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