Mathematics
Scientific paper
Jan 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994pasp..106...47m&link_type=abstract
Publications of the Astronomical Society of the Pacific, vol. 106, no. 695, p. 47-55
Mathematics
43
Functions (Mathematics), Globular Clusters, Mass Spectra, Stellar Luminosity, Stellar Spectra, Spectrum Analysis, Stellar Models
Scientific paper
Following Harris and Pudritz (1993, ApJ, submitted), it is assumed that a globular-cluster system (GCS) has a mass spectrum of the form N(m) approximately = m-alpha, where alpha may take on different characteristic values in selected mass ranges. From this, an analytical globular-cluster luminosity function (GCLF) is then derived. It is show that this GCLF is non-Gaussian, but will be peaked, unimodal, and symmetric (as is observed) if the mass spectral slope changes in a very specific way: there must be exactly one transition in alpha from greater than 1 to less than 1, and the relation absolute value of 1 - alpha = const. must hold. Similarly, the luminosity-weighted luminosity function (LWLF), which is a useful observable for the distant, very large GCSs in Virgo and beyond, is shown to be peaked, unimodal, and symmetric if there is exactly one transition from alpha greater than 2 to alpha less than 2, such that absolute value of 2 - alpha = const. The Gaussian approximation to the analytical GCLF is considered, and it is shown that the dispersion sigmaG is directly related to the mass spectral slope alpha. Implications for the use of the GCLF as a standard candle are briefly discussed.
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