view Abstract Citations References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Velocity distribution of K dwarf stars in the vicinity of the sun. Pillans, Helen M. Abstract Stars, in the vicinity of the sun, with known space velocities form a very incomplete and biased sample. In addition the calculated velocities are uncertain on account of observational errors in the proper motion, the radial velocity and the parallax. The effect of these two factors on the velocity ellipsoid for G8-K2 dwarf stars within 20 parsecs of the sun has been determined and found to decrease each of the three axes by approximately 20 per cent. Corrections for errors in the proper motions and the radial velocities were practically negligible; however, the parallax errors contributed about 8 per cent of this total observed reduction. Other characteristics of the velocity ellipsoid were unchanged; i.e., the three axes remained distinctly unequal and a vertex deviation of about 120 persisted. The incompleteness factors K(m, ) used as weights in obtaining the above results were found by taking the ratio of the theoretical N(m, i ) distribution, giving a total of 400 G8-K2 dwarf stars within the sphere of 20 parsecs surrounding the sun, to the observed A (m, ) distribution of the available 60 G8-K2 dwarf stars with parallaxes greater than or equal to o'.'050. The size of the factors varied from I to 12 depending upon the apparent magnitude and the proper motion of the star. The theoretical N(m, i ) distribution was calculated by transforming the three dimensional distribution function (AI, T, p) to F(m, , p) and integrating this with respect to p. The assumptions underlying this solution were that in the homogeneous, infinitesimal volume of space and for the small group of physically similar stars considered, M and T are stochastically independent of p and of each other, and that, to 20 parsecs, the stars are uniformly distributed, so that ~(p) = c$p4. The distributions M(M) and were calculated from the original data and later recalculated when approximate incompleteness factors had been found. The third approximation of the velocity ellipsoid derived with revised weights differed little from the second and was adopted. The effect of observational errors was taken care of by correcting the first and second order general moments of the space velocities and of the M(M) distribution. These corrections were approximately evaluated by series development and neglect of higher order terms. The basic parallax, radial velocity, and proper motion data were obtained from the Yale 1952 Parallax Catalogue, from the Mount Wilson 1950 Radial Velocity CaLalogue, both as yet unpublished, and from the General Catalogue of 33,342 Stars. University of Calsfornia, Berkeley, Ca 1sf. Publication: The Astronomical Journal Pub Date: October 1952 DOI: 10.1086/106797 Bibcode: 1952AJ.....57S.164P full text sources ADS |