Page 29 - 83 basic knowledge of astronomy

1. When κ ν = 0,
the solution of equation (36) is just a simple integral:

l
Z
0
0
I ν (l) = I ν (0) + ν (l )dl . (41)
0
2. When ν = 0,
the solution is an exponential function:
l
R
− κ ν (l )dl 0
0
I ν (l) = I ν (0)e 0 . (42)
If the medium is homogeneous, i.e. κ ν = constant everywhere, then

I ν (l) = I ν (0)e −κ ν l . (43)

Here,
κ ν > 0 (positive opacity) implies an exponential decay, which arises
from ordinary absorption, and
κ ν < 0 (negative opacity) implies an exponential growth, which arises
from maser amplification.

Maser Amplification

When the number density n n of particles at a higher energy level E n
is, for some reason, larger than n m at a lower energy level E m (such
a situation is called a “population inversion”), the opacity becomes
negative (κ ν < 0), and the radiation of the frequency corresponding to
the transition between the energy levels is exponentially amplified along
the initial direction of propagation (Figure 24). Since this amplification
is due to induced (or stimulated) emission, it is called a “MASER”
(Microwave Amplification of Stimulated Emission of Radiation). The
same mechanism in the visible light region of electromagnetic waves
is called the “LASER” (Light Amplification of Stimulated Emission of
Radiation).

If the thermal equilibrium condition is fulfilled in the gas medium, the
Boltzmann distribution always ensures n n < n m , and no maser amplifi-
cation can occur. Therefore, maser emission is essentially non–thermal.
We need some “pumping mechanism” which realizes the population in-
version in order to get the maser mechanism to work. In actual inter-
stellar space, strong infrared radiation from stars, or collisions of gas
molecules, may serve as a pumping mechanism.

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