MID-infrared Interferometric Instrument Research Articles

Spatially resolving the chemical composition of the planet building blocks

ABSTRACT The inner regions of protoplanetary discs (from ∼0.1 to 10 au) are the expected birthplace of planets, especially telluric. In those high-temperature regions, solids can experience cyclical annealing, vapourisation, and recondensation. Hot and warm dusty grains emit mostly in the infrared domain, notably in N-band (8–13 μm). Studying their fine chemistry through mid-infrared spectro-interferometry with the new Very Large Telescope Interferometer (VLTI) instrument Multi AperTure mid-Infrared SpectroScopic Experiment (MATISSE), which can spatially resolve these regions, requires detailed dust chemistry models. Using radiative transfer, we derived infrared spectra of a fiducial static protoplanetary disc model with different inner-disc (<1 au) dust compositions. The latter were derived from condensation sequences computed at local thermodynamic equilibrium (LTE) for three initial C/O ratios: subsolar (C/O = 0.4), solar (C/O = 0.54), and supersolar (C/O = 1). The three scenarios return very different N-band spectra, especially when considering the presence of sub-micron-sized dust grains. MATISSE should be able to detect these differences and trace the associated sub-au-scale radial changes. We propose a first interpretation of N-band ‘inner-disc’ spectra obtained with the former VLTI instrument MID-infrared Interferometric instrument (MIDI) on three Herbig stars (HD 142527, HD 144432, HD 163296) and one T Tauri star (AS 209). Notably, we could associate a supersolar (‘carbon-rich’) composition for HD 142527 and a subsolar (‘oxygen-rich’) one for HD 1444432. We show that the inner-disc mineralogy can be very specific and not related to the dust composition derived from spatially unresolved mid-infrared spectroscopy. We highlight the need for including more complex chemistry when interpreting solid-state spectroscopic observations of the inner regions of discs, and for considering dynamical aspects for future studies.

New evidence for the ubiquity of prominent polar dust emission in AGN on tens of parsec scales

ABSTRACT The key ingredient of active galactic nuclei (AGN) unification, the dusty obscuring torus was so far held responsible for the observed mid-infrared (MIR) emission of AGN. However, the best studied objects with Very Large Telescope Interferometer (VLTI)/MID-infrared Interferometric instrument (MIDI) show that instead a polar dusty wind is dominating these wavelengths, leaving little room for a torus contribution. But is this wind a ubiquitous part of the AGN? To test this, we conducted a straightforward detection experiment, using the upgraded Very Large Telescope (VLT)/VLT Imager and Spectrometer for mid-InfraRed (VISIR) for deep subarcsecond resolution MIR imaging of a sample of nine [O iv]-bright, obscured AGN, all of which were predicted to have detectable polar emission. Indeed, the new data reveal such emission in all objects but one. We further estimate lower limits on the extent of the polar dust and show that the polar dust emission is dominating the total MIR emission of the AGN. These findings support the scenario that polar dust is not only ubiquitous in AGN but also an integral part of its structure, processing a significant part of the primary radiation. The polar dust has to be optically thin on average, which explains e.g. the small dispersion in the observed MIR–X-ray luminosity correlation. At the same time, it has to be taken into account when deriving covering factors of obscuring material from MIR to bolometric luminosity ratios. Finally, we find a new tentative trend of increasing MIR emission size with increasing Eddington ratio.

New Evidence for the Dusty Wind Model: Polar Dust and a Hot Core in the Type-1 Seyfert ESO 323-G77*

Abstract Infrared interferometry of Seyfert galaxies has revealed that their warm (300–400 K) dust emission originates primarily from polar regions instead of from an equatorial dust torus as predicted by the classic AGN unification scheme. We present new data for the type 1.2 object ESO 323-G77 obtained with the MID-infrared interferometric Instrument and a new detailed morphological study of its warm dust. The partially resolved emission on scales between 5 and 50 mas (1.6–16 pc) is decomposed into a resolved and an unresolved source. Approximately 65% of the correlated flux between 8 and 13 μm is unresolved at all available baseline lengths. The remaining 35% is partially resolved and shows angular structure. From geometric modeling, we find that the emission is elongated along a position angle of 155° ± 14° with an axis ratio (major/minor) of 2.9 ± 0.3. Because the system axis is oriented in the position angle 174° ± 2°, we conclude that the dust emission of this object is also polar extended. A CAT3D-WIND radiative transfer model of a dusty disk and a dusty wind with a half opening angle of 30° can reproduce both the interferometric data and the SED, while a classical torus model is unable to fit the interferometric data. We interpret this as further evidence that a polar dust component is required even for low-inclination type 1 sources.

The VLTI/MIDI view on the inner mass loss of evolved stars from theHerschelMESS sample

The mass-loss process from evolved stars is a key ingredient for our understanding of many fields of astrophysics, including stellar evolution and the chemical enrichment of the interstellar medium via stellar yields. One the main unsolved questions is the geometry of the mass-loss process. Taking advantage of the results from the Herschel Mass loss of Evolved StarS (MESS) programme, we initiated a coordinated effort to characterise the geometry of mass loss from evolved red giants at various spatial scales. For this purpose we used the MID-infrared interferometric Instrument (MIDI) to resolve the inner envelope of 14 asymptotic giant branch stars (AGBs) in the MESS sample. In this contribution we present an overview of the interferometric data collected within the frame of our Large Programme, and we also add archive data for completeness. We studied the geometry of the inner atmosphere by comparing the observations with predictions from different geometric models. Asymmetries are detected for five O-rich and S-type, suggesting that asymmetries in the N band are more common among stars with such chemistry. We speculate that this fact is related to the characteristics of the dust grains. Except for one star, no interferometric variability is detected, i.e. the changes in size of the shells of non-mira stars correspond to changes of the visibility of less than 10%. The observed spectral variability confirms previous findings from the literature. The detection of dust in our sample follows the location of the AGBs in the IRAS colour-colour diagram: more dust is detected around oxygen-rich stars in region II and in the carbon stars in region VII. The SiC dust feature does not appear in the visibility spectrum of UAnt and SSct, which are two carbon stars with detached shells. This finding has implications for the theory of SiC dust formation.

DR Tauri: Temporal variability of the brightness distribution in the potential planet-forming region

We investigate the variability of the brightness distribution and the changing density structure of the protoplanetary disk around DR Tau, a classical T Tauri star. DR Tau is known for its peculiar variations from the ultraviolet (UV) to the mid-infrared (MIR). Our goal is to constrain the temporal variation of the disk structure based on photometric and MIR interferometric data. We observed DR Tau with the MID-infrared Interferometric instrument (MIDI) at the Very Large Telescope Interferometer (VLTI) at three epochs separated by about nine years, two months, respectively. We fit the spectral energy distribution and the MIR visibilities with radiative transfer simulations. We are able to reproduce the spectral energy distribution as well as the MIR visibility for one of the three epochs (third epoch) with a basic disk model. We were able to reproduce the very different visibility curve obtained nine years earlier with a very similar baseline (first epoch), using the same disk model with a smaller scale height. The same density distribution also reproduces the observation made with a higher spatial resolution in the second epoch, i.e. only two months before the third epoch.

Mid-infrared interferometry withKband fringe-tracking

Context: A turbulent atmosphere causes atmospheric piston variations leading to rapid changes in the optical path difference of an interferometer, which causes correlated flux losses. This leads to decreased sensitivity and accuracy in the correlated flux measurement. Aims: To stabilize the N band interferometric signal in MIDI (MID-infrared Interferometric instrument), we use an external fringe tracker working in K band, the so-called FSU-A (fringe sensor unit) of the PRIMA (Phase-Referenced Imaging and Micro-arcsecond Astrometry) facility at VLTI. We present measurements obtained using the newly commissioned and publicly offered MIDI+FSU-A mode. A first characterization of the fringe-tracking performance and resulting gains in the N band are presented. In addition, we demonstrate the possibility of using the FSU-A to measure visibilities in the K band. Methods: We analyzed FSU-A fringe track data of 43 individual observations covering different baselines and object K band magnitudes with respect to the fringe-tracking performance. The N band group delay and phase delay values could be predicted by computing the relative change in the differential water vapor column density from FSU-A data. Visibility measurements in the K band were carried out using a scanning mode of the FSU-A. Results: Using the FSU-A K band group delay and phase delay measurements, we were able to predict the corresponding N band values with high accuracy with residuals of less than 1 micrometer. This allows the coherent integration of the MIDI fringes of faint or resolved N band targets, respectively. With that method we could decrease the detection limit of correlated fluxes of MIDI down to 0.5 Jy (vs. 5 Jy without FSU-A) and 0.05 Jy (vs. 0.2 Jy without FSU-A) using the ATs and UTs, respectively. The K band visibilities could be measured with a precision down to ~2%.

Evidence of a metal-rich surface for the Asteroid (16) Psyche from interferometric observations in the thermal infrared

We describe the first determination of thermal properties and size of the M-type Asteroid (16) Psyche from interferometric observations obtained with the Mid-Infrared Interferometric Instrument (MIDI) of the Very Large Telescope Interferometer. We used a thermophysical model to interpret our interferometric data. Our analysis shows that Psyche has a low macroscopic surface roughness. Using a convex 3-D shape model obtained by Kaasalainen et al. (Kaasalainen, M., Torppa, J., Piironen, J. [2002]. Icarus 159, 369–395), we derived a volume-equivalent diameter for (16) Psyche of 247±25km or 238±24km, depending on the possible values of surface roughness. Our corresponding thermal inertia estimates are 133 or 114Jm−2s−0.5K−1, with a total uncertainty estimated at 40Jm−2s−0.5K−1. They are among the highest thermal inertia values ever measured for an asteroid of this size. We consider this as a new evidence of a metal-rich surface for the Asteroid (16) Psyche.

Catching the fish – Constraining stellar parameters for TX Piscium using spectro-interferometric observations

Stellar parameter determination is a challenging task when dealing with galactic giant stars. The combination of different investigation techniques has proven to be a promising approach. We analyse archive spectra obtained with the Short-Wavelength-Spectrometer (SWS) onboard of ISO, and new interferometric observations from the Very Large Telescope MID-infrared Interferometric instrument (VLTI/MIDI) of a very well studied carbon-rich giant: TX Psc. The aim of this work is to determine stellar parameters using spectroscopy and interferometry. The observations are used to constrain the model atmosphere, and eventually the stellar evolutionary model in the region where the tracks map the beginning of the carbon star sequence. Two different approaches are used to determine stellar parameters: (i) the 'classic' interferometric approach where the effective temperature is fixed by using the angular diameter in the N-band (from interferometry) and the apparent bolometric magnitude; (ii) parameters are obtained by fitting a grid of state-of-the-art hydrostatic models to spectroscopic and interferometric observations. We find a good agreement between the parameters of the two methods. The effective temperature and luminosity clearly place TX Psc in the carbon-rich AGB star domain in the H-R-diagram. Current evolutionary tracks suggest that TX Psc became a C-star just recently, which means that the star is still in a 'quiet' phase compared to the subsequent strong-wind regime. This is in agreement with the C/O ratio being only slightly larger than 1.

The geometry of the close environment of SV Piscium as probed by VLTI/MIDI

Context. SV Psc is an asymptotic giant branch (AGB) star surrounded by an oxygen-rich dust envelope. The mm-CO line profile of the object's outflow shows a clear double-component structure. Because of the high angular resolution, mid-IR interferometry may give strong constraints on the origin of this composite profile. Aims. The aim of this work is to investigate the morphology of the environment around SV Psc using high-angular resolution interferometry observations in the mid-IR with the Very Large Telescope MID-infrared Interferometric instrument (VLTI/MIDI). Methods. Interferometric data in the N-band taken at different baseline lengths (ranging from 32-64 m) and position angles (73- 142{\deg}) allow a study of the morphology of the circumstellar environment close to the star. The data are interpreted on the basis of 2-dimensional, chromatic geometrical models using the fitting software tool GEM-FIND developed for this purpose. Results. The results favor two scenarios: (i) the presence of a highly inclined, optically thin, dusty disk surrounding the central star; (ii) the presence of an unresolved binary companion at a separation of 13.7 AU and a position angle of 121.8{\deg} NE. The derived orbital period of the binary is 38.1 yr. This detection is in good agreement with hydrodynamic simulations showing that a close companion could be responsible for the entrainment of the gas and dust into a circumbinary structure.

Determination of physical properties of the Asteroid (41) Daphne from interferometric observations in the thermal infrared

We describe interferometric observations of the Asteroid (41) Daphne in the thermal infrared obtained with the Mid-Infrared Interferometric Instrument (MIDI) and the Auxiliary Telescopes (ATs) of the European Southern Observatory (ESO) Very Large Telescope Interferometer (VLTI). We derived the size and the surface thermal properties of (41) Daphne by means of a thermophysical model (TPM), which is used for the interpretation of interferometric data for the first time. From our TPM analysis, we derived a volume equivalent diameter for (41) Daphne of 189 km, using a non-convex 3-D shape model derived from optical lightcurves and adaptive optics images (B. Carry, private communication). On the other hand, when using the convex shape of Kaasalainen et al. (Kaasalainen, M., Mottola, S., Fulchignoni, M. [2002]. Icarus 159, 369–395) in our TPM analysis, the resulting volume equivalent diameter of (41) Daphne is between 194 and 209 km, depending on the surface roughness. The shape of the asteroid is used as an a priori information in our TPM analysis. No attempt is made to adjust the shape to the data. Only the size of the asteroid and its thermal parameters such as, albedo, thermal inertia and roughness are adjusted to the data. We estimated our model systematic uncertainty to be of 4% and of 7% on the determination of the asteroid volume equivalent diameter depending on whether the non-convex or the convex shape is used, respectively. In terms of thermal properties, we derived a value of the surface thermal inertia smaller than 50 J m −2 s −0.5 K −1 and preferably in the range between 0 and ∼30 J m −2 s −0.5 K −1. Our TPM analysis also shows that Daphne has a moderate macroscopic surface roughness.

On the anomalous silicate absorption feature of the prototypical Seyfert 2 galaxy NGC1068

Abstract The first detection of the silicate absorption feature in Active Galactic Nuclei (AGNs) was made at 9.7μm for the prototypical Seyfert 2 galaxy NGC1068 35 yr ago, indicating the presence of a large column of silicate dust in the line of sight to the nucleus. It is now well recognized that type 2 AGNs exhibit prominent silicate absorption bands, while the silicate bands of type 1 AGNs appear in emission. More recently, using the Mid-Infrared Interferometric Instrument on the Very Large Telescope Interferometer, Jaffe et al. for the first time spatially resolved the parsec-sized dust torus around NGC1068 and found that the 10μm silicate absorption feature of the innermost hot component exhibits an anomalous profile differing from that of the interstellar medium and that of common olivine-type silicate dust. While they ascribed the anomalous absorption profile to gehlenite (Ca2Al2SiO7, a calcium aluminium silicate species), we propose a physical dust model and argue that, although the presence of gehlenite is not ruled out, the anomalous absorption feature mainly arises from silicon carbide.

Resolving the Nucleus of Centaurus A at Mid-Infrared Wavelengths

AbstractWe have observed Centaurus A with the Mid-Infrared Interferometric Instrument (MIDI) at the Very Large Telescope Interferometer at resolutions of 7–15 mas (at 12.5 μm) and filled gaps in the (u, v) coverage in comparison to earlier measurements. We are now able to describe the nuclear emission in terms of geometric components and derive their parameters by fitting models to the interferometric data. With simple geometrical models, the best fit is achieved for an elongated disk with flat intensity profile with diameter 76 ± 9 × 35 ± 2 mas (1.41 ± 0.17 × 0.65 ± 0.03 pc) whose major axis is oriented at a position angle (PA) of 10.1 ± 2.2° east of north. A point source contributes 47 ± 11% of the nuclear emission at 12.5 μm. There is also evidence that neither such a uniform nor a Gaussian disk are good fits to the data. This indicates that we are resolving more complicated small-scale structure in active galactic nuclei with MIDI, as has been seen in Seyfert galaxies previously observed with MIDI. The PA and inferred inclination i = of the dust emission are compared with observations of gas and dust at larger scales.

Hydrodynamic Studies of Turbulent AGN Tori

Recently, the MID-infrared Interferometric instrument (MIDI) at the VLTI has shown that dust tori in the two nearby Seyfert galaxies NGC 1068 and the Circinus galaxy are geometrically thick and can be well described by a thin, warm central disk, surrounded by a colder and fluffy torus component. By carrying out hydrodynamical simulations with the help of the TRAMP code (Klahr et al. 1999), we follow the evolution of a young nuclear star cluster in terms of discrete mass-loss and energy injection from stellar processes. This naturally leads to a filamentary large scale torus component, where cold gas is able to flow radially inwards. The filaments join into a dense and very turbulent disk structure. In a post-processing step, we calculate spectral energy distributions and images with the 3D radiative transfer code MC3D Wolf (2003) and compare them to observations. Turbulence in the dense disk component is investigated in a separate project.

DUST EMISSION FROM A PARSEC-SCALE STRUCTURE IN THE SEYFERT 1 NUCLEUS OF NGC 4151

We report mid-infrared interferometric measurements (based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere, Chile, programme number 081.B-0092(A)) with ∼10 mas resolution, which resolve the warm (T = 285+25−50 K) thermal emission at the center of NGC 4151. Using pairs of Very Large Telescope 8.2 m telescopes with the Mid-infrared interferometric instrument and by comparing the data to a Gaussian model, we determined the diameter of the dust emission region, albeit only along one position angle, to be (2.0 ± 0.4) pc (FWHM). This is the first size and temperature estimate for the nuclear warm dust distribution in a Seyfert 1 galaxy. The parameters found are comparable to those in Seyfert 2 galaxies, thus providing direct support for the unified model. Using simple analytic temperature distributions, we find that the mid-infrared emission is probably not the smooth continuation of the hot nuclear source that is marginally resolved with K-band interferometry. We also detected weak excess emission around 10.5 μm in our shorter baseline observation, possibly indicating that silicate emission is extended to the parsec scale.

Resolving the obscuring torus in NGC 1068 with the power of infrared interferometry: revealing the inner funnel of dust

We present new interferometric data obtained with MIDI (MID infrared Interferometric instrument) for the Seyfert II galaxy NGC 1068, with an extensive coverage of sixteen uv points. These observations resolve the nuclear mid-infrared emission from NGC 1068 in unprecedented detail with a maximum resolution of 7 mas. For the first time, sufficient uv points have been obtained, allowing us to generate an image of the source using maximum entropy image reconstruction. The features of the image are similar to those obtained by modelling. We find that the mid-infrared emission can be represented by two components, each with a Gaussian brightness distribution. The first, identified as the inner funnel of the obscuring torus, is hot (800K), 1.35 parsec long, and 0.45 parsec thick in FWHM at a PA=-42 degrees (from north to east). It has an absorption profile different than standard interstellar dust and with evidence for clumpiness. The second component is 3 by 4 pc in FWHM with T=300K, and we identify it with the cooler body of the torus. The compact component is tilted by 45 degrees with respect to the radio jet and has similar size and orientation to the observed water maser distribution. We show how the dust distribution relates to other observables within a few parsecs of the core of the galaxy such as the nuclear masers, the radio jet, and the ionization cone. We compare our findings to a similar study of the Circinus galaxy and other relevant studies. Our findings shed new light on the relation between the different parsec-scale components in NGC 1068 and the obscuring torus.

High spatial resolution observations of the T Tau system — II. Interferometry in the mid-infrared

Each time the resolution was improved, observations of the young low-mass star T Tau led to new insights. Initially classified as the prototype of low-mass pre-main-sequence stars, measurements with high resolution techniques in the near-infrared revealed the existence of a deeply embedded companion only 0.7 arcsec to the south. Later on, this companion itself has been resolved into two sources with a separation of only about 50 mas. We investigated both the optically bright northern component and the embedded southern binary with the MID-infrared Interferometric instrument (MIDI). The resulting visibilities of the northern component decrease with wavelength, independent of the baseline's position angle. This is a clear sign of the large face-on circumstellar disc. With a simultaneous fit of a radiative transfer model to both the interferometric results and the spectral energy distribution, the properties of this disc can be determined without the high degeneracy of fits to the spectral energy distribution alone. Since the visibilities of the southern binary are clearly dominated by the typical sinusoidal binary signal, we could for the first time in the mid-infrared derive separate spectra for both components together with a very precise relative position. This position is in excellent agreement with the orbit found from a fit to the near-infrared adaptive optics measurements. The orbit with its small periastron distance indicates tidally truncated discs, which are consistent with the interferometric measurements. The peculiar properties of the infrared companion can be explained by the model of an intermediate mass star extincted by an almost edge-on disc.

Studies of active galactic nuclei with the VLT interferometer

The observation of extragalactic targets is the most challenging program for interferometric instruments operating at infrared wavelengths. Of them, only the nearest active galactic nuclei (AGN) are bright enough to be reached with the current instruments at the VLT Interferometer (VLTI). So far, two Seyfert galaxies, NGC 1068 and the Circinus galaxy, have been studied in detail with the MID-infrared interferometric instrument (MIDI). First results could also be obtained for the nearby radio galaxy Centaurus A. This lecture gives an account of the current state-of-the art: after spelling out the scientific questions, the investigations of the dust tori in NGC 1068 and Circinus are used to demonstrate the observational challenge and the achieved data quality. The results of these studies provide new astrophysical insights and their comparison with newly developed models of dust tori allows a better understanding the identified structures. Finally, the prospects for extending this kind of studies to more distant and fainter AGN with current and next-generation VLTI instruments are discussed.

The core flux of the brightest 10 $\mathsf{\mu}$m galaxies in the southern sky

Aims. Near diffraction-limited images have been taken at 8.9, 11.9, and 12.9 µm for the brightest extragalactic sources in the southern sky, in order to optimally plan N-band observations with MIDI (MID-infrared Interferometric instrument) at the VLTI. Methods. We have assembled a sample of 21 objects consisting of all the AGNs observable from Paranal observatory, Chile, plus three non-AGN objects, with an estimated N-band flux greater than 400 mJy. We used the TIMMI2 Mid Infrared instrument mounted on the ESO’s 3.6 m telescope to obtain near diffraction-limited images in order to establish the unresolved core flux within <0.5 arscsec. Results. Positions and core total fluxes were obtained for all sources in our sample and compared with similar investigations in the literature. We find that 15 AGN and the nuclear starburst in NGC 253 exhibit an unresolved core flux <300 mJy at 11.9 µm, making them promising targets for MIDI at the VLTI. For extended sources, near diffraction-limited images are presented and discussed.

The T Tauri star RY Tauri as a case study of the inner regions of circumstellar dust disks

Aims. We study the inner region (∼1.0 AU up to a few 10 AUs) of the circumstellar disk around the “classical” T Tauri star RY Tau. Our aim is to find a physical description satisfying the available interferometric data, obtained with the mid-infrared interferometric instrument at the Very Large Telescope Interferometer, as well as the spectral energy distribution in the visible to millimeter wavelength range. We also compare the findings with the results of similar studies, including those of intermediate-mass Herbig Ae/Be stars. Methods. Our analysis is done within the framework of a passively heated circumstellar disk, which is optionally supplemented by the effects of accretion and an added envelope. To achieve a more consistent and realistic model, we used our continuum transfer code MC3D. In addition, we studied the shape of the 10 µm silicate emission feature in terms of the underlying dust population, both for single-dish and for interferometric measurements. Results. We show that a modestly flaring disk model with accretion can explain both the observed spectral energy distribution and the mid-infrared visibilities obtained with the mid-infrared infrared instrument. We found an interesting ambiguity: a circumstellar active disk model with an added envelope, and a lower accretion rate than in the active disk model without envelope, could represent the observations equally as well. This type of model with the envelope should be considered a viable alternative in future models of other T Tauri stars. The approach of a disk with a puffed-up inner rim wall and the influence of a stellar companion is also discussed. We also investigate the influence of various fit parameters on the outcome of the radiative transfer modeling. From the study of the silicate emission feature we see evidence for dust evolution in a T Tauri star, with a decreasing fraction of small amorphous and an increasing fraction of crystalline particles closer to the star.

First AU-scale observations of V1647 Orionis with VLTI/MIDI

The young eruptive star V16470ri was observed with MIDI, the mid-infrared interferometric instrument at the Very Large Telescope Interferometer (VLTI), on March 2, 2005. We present the first spectrally resolved interferometric visibility points for this object. Our results show that (1) the mid-infrared emitting region is extended, having a size of ≈7 AU at 10μm; (2) no signatures of a close companion can be seen; (3) the 8-13μm spectrum exhibits no obvious spectral features. Comparison with similar observations of Herbig Ae stars suggests that V1647 Ori probably possesses a disk of moderate flaring. A simple disk model with T ∼ r -0.53 , Σ ∼ r -1.5 , M d = 0.05 M ⊙ is able to fit both the spectral energy distribution and the observed visibility values simultaneously.