Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.gao.spb.ru/english/as/j2014/presentations/tsvetkov.pdf Дата изменения: Sun Sep 28 20:11:01 2014 Дата индексирования: Sun Apr 10 05:53:49 2016 Кодировка: Поисковые слова: antarctica

A.S.Tsvetkov and V.V.Vityazev SPb University, Russia

COMPARISON OF ASTROMETRIC CATALOGUES UCAC4, XPM, PPMXL


MOTIVATION
The pre-GAIA modern astrometric catalogues UCAC4, PPMXL and XPM with full coverage of the sky provide a qualitatively new material for investigations in various fields of astronomy. According to inner logics of astrometry, the catalogues containing common stars should be compared. Aiming at the application to the stellar kinematics, we declare the first results of the comparison concerning the systematic differences of proper motions in the Galactic coordinate system


PPMXL
· · · · · At present, the largest catalogue of positions and proper motions is PPMXL It contains about 900 million objects and is probably full from the brightest stars down to about magnitude V=20 full-sky. In this work the stars down to J=17 are used only. The proper motions are in the ICRS reference frame. The mean errors of the proper motions range from 4 mas/y to more than 10 mas/y.
160 000 000 140 000 000 120 000 000 100 000 000 80 000 000 60 000 000 40 000 000 20 000 000 0

0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

J


· The UCAC4 is an all-sky catalogue containing about 113 million stars covering mainly the 8 to 16 magnitude range in a single bandpass between V and R. · The formal errors in PMs range from about 1 to 10 mas/y depending on magnitude and observing history. · Systematic errors in PMs are estimated to be about 1-4 mas/y. · The UCAC4 may be considered complete to about R=16. · It contains accurate positions and proper motions on the ICRS at a mean epoch around 2000
J

UCAC4

40 000 000 35 000 000 30 000 000 25 000 000 20 000 000 15 000 000 10 000 000 5 000 000 0

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

J


XPM
·
· ·

The XPM catalogue (2009) lists about 280 million stars distributed all over the sky in the magnitude range 12 100 000 000

80 000 000

60 000 000

40 000 000

20 000 000

0

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17

J


Distribution of common stars
160 000 000 140 000 000 120 000 000 100 000 000 80 000 000 60 000 000 40 000 000 20 000 000 0

PPMXL UCAC4 XPM

6

7

8

9

10

11

12

13 14

15

16

J


Systematic differences as Vector Field on a sphere
U(l , b) l cos b el beb
be
b

l cos b e

l


Representation of systematic differences by VSH
l cos b el beb


nkl

tnkl Tnkl


nkl

snkl S

nkl

Toroidal (Magnetic) Functions

Tnkl (l , b)

1 1 K nkl (l , b) K nkl (l , b) el eb b cos l n(n 1)

Spheroidal (Electric) Functions

S nkl (l , b)

1 n(n 1)

K (l , b) 1 K nkl (l , b) el nkl eb l b cos b


Differences of the mean PMs
To avoid a lot of problems with cross identification of stars we worked not with the PM differences of individual stars but with the differences of the mean PMs in the HEALPix areas. The number of pixels was taken to be 4800 with the area of each pixel 8.6 square degrees. After averaging the PMs of stars inside each pixel the differences UCAC4-PPMXL, XPM-UCAC4 and XPM-PPMXL were formed and referred to the centers of the pixels. These data was collected for the stars in the J magnitude bins 10-12, 12-14 and 14-16. Since the numbers of stars from different catalogues in the same pixel does not differ more than several per cents, we believe that our approach does not differs significantly from the case if the individual differences were used.

We calculated the expansion coefficients for the PM differences up to n=4


The coefficients for representation of the systematic differences in PM on VSH. Galactic coordinate system (mas/yr)
Triple index J=10-12
UCAC4-PPMXL
m

J=12-14
UCAC4-PPMXL

m

J=14-16
UCAC4-PPMXL

m

TS

Par 3 2 1

N 1 1 1 2 2 2 2 2 1 1 1 2 2 2 2 2

K 0 1 1 0 1 1 2 2 0 1 1 0 1 1 2 2

L 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1

XPM-PPMXL

XPM-PPMXL

XPM-PPMXL

T

1,25 0,35 -0,07 0,32 1,27 -1,16
-1,65 -0,37 1,87 4,50 1,60 -0,15 1,05 0,92 -0,53 -0,44 0,07

1,42 4,28 -2,60 0,19 2,43 -2,87
-2,18 -1,50 3,09 5,91 2,64 -0,94 2,65 0,83 -2,10 -1,35 0,13

1,04 1,38 -0,71 -0,08 2,57 -2,03
-2,34 -0,94 2,62 6,56 1,85 -0,37 1,77 1,09 -1,09 -1,35 0,08

-0,40 -0,53 -0,15 1,16 0,23 -0,55
-0,03 0,76 1,67 1,25 0,29 -1,82 -0,31 -0,03 -0,97 -0,44 0,09

-0,14 0,30 0,41 -0,01 2,70 -1,12
-2,09 -0,88 3,95 8,36 0,88 -0,63 1,66 0,32 -1,69 -1,76 0,09

-1,01 0,93 0,51 -0,14 1,93 -1,15
-2,28 -1,13 2,80 4,87 -0,31 -0,96 2,20 -0,06 -1,73 -1,70 0,09

S

W V U M11,33 M23 M13 M12 M11




Expansion coefficients
10

UCAC4-PPMXL (mas/yr)

8

6

4

10-12 12-14 14-16

2

8

7

6

5

4

3

2

0 1 -2

1

2

3

4

5

6

7

8

Toroidal
-4

Spheroidal


Expansion coefficients XPM-PPMXL (mas/yr)

7 6 5 4 3 2 1 0 8 -1 -2 -3 -4 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 10- 12 12- 14 14- 16

Toroidal

Spheroidal


Extreme values are [-20; +20] mas/y
Ranges of Systematic Differences via Magnitude
20

XPMPPMXL

Max MuL 18,3 9,2 8,4

Max MuB 13,6 10,1 9,8

Min MuL -15,9 -14,6 -11,9

Min MuB -13,6 -11,2 -17,1
mas/yr

10 0 10-12 -10 -20 12-14 14-16
Max MuL Max MuB Min MuL Min MuB

10-12 12-14 14-16

J

20,0

XPMUCAC4

Max MuL 18,9 7,6 5,7

Max MuB 15.5 8,5 8,0

Min MuL -17,3 -9,3 -7,5

Min MuB
mas/yr

10,0 0,0 10-12 -10,0 -20,0 12-14 14-16
Max MuL Max MuB Min MuL Min MuB

10-12 12-14 14-16

-11,3 -8,2 -5,7

J

UCAC4PPMXL

Max MuL 9,8 10,9 10,5

Max MuB 9,1 12,8 10,7

Min MuL -7,6 -9,6 -12,9

Min MuB -7,1
mas/yr

20,0 10,0 0,0 10-12 -10,0 -20,0 12-14 14-16
Max MuL Max MuB Min MuL Min MuB

10-12 12-14 14-16

-11,3 -16,0

J


Total power of the field via magnitude

P
200


nkp

2 2 (tnkp snkp )

150 UCAC4-PPMXL XPM-PPMXL XPM-UCAC4

100

50

0 10-12 12-14 14-16

J


How close the XPM is to PPMXL and UCAC4
The PPMXL and UCAC4 realize the reference frames which does not rotate with respect to the quasars, whereas the XPM frame is claimed not to be rotating with respect to galaxies. Theoretically both quasars and galaxies form quasi-inertial reference systems but due to different techniques of measurement the corresponding reference frames may differ systematically. The main goal of this paper is to calculate the systematic differences in proper motions and to see is there significant differences between the XPM galaxies frame and the PPMXL and UCAC4 quasars frames.


MUTUAL SPIN of frames (mas/y)


2 1 2 2

2 3

UCAC4-PPMXL SMALL

10-12 12-14 14-16 0.45 ± 0.21 0.65 ± 0.24 0.18 ± 0.26
SMALL LARGE SMALL SMALL

XPM-PPMXL XPM-UCAC4

1.80 ± 0.38 1.22 ± 0.27 0.51 ± 0.26
LARGE SMALL

1.62 ± 0.36 0.65 ± 0.22 0.37 ± 0.18
LARGE SMALL SMALL


MAGNITUDE EQUATION
UCAC4-PPMXL PM in longitude PM in latitude

Power 40,7

Magn. 10-12

Power 88.3

Magn. 12-14

Power 115.7

Magn. 14-16


MAGNITUDE EQUATION XPM-PPMXL
PM in longitude PM in latitude

Power 155,0

Magn. 10-12

Power 82,8

Magn. 12-14

Power 68,7

Magn. 14-16


MAGNITUDE EQUATION XPM-UCAC4
PM in longitude PM in latitude

Power 71,7

Magn. 10-12

Power 21,0

Magn. 12-14

Power 22,6

Magn. 14-16


Dependence of VSH coefficients on magnitude
2 ,5

mas/yr

1 ,5

UCAC4-PPMXL t101 B



0 ,5

-0,5

10-12

12-14

UCAC-PPMXL s220 A
-1,5

XPM-PPMXL t101 B

14-16

J



XPM-PPMXL s220 A
-2,5


Stellar kinematics
Since the connection of low order VSH coefficients of the decomposition with the Ogorodnikov-Milne coefficients the VSH coefficients of the systematic differences in PM direct reducing a kinematical parameter from the system to the system of another catalogue. For example, the UCAC4-PPMXL coefficients PMs is known may be used for of one catalogue

t101 1.25 0.07

s220 0.53 0.07 mas / y

yield the differences of the Oort constants

B 2.06 0.12

A 1.12 0.16 km / s / kpc

what is confirmed by direct evaluation of these parameters from proper motions of both the catalogues.


CONCLUSION
· The representation of the differences UCAC4-PPMXL, XPM-UCAC4 and XPM-PPMXL by vector spherical harmonics is made in the 10 to 16 J mag. range. The PM systematic differences turned out to be in the -20 to +20 mas/y range which surpass the announced values of the random errors The proper motion XPM catalogue has the least systematic deviation from the ICRS proper motion catalogue UCAC4 in the 12-16 J mag range. In other words the XPM and UCAC4 are more consistent than each of the two with the PPMXL. With 3 sigma confidence large spin of XPM with respect to PPMXL and UCAC4 was found in the 10-14 J mag range The values of spin for UCAC4 on PPMXL are small Magnitude Equation is manifested by the dependence of the maps and the VSH coefficients on J magnitude The influence of low order VSH coefficients on the determination of the Ogorodnikov-Milne coefficients is clarified.

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THANK YOU!