Astrophysics 2: Stellar and Circumstellar Physics

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Astrophysics 2: Stellar and Circumstellar Physics. 4. Stellar Winds (1). http://www.arc.hokkai-s-u.ac.jp/ ~okazaki/astrophys-2/. 4.1.1 Solar wind. 4.1 Observations of stellar winds. Radiative core Convective envelope, where dynamo process is going on

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### Astrophysics 2:Stellar and Circumstellar Physics

4. Stellar Winds (1)

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

4.1.1 Solar wind

### 4.1 Observations of stellar winds

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

Structure of the Sun

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

where

Therefore, the solar corona can’t be static.

4.1.2 Winds from massive stars: P Cygni profiles

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

Emission

Absorption

E

E

A

Total

observer

wavelength

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.
4.2.2 Hydrostatic equilibrium in the base of a wind

Eq of motion:

Eq of state:

### 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

4.2.3. General dynamical equations

Mass

Momentum

Internal energy

EOS

Mass loss rate

Momentum

Total energy

work

heating

conduction

kinetic energy

potential energy

### Energy requirement

work

heating

conduction

Driving mechanism of coronal winds = gas pressure gradient

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

Assumptions

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

Coronal wind

Corona

heating

Convective envelope

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

Wind eq:

Basic equations

Eq of continuity:

Eq of motion:

Eq of state:

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),

4.2.5 Temperature sensitivity of mass loss rate

At the bottom of a subsonic wind with

we have

4.3 Analogy of De laval nozzles

Critical solutions have an analogy with flows in rocket nozzles.

Basic equations

Eq of continuity:

Eq of motion:

Eq of state:

Flow eq:

Wind eq:

Flow eq:

Both equations would be identical if