumulated helicity injected by them. We also present two homologous flares that occurred in the immediate periphery of the rotating sunspots. The main results are as follows: i) anticlockwise rotational motions are identified in the main poles of positive polarities in the AR; the fastest of them is about 220° for six days. ii) The helicity injection inferred from such rotational motion during the interval from October 25 to 30 is about − 3.0×10⁴³ Mx², which is comparable that calculated by the local correlation tracking (LCT) method (− 5.2×10⁴³ Mx²) in the whole AR. It is suggested that both methods reveal the essential topological properties of the AR, even if the former includes only the major poles and the fine features of the magnetic field are neglected. iii) It is found that there is a good spatial and temporal correspondence between the onset of two homologous CME-associated flares and the rotational motion of sunspots. This suggests that the rotational motions of sunspots not only relate to the transport of magnetic energy and complexity from the low atmosphere to the corona but may also play a key role in the onset of the homologous flares. Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users.     

Solar Activity and Classical Physics

1 INTRODUCTION The Sun is close enough to observe in some detail, and it shows that a star is more than the traditional stable self-gravitating thermonuclear body established half a celltury ago. For the fact is that out of sight beneath the visible surface the outward flow of heat from the thermonuclear core drives hydrodynamics that generates magnetic fields. It is the complicated dynamics of those magnetic fields that produces the modern mysteries of the active Sun. The…     

High sensitivity polarimetry

Over the last decade spectro‐polarimetry evolved to ever higher sensitivity levels. New techniques and instruments allow us to address weak polarization signals, which are caused by scattering in the solar atmosphere. In this paper a review on the development of spectro‐polarimetric investigations of scattering physics and its coupling to the solar magnetic field will be given. Starting from a technical point of view it will be demonstrated how our understanding of scattering phenomena and their role in solar physics in general has reached its current state. An outlook on future spectro‐polarimetry with new large solar telescopes concludes this review.     

Interplanetary dust particles and solar radiation

The problem of the action of the solar radiation on the motion of interplanetary dust particle is discussed. Differences between the action of electromagnetic solar radiation and that of the solar wind are explained not only from the point of view of the physical nature of these phenomena but also from the point of view of dust particle's orbital evolution. As for the electromagnetic solar radiation, general equation of motion for the particle is written and the most important consequences are: (i) the process of inspiralling toward the Sun is not the only possible motion - even spiralling from the Sun is also possible, and, (ii) the orbital plane of the particle (its inclination) may change in time. As for the solar wind, the effect corresponding to the fact that solar wind particles spread out from the Sun in nonradial direction causes that the process of inspiralling toward the Sun is in more than 50% less effective than for radial spread out; in the region of the asteroid belt (long period orbits) the process of inspiralling is changed into offspiralling. Also shift in the perihelion of dust particle's orbit exists.     

Rotation of the solar core from BiSON and LOWL frequency observations

Determination of the rotation of the solar core requires very accurate data on splittings for the low-degree modes which penetrate to the core, as well as for modes of higher degree to suppress the contributions from the rest of the Sun to the splittings of the low-degree modes. Here we combine low-degree data based on 32 months of observations with the BiSON network and data from the LOWL instrument. The data are analysed with a technique that specifically aims at obtaining an inference of rotation that is localized to the core. Our analysis provides what we believe is the most stringent constraint to date on the rotation of the deep solar interior.     

太阳P模振动理论的研究

日震学是太阳物理的一个前沿分支学科,是根据太阳振动的观测来研究太阳的内部结构与运动的一种方法学。太阳５ｍｉｎ振动频率的理论计算和实测之间存在的显著偏差和振动模的激发问题一直是困扰日震学的两大难题,经过多年的研究仍然没有解决。然而太阳的表面层内绝热假设条件与真实情况有很大的偏差,我们认为绝大多数标准太阳模型的Ｐ模频率计算忽略了非绝热效应对频率的影响,忽略了振动的激发和衰减机制以及缺乏振动与对流湍流相互作用的知识。因此,我们必须发展非绝热理论来处理太阳５ｍｉｎ的振动问题     

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)     

The sun‐as‐a‐star solar spectrum

The Sun is the only star for which individual surface features can be observed directly. For other stars, the properties of starspots, stellar rotation, stellar flares, etc, are derived indirectly via variation of star‐integrated spectral line profiles or their luminosity measurements. Solar disk‐integrated and disk‐resolved observations allow for investigations of the contribution of individual solar disk features to sun‐as‐a‐star spectra. Here, we provide a brief overview of three sun‐as‐a‐star programs, currently in operation, and describe recent improvements in observations and data reduction for the Integrated Sunlight Spectrometer (ISS), one of three instruments comprising the Synoptic Optical Long‐term Investigations of the Sun (SOLIS) system. Next, we discuss studies employing sun‐as‐a‐star observations (including Ca II K line as proxy for total unsigned magnetic flux and 2800 MHz radio flux) as well as the effects of flares on solar disk‐integrated spectra. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

太阳5分钟振荡的激发机制

1 引言 太阳5分钟振荡是上世纪1个重要的发现[1],它使得人们可以通过观测太阳表面的振动来探测其内部的结构,日震学已取得了巨大的进展,然而我们至今仍不了解其脉动的激发机制,它依然是1个存在争议的问题.太阳位于造父变星脉动不稳定区之外,所以大多数人都相信,由于对流的阻尼,太阳是脉动稳定的,太阳和太阳型恒星的振荡都是由所谓的湍流随机激发机制所激发[2-8].     

Relativistic effects and solar oblateness from radar observations of planets and spacecraft

We used more than 250 000 high-precision American and Russian radar observations of the inner planets and spacecraft obtained in the period 1961–2003 to test the relativistic parameters and to estimate the solar oblateness. Our analysis of the observations was based on the EPM ephemerides of the Institute of Applied Astronomy, Russian Academy of Sciences, constructed by the simultaneous numerical integration of the equations of motion for the nine major planets, the Sun, and the Moon in the post-Newtonian approximation. The gravitational noise introduced by asteroids into the orbits of the inner planets was reduced significantly by including 301 large asteroids and the perturbations from the massive ring of small asteroids in the simultaneous integration of the equations of motion. Since the post-Newtonian parameters and the solar oblateness produce various secular and periodic effects in the orbital elements of all planets, these were estimated from the simultaneous solution: the post-Newtonian parameters are β = 1.0000 ± 0.0001 and γ = 0.9999 ± 0.0002, the gravitational quadrupole moment of the Sun is J₂ = (1.9 ± 0.3) × 10^?7, and the variation of the gravitational constant is ?/G = (?2 ± 5) × 10^?14 yr^?1. The results obtained show a remarkable correspondence of the planetary motions and the propagation of light to General Relativity and narrow significantly the range of possible values for alternative theories of gravitation.     

Signature of differential rotation in solar disk‐integrated chromospheric line emission

UARS SOLSTICE data have been subjected to Fourier and wavelet analyses in order to search for the signature of the solar rotation law in the disk‐integrated irradiance of UV lines. Lyman‐α, Mg II, and Ca II data show a different behaviour. In the SOLSTICE data there are significant temporal variations of the rotation rate of the UV tracers over 5—6 years. Often several distinct rotation periods appear almost simultaneously. Beside the basic period around 27 days there are signals at 32—35 days corresponding to the rotation rate at very high latitudes. For more than 5 years during another period of the solar cycle the rotational behaviour is quite different; there is an indication of differential rotation of active regions in these Ca II ground‐based data. The data contain a wealth of information about the solar differential rotation, but it proves difficult to disentangle the effects of the different emitting sources.     

Rotation speed and stellar axis inclination from p modes: how CoRoT would see other suns

In the context of future space-based asteroseismic missions, we have studied the problem of extracting the rotation speed and the rotation-axis inclination of solar-like stars from the expected data. We have focused on slow rotators (at most twice solar rotation speed), first, because they constitute the most difficult case and, secondly, because some of the Convection Rotation and planetary Transits ( CoRoT ) main targets are expected to have slow rotation rates. Our study of the likelihood function has shown a correlation between the estimates of inclination of the rotation axis i and the rotational splitting δν of the star. By using the parameters, i and  δν^⋆=δν sin  i   , we propose and discuss new fitting strategies. Monte Carlo simulations have shown that we can extract a mean splitting and the rotation-axis inclination down to solar rotation rates. However, at the solar rotation rate we are not able to correctly recover the angle i , although we are still able to measure a correct  δν^⋆  with a dispersion less than 40 nHz.