On the Information Contained in Center-to Limb Observations.

Abstract

view Abstract Citations References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On the Information Contained in Center-to Limb Observations. Cowley, Charles Abstract Several years ago Karl-Heinz B5hm published a note in the Astrophysical Journal (134, 264, 1961). The conclusions of this note were that center-to-limb observations at a given wavelength were unable to provide more information than is contained in a three-parameter formula for the source function in a stellar atmosphere. This analysis was based on an analogy between the limb-darkening equation, which may be expressed as a convolution, and ordinary distortion-rectification problems. Fourier techniques were employed. The analogy, however, is not sufficiently close. In the case of the distortion of a true line profile t(z) by an apparatus function a (~) to give an observed profile o(~), the functions t(x), a(~), and o(z) are transient functions whose Fourier transforms are well defined. The limb-darkening equation for I (cos 0) however, is only defined for values of cos 0 equal to or less than one, and greater than some limiting value at which the assumption of plane-parallel layers is no longer valid. I(cos 0) thus does not have a Fourier transform. Use was also made of the "sampling theorem" from information theory. However, in the application of this theorem the observable range of a function was confused with the range over which a function is finite. The sampling theorem deals with the latter quantity, while in limb-darkening problems we are concerned with the former, namely the observable range of I(cos 0). We conclude that there is no reason to suppose that improved limb-darkening observations will not require a four-, or perhaps even a five-parameter formula for their description. The three-parameter formulas that have been used in the past are plainly inadequate to describe both the rapid decrease of the source function toward small optical depths and the departures from linearity that occur near optical depth unity. Publication: The Astronomical Journal Pub Date: 1965 DOI: 10.1086/109614 Bibcode: 1965AJ.....70R.671C full text sources ADS |