Dynamical Evolution of Refractory Elements in an alpha-Protoplanetary Disk

Introduction: Planets form within protoplanetary disks surrounding protostars. Both the star and the disk originate from the collapse of a dense molecular cloud. The condensation of the earliest solids, Calcium Aluminium-rich Inclusions (CAIs), marks the time zero of the solar system (ss). These refractory minerals are increasingly thought to form contemporaneously with the assembly of the protoplanetary disk, as their existence requires extremely high temperatures and widespread distribution across the disk [1-2].
In contrast to carbonaceous meteorites (non-CI) and Earth, which are enriched in refractory elements as CAIs, non-carbonaceous chondrites (NCC), which should have formed closer to the Sun, exhibit a sub-solar abundance trend of refractory elements such as Al and Mg, both relative to Si. This could be due to the loss of a refractory-rich component from a disc with the original solar composition [3-4].
[5] has proposed an astrophysical scenario for the sequestration of refractory elements from the NCC source region, which suggests that massive olivine condensation increased the dust concentration in the disk as it cooled down, suppressing magneto-rotational instability and prompting the rapid formation of the first planetesimals. This process isolated the condensed solids, preventing their further interaction with gas-solid equilibrium chemistry. Later, as temperatures dropped further, new “residual condensates” could form from the residual gas. Then, NCCs likely formed from a mixture of these residual condensates and solar-composition materials, including local grains non-accreted into the first planetesimals and possibly grains migrating from outer regions to the residual region, without element fractionation.

Whereas there is a general agreement that CAIs may have condensed in high temperature conditions, a major conundrum is how to make Enstatite and Ordinary chondrites with non-solar composition (with lower Al/Si and Mg/Si ratios compared to solar) [5]. So, here, we individually track the different refractory components (Al, Mg, and Si) and investigate their radial distribution along the disk.
Methods: We simulate a 1D protoplanetary disk using a Python-based code DustPy, to evolve systems with gas and dust [7]. We initially distribute the gas surface density radially following [8]. We have also modeled the early infall into the disk by implementing an external source term, Sext, with a flux of mass of 0.5e-5MSun/year falling within 0.2au (Fig. 1).
Our planar disk extends from 0.1 to 100 au with 40 grid cells, from which 16 refined cells around 2 au. To accurately study dust growth evolution, each radial point contains 78 logarithmically spaced mass bins every mass decade, and the growth and fragmentation of dust is calculated using Smoluchowski's equation. We set the standard dust/gas ratio value to 0.01. The newly formed star has radius RStar = 0.1au, mass MStar = 0.3MSun. Dust grain sizes start with minimum radii of 0.5 microns and bulk densities of around 1.25 g cm-3.

Results: Figure 3 showcases the evolution of surface density of refractory elements (Al, Mg, and Si) when we apply the  phase equilibrium codeFASTCHEMCOND [10-11] in the post-simulation. The pressure maxima in surface density occurs now near 1au after hundreds of years due to evolution of pressure profile. As the infall material reaches the midplane, it accumulates in the inner disk region, increasing the pressure in it. This material moves outwards due to the viscous spreading, reaching the condensation zone (gray dotted line), when some gas starts to condensate. Figure 4 presents
the average radial velocity of gas and dust. Small dust grains are the most abundant in the first thousand years and they are strongly coupled to the gas flow. Fractionation of the element abundances are observed during all evolution of the disk, especially in the condensation fronts.
Our results show that the dynamical evolution of a viscously evolving protoplanetary disk, when coupled with realistic dust growth and condensation models, naturally leads to the fractionation of refractory elements such as Al, Mg, and Si. The emergence of a pressure bump near the MRI front, as a result of the viscosity transition, prevents the immediate inward drift of solids and promotes a local accumulation of their surface density. This process leads to variations in condensation of the gas, which results in element fractionation over time. These findings support the idea that the observed depletion of refractory elements in non-carbonaceous chondrites is caused by early disc processes.
Our next steps will investigate the relationship between radial mixing and chemical evolution as both the disk becomes accretionary and the global temperature of the disk cools.
References: [1] Drążkowska, J. & Dullemond, C. P. (2018) AAP, 614, A62 [2] Pignatale F. C. et al. (2018) AJL, 867, L23 [3] Larimer J. W. (1979) Icarus, 40, 446-454. [4] Alexander, C.M.O’D. (2019). Geochim. Cosmochim., 254, 246 [5] Morbidelli A. (2020) Earth and Planet. Sci. Letters 538,116220 [7] Charnoz S. et al. (2019), A&A 627, A50 [8] Lynden-Bell & Pringle (1974) MNRAS 168, 603-637 [9] Birnstiel T. et al. (2012) A&A 539, A148 [10] Zhu, Z. et al. (2010) ApJ, 713, 1134 [11] Kitzmann D. et al. (2024) MNRAS 527, 7263–7283 [12] Stock J. W. et al. (2018) MNRAS, 479, 865.

 

FIGURE 1: Surface density evolution (y-left) of gas (blue line) and 100 x dust (orange line). Dust-to-gas ratio (gray solid line, y-right) as a function of distance r over time. Dotted gray line stands for condensation temperature, Tcond, before which dust is evaporated.

 

 

FIGURE 2: The graph shows the temperature (blue line, y-left) and pressure (black line, y-right) profiles evolution as a function of distance r over time. It is possible to note the pressure bump rising around 2au.

 

FIGURE 3: Surface density profiles of aluminium (Al, orange), magnesium (Mg, red), and silicon (Si, cyan) in both dust and gas phases (solid and dashed lines, respectively). Dotted and dashed black lines stand for condensation and MRI temperatures, respectively.

 

FIGURE 4. Mean radial velocities of dust (orange line) and gas (blue line). Dotted and dashed gray lines stand for condensation and MRI temperatures, respectively.