Modeling gravitational instabilities in self-gravitating protoplanetary disks with adaptive mesh refinement techniques

The astonishing diversity in the observed planetary population requires theoretical efforts and advances in planet formation theories. Numerical approaches provide a method to tackle the weaknesses of current planet formation models and are an important tool to close gaps in poorly constrained areas. We present a global disk setup to model the first stages of giant planet formation via gravitational instabilities (GI) in 3D with the block-structured adaptive mesh refinement (AMR) hydrodynamics code ENZO. With this setup, we explore the impact of AMR techniques on the fragmentation and clumping due to large-scale instabilities using different AMR configurations. Additionally, we seek to derive general resolution criteria for global simulations of self-gravitating disks of variable extent. We run a grid of simulations with varying AMR settings, including runs with a static grid for comparison, and study the effects of varying the disk radius. Adopting a marginally stable disk profile (Q_init=1), we validate the numerical robustness of our model for different spatial extensions, from compact to larger, extended disks (R_disk = 10, 100 and 300 AU, M_disk ~ 0.05 M_Sun, M_star = 0.646 M_Sun). By combining our findings from the resolution and parameter studies we find a lower limit of the resolution to be able to resolve GI induced fragmentation features and distinct, turbulence inducing clumps. Irrespective of the physical extension of the disk, topologically disconnected clump features are only resolved if the fragmentation-active zone of the disk is resolved with at least 100 cells, which holds as a minimum requirement for all global disk setups. Our simulations illustrate the capabilities of AMR-based modeling techniques for planet formation simulations and underline the importance of balanced refinement settings to reproduce fragmenting structures.Comment: 12 pages, 12 figures; accepted for publication in A&A; for associated movie files, see http://timlichtenberg.net/publications/gi1

Hidden Water in Magma Ocean Exoplanets

We demonstrate that the deep volatile storage capacity of magma oceans has significant implications for the bulk composition, interior, and climate state inferred from exoplanet mass and radius data. Experimental petrology provides the fundamental properties of the ability of water and melt to mix. So far, these data have been largely neglected for exoplanet mass–radius modeling. Here we present an advanced interior model for water-rich rocky exoplanets. The new model allows us to test the effects of rock melting and the redistribution of water between magma ocean and atmosphere on calculated planet radii. Models with and without rock melting and water partitioning lead to deviations in planet radius of up to 16% for a fixed bulk composition and planet mass. This is within the current accuracy limits for individual systems and statistically testable on a population level. Unrecognized mantle melting and volatile redistribution in retrievals may thus underestimate the inferred planetary bulk water content by up to 1 order of magnitude

System-level fractionation of carbon from disk and planetesimal processing

Finding and characterizing extrasolar Earth analogs will rely on interpretation of the planetary system's environmental context. The total budget and fractionation between C-H-O species sensitively affect the climatic and geodynamic state of terrestrial worlds, but their main delivery channels are poorly constrained. We connect numerical models of volatile chemistry and pebble coagulation in the circumstellar disk with the internal compositional evolution of planetesimals during the primary accretion phase. Our simulations demonstrate that disk chemistry and degassing from planetesimals operate on comparable timescales and can fractionate the relative abundances of major water and carbon carriers by orders of magnitude. As a result, individual planetary systems with significant planetesimal processing display increased correlation in the volatile budget of planetary building blocks relative to no internal heating. Planetesimal processing in a subset of systems increases the variance of volatile contents across planetary systems. Our simulations thus suggest that exoplanetary atmospheric compositions may provide constraints on $when$ a specific planet formed.Comment: Accepted for publication in ApJL; 10 pages, 4 figures; summaries available at https://bit.ly/LichtenbergKrijt21blog (blog) and https://bit.ly/LichtenbergKrijt21video (video

The effects of short-lived radionuclides and porosity on the early thermo-mechanical evolution of planetesimals

The thermal history and internal structure of chondritic planetesimals, assembled before the giant impact phase of chaotic growth, potentially yield important implications for the final composition and evolution of terrestrial planets. These parameters critically depend on the internal balance of heating versus cooling, which is mostly determined by the presence of short-lived radionuclides (SLRs), such as aluminum-26 and iron-60, as well as the heat conductivity of the material. The heating by SLRs depends on their initial abundances, the formation time of the planetesimal and its size. It has been argued that the cooling history is determined by the porosity of the granular material, which undergoes dramatic changes via compaction processes and tends to decrease with time. In this study we assess the influence of these parameters on the thermo-mechanical evolution of young planetesimals with both 2D and 3D simulations. Using the code family I2ELVIS/I3ELVIS we have run numerous 2D and 3D numerical finite-difference fluid dynamic models with varying planetesimal radius, formation time and initial porosity. Our results indicate that powdery materials lowered the threshold for melting and convection in planetesimals, depending on the amount of SLRs present. A subset of planetesimals retained a powdery surface layer which lowered the thermal conductivity and hindered cooling. The effect of initial porosity was small, however, compared to those of planetesimal size and formation time, which dominated the thermo-mechanical evolution and were the primary factors for the onset of melting and differentiation. We comment on the implications of this work concerning the structure and evolution of these planetesimals, as well as their behavior as possible building blocks of terrestrial planets.Comment: 19 pages, 11 figures, 5 tables; accepted for publication in Icarus; for associated video files, see http://timlichtenberg.net/2015_porosity.html or http://dx.doi.org/10.1016/j.icarus.2016.03.00

Reduced Late Bombardment on Rocky Exoplanets around M Dwarfs

Ocean-vaporizing impacts of chemically reduced planetesimals onto the early Earth have been suggested to catalyze atmospheric production of reduced nitrogen compounds and trigger prebiotic synthesis despite an oxidized lithosphere. While geochemical evidence supports a dry, highly reduced late veneer on Earth, the composition of late-impacting debris around lower-mass stars is subject to variable volatile loss as a result of their hosts’ extended pre-main-sequence phase. We perform simulations of late-stage planet formation across the M-dwarf mass spectrum to derive upper limits on reducing bombardment epochs in Hadean-analog environments. We contrast the solar system scenario with varying initial volatile distributions due to extended primordial runaway greenhouse phases on protoplanets and the desiccation of smaller planetesimals by internal radiogenic heating. We find a decreasing rate of late-accreting reducing impacts with decreasing stellar mass. Young planets around stars „0.4 Me experience no impacts of sufficient mass to generate prebiotically relevant concentrations of reduced atmospheric compounds once their stars have reached the main sequence. For M-dwarf planets to not exceed Earth- like concentrations of volatiles, both planetesimals, and larger protoplanets must undergo extensive devolatilization processes and can typically emerge from long-lived magma ocean phases with sufficient atmophile content to outgas secondary atmospheres. Our results suggest that transiently reducing surface conditions on young rocky exoplanets are favored around FGK stellar types relative to M dwarfs

CO2 ocean bistability on terrestrial exoplanets

Cycling of carbon dioxide between the atmosphere and interior of rocky planets can stabilize global climate and enable planetary surface temperatures above freezing over geologic time. However, variations in global carbon budget and unstable feedback cycles between planetary sub-systems may destabilize the climate of rocky exoplanets toward regimes unknown in the Solar System. Here, we perform clear-sky atmospheric radiative transfer and surface weathering simulations to probe the stability of climate equilibria for rocky, ocean-bearing exoplanets at instellations relevant for planetary systems in the outer regions of the circumstellar habitable zone. Our simulations suggest that planets orbiting G- and F-type stars (but not M-type stars) may display bistability between an Earth-like climate state with efficient carbon sequestration and an alternative stable climate equilibrium where CO2 condenses at the surface and forms a blanket of either clathrate hydrate or liquid CO2. At increasing instellation and with ineffective weathering, the latter state oscillates between cool, surface CO2-condensing and hot, non-condensing climates. CO2 bistable climates may emerge early in planetary history and remain stable for billions of years. The carbon dioxide-condensing climates follow an opposite trend in pCO2 versus instellation compared to the weathering-stabilized planet population, suggesting the possibility of observational discrimination between these distinct climate categories

Impact splash chondrule formation during planetesimal recycling

Chondrules are the dominant bulk silicate constituent of chondritic meteorites and originate from highly energetic, local processes during the first million years after the birth of the Sun. So far, an astrophysically consistent chondrule formation scenario, explaining major chemical, isotopic and textural features, remains elusive. Here, we examine the prospect of forming chondrules from planetesimal collisions. We show that intensely melted bodies with interior magma oceans became rapidly chemically equilibrated and physically differentiated. Therefore, collisional interactions among such bodies would have resulted in chondrule-like but basaltic spherules, which are not observed in the meteoritic record. This inconsistency with the expected dynamical interactions hints at an incomplete understanding of the planetary growth regime during the protoplanetary disk phase. To resolve this conundrum, we examine how the observed chemical and isotopic features of chondrules constrain the dynamical environment of accreting chondrite parent bodies by interpreting the meteoritic record as an impact-generated proxy of planetesimals that underwent repeated collision and reaccretion cycles. Using a coupled evolution-collision model we demonstrate that the vast majority of collisional debris feeding the asteroid main belt must be derived from planetesimals which were partially molten at maximum. Therefore, the precursors of chondrite parent bodies either formed primarily small, from sub-canonical aluminum-26 reservoirs, or collisional destruction mechanisms were efficient enough to shatter planetesimals before they reached the magma ocean phase. Finally, we outline the window in parameter space for which chondrule formation from planetesimal collisions can be reconciled with the meteoritic record and how our results can be used to further constrain early solar system dynamics.Comment: 20 pages, 11 figures, 2 tables; accepted for publication in Icarus; associated blog article at goo.gl/5bDqG

CO2 Ocean Bistability on Terrestrial Exoplanets

Cycling of carbon dioxide between the atmosphere and interior of rocky planets can stabilize global climate and enable planetary surface temperatures above freezing over geologic time. However, variations in global carbon budget and unstable feedback cycles between planetary sub‐systems may destabilize the climate of rocky exoplanets toward regimes unknown in the Solar System. Here, we perform clear‐sky atmospheric radiative transfer and surface weathering simulations to probe the stability of climate equilibria for rocky, ocean‐bearing exoplanets at instellations relevant for planetary systems in the outer regions of the circumstellar habitable zone. Our simulations suggest that planets orbiting G‐ and F‐type stars (but not M‐type stars) may display bistability between an Earth‐like climate state with efficient carbon sequestration and an alternative stable climate equilibrium where CO(2) condenses at the surface and forms a blanket of either clathrate hydrate or liquid CO(2). At increasing instellation and with ineffective weathering, the latter state oscillates between cool, surface CO(2)‐condensing and hot, non‐condensing climates. CO(2) bistable climates may emerge early in planetary history and remain stable for billions of years. The carbon dioxide‐condensing climates follow an opposite trend in pCO(2) versus instellation compared to the weathering‐stabilized planet population, suggesting the possibility of observational discrimination between these distinct climate categories

Late metal-silicate separation on the IAB parent asteroid: Constraints from combined W and Pt isotopes and thermal modelling

The short-lived $^{182}$Hf-$^{182}$W decay system is a powerful chronometer for constraining the timing of metal-silicate separation and core formation in planetesimals and planets. Neutron capture effects on W isotopes, however, significantly hamper the application of this tool. In order to correct for neutron capture effects, Pt isotopes have emerged as a reliable in-situ neutron dosimeter. This study applies this method to IAB iron meteorites, in order to constrain the timing of metal segregation on the IAB parent body. The $\epsilon^{182}$W values obtained for the IAB iron meteorites range from -3.61 $\pm$ 0.10 to -2.73 $\pm$ 0.09. Correlating $\epsilon^{\mathrm{i}}$Pt with $^{182}$W data yields a pre-neutron capture $^{182}$W of -2.90 $\pm$ 0.06. This corresponds to a metal-silicate separation age of 6.0 $\pm$ 0.8 Ma after CAI for the IAB parent body, and is interpreted to represent a body-wide melting event. Later, between 10 and 14 Ma after CAI, an impact led to a catastrophic break-up and subsequent reassembly of the parent body. Thermal models of the interior evolution that are consistent with these estimates suggest that the IAB parent body underwent metal-silicate separation as a result of internal heating by short-lived radionuclides and accreted at around 1.4 $\pm$ 0.1 Ma after CAIs with a radius of greater than 60 km.Comment: 11 pages, 8 figures, 2 tables; open access article under the CC BY-NC-ND license (see http://creativecommons.org/licenses/by-nc-nd/4.0/

Behavioral Design in Online Supermarkets: How Virtual Shopping Cart Functions Impact Sustainable Consumption

In recent years, the negative environmental impact of consumers\u27 dietary habits has become more visible. Accordingly, in-store interventions to promote more sustainable (e.g., organic) food choices have received increased scholarly attention. Thereby, online grocery shopping is gaining momentum as web-applications provide decision support tools such as real-time spending feedback (RSF). Building on budgeting and spending literature, this study provides initial insights on the impact of RSF on consumers’ organic food choices in online supermarkets. Using a free simulation experimental approach, we were able to track participants’ real grocery shopping behavior within a realistic online shopping environment. Within a baseline (no RSF) and an intervention (RSF) condition (between subject design), we show that RSF facilitated participants to stay within their budget and significantly reduced underspending. Somewhat surprisingly in response to the RSF, participants who usually buy fewer organic products purchased significantly more organic food items, both in absolute and relative terms