Total Disk Mass Research Articles

A Dust-trapping Ring in the Planet-hosting Disk of Elias 2-24

Rings and gaps are among the most widely observed forms of substructure in protoplanetary disks. A gap–ring pair may be formed when a planet carves a gap in the disk, which produces a local pressure maximum following the gap that traps inwardly drifting dust grains and appears as a bright ring owing to the enhanced dust density. A dust-trapping ring would provide a promising environment for solid growth and possibly planetesimal production via the streaming instability. We present evidence of dust trapping in the bright ring of the planet-hosting disk Elias 2-24, from the analysis of 1.3 and 3 mm Atacama Large Millimeter/submillimeter Array observations at high spatial resolution (0.″029, 4.0 au). We leverage the high spatial resolution to demonstrate that larger grains are more efficiently trapped and place constraints on the local turbulence (8 × 10−4 < α turb < 0.03) and the gas-to-dust ratio (Σ g /Σ d < 30) in the ring. Using a scattering-included marginal probability analysis, we measure a total dust disk mass of Mdust=13.8−0.5+0.7×10−4M⊙ . We also show that at the orbital radius of the proposed perturber the gap is cleared of material down to a flux contrast of 10−3 of the peak flux in the disk.

AB Aur, a Rosetta stone for studies of planet formation

Context. Observational constraints on dust properties in protoplanetary disks are key to better understanding disk evolution, their dynamics, and the pathway to planet formation, but also surface chemistry, the main driver of chemical complexity. Aims. We continue our exploration of the protoplanetary disk around AB Aur by characterizing its dust properties at different millimeter wavelengths. Methods. We present new ALMA observations at 2.2 mm and VLA observations at 6.8 mm. Together with previous ALMA and NOEMA observations at 0.87 and 1.1 mm, these new observations are used to compute global spectral index profiles as well as spectral index maps to probe the dust properties throughout the disk. On the interpretation side, we present the results of a simple isothermal slab model to help constrain dust properties along the non-axisymmetric ring of continuum emission outside the millimeter cavity. We also present new results of dust radiative transfer calculations based on a disk-planet hydrodynamical simulation to explain how the azimuthal contrast ratio of the ring emission varies with millimeter wavelength. Results. The spectral energy distribution and the radial profiles of the spectral index indicate that the radiation from the compact source towards the center is not dominated by dust thermal emission, but most likely by free-free emission originating in the radio jet; it constitutes 93% of the emission at 6.8 mm, and 37% at 0.87 mm. The protoplanetary disk has a typical spectral index of 2.3, computed using the 0.87, 1.1, and 2.2 mm bands. We estimate a dust disk mass of 8 × 10−5 M⊙ which, assuming a mean gas-to-dust ratio of 40, gives a total disk mass of 3.2 × 10−3 M⊙. The azimuthal contrast ratio of the ring outside the millimeter cavity is smaller at 2.2 mm than at 1.1 mm, in agreement with previous findings. The VLA image shows several knots of 5σ emission all along the ring, which, with the help of our dust radiative transfer calculations, are consistent with the ring emission being nearly axisymmetric at that wavelength. The decrease in the azimuthal contrast ratio of the ring emission from 0.87 to 6.8 mm can be explained by a dust-losing decaying vortex at the outer edge of a planet gap.

Constraining the gas mass of Herbig disks using CO isotopologues

Context. The total disk mass sets the formation potential for exoplanets. Obtaining the disk mass is however not an easy feat, as one needs to consider the optical thickness, temperature, photodissociation, and freeze-out of potential mass tracers. Carbon-monoxide (CO) has been used as a gas mass tracer in T Tauri disks, but was found to be less abundant than expected due to the freeze-out and chemical conversion of CO on the surfaces of cold dust grains. The disks around more massive intermediate mass pre-main sequence stars called Herbig disks are likely to be warmer, allowing for the possibility of using CO as a more effective total gas mass tracer. Aims. This work aims to obtain the gas mass and size of Herbig disks observed with ALMA and compare these to previous works on T Tauri disks and debris disks. Methods. Using ALMA archival data and new NOEMA data of 12CO, 13CO, and C 18O transitions of 35 Herbig disks within 450 pc, the masses were determined using the thermo-chemical code Dust And Lines (DALI). A grid of models was run spanning five orders of magnitude in disk mass, for which the model CO line luminosities could be linked to the observed luminosities. Survival analysis was used to obtain cumulative distributions of the resulting disk masses. These were compared with dust masses from previous work to obtain gas-to-dust ratios for each disk. In addition, radii for all three isotopologues were obtained. Results. The majority of Herbig disks for which 13CO and C18O were detected are optically thick in both. For these disks, the line flux essentially only traces the disk size and only lower limits to the mass can be obtained. Computing the gas mass using a simple optically thin relation between line flux and column density results in an underestimate of the gas mass of at least an order of magnitude compared to the masses obtained with DALI. The inferred gas masses with DALI are consistent with a gas-to-dust ratio of at least 100. These gas-to-dust ratios are two orders of magnitude higher compared to those found for T Tauri disks using similar techniques, even over multiple orders of magnitude in dust mass, illustrating the importance of the chemical conversion of CO in colder T Tauri disks. Similar high gas-to-dust ratios are found for Herbig group I and II disks. Since group II disks have dust masses comparable to T Tauri disks, their higher CO gas masses illustrate the determining role of temperature. Compared to debris disks, Herbig disks have gas masses higher by four orders of magnitude. At least one Herbig disk, HD 163296, has a detected molecular disk wind, but our investigation has not turned up other detections of the CO disk wind in spite of similar sensitivities. Conclusions. Herbig disks are consistent with a gas-to-dust ratio of at least 100 over multiple orders of magnitude in dust mass. This indicates a fundamental difference between CO emission from Herbig disks and T Tauri disks, which is likely linked to the warmer temperature of the Herbig disks.

Analytical solutions for the evolution of MHD wind-driven accretion discs

ABSTRACT We present new analytical solutions for the evolution of protoplanetary discs (PPDs) where magnetohydrodynamic (MHD) wind-driven processes dominate. Our study uses a 1D model which incorporates equations detailing angular momentum extraction by MHD winds and mass-loss rates. Our solutions demonstrate that the disc retains its initial state during the early phases; however, it rapidly evolves towards a self-similar state in the later stages of disc evolution. The total disc mass undergoes a continuous decline over time, with a particularly rapid reduction occurring beyond a certain critical time threshold. This gradual decrease in mass is influenced by the wind parameters and the initial surface density of the disc. In the MHD wind-dominated regime, we show that the disc’s lifespan correlates positively with the magnetic lever arm up to a certain threshold, irrespective of the initial disc size. PPDs with a larger magnetic lever arm are found to maintain significantly higher total disc mass over extended periods compared to their counterparts. The mass ejection-to-accretion ratio increases in efficient wind scenarios and is further amplified by a steeper initial surface density profile. Our analysis also reveals varied evolutionary trajectories in the plane of accretion rate and total disc mass, influenced by magnetic parameters and initial disc size. In scenarios with efficient MHD winds, discs with bigger sizes have extended operation time for mechanisms governing planet formation.

Dynamical mass measurements of two protoplanetary discs

ABSTRACT ALMA observations of line emission from planet forming discs have demonstrated to be an excellent tool to probe the internal disc kinematics, often revealing subtle effects related to important dynamical processes occurring in them, such as turbulence, or the presence of planets, that can be inferred from pressure bumps perturbing the gas motion, or from the detection of the planetary wake. In particular, we have recently shown for the case of the massive disc in Elias 2-27 as how one can use such kind of observations to measure deviations from Keplerianity induced by the disc self-gravity, thus constraining the total disc mass with good accuracy and independently on mass conversion factors between the tracer used and the total mass. Here, we refine our methodology and extend it to two additional sources, GM Aur and IM Lup, for which archival line observations are available for both the 12CO and the 13CO line. For IM Lup, we are able to obtain a consistent disc mass of $M_{\rm disc}=0.1 \, \mathrm{M}_{\odot }$, implying a disc-star mass ratio of 0.1 (consistent with the observed spiral structure in the continuum emission) and a gas/dust ratio of ∼65 (consistent with standard assumptions), with a systematic uncertainty by a factor of ≃ 2 due to the different methods to extract the rotation curve. For GM Aur, the two lines we use provide slightly inconsistent rotation curves that cannot be attributed only to a difference in the height of the emitting layer, nor to a vertical temperature stratification. Our best-fitting disc mass measurement is $M_{\rm disc}=0.26 \, \mathrm{M}_{\odot }$, implying a disc-star mass ratio of ∼0.35 and a gas/dust ratio of ∼130. Given the complex kinematics in the outer disc of GM Aur and its interaction with the infalling cloud, the CO lines might not well trace the rotation curve and our results for this source should then be considered with some caution.

The impact of the presence of water ice on the analysis of debris disk observations

Context. The analysis of debris disk observations is often based on the assumption of a dust phase composed of compact spherical grains consisting of astronomical silicate. Instead, observations indicate the existence of water ice in debris disks. Aims. We quantify the impact of water ice as a potential grain constituent in debris disks on the disk parameter values estimated from photometric and spatially resolved observations in the mid- and far-infrared. Methods. We simulated photometric measurements and radial profiles of debris disks containing water ice and analyzed them by applying a disk model purely consisting of astronomical silicate. Subsequently, we quantified the deviations between the derived and the true parameter values. As stars in central positions we discuss a β Pic sibling and main-sequence stars with spectral types ranging from A0 to K5. To simulate observable quantities we employed selected observational scenarios regarding the choice of wavelengths and instrument characteristics. Results. For the β Pic stellar model and ice fractions ≥50% the derived inner disk radius is biased by ice sublimation toward higher values. However, the derived slope of the radial density profile is mostly unaffected. Along with an increasing ice fraction, the slope of the grain size distribution is overestimated by up to a median factor of ~1.2 for an ice fraction of 90%. At the same time, the total disk mass is underestimated by a factor of ~0.4. The reliability of the derived minimum grain size strongly depends on the spectral type of the central star. For an A0-type star the minimum grain size can be underestimated by a factor of ~0.2, while for solar-like stars it is overestimated by up to a factor of ~4–5. Neglecting radial profile measurements and using solely photometric measurements, the factor of overestimation increases for solar-like stars up to ~7–14.

Constraining protoplanetary disc mass using the GI wiggle

ABSTRACT Exoplanets form in protoplanetary accretion discs. The total protoplanetary disc mass is the most fundamental parameter, since it sets the mass budget for planet formation. Although observations with the Atacama Large Millimeter/Submillimeter array (ALMA) have dramatically increased our understanding of these discs, total protoplanetary disc mass remains difficult to measure. If a disc is sufficiently massive (≳10 per cent of the host star mass), it can excite gravitational instability (GI). Recently, it has been revealed that GI leaves kinematic imprints of its presence known as the ‘GI Wiggle’. In this work, we use numerical simulations to determine an approximately linear relationship between the amplitude of the wiggle and the host disc-to-star mass ratio, and show that measurements of the amplitude are possible with the spatial and spectral capabilities of ALMA. These measurements can therefore be used to constrain disc-to-star mass ratio.

Formation of Earth-sized planets within the Kepler-1647 system habitable zone

ABSTRACT The Kepler-1647 is a binary system with two Sun-type stars (≈1.22 and ≈0.97 M⊙). It has the most massive circumbinary planet (≈1.52 MJup) with the longest orbital period (≈1107.6 d) detected by the Kepler probe and is located within the habitable zone (HZ) of the system. In this work, we investigated the ability to form and house an Earth-sized planet within its HZ. First, we computed the limits of its HZ and performed numerical stability tests within that region. We found that HZ has three subregions that show stability, one internal, one co-orbital, and external to the host planet Kepler-1647b. Within the limits of these three regions, we performed numerical simulations of planetary formation. In the regions inner and outer to the planet, we used two different density profiles to explore different conditions of formation. In the co-orbital region, we used eight different values of total disc mass. We showed that many resonances are located within regions causing much of the disc material to be ejected before a planet is formed. Thus, the system might have two asteroid belts with Kirkwood gaps, similar to the Solar system’s main belt of asteroids. The co-orbital region proved to be extremely sensitive, not allowing the planet formation, but showing that this binary system has the capacity to have Trojan bodies. Finally, we looked for regions of stability for an Earth-sized moon. We found that there is stability for a moon with this mass up to 0.4 Hill’s radius from the host planet.

Predicting the Kinematic Evidence of Gravitational Instability

Abstract Observations with the Atacama Large Millimeter/Submillimeter Array (ALMA) have dramatically improved our understanding of the site of exoplanet formation: protoplanetary disks. However, many basic properties of these disks are not well understood. The most fundamental of these is the total disk mass, which sets the mass budget for planet formation. Disks with sufficiently high masses can excite gravitational instability and drive spiral arms that are detectable with ALMA. Although spirals have been detected in ALMA observations of the dust, their association with gravitational instability, and high disk masses, is far from clear. Here we report a prediction for kinematic evidence of gravitational instability. Using hydrodynamics simulations coupled with radiative transfer calculations, we show that a disk undergoing such instability has clear kinematic signatures in molecular line observations across the entire disk azimuth and radius, which are independent of viewing angle. If these signatures are detected, it will provide the clearest evidence for the occurrence of gravitational instability in planet-forming disks, and provide a crucial way to measure disk masses.

Effect of pebble flux-regulated planetesimal formation on giant planet formation

Context. The formation of gas giant planets by the accretion of 100 km diameter planetesimals is often thought to be inefficient. A diameter of this size is typical for planetesimals and results from self-gravity. Many models therefore use small kilometer-sized planetesimals, or invoke the accretion of pebbles. Furthermore, models based on planetesimal accretion often use the ad hoc assumption of planetesimals that are distributed radially in a minimum-mass solar-nebula way. Aims. We use a dynamical model for planetesimal formation to investigate the effect of various initial radial density distributions on the resulting planet population. In doing so, we highlight the directive role of the early stages of dust evolution into pebbles and planetesimals in the circumstellar disk on the subsequent planet formation. Methods. We implemented a two-population model for solid evolution and a pebble flux-regulated model for planetesimal formation in our global model for planet population synthesis. This framework was used to study the global effect of planetesimal formation on planet formation. As reference, we compared our dynamically formed planetesimal surface densities with ad hoc set distributions of different radial density slopes of planetesimals. Results. Even though required, it is not the total planetesimal disk mass alone, but the planetesimal surface density slope and subsequently the formation mechanism of planetesimals that enables planetary growth through planetesimal accretion. Highly condensed regions of only 100 km sized planetesimals in the inner regions of circumstellar disks can lead to gas giant growth. Conclusions. Pebble flux-regulated planetesimal formation strongly boosts planet formation even when the planetesimals to be accreted are 100 km in size because it is a highly effective mechanism for creating a steep planetesimal density profile. We find that this leads to the formation of giant planets inside 1 au already by pure 100 km planetesimal accretion. Eventually, adding pebble accretion regulated by pebble flux and planetesimal-based embryo formation as well will further complement this picture.

High-eccentricity migration of planetesimals around polluted white dwarfs

ABSTRACT Several white dwarfs (WDs) with atmospheric metal pollution have been found to host small planetary bodies (planetesimals) orbiting near the tidal disruption radius. We study the physical properties and dynamical origin of these bodies under the hypothesis that they underwent high-eccentricity migration from initial distances of several astronomical units. We examine two plausible mechanisms for orbital migration and circularization: tidal friction and ram-pressure drag in a compact disc. For each mechanism, we derive general analytical expressions for the evolution of the orbit that can be rescaled for various situations. We identify the physical parameters that determine whether a planetesimal’s orbit can circularize within the appropriate time-scale and constrain these parameters based on the properties of the observed systems. For tidal migration to work, an internal viscosity similar to that of molten rock is required, and this may be naturally produced by tidal heating. For disc migration to operate, a minimal column density of the disc is implied; the inferred total disc mass is consistent with estimates of the total mass of metals accreted by polluted WDs.

13C17O suggests gravitational instability in the HL Tau disc

ABSTRACT We present the first detection of the $^{13}\text{C}^{17}\text{O}$ J = 3–2 transition toward the HL Tau protoplanetary disc. We find significantly more gas mass (at least a factor of 10 higher) than has been previously reported using $\text{C}^{18}\text{O}$ emission. This brings the observed total disc mass to 0.2 M⊙, which we consider to be a conservative lower limit. Our analysis of the Toomre Q profile suggests that this brings the disc into the regime of gravitational instability. The radial region of instability (50–110 au) coincides with the location of a proposed planet-carved gap in the dust disc, and a spiral in the gas. We therefore propose that if the origin of the gap is confirmed to be due to a forming giant planet, then it is likely to have formed via the gravitational fragmentation of the protoplanetary disc.

Demographics of disks around young very low-mass stars and brown dwarfs in Lupus

We present new 890 μm continuum ALMA observations of five brown dwarfs (BDs) with infrared excess in Lupus I and III, which in combination with four previously observed BDs allowed us to study the millimeter properties of the full known BD disk population of one star-forming region. Emission is detected in five out of the nine BD disks. Dust disk mass, brightness profiles, and characteristic sizes of the BD population are inferred from continuum flux and modeling of the observations. Only one source is marginally resolved, allowing for the determination of its disk characteristic size. We conduct a demographic comparison between the properties of disks around BDs and stars in Lupus. Due to the small sample size, we cannot confirm or disprove a drop in the disk mass over stellar mass ratio for BDs, as suggested for Ophiuchus. Nevertheless, we find that all detected BD disks have an estimated dust mass between 0.2 and 3.2 M⊙; these results suggest that the measured solid masses in BD disks cannot explain the observed exoplanet population, analogous to earlier findings on disks around more massive stars. Combined with the low estimated accretion rates, and assuming that the mm-continuum emission is a reliable proxy for the total disk mass, we derive ratios of Ṁacc∕Mdisk that are significantly lower than in disks around more massive stars. If confirmed with more accurate measurements of disk gas masses, this result could imply a qualitatively different relationship between disk masses and inward gas transport in BD disks.

Stellar cosmic rays as an important source of ionisation in protoplanetary disks: a disk mass dependent process

Abstract We assess the ionising effect of low energy protostellar cosmic rays in protoplanetary disks around a young solar mass star for a wide range of disk parameters. We assume a source of low energy cosmic rays located close to the young star which travel diffusively through the protoplanetary disk. We use observationally inferred values from nearby star-forming regions for the total disk mass and the radial density profile. We investigate the influence of varying the disk mass within the observed scatter for a solar mass star. We find that for a large range of disk masses and density profiles that protoplanetary disks are “optically thin” to low energy (∼3 GeV) cosmic rays. At R ∼ 10 au, for all of the disks that we consider (Mdisk = 6.0 × 10−4 − 2.4 × 10−2M⊙), the ionisation rate due to low energy stellar cosmic rays is larger than that expected from unmodulated galactic cosmic rays. This is in contrast to our previous results which assumed a much denser disk which may be appropriate for a more embedded source. At R ∼ 70 au, the ionisation rate due to stellar cosmic rays dominates in ∼50% of the disks. These are the less massive disks with less steep density profiles. At this radius there is at least an order of magnitude difference in the ionisation rate between the least and most massive disk that we consider. Our results indicate, for a wide range of disk masses, that low energy stellar cosmic rays provide an important source of ionisation at the disk midplane at large radii (∼70 au).

Probing the Gas Content of Late-stage Protoplanetary Disks with N2H+

Abstract The lifetime of gas in circumstellar disks is a fundamental quantity that informs our understanding of planet formation. Studying disk gas evolution requires measurements of disk masses around stars of various ages. Because H2 gas is unobservable under most disk conditions, total disk masses are based on indirect tracers such as sub-mm dust and CO emission. The uncertainty in the relation between these tracers and the disk mass increases as the disk evolves. In a few well-studied disks, CO exhibits depletions of up to 100× below the assumed interstellar value. Thus, additional tracers are required to accurately determine the total gas mass. The relative lack of nitrogen found in solid solar system bodies may indicate that it persists in volatile form, making nitrogen-bearing species more robust tracers of gas in more evolved disks. Here we present Atacama Large Millimeter/submillimeter Array detections of N2H+ in two mature, ∼5–11 Myr old disks in the Upper Scorpius OB Association. Such detections imply the presence of H2-rich gas and sources of ionization, both required for N2H+ formation. The Upper Sco disks also show elevated N2H+/CO flux ratios when compared to previously observed disks with ≳10× higher CO fluxes. Based on line ratio predictions from a grid of thermochemical disk models, a significantly reduced CO/H2 abundance of &lt;10−6 for a gas-to-dust ratio of ≳100 is required to produce the observed N2H+ fluxes. These systems appear to maintain H2 gas reservoirs and indicate that carbon- and nitrogen-bearing species follow distinct physical or chemical pathways as disks evolve.

Constraining the Solar System's Debris Disk with In Situ New Horizons Measurements from the Edgeworth–Kuiper Belt

Abstract The solar system currently possesses two remnant debris disks leftover from the planetary formation era in the form of the asteroid belt and the Edgeworth–Kuiper Belt (EKB). Similar to other stellar systems, these debris disks continually generate submillimeter-sized dust grains through processes such as mutual collisions, interstellar dust grain bombardment, and sublimation/sputtering of larger grains. Here, we use recent in situ measurements by the New Horizons Student Dust Counter and an interplanetary dust dynamics model to constrain the overall structure and magnitude of the solar system’s debris disk, including the disk mass, optical depth, and surface brightness in both scattered light and thermal emission. We find that ∼99% of the solar system’s dust disk mass (grains with diameter &lt;1 mm) is contained within EKB and Oort Cloud cometary grains outside of 30 au, with the remaining ∼1% mass in the form of Jupiter-family cometary dust within 5 au. The total disk mass is estimated to be ∼8 × 10−7 M ⊕ with a total fractional luminosity of ∼5 × 10−7, confirming our solar system as a relatively dust-poor system compared to debris disks around similar-aged FGK stars. Finally, we estimate that Kuiper Belt Object collisional events such as that which created the Haumea family could transiently increase the current surface brightness of our debris disk by a factor of only ∼6, far less than median brightnesses seen in other nearby disks. This further supports the idea that the EKB has been largely depleted of its primordial mass relative to other stellar systems by instabilities triggered by planetary migration.

Time-dependent evolution of the protoplanetary discs with magnetic winds

ABSTRACT We study the evolution of the protoplanetary discs (PPDs) in the presence of magnetically driven winds with the stress relations motivated by the non-ideal MHD disc simulations. Contribution of the magnetic winds in the angular momentum removal and mass-loss is described using these relations which are quantified in terms of the plasma parameter. Evolution of the essential disc quantities including the surface density, accretion rate, and wind mass-loss rate are studied for a wide range of the model parameters. Two distinct phases of the disc evolution are found irrespective of the adopted input parameters. While at the early phase of the disc evolution, global disc quantities such as its total mass and magnetic flux undergo non-significant reductions, their rapid declines are found in the second phase of evolution. Duration of each phase, however, depends upon the model parameters including magnetic wind strength. Our model predicts that contributions of the magnetic winds in the disc evolution are significant during the second phase. We then calculated locus of points in the plane of the accretion rate and total disc mass corresponding to an ensemble of evolving PPDs. Our theoretical isochrone tracks exhibit reasonable fits to the observed PPDs in star-forming regions Lupus and σ-Orion.

New Constraints From Dust Lines on the Surface Densities of Protoplanetary Disks

Abstract We present new determinations of disk surface density, independent of an assumed dust opacity, for a sample of seven bright, diverse, protoplanetary disks using measurements of disk dust lines. We develop a robust method for determining the location of dust lines by modeling disk interferometric visibilities at multiple wavelengths. The disks in our sample have newly derived masses that are 9%–27% of their host stellar mass, substantially larger than the minimum mass solar nebula. All are stable to gravitational collapse, except for one that approaches the limit of Toomre-Q stability. Our mass estimates are 2–15 times larger than estimates from integrated optically thin dust emission. We derive depleted dust-to-gas ratios with typical values of ∼10−3 in the outer disk. Using coagulation models, we derive dust surface density profiles that are consistent with millimeter dust observations. In these models, the disks formed with an initial dust mass that is a factor of ∼10 greater than is presently observed. Of the three disks in our sample with resolved CO line emission, the masses of HD 163296, AS 209, and TW Hya are roughly 3, 115, and 40 times more massive than estimates from CO respectively. This range indicates that CO depletion is not uniform across different disks and that dust is a more robust tracer of total disk mass. Our method of determining surface density using dust lines is robust even if particles form as aggregates and is useful even in the presence of dust substructure caused by pressure traps. The low Toomre-Q values observed in this sample indicate that at least some disks do not accrete efficiently.

Possible Detection of Gamma-Rays from Epsilon Eridani

We use the Fermi-LAT gamma-ray observatory to search for gamma-ray emission from four nearby, debris disk-hosting main sequence stars: $\tau$ Ceti, $\epsilon$ Eridani, Fomalhaut, and Vega. For three stars ($\tau$ Ceti, Fomalhaut, and Vega), we establish upper limits that are consistent with theoretical expectations. For $\epsilon$ Eridani, we find a possible spatially coincident source with a soft energy spectrum of $dN/dE \sim E^{-3.6}$. However, at this stage we are unable to rule out that this emission is due to a more extended feature in the diffuse background. In the interpretation that the emission is due to $\epsilon$ Eridani, the $> 100$ MeV gamma-ray luminosity is $\sim 10^{27}$ erg/s $\simeq 3\times 10^{-7}$ L$_\odot$, which is $\sim 10^{10}$ times the gamma-ray luminosity from the disk of the quiet Sun. We find $\lesssim 2 \sigma$ evidence of source variability over a $\sim 7$ year timescale. In the interpretation that the gamma-ray emission from $\epsilon$ Eridani itself, we consider two possible models: 1) cosmic-ray collisions with solid bodies in the debris disk which extends out $\sim$60 AU from the host star, and 2) emission from the stellar activity. For the former model, assuming a total disk mass consistent with infrared measurements, we find that the size distribution of bodies is steeper than expected for a collisional cascade state. If confirmed as being associated with $\epsilon$ Eridani, this would be the first indication of gamma-ray emission from the vicinity of a main sequence star other than the Sun.

Growth and Settling of Dust Particles in Protoplanetary Nebulae: Implications for Opacity, Thermal Profile, and Gravitational Instability

Abstract Despite making a small contribution to total protoplanetary disk mass, dust affects the disk temperature by controlling the absorption of starlight. As grains grow from their initial interstellar-medium-like size distribution, settling depletes the disk’s upper layers of dust and decreases the optical depth, cooling the interior. Here we investigate the effect of collisional growth of dust grains and their dynamics on the thermal and optical profile of the disk, and explore the possibility that cooling induced by grain growth and settling could lead to gravitational instability. We develop a Monte Carlo dust collision model with a weighting technique and allow particles to collisionally evolve through sticking and fragmentation, along with vertical settling and turbulent mixing. We explore three disk models and perform simulations for both constant and spatially variable turbulence profile. We then calculate mean wavelength-dependent opacities for the evolving disks and perform radiative transfer to calculate the temperature profile. Finally, we calculate the Toomre Q parameter, a measure of the disk’s stability against self-gravity, after it reaches a steady-state dust-size distribution. We find that even weak turbulence can keep submicrometer-sized particles stirred in the disk’s upper layer, affecting its optical and thermal profiles, and the growth of large particles in the midplane can make a massive disk optically thick at millimeter wavelengths, making it difficult to calculate the surface density of dust available for planet formation in the inner disk. Also, for all our initially marginally stable annuli, we find a small but noticeable reduction in Q.