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

||ml

2|| ml

1|| ml

0m

zonal symmetric

antisymmetric sectoral

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Sectoral modes: Temperature mapping

T/T=10% 9|| ml

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Sectoral modes: Temperature mapping

V =3 km /s V =10 km /s9|| ml

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Sectoral modes: Velocity mapping

V =10 km /s 6|| ml

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Sym. tesseral modes: Temperature mapping

T/T=10%

i =55 i =70 i =85

3||,5 ml

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Sym. tesseral modes: Velocity mapping

i =60 i =85

V=9 km/s 4||,6 ml

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Antisym. tesseral mode: Temperature mapping

T=10%

i =55 i =85

4||,5 ml

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Antisym. tesseral modes: Velocity mapping

i =60 i =85

V=9 km/s 5||,6 ml

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Zonal modes: Velocity mapping

i =60 i =85

V=9 km/s 0||,3 ml

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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

2|| ml

1|| ml

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Inversions of real data: ω1 Sco

ω1 Sco, B1 V,

Cep-type star

T=25,000 K

log g=4.0

Telting & Schrijvers (1998)

Si III triplet at 4565 Å

Temperature mapping no assumptions Occamian approach Berdyugina et al. (2003)

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ω1 Sco: parameter estimates

Fourier analysis 15 cycles/day

13.8 cycles/day

19l

?l

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ω1 Sco: parameter estimates

Vsini period inclination

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ω1 Sco: final solution

7||,9 ml

8|| ml

9|| ml

10|| ml

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ω1 Sco: mode interference

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Conclusions (II):

Line-profile variations on ω1 Sco are caused by non-radial pulsations shaped as spherical harmonics

In ω1 Sco sectoral modes with and are possible

Interference of the two modes produces amplitude modulation

8|| ml 9|| ml

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Inversions of real data: HR 3831

HR 3831

roAp-type star

T=7650K

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

1|| ml

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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