The Occurrence of Planets.

I wish to point out several errors and an inconsistency in Harrison Brown's report, "Planetary systems associated with main-sequence stars" (1). He begins by extrapolating the Salpeter luminosity function, which is nearly linear over an interval of 12 magnitudes, down to planetary masses. He then assumes that stars and planets are formed independently in groups of random size distribution. He concludes that great numbers of planets should exist, both as companions of stars and in invisible clusters of planetary objects. There is considerable evidence, however, that his basic assumptions are unjustified. Brown's assumption that the Salpeter-van Rhijn luminosity function can be extrapolated down to low masses is extremely weak. The determination of the "observed" luminosity function is itself very difficult and uncertain because of the incompleteness and observational bias in the discovery of nearby stars. Recently, Wanner (2) has made a new determination of the luminosity function, using new and greatly extended observational data and an improved statistical technique. His luminosity function is practically constant from M, = +6 to +16; in fact it peaks at Ml,1= +9. If Brown had used Wanner's luminosity function instead of the Salpeter-van Rhijn function, he would have predicted only half a planet (in the range of mass from Jupiter to one "Mars-equivalent") per star. However, regardless of what luminosity function is adopted, the assumption that it represents a uniform massdistribution function that can be linearly extrapolated over several orders of magnitude is certainly unsound. For the general luminosity function represents a mixture of stellar populations, with different ages, chemical compositions, and places of origin; and the proportions of the mixture vary with luminosity. Even if the luminosity function itself were uniform and linear, the nonlinearity of the mass-luminosity relation would make the derived massfrequency function nonlinear. Brown tacitly admits this by restricting his mass-frequency function to stars fainter than Mv = 10, thereby abandoning the upper main sequence and making irrelevant his previous discussion of