We examine the evolution of the snow line in a protoplanetary disc that contains a dead zone (a region of zero or low turbulence). The snow line is within a self-gravitating part of the dead zone, and we obtain a fully analytic solution for its radius. Our formula could prove useful for future observational attempts to characterise the demographics of planets outside the snow line. External sources such as comic rays or X-rays from the central star can ionise the disc surface layers and allow the magneto-rotational instability to drive turbulence there. We show that provided that the surface density in this layer is less than about 50 g/cm^2, the dead zone solution exists, after an initial outbursting phase, until the disc is dispersed by photoevaporation. We demonstrate that the snow line radius is significantly larger than that predicted by a fully turbulent disc model, and that in our own solar system it remains outside of the orbital radius of the Earth. Thus, the inclusion of a dead zone into a protoplanetary disc model explains how our Earth formed with very little water.
Dust particles need to grow efficiently from micrometre sizes to thousands of kilometres to form planets. With the growth of millimetre to meter sizes being hindered by a number of barriers, the recent discovery that dust evolution is able to create `self-induced' dust traps shows promises. The condensation and sublimation of volatile species at certain locations, called snow lines, is also thought to be an important part of planet formation scenarios. Given that dust sticking properties change across a snow line, this raises the question: how do snow lines affect the self-induced dust trap fo…
CO is thought to be a vital building block for prebiotic molecules that are necessary for life. Thus, understanding where CO existed in a solid phase within the solar nebula is important for understanding the origin of life. We model the evolution of the CO snow line in a protoplanetary disk. We find that the current observed location of the CO snow line in our solar system, and in the solar system analogue TW Hydra, cannot be explained by a fully turbulent disk model. With time-dependent disk models we find that the inclusion of a dead zone (a region of low turbulence) can resolve this proble…
We model the evolution of the snow line in a protoplanetary disc. If the magneto-rotational instability (MRI) drives turbulence throughout the disc, there is a unique snow line outside of which the disc is icy. The snow line moves closer to the star as the infall accretion rate drops. Because the snow line moves inside the radius of the Earth's orbit, the formation of our water-devoid planet is difficult with this model. However, protoplanetary discs are not likely to be sufficiently ionised to be fully turbulent. A dead zone at the mid-plane slows the flow of material through the disc and a s…
Aims. We track the time evolution of planet traps and snowlines in a viscously evolving protoplanetary disk using an opacity table that accounts for the composition of the dust material. Methods. We coupled a dynamical and thermodynamical disk model with a temperature-dependent opacity table (that accounts for the sublimation of the main dust components) to investigate the formation and evolution of snowlines and planet traps during the first million years of disk evolution. Results. Starting from a minimum mass solar nebula (MMSN), we find that the disk mid-plane temperature profile shows sev…
Evolution of a snow line in an optically-thick protoplanetary disk is investigated with numerical simulations. The ice-condensing region in the disk is obtained by calculating the temperature and the density with the 1+1D approach. The snow line migrates as the mass accretion rate (\dot{M}) in the disk decreases with time. Calculations are carried out from an early phase with high disk accretion rates (\dot{M} \sim 10^{-7} M_sun/yr) to a later phase with low disk accretion rates (\dot{M} \sim 10^{-12} M_sun/yr) using the same numerical method. It is found that the snow line moves inward for \d…
The snow line in a protoplanetary disk demarcates regions with H$_2$O ice from regions with H$_2$O vapor. Where a planet forms relative to this location determines how much water and other volatiles it forms with. Giant planet formation may be triggered at the water snow line if vapor diffuses outward and is cold-trapped beyond the snow line faster than icy particles can drift inward. In this study we investigate the distribution of water across the snow line, considering three different radial profiles of the turbulence parameter $α(r)$, corresponding to three different angular momentum trans…
We present an observational reconstruction of the radial water vapor content near the surface of the TW Hya transitional protoplanetary disk, and report the first localization of the snow line during this phase of disk evolution. The observations are comprised of Spitzer-IRS, Herschel-PACS, and Herschel-HIFI archival spectra. The abundance structure is retrieved by fitting a two-dimensional disk model to the available star+disk photometry and all observed H2O lines, using a simple step-function parameterization of the water vapor content near the disk surface. We find that water vapor is abund…
Sharp chemical discontinuities can occur in protoplanetary discs, particularly at `snow-lines' where a gas-phase species freezes out to form ice grains. Such sharp discontinuities will diffuse out due to the turbulence suspected to drive angular momentum transport in accretion discs. We demonstrate that the concentration gradient - in the vicinity of the snow-line - of a species present outside a snow-line but destroyed inside is strongly sensitive to the level of turbulent diffusion (provided the chemical and transport time-scales are decoupled) and provides a direct measurement of the radial…
The low water content of the terrestrial planets in the solar system suggests that the protoplanets formed within the water snow line. Accurate prediction of the snow line location moving with time provides a clue to constrain the formation process of the planets. In this paper, we investigate the migration of the snow line in protoplanetary disks whose accretion is controlled by laminar magnetic fields, which have been proposed by various nonideal magnetohydrodynamic (MHD) simulations. We propose an empirical model of the disk temperature based on our nonideal MHD simulations, which show that…
Molecular snow lines in protoplanetary disks have been studied theoretically for decades because of their importance in shaping planetary architectures and compositions. The water snow line lies in the planet formation region at < 10 AU, and so far its location has been estimated only indirectly from spatially-unresolved spectroscopy. This work presents a proof-of-concept method to directly image the water snow line in protoplanetary disks through its physical and chemical imprint in the local dust properties. We adopt a physical disk model that includes dust coagulation, fragmentation, drift,…
Planetesimal formation stage represents a major gap in our understanding of the planet formation process. The late-stage planet accretion models typically make arbitrary assumptions about planetesimals and pebbles distribution while the dust evolution models predict that planetesimal formation is only possible at some orbital distances. We want to test the importance of water snow line for triggering formation of the first planetesimals during the gas-rich phase of protoplanetary disk, when cores of giant planets have to form. We connect prescriptions for gas disk evolution, dust growth and fr…
We introduce a new Lagrangian smooth-particle method to model the growth and drift of pebbles in protoplanetary disks. The Lagrangian nature of the model makes it especially suited to follow characteristics of individual (groups of) particles, such as their composition. In this work we focus on the water content of solid particles. Planetesimal formation via streaming instability is taken into account, partly based on previous results on streaming instability outside the water snowline that were presented in Schoonenberg & Ormel (2017). We validate our model by reproducing earlier results from…
Observationally inferred crystalline abundance in silicates in comets, which should have been formed in the outer region of a protoplanetary disk, is relatively high (~ 10-60%), although crystalline silicates would be formed by annealing of amorphous precursors in the disk inner region. In order to quantitatively address this puzzle, we have performed Monte Carlo simulation of advection/diffusion of silicate particles in a turbulent disk, in the setting based on pebble accretion model: pebbles consisting of many small amorphous silicates embedded in icy mantle are formed in the disk outer regi…
Snowlines of major volatiles regulate the gas and solid C/N/O ratios in the planet-forming midplanes of protoplanetary disks. Snow surfaces are the 2D extensions of snowlines in the outer disk regions, where radiative heating results in a decreasing temperature with disk height. CO and N$_2$ are two of the most abundant carriers of C, N and O. N$_2$H$^+$ can be used to probe the snow surfaces of both molecules, because it is destroyed by CO and formed from N$_2$. Here we present Atacama Large Millimeter/submillimeter Array (ALMA) observations of N$_2$H$^+$ at 0.2$''$-0.4$''$ resolution in the …
Context. The water snowline divides dry and icy solid material in protoplanetary disks, and has been thought to significantly affect planet formation at all stages. If dry particles break up more easily than icy ones, then the snowline causes a traffic jam, because small grains drift inward at lower speeds than larger pebbles. Aims. We aim to evaluate the effect of high dust concentrations around the snowline onto the gas dynamics. Methods. Using numerical simulations, we model the global radial evolution of an axisymmetric protoplanetary disk. Our model includes particle growth, evaporation a…
The terrestrial planets and the asteroids dominant in the inner asteroid belt are water poor. However, in the protoplanetary disk the temperature should have decreased below water condensation level well before the disk was photoevaporated. Thus, the global water depletion of the inner Solar System is puzling. We show that, even if the inner disk becomes cold, there cannot be direct condensation of water. This is because the snowline moves towards the Sun more slowly than the gas itself. The appearance of ice in a range of heliocentric distances swept by the snowline can only be due to the rad…
We investigate dust growth due to settling in a 1D vertical column of a protoplanetary disk. It is known from the observed 10 micron feature in disk SEDs, that small micron-sized grains are present at the disk atmosphere throughout the lifetime of the disk. We hope to explain such questions as what process can keep the disk atmospheres dusty for the lifetime of the disk and how does the particle properties change as a function of height above the midplane. We use a Monte Carlo code to follow the mass and porosity evolution of the particles in time. The used collision model is based on laborato…
We obtain a new set of analytical solutions for the evolution of a self-gravitating accretion disc by holding the Toomre parameter close to its threshold, and obtaining the stress parameter from the cooling rate. In agreement with the previous numerical solutions, furthermore, the accretion rate is assumed to be independent of the disc radius. Extreme situations where the entire disc is either optically thick or optically thin are studied independently and the obtained solutions can be used for exploring the early or the final phases of a protoplanetary disc evolution. Our solutions exhibit de…
Hydrodynamics modeling of the water snow line in young protoplanetary disks with dust-size-dependent opacities
Institut für Astro- und Teilchenphysik, Universität Innsbruck（因斯布鲁克大学天体与粒子物理研究所）；Research Institute of Physics, Southern Federal University（南联邦大学物理研究所）；Institute of Astronomy, Russian Academy of Sciences（俄罗斯科学院天文研究所）
The radial-dependent positions of snowlines of abundant oxygen- and carbon-bearing molecules in protoplanetary discs will result in systematic radial variations in the C/O ratios in the gas and ice. This variation is proposed as a tracer of the formation location of gas-giant planets. However, disc chemistry can affect the C/O ratios in the gas and ice, thus potentially erasing the chemical fingerprint of snowlines in gas-giant atmospheres. We calculate the molecular composition of hot Jupiter atmospheres using elemental abundances extracted from a chemical kinetics model of a disc midplane wh…
Content: For up to a few millions of years, pebbles must provide a quasi-steady inflow of solids from the outer parts of protoplanetary disks to their inner regions. Aims: We wish to understand how a significant fraction of the pebbles grows into planetesimals instead of being lost to the host star. Methods:We examined analytically how the inward flow of pebbles is affected by the snow line and under which conditions dust-rich (rocky) planetesimals form. When calculating the inward drift of solids that is due to gas drag, we included the back-reaction of the gas to the motion of the solids. Re…
Pressure maxima are regions in protoplanetary disks where pebbles can be trapped because of the local absence of pressure gradient. These regions could be ideal places to form planetesimals or to isolate isotopic reservoirs. Observations of protoplanetary disks show that dusty rings structures are common, and pressure maxima are sometime invoked as a possible explanation. In our Solar System, pressure bumps have been suggested as a possible mechanism for separating reservoirs with different nucleosynthetic compositions. In this letter we detail a mechanism by which pressure maxima form just in…
We present deep Herschel-PACS spectroscopy of far-infrared water lines from a sample of four protoplanetary disks around solar-mass stars, selected to have strong water emission at mid-infrared wavelengths. By combining the new Herschel spectra with archival Spitzer-IRS spectroscopy, we retrieve a parameterized radial surface water vapor distribution from 0.1-100 AU using two-dimensional dust and line radiative transfer modeling. The surface water distribution is modeled with a step model comprising of a constant inner and outer relative water abundance and a critical radius at which the surfa…
Most protoplanetary discs are thought to undergo violent and frequent accretion outbursts, during which the accretion rate and central luminosity are elevated for several decades. This temporarily increases the disc temperature, leading to the sublimation of ice species as snowlines move outwards. In this paper, we investigate how an FUor-type accretion outburst alters the growth and appearance of dust aggregates at different locations in protoplanetary discs. We develop a model based on the Monte Carlo approach to simulate locally the coagulation and fragmentation of icy dust particles and in…
A snow-line is the region of a protoplanetary disk at which a major volatile, such as water or carbon monoxide, reaches its condensation temperature. Snow-lines play a crucial role in disk evolution by promoting the rapid growth of ice-covered grains. Signatures of the carbon monoxide snow-line (at temperatures of around 20 kelvin) have recently been imaged in the disks surrounding the pre-main-sequence stars TW Hydra and HD163296, at distances of about 30 astronomical units (au) from the star. But the water snow-line of a protoplanetary disk (at temperatures of more than 100 kelvin) has not h…
In this paper, we analyse the upper limit fluxes of sub-millimeter ortho-H$_{2}$$^{16}$O 321 GHz, para-H$_{2}$$^{18}$O 322 GHz, and HDO 335 GHz lines from the protoplanetary disk around the Herbig Ae star HD 163296, using the Atacama Large Millimeter/Submillimeter Array (ALMA). These water lines are considered to be the best candidate sub-millimeter lines to locate the position of the H$_{2}$O snowline, on the basis of our previous model calculations. We compare the upper limit fluxes with the values calculated by our models with dust emission included, and we constrain the line emitting regio…
Volatile species in protoplanetary discs can undergo a phase change from vapour to solid. These "snow-lines" can play vital roles in planet formation at all scales, from dust coagulation to planetary migration. In the outer regions of protoplanetary discs, the temperature profile is set by the absorption of reprocessed stellar light by the solids. Further, the temperature profile sets the distribution of solids through sublimation and condensation at various snow-lines. Hence the snow-line position depends on the temperature profile and vice-versa. We show that this coupling can be thermally u…
Dust plays a key role in the formation of planets and its emission also provides one of our most accessible views of protoplanetary discs. If set by radiative equilibrium with the central star, the temperature of dust in the disc plateaus at around $10-20$K in the outer regions. However sufficiently nearby massive stars can heat the outer disc to substantially higher temperatures. In this paper we study the radiative equilibrium temperature of discs in the presence of massive external sources and gauge the effect that it has on millimetre dust mass estimates. Since millimetre grains are not en…
In most theories of planet formation, the snow-line represents a boundary between the emergence of the interior rocky planets and the exterior ice giants. The wide separation of the snow-line makes the discovery of transiting worlds challenging, yet transits would allow for detailed subsequent characterization. We present the discovery of Kepler-421b, a Uranus-sized exoplanet transiting a G9/K0 dwarf once every 704.2 days in a near-circular orbit. Using public Kepler photometry, we demonstrate that the two observed transits can be uniquely attributed to the 704.2 day period. Detailed light cur…
While giant planet occurrence rates increase with stellar mass, occurrence rates of close-in super-Earths decrease. This is in contradiction to the expectation that the total mass of the planets in a system scale with the protoplanetary disc mass and hence the stellar mass. Since the snow line plays an important role in the planet formation process we examine differences in the temperature structure of protoplanetary gas discs around stars of different mass. Protoplanetary discs likely contain a dead zone at the midplane that is sufficiently cold and dense for the magneto-rotational instabilit…
In the currently-favored paradigm of planet formation, the location of the snow line in the protoplanetary disk plays a crucial role. Determining the demographics of planets beyond the snow line of stars of various masses is thus essential for testing this model. Microlensing is sensitive to planets that are generally inaccessible to other methods, and in particular is most sensitive to cool planets at or beyond the snow line, including very low-mass (i.e. terrestrial) planets. Hence, microlensing is uniquely suited and so essential for a comprehensive study of this region. Microlensing is als…
Luminosity bursts in young FU Orionis-type stars warm up the surrounding disks of gas and dust, thus inflicting changes on their morphological and chemical composition. In this work, we aim at studying the effects that such bursts may have on the spatial distribution of dust grain sizes and the corresponding spectral index in protoplanetary disks. We use the numerical hydrodynamics code FEOSAD, which simulates the co-evolution of gas, dust, and volatiles in a protoplanetary disk, taking dust growth and back reaction on gas into account. The dependence of the maximum dust size on the water ice …
The spatial origin and detectability of rotational H2O emission lines from Herbig Ae type protoplanetary disks beyond 70 micron is discussed. We use the recently developed disk code ProDiMo to calculate the thermo-chemical structure of a Herbig Ae type disk and apply the non-LTE line radiative transfer code Ratran to predict water line profiles and intensity maps. The model shows three spatially distinct regions in the disk where water concentrations are high, related to different chemical pathways to form the water: (1) a big water reservoir in the deep midplane behind the inner rim, (2) a be…
The architectures of debris disks encode the history of planet formation in these systems. Studies of debris disks via their spectral energy distributions (SEDs) have found infrared excesses arising from cold dust, warm dust, or a combination of the two. The cold outer belts of many systems have been imaged, facilitating their study in great detail. Far less is known about the warm components, including the origin of the dust. The regularity of the disk temperatures indicates an underlying structure that may be linked to the water snow line. If the dust is generated from collisions in an exo-a…
Suggestions have been made that asteroid belts may be important both for the existence of life and perhaps even for the evolution of complex life on a planet. Using numerical models for protoplanetary discs we calculate the location of the snow line, and we propose that asteroid belts are most likely to form in its vicinity. We then show that observations of warm dust in exo-solar systems, thought to be produced by collisions between asteroids in a belt, indicate that asteroid belts (when they exist), indeed coincide with the radial location and the temperature of the snow line. Giant planets …
Recently, an Atacama Large Millimeter/submillimeter Array (ALMA) observation of the water snow line in the protoplanetary disk around the FU Orionis star V883 Ori was reported. The radial variation of the spectral index at mm-wavelengths around the snow line was interpreted as being due to a pileup of particles interior to the snow line. However, radial transport of solids in the outer disk operates on timescales much longer than the typical timescale of an FU Ori outburst ($10^{1}$--$10^{2}$ yr). Consequently, a steady-state pileup is unlikely. We argue that it is only necessary to consider w…
The early stages of planet formation are still not well understood. Coagulation models have revealed numerous obstacles to the dust growth, such as the bouncing, fragmentation and radial drift barriers. We study the interplay between dust coagulation and drift in order to determine the conditions in protoplanetary disk that support the formation of planetesimals. We focus on planetesimal formation via sweep-up and investigate whether it can take place in a realistic protoplanetary disk. We have developed a new numerical model that resolves spatial distribution of dust in the radial and vertica…
We investigate the effect of photodesorption on the snow line position at the surface of a protoplanetary disk around a Herbig Ae/Be star, motivated by the detection of water ice particles at the surface of the disk around HD142527 by Honda et al. For this aim, we obtain the density and temperature structure in the disk with a 1+1D radiative transfer and determine the distribution of water ice particles in the disk by the balance between condensation, sublimation, and photodesorption. We find that photodesorption induced by the far-ultraviolet radiation from the central star depresses the ice-…
We report the first detection of a gap and a ring in 336 GHz dust continuum emission from the protoplanetary disk around TW Hya, using the Atacama Large Millimeter/Submillimeter Array (ALMA). The gap and ring are located at around 25 and 41 au from the central star, respectively, and are associated with the CO snow line at ~30 au. The gap has a radial width of less than 15 au and a mass deficit of more than 23%, taking into account that the observations are limited to an angular resolution of ~15 au. In addition, the 13CO and C18O J = 3 - 2 lines show a decrement in CO line emission throughout…
Planets form in the disks around young stars. Their formation efficiency and composition are intimately linked to the protoplanetary disk locations of "snow lines" of abundant volatiles. We present chemical imaging of the CO snow line in the disk around TW Hya, an analog of the solar nebula, using high spatial and spectral resolution Atacama Large Millimeter/Submillimeter Array (ALMA) observations of N2H+, a reactive ion present in large abundance only where CO is frozen out. The N2H+ emission is distributed in a large ring, with an inner radius that matches CO snow line model predictions. The…
CO has long been thought to be the best tracer to measure gas masses as it is readily detected at (sub)mm wavelengths in many disks. Inferred gas masses from CO in recent ALMA observations of large samples of disks seem inconsistent with their inferred dust masses. The derived gas-to-dust mass ratios from CO are 1-2 orders of magnitude lower than $\sim$100 even if photodissociation and freeze-out are included. Herschel measurements of HD line emission imply gas masses in line with gas-to-dust mass ratios of 100. This suggests that at least one additional mechanism is removing gaseous CO. Here …
Accurate measurements of the physical structure of protoplanetary discs are critical inputs for planet formation models. These constraints are traditionally established via complex modelling of continuum and line observations. Instead, we present an empirical framework to locate the CO isotopologue emitting surfaces from high spectral and spatial resolution ALMA observations. We apply this framework to the disc surrounding IM Lupi, where we report the first direct, i.e. model independent, measurements of the radial and vertical gradients of temperature and velocity in a protoplanetary disc. Th…
Substructures in PPDs, whose ubiquity was unveiled by recent ALMA observations, are widely discussed regarding their possible origins. We carry out global full magnetohydrodynamic (MHD) simulations in axisymmetry, coupled with self-consistent ray-tracing radiative transfer, thermochemistry, and non-ideal MHD diffusivities. The abundance profiles of grains are also calculated based on the global dust evolution calculation, including sintering effects. We found that dust size plays a crucial role in the ring formation around the snow lines of protoplanetary disks (PPDs) through the accretion pro…
Measurements of the gas mass are necessary to determine the planet formation potential of protoplanetary disks. Observations of rare CO isotopologues are typically used to determine disk gas masses; however, if the line emission is optically thick this will result in an underestimated disk mass. With ALMA we have detected the rarest stable CO isotopologue, 13C17O, in a protoplanetary disk for the first time. We compare our observations with the existing detections of 12CO, 13CO, C18O and C17O in the HD163296 disk. Radiative transfer modelling using a previously benchmarked model, and assuming …
