Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.gao.spb.ru/english/as/j2014/presentations/vityazev.pdf Äàòà èçìåíåíèÿ: Sun Oct 19 21:15:31 2014 Äàòà èíäåêñèðîâàíèÿ: Sun Apr 10 05:53:52 2016 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: galactic plane

KINEMATICS DERIVED FROM NORTHERN AND SOUTHERN HEMISPHERES OF HUGE ASTROMETRIC CATALOGUES
V. VITYAZEV 1 , A. TSVETKOV 2 , 1 Saint-Petersburg State University 198504 Petrodvorets, Universitetsky pr., 28., S.Petersburg, Russia vityazev@list.ru 2 Saint-Petersburg State University 198504 Petrodvorets, Universitetsky pr., 28., S.Petersburg, Russia A.S.Tsvetkov@inbox.ru

ABSTRACT.
It is shown that the kinematic analysis of the UCAC4, PPMXL and XPM proper motions in northern and southern Galactic hemispheres detects retardation of the Galaxy's rotational velocity and acceleration of the expansion velocity of the stellar system with increasing the distance from the principal Galactic plane. The estimates of the vertical gradient of the Galactic rotation are UCAC4: 40.1 ± 0.2; PPMXL: 36.2 ± 0.4; XPM: 37.7 ± 0.1 km · s-1 · kpc-1 , while the values of the vertical gradient of the expansion velocity turned out to be UCAC4: 11.9 ± 0.2; PPMXL: 19.0 ± 1.1; XPM: 10.9 ± 0.3 km · s-1 · kpc-1 .

1. INTRODUCTION
Modern astrometric catalogues realizing the ICRS in optical waves with full coverage of the sky provide a qualitatively new material, in particular, for investigating the kinematics of nearby stars in both Galalactic hemispheres separately. In case of the Ogorodnikov­Milne model [1] the stellar velocity field is given by expression V = V0 + M + r + M - r , (1) where: V0 -- the velocity of the Sun with respect to given centroid of stars; M + -- the diverging matrix + + + + + + with the dilation coefficients M1 1 , M2 2 , M3 3 , and M1 2 , M1 3 M2 3 standing for shears in the galactic - planes (x, y ), (x, z ), (y , z ); M -- the rotation matrix with the components 1 , 2 3 . about axes x, y , z . Unfortunately, due to high correlations of the parameters the standard LS solutions of the OgorodnikovMilne equations on hemispheres are hardly to be trusted. To remedy this we use an approach the first step of which is the expansion of proper motions on a system of vector spherical harmonics which are orthonormal on a hemisphere. At the second step, the kinematical parameters are derived from the coefficients of the expansion. For more detail of the method the reader is referred to [2].

2. NUMERICAL RESULTS
We applied our method to proper motions of stars listed in the catalogues UCAC4 [3], PPMXL [4] and XPM [5]. The full description of the results may be found in [2]. The present paper is devoted to the "northern" and "southern" solutions only, since all the tree catalogues gave evidence that the parameters + + 1 , M2,3 , 2 , M1,3 have different signs in different hemispheres. + V Now, in the galactocentric cylindrical coordinate system [6] we have 1 - M32 = - zS , where VS is the circular velocity of the local reference frame around the galactic center. This quantity is identified with the Galaxy's rotational velocity in the solar neighborhood. From Table 1 which gives the numerical values + for the values 1 - M32 that we obtained from different samples of our catalogues, we see that the vertical V gradient of the Galaxy's rotational velocity zS has different signs in the northern and southern galactic hemispheres, with the velocity itself decreasing with increasing distance from the principal galactic plane. Again, from the Table 1 for the the vertical gradient of the expansion velocity of the stellar system + VR 2 + M13 = - z we may conclude that the expansion velocity increases with increasing distance from V VR the principal galactic plane. The estimates of both the gradients zS and z derived from all the catalogues under consideration are in good agreement. + 1 The values 1 + M32 = - R Vz which are associated with the local Galactic warp, and the radial + gradient of the vertical velocity field 2 - M13 = Vz turned out to be unreliable. R


+ + Table 1: Values 1 - M32 and 2 + M31 obtained from northern and southern galactic hemispheres of the UCAC4, PPMXL and XPM. Units: km · s-1 · kpc-1 .

11
+ (1 - M32 )N + (1 - M32 )S + (2 + M31 )N + (2 + M31 )S VR z VS z

m

12 0, 0, 0. 0, 0, 0, 1. 2. 1. 1, 2, 1, 1. 1. 1. 1, 1, 1, 8 9 6 8 9 6 8 8 7 8 8 6 4 4 0 4 4 0 39, -42, 40, -19, 13, 16, 40 -47, 43 -17, 21, 19, 33 -62 47 -9, 19, 14, 6 1 8 7 6 7

m

42, 4 -41, 5 42.0 -15, 6 11, 3 13, 5 51.3 -45.6 48.4 -20, 8 16, 2 18, 5 34.4 -63.0 48.7 - 6, 8 19, 9 13, 3

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0 1 0 0 1 0

, , , , , ,

+ (1 - M32 )N + (1 - M32 )S + (2 + M31 )N + (2 + M31 )S VR z VS z

.2 0 .6 3 6 4 .3 .3 .8 7 6 6

1. 1, 1. 1, 1, 1, 0. 0. 0. 0, 1, 0,

+ (1 - M32 )N + (1 - M32 )S + (2 + M31 )N + (2 + M31 )S VR z VS z

13m 14m Catalogue UCAC4 7 36, 9 ± 0, 5 35, 7 ± 1 -44, 6 ± 0, 8 -43, 2 ± 7 40, 8 ± 0, 5 39, 4 ± 7 -16, 3 ± 0, 5 -10, 9 ± 1 11, 8 ± 0, 8 12, 6 ± 7 14, 0 ± 0, 5 11, 7 ± Catalogue PPMXL 6 45.1 ± 1.7 47.8 ± 7 -40, 5 ± 1.7 -35.4 ± 2 42.8 ± 1.2 41.6 ± 7 -21, 1 ± 1, 7 -18, 1 ± 7 23, 4 ± 1, 7 25, 3 ± 2 22, 2 ± 1, 2 21, 7 ± Catalogue XPM 8 34.6 ± 0.5 37.7 ± 9 -56.6 ± 0.6 -49.1 ± 6 45.6 ± 0.4 43.4 ± 8 -8, 6 ± 0, 5 -6, 0 ± 0 17, 0 ± 0, 7 14, 3 ± 6 12, 8 ± 0, 4 10, 2 ±

15m 0, 0, 0, 0, 0, 0, 1. 1. 0. 1, 1, 0, 0. 0. 0. 0, 0, 0, 4 7 4 4 7 4 0 2 8 0 2 8 4 4 3 3 4 3 35, -42, 38, - 7, 9, 8, 2 3 7 8 5 6 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 0, 0, 0, 0, 0, 0, 3 4 3 3 4 3

16m 36, -41, 39, -6, 7, 6, 0 9 0 6 3 8 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 0, 0, 0. 0, 0, 0, 0, 0, 0. 0, 0, 0, 0. 0. 0. 0, 0, 0, 3 3 2 3 3 2 6 7 5 6 7 4 2 3 2 2 3 2

47.3 -33, 2 40.3 -16, 5 18, 9 17, 7 38.1 -42.1 40.1 - 4, 7 11, 5 8, 1

0, 7 0, 8 0.5 0, 7 0, 8 0, 5 0.3 0.4 0.2 0, 3 0, 4 0, 2

43.9 -29, 4 36.7 -11, 9 17, 9 14, 9 36.4 -39.8 38.1 -3, 9 8, 6 6, 3

3. CONCLUSIONS
The success of this paper is based on the vector spherical harmonics solutions of the OgorodnikovMilne equations on hemispheres which permitted to obtain the uncorrelated values of the kinematical parameters and to show that some of them have different signs in both hemispheres. The transition to the Galactocentrical cylinder coordinate system immediately made it clear that the change of signs is connected with the retardation of the Galaxy's rotational velocity and acceleration of the expansion velocity of the stellar system with increasing the distance from the principal Galactic plane.

4. ACKNOWLEDGEMENTS
This work was done with support of the St.Petersburg University Grant 6.0.161.2010.

5. REFERENCES
1. Du Mont B., 1997, "A three-dimensional analysis of the kinematics of 512 FK4 Sup. stars", A&A, 61, N 1. pp. 127-132. 2. V.V.Vityazev, A.S.Tsvetkov, 2014, "Intercomparison of kinematics derived from catalogues UCAC4, PPMXL and XPM with vector spherical harmonics", MNRAS 442, pp. 1249­1264. 3. Zacharias et al., 2013 "The Fourth US Naval Observatory CCD Astrograph Catalog (UCAC4)". , Astron. J., 145, p.44. 4. Roeser S. and al., 2010,"The PPMXL Catalog of positions and proper motions on the ICRF. Combining USNO-B1.0 with 2MASS ", Astron. J., 139, N 6, 2440 5. P. N. Fedorov, A. A. Myznikov and V. S. Akhmetov, 2009 "The XPM Catalogue. Absolute proper motions of 280 million stars", MNRAS . 393, 133. 6. M. Miyamoto, M. Soma, 1993, "Is the vorticity vector of the Galaxy perpendicular to the Galactic plane? I. Precessional corrections and equinoctial motion correction to the FK5 system,", Astron. J., 105, 2138.