You are here:

Astrophysics/Transfer equation for brightness temperature

Advertisement

Expert: - 3/10/2008


Question
What would be the transfer equation for the brightness temperature of radiation in the vicinity of a flare? (Note: not a homework question!)

Answer
Hello,

The transfer equation for the brightness temperature of radiation in the vicinity of a flare is expressed:

dT_b/ dx = A - (u_N  +  u_c)T_b

where T_b is the brightness temperature.  This is the temperature a black body should have for the spcific intensity (I) to produce a given frequency. (You may wish to go back to the second or third question you asked me last year, which dealt with specific intensity)

Recall the power radiated by a source can be expressed:

P(s) =  kT_b [OMEGA/ L^2]

where OMEGA denotes the solid angle, and L is the wavelength, k is Boltzmann's constant.

The other quantity to pay special attention to is the collisional absorption coefficient, u_c:

u_c =  w_p^2 f_ei/ w_t^2 v(g)

where w_p is the plasma frequency, f_ei is the electron -ion collision frequency, w_t is the frequency for the relevant EM wave, and v(g) is the group velocity for transverse EM waves:

v(g) =  c[1 - w_p(x)^2/ w_t^2]^1/2

Hope this sheds some light, and if you need to unravel anything more, let me know!  

Astrophysics

All Answers

Answers by Expert:

Ask Experts

Volunteer

Philip A. Stahl

Expertise

I specialize in stellar and solar astrophysics. Can answer any questions pertaining to these areas, the spectroscopic analysis of stars – as well as the magneto-hydrodynamics of sunspots and solar flares. Sorry – No homework problems done or research projects! I will provide hints on solutions.

Experience

Have published papers on the relationship between sunspot morphology and solar flares; discovery of SID flares related to this, constructed computerized stellar models; MHD research.

Organizations
American Astronomical Society (Solar physics and Dynamical astronomy divisions), American Geophysical Union, American Mathematical Society, Intertel.

Publications
Solar Physics, Journal of the Royal Astronomical Society of Canada, Journal of the Barbados Astronomical Society, Meudon Solar Flare Proceedings (Meudon, France). Books: 'Selected Analyses in Solar Flare Plasma Dynamics', 'Physics Notes for Advanced Level'.

Education/Credentials
B.A. degree in Astronomy; M.Phil. degree in Physics - specializing in solar physics.

Awards and Honors
Postgraduate research award- Barbados government; Studentship Award in Solar Physics - American Astronomical Society

©2012 About.com, a part of The New York Times Company. All rights reserved.