arXiv subjects

Soko Matsumura

Publications and source records attributed to Soko Matsumura.

At least 19 recordsLinked to original sources

arXiv2025

Similar-mass versus diverse-mass planetary systems in wind-driven accretion discs

Many close-in multiple-planet systems show a peas-in-a-pod trend, where neighbouring planets have similar sizes, masses, and orbital spacing. Others, including the Solar System, have a more diverse size and mass distribution. Classical planet formation models tend to produce the former rather than the latter, and the origin of this difference remains unclear. Recent studies suggest disc evolution is largely driven by magnetic winds rather than viscosity alone. In such wind-driven accretion discs, the mass accretion rate varies radially instead of being constant, as in classical viscous discs. We investigate how the wind's efficiency in removing disc mass affects planet formation and migration. We performed single-core planet formation simulations via pebble accretion in wind-driven accretion discs. We varied wind efficiency via the magnetic lever arm parameter $ λ$ and studied outcomes by considering a range of initial disc masses and accretion timescales. Our simulations show that higher $ λ$ discs, with less wind mass loss, lead to faster formation and migration, generating similar-mass planetary systems. Lower $ λ$ discs lead to slower formation and migration and more diverse-mass planetary systems. A mass jump occurs for all $ λ$ cases when planet formation and disc accretion timescales are comparable, but is larger for lower $ λ$ discs. Super-Earth systems with cold Jupiters form more frequently in metal-rich discs, consistent with observations. Our simulations suggest similar-mass and diverse-mass systems are approximately separated at $ λ\sim 2\text{--}3 $.

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arXiv2024

Giant planet formation in the solar system

The formation history of Jupiter has been of interest due to its ability to shape the solar system's history. Yet little attention has been paid to the formation and growth of Saturn and the other giant planets. Here, we explore the implications of the simplest disc and pebble accretion model with steady-state accretion on the formation of giant planets in the solar system through N-body simulations. We conducted a statistical survey of different disc parameters and initial conditions of the protoplanetary disc to establish which combination best reproduces the present outer solar system. We examined the effect of the initial planetesimal disc mass, the number of planetesimals and their size-frequency distribution slope, pebble accretion prescription, and sticking efficiency on the likelihood of forming gas giants and their orbital distribution. The results reveal that the accretion sticking efficiency is the most sensitive parameter for controlling the final masses and number of giant planets. We have been unable to replicate the formation of all three types of giant planets in the solar system in a single simulation. The probability distribution of the final location of the giant planets is approximately constant in $\log r$, suggesting there is a slight preference for formation closer to the Sun but no preference for more massive planets to form closer. The eccentricity distribution has a higher mean for more massive planets, indicating that systems with more massive planets are more violent. The formation timescales of the cores of the gas giants are distinct, suggesting that they formed sequentially.

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arXiv2024

Can the giant planets of the Solar System form via pebble accretion in a smooth protoplanetary disc?

Prevailing $N$-body planet formation models typically start with lunar-mass embryos and show a general trend of rapid migration of massive planetary cores to the inner Solar System in the absence of a migration trap. This setup cannot capture the evolution from a planetesimal to embryo, which is crucial to the final architecture of the system. We aim to model planet formation with planet migration starting with planetesimals of $\sim10^{-6}$ -- $10^{-4}M_\oplus$ and reproduce the giant planets of the Solar System. We simulated a population of 1,000 -- 5,000 planetesimals in a smooth protoplanetary disc, which was evolved under the effects of their mutual gravity, pebble accretion, gas accretion, and planet migration, employing the parallelized $N$-body code SyMBAp. We find that the dynamical interactions among growing planetesimals are vigorous and can halt pebble accretion for excited bodies. While a set of results without planet migration produces one to two gas giants and one to two ice giants beyond 6 au, massive planetary cores readily move to the inner Solar System once planet migration is in effect. Dynamical heating is important in a planetesimal disc and the reduced pebble encounter time should be considered in similar models. Planet migration remains a challenge to form cold giant planets in a smooth protoplanetary disc, which suggests an alternative mechanism is required to stop them at wide orbits.

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arXiv2021

The STAR-MELT Python package for emission line analysis of YSOs

We introduce the STAR-MELT Python package that we developed to facilitate the analysis of time-resolved emission line spectroscopy of young stellar objects. STAR-MELT automatically extracts, identifies and fits emission lines. We summarise our analysis methods that utilises the time domain of high-resolution stellar spectra to investigate variability in the line profiles and corresponding emitting regions. This allows us to probe the innermost disc and accretion structures of YSOs. Local temperatures and densities can be determined using Boltzmann statistics, the Saha equation, and the Sobolev large velocity gradient approximation. STAR-MELT allows for new results to be obtained from archival data, as well as facilitating timely analysis of new data as it is obtained. We present the results of applying STAR-MELT to three YSOs, using spectra from UVES, XSHOOTER, FEROS, HARPS, and ESPaDOnS. We demonstrate what can be achieved for data with disparate time sampling, for stars with different inclinations and variability types. For EX Lupi, we confirm the presence of a localised and stable stellar-surface hot spot associated with the footprint of the accretion column. For GQ Lupi A, we find that the maximum infall rate from an accretion column is correlated with lines produced in the lowest temperatures. For CVSO109 we investigate the rapid temporal variability of a redshifted emission wing, indicative of rotating and infalling material in the inner disc. Our results show that STAR-MELT is a useful tool for such analysis, as well as other applications for emission lines.

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arXiv2021

N-body simulations of planet formation via pebble accretion II. How various giant planets form

Aims. The connection between initial disc conditions and final orbital and physical properties of planets is not well-understood. In this paper, we numerically study the formation of planetary systems via pebble accretion and investigate the effects of disc properties such as masses, dissipation timescales, and metallicities on planet formation outcomes. Methods. We improved the N-body code SyMBA that was modified by taking account of new planet-disc interaction models and type II migration. We adopted the 'two-alpha disc' model to mimic the effects of both the standard disc turbulence and the mass accretion driven by the magnetic disc wind. Results. We successfully reproduced the overall distribution trends of semi-major axes, eccentricities, and planetary masses of extrasolar giant planets. We find that, when planet formation happens fast enough, giant planets are fully grown (Jupiter mass or higher) and are distributed widely across the disc. On the other hand, when planet formation is limited by the disc's dissipation, discs generally form low-mass cold Jupiters (CJs). Our simulations also naturally explain why hot Jupiters (HJs) tend to be alone and how the observed eccentricity-metallicity trends arise. The low-metallicity discs tend to form nearly circular and coplanar HJs in situ, because planet formation is slower than high-metallicity discs, and thus protoplanetary cores migrate significantly before gas accretion. The high-metallicity discs, on the other hand, generate HJs in situ or via tidal circularisation of eccentric orbits. Both pathways usually involve dynamical instabilities, and thus HJs tend to have broader eccentricity and inclination distributions. When giant planets with very wide orbits ('super-cold Jupiters') are formed, we find that they often belong to metal-rich stars, have eccentric orbits, and tend to have (~80%) companions interior to their orbits.

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arXiv2020

A new and simple prescription for planet orbital migration and eccentricity damping by planet-disc interactions based on dynamical friction

During planet formation gravitational interaction between a planetary embryo and the protoplanetary gas disc causes orbital migration of the planetary embryo, which plays an important role in shaping the final planetary system. While migration sometimes occurs in the supersonic regime, wherein the relative velocity between the planetary embryo and the gas is higher than the sound speed, migration prescriptions proposed thus far describing the planet-disc interaction force and the timescales of orbital change in the supersonic regime are inconsistent with one another. Here we discuss the details of existing prescriptions in the literature and derive a new simple and intuitive formulation for planet-disc interactions based on dynamical friction that can be applied in both supersonic and subsonic cases. While the existing prescriptions assume particular disc models, ours include the explicit dependence on the disc parameters; hence it can be applied to discs with any radial surface density and temperature dependence (except for the local variations with radial scales less than the disc scale height). Our prescription will reduce the uncertainty originating from different literature formulations of planet migration and will be an important tool to study planet accretion processes, especially when studying the formation of close-in low-mass planets that are commonly found in exoplanetary systems.

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arXiv2018

The curious case of Mars formation

Dynamical models of planet formation coupled with cosmochemical data from martian meteorites show that Mars' isotopic composition is distinct from that of Earth. Reconciliation of formation models with meteorite data require that Mars grew further from the Sun than its present position. Here, we evaluate this compositional difference in more detail by comparing output from two $N$-body planet formation models. The first of these planet formation models simulates what is termed the "Classical" case wherein Jupiter and Saturn are kept in their current orbits. We compare these results with another model based on the "Grand Tack", in which Jupiter and Saturn migrate through the primordial asteroid belt. Our estimate of the average fraction of chondrite assembled into Earth and Mars assumes that the initial solid disk consists of only sources of enstatite chondrite composition in the inner region, and ordinary chondrite in the outer region. Results of these analyses show that both models tend to yield Earth and Mars analogues whose accretion zones overlap. The Classical case fares better in forming Mars with its documented composition (29% to 68% enstatite chondrite plus 32% to 67% ordinary chondrite) though the Mars analogues are generally too massive. However, if we include the restriction of mass on the Mars analogues, the Classical model does not work better. We also further calculate the isotopic composition of $^{17} \rm O$, $^{50} \rm Ti$, $^{54} \rm Cr$, $^{142} \rm Nd$, $^{64} \rm Ni$, and $^{92} \rm Mo$ in the martian mantle from the Grand Tack simulations. We find that it is possible to match the calculated isotopic composition of all the above elements in Mars' mantle with their measured values, but the resulting uncertainties are too large to place good restriction on the early dynamical evolution and birth place of Mars.

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arXiv2018

Exoplanet Science Priorities from the Perspective of Internal and Surface Processes for Silicate and Ice Dominated Worlds

The geophysics of extrasolar planets is a scientific topic often regarded as standing largely beyond the reach of near-term observations. This reality in no way diminishes the central role of geophysical phenomena in shaping planetary outcomes, from formation, to thermal and chemical evolution, to numerous issues of surface and near-surface habitability. We emphasize that for a balanced understanding of extrasolar planets, it is important to look beyond the natural biases of current observing tools, and actively seek unique pathways to understand exoplanet interiors as best as possible during the long interim prior to a time when internal components are more directly accessible. Such pathways include but are not limited to: (a) enhanced theoretical and numerical modeling, (b) laboratory research on critical material properties, (c) measurement of geophysical properties by indirect inference from imprints left on atmospheric and orbital properties, and (d) the purpose-driven use of Solar System object exploration expressly for its value in comparative planetology toward exoplanet-analogs. Breaking down barriers that envision local Solar System exploration, including the study of Earth's own deep interior, as separate from and in financial competition with extrasolar planet research, may greatly improve the rate of needed scientific progress for exoplanet geophysics. As the number of known rocky and icy exoplanets grows in the years ahead, we expect demand for expertise in 'exogeoscience' will expand at a commensurately intense pace. We highlight key topics, including: how water oceans below ice shells may dominate the total habitability of our galaxy by volume, how free-floating nomad planets may often attain habitable subsurface oceans supported by radionuclide decay, and how deep interiors may critically interact with atmospheric mass loss via dynamo-driven magnetic fields.

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arXiv2018

Highly Volcanic Exoplanets, Lava Worlds, and Magma Ocean Worlds: An Emerging Class of Dynamic Exoplanets of Significant Scientific Priority

Highly volcanic exoplanets, which can be variously characterized as 'lava worlds', 'magma ocean worlds', or 'super-Ios' are high priority targets for investigation. The term 'lava world' may refer to any planet with extensive surface lava lakes, while the term 'magma ocean world' refers to planets with global or hemispherical magma oceans at their surface. 'Highly volcanic planets', including super-Ios, may simply have large, or large numbers of, active explosive or extrusive volcanoes of any form. They are plausibly highly diverse, with magmatic processes across a wide range of compositions, temperatures, activity rates, volcanic eruption styles, and background gravitational force magnitudes. Worlds in all these classes are likely to be the most characterizable rocky exoplanets in the near future due to observational advantages that stem from their preferential occurrence in short orbital periods and their bright day-side flux in the infrared. Transit techniques should enable a level of characterization of these worlds analogous to hot Jupiters. Understanding processes on highly volcanic worlds is critical to interpret imminent observations. The physical states of these worlds are likely to inform not just geodynamic processes, but also planet formation, and phenomena crucial to habitability. Volcanic and magmatic activity uniquely allows chemical investigation of otherwise spectroscopically inaccessible interior compositions. These worlds will be vital to assess the degree to which planetary interior element abundances compare to their stellar hosts, and may also offer pathways to study both the very young Earth, and the very early form of many silicate planets where magma oceans and surface lava lakes are expected to be more prevalent. We suggest that highly volcanic worlds may become second only to habitable worlds in terms of both scientific and public long-term interest.

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arXiv2017

N-body simulations of planet formation via pebble accretion I: First Results

Context. Planet formation with pebbles has been proposed to solve a couple of long-standing issues in the classical formation model. Some sophisticated simulations have been done to confirm the efficiency of pebble accretion. However, there has not been any global N-body simulations that compare the outcomes of planet formation via pebble accretion with observed extrasolar planetary systems. Aims. In this paper, we study the effects of a range of initial parameters of planet formation via pebble accretion, and present the first results of our simulations. Methods. We incorporate the pebble accretion model by Ida et al. (2016) in the N-body code SyMBA (Duncan et al. 1998), along with the effects of gas accretion, eccentricity and inclination damping and planet migration in the disc. Results. We confirm that pebble accretion leads to a variety of planetary systems, but have difficulty in reproducing observed properties of exoplanetary systems, such as planetary mass, semimajor axis, and eccentricity distributions. The main reason behind this is a too-efficient type I migration, which sensitively depends on the disc model. However, our simulations also lead to a few interesting predictions. First, we find that formation efficiencies of planets depend on the stellar metallicities, not only for giant planets, but also for Earths (Es) and Super-Earths (SEs). The dependency for Es/SEs is subtle. Although higher metallicity environments lead to faster formation of a larger number of Es/SEs, they also tend to be lost later via dynamical instability. Second, our results indicate that a wide range of bulk densities observed for Es and SEs is a natural consequence of dynamical evolution of planetary systems. Third, the ejection trend of our simulations suggest that one free-floating E/SE may be expected for two smaller-mass planets.

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arXiv2015

Effects of Dynamical Evolution of Giant Planets on the Delivery of Atmophile Elements During Terrestrial Planet Formation

Recent observations started revealing the compositions of protostellar discs and planets beyond the Solar System. In this paper, we explore how the compositions of terrestrial planets are affected by dynamical evolution of giant planets. We estimate the initial compositions of building blocks of these rocky planets by using a simple condensation model, and numerically study the compositions of planets formed in a few different formation models of the Solar System. We find that the abundances of refractory and moderately volatile elements are nearly independent of formation models, and that all the models could reproduce the abundances of these elements of the Earth. The abundances of atmophile elements, on the other hand, depend on the scattering rate of icy planetesimals into the inner disc as well as the mixing rate of the inner planetesimal disc. For the classical formation model, neither of these mechanisms are efficient and the accretion of atmophile elements during the final assembly of terrestrial planets appears to be difficult. For the Grand Tack model, both of these mechanisms are efficient, which leads to a relatively uniform accretion of atmophile elements in the inner disc. It is also possible to have a "hybrid" scenario where the mixing is not very efficient but the scattering is efficient. The abundances of atmophile elements in this case increases with orbital radii. Such a scenario may occur in some of the extrasolar planetary systems which are not accompanied by giant planets or those without strong perturbations from giants. We also confirm that the Grand Tack scenario leads to the distribution of asteroid analogues where rocky planetesimals tend to exist interior to icy ones, and show that their overall compositions are consistent with S-type and C-type chondrites, respectively.

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arXiv2014

Deep Thermal Infrared Imaging of HR 8799 bcde: New Atmospheric Constraints and Limits on a Fifth Planet

We present new $L^\prime$ (3.8 $μm$) and Br-$α$ (4.05 $μm$) data and reprocessed archival $L^\prime$ data for the young, planet-hosting star HR 8799 obtained with Keck/NIRC2, VLT/NaCo and Subaru/IRCS. We detect all four HR 8799 planets in each dataset at a moderate to high signal-to-noise (SNR $\gtrsim$ 6-15). We fail to identify a fifth planet, "HR 8799 f", at $r$ $<$ 15 $AU$ at a 5-$σ$ confidence level: one suggestive, marginally significant residual at 0.2" is most likely a PSF artifact. Assuming companion ages of 30 $Myr$ and the Baraffe (Spiegel \& Burrows) planet cooling models, we rule out an HR 8799 f with mass of 5 $M_{J}$ (7 $M_{J}$), 7 $M_{J}$ (10 $M_{J}$), and 12 $M_{J}$ (13 $M_{J}$) at $r_{proj}$ $\sim$ 12 $AU$, 9 $AU$, and 5 $AU$, respectively. All four HR 8799 planets have red early T dwarf-like $L^\prime$ - [4.05] colors, suggesting that their SEDs peak in between the $L^\prime$ and $M^\prime$ broadband filters. We find no statistically significant difference in HR 8799 cde's colors. Atmosphere models assuming thick, patchy clouds appear to better match HR 8799 bcde's photometry than models assuming a uniform cloud layer. While non-equilibrium carbon chemistry is required to explain HR 8799 bc's photometry/spectra, evidence for it from HR 8799 de's photometry is weaker. Future, deep IR spectroscopy/spectrophotometry with the Gemini Planet Imager, SCExAO/CHARIS, and other facilities may clarify whether the planets are chemically similar or heterogeneous.

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arXiv2014

The Brazil-nut effect and its application to asteroids

Out of the handful of asteroids that have been imaged, some have distributions of blocks that are not easily explained. In this paper, we investigate the possibility that seismic shaking leads to the size sorting of particles in asteroids. In particular, we focus on the so-called Brazil Nut Effect (BNE) that separates large particles from small ones under vibrations. We study the BNE over a wide range of parameters by using the N-body code PKDGRAV, and find that the effect is largely insensitive to the coefficients of restitution, but sensitive to friction constants and oscillation speeds. Agreeing with the previous results, we find that convection drives the BNE, where the intruder rises to the top of the particle bed. For the wide-cylinder case, we also observe a "whale" effect, where the intruder follows the convective current and does not stay at the surface. We show that the non-dimensional critical conditions for the BNE agree well with previous studies. We also show that the BNE is scalable for low-gravity environments and that the rise speed of an intruder is proportional to the square root of the gravitational acceleration. Finally, we apply the critical conditions to observed asteroids, and find that the critical oscillation speeds are comparable to the seismic oscillation speeds that are expected from non-destructive impacts.

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arXiv2013

Secular Orbital Evolution of Compact Planet Systems

Recent observations have shown that at least some close-in exoplanets maintain eccentric orbits despite tidal circularization timescales that are typically shorter than stellar ages. We explore gravitational interactions with a distant planetary companion as a possible cause of these non-zero eccentricities. For simplicity, we focus on the evolution of a planar two-planet system subject to slow eccentricity damping and provide an intuitive interpretation of the resulting long-term orbital evolution. We show that dissipation shifts the two normal eigenmode frequencies and eccentricity ratios of the standard secular theory slightly, and that each mode decays at its own rate. Tidal damping of the eccentricities drives orbits to transition between periods of pericenter circulation and libration, and the planetary system settles into a locked state where the pericenters are nearly aligned or anti-aligned. Once in the locked state, the eccentricities of the two orbits decrease very slowly due to tides rather than at the much more rapid single-planet rate, and thus eccentric orbits, even for close-in planets, can often survive much longer than the age of the system. Assuming that an observed close-in planet on an elliptical orbit is apsidally-locked to a more distant, and perhaps unseen companion, we provide a constraint on the mass, semi-major axis, and eccentricity of the companion. We find the observed two-planet system HAT-P-13 might be in just such an apsidally-locked state, with parameters that obey our constraint well. We also survey close-in single planets, and found that none provide compelling evidence for unseen companions. Instead, we suspect that (1) orbits are circular, (2) tidal damping rates are slower than our assumption, or (3) a recent event has excited these eccentricities. Our method should prove useful for interpreting the results of current and future planet searches.

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arXiv2013

A Combined VLT and Gemini Study of the Atmosphere of the Directly-Imaged Planet, beta Pictoris b

We analyze new/archival VLT/NaCo and Gemini/NICI high-contrast imaging of the young, self-luminous planet $β$ Pictoris b in seven near-to-mid IR photometric filters, using advanced image processing methods to achieve high signal-to-noise, high precision measurements. While $β$ Pic b's near-IR colors mimick that of a standard, cloudy early-to-mid L dwarf, it is overluminous in the mid-infrared compared to the field L/T dwarf sequence. Few substellar/planet-mass objects -- i.e. $κ$ And b and 1RXJ 1609B -- match $β$ Pic b's $JHK_{s}L^\prime$ photometry, and its 3.1 $μm$ and 5 $μm$ photometry are particularly difficult to reproduce. Atmosphere models adopting cloud prescriptions and large ($\sim$ 60 $μm$) dust grains fail to reproduce the $β$ Pic b spectrum. However, models incorporating thick clouds similar to those found for HR 8799 bcde but also with small (a few microns) modal particle sizes yield fits consistent with the data within uncertainties. Assuming solar abundance models, thick clouds, and small dust particles ($ $ = 4 $μm$) we derive atmosphere parameters of log(g) = 3.8 $\pm$ 0.2 and $T_{eff}$ = 1575--1650 $K$, an inferred mass of 7$^{+4}_{-3}$ $M_{J}$, and a luminosity of log(L/L$_{\odot}$) $\sim$ -3.80 $\pm$ 0.02. The best-estimated planet radius, $\approx$ 1.65 $\pm$ 0.06 $R_{J}$, is near the upper end of allowable planet radii for hot-start models given the host star's age and likely reflects challenges with constructing accurate atmospheric models. Alternatively, these radii are comfortably consistent with hot-start model predictions if $β$ Pic b is younger than $\approx$ 7 Myr, consistent with a late formation, well after its host star's birth $\sim$ 12$^{+8}_{-4}$ Myr ago.

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arXiv2013

Effects of Dynamical Evolution of Giant Planets on Survival of Terrestrial Planets

The orbital distributions of currently observed extrasolar giant planets allow marginally stable orbits for hypothetical, terrestrial planets. In this paper, we propose that many of these systems may not have additional planets on these "stable" orbits, since past dynamical instability among giant planets could have removed them. We numerically investigate the effects of early evolution of multiple giant planets on the orbital stability of the inner, sub-Neptune-like planets which are modeled as test particles, and determine their dynamically unstable region. Previous studies have shown that the majority of such test particles are ejected out of the system as a result of close encounters with giant planets. Here, we show that secular perturbations from giant planets can remove test particles at least down to 10 times smaller than their minimum pericenter distance. Our results indicate that, unless the dynamical instability among giant planets is either absent or quiet like planet-planet collisions, most test particles down to ~0.1 AU within the orbits of giant planets at a few AU may be gone. In fact, out of ~30 % of survived test particles, about three quarters belong to the planet-planet collision cases. We find a good agreement between our numerical results and the secular theory, and present a semi-analytical formula which estimates the dynamically unstable region of the test particles just from the evolution of giant planets. Finally, our numerical results agree well with the observations, and also predict the existence of hot rocky planets in eccentric giant planet systems.

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arXiv2012

Direct Imaging Confirmation and Characterization of a Dust-Enshrouded Candidate Exoplanet Orbiting Fomalhaut

We present Subaru/IRCS J band data for Fomalhaut and a (re)reduction of archival 2004--2006 HST/ACS data first presented by Kalas et al. (2008). We confirm the existence of a candidate exoplanet, Fomalhaut b, in both the 2004 and 2006 F606W data sets at a high signal-to-noise. Additionally, we confirm the detection at F814W and present a new detection in F435W. Fomalhaut b's space motion may be consistent with it being in an apsidally-aligned, non debris ring-crossing orbit, although new astrometry is required for firmer conclusions. We cannot confirm that Fomalhaut b exhibits 0.7-0.8 mag variability cited as evidence for planet accretion or a semi-transient dust cloud. The new, combined optical SED and IR upper limits confirm that emission identifying Fomalhaut b originates from starlight scattered by small dust, but this dust is most likely associated with a massive body. The Subaru and IRAC/4.5 micron upper limits imply M < 2 Mj, still consistent with the range of Fomalhaut b masses needed to sculpt the disk. Fomalhaut b is very plausibly "a planet identified from direct imaging" even if current images of it do not, strictly speaking, show thermal emission from a directly imaged planet.

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arXiv2012

Direct Detection and Orbit Analysis of the Exoplanets HR 8799 bcd from Archival 2005 Keck/NIRC2 Data

We present previously unpublished July 2005 $H$-band coronagraphic data of the young, planet-hosting star HR 8799 from the newly-released Keck/NIRC2 archive. Despite poor observing conditions, we detect three of the planetary companions (HR 8799 bcd), two of them (HR 8799 bc) without advanced image processing. Comparing these data with previously published 1998-2011 astrometry and that from re-reduced October 2010 Keck data constrains the orbits of the planets. Analyzing the planets' astrometry separately, HR 8799 d's orbit is likely inclined at least 25$^\circ$ from face-on and the others may be on in inclined orbits. For semimajor axis ratios consistent with a 4:2:1 mean-motion resonance, our analysis yields precise values for HR 8799 bcd's orbital parameters and strictly constrains the planets' eccentricities to be less than 0.18--0.3. However, we find no acceptable orbital solutions with this resonance that place the planets in face-on orbits; HR 8799 d shows the largest deviation from such orbits. Moreover, few orbits make HR 8799 d coplanar with b and c, whereas dynamical stability analyses used to constrain the planets' masses typically assume coplanar and/or face-on orbits. This paper illustrates the significant science gain enabled with the release of the NIRC2 archive.

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