History of Solar Oblateness

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Nugget
Number: 126
1st Author: Hugh Hudson
2nd Author: Jean-Pierre Rozelot
Published: 2010 April 26
Next Nugget: TBD
Previous Nugget: The Masuda Flare Revisited
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Introduction

Exact measurements of the shape of the Sun have a history extending well back into the 19th century (for full details, see reference [1]), and RHESSI is playing a small role in this continuing history (see two earlier nuggets (a, b) thanks to the small optical telescopes used for solar aspect sensing. These observations are serendipitous, as are those of SOHO/MDI and soon those of SDO/HMI. But there is also to be a dedicated space observatory actually designed for solar global observations, Picard, and we expect that it will make the definitive measurements over the next few years following its anticipated launch in June 2010.

The purpose of this Nugget is to show off some of the historical overview from [1], and to remind Nugget readers of the basic physics of the oblateness measurement. RHESSI has just completed its observations through the remarkable recent solar minimum and we see no particular reason why its data should not continue well into the operational lifetimes of SDO and Picard.

Why is the oblateness interesting?

Astrometry is one of the classical branches of astronomy, and precise determinations of the shape of the Sun make use of highly specialized techniques with similar fundamental problems of measurement. The oblateness of the Sun is normally defined as the (normalized) difference between equatorial and polar radii, and so it is a differential measurement as opposed to the absolute determination of the radius (or diameter), which is obviously much harder. Picard will make the first optimized absolute measurements from space, and the oblateness (and other shape features) an interesting and highly important byproduct of the measurement. The non-optimized RHESSI, SOHO, and now SDO measurements cannot be regarded as absolute and are restricted to shape alone.

The shape of the Sun, or any star, reflects what is going on inside it. Most trivially it is rotating, and so an equatorial bulge should appear. The Sun rotates slowly, and so this bulge is small (by one prediction, 7.98 mas, where the common unit mas is a milli-arc-sec, or closely 1 part per million of the full radius). More rapidly rotating stars can have substantial bulge, which leads to the interesting effect known as the von Zeipel theorem which implies that there is also a substantial dimming of the surface brightness at the equator of such a star. In the case of the Sun both rotational ellipticity and rotational dimming are tiny and therefore a wonderful challenge for observers.

Many other potential mechanisms could change the shape of the Sun. The surface is known to rotate differentially in the sense that the equator region has an angular velocity greater than the polar regions. There must be internal differential rotation as well, although it is increasingly well constrained by helioseismology, and what we see at the surface may conceal mass internal mass distributions that can affect the shape. Such effects are related to tests of relativity theory, from which Einstein famously explained the anomalous perihelion precession of Mercury. This was an amazing coup of 19th-century astrometry. Finally there are links to the solar cycle; for example a north-south meridional circulation is required to explain the 11-year cycle - a hot research topic nowadays because of the recent anomalous minimum. This could well have detectable effects at the surface of the Sun other than the subtle motions of magnetic elements that trace out the flow associated with the cycle.


References

A brief history of the solar oblateness. A review

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