The potential of combining MATISSE and ALMA observations: Constraining the structure of the innermost region in protoplanetary discs

In order to study the initial conditions of planet formation, it is crucial to obtain spatially resolved multi-wavelength observations of the innermost region of protoplanetary discs. We evaluate the advantage of combining observations with MATISSE/VLTI and ALMA to constrain the radial and vertical structure of the dust in the innermost region of circumstellar discs in nearby star-forming regions. Based on a disc model with a parameterized dust density distribution, we apply 3D radiative-transfer simulations to obtain ideal intensity maps. These are used to derive the corresponding wavelength-dependent visibilities we would obtain with MATISSE as well as ALMA maps simulated with CASA. Within the considered parameter space, we find that constraining the dust density structure in the innermost $5\,$au around the central star is challenging with MATISSE alone, whereas ALMA observations with reasonable integration times allow us to derive significant constraints on the disc surface density. However, we find that the estimation of the different disc parameters can be considerably improved by combining MATISSE and ALMA observations. For example, combining a 30-minute ALMA observation (at 310 GHz with an angular resolution of 0.03$^{\prime\prime}$) for MATISSE observations in the L and M bands (with visibility accuracies of about $3\,\%$) allows the radial density slope and the dust surface density profile to be constrained to within $\Delta \alpha=0.3$ and $\Delta (\alpha-\beta)=0.15$, respectively. For an accuracy of ${\sim 1\%}$ even the disc flaring can be constrained to within $\Delta \beta=0.1$. To constrain the scale height to within $5\,$au, M band accuracies of $0.8\,\%$ are required. While ALMA is sensitive to the number of large dust grains settled to the disc midplane we find that the impact of the surface density distribution of the large grains on the observed quantities is small.Comment: 12 pages, 12 figures, 1 table, accepted by A&

Self-scattering in protoplanetary disks with dust settling

Scattering of re-emitted flux is considered to be at least partially responsible for the observed polarisation in the (sub-)millimetre wavelength range of several protoplanetary disks. Although the degree of polarisation produced by scattering is highly dependent on the dust model, early studies investigating this mechanism relied on the assumption of single grain sizes and simple density distribution of the dust. However, in the dense inner regions where this mechanism is usually most efficient, the existence of dust grains with sizes ranging from nanometres to millimetres has been confirmed. Additionally, the presence of gas forces larger grains to migrate vertically towards the disk midplane, introducing a dust segregation in the vertical direction. Using polarisation radiative transfer simulations, we analyse the dependence of the resulting scattered light polarisation at 350 $\mu$m, 850 $\mu$m, 1.3 mm, and 2 mm on various parameters describing protoplanetary disks, including the effect of dust grain settling. We find that the different disk parameters change the degree of polarisation mostly by affecting the anisotropy of the radiation field, the optical depth, or both. It is therefore very challenging to deduce certain disk parameter values directly from polarisation measurements alone. However, assuming a high dust albedo, it is possible to trace the transition from optically thick to optically thin disk regions. The degree of polarisation in most of the considered disk configurations is lower than what is found observationally, implying the necessity to revisit models that describe the dust properties and disk structure.Comment: accepted by A&A, 7 pages, 8 figure

The influence of dust grain porosity on the analysis of debris disc observations

Debris discs are often modelled assuming compact dust grains, but more and more evidence for the presence of porous grains is found. We aim at quantifying the systematic errors introduced when modelling debris discs composed of porous dust with a disc model assuming spherical, compact grains. We calculate the optical dust properties derived via the fast, but simple effective medium theory. The theoretical lower boundary of the size distribution -- the so-called 'blowout size' -- is compared in the cases of compact and porous grains. Finally, we simulate observations of hypothetical debris discs with different porosities and feed them into a fitting procedure using only compact grains. The deviations of the results for compact grains from the original model based on porous grains are analysed. We find that the blowout size increases with increasing grain porosity up to a factor of two. An analytical approximation function for the blowout size as a function of porosity and stellar luminosity is derived. The analysis of the geometrical disc set-up, when constrained by radial profiles, are barely affected by the porosity. However, the determined minimum grain size and the slope of the grain size distribution derived using compact grains are significantly overestimated. Thus, the unexpectedly high ratio of minimum grain size to blowout size found by previous studies using compact grains can be partially described by dust grain porosity, although the effect is not strong enough to completely explain the trend.Comment: accepted by MNRA

Constraints on observing brightness asymmetries in protoplanetary disks at solar system scale

We have quantified the potential capabilities of detecting local brightness asymmetries in circumstellar disks with the Very Large Telescope Interferometer (VLTI) in the mid-infrared wavelength range. The study is motivated by the need to evaluate theoretical models of planet formation by direct observations of protoplanets at early evolutionary stages, when they are still embedded in their host disk. Up to now, only a few embedded candidate protoplanets have been detected with semi-major axes of 20-50 au. Due to the small angular separation from their central star, only long-baseline interferometry provides the angular resolving power to detect disk asymmetries associated to protoplanets at solar system scales in nearby star-forming regions. In particular, infrared observations are crucial to observe scattered stellar radiation and thermal re-emission in the vicinity of embedded companions directly. For this purpose we performed radiative transfer simulations to calculate the thermal re-emission and scattered stellar flux from a protoplanetary disk hosting an embedded companion. Based on that, visibilities and closure phases are calculated to simulate observations with the future beam combiner MATISSE, operating at the L, M and N bands at the VLTI. We find that the flux ratio of the embedded source to the central star can be as low as 0.5 to 0.6 % for a detection at a feasible significance level due to the heated dust in the vicinity of the embedded source. Furthermore, we find that the likelihood for detection is highest for sources at intermediate distances $r\approx2$-$5$ au and disk masses not higher than $\approx10^{-4}$ M$_{\odot}$

Constraining the magnetic field properties of Bok globule B335 using SOFIA/HAWC+

Thanks to their well-defined shape and mostly isolated locations, Bok globules are suitable objects for studying the physics of low-mass star formation. To study the magnetic field of the prototypical Bok globule B335, we obtained a spatially resolved polarization map with SOFIA/HAWC+ at a wavelength of 214$\,\mu$m. For the first time, these observations reveal that polarization holes in Bok globules, that is, the decrease in polarization degree towards their dense centers, also occur in the far-infrared wavelength regime. The observed polarization pattern is uniform with a mean polarization angle of 48$^\circ\pm$26$^\circ$ and a magnetic field strength of $\sim$ 142$\,\mu$G. Moreover, we use complementary polarimetic data for B335 obtained at near-infrared to millimeter wavelengths to analyze and constrain the magnetic field across different scales. By applying the 3D Monte-Carlo radiative transfer code POLARIS (Reissl et al. 2016), we developed a model for the density and magnetic field structure as well as for the dust properties of this globule. We conclude that the column density towards the center of B335 is too low to cause the observed polarization hole in B335 via dichroic absorption (Brauer et al. 2016). Furthermore, we conclude that the effect of self-scattering has no significant impact on the observed polarization. Adopting dust-grain alignment via the radiative torque mechanism, a combination of the interstellar radiation field and the central star as radiation sources is consistent with the decrease in polarization degree at the outer regions of B335 ($\approx\,$10$^4\,$au from the core). However, the model fails to explain the low polarization degree within the inner 5000 au.Comment: Accepted for publication in A&A, 11 pages, 10 figure

Three-dimensional continuum radiative transfer of polarized radiation in exoplanetary atmospheres

Polarimetry is about to become a powerful tool for determining the atmospheric properties of exoplanets. To provide the basis for the interpretation of observational results and for predictive studies to guide future observations, sophisticated analysis tools are required. Our goal is to develop a radiative transfer tool that contains all the relevant continuum polarization mechanisms for the comprehensive analysis of the polarized flux resulting from the scattering in the atmosphere of, on the surface of, and in the local planetary environment (e.g., planetary rings, exomoons) of extra-solar planets. Furthermore, our goal is to avoid common simplifications such as locally plane-parallel planetary atmospheres, the missing cross-talk between latitudinal and longitudinal regions, or the assumption of either a point-like star or plane-parallel illumination. As a platform for the newly developed numerical algorithms, we use the 3D Monte Carlo radiative transfer code POLARIS. The code is extended and optimized for the radiative transfer in exoplanetary atmospheres. We investigate the reflected flux and its degree of polarization for different phase angles for a homogeneous cloud-free atmosphere and an inhomogeneous cloudy atmosphere. To take advantage of the 3D radiative transfer and to demonstrate the potential of the code, the impact of an additional circumplanetary ring on the reflected polarized flux is studied. The presence of a circumplanetary ring consisting of small water-ice particles has a noticeable impact on the reflected polarized radiation. In particular, the reflected flux strongly increases at larger phase angles if the planetary orbit is seen edge-on because the considered particles tend to scatter forwards. In contrast, the degree of polarization decreases at these phase angles.Comment: Accepted for publication in A&A, 12 pages, 10 figure

Beobachtbarkeit von ausgewählten Strukturen und Staubeigenschaften zirkumstellarer Scheiben in verschiedenen Entwicklungsstadien

Protoplanetare Scheiben aus Gas und Staub sind die Geburtsstätten von Planeten. Die Planetenentstehung ist jedoch nicht geklärt, obwohl mehrere, plausible Theorien in der Fachliteratur zu finden sind. Durch die Beobachtung des Staubs ist es möglich, Aussagen über die Eigenschaften der Scheiben und eventuell vorhandener Planeten zu treffen. Auch Beobachtungen der deutlich älteren Trümmerscheiben können dabei helfen, die zeitliche Entwicklung zirkumstellarer Scheiben zu verstehen. In der Arbeit wird untersucht, ob man mit aktuellen, optischen Interferometern auf die Präsenz von Planeten in protoplanetaren Scheiben schließen und diese charakterisieren kann. Weiterhin wird gezeigt, welchen Einfluss die Porosität des Staubs auf die Modellierungsergebnisse von räumlich aufgelösten und unaufgelösten Beobachtungen von Trümmerscheiben hat. In der ersten Studie werden interferometrische Beobachtungen im Mittelinfrarot einer protoplanetaren Scheibe auf Variabilität untersucht. Außerdem wird mittels Strahlungstransport-Simulationen auf die Dichteverteilung des Staubs innerhalb der Scheibe geschlossen. Zusätzlich wird ein Satz photometrischer Beobachtungsdaten verwendet, um eventuelle Mehrdeutigkeiten des Scheibenmodells zu reduzieren. Der zweite Teil der Arbeit liefert Vorhersagen zur Detektierbarkeit von Helligkeitsasymmetrien in protoplanetaren Scheiben mit dem Interferometer MATISSE. Dazu werden Beobachtungen dieser Helligkeitsverteilungen simuliert und hinsichtlich der notwendigen Messunsicherheiten von MATISSE untersucht. In der dritten Studie werden Beobachtungen von Trümmerscheiben mit porösem Staub simuliert. Im Standardverfahren zur Anpassung eines Scheibenmodells an Beobachtungsdaten werden die Staubkörner als kompakt und sphärisch angenommen, obwohl es deutliche Hinweise auf die fraktale und poröse Gestalt des Staubs in Trümmerscheiben gibt. Es wird untersucht, inwiefern sich die Ergebnisse der Modellanpassung mit kompakten Körnern von den tatsächlichen Staub- und Scheibenparametern der Trümmerscheibe mit porösen Körnern unterscheidet

Interferometric study on the temporal variability of the brightness distributions of protoplanetary disks

Multi-epoch observations have revealed the variability of pre-main sequence stars and/or their environment. Moreover, structures in orbital motion around the central star, resulting from planet-disk interaction, are predicted to cause temporal variations in the brightness distributions of protoplanetary disks. Through repeated observations with the Very Large Telescope Interferometer (VLTI) over nearly two decades, the ESO Archive has become a treasure chest containing high-resolution multi-epoch near- and mid-infrared observations of the potential planet-forming regions in protoplanetary disks. We aim to investigate whether the existing multi-epoch observations provide evidence for the variability of the brightness distributions of the innermost few astronomical units of protoplanetary disks and to quantify any variations detected. We present different approaches to search for evidence of temporal variations based on multi-epoch observations obtained with the VLTI instruments PIONIER, AMBER, and MIDI for 68 pre-main sequence stars. For nine objects in our sample, multi-epoch data obtained using equal baselines are available that allow us to directly detect variations in the visibilities due to temporally variable brightness distributions. Significant variations of the near-infrared visibilities obtained in different epochs with PIONIER and/or AMBER for HD 50138, DX Cha, HD 142527, V856 Sco, HD 163296, and R CrA were found. By estimating the impact of a small variation of the baseline on the measured squared visibilities, we are able to compare the data of another 12 pre-main sequence stars. Thereby, we find evidence for temporal variations of the brightness distribution of one additional object, AK Sco. Besides the two binaries DX Cha and AK Sco, HD 50138 and V856 Sco also show signs of variability caused by variations of asymmetric structures in the brightness distribution.Comment: Accepted for publication in A&

Polarization reversal of scattered thermal dust emission in protoplanetary disks at submillimetre wavelengths

Investigation of the polarized light of protoplanetary disks is key for constraining dust properties, disk morphology, and embedded magnetic fields. However, different polarization mechanisms and the diversity of dust grain shapes and compositions lead to ambiguities in the polarization pattern. The so-called “self-scattering” of thermal, re-emitted radiation in the infrared and millimetre and submillimetre wavelengths is discussed as a major polarization mechanism. If the net flux of the radiation field is in the radial direction, it is commonly assumed that the polarization pattern produced by scattering in a protoplanetary disk shows concentric rings for disks seen in face-on orientation. We show that a change of 90° of the polarization vector orientation may occur and mimic the typical pattern of dichroic emission of dust grains aligned by a toroidal magnetic field in disks seen close to face-on. Furthermore, this effect of polarization reversal is a fast-changing function of wavelength and grain size, and is thus a powerful tool to constrain grain composition and size distribution present in protoplanetary disks. In addition, the effect may also provide unique constraints for the disk inclination, especially if the disk is seen close to face-on

Self-scattering on large, porous grains in protoplanetary disks with dust settling

Context. Observations of protoplanetary disks in the sub-millimetre wavelength range suggest that polarisation is caused by scattering of thermal re-emission radiation. Most of the dust models that are used to explain these observations have major drawbacks: they either use much smaller grain sizes than expected from dust evolution models, or result in polarisation degrees that are lower than observed. Aims. We investigate the effect of dust grain porosity on the observable polarisation due to scattering at sub-millimetre wavelengths arising from grain size distributions up to millimetre sizes, as they are expected to be present close to the midplane of protoplanetary disks. Methods. Using the effective medium theory, we calculated the optical properties of porous dust and used them to predict the behaviour of the observable polarisation degree due to scattering. Subsequently, Monte Carlo radiative transfer simulations for protoplanetary disks with porous dust grains were performed to analyse the additional effect of the optical depth structure, and thus the effect of multiple scattering events and inhomogeneous temperature distributions on the net observable polarisation degree. Results. We find that porous dust grains with moderate filling factors of about 10% increase the degree of polarisation compared to compact grains. For higher grain porosities, that is, grains with a filling factor of 1% or lower, the extinction opacity decreases, as does the optical depth of a disk with constant mass. Consequently, the unpolarised direct radiation dominates the scattered flux, and the degree of polarisation drops rapidly. Even though the simulated polarisation degree is higher than in the case of compact grains, it is still below the typical observed values for face-on disks. However, the polarisation degree can be increased when crucial model assumptions derived from disk and dust evolution theories, for instance, dust settling and millimetre-sized dust grains, are dropped. In the case of inclined disks, however, our reference model is able to achieve polarisation degrees of about 1%, and using higher disk masses, even higher than this