Indirect imaging of stellar nonradial pulsations

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Indirect imaging of stellar non-radial pulsations

• Svetlana V. Berdyugina
• University of Oulu, Finland
• Institute of Astronomy, ETH Zurich, Switzerland

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4. Mode identification

• Sectoral modes
• Symmetric tesseral modes
• Antisymmetric tesseral modes
• Zonal modes
• Inversion of real data

zonal
symmetric
antisymmetric
sectoral
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Sectoral modes Temperature mapping

• ?T/T10

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Sectoral modes Temperature mapping
?V 3 km /s
?V 10 km /s
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Sectoral modes Velocity mapping

• ?V 10 km /s

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Sym. tesseral modes Temperature mapping

• ?T/T10

i 55
i 70
i 85
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Sym. tesseral modes Velocity mapping

• ?V9 km/s

i 60
i 85
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Antisym. tesseral mode Temperature mapping

• ?T10

i 55
i 85
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Antisym. tesseral modes Velocity mapping

• ?V9 km/s

i 60
i 85
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Zonal modes Velocity mapping

• ?V9 km/s

i 60
i 85
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Conclusions (I)

• Sectoral modes are perfectly recovered
• Symmetrical tesseral modes with
  can be successfully recovered
• Antisymmetric tesseral modes with
  are difficult to recover
• Zonal modes are failed to be recovered
• Temperature and velocity mapping are equally good
  for mode identification

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Inversions of real data ?1 Sco

• ?1 Sco, B1 V,
• ? Cep-type star
• T25,000 K
• log g4.0
• Telting Schrijvers (1998)
• Si III triplet at 4565 Å
• Temperature mapping
• no assumptions
• Occamian approach
• Berdyugina et al. (2003)

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?1 Sco parameter estimates

• Fourier analysis
• 15 cycles/day
• 13.8 cycles/day

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?1 Sco parameter estimates
period
Vsini
inclination
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?1 Sco final solution
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?1 Sco mode interference
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Conclusions (II)

• Line-profile variations on ?1 Sco are caused by
  non-radial pulsations shaped as spherical
  harmonics
• In ?1 Sco sectoral modes with and
  are possible
• Interference of the two modes produces amplitude
  modulation

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Inversions of real data HR 3831

• HR 3831
• roAp-type star
• T7650K
• Nd III at 6145 Å
• 1860 spectra
• Velocity mapping
• Assumption on spherical harmonics
• Tikhonov regularization
• Kochukhov (2004)

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Inversions of real data HR 3831
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HR 3831 Magnetic field and Nd abundance
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Key issues

• Both temperature and velocity mapping are equally
  successful in mode identification
• Only rapidly rotating stars can be studied
• Simultaneous mapping of different parameters
  requires additional constraints (measurements or
  assumptions)

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Final conclusion
Stellar surface imaging is a useful technique for
studying stellar non-radial pulsations