How do the Sun's dimensions vary in time

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How do the Sun's dimensions vary in time?
J.P. Rozelot (1) C. Damiani (2)
(1) OCA-FIZEAU (UMR 6525), Université de
Nice-Sophia-Antipolis, Av. Copernic, 06130,
Grasse, France email rozelot_at_obs-azur.fr (2)
INAF-Osservatorio Astronomico di Roma , via
Frascati 33, 00040 Monteporzio Catone, Italia
email cilia.damiani_at_obspm.fr
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Solar Limb Astrometry Science

• What limb astrometry?
• The solar radius
• The solar radius variations with time
• The solar radius variations with central angle
  (shape)

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Solar Limb Astrometry Science

• What limb astrometry?
• The solar radius
• The solar radius variations with time
• The solar radius variations with central angle
  (shape)
• What are the pressing questions?
• Does the solar radius change with solar cycle?
• Knowledge of radius changes and irradiance or
  luminosity changes constrain the solar cycle
  mechanisms a long debated problem
• What is the Suns shape and is this consistent
  with solar system limits on its gravitational
  potential and the internal rotation rate?
• Low frequency limb oscillations (p-modes,
  g-modes, r-modes) sample the deepest parts of the
  solar interior

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Stellar Rotation

• Density r r -n and constant rotation w

• Solar case density r and rotation w non uniform

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Solar oblateness
Newcomb 1895 solar oblateness of 500 mas
would explain the discrepancy between the
prediction of Newtonian gravitational theory and
the perihelion advance of Mercury observed by Le
Verrier 1859. Ambronn and Schur heliometer
1892 and 1902 solar oblateness e 2.08 10-
6 From measurements made between 1874-1882
Auwers concluded D r 0.038
0.023 or e 3.96 10- 5
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Solar oblateness
Dicke R.H. and Goldenberg H.M. 1967 (Phys.
Rev. Lett., 18(9), 313) Dr 41.9 3.3
mas Many papers attempting to interpret the
results as other than a quadrupole moment. We
know today that such measurements were
inaccurate, but were a source of progress.
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What has been done?

• Princeton
• SCLERA
• Some balloon flights (SDS)
• Tourelle dome (50-cm) Pic du Midi, since 1993
• SOHO (MDI)
• RHESSI

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Results

• Sun e ? 8.86 10-6
• Less than 1.1 10-5
• Questions

Is the oblateness time dependent? If yes, which
physical mechanisms are involved? Are they
relevant to drive astrophysical phenomena?
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Observations at Pic du Midi Observatory (South
France, 2877 m)

• Start in April 1993, then each month on September
  1994-1996
• Interruption 1997-1999 due to buildings
  refurbishing
• September 2000 1rst to 4 th
• September 2001 3rd, 4th and 5th
• --gt exceptional meteorological conditions
• Moderate North-West wind
• Seeing average 18 cm
• September 2002, 2003,
• 2004, 2005 and 2006,
• July 2007 and 2008
• Turret dome (50-cm)

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Scanning Heliometer (Pic du Midi J. Rösch)
Rozelot, Lefebvre and Desnoux, 2003, Solar
Physics 217 3952, 2003.
Pic du Midi Heliometer is a device specially
designed for the solar shape observations Differ
ent from astrolabes
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Solar oblateness
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Solar oblateness
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Space Oblateness measurements
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• Solar shape and to 1rst order, oblateness,
  still very difficult to measure
• But exciting!
• Revival of interest due to dedicated space
  missions
• Balloon flights (SDS)
• (Courtesy S. Sabatino)

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Solar Disk Sextant

• Balloon flights (Yale University). Measurements
  40 km above sea level.

Courtesy Sofia Sabatino, April 2003
11 October 1990 ?
Maier, E., Twing, L., Sofia, S. 1992, Astrophys.
J. 389, 447. Sofia, S., Heaps, W., Twigg, L.W.
1994, Astrophys. J. 427, 1048 Egidi, R., Caccin,
B., Sofia, S., Heaps, W., Hoegy, W., Twigg, L.
2006, Solar Phys. 235, 410. Revised values
Sofia et al 2008, Solar Phys, 247 225.
.
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Solar astrometry from space Solar and
Heliospheric Observatory, Michelson Doppler
Imager (MDI)

• Satellite in halo orbit near L1
• Stable solar image limb fiducial
• MDI Imaging instrument with well defined thermal
  properties, .02 pointing errors

After M. Emilio, R. I. Bush, J. Kuhn, and P.
Scherrer 2007, ApJ., 660, L161L163
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Limb astrometry SOHO/MDI
6 pixel annulus
480pix
12 min cadence (antialiased) 30 degree roll
increments 512(360) angular bins 1.96 per pixel
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The solar limb shape (oblateness) changes (in
phase) with solar cycle
From SOHO experiment. After M. Emilio, R. I.
Bush, J. Kuhn, and P. Scherrer 2007, ApJ., 660,
L161L163
1997 (min)
2001 (max)
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RHESSI complex time dependence ()
The oblateness (axisymmetric quadrupole) term
dominates the shape and is
10.77 0.44
mas. Fivian, M. D., Hudson, H. S., Lin, R. P. and
Zahid, H. J. Sience express, 2 October 2008, p.
3 (mean value identical to already published
values obtained by means of the heliometer Rösch
et al., 1996,. Sol. Phys., 165,1)
() Reuven Ramaty High-Energy Solar Spectroscopic
Imager.
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Oblateness
X Rhessi
x
0
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RHESSI complex time dependence

Fivian, M. D., Hudson, H. S., Lin, R. P. and
Zahid, H. J. Sience express, 2 October 2008, p.
3 Rozelot, J.P. Damiani 2008, ApJ, Submitted
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Science Objectives 1/ Solar Shape Measures
Gravitational Potential and Solar Rotation
MULTIPOLAR GRAVITATIONAL MOMENTS
w w0 w2 m2
Rotation expansion of the form
Solar shape follows from the equation of
hydrostatic support,
p, r, f and w represent the pressure, density,
gravitational potential and rotation rate W is an
ill-defined characteristic surface rotation rate
related to w
Magnetic fields and non-rotational velocity
flows Complicate this result See Fazel et al,
2008, New Astronomy
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Science Objectives
2/ RELATIVISTIC CELESTIAL MECHANICS
J2 plays a role in the relativistic perihelion
precession of a planet with orbital parameter
(a, e, i)
42,98 arcsec/century
Post-Newtonian parameter encoding the amount of
non-linearity in the superposition law of
gravitation
A precise knowledge of J2 will be needed for
precise ephemeris.
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3/ Variation of the position of subsurface layers
Lefebvre Kosovichev, 2005, ApJ, 633,
L149 Lefebvre et al., 2007, ApJ, 658, L135
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Schematic view of the Leptocline
S. Lefebvre, P. A. P. Nghiem and S. Turck-Chièze
2009, ApJ., 690, 1272
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4/ Solar radius changes due to interior solar
cycle changes
So-called asphericity/luminosity parameter w
(Sofia, S., 1979 -- Lefebvre
Rozelot, AA, 2002)

• Ratio w ? (ln R)/ ?(R) / ? (ln L) / ?(L)
• Estimates are still non consistent
• How to measure a reliable w ?
• --gt Space dedicated missions

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Some global computations w Sofia et al. (1979)
7.510-2 Dearborn Blake (1980)
510-3 Gilliland (1980) 8.510-4 Sweigart
(1981) 0.71 Gough (1981) 510-4 Gough
(2001) 2.0 10-3 Sofia Chan (1982)
610-4 Gilliland (1982)
-210-5 Spruit (1982) 210-4 Newkirk
(1983) 610-4 Balmforth et al. (1996) 210-3
Lefebvre Rozelot (2004) and Fazel et al.
(2008) -1.5510-2 and -7.6110-3,
according to a linear variation of r with depth
or a non homologous variation. The second
estimate is more likely. Such a small value
suggests the existence of a reservoir where the
gravitational energy is stored or relaxed
depending of the variable rate of transport.
Brown (1987) (deduced from observations)
W lt5 10-2. A brief summary
of estimates taken in the existing literature
- 6.7 10-2 to 0.8 ? The sign is obviuously of
great importance.
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Space perspectives
And many others Astrometria, Spheris, etc
Crédit CEA
DynaMICCS
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Solar Dynamics Observer (SDO) HMI Optics
Package (HOP)P. Scherrer, R. Bush, A. Kosovichev
et al. (Stanford University-USA))
Connector Panel
Z
Focal Plane B/S
Fold Mirror
X
Shutters
Alignment Mech
Limb Sensor
Y
Oven Structure
Detector
Michelson Interf.
Lyot Filter
CEBs
Detector
Vents
Limb B/S
Front Window
Active Mirror
Polarization Selector
Focus/Calibration Wheels
OP Structure
Mechanical Characteristics Box 0.84 x 0.55 x
0.16 m Over All 1.19 x 0.83 x 0.29 m Mass 39.25
kg First Mode 63 Hz
Telescope
Support Legs (6)
Front Door
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(No Transcript)
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A changing solar shape ?

• Mechanisms
• Solar oblateness seems to vary in phase with
  solar activity, while it is quite proven that
  radius changes in opposite phase, at least near
  the surface.
• This could be explained by a complex mechanism
  involving changes in J2 and J4
• In a time of low activity, the equatorial
  diameter slightly increases under the influence
  of J2, with no effect of J4, so that the
  oblateness is decreasing (reverse mechanisms
  happen when the solar activity is higher

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Thanks to Dicke and Rösch,
And to all of you
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Slicing process
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Shift of the inflexion point and Fried Parameter

• FFTD
• PTh ? F Data

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Astrophysical relevance
zoom
Tremendous factor gained in few years
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Astrophysical relevance
There is room for Alternative gravitational
Theories Space Missions Beppi-Colombo,
Gaia Pireaux Rozelot, 2003, Adv. Sp. Res.
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Solar radius changes due to interior solar cycle
changes
So-called asphericity/luminosity parameter w
(Lefebvre Rozelot, AA, 2002)

• Ratio w ? (ln R)/ ?(R) / ? (ln L) / ?(L)
• Theoretically
• Sofia, Spruit, Deadborne, Brown
• 7.5 10-2 to 2 10-4 sign ?
• Observations 6.7 10-2 to 0.8
• How to measure a reliable w ?
• --gt Space dedicated missions

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Solar oscillations observed near surface probe
the interior

• P-modes essentially acoustic modes trapped
  between the interior, increasing sound speed
  gradient and the radiative solar surface
  boundary fundamental is about 1hr, but modes are
  observed in velocity and brightness with periods
  near 5 minutes
• G-modes bouyancy waves, evanescent through the
  convection zone, not detected, periods of 1 hour
  and longer
• R-modes coriolis restoring force, long period
  modes not (yet) observed (also Rossby waves)

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Solar Disk Sextant

• Balloon flights (Université de Yale).
  Measurements 40 km above sea level

S. Sofia and B. Caccin Rotation law w0
2.840 0.400 sin2(q) m rad s-1 J2 1.84
10-7 J4 9.83 10-7
Courtesy Sofia Sabatino, April 2003