assignment for astrophysics

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