Planets form in young circumstellar disks called protoplanetary disks. However, it is still difficult to catch planet formation in-situ. Nevertheless, from recent ALMA/SPHERE data, encouraging evidence of the direct and indirect presence of embedded planets has been identified in disks around young stars: co-moving point sources, gravitational perturbations, rings, cavities, and emission dips or shadows cast on disks. The interpretation of these observations needs a robust physical framework to deduce the complex disk geometry. In particular, protoplanetary disk models usually assume the gas pressure scale-height given by the ratio of the sound speed over the azimuthal velocity $H/r = c_{s\rm }/v_{\rm k}$. By doing so, \textit{radiative} pressure fields are often ignored, which could lead to a misinterpretation of the real vertical structure of such disks. We follow the evolution of a gaseous disk with an embedded Jupiter mass planet through hydrodynamical simulations, computing the disk scale-height including radiative pressure, which was derived from a generalization of the stellar atmosphere theory. We focus on the vertical impact of the radiative pressure in the vicinity of circumplanetary disks, where temperatures can reach $\gtrsim 1000$ K for an accreting planet, and radiative forces can overcome gravitational forces from the planet. The radiation-pressure effects create a vertical optically thick column of gas and dust at the proto-planet location, casting a shadow in scattered light. This mechanism could explain the peculiar illumination patterns observed in some disks around young stars such as HD 169142 where a moving shadow has been detected, or the extremely high aspect-ratio $H/r \sim 0.2$ observed in systems like AB Aur and CT Cha.
Detailed observations of gaps in protoplanetary disks have revealed structures that drive current research on circumstellar disks. One such feature is the two intensity nulls seen along the outer disk of the HD 142527 system, which are particularly well traced in polarized differential imaging. Here we propose that these are shadows cast by the inner disk. The inner and outer disk are thick, in terms of the unit-opacity surface in H-band, so that the shape and orientation of the shadows inform on the three-dimmensional structure of the system. Radiative transfer predictions on a parametric dis…
Three-dimensional hydrodynamic numerical simulations have demonstrated that the structure of a protoplanetary disc may be strongly affected by a planet orbiting in a plane that is misaligned to the disc. When the planet is able to open a gap, the disc is separated into an inner, precessing disc and an outer disc with a warp. In this work, we compute infrared scattered light images to investigate the observational consequences of such an arrangement. We find that an inner disc misaligned by a less than a degree to the outer disc is indeed able to cast a shadow at larger radii. In our simulation…
We explore whether protoplanetary disks with self-shadowing from puffed up inner rims exhibit observable features in scattered light images. We use both self-consistent hydrostatic equilibrium calculations and parameterized models to produce the vertically puffed up inner rims. We find that, in general, the transition between the shadowed and flared regions occurs in a smooth manner over a broad radius range, and no sudden jump exists at the outer edge of the shadow in either the disk temperature or density structures. As a result, a puffed up rim cannot create sharp ring/arc/spiral-arm-like f…
Understanding the diversity of planets requires to study the morphology and the physical conditions in the protoplanetary disks in which they form. We observed and spatially resolved the disk around the ~10 Myr old protoplanetary disk HD 100453 in polarized scattered light with SPHERE/VLT at optical and near-infrared wavelengths, reaching an angular resolution of ~0.02", and an inner working angle of ~0.09". We detect polarized scattered light up to ~0.42" (~48 au) and detect a cavity, a rim with azimuthal brightness variations at an inclination of 38 degrees, two shadows and two symmetric spi…
We show that the first order (non co-orbital) corotation torques are significantly modified by entropy gradients in a non-barotropic protoplanetary disk. Such non-barotropic torques can dramatically alter the balance that, for barotropic cases, results in the net eccentricity damping for giant gap-clearing planets embedded in the disk. We demonstrate that stellar illumination can heat the gap enough for the planet's orbital eccentricity to instead be excited. We also discuss the "Eccentricity Valley" noted in the known exoplanet population, where low-metallicity stars have a deficit of eccentr…
Theoretical models of protoplanetary disks including stellar irradiation often show a spontaneous amplification of scale height perturbations, produced by the enhanced absorption of starlight in enlarged regions. In turn, such regions cast shadows on adjacent zones that consequently cool down and shrink, eventually leading to an alternating pattern of overheated and shadowed regions. Previous investigations have proposed this to be a real self-sustained process, the so-called self-shadowing or thermal wave instability, which could naturally form frequently observed disk structures such as ring…
Starlight-driven flared-staircase geometry in radiation hydrodynamic models of protoplanetary disks
Max-Planck-Institut für Astronomie（马克斯·普朗克天文学研究所）；Fakultät für Physik und Astronomie, Universität Heidelberg（海德堡大学物理与天文学院）；Ludwig-Maximilians-Universität München（慕尼黑路德维希-马克西米利安大学）；Exzellenzcluster ORIGINS（ORIGINS卓越集群）
Dust evolution in protoplanetary disks from small dust grains to pebbles is key to the planet formation process. The gas in protoplanetary disks should influence the vertical distribution of small dust grains ($\sim$1 $μm$) in the disk.Utilizing archival near-infrared polarized light and millimeter observations, we can measure the scale height and the flare parameter $β$ of the small dust grain scattering surface and $^{12}$CO gas emission surface for three protoplanetary disks IM Lup, HD 163296, and HD 97048 (CU Cha). For two systems, IM Lup and HD 163296, the $^{12}$CO gas and small dust gra…
Substructure in externally irradiated protoplanetary disks, I. spirals and rings in two-dimensional radiation hydrodynamics
Ludwig-Maximilians-Universität München（路德维希-马克西米利安慕尼黑大学）；Astronomy Unit, School of Physics and Astronomy, Queen Mary University of London（伦敦大学玛丽女王学院物理与天文学系天文学单元）；Max Planck Institute for Astronomy（马克斯·普朗克天文学研究所）
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 due to an inclined (sub-)stellar companion embedded in the disk. We 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. We obtained J- and H-band observations in polarized scattered light with VLT/SPHERE that show strong azimuthal asymmetries. In the outer disk, beyond ~3…
We aim at estimating the dust scale height of protoplanetary disks from millimeter continuum observations. First, we present a general expression of intensity of a ring in a protoplanetary disk, and show that we can constrain the dust scale height by the azimuthal intensity variation. Then, we apply the presented methodology to the two distinct rings at 68 au and at 100 au of the protoplanetary disk around HD 163296. We constrain the dust scale height by comparing the DSHARP high-resolution millimeter dust continuum image with radiative transfer simulations using RADMC-3D. We find that h_d/h_g…
Probing disk dynamics and dust evolution through shadows in protoplanetary disks: A case study of the HD 142527 disk
Institute of Astronomy and Astrophysics, Academia Sinica（中央研究院天文及天文物理研究所）；Institute of Science Tokyo（东京科学大学）；The University of Tokyo（东京大学）；Kogakuin University（工学馆大学）
Spiral structures are a common feature in scattered-light images of protoplanetary disks, and of great interest as possible tracers of the presence of planets. However, other mechanisms have been put foward to explain them, including self-gravity, disk-envelope interactions, and dead zone boundaries. These mechanisms explain many spirals very well, but are unable to easily account for very loosely wound spirals and single spiral arms. We study the effect of light travel time on the shape of a shadow cast by a clump orbiting close (within ${\sim}1\,$au) of the central star, where there can be s…
Understanding the thermal structure of protoplanetary disks is crucial for modeling planet formation and interpreting disk observations. We present a new two-layer radiative transfer model for computing the thermal structure of axisymmetric irradiated disks. Unlike the standard two-layer model, our model accounts for the radial as well as vertical transfer of the starlight reprocessed at the disk surface. The model thus allows us to compute the temperature below "shadowed" surfaces receiving no direct starlight. Thanks to the assumed axisymmetry, the reprocessed starlight flux is given in one-…
Modeling the Evolution of Protoplanetary Disks: Two Pathways from Gravitational Instability to MHD Wind-Driven Accretion
Institute for Advanced Study, Tsinghua University（清华大学高等研究院）；Center for Computational Astrophysics, Flatiron Institute（Flatiron研究所计算天体物理中心）；Department of Astronomy, Tsinghua University（清华大学天文系）
We calculate simulated images of disks perturbed by embedded small planets. These 10-50 M_Earth bodies represent the growing cores of giant planets. We examine scattered light and thermal emission from these disks over a range of wavelengths, taking into account the wavelength-dependent opacity of dust in the disk. We also examine the effect of inclination on the observed perturbations. We find that the perturbations are best observed in the visible to mid-infrared. Scattered light images reflect shadows produced at the surface of perturbed disks, while the infrared images follow thermal emiss…
We carry out three-dimensional hydrodynamical simulations to study planet-disc interactions for inclined high mass planets, focusing on the disc's secular evolution induced by the planet. We find that, when the planet is massive enough and the induced gap is deep enough, the disc inside the planet's orbit breaks from the outer disc. The inner and outer discs precess around the system's total angular momentum vector independently at different precession rates, which causes significant disc misalignment. We derive the analytical formulae, which are also verified numerically, for: 1) the relation…
The variety of observed protoplanetary disks in polarimetric light motivates a taxonomical study to constrain their evolution and establish the current framework of this type of observations. We classified 58 disks with available polarimetric observations into six major categories (Ring, Spiral, Giant, Rim, Faint, and Small disks) based on their appearance in scattered light. We re-calculated the stellar and disk properties from the newly available GAIA DR2 and related these properties with the disk categories. More than a half of our sample shows disk sub-structures. For the remaining sources…
The morphological evolution of dusty disks around young (few Myr-old) stars is pivotal to better understand planet formation. Since both dust grains and the global disk geometry evolve on short timescale, high-resolution imaging of a sample of objects may provide important hints towards such an evolution. We enlarge the sample of protoplanetary disks imaged in polarized light with high-resolution by observing the Herbig Ae/Be stars HD163296, HD141569A, and HD150193A. We integrate our data with previous datasets to paint a larger picture of their morphology. We report a weak detection of the di…
We examine the observational consequences of partial gaps being opened by planets in protoplanetary disks. We model the disk using a static alpha-disk model with detailed radiative transfer, parametrizing the shape and size of the partially cleared gaps based on the results of hydrodynamic simulations. Shadowing and illumination by stellar irradiation at the surface of the gap leads to increased contrast as the gap trough is deepened by shadowing and cooling and the far gap wall is puffed up by illumination and heating. In calculating observables, we find that multiple scattering is important …
Diverse dust vertical height and settling strength conditions in protoplanetary discs
Mullard Space Science Laboratory, University College London（穆拉德太空科学实验室，伦敦大学学院）；Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台）；School of Astronomy and Space Science, University of Science and Technology of China（中国科学技术大学天文与空间科学学院）；Univ. Grenoble Alpes, CNRS, IPAG（格勒诺布尔阿尔卑斯大学，法国国家科学研究中心，IPAG）；School of Physical Science and Technology, Southwest Jiaotong University（西南交通大学物理科学与技术学院）；School of Natural Sciences, Center for Astronomy, University of Galway（戈尔韦大学自然科学与天文学中心）；Max-Planck Institute for Astronomy (MPIA)（马克斯·普朗克天文学研究所）
One of the striking discoveries of protoplanetary disc research in recent years are the spiral arms seen in several transitional discs in polarised scattered light. An interesting interpretation of the observed spiral features is that they are density waves launched by one or more embedded (proto-)planets in the disc. In this paper we investigate whether planets can be held responsible for the excitation mechanism of the observed spirals. We use locally isothermal hydrodynamic simulations as well as analytic formulae to model the spiral waves launched by planets. Then H-band scattered light im…
Molecules in the shadows of the protoplanetary disk HD 143006: Evidence for C/O $\gtrsim 1$ from simultaneously modeling fourteen ALMA lines
Space Research Institute, Austrian Academy of Sciences（奥地利科学院空间研究所）；Leibniz Institute for Astrophysics Potsdam (AIP)（波茨坦莱布尼茨天体物理研究所）；Space Research Organisation Netherlands（荷兰空间研究组织）；Department of Astronomy, University of Wisconsin-Madison（威斯康星大学麦迪逊分校天文学系）
利用 HD 143006 内盘投下的阴影，结合 ALMA 观测与 ProDiMo 模型，发现其外盘 C/O 略大于 1，并揭示慢热弛豫与紫外解吸对谱线形成的关键作用。
We investigate the dynamics of dust grains with various sizes in protoplanetary disk winds driven by magnetorotational turbulence, by simulating the time evolution of the dust grain distribution in the vertical direction. Small dust grains, which are well coupled to the gas, are dragged upward with the upflowing gas, while large grains remain near the midplane of a disk. Intermediate--size grains float at several scale heights from the midplane in time-averated force balance between the downward gravity and the upward gas drag. For the minimum mass solar nebula at 1 AU, dust grains with size o…
Dust gaps and rings appear ubiquitous in bright protoplanetary disks. Disk-planet interaction with dust-trapping at the edges of planet-induced gaps is one plausible explanation. However, the sharpness of some observed dust rings indicate that sub-mm-sized dust grains have settled to a thin layer in some systems. We test whether or not such dust around gas gaps opened by planets can remain settled by performing three-dimensional, dust-plus-gas simulations of protoplanetary disks with an embedded planet. We find planets massive enough to open gas gaps stir small, sub-mm-sized dust grains to hig…
Recent ALMA molecular line observations have revealed 3-D gas velocity structure in protoplanetary disks, shedding light on mechanisms of disk accretion and structure formation. 1) By carrying out viscous simulations, we confirm that the disk's velocity structure differs dramatically using vertical stress profiles from different accretion mechanisms. Thus, kinematic observations tracing flows at different disk heights can potentially distinguish different accretion mechanisms. On the other hand, the disk surface density evolution is mostly determined by the vertically integrated stress. The sh…
The chemical and physical evolution of primitive materials in protoplanetary disks are determined by the types of environments they are exposed to and their residence times within each environment. Here a method for calculating representative paths of materials in diffusive protoplanetary disks is developed and applied to understanding how the vertical trajectories that particles take impact their overall evolution. The methods are general enough to be applied to disks with uniform diffusivity, the so-called "constant-$α$" cases, and disks with a spatially varying diffusivity, such as expected…
Vertical Structure of Protoplanetary Disks in Scattered Light: A large sample analysis
School of Natural Sciences, Center for Astronomy, University of Galway（自然科学与天文学中心，高威大学）；School of Physics, Trinity College Dublin, The University of Dublin（三一学院都柏林，都柏林大学物理学院）；Leiden Observatory, Leiden University（莱顿天文台，莱顿大学）；INAF, Istituto di Radioastronomia（意大利国家天体物理研究所射电天文研究所）
Shadows in transitional disks are generally interpreted as signs of a misaligned inner disk. This disk is usually beyond the reach of current day high contrast imaging facilities. However, the location and morphology of the shadow features allow us to reconstruct the inner disk geometry. We derive analytic equations of the locations of the shadow features as a function of the orientation of the inner and outer disk and the height of the outer disk wall. In contrast to previous claims in the literature, we show that the position angle of the line connecting the shadows cannot be directly relate…
The formation of planets with gaseous envelopes takes place in protoplanetary accretion discs on time-scales of several millions of years. Small dust particles stick to each other to form pebbles, pebbles concentrate in the turbulent flow to form planetesimals and planetary embryos and grow to planets, which undergo substantial radial migration. All these processes are influenced by the underlying structure of the protoplanetary disc, specifically the profiles of temperature, gas scale height and density. The commonly used disc structure of the Minimum Mass Solar Nebular (MMSN) is a simple pow…
The HD 163296 disk shows ring and gap substructures with ALMA observations. In addition, this is the only disk where the rings and gaps are spatially resolved in millimeter-wave polarization measurements. In this paper, we conduct radiative transfer modeling that includes self-scattering polarization to constrain the grain size and its distribution. We found that the grain size and dust scale height are the key parameters for reproducing the radial and azimuthal distributions of the observed polarization signature. Radial variation is mainly determined by grain size. The polarization fraction …
Interpreting the scattering surface in protoplanetary disks
Università degli Studi di Milano（米兰大学）；University of Bologna（博洛尼亚大学）；INAF, Astrophysics and Space Science Observatory Bologna（意大利国家天体物理研究所博洛尼亚天文台）；Univ. Grenoble Alpes, CNRS, IPAG（格勒诺布尔阿尔卑斯大学、法国国家科学研究中心、IPAG实验室）；Istituto di Radioastronomia, INAF（意大利国家天体物理研究所射电天文研究所）；Max-Planck-Institut für Astronomie (MPIA)（马克斯·普朗克天文学研究所）；University Observatory, Faculty of Physics, Ludwig-Maximilians-Universität München（慕尼黑大学物理学院天文台）；Exzellenzcluster ORIGINS（ORIGINS卓越集群）
Planets are born in protostellar disks, which are now observed with enough resolution to address questions about internal gas flows. Candidates for driving the flows include magnetic forces, but ionization state estimates suggest much of the gas mass decouples from magnetic fields. Thus, hydrodynamical instabilities could play a major role. We investigate disk dynamics under conditions typical for a T Tauri system, using global 3D radiation hydrodynamics simulations with embedded particles and a resolution of 70 cells per scale height. Stellar irradiation heating is included with realistic dus…
Turbulence driven by magnetorotational instability (MRI) crucially affects the evolution of solid bodies in protoplanetary disks. On the other hand, small dust particles stabilize MRI by capturing ionized gas particles needed for the coupling of the gas and magnetic fields. To provide an empirical basis for modeling the coevolution of dust and MRI, we perform three-dimensional, ohmic-resistive MHD simulations of a vertically stratified shearing box with an MRI-inactive "dead zone" of various sizes and with a net vertical magnetic flux of various strengths. We find that the vertical structure o…
We study dust transport in turbulent protoplanetary disks using three-dimensional global unstratified magnetohydrodynamic (MHD) simulations including Lagrangian dust particles. The turbulence is driven by the magnetorotational instability (MRI) with either ideal or non-ideal MHD that includes ambipolar diffusion (AD). In ideal MHD simulations, the surface density evolution (except for dust that drifts fastest), turbulent diffusion, and vertical scale height of dust can all be reproduced by simple one-dimensoinal and/or analytical models. However, in AD dominated simulations which simulate prot…
During the evolution of protoplanetary disks into planetary systems we expect to detect signatures that trace mechanisms such as planet-disk interaction. Protoplanetary disks display a large variety of structures in recently published high-spatial resolution images. However, the three-dimensional morphology of these disks is often difficult to infer from the two-dimensional projected images we observe. We spatially resolve the disk around HD 34282 using VLT/SPHERE in polarimetric imaging mode. We retrieve a profile for the height of the scattering surface to create a height-corrected deproject…
We have obtained new images of the protoplanetary disk orbiting TW Hya in visible, total intensity light with the Space Telescope Imaging Spectrograph (STIS) on the Hubble Space Telescope (HST), using the newly commissioned BAR5 occulter. These HST/STIS observations achieved an inner working angle $\sim$0.2\arcsec, or 11.7~AU, probing the system at angular radii coincident with recent images of the disk obtained by ALMA and in polarized intensity near-infrared light. By comparing our new STIS images to those taken with STIS in 2000 and with NICMOS in 1998, 2004, and 2005, we demonstrate that T…
Some circumstellar disks are observed to show prominent spiral arms in infrared scattered light or (sub-)millimeter dust continuum. The spirals might be formed from self-gravity, shadows, or planet-disk interactions. Recently, it was hypothesized that massive vortices can drive spiral arms in protoplanetary disks in a way analogous to planets. In this paper, we study the basic properties of vortex-driven spirals by the Rossby Wave Instability in 2D hydrodynamics simulations. We study how the surface density contrast, the number, and the shape of vortex-driven spirals depend on the properties o…
We present multi-epoch Hubble Space Telescope imaging of the Great Disk Shadow in the Serpens star-forming region. The near-infrared images show strong variability of the disk shadow, revealing dynamics of the inner disk on time scales of months. The Great Shadow is projected onto the Serpens reflection nebula by an unresolved protoplanetary disk surrounding the young intermediate-mass star SVS2/CK3/EC82. Since the shadow extends out to a distance of at least 17,000 au, corresponding to a light travel time of 0.24 years, the images may reveal detailed changes in the disk scale height and posit…
While planet formation is thought to occur early in the history of a protoplanetary disk, the presence of planets embedded in disks, or of other processes driving disk evolution, might be traced from their imprints on the disk structure. We observed the T Tauri star HD 143006, located in the 5-11 Myr-old Upper Sco region, in polarized scattered light with VLT/SPHERE at near-infrared wavelengths, reaching an angular resolution of ~0.037" (~6 au). We obtained two datasets, one with a 145 mas diameter coronagraph, and the other without, enabling us to probe the disk structure down to an angular s…
Sharp density features in protoplanetary discs, for instance at the edge of a magnetically dead zone, have recently been proposed as effective barriers to slow down or even stop the problematically fast migration of planetary cores into their central star. Density features on a radial scale approaching the disc vertical scale height might not exist, however, since they could be Rayleigh (or more generally Solberg-Hoiland) unstable. Stability must be checked explicitly in one-dimensional viscous accretion disc models because these instabilities are artificially eliminated in the process of redu…
(Abridged) We present local 2D and 3D hybrid numerical simulations of particles and gas in the midplane of protoplanetary disks (PPDs) using the Athena code. The particles are coupled to gas aerodynamically, with particle-to-gas feedback included. Magnetorotational turbulence is ignored as an approximation for the dead zone of PPDs, and we ignore particle self-gravity to study the precursor of planetesimal formation. Our simulations include a wide size distribution of particles, ranging from strongly coupled particles with dimensionless stopping time tau_s=Omega t_stop=1e-4 to marginally coupl…
Herbig stars can be classified into group I and group II depending on the shape of the far-IR excess from the spectral energy distribution. This separation may be evolutionary and related to the vertical structure of these disks. We aim to determine the emission height of Herbig disks and compare the resulting vertical extent of both groups. ALMA Band 6 observations of 12CO emission lines at sufficient velocity and spatial resolution of eight Herbig disks (four group I and four group II sources) are used to determine the emission heights from the channel maps via geometrical methods developed …
The collision dynamics of dusty bodies are crucial for planetesimal formation. Especially decimeter agglomerates are important in the different formation models. Therefore, in continuation of our experiments on mutual decimeter collisions, we investigate collisions of centimeter onto decimeter dust agglomerates in a small drop tower under vacuum conditions (p<5*$10^{-1}$ mbar) at a mean collision velocity of 6.68 +- 0.67m/s. We use quartz dust with irregularly shaped micrometer grains. Centimeter projectiles with different diameters, masses and heights are used, their typical volume filling fa…
Turbulent motions are believed to regulate angular momentum transport and influence dust evolution in protoplanetary disks. Measuring the strength of turbulence is challenging through gas line observations because of the requirement for high spatial and spectral resolution data, and an exquisite determination of the temperature. In this work, taking the well-known HD 163296 disk as an example, we investigated the contrast of gaps identified in high angular resolution continuum images as a probe for the level of turbulence. With self-consistent radiative transfer models, we simultaneously analy…
Observations of protoplanetary disks show that some characteristics seem recurrent, even in star formation regions that are physically distant such as surface mass density profiles varying as $r^{-1}$, or aspect ratios about 0.03 to 0.23. Accretion rates are also recurrently found around $10^{-8} - 10^{-6}~\mathrm{M_{\odot}~yr^{-1}}$ for disks already evolved (Isella et al., 2009, Andrews et al., 2009, 2010). Several models have been developed in order to recover these properties. However, most of them usually simplify the disk geometry if not its mid-plane temperature. This has major conseque…
Azimuthally asymmetric structures have been discovered in millimeter continuum emission from many protoplanetary disks. One hypothesis is that they are vortices produced by the Rossby wave instability, for example at edges of planet-opened gaps or deadzones. Confirming the vortex nature of these structures will have profound implications to planet formation. One way to test the hypothesis is to compare the observed morphology of vortex candidates in near-infrared scattered light with theoretical expectations. To this end, we synthesize the appearance of vortices in H-band polarized light by co…
Gravitational instability (GI) controls the dynamics of young massive protoplanetary discs. Apart from facilitating gas accretion on to the central protostar, it must also impact on the process of planet formation: directly through fragmentation, and indirectly through the turbulent concentration of small solids. To understand the latter process, it is essential to determine the dust dynamics in such a turbulent flow. For that purpose, we conduct a series of 3D shearing box simulations of coupled gas and dust, including the gas's self-gravity and scanning a range of Stokes numbers, from 0.001 …
The model of a protoplanetary disk of a star with a low-mass companion ($M_2:M_1 \le 0.1$), moving on a circular orbit, which slightly inclined to the disk plane ($\le 10^{\circ}$), is considered. The SPH-method is used to calculate gas-dynamic ows. The motion of the companion on the orbit leads to the inhomogeneous distribution of the matter in the disk: there are a cleared gap, density waves and streams of matter. Because of the disturbances the inner part of the disk is tilted to its periphery and also do not coincides with the orbit plane of the companion. It leads to anisotropic illuminat…
