arXiv subjects

Chris W. Ormel

Publications and source records attributed to Chris W. Ormel.

45 records · Page 3Linked to original sources

arXiv2014

Hydrodynamics of Embedded Planets' First Atmospheres. I. A Centrifugal Growth Barrier for 2D Flows

In the core accretion paradigm of planet formation, gas giants only form a massive atmosphere after their progenitors exceeded a threshold mass: the critical core mass. Most (exo)planets, being smaller and rock/ice-dominated, never crossed this line. Nevertheless, they were massive enough to attract substantial amounts of gas from the disc, while their atmospheres remained in pressure-equilibrium with the disc. Our goal is to characterise the hydrodynamical properties of the atmospheres of such embedded planets and their implication for their (long-term) evolution. In this paper -- the first in series -- we start to investigate the properties of an isothermal and inviscid flow past a small, embedded planet by conducting local, 2D hydrodynamical simulations. Using the PLUTO code we confirm that the flow is steady and bound. This steady outcome is most apparent for the log-polar grid (with the grid spacing proportional to the distance from the planet). For low-mass planets, Cartesian grids are somewhat less efficient as they have difficulty to follow the circular, large speeds in the deep atmosphere. Relating the amount of rotation to the gas fraction of the atmosphere, we find that more massive atmospheres rotate faster -- a finding consistent with Kelvin's circulation theorem. Rotation therefore limits the amount of gas that planets can acquire from the nebula. Dependent on the Toomre-Q parameter of the circumstellar disc, the planet's atmosphere will reach Keplerian rotation before self-gravity starts to become important.

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arXiv2014

Hydrodynamics of Embedded Planets' First Atmospheres. II. A Rapid Recycling of Atmospheric Gas

Following Paper I we investigate the properties of atmospheres that form around small protoplanets embedded in a protoplanetary disc by conducting hydrodynamical simulations. These are now extended to three dimensions, employing a spherical grid centred on the planet. Compression of gas is shown to reduce rotational motions. Contrasting the 2D case, no clear boundary demarcates bound atmospheric gas from disc material; instead, we find an open system where gas enters the Bondi sphere at high latitudes and leaves through the midplane regions, or, vice versa, when the disc gas rotates sub-Keplerian. The simulations do not converge to a time-independent solution; instead, the atmosphere is characterized by a time-varying velocity field. Of particular interest is the timescale to replenish the atmosphere by nebular gas, $t_\mathrm{replenish}$. It is shown that the replenishment rate, $M_\mathrm{atm}/t_\mathrm{replenish}$, can be understood in terms of a modified Bondi accretion rate, $\sim$$R_\mathrm{Bondi}^2ρ_\mathrm{gas}v_\mathrm{Bondi}$, where $v_\mathrm{Bondi}$ is set by the Keplerian shear or the magnitude of the sub-Keplerian motion of the gas, whichever is larger. In the inner disk, the atmosphere of embedded protoplanets replenishes on a timescale that is shorter than the Kelvin-Helmholtz contraction (or cooling) timescale. As a result, atmospheric gas can no longer contract and the growth of these atmospheres terminates. Future work must confirm whether these findings continue to apply when the (thermodynamical) idealizations employed in this study are relaxed. But if shown to be broadly applicable, replenishment of atmospheric gas provides a natural explanation for the preponderance of gas-rich but rock-dominant planets like super-Earths and mini-Neptunes.

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arXiv2014

On the filtering and processing of dust by planetesimals 1. Derivation of collision probabilities for non-drifting planetesimals

Context. Circumstellar disks are known to contain a significant mass in dust ranging from micron to centimeter size. Meteorites are evidence that individual grains of those sizes were collected and assembled into planetesimals in the young solar system. Aims. We assess the efficiency of dust collection of a swarm of non-drifting planetesimals {\rev with radii ranging from 1 to $10^3$\,km and beyond. Methods. We calculate the collision probability of dust drifting in the disk due to gas drag by planetesimal accounting for several regimes depending on the size of the planetesimal, dust, and orbital distance: the geometric, Safronov, settling, and three-body regimes. We also include a hydrodynamical regime to account for the fact that small grains tend to be carried by the gas flow around planetesimals. Results. We provide expressions for the collision probability of dust by planetesimals and for the filtering efficiency by a swarm of planetesimals. For standard turbulence conditions (i.e., a turbulence parameter $α=10^{-2}$), filtering is found to be inefficient, meaning that when crossing a minimum-mass solar nebula (MMSN) belt of planetesimals extending between 0.1 AU and 35 AU most dust particles are eventually accreted by the central star rather than colliding with planetesimals. However, if the disk is weakly turbulent ($α=10^{-4}$) filtering becomes efficient in two regimes: (i) when planetesimals are all smaller than about 10 km in size, in which case collisions mostly take place in the geometric regime; and (ii) when planetary embryos larger than about 1000 km in size dominate the distribution, have a scale height smaller than one tenth of the gas scale height, and dust is of millimeter size or larger in which case most collisions take place in the settling regime. These two regimes have very different properties: we find that the local filtering efficiency $x_{filter,MMSN}$ scales with $r^{-7/4}$ (where $r$ is the orbital distance) in the geometric regime, but with $r^{-1/4}$ to $r^{1/4}$ in the settling regime. This implies that the filtering of dust by small planetesimals should occur close to the central star and with a short spread in orbital distances. On the other hand, the filtering by embryos in the settling regime is expected to be more gradual and determined by the extent of the disk of embryos. Dust particles much smaller than millimeter size tend only to be captured by the smallest planetesimals because they otherwise move on gas streamlines and their collisions take place in the hydrodynamical regime. Conclusions. Our results hint at an inside-out formation of planetesimals in the infant solar system because small planetesimals in the geometrical limit can filter dust much more efficiently close to the central star. However, even a fully-formed belt of planetesimals such as the MMSN only marginally captures inward-drifting dust and this seems to imply that dust in the protosolar disk has been filtered by planetesimals even smaller than 1 km (not included in this study) or that it has been assembled into planetesimals by other mechanisms (e.g., orderly growth, capture into vortexes). Further refinement of our work concerns, among other things: a quantitative description of the transition region between the hydro and settling regimes; an assessment of the role of disk turbulence for collisions, in particular in the hydro regime; and the coupling of our model to a planetesimal formation model.

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arXiv2014

An Atmospheric Structure Equation for Grain Growth

We present a method to include the evolution of the grain size and grain opacity $κ_\mathrm{gr}$ in the equations describing the structure of protoplanetary atmospheres. The key assumption of this method is that a single grain size dominates the grain size distribution at any height $r$. In addition to following grain growth, the method accounts for mass deposition by planetesimals and grain porosity. We illustrate this method by computation of a simplified atmosphere structure model. In agreement with previous works, grain coagulation is seen to be very efficient. The opacity drops to values much below the often-used `ISM-opacities' ($\sim$$1\ \mathrm{cm^2\ g}^{-1}$) and the atmosphere structure profiles for temperature and density resemble that of the grain-free case. Deposition of planetesimals in the radiative part of the atmosphere hardly influences this outcome as the added surface is quickly coagulated away. We observe a modest dependence on the internal structure (porosity), but show that filling factors cannot become too large because of compression by gas drag.

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arXiv2014

Planetesimal driven migration as an explanation for observations of high levels of warm, exozodiacal dust

High levels of exozodiacal dust have been observed in the inner regions of a large fraction of main sequence stars. Given the short lifetime of the observed small dust grains, these 'exozodis' are difficult to explain, especially for old (>100 Myr) stars. The exozodiacal dust may be observed as excess emission in the mid-infrared, or using interferometry. We hypothesise that exozodi are sustained by planetesimals scattered by planets inwards from an outer planetesimal belt, where collision timescales are long. In this work, we use N-body simulations to show that the outwards migration of a planet into a belt, driven by the scattering of planetesimals, can increase, or sustain, the rate at which planetesimals are scattered from the outer belt to the exozodi region. We hypothesise that this increase is sufficient to sustain the observed exozodi on Gyr timescales. No correlation between observations of an outer belt and an exozodi is required for this scenario to work, as the outer belt may be too faint to detect. If planetesimal driven migration does explain the observed exozodi, this work suggests that the presence of an exozodi indicates the presence of outer planets and a planetesimal belt.

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arXiv2013

The Fate of Planetesimals in Turbulent Disks with Dead Zones. I. The Turbulent Stirring Recipe

Turbulence in protoplanetary disks affects planet formation in many ways. While small dust particles are mainly affected by the aerodynamical coupling with turbulent gas velocity fields, planetesimals and larger bodies are more affected by gravitational interaction with gas density fluctuations. For the latter process, a number of numerical simulations have been performed in recent years, but a fully parameter-independent understanding has not been yet established. In this study, we present simple scaling relations for the planetesimal stirring rate in turbulence driven by magnetorotational instability (MRI), taking into account the stabilization of MRI due to Ohmic resistivity. We begin with order-of-magnitude estimates of the turbulence-induced gravitational force acting on solid bodies and associated diffusion coefficients for their orbital elements. We then test the predicted scaling relations using the results of recent Ohmic-resistive MHD simulations by Gressel et al. We find that these relations successfully explain the simulation results if we properly fix order-of-unity uncertainties within the estimates. We also update the saturation predictor for the density fluctuation amplitude in MRI-driven turbulence originally proposed by Okuzumi & Hirose. Combination of the scaling relations and saturation predictor allows to know how the turbulent stirring rate of planetesimals depends on disk parameters such as the gas column density, distance from the central star, vertical resistivity distribution, and net vertical magnetic flux. In Paper II, we apply our recipe to planetesimal accretion to discuss its viability in turbulent disks.

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arXiv2012

Rapid Formation of Saturn after Jupiter Completion

We have investigated Saturn's core formation at a radial pressure maximum in a protoplanetary disk, which is created by gap opening by Jupiter. A core formed via planetesimal accretion induces the fragmentation of surrounding planetesimals, which generally inhibits further growth of the core by removal of the resulting fragments due to radial drift caused by gas drag. However, the emergence of the pressure maximum halts the drift of the fragments, while their orbital eccentricities and inclinations are efficiently damped by gas drag. As a result, the core of Saturn rapidly grows via accretion of the fragments near the pressure maximum. We have found that in the minimum-mass solar nebula, kilometer sized planetesimals can produce a core exceeding 10 Earth masses within two million years. Since Jupiter may not have undergone significant type II inward migration, it is likely that Jupiter's formation was completed when the local disk mass has already decayed to a value comparable to or less than Jovian mass. The expected rapid growth of Saturn's core on a timescale comparable to or shorter than observationally inferred disk lifetime enables Saturn to acquire the current amount of envelope gas before the disk gas is completely depleted. The high heat energy release rate onto the core surface due to the rapid accretion of the fragments delays onset of runaway gas accretion until the core mass becomes somewhat larger than that of Jupiter, which is consistent with the estimate based on interior modeling. Therefore, the rapid formation of Saturn induced by gap opening of Jupiter can account for the formation of multiple gas giants (Jupiter and Saturn) without significant inward migration and larger core mass of Saturn than that of Jupiter.

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arXiv2010

Spectroscopic [CI] mapping of the infrared dark cloud G48.65-0.29

We report the first spectroscopic mapping of an atomic carbon line in an infrared dark cloud (IRDC). By observing the spatial distribution of the [CI] emission in an IRDC, comparing it with the 13CO emission and the known distribution of internal heating sources, we can quantify the role of internal and external UV irradiation in the production of atomic carbon. We used the 2x4 pixel SMART receiver of the KOSMA observatory on Gornergrat to map the [CI] 3P1 - 3P0 line in the IRDC G48.65-0.29 and compared the resulting spectra with data from the BU-FCRAO 13CO 1-0 Galactic Ring Survey. The [CI]/13CO effective beam temperature ratio falls at about 0.3 with local deviations by less than a factor two. All velocity components seen in 13CO are also detected in[CI]. We find, however, significant differences in the morphology of the brightest regions seen in the two tracers. While 13CO basically follows the column density distribution derived from the near-infrared (NIR) extinction and the submm continuum, the [CI] emission peaks at the locations of the two known NIR point sources. We find CI/CO abundance ratios between 0.07 and 0.13, matching the lower end of the range previously measured in star-forming regions. Evaluating the relative importance of the irradiation by embedded sources and by the Galactic interstellar UV field, we find that in G48.65-0.29 most [CI] emission can be attributed to externally illuminated surfaces. Embedded sources have a significant impact on the overall abundance distribution of atomic carbon as soon as they are found in an evolved state with noticeable NIR flux.

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arXiv2009

The outcome of protoplanetary dust growth: pebbles, boulders, or planetesimals? I. Mapping the zoo of laboratory collision experiments

The growth processes from protoplanetary dust to planetesimals are not fully understood. Laboratory experiments and theoretical models have shown that collisions among the dust aggregates can lead to sticking, bouncing, and fragmentation. However, no systematic study on the collisional outcome of protoplanetary dust has been performed so far so that a physical model of the dust evolution in protoplanetary disks is still missing. We intend to map the parameter space for the collisional interaction of arbitrarily porous dust aggregates. This parameter space encompasses the dust-aggregate masses, their porosities and the collision velocity. With such a complete mapping of the collisional outcomes of protoplanetary dust aggregates, it will be possible to follow the collisional evolution of dust in a protoplanetary disk environment. We use literature data, perform own laboratory experiments, and apply simple physical models to get a complete picture of the collisional interaction of protoplanetary dust aggregates. In our study, we found four different types of sticking, two types of bouncing, and three types of fragmentation as possible outcomes in collisions among protoplanetary dust aggregates. We distinguish between eight combinations of porosity and mass ratio. For each of these cases, we present a complete collision model for dust-aggregate masses between 10^-12 and 10^2 g and collision velocities in the range 10^-4 to 10^4 cm/s for arbitrary porosities. This model comprises the collisional outcome, the mass(es) of the resulting aggregate(s) and their porosities. We present the first complete collision model for protoplanetary dust. This collision model can be used for the determination of the dust-growth rate in protoplanetary disks.

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