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Title: Radiation-driven%20Winds%20from%20pulsating%20luminous%20Stars

Radiation-driven Winds from pulsating luminous
Ernst A. Dorfi Universität Wien Institut für
  • 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

  • ? Car will explode as Supernova, distance d7500
  • Massive object M120M? (1 M?2?1030kg)
  • Extremely luminous star L4?106L? (1
    L?3.8?1026 W)
  • Observed mass loss, lobes are expanding with 2300
  • 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
Adopted from Gautschy Saio 1996
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
  • 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
  • LBVs show outbursts on scale of several years

R40 in SMC
Sterken et al. 1998, y- and Hipparcos photometry
MOST light curve of WR123
Lefèvre at al. 2005, ApJ
  • Observations over 38 days
  • Clear signal with a period of P9.8 h

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
  • Model WR123U M25 M?, Teff33 900 K, L2.82
    105 L?

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
  • 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
    gtgt tdyn
  • Solve full set of Radiation Hydrodynamics (RHD),
    problem detailed properties of convection

Adaptive Grid
  • Fixed number of N grid points ri, 1?i?N, and
    grid points must remain monotonic riltri1
  • 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, XX(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
  • 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

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
  • 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
  • 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
  • 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

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 lt log Tlt
  • These high luminosity stars exhibit modes located
    more at the surface than classical pulsators

M 30 M? L 316 000 L? Teff 31 620 K
Pulsations with small amplitudes
M 20 M? L 66 000 L? Teff 27 100 K P
0.29 days
Radius R?
Synchronous motion of mass shells
Time in pulsation periods
Atmosphere with shock waves
M 25 M? L 282 000 L? Teff 33 900 K P
0.49 days
Shock wave
Ballistic motions on the scale of tff
Observations of stellar parameter
  • Effective temperature can decrease as mean radius
  • WR123R M25 M?, log L/L?5.5,
    Teff_i33 000K
  • Teff_puls31 700 K, ?T1300 K
  • Rph17.2R?, Rpuls18.7R?
  • P 0.72 d

Atmospheric dynamics
  • IRS16WS model L2.59106L?
  • Rotation plays important role in decoupling the
    stellar atmosphere from internal pulsations
  • Ballistic motions at different time scales
    introduce complex flows
  • vrot220 km/s, P3.471d, T25000K
  • vrot225 km/s, P3.728d, T24000K
  • Higher rotation rates lead to mass loss of about
    10-4 M?/yr

Light curves without mass loss
  • P3.728d, vrot225 km/s, T24000K, L2.59106L?
  • 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 0.5 mag in U,B
    to less than 0.25 mag 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 310-4M?/yr, vext550
  • Total mass loss rate probable reduced by

Motion of mass shells
Episodic mass loss
Ballistic motions
Shock formation
Regular interior pulsations
  • According to theory All luminous stars with
    LL?/MM?gt104 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

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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