Propagating Linear Waves in Convectively Unstable Stellar Models: A Perturbative Approach

Abstract

Linear time-domain simulations of acoustic oscillations are unstable in the stellar convection zone. To overcome this problem it is customary to compute the oscillations of a stabilized background stellar model. The stabilization affects the result, however. Here we propose to use a perturbative approach (running the simulation twice) to approximately recover the acoustic wave field while preserving seismic reciprocity. To test the method we considered a 1D standard solar model. We found that the mode frequencies of the (unstable) standard solar model are well approximated by the perturbative approach within 1 μHz for low-degree modes with frequencies near 3 mHz. We also show that the perturbative approach is appropriate for correcting rotational-frequency kernels. Finally, we comment that the method can be generalized to wave propagation in 3D magnetized stellar interiors because the magnetic fields have stabilizing effects on convection.

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Acknowledgements

The authors acknowledge research funding by the Deutsche Forschungsgemeinschaft (DFG) under the grant SFB 963/1 project A18. We used data provided by M. Rempel at the National Center for Atmospheric Research (NCAR). Support for the production of the data was provided by the NASA Solar Dynamics Observatory (SDO) Science Center program through grant NNH09AK021 awarded to NCAR and contract NNH09CE41C awarded to NWRA. The National Center for Atmospheric Research is sponsored by the National Science Foundation. LG acknowledges support from EU FP7 Collaborative Project Exploitation of Space Data for Innovative Helio- and Asteroseismology (SPACEINN). We used data provided by BiSON, funded by the UK Science and Technology Facilities Council (STFC). We thank Robert Cameron for comments.

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Correspondence to E. Papini.

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Papini, E., Gizon, L. & Birch, A.C. Propagating Linear Waves in Convectively Unstable Stellar Models: A Perturbative Approach. Sol Phys 289, 1919–1929 (2014). https://doi.org/10.1007/s11207-013-0457-7

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Keywords

  • Stellar models
  • Helioseismology
  • Magnetic fields
  • Numerical methods