Download presentation

Presentation is loading. Please wait.

Published byEdwin Culverhouse Modified over 2 years ago

1
Precision and accuracy in stellar oscillations modeling Marc-Antoine Dupret, R. Scuflaire, M. Godart, R.-M. Ouazzani, … 11 June 2014ESTER workshop, Toulouse1

2
11 June 2014ESTER workshop, Toulouse2 Precision and accuracy in stellar oscillations modeling Precision: Precise solution of given differential equations Accuracy: Set of differential equations accurately modeling stellar oscillations

3
11 June 2014ESTER workshop, Toulouse Precision in stellar oscillations modeling Numerical analyst point of view: Increasing the number of mesh points: “With 5000 mesh points, oscillation computations are precise …” Not enough in evolved stars Increasing the precision of the numerical scheme: High order of precision of finite differences. But don’t forget numerical stability (Reese 2013, A&A 555, 12, GYRE: Townsend & Teitler 2013, MNRAS 435, 3406) Spectral approach with orthogonal polynomials (TOP, ESTER, …) But sharp variations in stellar interiors Multi-domain (convective boundaries, opacities, …), approach huge core-surface contrast This is not always enough … 3

4
11 June 2014ESTER workshop, Toulouse Precision in stellar oscillations modeling: choosing the good variables Lagrangian or Eulerian perturbations ? General rule: Compare the orders of magnitude and choose the smallest 1.Gravitational potential The Cowling approximation is not so bad Always use the Eulerian perturbation of 2.Pressure P In dense cores, |P’| << | P| Use the Eulerian perturbation of P 4

5
11 June 2014ESTER workshop, Toulouse Lagrangian or Eulerian perturbations ? Pressure In a g-mode cavity where The Eulerian perturbation of P must be used 5 Precision in stellar oscillations modeling: choosing the good variables

6
11 June 2014ESTER workshop, Toulouse Lagrangian or Eulerian perturbations ? Lagrangian Eulerian if and only if hydrostatic equilibrium of the structure model In high density contrast stars, 10.000-50.000 points required Interpolating the structure models ? No: hydrostatic equilibrium too imprecise … Non-radial oscillations in high-density contrast stars (blue and red supergiants): - Eulerian pressure perturbation in the g-mode cavity - Models in hydrostatic equilibrium with enough mesh points (avoid interpolations) 6 Precision in stellar oscillations modeling: choosing the good variables

7
11 June 2014ESTER workshop, Toulouse Non-adiabatic oscillations in near-surface layers 7 Precision in stellar oscillations modeling: choosing the good variables must be used as variable in non-adiabatic oscillation codes or Lagrangian or Eulerian perturbations ? Lagrangian perturbation of state equation and opacities are simpler better to use them in the superficial non-adiabatic layers

8
11 June 2014ESTER workshop, Toulouse8 Precision in stellar oscillations modeling The first integral of Takata, a good test of precision Dipolar modes Equation of momentum conservation for the center of mass of each sphere M r : Takata 2005, PASJ 57, 375 Reduce by two orders the differential system Can be used as an a posteriori precision test in each layer Valid in the full non-adiabatic case Could be generalized to fast rotating stars Good test of precision of non-perturbative oscillation codes for fast rotating stars (ACOR, TOP, …)

9
11 June 2014ESTER workshop, Toulouse9 Precision in stellar oscillations modeling The first integral of Takata, a good test of precision Proof: Integration on an arbitrary volume: ||

10
11 June 2014ESTER workshop, Toulouse10 Precision in stellar oscillations modeling The first integral of Takata, a good test of precision First integral (general case): Dipolar mode, sphere:

11
11 June 2014ESTER workshop, Toulouse11 Precision in stellar oscillations modeling Using asymptotic JWKB solutions Full non-adiabatic case: see Dziembowski (1977) Continuous match to the numerical solution Does not increase precision, but decreases the number of mesh points Useful in the core of high density contrast stars Adiabatic-Cowling approximation, g-mode cavity with : Numerous nodes in high density contrast stars Quasi-adiabatic approximation: Power lost by the mode through radiative damping:

12
11 June 2014ESTER workshop, Toulouse12 Accuracy in stellar oscillations modeling Usual approximations in oscillation equations: Adiabaticity, slow rotation, no magnetic field, no tidal effects Acts as a forcing term in oscillation equations, boosting some modes through resonances and complicating spin-orbit synchronisation: Savonije et al. 1995, … Affects frequencies: Saio (1981), … Magnetic field: Lorentz force + perturbed induction equation Direct effect on frequencies, mode geometry and driving Perturbative approach: see e.g. Hasan et al. 1992, 2005; Cunha & Gough 2000 Non-perturbative approach: see e.g. Bigot & Dziembowski (2003), Saio (2005) Tidal influence of a companion:

13
11 June 2014ESTER workshop, Toulouse13 Accuracy in stellar oscillations modeling Rotation: Coriolis + centrifugal deformation Major effect on frequencies, mode geometry and driving Perturbative approach: see e.g. Dziembowski & Goode (1992), 2 nd order Soufi et al. 1998, 3 rd order Non-perturbative approach: Traditional approximation (spherical symetry, rigid rotation, horizontal Coriolis) Separabilityvery efficient computations Not so bad for g-modes of moderate rotators (Ballot et al. 2011) Perturbative structure models + full spectral expansion: Lee & Baraffe (1995), … Full 2D structure models + full spectral expansions: Major works of the Toulouse team (Dintrans, Lignières, Reese, Ballot 2000-2014), See their talks ! Ouazzani et al. (2012) 2D structure models + oscillations with finite differences: Clement 1998, Deupree 1995, …

14
11 June 2014ESTER workshop, Toulouse14 Accuracy in stellar oscillations modeling Non-adiabatic-energetic aspects in oscillations modeling: Predictions of mode excitation + normalized amplitudes and phases Heat engine pulsators: Range of unstable modes and instability strips Constrains opacities, time-dependent convection Stochastic excitation: Mode life-times line-widths in power spectrum Constrains time-dependent convection Improve accuracy of theoretical frequencies through a good oscillations modeling in the superficial layersPhysical treatment of surface effects Important for high-order p-modes (e.g. solar-like oscillations)

15
11 June 2014ESTER workshop, Toulouse15 Accuracy in stellar oscillations modeling Non-adiabatic-energetic aspects in oscillations modeling: Main challenges: Non-adiabaticity + rotation See talk of Daniel Reese Non-adiabaticity + magnetism: Saio (2005) Oscillations in the atmosphere: Dupret et al. (2002) Time-dependent convection Non-linear radial oscillations: e.g. Stellingwerf 1982, Kuhfuß 1986 Linear oscillations: Gough 1977 Balmforth 1992Houdek et al. (1999-…) Unno 1967 Gabriel 1996 Grigahcène, Dupret et al. (2005-…) Beyond the mixing-length theory: Xiong et al. (1997-2010) All these theories introduce free parameters !

16
11 June 2014ESTER workshop, Toulouse16 Accuracy in stellar oscillations modeling Non-adiabatic-energetic aspects in oscillations modeling: Time-dependent convection All current theories introduce free parameters or are contradicted by observations … What should be done ? What hydrodynamical simulations are telling us ? (Gastine & Dintrans 2011, Mundprecht et al. 2012) Going beyond the MLT, yes but …

Similar presentations

OK

1 Influence of the Convective Flux Perturbation on the Stellar Oscillations: δ Scuti and γ Doradus cases A. Grigahcène, M-A. Dupret, R. Garrido, M. Gabriel.

1 Influence of the Convective Flux Perturbation on the Stellar Oscillations: δ Scuti and γ Doradus cases A. Grigahcène, M-A. Dupret, R. Garrido, M. Gabriel.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on electronic configuration of elements Converter pub to ppt online templates Free download ppt on statistics for class 9 Ppt on reverse mortgage Ppt on human chromosomes pictures Ppt on bond length periodic table Ppt on ancient greek clothing Ppt on exterior angle theorem Seminar ppt on mobile number portability Ppt on obesity prevention initiative