Difference between revisions of "Radiative Processes in Astrophysics"

From AstroBaki
Jump to navigationJump to search
Line 1: Line 1:
# [[Radiation Lecture 01]]
+
# [[Radiation Lecture 01]] {{:Radiation_Lecture_01}}
 
# [[Radiation Lecture 02]]
 
# [[Radiation Lecture 02]]
 
# [[Radiation Lecture 03]]
 
# [[Radiation Lecture 03]]

Revision as of 03:39, 14 February 2010

  1. Radiation Lecture 01

Units

Here are some terms pertaining to telescope observations:

aperture area (), solid angle on sky (), exposure time (), collects energy (), over waveband (), but .

is the specific intensity per unit frequency.

Flux density is power per unit frequency passing through a differential area whose normal is . Thus, flux density is:

Proof that Specific Intensity is conserved along a ray

The power received by the telescope is:

where is the intensity as a function of right-ascension () and declination (). Say that is the surface luminosity of a patch of sky (that is, the emitted intensity). Then power emitted by patch of sky is:

Recognizing that :

This derivation assumes that we are in a vacuum and that the frequencies of photons are constant. If frequencies change, then though specific intensity is not conserved, is. Also, for redshift ,

so intensity decreases with redshift. Finally:

is conserved along a ray, where is the index of refraction.

The Blackbody

A blackbody is the simplest source: it absorbs and reemits radiation with 100% efficiency. The frequency content of blackbody radiation is given by the Planck Function:

(The Planck Function for Black Body Radiation)

Derivation:

The # density of photons having frequency between and has to equal the # density of phase-space cells in that region, multiplied by the occupation # per cell. Thus:

However,

so we have it. In the limit that :

Wein tail

If :

Rayleigh-Jeans tail Note that this tail peaks at . Also,

  1. Radiation Lecture 02
  2. Radiation Lecture 03
  3. Radiation Lecture 04
  4. Radiation Lecture 05
  5. Radiation Lecture 06
  6. Radiation Lecture 07
  7. Radiation Lecture 08
  8. Radiation Lecture 09
  9. Radiation Lecture 10
  10. Radiation Lecture 11
  11. Radiation Lecture 12
  12. Radiation Lecture 13
  13. Radiation Lecture 14
  14. Radiation Lecture 15
  15. Radiation Lecture 16
  16. Radiation Lecture 17
  17. Radiation Lecture 18
  18. Radiation Lecture 19
  19. Radiation Lecture 20
  20. Radiation Lecture 21
  21. Radiation Lecture 22
  22. Radiation Lecture 23
  23. Radiation Lecture 24