Radiative Transfer Homework: Slab of Stars & Dust | Get Help Now

In summary, we are trying to calculate the surface brightness of a galaxy consisting of a uniform slab of stars and dust. We assume that the slab has a thickness of L and an optical depth of \tau for a ray passing through it. We also assume that the emissivity of the stars and the density of the dust are constant throughout the slab and that there is no scattering due to the dust. Using the relevant equations, we find that the surface brightness observed is independent of inclination when the amount of dust becomes very large, and it is given by the integral of the emissivity over the slab.
  • #1
captain.joco
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Homework Statement


A galaxy consist of a uniform slab of stars mixed with dust. The slab has thickness L, and optical depth [tex]\tau[/tex] for a ray passing perpendicularly through the slab. assume the emmisivity of the stars [tex]\epsilon[/tex] and the density of dust is constand throught the slab. Further assume that no scattering occurs due to the dust.

Hence, calculate the surface brightness observed as function of inclination and show that it is independent of inclination if the amount of dust becoms very large.

Can I get some help please in how to set the problem up?

Thanks
 
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  • #2
. Homework Equations The relevant equations are the radiative transfer equation and the equation of conservation of energy. Radiative transfer equation: \frac{dI_\nu}{ds} = -\kappa_\nu I_\nu + \epsilon_\nuEquation of conservation of energy: I_\nu (s) = I_\nu(0)e^{-\tau_\nu(s)} + \int_0^s \epsilon_\nu(s') e^{-\tau_\nu(s-s')} ds'The Attempt at a Solution The surface brightness observed is given by I_\nu = I_\nu(0)e^{-\tau_\nu L \cos \psi} + \int_0^L \epsilon_\nu(s') e^{-\tau_\nu(L\cos \psi - s')} ds'where \psi is the angle between the ray and the normal to the slab. In the limit of large \tau, the first term can be neglected, and we get I_\nu = \int_0^L \epsilon_\nu(s') e^{-\tau_\nu(L\cos \psi - s')} ds'This expression for the surface brightness is independent of inclination, i.e., the angle \psi.
 

1. What is radiative transfer?

Radiative transfer is the process of energy transfer through a medium, such as light or heat, by means of electromagnetic radiation.

2. What is a slab of stars and dust in relation to radiative transfer?

A slab of stars and dust refers to a theoretical model used in radiative transfer studies. It consists of a layer of stars and a layer of dust, with the dust acting as an absorber and scatterer of radiation from the stars.

3. How does radiative transfer homework help in understanding the universe?

Studying radiative transfer through models, such as a slab of stars and dust, helps us understand the behavior of light and energy in different environments. This can provide insight into the physical properties of celestial objects and their interactions with each other.

4. What are some common challenges in solving radiative transfer homework?

Some common challenges in solving radiative transfer homework may include understanding the mathematical equations and models, dealing with complex data and calculations, and interpreting the results in a meaningful way.

5. How can I get help with my radiative transfer homework?

You can seek help from your professor, teaching assistant, or classmates. You can also refer to textbooks, online resources, or reach out to a tutor for additional support.

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