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KYA306 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 QuantitiesPhotoionization

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KYA306 AstrophysicsStellar Astrophysics Assignment #3M.docx

  • 1. KYA306 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?
  • 2. 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⌫,
  • 3. 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 QuantitiesPhotoionization