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Antranik A. Sefilian

Publications and source records attributed to Antranik A. Sefilian.

At least 19 recordsLinked to original sources
arXiv2026

Planet forming disk populations and their connection to the environment

Existing sub-mm observatories such as ALMA have provided statistics on the planet-forming mass reservoirs within circumstellar disks around stars in stellar clusters out to distances of $\sim$400pc. However, these disks are not where most planets form. Many stars, and hence planets, form in more massive clusters, which are only found at larger distances. Environmental conditions that affect disks - such as UV radiation field, ambient gaseous mass reservoir, and stellar density - change significantly as a function of cluster mass, implying that our current knowledge of the disk population from current facilities is severely biased. Characterising planet formation in stellar clusters towards the peak of the cluster mass function requires determining the distribution of planet forming disk masses out to $\sim$3kpc, which encapsulates the nearby parts of the Sagittarius arm of the Milky Way and contains multiple massive stellar clusters. ALMA2040 will provide the leap in sensitivity needed to move beyond detections of only a handful of disks and robustly measure the slope and median of the disk mass distribution at these distances. This will mark the transition from studying individual detections to population-level studies of planet formation across diverse cluster environments. This has synergy with existing and upcoming measurements of accretion rates in these distant clusters, which combined provide a measure of the accretion timescale, enabling us to distinguish various evolutionary pathways and assess how they depend on cluster mass and star-forming environment.

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arXiv2026

How eccentric is the debris disk of epsilon Eridani? ALMA reveals a near-circular belt

The nearby (3.2 pc) K2V star $ε$ Eridani hosts the closest detected debris disk and an exo-Jupiter analog ($ε$ Eridani b). In this work, we reanalyse ALMA Band 6 (1.29 mm) observations of $ε$ Eridani to assess whether its outer debris belt exhibits a non-zero eccentricity, potentially induced by planet-disk interactions. Considering two models, one that accounts for the disk's forced eccentricity ($e_\mathrm{f}$) and another that accounts for a proper eccentricity ($e_\mathrm{p}$), we place stringent (99.7th-percentile) upper limits of $e_\mathrm{f} < 2.6\%$ and $e_\mathrm{p} < 6.8\%$, respectively, and find tentative evidence for a non-zero forced eccentricity of $e_\mathrm{f} = 1.62^{+0.39}_{-0.40}\%$ at the $4σ$ level. This corresponds to the lowest millimeter-derived upper limit on the forced eccentricity of any debris disk to date, which, together with the low upper limit on the proper eccentricity, suggests that the outer belt is nearly circular and dynamically cold. We further explore planetary system architectures that are consistent with these ALMA-based results in combination with Spitzer/IRAC, JWST/NIRCam F444W, and JWST/MIRI F2550W data. Together, these analyses provide insight into potential planet-disk interactions in this nearby system, constraining any additional planet beyond $ε$ Eridani b to masses ranging from $\sim 2\times10^{-4}$ to $0.3\,M_\mathrm{Jup}$ at orbital separations of $\sim 6$-$60$ au.

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arXiv2026

Deep HST/STIS Coronagraphic Imaging of the $β$ Pictoris Debris Disk: On the Scattered Light Component of the Cat's Tail

The $β$ Pictoris debris disk is a unique system where mid-infrared coronagraphic imaging with JWST/MIRI revealed a new spatially resolved substructure known as the Cat's Tail. We present deep HST/STIS coronagraphic imaging of $β$ Pic in scattered light, combining six epochs of observations between 2012 and 2025, in search of the scattered light component of the Cat's Tail. We detect the disk out to a projected separation of 500 au for the first time with HST/STIS, achieving SNR > 100 across much of the midplane between 50 and 200 au. We report the detection of the visible/near-infrared scattered light component of the Cat's Tail substructure. We find through injection-recovery analysis that the scattered light component of the Cat's Tail has a total flux of $0.1-0.4\%$ of the MIRI F1550C flux. Using the measured STIS-to-MIRI flux ratio, we model the Cat's Tail grain properties and find that the grains are highly porous and almost entirely composed of organic refractory material, which is in agreement with findings with JWST/MIRI. We use the organics content of Solar System dwarf planets and dust in the local ISM as a proxy to estimate the size of the colliding progenitors that can produce enough organic refractory material seen in the Cat's Tail. We find that each colliding progenitor must have a mass of at least $1-3\times 10^{21}$ kg, comparable to Charon and Makemake in our Kuiper Belt. Additionally, we find a prominent warped morphology and surface brightness asymmetry in the outer dust halo of $β$ Pic. We compare the observed halo morphology and asymmetry to predicted vertical structures, which may arise from planet--disk interactions.

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arXiv2026

The JWST/NIRCam Scattered Light Disks GTO 2780 program: panchromatic coronagraphic imaging of the HD 10647, HD 32297, HD 61005, HD 107146, and HD 181327 debris disk systems

Debris disks, composed of rocks, boulders, planetesimals, and the dust produced in their collisions, present the most readily observable components of mature planetary systems. They also serve as valuable diagnostic tools, enabling studies of planetary dynamical interactions and mineral compositions. Observed from optical to radio wavelengths, each band reveals unique information about the dust populations. Optical and near-infrared observations are specifically sensitive to light scattered off the surfaces of the micron-sized particles. Here, we present results from the JWST/NIRCam GTO program 2780, designed to observe five disk systems previously identified to be exceptionally bright at optical wavelengths (HD 10647, HD 32297, HD 61005, HD 107146, and HD 181327) with six filters using the NIRCam coronagraphs. The NIRCam data complement previous shorter-wavelength images of these same systems. They reveal scattered light from the disks and from the extended halos of tiny grains under the influence of radiative forces, at high resolution and signal to noise. All the systems show evidence for water ice, although it can have differing radial distributions and tends to show stronger signatures in the halos. In the two cases we could analyze, the scattering phase function in the disks resembles the behavior of dust in the Solar System with evidence for enhanced forward scattering in the halos, consistent with the latter being composed of tiny grains. MIRI images for two systems are more centrally concentrated than the shorter wavelength ones, suggesting a role for dragged-in larger grains.

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arXiv2026

Viscously Stirring Particle Disks into Lorentzians and Gaussians to Infer Dynamical and Collisional Masses (ARKS XIII)

Disks (Keplerian or otherwise, particulate or fluid) are often assumed to have densities that drop off vertically as Gaussians. Recent mm-wave imaging of circumstellar debris disks contradicts this assumption, revealing vertical profiles in dust that resemble Lorentzians. As part of the ARKS ALMA Large Program, we show how Lorentzians and Gaussians define an evolutionary sequence for disks of gravitationally scattering (viscously stirring) particles. When orbits are crossing and eccentricities $e \gg$ inclinations $i$, each scattering can change a particle's inclination by $\pm \,Δi \propto i$. A random walk with fixed steps in $Δi/i = Δ\ln i$ produces a thick, log normal tail at large $i$ that leads to Lorentzian tails in density. This result holds independent of the origin of the large eccentricities, which may characterize either the stirrers or the objects being stirred; what matters is that relative motions parallel to the disk midplane are faster than perpendicular motions, and that vertical displacements during encounters are smaller than horizontal displacements. After enough scatterings, $i$ comes into equipartition with $e$, $Δi$ stops exponentiating, and the vertical density relaxes to a Gaussian. We identify four regimes of dispersion-dominated viscous stirring, three of which are out-of-equipartition and where $i$ is stirred faster than $e$. The stirrers for ARKS debris disks may range from Pluto to a few times Mars in size, and be sufficiently few as to be collisionless. Or the stirrers may be even smaller, and be so numerous and collide so frequently that they source the collisional cascades that produce observable dust.

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arXiv2026

Debris Disc Substructures Induced by Secular Planetary Perturbations

Observations of debris discs have the potential to provide us with valuable information about massive planets perturbing them gravitationally. In this work, we explore the evolution of the azimuthally-averaged (or axisymmetric) surface density (ASD) -- a characteristic routinely derived from observations -- in a disc secularly perturbed by an inner planet. We develop detailed analytical understanding of ASD evolution and verify it using a novel numerical framework DebrisPy, which we make publicly available. With these tools we show that in a secularly evolving disc ASD develops a set of sharp features -- weakly discontinuous peaks at eccentricity nulls and sharp discontinuities at caustic points where particle periastra or apoastra pile up -- marching out through the disc as it ages. We probe the dependence of these features on planetary eccentricity, ratio of the free to forced particle eccentricity, and underlying radial mass distribution, showing in particular that more eccentric planets produce more prominent ASD features. Convolution with the PSF of realistic observations (as well as the non-zero random free eccentricity of debris) smooths out these features, but they can still be detectable in high-resolution observations. Radial locations of secular ASD peaks follow a particular, well-defined pattern, which should unambiguously point to their secular nature in observations. We illustrate how both detection and non-detection of such secular features in observed discs can be used (in combination with other constraints) to measure or constrain key parameters of perturbing planets (even those not yet detected) -- mass, semi-major axis and eccentricity.

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arXiv2026

Extreme Debris Disks: Insights into Violent Collisions in Planet Formation and Destruction

Debris disks are dusty structures around mature stars, primarily identified by infrared excesses in the stellar spectra. A subset, known as extreme debris disks (EDDs), exhibits stochastic infrared variability, believed to result from large-scale violent collisions that contribute to the formation or destruction of rocky planetary bodies. We analyze JWST and Spitzer mid-infrared spectra for 21 EDDs to investigate the connection between impact-produced dust mineralogy and the age and dynamical state of these systems during various stages of planet formation and evolution. Our findings indicate that EDDs contain significantly more optically thin, small dust grains compared to those typically seen in protoplanetary and debris disks. Predominantly submicron in size, these grains are thermally altered, as shown by their high levels of silica and crystalline silicate composition. Along with stochastic infrared variability, these features define EDDs as a subclass of debris systems where dust is generated from large collisions between Moon- and Mars-sized bodies. Our results not only provide diagnostic information about the physical conditions of violent events during terrestrial planet formation, aiding in differentiating the complex outcomes of these impacts, but also offer a potential marker for identifying planetary systems experiencing dynamical instability.

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arXiv2026

A radially broad collisional cascade in the debris disk of $γ$ Ophiuchi observed by JWST

The A1V star $γ$ Oph, at a distance of 29.7 pc, is known from Spitzer imaging to host a debris disk with a large radial extent and from its spectral energy distribution to host inner warm dust. We imaged $γ$ Oph with JWST/MIRI at 15 and 25.5 $μ$m, revealing smooth and radially broad emission that extends to a radius of at least 250 au at 25.5 $μ$m. In contrast to JWST findings of an inner small-grain component with distinct ringed structures in Fomalhaut and Vega, the mid-infrared radial profile combined with prior ALMA imaging suggests a radially broad steady-state collisional cascade with the same grain size distribution throughout the disk. This further suggests that the system is populated by a radially broad planetesimal belt from tens of au or less to well over 200 au, rather than a narrow planetesimal belt from which the observed dust is displaced to appear broad. The disk is also found to be asymmetric, which could be modelled by a stellocentric offset corresponding to a small eccentricity of $\sim$0.03. Such a disk eccentricity could be induced by a mildly eccentric $<10\,M_\mathrm{Jup}$ giant planet outside 10 au, or a more eccentric companion up to stellar mass at a few au, without producing a resolvable radial gap in the disk.

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arXiv2026

The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) II. The radial structure of debris discs

The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) was recently completed to cover the lack of high-resolution observations of debris discs and to investigate the prevalence of substructures such as radial gaps and rings in a sample of 24 discs. This study characterises the radial structure of debris discs in the ARKS programme. To identify and quantify the disc substructures, we modelled all discs with a range of non-parametric and parametric approaches. We find that of the 24 discs in the sample, 5 host multiple rings, 7 are single rings that display halos or additional low-amplitude rings, and 12 are single rings with at most tentative evidence of additional substructures. The fractional ring widths that we measured are significantly narrower than previously derived values, and they follow a distribution similar to the fractional widths of individual rings resolved in protoplanetary discs. However, there exists a population of rings in debris discs that are significantly wider than those in protoplanetary discs. We also find that discs with steep inner edges consistent with planet sculpting tend to be found at smaller (<100 au) radii, while more radially extended discs tend to have shallower edges more consistent with collisional evolution. An overwhelming majority of discs have radial profiles well-described by either a double power law or double-Gaussian parametrisation. While our findings suggest that it may be possible for some debris discs to inherit their structures directly from protoplanetary discs, there exists a sizeable population of broad debris discs that cannot be explained in this way. Assuming that the distribution of millimetre dust reflects the distribution of planetesimals, mechanisms that cause rings in protoplanetary discs to migrate or debris discs to broaden soon after formation may be at play, possibly mediated by planetary migration or scattering.

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arXiv2026

The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) III: The vertical structure of debris disks

Debris disks -- collisionally sustained belts of dust and sometimes gas around main sequence stars -- are remnants of planet formation processes and are found in systems ${\gtrsim}10$ Myr old. Millimeter-wavelength observations are particularly important, as the grains probed by these observations are not strongly affected by radiation pressure and stellar winds, allowing them to probe the dynamics of large bodies producing dust. The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) is analyzing high-resolution observations of 24 debris disks to enable the characterization of debris disk substructures across a large sample for the first time. For the most highly inclined disks, it is possible to recover the vertical structure of the disk. We aim to model and analyze the most highly inclined systems in the ARKS sample in order to uniformly extract the vertical dust distributions for a sample of well-resolved debris disks. We employed both parametric and nonparametric methods to constrain the vertical dust distributions for the most highly inclined ARKS targets. We find a broad range of aspect ratios, revealing a wide diversity in vertical structure, with a range of best-fit parametric values of $0.0026 \leq h_{\rm HWHM} \leq 0.193$ and a median best-fit value of $h_{\rm HWHM}=0.021$. The results obtained by nonparametric modeling are generally consistent with the parametric modeling results. We find that five of the 13 disks are consistent with having total disk masses less than that of Neptune (17 $M_{\oplus}$), assuming stirring by internal processes (self-stirring and collisional and frictional damping). Furthermore, most systems show a significant preference for a Lorentzian vertical profile rather than a Gaussian.

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arXiv2026

The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) IX: Gas-driven origin for the continuum arc in the debris disc of HD 121617

Debris discs were long considered to be largely gas-free environments governed by collisional fragmentation, gravitational stirring, and radiative forces. Recent CO detections show that gas is present, but its abundance and origin remain uncertain. The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) revealed a narrow gas and dust ring in the disc HD 121617 with an asymmetric arc 40% brighter than the rest of the ring. We aim to constrain the total gas mass in HD 121617 assuming the dust arc is produced by hydrodynamical gas-dust interactions. We used the Dusty FARGO-ADSG code, modelling dust as Lagrangian particles, including radiation pressure and dust feedback, and varying the total gas mass. Simulations were compared to observations using radiative transfer. An unstable gas ring creates a size-dependent radial and azimuthal dust trap whose efficiency depends on gas mass. Two models, with 50 and 5 Earth masses of gas, reproduce both the ALMA band 7 arc and the outward offset of the VLT/SPHERE scattered-light ring via gas drag and radiation pressure. We infer a conservative gas-mass range of 2.5 to 250 Earth masses. If the ALMA asymmetry is caused by gas drag, the required gas mass compared with the observed CO implies substantial H2, consistent with primordial gas. HD 121617 would then be a hybrid disc between protoplanetary and debris stages. Since a planet could also create an arc, future observations are needed to distinguish these scenarios.

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arXiv2025

Testing the Impact of Planet-stirring, Self-stirring, and Mixed-stirring on Debris Disc Architecture: A Case Study of HD 16743

Dynamical interactions between planets and debris discs can excite the orbits of embedded planetesimals to such a degree that a collisional cascade is triggered, generating detectable amounts of dust. Millimetre wavelength observations are sensitive to emission from large and cold dust grains, which are unperturbed by radiation forces and act as a proxy for the location of the planetesimals. The influence of unseen planetary companions on debris discs can be inferred with high-resolution imaging observations at millimetre wavelengths, tracing the radial and vertical structure of these belts. Here we present a set of $N$-body simulations modelling ALMA observations of the HD~16743 debris disc. We consider a range of relative contributions from either a single planetary companion and/or a set of embedded massive planetesimals to reproduce the disc's observed radial and vertical structure. We compare our dynamical results for the limiting cases of planet-stirring and self-stirring, finding them to be consistent with theoretical expectations for each scenario. For the case of HD~16743, we find that a set of massive planetesimals on mildly eccentric orbits, confined to a relatively narrow range of semimajor axes (compared to the observed belt width), offers the best results to reproduce the vertical and radial extent of the observed emission. Our findings constrain the total planet-disk system mass. A combined giant and dwarf planet mass of $\geq~27~M_{\oplus}$ can reproduce the observed architecture, with the equipartition scenario requiring only half the disc mass of the self-stirring scenario.

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arXiv2025

JWST/MIRI Imaging of the Warm Dust Component of the Epsilon Eridani Debris Disk

We present JWST/MIRI observations of the debris disk surrounding the nearby, solar analog Epsilon Eridani obtained as part of the Archetypal Debris Disk GTO program. Multi-wavelength images from 15, 18, 21, and 25.5 $μm$ show a smooth dust distribution with no evidence of sculpting by massive planets outside of 5 au. Maps of the color temperature and opacity constrain the dust properties while radiative transfer modeling of a warm dust component traces the interaction between the debris disk and Epsilon Eri b ($\sim$3.5 au). Dynamical and collisional modeling further shows that the disk morphology is dominated by dust produced in the outer planetesimal belt ($\sim 70 \, au$) moving inward via stellar wind drag. We confirm the presence of a disk interior to the Epsilon Eri b orbit first detected from mid-IR interferometry. Drag dominated inner disk regions have also been observed around Vega and Fomalhaut hinting at the diversity of asteroid belt analogs.

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arXiv2025

The polar debris disc around 99 Herculis: A potential signpost for polar circumbinary planets

The nearby binary star system 99 Herculis (99 Her) is host to the only known polar-aligned circumbinary debris disc. We investigate the hypothesis that the narrow structure of this circumbinary disc is sculpted by the gravitational influence of one or more unseen polar circumbinary planets. We first establish the theoretically viable parameter space for a sculpting planet by considering dynamical stability and clearing mechanisms, including the chaotic zone, Hill radius, diffusion, and polar alignment timescales. We then use $N$-body simulations to test three specific architectures: a single planet interior to the disc, a single planet exterior, and a two-planet system bracketing the disc. Our simulations demonstrate that single-planet models are insufficient to reproduce the observed morphology, as they can only truncate one edge of the disc while leaving the other dynamically extended. In contrast, the two-planet shepherding model successfully carves both the inner and outer edges, confining the debris into a narrow, stable polar ring consistent with observations. We conclude that the structure of the 99 Her debris disc is most plausibly explained by the presence of two shepherding, polar circumbinary planets. We present a specific, testable model for this unique system, which elucidates the pivotal role of planetary bodies in sculpting the architecture of debris discs.

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arXiv2025

The vertical structure of debris discs and the role of disc gravity: A primer using a simplified model

Debris discs provide valuable insights into the formation and evolution of exoplanetary systems. Their structures are commonly attributed to planetary perturbations, serving as probes of as-yet-undetected planets. However, most studies of planet-debris disc interactions ignore the disc's gravity, treating it as a collection of massless planetesimals. Here, using an analytical model, we investigate how the vertical structure of a back-reacting debris disc responds to secular perturbations from an inner, inclined planet. Considering the disc's axisymmetric potential, we identify two dynamical regimes: planet-dominated and disc-dominated, which may coexist, separated by a secular-inclination resonance. In the planet-dominated regime ($M_d/m_p\ll1$), we recover the classical result: a transient warp propagates outward until the disc settles into a box-like structure centered around the planetary orbit's initial inclination $I_p(0)$, with a distance-independent aspect ratio $\mathcal{H}(R)\approx I_p(0)$. In contrast, in the disc-dominated regime ($M_d/m_p\gtrsim1$), the disc exhibits dynamical rigidity, remaining thin and misaligned, with significantly suppressed inclinations and a sharply declining aspect ratio, $\mathcal{H}(R)\propto I_p(0)R^{-7/2}$. In the intermediate regime ($M_d/m_p\lesssim1$), the system exhibits a secular-inclination resonance, leading to long-lived, warp-like structures and a bimodal inclination distribution, containing both dynamically hot and cold populations. We provide analytic formulae describing these effects as a function of system parameters. We also find that the vertical density profile is intrinsically non-Gaussian and recommend fitting observations with non-zero slopes of $\mathcal{H}(R)$. Our results may be used to infer planetary parameters and debris disc masses based on observed warps and scale heights, as demonstrated for HD 110058 and $β$ Pic.

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arXiv2025

The Influence of Cold Jupiters in the Formation of Close-in planets. II. Collisional Growth of Planetesimals

Exoplanet observations have shown that the occurrence and orbital architectures of close-in super-Earths and sub-Neptunes are shaped by the presence of outer gas giant planets. This influence may emerge during the formation stage or from later dynamical evolution by a yet elusive physical process. In this work, we investigate the early stages of planetesimal accretion, modeling the joint collisional and dynamical evolution of planetesimals under the gravitational influence of a cold Jupiter and a viscously-dissipating massive protoplanetary disk. We find that an initially extended planetesimal disk of small ($\sim 1-10$ km) bodies evolves into massive, compact ($Δa/a\lesssim 0.1$) rings of several Earth masses in Moon-sized objects centered at $\sim0.1-0.5$ au. This prevalent outcome is the result of an initial stage of planetesimal accretion over the first 10 kyrs, followed by orbital transport driven by a secular apsidal resonance sweeping inward on Myr timescales. Our findings highlight the crucial role of giant planets in redistributing solids within the inner disk. This redistribution of planetary building blocks may help explain why systems with giant companions often depart from the "peas-in-a-pod" architecture.

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arXiv2025

ALMA Reveals an Eccentricity Gradient in the Fomalhaut Debris Disk

We present evidence of a negative eccentricity gradient in the debris disk of the nearby A-type main sequence star, Fomalhaut. Fitting to the high-resolution, archival ALMA 1.32 mm continuum data for Fomalhaut (with a synthesised angular resolution of $0.76{\times}0.55''$; 4-6\,au), we present a model that describes the bulk properties of the disk (semi-major axis, width, and geometry) and its asymmetric morphology. The best-fit model incorporates a forced eccentricity gradient that varies with semi-major axis, $e_f\propto a^{n_\mathrm{pow}}$, a generalized form of the parametric models of Lynch & Lovell 2022, with $n_\mathrm{pow}{=}{-1.75}{\pm}0.16$. We show that this model is statistically preferred to models with constant forced and free eccentricities. In comparison to disk models with constant forced eccentricities, negative eccentricity gradient models broaden disk widths at pericenter versus apocenter, and increase disk surface densities at apocenter versus pericenter, both of which are seen in the Fomalhaut disk, and which we collectively term Eccentric Velocity Divergence. We propose single-planet architectures consistent with the model and investigate the stability of the disk over 440 Myr to planet-disk interactions via N-body modeling. We find that Fomalhaut's ring eccentricity plausibly formed during the protoplanetary disk stage, with subsequent planet-disk interactions responsible for carving the disk morphology.

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arXiv2024

Massive Debris Disks May Hinder Secular Stirring by Planetary Companions: An Analytic Proof of Concept

Debris disks or exo-Kuiper belts, detected through their thermal or scattered emission from their dusty components, are ubiquitous around main-sequence stars. Since dust grains are short-lived, their sustained presence is thought to require dynamical excitation, i.e., "stirring", of a massive reservoir of large planetesimals, such that mutual collisions are violent enough to continually supply fresh dust. Several mechanisms have been proposed to explain debris disk stirring, with the commonly accepted being long-term, secular planet-debris disk interactions. However, while effective, existing planet-stirring models are rudimentary; namely, they ignore the (self-)gravity of the disk, treating it as a massless reservoir of planetesimals. Here, using a simple analytical model, we investigate the secular interactions between eccentric planets and massive, external debris disks. We demonstrate that the disk gravity drives fast apsidal precession of both planetesimal and planetary orbits, which, depending on the system parameters, may well exceed the planet-induced precession rate of planetesimals. This results in strong suppression of planetesimal eccentricities and thus relative collisional velocities throughout the disk, often by more than an order of magnitude when compared to massless disk models. We thus show that massive debris disks may hinder secular stirring by eccentric planets orbiting near, e.g., the disk's inner edge, provided the disk is more massive than the planet. We provide simple analytic formulae to describe these effects. Finally, we show that these findings have important implications for planet inferences in debris-bearing systems, as well as for constraining the total masses of debris disks (as done for $β$ Pic).

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