Earth Masses Research Articles

Dust ring and gap formation by gas flow induced by low-mass planets embedded in protoplanetary disks. II. Time-dependent model

The observed dust rings and gaps in protoplanetary disks could be imprints of forming planets. Even low-mass planets in the 1--10 Earth-mass regime, which have not yet carved deep gas gaps, can generate such dust rings and gaps by driving a radially-outward gas flow, as shown in previous work. However, understanding the creation and evolution of these dust structures is challenging due to dust drift and diffusion, requiring an approach beyond previous steady state models. Here we investigate the time evolution of the dust surface density influenced by the planet-induced gas flow based on post-processing three-dimensional hydrodynamical simulations. We find that planets larger than a dimensionless thermal mass of $m=0.05$ corresponding to $0.3$ Earth mass at 1 au or 1.7 Earth masses at 10 au generate dust rings and gaps provided that solids have small Stokes numbers St and that the disk midplane is weakly turbulent ($ diff As dust particles pile up outside the orbit of the planet, the interior gap expands with time when the advective flux dominates over diffusion. Dust gap depths range from a factor of a few to several orders of magnitude, depending on planet mass and the level of midplane particle diffusion. We constructed a semi-analytic model describing the width of the dust ring and gap, and then compared it with the observational data. We find that up to 65<!PCT!> of the observed wide-orbit gaps could be explained as resulting from the presence of a low-mass planet, assuming diff and St However, it is more challenging to explain the observed wide rings, which in our model would require the presence of a population of small particles ($ Further work is needed to explore the role of pebble fragmentation, planet migration, and the effect of multiple planets.

Evolution of gas envelopes and outgassed atmospheres of rocky planets that formed via pebble accretion

In this work, we present results of numerical simulations of the formation and early evolution of rocky planets through pebble accretion, with an emphasis on hydrogen envelope longevity and the composition of the outgassed atmosphere. We modelled planets with a range in mass from 0.1 to 5 Earth masses that orbit between 0.7 and 1.7 AU. The composition of the outgassed atmosphere was calculated with the partial pressure of free oxygen fit to geophysical models of magma ocean self-oxidation. The combined X-ray and UV (XUV) radiation-powered photoevaporation is considered as the main driver of atmospheric escape. We modelled planets that remain below the pebble isolation mass and hence accrete tenuous envelopes only. We considered slow, medium, or fast initial stellar rotation for the temporal evolution of the XUV flux. The loss of the envelope is a key event that allows the magma ocean to crystallise and outgas its bulk volatiles. The atmospheric composition of the majority of our simulated planets is dominated by CO$_2$. Our planets accrete a total of 11.6 Earth oceans of water, the majority of which enters the core. The hydrospheres of planets lighter than the Earth reach several times the mass of the Earth's modern oceans, while the hydrospheres of planets ranging from 1 to 3.5 Earth masses are comparable to those of our planet. However, planets of 4-5 Earth masses have smaller hydrospheres due to the trapping of volatiles in their massive mantles. Overall, our simulations demonstrate that hydrogen envelopes are easily lost from rocky planets and that this envelope loss triggers the most primordial partitioning of volatiles between the solid mantle and the atmosphere.

Primitive asteroids as a major source of terrestrial volatiles.

The origins of Earth's volatiles are debated. Recent studies showed that meteorites display unique mass-independent isotopic signatures of the volatile element Zn, suggesting that Earth's Zn originated from materials derived from different regions of the Solar System. However, these studies largely omitted meteorites from the differentiated planetesimals thought to represent the Earth's building blocks, which underwent melting and substantial volatile loss. Here, we characterize the mass-independent Zn isotope compositions of meteorites from such planetesimals. We incorporate these results in mixing models that aim to reproduce Earth's abundance and isotope compositions of Zn and other elements. Our results suggest that, while differentiated planetesimals supplied ~70% of Earth's mass, they provided only ~10% of its Zn. The remaining Zn was supplied by primitive materials that did not experience melting and associated volatile loss. Combined with other findings, our results imply that an unmelted primitive material is likely required to establish the volatile budgets of the terrestrial planets.

Resonant amplitude distribution of the Hilda asteroids and the free-floating planet flyby scenario

In some recent work, we provided a quantitative explanation for the number asymmetry of Jupiter Trojans by hypothesizing a free-floating planet (FFP) flyby into the Solar System. In support of that explanation, this paper examines the influence of the same FFP flyby on the Hilda asteroids, which orbit stably in the 3:2 mean motion resonance with Jupiter. The observed Hilda population exhibits two distinct resonant patterns: (1) a lack of Hildas with resonant amplitudes <40° at eccentricities <0.1; (2) a nearly complete absence of Hildas with amplitudes <20°, regardless of eccentricity. Previous models of Jupiter migration and resonance capture could account for the eccentricity distribution of Hildas but have failed to replicate the unusual absence of those with the smallest resonant amplitudes, which theoretically should be the most stable. Here we report that the FFP flyby can trigger an extremely rapid outward migration of Jupiter, causing a sudden shift in the 3:2 Jovian resonance. Consequently, Hildas with varying eccentricities would have their resonant amplitudes changed by different degrees, leading to the observed resonant patterns. We additionally show that, in our FFP flyby scenario, these patterns are consistently present across different resonant amplitude distributions of primordial Hildas arising from various formation models. We also place constraints on the potential parameters of the FFP, suggesting it should have an eccentricity of 1-1.3 or larger, an inclination up to 30° or higher, and a minimum mass of about 50 Earth masses.

Statistics and Habitability of F-type Star–Planet Systems

F-type star–planet systems represent an intriguing case for habitability studies. Although F-type stars spend considerably less time on the main sequence (MS) than G-, K-, and M-type stars, they still offer a unique set of features, allowing for the principal possibility of exolife. Examples of these features include the increased widths of stellar habitable zones as well as the presence of enhanced UV flux, which in moderation may have added to the origin of life in the Universe. In this study, we pursue a detailed statistical analysis of the currently known planet-hosting F-type stars by making use of the NASA Exoplanet Archive. After disregarding systems with little or no information on the planet(s), we identify 206 systems of interest. We also evaluate whether the stars are on the MS based on various criteria. In one approach, we use the stellar evolution code MESA. Depending on the adopted criterion, about 60–80 stars have been identified as MS stars. In 18 systems, the planet spends at least part of its orbit within the stellar habitable zone. In one case, i.e., HD 111998, known as 38 Vir, the planet is situated in the habitable zone at all times. Our work may serve as a basis for future studies, including studies on the existence of Earth-mass planets in F-type systems, as well as investigations of possibly habitable exomoons hosted by exo-Jupiters, as the lowest-mass habitable zone planet currently identified has a mass estimate of 143 Earth masses.

A Relativistic Framework to Estimate Clock Rates on the Moon

As humanity aspires to explore the solar system and investigate distant worlds such as the Moon, Mars, and beyond, there is a growing need to estimate and model the rate of clocks on these celestial bodies and compare them with the rate of standard clocks on Earth. According to Einstein’s theory of relativity, the rate of a standard clock is influenced by the gravitational potential at its location and its relative motion. A convenient choice of local reference frames allows for the comparison of local time variations of clocks due to gravitational and kinematic effects. We estimate the rate of clocks on the Moon using a locally freely falling reference frame coincident with the center of mass of the Earth–Moon system. A clock near the Moon’s selenoid ticks faster than one near the Earth’s geoid, accumulating an extra 56.02 μs day−1 over the duration of a lunar orbit. This formalism is then used to compute the clock rates at Earth–Moon Lagrange points. Accurate estimation of the rate differences of coordinate times across celestial bodies and their intercomparisons using clocks on board orbiters at Lagrange points as time transfer links is crucial for establishing reliable communications infrastructure. This understanding also underpins precise navigation in cislunar space and on celestial bodies’ surfaces, thus playing a pivotal role in ensuring the interoperability of various position, navigation, and timing systems spanning from Earth to the Moon and to the farthest regions of the inner solar system.

Giant planet formation in the Solar System

The formation history of Jupiter has been of interest due to its ability to shape the solar system’s history. Yet little attention has been paid to the formation and growth of Saturn and the other giant planets. Here we explore through N-body simulations the implications of the simplest disc and pebble accretion model with steady-state accretion and an assumed ring structure in the disc at 5 AU on the formation of the giant planets in the solar system. We conducted a statistical survey of different disc parameters and initial conditions of the protoplanetary disc to establish which combination best reproduces the present outer solar system. We examined the effect of the initial planetesimal disc mass, the number of planetesimals and their size-frequency distribution slope, pebble accretion prescription and sticking efficiency on the likelihood of forming gas giants and their orbital distribution. The results reveal that the accretion sticking efficiency is the most sensitive parameter to control the final masses and number of giant planets. We have been unable to replicate the formation of all three types of giant planets in the solar system in a single simulation. The probability distribution of the final location of the giant planets is approximately constant in logr, suggesting there is a slight preference for formation closer to the Sun but no preference for more massive planets to form closer. The eccentricity distribution has a higher mean for more massive planets indicating that systems with more massive planets are more violent. We compute the average formation time for proto-Jupiter to reach 10 Earth masses to be 〈tc,J〉=1.1±0.3 Myr and for proto-Saturn 〈tc,S〉=3.3±0.4 Myr, while for the ice giants this increases to 〈tc,I〉=4.9±0.1 Myr. The formation timescales of the cores of the gas giants are distinct at >95% confidence, suggesting that they formed sequentially.

Comparative analysis of the impact on societies of silicon technology against that of steel

Silicon is one of the most important elements in the world today, and its content in the Earths crust reaches 26%, second only to oxygen. Iron is the fourth most abundant element in the Earths crust, accounting for more than 5% of the Earths mass. It makes up most of the Earths core. Both of them play a vital role in daily human life and economic development. Silicon electronics industry, computer, composite materials, life technology, and other important pillars. Iron is used in construction, manufacturing, transportation, and so on. This article will describe the discovery of two elements and their development history. In addition, this paper analyzes the similarities and differences between the two from different aspects, comparing their impact on society. Finally, this paper gives some prospects for them. The insight gained from this paper can reinforce the understanding of the history of its exploration and their different role in social development.

APPROACHES TO ASSESSING THE STABILITY OF BANK PROTECTION STRUCTURES OF WATERBODIES: ANALYSIS OF CONSTRUCTIONS AND MODELS FOR THEIR CALCULATION

The article analyzes the theoretical foundations for determining the stress state in a soil mass and the design of fastening the bank slope of reservoirs. Scientific research and theoretical principles on determining the forces that act on a bank protection structure have been systematized. Methodological approaches to the static calculation of bank protection for indirectly vertical structures are proposed, taking into account the relationship between the load on the structure and its deformation. The purpose of the research is to ensure the stability and reliability of bank protection structures and to substantiate directions for improving technical solutions in modern conditions. The work analyzes the use of various types of slope fastenings for bank protection structures in accordance with the requirements of State construction standards. It is proposed to focus research on sheet piling shore fastenings, as a modern and progressive technology for bank protection. The "soil massif - fastening structure" system is considered as a calculation model in the form of a one-sided type, which is an elastic element, which makes it possible to apply the modern apparatus of the theory of elasticity in considering this problem. This makes it possible to accept a linear relationship between stress and strain and obtain sufficient accuracy, which is confirmed by the available results of domestic and foreign research. For calculations of deformations, and assessment of the strength and stability of soil massifs and foundations, it is proposed to pay direct attention to the characteristics of the mechanical properties of soils, while three stages of foundation deformation are considered. The formulated differential equations of the equilibrium of the soil massif make it possible to solve a wide range of issues related to the limit equilibrium and to obtain the calculated parameters of the pressure of earth masses on the retaining walls of shore fortifications of the oblique-vertical type. The results of the research analysis are recommended for use in determining the main loads on hydraulic structures, substantiating technical solutions for the development and improvement of slope and slope-vertical types of bank protection of reservoirs.

Low-mass planets falling into gaps with cyclonic vortices

ABSTRACT We investigate the planetary migration of low-mass planets ($M_p\in [1,15]\, \mathrm{ M}_{\oplus }$, here $\mathrm{ M}_{\oplus }$ is the Earth mass) in a gaseous disc containing a previously formed gap. We perform high-resolution 3D simulations with the fargo3d code. To create the gap in the surface density of the disc, we use a radial viscosity profile with a bump, which is maintained during the entire simulation time. We find that when the gap is sufficiently deep, the spiral waves excited by the planet trigger the Rossby wave instability, forming cyclonic (underdense) vortices at the edges of the gap. When the planet approaches the gap, it interacts with the vortices, which produce a complex flow structure around the planet. Remarkably, we find a widening of the horseshoe region of the planet produced by the vortex at the outer edge of the gap, which depending on the mass of the planet differs by at least a factor of two with respect to the standard horseshoe width. This inevitably leads to an increase in the co-rotation torque on the planet and produces an efficient trap to halt its inward migration. In some cases, the planet becomes locked in co-rotation with the outer vortex. Under this scenario, our results could explain why low-mass planets do not fall towards the central star within the lifetime of the protoplanetary disc. Lastly, the development of these vortices produces an asymmetric temporal evolution of the gap, which could explain the structures observed in some protoplanetary discs.

Method for monitoring and forecasting landslide phenomenon based on machine learning

A landslide involves the downward movement of a mass of rock, debris, earth, or soil. Landslides happen when gravitational forces and other types of shear stresses on a slope surpass the shear strength of the materials. Additionally, landslides can be triggered by processes that weaken the shear strength of the slope's material. Shear strength primarily depends on two factors such as frictional strength, which is the resistance to movement between the interacting particles of the slope material, and cohesive strength, which is the bonding between those particles. A landslide is a terrible natural disaster that causes much damage to both human life and the economy. It often occurs in steep mountainous areas or hilly regions, ranging in scale from medium to large. It progresses slowly (20–50 mm/year), but when it occurs, it can move at a speed of 3 m/s. Therefore, early detection or prevention of this disaster is an essential and significant task. This paper developed a method to collect and analyze data, with the purpose of determining the possibility of landslide occurrences to reduce its potential losses.•The proposed method is convenient for users to grasp information of landslide phenomenon.•A machine learning model is applied to forecast landslide phenomenon.•Internet of things (IoT) system is utilized to manage and send a warning text to individual email address and mobile devices.

Planet Formation by Gas-assisted Accretion of Small Solids

We compute the accretion efficiency of small solids, with radii 1 cm ≤ R s ≤ 10 m, on planets embedded in gaseous disks. Planets have masses 3 ≤ M p ≤ 20 Earth masses (M ⊕) and orbit within 10 au of a solar mass star. Disk thermodynamics is modeled via 3D radiation-hydrodynamics calculations that typically resolve the planetary envelopes. Both icy and rocky solids are considered, explicitly modeling their thermodynamic evolution. The maximum efficiencies of 1 ≤ R s ≤ 100 cm particles are generally ≲10%, whereas 10 m solids tend to accrete efficiently or be segregated beyond the planet’s orbit. A simplified approach is applied to compute the accretion efficiency of small cores, with masses M p ≤ 1 M ⊕ and without envelopes, for which efficiencies are approximately proportional to Mp2/3 . The mass flux of solids, estimated from unperturbed drag-induced drift velocities, provides typical accretion rates dM p /dt ≲ 10−5 M ⊕ yr−1. In representative disk models with an initial gas-to-dust mass ratio of 70–100 and total mass of 0.05–0.06 M ⊙, the solids’ accretion falls below 10−6 M ⊕ yr−1 after 1–1.5 Myr. The derived accretion rates, as functions of time and planet mass, are applied to formation calculations that compute dust opacity self-consistently with the delivery of solids to the envelope. Assuming dust-to-solid coagulation times of ≈0.3 Myr and disk lifetimes of ≈3.5 Myr, heavy-element inventories in the range 3–7 M ⊕ require that ≈90–150 M ⊕ of solids cross the planet’s orbit. The formation calculations encompass a variety of outcomes, from planets a few times M ⊕, predominantly composed of heavy elements, to giant planets. The peak luminosities during the epoch of the solids’ accretion range from ≈10−7 to ≈10−6 L ⊙.

Randomness and retention: using weak mean motion resonances to constrain Neptune’s late-stage migration

ABSTRACT Planet–planetesimal interactions cause a planet to migrate, manifesting as a random walk in semimajor axis. In models for Neptune’s migration involving a gravitational upheaval, this planetesimal-driven migration is a side-effect of the dynamical friction required to damp Neptune’s orbital eccentricity. This migration is noisy, potentially causing Trans-Neptunian Objects (TNOs) in mean motion resonance to be lost. With N-body simulations, we validate a previously derived analytic model for resonance retention and determine unknown coefficients. We identify the impact of random-walk (noisy) migration on resonance retention for resonances up to fourth order lying between 39 and 75 au. Using a population estimate for the weak 7:3 resonance from the well-characterized Outer Solar System Origins Survey (OSSOS), we rule out two cases: (1) a planetesimal disc distributed between 13.3 and 39.9 au with ≳ 30 Earth masses in today’s size distribution and Tmig ≳ 40 Myr and (2) a top-heavy size distribution with ≳2000 Pluto-sized TNOs and Tmig ≳10 Myr, where Tmig is Neptune’s migration time-scale. We find that low-eccentricity TNOs in the heavily populated 5:2 resonance are easily lost due to noisy migration. Improved observations of the low-eccentricity region of the 5:2 resonance and of weak mean motion resonances with Rubin Observatory’s Legacy Survey of Space and Time will provide better population estimates, allowing for comparison with our model’s retention fractions and providing strong evidence for or against Neptune’s random interactions with planetesimals.

The metal-poor atmosphere of a potential sub-Neptune progenitor

Young transiting exoplanets offer a unique opportunity to characterize the atmospheres of freshly formed and evolving planets. We present the transmission spectrum of V1298 Tau b, a 23-Myr-old warm Jupiter-sized (0.91 ± 0.05 RJ, where RJ is the radius of Jupiter) planet orbiting a pre-main-sequence star. We detect a mostly clear primordial atmosphere with an exceptionally large atmospheric scale height, and a water vapour absorption at a 5σ level of significance, from which we estimate a planetary mass upper limit (23 Earth masses, 0.12 g cm−3 at a 3σ level). This is one of the lowest-density planets discovered so far. We retrieve a low atmospheric metallicity (logZ=−0.7−0.7+0.8solar\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\log{Z}=-0.{7}_{-0.7}^{+0.8}\\,{\\mathrm{solar}}$$\\end{document}), consistent with solar/sub-solar values. Our findings challenge the expected mass–metallicity relation from core-accretion theory. Our observations can instead be explained by in situ formation via pebble accretion together with ongoing evolutionary mechanisms. We do not detect methane, which hints at a hotter-than-expected interior from just the formation entropy of this planet. Our observations suggest that V1298 Tau b is likely to evolve into a sub-Neptune.

The Evolution of Geospheres on an Expanding Earth

The evolution of the geosphere is considered in the light of the expanding Earth hypothesis, an alternative concept of plate tectonics, the fifth axiom of which is the statement about the immutability of the mass and size of the Earth, as well as the mass of water on its surface. A new look at the evolution of the Earth and its geospheres (lithosphere, hydrosphere, cryosphere and biosphere.) is proposed. The physical mechanisms of the not yet understood processes of increasing its size with a simultaneous increase in mass are discussed. For the first time, a physical scenario of the expansion process is proposed. It consists in the constant absorption of dark matter by the Earth in the form of quark nuggets (strangelets), followed by their decay and transformation into ordinary matter. The expansion of the Earth makes it possible to explain not only the large size and mass of land animals at the end of the Paleozoic and Mesozoic, but also to establish the most probable causes of the movement of continents and Great Extinctions.

Al-Biruni A Scientist Beyond His Time

Abū Rayḥān Muḥammad ibn Aḥmad al-Bīrūnī (September 15, 973 – December 13, 1048), a celebrated intellectual from the Islamic world, is recognized as a prodigious genius who thrived in Central Asia over a millennium ago. His innovative work and discoveries often surpassed the understanding of his contemporaries. Al-Biruni's expertise extended across various domains, including astronomy, mathematics, geology, mineralogy, physics, and natural sciences. His contributions to these fields were so monumental that scholars considered him the most scientifically accomplished individual of his time. Al-Biruni's works encompassed concepts such as evolution, equatorial leveling, and astronomy, which were later popularized by renowned figures like Darwin, Mercator, Copernicus, Kepler, and Galileo. Furthermore, he proposed the idea of plate tectonics, which geologists would later confirm in the 1960s, by suggesting that parts of the Earth's crust move and geographic coordinates of cities change over time. With his profound comprehension, al-Biruni accurately explained the causes of orogeny and earthquakes through his insights on the shifts in the Earth's weight distribution, the formation of ridges, and the deepening of valleys. This exceptional scientist rightfully holds a distinguished position among Earth scientists of the previous millennium within the cultural sphere of Iran. Delving into his life and work instills awe in those who appreciate his lasting impact on the scientific community.

Oort Cloud and sednoid formation in an embedded cluster, I: Populations and size distributions

In this paper we report on massive computer simulations aimed to clarify the formation of an Oort Cloud and the adjoining sednoid population during the earliest times of the solar system due to the perturbing effects of the Sun’s birth aggregate, for which we use different embedded cluster models. We define the sednoid population to have semi-major axes between 100 and 1600 astronomical units, and it can be seen as the innermost extension of the Oort Cloud. By also restricting the orbits to perihelion distances exceeding 60 astronomical units, the sednoid population can be regarded as dynamically inert with respect to both planetary and Galactic influences. It includes the objects (90377) Sedna, 2012 VP113 and (541132) Leleākūhonua. We start by creating 12 cluster models, using the NBODY6++GPU code, with three random realisations of four physically different models. In each of these we select six random solar template stars and equip those with a planetary system composed of Jupiter, Saturn and 4000 massless planetesimals representing a population of stray planetesimals in the Jupiter–Saturn zone with a total mass assumed to be about 20 Earth masses. From dynamical simulations of all these 72 variants of the early solar system including the cluster perturbations, we derive the total numbers and orbital characteristics of the sednoid and Oort Cloud populations, including the size distributions resulting from the limiting effects of solar nebula gas drag on extraction efficiency. We find that the predicted number of sednoids varies dramatically depending on the orbital evolution of the solar template star in the cluster. In general, numbers consistent with the existence of the observed sednoids is an expected outcome only for a birth aggregate with a strong central condensation and a relatively long lifetime of the residual gas, whereas other cluster models tend to fail to explain this. In the most successful, concentrated cluster models, we predict the existence of an as yet unseen population of at least 108 km-sized sednoids. However, we note that these cluster models produce an overheated inclination distribution at variance with the observed inclinations. Hence, we conclude that our study points to a possible, severe problem of the embedded cluster scenario in explaining the origin of the sednoids. The Oort Cloud predicted to originate in local, Jupiter–Saturn planetesimals by our simulations amounts to ∼10% of the estimated, current size of the entire Oort Cloud. This shows that such comets, likely characterised by Earth-like D/H ratios, may be a minority though a significant one. In an accompanying paper we discuss the extraction dynamics in some detail, based on the same simulations as here.

Revised Architecture and Two New Super-Earths in the HD 134606 Planetary System

Multiplanet systems exhibit a diversity of architectures that diverge from the solar system and contribute to the topic of exoplanet demographics. Radial velocity (RV) surveys form a crucial component of exoplanet surveys, as their long observational baselines allow for searches for more distant planetary orbits. This work provides a significantly revised architecture for the multiplanet system HD 134606 using both HARPS and UCLES RVs. We confirm the presence of previously reported planets b, c, and d with periods of 12.0897−0.0018+0.0019 , 58.947−0.054+0.056 , and 958.7−5.9+6.3 days and masses of 9.14−0.63+0.65 , 11.0 ± 1, and 44.5 ± 2.9 Earth masses, respectively, with the planet d orbit significantly revised to over double that originally reported. We report two newly detected super-Earths, e and f, with periods of 4.31943−0.00068+0.00075 and 26.9−0.017+0.019 days and masses of 2.31−0.35+0.36 and 5.52−0.73+0.74 Earth masses, respectively. In addition, we identify a linear trend in the RV time series, and the cause of this acceleration is deemed to be a newly detected massive companion with a very long orbital period. HD 134606 now displays four low-mass planets in a compact region near the star, one gas giant further out in the habitable zone, an additional companion in the outer regime, and a low-mass M dwarf stellar companion at large separation, making it an intriguing target for system formation/evolution studies. The location of planet d in the habitable zone proves to be an exciting candidate for future space-based direct imaging missions, whereas continued RV observations of this system are recommended for understanding the nature of the massive, long-period companion.

Dust growth and pebble formation in the initial stages of protoplanetary disk evolution

Aims. The initial stages of planet formation may start concurrently with the formation of a gas-dust protoplanetary disk. This makes the study of the earliest stages of protoplanetary disk formation crucially important. Here we focus on dust growth and pebble formation in a protoplanetary disk that is still accreting from a parental cloud core. Methods. We have developed an original three-dimensional numerical hydrodynamics code, which computes the collapse of rotating clouds and disk formation on nested meshes using a novel hybrid Coarray Fortran-OpenMP approach for distributed and shared memory parallelization. Dust dynamics and growth are also included in the simulations. Results. We found that the dust growth from ~1 µm to 1–10 mm already occurs in the initial few thousand years of disk evolution but the Stokes number hardly exceeds 0.1 because of higher disk densities and temperatures compared to the minimum mass Solar nebular. The ratio of the dust-to-gas vertical scale heights remains rather modest, 0.2–0.5, which may be explained by the perturbing action of spiral arms that develop in the disk soon after its formation. The dust-to-gas mass ratio in the disk midplane is highly nonhomogeneous throughout the disk extent and is in general enhanced by a factor of several compared to the fiducial 1:100 value. Low St hinders strong dust accumulation in the spiral arms compared to the rest of the disk and the nonsteady nature of the spirals is also an obstacle. The spatial distribution of pebbles in the disk midplane exhibits a highly nonhomogeneous and patchy character. The total mass of pebbles in the disk increases with time and reaches a few tens of Earth masses after a few tens of thousand years of disk evolution. Conclusions. We found that protoplanetary disks with an age ≤20 kyr can possess notable amounts of pebbles and feature dust-togas density enhancements in the disk midplane. Hence, these young disks can already be ripe for the planet formation process to start. Multidimensional numerical models of disk formation that consider the coevolution of gas and dust including dust growth are important to improve our understanding of planet formation.

Which stars can form planets: Planetesimal formation at low metallicities

The diversity of exoplanets has been linked to the disc environment in which they form, where the host star metallicity and the formation pathways play a crucial role. In the context of the core accretion paradigm, the initial stages of planet formation require the growth of dust material from micrometre-sized to planetesimal-sized bodies before core accretion can kick in. Although numerous studies have been conducted on planetesimal formation, it is still poorly understood how this process takes place in low-metallicity stellar environments. In this work, we explore how planetesimals are formed in stellar environments with primarily low metallicities. We performed global 1D viscous disc evolution simulations, including the growth of dust particles and the evaporation and condensation of chemical species at ice lines. We followed the formation of planetesimals during disc evolution and tested different metallicities, disc sizes, and turbulent viscosity strengths. We find that at solar and sub-solar metallicities, there is a significant increase in the midplane dust-to-gas mass ratios at the ice lines, but this leads to planetesimal formation only at the water--ice line. In our simulations Fe/H $= -0.6$ is the lower limit of metallicity for planetesimal formation where a few Earth masses of planetesimals can form. Our results further show that for such extreme disc environments, large discs are more conducive than small discs for forming large amounts of planetesimals at a fixed metallicity because the pebble flux can be maintained for a longer time, resulting in a longer and more efficient planetesimal formation phase. At lower metallicities, planetesimal formation is less supported in quiescent discs compared to turbulent discs, which produce larger amounts of planetesimals, because the pebble flux can be maintained for a longer time. The amount of planetesimals formed at sub-solar metallicities in our simulations places a limit on core sizes that could potentially result only in the formation of super-Earths.