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ON THE GALACTIC ABERRATION CONSTANT
Z. MALKIN1,2 Pulkovo Observatory, St. Petersburg, Russia 2 St. Petersburg State University, St. Petersburg, Russia e-mail: malkin@gao.spb.ru
1

ABSTRACT. In this work, we analyzed all available determinations of the Galactic rotation parameters
R0 and 0 made during last 10 years to 2 A = R0 0 /c. We used several statisti realistic errors. In result, we obtained the GA constant. We suggest that the during coming years. derive the most probable value of the Galactic aberration constant cal methods to obtain reliable estimates of R0 and 0 and their the value of A = 5.0 ± 0.3 µas/yr as the current best estimate of proposed value of the GA constant can be safely used in practice

1. INTRODUCTION
Galactic aberration (GA) is a small effect in proper motion of about 5 µas/yr already noticeable in VLBI and other highly-accurate astrometric observations. However accounting for this effect during data processing faces difficulty caused by the uncertainty in the GA constant A = R0 2 /c, where R0 is the 0 Galactocentric distance of the Sun, 0 is the angular velocity of circular rotation of the Sun around the Galactic center, c is speed of light. The value of the GA constant can be derived either using the stellar astronomy methods or VLBI observations of the extragalactic radio sources. It seems that the former provide more accurate results, while the latter are still somewhat contradictory. So, we use the results of the observations of Galactic ob jects to improve A. Our previous estimate of the GA constant (Malkin 2011) yields the values of R0 = 8.2 kpc, 0 = 29.5 km s-1 kpc-1 , and A = 5.02 µas/yr. This work is performed to check and improve if necessary this estimate taking into account more recent measurements of the Galactic rotation parameters.

2. DERIVING THE BEST VALUE OF THE GA CONSTANT
In this work, we have used 35 R0 measurements and 30 0 measurements made during last 10 years. They are listed in Table 1. We consider the results obtained during last 5 years as the most reliable, especially for R0 estimates, for which the direct methods, such as measurements of the parallax or stellar orbits around the massive black hole, become routine starting from 2008. So, the results published in 2008­2013 were used to derive the final estimate of the GA constant. The results of 2003­2007 were processed for control of its stability. We have applied several statistical techniques mostly used in physics and metrology to these data, as described in Malkin (2012, 2013). Results of computation are presented in Table 2. The first line corresponds to the best current estimates of the GA constant, in our opinion. The second result obtained by using only direct R0 measurements is practically the same. It shows that the results of the direct determinations of R0 does not substantially differ (in average) from other estimates. The results obtained with all measurements of the Galactic rotation parameters made during last 10 years are given in the third line. We think it is less reliable than the first two ones. However, it allows one to get an impression about the stability of the GA constant in time. For comparison, the standard weighted mean estimate yields for the main variant corresponding to the first line of Table 2 (data interval of 2008­2013, all R0 measurements) R0 = 8.03 ± 0.06 kpc, 0 = 29.23 ± 0.19 km s-1 kpc-1 , A = 4.83 ± 0.07 µas/yr. Precision of these estimates seems to be too optimistic. Using combined estimate of different statistical techniques as suggested by Malkin (2012) provides more reliable A estimate with a realistic uncertainty. Further analysis has shown that error in 0 prevails in the A error. Besides, published 0 results are not statistically consistent, unlike R0 measurements. So, more attention is needed to compute the best estimate of 0 .

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R0 8.3 7.7 8.01 8.7 7.2 7.52 8.1 7.4 7.94 8.16 8.07 8.33 8.7 7.58 8.4 * 7.75 8.24 7.9 * 7.7 8.1 8.3 * 7.80 8.29 7.9 8.03 8.54 7.7 * 8.27 8.05 7.51 8.24 8.38 8.08 8.2 7.4

* * *

*

* *

0.3 0.15 0.44 0.6 0.3 0.36 0.7 0.3 0.45 0.5 0.35 0.35 0.5 0.40 0.6 0.5 0.43 0.75 0.4 0.6 1.1 0.26 0.16 0.36 0.70 0.42 0.4 0.29 0.45 0.23 0.43 0.18 0.44 0.35 0.21

Re f e r e n c e Gerasimenko, 2004 Babusiaux & Gilmore, 2005 Avedisova, 2005 Groenewegen & Blommaert, 2005 Bica, et al., 2006 Nishiyama, et al. 2006 Shen & Zhu, 2007 Bobylev, et al., 2007 Groenewegen, et al., 2008 Ghez, et al., 2008 Trippe, et al. 2008 Gillessen, et al., 2009 Vanhollebeke, et al., 2009 Dambis, 2009 Reid, et al., 2009 Ma jaess, et al., 2009 Matsunaga, et al., 2009 Reid, et al., 2009 Dambis, 2010 Ma jaess, 2010 Sato, et al., 2010 Ando, et al., 2011 McMillan, 2011 Matsunaga, et al., 2011 Liu & Zhu, 2011 Pietrukowicz, et al., 2012 Morris, et al., 2012 Schoenrich, 2012 Honma, et al., 2012 Bobylev, 2013 Matsunaga, et al., 2013 Reid, 2013 Zhu & Shen, 2013 Nataf, et al., 2013 Francis & Anderson, 2013
-1

0 27.6 32.8 25.3 28.0 29.45 29.96 26.0 30.7 27.67 28.06 30.2 30.3 29.8 31 27.27 30.65 31.0 27.3 28.7 30.4 31.5 29.27 28.8 27.5 28.78 31.09 31.63 28 29.0 32.38

1.7 1.2 2.6 0.6 0.15 1.29 0.3 1.0 0.61 1.04 1.0 0.9 1.0 1 1.04 0.85 1.2 0.8 1.3 1.5 0.9 1.04 0.8 0.5 1.04 0.78 3.31 2 1.0 1.04

Re f e r e n c e Bedin, et al., 2003 Olling & Denhen, 2003 Kalirai, et al., 2004 Bobylev, 2004 Reid & Brunthaler, 2004 Zhu, 2006 Bobylev et al., 2007 Lepine, et al., 2008 Bobylev, et al., 2008 Ghez, et al., 2008 Dambis, 2009 Reid, et al., 2009a Bovy, et al., 2009 Melnik & Dambis, 2009 Dambis, 2010 Macmillan & Binney, 2010 Bobylev & Ba jkova, 2010 Ando, et al., 2011 Nagayama, et al., 2011 Stepanishchev & Bobylev, 2011 Bobylev & Ba jkova, 2011 Liu & Zhu, 2011 Ba jkova & Bobylev, 2012 Bobylev & Ba jkova, 2012 Schoenrich, 2012 Honma, et al., 2012 Bobylev, 2013 Nagayama, et al., 2013 Reid, 2013 Bobylev & Ba jkova, 2013

Table 1: R0 [kpc] and 0 [km s

kp c

-1

] estimates. Direct R0 measurements are marked with asterisk.

Interval 2008­2013 2008­2013 2003­2013

R0 data all d i r ect all

R0 8.06 ± 0.12 8.14 ± 0.15 8.00 ± 0.14

0 29.59 ± 0.75 29.59 ± 0.75 29.28 ± 0.66
-1

A 4.96 ± 0.26 5.01 ± 0.27 4.83 ± 0.24
-1

Table 2: Results of computation of R0 [kpc], 0 [km s

kp c

], and A [µas/yr.].

3. CONCLUSION
We derived the current best estimate of the GA constant using all available measurements of the Galactic rotation parameters made during last 5 years, which yields the result A = 4.96 ± 0.26 µas/yr. For practical applications we suggest to use the value A = 5 µas/yr. Using this value of the GA constant allows one to eliminate about 90% of the GA effect. Remaining uncertainty in proper motion of about 0.5 µas/yr is negligible nowadays. Thus the proposed value of the GA constant can be safely used in practice during coming years, presumably for at least the nearest decade, until new VLBI and space observations provide substantially better result. Acknow ledgements. The author is grateful to the organizers of the conference for the travel support.

4. REFERENCES
Malkin, Z.M., 2011, Astron. Rep. 55, pp. 810­815. Malkin, Z., 2012, arXiv:1202.6128. Malkin, Z.M., 2013, Astron. Rep. 57, pp. 882­887. 45