23 Jul AccountingAssignment For Astrophysics
Stellar Astrophysics Assignment #3
March 21, 2017
Due: 4 April 2017
1 Radiation Quantities
X-ray photons are produced in a cloud of radius R at a uniform rate � photons s�1 cm�3. The cloud is a distance d away from the observer. The intervening medium is optically thin (neglect absorption). A detector at Earth records x-ray photons arriving from an angle within ±�✓ (the so-called “acceptance half-angle” or “beam” of the instrument) of normal to the detector, which has an e↵ective area �A.
a. Assume that the source is completely resolved. What is the observed intensity (photons s
�1 cm
�2 sr
�1 )
toward the centre of the cloud?
b. Assume that the source is completely unresolved. What is the observed average intensity when the
source lies within the beam of the detector?
2 Photoionization
Photoionization is the process in which a photon is absorbed by an atom or molecule and an electron is
ejected. An energy at least equal to the ionization potential is required. Let this energy be h⌫0 and let �⌫ be the cross-section for photoionization. Show that the number of photoionizations per unit volume per unit time is
4⇡n
Z 1
⌫0
�⌫J⌫ h⌫
d⌫ = cn
Z 1
⌫0
�⌫u⌫ h⌫
d⌫,
where n is the number density of absorbing atoms, u is the energy density of the radiation field at frequency ⌫, and J⌫ is the corresponding mean intensity.
1
- Radiation Quantities
- Photoionization
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