1 / 21

Effects to consider on oscillation frequencies

Effects to consider on oscillation frequencies. The effect of rotation (perturbative approach). J. C. Suárez et al. Instituto de Astrofísica de Andalucía (CSIC), Granada, Spain. Plan. Introduction Slow, Moderate & Fast rotators Main effects (perturbative approach) Differential rotation

ayala
Download Presentation

Effects to consider on oscillation frequencies

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Effects to consider on oscillation frequencies The effect of rotation (perturbative approach) J. C. Suárez et al. Instituto de Astrofísica de Andalucía (CSIC), Granada, Spain Joint Helas & CoRoT/ESTA Workshop

  2. Plan • Introduction • Slow, Moderate & Fast rotators • Main effects (perturbative approach) • Differential rotation • Échèlle Diagrams • Analysis of splitting asymmetries & rotation profile variations (RPV). Joint Helas & CoRoT/ESTA Workshop

  3. Introduction • Type of rotators: • Slow (ε,μ <<1) • Moderate (ε,μ ≤ 0.5) • Fast (ε,μ > 0.5) Slow-Moderate Fast Joint Helas & CoRoT/ESTA Workshop

  4. Perturbative approach • Effect of rotation separated in orders O(μ) • O(μ): slow rotation • O(μ2,μ3): moderate rotation Dziembowski & Goode (1992), Soufi et al. 1998 Joint Helas & CoRoT/ESTA Workshop

  5. Main effects • First order (Coriolis, geometric) • Symmetry in multiplets • Second order (Coriolis,Centrifugal) • Asymmetries in multiplets global shift splitting asymmetry m=-1 m=0 m=+1 Joint Helas & CoRoT/ESTA Workshop

  6. ω0 ~ ωj Near degeneracy • Close – frequency modes • Avoided crossing, mixed modes • Selection rules: Δm=0, Δℓ=0,2 Joint Helas & CoRoT/ESTA Workshop

  7. Effects on adiabatic frequencies Cubic effects (3rd order) Near degeneracy (2nd order) Centrifugal (2nd order) geff & Coriolis (1st order) No rotation: ω=ω0(0) Goupil al. 1999 Joint Helas & CoRoT/ESTA Workshop

  8. Differential rotation • Shellular rotation gives rise to additional terms • Eigenfunctions (CL, J0, D0, D1) • Structure terms (J0, D0, D1) Joint Helas & CoRoT/ESTA Workshop

  9. Differential rotation • Intermediate-mass, moderately rotating stars • DR vs. UR models • DR as shellular (local conservation of angular momentum) Suárez et al. 2006 A&A 449, 673 Joint Helas & CoRoT/ESTA Workshop

  10. Differential rotation. The effects on frequencies • Mainly affect ω1 & ω2 • Significant effects for g and mixed modes • Up to 3μHz for g-mixed and 1μHz for p modes Suárez et al. 2006 A&A 449, 673 Joint Helas & CoRoT/ESTA Workshop

  11. Differential rotation. The effects on eigenfunctions Suárez et al. 2006 A&A 449, 673 Joint Helas & CoRoT/ESTA Workshop

  12. Rotation & Échèlle diagrams ℓ=2 ℓ=0 ℓ=3 ℓ=1 • Solar-like pulsators (high-frequency modes excited) • Significant effects for large frequencies • Near degeneracy naturally affects small separation. Largest effects for ℓ=(0,2) modes. • m components may complicate diagnostics but amplitudes may alleviate the problem 20 km/s 30 km/s 50 km/s 1.5 M● Lochard et al. 2006, in prep Joint Helas & CoRoT/ESTA Workshop

  13. Rotation & Échèlle diagrams 1.5 M●, 30km/s • Seismic modelling based on δω fitting diagnostics generally neglect rotation. • For a 1.5 M● (MS, 1Gyr) model δω(Ω)- δω(0) ~1μHz • But rotation effects can be “depolluted” Ω=0 ~1.2 mHz Ω Lochard et al. 2006, in prep Joint Helas & CoRoT/ESTA Workshop

  14. Rotation & Échèlle diagrams • Main idea: to obtain the “true” (non-rotating) small separations from observed δω • Rotation depullution is performed for close modes a & b from the structure quantity Va~Vb Δν(Ω) Δν(t) Δν(0) Goupil et al. 2003 Joint Helas & CoRoT/ESTA Workshop

  15. Analysis of splitting asymmetries & RPV • Asymmetries of rotation splittings (Sj) are observed in pulsating stars (δ Scuti, β Cephei, etc.) • Rotation profile variations (RPV) affects the rotation splittings: asymmetries (Aj) • Study of RPV through Aj is a promising tool to search for the true RP. Suárez et al. 2006, in prep. Joint Helas & CoRoT/ESTA Workshop

  16. Analysis of splitting asymmetries & RPV • Aj cannot be explained by UR models • DR models in the approximation of shellular rotation. S2: Shellular-type S1: Linear-type. S3: Smoothed Prof. Suárez et al. 2006, in prep. Joint Helas & CoRoT/ESTA Workshop

  17. Analysis of splitting asymmetries & RPV • Aj(g) behaves differently to Aj(p) • Al of low-order g & p modes are the most affected RPV near the core (μ-gradient zone). S2 S1 S3 S2 S1 S3 Suárez et al. 2006, in prep Joint Helas & CoRoT/ESTA Workshop

  18. Analysis of splitting asymmetries & RPV • Asymmetries are directly proportional to the second –order term D0 • Analysis of D0 Kernels (work in progress) will help to understand the behaviour of Aj: • Mode dependency (n,ℓ) • RPV effects Suárez et al. 2006, in prep. Joint Helas & CoRoT/ESTA Workshop

  19. Bibliography • Zahn et al. 1992 A&A 265, 115 • Dziembowski & Goode 1992 A&A • Goupil et al. 2003 ESA Eddington Conference, SP • Soufi et al. 1998 A&A 334, 911 • Suárez et al. 2006 A&A 449, 673 Joint Helas & CoRoT/ESTA Workshop

  20. Analysis of splitting asymmetries & RPV • Low order, low-degree modes (g & mixed) modes are the most affected by variations near the core & the μ-gradient zone Suárez et al. 2006, in prep Joint Helas & CoRoT/ESTA Workshop

  21. Analysis of splitting asymmetries & RPV • RPV modify the asymmetry of rotationally split multiplets Suárez et al. 2006 Joint Helas & CoRoT/ESTA Workshop

More Related