The Physics of Mass Loss From Stars

1
The Physics of Mass Loss From Stars

• Jon E. Bjorkman
• Ritter Observatory

2
Fluid Equations

• Continuity
• Momentum
• Energy (Dominated by Heating/Cooling)
• Equation of State

3
Wind Mechanisms

• Pressure-Driven
• Coronal Winds
• Wave-Driven
• Accoustic Waves
• Alfven Waves
• Rotationally-Driven
• Centrifugal
• Magneto-centrifugal
• Radiation-Driven
• Dust
• Continuum Opacity
• Spectral Lines

4
Stellar Mass Loss

• Hydrostatic (Isothermal) Atmosphere
• Outer Boundary Condition
• (almost) Zero Pressure
• Impossible to build Static Star

5
Isothermal Winds

• Wind Equation
• Combined momentum and continuity equations
• Critical Point

Pushing on flow moves rc inward
6
X-Type Solution Topology
Bondi 1952
7
Boundary Conditions

• Two point boundary value problem
• Stellar Surface
• ISM
• Mass Loss Rate

8
Stellar Outflow
Decreasing PISM
Increasing
9
Stellar Outflow

• As PISM decreases
• flow initially subsonic
• v0 increases gt mass loss increases
• outer boundary determines mass loss rate
• Until solution passes through critical point
• v0 now constant gt mass loss constant
• flow is choked
• termination shock matches PISM
• outer boundary determines shock location
• Conclude
• Mass loss determined by critical point location

10
Effect of External Forces

• Supersonic Momentum Deposition
• Increases terminal speed
• Mass loss unchanged
• Subsonic Momentum Deposition
• Moves critical point inward
• Increases mass loss
• May indirectly affect terminal speed

11
Continuum-Driven Winds

• Radiative Acceleration
• Wind Equation
• AGB Stars
• Dust condenses in outflow

12
Line-Driven Winds

• Sobolev Optical Depth
• Line acceleration
• Optically thin lines
• Optically thick lines

13
Line-Driven Winds

• Line Acceleration
• CAK parameterization

14
Line Force
Abbott 1980
Abbott 1982
15
Line-Driven Winds

• Wind Equation

16
Line-Driven Winds

• Wind Acceleration
• Subsonic
• 1 positive soln
• Sonic
• 1 positive soln
• Supersonic
• 2 positive solns
• Critical
• 1 positive soln
• Plus one more negative solution

17
Line-Driven Winds
Abbott 1980
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CAK Critical Point Topology

• Quasi-Linearization
• Courant and Hilbert 1962
• Differentiate wind equation (so that it is linear
  in the derivatives)
• Wind Equation

19
CAK Critical Point Topology

• CAK critical point is X-type

Bjorkman 95
(D0)
20
Line-Driven Winds

• Mass Loss Rate
• At critical point
• flow speed speed of inward radiative-acoustic
  wave (Abbott 1980)
• Radiative force balances gravity (inertia)
• given yc, mass loss (r) is raised/lowered until
  there are the correct number of thin lines
  (Gayley 1995)

21
Line-Driven Winds

• Terminal Speed
• (formerly) optically thick lines gt G gt 1
• Provide acceleration in supersonic region
• Relative number of thick lines sets terminal
  speed
• Changes in line force (ionization shifts, d, etc)
  alter terminal speed

22
Temperature Dependence

• Dominant Driving Ions
• O Stars
• CNO
• B Stars
• Fe group

Abbott 1982
23
Bi-stable Winds

• Ionization shifts alter driving lines
• Mass increases discontinuously
• Terminal speed drops
• Caused by change of Fe III ionization (Vink, de
  Koter, Lamers 1999)

Pauldrach Puls 1990 Lamers Pauldrach 1991
24
Bi-Stable Winds

• Observed Terminal Speeds

Crowther, Lennon, Walborn 06 see also Evans et
al. 04, and Trundle et al. 04
Lamers, Snow, Lindholm 95 Kudritzki Puls 00
25
Weak Line-Driven Winds

• Breakdown of CAK parameterization
• Wind requires at least one optically thick line
• Abbott 1979
• Babel 1996

Abbott 1979
26
Weak Line-Driven Winds

• Gas not well coupled to driving ions
• Ion runaway heating
• Springmann Pauldrach 1992
• Gayley Owocki 1994
• Multicomponent Winds
• Babel 1995
• Krticka Kubat 2000, 2001
• Detailed multicomponent NLTE Model
• Krticka Kubat 2004
• Wind terminal speed is lowered
• removes discrepancies with observations

27
Metallicity Dependence

• Wind driven by metals
• Lower mass loss at low Z
• Vink et al. 2001
• See also Abbott 1982 Puls et al. 2000 Kudritzki
  2002
• Lower terminal speed
• Garmany Conti 85 Prinja 87 Leitherer et al.
  92

28
High Mass Loss

• Wind Momentum
• Single Scattering Limit
• Wind momentum problem (Barlow et al. 1981)
• Photon Tiring Limit
• Owocki Gayley 1997

29
Multiple Scattering
Abbott Lucy 1985
30
Multiple Scattering

• Theoretical performance factor
• Gayley, Owocki, Cranmer 1995
• Momentum problem is really an opacity problem
• must fill entire spectral region with lines
• Requires ionization stratification
• Lucy Abbott 93, Springmann 94,
• Yes, but ionization is tricky
• Schmutz 91, 94, 97 Shaerer and Schmutz 94

31
Line Driven Winds withMultiple Scattering

• Monte Carlo RT Simulation
• Kurucz line list (106 lines)
• Sample photon scatterings
• Measure line acceleration
• Measure energy transfer from photons to wind
• Lucy Abbott (1993) method
• Assume velocity law
• Use energy conservation to find mass loss rate

32
Line Driven Winds withMultiple Scattering

• Schaerer Schmutz 1994 Kudritzki 2002
• Use depth-dependent k a
• solve wind dynamics, including critical point
• Mihaylov Bjorkman (2004)
• sample MC line forces in each cell
• Gives (Cf)i and ai
• Solve for yi and integrate wind velocity
• Map solution topology

33
Multiple Scattering
Mihaylov 04
34
Ionization Effects
Mihaylov 04
35
Continuum Driven Winds

• Basic Requirement
• Nugis Lamers (2002)
• used Fe-bump (OPAL opacities)
• At sonic point
• Opacity must increase outward
• Eddington factor G 1

36
OPAL Opacities

• Sonic Point

Nugis Lamers 02
37
NLTE rad-hydro WR Wind
Gfäfener Hamann 2005
38
NLTE rad-hydro WR Wind
Gfäfener Hamann 2005
39
Instabilities, Clumps Porosity
Shaviv 01
Shaviv 00
40
Acknowledments