Opacity Formulae and Stellar Line Intensities

Abstract

view Abstract Citations (13) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Opacity Formulae and Stellar Line Intensities Russell, Henry Norris Abstract Theory-Formulae for the general opacity of a stellar atmosphere are reviewed, especially Pannekoek's approximations. General equations are derived (~ 5) for the numbers of neutral and ionized atoms and the optical depth in an atmosphere contain- ing two partially ionized elements and others not ionized, and simplified by the introduc- tion of functionsf, which are tabulated (~ 8). Solutions in which only one component is supposed to be partially ionized-the rest being completely ionized or completely neutral- are sufficient in almost all practical cases. The influence of variations in abundance, gravity, and temperature are discussed (~ 9-10). If the opacity depends wholly on the interaction of electrons and ions, the lines of any element wi]I have a maximum (for varying temperature) only if some other element of easier ionizatioii is present, and the position of the maximum will depend on the relative abundance of the two (~ 13-16). Opacity due to interaction of neutral atoms and electrons produces similar effects (~ 17). Equations are given for both cases and for the combination of the two. Applications-With the aid of empirical expressions for the surface gravity in stars of different temperatures (main sequence and giants) [~ i8J, the conditions for maxima of lines of H, Mg+, and Fe+ are worked out for atmospheres composed mainly of hydrogen (§~ 19-20) and of easily ionized atoms like sodium (~ 21). The observed low temperature for Fe+ (class F5) and the persistence of arc lines of Fe in the hotter stars can be explained in the former case, but not in the latter. Numerical values for the pressure are derived from the writer's data for the solar atmosphere (~ 22). From the maxima of Fe+ and Ti~ it follows (~ 23) that hydrogen is from 1000 to 2000 times more abundant than all the metals together. For a model atmosphere, containing i atom of K to 3 of Na, 12 of Fe, and i 6,ooo of H, the electron pressure and amount of matter above the photosphere are calculated for main-sequence stars and giants (Figs. i, 2; § 25). The numbers of atoms engaged in producing given spectral lines are then computed, approximate account being taken of the transition probabilities (~ 26; Figs. 3-8). The computed temperatures of maximum agree closely with observation, including the previously anomalous (K) line of Ca4. A moderate disagreement for H arid Mg+ may be explained by a contribution of neutral atoms to opacity (Figs. 6-7), but more probably arises from distortion of the energy- curve in stars of class A, making their color temperatures too high. The outstanding dis- cordance in the absolute-magnitude effect for H and He at high temperatures is attrib- uted to the Stark effect. The still more anomalous strength of the Balmer series and the enhanced lines in red giants is ascribed tentatively to large differences in tempera- ture within the atmosphere Publication: The Astrophysical Journal Pub Date: November 1933 DOI: 10.1086/143505 Bibcode: 1933ApJ....78..239R full text sources ADS | Related Materials (1) Reprint: 1933CMWCI.477....1R