E7 Atomic Physics and Spectral Lines

Topic

The central figure of this model is the atom—specifically the hydrogen atom, which serves as the baseline for all spectral diagnostics in astrophysics.

Bohr's model defines the possible energy levels of the hydrogen atom, with each successive level being less deep than the last as the identifying quantum number increases; the Lyman, Balmer, and Paschen series each correspond to a set of atomic transitions terminating at one of the three lowest energy levels, and the Rydberg formula assigns a precise, predictable wavelength to each of these transitions.

Thermal Doppler broadening—caused by the atom's own thermal velocity within the gas—determines the minimum possible width of the spectral line associated with each transition: the higher the gas temperature, the greater the thermal velocity of its atoms, resulting in an increasingly broad spectral line.

The Boltzmann equation, in turn, describes the relative population of each atomic energy level: at a given temperature, the fraction of atoms occupying an excited level decreases exponentially as the level's energy above the ground state increases. A rise in temperature leads to greater population of the atom's higher energy levels, whereas a larger energy gap between two levels results in lower occupancy of those higher levels.

The Saha equation extends this reasoning to atomic ionization: the ratio of ionized to neutral atoms increases with gas temperature and decreases as the number of free electrons surrounding the atom rises. Thus, from the hydrogen atom with which this document begins to the ionization state with which it concludes—encompassing the Bohr model, thermal Doppler broadening, and the Boltzmann equation—atomic physics dictates that the state of a given atom (its populated levels, line widths, and degree of ionization) completely determines the spectral classification of stellar atmospheres as well as the observed state of nebulae.

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