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Spectral Lines
 We saw earlier how the strength of absorption lines can
be related to the chemical abundance of a star, from the
Boltzmann and Saha equations
 However, stars do not have a uniform composition,
temperature or density and therefore a proper analysis
must account for where in the atmosphere the absorption
line is formed.
 The shape of the absorption line contains a lot of
information about the environment in which it is formed
 The strength of a line is usually expressed as an
equivalent width, that has units of
 F  F 
d
W   
wavelength:
 F 
 The opacity of the stellar material is
greatest at the deepest part of the absorption line
 The line is optically thin if the flux is not completely
blocked (some photons are escaping without being
absorbed).
 The central regions of the line must be formed at higher
(and cooler) regions of the atmosphere. The wings probe
deeper into the atmosphere.
c
c
Line Broadening
 Natural broadening
 Quantum mechanical effect due to
Heisenberg’s uncertainty principle
 The FWHM of the line is
2

1
c t
where t is the uncertainty in the timescale
of the energy transition
 Pressure broadening
 Interactions between atoms can perturb
the orbital energy levels. This is known as
collisional broadening (when referring to
individual collisions) or pressure
broadening (on a macroscopic scale)
 Approximately, the width of the line is
related to the particle number density (n),
cross-section () and
2
2kT
  n
c
m
temperature T
 Doppler broadening
 In thermal equilibrium, atoms in a gas are
moving with random velocities described
by the Maxwell-Boltzmann distribution.
   
v
c

2
kT
2 ln( 2)
c
m
Measuring abundances
 Problem: to find the number of absorbing atoms
per unit area, Nabs, that have electrons in a given
orbital.
 Boltzmann and Saha equations can be used to get
the orbital distribution if the density and
temperature are known
 Also need to know the probability that an
electron in one state can absorb a photon and
jump to another state
 i.e. if you want to relate the strength of a
line resulting from the n2→n3 transition to
the population of the n2 level, you need to
know how many n2 electrons made
transitions to higher levels, as well.
 These relative probabilities are the fvalues, or oscillator strengths.
 Can be determined theoretically (for
simple atoms) or measured experimentally.
 The f values for all transitions from a
given orbital add up to the number of
electrons in the atom. Therefore the
oscillator strength is the number of
electrons per atom participating in a given
transition