Protoplanetary Dust Research Articles

Scattering properties of protoplanetary dust analogs with microwave analogy: Rough compact grains

Context. Scattering simulations of perfect spheres are not sufficient to explain the observations of scattered light from protoplanetary and debris disks, especially when the dust sizes are on the same order of magnitude as the wavelength used to perform the observations. Moreover, examples of grains collected from the Solar System have proved that the morphology of interstellar dust is irregular. These pieces of evidence lead us to consider that the morphologies of the dust that participates in these circumstellar disks are more complex than those of spheres. Aims. We aim to measure and simulate the scattering properties of six rough compact grains to identify how their morphology affects their scattering properties. These grains are intended to be dust analogs of protoplanetary and debris disks. Their convexity ranges from 75% to 99%. Methods. Grains were 3D printed using stereolithography, and their shape and refractive index were controlled. These analogs were measured with our microwave-scattering experiment (microwave analogy) at wavelengths ranging from 16.7 mm to 100 mm, leading to size parameters from X = 1.07 to X = 7.73. In parallel, their scattering properties were simulated with our finite-element method (FEM), which contained the same geometric file as the 3D printed grains. Results. We retrieved five scattering properties of these grains, that is, the phase function, the degree of linear polarization (DLP), and three other Mueller matrix elements 〈Sij〉. Two types of studies were performed. First, a study of the scattering properties averaged over several orientations of grains at different wavelengths. Second, a study of the same scattering properties, for which a power-law size distribution effect was applied. Conclusions. The very good correspondence between the measured and simulated Mueller matrix elements demonstrated the accuracy of our measurement setup and the efficiency of our FEM simulations. For the first study, DLP proved to be a good indicator of the grain morphology in terms of convexity and shape anisotropy. For the second study, backscattering enhancements of the phase function were related to the grain convexity. The maximum DLP and its negative polarization branches as well as the 〈S22〉/〈S11〉 levels were related to the shape anisotropy of our grains.

The Empirical and Radiative Transfer Hybrid (EaRTH) Disk Model: Merging Analyses of Protoplanetary Dust Disk Mineralogy and Structure

Our understanding of how exoplanets form and evolve relies on analyses of both the mineralogy of protoplanetary disks and their detailed structures; however, these key complementary aspects of disks are usually studied separately. We present initial results from a hybrid model that combines the empirical characterization of the mineralogy of a disk, as determined from its mid-infrared spectral features, with the MCFOST radiative transfer disk model, a combination we call the Empirical and Radiative Transfer Hybrid (EaRTH) Disk Model. With the results of the mineralogy detection serving as input to the radiative transfer model, we generate mid-infrared spectral energy distributions (SEDs) that reflect both the mineralogical and structural parameters of the corresponding disk. Initial fits of the SED output by the resulting integrated model of Spitzer Space Telescope mid-infrared spectra of the protoplanetary disk orbiting the nearby T Tauri star MP Mus demonstrate the potential advantages of this approach by revealing details like the dominance of micron-sized olivine and micron-sized forsterite in this dusty disk. The simultaneous insight into disk composition and structure provided by the EaRTH Disk methodology should be directly applicable to the interpretation of mid-infrared spectra of protoplanetary disks that will be produced by the James Webb Space Telescope.

Water transport through mesoporous amorphous-carbon dust

The diffusion of water molecules through mesoporous dust of amorphous carbon (a-C) is a key process in the evolution of prestellar, protostellar, and protoplanetary dust, as well as in that of comets. It also plays a role in the formation of planets. Given the absence of data on this process, we experimentally studied the isothermal diffusion of water molecules desorbing from water ice buried at the bottom of a mesoporous layer of aggregated a-C nanoparticles, a material analogous to protostellar and cometary dust. We used infrared spectroscopy to monitor diffusion in low temperature (160 to 170 K) and pressure (6 × 10−5 to 8 × 10−4 Pa) conditions. Fick’s first law of diffusion allowed us to derive diffusivity values on the order of 10−2 cm2 s−1, which we linked to Knudsen diffusion. Water vapor molecular fluxes ranged from 5 × 1012 to 3 × 1014 cm−2 s−1 for thicknesses of the ice-free porous layer ranging from 60 to 1900 nm. Assimilating the layers of nanoparticles to assemblies of spheres, we attributed to this cosmic dust analog of porosity 0.80−0.90 a geometry correction factor, similar to the tortuosity factor of tubular pore systems, between 0.94 and 2.85. Applying the method to ices and refractory particles of other compositions will provides us with other useful data.

An inflationary disk phase to explain extended protoplanetary dust disks

Context. Understanding planetesimal formation is an essential first step towards understanding planet formation. The distribution of these first solid bodies drives the locations where planetary embryos, which eventually form fully-fledged planets, grow. Aims. We seek to understand the parameter space of possible protoplanetary disk formation and evolution models of our Solar System. A good protoplanetary disk scenario for the Solar System must meet at least the following three criteria: (1) It must produce an extended gas and dust disk (e.g. 45 au for the dust); (2) within the disk, the local dust-to-gas ratio in at least two distinct locations must sufficiently increase to explain the early formation of the parent bodies of non-carbonaceous and carbonaceous iron meteorites; and (3) dust particles, which have condensed at high temperatures (i.e. calcium–aluminium-rich inclusions), must be transported to the outer disk. Though current protoplanetary disk models are able to satisfy one or two of these criteria, none have been successful in recreating all three. We aim to find scenarios that satisfy all three. Methods. In this study we used a 1D disk model that tracks the evolution of the gas and dust disks. Planetesimals are formed within the disk at locations where the streaming instability can be triggered. We explored a large parameter space to study the effect of the disk viscosity, the timescale of infall of material into the disk, the distance within which material is deposited into the disk, and the fragmentation threshold of dust particles. Results. We find that scenarios with a large initial disk viscosity (α > 0.05), a relatively short infall timescale (Tinfall < 100–200kyr), and a small centrifugal radius (RC ~ 0.4 au; i.e. the distance within which material falls into the disk) result in disks that satisfy all three criteria needed to represent the protoplanetary disk of the Solar System. The large initial viscosity and short infall timescale result in a rapid initial expansion of the disk, which we dub the ‘inflationary phase’ of the disk. Furthermore, a temperature-dependent fragmentation threshold, which accounts for cold icy particles breaking more easily, results in larger and more massive disks. This, in turn, results in more ‘icy’ than ‘rocky’ planetesimals. Such scenarios are also better in line with our Solar System, which has small terrestrial planets and massive giant planet cores. Finally, we find that scenarios with large RC cannot transport calcium–aluminium-rich inclusions to the outer disk and do not produce planetesimals at two locations within the disk.

Size Dependence of the Bouncing Barrier in Protoplanetary Dust Growth

Understanding the collisional behavior of dust aggregates is essential in the context of planet formation. It is known that low-velocity collisions of dust aggregates result in bouncing rather than sticking when the filling factor of colliding dust aggregates is higher than a threshold value. However, a large discrepancy between numerical and experimental results on the threshold filling factor was reported so far. In this study, we perform numerical simulations using soft-sphere discrete element methods and demonstrate that the sticking probability decreases with increasing aggregate radius. Our results suggest that the large discrepancy in the threshold filling factor may reflect the difference in the size of dust aggregates in earlier numerical simulations and laboratory experiments.

Measuring Protoplanetary Disk Dust Masses in Lupus with Spectral Energy Distribution Modeling

Measuring Protoplanetary Disk Dust Masses in Lupus with Spectral Energy Distribution Modeling

Scattering properties of protoplanetary dust analogs with microwave analogy: Aggregates of fractal dimensions from 1.5 to 2.8

Context. The growth of dust grains in protoplanetary disks is not understood in detail. Several studies have proposed the presence of aggregates and irregular grains to overcome the physical barriers in grain growth models. In order to understand the scattering properties of these aggregates, laboratory measurements of light scattering and microwave scattering have been developed over the last 50 years. Aims. We aim to measure the scattering properties of different protoplanetary analog aggregates with fractal dimensions of 1.5, 1.7, 2.0, 2.5, and 2.8. Methods. We used the microwave scattering technique (microwave analogy) for the measurements. The analog particles were virtually generated and fabricated by 3D printing with a controlled size (scaling factor), geometry, and refractive index. The seven analogs were measured at wavelengths ranging from 16.7 mm to 100 mm, leading to aggregate size parameters ranging from Xagg = 1 to Xagg = 20. The results were compared to finite element method calculations of the same analogs for cross-validation. Results. The phase function and the degree of linear polarization were deduced from the scattered field measurements of the different aggregates. These scattering properties are compared and discussed as a function of the fractal dimension. Conclusions. The scattering properties of aggregates with different fractal dimensions are different. Three different realizations of aggregates with the same fractal dimension but different monomer configurations yield the same phase functions. We verified that the maximum degree of linear polarization is higher for porous aggregates than for compact aggregates. Furthermore, the maximum polarization occurs at larger scattering angles for high fractal dimensions, while the half width at half maximum of the phase functions present larger values for small fractal dimensions.

A dusty filament and turbulent CO spirals in HD 135344B - SAO 206462

ABSTRACT Planet–disc interactions build up local pressure maxima that may halt the radial drift of protoplanetary dust, and pile it up in rings and crescents. ALMA observations of the HD 135344B disc revealed two rings in the thermal continuum stemming from ∼mm-sized dust. At higher frequencies the inner ring is brighter relative to the outer ring, which is also shaped as a crescent rather than a full ring. In near-IR scattered light images, the disc is modulated by a two-armed grand-design spiral originating inside the ALMA inner ring. Such structures may be induced by a massive companion evacuating the central cavity, and by a giant planet in the gap separating both rings, that channels the accretion of small dust and gas through its filamentary wakes while stopping the larger dust from crossing the gap. Here we present ALMA observations in the J = (2 − 1) CO isotopologue lines and in the adjacent continuum, with up to 12 km baselines. Angular resolutions of ∼0${_{.}^{\prime\prime}}$03 reveal the tentative detection of a filament connecting both rings, and which coincides with a local discontinuity in the pitch angle of the IR spiral, proposed previously as the location of the protoplanet driving this spiral. Line diagnostics suggests that turbulence, or superposed velocity components, is particularly strong in the spirals. The 12CO(2-1) 3D rotation curve points at stellocentric accretion at radii within the inner dust ring, with a radial velocity of up to ${\sim}5{{\ \rm per\ cent}}\pm 0.5{{\ \rm per\ cent}}$ Keplerian, which corresponds to an excessively large accretion rate of ${\sim}2\times 10^{-6}\, M_\odot \,$yr−1 if all of the CO layer follows the 12CO(2-1) kinematics. This suggests that only the surface layers of the disc are undergoing accretion, and that the line broadening is due to superposed laminar flows.

Particle Dynamics in 3D Self-gravitating Disks. II. Strong Gas Accretion and Thin Dust Disks

Abstract Observations suggest that protoplanetary disks have moderate accretion rates onto the central young star, especially at early stages (e.g., HL Tau), indicating moderate disk turbulence. However, recent ALMA observations suggest that dust is highly settled, implying weak turbulence. Motivated by such tension, we carry out 3D stratified local simulations of self-gravitating disks, focusing on the settling of dust particles in actively accreting disks. We find that gravitationally unstable disks can have moderately high accretion rates while maintaining a relatively thin dust disk for two reasons. First, accretion stress from the self-gravitating spirals (self-gravity stress) can be stronger than the stress from turbulence (Reynolds stress) by a factor of 5–20. Second, the strong gravity from the gas to the dust decreases the dust scale height by another factor of ∼2. Furthermore, the turbulence is slightly anisotropic, producing a larger Reynolds stress than the vertical dust diffusion coefficient. Thus, gravitoturbulent disks have unusually high vertical Schmidt numbers (Sc z ) if we scale the total accretion stress with the vertical diffusion coefficient (e.g., Sc z ∼ 10–100). The reduction of the dust scale height by the gas gravity should also operate in gravitationally stable disks (Q > 1). Gravitational forces between particles become more relevant for the concentration of intermediate dust sizes, forming dense clouds of dust. After comparing with HL Tau observations, our results suggest that self-gravity and gravity among different disk components could be crucial for solving the conflict between the protoplanetary disk accretion and dust settling, at least at the early stages.

A dusty origin for the correlation between protoplanetary disc accretion rates and dust masses

ABSTRACT Recent observations have uncovered a correlation between the accretion rates (measured from the UV continuum excess) of protoplanetary discs and their masses inferred from observations of the submm continuum. While viscous evolution models predict such a correlation, the predicted values are in tension with data obtained from the Lupus and Upper Scorpius star-forming regions; for example, they underpredict the scatter in accretion rates, particularly in older regions. Here, we argue that since the submm observations trace the discs’ dust, by explicitly modelling the dust grain growth, evolution, and emission, we can better understand the correlation. We show that for turbulent viscosities with α ≲ 10−3, the depletion of dust from the disc due to radial drift means we can reproduce the range of masses and accretion rates seen in the Lupus and Upper Sco data sets. One consequence of this model is that the upper locus of accretion rates at a given dust mass does not evolve with the age of the region. Moreover, we find that internal photoevaporation is necessary to produce the lowest accretion rates observed. In order to replicate the correct dust masses at the time of disc dispersal, we favour relatively low photoevaporation rates ≲ 10−9 M⊙ yr−1 for most sources but cannot discriminate between EUV or X-ray-driven winds. A limited number of sources, particularly in Lupus, are shown to have higher masses than predicted by our models which may be evidence for variations in the properties of the dust or dust trapping induced in substructures.

Irregular Dust Features around Intermediate-mass Young Stars with GPI: Signs of Youth or Misaligned Disks?

Abstract We are undertaking a large survey of over 30 disks using the Gemini Planet Imager (GPI) to see whether the observed dust structures match spectral energy distribution predictions and have any correlation with stellar properties. GPI can observe near-infrared light scattered from dust in circumstellar environments using high-resolution Polarimetric Differential Imaging with coronagraphy and adaptive optics. The data have been taken in the J and H bands over two years, with inner working angles of 0.″08 and 0.″11, respectively. Ahead of the release of the complete survey results, here we present five objects with extended and irregular dust structures within 2″ of the central star. These objects are FU Ori, MWC 789, HD 45677, Hen 3-365, and HD 139614. The observed structures are consistent with each object being a pre-main-sequence star with protoplanetary dust. The five objects’ circumstellar environments could result from extreme youth and complex initial conditions, from asymmetric scattering patterns due to shadows cast by misaligned disks, or in some cases from interactions with companions. We see complex U ϕ structures in most objects that could indicate multiple scattering or result from the illumination of companions. Specific key findings include the first high-contrast observation of MWC 789 revealing a newly discovered companion candidate and arc, and two faint companion candidates around Hen 3-365. These two objects should be observed further to confirm whether the companion candidates are comoving. Further observations and modeling are required to determine the causes of the structures.

Including Dust Coagulation in Hydrodynamic Models of Protoplanetary Disks: Dust Evolution in the Vicinity of a Jupiter-mass Planet

Abstract Dust growth is often neglected when building models of protoplanetary disks due to its complexity and computational expense. However, it does play a major role in shaping the evolution of protoplanetary dust and planet formation. In this paper, we present a numerical model coupling 2D hydrodynamic evolution of a protoplanetary disk, including a Jupiter-mass planet, and dust coagulation. This is obtained by including multiple dust fluids in a single grid-based hydrodynamic simulation and solving the Smoluchowski equation for dust coagulation on top of solving for the hydrodynamic evolution. We find that fragmentation of dust aggregates trapped in a pressure bump outside of the planetary gap leads to an enhancement in the density of small grains. We compare the results obtained from the full-coagulation treatment to the commonly used, fixed-dust-size approach and to previously applied, less computationally intensive methods for including dust coagulation. We find that the full-coagulation results cannot be reproduced using the fixed-size treatment, but some can be mimicked using a relatively simple method for estimating the characteristic dust size in every grid cell.

Dust Evolution in Protoplanetary Discs and the Formation of Planetesimals

After 25 years of laboratory research on protoplanetary dust agglomeration, a consistent picture of the various processes that involve colliding dust aggregates has emerged. Besides sticking, bouncing and fragmentation, other effects, like, e.g., erosion or mass transfer, have now been extensively studied. Coagulation simulations consistently show that $\rm \mu$m-sized dust grains can grow to mm- to cm-sized aggregates before they encounter the bouncing barrier, whereas sub-$\rm \mu$m-sized water-ice particles can directly grow to planetesimal sizes. For siliceous materials, other processes have to be responsible for turning the dust aggregates into planetesimals. In this article, these processes are discussed, the physical properties of the emerging dusty or icy planetesimals are presented and compared to empirical evidence from within and without the Solar System. In conclusion, the formation of planetesimals by a gravitational collapse of dust "pebbles" seems the most likely.

The Physics of Protoplanetary Dust Agglomerates. X. High-velocity Collisions between Small and Large Dust Agglomerates as a Growth Barrier

Abstract In a protoplanetary disk, dust aggregates in the μm to mm size range possess mean collision velocities of 10–60 m s−1 with respect to dm- to m-sized bodies. We performed laboratory collision experiments to explore this parameter regime and found a size- and velocity-dependent threshold between erosion and growth. By using a local Monte Carlo coagulation calculation and along with a simple semi-analytical timescale approach, we show that erosion considerably limits particle growth in protoplanetary disks and leads to a steady-state dust-size distribution from μm- to dm-sized particles.

Gaps and rings carved by vortices in protoplanetary dust

Context. Large-scale vortices in protoplanetary disks are thought to form and survive for long periods of time. Hence, they can significantly change the global disk evolution and particularly the distribution of the solid particles embedded in the gas, possibly explaining asymmetries and dust concentrations recently observed at submillimeter and millimeter wavelengths. Aims. We investigate the spatial distribution of dust grains using a simple model of protoplanetary disk hosted by a giant gaseous vortex. We explore the dependence of the results on grain size and deduce possible consequences and predictions for observations of the dust thermal emission at submillimeter and millimeter wavelengths. Methods. Global 2D simulations with a bi-fluid code are used to follow the evolution of a single population of solid particles aerodynamically coupled to the gas. Possible observational signatures of the dust thermal emission are obtained using simulators of ALMA and Nest Generation Very Large Array (ngVLA) observations. Results. We find that a giant vortex not only captures dust grains with Stokes number St< 1 but can also affect the distribution of larger grains (with St ~ 1) carving a gap associated with a ring composed of incompletely trapped particles. The results are presented for different particle sizes and associated with their possible signatures in disk observations. Conclusions. Gap clearing in the dust spatial distribution could be due to the interaction with a giant gaseous vortex and their associated spiral waves without the gravitational assistance of a planet. Hence, strong dust concentrations at short sub-mm wavelengths associated with a gap and an irregular ring at longer mm and cm wavelengths could indicate the presence of an unseen gaseous vortex.

Low-velocity collision behaviour of clusters composed of sub-millimetre sized dust aggregates

The experiments presented aim to measure the outcome of collisions between sub-mm sized protoplanetary dust aggregate analogues. We also observed the clusters formed from these aggregates and their collision behaviour. The experiments were performed at the drop tower in Bremen. The protoplanetary dust analogue materials were micrometre-sized monodisperse and polydisperse SiO$_2$ particles prepared into aggregates with sizes between 120~$\mu$m and 250~$\mu$m. One of the dust samples contained aggregates that were previously compacted through repeated bouncing. During three flights of 9~s of microgravity each, individual collisions between aggregates and the formation of clusters of up to a few millimetres in size were observed. In addition, the collisions of clusters with the experiment cell walls leading to compaction or fragmentation were recorded. We observed collisions amongst dust aggregates and collisions between dust clusters and the cell aluminium walls at speeds ranging from about 0.1 cm/s to 20 cm/s. The velocities at which sticking occurred ranged from 0.18 to 5.0 cm/s for aggregates composed of monodisperse dust, with an average value of 2.1 cm/s for reduced masses ranging from 1.2x10-6 to 1.8x10-3 g with an average value of 2.2x10-4 g. From the restructuring and fragmentation of clusters composed of dust aggregates colliding with the aluminium cell walls, we derived a collision recipe for dust aggregates ($\sim$100 $\mu$m) following the model of Dominik \& Thielens (1997) developed for microscopic particles. We measured a critical rolling energy of 1.8x10-13 J and a critical breaking energy of 3.5x10-13 J for 100 $\mu$m-sized non-compacted aggregates.

Testing giant planet formation in the transitional disk of SAO 206462 using deep VLT/SPHERE imaging

Context. The SAO 206462 (HD 135344B) disk is one of the few known transitional disks showing asymmetric features in scattered light and thermal emission. Near-infrared scattered-light images revealed two bright outer spiral arms and an inner cavity depleted in dust. Giant protoplanets have been proposed to account for the disk morphology. Aims. We aim to search for giant planets responsible for the disk features and, in the case of non-detection, to constrain recent planet predictions using the data detection limits. Methods. We obtained new high-contrast and high-resolution total intensity images of the target spanning the Y to the K bands (0.95-2.3 mic) using the VLT/SPHERE near-infrared camera and integral field spectrometer. Results. The spiral arms and the outer cavity edge are revealed at high resolutions and sensitivities without the need for image post-processing techniques, which introduce photometric biases. We do not detect any close-in companions. For the derivation of the detection limits on putative giant planets embedded in the disk, we show that the knowledge of the disk aspect ratio and viscosity is critical for the estimation of the attenuation of a planet signal by the protoplanetary dust because of the gaps that these putative planets may open. Given assumptions on these parameters, the mass limits can vary from ~2-5 to ~4-7 Jupiter masses at separations beyond the disk spiral arms. The SPHERE detection limits are more stringent than those derived from archival NaCo/L' data and provide new constraints on a few recent predictions of massive planets (4-15 MJ) based on the spiral density wave theory. The SPHERE and ALMA data do not favor the hypotheses on massive giant planets in the outer disk (beyond 0.6). There could still be low-mass planets in the outer disk and/or planets inside the cavity.

Making Terrestrial Planets: High Temperatures, FU Orionis Outbursts, Earth, and Planetary System Architectures

Abstract Current protoplanetary dust coagulation theory does not predict dry silicate planetesimals, in tension with the Earth. While remedies to this predicament have been proposed, they have generally failed numerical studies, or are in tension with the Earth’s (low, volatility dependent) volatile and moderately volatile elemental abundances. Expanding on the work of Boley et al., we examine the implications of molten grain collisions and find that they may provide a solution to the dry silicate planetesimal problem. Furthermore, the source of the heating, whether it be a hot inner disk or an FU Orionis scale accretion event, would dictate the location of the resulting planetesimals, potentially controlling subsequent planetary system architectures. We hypothesize that systems that did undergo FU Orionis scale accretion events host planetary systems similar to our own, while ones that did not undergo such an accretion event instead host very close in, tightly packed planets such as those seen by Kepler.

THE ROLE OF PEBBLE FRAGMENTATION IN PLANETESIMAL FORMATION. I. EXPERIMENTAL STUDY

ABSTRACT Previous work on protoplanetary dust growth shows a halt at centimeter sizes owing to the occurrence of bouncing at velocities of ≳0.1 m s−1 and fragmentation at velocities ≳1 m s−1. To overcome these barriers, spatial concentration of centimeter-sized dust pebbles and subsequent gravitational collapse have been proposed. However, numerical investigations have shown that dust aggregates may undergo fragmentation during the gravitational collapse phase. This fragmentation in turn changes the size distribution of the solids and thus must be taken into account in order to understand the properties of the planetesimals that form. To explore the fate of dust pebbles undergoing fragmenting collisions, we conducted laboratory experiments on dust-aggregate collisions with a focus on establishing a collision model for this stage of planetesimal formation. In our experiments, we analyzed collisions of dust aggregates with masses between 0.7 and 91 g mass ratios between target and projectile from 1 to 126 at a fixed porosity of 65%, within the velocity range of 1.5–8.7 m s−1, at low atmospheric pressure of ∼10−3 mbar, and in free-fall conditions. We derived the mass of the largest fragment, the fragment size/mass distribution, and the efficiency of mass transfer as a function of collision velocity and projectile/target aggregate size. Moreover, we give recipes for an easy-to-use fragmentation and mass-transfer model for further use in modeling work. In a companion paper, we use the experimental findings and the derived dust-aggregate collision model to investigate the fate of dust pebbles during gravitational collapse.

Scattered light mapping of protoplanetary disks

High-contrast scattered light observations have revealed the surface morphology of several dozens of protoplanetary disks at optical and near-infrared wavelengths. Inclined disks offer the opportunity to measure part of the phase function of the dust grains that reside in the disk surface which is essential for our understanding of protoplanetary dust properties and the early stages of planet formation. We aim to construct a method which takes into account how the flaring shape of the scattering surface of an (optically thick) protoplanetary disk projects onto the image plane of the observer. This allows us to map physical quantities (scattering radius and scattering angle) onto scattered light images and retrieve stellar irradiation corrected (r^2-scaled) images and dust phase functions. We apply the method on archival polarized intensity images of the protoplanetary disk around HD 100546 that were obtained with VLT/SPHERE in R'-band and VLT/NACO in H- and Ks-band. The brightest side of the r^2-scaled R'-band polarized intensity image of HD 100546 changes from the far to the near side of the disk when a flaring instead of a geometrically flat disk surface is used for the r^2-scaling. The decrease in polarized surface brightness in the scattering angle range of ~40-70 deg is likely a result of the dust phase function and degree of polarization which peak in different scattering angle regimes. The derived phase functions show part of a forward scattering peak which indicates that large, aggregate dust grains dominate the scattering opacity in the disk surface. Projection effects of a protoplanetary disk surface need to be taken into account to correctly interpret scattered light images. Applying the correct scaling for the correction of stellar irradiation is crucial for the interpretation of the images and the derivation of the dust properties in the disk surface layer.