Page 11 - 83 basic knowledge of astronomy

opening angle intersect a sphere of radius r, forming a cross–section of area
σ, and let the source be seen to subtend a solid angle Ω at this radius. The
power of the radiation with bandwidth ∆ν passing through this cross–section
is W = I ν Ω σ∆ν, which must be constant at any radius along the tube, as
long as the radius is much larger than the source size. Now, the solid angle of
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the source Ω and the area of the cross–section σ vary as Ω ∝ r −2 and σ ∝ r ,
respectively. Therefore, the monochromatic intensity I ν = W/(Ω σ ∆ν)
must be constant along the path.

7.3 ‘Spectral Flux Density’ or ‘Flux Density’ or ‘Flux’
S ν

The spectral flux density S ν is the quantity of radiation energy incoming
through a cross section of unit area, per unit frequency bandwidth, and
per unit time. A special unit called ‘Jansky (Jy)’ is widely used in radio
astronomy for the spectral flux density. This unit is defined as: 1 Jy = 10 −26
−1
W m −2 Hz .
s

θ

∆σ

Figure 10: Definition of spectral flux density S ν .

The spectral flux density S ν is related to the intensity I ν by an integral
over a solid angle Ω:

ZZ
S ν = I ν (s) cos θ dΩ,
Ω
ZZ
= I ν (θ, φ) cos θ sin θ dθ dφ, (2)
Ω

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