Symmetric Objects Research Articles

Polygons have a small facilitatory effect on extraretinal symmetry perception.

Symmetrical objects only project a symmetrical image onto the retina when viewed from certain angles. Previous work has investigated the ERP response to visual symmetry in frontoparallel and perspective views. When participants are attending to regularity, the ERPs are the same. When participants are attending to colour, the response to perspective symmetry is reduced. We term this reduction ‘perspective cost’. We predicted that perspective cost would be lessened if the stimuli were polygons rather than dot patterns. This prediction was confirmed in a new experiment. This result suggests some stimuli may support automatic 3D interpretation better than others. However, the facilitatory effect of polygons was relatively small, and perspective cost was not eliminated. Furthermore, this study also revealed that attention to symmetry is not always sufficient to eliminate perspective cost.

Anisotropic interior models with Kohler–Chao–Tikekar-like complexity factor

This work explores the construction of spherically symmetric models of stellar interiors by incorporating the null complexity factor (CF) as an additional constraint. This supplementary condition helps us to close an array of stellar structure equations resulting from the process of gravitational decoupling. By making use of MGD-type gravitational decoupling we analyze the role of gravitational decoupling and its impact on the complexity of static, self-gravitational systems. We begin by considering an anisotropic seed solution described by the Kohler–Chao–Tikekar metric ansatz. We then apply the minimal geometric deformation technique to this seed solution, imposing the constraint that the effective anisotropic factor vanishes. This constraint leads to the generation of an isotropic stellar solution. Furthermore, we construct a second family of solutions in which the CF, remains the same for both the seed solution and its minimally deformed counterpart. Our analysis further investigated the influence of both the deformation parameter and the CF on the structural properties of the static and spherically symmetric stellar objects.

Anisotropic compact stellar model: a vanishing complexity approach

In this article, we develop a new class of solutions that describe stellar structures of recently observed pulsars. We adopt the condition of the vanishing complexity proposed by Herrera (Phys Rev D 97:044010, 2018) and an appropriate metric potential for generating the solutions. The solutions which are obtained from the complexity-free conditions, are physically well-behaved and satisfy all the rigorous conditions to describe static and spherically symmetric realistic compact objects. The features of observed anisotropic compact stars including Vela X-1, LMC X-4, Cen X-3, and EXO 1785-248 are validated with our model. It is further shown that the solutions supporting matter configurations are physically plausible, stable with positive anisotropy, and in an equilibrium state as verified by investigating the generalized TOV equation in the case of our model.

Energy exchange between charged relativistic fluids in f(T) gravity

This study focuses on the effects of a polytropic fluid on a charged gravitational source within f(T) gravity, where T is the torsion scalar. We investigate how the electromagnetic field affects the flow of energy in spherically symmetric and static celestial objects that contain relativistic fluids. By using the gravitational decoupling technique, we analyze the effects of polytropic fluid on the dynamics of the gravitational source, accompanied by the matching of the interior geometry with an exterior at the hypersurface Σ. Finally, with the help of the Tolman IV solution, we observe the conduct of energy conditions with the existence of charge using f(T) field equations and got the intended outcomes.

Role of complexity on the minimal deformation of black holes

Abstract We investigate spherically symmetric classes of anisotropic solutions within the realm of a schematic gravitational decoupling scheme, primarily decoupling through minimal geometric deformation, applied to non-rotating, ultra-compact, self-gravitational fluid distributions. In this respect, we employ the minimal complexity factor scheme to generate physically realistic models for anisotropic matter distributions, using a well-behaved model. The zero-complexity factor condition enables us to determine the deformation function for solving the decoupled system. We explore all the structure-defining scalar variables, such as density inhomogeneity, strong energy condition, density homogeneity, and the complexity factor (an alloy of density inhomogeneity and pressure anisotropy) for the decoupling constant ranging between 0 and 1. We observe that the anisotropy vanishes when the coupling constant is set to unity. This finding holds significance as it implies that, in the context of a zero-complexity factor approach, an anisotropic matter distribution becomes perfect without requiring any isotropy requirements. This work effectively explored the impact of complexity on the composition of self-gravitational stellar distributions. This effective approach enables the development of new, physically realistic isotropic stellar models for anisotropic matter distributions. Additionally, our findings indicate that the complexity factor in static, spherically symmetric self-gravitational objects can significantly affect the nature of the matter distribution within these systems. It is concluded that the minimally deformed Durgapal-IV model features an increasing pressure profile, and the local anisotropy of pressure vanishes throughout the model under complexity-free conditions.

Lane-Emden equations for Relativistic Anisotropic Polytropes

Abstract In this research work, spherically symmetric compact objects with anisotropic matter are studied within the framework of general relativity. For this purpose, the equation of state of the master polytrope P = Kργ + αρ − β is employed, which prevents the divergence of the tangential velocity at the object’s surface and generalizes the treatment of the equation of state. The corresponding Lane-Emden equation is derived and integrated using an anisotropy function that encompasses conformally flat polytropes and vanishing compactness factor. Furthermore, the physical acceptability conditions of the solutions are analyzed.

On the Origin of the X-Ray Emission in Heavily Obscured Compact Radio Sources

X-ray continuum emission of active galactic nuclei (AGNs) may be reflected by circumnuclear dusty tori, producing prominent fluorescence iron lines at X-ray frequencies. Here, we discuss the broadband emission of three radio-loud AGNs belonging to the class of compact symmetric objects (CSOs), with detected narrow Fe Kα lines. CSOs have newly born radio jets, forming compact radio lobes with projected linear sizes of the order of a few to hundreds of parsecs. We model the radio-to-γ-ray spectra of compact lobes in J1407+2827, J1511+0518, and J2022+6137, which are among the nearest and the youngest CSOs known to date, and are characterized by an intrinsic X-ray absorbing column density of N H > 1023 cm−2. In addition to the archival data, we analyze the newly acquired Chandra X-ray Observatory and Submillimeter Array (SMA) observations, and also refine the γ-ray upper limits from Fermi Large Area Telescope monitoring. The new Chandra data exclude the presence of the extended X-ray emission components on scales larger than 1.″5. The SMA data unveil a correlation between the spectral index of the electron distribution in the lobes and N H, which can explain the γ-ray quietness of heavily obscured CSOs. Based on our modeling, we argue that the inverse-Compton emission of compact radio lobes may account for the intrinsic X-ray continuum in all these sources. Furthermore, we propose that the observed iron lines may be produced by a reflection of the lobes’ continuum from the surrounding cold dust.

Emergence of brain-like mirror-symmetric viewpoint tuning in convolutional neural networks.

Primates can recognize objects despite 3D geometric variations such as in-depth rotations. The computational mechanisms that give rise to such invariances are yet to be fully understood. A curious case of partial invariance occurs in the macaque face-patch AL and in fully connected layers of deep convolutional networks in which neurons respond similarly to mirror-symmetric views (e.g. left and right profiles). Why does this tuning develop? Here, we propose a simple learning-driven explanation for mirror-symmetric viewpoint tuning. We show that mirror-symmetric viewpoint tuning for faces emerges in the fully connected layers of convolutional deep neural networks trained on object recognition tasks, even when the training dataset does not include faces. First, using 3D objects rendered from multiple views as test stimuli, we demonstrate that mirror-symmetric viewpoint tuning in convolutional neural network models is not unique to faces: it emerges for multiple object categories with bilateral symmetry. Second, we show why this invariance emerges in the models. Learning to discriminate among bilaterally symmetric object categories induces reflection-equivariant intermediate representations. AL-like mirror-symmetric tuning is achieved when such equivariant responses are spatially pooled by downstream units with sufficiently large receptive fields. These results explain how mirror-symmetric viewpoint tuning can emerge in neural networks, providing a theory of how they might emerge in the primate brain. Our theory predicts that mirror-symmetric viewpoint tuning can emerge as a consequence of exposure to bilaterally symmetric objects beyond the category of faces, and that it can generalize beyond previously experienced object categories.

PCKRF: Point Cloud Completion and Keypoint Refinement With Fusion Data for 6D Pose Estimation.

Some robust point cloud registration approaches with controllable pose refinement magnitude, such as ICP and its variants, are commonly used to improve 6D pose estimation accuracy. However, the effectiveness of these methods gradually diminishes with the advancement of deep learning techniques and the enhancement of initial pose accuracy, primarily due to their lack of specific design for pose refinement. In this paper, we propose Point Cloud Completion and Keypoint Refinement with Fusion Data (PCKRF), a new pose refinement pipeline for 6D pose estimation. The pipeline consists of two steps. First, it completes the input point clouds via a novel pose-sensitive point completion network. The network uses both local and global features with pose information during point completion. Then, it registers the completed object point cloud with the corresponding target point cloud by our proposed Color supported Iterative KeyPoint (CIKP) method. The CIKP method introduces color information into registration and registers a point cloud around each keypoint to increase stability. The PCKRF pipeline can be integrated with existing popular 6D pose estimation methods, such as the full flow bidirectional fusion network, to further improve their pose estimation accuracy. Experiments demonstrate that our method exhibits superior stability compared to existing approaches when optimizing initial poses with relatively high precision. Notably, the results indicate that our method effectively complements most existing pose estimation techniques, leading to improved performance in most cases. Furthermore, our method achieves promising results even in challenging scenarios involving textureless and symmetrical objects. Our source code is available at https://github.com/zhanhz/KRF.

Realistic compact objects in the f(R, T) gravity in the background of polytropic and barotropic gas models

The f(R, T) gravity in the background of the polytropic and barotropic fluid has been investigated in this work. We have selected the TOV equation to determine the internal spacetime of a spherically symmetric galactic object. With the use of the Einstein equation, we have selected KB-spacetime to calculate the mass, compactness, and surface redshift of a spherically symmetric body. Explicit conditions for model parameters have been constructed for the boundary conditions of the interior and exterior spacetime, and the Schwarzschild solution has been employed in the modified f(R, T) gravity theory to evaluate different matching criteria. An increasing pattern in compactness with respect to the different radii is evident in the graphical representation of the compactness evolution for each of the individual star models. After selecting a non-vacuum field equation for higher order curvature, we reformulated f(R, T) for R and T. As a result, the tangential pressure, radial pressure, and matter density have all been calculated. According to the study, as the radius goes to infinity, the tangential and radial pressures display asymptotic flatness and converge to zero. Polytropic and barotropic gas EoS have been adopted since the star model confronts the presence of an isotropic fluid backdrop. It has been noted that in a polytropic background, density and pressure increase with distance from the star’s core, but in a barotropic background, the pressure exhibits an ascending pattern as a function of radius.

Investigating X-ray emission in the GeV-emitting compact symmetric objects PKS 1718–649 and TXS 1146+596

Aims. Compact symmetric objects (CSOs) are thought to represent the first step in the evolutionary path of radio galaxies. In the present study, we investigated the X-ray emission of two CSOs confirmed to emit at GeV energies: PKS 1718–649 and TXS 1146+596. Unveiling the origin of their observed high-energy emission is crucial to establishing the physical parameters of the radio source and understanding how CSOs interact with the surrounding medium. Methods. We combined archival and new NuSTAR observations of PKS 1718–649 and TXS 1146+596 to have broadband X-ray coverage. For both sources, we modeled the broadband spectral energy distribution (SED) from the radio band up to γ-rays in order to derive their physical parameters. We also discuss the role of the ambient medium in confining the source expansion, which we investigate using X-ray obscuration. Results. For the first time, we report X-ray detections of PKS 1718–649 and 1146+596 with NuSTAR at energies higher than 10 keV. Combining Chandra and NuSTAR observations of TXS 1146+596, we reveal the presence of a multitemperature thermal component dominating the soft X-ray spectrum, and we interpret this finding as indicative of an AGN feedback process in action in this source. In addition, we show that two emitting electron populations are necessary to reproduce the observed broadband SED of TXS 1146+596: in our models, the X-ray emission could either be produced by synchrotron radiation or by a weak X-ray corona, or could be an ADAF-type emission. Interestingly, an additional X-ray component, namely a weak corona, is also required for PKS 1718–649. Moreover, we argue that heavily obscured and possibly frustrated sources tend to show different radio sizes with respect to those that are unobscured and free to expand.

The nature of compact radio-loud AGN: a systematic look at the LOFAR AGN population

ABSTRACT We investigate the nature of low-luminosity radio-loud active galactic nuclei (RLAGN) selected from the LOFAR Two-metre Sky Survey (LoTSS) first data release (DR1). Using optical, mid-infrared, and radio data, we have conservatively selected 55 radiative AGN candidates from DR1 within the redshift range 0.03 < z < 0.1. We show using high-frequency Karl G. Jansky Very Large Array (VLA) observations that 10 out of 55 objects show radio emission on scales >1–3 kpc, 42 are compact at the limiting resolution of 0.35 arcsec (taking an upper limit on the projected physical size, this corresponds to less than 1 kpc), and three are undetected. The extended objects display a wide range of radio morphologies: two-jet (5), one-jet (4), and double-lobed (1). We present the radio spectra of all detected radio sources which range from steep to flat/inverted and span the range seen for other compact radio sources such as compact symmetric objects (CSOs), compact steep spectrum (CSS) sources, and gigahertz peaked-spectrum (GPS) sources. Assuming synchrotron self-absorption (SSA) for flat/inverted radio spectrum sources, we predict small physical sizes for compact objects to range between 2 and 53 pc. Alternatively, using free–free absorption (FFA) models, we have estimated the free electron column depth for all compact objects, assuming a homogeneous absorber. We find that these objects do not occupy a special position on the power/linear size (P − D) diagram but some share a region with radio-quiet quasars (RQQs) and the so-called ‘FR0’ sources in terms of radio luminosity and linear size.

Gravitational fields of axially symmetric compact objects in 5D space–time–matter gravity

In the standard Einstein’s theory the exterior gravitational field of any static and axially symmetric stellar object can be described by means of a single function from which we obtain a metric into a four-dimensional space–time. In this work we present a generalization of those so called Weyl solutions to a space–time–matter metric in a five-dimensional manifold within a non-compactified Kaluza–Klein theory of gravity. The arising field equations reduce to those of vacuum Einstein’s gravity when the metric function associated to the fifth dimension is considered to be constant. The calculation of the geodesics allows to identify the existence or not of different behaviours of test particles, in orbits on a constant plane, between the two metrics. In addition, static solutions on the hypersurface orthogonal to the added dimension but with time dependence in the five-dimensional metric are also obtained. The consequences on the variation of the rest mass, if the fifth dimension is identified with it, are studied.

Small-scale radio jets and tidal disruption events: a theory of high-luminosity compact symmetric objects

ABSTRACT Double lobe radio sources associated with active galactic nuclei represent one of the longest studied groups in radio astronomy. A particular subgroup of double radio sources comprises the compact symmetric objects (CSOs). CSOs are distinguished by their prominent double structure and subkpc total size. It has been argued that the vast majority of high-luminosity CSOs (CSO 2s) represent a distinct class of active galactic nuclei with its own morphological structure and lifecycle. In this work, we present theoretical considerations regarding CSO 2s. We develop a semi-analytic evolutionary model, inspired by the results of large-scale numerical simulations of relativistic jets, that reproduces the features of the radio source population. We show that CSO 2s may be generated by finite energy injections and propose stellar tidal disruption events as a possible cause. We find that tidal disruption events of giant branch stars with masses ≳1 M⊙ can fuel these sources and discuss possible approaches to confirming this hypothesis. We predict that if the tidal disruption scenario holds, CSO 2s with sizes less than 400 pc should outnumber larger sources by more than a factor of 10. Our results motivate future numerical studies to determine whether the scenarios we consider for fuelling and source evolution can explain the observed radio morphologies. Multiwavelength observational campaigns directed at these sources will also provide critical insight into the origins of these objects, their environments, and their lifespans.

Lobe-dominated γ-Ray Emission of Compact Symmetric Objects

The γ-ray emitting compact symmetric objects (CSOs) PKS 1718–649, NGC 3894, and TXS 0128+554 are lobe-dominated in the radio emission. In order to investigate their γ-ray radiation properties, we analyze the ∼14 yr Fermi/LAT observation data of the three CSOs. They all show the low luminosity (1041–1043 erg s−1) and no significant variability in the γ-ray band. Their γ-ray average spectra can be well fitted by a power-law function. These properties of γ-rays are clearly different from the γ-ray emitting CSOs CTD 135 and PKS 1413+135, for which the γ-rays are produced by a restarted aligned jet. In the L γ − Γ γ plane, the three CSOs are also located at the region occupied by radio galaxies (RGs) while CTD 135 and PKS 1413+135 display a similar feature to blazars. Together with a similar radio emission property to γ-ray emitting RGs Cen A and Fornax A, we speculate that the γ-rays of the three CSOs stem from their extended mini-lobes. The broadband spectral energy distributions of the three CSOs can be well explained by the two-zone leptonic model, where their γ-rays are produced by the inverse Compton process of the relativistic electrons in extended regions. By extrapolating the observed Fermi/LAT spectra to the very high energy band, we find that TXS 0128+554 among the three CSOs may be detected by the Cherenkov Telescope Array in the future.

Predicting the upper bound of two-dimensional flow regimes of symmetric objects through two-dimensional computations

The onset of secondary wake instability is generally predicted via experiments, linear stability analysis, and three-dimensional direct numerical simulations. The current work stems from an open question that is very intriguing and fundamental: Can the upper bound of a two-dimensional flow be predicted purely on the basis of two-dimensional computational results? It is found that spatial distribution of a field variable, i.e., streamwise velocity in the vortex formation region, aids in determining the upper limit of a two-dimensional flow regime of a symmetric object. The vortex formation length attains its least value at the second critical Reynolds number. In addition, streamwise extents of mean wake and vortex formation region along wake axis become the same. Under this circumstance, the streamwise velocity at the terminal point of vortex formation region is such that its mean value vanishes while intensity of fluctuations or corresponding Reynolds stress becomes the maximum. The predicted values of critical Reynolds numbers for circular, square, and diamond cross sections exhibit excellent agreement with the results available in the literature.

Compact Symmetric Objects. III. Evolution of the High-luminosity Branch and a Possible Connection with Tidal Disruption Events

We use a sample of 54 compact symmetric objects (CSOs) to confirm that there are two unrelated CSO classes: an edge-dimmed, low-luminosity class (CSO 1), and an edge-brightened, high-luminosity class (CSO 2). Using blind tests, we show that CSO 2s consist of three subclasses: CSO 2.0, having prominent hot spots at the leading edges of narrow jets and/or narrow lobes; CSO 2.2, without prominent hot spots and with broad jets and/or lobes; and CSO 2.1, which exhibit mixed properties. Most CSO 2s do not evolve into larger jetted active galactic nuclei (AGN), but spend their whole life cycle as CSOs of size ≲500 pc and age ≲5000 yr. The minimum energies needed to produce the radio luminosity and structure in CSO 2s range from ∼10−4 M ⊙ c 2 to ∼7 M ⊙ c 2. We show that the transient nature of most CSO 2s, and their birth rate, can be explained through ignition in the tidal disruption events of stars. We also consider possibilities of tapping the spin energy of the supermassive black hole, and tapping the energy of the accretion disk. Our results demonstrate that CSOs constitute a large family of AGN in which we have thus far studied only the brightest. More comprehensive CSO studies, with higher sensitivity, resolution, and dynamic range, will revolutionize our understanding of AGN and the central engines that power them.

Compact Symmetric Objects. II. Confirmation of a Distinct Population of High-luminosity Jetted Active Galaxies

Compact symmetric objects (CSOs) are compact (<1 kpc), jetted active galactic nuclei (AGN), whose jet axes are not aligned close to the line of sight, and whose observed emission is not predominantly relativistically boosted toward us. Two classes of CSOs have previously been identified: approximately one-fifth are edge dimmed and the rest are edge brightened. We designate these as CSO 1s and 2s, respectively. This paper focuses almost exclusively on CSO 2s. Using complete samples of CSO 2s we present three independent lines of evidence, based on their relative numbers, redshift distributions, and size distributions, which show conclusively that the vast majority (>99%) of CSO 2s do not evolve into larger-scale radio sources. These CSO 2s belong to a distinct population of jetted AGN, which should be characterized as “short-lived,” as opposed to “young,” compared to the classes of larger jetted AGN. We show that there is a sharp upper cutoff in the CSO 2 size distribution at ≈500 pc. The distinct differences between most CSO 2s and other jetted AGN provides a crucial new time domain window on the formation and evolution of relativistic jets in AGN and the supermassive black holes that drive them.

Compact Symmetric Objects. I. Toward a Comprehensive Bona Fide Catalog

Compact symmetric objects (CSOs) are jetted active galactic nuclei (AGN) with overall projected size <1 kpc. The classification was introduced to distinguish these objects from the majority of compact jetted AGN in centimeter-wavelength very long baseline interferometry observations, where the observed emission is relativistically boosted toward the observer. The original classification criteria for CSOs were (i) evidence of emission on both sides of the center of activity and (ii) overall size <1 kpc. However, some relativistically boosted objects with jet axes close to the line of sight appear symmetric and have been misclassified as CSOs, thereby undermining the CSO classification. This is because two essential CSO properties, pointed out in the original papers, have been neglected: (iii) low variability and (iv) low apparent speeds along the jets. As a first step toward creating a comprehensive catalog of “bona fide” CSOs, we identify 79 bona fide CSOs, including 15 objects claimed as confirmed CSOs here for the first time, that match the CSO selection criteria. This sample of bona fide CSOs can be used for astrophysical studies of CSOs without contamination by misclassified CSOs. We show that the fraction of CSOs in complete flux density limited AGN samples with S 5GHz > 700 mJy is between (6.8 ± 1.6)% and (8.5 ± 1.8)%.

A comparison of compact, presumably young with extended, evolved radio active galactic nuclei

Context. The triggering and evolution of active galactic nuclei (AGNs) and the interaction of the AGN with its host galaxy is an important topic in extragalactic astrophysics. Radio sources with peaked spectra (peaked spectrum sources, PSS) and compact symmetric objects (CSO) are powerful, compact, and presumably young AGNs and therefore particularly suitable to study aspects of the AGN-host connection. Aims. We use a statistical approach to investigate properties of a PSS-CSO sample that are related to host galaxies and could potentially shed light on the link between host galaxies and AGNs. The main goal is to compare the PSS-CSO sample with a matching comparison sample of extended sources (ECS) to see if the two have significant differences. Methods. We analysed composite spectra, diagnostic line diagrams, multi-band spectral energy distributions (MBSEDs), star formation (SF) indicators, morphologies, and cluster environments for a sample of 121 PSSs and CSOs for which spectra are available from the Sloan Digital Sky Survey (SDSS). The statistical results were compared with those of the ECS sample, where we generally considered the two subsamples of quasi-stellar objects (QSOs) and radio galaxies separately. The analysis is based on a large set of archival data in the spectral range from the ultraviolet to mid-infrared. Results. We find significant differences between the PSS-CSO and the ECS sample. In particular, we find that the ECS sample has a higher proportion of passive galaxies with a lower star formation activity. This applies to both sub-samples (QSOs or radio galaxies) as well as to the entire sample. The star formation rates of the PSS-CSO host galaxies with available data are typically in the range ∼0 to 5 ℳ⊙ yr−1, and the stellar masses are in the range 3 × 1011 to 1012 ℳ⊙. Secondly, in agreement with previous results, we find a remarkably high proportion of PSS-CSO host galaxies with merger signatures. The merger fraction of the PSS-CSO sample is 0.61 ± 0.07, which is significantly higher than that of the comparison sample (0.15 ± 0.06). We suggest that this difference can be explained by assuming that the majority of the PSSs and CSOs cannot evolve to extended radio sources and are therefore not represented in our comparison sample.