Galactic Rotation Parameters Research Articles

К определению постоянной Галактической аберрации

Galactic aberration in proper motions (GA) has an amplitude (also known as the Galactic aberration constant) of about 5 µas/yr, which is substantial for the modern highly accurate astrometric observations such as Gaia and radio astrometry. There are several determination of the GA constant, but they don’t agree well. The estimates derived from radio astrometry (VLBI) and Gaia observations differ significantly, so it would be very desirable to involve another independent method to solve the problem of inconsistency between these two methods. In this paper, determination of the GA constant from the Galactic rotation parameters determined by methods of stellar astronomy is carried out. Obtained result showed that the GA constant estimate obtained from stellar astronomy agrees within errors with the estimate obtained from Gaia and does not agree well with the estimate based on VLBI observations of extragalactic radio sources.

On the Most Reliable Value of the Galactic Aberration Constant

Galactic aberration (GA) is a small effect in proper motions of celestial objects with an amplitude of about 5 μas yr−1 already noticeable in highly accurate astrometric observations such as VLBI and Gaia. However accurate accounting for this effect faces difficulty caused by the uncertainty in the GA amplitude (GA constant). Its estimates derived from VLBI and Gaia data processing differ significantly, so it would be very desirable to involve another independent method to solve the problem of inconsistency between these two methods. Such a method, that I consider in this paper, is using determination of the Galactic rotation parameters by methods of stellar astronomy. The result obtained in this study showed that the GA constant estimate obtained from stellar astronomy is closer to the estimate obtained from Gaia.

Наиболее интересные результаты изучения Галактики по OB-звездам

A review of the main results of studying the structure and kinematics of the Galaxy obtained by various research teams using OB stars is given. The main attention is paid to the results of the authors of this work. The following questions are considered: a) the nature of the spatial distribution of OB stars in the Galaxy; b) the use of OB stars to refine the parameters of the spiral pattern of the Galaxy; c) refinement of the Galactic rotation parameters and perturbation velocities caused by the influence of the Galactic spiral density wave using OB stars; d) spatial and kinematic relationship of OB stars with galactic warp; e) analysis of the motion of some runaway OB stars.

Analysis of the Distance Scales by Cepheids from the Gaia EDR3 Catalogue Data

We study the kinematics of a sample of classical Cepheids younger than 120 Myr. For these stars, the estimates of distances taken from Skowron et al., which are based on the period–luminosity relation, and the line-of-sight velocities and the proper motions from the Gaia catalog are available. There are also distance estimates derived from the trigonometric parallaxes contained in the Gaia ERD3 catalog. A method, which relies on comparison of the first-order derivative of the Galactic rotation angular velocity, showed the need to lengthen the distance scales determined by Skowron et al. by about 10%. This conclusion was confirmed by direct comparison to the distances predicted on using the trigonometric parallaxes. With taking into account this result, we obtained new estimates of the Galactic rotation parameters and the parameters of a spiral density wave.

Parameters of the Galactic Spiral Density Wave from Masers with Parallax Errors Less Than 10$$\boldsymbol{\%}$$

We have studied the kinematics of Galactic masers and radio stars with measured VLBI trigonometric parallaxes and proper motions. We have considered masers with relative trigonometric parallax errors less than 10\% and determined the Galactic rotation parameters from them. In particular, the linear rotation velocity of the Galaxy at the solar distance $R_0$ has been found to be $244.4\pm4.3$ km s$^{-1}$ (for the adopted $R_0=8.1\pm0.1$ kpc). We have performed a joint and separate spectral analysis of the radial, residual tangential, and vertical maser velocities. For example, from the vertical maser velocities we have estimated the velocity perturbation amplitude $f_W=5.2\pm1.5$ km s$^{-1}$ with the wavelength $\lambda_W=2.6\pm0.7$ kpc, arguing for the influence of the spiral density wave on the vertical stellar velocities. Based on 104 masers within 3 kpc of the Sun, as a result of the joint solution, we have estimated the radial, $f_R=6.7\pm1.1$ km s$^{-1}$, and tangential, $f_\theta=2.6\pm1.2$ km s$^{-1}$, velocity perturbations, the perturbation wavelength $\lambda=2.1\pm0.3$ kpc, and the Sun's phase in the Galactic spiral density wave $\chi_\odot=-148\pm15^\circ$. We have confirmed the presence of the Radcliffe wave in the spatial distribution of masers and radio stars belonging to the Local Arm.

Kinematics of the Galaxy from Young Open Star Clusters with Data from the Gaia EDR3 Catalogue

We have analyzed the kinematics of open star clusters (OSCs) with the proper motions and distances calculated by Hao et al. based on Gaia EDR3 data. The mean line-of-sight velocities are known for a number of clusters from this list. We show that the Galactic rotation parameters determined from samples of OSCs with various ages are in good agreement between themselves. The most interesting results have been obtained from a sample of 967 youngest OSCs with a mean age of 18 Myr. In particular, we have found the following parameters of the angular velocity of Galactic rotation using only their proper motions and distances: $\Omega_0 =28.01\pm0.15$ km s$^{-1}$ kpc$^{-1},$ $\Omega^{'}_0=-3.674\pm0.040$ km s$^{-1}$ kpc$^{-2},$ and $\Omega^{''}_0=0.565\pm0.023$ km s$^{-1}$ kpc$^{-3}$. The circular rotation velocity of the solar neighborhood around the Galactic center here is $V_0=226.9\pm3.1$ km s$^{-1}$ for the adopted Galactocentric distance of the Sun $R_0=8.1\pm0.1$ kpc. The parameters of the spiral density wave have been determined from the space velocities of 233 young clusters. The amplitudes of the radial and tangential velocity perturbations produced by the spiral density wave are $f_R=9.1\pm0.8$ km s$^{-1}$ and $f_\theta=4.6\pm1.2$ km s$^{-1}$, respectively; the perturbation wavelengths are $\lambda_R=3.3\pm0.5$ kpc and $\lambda_\theta=2.6\pm0.6$ kpc for the the adopted four-armed spiral pattern. The Sun's phase in the spiral density wave has been found to be $(\chi_\odot)_R\approx-180^\circ$.

Spiral density-wave structure parameters in the solar neighbourhood derived from longitudinal velocities of Gaia EDR3 OB stars: 3D approach

ABSTRACT Distances and transverse along the Galactic longitude velocities vl of 2640 Gaia EDR3 O–B2 stars of Xu et al. within 2.5 kpc from the Sun and 250 pc from the Galactic plane with relative distance and velocity accuracies of <10 and <50 per cent are selected. Under the assumption of spiral density waves, both Galactic differential rotation parameters and parameters of the wave structure in this solar neighbourhood are derived from observed vl. In contrast to all preceding studies, we take into account the effect of small but finite thickness of the disc of the Galaxy on even parity (‘sausage’) gravity perturbations of the kind investigated by Lin and Shu. As previously predicted by the modified theory of 3D density waves, two scales of periodic rarefaction–compression irregularity of the vl velocity field with the radial λ0 ≈ 1.5 kpc and vertical ξ0 ≈ 1.0 kpc wavelengths in the form of a spiral wave propagating in the disc are revealed. The Gaia’s DR2 line-of-sight and EDR3 longitudinal velocities analyses performed in the last papers of a series exhibit consistent findings, thus providing a further evidence to support the Lin–Shu density-wave proposal.

Galactic Rotation Parameters Based on Stars from Active Star-Forming Regions with Data from the Gaia DR2 Catalogue

We have studied a sample of more than 25 000 young stars with proper motions and trigonometric parallaxes from the Gaia DR2 catalogue. The relative errors of their parallaxes do not exceed 10\%. The selection of stars belonging to active star-forming regions was made by Marton et al. based on data from the Gaia DR2 catalogue by invoking infrared measurements from the WISE and Planck catalogues. Low-mass T Tauri stars constitute the majority of sample stars. The following parameters of the angular velocity of Galactic rotation have been found from them: $\Omega_0 =28.40\pm0.11$ km s$^{-1}$ kpc$^{-1}$, $\Omega^{'}_0=-3.933\pm0.033$ km s$^{-1}$ kpc$^{-2}$ and $\Omega^{''}_0=0.804\pm0.040$ km s$^{-1}$ kpc$^{-3}$. The Oort constants are $A=15.73\pm0.32$ km s$^{-1}$ kpc$^{-1}$ and $B=-12.67\pm0.34$ km s$^{-1}$ kpc$^{-1}$, while the circular rotation velocity of the solar neighborhood around the Galactic center is $V_0=227\pm4$ km s$^{-1}$ for the adopted Galactocentric distance of the Sun $R_0=8.0\pm0.15$ kpc.

Kinematics of Stars from the TGAS (Gaia DR1) Catalogue

Based on the stellar proper motions of the TGAS (Gaia DR1) catalogue, we have analyzed the velocity field of main-sequence stars and red giants from the TGAS catalogue with heliocentric distances up to 1.5 kpc. We have obtained four variants of kinematic parameters corresponding to different methods of calculating the distances from the parallaxes of stars measured with large relative errors. We have established that within the Ogorodnikov–Milne model changing the variant of distances affects significantly only the solar velocity components relative to the chosen centroid of stars, provided that the solution is obtained in narrow ranges of distances (0.1 kpc). The estimates of all the remaining kinematic parameters change little. This allows the Oort coefficients and related Galactic rotation parameters as well as all the remaining Ogorodnikov–Milne model parameters (except for the solar terms) to be reliably estimated irrespective of the parallax measurement accuracy. The main results obtained from main-sequence stars in the range of distances from 0.1 to 1.5 kpc are: A = 16.29 ± 0.06 km s−1 kpc−1, B = −11.90 ± 0.05 km s−1 kpc−1, C = −2.99 ± 0.06 km s−1 kpc−1, K = −4.04 ± 0.16 km s−1 kpc−1, and the Galactic rotation period P = 217.41 ± 0.60 Myr. The analogous results obtained from red giants in the range from 0.2 to 1.6 kpc are: the Oort constants A = 13.32 ± 0.09 km s−1 kpc−1, B = −12.71 ± 0.06 km s−1 kpc−1, C = −2.04 ± 0.08 km s−1 kpc−1, K = −2.72 ± 0.19 km s−1 kpc−1, and the Galactic rotation period P = 236.03 ± 0.98 Myr. The Galactic rotation velocity gradient along the radius vector (the slope of the Galactic rotation curve) is −4.32 ± 0.08 km s−1 kpc−1 for main-sequence stars and −0.61 ± 0.11 km s−1 kpc−1 for red giants. This suggests that the Galactic rotation velocity determined from main-sequence stars decreases with increasing distance from the Galactic center faster than it does for red giants.

OB Stars and Cepheids From the Gaia TGAS Catalogue: Test of their Distances and Proper Motions

Abstract We consider young distant stars from the Gaia TGAS catalog. These are 250 classical Cepheids and 244 OB stars located at distances up to 4 kpc from the Sun. These stars are used to determine the Galactic rotation parameters using both trigonometric parallaxes and proper motions of the TGAS stars. In this case the considered stars have relative parallax errors less than 200%. Following the well-known statistical approach, we assume that the kinematic parameters found from the line-of-sight velocities Vr are less dependent on errors of distances than the found from the velocity components Vl. From values of the first derivative of the Galactic rotation angular velocity ′0, found from the analysis of velocities Vr and Vl separately, the scale factor of distances is determined.We found that from the sample of Cepheids the scale of distances of the TGAS should be reduced by 3%, and from the sample of OB stars, on the contrary, the scale should be increased by 9%.

Vertical distribution and kinematics of protoplanetary nebulae in the galaxy

The catalogue of protoplanetary nebulae by Vickers et al. has been supplemented with the line-of-sight velocities and proper motions of their central stars from the literature. Based on an exponential density distribution, we have estimated the vertical scale height from objects with an age less than 3 Gyr belonging to the Galactic thin disk (luminosities higher than 5000 Lo) to be h=146+/-15 pc, while from a sample of older objects (luminosities lower than 5000 Lo) it is h=568+/-42 pc. We have produced a list of 147 nebulae in which there are only the line-of-sight velocities for 55 nebulae, only the proper motions for 25 nebulae, and both line-of-sight velocities and proper motions for 67 nebulae. Based on this kinematic sample, we have estimated the Galactic rotation parameters and the residual velocity dispersions of protoplanetary nebulae as a function of their age. We have established that there is a good correlation between the kinematic properties of nebulae and their separation in luminosity proposed by Vickers. Most of the nebulae are shown to be involved in the Galactic rotation, with the circular rotation velocity at the solar distance being V_0=227+/-23 km/s. The following principal semiaxes of the residual velocity dispersion ellipsoid have been found: (sigma1, sigma2, sigma3) = (47, 41, 29) km/s from a sample of young protoplanetary nebulae (with luminosities higher than 5000 Lo), (sigma1, sigma2, sigma3) = (50, 38, 28) km/s from a sample of older protoplanetary nebulae (with luminosities of 4000 Lo or 3500 Lo), and (sigma1, sigma_2, sigma3) = (91, 49, 36) km/s from a sample of halo nebulae (with luminosities of 1700 Lo).

Kinematics of the galaxy from OB stars with proper motions from the Gaia DR1 catalogue

We consider two previously studied samples of OB stars with different distance scales. The first one consists of 98 massive spectroscopic binary stars with photometric distances, and the second one consists on 140 OB stars with the distances determined along the lines of interstellar calcium. The OB stars are located at distances up to 7 kpc from the Sun. They are identified with the Gaia DR1 catalog. It is shown that the use of the proper motions, taken from the Gaia DR1 catalog, allows to reduce random errors of determination of the Galactic rotation parameters in comparison with the previously known ones. From the analysis of 208 OB stars from the Gaia DR1 catalog with proper motions and parallaxes with relative errors less than 200% we found the Galactic kinematic parameters. In addition the Galactic rotation parameters were obtained from only line-of-sight velocities of the same stars. From the comparison of the two values of \Omega^{'}_0 a distance scale of the Gaia DR1 catalog was determined as a value close to unit, namely 0.96. From 238 OB-stars of the united sample with photometric distances for stars of the first sample and distances in the calcium scale for stars of the second sample, line-of-sight velocities and proper motions from the Gaia DR1 catalog, were found the following kinematic parameters: (U,V,W)_\odot=(8.19,9.28,8.79)+/-(0.74,0.92,0.74) km/s, \Omega_0=31.53+/-0.54 km/s/kpc, \Omega^{'}_0=-4.44+/-0.12 km/s/kpc^2, \Omega^{"}_0=0.706+/-0.100 km/s/kpc^3, here Oort constants: A=-17.77+/-0.46 km/s/kpc, B=13.76+/-0.71 km/s/kpc and V_0=252+/-8 km/s.

FIRST PARALLAX MEASUREMENTS TOWARD A 6.7 GHz METHANOL MASER WITH THE AUSTRALIAN LONG BASELINE ARRAY—DISTANCE TO G 339.884−1.259.

We have conducted the first parallax and proper motion measurements of 6.7 GHz methanol maser emission using the Australian Long Baseline Array (LBA). The parallax of G339.884$-$1.259 measured from five epochs of observations is 0.48$\pm $0.08 mas, corresponding to a distance of $2.1^{+0.4}_{-0.3}$ kpc, placing it in the Scutum spiral arm. This is consistent (within the combined uncertainty) with the kinematic distance estimate for this source at 2.5$\pm $0.5 kpc using the latest Solar and Galactic rotation parameters. We find from the Lyman continuum photon flux that the embedded core of the young star is of spectral type B1, demonstrating that luminous 6.7 GHz methanol masers can be associated with high-mass stars towards the lower end of the mass range.

Erratum: On the implications of the Galactic aberration in proper motions for celestial reference frame

During the last years, much attention has been paid to the astrometric implications of the galactic aberration in proper motions (GA). This effect causes systematic errors in astrometric measurements at a microarcsecond level. Some authors consider it so serious that it requires redefinition of the celestial reference system (CRF). We argue that such attention to the GA is too much exaggerated. It is just a small astrometric correction that must be taken into account during highly accurate astrometric and geodetic data processing. The accuracy of this correction depends on accuracy of the Galactic rotation parameters and, for most application, on the accuracy of the rotation matrix between Galactic and equatorial systems. Our analysis has shown that our today knowledge of these two factors is sufficient to compute the GA correction with accuracy of better than 10%. The remaining effect at a level of few tenths microarcsecond/yr is negligible nowadays. Another consequence of introducing the GA correction is necessity to return to classical astrometric modeling of the VLBI-derived extragalactic radio source position by the linear trend model. Changing the current paradigm of VLBI-derived CRF based on assumption of zero motion of radio sources to classical one leads to bias in the radio source positions up to several tens microarcseconds for catalog at epoch J2000.0.

On the implications of the Galactic aberration in proper motions for the Celestial Reference Frame

During the last few years, much attention has been paid to the astrometric implications of the galactic aberration in proper motions (GA). This effect causes systematic errors in astrometric measurements at a μas level. Some authors consider it so serious that it requires redefinition of the Celestial Reference Frame (CRF). We argue that such attention to the GA is exaggerated too much. It is just a small astrometric correction that must be taken into account during highly accurate astrometric and geodetic data processing. The accuracy of this correction depends on the accuracy of the Galactic rotation parameters and, for most applications, on the accuracy of the rotation matrix between Galactic and equatorial systems. Our analysis has shown that our current knowledge of these two factors is sufficient to compute the correction of the GA with an accuracy better than 10 per cent. The remaining effect at the level of a few tenths μas yr−1 is negligible nowadays. Another consequence of introducing the GA correction is the necessity to return to classical astrometric modelling of the extragalactic radio source position – derived by very-long-baseline interferometry (VLBI) – by the linear trend model. Changing the current paradigm of the VLBI-derived CRF, based on the assumption of zero motion of radio sources, to classical one leads to bias in the radio source positions of up to several tens of μas for a catalogue at epoch J2000.0.

Determination of galactic rotation parameters and the solar galactocentric distance R 0 from 73 masers

We have determined the Galactic rotation parameters and the solar Galactocentric distance R 0 by simultaneously solving Bottlinger’s kinematic equations using data on masers with known line-of-sight velocities and highly accurate trigonometric parallaxes and proper motions measured by VLBI. Our sample includes 73 masers spanning the range of Galactocentric distances from 3 to 14 kpc. The solutions found are Ω0 = 28.86 ± 0.45 km s−1 kpc−1, Ω′0 = −3.96 ± 0.09 km s−1 kpc−2, Ω″0 = 0.790 ± 0.027 km s−1 kpc−3, and R 0 = 8.3 ± 0.2 kpc. In this case, the linear rotation velocity at the solar distance R 0 is V = 241 ± 7 km s−1. Note that we have obtained the R 0 estimate, which is of greatest interest, from masers for the first time; it is in good agreement with the most recent estimates and even surpasses them in accuracy.

Galactic parameters from masers with trigonometric parallaxes

Spatial velocities of all currently known 28 masers having trigonometric parallaxes, proper motion and line-of-site velocities are reanalyzed using Bottlinger's equations. These masers are associated with 25 active star-forming regions and are located in the range of galactocentric distances 3<R<14 kpc. To determine the Galactic rotation parameters, we used the first three Taylor expansion terms of angular rotation velocity {\Omega} at the galactocentric distance of the Sun R0=8 kpc. We obtained the following solutions: {\Omega}o=-31.0 +/- 1.2 km/s/kpc, {\Omega}o'=4.46 +/- 0.21 km/s/kpc^2, {\Omega}o"=-0.876 +/- 0.067 km/s/kpc^3, Oort constants: A=17.8 +/- 0.8 km/s/kpc, B=-13.2 +/- 1.5 km/s/kpc and circular velocity of the Solar neighborhood rotation Vo=248 +/- 14 km/s. Fourier analysis of galactocentric radial velocities of masers VR allowed us to estimate the wavelength {\lambda}=2.0 +/- 0.2 kpc and peak velocity f_R=6.5 +/- 2 km/s of periodic perturbations from the density wave and velocity of the perturbations 4 +/- 1 km/s near the location of the Sun. Phase of the Sun in the density wave is estimated as {\chi}o ~ -130^o +/- 10^o. Taking into account perturbations evoked by spiral density wave we obtained the following non-perturbed components of the peculiar Solar velocity with respect to the local standard of rest (LSR) (Uo,Vo,Wo)LSR=(5.5,11,8.5) +/- (2.2,1.7,1.2) km/s.

Peculiarities of galactic rotation in the solar neighborhood from the data on red clump giants

The three-dimensional Ogorodnikov-Milne model was used to investigate the local velocity field on the basis of the tangential velocities of more than 53 000 red giants which were identified as most probable Red Clump members from the Tycho-2 catalog. Galactic rotation parameters were determined for two star groups at the galactic latitudes |b| < 30° and |b| ≥ 30°. The galactic rotation of the first star group was found to have some peculiarities characterized by the statistically significant parameters of contraction (K = −6.3 ± 1.1 km s−1 kpc−1) and phase shift (ϕ = 6.9° ± 0.6°) in the Ogorodnikov-Miln model. The vertex deflection and the semiaxes of peculiar velocity ellipsoid were determined for both star groups together with the components of the Sun’s motion with respect to these groups. The greatest distinction between two groups manifests itself in the vertex deflection, which is equal to 5.9° ± 0.7° at |b| < 30° and 0.1° ± 0.6° at |b| ≥ 30°.

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

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.

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

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.