The non-ballistic superluminal motion in the plane of the sky

Faster-than-light or superluminal motion was originally predicted as a relativistic illusion of ballistic moving ejecta, and confirmed in a few tens of sources observationally. However, the recent results of the long-term multi-epoch observations of quasars, active galaxies, tracing the structure further along the jets and following the motion of individual features for longer time, rise questions that are difficult to understand by the standard ballistic model. I.e., the ejecta are aligned with the local jet direction, instead of the core; and within individual jets apparently inward-moving features are observed. Here we show that these unexpected phenomena, although only a small fraction among large samples, indicate the existence of non-ballistic jet motion, in which a continuous jet produces a discrete hot spot. And the precession of such a hot spot in the plane of the sky appears superluminal. Therefore, an unified and simple interpretation to the new results is obtained, which can be further tested through its predictions on the evolution of ejecta. The study is of importance in the understanding of the nature of superluminal motion, the interaction of jets and surrounding materials, as well as the common physics underlying quasars and microquasars.Comment: 7 pages, 7 figures, accepted to MNRA

The non-ballistic superluminal motion in the plane of the sky-II

The model of non-ballistic jet motion proposed in 2008 provides a simple explanation to the inward jet motion and bent jet. Recently, evidences of such a non-radial motion increase rapidly, and more complicated morphologies appear. On the other hand, the ballistic plus precession model likely holds in majority samples of jet motion. This paper discusses the relationship between the ballistic and non-ballistic model of jet motion, which suggests that the interaction of ejectors with ambient matter can produce knots at different stages of evolution and hence different separations to the core. And as a jet precesses, knots produced between the core and the deceleration radius result in spiral pattern expected by the model of ballistic plus precession; and knots generated at the deceleration radius display non-radial motion such as bent jet or oscillation of ridge-line. This paper develops the first non-ballistic model in four aspects. Firstly, it provides a numerical simulation to the production of multi-knot for a precessing jet. Secondly, it fits the precession behavior of multi-knot and interprets the oscillation of ridge lines like S5 1803+784. Thirdly, it gives an unified interpretation to the bent jet applicable to both multi-knot and single knot. And fourthly, the problem of very large numbers of observed outward motions as opposed to the inward ones is addressed in a new scope.Comment: 9 pages, 6 figures, accepted by MNRA

The innermost jet in the hidden ultra-luminous X-ray source Cygnus X-3

Cygnus X-3 is a high-mass X-ray binary with a compact object accreting matter from a Wolf-Rayet donor star. Recently, it has been revealed by the Imaging X-ray Polarimetry Explorer (IXPE) as a hidden Galactic ultra-luminous X-ray (ULX) source with a luminosity above the Eddington limit along the direction of a narrow (opening angle <~32 degree) funnel. In between the IXPE observations, we observed Cyg X-3 with the European VLBI (very long baseline interferometry) Network at 22 GHz and the NICER X-ray instrument. To probe possible relations between the X-ray funnel and the potential radio jet from the ULX, we analyzed the simultaneous multi-wavelength data. Our high-resolution VLBI image reveals an elongated structure with a position angle of -3.2+/-0.4 degree, accurately perpendicular to the direction of the linear X-ray polarization. Because Cyg X-3 was in the radio quiescent state on 2022 November 10, we identify the mas-scale structure as the innermost radio jet. The finding indicates that the radio jet propagates along and within the funnel. Moreover, the jet is marginally resolved in the transverse direction. This possibly results from the strong stellar winds and the rapid orbital motion of the binary system.Comment: 7 pages, 8 figures, accepted for publication in MNRAS Letter