Limb distortions related to solar magnetic activity

Solar limb astrometry with RHESSI

H.S. Hudson, M.D. Fivian,

B.M. Wilson, & H.J. Zahid

Space Sciences Lab, UC Berkeley

Background Information I

Differential observationsThe absolute value of the radius is an important but perhaps boring property of the Sun that needs precise determination. RHESSI is not designed to do this, but it can study the detailed shape of the limb, and to some extent its time variations. All RHESSI limb measurements are differential measurements enabled by its rotation.

Brief history of radius observationsThe modern era began with Dicke’s “Oblateness Telescope,” which began the series of determinationssummarized by Kuhn et al. (ApJ 613, 1241) in the plot on the left. Note that the error ranges consistently disagree - is this because of error underestimation,disagreement on measurement algorithms, or true time variability?

The RHESSI aspect system includes a set of three small optical systems for defining Sun center coordinates. These consist of simple lenses, passband filters, and linear CCDs. RHESSI rotates at about 15 rpm and thereby repeatedly determines the limb shape as a byproduct as in Dicke’sOblateness Telescope, but in space.

Measurement principle of the RHESSI Solar Aspect Sensor (SAS)

• Sensor: 1024-pixel linear CCD, 1.73 arc sec/pixel• Spectral band: 670 nm @ 12 nm FWHM• Readout: limbs ~100 sec-1, 4 pixels; chords ~1 min-1

• Duty cycle: low Earth orbit, 96 min period, 63-80% sunlight

Left: the geometry of the limb measurement,showing the CCDs as intersecting the limbat two points each (small circles). We construct an “residual triangle” to locate sun center, as shown. In general it has adimension of order 0.1 arc s. The dotted lines show how this error propagates toradius error. We correct for systematic displacements, e.g. due to the solaroblateness itself.

Upper left, a representative scan (CCD image); Upper right, the three detector signal levels vs time;Lower left, illustration of fit to limb profile; Lower right, derivative of mean limb profile.

Data

Upper plot, individual radius points for oneRHESSI orbit; lower left, their histogram;lower right, histogram mean values for successive orbits (preliminary view)

The p-modes have a clear presence

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

August 2004: 57-orbit summed power spectrum. SeeKuhn et al. (2000) for k-diagram of MDI limb data:the limb data emphasize m ~ l.

Solar oblateness*

View of RHESSI precision:Oblateness 9.72 +/- 0.19 mas(random error ~10-4 pixels). Notethe excesses due to faculae.

The text below shows the state of theart in the 19th century - visual observationswith heliometers (Auwers, 1891)

* See presentation by M. Fivian, paper 30.05

Synoptic-chart representation of RHESSIlimb shape: spots and faculae

These three stackplots show normalized radius (range of grayscale 300 mas) by 96-minute orbit, as shown. The time ranges are: bottom, 2005 Apr. 1 - Jul. 3; middle 2005 Jan. 1 - Apr. 4, top 2004 Jul. 4 - Oct. 4. Bar at lower left shows a half-rotation.

6-Jul-04 ~18:10

Potentially observable limb features

• p-modes !

• g-modes

• r-modes ?

• Granulation

• Other convective motions

• Sunspots !

• Faculae !

• Active network

• Flares

• Prominences

• Coronal holes

• ?

• Oblateness !

• Higher-order shape terms

• Gravitational moments J2, J4…

• Global temperature variation

• Limb-darkening functions

• Planetary tides

• Dynamo signatures

• ?

Solar radius determinations are in principlesensitive to many sources of distortion, as listed here (left: local; below: global). Red indicates items inherently magnetic in origin. Exclamation points indicate items already detected.

The Wilson effectThe Wilson effect

The Wilson effect is the systematic variation of umbra/penumbra morphology as a function of limb distance. It was described in the 18th century by Alexander Wilson of Glasgow (image at right). The effect suggests an excavation of the photosphere such that the umbra lies a few hundred km below the mean level. See Solanki (2003)for a review.

Wilson was a professor of astronomy, but was also aphysician, meteorologist, and font designer.

RHESSI observations of the Wilson effect

The RHESSI observations convolve position and brightness.Disentangling these effects will require detailed MHD/RTmodeling, something that is not currently accomplished. The effectivelimb displacement has the correct order of magnitude for theWilson effect as inferred indirectly.

The Wilson effect: observation and modeling

Typical RHESSI limb at 1,000 xmagnification, showing spot transit

Models of limb transit for simple cylindersof radius 20-50 Mm and depth (Wilsondepression) 200 km. Geometry prevents the tangent ray from reaching the umbralphotosphere for reasonable spot sizes and deep depressions.

The problems of faculae: first learning from them;second, screening against their presence

Granulation, solfläckar och facklor nära solranden (from the Swedish

Solar Telescope homepage)

The facular contrast depends upon flows and structure in the photosphere. The plots below show models by Steiner (2005) relating such properties to view angles of +- 45o.

Ideally we will measure “pure” solar global properties best after eliminating facular confusion.

Conclusions

• The RHESSI solar aspect sensor determines the limb shape with great precision

• There are many applications of such differential observations of the solar radius, with connections to helioseismology

• We believe that magnetic effects (faculae and network) will restrict many data analyses

• We hope to use the results of numerical models to help understand the limb-darkening function