A quantification of hydrodynamical effects on protoplanetary dust growth

Context. The growth process of dust particles in protoplanetary disks can be modeled via numerical dust coagulation codes. In this approach, physical effects that dominate the dust growth process often must be implemented in a parameterized form. Due to a lack of these parameterizations, existing studies of dust coagulation have ignored the effects a hydrodynamical gas flow can have on grain growth, even though it is often argued that the flow could significantly contribute either positively or negatively to the growth process. Aims. We intend to provide a quantification of hydrodynamical effects on the growth of dust particles, such that these effects can be parameterized and implemented in a dust coagulation code. Methods. We numerically integrate the trajectories of small dust particles in the flow of disk gas around a proto-planetesimal, sampling a large parameter space in proto-planetesimal radii, headwind velocities, and dust stopping times. Results. The gas flow deflects most particles away from the proto-planetesimal, such that its effective collisional cross section, and therefore the mass accretion rate, is reduced. The gas flow however also reduces the impact velocity of small dust particles onto a proto-planetesimal. This can be beneficial for its growth, since large impact velocities are known to lead to erosion. We also demonstrate why such a gas flow does not return collisional debris to the surface of a proto-planetesimal. Conclusions. We predict that a laminar hydrodynamical flow around a proto-planetesimal will have a significant effect on its growth. However, we cannot easily predict which result, the reduction of the impact velocity or the sweep-up cross section, will be more important. Therefore, we provide parameterizations ready for implementation into a dust coagulation code.Comment: 9 pages, 6 figures; accepted for publication in A&A; v2 matches the manuscript sent to the publisher (very minor changes

Breaking through: The effects of a velocity distribution on barriers to dust growth

It is unknown how far dust growth can proceed by coagulation. Obstacles to collisional growth are the fragmentation and bouncing barriers. However, in all previous simulations of the dust-size evolution in protoplanetary disks, only the mean collision velocity has been considered, neglecting that a small but possibly important fraction of the collisions will occur at both much lower and higher velocities. We study the effect of the probability distribution of impact velocities on the collisional dust growth barriers. Assuming a Maxwellian velocity distribution for colliding particles to determine the fraction of sticking, bouncing, and fragmentation, we implement this in a dust-size evolution code. We also calculate the probability of growing through the barriers and the growth timescale in these regimes. We find that the collisional growth barriers are not as sharp as previously thought. With the existence of low-velocity collisions, a small fraction of the particles manage to grow to masses orders of magnitude above the main population. A particle velocity distribution softens the fragmentation barrier and removes the bouncing barrier. It broadens the size distribution in a natural way, allowing the largest particles to become the first seeds that initiate sweep-up growth towards planetesimal sizes.Comment: 4 pages, 3 figures. Accepted for publication as a Letter in Astronomy and Astrophysic

Collisions of small ice particles under microgravity conditions - II. Does the chemical composition of the ice change the collisional properties?

Context. Understanding the collisional properties of ice is important for understanding both the early stages of planet formation and the evolution of planetary ring systems. Simple chemicals such as methanol and formic acid are known to be present in cold protostellar regions alongside the dominant water ice; they are also likely to be incorporated into planets which form in protoplanetary disks, and planetary ring systems. However, the effect of the chemical composition of the ice on its collisional properties has not yet been studied.Aims. Collisions of 1.5 cm ice spheres composed of pure crystalline water ice, water with 5% methanol, and water with 5% formic acid were investigated to determine the effect of the ice composition on the collisional outcomes.Methods. The collisions were conducted in a dedicated experimental instrument, operated under microgravity conditions, at relative particle impact velocities between 0.01 and 0.19 ms-1, temperatures between 131 and 160 K and a pressure of around 10-5Results. A range of coefficients of restitution were found, with no correlation between this and the chemical composition, relative impact velocity, or temperature.Conclusions. We conclude that the chemical composition of the ice (at the level of 95% water ice and 5% methanol or formic acid) does not affect the collisional properties at these temperatures and pressures due to the inability of surface wetting to take place. At a level of 5% methanol or formic acid, the structure is likely to be dominated by crystalline water ice, leading to no change in collisional properties. The surface roughness of the particles is the dominant factor in explaining the range of coefficients of restitution

Cepheid limb darkening, angular diameter corrections, and projection factor from static spherical model stellar atmospheres

Context. One challenge for measuring the Hubble constant using Classical Cepheids is the calibration of the Leavitt Law or period-luminosity relationship. The Baade-Wesselink method for distance determination to Cepheids relies on the ratio of the measured radial velocity and pulsation velocity, the so-called projection factor and the ability to measure the stellar angular diameters. Aims. We use spherically-symmetric model stellar atmospheres to explore the dependence of the p-factor and angular diameter corrections as a function of pulsation period. Methods. Intensity profiles are computed from a grid of plane-parallel and spherically-symmetric model stellar atmospheres using the SAtlas code. Projection factors and angular diameter corrections are determined from these intensity profiles and compared to previous results. Results. Our predicted geometric period-projection factor relation including previously published state-of-the-art hydrodynamical predictions is not with recent observational constraints. We suggest a number of potential resolutions to this discrepancy. The model atmosphere geometry also affects predictions for angular diameter corrections used to interpret interferometric observations, suggesting corrections used in the past underestimated Cepheid angular diameters by 3 - 5%. Conclusions. While spherically-symmetric hydrostatic model atmospheres cannot resolve differences between projection factors from theory and observations, they do help constrain underlying physics that must be included, including chromospheres and mass loss. The models also predict more physically-based limb-darkening corrections for interferometric observations.Comment: 8 pages, 6 figures, 2 tables, accepted for publication in A&

Building the cosmic distance scale: from Hipparcos to Gaia

Hipparcos, the first ever experiment of global astrometry, was launched by ESA in 1989 and its results published in 1997 (Perryman et al., Astron. Astrophys. 323, L49, 1997; Perryman & ESA (eds), The Hipparcos and Tycho catalogues, ESA SP-1200, 1997). A new reduction was later performed using an improved satellite attitude reconstruction leading to an improved accuracy for stars brighter than 9th magnitude (van Leeuwen & Fantino, Astron. Astrophys. 439, 791, 2005; van Leeuwen, Astron. Astrophys. 474, 653, 2007). The Hipparcos Catalogue provided an extended dataset of very accurate astrometric data (positions, trigonometric parallaxes and proper motions), enlarging by two orders of magnitude the quantity and quality of distance determinations and luminosity calibrations. The availability of more than 20000 stars with a trigonometric parallax known to better than 10% opened the way to a drastic revision of our 3-D knowledge of the solar neighbourhood and to a renewal of the calibration of many distance indicators and age estimations. The prospects opened by Gaia, the next ESA cornerstone, planned for launch in June 2013 (Perryman et al., Astron. Astrophys. 369, 339, 2001), are still much more dramatic: a billion objects with systematic and quasi simultaneous astrometric, spectrophotometric and spectroscopic observations, about 150 million stars with expected distances to better than 10%, all over the Galaxy. All stellar distance indicators, in very large numbers, will be directly measured, providing a direct calibration of their luminosity and making possible detailed studies of the impacts of various effects linked to chemical element abundances, age or cluster membership. With the help of simulations of the data expected from Gaia, obtained from the mission simulator developed by DPAC, we will illustrate what Gaia can provide with some selected examples.Comment: 16 pages, 16 figures, Conference "The Fundamental Cosmic Distance scale: State of the Art and the Gaia perspective, 3-6 May 2011, INAF, Osservatorio Astronomico di Capodimonte, Naples. Accepted for publication in Astrophysics & Space Scienc

Explaining millimeter-sized particles in brown dwarf disks

Context. Planets have been detected around a variety of stars, including low-mass objects, such as brown dwarfs. However, such extreme cases are challenging for planet formation models. Recent sub-millimeter observations of disks around brown dwarf measured low spectral indices of the continuum emission that suggest that dust grains grow to mm-sizes even in these very low mass environments. Aims. To understand the first steps of planet formation in scaled-down versions of T-Tauri disks, we investigate the physical conditions that can theoretically explain the growth from interstellar dust to millimeter-sized grains in disks around brown dwarf. Methods. We modeled the evolution of dust particles under conditions of low-mass disks around brown dwarfs. We used coagulation, fragmentation, and disk-structure models to simulate the evolution of dust, with zero and non-zero radial drift. For the non-zero radial drift, we considered strong inhomogeneities in the gas surface density profile that mimic long-lived pressure bumps in the disk. We studied different scenarios that could lead to an agreement between theoretical models and the spectral slope found by millimeter observations. Results. We find that fragmentation is less likely and rapid inward drift is more significant for particles in brown dwarf disks than in T-Tauri disks. We present different scenarios that can nevertheless explain millimeter-sized grains. As an example, a model that combines the following parameters can fit the millimeter fluxes measured for brown dwarf disks: strong pressure inhomogeneities of ~40% of amplitude, a small radial extent ~15 AU, a moderate turbulence strength α_(turb) = 10^(-3), and average fragmentation velocities for ices v_f = 10 m s^(-1)

The Large Magellanic Cloud and the Distance Scale

The Magellanic Clouds, especially the Large Magellanic Cloud, are places where multiple distance indicators can be compared with each other in a straight-forward manner at considerable precision. We here review the distances derived from Cepheids, Red Variables, RR Lyraes, Red Clump Stars and Eclipsing Binaries, and show that the results from these distance indicators generally agree to within their errors, and the distance modulus to the Large Magellanic Cloud appears to be defined to 3% with a mean value of 18.48 mag, corresponding to 49.7 Kpc. The utility of the Magellanic Clouds in constructing and testing the distance scale will remain as we move into the era of Gaia.Comment: 23 pages, accepted for publication in Astrophysics and Space Science. From a presentation at the conference The Fundamental Cosmic Distance Scale: State of the Art and the Gaia Perspective, Naples, May 201

Planetesimal formation by sweep-up: How the bouncing barrier can be beneficial to growth

The formation of planetesimals is often accredited to collisional sticking of dust grains. The exact process is unknown, as collisions between larger aggregates tend to lead to fragmentation or bouncing rather than sticking. Recent laboratory experiments have however made great progress in the understanding and mapping of the complex physics involved in dust collisions. We want to study the possibility of planetesimal formation using the results from the latest laboratory experiments, particularly by including the fragmentation with mass transfer effect, which might lead to growth even at high impact velocities. We present a new experimentally and physically motivated dust collision model capable of predicting the outcome of a collision between two particles of arbitrary masses and velocities. It is used together with a continuum dust-size evolution code that is both fast in terms of execution time and able to resolve the dust well at all sizes, allowing for all types of interactions to be studied without biases. We find that for the general dust population, bouncing collisions prevent the growth above millimeter-sizes. However, if a small number of cm-sized particles are introduced, for example due to vertical mixing or radial drift, they can act as a catalyst and start to sweep up the smaller particles. At a distance of 3 AU, 100-meter-sized bodies are formed on a timescale of 1 Myr. We conclude that direct growth of planetesimals might be a possibility thanks to a combination of the existence of a bouncing barrier and the fragmentation with mass transfer effect. The bouncing barrier is here even beneficial, as it prevents the growth of too many large particles that would otherwise only fragment among each other, and creates a reservoir of small particles that can be swept up by larger bodies. However, for this process to work, a few seeds of cm in size or larger have to be introduced.Comment: 17 pages, 13 figures. Accepted for publication in Astronomy and Astrophysic

Modeling dust growth in protoplanetary disks: The breakthrough case

Context. Dust coagulation in protoplanetary disks is one of the initial steps toward planet formation. Simple toy models are often not sufficient to cover the complexity of the coagulation process, and a number of numerical approaches are therefore used, among which integration of the Smoluchowski equation and various versions of the Monte Carlo algorithm are the most popular. Aims. Recent progress in understanding the processes involved in dust coagulation have caused a need for benchmarking and comparison of various physical aspects of the coagulation process. In this paper, we directly compare the Smoluchowski and Monte Carlo approaches to show their advantages and disadvantages. Methods. We focus on the mechanism of planetesimal formation via sweep-up growth, which is a new and important aspect of the current planet formation theory. We use realistic test cases that implement a distribution in dust collision velocities. This allows a single collision between two grains to have a wide range of possible outcomes but also requires a very high numerical accuracy. Results. For most coagulation problems, we find a general agreement between the two approaches. However, for the sweep-up growth driven by the “lucky” breakthrough mechanism, the methods exhibit very different resolution dependencies. With too few mass bins, the Smoluchowski algorithm tends to overestimate the growth rate and the probability of breakthrough. The Monte Carlo method is less dependent on the number of particles in the growth timescale aspect but tends to underestimate the breakthrough chance due to its limited dynamic mass range. Conclusions. We find that the Smoluchowski approach, which is generally better for the breakthrough studies, is sensitive to low mass resolutions in the high-mass, low-number tail that is important in this scenario. To study the low number density features, a new modulation function has to be introduced to the interaction probabilities. As the minimum resolution needed for breakthrough studies depends strongly on setup, verification has to be performed on a case by case basis