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Astrophysics 2: Stellar and Circumstellar PhysicsPowerPoint Presentation

Astrophysics 2: Stellar and Circumstellar Physics

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### Astrophysics 2:Stellar and Circumstellar Physics

### 4.1 Observations of stellar winds

### In the base of a wind, the atmosphere is exponentially stratified with a scale height much smaller than the stellar radius.

### Energy requirement

### 4.2.4 A simple model of coronal wind: an isothermal wind

4. Stellar Winds (1)

http://www.arc.hokkai-s-u.ac.jp/ ~okazaki/astrophys-2/

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

Structure of the Sun

Northern lights wind

Why the solar wind blows? (Parker 1958) wind

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

where wind

Therefore, the solar corona can’t be static.

4.1.2 Winds from massive stars: P Cygni profiles wind

P Cygni profile: Profile characterized by strong emission lines with corresponding blueshifted absorption lines.

P Cygni profiles: lines from an expanding atmosphere/stellar wind

Emission

Absorption

E

E

A

Total

observer

wavelength

Formation of a P Cygni Line- Profile wind

By S. Owocki

4.2 General equations and formalism for stellar winds wind

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.

4.2.2 Hydrostatic equilibrium in the base of a wind wind

Eq of motion:

Eq of state:

T varies gradually

e.g., Solar photosphere

4.2.3. General dynamical equations stratified with a scale height much smaller than the stellar radius.

Mass

Momentum

Internal energy

EOS

Steady, spherical expansion stratified with a scale height much smaller than the stellar radius.

Mass loss rate

Momentum

Total energy

work

heating

conduction

kinetic energy stratified with a scale height much smaller than the stellar radius.

potential energy

work

heating

conduction

Driving mechanism of coronal winds = gas pressure gradient stratified with a scale height much smaller than the stellar radius.

Assumptions

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

Coronal wind stratified with a scale height much smaller than the stellar radius.

Corona

heating

Convective envelope

Coronal winds are driven by gas pressure due to a high T in the corona.

Wind eq: stratified with a scale height much smaller than the stellar radius.

Basic equationsEq of continuity:

Eq of motion:

Eq of state:

Wind eq has a singularity at stratified with a scale height much smaller than the stellar radius.

- 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),

Solution curves for an isothermal coronal wind stratified with a scale height much smaller than the stellar radius.

(transonic solution)

4.2.5 Temperature sensitivity of mass loss rate stratified with a scale height much smaller than the stellar radius.

At the bottom of a subsonic wind with

we have

The density distribution is stratified with a scale height much smaller than the stellar radius.

Mass loss rate is very sensitive to the temperature! stratified with a scale height much smaller than the stellar radius.

Mass loss rateMass loss rate vs. temperature stratified with a scale height much smaller than the stellar radius.

(Owocki 2000)

4.3 Analogy of De laval nozzles stratified with a scale height much smaller than the stellar radius.

Critical solutions have an analogy with flows in rocket nozzles.

Basic equations stratified with a scale height much smaller than the stellar radius.

Eq of continuity:

Eq of motion:

Eq of state:

Flow eq:

Wind eq: stratified with a scale height much smaller than the stellar radius.

Flow eq:

Both equations would be identical if

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