Supplementary Material for "Identifying compact symmetric objects with high-precision VLBI and Gaia astrometry"

Astronomy &Astrophysics manuscript no. output ©ESO 2025 October 6, 2025 Supplementary Material for “Identifying compact symmetric objects with high-precision VLBI and Gaia astrometry” T. An1,2,⋆, Y. Zhang1,2, S. Frey3,4,5, W.A. Baan6,1,7and A. Wang1 1Shanghai Astronomical Observatory, Key Laboratory of Radio Astronomy, CAS, 80 Nandan Road, Shanghai 200030, China 2State Key Laboratory of Radio Astronomy and Technology, A20 Datun Road, Chaoyang District, Beijing, P. R. China 3Konkoly Observatory, HUN-REN Research Center for Astronomy and Earth Sciences, Konkoly Thege Miklós út 15-17, H-1121 Budapest, Hungary 4CSFK, MTA Centre of Excellence, Konkoly Thege Miklós út 15-17, H-1121 Budapest, Hungary 5Institute of Physics and Astronomy, ELTE Eötvös Loránd University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary 6Xinjiang Astronomical Observatory, CAS, 150 Science-1 Street, Ürümqi, Xinjiang 830011, P.R. China 7Netherlands Institute for Radio Astronomy, ASTRON, Oude Hoogeveensedijk 4, 7991PD Dwingeloo, The Netherlands Received 2025; accepted 2025 ABSTRACT This Supplementary Material provides the extended data tables, figures, and methodological details supporting the analysis presented in the main paper. It includes the complete CSO candidate sample, parameter lists and additional diagnostic plots. Key words. galaxies: active — galaxies: nuclei — galaxies: jets — quasars: general — radio continuum: galaxies — astrometry 1. Additional tables and figures This section compiles the materials supporting our CSO classifications. Table 1lists the full candidate catalog (coordinates, redshifts, optical IDs, classifications). Table 2reports the astrometry (angular scales, Gaia-radio offsets, and Gaia quality metrics) used in our method. Tables 3–8give VLBI imaging, model-fitting, and spectral-analysis parameters. Figure 1shows the redshift distribution of the sample. Figures 2–4show multifrequency VLBI maps, spectral-index images, and Gaia overlays that separate genuine CSOs, where the optical nucleus lies between symmetric lobes, from core-jet sources, where it sits at one end. Figure 5displays the light curves of confirmed CSOs. Figure 6shows component proper motions of each CSO. 2. Gaia +VLBI cross-match We compiled Gaia astrometric positions for our sources directly from the Gaia database1. For VLBI data, we used the Radio Fundamental Catalogue (RFC, Petrov & Kovalev 2025)2, which currently includes over 20,000 objects with typically sub-mas precision in absolute VLBI astrometry, achieved through observations from various astrometry and geodesy programs. This precision makes the RFC an invaluable resource for aligning the optical and radio extragalactic reference frameworks (as demonstrated by Bourda et al. 2008). In our analysis, we cross-matched the Gaia DR3 catalog (Gaia Collaboration et al. 2016,2023) with the VLBI sample from Section 2.2 in the main paper, employing a search radius of 1′′ to identify optical counterparts to the radio sources. Out of 105 VLBI-identified CSO candidates, 40 have Gaia counter- ⋆Corresponding author: [email protected] 1https://gea.esac.esa.int/archive/ 2http://astrogeo.org/ 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Redshift 0 2 4 6 8 Number of Sources Core-jet CSO candidate CSO Fig. 1. Redshift distribution of the sample, including the confirmed CSO, CSO candidate (CSOc), and core–jet (CJ) sources. parts (Fig. 1 in the main paper). The modest match rate (38%) provide important physical insight, suggesting that most CSO nuclei are optically faint or obscured, highlighting the fundamental challenge in CSO identification and the value of our combined Gaia+VLBI approach. This finding demonstrates why radio–only identification methods have proven insufficient and validates our multi–wavelength strategy. Since both Gaia and VLBI catalogs remain in continuous updates, the sample sizes analyzed in this paper are slightly larger than in those used in previous studies. The astrometric precision of both Gaia and VLBI is critical for aligning optical and radio positions. Gaia DR3 provides unprecedented astrometric precision with typical uncertainties of ∼0.04 mas for bright sources (apparent optical magnitude Article number, page 1 of 28 A&A proofs: manuscript no. output Table 1. The CSO candidate sample collected in this paper. Source name Right ascension (h m s), declination (◦ ′ ′′)zType Ref. Classification J0003+2129 00:03:19.350009 +21:29:44.50822 0.450 Q 2 CJ J0005+0524 00:05:20.215504 +05:24:10.80305 1.887 Q 2 CJ J0048+3157 00:48:47.141485 +31:57:25.08483 0.015 G 2 CSO J0119+3210 01:19:35.001084 +32:10:50.06103 0.0602 G 2 CSOc J0650+6001 06:50:31.254327 +60:01:44.55477 0.455 Q 1,2 CSOc J0741+2706 07:41:25.732847 +27:06:45.39211 0.772 Q 3 CSO J0753+4231 07:53:03.337437 +42:31:30.76470 3.594 Q 1,3 CJ J0831+4608 08:31:39.802592 +46:08:00.77140 0.131 G 3 CSOc J0832+1832 08:32:16.040301 +18:32:12.13265 0.154 G 3 CSO J0906+4636 09:06:15.539809 +46:36:19.02416 0.0847 G 3 CSOc J0943+1702 09:43:17.223952 +17:02:18.96252 1.600 Q 3 CSOc J1110+4817 11:10:36.324124 +48:17:52.44997 0.742 Q 3 CSO J1111+1955 11:11:20.065601 +19:55:36.00040 0.299 G 1,2,3 CSO J1148+5924 11:48:50.358181 +59:24:56.38223 0.0108 G 1,3 CSOc J1148+5254 11:48:56.569098 +52:54:25.32250 1.638 Q 2 CJ J1158+2450 11:58:25.787561 +24:50:17.96392 0.203 G 3 CSO J1234+4753 12:34:13.330774 +47:53:51.23687 0.373 Q 3 CSO J1244+4048 12:44:49.187531 +40:48:06.16239 0.814 Q 1,3 CSO J1247+6723 12:47:33.329586 +67:23:16.44894 0.107 G 2 CSO J1254+1856 12:54:33.271499 +18:56:01.90866 0.125 G 3 CSOc J1256+5652 12:56:14.233979 +56:52:25.23760 0.0417 G 2 CSO J1309+4047 13:09:41.508928 +40:47:57.23878 2.908 Q 2 CSOc J1310+3403 13:10:04.433638 +34:03:09.10854 0.960 G 3 CSO J1311+1417 13:11:07.824225 +14:17:46.64778 1.955 Q 1 CJ J1326+3154 13:26:16.511702 +31:54:09.52057 0.368 G 2,3 CSO J1335+4542 13:35:21.962189 +45:42:38.23218 2.451 Q 2 CJ J1358+4737 13:58:40.666477 +47:37:58.31155 0.230 G 3 CSO J1407+2827 14:07:00.394417 +28:27:14.69011 0.077 G 2 CSO J1511+0518 15:11:41.266365 +05:18:09.25931 0.084 G 2 CSO J1559+5924 15:59:01.701929 +59:24:21.83416 0.060 G 2,3 CSOc J1602+2418 16:02:13.838513 +24:18:37.79350 1.791 Q 3 CSO J1616+0459 16:16:37.556823 +04:59:32.73651 3.215 Q 2 CJ J1755+6236 17:55:48.435228 +62:36:44.12661 0.0276 G 2 CSO J1815+6127 18:15:36.792244 +61:27:11.64744 0.601 Q 1 CSO J1816+3457 18:16:23.901115 +34:57:45.74704 0.245 G 1,2 CJ J1823+7938 18:23:14.108654 +79:38:49.00188 0.224 Q 1,2 CSOc J1945+7055 19:45:53.519774 +70:55:48.72880 0.101 G 1,2 CSO J2022+6136 20:22:06.681748 +61:36:58.80472 0.227 G 1,2 CJ J2245+0324 22:45:28.284742 +03:24:08.86404 1.350 Q 1 CJ J2355+4950 23:55:09.458159 +49:50:08.33951 0.238 G 1,2 CSO Notes. Column (1): source name. Column (2): Equatorial coordinates from Astrogeo (Petrov & Kovalev 2025). Column (3): Spectroscopic or photometric redshifts collected from the NASA/IPAC Extragalactic Database (https://ned.ipac.caltech.edu/) or SIMBAD (https:// simbad.u-strasbg.fr/). Column (4) lists the optical identification of the source type from SIMBAD. Q – quasar; G – galaxy. Column (5) lists the references to the sources. Column (6) presents the classification of the radio morphology: CSO – confirmed CSO with Gaia-identified AGN between two radio components; CJ – one-sided core–jet with Gaia-identified AGN at the end of the radio structure; CSO candidate – sources with large optical–radio offset remain as CSO candidates. References: 1 – Peck & Taylor (2000); 2 – An & Baan (2012); 3 – Tremblay et al. (2016). G<14mag) and ∼0.7 mas for fainter sources (G=20mag). The RFC delivers sub-mas astrometric accuracy for bright radio AGN, with typical uncertainties ranging from ∼0.1 to 1 mas. When combining Gaia and VLBI positions, the final uncertainty is estimated to be less than 1 mas for most sources, much smaller than the typical separation between the core and hotspots in CSOs (several to tens of mas), providing a robust foundation for the Gaia+VLBI method. Table 2presents the CSO candidate sample collected in this study, detailing key parameters such as host galaxy type, angular scale, and astrometric offsets between VLBI and Gaia positions. The majority of the CSOs and candidates in this sample are clustered at moderate redshifts (z<1.0), while core–jet sources show a broader redshift range, often extending to higher redshift values (Fig. 1). This distribution likely reflects both physical differences in the populations and selection effects, with CSOs lacking the Doppler–boosted emission that makes core– jet sources detectable at higher redshifts. The cross-matched CSO candidates include a heterogeneous mix of quasars, radio galaxies, and other AGN types (e.g. Seyfert galaxies, BL Lac objects, or unclassified AGN), with quasars making up ∼40% of the matches. This prevalence of quasars reflects multiple factors: Gaia’s sensitivity to point–like optical sources, the higher intrinsic luminosity of quasars enabling detection at greater distances, and VLBI survey biases favoring sources with compact, bright radio components (Petrov et al. Article number, page 2 of 28 T. An , Y. Zhang , S. Frey, W.A. Baan and A. Wang: Identifying CSOs with Gaia and VLBI Table 2. Properties of the CSO candidate sample collected in this paper. Name Type Angular scale Scale OffsetRA OffsetDEC AEN AENS G (mas) (pc) (mas) (mas) (mas) (mag) CSO J0048+3157 G 11.70 3.59 10.05±1.98 −40.93±1.30 9.21 418.29 17.95 J0741+2706 G 16.90 125.32 7.05±0.75 −0.04±0.75 0.00 0.00 19.49 J0832+1832 G 7.90 21.15 6.14±2.55 2.30±1.71 7.12 19.90 20.07 J1110+4817 Q 22.30 162.87 −6.71±2.62 −10.33±2.63 3.08 1.28 20.73 J1111+1955 G 17.20 76.45 4.06±14.48 −5.80±9.15 18.47 107.18 21.25 J1158+2450 G 8.70 28.89 2.29±1.61 1.51±1.05 4.38 12.81 19.91 J1234+4753 Q 9.70 49.85 −0.97±0.41 0.90±0.38 0.20 2.24 16.84 J1244+4048 Q 29.20 220.43 −0.82±0.62 −0.61±0.80 0.00 0.00 19.75 J1247+6723 G 8.20 16.09 −12.73±5.52 10.37±3.90 18.62 89.49 20.23 J1256+5652 G 47.10 39.19 1.18±0.45 0.11±0.33 0.06 2.55 13.54 J1310+3403 G 15.50 122.88 3.28±6.98 5.62±6.60 9.59 26.84 21.10 J1326+3154 G 56.60 288.74 23.23±2.66 −25.85±2.36 8.56 10.49 20.94 J1358+4737 G 6.60 24.25 −3.15±2.81 1.69±3.19 10.92 101.41 20.59 J1407+2827 G 7.20 10.45 0.95±0.36 0.40±0.48 0.39 9.98 16.35 J1511+0518 G 5.00 7.89 5.74±0.68 −11.01±0.84 2.07 10.69 18.74 J1602+2418 Q 7.50 63.35 −4.92±0.36 1.98±0.53 0.05 0.04 18.02 J1755+6236 G 46.10 25.08 −6.46±2.00 0.40±1.65 2.72 2.17 20.10 J1815+6127 Q 11.00 73.59 0.17±0.95 −3.46±0.79 0.00 0.00 19.95 J1945+7055 G 32.70 60.84 24.11±6.28 −22.00±6.23 27.65 225.44 20.85 J2355+4950 G 49.80 188.92 −5.34±5.82 9.04±5.42 26.44 113.70 21.13 Core–Jet J0003+2129 Q 4.20 24.19 5.58±4.24 −2.38±2.88 7.13 5.11 21.02 J0005+0524 Q 2.30 19.36 0.10±0.31 −0.24±0.53 0.00 0.00 16.10 J0753+4231 Q 12.00 86.99 0.80±0.44 2.02±0.47 0.22 0.53 17.90 J1148+5254 Q 7.90 66.92 −1.09±0.43 1.04±0.35 0.10 1.13 16.21 J1311+1417 Q 5.20 43.62 1.40±0.85 4.36±0.64 0.87 0.90 19.81 J1335+4542 Q 2.00 16.20 1.01±0.37 −0.47±0.39 0.00 0.00 17.70 J1616+0459 Q ... ... −0.36±0.55 0.29±0.58 0.00 0.00 19.34 J1816+3457 G 35.90 138.21 −4.72±4.31 1.76±4.50 17.63 22.04 21.16 J2022+6136 G 7.10 25.83 13.18±3.26 12.20±4.54 8.92 13.09 20.68 J2245+0324 Q 10.70 89.96 0.00±0.47 0.21±0.64 0.00 0.00 18.81 CSO candidates J0119+3210 G ... ... −246.77±12.29 58.43±10.31 36.83 193.96 20.37 J0650+6001 Q 6.80 39.41 −0.18±1.25 −3.06±1.33 1.02 0.32 20.72 J0831+4608 G 4.50 10.50 −6.99±6.10 −7.31±4.13 17.68 301.92 20.38 J0906+4636 G 1.70 2.71 −5.69±1.08 7.85±1.06 4.23 30.38 19.26 J0943+1702 Q 13.60 115.21 −2.07±8.09 7.06±10.00 1.95 0.38 20.88 J1148+5924 G 22.80 5.60 −91.04±10.14 68.36±14.50 33.91 417.58 19.15 J1254+1856 G 3.30 6.90 −11.58±2.19 14.69±1.92 8.64 66.16 19.88 J1309+4047 Q 1.30 10.09 −0.82±1.29 −3.89±1.33 0.14 0.24 18.19 J1559+5924 G 7.80 9.07 25.83±2.40 7.88±2.41 9.98 61.47 19.25 J1823+7938 Q 15.70 56.54 −3.11±1.51 3.60±0.98 3.24 8.21 19.85 Notes. Column (1): source name; Column (2): host galaxy type. Q – quasar; G – galaxy; Column (3): angular size of the source from our images in mas; Column (4): linear scale of the sources in pc; Column (5)–(6): angular distance (in mas) between the X-band peak and the Gaia position along RA (∆RAcosδ) and DEC(∆DEC ); Column (7): astrometric excess noise factor from Gaia DR3; Column (8): astrometric excess noise significance from Gaia DR3; Column (9): mean G-band magnitude from Gaia DR3. 2019). Understanding these selection effects is crucial when interpreting our results and their implications for CSO evolution. The astrometric excess noise (AEN) from Gaia, presented in Table 2, offers valuable insights into the host galaxy properties. AEN values for CSOs are consistently larger than those for core–jet sources, while CSO candidates exhibit even higher AEN values than confirmed CSOs. This trend aligns with the observational evidence that CSOs are predominantly hosted by galaxies, whereas core–jet sources are typically associated with quasars, whose compact, bright nuclei dominate their optical emission. The higher AEN values for CSOs likely reflect the extended and complex optical morphologies of their host galaxies, which can introduce additional scatter in Gaia’s astrometric measurements. In contrast, the lower AEN values for core–jet sources correspond to the more point-like optical appearance of quasars, dominated by bright nuclear emission. These variations in AEN provide a quantitative measure that complements radio-based classifications and offer important insights into the diverse optical characteristics of AGN hosts. Article number, page 3 of 28 A&A proofs: manuscript no. output Table 3. Image parameters of 20 confirmed CSOs shown in Fig. 2. Name Epoch Freq. Speak σ θbeam (GHz) (mJy beam−1) (mJy beam−1) (mas, mas, ◦) J0048+3157 2018-09-01 8.7 269.3 0.21 (1.0, 2.1, −7.3) 2.3 105.7 0.52 (3.6, 8.2, -7.8) J0741+2706 2018-11-18 8.7 245.3 0.17 (1.1, 2.3, −9.7) 2.3 732.6 0.55 (3.6, 8.8, −10) J0832+1832 2017-06-10 8.7 116.7 0.23 (1.1, 2.1, 1.0) 2.3 231.8 0.48 (3.8, 7.7, 0.0) J1110+4817 2018-02-09 8.7 37.7 0.24 (1.2, 1.7, −21.2) 2.3 175.5 0.56 (4.5, 6.7, −21.1) J1111+1955 2018-03-26 8.7 68.9 0.30 (1.1, 2.4, −7.7) 2.3 498.8 0.85 (3.7, 9.4, −7.0) J1158+2450 2017-05-01 8.7 301.5 0.31 (1.0, 1.9, −1.5) 2.3 423.6 0.91 (4.1, 7.5, −3.4) J1234+4753 2018-06-09 8.7 142.3 0.19 (1.1, 1.5, 1.7) 2.3 208.9 0.46 (4.1, 5.5, −1.2) J1244+4048 2018-07-01 8.7 86.8 0.53 (1.1, 1.6, 9.3) 2.3 142.9 0.69 (3.8, 6.1, 3.3) J1247+6723 2017-05-27 8.7 57.8 0.22 (1.3, 1.5, −22.7) 2.3 138.7 0.30 (4.6, 5.4, -20.8) J1256+5652 2018-12-04 8.7 283.7 0.17 (1.1, 1.3, 13.8) 2.3 148.2 0.37 (4.3, 5.3, 12.4) J1310+3403 2006-07-17 4.8 46.6 0.25 (1.9, 2.9, −7.3) J1326+3154 2011-05-15 8.7 77.1 0.52 (1.1, 2.0, 3.4) 2.3 459.2 2.72 (3.8, 7.1, −2.1) J1358+4737 2017-08-12 8.7 172.3 0.25 (1.1, 1.6, 1.8) 2.3 480.0 0.42 (3.9, 5.7, 0.7) J1407+2827 2018-08-14 8.7 537.5 2.30 (1.3, 2.7, −23.4) 2.3 1312.3 1.83 (4.4, 11.2, −27.4) J1511+0518 2017-02-20 8.7 349.5 0.29 (0.9, 2.0, −0.1) 2.3 263.0 0.62 (3.4, 7.7, -3.2) J1602+2418 2018-04-29 8.7 50.3 0.19 (0.9, 1.9, 0.0) 2.3 214.6 0.54 (3.7, 7.6, −3.1) J1755+6236 2018-12-20 8.7 26.2 0.23 (1.2, 2.0, 69.2) 2.3 43.3 0.72 (4.6, 11.6, −45.1) J1815+6127 2017-01-16 8.7 92.0 0.26 (1.4, 1.7, 24.5) 2.3 403.9 0.47 (5.4, 6.3, 21.9) J1945+7055 2018-12-10 8.7 65.8 0.28 (1.1, 1.5, 25.1) 2.3 338.4 0.86 (3.9, 5.3, 20.2) J2355+4950 2017-04-25 8.6 259.4 0.91 (1.2, 1.5, 57.3) 2.3 892.3 1.27 (3.7, 4.2, 70.3) Notes. Column (1): source name; Column (2): observing epoch; Column (3): frequency; Column (4): peak intensity; Column (5): rms noise of the post-fit image; Column (6): restoring beam shape (major axis, minor axis, and position angle of the elliptical Gaussian beam; the position angle is measured from north to east). In typical AGN dominated by compact radio cores, the image center aligns with the actual source coordinate. However, in CSOs, where emission is dominated by lobes and hotspots, self-calibration in VLBI processing can shift the image center to the brightest component, which may not be the core. To reconcile Gaia positions with VLBI images, we implemented rigorous astrometric corrections, leveraging absolute RFC positions derived from group–delay measurements at Sand X-band (central frequencies at 2.3 and 8.4 GHz) minimally affected by source structure and calibration errors (Porcas 2009). This critical step ensures accurate registration between optical and radio reference frames, forming the foundation of our classification methodology. Additionally, we account for frequency-dependent core shifts using multi-frequency VLBI data whenever available (Lobanov 1998), where a robust optically thin jet component was used for each source. This correction is essential for accurate VLBI component identification across different observing frequencies and prevents potential misclassifications due to frequency-dependent position shifts. This Gaia+VLBI method provides a uniquely powerful and precise approach to confirming genuine CSOs, overcoming the fundamental limitations of traditional morphological analyses that relied on detecting often invisible radio cores. By definitively pinpointing the AGN position, our approach enables accurate determination of radio structure orientation and detailed study of jet kinematics, significantly enhancing our understanding of CSO physics and their evolutionary pathways. Article number, page 4 of 28 T. An , Y. Zhang , S. Frey, W.A. Baan and A. Wang: Identifying CSOs with Gaia and VLBI Table 4. Image information of the 10 confirmed core–jet sources shown in Fig. 3. Name Epoch Freq. Speak σ θbeam (GHz) (mJy beam−1) (mJy beam−1) (mas, mas, ◦) J0003+2129 2018-07-01 8.7 123.4 0.23 (1.7, 2.6, −14.2) 2.3 160.3 0.44 (3.6, 8.1, −4.5) J0005+0524 2018-11-03 8.7 74.2 0.21 (1.0, 2.4, −4.4) 2.3 165.6 0.42 (3.8, 10.1, −7.2) J0753+4231 2018-06-09 8.7 120.0 0.21 (1.2, 1.7 ,10.7) 2.3 300.1 0.64 (4.0, 6.2, 3.6) J1148+5254 2017-08-05 8.7 465.9 0.32 (1.2, 1.4, 10.3) 2.3 241.6 0.46 (4.3, 5.4, 10.0) J1311+1417 2018-12-10 8.7 75.3 0.15 (2.3 ,1.0, −4.4) 2.3 520.8 0.32 (9.9, 3.4, −9.4) J1335+4542 2017-07-16 8.7 515.6 0.30 (1.0, 1.5, 3.0) 2.3 473.1 0.55 (3.8, 5.8, −0.9) J1616+0459 2009-05-14 8.6 542.7 0.57 (1.1, 2.3, 3.4) 2.3 592.6 0.61 (4.9, 8.7, 5.0) J1816+3457 2017-03-23 8.7 52.5 0.57 (1.2, 2.6, 7.5) 2.3 187.8 0.72 (4.5, 9.0, 5.4) J2022+6136 2015-08-24 7.6 1268.9 0.76 (1.3, 2.7, −53.4) 4.3 1114.0 1.81 (2.3, 4.8, −55.9) J2245+0324 2018-11-18 8.7 176.9 0.23 (1.1, 2.4, 3.5) 2.3 316.4 0.48 (4.1, 9.3, −1.8) Notes. Column (1): source name; Column (2): observing epoch; Column (3): frequency; Column (4): peak intensity; Column (5): rms noise of the post-fit image; Column (6): restoring beam shape (major axis, minor axis, and position angle of the elliptical Gaussian beam; the position angle is measured from north to east). Table 5. Image information of the remaining 10 unclassified sources shown in Fig. 4. Name Epoch Freq. Peak σ θbeam (GHz) (mJy/b) (mJy/b) (mas, mas, ◦) J0119+3210 2017-06-10 8.7 61.6 0.97 (2.3, 1.2, −4.4) 2.3 220.1 8.54 (4.2,8.3, −4.5) J0650+6001 2017-07-16 8.7 573.7 0.52 (1.1, 1.3 , 36.8) 2.3 775.3 0.62 (4.8, 4.2, 33.2) J0831+4608 2006-05-31 4.8 44.8 0.27 (2.0, 2.6, −12.6) J0906+4636 2017-07-16 8.7 95.7 0.24 (1.0, 1.5, 11.8) 2.3 70.6 0.48 (4.0,5.9,10.7) J0943+1702 2017-08-05 8.7 188.3 0.21 (1.0, 2.4, −7.8) 2.3 122.5 0.37 (3.7, 9.1, −9.5) J1148+5924 2017-08-05 8.7 187.7 0.31 (1.2, 1.4, 13.8) 2.3 115.9 0.71 (4.5,5.4,12.3) J1254+1856 2006-02-25 8.4 78.3 0.22 (1.1, 2.5, 5.3) 4.8 75.5 0.25 (2.1,3.4,−3.5) J1309+4047 2022-07-26 7.6 36.8 0.42 (2.6, 0.9, 4.5) 2.3 77.1 0.41 (1.5, 4.4, 1.5) J1559+5924 2017-05-12 8.7 43.4 0.21 (1.2, 1.4, −66.2) 2.3 113.5 0.43 (4.9,5.5,-45.9) J1823+7938 2000-12-04 8.6 182.4 0.32 (1.1, 1.6, 46.5) 2.3 185.7 2.62 (4.9, 6.1, 41.3) Notes. Column (1): source name; Column (2): observing epoch; Column (3): frequency; Column (4): peak intensity; Column (5): rms noise of the post-fit image; Column (6): restoring beam shape (major axis, minor axis, and position angle of the elliptical Gaussian beam; the position angle is measured from north to east). 3. VLBI data reduction and analysis 3.1. Continuum images We obtained archive VLBI data for 40 CSO candidates from the Astrogeo database. Most of these data originate from astrometric VLBI projects, such as the VLBA Calibrator Surveys (e.g. Beasley et al. 2002;Fomalont et al. 2003;Petrov et al. 2005, 2006;Kovalev et al. 2007;Petrov et al. 2008;Petrov 2016), and consist of pre-processed and self-calibrated visibility data, often including simultaneous S-band (2.3 GHz) and X-band (8.4 GHz) observations. For these pre-calibrated datasets, we used standard hybrid mapping using the software package Difmap (Shepherd 1997), iteratively performing clean deconvolution and selfcalibration to refine the imaging quality. Article number, page 5 of 28 A&A proofs: manuscript no. output Table 6. Proper motions of the core–jet sample in Fig. 7. Name Comp. µrad βapp PAvar (mas yr−1) (c) (◦yr−1) J0003+2129 J2 0.055±0.002 1.50±0.04 0.49±0.01 J1 0.058±0.008 1.57±0.23 −0.04 ±0.08 J0005+0524 J1 0.070±0.001 5.55±0.10 −1.36 ±0.12 J1311+1417 J1 0.031±0.004 2.54±0.32 −0.16 ±0.07 J1335+4542 J3 0.025±0.001 2.28±0.05 −0.53 ±0.47 J2 0.022±0.001 2.03±0.05 0.02±0.05 J1 0.050±0.001 4.53±0.11 0.02±0.02 J2022+6136 J2-J1 0.083±0.001 1.20±0.01 0.02±0.03 J2245+0324 J1 0.010±0.001 0.67±0.05 −0.14 ±0.01 Notes. Column (1): source name; Column (2): component ID; Column (3): radial proper motion of the component with respect to the core; Column (4): position angle change of the component with respect to the core, measured from north to east. We implemented a rigorous quality control process, inspecting each dataset and selecting epochs with optimal signal-tonoise ratio (typically >10 for the weakest source compoents of interest) and (u,v)-coverage at X-band to ensure the highest possible fidelity in our resulting images. When X-band data were unavailable, we substituted C-band (4.8 GHz) observations, maintaining consistent resolution across the sample. Continuum images were produced for each selected epoch, with Gaia DR3 positions overlaid to compare the optical centroid with the VLBI radio structure, focusing on the core identification (Figs. 2,3, and 4). This approach allows us to directly assess the alignment between the optical and radio emission, aiding in CSO classification and understanding source morphology. 3.2. Spectral index map Accurate spectral index measurements require quasisimultaneous multi-frequency observations. The simultaneous dual–frequency (2.3/8.4 GHz) VLBI data from the astrometry program provide an ideal opportunity to construct reliable spectral index maps largely free from variability effects, offering critical diagnostic information about emission mechanisms in different regions of the source. We first produced FITS images from the calibrated visibility data for both the Sand X-band (typically 2.3 GHz and 8.4 GHz, respectively), ensuring they had the same pixel size and map dimensions. We have used a common visibility range in wavelength units at both frequencies to ensure consistency in the spectral index calculation. Standard imaging and self-calibration procedures were performed using the AIPS task IMAGR. If Sband data were unavailable, C-band images (typically 4.8 GHz or 5 GHz) were used as a substitute. To ensure that the spectral index calculation is sensitive to emission on similar angular scales and avoids artificial spectral features due to resolution differences, we matched the angular resolution. Specifically, we convolved the higher-resolution Xband images with a Gaussian beam matching that of the lowerfrequency images using the AIPS task CONVL and Difmap task restore. In order to precisely align multi–frequency images, a critical requirement for meaningful spectral analysis, we used optically thin, steep–spectrum components (typically hotspots or lobes) as reference points where available and clearly identifiable in both bands. These features are generally less affected by frequency-dependent position shifts and maintain consistent positions. Only sources with reliable component identification allowing for unambiguous alignment were used for spectral index mapping. The images were shifted based on calculated offsets using AIPS task OGEOM to guarantee that the same physical components were superimposed across frequencies. The spectral index (α, defined via Sν∝ν−α) maps were then generated from the aligned, resolution-matched images, using the AIPS task COMB with the OPCODE=’SPIX’. To ensure reliability, pixels in the input total intensity maps falling below a signal-to-noise ratio (SNR) threshold, typically set at 5 times image rms noise, were usually blanked before or during the spectral index calculation, thereby excluding low-SNR pixels from the final spectral index map. The resulting spectral index distributions for each CSO and core–jet source are shown in Figs. 2and 3. Spectral index maps help distinguish between core and jet components: cores typically exhibit flat or inverted spectra (α≲0.5), while jets and hotspots have steep spectra (α≳0.5) (Kellermann et al. 1994). This additional spectral information enhances source classification and helps elucidate their physical properties. For J1310+3403, only 4.8-GHz data were available from the archive, so a spectral index map could not be constructed. For the CSOc sources, we made spectral index maps, except for J0119+3210, J0906+4636 and J0831+4608. The first two sources lack reliable optically thin components for alignments and the last one only has 4.8-GHz data from the archive (see Fig. 4). 3.3. Proper motion analysis Proper motion measurements help constrain CSO expansion speeds, which are crucial for estimating kinematic ages and understanding evolutionary stages. In core–jet sources, jet speeds provide insights into jet dynamics and relativistic beaming effects. We analyzed the kinematics of CSOs and core–jet sources using multi-epoch VLBI data. In CSOs, we measured the separation speed between terminal hotspots or hotspot–core, while in core–jet sources, we tracked jet components relative to the core. We used the modelfit task in Difmap, employing circular Gaussian components to represent emission features. This approach provided a simple and consistent model for the compact structures observed. Given the varying data quality across epochs, we focused on fitting the brightest components that could be reliably identified across all epochs. If two components were too close or if the deconvolved size was significantly smaller than the restoring beam, we replaced the Gaussian with a point-source model. Our primary concern was determining component positions accurately rather Article number, page 6 of 28 T. An , Y. Zhang , S. Frey, W.A. Baan and A. Wang: Identifying CSOs with Gaia and VLBI than modeling exact shapes or sizes; thus, using circular Gaussians or point sources did not significantly affect the proper motion results. Table 7and 8list the model fitting parameters, including integrated flux density (Stot), radial separation (R) with respect to the Gaia position and the position angle (PA) measured from north to east, component size θFWHM (full width at half maximum of the fitted Gaussian), and brightness temperature (Tb). The error estimates are described in Appendix 4. Of these identified CSO and core–jet sources, 21 have multiple X-band VLBI epochs, allowing measurement of hotspot separation speeds or jet proper motions over time baselines ranging from a few years to 25 years (the earliest data are from 1994). For sources with more than two epochs available, we derived proper motions using linear regression of component positions over time. For those with only two epochs, we calculated apparent speeds based on positional changes between these epochs. Two sources (e.g. J1755+6236/NGC 6251, J2355+4950) were excluded from proper motion analysis due to insufficient time baselines, poor data quality, or ambiguous component identification. In some CSOs, we also measured the proper motions of inner jet components in addition to terminal hotspots to gain further insights into kinematics and dynamical evolution. 3.4. Error analysis and identification reliability To ensure the robustness of our CSO identifications, we conducted a comprehensive error analysis incorporating all potential sources of uncertainty in both Gaia and VLBI measurements. Gaia position errors range from 0.04 to 0.7 mas. Chromatic errors arising from the wavelength-dependent point-spread function of the Gaia optics can shift positions, particularly for AGN with significant ultraviolet or infrared emission (Lindegren et al. 2018). Proper motion and parallax uncertainties were accounted for, though they are generally negligible for distant extragalactic sources (Fabricius et al. 2021). For VLBI measurements, we accounted for thermal noise, tropospheric delay (introducing position errors of ∼0.1–1 mas), and ionospheric effects, which are more pronounced at lower frequencies (Sovers et al. 1998). Source structure effects were critically assessed, as extended or complex radio morphologies can cause significant astrometric shifts if not properly modeled (Charlot 1990;Porcas 2009). This is especially relevant for CSOs, where core emission is often weak or obscured, and dominant emission arises from the lobes or hotspots. Gaia and VLBI position errors were combined in quadrature, providing a conservative estimate of the total uncertainty in optical–radio alignment. We used a Monte Carlo approach, generating 1000 realizations of Gaia and VLBI positions for each source, based on Gaussian error distributions. For each realization, we calculated the offset between Gaia and VLBI positions, determining the likelihood that the optical position matches a particular radio component. This comprehensive error analysis enhances the credibility of our results and allows for nuanced interpretation of borderline cases, contributing to refined CSO identification methodologies. By quantifying the reliability of each identification, we provide a solid foundation for subsequent analyses of CSO properties, such as kinematic ages and expansion speeds, and demonstrate the power of combining optical and radio astrometry for future studies. 4. Error analysis of the VLBI components The errors of the fitted Gaussian components are mainly introduced by Fomalont (1999) and modified for the strong side lobes of VLBI observations: SNR =Speak σpeak (1) σpeak =σ(2) σint =σ×√1+Sint Speak (3) σpos =θbeam 2 SNR (4) σsize =θbeam 2 SNR (5) σPA =arctan (σpos R),(6) where SNR is the signal-to-noise ratio, σthe rms noise of the image, σpeak the post-fit root-mean-square error of the fitted component, σint the uncertainty of the integrated flux density, σpos and σsize the uncertainty of the fitted component position and size, σPA the uncertainty of the fitted component position angle, Speak the peak intensity of the component, Sint the total integrated flux density, θbeam is the full width at half maximum (FWHM) size of the restoring beam, √bmaj ·bmin, and Rthe radial distance of the component with respect to the core. Additional calibration errors depend on the accuracy of the visibility amplitude calibration. According to the VLBA observational status report3, the fractional calibration error for flux density is about 5% at 1.5–15 GHz frequency bands. We thus apply 5% as the calibration error for the peak intensities and total flux densities. 5. Core brightness temperature and radio luminosity We computed two fundamental physical parameters of the CSOs: the core (or bright hotspot) brightness temperature and the radio luminosity. The brightness temperature, TB, was calculated following Kellermann & Owen (1988): TB=1.22 ×1012 K(Stot Jy )(θFWHM mas )−2(ν GHz)−2(1 +z),(7) where νis the observing frequency, zthe redshift, θFWHM the angular size of the component, and Stot its integrated flux density. The monochromatic radio power at 1.4 GHz was derived as P1.4 GHz =4πD2 LS1.4 GHz(1 +z)−(α+1),(8) where DLis the luminosity distance, S1.4 GHz the observed 1.4 GHz flux density, and αthe spectral index. For GHz-peaked sources with turnover above 1.4 GHz (optically thick at this frequency), we used flux densities at higher frequencies and extrapolated to 1.4 GHz with the optically thin spectral index from our multi-frequency data. This yields a more reliable intrinsic power estimate, less affected by absorption at 1.4 GHz. 3https://science.nrao.edu/facilities/vlba/docs/ manuals/oss Article number, page 7 of 28 A&A proofs: manuscript no. output 6. The reliability of Gaia positions correlating with VLBI observations As discussed in Section 2 of the main paper, Gaia astrometry can be impacted by astrometric excess noise (AEN) and its significance (AENS), which quantify departures from the fiveparameter solution and may arise from extended hosts or subkpc optical jets (see also Lindegren et al. 2012; DR3 docs4). These metrics have been used, together with Gmagnitude, to select dual-AGN candidates (e.g. Chen et al. 2023;Schwartzman et al. 2024); for example, Schwartzman et al. (2024) adopted AENS >5, G<20, and z>0.5 to mitigate spurious jitter from large nearby galaxies. Table 2lists, for each source, the VLBI angular scale, AEN/AENS, and G. In our sample, confirmed CSOs and CSO candidates cluster at elevated AEN/AENS (jittering), consistent with extended optical hosts, whereas confirmed sources with z>0.5 generally have clean Gaia detections. These trends align with the reliability caveats summarised in Section 2.3 of the main paper and inform our conservative use of Gaia–VLBI offsets in classification. 7. Correlation analysis of the jet parameters To quantitatively investigate the relationships in Figure 2 of the main paper between key physical parameters in our CSO sample, we performed comprehensive correlation analyses using three complementary statistical methods: Pearson (parametric), Spearman (non-parametric rank), and Kendall (non-parametric rank) correlation coefficients. These different approaches allow us to identify both linear and non-linear relationships while assessing robustness against outliers and non-normal distributions. We primarily use the results of the Pearson method for evaluation, with Spearman and Kendall methods as supplementary checks. Table 9summarizes the correlation coefficients and p-values for the key parameter pairs across the three statistical methods. Statistical significance was assessed using p-values, with p< 0.05 considered statistically significant. Radio power shows a moderate and highly significant correlation with both projected size (r=0.483, p=0.004) and hotspot velocity (r=0.481, p=0.004), implying that more powerful sources are generally larger and host faster–moving hotspots (Fig. 2-aand b, the main paper). Projected size additionally correlates with hotspot velocity (Fig. 2-cof the main paper) and with spectral index (Fig. 2-hof the main paper), indicating that large CSOs can maintain relatively high advance speeds while exhibiting steeper synchrotron spectra. A significant negative correlation between hotspot velocity and kinematic age (r=−0.44, p=0.009) reveals systematic hotspot deceleration as a source ages (Fig. 2-eof the main paper), likely due to increasing ram pressure as hotspots encounter denser ambient medium at larger radii, combined with growing instabilities at the working surface and possible entrainment of ambient material. The size–age link (Fig. 2-fof the main paper) shows only marginal significance (p≈0.054). This weak correlation suggests that while older sources tend to be somewhat larger, the relationship is complicated by varying expansion rates, environmental interactions, and possible episodic jet activity. Some sources may experience periods of rapid expansion followed by 4https://gea.esac.esa.int/archive/documentation/GDR3/ pdf/GaiaDR3_documentation_1.2.pdf stagnation, while others maintain steady but slow growth, leading to considerable scatter in the size-age plot. The positive correlation between projected size and spectral index (r=0.39, p=0.0241, Fig. 2-hof the main paper) reflects synchrotron aging processes, where larger sources contain older electron populations that have experienced more radiative cooling and adiabatic expansion, resulting in steeper spectra. These correlation analyses highlight the interplay between jet power, physical size, hotspot dynamics, and evolutionary processes in CSOs, providing insights into their growth and interaction with the surrounding medium. Article number, page 8 of 28 T. An , Y. Zhang , S. Frey, W.A. Baan and A. Wang: Identifying CSOs with Gaia and VLBI Table 7. Model-fitting parameters of VLBI components for CSOs. . Name Epoch Label Sint RPA θFWHM Tb (mJy) (mas) (◦) (mas) (K) (1) (2) (3) (4) (5) (6) (7) (8) J0832+1832 1996/01/02 E 168.6±8.5 / / 0.13±0.01 (2.0±0.2)×1011 W 86.6±7.7 7.37±0.16 46.6±0.4 2.37±0.11 (3.1±0.3)×108 2012/02/20 E 140.1±7.8 / / 0.46±0.03 (1.3±0.2)×1010 W 76.6±12.0 7.31±0.24 45.1±1.0 2.00±0.25 (3.9±0.9)×108 2014/06/09 E 78.7±4.3 / / 0.33±0.03 (1.3±0.2)×1010 W 36.3±3.7 7.40±0.21 44.9±0.6 2.07±0.16 (1.6±0.2)×108 2017/06/10 E 133.4±10.1 / / 0.80±0.07 (3.9±0.6)×109 W 92.5±14.5 7.50±0.18 45.8±0.9 2.24±0.23 (3.5±0.7)×108 2018/07/31 E 71.4±6.5 / / 0.71±0.09 (2.7±0.5)×109 W 33.1±8.0 7.87±0.19 45.9±1.3 1.93±0.35 (1.7±0.6)×108 J1110+4817 2007/08/01 NE1 81.1±4.2 / / ≤0.32 ≥2.3×1010 NE2 14.5±1.7 6.03±0.33 −161.8±1.3 1.15±0.28 (3.1±1.1)×108 SW 8.3±1.5 22.38±0.34 −145.8±0.5 ≤1.18 ≥1.7×108 2014/08/09 NE1 44.0±2.3 / / 0.36±0.02 (9.7±0.9)×109 NE2 8.8±0.9 5.93±0.17 −158.2±0.6 1.45±0.12 (1.2±0.2)×108 SW 10.5±1.0 22.68±0.16 −143.8±0.2 1.85±0.12 (8.7±1.2)×107 2017/02/24 NE1 47.6±2.9 / / 0.39±0.04 (8.6±1.2)×109 NE2 8.3±0.8 5.85±0.15 −161.8±0.4 0.58±0.09 (6.9±1.6)×108 SW 6.6±0.5 22.24±0.15 −144.6±0.1 1.25±0.08 (1.2±0.1)×108 2018/02/09 NE1 39.8±2.9 / / 0.68±0.07 (2.4±0.4)×109 NE2 9.0±0.8 5.78±0.17 −162.2±0.5 1.21±0.10 (1.8±0.3)×108 SW 9.1±0.7 22.19±0.16 −145.2±0.1 0.72±0.07 (4.9±0.8)×108 J1111+1955 2015/03/17 W 69.5±5.1 / / ≤0.38 ≥1.0×1010 E 15.3±2.8 16.30±0.21 118.0±0.4 ≤0.68 ≥6.9×108 2017/01/16 W 99.5±13.2 / / 1.86±0.20 (6.0±1.2)×108 E 42.5±2.9 16.85±0.14 117.6±0.1 0.65±0.06 (2.1±0.3)×109 2018/03/26 W 124.0±21.5 / / 2.06±0.27 (6.1±1.5)×108 E 52.9±5.6 17.19±0.17 117.9±0.2 0.84±0.13 (1.6±0.4)×109 Notes. 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A., et al. 2016, MNRAS, 459, 820 Article number, page 9 of 28 A&A proofs: manuscript no. output                                mJy / b               mJy / b 20020 Relative RA (mas) 20 0 20 Relative DEC (mas) 2.3-8.7 GHz 2018-06-09 J1234+4753 0.5 0.0 0.5 1.0 1.5                                 mJy / b                  mJy / b 402002040 Relative RA (mas) 40 20 0 20 40 Relative DEC (mas) 2.3-8.7 GHz 2018-07-01 J1244+4048 0.5 0.0 0.5 1.0 1.5                               mJy / b                  mJy / b                                            mJy / b                 mJy / b 200204060 Relative RA (mas) 60 40 20 0 20 Relative DEC (mas) 2.3-8.7 GHz 2018-08-10 J1326+3154 0.5 0.0 0.5 1.0 1.5                               mJy / b                 mJy / b 201001020 Relative RA (mas) 20 10 0 10 20 Relative DEC (mas) 2.3-8.7 GHz 2018-09-02 J1358+4737 0.5 0.0 0.5 1.0 1.5 Fig. 2. Continued. Article number, page 16 of 28 T. An , Y. Zhang , S. Frey, W.A. Baan and A. Wang: Identifying CSOs with Gaia and VLBI                              mJy / b                 mJy / b 2010010 Relative RA (mas) 20 10 0 10 20 Relative DEC (mas) 2.3-8.7 GHz 2018-04-29 J1602+2418 0.5 0.0 0.5 1.0 1.5                              mJy / b                 mJy / b                                                mJy / b               mJy / b 20020 Relative RA (mas) 20 0 20 Relative DEC (mas) 2.3-8.7 GHz 2017-01-16 J1815+6127 0.5 0.0 0.5 1.0 1.5                                  mJy / b                  mJy / b 402002040 Relative RA (mas) 60 40 20 0 20 40 Relative DEC (mas) 2.3-8.6 GHz 2017-04-25 J2355+4950 0.5 0.0 0.5 1.0 1.5             Fig. 2. Continued. Article number, page 17 of 28 A&A proofs: manuscript no. output                             mJy / b                  mJy / b                                            mJy / b                   mJy / b 402002040 Relative RA (mas) 40 20 0 20 40 Relative DEC (mas) 2.3-8.7 GHz 2017-05-27 J1247+6723 0.5 0.0 0.5 1.0 1.5                             mJy / b                 mJy / b                                            mJy / b                  mJy / b                                                   mJy / b                    mJy / b 402002040 Relative RA (mas) 40 20 0 20 Relative DEC (mas) 2.3-8.7 GHz 2018-12-10 J1945+7055 0.5 0.0 0.5 1.0 1.5 Fig. 2. Continued. Article number, page 18 of 28 T. An , Y. Zhang , S. Frey, W.A. Baan and A. Wang: Identifying CSOs with Gaia and VLBI                               mJy / b                   mJy / b                                             mJy / b                 mJy / b                                              mJy / b                   mJy / b                                               mJy / b                 mJy / b                                              mJy / b                mJy / b               Fig. 3. VLBI images of confirmed core–jet sources overlaid with their Gaia positions located at the presumable jet bases. The red crosses mark the Gaia positions and the orange crosses overlaid with caps represent the positional errors of the Gaia positions with respect to their VLBI peaks. The spectral index maps are also presented. The Gaia position is associated with the brightest component at the end of the jet, which denotes the AGN location. Article number, page 19 of 28 A&A proofs: manuscript no. output                                  mJy / b                 mJy / b                                           mJy / b                mJy / b                                      mJy / b              mJy / b                                            mJy / b                mJy / b                                           mJy / b                   mJy / b                 Fig. 3. Continued. Article number, page 20 of 28 T. An , Y. Zhang , S. Frey, W.A. Baan and A. Wang: Identifying CSOs with Gaia and VLBI                              mJy / b                mJy / b                            C S N                  mJy / b                   mJy / b 402002040 Relative RA (mas) 40 20 0 20 40 Relative DEC (mas) 2.3-8.7 GHz 2017-08-05 J0943+1702 0.5 0.0 0.5 1.0 1.5                             mJy / b                  mJy / b                                             mJy / b                mJy / b                                              mJy / b                mJy / b                 Fig. 4. VLBI images of the 10 remaining candidate CSOs showing a large offset between the peaks of the optical and radio emissions. However, their VLBI images still display the characteristic triple morphology typical of CSOs. For J0119+3210 and J0906+4636, no optically thin components can be found to link the dual-band images, therefore no spectral index maps can be made. For J0831+4608, only one C-band (4.8 GHz) image is available. Article number, page 21 of 28 A&A proofs: manuscript no. output                            mJy / b                  mJy / b                                              mJy / b              mJy / b 20020 Relative RA (mas) 20 0 20 Relative DEC (mas) 2.3-8.6 GHz 2000-12-04 J1823+7938 0.5 0.0 0.5 1.0 1.5                               mJy / b                 mJy / b                              mJy / b                mJy / b            Fig. 4. Continued. Article number, page 22 of 28 T. An , Y. Zhang , S. Frey, W.A. Baan and A. Wang: Identifying CSOs with Gaia and VLBI 1995 1998 2001 2004 2007 2010 2013 2016 2019 Epoch (year) 200 300 400 500 600 700 800 Flux Density (mJy) J0832+1832 Total_X Total_S 2008 2010 2012 2014 2016 2018 Epoch (year) 50 100 150 200 250 300 350 400 450 Flux Density (mJy) J1110+4817 Total_X Total_S 2016 2017 2018 Epoch (year) 400 600 800 1000 1200 Flux Density (mJy) J1111+1955 Total_X Total_S 1998 2001 2004 2007 2010 2013 2016 Epoch (year) 200 400 600 800 1000 Flux Density (mJy) J1158+2450 Total_X Total_S 1998 2001 2004 2007 2010 2013 2016 2019 Epoch (year) 200 250 300 350 400 Flux Density (mJy) J1234+4753 Total_X Total_S 2012 2013 2014 2015 2016 2017 2018 Epoch (year) 200 400 600 800 Flux Density (mJy) J1244+4048 Total_X Total_S 2008 2010 2012 2014 2016 2018 Epoch (year) 100 150 200 250 Flux Density (mJy) J1247+6723 Total_X Total_S 1995 1998 2001 2004 2007 2010 2013 2016 2019 Epoch (year) 150 200 250 300 350 400 Flux Density (mJy) J1256+5652 Total_X Total_S 2006 2008 2010 2012 2014 2016 2018 Epoch (year) 200 300 400 500 600 700 Flux Density (mJy) J1358+4737 Total_X Total_S 19961998 20002002 20042006 20082010 20122014 Epoch (year) 1000 1200 1400 1600 1800 Flux Density (mJy) J1407+2827 Total_X Total_S 2002 2004 2006 2008 2010 2012 2014 2016 2018 Epoch (year) 300 400 500 600 700 Flux Density (mJy) J1511+0518 Total_X Total_S 2008 2010 2012 2014 2016 2018 Epoch (year) 100 150 200 250 300 Flux Density (mJy) J1602+2418 Total_X Total_S 2015 2016 2017 2018 Epoch (year) 200 300 400 500 600 700 800 900 1000 Flux Density (mJy) J1815+6127 Total_X Total_S 1995 1998 2001 2004 2007 2010 2013 2016 2019 Epoch (year) 300 400 500 600 700 800 900 1000 1100 Flux Density (mJy) J1945+7055 Total_X Total_S 1995 1998 2001 2004 2007 2010 2013 2016 2019 Epoch (year) 300 400 500 600 700 Flux Density (mJy) J2245+0324 Total_X Total_S Fig. 5. Light curve of total flux densities for confirmed CSOs (if data available). The 8.4-GHz total flux densities (Total_X) are shown as black dots and 2.3-GHz (Total_S) are displayed as gray dots Article number, page 23 of 28 A&A proofs: manuscript no. output                                                                                                                                                                                                                                                                                         Fig. 6. Proper motion of different components in each confirmed CSO. Article number, page 24 of 28 T. An , Y. Zhang , S. Frey, W.A. Baan and A. Wang: Identifying CSOs with Gaia and VLBI                                                              ‘                                                                       Fig. 7. Proper motion of different components in each core–jet source. Article number, page 25 of 28