<figure><img src="image_1.png" /></figure>

# Long-term Astrometric Monitoring of the Galactic Center Magnetar PSR J1745−2900

Geoffrey C. Bower<sup>1,2,3</sup>, Adam T. Deller<sup>4</sup>, Paul B. Demorest<sup>5</sup>, Jason Dexter<sup>6</sup>, Andreas Brunthaler<sup>7</sup>, Gregory Desvignes<sup>7,8</sup>, Ralph P. Eatough<sup>7,9</sup>, Heino Falcke<sup>10</sup>, Ciriaco Goddi<sup>11,12,13,14</sup>, Michael Kramer<sup>7</sup>, and F. Yusef-Zadeh<sup>15</sup>

*Received 2025 February 4; revised 2025 May 2; accepted 2025 June 2; published 2025 July 22*

## Abstract

We present new astrometric observations of the Galactic center magnetar PSR J1745−2900 with the Very Long Baseline Array. Combined with previously published measurements in 10 epochs that spanned 477 days, the complete data set consists of 25 epochs and 41 independent measurements that span 1984 days. These data constrain the proper motion to an accuracy of ≲2% and set an upper limit on the absolute value of the magnetar's acceleration of ≲(0.4, 0.2) mas yr⁻<fnref n="2" /> in the two celestial coordinates, consistent with the maximum value of ~0.03 mas yr⁻<fnref n="2" /> expected for an orbit around Sgr A*. Future measurements have the potential to detect the acceleration of PSR J1745−2900 due to Sgr A* should PSR J1745−2900 rebrighten. We consider several potential sources of systematic variations in the astrometric residuals after fitting for standard parameters, including refractive wander, changes in the structure of Sgr A*, and the presence of an unseen binary companion. While a stellar companion model can be fit to the astrometric data, pulse period measurements are inconsistent with that model. No changes in the apparent image size of the magnetar were detected over the duration of these observations, indicating a lack of change in the properties of the line-of-sight scattering during this period. We also show that the upper limit to the mean core shift of Sgr A* is consistent with expectations for a compact jet or symmetric accretion flow.

*Unified Astronomy Thesaurus concepts: Pulsars (1306); Radio pulsars (1353); Binary pulsars (153); Galactic center (565); Black holes (162); Interstellar scattering (854); Radio astrometry (1337); Astrometry (80); Very long baseline interferometry (1769); Magnetars (992)*

## 1. Introduction

Pulsars in the Galactic center (GC) are powerful tools to probe the interstellar medium, star formation and stellar death in extreme environments, and general relativity. A pulsar in a close orbit around Sgr A*, the $4 \times 10^6 M_{\odot}$ black hole in the GC, would provide unprecedented accuracy in the measurement of the black hole's mass and spin, and would also test nonstandard theories of gravity and black holes (K. Liu et al. 2012; D. Psaltis et al. 2016). Timing of such a pulsar would strongly complement measurements from near-infrared (NIR) stellar astrometry (T. Do et al. 2019; GRAVITY Collaboration et al. 2019) and black hole imaging by the Event Horizon Telescope (EHT; Event Horizon Telescope Collaboration et al. 2022a).

A large number of GC pulsars has been predicted as a result of the known populations of high-mass stars in the central

parsecs (E. Pfahl & A. Loeb 2004). Diffuse gamma-ray emission has also been interpreted as the result of a population of millisecond pulsars (C. Gordon & O. Macías 2013). Extensive searches have been conducted at a wide range of radio wavelengths; however, they only revealed a small number of confirmed pulsars in the central tens of parsecs (S. Johnston et al. 2006; J. S. Deneva et al. 2009; J. P. Macquart et al. 2010; R. P. Eatough et al. 2021; P. Torne et al. 2023; D. A. Frail et al. 2024), including the recently discovered millisecond pulsar J1744−2946 at a distance of ~1 deg from Sgr A* (M. E. Lower et al. 2024). Deep X-ray observations of the GC have also failed to detect a large number of pulsar candidates (M. P. Muno et al. 2009).

The absence of radio wavelength detections has primarily been explained as the result of the effects of strong interstellar scattering in the GC, which can smear the pulsed radio emission to a timescale longer than the pulse period. The interstellar scattering properties are primarily determined by the angular broadening of Sgr A* (G. C. Bower et al. 2006; M. D. Johnson et al. 2018), with supporting evidence from the

<figure><img src="image_2.png" /></figure>

Original content from this work may be used under the terms of the [Creative Commons Attribution 4.0 licence](https://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

<footnote n="1"><sup>1</sup> East Asian Observatory, 660 N. A'ohoku Pl., Hilo, HI 96720, USA; gbower@asiaa.sinica.edu.tw</footnote>

<footnote n="2"><sup>2</sup> Academia Sinica Institute of Astronomy and Astrophysics, 645 N. A'ohoku Pl., Hilo, HI 96720, USA</footnote>

<footnote n="3"><sup>3</sup> Department of Physics and Astronomy, University of Hawaii at Manoa, 2505 Correa Road, Honolulu, HI 96822, USA</footnote>

<footnote n="4"><sup>4</sup> Centre for Astrophysics and Supercomputing, Swinburne University of Technology, John St., Hawthorn, VIC 3122, Australia</footnote>

<footnote n="5"><sup>5</sup> National Radio Astronomy Observatory, P.O. Box O, Socorro, NM 87801, USA</footnote>

<footnote n="6"><sup>6</sup> JILA and Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80309, USA</footnote>

<footnote n="7"><sup>7</sup> Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, D-53121 Bonn, Germany</footnote>

<footnote n="8"><sup>8</sup> LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université de Paris, 5 place Jules Janssen, F-92195 Meudon, France</footnote>

<footnote n="9"><sup>9</sup> National Astronomical Observatories, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing 100101, People's Republic of China</footnote>

<footnote n="10"><sup>10</sup> Department of Astrophysics, Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Radboud University, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands</footnote>

<footnote n="11"><sup>11</sup> Universidade de São Paulo, Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Departamento de Astronomia, São Paulo, SP 05508-090, Brazil</footnote>

<footnote n="12"><sup>12</sup> Dipartimento di Fisica, Università degli Studi di Cagliari, SP Monserrato-Sestu km 0.7, I-09042 Monserrato, Italy</footnote>

<footnote n="13"><sup>13</sup> INAF—Osservatorio Astronomico di Cagliari, via della Scienza 5, I-09047 Selargius (CA), Italy</footnote>

<footnote n="14"><sup>14</sup> INFN, Sezione di Cagliari, Cittadella Univ., I-09042 Monserrato (CA), Italy</footnote>

<footnote n="15"><sup>15</sup> Department of Physics and Astronomy, CIERA, Northwestern University, 2145 Sheridan Road, Evanston, IL 60207, USA</footnote>
angular broadening of stellar hydroxyl masers (H. J. van Langevelde et al. 1992), counts of extragalactic background sources (T. J. W. Lazio & J. M. Cordes 1998a, 1998b), and other measurements. High-frequency radio observations have been used as a means to mitigate the strong frequency dependence of temporal broadening. However, typical pulsar spectra also decrease steeply with increasing frequency, reducing the number of detectable objects. Future searches with the Square Kilometre Array and with the ngVLA may be able to overcome these combined challenges (G. C. Bower et al. 2018).

The GC magnetar PSR J1745−2900 was discovered in 2013 through a luminous X-ray burst (J. A. Kennea et al. 2013; K. Mori et al. 2013) that was soon followed by the discovery of radio pulsations (R. P. Eatough et al. 2013). Given the projected distance of ~0.1 pc from Sgr A*, its large dispersion measure (DM) and rotation measure (RM), and the high X-ray column density, PSR J1745−2900 appears to be the first pulsar known to be in orbit around Sgr A*, with a period >700 yr (G. C. Bower et al. 2015). Astrometric observations showed that the pulsar has a proper motion consistent with originating from the clockwise (CW) stellar disk, which includes many O- and B-type stars that could serve as progenitors for a neutron star or magnetar (G. C. Bower et al. 2015). The magnetar has mostly faded in X-rays and radio emission in the years since its initial discovery (e.g., V. M. Kaspi et al. 2014; F. Yusef-Zadeh et al. 2015; R. Eatough et al. 2025, in preparation).

The low radio frequency detection of PSR J1745−2900 and a combination of the temporal and angular broadening properties has revised our understanding of the scattering properties toward PSR J1745−2900 and Sgr A* (G. C. Bower et al. 2014; L. G. Spitler et al. 2014). The measured angular broadening toward PSR J1745−2900 is consistent with that of Sgr A*, while the temporal broadening is much less than predicted if the scattering arises in the GC region. Rather, the scattering appears to originate from a screen situated at a distance of $\Delta \sim 5$ kpc from the GC, which cannot be responsible for the absence of other pulsars as the result of temporal broadening. Patchiness in the interstellar medium (ISM; where other sightlines do experience heavier temporal broadening) has been invoked as a possible geometry that would still lead to obscuration of a significant fraction of the GC pulsar population (L. G. Spitler et al. 2014). Studies of other GC pulsars suggest that scattering toward these sources arises at a range of distances along the line of sight (J. Dexter et al. 2017). Alternatively, the extreme densities and magnetic field strengths of the GC may lead to other paths for star formation that favor the creation of short-lived magnetars over ordinary pulsars (J. Dexter & R. M. O'Leary 2014). Detailed modeling that incorporates search sensitivities is necessary to constrain the GC pulsar population (J. Chennamangalam & D. R. Lorimer 2014).

Very long baseline interferometry (VLBI) imaging and astrometry of PSR J1745−2900 have been critical for addressing the source of interstellar scattering and for demonstrating the likely origin of the magnetar in the CW stellar disk. Continued VLBI imaging probes the structure of the scattering medium as the pulsar and the Sun move relative to the scattering medium (or mediums). Continued VLBI astrometry has the power to detect the acceleration of the magnetar due to the gravity of Sgr A*, confirming that it is in a bound orbit. Additionally, astrometry can probe wavelength- and temporal-

dependent changes in the structure of Sgr A*, which serves as the astrometric reference source.

In this paper, we extend the results first reported in G. C. Bower et al. (2014) and G. C. Bower et al. (2015) with new observations from the Very Long Baseline Array (VLBA). Section 2 presents the observations and data reduction. Section 3 presents the astrometric analysis. Section 4 presents the results on astrometry, scattering, and Sgr A*, incorporating new timing measurements from R. Eatough et al. (2025, in preparation). Section 5 summarizes the conclusions.

## 2. Observations and Data Reduction

G. C. Bower et al. (2015) reported 15 independent position measurements in 10 epochs made with the VLBA over 477 days, beginning at MJD 56422. New observations were obtained over the MJD range 57073–58406 with 26 independent position measurements in 15 epochs. The total span of the complete data set is 1984 days with 41 independent position measurements in 25 epochs. The observations used all available VLBA antennas, sometimes including a single “Y1” antenna from the Very Large Array (VLA) that provided additional short baselines. Receivers were tuned to several different frequencies, represented by the bands $X$ (8.6 GHz, 3.4 cm), $Ku$ (15.3 GHz, 2.0 cm), $K$ (21.9 GHz, 1.3 cm), and $Q$ (43.1 GHz, 0.7 cm). Data were recorded with bit rates of 2048 Mb s⁻¹ from each station. Each observation was correlated three times: once at the location of Sgr A*, and twice at the location of PSR J1745−2900. In the first correlation centered at PSR J1745−2900, pulsar gating was applied using the capabilities of the DiFX software correlator (A. T. Deller et al. 2007) to retain only the ~5% of the pulse period that contained significant pulsed emission, while the second generated a standard continuum visibility data set. An integration time of 3.76355 s was used, meaning that one pulse would be contained in each integration. Using the tools described in G. C. Bower et al. (2015), a scaled version of the continuum visibilities was subtracted from the gated data set, effectively removing the (time- and bandwidth-smeared) contribution of Sgr A* from the PSR J1745−2900 visibility data set and significantly improving the fidelity of the final images.

Data analysis was performed using AIPS following the same procedures in G. C. Bower et al. (2015). The primary steps in this analysis include amplitude calibration, instrumental and atmospheric delay and phase calibration on Sgr A*, and transfer of solutions to the magnetar. Delay, rate, and gain solutions on Sgr A* were derived using the same (observing band-dependent) models used in G. C. Bower et al. (2015), whose apparent, angular-broadened size as a function of wavelength are consistent with past measurements (G. C. Bower et al. 2006). Astrometric results are obtained from fitting in the image domain and are reported in Table 1. As a result of this calibration scheme, the fundamental measurement of this experiment is the position of the magnetar relative to the position of Sgr A*.

In G. C. Bower et al. (2015), we determined ICRF positions for the magnetar using the astrometry from M. J. Reid & A. Brunthaler (2004) with a proper motion of Sgr A* $\mu_{SgrA*} = (-3.151, -5.547)$ mas yr⁻¹ and position (17:45:40.0366, −29:00:28.217) at epoch 2014.145 (MJD = 56710). In this paper, we update the reference position and proper motion based on more recent measurements. We adopt a proper motion $\mu_{SgrA*} = (-3.156, -5.585)$ mas yr⁻¹ from M. J. Reid & A. Brunthaler (2020), which is consistent within the errors of the 2004 measurement. An improved value for the position has
<table><caption>**Table 1**
Observed Positions of PSR J1745-2900</caption><thead><tr><th>MJD</th><th>Band</th><th>ICRF R.A.<br>(J2000)</th><th>ICRF Decl.<br>(J2000)</th><th>Δα<br>(mas)</th><th>Δδ<br>(mas)</th></tr></thead><tbody><tr><td>56422</td><td>X</td><td>17 45 40.164031 ± 0.000020</td><td>-29 00 29.8902 ± 00.0002</td><td>1699.97 ± 0.26</td><td>-1683.38 ± 0.20</td></tr><tr><td>56444</td><td>X</td><td>17 45 40.163981 ± 0.000012</td><td>-29 00 29.8904 ± 00.0001</td><td>1699.50 ± 0.16</td><td>-1683.24 ± 0.10</td></tr><tr><td>56473</td><td>Ku</td><td>17 45 40.163917 ± 0.000008</td><td>-29 00 29.8904 ± 00.0001</td><td>1698.91 ± 0.10</td><td>-1682.80 ± 0.10</td></tr><tr><td>56486</td><td>X</td><td>17 45 40.163876 ± 0.000008</td><td>-29 00 29.8907 ± 00.0001</td><td>1698.49 ± 0.10</td><td>-1682.90 ± 0.10</td></tr><tr><td>56658</td><td>Ku</td><td>17 45 40.163918 ± 0.000007</td><td>-29 00 29.8902 ± 00.0001</td><td>1700.52 ± 0.09</td><td>-1679.79 ± 0.10</td></tr><tr><td>...</td><td>X</td><td>17 45 40.163930 ± 0.000010</td><td>-29 00 29.8902 ± 00.0001</td><td>1700.68 ± 0.13</td><td>-1679.79 ± 0.10</td></tr><tr><td>56710</td><td>Ku</td><td>17 45 40.163903 ± 0.000005</td><td>-29 00 29.8902 ± 00.0001</td><td>1700.77 ± 0.07</td><td>-1679.00 ± 0.10</td></tr><tr><td>...</td><td>X</td><td>17 45 40.163891 ± 0.000014</td><td>-29 00 29.8904 ± 00.0002</td><td>1700.62 ± 0.18</td><td>-1679.20 ± 0.20</td></tr><tr><td>56750</td><td>K</td><td>17 45 40.163889 ± 0.000004</td><td>-29 00 29.8903 ± 00.0001</td><td>1700.94 ± 0.05</td><td>-1678.49 ± 0.10</td></tr><tr><td>...</td><td>Q</td><td>17 45 40.163892 ± 0.000003</td><td>-29 00 29.8901 ± 00.0001</td><td>1700.98 ± 0.04</td><td>-1678.29 ± 0.10</td></tr><tr><td>56772</td><td>X</td><td>17 45 40.163900 ± 0.000016</td><td>-29 00 29.8900 ± 00.0002</td><td>1701.27 ± 0.21</td><td>-1677.86 ± 0.20</td></tr><tr><td>...</td><td>Ku</td><td>17 45 40.163858 ± 0.000008</td><td>-29 00 29.8903 ± 00.0001</td><td>1700.72 ± 0.10</td><td>-1678.16 ± 0.10</td></tr><tr><td>56892</td><td>Ku</td><td>17 45 40.163850 ± 0.000028</td><td>-29 00 29.8902 ± 00.0003</td><td>1701.65 ± 0.37</td><td>-1676.15 ± 0.30</td></tr><tr><td>56899</td><td>K</td><td>17 45 40.163904 ± 0.000025</td><td>-29 00 29.8902 ± 00.0003</td><td>1702.42 ± 0.33</td><td>-1676.06 ± 0.30</td></tr><tr><td>...</td><td>Q</td><td>17 45 40.163868 ± 0.000005</td><td>-29 00 29.8900 ± 00.0001</td><td>1701.95 ± 0.07</td><td>-1675.90 ± 0.10</td></tr><tr><td>57073</td><td>X</td><td>17 45 40.163893 ± 0.000047</td><td>-29 00 29.8905 ± 00.0004</td><td>1703.78 ± 0.62</td><td>-1673.72 ± 0.40</td></tr><tr><td>...</td><td>Ku</td><td>17 45 40.163846 ± 0.000010</td><td>-29 00 29.8898 ± 00.0002</td><td>1703.16 ± 0.13</td><td>-1673.02 ± 0.20</td></tr><tr><td>57220</td><td>Ku</td><td>17 45 40.163862 ± 0.000016</td><td>-29 00 29.8894 ± 00.0003</td><td>1704.65 ± 0.21</td><td>-1670.33 ± 0.30</td></tr><tr><td>...</td><td>K</td><td>17 45 40.163824 ± 0.000026</td><td>-29 00 29.8893 ± 00.0006</td><td>1704.15 ± 0.34</td><td>-1670.28 ± 0.60</td></tr><tr><td>57387</td><td>Ku</td><td>17 45 40.163806 ± 0.000004</td><td>-29 00 29.8895 ± 00.0001</td><td>1705.36 ± 0.05</td><td>-1667.87 ± 0.10</td></tr><tr><td>...</td><td>K</td><td>17 45 40.163800 ± 0.000003</td><td>-29 00 29.8893 ± 00.0001</td><td>1705.28 ± 0.04</td><td>-1667.72 ± 0.10</td></tr><tr><td>57564</td><td>Ku</td><td>17 45 40.163708 ± 0.000004</td><td>-29 00 29.8893 ± 00.0001</td><td>1705.60 ± 0.05</td><td>-1664.98 ± 0.10</td></tr><tr><td>...</td><td>K</td><td>17 45 40.163696 ± 0.000004</td><td>-29 00 29.8891 ± 00.0001</td><td>1705.44 ± 0.05</td><td>-1664.84 ± 0.10</td></tr><tr><td>...</td><td>X</td><td>17 45 40.163781 ± 0.000015</td><td>-29 00 29.8897 ± 00.0003</td><td>1704.77 ± 0.20</td><td>-1668.60 ± 0.30</td></tr><tr><td>57718</td><td>Ku</td><td>17 45 40.163653 ± 0.000030</td><td>-29 00 29.8886 ± 00.0005</td><td>1706.21 ± 0.39</td><td>-1661.98 ± 0.50</td></tr><tr><td>...</td><td>K</td><td>17 45 40.163619 ± 0.000015</td><td>-29 00 29.8883 ± 00.0003</td><td>1705.76 ± 0.20</td><td>-1661.68 ± 0.30</td></tr><tr><td>57923</td><td>Ku</td><td>17 45 40.163609 ± 0.000006</td><td>-29 00 29.8887 ± 00.0001</td><td>1707.41 ± 0.08</td><td>-1658.95 ± 0.09</td></tr><tr><td>58060</td><td>Ku</td><td>17 45 40.163611 ± 0.000006</td><td>-29 00 29.8883 ± 00.0001</td><td>1708.62 ± 0.08</td><td>-1656.45 ± 0.08</td></tr><tr><td>...</td><td>K</td><td>17 45 40.163574 ± 0.000005</td><td>-29 00 29.8886 ± 00.0001</td><td>1708.14 ± 0.07</td><td>-1656.76 ± 0.09</td></tr><tr><td>58062</td><td>Ku</td><td>17 45 40.163561 ± 0.000010</td><td>-29 00 29.8884 ± 00.0001</td><td>1707.99 ± 0.13</td><td>-1656.45 ± 0.12</td></tr><tr><td>...</td><td>K</td><td>17 45 40.163566 ± 0.000008</td><td>-29 00 29.8884 ± 00.0002</td><td>1708.05 ± 0.10</td><td>-1656.51 ± 0.15</td></tr><tr><td>58070</td><td>Ku</td><td>17 45 40.163554 ± 0.000011</td><td>-29 00 29.8887 ± 00.0002</td><td>1707.96 ± 0.14</td><td>-1656.63 ± 0.15</td></tr><tr><td>...</td><td>K</td><td>17 45 40.163561 ± 0.000006</td><td>-29 00 29.8885 ± 00.0001</td><td>1708.06 ± 0.08</td><td>-1656.42 ± 0.11</td></tr><tr><td>58137</td><td>K</td><td>17 45 40.163532 ± 0.000026</td><td>-29 00 29.8883 ± 00.0006</td><td>1708.25 ± 0.34</td><td>-1655.21 ± 0.60</td></tr><tr><td>58178</td><td>K</td><td>17 45 40.163528 ± 0.000008</td><td>-29 00 29.8881 ± 00.0002</td><td>1708.55 ± 0.10</td><td>-1654.46 ± 0.16</td></tr><tr><td>58274</td><td>K</td><td>17 45 40.163514 ± 0.000010</td><td>-29 00 29.8885 ± 00.0003</td><td>1709.20 ± 0.13</td><td>-1653.36 ± 0.29</td></tr><tr><td>58318</td><td>K</td><td>17 45 40.163528 ± 0.000015</td><td>-29 00 29.8881 ± 00.0003</td><td>1709.76 ± 0.20</td><td>-1652.25 ± 0.33</td></tr><tr><td>58405</td><td>Ku</td><td>17 45 40.163542 ± 0.000015</td><td>-29 00 29.8871 ± 00.0002</td><td>1710.70 ± 0.20</td><td>-1649.99 ± 0.20</td></tr><tr><td>...</td><td>K</td><td>17 45 40.163482 ± 0.000014</td><td>-29 00 29.8877 ± 00.0003</td><td>1709.91 ± 0.18</td><td>-1650.54 ± 0.30</td></tr><tr><td>58406</td><td>Ku</td><td>17 45 40.163542 ± 0.000015</td><td>-29 00 29.8871 ± 00.0002</td><td>1710.71 ± 0.20</td><td>-1649.98 ± 0.20</td></tr><tr><td>...</td><td>K</td><td>17 45 40.163492 ± 0.000014</td><td>-29 00 29.8880 ± 00.0003</td><td>1710.05 ± 0.18</td><td>-1650.88 ± 0.25</td></tr></tbody></table>

Note. The horizontal line indicates the separation between previously published (G. C. Bower et al. 2015, 2016) and new data.

also been presented in D. Gordon et al. (2023), which we adopt here: (17:45:40.034047, -29:00:28.21601) at epoch 2015.0. This position corresponds to a shift of (40.1, 8.8) mas relative to the position from M. J. Reid & A. Brunthaler (2004) at epoch 2015.0. Coordinates in the ICRF (Δα, Δδ) are given relative to this new fiducial Sgr A* position and proper motion. For epochs published in G. C. Bower et al. (2015), the ICRF values reported here are an update. The relative position of the magnetar to Sgr A* as a function of time are shown in Figure 1.

We also produce fits to the observed (scatter-broadened) size of the magnetar based on the fitting of a two-dimensional Gaussian component to the clean image followed by deconvolution of the synthesized beam (Table 2). We note that this approach is sensitive to the modeled size of Sgr A* (as it is used as a calibration source) and, furthermore, that image deconvolution (and the alternative approach of visibility model fitting) are increasingly challenging at low signal-to-noise

ratios (S/Ns) and for highly resolved sources. Accordingly, we produce these fits only for a single band (2 cm) where we have the most significant detections (S/N > 30).

### 3. Astrometric Analysis

We analyze the relative astrometric data in the same manner as in G. C. Bower et al. (2015). The fitting is done relative to the following functional form:

$$ \begin{aligned} \Delta\alpha &= \Delta\alpha_0 + f_{\alpha}(\pi, \alpha, \delta) + \mu_{\alpha} * (\text{MJD} - \text{MJD}_0) \\ &\quad + \frac{1}{2}a_{\alpha} * (\text{MJD} - \text{MJD}_0)^2 - \Phi_{\alpha} \lambda \\ \Delta\delta &= \Delta\delta_0 + f_{\delta}(\pi, \alpha, \delta) + \mu_{\delta} * (\text{MJD} - \text{MJD}_0) \\ &\quad + \frac{1}{2}a_{\delta} * (\text{MJD} - \text{MJD}_0)^2 - \Phi_{\delta} \lambda. \end{aligned} \quad (1) $$
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Position as a function of time for PSR J1745−2900 relative to Sgr A*. Different colors are used to identify the wavelength of the observations. The solid black line shows the best-fit proper motion in each coordinate with $\mu_{\alpha} = 2.04$ mas yr$^{-1}$ and $\mu_{\delta} = 6.07$ mas yr$^{-1}$. Fits including acceleration and core shift are indistinguishable on this scale.</figcaption></figure>

<table><caption>**Table 2**
Observed Sizes of PSR J1745−2900 at 2 cm Wavelength</caption><thead><tr><th>MJD</th><th>Major Axis<br>(mas)</th><th>Minor Axis<br>(mas)</th><th>Position Angle<br>(deg)</th></tr></thead><tbody><tr><td>56473</td><td>5.4<sup>+0.5</sup><sub>-0.5</sub></td><td>2.3<sup>+1.0</sup><sub>-2.0</sub></td><td>78<sup>+10</sup><sub>-9</sub></td></tr><tr><td>56658</td><td>4.9<sup>+0.6</sup><sub>-0.5</sub></td><td>3.0<sup>+1.1</sup><sub>-1.7</sub></td><td>78<sup>+17</sup><sub>-16</sub></td></tr><tr><td>56710</td><td>5.0<sup>+0.3</sup><sub>-0.3</sub></td><td>2.1<sup>+0.7</sup><sub>-1.1</sub></td><td>84<sup>+6</sup><sub>-7</sub></td></tr><tr><td>56772</td><td>5.5<sup>+0.5</sup><sub>-0.5</sub></td><td>3.6<sup>+0.8</sup><sub>-1.0</sub></td><td>79<sup>+13</sup><sub>-13</sub></td></tr><tr><td>56892</td><td>7.0<sup>+1.9</sup><sub>-2.1</sub></td><td>2.3<sup>+3.1</sup><sub>-2.3</sub></td><td>77<sup>+28</sup><sub>-24</sub></td></tr><tr><td>57387</td><td>5.0<sup>+0.3</sup><sub>-0.3</sub></td><td>2.9<sup>+0.6</sup><sub>-0.8</sub></td><td>80<sup>+9</sup><sub>-8</sub></td></tr><tr><td>57564</td><td>5.3<sup>+0.3</sup><sub>-0.3</sub></td><td>2.6<sup>+0.5</sup><sub>-0.6</sub></td><td>83<sup>+6</sup><sub>-5</sub></td></tr><tr><td>57923</td><td>5.1<sup>+0.5</sup><sub>-0.5</sub></td><td>2.7<sup>+0.7</sup><sub>-0.9</sub></td><td>75<sup>+10</sup><sub>-9</sub></td></tr><tr><td>58070</td><td>4.7<sup>+0.5</sup><sub>-4.7</sub></td><td>1.6<sup>+2.9</sup><sub>-1.6</sub></td><td>85<sup>+9</sup><sub>-9</sub></td></tr><tr><td>Average</td><td>5.2 ± 0.2</td><td>2.7 ± 0.4</td><td>81 ± 3</td></tr></tbody></table>

**Note.** The horizontal line indicates the separation between previously published (G. C. Bower et al. 2015, 2016) and new data.

Fitted terms include the parallax ($\pi$), proper motion ($\mu_{\alpha}$, $\mu_{\delta}$), acceleration ($a_{\alpha}$, $a_{\delta}$), and core shift ($\Phi_{\alpha}$, $\Phi_{\delta}$) as a function of wavelength $\lambda$. ($f_{\alpha}$, $f_{\delta}$) are the predictions for the effect of the

parallax $\pi$ at a given position $(\alpha, \delta)$, relative to the parallax of Sgr A*. The mean epoch of the data is MJD$_0 = 57424.7$. Fits are obtained for progressively more complex sets of parameters: first, proper motion only; second, proper motion plus acceleration; third, proper motion plus core shift; fourth, proper motion plus acceleration and core shift; and fifth, proper motion plus parallax. The results of the first four fits are summarized in Table 3, with residuals to principal models shown in Figure 2. The first two fits are performed with both bootstrap and least squares (LSQ) methods as a means of confirming the accuracy of error estimates (Figure 3). The bootstrap method uses $10^4$ astrometric series via sampling with replacement. We find good consistency in estimates of parameters and their errors across different fits and methods.

The LSQ methods produce a $\chi^2$ statistic that can be used to validate the quality of the fit. Declination (decl.) fits improve with the introduction of an acceleration term but do not improve with the introduction of the core shift term. Residuals remain significantly in excess of 1, however, indicative of the presence of systematic errors or underestimated thermal errors. When we add in a quadrature systematic uncertainty of ~0.15 mas to all measurements, we find $\chi^2 \sim 1$ for all decl. fits.
<table><caption>**Table 3**

Astrometric Fits for PSR J1745−2900</caption><thead><tr><th>Parameter</th><th>Units</th><th>PM Bootstrap</th><th>PM Bootstrap + Accel.</th><th>PM LSQ</th><th>PM + Accel.</th><th>PM + Core Shift</th><th>PM + Accel. + Core Shift</th></tr></thead><tbody><tr><td>Δα<sub>0</sub></td><td>(mas)</td><td>1704.86 ± 0.11</td><td>1705.12 ± 0.17</td><td>1704.86 ± 0.07</td><td>1705.15 ± 0.08</td><td>1704.89 ± 0.18</td><td>1705.09 ± 0.15</td></tr><tr><td>Δδ<sub>0</sub></td><td>(mas)</td><td>-1667.13 ± 0.03</td><td>-1667.27 ± 0.05</td><td>-1667.13 ± 0.03</td><td>-1667.27 ± 0.05</td><td>-1667.18 ± 0.09</td><td>-1667.24 ± 0.08</td></tr><tr><td>μ<sub>α</sub></td><td>(mas yr<sup>-1</sup>)</td><td>2.04 ± 0.04</td><td>2.01 ± 0.03</td><td>2.04 ± 0.04</td><td>2.01 ± 0.04</td><td>2.04 ± 0.04</td><td>2.01 ± 0.04</td></tr><tr><td>μ<sub>δ</sub></td><td>(mas yr<sup>-1</sup>)</td><td>6.07 ± 0.02</td><td>6.09 ± 0.02</td><td>6.07 ± 0.02</td><td>6.09 ± 0.02</td><td>6.08 ± 0.02</td><td>6.09 ± 0.02</td></tr><tr><td>a<sub>α</sub></td><td>(mas yr<sup>-2</sup>)</td><td>...</td><td>-0.238 ± 0.089</td><td>...</td><td>-0.252 ± 0.052</td><td>...</td><td>-0.256 ± 0.054</td></tr><tr><td>a<sub>δ</sub></td><td>(mas yr<sup>-2</sup>)</td><td>...</td><td>0.089 ± 0.033</td><td>...</td><td>0.089 ± 0.027</td><td>...</td><td>0.094 ± 0.029</td></tr><tr><td>Φ<sub>α</sub></td><td>(mas cm<sup>-1</sup>)</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.02 ± 0.10</td><td>-0.04 ± 0.08</td></tr><tr><td>Φ<sub>δ</sub></td><td>(mas cm<sup>-1</sup>)</td><td>...</td><td>...</td><td>...</td><td>...</td><td>-0.03 ± 0.04</td><td>0.02 ± 0.04</td></tr><tr><td>χ<sup>2</sup><sub>α</sub>/d.o.f.<sub>α</sub></td><td>...</td><td>...</td><td>...</td><td>852.9/39</td><td>530.1/38</td><td>851.9/38</td><td>527.3/37</td></tr><tr><td>χ<sup>2</sup><sub>δ</sub>/d.o.f.<sub>δ</sub></td><td>...</td><td>...</td><td>...</td><td>85.4/39</td><td>66.0/38</td><td>84.2/38</td><td>65.7/37</td></tr><tr><td colspan="8" style="text-align: center;">Fits without first four epochs</td></tr><tr><td>Δα<sub>0</sub></td><td>(mas)</td><td>1704.88 ± 0.11</td><td>1705.11 ± 0.18</td><td>1704.88 ± 0.06</td><td>1705.14 ± 0.08</td><td>1704.71 ± 0.19</td><td>1705.01 ± 0.17</td></tr><tr><td>Δδ<sub>0</sub></td><td>(mas)</td><td>-1667.14 ± 0.03</td><td>-1667.27 ± 0.06</td><td>-1667.14 ± 0.03</td><td>-1667.27 ± 0.05</td><td>-1667.17 ± 0.09</td><td>-1667.27 ± 0.09</td></tr><tr><td>μ<sub>α</sub></td><td>(mas yr<sup>-1</sup>)</td><td>2.00 ± 0.04</td><td>2.00 ± 0.03</td><td>2.01 ± 0.04</td><td>2.00 ± 0.04</td><td>2.00 ± 0.04</td><td>2.00 ± 0.04</td></tr><tr><td>μ<sub>δ</sub></td><td>(mas yr<sup>-1</sup>)</td><td>6.09 ± 0.02</td><td>6.09 ± 0.02</td><td>6.09 ± 0.02</td><td>6.09 ± 0.02</td><td>6.09 ± 0.02</td><td>6.09 ± 0.02</td></tr><tr><td>a<sub>α</sub></td><td>(mas yr<sup>-2</sup>)</td><td>...</td><td>-0.223 ± 0.103</td><td>...</td><td>-0.242 ± 0.057</td><td>...</td><td>-0.237 ± 0.057</td></tr><tr><td>a<sub>δ</sub></td><td>(mas yr<sup>-2</sup>)</td><td>...</td><td>0.094 ± 0.042</td><td>...</td><td>0.096 ± 0.033</td><td>...</td><td>0.096 ± 0.034</td></tr><tr><td>Φ<sub>α</sub></td><td>(mas cm<sup>-1</sup>)</td><td>...</td><td>...</td><td>...</td><td>...</td><td>-0.11 ± 0.11</td><td>-0.08 ± 0.10</td></tr><tr><td>Φ<sub>δ</sub></td><td>(mas cm<sup>-1</sup>)</td><td>...</td><td>...</td><td>...</td><td>...</td><td>-0.02 ± 0.05</td><td>0.00 ± 0.05</td></tr><tr><td>χ<sup>2</sup><sub>α</sub>/d.o.f.<sub>α</sub></td><td>...</td><td>...</td><td>...</td><td>681.6/35</td><td>445.7/34</td><td>662.5/34</td><td>436.6/33</td></tr><tr><td>χ<sup>2</sup><sub>δ</sub>/d.o.f.<sub>δ</sub></td><td>...</td><td>...</td><td>...</td><td>69.8/35</td><td>56.0/34</td><td>69.5/34</td><td>56.0/33</td></tr><tr><td colspan="8" style="text-align: center;">Fits with estimated systematic uncertainty included</td></tr><tr><td>Δα<sub>0</sub></td><td>(mas)</td><td>1704.78 ± 0.07</td><td>1704.96 ± 0.13</td><td>1704.78 ± 0.07</td><td>1704.96 ± 0.12</td><td>1704.69 ± 0.20</td><td>1704.80 ± 0.20</td></tr><tr><td>Δδ<sub>0</sub></td><td>(mas)</td><td>-1667.11 ± 0.04</td><td>-1667.27 ± 0.06</td><td>-1667.11 ± 0.04</td><td>-1667.27 ± 0.06</td><td>-1667.17 ± 0.11</td><td>-1667.24 ± 0.10</td></tr><tr><td>μ<sub>α</sub></td><td>(mas yr<sup>-1</sup>)</td><td>2.01 ± 0.04</td><td>2.01 ± 0.04</td><td>2.01 ± 0.04</td><td>2.01 ± 0.04</td><td>2.02 ± 0.04</td><td>2.03 ± 0.04</td></tr><tr><td>μ<sub>δ</sub></td><td>(mas yr<sup>-1</sup>)</td><td>6.09 ± 0.02</td><td>6.10 ± 0.02</td><td>6.09 ± 0.02</td><td>6.10 ± 0.02</td><td>6.09 ± 0.02</td><td>6.09 ± 0.02</td></tr><tr><td>a<sub>α</sub></td><td>(mas yr<sup>-2</sup>)</td><td>...</td><td>-0.113 ± 0.074</td><td>...</td><td>-0.111 ± 0.057</td><td>...</td><td>-0.125 ± 0.059</td></tr><tr><td>a<sub>δ</sub></td><td>(mas yr<sup>-2</sup>)</td><td>...</td><td>0.098 ± 0.037</td><td>...</td><td>0.100 ± 0.030</td><td>...</td><td>0.104 ± 0.032</td></tr><tr><td>Φ<sub>α</sub></td><td>(mas cm<sup>-1</sup>)</td><td>...</td><td>...</td><td>...</td><td>...</td><td>-0.04 ± 0.10</td><td>-0.09 ± 0.10</td></tr><tr><td>Φ<sub>δ</sub></td><td>(mas cm<sup>-1</sup>)</td><td>...</td><td>...</td><td>...</td><td>...</td><td>-0.03 ± 0.05</td><td>0.02 ± 0.05</td></tr><tr><td>χ<sup>2</sup><sub>α</sub>/d.o.f.<sub>α</sub></td><td>...</td><td>...</td><td>...</td><td>51.1/39</td><td>46.4/38</td><td>50.9/38</td><td>45.3/37</td></tr><tr><td>χ<sup>2</sup><sub>δ</sub>/d.o.f.<sub>δ</sub></td><td>...</td><td>...</td><td>...</td><td>45.3/39</td><td>34.9/38</td><td>44.9/38</td><td>34.8/37</td></tr></tbody></table>

Note. PM and Accel. refer to proper motion and acceleration fits, respectively.

R.A. fits, on the other hand, show $\chi^2 \gg 1$. In particular, and as already noted by G. C. Bower et al. (2015), the first four epochs appear substantially discrepant. We test the contribution of the first four epochs to the final results by excluding them from the fitting. These results are shown in the middle section of Table 3. While exclusion of these first four epochs does improve $\chi^2$, we find that there is still a significant contribution from the full range of epochs. We find that inclusion of an R.A. systematic uncertainty term of 0.35 mas to each epoch produces $\chi^2 \sim 1$.

The ~2:1 ratio of these systematic error estimates suggests an origin associated with the scattering medium, which produces images that are elongated east-west with a 2:1 axial ratio, unlike the synthesized beam, which is elongated north-south. The scattering size is ~1.4 mas in the major axis at a wavelength of 1.3 cm. Accordingly, for the substantial majority of these measurements, this systematic error term is consistent with a scaling of one-quarter of the beam or less. While many of the plausible sources of error could reasonably be expected to scale positively with the observing wavelength (as the apparent source size is also increasing with wavelength), we note that we see no evidence that this is the case.

However, the observations with both the lowest and highest observing wavelengths are clustered in time early in the observing campaign, meaning that separating time-dependent effects from wavelength-dependent effects is not straightforward. Selection of only the Ku band data, which is often of the highest significance, does not reduce the scatter in R.A. residuals.

The choice of a reduced data set or the inclusion of systematic error changes the precise values of fitted parameters but does not change these values systematically or significantly. Results for proper motion, acceleration, and core shift in both coordinates remain within $1\sigma$ of each other regardless of the choices that are made.

# 4. Results

## 4.1. Astrometric Constraints

The proper motion constraint obtained through these measurements is independent within the errors of whether we fit for additional terms for acceleration, parallax, or core shift. The proper motion value is also consistent with the measurement previously reported in G. C. Bower et al. (2015)
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Astrometric residuals after the fit for proper motion (upper left), and after the fit for proper motion, acceleration, and core shift (lower left).</figcaption></figure>

with a fivefold reduction in the measurement uncertainty. Thus, the central conclusion remains that the proper motion of the magnetar is consistent with neighboring stars in the CW disk of stars and supports the conclusion that the magnetar originated from this stellar disk with a modest initial velocity kick.

For the expected case of the pulsar in orbit around Sgr A* at a radius $r \lesssim 1$ pc, we expect the measured parallax relative to

Sgr A* to be reduced by a factor of $r/D \lesssim 10^{-5} \times$, the expected value for a distant background source, where D is the distance from the Sun to the GC, leading to an expected value on the scale of nanoarcseconds. The current constraint $\pi < 0.4$ mas (Figure 3) is therefore consistent with the pulsar being located at the GC.

In the case that the magnetar is at a minimal separation from Sgr A* given by the projected distance, the maximal
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Upper left: empirical probability density distribution of proper motion solutions from the bootstrap resampling method. Upper right: distribution of the measured parallax π of the magnetar referenced to Sgr A*. The upper limit at 95% confidence of π < 0.6 mas is consistent with the expectation that the magnetar is located in the GC. Lower left: empirical probability density distribution of acceleration from the bootstrap resampling method. Vertical dotted lines indicate the maximum acceleration terms as the result of acceleration by Sgr A*.</figcaption></figure>

acceleration in each coordinate is determined by the inverse-
square law to be |a| ≈ 0.029 mas yr⁻². The uncertainty in the
acceleration estimate exceeds this value, albeit only minimally
in the case of the decl. coordinate. One can estimate the
requirements for a future detection of the acceleration in the
event that the magnetar rebrightens. A second measurement of
the proper motion with the obtained uncertainty of
(0.06, 0.02) mas yr⁻¹ in the two coordinates obtained at a
separation of 10 yr would provide a (5, 10)σ detection of the
acceleration. Such a detection would provide definitive
confirmation that the magnetar is bound to Sgr A* and a
direct measure of the separation of these two sources. A
sample of stars at similar radii have measured accelerations
from over two decades of NIR astrometric monitoring
(A. Young et al. 2023).

As noted above, the measured positions in decl. are
consistent with no variations from linear motion with the
inclusion of a small systematic error. On the other hand,
residuals in R.A. show large variations that have the
appearance of systematic changes. In G. C. Bower et al.
(2015), we identify two sources of calibration error that could
introduce systematic astrometric errors: first, errors in the

scattering model for Sgr A* that are proportionally larger in
R.A. than decl., and second, calibration of the phased VLA
used in the first four epochs. The latter of these does not apply
to the long timescale variations seen in these data.
Astrophysical sources of systematic error could arise from
changes in the apparent centroid position of Sgr A*, which we
discuss in Section 4.3, refractive image wander, and the
influence of a binary companion.

Refractive wander occurs as the result of changes of the
large-scale index of refraction due to the relative motion of the
source and the turbulent scattering screen. The refractive
timescale $\tau_R \sim d\theta/v$, where d is the distance from the Earth to
the scattering screen, $\theta$ is the angular broadening, and $v$ is the
relative velocity. For $d \approx 3$ kpc and $v \approx 250$ km s$^{-1}$, we find
$\tau_R \gtrsim 300$ days at $\lambda = 2$ cm. Notably, refractive wander is
wavelength dependent, whereas the systematic error in our
residuals does not exhibit an obvious wavelength dependence.
This absence is reflected in the null detections of a systematic
core shift, which scales with $\lambda$. Further, if the plasma column
probed by the magnetar sightline is broadly comparable to that
probed by Sgr A*, the long-term stability of the apparent size
(G. C. Bower et al. 2006; I. Cho et al. 2022) and proper motion
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Lomb–Scargle periodogram of the astrometric and timing data (R. Eatough et al. 2025, in preparation). Periodic signals comparable to the data set length are often indicative of red noise variability. A linear trend has been removed from the timing residuals before calculation of the periodogram. Calculation of the periodogram without the linear trend does not significantly alter the results.</figcaption></figure>

(M. J. Reid & A. Brunthaler 2020) of Sgr A* argues against substantial refractive wander effects.

We consider the possibility of a binary companion to the magnetar as the source of the astrometric residuals. By eye, an apparent ~1 mas sinusoidal variation in the R.A. can be seen, with a period comparable to the data set length. A Lomb–Scargle periodogram analysis confirms that there is significant power on the longest timescale ~1600 days (Figure 4). For the decl. residuals, we see no timescales on which there is significant periodicity up to the length of the data set. A fit to the astrometric residuals for a binary companion reveals a set of orbits that match the broad features of the data (Figure 5). The best-fit solution finds a period *P* = 1600 ± 200 days, an inclination angle *i* = 95° ± 23° (i.e., nearly face on), and a semimajor axis *a* = 3.3 ± 1.0 au. Markov Chain Monte Carlo optimization shows broad distributions around these quantities. The most highly inclined orbits provide the least constraint on the semimajor axis and eccentricity. For a pulsar mass *M*<sub>P</sub> = 1.4*M<sub>☉</sub>*, the companion mass has a median value *M*<sub>2</sub> = 5.5*M<sub>☉</sub>* but with ±2*σ* values that range from 0.9 < *M*<sub>2</sub> < 35*M<sub>☉</sub>*. High-mass stellar companions are ruled out by NIR imaging, which have main-sequence detection limits of ≳3*M<sub>☉</sub>.

(R. Genzel et al. 2010; B. Ali et al. 2020), meaning that any such putative companion would necessarily be a neutron star or black hole—possibly making PSR J1745−2900 the first pulsar–black hole binary.

A binary companion will introduce a residual in the timing of the pulsar signal with the same period as the astrometric variations. A 10*M<sub>☉</sub>* companion at a separation of 1 mas would accelerate the pulsar, producing a change *P* ~ 10<sup>-11</sup>, which is comparable to the observed *P* = -6 × 10<sup>12</sup> (V. M. Kaspi et al. 2014). However, timing measurements for the magnetar are difficult, given the unstable magnetar pulse profile, the possibility of glitches in the timing, the long-term reduction in the pulse flux density, and general timing noise seen in magnetars and young pulsars. Timing analysis of an extensive data set spanning ~3400 days does not find evidence for a periodic signal consistent with the astrometric period (R. Eatough et al. 2025, in preparation). The periodogram of the pulse period reveals peak power at ~3100 days (Figure 4), nearly twice the period favored by variations in the VLBI positions in R.A. In the case of both the astrometric and timing data, the peak period is close to the observational duration. Additionally, the best-fit astrometric
<figure><img src="image_7.png" /><figcaption>**Figure 5.** The binary model (solid lines) from fitting astrometric data alone, plotted against the residual period from R. Eatough et al. (2025, in preparation) (top) and the astrometric data in R.A. (middle) and decl. (bottom). The plotted binary model has a semimajor axis *a* = 3.3 au, inclination angle *i* = −83°, and period *P* = 1600 days. A linear trend has been removed from the period to produce the residual value. While the magnitude of the variations are comparable between the period and astrometric data, there is no good correlation between the two. More sophisticated modeling of variations in the period by R. Eatough et al. (2025, in preparation) limits the residuals to be much less than predicted by the VLBI orbital fit.</figcaption></figure>

model is a poor fit to the timing data (Figure 5). Joint fits fail to find an adequate solution without the introduction of large systematic errors. R. Eatough et al. (2025, in preparation) conduct a more extensive binary analysis of the timing data that incorporates red noise corresponding to intrinsic magnetar pulse properties and also find that a high-mass companion to the magnetar is ruled out.

We conclude that no potential effect considered here provides a compelling explanation for the residual astrometric variations. The inconsistency between the pulsar period measurements and the astrometry appears to eliminate a binary companion model. The alternative explanations of refractive wander and variations in the morphology of Sgr A* could potentially produce residuals of the appropriate magnitude. The absence of a clear signature of a frequency-dependent effect, however, undermines the case for refractive wander. Structural changes in Sgr A* may also be inconsistent with the long-term accuracy of the independent astrometry and morphology measurements made of Sgr A*. We do note,

though, that many of those measurements are made at shorter wavelengths, where effects may be smaller.

## 4.2. Angular Broadening and the Detectability of Pulsars in the GC

The apparent size of the magnetar as a function of time for the *Ku* band (15 GHz) is shown in Figure 6, including results previously reported. For these high S/N epochs, we see no evidence for change in major axis size, minor axis size, and position angle over time. The mean sizes are consistent with past measurements of the magnetar reported in G. C. Bower et al. (2015) and, therefore, also with past measurements of Sgr A*. We set $3\sigma$ upper limits on a linear change in the major axis of $<0.3 \text{ mas yr}^{-1}$, approximately $<6\%$ per year.

The sizes for the magnetar are derived following self-calibration of the visibilities on Sgr A* with a standard model. This self-calibration does not force the magnetar size to be the same as Sgr A*, but it *does* enforce a time-independent size for Sgr A*. Thus, the results do rule out independent variations of
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Apparent size of the magnetar at 2 cm wavelength as a function of time for Gaussian deconvolutions of the image size in major axis (top), minor axis (middle), and position angle (bottom) parameters. Observations previously reported in G. C. Bower et al. (2015) are before MJD 57000. The red dashed line is the weighted mean for each parameter.</figcaption></figure>

the magnetar size relative to Sgr A*, but they do not rule out coherent variations in the size of the two sources. However, variations in the size of Sgr A* have been explored extensively without evidence for secular changes (G. C. Bower et al. 2006; I. Cho et al. 2022).

The timescale for refractive variations at 15 GHz is ≳300 days, significantly shorter than the >4 yr timescale of the magnetar measurements. This stability is in contrast to the variations seen with other interstellar propagation measurements seen toward the magnetar. Both the DM and the RM have been seen to vary over a range of timescales (G. Desvignes et al. 2018). The DM has a component that arises from the integrated electron population along the line of sight and varies by less than 1% over 4 yr. On the other hand, the RM varies by ~5% on a range of timescales. The majority of the RM likely arises from the central ~10 pc, consistent with the profile of electron densities traced by diffuse X-ray gas (and magnetic fields), with variations arising from the most turbulent components of the plasma at a distance of ~0.1 pc from Sgr A* (R. P. Eatough et al. 2013). The lack of similar variations in the scattering properties further supports the interpretation that the different propagation effects arise from different regions of the ISM.

The angular broadening is dominated by material arising at a distance of ~5 kpc from the GC, most likely associated with a supernova remnant in a spiral arm (G. C. Bower et al. 2014; J. Dexter et al. 2017). Additionally, modeling the source structure as a function of the pulse phase suggests additionally that the scattering is dominated by a single screen (O. Wucknitz 2014). This single scattering screen would be insufficient to obscure ordinary pulsars in the GC from existing searches. Nevertheless, given the potential significance of scattering, we consider the degree to which a second scattering screen can be constrained by these data. We can take the upper limit on secular variation of the major axis (or the uncertainty in the major axis) as an estimate of the contribution of an additional, time-variable GC component to the angular broadening.

The temporal scattering timescale $\tau$ for a single thin scattering screen is related to the angular broadening by the following equation:

$$ \tau = 6.2 \text{ s} \times \left( \frac{D}{8.3 \text{ kpc}} \right) \left( \frac{\theta_1}{1.3} \right)^2 \left( \frac{D}{\Delta} - 1 \right) \nu^{-4}, \quad (2) $$

where $D = 8.3$ kpc (T. Do et al. 2019; GRAVITY Collaboration et al. 2022) is the distance to the GC, $\Delta$ is the distance
from the pulsar to the scattering screen, and $\nu$ is the observing frequency in GHz (J. M. Cordes & T. J. W. Lazio 1997). $\theta_1$ is the observed angular size extrapolated to a frequency of 1.0 GHz using a scaling of $\nu^{-2}$. If we substitute the mean scattering properties of the magnetar into Equation (2), we find a distance $\Delta = 5.8 \pm 0.3$ kpc.

Now, we can add in a second thin scattering screen closer to Sgr A* and at a sufficiently large separation from the dominant scattering screen at distance $\Delta$ such that the scattering angular diameters add in quadrature, and the temporal broadening is the sum of the two properties of the two screens. We assume that this second scattering screen was not present at the beginning of the observations of PSR J1745-2900 when the scattering size was $\theta$ and was present at the end of the observations. Observationally, we constrain that the observed scattering size has not changed by more than the limit on the total secular change $\delta\theta$ in the source size. In this case, the maximum angular broadening attributed to the second scattering screen is $\theta_1^s = \sqrt{2\theta\delta\theta} = 0.4$ at 1 GHz. We also require that the temporal broadening cannot have changed so much that the pulses would be temporally broadened significantly, which depends on the distance $\Delta^s$ of the second scattering screen from the GC. Under these assumptions, a secondary scattering screen at $\Delta^s \lesssim 3$ kpc would produce additional scattering $\tau^s > 1$ s, making the magnetar unobservable. Smaller variations in the angular broadening, therefore, would be consistent with PSR J1745-2900 remaining observable throughout these observations. An order of magnitude improvement in the uncertainty of the angular broadening would set a limit $\Delta^s \gtrsim 0.5$ kpc.

Together, these results find no evidence for the existence of a second strong scattering screen in the GC that would obscure a population of GC pulsars. To accommodate such a model, the ionized ISM must be patchy on scales larger than the distance traversed by the pulsar in the course of these observations, ~200 au, larger than estimates of the inner scale of turbulence. Based on diffractive properties of the scattering, the inner scale of turbulence is estimated to be 800 ± 200 km (M. D. Johnson et al. 2018). On larger scales, S. Roy (2013) estimated patchiness in the ionized ISM of the GC to exist on a scale of 10', approximately 20 pc. Filaments and other features in the GC can have much smaller angular scales (I. Heywood et al. 2022).

### 4.3. Constraints on Sgr A*

A wide variety of constraints have not yet resolved the question of whether Sgr A* has a jet feature. Most recently, analysis of EHT images and polarimetric data with GRMHD models suggests that a small-scale jet may be present, but definitive evidence does not exist (Event Horizon Telescope Collaboration et al. 2022b, 2024). One of the expected signatures of an inhomogeneous jet would be the presence of a core shift, i.e., a shift in the centroid of Sgr A* proportional to wavelength, as a result of variations in the optical depth (R. D. Blandford & A. Königl 1979; H. Falcke et al. 2009; M. Mościbrodzka et al. 2014; R. Fraga-Encinas et al. 2023). This effect has been clearly seen in the jet of M87 (K. Hada et al. 2011). Since the pulsar positions are measured relative to Sgr A* in each epoch, the wavelength dependence of the positions can be used to constrain the core shift.

With a much smaller subset of observations, G. C. Bower et al. (2015) searched inconclusively for this effect. With the much larger sample of epochs with two frequency measurements in this paper, and excluding the anomalous first four epochs, we find a mean value for the core shift $\Phi = (-0.11 \pm 0.11, -0.02 \pm 0.05)$ mas cm$^{-1}$, which is also consistent with zero. Different methods of estimation of the mean core shift in Table 3 give similar values and uncertainties. Individual epochs, however, show a large scatter that formally indicates detection in those epochs. The origin of this scatter is unclear, but it is possibly related to the sources of systematic error discussed previously for the overall position errors or to intrinsic effects in Sgr A*. The east-west scatter is significantly larger than the north-south scatter, consistent with an origin related to the scattering asymmetry.

The measured average meets the expectations for jet models, which predict $\Phi \sim 0.1$ mas cm$^{-1}$, comparable to the uncertainty that we achieve with these measurements (M. Mościbrodzka et al. 2014). We show two of these models for inclination angles of 30° and 60° in Figure 7. Constraints based on EHT observations favor models with $i < 60°$ (Event Horizon Telescope Collaboration et al. 2022b). These more recent models based on EHT observations predict a core shift of a similar magnitude. It is also possible that the scatter in individual measurements is the result of changes in the large-scale structure of Sgr A* as the result of turbulent jet outflows or structures in the accretion flow. Time-variable structures of this kind could have characteristic timescales as short as the variability timescales measured for Sgr A* at these wavelengths, i.e., tens of minutes to hours (e.g., C. D. Brinkerink et al. 2015).

## 5. Conclusions

We have presented extensive new astrometric and high-resolution imaging observations of the GC magnetar PSR J1745-2900, extending until the magnetar flux density weakened to undetectable levels. The results provide significantly higher accuracy and greater temporal coverage that support previously published conclusions. The primary results are:

1. The proper motion remains consistent with the population of stars from the CW stellar disk, supporting an origin with modest kick velocity from a star in that disk.

2. Significantly stronger limits are set on the tangential acceleration of PSR J1745-2900, which remain consistent with the expectations for the maximum acceleration due to Sgr A*. If the magnetar rebrightens, new observations will have the power to detect the acceleration rapidly given the much longer time baseline.

3. Astrometric residuals in R.A. exhibit an apparently sinusoidal variation with a period of ~1600 days. Pulse period measurements are, however, inconsistent with a binary companion explanation of the astrometric data. Alternative possibilities for the variation, regardless of whether or not it is periodic or red noise, are refractive wander and changes in the structure of Sgr A*. None of these models are entirely good fits to all of the data.

4. The stable apparent size of the magnetar over the duration of these observations stands in contrast to the
<figure><img src="image_9.png" /><figcaption>**Figure 7.** Core shift for the epochs with two frequency observations (black squares) and for the fitted average over all epochs (red circle). Note that the mean core shift includes data from epochs in which both one and two frequency band observations are included, but that single-epoch core shifts are estimated only when more than one frequency is present. The light and dark blue curves show the core shift estimated from GRMHD jet simulations with an inclination angle of 30° and 60° oriented toward different position angles. The average observed core shift is consistent with predictions from the jet model (and with no-jet models), but individual epochs show substantially more scatter.</figcaption></figure>

highly variable RM, supporting a picture in which these propagation effects originate from different regions of the ISM. The results remain consistent with a single turbulent plasma screen at a distance ~5 kpc away from Sgr A*.

5. The results are consistent with a minimal stable core shift, as expected from a compact jet or accretion disk. Individual epochs, however, show significant scatter in the apparent core shift that may be the result of changing structures in Sgr A*, propagation effects, and/or systematic errors in the calibration and imaging.

If PSR J1745-2900 rebrightens so that it is detectable in astrometric experiments, future measurements can measure the acceleration due to Sgr A* and resolve the question of the presence of a binary companion or other sources of apparent short-term position variation. This complex set of results from a single, unique GC pulsar highlights the rich science to be gleaned from searches for and characterization of pulsars in this region with existing and future instruments.

## Acknowledgments

The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. We acknowledge financial support by the Italian Ministry of University and Research (MUR)—Project CUP F53D23001260001, funded by the European Union—NextGenerationEU. This work was partially supported by FAPESP (Fundação de Amparo á Pesquisa do Estado de São Paulo) under grant 2021/01183-8. We acknowledge the European Research Council (ERC) Synergy Grant “BlackHoleCam: Imaging the Event Horizon of Black Holes” (grant 610058) and Synergy Grant “BlackHolistic: Color Movies of Black Holes: Understanding Black Hole Astrophysics from the Event Horizon to Galactic Scales” (grant 10107164).

## ORCID iDs

Geoffrey C. Bower https://orcid.org/0000-0003-4056-9982
Adam T. Deller https://orcid.org/0000-0001-9434-3837
Paul B. Demorest https://orcid.org/0000-0002-6664-965X
Jason Dexter https://orcid.org/0000-0003-3903-0373

Andreas Brunthaler https://orcid.org/0000-0003-4468-761X

Gregory Desvignes https://orcid.org/0000-0003-3922-4055

Ralph P. Eatough https://orcid.org/0000-0001-6196-4135

Heino Falcke https://orcid.org/0000-0002-2526-6724

Ciriaco Goddi https://orcid.org/0000-0002-2542-7743

Michael Kramer https://orcid.org/0000-0002-4175-2271

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