The Galactic Center: An Improved Astrometric Reference Frame for Stellar Orbits around the Supermassive Black Hole

Maser stars that are detected in both the IR and radio are used to bring the IR stellar positions into an Sgr A* (radio) rest frame. Reid et al. (2007) presented radio data of masers that were based on five epochs of observations over the period of 1995–2006. In this paper, we use radio positions and proper motions from M. Reid (2018, private communication) that have been updated with two additional epochs of observations.

All the data for the IR observations of SiO masers in the Galactic Center region were obtained using the laser guide-star adaptive optics (LGSAO; van Dam et al. 2006; Wizinowich et al. 2006) facility on the Keck II telescope at the W. M. Keck Observatory. Images were obtained with a near-infrared facility imager (NIRC2; PI: K. Matthews) through the K' (λらむだ₀ = 2.12 μみゅーm, Δでるたλらむだ = 0.35 μみゅーm) bandpass. The camera has 1024 × 1024 pixels, with a plate scale of 9.952 mas per pixel (Yelda et al. 2010). Since 2014, the AO system and NIRC2 camera were realigned, and the plate scale was changed to 9.971 mas per pixel (Service et al. 2016). All maser observations were performed with the position angle set to zero. USNO 0600-28577051, which is offset by 94E and 695N from Sgr A*, served as the tip–tilt star for all of the LGSAO observations. The integration time for each exposure on the Galactic Center (GC) masers was 10.86 s for most epochs, and each comprised 60 co-added 0.181 s exposures in order to avoid saturating the bright masers. The integration time for the central 10'' field is much longer than the maser observations, with each exposure being 28 s, because this field was chosen both to include Sgr A* and to avoid bright stars that would saturate, such that a longer exposure time was possible.

We used a widely dithered (6'' × 6'') nine-point box pattern with multiple images at each of the nine positions. The number of exposures per dither position changed throughout the 13 years of observations, varying from 3 to 18. Starting in 2012, additional observations of a four-point box pattern (with a smaller dither of 3'' × 3''), with multiple images per dither position, were also obtained in order to average down astrometric errors from unaccounted for field variability in the point-spread function (PSF) due to atmospheric and instrumental aberrations. The data from the four-point box pattern had not been incorporated in any previous analysis. Figure 1 shows the two mosaic patterns covering an area large enough to include seven masers closest to the GC. Figure 1 also shows the positions of the seven masers. The full field of the maser mosaic is 22'' × 22'', corresponding to ∼0.88 pc × 0.88 pc at the distance of R₀ = 8.0 kpc. A summary of the IR observations and the delivered image quality is given in Table 1. Yelda et al. (2010) included the maser observations from 2005 to 2010. Boehle et al. (2016) then incorporated three additional epochs of maser observations spanning 2011–2013. However, they did not include the inner 2 × 2 dither positions in the construction of the reference frame. The new maser observations added in this paper since Boehle et al. (2016) are indicated by asterisks in Table 1.

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Table 1.  Summary of GC Maser Mosaic Images

Date	${t}_{\exp ,i}$ × Co-add	Nexpa	${K}_{{\rm{lim}}}^{{\prime} }$ b	FWHMc	Strehld	Nstarse	${\sigma }_{\mathrm{pos}}$ f
(UT)	(s)	per dither position	(mag)	(mas)			(mas)
2005 Jun 30	0.181 × 60	2 (3 × 3)	15.18	60.1	0.32	1143	1.25
2006 May 3	0.181 × 60	3 (3 × 3)	15.57	61.2	0.28	1242	1.10
2007 Aug 12	0.181 × 60	3 (3 × 3)	15.66	56.6	0.29	1474	1.15
2008 May 15	0.181 × 60	3 (3 × 3)	15.92	53.5	0.35	1861	1.05
2009 Jun 28	0.181 × 60	9 (3 × 3)	16.12	63.5	0.26	2274	1.10
2010 May 4	0.181 × 10	18 (3 × 3)	15.52	67.6	0.25	1110	1.25
2011 Jul 20	0.181 × 60	6 (3 × 3)	15.87	63.2	0.27	2033	1.20
2012 May 15	0.181 × 60	6 (3 × 3) + 3 (2 × 2)g	15.82	55.9	0.34	2226	1.10
2013 Jul 2	0.181 × 60	18 (3 × 3) + 4 (2 × 2)g	16.11	59.1	0.31	2745	1.20
2014 May 20	0.181 × 60	18 (3 × 3)g + 3 (2 × 2)g	16.14	65.8	0.24	2586	1.20
2015 Jul 10	0.181 × 60	18 (3 × 3)g + 3(2 × 2)g	16.44	65.4	0.27	3216	1.20
2016 May 15	0.181 × 60	18 (3 × 3)g + 3 (2 × 2)g	15.99	80.1	0.19	2329	1.30
2017 May 5	0.181 × 60	18 (3 × 3)g + 18 (2 × 2)g	16.51	58.9	0.31	3265	1.20

Notes.

^aNumber of exposures per dither position. The dither pattern is indicated in brackets. ^b ${K}_{{\rm{lim}}}^{{\prime} }$ is the magnitude at which the cumulative distribution function of the observed K' magnitudes reaches 90% of the total sample size. ^cMean FWHM of stars detected in each epoch. ^dMean Strehl ratio of stars detected in each epoch. ^eNumber of stars detected in each epoch. ^fMean total astrometric measurement error. ^gMaser data that had not been used in previous reference frame analyses.

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The new NIRC2 data were reduced following the methods described in Yelda et al. (2014). Each NIRC2 frame was sky-subtracted, flat-fielded, corrected for bad pixels, and also corrected for the effects of optical distortion and differential atmospheric refraction (Yelda et al. 2010; Service et al. 2016). The sky background was estimated by taking the median of sky exposures nightly. For optical distortion correction, two independent lookup tables are used. The AO was realigned in 2015, thus the optical distortion correction determined by Yelda et al. (2010) is applied for the data taken prior to 2015, while the correction by Service et al. (2016) is used for data taken in 2015 and later.

For each dither position, a bright isolated star is selected whose position is used to register and mosaic together multiple exposures. The final image for each dither position was created by including only those frames having an FWHM less than 1.25 times the smallest FWHM value measured for the dither position. If the number of exposures per dither position was only 3, which was the case for most of the earlier observations, and for the 2 × 2 dither pattern for all years except 2017, all exposures were used to create the final image at each dither position. Furthermore, the frames for each dither position were subdivided into three independent subsets. Each subset consisted of frames of similar FWHM and Strehl ratio. The images in each subset were then combined to make three "submap" images for each dither position. The standard deviation of measured positions over the three submap images was used for initial estimates of astrometric uncertainties. The positional uncertainties estimated from submaps range from 0.06 pixels (∼0.6 mas) on average for stars brighter than K' = 12 up to ∼0.1 pixel for stars with 14 < K' < 15. The signal-to-noise ratio (S/N) is ∼10,000 for K ∼ 12 stars. For fainter K ∼ 14–15 mag stars, the S/N is ∼4000. The astrometric uncertainties are larger, in general, in the maser mosaic data than in the central 10'' data. This is because the central 10'' observations are much longer and deeper; the central 10'' data comprise hundreds of frames, each with a total exposure time of 2.8 s × 10 co-adds.

With the fully reduced dithered images, the next step is to make a master starlist consisting of values of stellar positions and proper motions. Instead of creating a mosaicked image, we first extract stellar positions from the combined images at each dither position and then mosaic the starlists as described below (Yelda et al. 2014).

First, the photometry and astrometry were extracted on each dither position for each epoch using the AIROPA package developed by the UCLA Galactic Center group (Witzel et al. 2016), based on the PSF-fitting code StarFinder (Diolaiti et al. 2000). This package was designed to take atmospheric turbulence profiles, instrumental aberration maps, and images as inputs and then fit field-variable PSFs to deliver improved photometry and astrometry on crowded fields. Although a single PSF was applied for the data used in this paper, the PSF extraction benefited from a much improved method because AIROPA uses improved StarFinder subroutines. For each dither position, we selected ∼30–60 isolated stars spread throughout the NIRC2 field of view, which are combined to create a single PSF model. This PSF is then used to extract positions and fluxes using PSF-fitting methods. A similar analysis is performed on the three submap images as well.

The starlists from all the dither positions were then combined together to create one master starlist for each epoch, by following the iterative steps described below. (1) First, we use the positions of stars presented in Table 6 of Boehle et al. (2016) (hereafter GC starlist) as a starting point to launch an iterative process of mosaicking together starlists from individual mosaic positions to create a combined single master starlist for each epoch of NIRC2 observation. The GC starlist comprises ∼830 stars, spanning the same region as the maser frames. The positions given in arcseconds and proper motion values given in mas yr⁻¹ had been determined from the previous construction of the reference frame, in which accelerating sources were excluded (see Section 3 for details). An initial guess for the positions of stars in any given epoch can then be estimated using the values given in this GC starlist. Matching and transforming a starlist from one dither position to the GC starlist is performed by fitting a third-order, 20-parameter (10 in each dimension) polynomial to the positional offsets of ∼100 stars. The third-order fit was used in order to take care of the time-dependent residuals, likely stemming from the variable PSF, that were present after the corrections for geometric distortion (Yelda et al. 2010; Service et al. 2016) were applied. More details are given in the Appendix. This transformation step was iterated as each iteration added more stars, and thus a better transformation was calculated. This matching procedure is repeated for all observed dither positions.

(2) Now we have either 9 or 13 transformed starlists in arcseconds for each epoch, depending on how many dither positions were observed (see Table 1). Next, all the starlists for a given epoch are combined together to create one master list, spanning ∼22 × 22 arcsec per epoch. For stars found in the overlap regions, the mean positions were used, with the standard deviation of the mean used as the positional uncertainties. The typical astrometric uncertainties in the mosaicked image range from ∼0.05 mas for stars brighter than K ∼ 12 mag up to ∼2 mas for K ∼ 15 mag. For comparison, the mean uncertainties in the central 10'' data, which are much deeper than the maser mosaic observations, are around ∼0.09 mas.

(3) The newly created mosaicked master list is used as the reference starlist and steps 1 and 2 above are repeated six times. After three or four iterations, the standard deviation of the match between the reference starlist and the mosaicked starlist for each mosaic position converges to <1 mas (∼0.1 pixel).

The accuracy of the stellar positions after the first iteration in step 2 is 1.7 mas in the east and 2.2 mas in the north, which decrease to 1.3 and 1.8 mas for subsequent iterations. The uncertainty in the N/S direction is worse than in the E/W. This is likely due to the position of the tip–tilt star located NNE of the entire maser mosaic field, which causes the PSF to be elongated in that direction and leads to poorer measurement precision. The numbers of stars and mean position uncertainties for each epoch are listed in Table 1.

The goal of constructing the IR astrometric reference frame is to produce a set of secondary astrometric standard stars whose proper motions are linear and well measured. Their positions at a given epoch can then be used to define the coordinate system for that epoch. Stellar positions from multiple epochs can then be aligned together in the IR reference frame to derive the proper motions and accelerations of those stars in the region close to Sgr A* for determinations of orbits.

We start out with 13 starlists, each produced from one epoch of NIRC2 mosaic observations of SiO masers by following the procedure described in the previous section. The 13 sets of data span 13 years from 2005 to 2017. First, the seven maser positions from the individual starlist per epoch need to be transformed to their radio positions propagated to the corresponding epoch. The radio maser positions are calculated from the proper motion measurements given by M. Reid (2018, private communication).

We note that the intrinsic size of Sgr A* is less than 1 au, corresponding to ∼0.13 mas at the distance of the Galactic Center (Reid & Brunthaler 2004). Thus the uncertainty in the reference frame resulting from the error in the size measurement of Sgr A* is minimal. In addition, the position of Sgr A* in the radio is determined with an uncertainty of ∼1 mas. We also note that Sgr A*'s proper motion is −3.151 ± 0.018 mas yr⁻¹ and 5.547 ± 0.026 mas yr⁻¹ in the east and south directions respectively (Reid & Brunthaler 2004), with respect to background QSOs. However, the reference frame being derived in this paper is based on the assumption that Sgr A* is at rest. In other words, our frame is relative to Sgr A*.

Compared to the radio data used in Yelda et al. (2010), one or two additional astrometric points for each maser were included in the derivation of proper motions. For the radio positions and proper motions, it is assumed that Sgr A* is at the Galactic Center and at rest. Thus ideally the same assumption holds for the IR reference frame. The positional uncertainties in the propagated radio measurements vary from 0.3 to 5 mas depending on the maser, with a mean of ∼1.35 mas. For the alignment of IR and radio positions of the masers, six independent parameters were used (translation, rotation, and pixel scale independently in the east and north, to first order). The transformed IR starlist is now in the astrometric reference frame in which the Sgr A* radio source is at rest. This exercise was repeated for all 13 epochs, resulting in a set of 13 starlists that are all in the same radio astrometric reference frame.

The errors in the transformation of the IR positions to the radio Sgr A* rest frame in each epoch were calculated by a jackknife method, in which one maser was dropped from the alignment at a time. The standard deviation of seven "drop-one-maser" cases for each star was adopted as the positional uncertainty. The total astrometric uncertainty for a star's position in every epoch is estimated by combining the positional, alignment, and distortion correction errors. For the error in distortion correction, the average value of 1 mas, as derived by Yelda et al. (2010) and Service et al. (2016), was added to the astrometric errors in the east and north.

Next, the proper motions for all astrometric secondary standard stars are determined. The 13 epochs of starlists are in a common coordinate system and are cross-matched to identify each star across all epochs. The proper motions are then determined by fitting a linear velocity model to each star's positions over time. The proper motion errors were estimated using a jackknife resampling method. Out of ∼3900 stars detected in the entire maser mosaic field, 1008 stars were detected in at least 12 of the 13 epochs. For a star to be included in the secondary astrometric standard starlist, it needed to meet the following conditions: magnitude of proper motion in both the x and y directions <10 mas yr⁻¹, uncertainties in the x and y proper motions <0.2 mas yr⁻¹, and both χかい² values in x and y directions for proper motion fits less than 20, to exclude accelerating stars. The final secondary standard starlist contains 748 stars. Table 2 lists the properties of secondary IR astrometric standard stars.

Table 2.  Secondary IR Astrometric Standard and PSF Stars in the Galactic Center

												Astrometric
Name	K'	${T}_{0,\mathrm{IR}}$	Radius	ΔでるたR.A.	${\sigma }_{{\rm{R}}.{\rm{A}}.}$ a	ΔでるたDecl.	${\sigma }_{\mathrm{Decl}.}$ a	vR.A.	${\sigma }_{{v}_{{\rm{R}}.{\rm{A}}.}}$ b	vDecl.	${\sigma }_{{v}_{\mathrm{Decl}.}}$ b	Standardc	PSF Stard
	(mag)	(yr)	(arcsec)	(arcsec)	(mas)	(arcsec)	(mas)	(mas yr−1)	(mas yr−1)	(mas yr−1)	(mas yr−1)
S0-6	14.3	2010.86	0.36	0.0154	0.2000	−0.3563	0.2200	−5.057	0.051	3.065	0.075	Y
S0-11	15.4	2011.37	0.49	0.4896	0.2200	−0.0657	0.4300	−3.637	0.033	−2.530	0.080	Y
S0-7	15.4	2012.37	0.54	0.5268	0.2600	0.1002	0.2900	5.711	0.052	0.727	0.069	Y
S0-13	13.5	2011.00	0.69	0.5575	0.2000	−0.4073	0.2400	1.874	0.048	3.136	0.063	Y
S0-12	14.4	2011.53	0.69	−0.5497	0.2200	0.4198	0.2100	1.060	0.045	3.399	0.055	Y	C_SW
S0-31	15.1	2012.08	0.73	0.5810	0.4400	0.4470	0.8200	6.377	0.116	0.885	0.273	N	C_SW
S0-14	13.9	2011.40	0.81	−0.7533	0.2200	−0.2888	0.2800	2.514	0.051	−1.446	0.082	Y	C_NW, C_SW, W
S1-5	12.7	2011.08	0.94	0.3142	0.2400	−0.8833	0.1800	−3.671	0.067	4.304	0.053	Y

Notes.

^aPositional errors include errors due to centroiding, alignment, and residual distortion (1 mas), but do not include the error in position of Sgr A* (0.01 mas and −0.16 mas in R.A. and decl. respectively). ^bVelocity errors do not include the error in velocity of Sgr A* (0.018 mas yr⁻¹ and 0.004 mas yr⁻¹ in R.A. and decl. respectively. ^cIndicates whether the star is a secondary astrometric standard. ^dIndicates for which mosaic field the star was used to create a PSF.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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In Figure 5, the stability of the reference frame derived in this paper is compared with those of previously published results. In Yelda et al. (2010), six epochs of maser data were used, instead of 13 used in this paper. When comparing the stability of the reference frame, the uncertainty in distortion correction of 1 mas that was added in the formal IR error (see Table 3) is subtracted, because we would like to focus on the improvement made in the methods used to construct the reference frame. Without this uncertainty, the reference frame of Yelda et al. (2010) yields uncertainties in Sgr A*'s position of 0.319 mas and 0.382 mas in the east and north directions respectively. In this paper, Sgr A*'s position is estimated with uncertainties of 0.122 mas and 0.157 mas in the east and north directions respectively, indicating that the reference frame has been improved by a factor of ∼2.5 in position. The uncertainties in the proper motions of Sgr A* in the IR reference frame are 0.02 and 0.03 mas yr⁻¹ in the east and north directions, respectively, compared to 0.09 and 0.14 mas yr⁻¹ reported by Yelda et al. (2010). The orbital analysis of Boehle et al. (2016) was based on a reference frame that had three epochs of maser observations (2011–13) in addition to those used in Yelda et al. (2010). The uncertainties in the proper motions in the east and north directions of Sgr A* were 0.056 and 0.060 mas yr⁻¹ respectively.

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Using the NACO imager on VLT, Plewa et al. (2015) reports a stability of ∼0.17 mas in position and ∼0.07 mas yr⁻¹ in velocity. Their analysis used eight masers because their mosaicked field covered 42 arcsec × 42 arcsec. However, their maser sample did not include IRS 7. IRS 7 is a supergiant and its SiO maser features originate from a much larger maser emission region than the other masers used (Reid et al. 2003) by a factor of ∼2, which is reflected in larger uncertainties in the star's radio positions and proper motions. To see how much effect this one star has on the IR reference frame, we construct the reference frame without IRS 7. Excluding IRS 7, we obtain combined positional and velocity uncertainties of 0.17 mas and 0.031 mas yr⁻¹ respectively. The velocity stability of our sample of six masers, without IRS 7, is still a factor of 2 better than the one reported by Plewa et al. (2015). This is because IRS 7 has less influence on the overall reference frame due to the very large errors assigned to its radio velocities. The maser sample used by Plewa et al. (2015) also had one less epoch of the radio observations. Furthermore, their IR observations included data through 2013, while our IR data extend four additional years. As explained in Section 5, the IR data and the method used to create the reference frame presented in this paper were modified significantly compared to those used in Yelda et al. (2010). The comparison of the reference frame of Boehle et al. (2016) with that of Plewa et al. (2015) is likely more appropriate, because both use the maser data through 2013.

The stability of the reference frame improved by a factor of ∼5 compared to that of Yelda et al. (2010), to which the change in each one of the above five processes contributed. Of the five, the number of epochs of maser mosaic observations has had the most significant effect on the improvement of the stability of the reference frame . If we were to build the reference frame using seven epochs of data spanning the years 2005–2011, with all other conditions remaining the same, the uncertainties in the velocities in the reference frame would increase to 0.023 and 0.043 mas yr⁻¹ for V_R.A. and V_decl. (from 0.018 and 0.025 mas yr⁻¹). However, if we used seven epochs spread over 13 years from 2005 through 2017, skipping every other year, then the velocity uncertainties would remain similar (0.021 and 0.025 mas yr⁻¹). Thus it is not just the number of epochs that is important in creating a stable reference frame, but the range of dates of observations. The longer the time baseline, the more accurate the reference frame becomes. We attribute this to the improved precision and accuracy of the proper motions of the secondary astrometric stars.

The IR astrometric reference frame is stable within 0.03 mas yr⁻¹ (Table 3). However, this is based on the radio observations of proper motions of seven SiO masers only. There are 16 masers that can be used potentially to create the radio Sgr A* rest reference frame (Reid et al. 2003). However, given the field of view of NIRC2 and the feasibility of telescope scheduling, we have only been able to mosaic together a field large enough to cover the seven masers closest to Sgr A*. Because of dependence of this field on a small number of astrometric anchor points, we examine in this section how sensitive the global parameters of the SMBH are to the selection of masers.

We have applied a jackknife resampling method, in which one maser at a time is excluded from the construction of the reference frame. The proper motions of secondary astrometric standard stars derived from the radio positions of the remaining six masers change systematically. As mentioned above, the positional uncertainties of secondary astrometric stars are calculated by taking the average of seven drop-one-maser cases, with the assumption that this does not lead to any systematic uncertainties that might depend on the location of the star on the maser mosaic field. In order to evaluate whether this is the case, we have estimated first the deviation of the astrometric and proper motion values of one of the jackknife cases from those in the case in which all seven masers were used. The weighted standard deviations of seven cases were then calculated and plotted as color maps in Figure 6. The positions in the epoch 2000.0 were used for the astrometric comparison in Figure 6.

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In Figure 7, the comparisons of IR and radio positions of masers in all seven jackknife cases are shown. The case in which all masers are used is also included in this figure as the "all" case. Each jackknife case agrees with each other, and also with the "include all" case within 1σしぐま, suggesting that the selection of masers should not affect the zero-point of the IR astrometric reference frame. We further investigate how the SMBH parameters may be affected by the maser selection in the next section.

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Since the IR positions of all stars on the master starlist per epoch are transposed to the radio Sgr A* rest frame, if the perfect reference frame is achieved, the mean position and proper motion of Sgr A* in the IR reference frame should be zero. If not, the orbit of, for example, S0-2 would exhibit a shift resulting in an unclosed orbit, as the zero-point of each coordinate system would systematically wander. For the reference frame being presented in this paper, as seen in Table 3, the agreement between the IR and radio maser positions and proper motions is consistent with zero within uncertainties. The star S0-2 has a period of 16yr, and its positions, spanning the period 1995–2017, are shown in the right panel of Figure 8 after being cross-epoch aligned to the common reference frame (S. Jia et al. 2018, in preparation), with the orbit model fit superposed in black. Plotted in the left panel in the same figure are the astrometric points of S0-2 cross-epoch aligned using the reference frame used in Boehle et al. (2016), with the orbit model fit superposed. The same set of NIRC2 and radial velocity data were used in both orbits shown in Figure 8; the only difference between the two orbits is the reference frame used. With the previous reference frame, the shift in the radial position of S0-2 was roughly 0.75 mas yr⁻¹, which is clearly seen in Figure 8 as the gap in the orbit in the northeast direction from Sgr A*, whereas with the newer current reference frame the same shift is ∼0.05 mas yr⁻¹, an order of magnitude better. Since the analysis of Boehle et al. (2016), the speckle holography data have been reanalyzed and updated. The orbit-fitting results shown in this paper utilize the updated newer version (S. Jia et al. 2018, in preparation). However, when estimating the orbit of S0-2 using the previous version of speckle holography data, but using the most current reference frame being presented here, the orbit is much more "closed," similar to the one shown in Figure 8, than the one presented by Boehle et al. (2016), suggesting that the new reference frame plays a larger role in refining the S0-2 orbit than the reanalyzed NIRC2 speckle data.

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We further examine how each jackknife reference frame affects the black hole parameters determined from the orbit fitting following the procedure described in detail in Ghez et al. (2005b, 2008) and Boehle et al. (2016). Each jackknife reference frame, as described in the previous section, is used for cross-epoch alignment of central 10'' data, followed by the orbit-fitting procedure for each case to estimate the parameters of the Galactic Center SMBH (see Ghez et al. 2008; Boehle et al. 2016). The case in which no maser is dropped is the same alignment of cross-epoch central 10'' data presented in S. Jia et al. (2018, in preparation). Examining the statistical bias of SMBH parameters using the seven subset reference frames by applying the equations in Appendix C of Boehle et al. (2016), we estimate that the measurements are biased at a 2σしぐま level.

One of the motives for improving the IR reference frame has been the opportunity to be able to test general relativity as S0-2 reached its closest approach to the SMBH in 2018. Furthermore, observations of the apocenter shift of S0-2 should be possible in future, if the uncertainty in the stability of the reference frame of ∼0.02 mas yr⁻¹ is achieved (Weinberg et al. 2005). Yelda et al. (2010) reported that this stability would not be achieved until ∼2022 based on six epochs of maser observations. We are now able to revisit this question with more than twice the amount of data. Figure 9 shows the improvement in the reference frame. It displays the uncertainty in the velocity of Sgr A* in the IR reference frame as a function of time. The trends presented in Yelda et al. (2010) are represented in this figure by dashed lines. By the year 2020, with three additional epochs of maser data starting in 2018, the combined stability of ∼0.02 mas yr⁻¹, shown by a gray horizontal line, can be reached.

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Another method of examining how well the IR astrometric reference frame is determined is to compare the position of Sgr A*-IR on maser mosaic frames with the predicted radio position of Sgr A*. Sgr A*-IR is highly variable (Genzel et al. 2003; Ghez et al. 2004, 2005a; Witzel et al. 2018), and it is not often detectable, especially in short-exposure maser mosaics. However, we make use of the central 10'' data by examining single frames from a given epoch, which allows us to pinpoint the location of Sgr A*-IR when it flares. The position of Sgr A*-IR is then located on the maser mosaic field if the maser and central 10'' observations were taken within approximately a month of each other. Otherwise, the stars closest to the SMBH would have moved far enough that the location of Sgr A*-IR cannot be determined accurately enough. We have examined each epoch of data and found that Sgr A*-IR is visible in three epochs: 2008, 2010, and 2014. The results are shown in Figure 10. The R.A. and decl. positions of Sgr A*-IR in three epochs are shown as a function of time, with the predicted positions and uncertainties determined from the reference frame, as shown in Table 3, overplotted. With the exception of the 2014 decl. position, the position of Sgr A*-IR agrees well with the zero-point of the reference frame. Sgr A*-IR is fainter in 2014 than in the other two epochs, which may explain the slight discrepancy.

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