December 14, 2007, AGU Fall Meeting, San Francisco, (SH53A-1076) 1

Solar Shape Measurements from RHESSI

‘A Large Excess Oblateness ?’

M.D. Fivian, H.S. Hudson, R.P. Lin, H.J. Zahid

Space Sciences Laboratory, UC Berkeley

M. D. Fivian et al.: Solar Shape Measurements from RHESSI 2

Abstract

The Solar Aspect System of the RHESSI spacecraft scans the limb at the ~4 sec rotation period of the spacecraft, producing a large quantity of precise differential measurements of the solar radius at optical wavelengths (monochromatic at 670 nm). These data provide the most precise determinations of the oblateness prior in particular to the launch of the Picard mission in 2008. The observation of standing waves in the body of the Sun (helioseismology) provided the first direct way to study the interior of a star. The astrometric shape of the solar limb gives independent constraints on interior structures and flows; the surface rotation predicts an oblate ellipsoid with an equator-pole radius difference of some 8 mas (~0.001%). Here we report the most accurate observations to date of the solar shape, which show a much larger apparent oblateness with an equator-pole radius difference of 13.72± 0.44 mas. This new component can easily be distinguished spatially from the effects of faculae in the active latitude zones. Comparison with earlier observations suggests that this excess oblateness results from solar magnetic activity, as do the frequency variations of the helioseismic modes. However, correcting carefully for facular activity and subsequent instrumental effects leads to an oblateness of 8.7± 0.2 mas, a value consistent with predictions.

M. D. Fivian et al.: Solar Shape Measurements from RHESSI 3

RHESSI/SAS Instrument

The Solar Aspect System (SAS) focuses three optical, narrow bandwidth images of the solar disk onto three linear CCDs.

M. D. Fivian et al.: Solar Shape Measurements from RHESSI 4

RHESSI/SAS Instrument

A solar profile (top figure) is measured on each of the three independent sub-systems and the location of the solar limb can be determined. Conceptually overlaying those measurements leads to six instantaneous radius measurements.

M. D. Fivian et al.: Solar Shape Measurements from RHESSI 5

RHESSI: Solar Aspect System

Sensor Calibration Limb position

Geometrical Calibration Sun center and Radii

M. D. Fivian et al.: Solar Shape Measurements from RHESSI 6

Potentially Observable Limb Features

• p-modes !• g-modes• r-modes ?• Granulation • Other convective motions• Sunspots !• Faculae !• Active network !• Filament channels !• Flares• Prominences• Coronal holes• ?

• Oblateness !• Higher-order shape terms• Gravitational moments J2,

J4…• Global temperature variation• Limb-darkening functions• Planetary tides• Dynamo signatures• ?

Local Features Global Features

M. D. Fivian et al.: Solar Shape Measurements from RHESSI 7

Historical Results

First Oblateness Measurement(Auwers, 1891)

Absolute Radius Measurements(Kuhn, ApJ 613,1241,2004)

M. D. Fivian et al.: Solar Shape Measurements from RHESSI 8

Iterative Calculation of Radii

Data Sets

Processes

Data Generating Sequence

M. D. Fivian et al.: Solar Shape Measurements from RHESSI 9

Sensor Calibration

Measured profile:

Optical profile:

d(x,t): dark levelg(x,t) = r(t) f(x): variable gainr(t) : responsivityf(x) : flat-fieldc0,c1: parameters of odd-even model

Reconstructed Optical Solar Profile:

M. D. Fivian et al.: Solar Shape Measurements from RHESSI 10

Deconvolution of the Solar Profile

The deconvolution of the measured solar profile (blue) provides a precise measurement of the location of the limb. A parameterized point-spread function (red) and limb darkening function (green) is forward-fitted to the measured profile. The dotted lines in black show three components of the PSF. (note: the tail of the PSF is approximated by a gaussian with FWHM of appr. 30 arc minutes.)

M. D. Fivian et al.: Solar Shape Measurements from RHESSI 11

Forward-fitted Point-Spread Function

Yellow: Fitted point-spread function.

Red: Components of the fitted point-spread function.

Blue: Spatial derivative of the measured solar limb profile provides a first-order approximation of the PSF.

M. D. Fivian et al.: Solar Shape Measurements from RHESSI 12

Fitted Solar Profile and Residuals

The solid line shows the fitted model of the solar profile at the extreme limb. The fit-residuals (enlarged by a factor 20) are added to the model and are plotted in red.

The residuals are measured relative to a normalized solar profile. Aside from the noise caused by the sensors, the residuals show systematic errors in the order of 10^-3.

M. D. Fivian et al.: Solar Shape Measurements from RHESSI 13

Statistical Error in Limb Profile

Accumulating limb data over a time range of 3 month provides excellent statistics of the measured averaged limb profile. The top panel shows the rms error in the 10 milli arc second bins in the range of -20 to 20 arc seconds at the limb. The lower panel shows the inferred uncertainty in the measured position of the limb.

M. D. Fivian et al.: Solar Shape Measurements from RHESSI 14

Timeseries of Geometry ParametersP

late

Sca

les

[106

]

Redundances in the data provides the calibration of the geometry of the telescope. The plots on the left show time series of calibration parameters. Note: the slow change in radial dimensions in mid July of the shown time range is due to slow changes in the average temperature of the telescope due to changes in eclipse time of the RHESSI orbit.

Tw

ist

Rad

ial D

imen

sio

ns [

μm

]

M. D. Fivian et al.: Solar Shape Measurements from RHESSI 15

Confusion/Signal of Magnetic Activity

N

W

S

E

N

Illustration of the problems involved with rejecting active-region "noise" in precise shape determination. The grayscale at the bottom shows about one week's data on one-orbit averages, with time on the X-axis and position angle on the Y-axis. The plots show the limb profiles averaged to the left (26-29 June, 2004)) and to the right (1.4 days from 29 June 2004, 22:44 UT) of the yellow line, respectively.

M. D. Fivian et al.: Solar Shape Measurements from RHESSI 16

Synoptic View of Radius Measurements

M. D. Fivian et al.: Solar Shape Measurements from RHESSI 17

Masking RHESSI data using EIT 284Å

EIT 284Å data is used to mask areas of facular activity at limb.

With varying threshold areas of facular activity are masked in the RHESSI data.

M. D. Fivian et al.: Solar Shape Measurements from RHESSI 18

Oblateness Measurement vs. Masking Cut

Increasing the threshold for masking areas of facular activity more and more data is cut from the data set and the oblateness measurement is approaching a minimum, an oblateness corrected for facular contamination. Note: As even more data is cut, the oblateness shows a slow run-away.

M. D. Fivian et al.: Solar Shape Measurements from RHESSI 19

Stacked Radius Data with Fitted Components

(for caption see next page)

M. D. Fivian et al.: Solar Shape Measurements from RHESSI 20

SDS/MDI/RHESSI data vs. 10.7cm Radio Flux

As has been observed before using MDI data, RHESSI sees a large excess oblateness which can be correlated with the solar cycle by comparing to the 10.7cm radio flux. However, a carefully corrected value (for facular activity, network, filament channels, but also instrumental effects) shows an oblateness consistent with predictions (dashed line).

SDS

MDI

RHESSI

M. D. Fivian et al.: Solar Shape Measurements from RHESSI 21

Conclusions

• The RHESSI aspect sensors provide radius determinations of  unprecedented precision

• Since the RHESSI launch early February 2002 over 1010 single data points have been acquired providing excellent statistics over 5 years

• At this new level of precision, we find strong signatures of solar  magnetism

• The data will allow us to constrain solar interior models,  supplementing helioseismology  in a fundamentally new manner

• The data show a large, smooth and broadly distributed excess oblateness of 13.7 mas

• Masking the data of potential facular contamination using EIT images and regularizing the statistics of radius measurements leads to a preliminary resulting oblateness measurement of 8.7 +/- 0.2 mas. This measurement would be consistent with theoritical predictions