VLBA Research Articles

Monitoring Of Jets in Active Galactic Nuclei with VLBA Experiments. XVIII. Kinematics and Inner Jet Evolution of Bright Radio-loud Active Galaxies

Abstract We have analyzed the parsec-scale jet kinematics of 447 bright radio-loud active active galactic nuclei (AGN), based on 15 GHz Very Long Baseline Array (VLBA) data obtained between 1994 August 31 and 2019 August 4. We present new total intensity and linear polarization maps obtained between 2017 January 1 and 2019 August 4 for 143 of these AGN. We tracked 1923 bright features for five or more epochs in 419 jets. The majority (60%) of the well-sampled jet features show either accelerated or nonradial motion. In 47 jets there is at least one nonaccelerating feature with an unusually slow apparent speed. Most of the jets show variations of 10°–50° in their inner jet position angle (PA) over time, although the overall distribution has a continuous tail out to 200°. AGN with spectral energy distributions peaked at lower frequencies tend to have more variable PAs, with BL Lac objects being less variable than quasars. The Fermi Large Area Telescope (LAT) gamma-ray-associated AGN also tend to have more variable PAs than the non-LAT AGN in our sample. We attribute these trends to smaller viewing angles for the lower spectral peaked and LAT-associated jets. We identified 13 AGN where multiple features emerge over decade-long periods at systematically increasing or decreasing PAs. Since the ejected features do not fill the entire jet cross section, this behavior is indicative of a precessing flow instability near the jet base. Although some jets show indications of oscillatory PA evolution, we claim no bona fide cases of periodicity since the fitted periods are comparable to the total VLBA time coverage.

TXS 0128+554: A young gamma‐ray emitting active galactic nucleus with episodic jet activity

AbstractWe carried out a Chandra X‐ray and multi‐frequency very long baseline array (VLBA) study of TXS 0128+554, which is associated with the Fermi γ‐ray source 4FGL J0131.2+5547. The active galactic nuclei (AGN) is unresolved in a 19.3 ks Chandra X‐ray image, and its X‐ray spectrum is well fit by a simple absorbed power law model, with no distinguishable spectral features. Its relatively soft X‐ray spectrum compared to other compact symmetric object (CSOs) may be indicative of a thermal emission component, for which we were able to obtain an upper‐temperature limit of kT <0.08 keV. The compact radio morphology and advanced speed of indicating a kinematic age of 82 ±17 years, placing TXS 0128+554 among the youngest members of the CSO class. The lack of compact, inverted spectrum hotspots, and an emission gap between the bright inner jet and outer radio lobe structure indicate that the jets have undergone episodic activity, and were re‐launched a decade ago. The predicted γ‐ray emission from the lobes, based on an inverse Compton‐emitting cocoon model, is three orders of magnitude below the observed Fermi‐LAT flux. A comparison to other Fermi‐detected and non‐Fermi detected CSOs with redshift indicates that the γ‐ray emission likely originates in the inner jet/core region, and that nearby, recently launched AGN jets are primary candidates for detection by Fermi.

1321+045: A compact steep‐spectrum radio source in a cool‐core galaxy cluster

AbstractCluster‐central gigahertz peak and compact steep‐spectrum (CSS) sources offer an opportunity to study the earliest phases of active galactic nucleus (AGN) feedback, but few have yet been examined in detail. We present results from radio and X‐ray observations of 1321+045, a CSS source in a 4.4 keV cluster at . The cluster has a strongly cooling core, and disturbances from a minor cluster merger may have triggered a period of jet activity which formed the 16 kpc radio lobes ago. However, new very long baseline array (VLBA) imaging shows a ∼20 pc jet on a different projected axis, which is probably only a few hundred years old. We consider possible histories for the system, with either one or two periods of jet activity. While this single system is informative, a broader study of the youngest cluster‐central radio sources is desirable.

The Nature of Jets in Double-peaked Emission-line AGN in the KISSR Sample

Abstract Double-peaked emission-line AGN (DPAGN) have been regarded as binary black hole candidates. We present here results from parsec-scale radio observations with the Very Long Baseline Array (VLBA) of five DPAGN belonging to the KISSR sample of emission-line galaxies. This work concludes our pilot study of nine type 2 Seyfert and LINER DPAGN from the KISSR sample. In the nine sources, dual compact cores are only detected in the “offset AGN,” KISSR 102. However, the overall incidence of jets in the eight sources that were detected with the VLBA is ≥60%. We find a difference in the “missing flux density” going from the Very Large Array to VLBA scales between Seyferts and LINERs, with LINERs showing less missing flux density on parsec-scales. Using the emission-line modeling code, MAPPINGS III, we find that the emission lines are likely to be influenced by jets in 5/9 sources. Jet-medium interaction is the likely cause of the emission-line splitting observed in the SDSS spectra of these sources. Jets in radio-quiet AGN are therefore energetically capable of influencing their parsec- and kpc-scale environments, which makes them agents of “radio AGN feedback” (similar to radio-loud AGN).

Detection of a parsec-scale jet in a radio-quiet narrow-line Seyfert 1 galaxy with highly accreting supermassive black hole

ABSTRACT The jet in active galactic nuclei (AGN) is a key ingredient in understanding the co-evolution of galaxies and their central supermassive black holes (SMBHs). Unfortunately, the mechanism of jet launching and collimation is still elusive. The observational evidence of decreasing radio loudness with increasing Eddington ratio implies that the jet should be coupled with the accretion process. To further explore the relationship between the jet and accretion, it is necessary to extend our knowledge of the jet to an extreme end of the Eddington ratio distribution of AGN. Using Very Long Baseline Array (VLBA), we report the detection of the parsec-scale radio structure in Mrk 335, a radio-quiet narrow-line Seyfert 1 galaxy with an Eddington ratio close to/above unity. The VLBA image at 1.5 GHz reveals an elongated structure extending ∼20 pc in north–south direction with a peak flux density of 1.98 ± 0.05 mJy beam−1 and radio brightness temperatures as high as 6 × 107 K. This feature provides a strong evidence of a parsec-scale (bipolar) jet launched from a highly accreting SMBH. We discuss the result by comparing Mrk 335 with other highly accreting systems, e.g. Galactic black holes and tidal disruption events, and recall the discovery of collimated corona in the vicinity of SMBH in Mrk 335 by previous X-ray observations, whose relation to the parsec-scale radio jet should be explored by future simultaneous X-ray spectroscopy and high resolution radio observations.

The use of astronomy VLBA campaign MOJAVE for geodesy

We investigated the suitability of the astronomical 15 GHz Very Long Baseline Array (VLBA) observing program MOJAVE-5 for estimation of geodetic parameters, such as station coordinates and Earth orientation parameters. We processed a concurrent dedicated VLBA geodesy program observed at 2.3 GHz and 8.6 GHz starting on September 2016 through July 2020 as reference dataset. We showed that the baseline length repeatability from MOJAVE-5 experiments is only a factor of 1.5 greater than from the dedicated geodetic dataset and still below 1 ppb. The wrms of the difference of estimated Earth orientation parameters with respect to the reference IERS C04 time series are a factor of 1.3 to 1.8 worse. We isolated three major differences between the datasets in terms of their possible impact on the geodetic results, i.e. the scheduling approach, treatment of the ionospheric delay, and selection of target radio sources. We showed that the major factor causing discrepancies in the estimated geodetic parameters is the different scheduling approach of the datasets. We conclude that systematic errors in MOJAVE-5 dataset are low enough for these data to be used as an excellent testbed for further investigations on the radio source structure effects in geodesy and astrometry.

Parsec-scale properties of eight Fanaroff–Riley type 0 radio galaxies

ABSTRACT We report the high-resolution radio observations of eight Fanaroff–Riley type 0 radio galaxies (FR 0s), selected from the published FR 0 sample. These observations were carried out with the Very Long Baseline Array (VLBA) and European VLBI Network (EVN) at frequencies of 5 and 8 GHz with a highest resolution of ∼0.6 milliarcsec. All eight sources show compact structures on projected physical sizes of 0.3–10 parsec. Six sources show a two-sided structure and two sources show a one-sided jet structure. J1025+1022 shows an X-shaped jet structure, which could result from a reorientation of the jet axis due to a restart of the central engine or a projection of a highly curved inner jet. However, more studies are needed to examine these scenarios. Proper motions for 22 jet components of the eight sources are determined to be between $-0.08\, c$ and $0.51\, c$. Although most of the sources exhibit flat spectra, other observed characteristics, such as low-amplitude flux density variations, low jet proper motion speeds and symmetric two-sided jet structures, tend to support the fact that the parsec-scale FR 0 jets are mildly relativistic with lower bulk Lorentz factors and larger viewing angles.

The Search for Binary Supermassive Black Holes among Quasars with Offset Broad Lines Using the Very Long Baseline Array

Abstract In several previous studies, quasars exhibiting broad emission lines with ≳1000 km s−1 velocity offsets with respect to the host galaxy rest frame have been discovered. One leading hypothesis for the origin of these velocity-offset broad lines is the dynamics of a binary supermassive black hole (SMBH). We present high-resolution radio imaging of 34 quasars showing these velocity-offset broad lines with the Very Long Baseline Array (VLBA), aiming to find evidence for the putative binary SMBHs (such as dual radio cores), and testing the competing physical models. We detect exactly half of the target sample from our VLBA imaging, after implementing a 5σ detection limit. While we do not resolve double radio sources in any of the targets, we obtain limits on the instantaneous projected separations of a radio-emitting binary for all of the detected sources under the assumption that a binary still exists within our VLBA angular resolution limits. We also assess the likelihood that a radio-emitting companion SMBH exists outside of our angular resolution limits, but its radio luminosity is too weak to produce a detectable signal in the VLBA data. Additionally, we compare the precise sky positions afforded by these data to optical positions from both the SDSS and Gaia DR2 source catalogs. We find projected radio/optical separations on the order of ∼10 pc for three quasars. Finally, we explore how future multi-wavelength campaigns with optical, radio, and X-ray observatories can help discriminate further between the competing physical models.

Stellar intensity interferometry of Vega in photon counting mode

ABSTRACT Stellar intensity interferometry is a technique based on the measurement of the second-order spatial correlation of the light emitted from a star. The physical information provided by these measurements is the angular size and structure of the emitting source. A worldwide effort is presently underway to implement stellar intensity interferometry on telescopes separated by long baselines and on future arrays of Cherenkov telescopes. We describe an experiment of this type, realized at the Asiago Observatory (Italy), in which we performed for the first time measurements of the correlation counting photon coincidences in post-processing by means of a single photon software correlator and exploiting entirely the quantum properties of the light emitted from a star. We successfully detected the temporal correlation of Vega at zero baseline and performed a measurement of the correlation on a projected baseline of ∼2 km. The average discrete degree of coherence at zero baseline for Vega is $\lt g^{(2)} \gt \, = 1.0034 \pm 0.0008$, providing a detection with a signal-to-noise ratio S/N ≳ 4. No correlation is detected over the km baseline. The measurements are consistent with the expected degree of spatial coherence for a source with the 3.3 mas angular diameter of Vega. The experience gained with the Asiago experiment will serve for future implementations of stellar intensity interferometry on long-baseline arrays of Cherenkov telescopes.

Resolving the inner jet of PKS 1749+096 with super-resolution VLBA images at 7 mm

High resolution imaging of inner jets in Active Galactic Nuclei (AGNs) with Very Long Baseline Interferometry (VLBI) at millimeter wavelengths provides deep insight into the launching and collimation mechanisms of relativistic jets. The BL Lac object, PKS 1749+096, shows a core-dominated jet pointing toward the northeast on parsec-scales revealed by various VLBI observations. In order to investigate the jet kinematics, in particular, the orientation of the inner jet on the smallest accessible scales and the basic physical conditions of the core, in this work we adopted a super-resolution technique, the Bi-Spectrum Maximum Entropy Method (BSMEM), to reanalyze VLBI images based on the Very Long Baseline Array (VLBA) observations of PKS 1749+096within the VLBA-BU-BLAZAR 7mm monitoring program. These observations include a total of 105 epochs covering the period from 2009 to 2019. We found that the stacked image of the inner jet is limb-brightened with an apparent opening angle of 50 ° 0 ± 8 ° 0 and 42 ° 0 ± 6° 0 at the distances of 0.2 and 0.3 mas (0.9 and 1.4 pc) from the core, corresponding to an intrinsic jet opening angle of 5° 2 ± 1 ° 0 and 4° 3 ± 0° 7, respectively. In addition, our images show a clear jet position angle swing in \\sr within the last ten years. We discuss the possible implications of jet limb brightening and the connection of the position angle with jet peak flux density and gamma-ray brightness.

Analysis and Optimization of Long Baseline Acoustic Positioning Error of Synchronous Responsive Type

In order to solve the problem of large time delay and low accuracy of position determination when the long-baseline positioning system is operating at large depths, the underwater acoustic positioning technology of the long-baseline array is studied and the long-baseline synchronization positioning error analysis is carried out, and the simulation verification is carried out by MATLAB. A method for optimizing the underwater acoustic positioning algorithm is proposed. After optimizing the positioning algorithm, in the case of a water depth of 6000 M and a positioning area of 1000*1000m2, the total positioning error of the sitting-bottom long baseline is reduced from the meter level to the decimeter level, and the positioning accuracy is greatly improved. An improved synchronous response type is determined The underwater acoustic positioning can realize the underwater large-scale, high-precision and high-real-time positioning.

The peculiar WAT NGC 2329 with Seyfert/FR I-like radio lobes

ABSTRACT We report the complex radio properties of the radio galaxy NGC 2329 that resides in the centre of the galaxy cluster Abell 569. For this study, we have used archival data from the Very Large Array (VLA) at various resolutions and frequencies, as well as the Very Long Baseline Array (VLBA). While the wide-angle tailed (WAT) Fanaroff–Riley type I (FR I) radio morphology of the source has been discussed widely in the literature, the nature of the inner lobes has not been as widely discussed. In particular, we note that the inner lobes resemble the bubble-like radio structures observed in Seyfert galaxies. Polarization-sensitive data from the VLA clearly show magnetic field structures consistent with FR Is for the outer lobes and Seyferts for the inner lobes in NGC 2329. FR Is are classified as radio-loud (RL) active galactic nuclei (AGN) and Seyferts as radio-quiet (RQ) AGN, making this source unique. The VLBA shows a one-sided radio jet suggesting a relativistic pc-scale outflow, leading into the inner lobes. Electron lifetime estimates suggest that the outer FR I-like lobes are nearly twice as old (∼45 Myr) as the inner Seyfert-like lobes (∼25 Myr). Gas inflow in this merging cluster seems to have rejuvenated the AGN about ∼25 Myr ago, and may have caused a change in the accretion disc state. The complex composite radio morphology of NGC 2329 suggests that the RL/RQ dichotomy is a function of time in the lifecycle of an AGN.

Resolving the Radio Emission from the Quasar P172+18 at z = 6.82

Abstract We present high angular resolution imaging of the quasar PSO J172.3556+18.7734 at z = 6.82 with the Very Long Baseline Array (VLBA). This source currently holds the record of being the highest redshift radio-loud quasar. These observations reveal a dominant radio source with a flux density of 398.4 ± 61.4 μJy at 1.53 GHz, a deconvolved size of 9.9 × 3.5 mas (52.5 × 18.6 pc), and an intrinsic brightness temperature of (4.7 ± 0.7) × 107 K. A weak unresolved radio extension from the main source is also detected at the ∼3.1σ level. The total flux density recovered with the VLBA at 1.53 GHz is consistent with that measured with the Very Large Array (VLA) at a similar frequency. The quasar is not detected at 4.67 GHz with the VLBA, suggesting a steep spectral index with a limit of 1.55. The quasar is also not detected with the VLBA at 7.67 GHz. The overall characteristics of the quasar suggest that it is a very young radio source similar to lower redshift gigahertz peaked spectrum radio sources, with an estimated kinematic age of ∼103 yr. The VLA observations of this quasar revealed a second radio source in the field 23.″1 away. This radio source, which does not have an optical or IR counterpart, is not detected with the VLBA at any of the observed frequencies. Its nondetection at the lowest observed VLBA frequency suggests that it is resolved out, implying a size larger than ∼0.″17. It is thus likely situated at lower redshift than the quasar.

Observing the Time Evolution of the Multicomponent Nucleus of 3C 84

Abstract The advent of global millimeter-band very long baseline interferometry (VLBI) in recent years has finally revealed the morphology of the base of the two most prominent nearby, bright, extragalactic radio jets in M87 and 3C 84. The images are quite surprising considering the predictions of jet theory and current numerical modeling. The jet bases are extremely wide compared to expectations, and the nucleus of 3C 84 is very complicated. It appears as a double nucleus in 86 GHz observations with 50 μas resolution and a triple nucleus with 30 μas resolution with space-based VLBI by RadioAstron at 22 GHz. What is even odder is that the double and triple nuclei are arranged along an east–west line that is approximately orthogonal to the north–south large-scale jet on 150 μas−4 mas scales. We explore the emergence of an (east–west) double nucleus in the lower-resolution 43 GHz Very Long Baseline Array (VLBA) imaging from 2018 August to 2020 April. The double nucleus is marginally resolved. We exploit the east–west resolution associated with the longest baselines, ∼0.08 mas, to track a predominantly east–west separation speed of ≈0.086 ± 0.008c. We estimate that the observed mildly relativistic speed persists over a deprojected distance of ∼1900–9800 times the central, supermassive black hole gravitational radius (∼0.3–1.5 lt-yr) from the point of origin.

A ring accelerator? Unusual jet dynamics in the IceCube candidate PKS 1502+106

ABSTRACT On 2019/07/30.86853 ut, IceCube detected a high-energy astrophysical neutrino candidate. The Flat Spectrum Radio Quasar PKS 1502+106 is located within the 50 per cent uncertainty region of the event. Our analysis of 15 GHz Very Long Baseline Array (VLBA) and astrometric 8 GHz VLBA data, in a time span prior and after the IceCube event, reveals evidence for a radio ring structure that develops with time. Several arc-structures evolve perpendicular to the jet ridge line. We find evidence for precession of a curved jet based on kinematic modelling and a periodicity analysis. An outflowing broad line region (BLR) based on the C iv line emission (Sloan Digital Sky Survey) is found. We attribute the atypical ring to an interaction of the precessing jet with the outflowing material. We discuss our findings in the context of a spine-sheath scenario where the ring reveals the sheath and its interaction with the surroundings (narrow line region, NLR, clouds). We find that the radio emission is correlated with the γ-ray emission, with radio lagging the γ-rays. Based on the γ-ray variability time-scale, we constrain the γ-ray emission zone to the BLR (30–200 rg) and within the jet launching region. We discuss that the outflowing BLR provides the external radiation field for γ-ray production via external Compton scattering. The neutrino is most likely produced by proton–proton interaction in the blazar zone (beyond the BLR), enabled by episodic encounters of the jet with dense clouds, i.e. some molecular cloud in the NLR.

A compact core-jet structure in the changing-look Seyfert NGC 2617

ABSTRACT The nearby face-on spiral galaxy NGC 2617 underwent an unambiguous ‘inside–out’ multiwavelength outburst in Spring 2013, and a dramatic Seyfert-type change probably between 2010 and 2012, with the emergence of broad optical emission lines. To search for the jet activity associated with this variable accretion activity, we carried out multiresolution and multiwavelength radio observations. Using the very long baseline interferometric (VLBI) observations with the European VLBI Network at 1.7 and 5.0 GHz, we find that NGC 2617 shows a partially synchrotron self-absorbed compact radio core with a significant core shift, and an optically thin steep-spectrum jet extending towards the north up to about 2 pc in projection. We also observed NGC 2617 with the electronic Multi-Element Remotely Linked Interferometer Network at 1.5 and 5.5 GHz, and revisited the archival data of the Very Large Array (VLA) and the Very Long Baseline Array (VLBA). The radio core had a stable flux density of ∼1.4 mJy at 5.0 GHz between 2013 June and 2014 January, in agreement with the expectation of a supermassive black hole in the low accretion rate state. The northern jet component is unlikely to be associated with the ‘inside–out’ outburst of 2013. Moreover, we report that most optically selected changing-look active galactic nuclei (AGN) at z < 0.83 are sub-mJy radio sources in the existing VLA surveys at 1.4 GHz, and it is unlikely that they are more active than normal AGN at radio frequencies.

The JPL Planetary and Lunar Ephemerides DE440 and DE441

Abstract The planetary and lunar ephemerides called DE440 and DE441 have been generated by fitting numerically integrated orbits to ground-based and space-based observations. Compared to the previous general-purpose ephemerides DE430, seven years of new data have been added to compute DE440 and DE441, with improved dynamical models and data calibration. The orbit of Jupiter has improved substantially by fitting to the Juno radio range and Very Long Baseline Array (VLBA) data of the Juno spacecraft. The orbit of Saturn has been improved by radio range and VLBA data of the Cassini spacecraft, with improved estimation of the spacecraft orbit. The orbit of Pluto has been improved from use of stellar occultation data reduced against the Gaia star catalog. The ephemerides DE440 and DE441 are fit to the same data set, but DE441 assumes no damping between the lunar liquid core and the solid mantle, which avoids a divergence when integrated backward in time. Therefore, DE441 is less accurate than DE440 for the current century, but covers a much longer duration of years −13,200 to +17,191, compared to DE440 covering years 1550–2650.

Parsec-scale Properties of Steep- and Flat-spectrum Extragalactic Radio Sources from a VLBA Survey of a Complete North Polar Cap Sample

Abstract We observed with the Very Long Baseline Array (VLBA) at 2.3 and 8.6 GHz a complete flux-density-limited sample of 482 radio sources with decl. > +75° brighter than 200 mJy at 1.4 GHz drawn from the NVSS catalog. A total of 34% of the sources show parsec-scale emission above the flux density detection limit of 30 mJy; their accurate positions and parsec-scale structure parameters are determined. Among all the sources detected at least at the shortest VLBA baselines, the majority, or 72%, have a steep single-dish spectrum. The fraction of the sources with a detectable parsec-scale structure is above 95% among the flat-spectrum objects and close to 25% among the steep-spectrum objects. We identified 82 compact steep-spectrum source candidates, which make up 17% of the sample; most of them are reported for the first time. The compactness and the brightness temperature of the sources in our sample show a positive correlation with single-dish and VLBA spectral indices. All the sources with a significant 8 GHz variability were detected by the VLBA snapshot observations, which independently confirmed their compactness. We demonstrated that 54% of the sources detected by the VLBA at 2.3 GHz in our sample have a steep VLBA spectrum. The compact radio emission of these sources is likely dominated by optically thin jets or mini-lobes, not by an opaque jet core. These results show that future VLBI surveys aimed at searching for new sources with parsec-scale structure should include not only flat-spectrum sources but also steep-spectrum ones in order to reach an acceptable level of completeness.

Fundamental Reference AGN Monitoring Experiment (FRAMEx). I. Jumping Out of the Plane with the VLBA

Abstract We present the first results from the Fundamental Reference active galactic nucleus (AGN) Monitoring Experiment, an observational campaign dedicated to understanding the physical processes that affect the apparent positions and morphologies of AGNs. In this work, we obtained simultaneous Swift X-ray Telescope and Very Long Baseline Array (VLBA) radio observations for a snapshot campaign of 25 local AGNs that form a volume-complete sample with hard X-ray (14–195 keV) luminosities above 1042 erg s−1, out to a distance of 40 Mpc. Despite achieving an observation depth of ∼20 μJy, we find that 16 of 25 AGNs in our sample are not detected with the VLBA on milliarcsecond (subparsec) scales, and the corresponding core radio luminosity upper limits are systematically below predictions from the Fundamental Plane of black hole activity. Using archival Jansky Very Large Array (VLA) radio measurements, our sample jumps back onto the Fundamental Plane, suggesting that extended radio emission is responsible for the apparent correlation between radio emission, X-ray emission, and black hole mass. We suggest that this discrepancy is likely due to extranuclear radio emission produced via interactions between the AGN and host environment. We compare VLBA observations of AGNs to VLA observations of nearby Galactic black holes, and we find a mass-independent correlation between radio and X-ray luminosities of black holes of / ∼10−6, in line with predictions for coronal emission, but allowing for the possibility of truly radio-silent AGNs.

A VLBA Survey of Radio Stars in the Orion Nebula Cluster. II. Astrometry

Abstract From Very Long Baseline Array (VLBA) observations we previously identified a population of 123 young stellar systems with nonthermal radio emission toward the core of the Orion Nebula Cluster (ONC). We find optical sources in the Gaia DR2 catalog for 34 of them within 0.″2 of the radio positions. Most of the radio sources are likely companions of Gaia detections. However, there are 11 stars whose VLBA positions differ from Gaia by <1.6 mas, and some of these radio sources probably are the direct counterparts of the optical stars. We are able to obtain radio proper motions for 23 stars. Combining the stellar proper motions derived from the VLBA and Gaia DR2 data we find the global motion and velocity dispersion of the ONC to be (μ α ∗, μ δ ) = (1.20 ± 0.09, 0.18 ± 0.09) mas yr−1 and ( σ μ α ∗ , σ μ δ ) = (0.84 ± 0.09, 1.30 ± 0.09) mas yr−1. Finally, we looked for ordered motions by estimating the means of scalar and vectorial products, which results in v · r ˆ ¯ = − 0.61 ± 1.00 km s−1 and v × r ˆ ¯ = 0.57 ± 0.95 km s−1. These do not show indications that the young stellar cluster is in expansion, contraction, or rotation.