Radiation-driven Winds from

pulsating luminous Stars

Radiation-driven Winds from

pulsating luminous Stars

Ernst A. Dorfi

Universität Wien

Institut für Astronomie

OutlineOutline

XLA Data for stellar objects

Luminous massive stars

Computational approach

Stellar Pulsations

Dynamical atmospheres and mass loss

Conclusions and Outlook

XLA Data for Stellar AstrophysicsXLA 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-ProgenitorSN-Progenitor

Car will explode as Supernova, distance d=7500 ly

Massive object: M~120M (1 M=2●1030kg)

Extremely luminous star: L~4●106L (1

L=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

Adopted from Gautschy & Saio 1996

Theoretical HRDTheoretical HRD

WR123WN8IRS16SW

Some Properties of LBVsSome 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 LBVsObserved light curves of LBVs

Luminous Blue Variables exhibit so-called micro-variability

LBVs show outbursts on scale of several years

Sterken et al. 1998, y- and Hipparcos photometry

R40 in SMC

MOST light curve of WR123MOST 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 pulsationsGrowth 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=25 M, Teff=33

900 K, L=2.82 • 105 L

Dorfi, Gautschy, Saio, 2006

Computational RequirementsComputational 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 GridAdaptive 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 RHDComputational 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 RHDAdaptive 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:

1st-order TVD

2nd-order TVD

Temporal discretizationTemporal discretization

2nd-order temporal discretization to reduce artificial damping of oscillations

Smallest errors in case of time-centered variables

Linear vs. non-linear pulsationsLinear 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 = 316 000 L

Teff = 31 620 K

M = 20 M

L = 66 000 L

Teff = 27 100 KP = 0.29 days

Pulsations with small amplitudesPulsations with small amplitudes

Synchronous motion of mass shells

Time in pulsation periods

Ra

diu

s [R

]

Atmosphere with shock wavesAtmosphere with shock waves

Shock wave

Ballistic motions on the scale of tff

M = 25 M

L = 282 000 L

Teff = 33 900 KP = 0.49 days

Observations of stellar parameterObservations of stellar parameter

Effective temperature can decrease as mean radius increases

WR123R: M=25 M, log L/L=5.5, Teff_i=33 000K

Teff_puls=31 700 K, ΔT=1300 K

Rph=17.2R, Rpuls=18.7R

P = 0.72 d

Atmospheric dynamicsAtmospheric 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=220 km/s, P=3.471d, T=25000K

vrot=225 km/s, P=3.728d, T=24000K

Higher rotation rates lead to mass loss of about 10-4 M/yr

Light curves without mass lossLight 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 0.5 mag in U,B to less than 0.25 mag in H,K

Initiating mass lossInitiating 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 lossPulsation 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=550 km/s

Total mass loss rate probable reduced by angle-dependence

Motion of mass shellsMotion of mass shells

Photosphere

Episodic mass loss

Shock formation

Ballistic motions

Regular interior pulsations

ConclusionsConclusions

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 OutlookComputational 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