diff --git "a/6NE5T4oBgHgl3EQfPg5N/content/tmp_files/load_file.txt" "b/6NE5T4oBgHgl3EQfPg5N/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/6NE5T4oBgHgl3EQfPg5N/content/tmp_files/load_file.txt" @@ -0,0 +1,754 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf,len=753 +page_content='Astronomy & Astrophysics manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' dust_filtering ©ESO 2023 January 16, 2023 Leaky Dust Traps: How Fragmentation impacts Dust Filtering by Planets Sebastian Markus Stammler1, Tim Lichtenberg2, Joanna Dr˛a˙zkowska3, and Tilman Birnstiel1, 4 1 University Observatory, Faculty of Physics, Ludwig-Maximilians-Universität München, Scheinerstr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 1, 81679, Munich, Germany 2 Kapteyn Astronomical Institute, University of Groningen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Box 800, 9700 AV Groningen, The Netherlands 3 Max Planck Institute for Solar System Research, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany 4 Exzellenzcluster ORIGINS, Boltzmannstr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2, D-85748 Garching, Germany January 16, 2023 ABSTRACT The nucleosynthetic isotope dichotomy between carbonaceous and non-carbonaceous meteorites has been interpreted as evidence for spatial separation and coexistence of two distinct planet-forming reservoirs for several million years in the solar protoplanetary disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Rapid formation of Jupiter’s core within one million years after CAIs has been suggested as a potential mechanism for spatial and temporal separation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' In this scenario, Jupiter’s core would open a gap in the disk and trap inwards-drifting dust grains in the pressure bump at the outer edge of the gap, separating the inner and outer disk materials from each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' We performed simulations of dust particles in a protoplanetary disk with a gap opened by an early formed Jupiter core, including dust growth and fragmentation as well as dust transport using the dust evolution software DustPy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Our numerical experiments indicate that particles trapped in the outer edge of the gap rapidly fragment and are transported through the gap, contaminating the inner disk with outer disk materials on a timescale that is inconsistent with the meteoritic record.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' This suggests that other processes must have initiated or at least contributed to the isotopic separation between the inner and outer Solar System.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Key words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Meteorites, meteors, meteoroids — Methods: numerical — Protoplanetary disks — Planets and satellites: formation – Planets and satellites: composition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Introduction Recent high-precision isotopic measurements reveal a di- chotomy between carbonaceous and non-carbonaceous mete- orites indicating that both have been formed in separate reser- voirs within the early Solar System (Trinquier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2007, 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Leya et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Warren 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Mezger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Kleine et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Kruijer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' (2017) and Desch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' (2018) argued that these reservoirs must have been well separated for at least two million years without interchanging solid material, proposing the rapid formation of Jupiter’s core opening a gap in the protoplan- etary disk as possible mechanism to prevent the mixing of both reservoirs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The physical origin of the isotopic separation is a po- tential critical clue to the timescales of planet formation in both the inner and outer Solar System (Nimmo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2018), and thus ultimately the origin of the chemical abundances in the terres- trial planets and similar exoplanets (Krijt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Lichten- berg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' This concept of a gap-opening Jupiter preventing dust reser- voir mixing, however, intimately depends on the evolution of the dust flux during the evolution of the protoplanetary disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Dust particles in protoplanetary disks are subject to gas drag and drift (Whipple 1973;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Weidenschilling 1977;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Takeuchi & Lin 2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The radial dust velocity is given by: vd = vg 1 St2 + 1 + 2vP St St2 + 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' (1) The Stokes number St is an aerodynamic measure and propor- tional to the particle size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Small particles with small Stokes num- bers are dragged along with the gas with velocity vg as can be seen by Equation 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The gas is, in contrast to the dust, pressure supported and orbits the star with sub-Keplerian velocities in a typical smooth disk with inward pointing pressure gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The dust particles, on the other hand, are not pressure supported, ex- change angular momentum with the gas and drift in direction of pressure gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Intermediate particle sizes are most affected by this effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Small particles are well coupled to the gas, while large particles are completely decoupled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' From Equation 1 it can be seen that particles with Stokes number of unity will experi- ence maximum drift in direction of the pressure gradient with velocity vP, which is given by: vP = 1 2 c2 s vK ∂ log P ∂ log r , (2) with the sound speed cs, pressure P, and the Keplerian velocity vK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Particles typically grow to maximum sizes with Stokes num- bers between 10−2 to 10−1 (see Birnstiel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2012), depending on the disk parameters, and are therefore affected by radial drift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Growing planets can perturb the pressure structure in the disk by opening a gap in the gas (Paardekooper & Mellema 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Rice et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' At the outer edge of the gap the pressure gradi- ent reverses and is pointing outward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' If the pressure pertubation is large enough, large dust pebbles that are affected by drift can be prevented from crossing the gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The planetary mass at which the pressure pertubation is large enough to stop particle dift is called pebble isolation mass (see Lambrechts et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Bitsch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2018) and is given by Drazkowska et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' (2022) as: Miso ≃ 25 M⊕ �HP/r 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='05 �3 M⋆ M⊙ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' (3) Article number, page 1 of 8 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='05505v1 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='EP] 13 Jan 2023 A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' dust_filtering From NASA’s Juno mission Jupiter’s core is estimated to have a mass of up to 25 M⊕ (Wahl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2017) and would have therefore been able to open a gap and stop the flux of dust peb- bles in the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' A rapid formation of Jupiter’s core could there- fore explain two isolated dust reservoirs with the dust in the outer disk forming the carbonaceous and the dust in the inner disk the non-carbonaceous bodies in the Solar System.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Dr˛a˙zkowska et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' (2019), however, showed in two- dimensional hydrodynamic simulations of gas and dust includ- ing collisional dust evolution, that the pressure bump at the outer edge of planetary gaps does not only show an accumulation of large dust pebbles, but also of small dust particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' But in con- trast to large pebbles, these small particles are not trapped by the pressure bump, they are produced in situ by collisions of large particles leading to fragmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' These small fragments can escape the pressure bump due to diffusion and gas drag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The equations of motion of the dust particles are given by: ∂ ∂tΣd + 1 r ∂ ∂r � rΣdvd − rDΣg ∂ ∂r �Σd Σg �� = 0, (4) with the dust diffusivity given by Youdin & Lithwick (2007) as D = δrc2 s ΩK 1 St2 + 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' (5) with δr being a free parameter that defines the strength of radial dust diffusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Small particles are therefore most affected by dif- fusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' If the diffusivity is high enough, these small particles can diffuse out of the pressure maximum and are dragged with the gas through the gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' If this is the case the inner disk would be contaminated with dust from the outer disk negating the idea of two distinct dust reservoirs separated by an early formed Jupiter core.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' In this letter we test this hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' In section 2 we present a toy model which initially has dust placed only outside of the planet to show as a proof of concept, that solid material can pen- etrate planetary gaps if the dust is subject to fragmentation and diffusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' In section 3 we investigate the influence of the plan- etary mass and the dust diffusivity on the dust permeability of planetary gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' In section 4 we present models with a realis- tic evolution of the planetary mass, as it has been suggested for Jupiter, for models with both fragmentation and bouncing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Fi- nally, in section 5 we discuss our results, before we conclude in section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Toy Model To investigate the influence of a planet on the dust flux in the inner disk, we model dust coagulation and transport in a proto- planetary disk with a planet opening a gap at 5 AU using the dust evolution software DustPy1 (Stammler & Birnstiel 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' In a first simplified toy model, we initialize the disk only with dust outside of a Saturn mass planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Therefore, any dust flux mea- sured inside the planet must have crossed the gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' We use this simplified model to investigate different scenarios: dust growth limited by fragmentation, dust growth limited by bouncing, and unlimited dust growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Furthermore, we compare the toy model to a model without a gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' We initialize the gas surface density with the self similar so- lution of Lynden-Bell & Pringle (1974): Σg (r) = Mdisk 2πr2c � r rc �−1 exp � − r rc � (6) 1 DustPy v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='1 has been used for the simulations presented in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' with a cutoff radius of rc = 30 AU and an initial disk mass of Mdisk = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='05 M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' We impose a gap onto this gas surface density profile originating from a Saturn mass planet located at 5 AU, for which we use the gap profile fits provided by Kanagawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' To maintain this gap profile F (r) throughout the sim- ulation we impose the inverse of this profile onto the turbulent viscosity parameter α, since the product of gas surface density and viscosity is constant in quasi steady-state: α (r) = α0 F (r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' (7) In the default setup, we use α0 = δr = 10−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Please note, that this change in α (r) does not affect the turbulent diffusion of the dust particles, since δr is a constant in our models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' We initialize the dust surface density with a constant gas-to- dust ratio of 100 and the dust size distribution according Mathis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' (1977) as n (a) = a−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='5 with a maximum initial particle size of 1 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' In the toy model we initially have dust only outside of 15 AU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' DustPy simulates dust growth by solving the Smoluchowski equation of a dust mass distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Dust transport is simulated by solving Equation 4 for every dust size individually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The gas surface density is evolved by solving the viscous advection-diffusion equation ∂ ∂tΣg + 1 r ∂ ∂r � rΣgvg � = 0 (8) with the gas velocity given by Lynden-Bell & Pringle (1974) as vg = − 3 Σg √r ∂ ∂r � Σgν √r � (9) and the kinematic viscosity given by ν = αcsHP (10) with the sound speed cs = � kBT/µ, the pressure scale height HP = cs/ΩK, and the viscosity parameter α given by Equation 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' We run five different flavors of the toy model: one with a fragmentation velocity of vfrag = 10 m/s (fiducial), one with no fragmentation at all, one with a fragmentation velocity of 1 m/s, one with bouncing as described by Windmark et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' (2012), and one without a gap, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' F (r) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' In the default collision model used by DustPy particles fragment once their relative collision velocities exceed the fragmentation velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Fragmenting colli- sions of equal size particles lead to catastrophic fragmentation of both collision partners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' If the target particle is significantly larger, only the projectile particle fragments entirely while erod- ing mass off the target particle (Schräpler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Hasegawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The transition between pure sticking and fragmenta- tion is smooth, since DustPy is assuming a velocity distribution of possible collision velocities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' For details on the collision model we refer to Stammler & Birnstiel (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Panel A of Figure 1 shows the initial dust distribution with dust located outside of 15 AU with particles sizes up to 1 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The white lines are contour lines of Stokes numbers St = � 10−3, 10−2, 10−1, 100� with the bold white line corresponding to St = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Panel B shows the fiducial simulation with a Saturn mass planet at 5 AU and the fragmentation velocity vfrag = 10 m/s after 1 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Particles trapped in the pressure bump outside the planetary gap can reach sizes with Stokes numbers of up to St = 10−1 corresponding to particle sizes of a few centimeters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' It can be seen that even small particles are accumulated in the pressure bump, even though their Stokes numbers are too small Article number, page 2 of 8 Sebastian Markus Stammler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' : Leaky Dust Traps: How Fragmentation impacts Dust Filtering by Planets ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='101 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='102 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='Distance from star [AU] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='101 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='102 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='Particle size [cm] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='A: initial ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='101 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='102 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='Distance from star [AU] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='101 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='102 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='Particle size [cm] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='B: fiducial ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='101 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='102 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='Distance from star [AU] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='101 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='102 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='Particle size [cm] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='C: without planet ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='101 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='102 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='Distance from star [AU] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='101 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='102 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='Particle size [cm] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='D: no fragmentation ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='101 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='102 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='Distance from star [AU] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='101 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='102 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='Particle size [cm] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='E: vfrag = 1 m/s ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='101 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='102 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='Distance from star [AU] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='101 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='102 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='Particle size [cm] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='F: bouncing ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='101 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='dust [g/cm²] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Panel A: Initial dust distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The white lines correspond to Stokes numbers of St = � 10−3, 10−2, 10−1, 100� with the bold white line corresponding to St = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' All other panels show snapshots of models at 1 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Panel B: The fiducial toy model with a Saturn mass planet at 5 AU and a fragmentation velocity of 10 m/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Panel C: Model without a planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The vertical dashed lines are the location at which the dust flux is measured in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Panel D: Model without fragmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Panel E: Model with a reduced fragmentation velocity of 1 m/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Bottom right: Model with bouncing instead of fragmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' to be affected by drift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' These small dust particles are produced by collisional fragmentation of larger particles trapped in the bump.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' They diffuse out of the bump and are dragged with the gas contaminating the inner disk with outer disk material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' It can be seen that particles with Stokes numbers of about St = 10−2, corresponding to particle sizes of a few millimeter, can diffuse through the gap into the inner disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Particles in the inner disk can again grow to centimeter sizes and can contribute to phe- nomena like the streaming instability or pebble accretion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Panel C shows a simulation with identical initial conditions but with- out a planet opening a gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The vertical yellow and green dashed lines in panels B and C are the locations at which the dust fluxes shown in Figure 2 are measured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The dust fluxes at the outer disk are identical in both sim- ulations with the solid and dashed green lines overlapping in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The fluxes in the inner disk, however, differ in both simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The onset of dust flux in the inner disk in the sim- ulation with a planet is delayed by about 20 000 yr compared to the simulations without a planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Without a planet, the large dust particles can freely drift into the inner disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' With a planet, how- ever, they are first trapped in the pressure bump at the outer edge of the gap, fragment down to smaller sizes, and diffuse out of the pressure bump before the gas can drag them into the inner disk where they grow to larger particles again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Due to this delayed processing the maximum dust flux is reduced by about one or- der of magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The duration, however, is prolonged such that Article number, page 3 of 8 A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' dust_filtering 103 104 105 106 107 Time [yrs] 10 7 10 6 10 5 10 4 10 3 10 2 Dust flux [M /yr] r = 2 AU r = 15 AU with planet w/o planet 103 104 105 106 107 Time [yrs] 10 2 10 1 100 Fraction of total dust mass accreted Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Top: Comparison of the dust flux in the inner disk (at 2 AU) and outer disk (at 15 AU) in the toy model with a Saturn mass planet at 5 AU (panel B in Figure 1) and a model without a planet (panel C in Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Both green 15 AU lines overlap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Bottom: Total dust mass accreted through the inner disk over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' the total mass of dust flowing through the inner disk is identical after 10 Myr as can be seen in the bottom panel of Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The Saturn mass planet did not separate the inner from outer disk material, but only delayed the material transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Panel D of Figure 1 shows a simulation without fragmen- tation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' In this scenario, particles sizes are limited only by the radial drift, consistent with the model presented by Kobayashi & Tanaka (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' In the center of the pressure bump, the pressure gradient is zero and the growth is in principle unlimited until the particles accumulate at the upper end of the simulation grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' This scenario most closely represents the separation of inner and outer dust reservoirs with only very few particles being able to diffuse through the gap, because they were not able to grow to large par- ticles quickly enough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' It is, however, rather unlikely that the dust particles do not fragment or get eroded at some point given the relative velocities they typically experience (see Blum & Münch 1993;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Wada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Schräpler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Panel E of Figure 1 shows a model with a fragmentation ve- locity of 1 m/s as indicated by recent experiments (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Blum 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Gundlach et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Musiolik & Wurm 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' In this case, the particles cannot reach particles sizes large enough to be efficiently trapped in the pressure bump.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The objective is therefore to halt particle growth without pro- ducing small particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' This can be achieved if the growth is lim- ited by bouncing, when particles simply bounce of each other without growing or fragmenting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Panel F of Figure 1 shows a simulation with the bouncing barrier implemented as described by Windmark et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' In this model, bouncing starts when 103 104 105 106 107 Time [yrs] 10 7 10 6 10 5 10 4 10 3 Pebble flux [M /yr] 103 104 105 106 107 Time [yrs] 10 4 10 3 10 2 10 1 100 Fraction of dust mass accreted no planet 30 M 50 M Msat, r = 10 2 Msat, r = 10 3 Msat, r = 10 4 Msat, r = 10 5 200 M Mjup Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Top: Dust flux through the planetary gap in models with different planet masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The blue line is for a model without a planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The dashed, dotted, and dash-dotted red lines show additional simulations with a Saturn mass planet for different radial dust diffusivity parameters δr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Bottom: Total fraction of outer dust mass accreted through the planetary gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' the relative velocity reaches a few centimeters per second.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' In this case, however, the particles only reach sizes of a few 100 µm corresponding to Stokes numbers lower than 10−3, which is too small to be efficiently trapped in the pressure bump created by the planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The particles can diffuse through the gap and contam- inate the inner disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Full Disk Models The toy model in section 2 served as a proof of concept that planets do not prevent dust flux if particles are subject to frag- mentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' In this section we discuss full disk models with dif- ferent planet masses in which dust is initialized in the entire disk to investigate the dust permeability of the gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The top panel of Figure 3 shows the dust flux through the planetary gap for differ- ent planet masses from 30 Earth masses to one Jupiter mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' In the case of a Saturn mass planet we additionally performed sim- ulations with different dust diffusivity parameters δr (see Equa- tion 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The bottom panel of Figure 3 shows the total fraction of outer disk dust material that has been accreted through the gap over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' In all models the planets have their respective masses already from the beginning of the simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The smallest planetary mass considered here is 30 M⊕, which is already higher than the upper estimate of Jupiter’s core mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The largest mass considered is 1 Mjup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The smallest planetary mass is not capable of efficiently suppressing the dust flux through the gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' After about 300 000 yr almost the entire dust Article number, page 4 of 8 Sebastian Markus Stammler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' : Leaky Dust Traps: How Fragmentation impacts Dust Filtering by Planets mass (horizontal line in bottom panel) of the outer disk has been accreted through the gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Increasing the planetary mass simply delays the accretion time, but is not able to prevent accretion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The maximum delay of accretion seems to be achieved already with a 200 M⊕ planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Increasing the planet mass further to a Jupiter mass planet does not significantly change the accretion history.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' At the end of the simulation at 10 Myr about 80 % of the dust mass has been accreted through the gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The dust diffusivity δr has a more significant influence on the accretion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Increasing the diffusivity by a factor of 10 to δr = 10−2 in the Saturn mass simulation has the same effect as reducing the planet mass by a factor of about 2, mimicking the accretion his- tory of a 40 M⊕ planet with diffusivity of δr = 10−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Note that we only changed δr, while keeping α0 = 10−3 and therefore keeping the shape of planetary gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The relative collision velocities of the dust particles are not affected by this change in δr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Decreas- ing δr by a factor of 10 is more efficient in retaining the dust than having a Jupiter mass planet with the standard diffusivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' In this case only about 10 % of the dust mass has been accreted at the end of the simulation after 10 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Lowering the diffusivity even further to δr = 10−5 reduces the dust permeability further to a about 5 % of the outer disk mass after 10 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' It is however noted that the fraction of outer disk material present in the inner disk is usually significantly larger, since the inner disk material is accreted onto the star on short timescales and only re-supplied with outer disk material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Time-dependent planet mass In the previous models we assumed that the planets are fully formed from the beginning of the simulation and the planet mass does not evolve over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Kruijer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' (2017) argue that the two dust reservoirs have been separated from about 1 Myr to 3−4 Myr after CAI formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' They therefore claim that Jupiter’s core must have been massive enough to open a gap at 1 Myr and must have reached a mass of about 50 M⊕ after 4 Myr to be able to scatter planetesimals from the outer disk to the inner disk where they are observed today in the asteroid belt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' We there- fore performed simulations with a time-dependent planet mass as shown in the top left panel of Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The solid blue line shows an evolutionary track where the planet reaches 30 M⊕ af- ter 1 Myr, 50 M⊕ after 4 Myr and a final mass of Mjup at the end of the simulation after 10 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The bottom left panel of Figure 4 shows the fraction of mass accreted through the planetary gap normalized to the dust mass in the outer disk at 1 Myr when the planet was massive enough to open a gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' We performed simulations with different values of the dust diffusivity δr between 10−5 and 10−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' In the standard run with δr = 10−3 about 80 % of the dust mass has been accreted through the gap after 4 Myr (vertical solid line) when the assem- bly of the meteorite parent bodies has been completed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Even in the low diffusivity run with δr = 10−5 about 60 % of the mass has been accreted though the gap between 1 Myr and 4 Myr, strongly contaminating the inner disk with dust from the outer reservoir on a system-wide scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Lowering the dust diffusivity to very low values does not help keeping both reservoirs separated, since the planet mass is too low in this scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The bottom right panel of Figure 4 shows a model with bouncing instead of fragmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The solid blue line shows a model with radial dust diffusivity δr = 10−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' As already shown in section 2, this is not sufficient to stop dust accretion through the gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Only after 7 Myr when the planet already reached a mass of about 200 M⊕ the gap is deep enough and accretion is halted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Allowing the planet to reach these masses at earlier times would, however, not change the dust redistribution, since these massive planets are able to scatter planetesimals from the outer disk into the inner disk, which is inconsistent with observations from the meteoritic record at these early times (Deienno et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The green solid line shows a model with δr = δt = δz = 10−5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The parameters δt and δz are similar to δr and parametrize the strength of turbulent motion and vertical settling of the particles (see Stammler & Birnstiel 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Pinilla et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2021, for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' In that way the relative velocities between the particles are re- duced, allowing them to grow to larger sizes before being lim- ited by bouncing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' They can therefore be trapped by gaps created by smaller mass planets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' However, even in that case accretion is only halted after abut 3 Myr, when the planet reached a mass of about 40 M⊕.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The dashed green line shows a model where the planet reaches a mass of 40 M⊕ already after 1 Myr (dashed line in top left panel of Figure 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' In this case accretion of dust through the gap is efficiently stopped at 1 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The top right panel of Fig- ure 4 shows a snapshot of this simulation after 4 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The inner disk is heavily depleted in dust, all of which has been accreted onto the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The dust mass in the inner disk at this stage was all supplied from the outer disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Meteoritic bodies formed in the inner disk would therefore be entirely made out of outer disk material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Discussion Isotopic measurements of meteoritic material indicate that me- teorites must have formed in two dust reservoirs, that coexisted spatially separated for several million years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The early formation of Jupiter’s core has been proposed as natural explanation for the observed separation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' A planet exceeding the pebble isolation mass opens a gap in the gas disk creating a pressure bump at the outer edge of the gap, which can trap large dust particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Two- dimensional hydrodynamical simulations by Dr˛a˙zkowska et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' (2019) including dust coagulation and fragmentation showed an overabundance of small dust particles at the location of the pres- sure bump, which should be too small to be efficiently trapped.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' These particles were created in fragmenting collision of large dust pebbles that have been trapped in the pressure bump.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' These small dust fragments can diffuse out of the bump and can be dragged by the gas through the gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Our simulations in this work suggest that collisional frag- mentation of dust pebbles in pressure bumps and subsequent dif- fusion of small fragments can act as a leak for dust traps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' As can be seen by Figure 3, gaps opened by planets can only de- lay but not fully prevent dust accretion if particles are subject to fragmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' To act as an efficient dust barrier, particles need to grow to large pebbles that can be trapped without producing small particles as shown in the panel D of Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' We investigated different planet masses and showed in Fig- ure 3 that no planet mass was able to completely isolate the inner disk from outer dust material on timescales that are relevant for the assumed reservoir separation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Even an initial gap formed by a fully-grown Jupiter mass planet would leak 20 % of the outer disk material into the inner disk within 1 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Smaller proto- Jupiter masses typically lead to complete homogenization within ∼ 105 to at maximum a few 106 yr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' This presents a problem for the suggestion that the age differences in carbonaceus and non-carbonaceous meteorites may be used as a tracer to track the growth timescale of proto-Jupiter within the disk (Kruijer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Alibert et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2018): the initial spatial distribution of nucleosynthetic isotopes at the end of disk infall is degenerate Article number, page 5 of 8 A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' dust_filtering 0 2 4 6 8 10 Time [Myr] 0 50 100 150 200 250 300 Planet mass [M ] default model rapid early growth 1 2 3 4 5 6 7 8 9 10 Time [Myr] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='0 Fraction of dust mass accreted Fragmentation r = 10 3 r = 10 4 r = 10 5 1 2 3 4 5 6 7 8 9 10 Time [Myr] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='0 Fraction of dust mass accreted Bouncing i = 10 3 i = 10 5 i = 10 5 101 102 Distance from star [AU] 10 4 10 3 10 2 10 1 100 101 102 Particle size [cm] 10 5 10 4 10 3 10 2 10 1 100 101 dust [g/cm²] Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Top left: Evolution of the planetary mass in the time-dependent model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The solid line shows the default model where the planet reaches 20 M⊕ at 1 Myrs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The dashed line shows the evolution in a model with rapid early growth in which the planet reaches 40 M⊕ at 1 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Bottom left: Fraction of outer disk dust mass accreted through the gap after 1 Myr in the default planetary mass evolution model for different values of dust diffusivity δr with fragmentation limited growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Bottom right: The solid lines show the fraction of outer disk material accreted through the gap after 1 Myr for bouncing limited growth for different values of the δi parameters in the default planetary growth model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The dashed green line shows a model of bouncing limited growth with δi = 10−5 and rapid early growth of the planet (dashed line in top left panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The vertical lines mark 4 Myr until which both reservoirs need to be separated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Top right: Snapshot of the dust distribution at 4 Myr for the model with bouncing limited growth and δi = 10−5 (dashed green line in bottom right panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The inner disk is depleted in dust and only supplied with small amounts of outer disk material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' with different Jupiter growth tracks in the Jupiter barrier hypoth- esis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Only significantly lowering the dust diffusivity to a value of δr = 10−5 could decrease the dust permeability such that the inner disk is only contaminated with a few percent of outer disk material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' However, isolating the inner disk from dust flux would quickly drain the inner disk from solids that got accreted onto the star, which was also previously noted by Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' At later stages the dust in the inner disk then consists to large parts of outer disk material that has been slowly diffused through the gap, which is inconsistent with the meteoritic record.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The situation gets worse when using a more realistic evo- lution of the planetary mass, assuming Jupiter’s core reached a mass of 20 M⊕ after 1 Myr and 50 M⊕ after 4 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' These masses are not large enough to isolate the inner disk even in models with very low diffusivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Even in the most optimistic cases at least 60 % of the outer disk dust has been accreted through the planetary gap after 4 Myr as can be seen by Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' However, increasing the core mass even more and earlier would enable Jupiter to scatter outer disk planetesimals into the inner disk pol- luting the inner dust reservoir, which has not been accounted for in this simple model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Only in models with bouncing lim- ited growth without small particles, early planetary growth and reduced relative particle collision velocities, the inner disk can be efficiently isolated from the inner disk as seen by Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' In these cases, however, the inner disk is quickly depleted from dust and only re-supplied from small amount of outer disk ma- terial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Meteoritic bodies formed in the inner disk after this point would therefore consist almost entirely of outer disk material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Dr˛a˙zkowska et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' (2019) noted that the shape of planetary gaps in two-dimensional simulations is not axisymmetric, which is ignored in the simple one-dimensional model in this publi- cation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' They further noted, however, that the asymmetry at the planet location would increase the dust flux through the gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Weber et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' (2018) compared one- and two-dimensional simula- tions of dust transport through planetary gaps and indeed found that gaps in two-dimensional simulations are more permeable to dust particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Our one-dimensional simulations, therefore, need to be considered more conservative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' If it is not possible to sepa- rate two reservoirs in one-dimensional models, it is less likely to do so in higher dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' We furthermore assumed a dust fragmentation velocity of 10 m/s, which may be rather high even for icy particles as in- dicated by recent laboratory experiments which are suggesting values of 1 m/s (see Blum 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Gundlach et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Musiolik & Wurm 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Lowering the fragmentation velocity, however, generally decreases the particle sizes making them even less likely to be trapped in pressure bumps (see panel E in Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Other experiments indicate a significantly higher fragmentation Article number, page 6 of 8 Sebastian Markus Stammler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' : Leaky Dust Traps: How Fragmentation impacts Dust Filtering by Planets velocity (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Kimura et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2020) than the 10 m/s used in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' The exact value of the fragmentation velocity, however, does not significantly influence the problem of inner disk con- tamination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Either the fragmentation velocity is exceeded, which will lead to pollution of the inner disk with outer disk material (see panel B of Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Or the fragmentation velocity is larger than the maximum collision velocity of dust particles in the disk, in which case the particles will efficiently grow to larger parti- cles, that are being trapped in the outer edge of the disk, which will quickly deplete the inner disk (see panel D in Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Similarily, the porosity evolution may have an effect on the collisional physics of dust particles (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Suyama et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Krijt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Kobayashi & Tanaka 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' However, as for the fragmentation velocity the details of the collision model do not have a strong effect on the outcome of the simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Either the particles fragment and the inner disk is polluted with outer disk material, or the particles grow unhindered to large particles that are trapped in the pressure bump, which is quickly depleting the inner disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' We furthermore did not consider the formation of planetes- imals in the pressure bump in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Previous publications have shown that the conditions in pressure maxima at the outer edges of gaps can facilitate planetesimal formation (Stammler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Miller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2021) or even the formation of planets (Lau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Jiang & Ormel 2023).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' One could conceive that small dust fragments could not penetrate the inner disk because they are quickly converted into planetesimals before they could transverse the gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' This would, however, require a nearly per- fect planetesimal formation efficiency to efficiently isolate both dust reservoirs, which has not been observed in previous simu- lations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Additionally, planetesimals formed at gap edges quickly have been shown in simulations to quickly ablate (Eriksson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Enstatite and ordinary chondrites would thus have to be explained by planetesimal formation where the dust is replen- ished by, for instance, late-stage planetesimal collisions in the NC reservoir (Dullemond et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Lichtenberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Bernabò et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' This suggests that it is unlikely that the formation of Jupiter could have solely separated both dust reservoirs in the Solar Sys- tem if the dust particles were subject to fragmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' This does not only apply to gaps created by planets, but also to other sub- structures of non-planetary origin where particles are trapped in pressure maxima as described in Brasser & Mojzsis (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Other suggested mechanisms to explain the observations include a temporal change in the isotopic content of inward-streaming dust grains (Schiller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2018), and the formation of multi- ple distinct planetesimal populations in the inner and outer disk (Lichtenberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Morbidelli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Izidoro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' How these physical mechanisms are con- nected to the structures and gaps seen in ALMA disks (Miotello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2022) and the underlying mechanisms of protoplanet for- mation (Drazkowska et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2022) and differentiation (Lichten- berg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 2022) remain to be explored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Conclusions Protoplanet-induced gaps in circumstellar disks are not able to efficiently separate dust in the inner disk from dust in the outer disk on million-year timescales if the particles are subject to fragmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Particles limited by bouncing without producing small fragments are usually too small to be trapped by pressure bumps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Only significantly reducing the relative collision veloci- ties allows particles to be efficiently trapped in pressure bumps within 1 Myr, if the planet grew to 40 M⊕.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' In this case, however, the inner disk is quickly depleted from dust making it difficult to form meteoritic bodies in situ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Our simulations suggest that other physical mechanism must have initiated or at least substantially contributed to the large-scale separation of nucleosynthetic iso- topes observed in the planetary materials of the inner and outer Solar System.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Acknowledgements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' This project has received funding from the European Re- search Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No 714769.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' This project has re- ceived funding by the Deutsche Forschungsgemeinschaft (DFG, German Re- search Foundation) through grants FOR 2634/1 and 361140270.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' This research was supported by the Munich Institute for Astro-, Particle and BioPhysics (MIAPbP) which is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC- 2094 – 390783311.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' JD was funded by the European Union under the Euro- pean Union’s Horizon Europe Research & Innovation Programme 101040037 (PLANETOIDS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Views and opinions expressed are however those of the au- thors only and do not necessarily reflect those of the European Union or the Eu- ropean Research Council.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' Neither the European Union nor the granting authority can be held responsible for them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' TL was supported by grants from the Simons Foundation (SCOL Award No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' 611576) and the Branco Weiss Foundation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=' References Alibert, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=', Venturini, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=', Helled, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6NE5T4oBgHgl3EQfPg5N/content/2301.05505v1.pdf'} +page_content=', et al.' metadata={'source': 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