Astronomy Principles and Practice Fourth Edition.pdf

230 The radiation laws
In most physical situations, practical determination of natural emission widths is compromised by
a variety of physical causes affecting the behaviour of the radiating atoms. Certainly this is the case
in the general astrophysical environments as highlighted in the next three subsections which serve as
examples of the importance of recording the details of spectral line profiles.
15.8.4 Thermal line broadening
If atoms are contained in a hot gas cloud and are giving rise to emission lines in their spectra, then the
profiles are likely to be broadened by thermal Doppler effects.
As a result of the local temperature, the atoms acquire a distribution of kinetic energies referred to
as the Maxwell distribution. Within such a radiating cloud some atoms will be receding and others will
be approaching the observer such that at the times of the emissions, individual contributions may be
red or blue shifted as a result of the Doppler effect. The overall shape of the emission line is, therefore,
broadened into a ‘bell-shaped’ profile with the halfwidth dependent on the temperature.
A typical kinetic energy of an atom may be obtained by taking the most probable value of the
Maxwell distribution this being
1
2 mv2 = kT
where k is Boltzmann’s constant. Hence,
√
2kT
v ∼
m
If, for example, a cloud of hydrogen is considered to be at a temperature of 10 000 K, a typical value
for the velocity is
v ∼
√
2 × 1·38 × 10 −23 × 10 4
1·7 × 10 −27 ms −1
giving a value for v ∼ 1 × 10 4 ms −1 . The Doppler shift associated with such a velocity is readily
detectable. It is obvious that thermal Doppler broadening would be less apparent for the heavier atomic
species.
15.8.5 Collisional line broadening
For atoms which are radiating in an environment subject to a high pressure, the energy levels of the
radiating or absorbing atom may be influenced by local charged particles (ions and electrons). In a
gas, such perturbations are random and give rise to a broadening of the line—the Stark effect. There
will be a high probability that the radiating atoms will suffer collisional impacts with adjacent atoms
during the time interval of the individual emissions. As a result, the frequency associated with the
emission will be blurred. Overall, the assembly of radiating atoms provides spectral line profiles which
are broadened by the process according to the local density or pressure.
15.8.6 Line broadening by rotation
When a telescope–spectrometer combination is applied to a stellar radiation, the resultant spectrum
results from the light received from the whole of the presented stellar disc.
For rotating stars, this means that the generated absorption lines from each location on the disc
are subject to Doppler displacements according to their position and line-of-sight velocity. Radiation
from the approaching limb will be blue shifted, while that from the receding limb will be red shifted.
Integration of these effects over the presented disc produces an overall absorption line profile which is
saucer-shaped. From observations of the line profile spread, the projected equatorial velocity, V sin i,
of the star can be determined.