Mass loss and the Eddington Limit

1
Mass loss and the Eddington Limit
Stan Owocki Bartol Research Institute University
of Delaware
Collaborators Nir Shaviv Hebrew U.,
Israel Ken Gayley U. Iowa A-J van Marle U.
Delaware Rich Townsend U. Delaware Nathan
Smith U.C. Berkley
2
Continuum opacity fromFree Electron Scattering
e-
Thompson Cross Section
th
sTh 8p/3 re2 2/3 barn 0.66 x 10-24 cm2

3
Eddington limit
Radiative Force
Gravitational Force
4
Stellar Luminosity vs. Mass
L M 3.5
5
Basic Stellar Structure -gt L M3
Hydrostatic equilibrium (Gltlt1)
Radiative diffusion
6
Basic Stellar Structure -gt L M3
Hydrostatic equilibrium (Gltlt1)
gt
gt
Radiative diffusion
7
Basic Stellar Structure -gt L M3
Hydrostatic equilibrium (Gltlt1)
Radiative diffusion
8
Basic Stellar Structure -gt L M3
Hydrostatic equilibrium (Gltlt1)
Radiative diffusion
9
Mass-Luminosity Relation
M1
???
M3.5
10
Interior Radiation Pressure
11
Interior Radiation Pressure
12
Key points

• Stars with M 100 Msun have L 106 Lsun gt
  near Eddington limit!
• Suggests natural explanation why we dont see
  stars much more luminous ( massive)
• Prad gt Pgas gt Instabilities gt Extreme mass loss

13
Line-Driven Stellar Winds

• Stars near but below the Edd. limit have stellar
  winds
• Driven by line scattering of light by electrons
  bound to metal ions
• This has some key differences from free electron
  scattering...

14
Line Scattering Bound Electron Resonance
for high Quality Line Resonance, cross section gtgt
electron scattering
15
Driving by Line-Opacity
Optically thin
16
CAK Line-Driven Wind
17
Mdot increases with Ge
18
Optically Thick Line-Absorption in an
Accelerating Stellar Wind
For strong, optically thick line
19
CAK model of steady-state wind
Equation of motion
inertia
gravity
CAK line-force
20
CAK model of steady-state wind
21
Summary Key CAK Scaling Results
e.g., for a1/2
Mass Flux
22
Key points

• Stars with M 100 Msun have L 106 Lsun gt
  near Eddington limit!
• Suggests natural explanation why we dont see
  stars much more luminous ( massive)
• Prad gtPgas gt Instabilities gt Extreme mass loss
• Can not be line-driven?
• But continuum driving needs to be regulated.

23
How is such a wind affected by (rapid) stellar
rotation?
24
Gravity Darkening
increasing stellar rotation
25
Effect of gravity darkening on line-driven mass
flux
Recall
e.g., for
26
Effect of rotation on flow speed

27
Eta Carinae
28
Historical Light Curve
29
Smith et al. 2002
30
Eta Cars Extreme Properties
Present day
31
Line-driving cant explain h Cars mass loss

• Must be continuum driven with L gt LEdd
• But how is this regulated when G L/M const.?
• Perhaps by porosity of structured medium?
• Structure could arise from instabilities, or
  fallback from stagnation in photon tiring
  limited wind.

32
Lines cant drive h Carinaes mass loss
33
3 Key points about h Cars eruption

• Mdot gt 103 Mdot(CAK)
• can NOT be line-driven!
• Lobs gt LEdd
• gt super-Eddington (by factor gt 5!)
• Lobs MdotV2/2
• Mdot limited by energy or photon-tiring

34
Stagnation of photon-tired outflow
35
Stagnation of photon-tired outflow
36
Stagnation of photon-tired outflow
Max mass loss
37
Stagnation of photon-tired outflow
38
Lines cant drive h Carinaes mass loss
39
Lines cant drive h Carinaes mass loss
40
(No Transcript)
41
(No Transcript)
42
Flow Stagnation
43
Flow Stagnation
44
Photon Tiring Flow Stagnation
45
CAK model of steady-state wind
Equation of motion
inertia
gravity
CAK line-force
Solve for
46
Radiation vs. Gas Pressure
Radiative diffusion
Hydrostaticequilibrium
47
Shaviv 2001
48
Line-driving cant explain h Cars mass loss

• Must be continuum driven with L gt LEdd
• But how is this regulated when G L/M const.?
• Perhaps by porosity of structured medium?
• Structure could arise from instabilities, or
  fallback from stagnation in photon tiring
  limited wind.

49
Super-Eddington Continuum-Driven Winds
moderated by porosity
50
G. Dinderman Sky Tel.
51
(No Transcript)
52
Convective Instability

• Classically expected when dT/dr gt dT/drad
• e.g., hot-star core e T10-20 cool star env. k
  increase
• But G(r) -gt 1 gt decreases dT/drad gt convection
• e.g., if Ge1/2 gt M(r) lt M/2 convective!
• For high density interior gt convection efficient
  
• Lconv gt Lrad - LEdd gt Grad (r) lt 1 hydrostatic
  equilibrium
• Near surface, convection inefficient gt
  super-Eddington
• but any flow would have M L/a2
• implies wind energy Mvesc2 gtgt L
• wouldtire radiation, stagnate outflow
• suggests highly structured, chaotic surface

.
.
53
Initiating Mass Loss from Layer of Inefficient
Convection
gt flow would stagnate due to photon tiring
54
Porosity
Same amount of material More light gets
through Less interaction between matter and
light
Incident light
55
Porous Envelope
Porosity length size/filling factor h ? l/f
h'r
56
Porous envelopes
l0.05r
l0.1r
l0.2r
h0.5r
hºl/f
hr
h2r
57
ExpandingPorous envelopes
l0.05r
l0.1r
l0.2r
h0.5r
hºl/f
hr
h2r
58
Pure-abs. model for blob opacity
59
Monte Carlo
60
Monte Carlo results for eff. opacity vs. density
in a porous medium
critical density rc
Log(eff. opacity)
blobs opt. thin
blobs opt. thick
Log(average density)
61
Key Point
Blobs become opt. thick for densities above
critical density rc, defined by
62
Super-Eddington Wind
Shaviv 98-02

• Wind driven by continuum opacity in a porous
  medium when G gt1

At sonic point
porosity-length ansatz
63
Power-law porosity
At sonic point
64
Results for Power-law porosity model
65
Effect of gravity darkening on porosity-moderated
mass flux
66
Eta Carinae
67
Summary Themes

• Continuum vs. Line driving
• Prolate vs. Oblate mass loss
• Porous vs. Smooth medium

68
Future Work

• Radiation hydro simulations of porous driving
• Cause of L gt LEdd?
• Interior vs. envelope energy source
• Cause of rapid rotation
• Angular momentum loss/gain
• Implications for
• Collapse of rotating core, Gamma Ray Bursts
• Low-metalicity mass loss, First Stars

69
X-ray lightcurve for h Car
70
(No Transcript)
71
(No Transcript)
72
POWR model for opacity
73
POWR model of radiative flux
74
POWR model of radiative force
75
Mdot increases with GEdd
76
Mdot increases with Ge