arXiv subjects

Eve J. Lee

Publications and source records attributed to Eve J. Lee.

60 records · Page 4Linked to original sources

arXiv2016

Correlations between compositions and orbits established by the giant impact era of planet formation

The giant impact phase of terrestrial planet formation establishes connections between super-Earths' orbital properties (semimajor axis spacings, eccentricities, mutual inclinations) and interior compositions (the presence or absence of gaseous envelopes). Using N-body simulations and analytic arguments, we show that spacings derive not only from eccentricities, but also from inclinations. Flatter systems attain tighter spacings, a consequence of an eccentricity equilibrium between gravitational scatterings, which increase eccentricities, and mergers, which damp them. Dynamical friction by residual disk gas plays a critical role in regulating mergers and in damping inclinations and eccentricities. Systems with moderate gas damping and high solid surface density spawn gas-enveloped super-Earths with tight spacings, small eccentricities, and small inclinations. Systems in which super-Earths coagulate without as much ambient gas, in disks with low solid surface density, produce rocky planets with wider spacings, larger eccentricities, and larger mutual inclinations. A combination of both populations can reproduce the observed distributions of spacings, period ratios, transiting planet multiplicities, and transit duration ratios exhibited by Kepler super-Earths. The two populations, both formed in situ, also help to explain observed trends of eccentricity vs. planet size, and bulk density vs. method of mass measurement (radial velocities vs. transit timing variations). Simplifications made in this study --- including the limited timespan of the simulations, and the approximate treatments of gas dynamical friction and gas depletion history --- should be improved upon in future work to enable a detailed quantitative comparison to the observations.

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arXiv2015

Breeding Super-Earths and Birthing Super-Puffs in Transitional Disks

The riddle posed by super-Earths (1-4$R_\oplus$, 2-20$M_\oplus$) is that they are not Jupiters: their core masses are large enough to trigger runaway gas accretion, yet somehow super-Earths accreted atmospheres that weigh only a few percent of their total mass. We show that this puzzle is solved if super-Earths formed late, as the last vestiges of their parent gas disks were about to clear. This scenario would seem to present fine-tuning problems, but we show that there are none. Ambient gas densities can span many (up to 9) orders of magnitude, and super-Earths can still robustly emerge after $\sim$0.1-1 Myr with percent-by-weight atmospheres. Super-Earth cores are naturally bred in gas-poor environments where gas dynamical friction has weakened sufficiently to allow constituent protocores to merge. So little gas is present at the time of core assembly that cores hardly migrate by disk torques: formation of super-Earths can be in situ. The picture --- that close-in super-Earths form in a gas-poor (but not gas-empty) inner disk, fed continuously by gas that bleeds inward from a more massive outer disk --- recalls the largely evacuated but still accreting inner cavities of transitional protoplanetary disks. We also address the inverse problem presented by super-puffs: an uncommon class of short-period planets seemingly too voluminous for their small masses (4-10$R_\oplus$, 2-6$M_\oplus$). Super-puffs easily acquire their thick atmospheres as dust-free, rapidly cooling worlds outside $\sim$1 AU where nebular gas is colder, less dense, and therefore less opaque. Unlike super-Earths which can form in situ, super-puffs migrated in to their current orbits; they are expected to form the outer links of mean-motion resonant chains, and to exhibit greater water content. We close by confronting observations and itemizing remaining questions.

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arXiv2015

To Cool is to Accrete: Analytic Scalings for Nebular Accretion of Planetary Atmospheres

Planets acquire atmospheres from their parent circumstellar disks. We derive a general analytic expression for how the atmospheric mass grows with time $t$, as a function of the underlying core mass $M_{\rm core}$ and nebular conditions, including the gas metallicity $Z$. Planets accrete as much gas as can cool: an atmosphere's doubling time is given by its Kelvin-Helmholtz time. Dusty atmospheres behave differently from atmospheres made dust-free by grain growth and sedimentation. The gas-to-core mass ratio (GCR) of a dusty atmosphere scales as GCR $\propto t^{0.4} M_{\rm core}^{1.7} Z^{-0.4} μ_{\rm rcb}^{3.4}$, where $μ_{\rm rcb} \propto 1/(1-Z)$ (for $Z$ not too close to 1) is the mean molecular weight at the innermost radiative-convective boundary. This scaling applies across all orbital distances and nebular conditions for dusty atmospheres; their radiative-convective boundaries, which regulate cooling, are not set by the external environment, but rather by the internal microphysics of dust sublimation, H$_2$ dissociation, and the formation of H$^-$. By contrast, dust-free atmospheres have their radiative boundaries at temperatures $T_{\rm rcb}$ close to nebular temperatures $T_{\rm out}$, and grow faster at larger orbital distances where cooler temperatures, and by extension lower opacities, prevail. At 0.1 AU in a gas-poor nebula, GCR $\propto t^{0.4} T_{\rm rcb}^{-1.9} M_{\rm core}^{1.6} Z^{-0.4} μ_{\rm rcb}^{3.3}$, while beyond 1 AU in a gas-rich nebula, GCR $\propto t^{0.4} T_{\rm rcb}^{-1.5} M_{\rm core}^1 Z^{-0.4}μ_{\rm rcb}^{2.2}$. We confirm our analytic scalings against detailed numerical models for objects ranging in mass from Mars (0.1 $M_\oplus$) to the most extreme super-Earths (10-20 $M_\oplus$), and explain why heating from planetesimal accretion cannot prevent the latter from undergoing runaway gas accretion.

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arXiv2015

A Metallicity Recipe for Rocky Planets

Planets with sizes between those of Earth and Neptune divide into two populations: purely rocky bodies whose atmospheres contribute negligibly to their sizes, and larger gas-enveloped planets possessing voluminous and optically thick atmospheres. We show that whether a planet forms rocky or gas-enveloped depends on the solid surface density of its parent disk. Assembly times for rocky cores are sensitive to disk solid surface density. Lower surface densities spawn smaller planetary embryos; to assemble a core of given mass, smaller embryos require more mergers between bodies farther apart and therefore exponentially longer formation times. Gas accretion simulations yield a rule of thumb that a rocky core must be at least 2$M_\oplus$ before it can acquire a volumetrically significant atmosphere from its parent nebula. In disks of low solid surface density, cores of such mass appear only after the gas disk has dissipated, and so remain purely rocky. Higher surface density disks breed massive cores more quickly, within the gas disk lifetime, and so produce gas-enveloped planets. We test model predictions against observations, using planet radius as an observational proxy for gas-to-rock content and host star metallicity as a proxy for disk solid surface density. Theory can explain the observation that metal-rich stars host predominantly gas-enveloped planets.

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arXiv2015

Time Varying Dynamical Star Formation Rate

We present numerical evidence of dynamic star formation in which the accreted stellar mass grows superlinearly with time, roughly as $t^2$. We perform simulations of star formation in self-gravitating hydrodynamic and magneto-hydrodynamic turbulence that is continuously driven. By turning the self-gravity of the gas in the simulations on or off, we demonstrate that self-gravity is the dominant physical effect setting the mass accretion rate at early times before feedback effects take over, contrary to theories of turbulence-regulated star formation. We find that gravitational collapse steepens the density profile around stars, generating the power-law tail on what is otherwise a lognormal density probability distribution function. Furthermore, we find turbulent velocity profiles to flatten inside collapsing regions, altering the size-linewidth relation. This local flattening reflects enhancements of turbulent velocity on small scales, as verified by changes to the velocity power spectra. Our results indicate that gas self-gravity dynamically alters both density and velocity structures in clouds, giving rise to a time-varying star formation rate. We find that a substantial fraction of the gas that forms stars arrives via low density flows, as opposed to accreting through high density filaments.

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arXiv2014

Make Super-Earths, Not Jupiters: Accreting Nebular Gas onto Solid Cores at 0.1 AU and Beyond

Close-in super-Earths having radii 1--4 $R_\oplus$ may possess hydrogen atmospheres comprising a few percent by mass of their rocky cores. We determine the conditions under which such atmospheres can be accreted by cores from their parent circumstellar disks. Accretion from the nebula is problematic because it is too efficient: we find that 10-$M_\oplus$ cores embedded in solar metallicity disks tend to undergo runaway gas accretion and explode into Jupiters, irrespective of orbital location. The threat of runaway is especially dire at $\sim$0.1 AU, where solids may coagulate on timescales orders of magnitude shorter than gas clearing times; thus nascent atmospheres on close-in orbits are unlikely to be supported against collapse by planetesimal accretion. The time to runaway accretion is well approximated by the cooling time of the atmosphere's innermost convective zone, whose extent is controlled by where H$_2$ dissociates. Insofar as the temperatures characterizing H$_2$ dissociation are universal, timescales for core instability tend not to vary with orbital distance --- and to be alarmingly short for 10-$M_\oplus$ cores. Nevertheless, in the thicket of parameter space, we identify two scenarios, not mutually exclusive, that can reproduce the preponderance of percent-by-mass atmospheres for super-Earths at $\sim$0.1 AU, while still ensuring the formation of Jupiters at $\gtrsim 1$ AU. Scenario (a): planets form in disks with dust-to-gas ratios that range from $\sim$20$\times$ solar at 0.1 AU to $\sim$2$\times$ solar at 5 AU. Scenario (b): the final assembly of super-Earth cores from mergers of proto-cores --- a process that completes quickly at $\sim$0.1 AU once begun --- is delayed by gas dynamical friction until just before disk gas dissipates completely.

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