arXiv subjects

Philip J. Armitage

Publications and source records attributed to Philip J. Armitage.

At least 37 records · Page 2Linked to original sources

arXiv2023

Tidal truncation of circumplanetary disks fails above a critical disk aspect ratio

We use numerical simulations of circumplanetary disks to determine the boundary between disks that are radially truncated by the tidal potential, and those where gas escapes the Hill sphere. We consider a model problem, in which a coplanar circumplanetary disk is resupplied with gas at an injection radius smaller than the Hill radius. We evolve the disk using the PHANTOM Smoothed Particle Hydrodynamics code until a steady-state is reached. We find that the most significant dependence of the truncation boundary is on the disk aspect ratio $H/R$. Circumplanetary disks are efficiently truncated for $H/R \lesssim 0.2$. For $H/R \simeq 0.3$, up to about half of the injected mass, depending on the injection radius, flows outwards through the decretion disk and escapes. As expected from analytic arguments, the conditions ($H/R$ and Shakura-Sunyaev $α$) required for tidal truncation are independent of planet mass. A simulation with larger $α=0.1$ shows stronger outflow than one with $α=0.01$, but the dependence on transport efficiency is less important than variations of $H/R$. Our results suggest two distinct classes of circumplanetary disks: tidally truncated thin disks with dust-poor outer regions, and thicker actively decreting disks with enhanced dust-to-gas ratios. Applying our results to the PDS 70c system, we predict a largely truncated circumplanetary disk, but it is possible that enough mass escapes to support an outward flow of dust that could explain the observed disk size.

astro-ph.EP↗

arXiv2023

The role of the drag force in the gravitational stability of dusty planet-forming disc -- II. Numerical simulations

Young protostellar discs are likely to be both self-gravitating, and to support grain growth to sizes where the particles decoupled from the gas. This combination could lead to short-wavelength fragmentation of the solid component in otherwise non-fragmenting gas discs, forming Earth-mass solid cores during the Class 0/I stages of Young Stellar Object evolution. We use three-dimensional smoothed particle hydrodynamics simulations of two-fluid discs, in the regime where the Stokes number of the particles St>1, to study how the formation of solid clumps depends on the disc-to-star mass ratio, the strength of gravitational instability, and the Stokes number. Gravitational instability of the simulated discs is sustained by local cooling. We find that the ability of the spiral structures to concentrate solids increases with the cooling time, and decreases with the Stokes number, while the relative dynamical temperature between gas and dust of the particles decreases with the cooling time and the disc-to-star mass ratio, and increases with the Stokes number. Dust collapse occurs in a subset of high disc mass simulations, yielding clumps whose mass is close to linear theory estimates, namely 1-10 Earth masses. Our results suggest that if planet formation occurs via this mechanism, the best conditions correspond to near the end of the self-gravitating phase, when the cooling time is long and the Stokes number close to unity.

astro-ph.EP↗

arXiv2023

Saturation of the magnetorotational instability and the origin of magnetically elevated accretion discs

We propose that the strength of angular momentum transport in accretion discs threaded by net vertical magnetic field is determined by a self-regulation mechanism: the magnetorotational instability (MRI) grows until its own turbulent resistivity damps the fastest growing mode on the scale of the disc thickness. Given weak assumptions as to the structure of MRI-derived turbulence, supported by prior simulation evidence, the proposed mechanism reproduces the known scaling of the viscous $α$-parameter, $α\propto β_z^{-1/2}$. Here, $β_z = 8πp_g/B_{z0}^2$ is the initial plasma $β$-parameter on the disc midplane, $B_{z0}$ is the net field, and $p_g $ is the midplane gas pressure. We generalize the argument to discs with strong suprathermal toroidal magnetic fields, where the MRI growth rate is modified from the weak-field limit. Additional sources of turbulence are required if such discs are to become magnetically elevated, with the increased scale heights near the midplane that are seen in simulations. We speculate that tearing modes, associated with current sheets broadened by the effective resistivity, are a possible source of enhanced turbulence in elevated discs.

astro-ph.HE↗

arXiv2023

Revisiting collisional dust growth in Class 0/I protostellar disks: Sweep-up can convert a few $10 M_\oplus$ of dust into kg pebbles in 0.1 Myr

Recent observations suggest that the first stages of planet formation likely take place in the Class 0/I phase of Young Stellar Object evolution, when the star and the disk are still embedded in an infalling envelope. In this study we perform grain coagulation calculations to investigate the very first stage of planet formation, the collisional growth of dust grains, in Class 0/I disks. We find that the slow increase in grain mass by high-velocity collision with much smaller grains ("sweep-up") allows $\sim 50 M_\oplus$ of grains to grow well beyond the fragmentation barrier into $\sim$kg pebbles by the end of Class 0/I (0.1 Myr). We analyze the linear growth and saturation of sweep-up to understand our results quantitatively, and test whether the sweep-up outcome is sensitive to disk parameters and details of the grain coagulation model. The sweep-up pebble population could be important for planet formation, because they are less well-coupled to the gas (compared to the main population below the fragmentation barrier) and therefore more favorable to known mechanisms of dust clump formation (which initiate planetesimal formation). It also contains enough mass to form all planet cores, based on observational estimates of the planet mass budget. Our findings motivate future studies of grain growth and planetesimal formation in Class 0/I disks, including the subsequent evolution of this sweep-up population.

astro-ph.EP↗

arXiv2022

The role of the drag force in the gravitational stability of dusty planet forming disc -- I. Analytical theory

Recent observations show that planet formation is already underway in young systems, when the protostar is still embedded into the molecular cloud and the accretion disc is massive. In such environments, the role of self gravity (SG) and gravitational instability (GI) is crucial in determining the dynamical evolution of the disc. In this work, we study the dynamical role of drag force in self-gravitating discs as a way to form planetesimals in early protoplanetary stages. We obtain the dispersion relation for density-wave perturbations on a fluid composed of two phases (gas and dust) interacting through the common gravitation field and the mutual drag force, and we find that the stability threshold is determined by three parameters: the local dust-to-gas density ratio, the dust relative temperature and the relevant Stokes number. In a region of parameters space, where young protoplanetary discs are likely to be found, the instability can be dust driven, occurring at small wavelengths. In this regime, the Jeans mass is much smaller than the one predicted by the standard gravitational instability model. This mechanism can be a viable way to form planetary cores in protostellar discs, since their predicted mass is about 10 Earth masses.

astro-ph.EP↗

arXiv2022

A Neural Network Subgrid Model of the Early Stages of Planet Formation

Planet formation is a multi-scale process in which the coagulation of $\mathrm{μm}$-sized dust grains in protoplanetary disks is strongly influenced by the hydrodynamic processes on scales of astronomical units ($\approx 1.5\times 10^8 \,\mathrm{km}$). Studies are therefore dependent on subgrid models to emulate the micro physics of dust coagulation on top of a large scale hydrodynamic simulation. Numerical simulations which include the relevant physical effects are complex and computationally expensive. Here, we present a fast and accurate learned effective model for dust coagulation, trained on data from high resolution numerical coagulation simulations. Our model captures details of the dust coagulation process that were so far not tractable with other dust coagulation prescriptions with similar computational efficiency.

astro-ph.EP↗

arXiv2022

Instability from high-order resonant chains in wide-separation massive planet systems

Diversity in the properties of exoplanetary systems arises, in part, from dynamical evolution that occurs after planet formation. We use numerical integrations to explore the relative role of secular and resonant dynamics in the long-term evolution of model planetary systems, made up of three equal mass giant planets on initially eccentric orbits. The range of separations studied is dominated by secular processes, but intersects chains of high-order mean-motion resonances. Over time-scales of $10^8$ orbits, the secular evolution of the simulated systems is predominantly regular. High-order resonant chains, however, can be a significant source of angular momentum deficit (AMD), leading to instability. Using a time-series analysis based on a Hilbert transform, we associate instability with broad islands of chaotic evolution. Previous work has suggested that first-order resonances could modify the AMD of nominally secular systems and facilitate secular chaos. We find that higher-order resonances, when present in chains, can have similar impacts.

astro-ph.EP↗

arXiv2022

Lecture notes on accretion disk physics

These notes introduce and review some of the physical principles underlying the theory of astrophysical accretion, emphasizing the central roles of angular momentum transport, angular momentum loss, and radiative cooling in determining the structure and evolution of accretion flows. Additional topics covered include the effective viscous theory of thin disks, classical instabilities of disk structure, the evolution of warped or eccentric disks, and the basic properties of waves within disks.

astro-ph.HE↗

arXiv2021

MHD disc winds can reproduce fast disc dispersal and the correlation between accretion rate and disc mass in Lupus

The final architecture of planetary systems depends on the extraction of angular momentum and mass-loss processes of the discs in which they form. Theoretical studies proposed that magnetized winds launched from the discs (MHD disc winds) could govern accretion and disc dispersal. In this work, we revisit the observed disc demographics in the framework of MHD disc winds, combining analytical solutions of disc evolution and a disc population synthesis approach. We show that MHD disc winds alone can account for both disc dispersal and accretion properties. The decline of disc fraction over time is reproduced by assuming that the initial accretion timescale (a generalization of the viscous timescale) varies from disc to disc and that the decline of the magnetic field strength is slower than that of the gas. The correlation between accretion rate and disc mass, and the dispersion of the data around the mean trend as observed in Lupus is then naturally reproduced. The model also accounts for the rapidity of the disc dispersal. This paves the way for planet formation models in the paradigm of wind-driven accretion.

astro-ph.EP↗

arXiv2021

Secular evolution of MHD wind-driven discs: analytical solutions in the expanded α-framework

The evolution of protoplanetary discs and the related process of planet formation is regulated by angular momentum transport and mass-loss processes. Over the past decade, the paradigm of viscosity has been challenged and MHD disc winds appear as a compelling scenario to account for disc accretion. In this work, we aim to construct the equivalent of the widely used analytical description of viscous evolution for the MHD wind case. The transport of angular momentum and mass induced by the wind is parameterized by an $α$-like parameter and by the magnetic lever arm parameter $λ$. Extensions of the paradigmatic Lynden-Bell and Pringle similarity solutions to the wind case are presented. We show that wind-driven accretion leads to a steeper decrease in the disc mass and accretion rate than in viscous models due to the absence of disc spreading. If the decline of the magnetic field strength is slower than that of the gas surface density, the disc is dispersed after a finite time. The evolution of the disc in the $\dot{M}_*-M_D$ plane is sensitive to the wind and turbulence parameters. A disc population evolving under the action of winds can exhibit a correlation between $\dot{M}_*$ and $M_D$ depending on the initial conditions. The simplified framework proposed in this work opens to a new avenue to test the effectiveness of wind-driven accretion from the observed disc demographics and constitutes an important step to include wind-driven accretion in planet population synthesis models.

astro-ph.SR↗

arXiv2021

Global 3D Radiation Hydrodynamic Simulations of Proto-Jupiter's Convective Envelope

The core accretion model of giant planet formation has been challenged by the discovery of recycling flows between the planetary envelope and the disc that can slow or stall envelope accretion. We carry out 3D radiation hydrodynamic simulations with an updated opacity compilation to model the proto-Jupiter's envelope. To isolate the 3D effects of convection and recycling, we simulate both isolated spherical envelopes and envelopes embedded in discs. The envelopes are heated at given rates to achieve steady states, enabling comparisons with 1D models. We vary envelope properties to obtain both radiative and convective solutions. Using a passive scalar, we observe significant mass recycling on the orbital timescale. For a radiative envelope, recycling can only penetrate from the disc surface until $\sim$0.1-0.2 planetary Hill radii, while for a convective envelope, the convective motion can "dredge up" the deeper part of the envelope so that the entire convective envelope is recycled efficiently. This recycling, however, has only limited effects on the envelopes' thermal structure. The radiative envelope embedded in the disc has identical structure as the isolated envelope. The convective envelope has a slightly higher density when it is embedded in the disc. We introduce a modified 1D approach which can fully reproduce our 3D simulations. With our updated opacity and 1D model, we recompute Jupiter's envelope accretion with a 10 $M_{\oplus}$ core, and the timescale to runaway accretion is shorter than the disc lifetime as in prior studies. Finally, we discuss the implications of the efficient recycling on the observed chemical abundances of the planetary atmosphere (especially for super-Earths and mini-Neptunes).

astro-ph.EP↗

arXiv2021

Dynamical stability of giant planets: the critical adiabatic index in the presence of a solid core

The dissociation and ionization of hydrogen, during the formation of giant planets via core accretion, reduces the effective adiabatic index $γ$ of the gas and could trigger dynamical instability. We generalize the analysis of Chandrasekhar, who determined that the threshold for instability of a self-gravitating hydrostatic body lies at $γ=4/3$, to account for the presence of a planetary core, which we model as an incompressible fluid. We show that the dominant effect of the core is to stabilize the envelope to radial perturbations, in some cases completely (i.e. for all $γ> 1$). When instability is possible, unstable planetary configurations occupy a strip of $γ$ values whose upper boundary falls below $γ=4/3$. Fiducial evolutionary tracks of giant planets forming through core accretion appear unlikely to cross the dynamical instability strip that we define.

astro-ph.EP↗

arXiv2021

Primordial giant planet obliquity driven by a circumplanetary disk

Detached circumplanetary disks are unstable to tilting as a result of the stellar tidal potential. We examine how a tilted circumplanetary disk affects the evolution of the spin axis of an oblate planet. The disk is evolved using time-dependent equations for linear wave-like warp evolution, including terms representing the effect of the tidal potential and planetary oblateness. For a disk with a sufficiently large mass, we find that the planet spin quickly aligns to the misaligned disk. The tilt of the planetary spin axis then increases on the same timescale as the disk. This can be an efficient mechanism for generating primordial obliquity in giant planets. We suggest that directly imaged exoplanets at large orbital radii, where the disk mass criterion is more likely to be satisfied, could have significant obliquities due to the tilt instability of their circumplanetary disks.

astro-ph.EP↗

arXiv2021

Partial tidal disruption events by stellar mass black holes: gravitational instability of stream and impact from remnant core

In dense star clusters, such as globular and open clusters, dynamical interactions between stars and black holes (BHs) can be extremely frequent, leading to various astrophysical transients. Close encounters between a star and a stellar mass BH make it possible for the star to be tidally disrupted by the BH. Due to the relative low mass of the BH and the small cross section of the tidal disruption event (TDE) for cases with high penetration, disruptions caused by close encounters are usually partial disruptions. The existence of the remnant stellar core and its non-negligible mass compared to the stellar mass BH alters the accretion process significantly. We study this problem with SPH simulations using the code {\tt Phantom}, with the inclusion of radiation pressure, which is important for small mass BHs. Additionally, we develop a new, more general method of computing the fallback rate which does not rely on any approximation. Our study shows that the powerlaw slope of the fallback rate has a strong dependence on the mass of the BH in the stellar mass BH regime. Furthermore, in this regime, self-gravity of the fallback stream and local instabilities become more significant, and cause the disrupted material to collapse into small clumps before returning to the BH. This results in an abrupt increase of the fallback rate, which can significantly deviate from a powerlaw. Our results will help in the identification of TDEs by stellar mass BHs in dense clusters.

astro-ph.HE↗

arXiv2021

Kozai-Lidov oscillations triggered by a tilt instability of detached circumplanetary discs

Circumplanetary discs can be linearly unstable to the growth of disc tilt in the tidal potential of the star-planet system. We use three-dimensional hydrodynamical simulations to characterize the disc conditions needed for instability, together with its long term evolution. Tilt growth occurs for disc aspect ratios, evaluated near the disc outer edge, of $H/r\gtrsim 0.05$, with a weak dependence on viscosity in the wave-like regime of warp propagation. Lower mass giant planets are more likely to have circumplanetary discs that satisfy the conditions for instability. We show that the tilt instability can excite the inclination to above the threshold where the circumplanetary disc becomes unstable to Kozai--Lidov (KL) oscillations. Dissipation in the Kozai--Lidov unstable regime caps further tilt growth, but the disc experiences large oscillations in both inclination and eccentricity. Planetary accretion occurs in episodic accretion events. We discuss implications of the joint tilt--KL instability for the detectability of circumplanetary discs, for the obliquity evolution of forming giant planets, and for the formation of satellite systems.

astro-ph.EP↗

arXiv2021

A Bayesian neural network predicts the dissolution of compact planetary systems

Despite over three hundred years of effort, no solutions exist for predicting when a general planetary configuration will become unstable. We introduce a deep learning architecture to push forward this problem for compact systems. While current machine learning algorithms in this area rely on scientist-derived instability metrics, our new technique learns its own metrics from scratch, enabled by a novel internal structure inspired from dynamics theory. Our Bayesian neural network model can accurately predict not only if, but also when a compact planetary system with three or more planets will go unstable. Our model, trained directly from short N-body time series of raw orbital elements, is more than two orders of magnitude more accurate at predicting instability times than analytical estimators, while also reducing the bias of existing machine learning algorithms by nearly a factor of three. Despite being trained on compact resonant and near-resonant three-planet configurations, the model demonstrates robust generalization to both non-resonant and higher multiplicity configurations, in the latter case outperforming models fit to that specific set of integrations. The model computes instability estimates up to five orders of magnitude faster than a numerical integrator, and unlike previous efforts provides confidence intervals on its predictions. Our inference model is publicly available in the SPOCK package, with training code open-sourced.

astro-ph.EP↗

arXiv2020

Survivor bias: divergent fates of the Solar System's ejected vs. persisting planetesimals

The orbital architecture of the Solar System is thought to have been sculpted by a dynamical instability among the giant planets. During the instability a primordial outer disk of planetesimals was destabilized and ended up on planet-crossing orbits. Most planetesimals were ejected into interstellar space but a fraction were trapped on stable orbits in the Kuiper belt and Oort cloud. We use a suite of N-body simulations to map out the diversity of planetesimals' dynamical pathways. We focus on two processes: tidal disruption from very close encounters with a giant planet, and loss of surface volatiles from repeated passages close to the Sun. We show that the rate of tidal disruption is more than a factor of two higher for ejected planetesimals than for surviving objects in the Kuiper belt or Oort cloud. Ejected planetesimals are preferentially disrupted by Jupiter and surviving ones by Neptune. Given that the gas giants contracted significantly as they cooled but the ice giants did not, taking into account the thermal evolution of the giant planets decreases the disruption rate of ejected planetesimals. The frequency of volatile loss and extinction is far higher for ejected planetesimals than for surviving ones and is not affected by the giant planets' contraction. Even if all interstellar objects were ejected from Solar System-like systems, our analysis suggests that their physical properties should be more diverse than those of Solar System small bodies as a result of their divergent dynamical histories. This is consistent with the characteristics of the two currently-known interstellar objects.

astro-ph.EP↗

arXiv2020

Turbulence Regulates the Rate of Planetesimal Formation via Gravitational Collapse

We study how the interaction between the streaming instability and intrinsic gas-phase turbulence affects planetesimal formation via gravitational collapse in protoplanetary disks. Turbulence impedes the formation of particle clumps by acting as an effective turbulent diffusivity, but it can also promote planetesimal formation by concentrating solids, for example in zonal flows. We quantify the effect of turbulent diffusivity using numerical simulations of the streaming instability in small local domains, forced with velocity perturbations that establish approximately Kolmogorov-like turbulence. We find that planetesimal formation is suppressed by turbulence once velocity fluctuations exceed $\langle δv^2 \rangle \simeq 10^{-3.5} - 10^{-3} c_s^2$. Turbulence whose strength is just below the threshold reduces the rate at which solids are bound into clumps. Our results suggest that the well-established turbulent thickening of the mid-plane solid layer is the primary mechanism by which turbulence influences planetesimal formation and that planetesimal formation requires a mid-plane solid-to-gas ratio $ε\gtrsim 0.5$. We also quantify the initial planetesimal mass function using a new clump-tracking method to determine each planetesimal mass shortly after collapse. For models in which planetesimals form, we show that the mass function is well-described by a broken power law, whose parameters are robust to the inclusion and strength of imposed turbulence. Turbulence in protoplanetary disks is likely to substantially exceed the threshold for planetesimal formation at radii where temperatures $T \gtrsim 10^3 \ {\rm K}$ lead to thermal ionization. Planetesimal formation may therefore be unviable in the inner disk out to 2-3 times the dust sublimation radius.

astro-ph.EP↗