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Radiation-driven Winds from pulsating luminous Stars

Radiation-driven Winds from pulsating luminous Stars. Ernst A. Dorfi Universit ä t Wien Institut f ü r Astronomie. Outline. XLA Data for stellar objects Luminous massive stars Computational approach Stellar Pulsations Dynamical atmospheres and mass loss Conclusions and Outlook.

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Radiation-driven Winds from pulsating luminous Stars

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  1. Radiation-driven Winds frompulsating luminous Stars Ernst A. Dorfi Universität Wien Institut für Astronomie

  2. Outline • XLA Data for stellar objects • Luminous massive stars • Computational approach • Stellar Pulsations • Dynamical atmospheres and mass loss • Conclusions and Outlook

  3. XLA Data for Stellar Astrophysics • Nuclear cross sections for energy generation as well as nucleosynthesis • Stellar opacities for radiative transfer, grey or frequency-integrated (OPAL and OP-projects), new values solved a number of discrepancies between observations and theory (molecular opacities still needed) • Equation of State, hot dense plasmas (but also cold dense plasmas for ‘planets’) • Optical constants for dust particles

  4. SN-Progenitor •  Car will explode as Supernova, distance d=7500 ly • Massive object: M~120M (1M=2●1030kg) • Extremely luminous star: L~4●106L (1L=3.8●1026 W) • Observed mass loss, lobes are expanding with 2300 km/s • Central source and hot shocked gas between 3-60 ●106 K, X-ray emission • Giant eruptions between1837 and1856 • Questions: mass loss, giant eruptions, variability, rotation, binarity, ...  Car: HST/NASA  Car: CHANDRA

  5. IRS16SW WN8 WR123 Theoretical HRD Adopted from Gautschy & Saio 1996

  6. Some Properties of LBVs • LBVs are the most luminous stellar objects with luminosities up to 106L • Radiation pressure dominates most of the radial extension of the stars • LBVs are poorly observed (sampled) variable stars, small and large scale variations, large outbursts on scales of several decades, poorly determined stellar parameter • More theoretical work on variability necessary: regular pulsations of LBVs on a time scale of days or less (Dorfi & Gautschy), strange modes in the outer layers, LBV phenomenon due to dynamically unstable oscillations near the Eddington-limit (Stothers & Chin, Glatzel & Kiriakidis) • Theoretical LBVs light curves: complicated structures due to shock waves running through the stellar atmosphere

  7. Observed light curves of LBVs • Luminous Blue Variables exhibit so-called micro-variability • LBVs show outbursts on scale of several years R40 in SMC Sterken et al. 1998, y- and Hipparcos photometry

  8. MOST light curve of WR123 • Observations over 38 days • Clear signal with a period of P=9.8 h Lefèvre at al. 2005, ApJ

  9. Growth of pulsations • Pulsations initiated by a small random perturbation: 5 km/s • Initial linear growth (dotted line), stellar atmosphere can adjust on a different time scale • Final amplitude when kinetic energy becomes constant • Model WR123U: M=25M, Teff=33900 K, L=2.82 • 105L Dorfi, Gautschy, Saio, 2006

  10. Computational Requirements • Resolve relevant features within one single computation like driving zone, ionization zones, opacity changes, shock waves, stellar winds, … global simulations • Kinetic energy is small fraction of the total energy • Steep gradients within the stellar atmosphere and/or possible changes of the atmospheric stratification due to energy deposition may change boundary conditions • Long term evolution of stellar pulsations, secular changes on thermal time scales, i.e. tKH >> tdyn • Solve full set of Radiation Hydrodynamics (RHD), problem: detailed properties of convection

  11. Adaptive Grid • Fixed number of N grid points: ri, 1iN, and grid points must remain monotonic: ri<ri+1 • Grid is rearranged at every time-step • Additional grid equation is solved together with the physical equations • Grid points basically distributed along the arc-length of a physical quantities (Dorfi & Drury, 1986, JCP) • Physical equations are transformed into the moving coordinate system • Computation of fluxes relative to the moving spherical grid

  12. Computational RHD • All variables depend on time and radius, X=X(r,t) • Equations are discretized in a conservative way, i.e. global quantities are conserved, correct speed of propagating waves • Adaptive grid to resolve steep features within the flow • Implicit formulation, large time steps are possible, solution of a non-linear system of equations at every new time step • Flexible approach to incorporate also new physics

  13. Adaptive conservative RHD • Integration over finite but time-dependent volume V(t) due to moving grid points • Advection terms calculated from fluxes over cell boundaries • Relative velocities between mater and grid motion: urel = u - ugrid

  14. Equations of RHD (1) • Equation of continuity (conservation of mass) • Equation of motion (conservation of linear momentum), including artificial viscosity uQ

  15. Equations of RHD (2) • Equation of internal gas energy (including artificial viscous energy dissipation Q) • Poisson equation leads to gravitational potential, integrated mass m(r) in spherical symmetry

  16. Equations of RHD (3) • 0th - moment of the RTE, radiation energy density • 1th- moment of RTE, equation of radiative flux

  17. Advection (I) • Transport through moving shells as accurate as possible • Usage of a staggered mesh, i.e. variables located at cell center or cell boundary • Fulfil accuracy as well as stability criteria for sub- and supersonic flow • Avoid numerical oscillations, so-called TVD-schemes • Ensure correct propagation speed of waves

  18. Advection (II) • TVD-schemes are based on monotonicity criteria of the consecutive ratio R • Correct propagation speed of waves requires ψ(1)=1 • Monotonic advection scheme according to van Leer (1979) essential for stellar pulsations: 2nd-order TVD 1st-order TVD

  19. Temporal discretization • 2nd-order temporal discretization to reduce artificial damping of oscillations • Smallest errors in case of time-centered variables

  20. Linear vs. non-linear pulsations • Work integrals based on linear as well as full RHD-computations, remarkable correspondence (normalized to unity in the damping region) • Driving and damping mechanisms are identical for both approaches • Pulsations are triggered by the iron metals bump in the Rosseland-mean opacities (5.0 < log T< 5.3) • These high luminosity stars exhibit modes located more at the surface than classical pulsators • M = 30 M • L = 316000L • Teff= 31620K

  21. Pulsations with small amplitudes • M = 20M • L = 66000L • Teff = 27100K • P = 0.29days Radius [R] Synchronous motion of mass shells Time in pulsation periods

  22. Atmosphere with shock waves • M = 25M • L = 282000L • Teff= 33900K • P = 0.49days Shock wave Ballistic motions on the scale of tff

  23. Observations of stellar parameter • Effective temperature can decrease as mean radius increases • WR123R:M=25 M, log L/L=5.5, Teff_i=33000K • Teff_puls=31700K, ΔT=1300K • Rph=17.2R, Rpuls=18.7R • P = 0.72d

  24. Atmospheric dynamics • IRS16WS model: L=2.59•106L • Rotation plays important role in decoupling the stellar atmosphere from internal pulsations • Ballistic motions at different time scales introduce complex flows • vrot=220km/s, P=3.471d, T=25000K • vrot=225km/s, P=3.728d, T=24000K • Higher rotation rates lead to mass loss of about 10-4 M/yr

  25. Light curves without mass loss • P=3.728d, vrot=225 km/s, T=24000K, L=2.59•106L • Shocks, dissipation of kinetic energy, large variations in the optical depth • Looks rather irregular and pulsation can be hidden within atmospherical dynamics • Large expansion of photosphere around 10 and 20 days clearly visible • Typical amplitudes decrease from 0.5mag in U,B to less than 0.25mag in H,K

  26. Initiating mass loss • Pulsation perturbed by increase rotational velocity from 225km/s to 230 km/s • After 4 cycles outermost mass shell accelerated beyond escape velocity • Outer boundary: from Lagrangian to outflow at 400 R, advantage of adaptive grid • Gas velocity varies there around 550 km/s escape velocity

  27. Pulsation and mass loss • Pulsation still exists, very different outer boundary condition • Large photosphere velocity variations due to changes in the optical depth • Mean equatorial mass loss: 3•10-4M/yr, vext=550km/s • Total mass loss rate probable reduced by angle-dependence

  28. Motion of mass shells Episodic mass loss Photosphere Ballistic motions Shock formation Regular interior pulsations

  29. Conclusions • According to theory: All luminous stars with L[L]/M[M]>104 exhibit strange modes located at the outer stellar layers • All stars in the range of 106L should be unstable, but no simple light curves expected • Complicated, dynamical stellar atmospheres, difficulties to detect pulsations due to shocks, irregularities, non-radial effects, rotation, dM/dt ~ 10-4M/yr • In many cases the resulting light curves as well as the radial oscillations can become rather irregular and difficult to analyze • These oscillations will affect mass loss and angular momentum loss as well as further stellar evolution

  30. Computational Outlook • Include better description of convective energy and momentum transport into the code • Include Doppler-Effects in the opacities, additional opacity may cause large-scale outbursts, even without rotation • Non-grey radiative transport on a small number (about 50) of frequency points • 2-dimensional adaptive, implicit calculations based on the same numerical methods Stökl & Dorfi, CPC, 2008

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