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Radiation-driven Winds frompulsating luminous Stars

Ernst A. Dorfi

Universität Wien

Institut für Astronomie

Outline

- XLA Data for stellar objects
- Luminous massive stars
- Computational approach
- Stellar Pulsations
- Dynamical atmospheres and mass loss
- Conclusions and Outlook

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

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

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

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

MOST light curve of WR123

- Observations over 38 days
- Clear signal with a period of P=9.8 h

Lefèvre at al. 2005, ApJ

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

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

Adaptive Grid

- Fixed number of N grid points: ri, 1iN, 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

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

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

Equations of RHD (1)

- Equation of continuity (conservation of mass)
- Equation of motion (conservation of linear momentum), including artificial viscosity uQ

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

Equations of RHD (3)

- 0th - moment of the RTE, radiation energy density
- 1th- moment of RTE, equation of radiative flux

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

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

Temporal discretization

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

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

Pulsations with small amplitudes

- M = 20M
- L = 66000L
- Teff = 27100K
- P = 0.29days

Radius [R]

Synchronous motion of mass shells

Time in pulsation periods

Atmosphere with shock waves

- M = 25M
- L = 282000L
- Teff= 33900K
- P = 0.49days

Shock wave

Ballistic motions on the scale of tff

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

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

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

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

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

Motion of mass shells

Episodic mass loss

Photosphere

Ballistic motions

Shock formation

Regular interior pulsations

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

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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