Peering into the Heart of Darkness with VLBA: Radio-quiet Active Galactic Nucleus in the JWST North Ecliptic Pole Time-domain Field Payaswini Saikia, Ramon Wrzosek, Joseph Gelfand, Walter Brisken, W. D. Cotton, S. P. Willner, Hansung B. Gim, et al. Accessibility Disclaimer: For a more accessible version of this document, please submit an accessibility request form through the Montana State University Library website. Made available through Montana State University’s ScholarWorks B_ MONTANA STATE UNIVERSITY LIBRARY Peering into the Heart of Darkness with VLBA: Radio-quiet Active Galactic Nucleus in the JWST North Ecliptic Pole Time-domain Field Payaswini Saikia1 , Ramon Wrzosek1 , Joseph Gelfand1 , Walter Brisken2, William Cotton2 , S. P. Willner 3 , Hansung B. Gim4 , Rogier A. Windhorst5 , Vicente Estrada-Carpenter6 , Ivan Yu. Katkov1,7 , Ingyin Zaw1 , Michael J. Nicandro Rosenthal8 , Hanaan Shafi1 , Kenneth Kellermann2 , James Condon9 , Anton M. Koekemoer10 , Christopher J. Conselice11 , Rafael Ortiz, III5 , Christopher N. A. Willmer12 , Brenda Frye13 , Norman A. Grogin10 , Heidi B. Hammel14 , Seth H. Cohen5 , Rolf A. Jansen5 , Jake Summers5 , Jordan C. J. D’Silva15,16 , Simon P. Driver15 , Nor Pirzkal10 , Haojing Yan17 , and Min S. Yun18 1 Center for Astrophysics and Space Science (CASS), New York University Abu Dhabi, PO Box 129188, Abu Dhabi, UAE; ps164@nyu.edu 2 National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903, USA 3 Center for Astrophysics, Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA 4 Department of Physics, Montana State University, P.O. Box 173840, Bozeman, MT 59717, USA 5 School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287-1404, USA 6 Institute for Computational Astrophysics and Department of Astronomy & Physics, Saint Mary’s University, 923 Robie Street, Halifax, Nova Scotia B3H 3C3, Canada 7 Sternberg Astronomical Institute, M.V. Lomonosov Moscow State University, 13 Universitetsky prospect, Moscow, 119991, Russia 8 Department of Astronomy, University of Wisconsin-Madison, 475 North Charter Street, Madison, WI 53706, USA 9 Unaffiliated, 2571 Old Lynchburg Road, North Garden, VA 22959, USA 10 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA 11 Jodrell Bank Centre for Astrophysics, Alan Turing Building, University of Manchester, Oxford Road, Manchester M13 9PL, UK 12 Steward Observatory, University of Arizona, 933 N Cherry Ave, Tucson, AZ, 85721-0009, USA 13 Department of Astronomy/Steward Observatory, University of Arizona, 933 N Cherry Ave, Tucson, AZ, 85721-0009, USA 14 Association of Universities for Research in Astronomy, 1331 Pennsylvania Ave NW, Suite 1475, Washington, DC 20005, USA 15 International Centre for Radio Astronomy Research (ICRAR) and the International Space Centre (ISC), The University of Western Australia, M468, 35 Stirling Highway, Crawley, WA 6009, Australia 16 ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia 17 Department of Physics and Astronomy, University of Missouri, Columbia, MO 65211, USA 18 Department of Astronomy, University of Massachusetts, Amherst, MA 01003, USA Received 2025 May 16; revised 2025 June 8; accepted 2025 June 21; published 2025 August 1 Abstract We present initial results from the 4.8 GHz Very Long Baseline Array (VLBA) survey of the JWST North Ecliptic Pole Time-Domain Field (TDF). From 106 radio sources found in the Karl G. Jansky Very Large Array (VLA) observations in the TDF, we detected 12 sources (∼11% detection rate) at ∼3.3 µJy rms sensitivity and ∼4 mas resolution. Most detections exhibit parsec-scale emission (less than 40 pc) with high VLBA/VLA flux density ratios and brightness temperatures exceeding 105 K, confirming nonthermal active galactic nucleus (AGN) activity. Spectral indices ≳ −0.5 correlate with higher VLBA/VLA flux ratios, consistent with synchrotron emission from AGN coronae or jets. In the majority of our sources, star formation contributes less than 50% of the total VLBA radio emission, with a few cases where the emission is almost entirely AGN driven. Although the radio emission from radio quiet AGN is thought to be primarily driven by star formation, our VLBA observations confirm that there is also often a contribution at various levels from black hole driven AGN. Eight VLBA detections have JWST/NIRCam counterparts, predominantly early-type, bulge-dominated galaxies, which we use to get an estimate of the redshift and star formation rate (SFR). Wide-field Infrared Survey Explorer colors indicate that VLBA detections are either AGN or intermediate-disk-dominated systems, while VLBA nondetections correspond to extended, star-forming galaxies. We compare SFRs derived from previous SCUBA-2 850 µm observations with new JWST-based estimates, and discuss the observed discrepancies, highlighting JWST’s improved capability to disentangle AGN activity from star formation. Unified Astronomy Thesaurus concepts: Active galactic nuclei (16); Active galaxies (17); High energy astrophysics (739); Radio galaxies (1343); Radio sources (1358) 1. Introduction Growing evidence suggests that galaxies and their super- massive black holes (SMBHs) strongly influence each other’s properties and evolution. Feedback from SMBH (MBH ≳ 106M⊙) in active galactic nuclei (AGN) also affects stellar populations, as indicated by the linear correlation between galactic bulge and SMBH masses (K. Gebhardt et al. 2000), and the quenching of star formation (SF) in AGN host galaxies (P. F. Hopkins et al. 2008). Further interconnection is observed in an order of magnitude decline since cosmic noon (z ∼ 2) of the comoving star formation rate (SFR) density, the mean specific SFR (sSFR ≡ SFR/M〉) of galaxies, and SMBH growth rates (P. Madau & M. Dickinson 2014; J. C. J. D’Silva et al. 2023). Radio-continuum milliarcsecond resolution studies have found that >50% of the emission of compact The Astrophysical Journal 989:29 (24pp), 2025 August 10 https://doi.org/10.3847/1538-4357/ade709 © 2025. The Author(s). Published by the American Astronomical Society. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1 OPEN ACCESS ® CrossMark e e e e ® ® e e e ® e e e e e ® e e e ® ® e e e ® ® e e ® l® G.LJ https://orcid.org/0000-0002-5319-6620 https://orcid.org/0000-0002-2200-0592 https://orcid.org/0000-0003-4679-1058 https://orcid.org/0000-0001-7363-6489 https://orcid.org/0000-0002-9895-5758 https://orcid.org/0000-0003-1436-7658 https://orcid.org/0000-0001-8156-6281 https://orcid.org/0000-0001-8489-2349 https://orcid.org/0000-0002-6425-6879 https://orcid.org/0000-0002-5208-1426 https://orcid.org/0000-0003-3910-6446 https://orcid.org/0000-0001-9012-4020 https://orcid.org/0000-0002-0093-4917 https://orcid.org/0000-0003-4724-1939 https://orcid.org/0000-0002-6610-2048 https://orcid.org/0000-0003-1949-7638 https://orcid.org/0000-0002-6150-833X https://orcid.org/0000-0001-9262-9997 https://orcid.org/0000-0003-1625-8009 https://orcid.org/0000-0001-9440-8872 https://orcid.org/0000-0001-8751-3463 https://orcid.org/0000-0003-3329-1337 https://orcid.org/0000-0003-1268-5230 https://orcid.org/0000-0002-7265-7920 https://orcid.org/0000-0002-9816-1931 https://orcid.org/0000-0001-9491-7327 https://orcid.org/0000-0003-3382-5941 https://orcid.org/0000-0001-7592-7714 https://orcid.org/0000-0001-7095-7543 mailto:ps164@nyu.edu http://astrothesaurus.org/uat/16 http://astrothesaurus.org/uat/17 http://astrothesaurus.org/uat/739 http://astrothesaurus.org/uat/739 http://astrothesaurus.org/uat/1343 http://astrothesaurus.org/uat/1358 https://doi.org/10.3847/1538-4357/ade709 https://crossmark.crossref.org/dialog/?doi=10.3847/1538-4357/ade709&domain=pdf&date_stamp=2025-08-01 https://creativecommons.org/licenses/by/4.0/ radio sources, which are unresolved by the NSF’s Karl G. Jansky Very Large Array (VLA),19 is produced by AGN accretion processes, while the rest might be traced to SF processes (A. Maini et al. 2016; N. Herrera Ruiz et al. 2017; J. F. Radcliffe et al. 2018). Notably, for the fainter source population, SF dominates on kiloparsec scales or larger, which are often marginally resolved or entirely unresolved by the VLA (W. D. Cotton et al. 2018). The origin of this radio emission in faint sources is still uncertain. Deep-field and multiwavelength studies are essential to study radio-quiet (RQ) AGN, which represent more than 90% of the detected AGN (P. Padovani 2017). The high sensitivity of deep-field radio surveys makes them the most effective way to study AGN emission mechanisms, and their effects on the surrounding media can be analyzed with multiwavelength follow-ups (V. Smolcic et al. 2015; A. Maini et al. 2016; P. Saikia et al. 2018). However, in order to distinguish between the SF radio emission and the AGN radio emission, fainter RQ AGN samples must be targeted to eliminate the Very Long Baseline Interferometry (VLBI) bias toward AGN-dominated sources (P. Padovani 2016). In the case of RQ AGN, different correlations (see also Table 1) can help distinguish between different emission mechanisms (F. Panessa et al. 2019). In most cases, RQ AGN emission has been observed to be synchrotron radiation, emitted by relativistic electrons that are accelerated by moving shocks in organized AGN outflows (N. L. Zakamska & J. E. Greene 2014). However, various mechanisms, such as SF, winds, and/or low-power jets driven by an AGN, free–free emission from photoionized gas, and coronal activity in the innermost accretion disk, could also contribute to radio emission in these sources (F. Panessa et al. 2019). A comprehensive study of 144 bright quasars (PG quasar sample) led A. Laor et al. (2019) to discover that the radio spectral index ( ; Flux density Sν ∝ ν ), the variability of the AGN’s radio emission, and the Eddington ratios ( L LEdd )20 are correlated with the emission mechanisms of the AGN. As can be seen in Table 1, RQ AGN with higher Eddington ratios (>0.3) have a “steeper spectra” than those with lower Eddington ratios. This suggests that the origin of the AGN’s radio emission strongly depends on the accretion modes onto the SMBH (see also Table 1). Deep multiwavelength surveys of the extragalactic sky can be used to determine the evolution of galaxies and AGNs earlier in the history of the cosmos. The James Webb Space Telescope (JWST) North Ecliptic Pole (NEP) Time-Domain Field (TDF) is a 14 diameter field that was observed by the JWST Guaranteed Time Observations program (JWST-GTO- 2738; PI: R. A. Windhorst). The JWST NEP TDF (hereafter TDF) has been chosen to study the nature of AGN given its optimal properties for time-domain observations at multiple wavelengths (R. A. Jansen & R. A. Windhorst 2018). The TDF is notable for its continuous accessibility by the JWST, low galactic extinction, low zodiacal foreground light, and absence of bright galactic stars (free from sources brighter than mAB ∼ 16). The field has a wealth of multiwavelength ancillary data obtained with both ground-based and space- based surveys, as tabulated by R. Jansen21 and X. Zhao et al. (2024); which has several dedicated surveys in optical wavelengths (56 narrowband optical filters plus u, g, r, and i filters, as part of the Javalambre-Physics of the Accelerating Universe Astrophysical Survey; A. Hernán-Caballero et al. 2023), including a time-domain optical study (at visible wavelengths using TREASUREHUNT Hubble Space Tele- scope data; R. O’Brien et al. 2024), near-infrared (NIR; Y, J, H, and K imaging obtained using the MMT-Magellan Infrared Imager and Spectrometer (MMIRS) on the MMT; C. N. A. Willmer et al. 2023), X-rays (3−24 keV and 0.5−10 keV fluxes with NuSTAR and XMM-Newton; X. Zhao et al. 2024), radio (3 GHz observations using the VLA; M. Hyun et al. 2023), and submillimeter (850 µm observations with the Submillimetre Common-user Bolometer Array 2, hereafter SCUBA-2, of the James Clerk Maxwell Telescope, hereafter JCMT; M. Hyun et al. 2023). The initial JWST survey of the field, conducted as part of the Prime Extragalactic Areas for Reionization and Lensing Science (PEARLS) TDF program (using NIRCam infrared observa- tions to search for radio counterparts; S. P. Willner et al. 2023), has already been completed, along with a detailed visual search for galaxies exhibiting central pointlike features in the TDF (R. Ortiz et al. 2024). A high-resolution radio survey of the field is necessary to study how different accretion modes affect AGN emission, to understand how AGN affects galaxy formation and evolution, and to explore the origin of low-luminosity AGN emission, which is poorly understood especially in the case of RQ AGN. The observations in this paper are part of a radio program using the VLA and the Very Long Baseline Array (VLBA) to generate a list of extragalactic radio sources using the VLA and then identify which ones contain a significant AGN component using the VLBA. The purpose of the VLBA TDF deep survey is to identify and determine the nature of RQ AGN and to image the sources with milliarcsecond resolution and microJansky (µJy) rms sensitivity. Similar deep surveys with the VLBA and other VLBI telescopes have already been conducted in different fields, as outlined in Table 2. These surveys have proved that the methodology is successful, obtaining several detections at ∼1.4 GHz. Data have been published from the Hubble Deep Field (HDF; M. A. Garrett et al. 2001), the VLBA and Green Bank Telescope (GBT) NOAO Boötes Field (M. A. Garrett et al. 2005), the Lockman Hole/XMM (E. Middelberg et al. 2013), Hubble Deep Field North (HDF-N) and Hubble Flanking Fields (HFF; S. Chi et al. 2013), the COSMOS Field (N. Herrera Ruiz et al. 2017, 2018), the northern Square Kilometre Array PAthfinder Radio Continuum Surveys (SPARCS) reference field (A. Njeri et al. 2023), and the GOODS-N Field (J. F. Radcliffe et al. 2018). Compared with these deep surveys, the data presented in this paper are among the most sensitive (only one other field is comparable), while also being at a significantly higher frequency (4.8 GHz, while all the other fields are at 1.4–1.6 GHz), making the detected sources less susceptible to synchrotron self-absorption. This paper presents initial findings from the 4.8 GHz VLBA TDF deep-field survey, based on 55.3 effective hr of VLBA observations with an rms sensitivity of ∼3.3 µJy beam−1 and a 19 The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. 20 Ratio of the bolometric luminosity L and the Eddington luminosity LEdd of the AGN. LEdd is the maximum luminosity that the AGN can achieve when its radiation pressure and gravitational force are balanced. 21 http://lambda.la.asu.edu/jwst/neptdf/ 2 The Astrophysical Journal 989:29 (24pp), 2025 August 10 Saikia et al. http://lambda.la.asu.edu/jwst/neptdf/ resolution of 4 mas. The paper is organized as follows: In Section 2, we discuss the VLBA observations of the TDF, including source selection and data reduction methods. Section 3 discusses the multiwavelength counterparts of our sample, particularly focusing on optical (the Sloan Digital Sky Survey, hereafter SDSS), millimeter (SCUBA-2), and infrared (Wide-field Infrared Survey Explorer, hereafter WISE, JWST) wavelengths. Section 4 presents the radio wavelength analysis from the VLBA and previous multiwavelength detections. In Section 5, we discuss our findings, and in Section 6, we provide a summary of our results and present the conclusions of the study. Finally, Appendix A includes a catalog of VLBA nondetections and a mosaic of their JWST counterparts. Throughout this paper, we adopt the ΛCDM cosmology parameters with the Hubble constant H0 = 67.66 km s−1 Mpc−1, matter density parameter ΩM = 0.3111, and dark-energy density parameter ΩΛ = 0.6889 (Planck Collaboration et al. 2020). 2. Observations and Data Reductions 2.1. Sample We used the 3 GHz VLA observations of the TDF consisting of 588 objects (M. Hyun et al. 2023), to identify pointlike sources. The parent sample is comprised of unresolved objects at 3 GHz, with a single phase calibrator, achieving an rms sensitivity of 1 µJy beam−1 at a resolution of 0.7. A central portion of the TDF was observed with the VLBA under project codes BB388 and BB397 (PI: W. Brisken). The field was centered on a VLBA calibrator source J1723∫6547. The chosen field contains no other strong radio source. For the VLBA observations, we employed a single-pointing strategy centered on the same position as the VLA 3 GHz observations, using the same phase calibrator for consistency and phase referencing. All VLA-detected radio sources that were unresolved and exhibited flux densities �5σ above the local rms noise were selected as candidates for VLBA follow-up. Due to the smaller primary beam of the VLBA at 4.8 GHz, the effective field of view was more limited, resulting in a reduced number of detectable sources. The initial VLBA correlation was performed with the pointing center on the phase calibrator, after which multiple recorrelations were carried out at different phase centers (PCs), targeting the brightest VLA sources. The target selection for recorrelation was constrained to sources within 6 of the pointing center, where the primary-beam response falls to 0.25. This resulted in a total sample of 106 sources within 1.5 radius of the VLA position. 2.2. Observations The VLBA observations were made at a central observing frequency of 4832 MHz and bandwidth of 256 MHz using both right and left circular polarizations. The specific observing setup was chosen to maximize instantaneous sensitivity and minimize the effects of radio frequency interference. At the observing frequency, the central calibrator source had a flux density of ∼160 mJy, sufficient to allow self-calibration. The circumpolar VLBA calibrator J2005∫7752 with ∼1.0 Jy flux density at 5 GHz was observed approximately once every 90 minutes to serve as a bandpass calibrator. Table 2 VLBI Deep Surveys Field(s) Telescopes Central ν Detections Detection Fraction Sensitivity References (GHz) (%) (µJy beam−1) HDF EVN 1.6 2 40 33 M. A. Garrett et al. (2001) NOAO Boötes VLBA∫GBT 1.4 9 15 9 M. A. Garrett et al. (2005) Lockman Hole VLBA 1.4 65 30 20 E. Middelberg et al. (2013) HDF-N and HFF Global VLBI 1.4 21 23 7.3 S. Chi et al. (2013) COSMOS VLBA 1.54 468 20 10 N. Herrera Ruiz et al. (2017) COSMOS VLBA∫GBT 1.54 35 20 3.5 N. Herrera Ruiz et al. (2018) GOODS-N EVN 1.6 31 10 9 J. F. Radcliffe et al. (2018) SPARCS EVN∫e-Merlin 1.6 11 21 6–10 A. Njeri et al. (2023) NEP VLBA 4.8 12 20 3.3 Present work Note. The table presents a compilation of deep radio surveys conducted in various fields using VLBI techniques. It includes the field name, telescope and central frequency, number of detections, detection fraction relative to the total observed sample, achieved sensitivity, and relevant references. European VLBI Network (EVN). Table 1 AGN emission mechanisms Spectral Index Emission VLBI Radio Eddington Variability Physical ( ) Mechanism Morphology Ratio Mechanism (1) (2) (3) (4) (5) (6) ≲−0.5 Opt. thin synchrotron Highly elongated >0.3 (High) Y Jet (steep) L Aspherical L N AGN-driven wind ≳−0.5 Opt. thick synchrotron Pointlike ∼0.3 (Low) Y Coronal emission (flat) Opt. thin bremsstrahlung Diffuse L N Broad-line region Note. Expected properties of proposed AGN emission mechanisms, and correlations with (1) spectral indices, (2) emis-sion mechanisms, (3) radio morphology on VLBI scales, (4) Eddington ratios, (5) the variability observed, and (6) physicalmechanisms responsible for the observed radio emission F. Panessa et al. (2019). 3 The Astrophysical Journal 989:29 (24pp), 2025 August 10 Saikia et al. II The observations were well suited as “filler” observations at the VLBA. The TDF can be observed with the VLBA for about 18 hr each day. A series of template observing files were provided to VLBA Operations, which scheduled observations whenever conditions were poor for other observations in the dynamic queue. This paper presents an analysis based on the first 137 hr of observing time allocated at the VLBA for this program, including calibration and overheads, corresponding to 55.3 effective on-source hr after accounting for periods when the full array was not available. A subsequent publication will follow with a complete data reduction. The ultimate ambition of the VLBA deep-field imaging is to amass 500 hr of VLBA observing time with a goal of reaching approximately ∼1.3 µJy beam−1 image sensitivity at the center of the field. 2.3. Correlation We correlated the observations with the DiFX correlator (A. T. Deller et al. 2011). The multiphase-center mode was used to allow the formation of separate correlated data sets for the central calibrator source and all 106 additional fields. In this mode, the data were correlated with 31.25 kHz spectral resolution and 40 ms time resolution, sufficient to avoid bandwidth and time smearing anywhere in the VLBA primary beam. After each of these subintegrations, visibility spectra were appropriately phase shifted to correspond to each of the PCs correlated. Time and spectral averaging was then performed separately for each PC to achieve a final resolution of 0.5 MHz. The correlation parameters led to a usable field of view for each PC of about 4″. 2.4. Calibration Calibration and imaging were performed in the Astronom- ical Image Processing System (AIPS) data reduction package (E. W. Greisen 2003). A data reduction pipeline was used to process all of the data consistently. There were two independent steps in the calibration: determination and application. Rather than developing a pipeline with complex logic in the “POPS” language that AIPS uses, Python language programs were used to generate explicit scripts based on a project status file, which contained relevant information for each observation. The calibration determination was performed on a per- observation basis. Data validity flags from the VLBA online system were applied. In a small number of cases, an antenna was excluded from analysis due to poor sensitivity not captured by the online system. Furthermore, some low-altitude data were discarded when the phases were changing rapidly. The calibration routine followed the method suggested by R. C. Walker (2014). The bright calibrator J2005∫7752 was used for determining the residual delays and complex bandpass. The central source J1723∫6547 was used for determination of delays and complex gains (using AIPS tasks FRING and CALIB, respectively). A high-fidelity source model for J1723∫6547, constructed from the combined 137 hr of observing, was used in the complex gain determination. When determining the gains, constraints ensured that only antennas that experienced the best weather could affect the overall gain scaling. This was in lieu of determining corrections due to atmospheric opacity, which are typically not important at 5 GHz observing frequency. The product of this pipeline step consisted of three tables: an AIPS flagging (FG) table containing the final set of data validity flags, an AIPS bandpass (BP) table containing the complex bandpass table, and an AIPS calibration (CL) task containing the delays and complex gains. The calibration was applied on a per-phase-center basis, where data from all relevant observations for a given PC were combined to create a single calibrated data set. We loaded the correlated data for each observation into AIPS, with each observation occupying its own catalog entry. Subsequently, the FG, BP, and CL tables from the prior calibration step for the corresponding observation were loaded. To transfer the calibration from J1723∫6547 to the target PC, a source renumbering was required in the CL table. This nonstandard operation was executed using the AIPS task TABED with OPTYPE=“REPL.” The AIPS task SPLIT was used to apply the calibration values, creating new databases with corrected visibilities. Finally, the AIPS task DBAPP was used to append all of the calibrated observations into a single database ready for imaging. This “in-beam” calibration scheme works very well for two reasons: (1) the calibration was determined con- temporaneously, so no interpolation was required; (2) the angle between the calibrator source and the target field was less than 6 , leaving only very small angular gradients uncorrected. 2.5. Imaging We Fourier transformed, cleaned, and imaged the source fields (UV data) with IMAGR, averaging together all 256 frequency channels (STOKES = I). We used natural weighting (ROBUST = 5) to minimize the rms noise. The central ×1 .6 1 .6 around each PC was imaged using 4096 pixels along each axis, and the average synthesized beam in each image was 4 × 3.5 mas. The typical sensitivity loss from delay and time smearing at 6″ offset is ∼48%. Source detection required the cleaned image to contain a source with a peak flux >5σ above the background noise. After initial imaging, we analyzed fields with clear detections using AIPS’ JMFIT. We applied primary-beam corrections to the peak flux density (Speak) and integrated flux density (Sint) of the source. To check for possible coordinate shifting, we reimaged the fields with no detections with 6″ sides and 12,000 pixels in each axis. No additional detections were found. 2.6. Source Properties Of the sample of 106 radio VLA sources, 12 gave VLBA detections. We measured the source properties from the images by fitting them with Gaussian and point models vis AIPS JMFIT, the point model being a Gaussian with a size fixed to that of the synthesized beam. Figure 1 presents a comparison between the flux densities obtained from the point model and the Gaussian model. Higher-resolution imaging was also used to check for potential structures in the detected sources. However, this increase of angular resolution comes at the cost of higher image noise. Only PC 64 appears resolved, but no specific structures were detected. PC 67 also exhibits a slight indication of being resolved, but the significance is low. For the other fields, we applied a point-model fit (DOWIDTH = −1). The resultant images are plotted in Figure 2. 4 The Astrophysical Journal 989:29 (24pp), 2025 August 10 Saikia et al. If " 3. Multiwavelength Counterparts 3.1. VLA Counterparts The VLA survey of the TDF served as the parent sample for selecting our VLBA PCs (M. Hyun et al. 2023). The VLA sample was observed at 3 GHz with an rms sensitivity of 1 µJy beam−1 at a resolution of 0.7. To account for positional uncertainties in the VLA, we searched for VLBA detections within a 1.5 radius around each VLA coordinate. The VLA counterparts for eight of the VLBA detections are shown in Figure 3 as illustrative examples. To estimate the radio spectral index from the VLA 3 GHz data (M. Hyun et al. 2023), we subdivided the 2 GHz bandwidth into 25 subbands, each with a 3% fractional bandwidth. We generated images for each subband indepen- dently but performed joint CLEANing to improve the signal quality while accounting for frequency-dependent variations in sky brightness and antenna gain. For each source in our catalog, we interpolated the flux densities from these subband images, applying frequency-dependent gain corrections, then fit a spectrum for each source to yield an estimated spectral index. We adopt the convention Sν ∝ ν , where Sν represents the integrated radio flux density, and denotes the intrinsic spectral index of the source. Due to limitations in precise primary-beam correction with frequency, these spectral indices are uncertain, but they indicate the general spectral behavior of the sources. 3.2. WISE Counterparts We conducted a search for mid-infrared (MIR) counterparts of our VLBA sources in the WISE mission catalog (E. L. Wright et al. 2010), across four wavelength bands: 3.4 µm (W1), 4.6 µm (W2), 12 µm (W3), and 22 µm (W4). Using a 10″ cone search radius of our VLBA positions, we find that all of our VLBA detections, except for PC 25, have WISE counterparts. 3.3. SCUBA Counterparts We also crossmatched the radio sample with the 850 µm observations of the TDF with the Submillimeter Common-user Bolometer Array 2 (SCUBA-2) of the JCMT (M. Hyun et al. 2023). The survey was carried out over an area of approximately 0.087 deg2 in the TDF, achieving a mean 1σ sensitivity of 1.0 mJy beam−1 . For the discussion on the SCUBA counterparts, we use the SCUBA−VLA associations identified by M. Hyun et al. (2023). Currently, the SCUBA −VLA crossmatch yielded a total of 85 sources, but only 17 of these sources matched with our VLBA PCs, with 3 of them being detections (PC 26, 46, and 71) and the remaining 14 being nondetections. However, because of the relatively poor angular resolution of SCUBA observations and the resulting positional uncertainties, we remain cautious about confidently associating them with specific VLA sources. More precise submillimeter positions are needed to fully leverage the potential of SCUBA-2 data. 3.4. JWST/NIRCam Counterparts To further investigate potential infrared counterparts of the VLBA-detected sources, we crossmatched our sample with JWST PEARLS observations from the literature. S. P. Willner et al. (2023) described the association between the M. Hyun et al. (2023) VLA sources and the first spoke of the JWST/ NIRCam imaging of the TDF. NIRCam has now observed the remaining three spokes, and S. Willner et al. (2025, in preparation) will describe the results. In brief, nearly all of the 211 VLA radio sources within the NIRCam area have an NIRCam counterpart, and more than 80% of the counterparts have magnitudes [F444W] ∼ 22 AB. All eight of the VLBA- detected sources within the NIRCam area have counterparts, the faintest of which has [F444W] ≈ 21.4 AB. Figure 3 presents, for the first time, postage-stamp images of these VLBA detections across seven JWST NIRCam bands (F090W, F115W, F150W, F200W, F277W, F356W, and F444W) using ASTROCUT22 (C. E. Brasseur et al. 2019). Four counterparts have spectroscopic redshifts, and the remainder have photometric redshifts (see Section 4.8 for more details). We also crossmatched our observations with the 66 galaxies observed by JWST/NIRCam in R. Ortiz et al. (2024) that looked for galaxies with clear point-source centers indicative of AGN, and found that three of our VLBA detections (PC 3, 7, and 64) are included in their sample. We further expand on the optical-NIR properties of our detections in Section 4.7. 3.5. SDSS Counterparts A search for optical counterparts within 1″ of our VLBA sample in the SDSS archive identified 34 matches. Among these, three sources were detected with the VLBA (PC 24, 41, and 64). All optical counterparts are within 0.1 of their corresponding radio positions and have photometric redshifts zph ∼ 0.3. The nondetected sources, on the contrary, exhibit a broad range of distances (0.1 ∼ zph ∼ 0.8). This spread in redshift may suggest diverse evolutionary Figure 1. Point-model vs. Gaussian-model peak flux densities (natural weighting before primary-beam correction). The sources are labeled with their VLBA PC numbers (see Figure 2 for the complete VLBA snapshots, and Table 3 for the coordinates). The dashed line shows equality. All sources except PC 64 (VLA ID 528) lie close to the identity line. PC 64 (VLA ID 528) was the only one resolved with the current beam settings, while PC 67 (VLA ID 554) shows hints of being marginally resolved. 22 https://astrocut.readthedocs.io/en/latest/ 5 The Astrophysical Journal 989:29 (24pp), 2025 August 10 Saikia et al. II I y = x I I I I I I I I I 20 40 60 80 100 12 0 Gaussian-fit VLBA Speak (µJy/beam) II - - - 140 II https://astrocut.readthedocs.io/en/latest/ stages or environments among these sources, potentially contributing to their nondetection in the higher-resolution VLBA observations. Legacy survey cutouts (A. Dey et al. 2019) of the three optical counterparts to our VLBA detections are shown in Figure 4, where we present red, green, and blue (RGB) images Figure 2. Natural weighting (ROBUST = 5) 4.8 GHz VLBA images. Sources are identified in each panel. Image rms and contour levels are: (a) PC 3 (image rms = 3.5 µJy beam−1; contours = 3σ, 5σ, 10σ), (b) PC 7 (6.2 µJy beam−1; 3σ, 5σ, 10σ, 15σ), (c) PC 14 (3.5 µJy beam−1; 3σ, 5σ, 7.5σ), (d) PC 24 (4.0 µJy beam−1; 3σ, 5σ, 10σ, 15σ), (e) PC 25 (3.5 µJy beam−1; 3σ, 5σ, 7.5σ), (f) PC 26 (3.5 µJy beam−1; 3σ, 5σ, 10σ), (g) PC 41 (3.1 µJy beam−1; 3σ, 5σ, 10σ), (h) PC 46 (3.2 µJy beam−1; 3σ, 5σ, 7.5σ), (i) PC 47 (3.1 µJy beam−1; 3σ, 5σ, 7.5σ), (j) PC 64 (4.6 µJy beam−1; 3σ, 5σ, 10σ, 20σ), (k) PC 67 (4.7 µJy beam−1; 3σ, 5σ, 10σ, 20σ), and (l) PC 71 (4.8 µJy beam−1; 3σ, 5σ, 7.5σ). Image rms and color bar indicate the surface brightness uncorrected for primary-beam attenuation, and the crosshatched ellipses shows the restored beams. 6 The Astrophysical Journal 989:29 (24pp), 2025 August 10 Saikia et al. PC 3 (VLA ID 124) 'f PC 7 (VLA ID 141) PC 14 (VLA ID 182) Q) l!) ... 0 d, l!) ci N - l!l 0 0 r--. l!) 0 0 d, ci 0 . N 0 "' ..., 0 'f Q) Q) l!) en l!) l!) 0 l!) f::? d, 0 d, "' 0 ci - 0 N 0 ., r--. en O ci :g ci l!) (.) w d, 0 0 l!) l!) C) 0 "" 0 0 0 ci 0 ci -0.04 -0.045 -0.05 0.165 0.16 0.155 0.04 0.035 0.03 'f PC 24 (VLA ID 260) PC 25 (VLA ID 262) Q) PC 26 (VLA ID 279) l!) "' 'f d, l!) r--. 0 Q) 0 ... 9 ... a o 0 l!) 'f l!) 0 ci N d, Q) d, ..., "' N "' 0 l!) ill I!) l!) l!) 0 f::?"" 9 l!) "'0 d, d, - ci N l!) l!) N ., C) en 0 d, "' l!) ci 0 'f (.) d, "" w 0 Q) 0 "" 9 0 ci C) 0 0 0 ci 0 0.05 0.045 0.04 -0.075 -0.08 -0.085 0.01 0.005 0 l!) l!) l!) PC 41 (VLA ID 382) d, PC 46 (VLA ID 403) d, PC 47 (VLA ID 434) d, "' 0 N l!) N ... ci l!) 9 l!) l!) d, d, -o 0 . "l "l oO l!) 0 d, N ..., N 0 l!) l!) Q) C) l!) l!) d, en 0 d, f::? l!) ci 9 m a l!) l!) l!) "' d, d, d, 0 l!) l!) (.) C) ci l!) ci w 0 l!) 0 ci ... 9 0 0 0 ci 0 -0.015 -0.02 -0.025 0.115 0.11 0.105 -0.035 -0.04 -0.045 'i 'i l!) PC 64 (VLA ID 528) Q) Q) d, PC 67 (VLA ID 554) N PC 71 (VLA ID 614) ... 0 "' 9 0 l!) 0 9 d, 0 "' 0 0 @ "' ..., 9 l!) 0 N l!) Q) 'f l!) l!) 0 d, en f::? "' d, 9 N Q) 0 l!) 9 l!) ., en l!) l!) "' 0 0 d, (.) 9 "' w 0 0 ... 9 0 N 9 0 0 0 0 9 -0.03 -0.025 0.02 0.015 -0.045 -0.05 -0.055 -0.06 -0.01 -0.015 -0.02 RA offset (arcsec; J2000) RA offset (arcsec; J2000) RA offset (arcsec; J2000) constructed from the g, r, and z bands, each with a size of 200 pixels and a pixel scale of 0.12 per pixel. . Results 4.1. Detection Rate We observed a targeted sample of 106 VLA sources in the TDF (M. Hyun et al. 2023) with the VLBA at 4.8 GHz. This significantly improved the resolution of the TDF in radio bands from 0.7 with the VLA to 4 mas with the VLBA. We detected 12 of 106 sources, or a VLBA detection fraction of ∼11% (∼3.3 µJy rms sensitivity). For brighter radio sources with VLA 3 GHz flux densities greater than 50 µJy, the detection rate increases to ∼35%. Table 3 gives the source properties of the detections. The deconvolved images of the detected sources are shown in Figure 2. Figure 3. Negative images of the eight VLBA-detections in the JWST/NIRCam area. The leftmost panels show the 3 GHz VLA radio image with the source ID included (M. Hyun et al. 2023). Other panels show the NIRCam images in the filters of F090W, F115W, F150W, F200W, F277W, F356W, and F444W. Each panel is 3″ × 3″. The green “∫” sign on the first postage stamp indicates the VLBA positions. The magenta circle indicates the VLA beam size of 0.7, centered around the VLA position. A logarithmic scale has been implemented for visualization. For the VLA images, the minimum value is fixed at −3 µJy, and the maximum is set to the 99.9999th percentile of the data. For the JWST images, the display range spans from the 0.01st percentile to the 99th percentile of the data. 7 The Astrophysical Journal 989:29 (24pp), 2025 August 10 Saikia et al. 124 141 182 260 382 403 434 528 II II 4.2. Resolved Source PC 64 (VLA ID 528) The only significantly resolved source (PC 64 or VLA ID 528) was refitted with two Gaussian components with results in Table 4. Both Gaussians had very similar centroids, but the physical sizes differ. The first component is elongated with the axis ratio 4.3. The second component has a radio-emitting region approximately 40 pc larger than that of the first. It exhibits a rounder structure, with the axis ratio 1.5. The first component could be a small jet, while the second component could be an AGN core or plasma heated when the small jet is terminated/interacts with the surrounding medium. 4.3. Brightness Temperature The brightness temperature (TB) of each of the 12 detections is calculated according to the following equation: ( ) ( ) ( )= +T k S z 2 ln 2 1 1b int 2 where λ = 0.0623 m (ν = 4.8 GHz), Boltzmann’s constant k = 1.380649 × 10−23 JK−1, z is taken to be 0 for all the sources as we do not have information regarding the redshift of these sources, and solid angle Ω = π (deconvolved major axis × deconvolved minor axis). For unresolved sources, we define the deconvolved size ≡ beam sizes, and the size of the radio-emitting region remains indeterminate, allowing only lower limits to be estimated for the brightness temperature. We find that the brightness temperatures for all the detected sources exceed 105 K. The TB values, listed in Table 5, are significantly higher than those typically produced by SF processes (J. J. Condon 1992). In nearby galaxies, such high- brightness temperatures can arise from AGN, as well as supernovae or their remnants. However, in more distant galaxies (z > 0.1), brightness temperatures in excess of 105 K can be reliably linked to accretion-related AGN emission, as the high energies required for such TB values point to an AGN origin (L. J. Kewley et al. 2000). 4.4. Radio Fluxes and Spectral Indices Figure 5 presents the distribution of 3 GHz peak flux densities for the VLA sample. When observed, nearly all of the brightest VLA sources were detected by the VLBA. All detected sources have S(3 GHz) > 50 µJy, highlighting a flux threshold for VLBA detection. The VLBA coordinates for all 12 detected sources are within 0.03 of the VLA positions. The VLBA nondetections could just be a matter of sensitivity, although two VLA sources with flux densities above 200 mJy (PC 6 and 33) were undetected in our VLBA survey. These two cases may exhibit intrinsically diffuse radio emission, i.e., substantial SF activity creating their VLA flux density. Such extended emission would be resolved in the VLBA observa- tions. Another possibility is that PC 6 and PC 33 exhibit intrinsic radio variability on long timescales. Although deep- field surveys have generally found the µJy−mJy radio sky to be quiescent (J. F. Radcliffe et al. 2019), variability at these flux densities has been reported in other studies (P. J. Hancock et al. 2016; K. P. Mooley et al. 2016), making this a plausible explanation for the observed nondetections. The radio spectral indices of the VLBA detections are centered around ∼ −0.4, and the majority of detections show ≳ −0.5 (Figure 6). In contrast, sources that are not detected with the VLBA predominantly have ≲ −0.5. Sources 1, 27, and 40 (VLA IDs 113, 282, and 379) have a flat or inverted spectral index and would be expected to appear in VLBA observations. However, these sources have VLA peak flux densities between 30 and 95 µJy, likely rendering them too faint for VLBA detection. Alternatively, their radio Figure . Legacy survey cutouts of the three optical counterparts of our VLBA detections (PC 24, 41, and 64). These are RGB images made from the g, r, and z bands, with a size of 200 pixels, and a pixscale of 0.12 per pixel. In all the cutouts, north is oriented at the top, and east to the left. 8 The Astrophysical Journal 989:29 (24pp), 2025 August 10 Saikia et al. PC 24 (VLA ID 260) • • PC 41 (VLA ID 382) PC 64 (VLA ID 528) II emission may be variable, potentially resulting in a diminished flux density during the VLBA observation epochs. In contrast, sources 46 and 64 (VLA IDs 403 and 528), which exhibit very steep spectra, were detected with the VLBA. This could indicate that at least some of their radio emission is from vigorous SF within the host galaxy, with an AGN component giving the VLBA signal. Alternatively, these detections may represent the AGN jets, observable at VLBA resolutions. E. Middelberg et al. (2013) conducted a VLBI survey of 217 radio sources in the Lockman Hole/XMMfield and found that most of the detections had aflat spectral index. Despite our sample being approximately 5 times fainter than and at a higher frequency (4.8 GHz instead of 1.4 GHz) than that of E. Middelberg et al. (2013), the same trend in the spectral index distribution suggests that we are observing a similar population at lower luminosities or greater distances. Figure 7 compares the VLBA/VLAflux density ratio with the VLA spectral index. The VLBA/VLAflux density ratio increases with flatter spectral indices. This trend can be attributed to synchrotron self-absorption, which requires higher densities (indicated by a higher VLBA/VLA ratio) and results in a characteristicflat spectrum. The compactness of these high-density sources makes them more likely to be detected by the VLBA. However, the question remains as to Table 3 VLBA Detections Source VLBAVLA PC VLA IDJ2000J2000∆Speak S/NS3 GHzSpec. Index () (hh mm ss) (deg arcmin arcsec) (mas) (µJy bm−1) (µJy) (1) (2)(3)(4) (5) (6) (7) (8)(9) 3 12417 22 30.3766∫65 51 07.90980.1143 ± 1133.1472.0 ± 12.3−0.37 ± 0.20 7 14117 22 33.3964∫65 47 57.78620.1174 ± 638.51071.0 ± 25.7−0.51 ± 0.20 14 18217 22 38.9746∫65 51 43.02700.178 ± 1016.374.3 ± 2.6−0.01 ± 0.20 24 26017 22 53.1466∫65 48 47.38700.153 ± 414.357.4 ± 2.0−0.17 ± 0.32 25 26217 22 53.7332∫65 52 17.74100.167 ± 816.4117.0 ± 3.7−0.41 ± 0.23 26 27917 22 55.6433∫65 53 01.38090.1148 ± 1132.5223.0 ± 6.8−0.50 ± 0.21 41 38217 23 11.9299∫65 50 14.33670.240 ± 49.1100.3 ± 7.1−0.09 ± 0.31 46 40317 23 16.9409∫65 50 45.46540.327 ± 47.5181.0 ± 6.5−0.90 ± 0.22 47 43417 23 22.5065∫65 49 45.63460.323 ± 46.850.5 ± 1.8−0.41 ± 0.33 64 52817 23 40.6700∫65 49 52.81340.1159 ± 549.6512.0 ± 15.4−1.00 ± 0.20 67 55417 23 45.4225∫65 43 57.53300.1274 ± 1146.0286.0 ± 8.70.51 ± 0.21 71 61417 23 59.7510∫65 45 48.33400.1109 ± 1221.6195.0 ± 6.0−0.43 ± 0.22 Note. (1): phase center (PC) number, used as reference for the VLBA sources in this project. (2): VLA ID (M. Hyun et al. 2023). (3), (4): R.A. () and decl. () (J2000) of the source, measured with the VLBA (natural weighting). (5): position uncertainty (∆) for the source. (6): peak (Speak) VLBAflux density of the source (4.8 GHz) after primary-beam correction. (7): signal-to-noise ratio (S/N) from the ratio of uncorrected Speak over image rms. (8): VLA 3 GHzflux density, corrected for the primary beam, and its uncertainty (M. Hyun et al. 2023). (9): spectral index of the VLA 3 GHz counterpart. Table Resolved Source Data: PC 64 (VLA ID 528) Component Maj/Min AxesPhysical SizeSint L4.8 GHzν L (mas) (pc)(erg s −1 cm −2 Hz −1 )(WHz −1 ) (W) First Gaussian 3.5 ± 0.318.7 ± 1.6(1.7 ± 0.1) × 10−27(8.88 ± 0.35) × 10 22 (4.26 ± 0.17) × 10 32 0.8 ± 0.6 4.3 ± 3.2LLL Second Gaussian 11.3 ± 1.260.3 ± 6.4(2.8 ± 0.3) × 10 −27 (14.61 ± 1.17) × 10 22 (7.01 ± 0.56) × 10 32 7.9 ± 0.9 42.1 ± 4.8LLL Note. L4.8 GHz and physical sizes calculated using the redshift z = 0.3760 (see Table 6). Table 5 Brightness Temperatures (Tb) of the VLBA Detections PC VLA ID♦Maj minΩ Tb (mas) (mas) (10−16 sr) (10 5 K) (1) (2)(3)(4) (5) (6) 3 1244.53.812.4>4.5 7 1414.23.811.8>5.8 14 1824.43.812.1>2.5 24 2602.52.13.8>5.4 25 2624.33.711.9>2.2 26 2794.43.912.5>4.6 41 3823.93.710.6>1.5 46 4034.03.711.0>1.0 47 4343.93.710.7>0.9 64 528+ 4.90.3 0.2+ 3.00.2 0.3 11.1+ 11.31.0 1.4 67 5544.22.78.5>12.7 71 6144.32.88.9>4.8 Note. (1): phase center (PC) number, used as reference for the VLBA sources in this project. (2): VLA ID of the 3 GHz counterparts (M. Hyun et al. 2023). ((3), (4)): deconvolved major (♦Maj) and minor ( min) axes of the VLBA detections. For the unresolved sources, the deconvolved maj/min axes are defined as the respective beam sizes, given that this would be their maximum angular size to remain unresolved (thus, the TB are lower limits). (5): solid angle (Ω) in steradians. (6): brightness temperature (TB) per Equation (1). 9 The Astrophysical Journal 989:29 (24pp), 2025 August 10 Saikia et al. why these compact cores do not produce larger-scale radio emission, despite there being no apparent restriction that prevents it. We calculated the expected VLA 4.8 GHz flux densities using spectral indices from the VLA 3 GHz observations. By analyzing which fraction of the predicted VLA emission was detected by the VLBA, we found a strong correlation between this fraction and the VLA spectral index. Figure 8 plots the VLBA 4.8 GHz peak flux density versus the predicted VLA 4.8 GHz peak flux density. The ≳ −0.5 sources have a higher fraction (located closer to the equality/dashed line) than steeper-spectrum sources. This suggests that the flatter- spectrum sources are truly compact and produce optically thick, probably self-absorbed, synchrotron emission. In con- trast, the steeper-spectrum sources are physically larger and produce optically thin synchrotron emission (K. I. Kellermann & I. I. K. Pauliny-Toth 1981). 4.5. Mid-infrared Colors We analyzed the MIR colors of the detected sources’ WISE counterparts, and classified the sources following the frame- work outlined by T. H. Jarrett et al. (2017). This separated the sources into four main categories: spheroid dominated, intermediate disk dominated, SF dominated, and AGN dominated (see Figure 9). This classification is refined using the AGN selection threshold from D. Stern et al. (2012), above which MIR emission is indicative of dust heated by AGN. Additionally, we included the “SF sequence” from T. H. Jarrett et al. (2019), which illustrates the typical color progression for normal galaxies ranging from quiescent to highly star forming. The WISE classification was developed for low redshifts and might need to be adjusted for higher redshifts. As shown in Figure 9, four VLBA-detected sources were detected in all the WISE bands. These are mostly classified as intermediate-disk or AGN-dominated galaxies, and none fall into the SF region. In contrast, many of the VLBA nondetected sources are in the SF region, indicating different primary emission sources between detections and nondetections, consistent with VLBA detections being AGN. 4.6. Physical Properties from Submillimeter Detections M. Hyun et al. (2023) crossmatched the VLA radio sample of the TDF with their 850 µm SCUBA-2 observations, identifying 85 possible VLA counterparts of SCUBA-2 sources, of which 17 match our VLBA PCs. Three of these (PC 26, 46, and 71) were detected by VLBA, while the remaining 14 were nondetections. The three VLBA-detected sources in the SCUBA sample are at redshifts of approximately z ∼ 1.5 with estimated stellar ages ranging from approximately 80 to 500 Myr. The physical properties derived from SCUBA-2 for the parent galaxies of VLBA detections show no substantial differences from the nondetections in key attributes such as stellar mass, SFR, or other derived galaxy parameters. Figure 5. Distribution of VLA peak flux densities (Speak) of the VLBA observed sources. The VLBA detections are depicted in red bins with horizontal dashes, and the nondetections in yellow bins with forward slashes. The complete VLA sample of the TDF (M. Hyun et al. 2023) are shown with empty green steps. The eight brightest VLA sources, with flux density in excess of 1100 mJy, are off scale to the right. Figure 6. Distribution of spectral indices (measured from VLA 3 GHz observation; M. Hyun et al. 2023) for the VLBA detections (red bins with horizontal dashes) and nondetections (yellow bins with forward slashes) in the TDF. Figure 7. VLBA/VLA flux density ratio vs. VLA spectral index of the VLBA-detected sources in the TDF (red stars) and the Lockman Hole/XMM field (blue squares; E. Middelberg et al. 2013). The TDF fluxes were measured at 4.8 GHz with the VLBA and at 3 GHz with the VLA, with the latter being extrapolated to 4.8 GHz using the source’s radio spectral index. In contrast, the Middelberg fluxes (for both VLA and VLBA) were measured at 1.4 GHz. 10 The Astrophysical Journal 989:29 (24pp), 2025 August 10 Saikia et al. 1000 ~-------------------~ 100 a; 10 ::, z a; ..0 E ::, z 0.1 16 14 12 10 8 6 4 2 200 c::::J Complete VLA Sample rzz:J VLBA Non-detections - VLBA Detections 400 600 800 1000 VLA flux density (3 GHz, mJy) [ZZl VLBA Non-detections -VLBA Detections -1 .25 -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 VLA Spectral Index 1.4~------------------~ 1.2 182 0.0 .L,---~ ~----~---~----,...., -1.0 -0 .5 0.0 0.5 1.0 VLA Spectral index All three VLBA detections show low JCMT peak flux densities compared to the nondetections (Figure 10, top panel), which could suggest comparatively lower levels of SF in the host galaxies of these three sources, and/or less dusty star- forming galaxies. To investigate this further, we examined the SCUBA- derived physical properties, focusing on the SFR of both detected and undetected sources (M. Hyun et al. 2023). Surprisingly, we found that the estimated SFRs were relatively high even for the detected sources (in the range of ∼450−700 M⊙ yr −1), contrary to what might be expected based on their lower JCMT flux densities (see Figure 10, bottom panel). This discrepancy between peak flux density and measured SFR raises interesting questions about the underlying mechanisms in these galaxies, suggesting that, while the SCUBA flux density could reflect localized SF activity, the total SFR measurements derived from SCUBA may still capture broader SF processes across the host galaxy (see Section 5.2 for a complete discussion). Further detailed analysis would be necessary to resolve these contrasting indicators of SF in VLBA-detected sources versus nondetections. However, we also note that, because of the limited angular resolution and positional uncertainties of SCUBA observations, we remain cautious in associating the SCUBA counterparts with specific radio sources. 4.7. Properties of the Sources from Infrared Detections To understand the nature of infrared counterparts, we crossmatched our VLBA-detected sources with JWST PEARLS observations. S. P. Willner et al. (2023) carried out Figure 8. VLBA 4.8 GHz vs. predicted VLA 4.8 GHz peak flux density (Speak), color coded by spectral index . Each source is labeled according to the classification of their WISE counterparts, with the diamonds depicting the AGN-dominated galaxies, and the squares depicting the non-AGN dominated, and marked using their respective VLA IDs. The red dashed line represents the location where the observed VLBA 4.8 GHz flux density (S4.8) is equal to the predicted VLA S4.8. The blue dotted line represents the location where the observed VLBA S4.8 is equal to half of the predicted VLA S4.8. “Flatter spectrum” sources ( ≳ −0.5) are closer to the 1:1 equality/dashed line. The only resolved detection (VLA ID 528, or PC 64) is presented both with detected VLBA Sint (labeled as 528) and Speak (labeled as 528〉). Figure 9. WISE color–color diagram showing W1 − W2 vs. W2 − W3 colors for the VLBA detections with WISE measurements (red diamonds), VLBA detections with WISE upper limits (green circles), and nondetectons (blue open squares). Lines mark the T. H. Jarrett et al. (2017) categories: spheroid- dominated, intermediate-disk, active star formation region, and AGN- dominated galaxies. The horizontal green dashed line represents the AGN threshold (D. Stern et al. 2012), above which sources are likely influenced by AGN dust. The magenta dashed curve shows the “star formation sequence” from T. H. Jarrett et al. (2019), depicting the typical color transition of galaxies from quiescent to actively forming stars. Figure 10. Top: JCMT flux density vs. VLA 3 GHz flux density for VLBA detections in blue circles and nondetections in red diamonds. Detections are identified by their corresponding VLA IDs. Bottom: histogram depicting the SFR distribution (in logarithmic scale) of the complete SCUBA sample (green empty steps), VLBA detections (red bins filled with horizontal lines), and nondetections (yellow bins filled with forward slashes). 11 The Astrophysical Journal 989:29 (24pp), 2025 August 10 Saikia et al. 320 --- y=x ..528' ~ 554 -s;:; -, 3,160 .?:- "iii C ,'g 80 X :::, u::: 40 (!) co «i ca 20 ....J > oi l1l .s N s: I 3: 1.5 0.5 § 0 0 Y= 1/2x / - T403 "f< 40 80 160 320 640 VLA 4.8 GHz Predicted flux density (µJy) VLBA Non-Detections f--------+----- VLBA Detections VLBA Detections with WISE upper-limits SF sequence 141 • r -AGN a;;d ;.t,;ma·1 I f ft ·:t_:,pt .2f 2 0 r 4 - / Spheroids Intermediate disks Active star-forming region 2 3 4 WISE W2-W3 (mag) 0.6 0.4 0.2 0 X Q) -0 .!: -0.2 0 Q) -0.4 b5° -0.6 -0.8 ·1 5 250 -s;:; -, 3,200 .?:- 'iii C Q) -0 150 X :::, -= "' + 279 + 403 - VLBA Detections 1- VLBA Non-Detections 100 · N I CD (") 50 ::5 > 25 20 ll 15 E :::, z 10 5 • 00 10 20 30 40 50 60 70 JCMT 850 µm peak flux density (mJy) c::::J Complete SCUBA Sample l2ZI VLBA Non-detections - VLBA Detections 80 O L_....EZL-~~J_12J~ --ll:::===i.J -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Log SFR (M 0 /yr) JWST/NIRCam observations covering a 16 arcmin2 region of the TDF and detected 4.4 µm counterparts for 62 of the 63 VLA radio sources, of which only one overlaps with our VLBA-detected sample. Willner et al. (2025, in preparation) has examined new NIRCam data of the JWST counterparts for the radio sources at the TDF. In these, we have identified a total of eight matches with our VLBA-detected sources, while the remaining four sources were outside the NIRCam coverage (Figure 3). Each detected source is located within a galactic nucleus, with some host galaxies showing late-type features. All sources exhibit a compact NIR nucleus, although only some show clear point-source signatures. PC 3 (VLA ID 124) is elongated with a bright nucleus, potentially with a spiral disk where SF could contribute to the radio flux. PC 7 (VLA ID 141) has an elongated disk, possibly with ongoing SF. PC 14 (VLA ID 182) is a bright elliptical with a compact red nucleus but no clear point-source signature and is notable for lensing a background galaxy into an Einstein ring (N. J. Adams et al. 2025, in preparation). PC 24 (VLA ID 260) is another bright elliptical but with a distinct point-source nucleus. PC 41 (VLA ID 382) is a radio source with a large elliptical NIRCam counterpart with a bright but extended nucleus. PC 46 (VLA ID 403) appears as a red disk, potentially spiral, with a compact red nucleus. PC 47 (VLA ID 434) is a very red source with a prominent dust lane, resembling a disk with a bright nucleus at longer wavelengths. PC 64 (VLA ID 528) is a large, smooth face-on disk with a bright point-source nucleus. R. Ortiz et al. (2024) identified a sample of 66 galaxies in JWST/NIRCam, with point-source features in their cores. 13 of these have VLBA observations, and 3 were detected (PC 3, 7, and 64). Among the detections, PC 64 (VLA ID 528) was classified by R. Ortiz et al. (2024) as a point-source galaxy core, indicating that its infrared emission probably originates from the AGN. In contrast, PC 3 (VLA ID 124) and PC 7 (VLA ID 141) were classified as compact stellar bulges. For all three sources, the median fractional AGN contribution to their 0.1–30 µm flux is approximately 0.21–0.25. Interestingly, among the 10 VLBA nondetections, 9 were classified as bulges, while 4 (PC 21, 33, 57, and 95) appeared as point sources, suggesting that the infrared emission in these sources is likely dominated by a central AGN. Hence, their nondetec- tion at VLBA scales is intriguing. For the VLBA nondetections, 49 of 94 have been detected with NIRCam. The VLBA-undetected sources with S(3 GHz) > 100 µJy show no major differences from the detected sources except for PC 70 (VLA ID 593). For the remaining sources, it is unclear whether they were too resolved for the VLBA to detect or simply fell below the VLBA’s sensitivity limit. PC 6 (VLA ID 134) is a face-on, reddened disk with a point-source nucleus, except for one spiral-shaped region; given its S(3 GHz) = 340 µJy, its nondetection is surprising. PC 10 (VLA ID 150) appears to be part of a complex major merger with patchy dust and a pointlike nucleus. PC 33 (VLA ID 314) is dominated by a point-source nucleus (R. Ortiz et al. 2024), has faint red irregular patches, and is another surprising VLBA nondetection. PC 35 (VLA ID 319) is a nearly face-on spiral with a very bright nucleus. PC 70 (VLA ID 593) is a spiral with multiple bright spots, likely H II regions, with an extended and faint nucleus. The remaining two bright VLA radio sources that were not detected with the VLBA (PC 303 and PC 587) have no NIRCam images yet. 4.8. Redshift and SFR Measurements We used the NIRISS spectra of JWST for the detected galaxies to obtain a measurement of the associated SFR (see Table 6, Figure 11). We note that, although PC 64 (VLA ID 528) was covered in JWST NIRCam, it does not have coverage in NIRISS. We constrained the SFR using the NIRISS spectra by simultaneously fitting the photometric data and NIRISS grism spectra using the method outlined by V. Estrada-Carpe- nter et al. (2023), the flexible SF histories of Dense Basis (K. Iyer & E. J. Gawiser 2017), and SED models from the flexible stellar population synthesis models (C. Conroy & J. E. Gunn 2010) utilizing the MILeS and BaSeL libraries and Kroupa initial mass function (P. Kroupa 2001). We also provide the redshifts of the eight detected objects within the NIRCam field of view. The redshifts given to four decimal places are derived from Binospec spectroscopy, whereas those with two decimal places are photometric estimates. The number of decimal digits reflects the associated uncertainty. Further details on how redshifts were measured, including the full set of host-galaxy properties based on these new infrared observations, will be presented in Willner et al. (2025, in preparation). The measured redshifts were used to estimate the size of the emission regions and the radio luminosity of the sources (see Table 6). 5. Discussion We conducted a detailed analysis of 106 radio sources in the NEP field using high-resolution VLBA observations, detecting 12 sources. 5.1. Origin of the Radio Emission Radio sources are commonly classified as AGN or non- AGN by analyzing their spectral index (K. I. Kellermann 1964; A. G. Pacholczyk 1970). AGN are typically identified by flat or inverted spectral indices ( ≳ 0.7), which suggest compact, optically thick synchrotron sources. In contrast, “steep” indices ( ∼ −1.0) are linked to optically thin emission from radio lobes, often indicating older particle populations. For intermediate indices ∼ −0.7, classification Table 6 Redshift and SFR of the VLBA-detected Sources within the NIRCam Field of View PC VLA ID Redshift 4.8 GHz Luminosity Size SFR (W Hz−1) (pc) (M⊙ yr −1) 3 124 1.05 (8.90 ± 0.68) × 1023 ∼37 +0.02 0.02 0.13 7 141 1.0175 (1.00 ± 0.03) × 1024 ∼35 +1.8 0.8 2.1 14 182 1.02 (4.52 ± 0.58) × 1023 ∼36 +0.3 0.3 1.1 24 260 0.5445 (6.63 ± 0.50) × 1022 ∼17 +0.1 0.09 1.2 41 382 0.3741 (2.05 ± 0.20) × 1022 ∼20 +0.04 0.01 0.05 46 403 1.42 (3.54 ± 0.52) × 1023 ∼35 +55.6 35.6 31.0 47 434 0.95 (1.12 ± 0.19) × 1023 ∼32 +860.0 278.7 156.4 64 528 0.3760 (8.26 ± 0.26) × 1022 ∼22 L Note. Redshift and SFR (M⊙ yr −1) of the eight VLBA-detected sources within the NIRCam field of view. Radio luminosity (W Hz−1) and the physical size of the emission region, derived using the measured redshifts. All of the sources listed here are unresolved, and we used the beam size to estimate the maximum possible extent of the emission region. An SFR estimate for PC 64 is not available as it falls outside the NIRISS field of view. 12 The Astrophysical Journal 989:29 (24pp), 2025 August 10 Saikia et al. becomes ambiguous, as both AGN and starburst galaxies can produce these values through ongoing synchrotron particle injections (A. G. Pacholczyk 1970). As illustrated in Figure 8, compact VLBA detections in our sample typically display flat spectral indices ( ≳ −0.5), which are characteristic of compact AGN structures. Conversely, VLBA detections with more spatially extended, kiloparsec-scale emission exhibit steeper spectral indices ( ≲ −0.5). The sharp rise in the VLBA/VLA flux density ratio around the spectral index ( ≳ −0.5, Figure 7) likely reflects two distinct accretion regimes (see Table 1). These regimes correspond to different Eddington ratios, representing distinct modes of accretion onto SMBHs. Assuming this relationship holds, the origin of radio emission in these two cases could differ significantly. Specifically, AGNs with flat-spectrum indices tend to exhibit compact, parsec-scale radio emission (indicated by a high VLBA/VLA flux density ratio), whereas those with steeper spectra are associated with larger-scale emission. Figure 12 shows the distribution of the VLBI-detected sources in the redshift–radio luminosity plane. We use the selection criteria of M. Magliocchetti et al. (2018) to separate AGN-dominated and SF-dominated radio emission, which defines Pcross as the luminosity above which AGN-driven radio emission overtakes that from SF in a radio-selected population. At z ∼ 1.8, Pcross is determined using the radio luminosity functions of K. McAlpine et al. (2013). Beyond z > 1.8, the radio luminosity function of SF galaxies declines rapidly, and Pcross is fixed at 1023.5 W Hz−1, ensuring that the contamina- tion from star-forming galaxies remains below 10% (M. Mag- liocchetti et al. 2018). As evident in Figure 12, all our VLBI sources lie above this threshold, confirming that our observa- tions primarily probe AGN-related radio emission. The high-brightness temperatures observed in our detections also imply that the compact radio emission originates from AGNs (see Table 5), which are typically associated with relatively low SFR. WISE infrared counterparts for the VLBA detections were primarily either AGN or intermediate-disk dominated, as evidenced by MIR colors typical of AGN, while none of the VLBA detections are classified as purely star forming. Many nondetected sources, however, exhibited WISE classifications pointing to active SF, indicating that our VLBA detections probe AGN driven radio emission. 5.2. Star Formation Rate VLBA-detected sources that have a JWST counterpart have SFR significantly lower than nondetected sources with JWST counterparts. This is consistent with AGN-dominated emis- sion. Among the seven VLBA-detected sources with available JWST spectra, five exhibit very low SF activity, with SFR values below 1 M⊙ yr −1 . The only two sources with sig- nificantly higher SFRs are PC 46 (VLA ID 403) and PC 47 (VLA ID 434), which may be AGN-starburst composites where AGN activity coexists with substantial SF, similar to NGC 1068 and NGC 4945 (e.g., J. P. Lenain et al. 2010; J. P. Pérez-Beaupuits et al. 2011) or a transition phase from SF dominated to AGN dominated. Both sources display complex morphologies in their JWST counterparts (Figure 3), sugges- tive of mergers, further supporting the idea that their radio emission arises from a combination of starburst activity and a compact AGN. For PC 46 (VLA ID 403), the low VLBA/ VLA flux ratio (∼0.2) suggests that the starburst component is probably resolved by VLBA. However, an intriguing contrast is seen in PC 47 (VLA ID 434), where the high VLBA/VLA ratio (∼0.6) indicates that the majority of its radio emission originates from an AGN. Hence, the unusually high SFR in this source is particularly interesting. For the three VLBA-detected sources with SCUBA counterparts, the SFR values are surprisingly high. We caution that more precise submillimeter positions are necessary to confidently identify the true VLA counterparts within the SCUBA positional uncertainties; moreover, even if the associations are correct, the elevated SFR estimates for SCUBA-detected sources may still be affected by methodo- logical uncertainties. SCUBA’s SFR and redshift estimates rely on multiwavelength spectral energy distribution (SED) fitting, which integrates data from optical, NIR, and MIR photometry, deboosted 850 µm measurements, and 3 GHz VLA data for submillimeter galaxies (M. Hyun et al. 2023). Figure 12. 4.8 GHz radio luminosity (in logarithmic scale) vs. redshift for the VLBI detections. The detected sources are labeled using their VLA IDs. The solid black line represents the threshold, Pcross, which separates AGN- dominated and star formation-dominated radio emission, based on the selection criteria of M. Magliocchetti et al. (2018). The gray-shaded region marks the regime in which SF is expected to be the dominant contributor to radio emission, while the area above the gray-shaded region corresponds to the AGN-dominated regime. Figure 11. SFR distribution (in logarithmic scale) of the complete VLA sample with published JWST counterparts (green empty steps) and nondetections (yellow bins filled with forward slashes). We also plot the SFR measured from JWST counterparts of the VLBA detections (red bins filled with horizontal lines) with both published as well as the new SFR measurements reported in this paper. 13 The Astrophysical Journal 989:29 (24pp), 2025 August 10 Saikia et al. 20 c::::J Complete VLA Sample 1024 1~ [ZZJ VLBA Non-detections 18~ 17.5 -VLBA Detections N" 40, J: 15 i a; >- 44 ..o 12.5 '1ii 1023 52 \ E 0 6q. C: '-<£ z,'-J, ::::, 10 .E z ::::, °'"''I>~"' _J 0o""- 0o 7.5 0 387. '?-ci' fP"' '6