1. 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

2. Background Information I Differential observations The 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 observations The modern era began with Dicke’s “Oblateness Telescope,” which began the series of determinations summarized 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?

3. 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’s Oblateness Telescope, but in space.

4. 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 limb at two points each (small circles). We construct an “residual triangle” to locate sun center, as shown. In general it has a dimension of order 0.1 arc s. The dotted lines show how this error propagates to radius error. We correct for systematic displacements, e.g. due to the solar oblateness itself.

5. 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.

6. Data Upper plot, individual radius points for one RHESSI orbit; lower left, their histogram; lower right, histogram mean values for successive orbits (preliminary view)

7. The p-modes have a clear presence August 2004: 57-orbit summed power spectrum. See Kuhn et al. (2000) for k-  diagram of MDI limb data: the limb data emphasize m ~ l.

8. Solar oblateness* View of RHESSI precision: Oblateness 9.72 +/- 0.19 mas (random error ~10 -4 pixels). Note the excesses due to faculae. The text below shows the state of the art in the 19th century - visual observations with heliometers (Auwers, 1891) * See presentation by M. Fivian, paper 30.05

9. Synoptic-chart representation of RHESSI limb 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

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 principle sensitive 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.

11. The 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 a physician, meteorologist, and font designer. RHESSI observations of the Wilson effect The RHESSI observations convolve position and brightness. Disentangling these effects will require detailed MHD/RT modeling, something that is not currently accomplished. The effective limb displacement has the correct order of magnitude for the Wilson effect as inferred indirectly.

12. The Wilson effect: observation and modeling Typical RHESSI limb at 1,000 x magnification, showing spot transit Models of limb transit for simple cylinders of radius 20-50 Mm and depth (Wilson depression) 200 km. Geometry prevents the tangent ray from reaching the umbral photosphere for reasonable spot sizes and deep depressions.

13. 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 +- 45 o. Ideally we will measure “pure” solar global properties best after eliminating facular confusion.

14. 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