Rotating Accretion Disk Research Articles

A Rotating Accretion Disk around MWC 297, a Young B1.5Ve Star

High-resolution spectra with iSHELL on IRTF in the K and M bands of the young, heavily accreting B1.5Ve star MWC 297 show numerous double-peaked CO lines. These CO lines originate in an inclined gaseous disk in Keplerian rotation. MWC 297 is the only early B star known to show a Keplerian disk in CO. Analysis of the spectra shows that 12CO 1–0 is optically thick for the low excitation lines. Even the 13CO 1–0 and 12CO 2–1 have somewhat optically thick lines at low J levels. We find that the CO emission in the disk can be fitted with CO being in a narrow ring at a radius of 12 au, with a temperature of 1500 K and a CO column density of 1.6 × 1018 cm−2. This model underestimates the line strength of high-J lines, indicating that they are excited by fluorescence. The CO overtone lines have a similar temperature. The 13CO lines are much brighter than expected from interstellar isotope ratios. The 13CO lines are wider than the 12CO ones, suggesting different excitation conditions. The same is true for 12CO 2–1. We see strong absorption in 12CO and 13CO 1–0 at low J levels, which is due to two cold foreground clouds. These clouds, one with a temperature of 8.3 K and a column density of 6.7 1017 cm−2 and the other one colder and with lower column density, can fully account for the observed extinction toward MWC 297.

Mid-infrared and Maser Flux Variability Correlation in Massive Young Stellar Object G036.70+00.09

We present the discovery of the simultaneous flux variation of a massive young stellar object (MYSO) G036.70+00.09 (G036.70) both in the maser emission and mid-infrared (MIR; λ = 3–5 μm) bands. Using the ALLWISE and NEOWISE archival databases that cover a long time span of approximately 10 yr with a cadence of 6 months, we confirm that G036.70 indicates a stochastic year-long MIR variability with no signs of a WISE band color change of W1 (3.4 μm) −W2 (4.6 μm). Cross-matching the MIR data set with the high-cadence 6.7 GHz class II methanol maser flux using the Hitachi 32 m radio telescope that discovered its periodicity in the methanol maser of 53.0–53.2 days, we also determine the flux correlations between the two bands at two different timescales, year-long and day-long, both of which have never been reported in MYSOs, except when they are in the accretion burst phase. The results of our study support the scenario that a class II methanol maser is pumped up by infrared emission from accreting disks of MYSOs. We also discuss the possible origins of MIR and maser variability. To explain the two observed phenomena, a stochastic year-long MIR variability with no signs of significant color change and maser-MIR variability correlation or a change in mass accretion rate and line-of-sight extinction because of the nonaxisymmetric dust density distribution in a rotating accretion disk are possible origins. Observations through spectroscopic monitoring of accretion-related emission lines are essential for determining the origin of the observed variability in G036.70.

New explanation of opposite position angles in red and blue wings of spectral lines

ABSTRACTWe consider the emission of resonance line radiation from rotating circular accretion disc with the progressive increasing height (the inclined ring). Our theory can also be applied to the rotating spot-like sources of resonance radiation. We assume that the atmosphere of inclined ring is homogeneous. In this case, the every part of ring emits the radiation with the wave electric field oscillations perpendicular to plane $(\boldsymbol{nN^{\prime }})$, where ${\boldsymbol{n}}$ is the direction to a telescope and $\boldsymbol{N^{\prime }}$ is the normal to considered local surface of a ring. Geometrical consideration shows that the radiation polarization angle χ (frequently denoted as position angle or PA) depends on the inclination angle α of the ring relative to the central plane of accretion disc, the inclination angle θ of the central plane of accretion disc with the normal $\boldsymbol{N}$, and on azimuthal angle φ of radiating part on the ring. The right and left parts of a ring according to the symmetry plane $(\boldsymbol{nN})$ give rise to opposite polarization angles. For rotating accretion disc, due to Doppler’s effect, this means that polarization angles have opposite signs in the red and blue wings of emerging spectral line radiation. Such behaviour is observed in many objects.

Intensity and Polarization of Radiation Emerging from Rotating Accretion Disc with Increasing Height

We consider the radiation emission in continuum and spectral lines from rotating accretion disc with the progressive increasing height. It is known that for the plane accretion disc with homogeneous atmosphere the wave electric field E is perpendicular to the plane between line of sight n and the normal to the disc N. For the expanding accretion disc the wave electric field from every inclined cone-like part with given azimuthal angle φ has direction perpendicular to the plane between n and local normal N′ to the inclined surface. This behaviour is the consequence of homogeneity of inclined atmosphere and has purely geometrical origin. The geometrical consideration shows that the position angles of polarized radiation in the right and left parts relative to plane (nN) of the inclined accretion disc have opposite values. Therefore, for inclined accretion disc the integral continuum radiation has the usual polarization angle perpendicular to the plane (nN), but smaller degree of polarization and less alongated along the normal N than that for the plane accretion disc. For spectral line, due to the Doppler effect, the polarization (position) angles have opposite signs for the red and blue wings. Such behaviour is frequently observed in Hα-radiation.

Striped Blandford/Znajek jets from advection of small-scale magnetic field

ABSTRACT Black hole – accretion disc systems are the central engines of relativistic jets from stellar to galactic scales. We numerically quantify the unsteady outgoing Poynting flux through the horizon of a rapidly spinning black hole endowed with a rotating accretion disc. The disc supports small-scale, concentric, flux tubes with zero net magnetic flux. Our general relativistic force-free electrodynamics simulations follow the accretion on to the black hole over several hundred dynamical time-scales in 3D. For the case of counter-rotating accretion discs, the average process efficiency reaches up to 〈ϵ〉 ≈ 0.43, compared to a stationary energy extraction by the Blandford/Znajek process. The process efficiency depends on the cross-sectional area of the loops, i.e. on the product l × h, where l is the radial loop thickness and h its vertical scale height. We identify a strong correlation between efficient electromagnetic energy extraction and the quasi-stationary setting of ideal conditions for the operation of the Blandford/Znajek process (e.g. optimal field line angular velocity and fulfillment of the so-called Znajek condition). Remarkably, the energy extraction operates intermittently (alternating episodes of high and low efficiency) without imposing any large-scale magnetic field embedding the central object. Scaling our results to supermassive black holes, we estimate that the typical variability time-scale of the system is of the order of days to months. Such time-scales may account for the longest variability scales of TeV emission observed, e.g. in M87.

The HH 212 Interstellar Laboratory: Astrochemistry as a Tool To Reveal Protostellar Disks on Solar System Scales around a Rising Sun

The investigation of star-forming regions has enormously benefited from the recent advent of the ALMA interferometer working in the millimeter- and submillimeter-wavelength spectral windows. More specifically, the unprecedented combination of high-sensitivity and high-angular resolution provided by ALMA allows one to shed light on the jet/disk systems associated with a Sun-like mass protostar. In this context, astrochemistry also possesses the possibility to analyze complex spectra obtained using large bandwidths: several interstellar complex organic molecules (iCOMs; C-bearing species with at least six atoms) have been detected and imaged around protostars, often thanks to a large number of rotational–vibrational lines. This in turn boosted the study of the astrochemistry at work during the earliest phases of star formation paving the way to the chemical complexity in planetary systems where Life could emerge. There is mounting evidence that the observations of iCOMs (e.g., CH3CHO or NH2CHO) can be used as unique tools to shed light on Solar System scales (<50 au) on the molecular content of protostellar disk. The increase of iCOMs abundance occur only under very selective physical conditions, such as those associated low-velocity shocks found where the infalling envelope is impacting the rotating accretion disk. The imaging of these regions with simpler molecules such as CO or CS is indeed paradoxically hampered by their high abundances and consequently high line opacities which do not allow the observers to disentangle all the emitting components at these small scales. In this respect, we review the state-of-the art of the ALMA analysis about the standard Sun-like star forming region in Orion named HH 212, associated with a pristine jet-disk protostellar system. We enrich the discussion with unpublished ALMA data sets, showing (i) how all of the physical components involved in the formation of a Sun-like star can be revealed only by observing different molecular tracers, and (ii) how the observation of iCOMs emission, observed to infer the chemical composition of star-forming regions, can be used also as a unique tracer to image protostellar disks on Solar System scales, that is, where planets will eventually form.

Resonance line in rotating accretion disc

We study the resonance line emission from the rotating plane optically thick accretion disc, consisting of free electrons and resonant atoms. We use the standard assumption that the source of continuum radiation is located near central plane of the accretion disc, where the temperature is the highest. This corresponds to the Milne problem consideration for continuum. We shortly discuss the impossibility of the Milne problem for the resonance radiation. We assume that the resonant atoms are located in a thin layer of an accretion disc near the surface. In this case the resonance line emission arises due to scattering of a continuum on the resonant atoms. In thin layer we can neglect the multiple scattering of the resonance radiation on the resonant atoms. We consider the axially symmetric problems, where the Stokes parameter U =0. We take into account the Doppler effect for the frequencies of the resonance line. The three types of the resonant atom sources are considered (see Figs.1-3). The first source is the axially symmetric continuous distribution of the resonant atoms along the circular orbit. The second spot-like source rotates in the orbit. The third type presents two spot-like sources located in the orbit contrary one to another. In the first and third cases the shape of the emitting resonance line is symmetric, i.e. the right and left wings have the similar shapes. In the second case the resonance line has asymmetric shape. The shape of the emerging line depends significantly on the ratio of the rotation velocity value to the velocity, characterizing the Doppler width. It also depends on the ratio of the electron number density to the number density of resonant atoms. The results of the calculations characterize the different observational effects of H$\alpha$ radiation in the accretion discs and can be used for estimations of the parameters mentioned above.

Rotating accretion flows in D dimensions: Sonic points, critical points, and photon spheres

We give the formulation and the general analysis of the rotational accretion problem on $D$-dimensional spherical spacetime and investigate sonic points and critical points. First, we construct the simple two-dimensional rotating accretion flow model in general $D$-dimensional static spherically symmetric spacetime and formulate the problem. The flow forms a two-dimensional disk lying on the equatorial plane and the disk is assumed to be geometrically thin and has uniform distribution in the polar angle directions. Analyzing the critical point of the problem, we give the conditions for the critical point and its classification explicitly and show the coincidence with the sonic point for generic equation of state (EOS). Next, adopting the EOS of ideal photon gas to the analysis, we reveal that there always exists a correspondence between the sonic points and the photon spheres of the spacetime. Our main result is that the sonic point of the rotating accretion flow of ideal photon gas must be on (one of) the unstable photon sphere(s) of the spacetime in arbitrary spacetime dimensions. This paper extends this correspondence for spherical flows shown in the authors' previous work to rotating accretion disks.

The reverberation signatures of rotating disc winds in active galactic nuclei

The broad emission lines (BELs) in active galactic nuclei (AGN) respond to ionizing continuum variations. The time and velocity dependence of their response depends on the structure of the broad-line region: its geometry, kinematics and ionization state. Here, we predict the reverberation signatures of BELs formed in rotating accretion disc winds. We use a Monte Carlo radiative transfer and ionization code to predict velocity-delay maps for representative high- (C$~IV$) and low-ionization (H$\alpha$) emission lines in both high- and moderate-luminosity AGN. Self-shielding, multiple scattering and the ionization structure of the outflows are all self-consistently taken into account, while small-scale structure in the outflow is modelled in the micro-clumping approximation. Our main findings are: (1) The velocity-delay maps of smooth/micro-clumped outflows often contain significant negative responses. (2)~The reverberation signatures of disc wind models tend to be rotation dominated and can even resemble the classic "red-leads-blue" inflow signature. (3) Traditional "blue-leads-red" outflow signatures can usually only be observed in the long-delay limit. (4) Our models predict lag-luminosity relationships similar to those inferred from observations, but systematically underpredict the observed centroid delays. (5) The ratio between "virial product" and black hole mass predicted by our models depends on viewing angle. Our results imply that considerable care needs to be taken in interpreting data obtained by observational reverberation mapping campaigns. In particular, basic signatures such as "red-leads-blue", "blue-leads-red" and "blue and red vary jointly" are not always reliable indicators of inflow, outflow or rotation. This may help to explain the perplexing diversity of such signatures seen in observational campaigns to date.

OPTICAL AND NEAR-INFRARED SPECTROSCOPY OF THE BLACK HOLE SWIFT J1753.5–0127

We report on a multiwavelength observational campaign of the black hole X-ray binary Swift J1753.5-0127 that consists of an ESO/X-shooter spectrum supported by contemporaneous Swift/XRT+UVOT and ATCA data. ISM absorption lines in the X-shooter spectrum allows us to determine E(B-V)=0.45+/-0.02 along the line-of-sight to the source. We also report detection of emission signatures of He II at 4686 angstrom, H alpha, and, for the first time, H I at 10906 angstrom and Paschen Beta. The double-peaked morphology of these four lines is typical of the chromosphere of a rotating accretion disk. Nonetheless, the paucity of disk features points towards a low level of irradiation in the system. This is confirmed through spectral energy distribution modeling and we find that the UVOT+X-shooter continuum mostly stems from the thermal emission of a viscous disk. We speculate that the absence of reprocessing is due to the compactness of an illumination-induced envelope that fails to reflect enough incoming hard X-ray photons back to the outer regions. The disk also marginally contributes to the Compton-dominated X-ray emission and is strongly truncated, with an inner radius about a thousand times larger than the black hole's gravitational radius. A near-infrared excess is present, and we associate it with synchrotron radiation from a compact jet. However, the measured X-ray flux is significantly higher than what can be explained by the optically thin synchrotron jet component. We discuss these findings in the framework of the radio quiet versus X-ray bright hypothesis, favoring the presence of a residual disk, predicted by evaporation models, that contributes to the X-ray emission without enhancing the radio flux.

The effect of gaseous accretion disk on dynamics of the stellar cluster in AGN

AbstractThere is a supermassive black hole, a gaseous accretion disk and compact star cluster in the center of active galactic nuclei, as known today. So the activity of AGN can be represented as the result of interaction of these three subsystems. In this work we investigate the dynamical interaction of a central star cluster surrounding a supermassive black hole and a central accretion disk. The dissipative force acting on stars in the disk leads to an asymmetry in the phase space distribution of the central star cluster due to the rotating accretion disk. In our work we present some results of Stardisk model, where we see some changes in density and phase space of central star cluster due to influence of rotating gaseous accretion disk.

Inconsistency in the standard model for stellar thin accretion disks

We analyze the configuration of a thin rotating accretion disk, which is embedded in a magnetic field inducing a backreaction in the gravitating plasma. The aim of this study is to determine the conditions under which the gaseous accretion model of Shakura can be reconciled with the magneto-hydrodynamical picture requested to trigger the underlying turbulent behavior. We focus our attention to the generalized Ohm equation in order to understand if the plasma backreaction is able to provide the proper toroidal current, allowing a non-zero infalling velocity. In the limit of linear plasma backreaction, this analysis shows how the Shakura profile of accretion turns out to be inconsistent. In particular, comparing the azimuthal and the generalized Ohm equilibrium equations, we argue that it is not possible to maintain a constant rate of accretion. A non-stationary scenario for the disk configuration is then outlined and it results into a transient process which is however associated to a vanishing accretion rate.

X-ray variations in the inner accretion flow of dwarf novae

We show for five DN systems, SS Cyg, VW Hyi, RU Peg, WW Cet and T Leo that the UV and X-ray power spectra of their time variable light curves are similar in quiescence. All of them show a break in their power spectra, which in the framework of the model of propagating fluctuations indicates inner disk truncation. We derive the inner disk radii for these systems in a range (10-3)$\times10^{9}$ cm. We analyze the RXTE data of SS Cyg in outburst and compare it with the power spectra, obtained during the period of quiescence. We show that during the outburst the disk moves towards the white dwarf and recedes as the outburst declines. We calculate the correlation between the simultaneous UV and X-ray light curves of the five DN studied in this work, using the XMM-Newton data obtained in the quiescence and find X-ray time lags of 96-181 sec. This can be explained by the travel time of matter from a truncated inner disk to the white dwarf surface. We suggest that, in general, DN may have truncated accretion disks in quiescence which can also explain the UV and X-ray delays in the outburst stage and that the accretion may occur through coronal flows in the disk (e.g., rotating accretion disk coronae). Within a framework of the model of propagating fluctuations the comparison of the X-ray/UV time lags observed by us in the case of DN systems with those, detected for a magnetic Intermediate Polar allows us to make a rough estimate of the viscosity parameter $\alpha\sim0.25$ in the innermost parts of the accretion flow of DN systems.

ENHANCED ACCRETION RATES OF STARS ON SUPERMASSIVE BLACK HOLES BY STAR-DISK INTERACTIONS IN GALACTIC NUCLEI

We investigate the dynamical interaction of a central star cluster surrounding a super-massive black hole and a central accretion disk. The dissipative force acting on stars in the disk leads to an enhanced mass flow towards the super-massive black hole and to an asymmetry in the phase space distribution due to the rotating accretion disk. The accretion disk is considered as a stationary Keplerian rotating disk, which is vertically extended in order to employ a fully self-consistent treatment of stellar dynamics including the dissipative force originating from star-gas ram pressure effects. The stellar system is treated with a direct high-accuracy N-body integration code. A star-by-star representation, desirable in N-body simulations, cannot be extended to real particle numbers yet. Hence, we carefully discuss the scaling behavior of our model with regard to particle number and tidal accretion radius. The main idea is to find a family of models for which the ratio of two-body relaxation time and dissipation time (for kinetic energy of stellar orbits) is constant, which then allows us to extrapolate our results to real parameters of galactic nuclei. Our model is derived from basic physical principles and as such it provides insight into the role of physical processes in galactic nuclei, but it should be regarded as a first step towards more realistic and more comprehensive simulations. Nevertheless, the following conclusions appear to be robust: the star accretion rate onto the accretion disk and subsequently onto the super-massive black hole is enhanced by a significant factor compared to purely stellar dynamical systems neglecting the disk. This process leads to enhanced fueling of central disks in active galactic nuclei and to an enhanced rate of tidal stellar disruptions. [Abridged]

Wave modes from the magnetorotational instability in accretion discs

AbstractThe magnetorotational instability (MRI) is widely believed to be the source of turbulence in accretion discs. This turbulence is responsible for the anomalous angular momentum transport in accretion discs. The turbulence will affect other aspects of the dynamics of the disc as well, and we will concentrate on two such issues: a) what kind of oscillations can be excited by the turbulence itself, and b) how the turbulence is interacting with modes that have been excited by some other agent. This is of interest in understanding the quasi-periodic oscillations (QPOs) that have been observed in the X-ray light curves of accreting neutron star and black hole binaries. We carry out local three dimensional (3D) magnetohydrodynamic simulations of a keplerian differentially rotating accretion disc, using a shearing box configuration taking in account the effects of the vertical stratification.

SHEAR-DRIVEN INSTABILITIES IN HALL-MAGNETOHYDRODYNAMIC PLASMAS

The large-scale dynamics of plasmas is well described within the framework of magnetohydrodynamics (MHD). However, whenever the ion density of the plasma becomes sufficiently low, the Hall effect is likely to become important. The role of the Hall effect has been studied in several astrophysical plasma processes, such as magnetic reconnection, magnetic dynamo, MHD turbulence or MHD instabilities. In particular, the development of small-scale instabilities is essential to understand the transport properties in a number of astrophysical plasmas. The magneto-rotational instability, which takes place in differentially rotating accretion disks embedded in relatively weak magnetic fields, is just one example. The influence of the large-scale velocity flows on small-scale instabilities is often approximated by a linear shear flow. In this paper we quantitatively study the role of the Hall effect on plasmas embedded in large-scale shear flows. More precisely, we show that a new instability develops as long as the Hall effect is present, which we therefore term as the Hall magneto-shear instability. As a particular case, we recover the so-called magneto-rotational instability and quantitatively assess the role of the Hall effect on its development and evolution.

A DETAILED STUDY OF THE ACCRETION DISK SURROUNDING THE HIGH-MASS PROTOSTAR NGC 7538 S

We present deep high angular resolution observations of the high-mass protostar NGC 7538S, which is in the center of a cold dense cloud core with a radius of 0.5 pc and a mass of ~2,000 Msun. These observations show that NGC 7538S is embedded in a compact elliptical core with a mass of 85 - 115 Msun. The star is surrounded by a rotating accretion disk, which powers a very young, hot molecular outflow approximately perpendicular to the rotating accretion disk. The accretion rate is very high, ~ 1.4 - 2.8 10^-3 Msun yr^-1. Evidence for rotation of the disk surrounding the star is seen in all largely optically thin molecular tracers, H13CN J = 1-0, HN13C J = 1-0, H13CO+ J = 1-0, and DCN J = 3-2. Many molecules appear to be affected by the hot molecular outflow, including DCN and H13CO+. The emission from CH3CN, which has often been used to trace disk rotation in young high-mass stars, is dominated by the outflow, especially at higher K-levels. Our new high-angular resolution observations show that the rotationally supported part of the disk is smaller than we previously estimated. The enclosed mass of the inner, rotationally supported part of the disk (D ~ 5", i.e 14,000 AU) is ~ 14 - 24 Msun.

THE EVOLUTION OF QUASAR C IV AND Si IV BROAD ABSORPTION LINES OVER MULTI-YEAR TIMESCALES

We investigate the variability of CIV 1549A broad absorption line (BAL) troughs over rest-frame time scales of up to ~7 yr in 14 quasars at redshifts z>2.1. For 9 sources at sufficiently high redshift, we also compare CIV and SiIV 1400A absorption variation. We compare shorter- and longer-term variability using spectra from up to four different epochs per source and find complex patterns of variation in the sample overall. The scatter in the change of absorption equivalent width (EW), Delta EW, increases with the time between observations. BALs do not, in general, strengthen or weaken monotonically, and variation observed over shorter (<months) time scales is not predictive of multi-year variation. We find no evidence for asymmetry in the distribution of Delta EW that would indicate that BALs form and decay on different time scales, and we constrain the typical BAL lifetime to be >~30 yr. The BAL absorption for one source, LBQS 0022+0150, has weakened and may now be classified as a mini-BAL. Another source, 1235+1453, shows evidence of variable, blue continuum emission that is relatively unabsorbed by the BAL outflow. CIV and SiIV BAL shape changes are related in at least some sources. Given their high velocities, BAL outflows apparently traverse large spatial regions and may interact with parsec-scale structures such as an obscuring torus. Assuming BAL outflows are launched from a rotating accretion disk, notable azimuthal symmetry is required in the outflow to explain the relatively small changes observed in velocity structure over times up to 7 yr.

Modelling the orientation of accretion discs in quasars using Hα emission

Infrared spectroscopy of the H-alpha emission lines of a sub-sample of 19 high-redshift (0.8 < z < 2.3) Molonglo quasars, selected at 408 MHz, is presented. These emission lines are fitted with composite models of broad and narrow emission, which include combinations of classical broad-line regions of fast-moving gas clouds lying outside the quasar nucleus, and/or a theoretical model of emission from an optically-thick, flattened, rotating accretion disk. All bar one of the nineteen sources are found to have emission consistent with the presence of an optically-emitting accretion disk, with the exception appearing to display complex emission including at least three broad components. Ten of the quasars have strong Bayesian evidence for broad-line emission arising from an accretion disk together with a standard broad-line region, selected in preference to a model with two simple broad lines. Thus the best explanation for the complexity required to fit the broad H-alpha lines in this sample is optical emission from an accretion disk in addition to a region of fast-moving clouds. We derive estimates of the angle between the rotation axis of the accretion disk and the line of sight. A weak correlation is found between the accretion disk angle and the logarithm of the low-frequency radio luminosity. This is direct, albeit tenuous, evidence for the receding torus model. Velocity shifts of the broad H-alpha components are analysed and the results found to be consistent with a two-component model comprising one single-peaked broad line emitted at the same redshift as the narrow lines, and emission from an accretion disk which appears to be preferentially redshifted with respect to the narrow lines for high-redshift sources and blueshifted relative to the narrow lines for low-redshift sources.

JD7 -Astrophysical Outflows and Associated Accretion Phenomena

Highly collimated supersonic jets and outflows are very frequent in several astrophysical environments. They are seen in young stellar objects (YSOs), proto-planetary nebulae, compact objects (like galactic black holes or microquasars, and X-ray binary stars), active galactic nuclei, and are also possibly associated to gamma-ray bursts (GRBs) and to ultra-high energy cosmic rays sources (UHECRs). Despite their different physical scales, all these outflow classes have strong morphological similarities, but questions such as - what physics do they share? - or - can we find a universal mechanism of acceleration and collimation that operates in all classes? - remain matters of debate. The most accepted mechanism for their origin relies on a rotating accretion disk threaded by perpendicular large-scale magnetic fields and, though most of the systems producing jets contain an accretion disk around the central source, the real role that rotation and magnetic fields play in these processes is still not fully understood, nor are the highly non-linear physical processes connected to these jet-disk systems in the large parameter space involved.