Page 12 - 83 basic knowledge of astronomy

where Ω could be, for example, a solid angle subtended by a radio source
(see Figure 10).

7.4 Power/Energy/Radiation Flux Density S

The power/energy/radiation flux density S is the quantity of radiation en-
ergy, over the whole frequency range, incoming through a cross section of
unit area, per unit time. Therefore,
∞
Z
S = S ν dν. (3)
0
When we are interested in the “received” power flux density only, we
restrict the range of integration to the observing bandwidth ∆ν, i.e.,
Z
S = S ν dν. (4)
∆ν
−2
The unit of power flux density is: W m .

7.5 Spectral Energy Density per Unit Solid Angle u ν

The spectral energy density per unit solid angle, u ν (s), is the volume density
of the radiation energy incident from a certain direction s, per unit solid
−1
angle, and per unit frequency bandwidth. The unit is J m −3 Hz −1 sr .
dσ
s

c dt

Figure 11: Radiation energy per unit solid angle in a tube.

Let us consider a cylindrical tube with a cross section of area dσ perpen-
dicular to the ray propagation direction, and with a length cdt, which is the
distance travelled by the radiation during a time interval dt at light speed c
8
−1
( = 2.998 × 10 m s ) (see Figure 11). The radiation energy dU ν (J Hz −1
−1
sr ) per unit solid angle, and per unit frequency bandwidth, contained in
the cylinder may be expressed either in terms of the spectral energy density
per unit solid angle, u ν (s), or in terms of the intensity I ν (s), as:
dU ν = u ν (s) cdt dσ,
dU ν = I ν (s) dt dσ. (5)

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