Download Light perturbation from stellar non radial oscillations: an application

GETTING READY for PICARD
HELIOSEISMOLOGY
PROGRAM December 3-4 2008
Light Perturbations
from stellar non-radial oscillations
an application to solar limb
observations
Thierry Toutain /Janine Provost
School of Phys. and Astron. Birmingham / UNS CNRS OCA Cassiopée
Purpose: estimate, on the solar disk, the relative perturbation of the
intensity emitted by the photosphere in the visible continuum due to nonradial oscillations.
Pioneering work by Dziembowski(1977).
Buta and Smith (1979) +adiabatic oscillation and black-body
approximation.
Berthomieu and Provost (1990) + thickness of the photosphere and grey
photosphere approximation.
Toutain and Gouttebroze (1993), Staude (1994) + some radiative
transfer.
Toutain, Berthomieu and Provost (1999) + sphericity of the photosphere
(to allow for calculations of intensity perturbation at the limb).
3/12/2008
Th. Toutain, J. Provost
Getting ready for Picard helioseismology program
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Model of intensity
on the solar disk
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Getting ready for Picard helioseismology program
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Getting ready for Picard helioseismology program
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Emerging Intensity across the solar disk
(μ0 = cos θ0)
center
limb
Sphericity of the emitting layers cannot be neglected
for the outer ~3% (~30”) of the disk because the total optical depth
along the line of sight drops quickly below 1.
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Th. Toutain, J. Provost
Getting ready for Picard helioseismology program
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Perturbation of the intensity
which perturbation formalism to use:
Eulerian or Lagrangian?
Eulerian: integrate perturbation along the line of sight
(Toutain and Gouttebroze,1993; )
Lagrangian: follow fluid elements (Berthomieu and
Provost,1990), distorted line of sight?
Schematic shape of a star perturbed by a l=2 oscillation
As shown by Toutain, Berthomieu and Provost (1999) the 2 formalisms,
lagrangian and eulerian, lead to a same intensity perturbation, except at the
limb (blue region) where fluid elements moving out the line of sight are not
always replaced with similar fluid elements. So Eulerian formalism is
requested to study intensity perturbation at the solar limb.
3/12/2008
Th. Toutain, J. Provost
Getting ready for Picard helioseismology program
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Intensity perturbation across the solar disk
for a radial p-mode
limb
center
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Th. Toutain, J. Provost
Getting ready for Picard helioseismology program
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Intensity perturbation across the solar disk
for a l=1 p-mode
m=0
m=1
3/12/2008
Th. Toutain, J. Provost
Getting ready for Picard helioseismology program
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Intensity perturbation across the solar disk
for a l=1 g-mode
m=0
m =1
3/12/2008
Th. Toutain, J. Provost
Getting ready for Picard helioseismology program
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Results
• Taking into account sphericity of the
photosphere reveals a possible significant
increase of the relative intensity perturbation
at the solar limb for some modes of oscillation:
- both for p and g-modes
- and only for l+m even modes
• The effect on the full-disk perturbation is
expected to be small
3/12/2008
Th. Toutain, J. Provost
Getting ready for Picard helioseismology program
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Explanation:
Near the limb the photosphere is transparent and the intensity
perturbations are driven by the global upward/downward motions of the
photosphere which change the opacity of the layer crossing the line of
sight. The perturbation is then roughly proportional to the derivative of
the intensity:
DI/ I(0) ~ 1/ I(0).dI(0)/dm .Plm(m)
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Th. Toutain, J. Provost
Getting ready for Picard helioseismology program
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Limitations
•
•
•
•
Adiabatic eigenfunctions
Simplified radiative transfer (only ion H-)
No interaction between convection and oscillations
Amplitude estimate assuming energy equipartition
or surface velocity (excitation mechanism?)
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Th. Toutain, J. Provost
Getting ready for Picard helioseismology program
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Observational evidences?
(1)
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Th. Toutain, J. Provost
Getting ready for Picard helioseismology program
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Observational evidences?
(2)
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Th. Toutain, J. Provost
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Theory / MDI observations
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Th. Toutain, J. Provost
(Toner et al 1999)
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Conclusion
• Because of the sharp fall-off of the visible
continuum intensity near the solar limb we
expect solar oscillations (both p and g-modes) to
produce larger relative intensity perturbations.
• Study of limb intensity p-mode signals both with
LOI and MDI seems to suggest a significant
increase of the signal at the limb ( factor 2-3).
• Need more evidences for p modes and check for
a possible g-mode signature with new
instruments (PICARD...).
3/12/2008
Th. Toutain, J. Provost
Getting ready for Picard helioseismology program
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