Radiation Lecture 01

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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,