How to model light from a star?

[Haorong Wu]

I am aware that a laser could be modeled as a Gaussian beam, e.g., $$E=E_0\frac{w_0}{w_z}\exp (\frac {-r^2}{w^2_z}) \exp (-i(kz+k \frac {r^2}{2R(z)}-\psi(z))).$$

Now I want to study the propagation of light emitted from stars. But I am not sure how to model it, especially by some kind of functions.

I am particularly interested in the situation where the light has traveled a great deal of distance. Since it then can be treated as parallel beam, I argue that they can be model as a Gaussian beam with the waist radius equal to the radius of the star, given a certain frequency. Does this make sense?

What key words should I search in google scholar?

Thanks!

 

[Baluncore]

The light emitted from a star is not a narrow parallel beam, it is radial.
What is your reason for needing a model?
How will you model the aperture of your observer?
Are you modelling the light in free space, or light reaching the surface of the Earth?

 

[anuttarasammyak]

How about it ?
$$E^2_{av}=B^2_{av}=\frac{S}{8\pi R^2}$$
$$\mathbf{E}\times\mathbf{R}=0,\mathbf{B}\times\mathbf{R}=0$$
where $\mathbf{R}$ is vector from the star to the Earth.

 

[Haorong Wu]

The light emitted from a star is not a narrow parallel beam, it is radial.
What is your reason for needing a model?
How will you model the aperture of your observer?
Are you modelling the light in free space, or light reaching the surface of the Earth?

Thanks, @Baluncore .

Initially, it is radial. But I am taught that when solar light reach the Earth, it can be treated as parallel light. I am not sure is this argument correct.

I am studying the propagation of light near a black hole. Well, most of light comes from stars, so I would like to model it.

To be specific, I am using the covariant wave equation, from Spacetime and geometry, $$\square \psi=[g^{00} \partial^2_0+\frac 1 2 g^{00}g^{ij}(\partial_i g_{00})\partial_j+g^{ij}\partial_i\partial_j-g^{ij}\Gamma^k_{ij}\partial_k]\psi=0 $$ where $\psi$ describe the light. For a laser, $\psi$ can be the Gaussian beam.

The emitting and observation parts are out of my consideration.

 

[Haorong Wu]

Hi, @anuttarasammyak.

At first sight, those equations seem familiar. But I do not understand them. What $av$ stands for? Anyway, I could understand that the first equation means the energy carried by electric or magnetic field.

But I do not understand the second one. Why $\mathbf E \times \mathbf r=0$? Should not $\mathbf E$ be perpendicular to $\mathbf r$?

 

[anuttarasammyak]

I meant av as time average but now I think it is unnecessary for incoherent light.
Electromagnetic wave is a transverse wave.

 

[Haorong Wu]

I meant av as time average but now I think it is unnecessary for incoherent light.
Electromagnetic wave is a transverse wave.

But for a transverse wave, do you mean $\mathbf E \cdot \mathbf r=0$?

 

[anuttarasammyak]

Yea, I was wrong.

 

[anuttarasammyak]

where R is vector from the star to the Earth.

I made a rough definition "to the Earth" because vectors from the center of star to south pole and to north pole differ slightly. In good approximation you observe light from the stars are plane wave though they actually are sphere wave.