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 ...