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 l.jpg

Astrophysics 2:Stellar and Circumstellar Physics

4. Stellar Winds (1)

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


4 1 observations of stellar winds l.jpg

4.1.1 Solar wind

4.1 Observations of stellar winds

  • Radiative core

  • 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 l.jpg
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


Slide7 l.jpg

where wind

Therefore, the solar corona can’t be static.


4 1 2 winds from massive stars p cygni profiles l.jpg
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 l.jpg
P Cygni profiles: lines from an expanding atmosphere/stellar wind

Emission

Absorption

E

E

A

Total

observer

wavelength




4 2 general equations and formalism for stellar winds l.jpg
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 l.jpg
4.2.2 Hydrostatic equilibrium in the base of a wind wind

Eq of motion:

Eq of state:

T varies gradually


Slide14 l.jpg

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

Mass loss rate

Momentum

Total energy

work

heating

conduction


Energy requirement l.jpg

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

potential energy

Energy requirement

work

heating

conduction


4 2 4 a simple model of coronal wind an isothermal wind l.jpg

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

4.2.4 A simple model of coronal wind: an isothermal wind

Assumptions

  • Steady & spherically symmetric.

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


Slide19 l.jpg

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.


Basic equations l.jpg

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

Basic equations

Eq of continuity:

Eq of motion:

Eq of state:


Slide21 l.jpg

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


Mass loss rate l.jpg

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

Mass loss rate


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

(Owocki 2000)


4 3 analogy of de laval nozzles l.jpg
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 equations28 l.jpg
Basic equations stratified with a scale height much smaller than the stellar radius.

Eq of continuity:

Eq of motion:

Eq of state:

Flow eq:


Slide29 l.jpg

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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