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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