Magnetic fields in circumstellar disks: The potential of Zeeman observations

Magnetic fields in circumstellar disks: The potential of Zeeman observations

Authors:

Brauer et al

Abstract:

Context.

Recent high angular resolution polarimetric continuum observations of circumstellar disks provide new insights into their magnetic field. However, direct constraints are limited to the plane of sky component of the magnetic field. Observations of Zeeman split spectral lines are a potential approach to enhance these insights by providing complementary information.

Aims.

We investigate which constraints for magnetic fields in circumstellar disks can be obtained from Zeeman observations of the 113 GHz CN lines. Furthermore, we analyze the requirements to perform these observations and their dependence on selected quantities.

Methods.

We simulate the Zeeman splitting with the radiative transfer (RT) code POLARIS (Reissl et al. 2016) extended by our Zeeman splitting RT extension ZRAD (Brauer et al. 2017), which is based on the line RT code Mol3D (Ober et al. 2015).

Results.

We find that Zeeman observations of the 113 GHz CN lines provide significant insights into the magnetic field of circumstellar disks. However, with the capabilities of recent and upcoming instrument/observatories, even spatially unresolved observations would be challenging. Nevertheless, these observations are feasible for the most massive disks with a strong magnetic field and high abundance of CN/H. The most restrictive quantity is the magnetic field strength, which should be at least in the order of ∼1 mG. In addition, the inclination of the disk should be around 60deg to preserve the ability to derive the line-of-sight (LOS) magnetic field strength and to obtain a sufficiently high circularly polarized flux.

A precessing Be disk as a possible model for occultation events in GX 304-1

A precessing Be disk as a possible model for occultation events in GX 304-1

Authors:

Kühnel et al

Abstract:

We report on the RXTE detection of a sudden increase in the absorption column density, NH, during the 2011 May outburst of GX 304-1. The NH increased up to ∼16×1022 atoms cm−2, which is a factor of 3-4 larger than what is usually measured during the outbursts of GX 304-1 as covered by RXTE. Additionally, an increase in the variability of the hardness ratio as calculated from the energy resolved RXTE-PCA light curves is measured during this time range. We interpret these facts as an occultation event of the neutron star by material in the line of sight. Using a simple 3D model of an inclined and precessing Be disk around the Be type companion, we are able to qualitatively explain the NH evolution over time. We are able to constrain the Be-disk density to be on the order of 10−11 g cm−3. Our model strengthens the idea of inclined Be disks as origin of double-peaked outbursts as the derived geometry allows accretion twice per orbit under certain conditions.

ALMA Measurements of Circumstellar Material in the GQ Lup System

ALMA Measurements of Circumstellar Material in the GQ Lup System

Authors:

MacGregor et al

Abstract:

We present ALMA observations of the GQ Lup system, a young Sun-like star with a substellar mass companion in a wide-separation orbit. These observations of 870 μm continuum and CO J=3-2 line emission with beam size ∼0.3″ (∼45 AU) resolve the disk of dust and gas surrounding the primary star, GQ Lup A, and provide deep limits on any circumplanetary disk surrounding the companion, GQ Lup b. The circumprimary dust disk is compact with a FWHM of 59±12 AU, while the gas has a larger extent with a characteristic radius of 46.5±1.8 AU. By forward-modeling the velocity field of the circumprimary disk based on the CO emission, we constrain the mass of GQ Lup A to be M∗=(1.03±0.05)∗(d/156 pc) M⊙, where d is a known distance, and determine that we view the disk at an inclination angle of 60.5∘±0.5∘ and a position angle of 346∘±1∘. The 3σ upper limit on the 870 μm flux density of any circumplanetary disk associated with GQ Lup b of <0.15 mJy implies an upper limit on the dust disk mass of <0.04 M⊕ for standard assumptions about optically thin emission. We discuss proposed mechanisms for the formation of wide-separation substellar companions given the non-detection of circumplanetary disks around GQ Lup b and other similar systems.

Grand Design Spiral Arms in A Young Forming Circumstellar Disk

Grand Design Spiral Arms in A Young Forming Circumstellar Disk

Authors:

Tomida et al

Abstract:

We study formation and long-term evolution of a circumstellar disk in a collapsing molecular cloud core using a resistive magnetohydrodynamic simulation. While the formed circumstellar disk is initially small, it grows as accretion continues and its radius becomes as large as 200 AUs toward the end of the Class-I phase. A pair of grand-design spiral arms form due to gravitational instability in the disk, and they transfer angular momentum in the highly resistive disk. Although the spiral arms disappear in a few rotations as expected in a classical theory, new spiral arms form recurrently as the disk soon becomes unstable again by gas accretion. Such recurrent spiral arms persist throughout the Class-0 and I phase. We then perform synthetic observations and compare our model with a recent high-resolution observation of a young stellar object Elias 2-27, whose circumstellar disk has grand design spiral arms. We find an excellent agreement between our theoretical model and the observation. Our model suggests that the grand design spiral arms around Elias 2-27 are consistent with material arms formed by gravitational instability. It also implies that the age of Elias 2-27 can be younger than the previous estimate.

First Detection of Hydrogen in the β Pictoris Gas Disk

First Detection of Hydrogen in the β Pictoris Gas Disk

Authors:

Wilson et al

Abstract:

The young and nearby star \beta\ Pictoris (\beta\ Pic) is surrounded by a debris disk composed of dust and gas known to host a myriad evaporating exocomets, planetesimals and at least one planet. At an edge-on inclination, as seen from Earth, this system is ideal for debris disk studies providing an excellent opportunity to use absorption spectroscopy to study the planet forming environment. Using the Cosmic Origins Spectrograph (COS) instrument on the Hubble Space Telescope (HST) we observe the most abundant element in the disk, hydrogen, through the HI Lyman \alpha\ (Ly-\alpha\) line. We present a new technique to decrease the contamination of the Ly-\alpha\ line by geocoronal airglow in COS spectra. This Airglow Virtual Motion (AVM) technique allows us to shift the Ly-\alpha\ line of the astrophysical target away from the contaminating airglow emission revealing more of the astrophysical line profile. The column density of hydrogen in the \beta\ Pic stable gas disk at the stellar radial velocity is measured to be log(NH/1cm2)≪18.5. The Ly-\alpha\ emission line profile is found to be asymmetric and we propose that this is caused by HI falling in towards the star with a bulk radial velocity of 41±6 km/s relative to \beta\ Pic and a column density of log(NH/1cm2)=18.6±0.1. The high column density of hydrogen relative to the hydrogen content of CI chondrite meteorites indicates that the bulk of the hydrogen gas does not come from the dust in the disk. This column density reveals a hydrogen abundance much lower than solar, which excludes the possibility that the detected hydrogen could be a remnant of the protoplanetary disk or gas expelled by the star. We hypothesise that the hydrogen gas observed falling towards the star arises from the dissociation of water originating from evaporating exocomets.

Explorations of Dusty Debris Disk Geometry

Explorations of Dusty Debris Disk Geometry

Authors:

Dennihy et al

Abstract:

As the sample of white dwarfs with signatures of planetary systems has grown, statistical studies have begun to suggest our picture of compact debris disk formation from disrupted planetary bodies is incomplete. Here we present the results of an effort to extend the preferred dust disk model introduced by \citet{jur03} to include elliptical geometries. We apply this model the observed distribution of fractional infrared luminosities, and explore the difference in preferred parameter spaces for a circular and highly elliptical model on a well-studied dusty white dwarf.

Protoplanetary and Transitional Disks in the Open Stellar Cluster IC 2395

Protoplanetary and Transitional Disks in the Open Stellar Cluster IC 2395

Authors:

Balog et al

Abstract:

We present new deep UBVRI images and high-resolution multi-object optical spectroscopy of the young (~ 6 - 10 Myr old), relatively nearby (800 pc) open cluster IC 2395. We identify nearly 300 cluster members and use the photometry to estimate their spectral types, which extend from early B to middle M. We also present an infrared imaging survey of the central region using the IRAC and MIPS instruments on board the Spitzer Space Telescope, covering the wavelength range from 3.6 to 24 microns. Our infrared observations allow us to detect dust in circumstellar disks originating over a typical range of radii ~ 0.1 to ~ 10AU from the central star. We identify 18 Class II, 8 transitional disk, and 23 debris disk candidates, respectively 6.5%, 2.9%, and 8.3% of the cluster members with appropriate data. We apply the same criteria for transitional disk identification to 19 other stellar clusters and associations spanning ages from ~ 1 to ~ 18 Myr. We find that the number of disks in the transitional phase as a fraction of the total with strong 24 micron excesses ([8] - [24] > 1.5) increases from 8.4 +\- 1.3% at ~ 3 Myr to 46 +\- 5% at ~ 10 Myr. Alternative definitions of transitional disks will yield different percentages but should show the same trend.

Non-axisymmetric instabilities in disks with imposed zonal flows

Non-axisymmetric instabilities in discs with imposed zonal flows

Authors:

Vanon et al

Abstract:

We conduct a linear stability calculation of an ideal Keplerian flow on which a sinusoidal zonal flow is imposed. The analysis uses the shearing sheet model and is carried out both in isothermal and adiabatic conditions, with and without self-gravity (SG). In the non-SG regime a structure in the potential vorticity (PV) leads to a non-axisymmetric Kelvin-Helmholtz (KH) instability; in the short-wavelength limit its growth rate agrees with the incompressible calculation by Lithwick (2007), which only considers perturbations elongated in the streamwise direction. The instability's strength is analysed as a function of the structure's properties, and zonal flows are found to be stable if their wavelength is ≳8H, where H is the disc's scale height, regardless of the value of the adiabatic index γ. The non-axisymmetric KH instability can operate in Rayleigh-stable conditions, and it therefore represents the limiting factor to the structure's properties. Introducing SG triggers a second non-axisymmetric instability, which is found to be located around a PV maximum, while the KH instability is linked to a PV minimum, as expected. In the adiabatic regime, the same gravitational instability is detected even when the structure is present only in the entropy (not in the PV) and the instability spreads to weaker SG conditions as the entropy structure's amplitude is increased. This eventually yields a non-axisymmetric instability in the non-SG regime, albeit of weak strength, localised around an entropy maximum.

Evidence of Magnetic Braking in the HH 111 Protostellar System?

ANGULAR MOMENTUM LOSS IN THE ENVELOPE–DISK TRANSITION REGION OF THE HH 111 PROTOSTELLAR SYSTEM: EVIDENCE FOR MAGNETIC BRAKING?

Authors:

Lee et al

Abstract:

HH 111 is a Class I protostellar system at a distance of ~400 pc, with the central source VLA 1 associated with a rotating disk deeply embedded in a flattened envelope. Here we present the observations of this system at ~0farcs6 (240 au) resolution in C18O (J = 2 — 1) and a 230 GHz continuum obtained with the Atacama Large Millimeter/Submillimeter Array, and in SO (${N}_{J}\,=\,{5}_{6}-{4}_{5}$) obtained with the Submillimeter Array. The observations show for the first time how a Keplerian rotating disk can be formed inside a flattened envelope. The flattened envelope is detected in C18O, extending out to gsim2400 au from the VLA 1 source. It has a differential rotation, with the outer part (gsim2000 au) better described by a rotation that has constant specific angular momentum, and the innermost part (lesssim160 au) by a Keplerian rotation. The rotationally supported disk is therefore relatively compact in this system, which is consistent with the dust continuum observations. Most interestingly, if the flow is in steady state, there is a substantial drop in specific angular momentum in the envelope–disk transition region from 2000 to 160 au, by a factor of ~3. Such a decrease is not expected outside a disk formed from simple hydrodynamic core collapse, but can happen naturally if the core is significantly magnetized, because magnetic fields can be trapped in the transition region outside the disk by the ram pressure of the protostellar accretion flow, which can lead to efficient magnetic braking. In addition, SO shock emission is detected around the outer radius of the disk and could trace an accretion shock around the disk.

Fragmentation of protoplanetary disks around M-dwarfs

Fragmentation of protoplanetary disks around M-dwarfs

Authors:

Backus et al

Abstract:

We investigate the conditions required for planet formation via gravitational instability (GI) and protoplanetary disk (PPD) fragmentation around M-dwarfs. Using a suite of 64 SPH simulations with 106 particles, the parameter space of disk mass, temperature, and radius is explored, bracketing reasonable values based on theory and observation. Our model consists of an equilibrium, gaseous, and locally isothermal disk orbiting a central star of mass M∗=Msol/3. Disks with a minimum Toomre Q of Qmin≲0.9 will fragment and form gravitationally bound clumps. Some previous literature has found Qmin

The circumstellar disk of FS Tau B- A self-consistent model based on observations in the mid-infrared with NACO -

The circumstellar disk of FS Tau B- A self-consistent model based on observations in the mid-infrared with NACO -

Authors:

Kirchschlager et al

Abstract:

Protoplanetary disks are a byproduct of the star formation process. In the dense mid-plane of these disks, planetesimals and planets are expected to form. The first step in planet formation is the growth of dust particles from submicrometer-sized grains to macroscopic mm-sized aggregates. The grain growth is accompanied by radial drift and vertical segregation of the particles within the disk. To understand this essential evolutionary step, spatially resolved multi-wavelength observations as well as photometric data are necessary which reflect the properties of both disk and dust. We present the first spatially resolved image obtained with NACO at the VLT in the Lp band of the near edge-on protoplanetary disk FS Tau B. Based on this new image, a previously published Hubble image in H band and the spectral energy distribution from optical to millimeter wavelengths, we derive constraints on the spatial dust distribution and the progress of grain growth. For this purpose we perform a disk modeling using the radiative transfer code MC3D. Radial drift and vertical sedimentation of the dust are not considered. We find a best-fit model which features a disk extending from 2 AU to several hundreds AU with a moderately decreasing surface density and Mdisk = 2.8 × 10−2M⊙. The inclination amounts to i = 80°. Our findings indicate that substantial dust grain growth has taken place and that grains of a size equal to or larger than 1 mm are present in the disk. In conclusion, the parameters describing the vertical density distribution are better constrained than those describing the radial disk structure.

Composite Circumstellar Dust Grains

Composite Circumstellar Dust Grains

Authors:

Gupta et al

Abstract:

We calculate the absorption efficiencies of composite silicate grains with inclusions of graphite and silicon carbide in the spectral range 5–25μm. We study the variation in absorption profiles with volume fractions of inclusions. In particular we study the variation in the wavelength of peak absorption at 10 and 18 μm. We also study the variation of the absorption of porous silicate grains. We use the absorption efficiencies to calculate the infrared flux at various dust temperatures and compare with the observed infrared emission flux from the circumstellar dust around some M-Type & AGB stars obtained from IRAS and a few stars from Spitzer satellite. We interpret the observed data in terms of the circumstellar dust grain sizes; shape; composition and dust temperature.

INVESTIGATING THE CIRCUMSTELLAR DISK OF THE Be SHELL STAR 48 LIBRAE

INVESTIGATING THE CIRCUMSTELLAR DISK OF THE Be SHELL STAR 48 LIBRAE

Authors:

Silaj et al

Abstract:

A global disk oscillation implemented in the viscous decretion disk (VDD) model has been used to reproduce most of the observed properties of the well known Be star ζ Tau. 48 Librae shares several similarities with ζ Tau—they are both early-type Be stars, display shell characteristics in their spectra, and exhibit cyclic V/R variations—but has some marked differences as well, such as a much denser and more extended disk, a much longer V/R cycle, and the absence of the so-called triple-peak features. We aim to reproduce the photometric, polarimetric, and spectroscopic observables of 48 Librae with a self-consistent model, and to test the global oscillation scenario for this target. Our calculations are carried out with the three-dimensional NLTE radiative transfer code HDUST. We employ a rotationally deformed, gravity-darkened central star surrounded by a disk whose unperturbed state is given by the VDD model. A two-dimensional global oscillation code is then used to calculate the disk perturbation and superimpose it on the unperturbed disk. A very good, self-consistent fit to the time-averaged properties of the disk is obtained with the VDD. The calculated perturbation has a period P = 12 years, which agrees with the observed period, and the behavior of the V/R cycle is well reproduced by the perturbed model. The perturbed model improves the fit to the photometric data and reproduces some features of the observed spectroscopic data. Some suggestions to improve the synthesized spectroscopy in a future work are given.

M Dwarf AWI0005x3s has Peter Pan Protoplanetary Disk

A group of citizen scientists and professional astronomers, including Carnegie's Jonathan Gagné, joined forces to discover an unusual hunting ground for exoplanets. They found a star surrounded by the oldest known circumstellar disk--a primordial ring of gas and dust that orbits around a young star and from which planets can form as the material collides and aggregates.

Led by Steven Silverberg of University of Oklahoma, the team described a newly identified red dwarf star with a warm circumstellar disk, of the kind associated with young planetary systems. Circumstellar disks around red dwarfs like this one are rare to begin with, but this star, called AWI0005x3s, appears to have sustained its disk for an exceptionally long time. The findings are published by The Astrophysical Journal Letters.

"Most disks of this kind fade away in less than 30 million years," said Silverberg. "This particular red dwarf is a candidate member of the Carina stellar association, which would make it around 45 million years old [like the rest of the stars in that group]. It's the oldest red dwarf system with a disk we've seen in one of these associations."

link.

Watching the Variation in Composition of the Debris Disk Around White Dwarf WD 1145+017

Spectroscopic Evolution of Disintegrating Planetesimals: Minutes to Months Variability in the Circumstellar Gas Associated with WD 1145+017

Authors:

Redfield et al

Abstract:

With the recent discovery of transiting planetary material around WD 1145+017, a critical target has been identified that links the evolution of planetary systems with debris disks and their accretion onto the star. We present a series of observations, five epochs over a year, taken with Keck and the VLT, which for the first time show variability of circumstellar absorption in the gas disk surrounding WD 1145+017 on timescales of minutes to months. Circumstellar absorption is measured in more than 250 lines of 14 ions among ten different elements associated with planetary composition, e.g., O, Mg, Ca, Ti, Cr, Mn, Fe, Ni. Broad circumstellar gas absorption with a velocity spread of 225 km/s is detected, but over the course of a year blue shifted absorption disappears while redshifted absorption systematically increases. A correlation of equivalent width and oscillator strength indicates that the gas is not highly optically thick (median tau approximately 2). We discuss simple models of an eccentric disk coupled with magnetospheric accretion to explain the basic observed characteristics of these high resolution and high signal-to-noise observations. Variability is detected on timescales of minutes in the two most recent observations, showing a loss of redshifted absorption for tens of minutes, coincident with major transit events and consistent with gas hidden behind opaque transiting material. This system currently presents a unique opportunity to learn how the gas causing the spectroscopic, circumstellar absorption is associated with the ongoing accretion evidenced by photospheric contamination, as well as the transiting planetary material detected in photometric observations.

Variability of the planetary debris disc at the white dwarf SDSS J104341.53+085558.2

Another one grinds the dust: Variability of the planetary debris disc at the white dwarf SDSS J104341.53+085558.2

Authors:

Manser et al

Abstract:

We report nine years of optical spectroscopy of the metal-polluted white dwarf SDSS J104341.53+085558.2, which presents morphological variations of the line profiles of the 8600 \AA\ Ca II triplet emission from the gaseous component of its debris disc. Similar changes in the shape of the Ca II triplet have also been observed in two other systems that host a gaseous disc, and are likely related to the same mechanism. We report the Mg, Si, and Ca abundances of the debris detected in the photosphere of SDSS J1043+0855, place upper limits on O and Fe, and derive an accretion rate of (2.5 - 12)x108 g/s, consistent with those found in other systems with detected debris discs. The Mg/Si ratio and the upper limit on the Fe/Si ratio of the accreted material broadly agree with those found for the crust of the Earth. We also review the range of variability observed among white dwarfs with planetary debris discs.

Planetary engulfment as a trigger for white dwarf pollution

Planetary engulfment as a trigger for white dwarf pollution 

Authors:

Petrovich et al

Abstract:

The presence of a planetary system can shield a planetesimal disk from the secular gravitational perturbations due to distant outer massive objects (planets or stellar companions). As the host star evolves off the main sequence to become a white dwarf, these planets can be engulfed, triggering secular instabilities and leading to the tidal disruptions of small rocky bodies. These disrupted bodies can feed the white dwarfs with rocky material and possibly explain the high-metallicity material in their atmospheres. We illustrate how this mechanism can operate when the gravitational perturbations are due to the Kozai-Lidov mechanism from a stellar binary companion. We show that this mechanism can explain the observed levels of accretion if: (1) the planetary engulfment happens fast compared to the secular timescale, which is generally the case for wide binaries (>100 AU) and planetary engulfment during the Asymptotic Giant Branch; (2) the planetesimal disk has a total mass of ∼10−4−10−2M⊕. We show that this new mechanism can provide a steady supply of material throughout the entire life of the white dwarfs for all cooling ages and can account for a large fraction (up to nearly half) of the observed polluted WDs.

Dipper disks not inclined towards edge-on orbits

Dipper disks not inclined towards edge-on orbits

Authors:

Ansdell et al

Abstract:

The so-called "dipper" stars host circumstellar disks and have optical and infrared light curves that exhibit quasi-periodic or aperiodic dimming events consistent with extinction by transiting dusty structures orbiting in the inner disk. Most of the proposed mechanisms explaining the dips---i.e., occulting disk warps, vortices, and forming planetesimals---assume nearly edge-on viewing geometries. However, our analysis of the three known dippers with publicly available resolved sub-mm data reveals disks with a range of inclinations, most notably the face-on transition disk J1604-2130 (EPIC 204638512). This suggests that nearly edge-on viewing geometries are not a defining characteristic of the dippers and that additional models should be explored. If confirmed by further observations of more dippers, this would point to inner disk processes that regularly produce dusty structures far above the outer disk midplane in regions relevant to planet formation.

RAPID CIRCUMSTELLAR DISK EVOLUTION AND AN ACCELERATING STAR FORMATION RATE IN THE INFRARED DARK CLOUD M17 SWex

RAPID CIRCUMSTELLAR DISK EVOLUTION AND AN ACCELERATING STAR FORMATION RATE IN THE INFRARED DARK CLOUD M17 SWex

Authors:

Povich et al

Abstract:

We present a catalog of 840 X-ray sources and first results from a 100 ks Chandra X-ray Observatory imaging study of the filamentary infrared (IR) dark cloud G014.225–00.506, which forms the central regions of a larger cloud complex known as the M17 southwest extension (M17 SWex). In addition to the rich population of protostars and young stellar objects with dusty circumstellar disks revealed by archival data from the Spitzer Space Telescope, we discover a population of X-ray-emitting, intermediate-mass pre-main-sequence stars that lack IR excess emission from circumstellar disks. We model the IR spectral energy distributions of this source population to measure its mass function and place new constraints on the destruction timescales for the inner dust disk for 2–8 M ☉ stars. We also place a lower limit on the star formation rate (SFR) and find that it is quite high ($\dot{M}\geqslant 0.007$ M ☉ yr−1), equivalent to several Orion Nebula Clusters in G14.225–0.506 alone, and likely accelerating. The cloud complex has not produced a population of massive, O-type stars commensurate with its SFR. This absence of very massive (gsim20 M ☉) stars suggests that either (1) M17 SWex is an example of a distributed mode of star formation that will produce a large OB association dominated by intermediate-mass stars but relatively few massive clusters, or (2) the massive cores are still in the process of accreting sufficient mass to form massive clusters hosting O stars.

Polarimetry and flux distribution in the debris disk around HD 32297

Polarimetry and flux distribution in the debris disk around HD 32297

Authors:

Asensio-Torres et al

Abstract:

We present high-contrast angular differential imaging (ADI) observations of the debris disk around HD 32297 in H-band, as well as the first polarimetric images for this system in polarized differential imaging (PDI) mode with Subaru/HICIAO. In ADI, we detect the nearly edge-on disk at >5sigma levels from ~0.45 arcsec to ~1.7 arcsec (50-192 AU) from the star and recover the spine deviation from the midplane already found in previous works. We also find for the first time imaging and surface brightness (SB) indications for the presence of a gapped structure on both sides of the disk at distances of ~0.75 arcsec (NE side) and ~0.65 arcsec (SW side). Global forward-modelling work delivers a best-fit model disk and well-fitting parameter intervals that essentially match previous results, with high-forward scattering grains and a ring located at 110 AU. However, this single ring model cannot account for the gapped structure seen in our SB profiles. We create simple double ring models and achieve a satisfactory fit with two rings located at 60 and 95 AU, respectively, low-forward scattering grains and very sharp inner slopes. In polarized light we retrieve the disk extending from ~0.25-1.6 arcsec, although the central region is quite noisy and high S/N are only found in the range ~0.75-1.2 arcsec. The disk is polarized in the azimuthal direction, as expected, and the departure from the midplane is also clearly observed. Evidence for a gapped scenario is not found in the PDI data. We obtain a linear polarization degree of the grains that increases from ~10% at 0.55 arcsec to ~25% at 1.6 arcsec. The maximum is found at scattering angles of ~90degrees, either from the main components of the disk or from dust grains blown out to larger radii.