The galactic motion field of K0-5 giants from Hipparcos data

Abstract

We have investigated the motions of all K0-5 stars which have a proper motion in the Hipparcos catalogue and a known luminosity class III (due to the incompleteness of the ongoing classification, the distribution of these stars at the celestial sphere is rather uneven). We have used the apparent magnitudes and colours together with adopted means and dispersions of the absolute values in order to estimate distances. The fulfilment of two one-sided conditions has been ensured: the stars should only be reddened and their photometric parallaxes should be consistent with the trigonometric ones; this is practically a one-sided condition, if, as usual, the trigonometric parallax is near zero (every condition to be demanded within s dispersions). Our final total sample contains 8349 stars. We did not demand the knowledge of radial velocities or metallicities, nor did we use them in the rather small fraction of our stars which they were known for. The estimated photometric distances have a logarithmic mean of 280 pc and an error of typically 25%. The proper motions were represented by a kind of ‘adaptive’ model, using a three dimensional expansion in a series of orthogonal functions of galactic latitude, longitude and of the logarithm of the distance. Our programme searches automatically for significant functions. Usually, we have selected those which could arise by chance with a 5% probability only or less than 5% (in some cases we additionally have treated the data with a corresponding limit of 1%). Most of the found significant functions belong to exact or approximate equivalents of known standard motions, especially the average ensemble motion and the two first order parameters of galactic rotation. The data were treated first for each spectral subclass separately and then - since the differences were not pronounced - as a united sample. For the united sample, the ensemble motion with respect to the sun is (U0, V0, W0) = (—9.0 ± 0.5, —21.0 ± 0.5, —7.7 ± 0.4) km/s and with respect to the local standard of rest (U, V, W)LSR = (+1, —16, —1) km/s As galactic rotation parameters we obtain Q = —1.81 ± 0.51 mas/yr, P = +2.92 ± 0.32 mas/yr (the first being corrected for asymmetric drift with the aim to represent the circular velocity). Beyond these standard motions, three non-standard functions appear. One of those has a 4 s coefficient and corresponds to a distance dependent galactic shear parameter C. If we were to demand that this term vanishes, Q would change towards —2.60 mas/yr - in agreement with the value from Hipparcos Cepheids. The residuals against the systematic motions are used to obtain the 3 axes of a velocity ellipsoid (assumed to be aligned to the galactic axes) σ(U) = 37.5 ± 0.3 km/s, σ(V) = 26.9 ± 0.4 km/s, σ(W) = 20.1 ± 0.7 km/s. The two quantities V0 and σ(U) mutually fulfill the asymmetric drift relation. From the total dispersion an age of the order 4 · 109 years can be obtained. These figures agree with those of nearby old giants, but they now refer to a much larger volume and number of stars. All dispersions depend on the distance z perpendicular to the galactic plane. Most distinctly, the dispersion perpendicular to the galactic plane cannot be described by one isothermal component. σ(W) increases with |z|; the distribution of the W-velocities near the galactic plane is non-Gaussian in the sense that the central peak is more populated. Thus at least 3 components would be required if a description with isothermal components were wanted.