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Pulkovo Observatory and St. Petersburg State University, Russia ABSTRACT. We analyzed all available determina- tion of the Galactic rotation parameters R0 and Ω0 madeduring last 10 years to derive the most probable value ofthe Galactic aberration constant A = R0Ω20/c. We usedseveral statistical methods to obtain reliable estimatesof R0 and Ω0 and their realistic errors. Finally we haveobtained the value A = 5.0 ± 0.3 µas/yr as the currentbest estimate of the GA constant. We suggest that theproposed value of the GA constant can be safely usedin practice during coming years.
Galactic aberration (GA) is a small effect in proper motion of about 5 µas/yr already noticeable in VLBI and other highly-accurateastrometric observations. However accounting for this effect duringdata processing faces difficulty caused by the uncertainty in the GAconstant A = R0Ω20/c, where R0 is the Galactocentric distance ofthe Sun, Ω0 is the angular velocity of circular rotation of the Sunaround 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 extragalac-tic radio sources. It seems that the former provide more accurateresults, while the latter are still somewhat contradictory. So, we usethe results of the observations of Galactic objects to improve A. Ourprevious estimate of the GA constant (Malkin 2011) yields the valuesR0 = 8.2 kpc, Ω0 = 29.5 km s−1 kpc−1, A = 5.02 µas/yr. This workis performed to check and improve if necessary this estimate tak-ing into account more recent measurements of the Galactic rotationparameters.
DERIVING OF THE BEST VALUE OFTHE GA CONSTANT In this work, we have used 35 R0 measurements and 30 Ω0 mea- surements made during last 10 years. They are listed in Tables 1and 2. We consider the results obtained during last 5 years as themost reliable, especially for R0 estimates, for which the direct meth-ods, such as measurements of the parallax or stellar orbits aroundthe massive black hole, become routine starting from 2008. So, theresults published in 2008–2013 were used to derive the final estimateof the GA constant. The results of 2003–2007 were processed forcontrol 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 3. The first linecorresponds to the best current estimates of the GA constant, in ouropinion. The second result obtained using direct R0 measurementsonly is practically the same. It shows that the results of the directdeterminations of R0 does not substantially differ (in average) from other estimates. The results obtained with all the measurements ofthe Galactic rotation parameters made during last 10 years are givenin the third line. We think it is less reliable than the first two ones.
However, it allows us to get an impression about the stability of theGA constant in time.
For comparison, using the standard weighted mean estimate, we have got for the main variant for the data interval 2008–2013 andusing all R0 measurements (i.e. corresponding to the first line ofTable 3): R0 = 8.14 ± 0.08 kpc, Ω0 = 29.22 ± 0.20 km s−1 kpc−1,A = 4.89 ± 0.08 µas/yr. Precision of these estimates seems to be toooptimistic. Using combined value from different statistical techniquesas suggested by Malkin (2012) provides more reliable A estimate withrealistic uncertainty.
More detailed analysis has shown that the error in Ω0 prevails in the A error. Besides, published Ω0 results are not statisticallyconsistent, unlike R0 measurements. So, more attention is needed tocompute the best estimate of Ω0.
We derived the current best estimate of the GA constant using all available measurements of the Galactic rotation parameters madeduring 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 us to eliminate at least90% of the GA effect. Remaining uncertainty in proper motion ofabout 0.5 µas/yr is negligible nowadays. Thus the proposed value ofthe GA constant can be safely used in practice during coming years,presumably for at least the nearest decade, until new VLBI and spaceobservations provide substantially better result.
Table 1. R0 estimates used in this study, kpc. Direct R0 measure-ments are marked with asterisk.
Table 2. Ω0 estimates used in this study, [km s−1 kpc−1].
Table 3. Results of computation of the mean R0 [kpc], Ω0 [km s−1kpc−1], and the GA constant A [µas/yr.].
Malkin, Z.M., 2011,“The Influence of Galactic Aberration on Pre- cession Parameters Determined from VLBI Observations”, Astron.
Rep. 55, pp. 810–815.
Malkin, Z., 2012, “The current best estimate of the Galactocentric distance of the Sun based on comparison of different statisticaltechniques”, arXiv:1202.6128.
Malkin, Z.M., 2013, “On the Calculation of Mean-Weighted Value in Astronomy”, Astron. Rep. 57(11), 882–887.

Source: http://syrte.obspm.fr/journees2013/powerpoint/malkin_poster_ga_jsr13.pdf