Formation of multi-planetary systems via pebble accretion in externally photoevaporating discs in stellar clusters

TL;DR

The paper addresses how external photoevaporation in stellar clusters influences the formation and final architectures of multi-planet systems formed via pebble accretion. It combines N-body dynamics (Mercury-6) with a 1-D viscous disc model that includes time-dependent external FUV-driven mass loss, plus detailed prescriptions for pebble production, migration, and gas accretion. The study finds that external photoevaporation reduces the pebble reservoir and thus planetary growth, particularly in low-mass discs, while disc mass and planet-planet interactions in higher-mass discs dominate the final architecture, often masking PE effects. The results imply environment-driven differences in planetary demographics, notably fewer and less massive close-in planets in strongly irradiated, low-mass discs and a richer population of small terrestrial wide-orbit planets in scenarios with longer shielding times; resonant configurations remain rare, and future work should couple planet formation models with evolving cluster FUV tracks for realistic predictions.

Abstract

In this paper, we investigate how external photo-evaporation influences the formation, dynamical evolution and the resultant planetary architecture of multi-planet systems born in stellar clusters. We use a model of N-body simulations of multiple planet formation via pebble accretion coupled with a 1-D viscous disc subject to external photo-evaporation. We found that external photo-evaporation reduces the planet growth by reducing the pebble mass reservoir in discs containing multiple planetary embryos across a wide range of disc masses, and is particularly effective in suppressing planet growth in less initially massive discs (< 0.1 M$_{\odot}$). However, in more initially massive ($\geq$ 0.1 M$_{\oplus}$) discs planets lost due to planet-planet interactions dominate the outcome for final resultant total planet mass, masking the effects of external photo-evaporation in curbing the planet mass growth. In terms of the final resulting planetary architectures, the signature of external photo-evaporation is visible in less massive (< 0.1 M$_{\odot}$) discs, with fewer numbers and lower masses of planets surviving in discs irradiated with stronger external FUV radiation. External photo-evaporation also leaves a signature for the wide orbit (> 10 au) terrestrial planets (0.1 - 1 M$_{\oplus}$), with fewer planets populating this region for stronger FUV field. Finally, the 1st-order resonant pairs fraction decreases with stronger FUV radiation, although the resonant pairs occur rarely regardless of the FUV radiation environment, due to the small number of planets that survive gravitational encounters.

Figures (9)

• Figure 1: Two examples of some of the time varying FUV tracks implemented the simulation described by equation \ref{['eqn:FUV_track']}. The blue curve shows an FUV field track with a shielding time $t_{\textrm{sh}} =$ 2 Myrs and a maximum FUV field strength ${F_{\textrm{FUV, max}}} =$$10^3$ G$_0$. The orange curve shows an FUV field track with a shielding time $t_{\textrm{sh}} =$ 1 Myrs and a maximum FUV field strength ${F_{\textrm{FUV, max}}} =$$10^5$ G$_0$.
• Figure 2: The total final planet mass made per disc (averaged over 5 realisations of the same parameters, counting all planets regardless of whether they are lost due to gravitational interactions) as a function of shielding timescale $t_{\textrm{sh}}$ for planets within various ranges of initial semi-major axis (different colors) in discs irradiated by F$_{\textrm{FUV, max}}$ = $10^5$ G$_0$).
• Figure 3: Top panels: evolution of surface density (with lines plotted every 50000 years) for discs with initial mass $M_{d}$ = 0.1 M$_{\oplus}$ which are subject to an external FUV radiation field strength of F$_{\textrm{FUV,max}} = 10^5\,G_0$. The left panel shows the disc that is not shielding and the right panel shows the disc that is shielding for 1.5 Myr. The bottom panels show the evolution of mass $M_p$ and semi-major axis of all the planetary embryos in the disc. The colour indicates the simulation time, and only the first 2.5 million years of the evolution is plotted, as the rapid disc depletion by the strong FUV field makes the gas disc evolution cease after only 1.3 Myr for the left hand non-shielded disc, and only 2.56 Myr for the right hand disc with $t_{\textrm{sh}}$ = 1.5 Myr. The red dashed line indicates the inner grid domain edge, and grey dashed line indicates the inner disc edge. On the bottom panels, the red solid circle and black empty circle indicate bodies that grew to a final mass $\geq 0.1$ M$_{\oplus}$. The red solid circle indicates the final mass and semi-major axis of the ones which survived in the disc by the end of the simulation, the black empty circle indicates the final mass and semi-major axis of the ones that were lost during the simulation due to planet-planet interactions. The small red cross indicates the final mass and semi-major axis the bodies with final mass $< 0.1$$M_{\oplus}$, and the big grey cross indicates the bodies that merged with another body via collision.
• Figure 4: Plots of final planet masses in discs of varying initial masses that are subject to different FUV radiation strengths indicated by different colors: 10 G$_0$ (blue), $10^3$ G$_0$ (orange), $10^5$ G$_0$ (green). Top panels: the top left panel shows the total final planet masses formed in discs regardless of whether the formed planets were later lost; the top right panel shows the total final planet masses left in discs at the end of simulations after some planets were lost due to planet-planet interactions. The dots shows the value of total final planet mass in each of 5 runs with the same parameters, and solid line shows the averaged value of the 5 runs. Bottom panels: bottom left panel shows the ratio of final planet mass made (averaged over 5 runs) in discs subject to different radiation strengths compared to the planets made in disc subject to weakest radiation (10 G$_0$); bottom right panel shows the ratio of the final planet mass remaining (averaged over 5 runs) in discs subject to different radiation strengths compared to the planets remaining in discs subject to the weakest radiation (10 G$_0$).
• Figure 5: Number of planets (mass $M_p \geq$ 10 M$_\oplus$) per disc (averaged over 5 realisations of the same parameters) as a function of varying initial disc masses, radiated by different FUV radiation strengths indicated by different colors: 10 G$_0$ (blue), $10^3$ G$_0$ (orange), $10^5$ G$_0$ (green). Top panel: number of planets with M$_p \geq$ 10 M$_\oplus$ formed in discs, regardless of whether the formed planets were later lost. Middle panel: number of planets with $M_p \geq$ 10 M$_\oplus$ left in discs with varying masses at the end of simulations after some planets lost due to planet-planet interactions. Bottom panel: fraction of the formed planets that were lost due to planet-planet interaction in discs with varying initial masses.