Bright Ring Research Articles

Inverse response behaviour in the bright ring radius measurement of the Czochralski process II: Mitigation by control

This is the second part of a two-article series investigating the presence of an inverse response in the measurement of the ingot radius in the Czochralski process for monocrystalline silicon production, when the ingot radius is deduced from a camera image of the bright ring at the meniscus connecting the solid crystal to the silicon melt. Such inverse responses are known to pose a fundamental limitation in achievable control performance. However, for the bright ring radius measurement, the inverse response is an artefact of the measurement technique and does not appear in the physical variable one wants to control (the actual crystal radius). The present article addresses control for the mitigation of the inverse response behaviour, using a combination of parallel compensation and feedback control. The proposed design is validated against simulations where the production process is subjected to temperature disturbances.

High resolution observations of molecular emission lines toward the CI Tau proto-planetary disc: planet-carved gaps or shadowing?

Abstract Recent observations have revealed that most proto-planetary discs show a pattern of bright rings and dark gaps. However, most of the high-resolution observations have focused only on the continuum emission. In this Paper we present high-resolution ALMA band 7 (0.89mm) observations of the disc around the star CI Tau in the 12CO & 13CO J = 3–2 and CS J = 7–6 emission lines. Our recent work demonstrated that the disc around CI Tau contains three gaps and rings in continuum emission, and we look for their counterparts in the gas emission. While we find no counterpart of the third gap and ring in 13CO, the disc has a gap in emission at the location of the second continuum ring (rather than gap). We demonstrate that this is mostly an artefact of the continuum subtraction, although a residual gap still remains after accounting for this effect. Through radiative transfer modelling we propose this is due to the inner disc shadowing the outer parts of the disc and making them colder. This raises a note of caution in mapping high-resolution gas emission lines observations to the gas surface density – while possible, this needs to be done carefully. In contrast to 13CO, CS emission shows instead a ring morphology, most likely due to chemical effects. Finally, we note that 12CO is heavily absorbed by the foreground preventing any morphological study using this line.

In vivo reflectance confocal microscopy for evaluating seborrheic keratosis, verruca plana, syringoma and lichen nitidus.

In clinical, common facial papule dermatosis such as seborrheic keratosis (SK), verruca plana (VP), syringoma and lichen nitidus (LN) is often misdiagnosed. Summarizing in vivo reflectance confocal microscopy (RCM) features of the facial papule dermatosis is helpful in the diagnosis of ambiguous lesions. The purpose of this study was to evaluate the features of SK, VP, syringoma, and LN in RCM. We recruited 144 patients referred for unequivocal facial papule dermatosis including 60 patients with SK, 60 patients with VP, 10 patients with syringoma, and 14 patients with LN. The RCM images were evaluated at the epidermis, the dermoepidermal junction, and the dermis from both papule lesions and normal skin. In the epidermis, the cerebriform shape was the main RCM characteristic of SK and the "petal-like" structure was the main RCM characteristic of VP. In the dermoepidermal junction, the RCM features we found were as follows: For SK, the bright dermal papillary rings, the abnormal dermal papilla and the looped vessels were also observed at the abnormal dermal papilla. For VP, the bright dermal papillary rings and the point-like blood vessels were also observed at the round dermal papills. For LN, the round, enlarged, well-circumscribed dermal papillae and the enlarged dermal papillaes were heavily laden with individual highly refractive cells. In the dermis, RCM examination revealed brightly refractile teratogenous sweat tube, designing variably visible bright "moon" structures in all syringoma patients. Considering our results, RCM may be useful to non-invasively discriminate SK, VP, syringoma and LN in vivo.

Combination of Lymphatic and Intravenous Contrast-Enhanced Ultrasound for Evaluation of Cervical Lymph Node Metastasis from Papillary Thyroid Carcinoma: A Preliminary Study

The aim of this prospective study was to evaluate the value of the combination of lymphatic contrast-enhanced ultrasound (LCEUS) and intravenous contrast-enhanced ultrasound (IVCEUS) for the identification of cervical lymph node metastasis (CLNM) from papillary thyroid carcinoma (PTC). From November 2018 to March 2019, 24 consecutive patients with PTC were evaluated. All patients underwent routine US, LCEUS and IVCEUS. Pathology was used as the gold standard. After injection of a contrast agent into the thyroid parenchyma, lymphatic vessels and lymph nodes (LNs) could be exclusively displayed as hyper-enhancement on LCEUS. Benign LNs displayed a complete bright ring (100%) and homogeneous perfusion (88.9%) on LCEUS, while displaying centrifugal perfusion (66.7%) and homogenous enhancement (88.9%) on IVCEUS. Perfusion defects (94.9%) and interruption of the bright ring (71.8%) were the two characteristic LCEUS signs for diagnosing CLNM. On IVCEUS, CLNM appeared as centripetal perfusion (59.0%) and heterogeneous enhancement (59.0%). After comparison with pathology, perfusion defect was correlated to the metastatic foci in the medulla and interruption of the bright ring to the tumor seeding in the marginal sinus (all p values <0.05). LCEUS had more value (area under the receiver operating characteristic curve [AUC] = 0.850, 95% confidence interval [CI]: 0.682–1.000) in diagnosing CLNM than IVCEUS (AUC = 0.692, 95% CI: 0.494–0.890) and routine US (AUC = 0.581, 95% CI: 0.367–0.796). The combination of LCEUS and IVCEUS has the highest diagnostic value (AUC = 0.863, 95% CI: 0.696–1.000). LCEUS had higher diagnostic value than IVCEUS and US for CLNM from PTC. The combination of LCEUS and IVCEUS has the highest diagnostic value for CLNM.

First Report of Alfalfa mosaic virus in Chayote in Italy.

Chayote (Sechium edule (Jacq.) Sw.) is a vigorous perennial and climbing cucurbits, native to Mesoamerica, and cultivated for alimentary purposes in the American continent, Australia, New Zealand, South Europe, Asia and Africa. During spring 2019, some chayote plants showing bright yellow vein banding rings and lines were observed in a private garden in South Italy (Campania region). Symptoms coalesced in some leaves, covering almost the whole foliar area. Double-stranded RNAs were extracted from symptomatic leaves of a single chayote plant and reverse-transcribed, randomly amplified, and submitted to Illumina sequencing (Marais et al., 2018). Reads were assembled using CLC Genomics Workbench 11.1 (http://www.clcbio.com). Contigs were then annotated by Blastn and Blastx comparison with the Genbank database, which allowed the identification of eight contigs of between 380 and 980 nucleotides sharing significant identity with alfalfa mosaic virus (AMV) genomic RNAs. No other viral contigs were identified. Mapping of reads on AMV genomic RNAs identified 4,209 AMV reads (1.26% of total reads) and allowed the scaffolding of the contigs into three scaffolds corresponding to the three AMV genomic RNAs. To complete the sequence of the AMV chayote isolate genome (named See-1), primers were designed from the contig sequences and used to amplify RACE PCR products spanning the 5' and 3' terminal regions of the three genomic RNAs using the SMARTer™ RACE cDNA Amplification Kit (Clontech, China). All amplicons were cloned into the pGEM-T vector (Promega, USA) and sequenced (three clones for each amplicon) by Microsynth Seqlab (Microsynth AG, Switzerland). Finally, the complete genomic sequences of the three RNAs were assembled by MacVector 17.5 (MacVector Inc., USA). The RNA1, RNA2 and RNA3 of See-1 are 3,643, 2,593 and 2,037 nt respectively (GenBank accession Nos. MT093209 to MT093211), and share the highest nt sequence identity with the RNA1 and RNA3 of AMV isolate (HZ) from tobacco (99.5% for RNA1, HQ316635; 98.7% for RNA3, HQ316637) and with the RNA2 of isolate AMV-Gym from Gynostemma pentaphyllum (98.1%, MH332898), both from China. AMV isolate See-1 was classified as belonging to subgroup I based on the presence of a BamH I and two AvaII sites in the CP ORF (Parrella et al., 2000). Reverse transcription polymerase chain reaction, using primers targeting the CP gene (Parrella et al., 2000), confirmed AMV infection in three symptomatic cayote plants including that used for Illumina sequencing, with 100% of nt sequence identity of amplicons. Three plants each of Chenopodium amaranticolor, Nicotiana benthamiana and Solanum lycopersicon were mechanically inoculated with sap from isolate See-1 infected plant, leading to the appearance of typical AMV symptoms in all three hosts ten days post-inoculation (Jaspars & Bos, 1980). This note describes the first detection of AMV in cayote in Italy and, to the best of our knowledge, in the world. In some areas of Southern Italy, climatic conditions are favorable enough to allow chayote development in the wild. Further studies would be desirable to determine the distribution and incidence of AMV in chayote and to understand the possibility that this species may play a role in AMV epidemiology, representing a threat to other susceptible crops.

Observational signatures of strongly naked singularities: image of the thin accretion disk

We study the optical appearance of a thin accretion disk around the strongly naked static Janis–Newman–Winicour singularity. The solution does not possess a photon sphere, which results in the formation of a complex structure of bright rings in the central region of the disk image. Such structure is absent in the case of the Schwarzschild black hole with a thin accretion disk, where instead of the image we observe the black hole shadow. Some of the rings emit with the maximal observable radiation flux from the accretion disk, and should be experimentally detectable. Thus, this qualitatively new feature can be used to distinguish observationally black holes from naked singularities. We elucidate the appearance of the ring structure by revealing the physical mechanism of its formation, and explaining the nature of each of the ring images. We make the conjecture that a similar structure would also appear for other solutions without a photon sphere and it can serve as a general observational signature for distinguishing compact objects possessing no photon sphere from black holes.

Sol–gel auto-ignition fabrication of Gd3+ incorporated Ni0.5Co0.5Fe2O4 multifunctional spinel ferrite nanocrystals and its impact on structural, optical and magnetic properties

Monophasic nanocrystals of rare earth gadolinium (Gd3+) ion doped nickel–cobalt ferrite, Ni0.5Co0.5GdyFe2−yO4 (y = 0.00, 0.025, 0.050, 0.075, 0.100 and 0.125) have been synthesized by l-ascorbic acid assisted sol–gel auto-ignition process. Thermogravimetric and differential scanning calorimetry, X-ray diffraction, Fourier transform infrared spectroscopy (FTIR), transmission electron microscopy (TEM) with selected area electron diffraction (SAED) patterns, ultraviolet–visible spectrophotometry and vibrating sample magnetometer were employed to characterize the microstructure, optical and magnetic properties. Structural investigations verified the presence of cubic spinel phase short of any contamination peak. The average crystallite size was seen in nano-regime dimensions and well confirmed by TEM results. SAED patterns showed bright and intense ring of (311) plane revealed the establishment of spinel ferrite nanocrystals. Lattice constant (a) increases steadily with the rise in Gd3+ content following the Vegard’s law. FTIR spectra confirmed the creation of spinel ferrite structural geometry. Saturation magnetization (Ms) and a remanence magnetization (Mr) decreased from 29.77 to 20.78 emu/g and 21.62 to 15.79 emu/g, respectively, with increasing the Gd3+ content. However, coercivity (Hc) is significantly increased. The highest value of Hc = 1132 Oe was found for y = 0.075 sample. The reduction in Ms values can be justified owing to the replacement of Fe3+ existing at the octahedral [B]-sites by the Gd3+ ions which is paramagnetic at room temperature. The elucidation of magnetic parameters with Gd3+ doping was attributed to the discrepancy of anisotropy constant, the paramagnetic nature of Gd3+ and crystallite size effect.

Suppressed twist in droplets of cholesteric rod-like virus as identified by single particle imaging

ABSTRACT The director field configuration of a colloidal chiral nematic liquid crystal confined in droplets is studied in this work. We employ microfluidics to produce monodisperse droplets containing nematic dispersions of fd virus surrounded by a carrier oil phase, while we vary the size of the droplet as well as the concentration of the virus. The resulting director fields within the droplets are studied at the single-molecule level, using confocal microscopy. The 3-D structures are linked to polarisation microscopy observations of bright rings, which can be attributed to a cholesteric twist of the director field. We identify boundaries of concentration and size where one and two rings are observed, suggesting suppression of the cholesteric twist by confinement. Single particle confocal observations confirm that indeed the twist in the director field underlies the ring formation, but they also show that the twist is non-monotonous throughout the droplet and much smaller than observed in bulk.

Precisely controlled shape and size of gold nanostructures by seed-mediated reduction reaction method

Here we present synthesis of different shapes and sizes of Au nanostructures using seed-mediated growth method. The effect of concentration of seed solution (SS), reducing reagent, and capping molecule are investigated. Further, the growth mechanism involved of nanoshapes is discussed. A systematic red shift in the surface plasmon resonance peak observed with the decreasing SS in NP suspension demonstrates the growth of different sizes of NPs. Two surface resonance peaks (TSPR and LSPR) exhibited in the optical spectra of NRs suspension confirms the growth of NRs. The aspect ratio of NR was found increased from 1.8 to 3.2 with increasing the contents of AgNO3. For lower pH, the fixed position of TSPR peak confirms the growth of uniform diameter of NBPs. The increased transverse and longitudinal length of Au NBPs is proposed due to the absorption of more Au(0) ions on the facets of Au seed particles. A broad absorbance pattern revealed in visible to near-infrared region for NSR suspensions was due to the complex response from the branches and plamon response of nanostar core. The Ag + ions combine with the halide significantly influence the shape and growth of NSRs. XRD data revealed that the NRs and NBPs were preferential orientation (111) crystalline rich, whereas NSRs were not abundant in (111) and (200) facets. TEM images confirm the change in shape and size of nanostructures by changing the SS, AgNO3, HCl, and AA in the respective solutions of NPs, NRs, NBPs, and NSRs. A clear lattice fringe in HRTEM images with inter-planner distance ~ 2.27 A corresponds to (111) Bragg reflection and dotted bright circular rings evident the good crystallinity of Au nanostructures with FCC crystal structure. The ability to produce the controlled shape and size of Au nanostructures could be beneficial for solar cell applications to enhance the absorption of electromagnetic radiation in the visible region.

Annular substructures in the transition disks around LkCa 15 and J1610

We present high-resolution millimeter continuum ALMA observations of the disks around the T Tauri stars LkCa 15 and 2MASS J16100501-2132318 (hereafter, J1610). These transition disks host dust-depleted inner regions, which have possibly been carved by massive planets, and they are of prime interest to the study of the imprints of planet-disk interactions. While at moderate angular resolution, they appear as a broad ring surrounding a cavity, the continuum emission resolves into multiple rings at a resolution of ~60 × 40 mas (~7.5 au for LkCa 15, ~6 au for J1610) and ~7μJy beam−1rms at 1.3 mm. In addition to a broad extended component, LkCa 15 and J1610 host three and two narrow rings, respectively, with two bright rings in LkCa 15 being radially resolved. LkCa 15 possibly hosts another faint ring close to the outer edge of the mm emission. The rings look marginally optically thick, with peak optical depths of ~0.5 (neglecting scattering), in agreement with high angular resolution observations of full disks. We performed hydrodynamical simulations with an embedded, sub-Jovian-mass planet and show that the observed multi-ringed substructure can be qualitatively explained as the outcome of the planet-disk interaction. We note, however, that the choice of the disk cooling timescale alone can significantly impact the resulting gas and dust distributions around the planet, leading to different numbers of rings and gaps and different spacings between them. We propose that the massive outer disk regions of transition disks are favorable places for planetesimals, and possibly second-generation planet formation of objects with a lower mass than the planets carving the inner cavity (typically fewMJup), and that the annular substructures observed in LkCa 15 and J1610 may be indicative of planetary core formation within dust-rich pressure traps. Current observations are compatible with other mechanisms contributing to the origin of the observed substructures, in particular with regard to narrow rings generated (or facilitated) at the edge of the CO and N2snowlines.

Features of dermatofibroma in reflectance confocal microscopy.

Dermatofibroma (DF) is a common benign skin lesion in a majority of cases located on the legs or upper limbs. The etiology of DF is still unclear. Reflectance confocal microscopy features of DF were described. Forty patients with DF diagnosis confirmed by dermoscopy were examined using reflectance confocal microscopy VivaScope 1500 from March 2018 to April 2019. DF was more common in females (80%) than males (20%). Thirty-six lesions (90%) were located on the limbs while four (10%) were on the trunk. Dermoscopically, 18 lesions (45%) revealed typical features: central white area with a brown network in the periphery. Twenty-two DFs (55%) were found with a central white patch and globular-like structures, surrounded by a thin brown network. In reflectance confocal microscopy, all revealed a typical honeycombed pattern, although in some cases (30%), streaming was observed. In two lesions (5%) in epidermis, few dendritic cells were observed, and one DF revealed roundish pagetoid cells (2.5%). The dermoepidermal junction (DEJ) in all lesions was abounded in dilated vessels. The most common observable feature of DF was bright "rings" composed of monomorphic, regular cells surrounding dark dermal papillae. In five lesions (12.5%), rings were "double" because of exceptionally pigmented DF. Reflectance confocal microscopy enables us to describe microscopic features of DF. There are four confocal microscopic features observable in each DF: in the epidermis, normal honeycombed pattern, sometimes with local streaming, in DEJ, edged papillae, bright rings, and dilated vessels.

The Classification and Characteristics of Black Holes

Scientists have obtained the first image of a black hole, using Event Horizon Telescope observations of the center of the galaxy M87. The image shows a bright ring formed as light bends in the intense gravity around a black hole that is 6.5 billion times more massive than the Sun. It is consistent with what General Relativity predicts. One of the famous predictions of general relativity is that of black holes. With the birth of the first image of a black hole, this article will discuss the classification of blackholes.

Screening of Phosphate-Resolving Bacteria in Rhizosphere of Cold Sunflower and Physiological and Biochemical Study

The purpose of the experiment is to obtain high-efficiency microbial phosphorus dephosphorization fertilizer, increase the soluble phosphorus content of the soil, and promote plant growth. The phosphorus detoxifying bacteria in sunflower rhizosphere were studied through dilution and coating plate method, molybdenum-antimony anti-spectrophotometry, plate culture, physiological and biochemical detection. 10 strains were isolated and purified to form bright rings, D/d value is between 1.10-4.35. The quantitative analysis of the pressure showed that BX2 had the best effect in dissolving phosphorus. The available phosphorus increment was 38.59μg/mL, BX7 had the lowest phosphorus dissolving effect, and the effective phosphorus increase was only 1.77μg/mL. These strains of BX2, BX3, BX5, BX9 and BX10 have excellent phosphorus-dissolving properties, providing necessary conditions for the subsequent development of microbial fertilizer.

Syntheses and characterizations of GO/Mn3O4 nanocomposite film electrode materials for supercapacitor applications

We have, in this study; used simple, in-expensive and environmentally-friendly successive ionic layer adsorption and reactions (SILAR) deposition procedure to successfully grow GO/Mn3O4 thin film electrode materials. The deposited films were examined for their surface morphology using scanning electron microscopy (SEM) while its morphology and structure was confirmed using transmission electron microscopy (TEM) and selected area electron diffractometry (SAED) respectively. X-ray diffraction (XRD) was used to study their structural properties while their supercapacitive studies were obtained using cyclic voltammetry (CV), galvanostatic charge–discharge (GCD) and electrochemical impedance spectroscopy (EIS) techniques. All deposited films were scanned in 1 M solution of Na2SO4 electrolyte. The SEM images of the deposited films revealed highly porous interconnected morphology with Mn3O4 densely dispersed among graphene oxide (GO). Individual peaks of Mn3O4 and GO compounds indicating uniform spread of Mn3O4 inside the porous matrix of GO were observed from the XRD. Mn3O4 nanograins well-dispersed on the surface were further confirmed through the TEM images while bright concentric rings confirming the polycrystalline nature of the films were observed from SAED images. The film deposited at 40 cycles yielded the maximum specific capacitance of 532.54 Fg−1at 5 mVs−1 scan rate. The results of the electrochemical studies show that the GO/Mn3O4 composite films synthesized by SILAR could be a promising material for supercapacitors.

Circular Dammann gratings for enhanced control of the ring profile of perfect optical vortices

Perfect optical vortices (POVs) provide a solution to address the challenge induced by strong dependence of classical optical vortices on their carried topological charges. However, traditional POVs are all shaped into bright rings with a single main lobe along the radial direction. Here we propose a method for enhanced control on the ring profile (the radial intensity profile of circular rings) of POVs based on modulated circular sine/cosine radial functions, which is realized by a circular Dammann grating embedded with a spiral phase. Specifically, a type of “absolute” dark POVs surrounded by two bright lobe rings in each side is presented, which provides a perfect annular potential well along those dark impulse rings for trapping low-index particles, cells, or quantum gases. In addition, several POVs with different ring profiles, including conventional POVs with bright rings, the dark POVs mentioned above, and also POVs with tunable ring profiles, are demonstrated. This work opens up new possibilities to controllably tune the ring profile of perfect vortices, and this type of generalized POVs will enrich the content of singular optics and expand the application scope of perfect vortices in a range of areas including optical manipulation, both quantum and classical optical communications, enhanced optical imaging, and also novel structured pumping lasers.

Spirals inside the millimeter cavity of transition disk SR 21

Context. Hydrodynamical simulations of planet-disk interactions suggest that planets may be responsible for a number of the substructures frequently observed in disks in both scattered light and dust thermal emission. Despite the ubiquity of these features, direct evidence of planets embedded in disks and of the specific interaction features like spiral arms within planetary gaps are still rare. Aims. In this study we discuss recent observational results in the context of hydrodynamical simulations in order to infer the properties of a putative embedded planet in the cavity of a transition disk. Methods. We imaged the transition disk SR 21 in H-band in scattered light with SPHERE/IRDIS and in thermal dust emission with ALMA band 3 (3 mm) observations at a spatial resolution of 0.1″. We combine these datasets with existing Band 9 (430 μm) and Band 7 (870 μm) ALMA continuum data. Results. The Band 3 continuum data reveals a large cavity and a bright ring peaking at 53 au strongly suggestive of dust trapping. The ring shows a pronounced azimuthal asymmetry, with a bright region in the northwest that we interpret as a dust overdensity. A similarly asymmetric ring is revealed at the same location in polarized scattered light, in addition to a set of bright spirals inside the millimeter cavity and a fainter spiral bridging the gap to the outer ring. These features are consistent with a number of previous hydrodynamical models of planet-disk interactions, and suggest the presence of a ∼1 MJup planet at 44 au and PA = 11 deg. This makes SR21 the first disk showing spiral arms inside the millimeter cavity, and the first disk for which the location of a putative planet can be precisely inferred. Conclusions. The main features of SR 21 in both scattered light and thermal emission are consistent with hydrodynamical predictions of planet-disk interactions. With the location of a possible planet being well constrained by observations, it is an ideal candidate for follow-up observations to search for direct evidence of a planetary companion still embedded in its disk.

Black Hole Parameter Estimation from Its Shadow

Abstract The Event Horizon Telescope (EHT), a global submillimeter wavelength very long baseline interferometry array, unveiled event-horizon–scale images of the supermassive black hole M87* as an asymmetric bright emission ring with a diameter of 42 ± 3 μas, and it is consistent with the shadow of a Kerr black hole of general relativity. A Kerr black hole is also a solution of some alternative theories of gravity, while several modified theories of gravity admit non-Kerr black holes. While earlier estimates for the M87* black hole mass, depending on the method used, fall in the range , the EHT data indicated a mass for the M87* black hole of (6.5 ± 0.7) × 109 M ⊙. This offers another promising tool to estimate black hole parameters and to probe theories of gravity in its most extreme region near the event horizon. The important question arises: Is it possible by a simple technique to estimate black hole parameters from its shadow, for arbitrary models? In this paper, we present observables, expressed in terms of ordinary integrals, characterizing a haphazard shadow shape to estimate the parameters associated with black holes, and then illustrate its relevance to four different models: Kerr, Kerr–Newman, and two rotating regular models. Our method is robust, accurate, and consistent with the results obtained from existing formalism, and it is applicable to more general shadow shapes that may not be circular due to noisy data.

Static spherically symmetric configurations with N nonlinear scalar fields: Global and asymptotic properties

In case of a spherically symmetric non-linear scalar field (SF) in flat space, besides singularity at the center, spherical singularities can occur for non-zero values of radial variable $r>0$. We show that in the General Relativity the gravitational field suppresses the occurrence of the spherical singularities under some generic conditions. Our consideration deals with asymptotically flat space-times around static spherically symmetric configurations in presence of $N$ non-linear SFs, which are minimally coupled to gravity. Constraints are imposed on the SF potentials, which guarantee a monotonicity of the fields as functions of radial variable; also the potentials are assumed to be exponentially bounded. We give direct proof that solutions of the joint system of Einstein -- SF equations satisfying the conditions of asymptotic flatness are regular for all values of $r$, except for naked singularities in the center $r=0$ in the Schwarzschild (curvature) coordinates. Asymptotic relations for SF and metric near the center are derived, which appear to be remarkably similar to the case of the Fisher solution for free SF. These relations determine two main types of the corresponding geodesic structure when photons can be captured by the singularity or not depending on the existence of the photon sphere. To illustrate, the case of one SF with monomial potential is analyzed in detail numerically. We show that the image of the accretion disk around the singularity, observed from infinity, can take the form of a bright ring with a dark spot in the center, like the case of an ordinary black hole.

Shadowing and multiple rings in the protoplanetary disk of HD 139614

Context. Shadows in scattered light images of protoplanetary disks are a common feature and support the presence of warps or misalignments between disk regions. These warps are possibly caused by an inclined (sub-)stellar companion embedded in the disk. Aims. We aim to study the morphology of the protoplanetary disk around the Herbig Ae star HD 139614 based on the first scattered light observations of this disk, which we model with the radiative transfer code MCMax3D. Methods. We obtained J- and H-band observations that show strong azimuthal asymmetries in polarized scattered light with VLT/SPHERE. In the outer disk, beyond ~30 au, a broad shadow spans a range of ~240 deg in position angle, in the east. A bright ring at ~16 au also shows an azimuthally asymmetric brightness, with the faintest side roughly coincidental with the brightest region of the outer disk. Additionally, two arcs are detected at ~34 and ~50 au. We created a simple four-zone approximation to a warped disk model of HD 139614 in order to qualitatively reproduce these features. The location and misalignment of the disk components were constrained from the shape and location of the shadows they cast. Results. We find that the shadow on the outer disk covers a range of position angles too wide to be explained by a single inner misaligned component. Our model requires a minimum of two separate misaligned zones – or a continuously warped region – to cast this broad shadow on the outer disk. A small misalignment of ~4° between adjacent components can reproduce most of the observed shadow features. Conclusions. Multiple misaligned disk zones, potentially mimicking a warp, can explain the observed broad shadows in the HD 139614 disk. A planetary mass companion in the disk, located on an inclined orbit, could be responsible for such a feature and for the dust-depleted gap responsible for a dip in the SED.

Pebble drift and planetesimal formation in protoplanetary discs with embedded planets

Nearly axisymmetric gaps and rings are commonly observed in protoplanetary discs. The leading theory regarding the origin of these patterns is that they are due to dust trapping at the edges of gas gaps induced by the gravitational torques from embedded planets. If the concentration of solids at the gap edges becomes high enough, it could potentially result in planetesimal formation by the streaming instability. We tested this hypothesis by performing global 1D simulations of dust evolution and planetesimal formation in a protoplanetary disc that is perturbed by multiple planets. We explore different combinations of particle sizes, disc parameters, and planetary masses, and we find that planetesimals form in all of these cases. We also compare the spatial distribution of pebbles from our simulations with protoplanetary disc observations. Planets larger than one pebble isolation mass catch drifting pebbles efficiently at the edge of their gas gaps, and depending on the efficiency of planetesimal formation at the gap edges, the protoplanetary disc transforms within a few 100 000 yr to either a transition disc with a large inner hole devoid of dust or to a disc with narrow bright rings. For simulations with planetary masses lower than the pebble isolation mass, the outcome is a disc with a series of weak ring patterns but there is no strong depletion between the rings. By lowering the pebble size artificially to a 100 micrometer-sized “silt”, we find that regions between planets get depleted of their pebble mass on a longer time-scale of up to 0.5 million years. These simulations also produce fewer planetesimals than in the nominal model with millimeter-sized particles and always have at least two rings of pebbles that are still visible after 1 Myr.