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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2. Stellar surface imaging

• Surface inhomogeneities
• Line profile distortions
• Localization of inhomogeneities
• Observational requirements
• Input parameters
• Inversion tests

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Stellar surface imaging
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Stellar surface imaging

• Deutsch (1958)
• The first idea to use spectral line profiles for
  mapping the stellar surfaces
• Stellar Surface Imaging
• Doppler Imaging
• Based on the analysis of Doppler shifts in line
  profiles
• Surface inhomogeneities
• Produce distortions which move across profiles as
  the star rotates
• Time series allows for mapping the stellar surface

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Surface inhomogeneities

• Temperature
• Starspots on cool magnetically active stars
• Abundances
• magnetic Ap stars
• Magnetic field
• cool active stars
• magnetic Ap stars
• white dwarfs
• Non-Radial Pulsations
• Rapidly rotating O-B-A stars

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Local line profiles

• Disk integration
• Mapping
• Brightness
• Temperature
• Elemental abundance
• Magnetic field
• Velocity field

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Line profile distortions

• Lines of constant radial velocity

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Line profile distortions
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Line profile distortions
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How to locate a spot
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Requirements

• Observations
• high spectral resolution ???? ? 30 000
• high signal-to-noise ratio S/N ? 200
• good phase coverage
• a few sensitive spectral lines
• stellar rotation ? 20 km/s.
• Calculation technique
• local line profiles accounting for many spectral
  lines
• integration over the stellar surface
• inversion technique involving as few as possible
  a priori assumptions

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Input parameters

• Geometrical parameters
• rotation velocity Vsini
• inclination i
• pulsation frequency
• period of rotation P
• Physical parameters
• effective temperature Teff
• surface gravity log g
• microturbulent velocity
• macroturbulent velocity
• instrumental broadening

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Inversion tests

• Teff5000K, Tspot3500K,
• log g3.5, i60?,
• Vsini 50 km/s,
• 20 phases, OA

• S/N200

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Inversion tests

• Teff5000K, Tspot3500K,
• log g3.5, i60?,
• Vsini 50 km/s
• 20 phases, OA

• S/N200

• S/N100

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Inversion tests

• Teff5000K, Tspot3500K,
• log g3.5, i60?,
• Vsini 50 km/s,
• 20 phases, OA

• Vsini48 km/s

• Vsini52 km/s

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Inversion tests

• Teff5000K, Tspot3500K,
• log g3.5, i60?,
• Vsini 50 km/s,
• 22 phases, OA

• i50?

• i70?

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MEM vs TR
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TR vs OA
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Intrinsic limitations of Doppler Imaging

• appearance of polar caps or equatorial belts due
  to wrong values of e.g. v sin i and inclination
  i.
• appearance of numerous false features due to low
  S/N, errors in atomic parameters, missing blends,
  and phase gaps.
• almost total ambiguity between the hemispheres,
  if the inclination of the star is about 90?.
• a lack of latitude resolution near the equator.

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3. Imaging of non-radial pulsations

• Temperature mapping
• No assumptions
• (Berdyugina et al. 2003, OA)
• Velocity mapping
• Assumption on the shape of pulsations is needed
• (Kochukhov 2004, TR)

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Temperature mapping ?T10

• Teff25000K, log g4.0, i60?,
• Vsini 100 km/s, S/N500, 22 phases, OA

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Temperature mapping ?T10

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Parameter errors Vsini
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Parameter errors Inclination
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Parameter errors Period
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Temperature mapping Velocity variations
?V 3 km/s
?V 10 km/s
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Temperature mapping
Involves no assumptions on the shape of
pulsations
Can be used to verify the geometry of non-radial
pulsations
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Velocity mapping

• Vector field
• Kochukhov (2004)
• Geometry of NRP
• Velocity vector Fourier series
• Mapping Fourier coefficients

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Velocity mapping

• Teff8000K, log g4.0, i60?,
• Vsini 40 km/s, S/N300, 500 phases

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Key issues

• Stellar surface imaging
• Doppler shifts ? stellar maps
• High-quality spectral observations are needed
• Rapidly rotating stars are the main targets
• Uncertainties in stellar parameters produce
  spurious features
• Regularization strongly influences the solution
• Temperature mapping of NRP involves no
  assumptions
• Velocity mapping requires an assumption on the
  geometry of NRP