Astrophysics 2: Stellar and Circumstellar Physics

1
Astrophysics 2Stellar and Circumstellar Physics
4. Stellar Winds (1)
http//www.arc.hokkai-s-u.ac.jp/
okazaki/astrophys-2/
2
4.1 Observations of stellar winds
4.1.1 Solar wind

• Radiative core
• Convective envelope, where dynamo process is
  going on
• Corona, where the solar wind begins to blow

Structure of the Sun
3
Interaction of the Earths magnetosphere with the
solar wind
4
Northern lights
5
Boundary between the solar system and the
interstellar space
6
Why the solar wind blows? (Parker 1958)
Suppose the solar corona is static, then the
equation of motion is given by
If we assume the corona to be isothermal, i.e.,
with being the isothermal
sound speed, we have
7
where
Therefore, the solar corona cant be static.
8
4.1.2 Winds from massive stars P Cygni profiles
P Cygni profile Profile characterized by strong
emission lines with corresponding blueshifted
absorption lines.
9
P Cygni profiles lines from an expanding
atmosphere/stellar wind
Emission
Absorption
E
E
A
Total
wavelength
observer
10
http//casswww.ucsd.edu/public/tutorial/Stars.html
11
Formation of a P Cygni Line- Profile
By S. Owocki
12
4.2 General equations and formalism for stellar
winds
4.2.1 What is a stellar wind?

• A stellar wind is
• a sustained outflow in the outer layers of a
  star, through which the star loses its mass
  continuously.
• a source of mass, angular momentum, and energy
  to the interstellar matter.

13
4.2.2 Hydrostatic equilibrium in the base of a
wind
Eq of motion
Eq of state
T varies gradually
14
In the base of a wind, the atmosphere is
exponentially stratified with a scale height much
smaller than the stellar radius.
e.g., Solar photosphere
15
4.2.3. General dynamical equations
Mass
Momentum
Internal energy
EOS
16
Steady, spherical expansion
Mass loss rate
Momentum
Total energy
work
heating
conduction
17
Energy requirement
kinetic energy
potential energy
work
heating
conduction
18
4.2.4 A simple model of coronal wind an
isothermal wind
Driving mechanism of coronal winds gas pressure
gradient
Assumptions

• Steady spherically symmetric.
• Forces taken into account are only gravity and
  pressure gradient force.

19
Coronal winds are driven by gas pressure due to a
high T in the corona.
20
Basic equations
Eq of continuity
Eq of motion
Eq of state
21
Wind eq has a singularity at

• The critical point is at

• The critical point is of saddle type (x-type),
  which is stable for perturbations

• At the critical point,

(sonic point),
22
Solution curves for an isothermal coronal wind
(transonic solution)
23
4.2.5 Temperature sensitivity of mass loss rate
At the bottom of a subsonic wind with
we have
24
The density distribution is
25
Mass loss rate
26
Mass loss rate vs. temperature
(Owocki 2000)
27
4.3 Analogy of De laval nozzles
Critical solutions have an analogy with flows in
rocket nozzles.
28
Basic equations
Eq of continuity
Eq of motion
Eq of state
Flow eq
29
Wind eq
Flow eq
Both equations would be identical if