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Astron. Astrophys. 327, 1155-1163 (1997)

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A numerical simulation of the Wilson-Bappu relationship

Q.-Q. Cheng , O. Engvold and O. Elgaroy

Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029 Blindern, N-0315 Oslo, Norway

Received 26 May 1997 / Accepted 11 July 1997


A numerical investigation of Wilson-Bappu relationship for CaII H and K lines in a series of non-active late-type main sequence stars is performed. Atmospheric models are constructed with given effective temperatures and surface gravities using a time-dependent hydrodynamic code. Mechanical heating by acoustic waves is included in the simulations. Radiative energy losses are treated by using tabulated Rosseland mean opacities in the photosphere, solving the transfer equation for the strongest lines in the chromosphere, and assuming optically thin emissivities in the corona.

In the static (time-averaged) atmospheres, we find that the calculated profiles of the CaII K line for different stars show a Wilson-Bappu relationship which is in good agreement with the empirical form. In different stars the lines are formed at an atmospheric height where the column mass density, which is related to the line opacity, is different, and the full width at half maximum of the CaII line emission core broadens as a result of increasing column mass density in the chromosphere. A correct choice of turbulence velocity is important for the calculation of line width in later dwarf stars.

It is well known that stellar atmospheres are dynamic. A more realistic approach is therefore to average line profiles resulting from dynamic atmospheres that represent different instants (phases) of acoustic waves. We find that the time-averaged line profiles in dynamic atmospheres are asymmetric with strong emission on the violet side of the line center. With increasing atmospheric heating the line intensity increases and the base emission line width broadens, while the variation of peak width is not significant.

Key words: hydrodynamics – lines: profiles – star: atmospheres; chromospheres; late-type; fundamental parameters

Send offprint requests to: Q.-Q. Cheng


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© European Southern Observatory (ESO) 1997

Online publication: April 6, 1998