radiation driven winds from pulsating luminous stars
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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
Radiation-driven Winds frompulsating luminous Stars

Ernst A. Dorfi

Universität Wien

Institut für Astronomie

  • 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
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, ...



theoretical hrd




Theoretical HRD

Adopted from Gautschy & Saio 1996

some properties of lbvs
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
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
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
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
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
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
computational rhd
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
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
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
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
Equations of RHD (3)
  • 0th - moment of the RTE, radiation energy density
  • 1th- moment of RTE, equation of radiative flux
advection i
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
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
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
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
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
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
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
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
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
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 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
Motion of mass shells

Episodic mass loss


Ballistic motions

Shock formation

Regular interior pulsations

  • 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
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