The local standard of rest and the well in the vel

Authors: Charles Francis Erik Anderson

Publish Date: 2014/04/03

Volume: 118, Issue: 4, Pages: 399-413

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Abstract

It is now recognised that the traditional method of calculating the LSR fails We find an improved estimate of the LSR by making use of the larger and more accurate database provided by XHIP and repeating our preferred analysis from Francis and Anderson New Astron 14615–629 2009a We confirm an unexpected high value of U 0 by calculating the mean for stars with orbits sufficiently inclined to the galactic plane that they do not participate in bulk streaming motions Our best estimate of the solar motion with respect to the LSR U 0 V 0 W 0 = 141 pm 11 146 pm 04 69 pm 01 km s1Kepler’s second law is an expression of conservation of angular momentum and holds for planar orbits in any axisymmetric potential Assuming a wellmixed distribution in which orbital eccentricities are low the greater density of stars towards the centre of the Galaxy will not greatly affect calculation If the number of stars on the outer part of the orbit lagging the LSR outnumbers the number on the inner part leading the LSR by 7030 it is because the time on the outer part of the orbit is greater by roughly this ratio so the velocity is less and the radial distance is greater by the square root of this ratio ie by a factor greater than 15 contradicting the assumption that orbital eccentricities are low Then for galactic rotation theta 0 approx 200 km s1 azimuthal velocities will range from sim 160 to sim 240 km s1 and dispersion in V will be about 40 km s1 around twice the observed value of 21 km s1 for disc starsA simple estimate of the probability that the well at U V = 125 14 km s1 seen in Fig 2 could arise by chance can be found by defining one hundred 2times 2 km2 s2 bins centred at even integer velocities in the ranges 24le U le 6 24le V le 6 km s1 The bins contain 3 824 stars The bin centred at 12 14 km s1 contains only 21 stars For a uniform distribution the null hypothesis the number of stars in each bin is given by a binomial distribution mathsf B 3 824 001 for which the probability of finding 21 or fewer stars in a bin is 00017 giving a 998  significance level The use of a uniform probability distribution underestimates the statistical significance of the well because there is generally a greater probability of finding data towards the centre of a distribution

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