Abstract
This article surveys the development of observational understanding of the interior rotation of the Sun and its temporal variation over approximately forty years, starting with the 1960s attempts to determine the solar core rotation from oblateness and proceeding through the development of helioseismology to the detailed modern picture of the internal rotation deduced from continuous helioseismic observations during solar cycle 23. After introducing some basic helioseismic concepts, it covers, in turn, the rotation of the core and radiative interior, the “tachocline” shear layer at the base of the convection zone, the differential rotation in the convection zone, the near-surface shear, the pattern of migrating zonal flows known as the torsional oscillation, and the possible temporal variations at the bottom of the convection zone. For each area, the article also briefly explores the relationship between observations and models.
Highlights
The internal rotation of the Sun is intimately related to the processes that drive the activity cycle. Brown et al (1989) stated that, “Knowledge of the internal rotation of the Sun with latitude, radius, and time is essential for a complete understanding of the evolution and the present properties of the Sun,” and this remains true today.The Sun rotates on its axis approximately once every 27 days; the rotation is not uniform, being substantially slower near the poles than at the equator
The pattern repeats – not precisely – with each 11year activity cycle, each equatorward-migrating flow band exists for about eighteen years, emerging at mid-latitudes soon after the maximum of one cycle and disappearing at the equator a couple of years after the minimum of the following cycle; the band of faster rotation associated with the activity of cycle 22 was still visible at the beginning of Global Oscillation Network Group (GONG) and Michelson Doppler Imager (MDI) observations in early cycle 23, and the band that is expected to accompany cycle 24 became visible around 2002, or 2005 – 2006
Because of the surprising nature of many of the findings, it has been important to have more than one source of observations, so that it is possible to distinguish between real solar features – especially the unexpected ones – and systematic error
Summary
The raw data of helioseismology consist of measurements of the photospheric Doppler velocity – or in some cases intensity in a particular wavelength band – taken at a cadence of about one minute and generally collected with as little interruption as possible over periods of months or years; the measurements can be either imaged or integrated (“Sun as a Star”). As was first discovered by Deubner (1975), the velocity or intensity variations at the solar surface have a spectrum in k − ω or l − ν space that reveals their origin in acoustic modes propagating in a cavity bounded above by the solar surface and below by the wavelength-dependent depth at which the waves are refracted back towards the surface These “p modes” can be classified by their radial order n, spherical harmonic degree l, and azimuthal order m; as discussed, for example, in Section 2.2 of Birch and Gizon (2005), the radial displacement of a fluid element at time t, latitude θ and longitude φ can be written in the form l δr(r, θ, φ, t) = ∑︁ anlmξnl(r)Ylm(θ, φ)eiωnlmt,. The power in the modes peaks at about 3 mHz, or a period of 5 minutes; useful measurements can be made for modes between about 1.5 and 5 mHz, with the frequency determination becoming more challenging at the extremes due to signal-to-noise issues and, at the high-frequency end, to the increasing breadth of the peaks
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