1. V.S. Akhmetov, P.N. Fedorov, A.B. Velichko Institute of Astronomy, V.N.Karazin Kharkiv National University, Kharkiv, Ukraine
The PMA catalog. Astrometric and multiband photometric data for more than 400 millions objects.
International meeting on variable stars research
KOLOS 2016
December 1-3, 2016
Vihorlat Observatory Humenne, Slovakia

2. INTRODUCTION
1. We combined the data from the Gaia DR1 and Two-Micron All Sky Survey (2MASS) catalogues in order to derive the absolute proper motions more than 400 million stars distributed all over the sky in the stellar magnitude range 10<G<20 (Gaia magnitude) that been named PMA.
2. For provide quick access to modern astronomical catalogs that contains data for celestial objects including stars, galaxies, quasars and others objects has been developed database.
3. We present some problems of creation new high-density astrometric catalog of more then one billion positions and absolute proper motions objects obtained from the SuperCOSMOS Science Archive, the XPMA catalogue. It contains positions and absolute proper motions with the magnitudes up to B < 23 mag.
4. . We present some methods for astrometric and kinematics research of large catalogs.

3. GAIA - Global Astrometric Interferometer for Astrophysics
Copyright: ESA

4. 2MASS(PSC) Two Micron All Sky Survey (Point Source Catalog)
2MASS used two highly-automated 1.3-m telescopes, one at Mt. Hopkins, AZ, and one at CTIO, Chile. Each telescope is equipped with a three-channel camera, each channel consisting of a 256W256 array of HgCdTe detectors, capable of observing the sky simultaneously at J (1.25 µm), H (1.65 µm), and Ks (2.17 µm). The northern 2MASS facility began routine operations in 1997 June, and the southern facility in 1998 March. Survey operations were complete for both hemispheres on 2001 February 15. The final release contains position and 3 band near-infrared photometry of 470,992,970 objects. Copyright:

5. Preliminary pixelization of data using HEALPix library (Gorsky et al

6. Preliminary pixelization of data using RADEC_PIX library (Akhmetov)
sd= side of declination
sr = side of right ascension
nd =180.0/sd ; //count of declination zone
nr = 360.0/(sr/cos((-90.0+sd/2.0+j*sd)*M_PI/180.0))); //count of pixels in j zone
For pixel = 6ox6o sd=6o, sr=6o Count pixels = 1132 (0 1 2 …..1131)

7. Preliminary pixelization of data using RADEC_PIX library (Akhmetov)
For pixel = 10ox10o
count 404 o

8. Pixelization of data using RADEC_PIX library (Akhmetov) on the left and HEALPix library (Gorsky et al., 2005) on the right o
Because of a very large difference of stellar density at the different galactic latitudes, we used a two-step cross-identification procedure with a circular window of adjustable size. At the first stage, a circular window of 0.5 arcsec in radius was used in each field.
After that, the procedure of error correction was applied.
To eliminate some and irregular distortions of a discontinuous type, we applied the two-dimensional median filter.

9. The coordinate differences of right ascension for GAIA minus PSC has been divided on difference of epoch observations (15 years) as a function of coordinate. Top before and down after corrections.

10. The coordinate differences of declination for GAIA minus PSC has been divided on difference of epoch observations (15 years) as a function of coordinate. Top before and down after corrections.

11. Median correction for RA (left) and for DEC (right) as function from RA and DEC

12. Cross-identification of objects
After the procedure of position correction in PSC data, we used next step cross-identification. We used various windows with sizes varying from 0.1 to 13 arcsec with a step o 0.1 arcsec, and counted the increment of a number of stars dN (circular dots), which fell into the annular zones with radii R and R + dR. This increment shown in Fig. as a function of the ring radius can be represented by a sum of two functions. One of them is the density distribution function of angular distances for the nearest neighbours in each field for the random (Poisson) distribution of star positions. The second one is the function of a uniform density distribution of stars over the via radius where the probability of misidentification reaches the probability of omitting a star with a considerable proper motion. The value of the computed window radius varies from 1.6 to 6 arcsec, depending on a particular field. It should be noted that such cross-identification is usually named positional association and is not necessarily an exact identification.

13. Stars-galaxy classification

14. PMA catalog – Proper Motion Absolute
2MASS
470 millions
j, h, k photometry
position on~2000
GAIA
1 142 millions
G-photometry
position on 2015
Cross-matching
Catalogues
GSC2.3
910 millions
B,R,V,I photometry
WISE
570 millions
w1,w2,w3,w4 photometry
PMA
Absolute Proper Motions
410 million of objects
multiband photometric data

15. Comparison of PMА stars proper motion with UCAC4 catalog data
PMA MuRA
UCAC4 MuRA
RA, degree
Catalog UCAC4 is a compiled, all-sky star catalog covering mainly the 8 to 16 magnitude range in a single band- pass between V and R. Positional errors are about 15 to 20 mas for stars in the 10 to 14 mag range. Proper motions have been derived for most of the about 113 million stars. (Zacharias N. et al., 2013)

16. The PMA catalogue as a realization of the extragalactic reference system in optical and near infrared wavelengths.
1. The PMA system of absolute proper motions was obtained by direct linking to the extragalactic reference frame that is specified using approximately 4 million galaxies distributed over the sky excluding a small region near the Galactic Centre. 2. The PMA reference frame is non-rotating with respect to extragalactic objects within 0.3 mas/yr. 3. The proper motions errors are about mas/yr for G magnitude range and about mas/yr for fainter stars.

17. SuperCOSMOS Science Archive (SSA)
surveyID
surveyName
numObject
meanEpoch
fieldOfView
decMin
decMax
numFields
magLimit
109
year
degree
mag 1
SERC-J
1.1 6
-90 3
894 23 2
SERC-R
1.00 22
SERC-I
0.82 19 4
ESO-R     5
-17.25
606
POSSI-E(N)     90
644
POSSII-B
0.60
824
22.5 7
POSSII-R
0.66
20.8 8
POSSII-I
0.54
19.5 9
POSSI-E(S)    
-18
245

18. Deriving the objects position for SERC and POSS survey.
1. Removing the junk detections;
2. Astrometric reduction of the measured x and y positions on plates to tangential coordinates (ξ, η) and transformation to the spherical coordinates of objects in each field to the epoch of its observation.
3. Removing the position-dependent and magnitude- dependent systematic errors.
4. Stars-galaxy classification. Using galaxies for absolute calibration of the proper motion XPMA stars.
XPMA – eXtended Proper Motion Absolute catalog

19. Removing the junk detections
Removing the junk detections. Each set of plate detections has been run through an automated junk detection algorithm to remove any objects that are a result of curvi-linear lines, circular or halo-type artifacts on the source photographic material.

20. The result automated junk detection algorithm.

21. PlateID=66121 (SERC-J) with globular cluster М80 (RA= 16h17m2
PlateID=66121 (SERC-J) with globular cluster М80 (RA= 16h17m2.4s DEC= ’ 33.9”)

22. 2. Astrometric reduction of the measured x and y positions on plates to tangential coordinates (ξ, η).
Since the astrometric reduction of observations taken at the
Schmidt telescopes with the use of only the classic method
is often inefficient, we had to apply a two-step procedure.
The first step we applied the reduction model using the fifth- order polinomial model reduction as function from magnitude.
At the second step, to eliminate some residual and irregular distortions of a discontinuous type, we applied the two- dimensional median filter.
The stars from PMA(400 million) catalogue were used as the reference ones.

23. Mean vector residual map using a third-order polynomial plate model (left) and a fifth-order one (right)

24. Removing the position- and magnitude-dependent systematic errors
- VectorPM =

25. η = b1+b2x+b3y+b4xy+b5y2+b6x2y+b7y3+b8x4y+b9x2y3
All reference stars have been binned in magnitude range with step one magnitude for obtaining parameters polynomial model reduction for each bins.
ξ = a1+a2x+a3y+a4x2+a5xy+a6x3+a7xy2+a8x3y2+a9xy4
η = b1+b2x+b3y+b4xy+b5y2+b6x2y+b7y3+b8x4y+b9x2y3

26. Mean vector residual between solution for the least squares method using the double (C++) and the GMP library in numerical computations.
DOUBLE has 16 decimal digits precision.(52 bit)
X range ±1.6*105
Y range ± 1.6*105
(105 )1 ……..(105 )5
(105 )1 ((105 )1)2 …..(105 )5+1
…………………………….
(105 )5 ((105 )5+1 ….((105 )5)2
Solving the system of conditional equations with the use numerical computations with arbitrary precision for the least squares method provides the most probable unbiased values of unknown quantities

27. Schema for obtain the stars proper motion of XPMA catalogue
POSS2-B,R,I
SERC–R,I
position on 1995, 1990
POSS1-R
SERC–J(B)
position on 1953, 1980
Cross-matching
Catalogues
2MASS(j,h,k)
position on 2000
WISE(w1,w2,w3,w4)
position on 2010
GAIA (Gmag)
position on 2015
XPMA Proper Motion
1 billion of objects

28. Astrometric and kinematics research of large catalogs
For provide quick access to modern astronomical catalogs that contains data for celestial objects including stars, galaxies, quasars and others objects has been developed database MSSQL (Windows) and PostgreSQL (Linux).
The software for astrometric catalogs analysis by means of the Roland Wielens method has been created.
The kinematics studies of the Galaxy using classical Ogorodnikov-Milne model presented in OGMUI software.
The software for cross-matching large catalogues and statistic analysis has been created.

30. http://astrodata. univer. kharkov
Astronomical Catalogs Database

31. R. Wielen. A method for determining the individual accuracy of astrometric catalogues. (Astronomy and Astrophysics, 302, (1995).
The method described by Roland Wielen is very efficient provided the data under
comparison are independent quantities. In this case, dispersion of positions or proper motion
differences is equal to the sum of their dispersions, because the index of correlation
between the data sets is zero. With three or more independent catalogues, it is easy to estimate
the external accuracy of each of them:
where D12, D13 and D23 are dispersions of the differences of positions or proper motions for
two catalogues under consideration. Before proceeding to the calculation of the dispersions,
we need to ascertain that the correct values will be obtained. The assumption that the initial
random quantities are centered, i.e. the mean value of each of them is zero, may be a possible
source of incorrectness. In general, the mean value is non-zero because of systematic errors
in the catalogues. If this non-zero mean is constant or varies with magnitude smoothly, then
the dispersion of the differences can be calculated. In the case, when the systematic differences
vary fast or have breaks, the method does not work. Therefore, it is important to determine
behaviors of the systematic differences. Fortunately, the systematic differences of proper motions
are smooth functions of magnitude.

32. The software for astrometric catalogs analysis by means the Roland Wielens method.

33. The systematic differences and standard deviations of the star magnitude obtained by the method of Wielen for FON3, XPM, UCAC4 and PPMXL depending on the magnitude B of FON3.

34. Ogorodnikov-Milne equations
where X0, Y0, Z0 – component velocity vector of solar motion
M32-, M13-, M21-, – component vector of solid body rotation of circum-solar stars in the neighbourhood of the Sun.
M12+, M13+, M23+ – component deformation tensor of the velocities field of this system.
1/r = 1. In this case all parameter obtained to sphere with 1 kpc radius.

35. OGorodnikov-Milne User Interface the software for kinematics research.

36. Using the Ogorodnikov-Milne model and statistical parallaxes, it is possible to find the linear velocity of the solar motion as dependence from distance.

37. Statistic analysis TGAS-TYC2

38. CONCLUSIONS
The PMA catalogue contains positions and absolute proper motions with the magnitudes up to B < 20 mag of about 410 million objects.
The stellar proper motion errors are typically in the mas/yr range.
Removed the systematic zonal errors in position of 2MASS catalogue objects by means of a 2-dimensional median filter.
The PMA system of absolute proper motions was obtained by direct linking to the extragalactic reference frame that is specified using approximately 4 million galaxies distributed over the sky excluding a small region near the Galactic Centre.
The PMA data are supplemented by WISE and GSC2.3 photometry almost for all objects.
Next step
Combine all POSS and SERC survey, 2MASS, WISE and GAIA data for creating more then one billion absolute proper motion of stars.
Classification objects using photometric diagrams and stars proper motion.
Astrometric and kinematics research of one billion absolute proper motion of stars XPMA catalog. Comparison with GAIA data

39. Thank you for attention! akhmetovvs@gmail.com