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At least 865 records · Page 48

MASS-RADIUS RELATIONSHIPS FOR VERY LOW MASS GASEOUS PLANETS

Recently, the Kepler spacecraft has detected a sizable aggregate of objects, characterized by giant-planet-like radii and modest levels of stellar irradiation. With the exception of a handful of objects, the physical nature, and specifically the average densities, of these bodies remain unknown. Here, we propose that the detected giant planet radii may partially belong to planets somewhat less massive than Uranus and Neptune. Accordingly, in this work, we seek to identify a physically sound upper limit to planetary radii at low masses and moderate equilibrium temperatures. As a guiding example, we analyze the interior structure of the Neptune-mass planet Kepler-30d and show that it is acutely deficient in heavy elements, especially compared with its solar system counterparts. Subsequently, we perform numerical simulations of planetary thermal evolution and in agreement with previous studies, show that generally, 10-20 M{sub Circled-Plus }, multi-billion year old planets, composed of high density cores and extended H/He envelopes can have radii that firmly reside in the giant planet range. We subject our results to stability criteria based on extreme ultraviolet radiation, as well as Roche-lobe overflow driven mass-loss and construct mass-radius relationships for the considered objects. We conclude by discussing observational avenues that may be used to confirm or repudiate the existence of putative low mass, gas-dominated planets.

79 ASTRONOMY AND ASTROPHYSICS↗

THE EFFECT OF METALLICITY-DEPENDENT T-τ RELATIONS ON CALIBRATED STELLAR MODELS

Mixing length theory is the predominant treatment of convection in stellar models today. Usually described by a single free parameter, α, the common practice is to calibrate it using the properties of the Sun, and apply it to all other stellar models as well. Asteroseismic data from Kepler and CoRoT provide precise properties of other stars which can be used to determine α as well, and a recent study of stars in the Kepler field of view found α to vary with metallicity. Interpreting α obtained from calibrated stellar models, however, is complicated by the fact that the value for α depends on the surface boundary condition of the stellar model, or T-τ relation. Calibrated models that use typical T-τ relations, which are static and insensitive to chemical composition, do not include the complete effect of metallicity on α. We use three-dimensional radiation-hydrodynamic simulations to extract metallicity-dependent T-τ relations and use them in calibrated stellar models. We find the previously reported α-metallicity trend to be robust, and not significantly affected by the surface boundary condition of the stellar models.

79 ASTRONOMY AND ASTROPHYSICS↗

FORMATION OF CLOSE IN SUPER-EARTHS AND MINI-NEPTUNES: REQUIRED DISK MASSES AND THEIR IMPLICATIONS

Recent observations by the Kepler space telescope have led to the discovery of more than 4000 exoplanet candidates consisting of many systems with Earth- to Neptune-sized objects that reside well inside the orbit of Mercury around their respective host stars. How and where these close-in planets formed is one of the major unanswered questions in planet formation. Here, we calculate the required disk masses for in situ formation of the Kepler planets. We find that if close-in planets formed as isolation masses, then standard gas-to-dust ratios yield corresponding gas disks that are gravitationally unstable for a significant fraction of systems, ruling out such a scenario. We show that the maximum width of a planet's accretion region in the absence of any migration is 2v {sub esc}/Ω, where v {sub esc} is the escape velocity of the planet and Ω is the Keplerian frequency, and we use it to calculate the required disk masses for in situ formation with giant impacts. Even with giant impacts, formation without migration requires disk surface densities in solids at semi-major axes of less than 0.1 AU of 10{sup 3}-10{sup 5} g cm{sup –2}, implying typical enhancements above the minimum-mass solar nebular (MMSN) by at least a factor of 20. Corresponding gas disks are below but not far from the gravitational stability limit. In contrast, formation beyond a few AU is consistent with MMSN disk masses. This suggests that the migration of either solids or fully assembled planets is likely to have played a major role in the formation of close-in super-Earths and mini-Neptunes.

79 ASTRONOMY AND ASTROPHYSICS↗

THE MASS-DEPENDENCE OF ANGULAR MOMENTUM EVOLUTION IN SUN-LIKE STARS

To better understand the observed distributions of the rotation rate and magnetic activity of Sun-like and low-mass stars, we derive a physically motivated scaling for the dependence of the stellar wind torque on the Rossby number. The torque also contains an empirically derived scaling with stellar mass (and radius), which provides new insight into the mass-dependence of stellar magnetic and wind properties. We demonstrate that this new formulation explains why the lowest mass stars are observed to maintain rapid rotation for much longer than solar-mass stars, and simultaneously why older populations exhibit a sequence of slowly rotating stars, in which the low-mass stars rotate more slowly than solar-mass stars. The model also reproduces some previously unexplained features in the period-mass diagram for the Kepler field, notably: the particular shape of the ''upper envelope'' of the distribution, suggesting that ∼95% of Kepler field stars with measured rotation periods are younger than ∼4 Gyr; and the shape of the ''lower envelope'', corresponding to the location where stars transition between magnetically saturated and unsaturated regimes.

79 ASTRONOMY AND ASTROPHYSICS↗

A LOW STELLAR OBLIQUITY FOR WASP-47, A COMPACT MULTIPLANET SYSTEM WITH A HOT JUPITER AND AN ULTRA-SHORT PERIOD PLANET

We have detected the Rossiter–Mclaughlin effect during a transit of WASP-47b, the only known hot Jupiter with close planetary companions. By combining our spectroscopic observations with Kepler photometry, we show that the projected stellar obliquity is λ = 0° ± 24°. We can firmly exclude a retrograde orbit for WASP-47b, and rule out strongly misaligned prograde orbits. Low obliquities have also been found for most of the other compact multiplanet systems that have been investigated. The Kepler-56 system, with two close-in gas giants transiting their subgiant host star with an obliquity of at least 45{sup ◦}, remains the only clear counterexample.

79 ASTRONOMY AND ASTROPHYSICS↗

Prospects for Galactic and stellar astrophysics with asteroseismology of giant stars in the TESS continuous viewing zones and beyond

ABSTRACT The NASA Transiting Exoplanet Survey Satellite (NASA-TESS) mission presents a treasure trove for understanding the stars it observes and the Milky Way, in which they reside. We present a first look at the prospects for Galactic and stellar astrophysics by performing initial asteroseismic analyses of bright (G < 11) red giant stars in the TESS southern continuous viewing zone (SCVZ). Using three independent pipelines, we detect νmax and Δν in 41 per cent of the 15 405 star parent sample (6388 stars), with consistency at a level of $\sim \! 2{{\ \rm per\ cent}}$ in νmax and $\sim \! 5{{\ \rm per\ cent}}$ in Δν. Based on this, we predict that seismology will be attainable for ∼3 × 105 giants across the whole sky and at least 104 giants with ≥1 yr of observations in the TESS-CVZs, subject to improvements in analysis and data reduction techniques. The best quality TESS-CVZ data, for 5574 stars where pipelines returned consistent results, provide high-quality power spectra across a number of stellar evolutionary states. This makes possible studies of, for example, the asymptotic giant branch bump. Furthermore, we demonstrate that mixed ℓ = 1 modes and rotational splitting are cleanly observed in the 1-yr data set. By combining TESS-CVZ data with TESS-HERMES, SkyMapper, APOGEE, and Gaia, we demonstrate its strong potential for Galactic archaeology studies, providing good age precision and accuracy that reproduces well the age of high [α/Fe] stars and relationships between mass and kinematics from previous studies based on e.g. Kepler. Better quality astrometry and simpler target selection than the Kepler sample makes this data ideal for studies of the local star formation history and evolution of the Galactic disc. These results provide a strong case for detailed spectroscopic follow-up in the CVZs to complement that which has been (or will be) collected by current surveys.

Mackereth, J. Ted↗

Survival function analysis of planet size distribution with Gaia Data Release 2 updates

Applying the survival function analysis to the planet radius distribution of the Kepler confirmed/candidate planets, we have identified two natural divisions of planet radius at 4 Earth radii (R ⊕ ) and 10 R ⊕ . These divisions place constraints on planet formation and interior structure model. The division at 4 R ⊕ separates small exoplanets from large exoplanets above. When combined with the recently discovered radius gap at 2 R ⊕ , it supports the treatment of planets in between 2 and 4 R ⊕ as a separate group, likely water worlds. For planets around solar-type FGK main-sequence stars, we argue that 2 R ⊕ is the separation between water-poor and water-rich planets, and 4 R ⊕ is the separation between gas-poor and gas-rich planets. Here, we confirm the slope of the survival function in between 4 and 10 R ⊕ to be shallower compared to either ends, indicating a relative paucity of planets in between 4 and 10 R ⊕ , namely the sub-Saturnian desert there. We name them transitional planets, as they form a bridge between the gas-poor small planets and gas giants. Accordingly, we propose the following classification scheme: (<2 R ⊕ ) rocky planets, (2–4 R ⊕ ) water worlds, (4–10 R ⊕ ) transitional planets, and (>10 R ⊕ ) gas giants.

79 ASTRONOMY AND ASTROPHYSICS↗

Distributed Workflows for Modeling Experimental Data

Modeling helps explain the fundamental physics hidden behind experimental data. In the case of material modeling, running one simulation rarely results in output that reproduces the experimental data. Often one or more of the force field parameters are not precisely known and must be optimized for the output to match that of the experiment. Since the simulations require high performance computing (HPC) resources and there are usually many simulations to run, a workflow is very useful to prevent errors and assure that the simulations are identical except for the parameters that need to be varied. These workflows are usually distributed because the simulations require HPC, but the optimization and steps to compare the simulation results and experimental data are done on a local workstation. We will present results from force field refinement of data collected at the Spallation Neutron Source using Kepler, Pegasus, and Beam workflows and discuss what we have learned from using these workflows.

Lynch, Vickie E.↗

Validation of transfer map calculation for electrostatic deflectors in the code COSY INFINITY

The code COSY INFINITY uses a beamline coordinate system with a Frenet–Serret frame relative to the reference particle, and calculates differential algebra-valued transfer maps by integrating the ODEs of motion in the respective vector space over a differential algebra (DA). In our work, we described and performed computation of the DA transfer map of an electrostatic spherical deflector in a laboratory coordinate system using two conventional methods: (1) by integrating the ODEs of motion using a numerical integrator and (2) by computing analytically and in closed form the properties of the respective elliptical orbits from Kepler theory. We compared the resulting transfer maps with (3) the DA transfer map of COSY INFINITY’s built-in electrostatic spherical deflector element ESP and (4) the transfer map of the electrostatic spherical deflector computed using the program GIOS, which uses analytic formulas from a paper1 by Hermann Wollnik regarding second-order aberrations. In addition to the electrostatic spherical deflector, we studied an electrostatic cylindrical deflector, where the Kepler theory is not applicable. We computed the DA transfer map by the ODE integration method (1), and we compared it with the transfer maps by (3) COSY INFINITY’s built-in electrostatic cylindrical deflector element ECL and (4) GIOS. The transfer maps of electrostatic spherical and cylindrical deflectors obtained using the direct calculation methods (1) and (2) are in excellent agreement with those computed using (3) COSY INFINITY. On the other hand, we found a significant discrepancy with (4) the program GIOS.

43 PARTICLE ACCELERATORS↗

Field-Flow Fractionation of Carbon Nanotubes and Related Materials

During the grant period, we carried out FFF studies of carbonaceous soot, single-walled and multi-walled carbon nanotubes, carbon nano-onions and polyoxometallates. FFF alone does not provide enough information to fully characterize samples, so our suite of characterization techniques grew to include light scattering (especially Photon Correlation Spectroscopy), scanning and transmission electron microscopy, thermogravimetric analysis and spectroscopic methods. We developed convenient techniques to deposit and examine minute FFF fractions by electron microscopy. In collaboration with Arthur Cammers (University of Kentucky), we used Flow Field-Flow Fractionation (Fl-FFF) to monitor the solution-phase growth of keplerates, a class of polyoxometallate (POM) nanoparticles. We monitored the evolution of Mo-POM nanostructures over the course of weeks by by using flow field-flow fractionation and corroborated the nanoparticle structures by using transmission electron microscopy (TEM). Total molybdenum in the solution and precipitate phases was monitored by using inductively coupled plasma analyses, and total Mo-POM concentration by following the UV-visible spectra of the solution phase. We observe crystallization-driven formation of (Mo132) keplerate and solution phase-driven evolution of structurally related nanoscopic species (3-60 nm). FFF analyses of other classes of materials were less successful. Attempts to analyze platelets of layered materials, including exfoliated graphite (graphene) and TaS2 and MoS2, were disappointing. We were not able to optimize flow conditions for the layered materials. The metal sulfides react with the aqueous carrier liquid and settle out of suspension quickly because of their high density.

36 MATERIALS SCIENCE↗

Tatooine nurseries: Structure and evolution of circumbinary protoplanetary disks

Recent discoveries of circumbinary planets by the Kepler mission provide motivation for understanding their birthplaces—protoplanetary disks around stellar binaries with separations ≲1 AU. We explore properties and evolution of such circumbinary disks focusing on modification of their structure caused by tidal coupling to the binary. We develop a set of analytical scaling relations describing viscous evolution of the disk properties, which are verified and calibrated using 1D numerical calculations with realistic inputs. Injection of angular momentum by the central binary suppresses mass accretion onto the binary and causes radial distribution of the viscous angular momentum flux F{sub J} to be different from that in a standard accretion disk around a single star with no torque at the center. Disks with no mass accretion at the center develop an F{sub J} profile that is flat in radius. Radial profiles of temperature and surface density are also quite different from those in disks around single stars. Damping of the density waves driven by the binary and viscous dissipation dominates heating of the inner disk (within 1–2 AU), pushing the ice line beyond 3–5 AU, depending on disk mass and age. Irradiation by the binary governs disk thermodynamics beyond ∼10 AU. However, self-shadowing by the hot inner disk may render central illumination irrelevant out to ∼20 AU. Spectral energy distribution of a circumbinary disk exhibits a distinctive bump around 10 μm, which may facilitate identification of such disks around unresolved binaries. Efficient tidal coupling to the disk drives orbital inspiral of the binary and may cause low-mass and relatively compact binaries to merge into a single star within the disk lifetime. We generally find that circumbinary disks present favorable sites for planet formation (despite their wider zone of volatile depletion), in agreement with the statistics of Kepler circumbinary planets.

79 ASTRONOMY AND ASTROPHYSICS↗

Atmospheres of low-mass planets: The “boil-off”

We show that, for a low-mass planet that orbits its host star within a few tenths of an AU (like the majority of the Kepler planets), the atmosphere it was able to accumulate while embedded in the protoplanetary disk may not survive unscathed after the disk disperses. This gas envelope, if more massive than a few percent of the core (with a mass below 10M{sub ⊕}), has a cooling time that is much longer than the timescale on which the planet exits the disk. As such, it could not have contracted significantly from its original size, of the order of the Bondi radius. So a newly exposed protoplanet would be losing mass via a Parker wind that is catalyzed by the stellar continuum radiation. This represents an intermediate stage of mass-loss, occurring soon after the disk has dispersed, but before the EUV/X-ray driven photoevaporation becomes relevant. The surface mass-loss induces a mass movement within the envelope that advects internal heat outward. As a result, the planet atmosphere rapidly cools down and contracts, until it has reached a radius of the order of 0.1 Bondi radius, at which time the mass-loss effectively shuts down. Within a million years after the disk disperses, we find a planet that has only about 10% of its original envelope, and a Kelvin–Helmholtz time that is much longer than its actual age. We suggest that this “boil-off” process may be partially responsible for the lack of planets above a radius of 2.5R{sub ⊕} in the Kepler data, provided planet formation results in initial envelope masses of tens of percent.

79 ASTRONOMY AND ASTROPHYSICS↗

A granulation “Flicker”-based measure of stellar surface gravity

In our previous work we found that high-quality light curves, such as those obtained by Kepler, may be used to measure stellar surface gravity via granulation-driven light curve “flicker” (F{sub 8}). Here, we update and extend the relation originally presented by Bastien et al. in 2013 after calibrating F{sub 8} against a more robust set of asteroseismically derived surface gravities. We describe in detail how we extract the F{sub 8} signal from the light curves, including how we treat phenomena, such as exoplanet transits and shot noise, that adversely affect the measurement of F{sub 8}. We examine the limitations of the technique, and, as a result, we now provide an updated treatment of the F{sub 8}-based log g error. We briefly highlight further applications of the technique, such as astrodensity profiling or its use in other types of stars with convective outer layers. We discuss potential uses in current and upcoming space-based photometric missions. Finally, we supply F{sub 8}-based log g values, and their uncertainties, for 27,628 Kepler stars not identified as hosts of transiting planets, with 4500 K < T{sub eff} < 7150 K, 2.5 < log g < 4.6, K{sub p} ≤ 13.5, and overall photometric amplitudes <10 parts per thousand.

79 ASTRONOMY AND ASTROPHYSICS↗

Zodiacal exoplanets in time (Zeit). I. A Neptune-sized planet orbiting an M4.5 dwarf in the Hyades star cluster

Studying the properties of young planetary systems can shed light on how the dynamics and structure of planets evolve during their most formative years. Recent K2 observations of nearby young clusters (10–800 Myr) have facilitated the discovery of such planetary systems. Here we report the discovery of a Neptune-sized planet transiting an M4.5 dwarf (K2-25) in the Hyades cluster (650–800 Myr). The light curve shows a strong periodic signal at 1.88 days, which we attribute to spot coverage and rotation. We confirm that the planet host is a member of the Hyades by measuring the radial velocity of the system with the high-resolution near-infrared spectrograph Immersion Grating Infrared Spectrometer. This enables us to calculate a distance based on K2-25's kinematics and membership to the Hyades, which in turn provides a stellar radius and mass to ≃5%–10%, better than what is currently possible for most Kepler M dwarfs (12%–20%). We use the derived stellar density as a prior on fitting the K2 transit photometry, which provides weak constraints on eccentricity. Utilizing a combination of adaptive optics imaging and high-resolution spectra, we rule out the possibility that the signal is due to a bound or background eclipsing binary, confirming the transits’ planetary origin. K2-25b has a radius (3.43{sub −0.31}{sup +0.95} R{sub ⊕}) much larger than older Kepler planets with similar orbital periods (3.485 days) and host-star masses (0.29 M{sub ⊙}). This suggests that close-in planets lose some of their atmospheres past the first few hundred million years. Additional transiting planets around the Hyades, Pleiades, and Praesepe clusters from K2 will help confirm whether this planet is atypical or representative of other close-in planets of similar age.

79 ASTRONOMY AND ASTROPHYSICS↗

Two small temperate planets transiting nearby M dwarfs in K2 campaigns 0 and 1

The prime Kepler mission revealed that small planets (<4 R{sub ⊕}) are common, especially around low-mass M dwarfs. K2, the repurposed Kepler mission, continues this exploration of small planets around small stars. Here we combine K2 photometry with spectroscopy, adaptive optics imaging, and archival survey images to analyze two small planets orbiting the nearby field-age M dwarfs, K2-26 (EPIC 202083828) and K2-9. K2-26 is an M1.0±0.5 dwarf at 93 ± 7 pc from K2 Campaign 0. We validate its planet with a day period of 14.5665 and estimate a radius of 2.67{sub −0.42}{sup +0.46} R{sub ⊕}. K2-9 is an M2.5±0.5 dwarf at 110 ± 12 pc from K2 Campaign 1. K2-9b was first identified by Montet et al.; here we present spectra and adaptive optics imaging of the host star and independently validate and characterize the planet. Our analyses indicate K2-9b is a 2.25{sub −0.96}{sup +0.53} R{sub ⊕} planet with a 18.4498 day period. K2-26b exhibits a transit duration that is too long to be consistent with a circular orbit given its measured stellar radius. Thus, the long transits are likely due to the photoeccentric effect and our transit fits hint at an eccentric orbit. Both planets receive low incident flux from their host stars and have estimated equilibrium temperatures <500 K. K2-9b may receive approximately Earth-like insolation. However, its host star exhibits strong GALEX UV emission which could affect any atmosphere it harbors. K2-26b and K2-9b are representatives of a poorly studied class of small planets with cool temperatures that have radii intermediate to Earth and Neptune. Future study of these systems can provide key insight into trends in bulk composition and atmospheric properties at the transition from silicate dominated to volatile rich bodies.

79 ASTRONOMY AND ASTROPHYSICS↗

THE VARYING LIGHT CURVE AND TIMINGS OF THE ULTRASHORT-PERIOD CONTACT BINARY KIC 9532219

KIC 9532219 is a W UMa-type eclipsing binary with an orbital period of 0.1981549 days that is below the short-period limit (∼0.22 days) of the period distribution for contact binaries. The Kepler light curve of the system exhibits striking changes in both eclipse depths and light maxima. Applying third-body and spot effects, the light-curve synthesis indicates that the eclipsing pair is currently in a marginal contact stage with a mass ratio of q = 1.20, an orbital inclination of i = 66.°0, a temperature difference of T{sub 1}–T{sub 2} = 172 K, and a third light of l{sub 3} = 75.9%. To understand the light variations with time, we divided up the light curve into 312 segments and analyzed them separately. The results reveal that variation of eclipse depth is primarily caused by changing amounts of contamination due to the nearby star KIC 9532228 between the Kepler Quarters and that the variable O’Connell effect originates from the starspot activity on the less massive primary component. Based on our light-curve timings, a period study of KIC 9532219 indicates that the orbital period has varied as a combination of a downward parabola and a light-travel-time (LTT) effect due to a third body, which has a period of 1196 days and a minimum mass of 0.0892 M{sub ⊙} in an orbit of eccentricity 0.150. The parabolic variation could be a small part of a second LTT orbit due to a fourth component in a wider orbit, instead of either mass transfer or angular momentum loss.

79 ASTRONOMY AND ASTROPHYSICS↗

REDUCED ACTIVITY AND LARGE PARTICLES FROM THE DISINTEGRATING PLANET CANDIDATE KIC 12557548b

The intriguing exoplanet candidate KIC 12557548b is believed to have a comet-like tail of dusty debris trailing a small rocky planet. The tail of debris scatters up to 1.3% of the stellar light in the Kepler observatory’s bandpass (0.42–0.9 μ m). Observing the tail’s transit depth at multiple wavelengths can reveal the composition and particle size of the debris, constraining the makeup and lifetime of the sub-Mercury planet. Early dust particle size predictions from the scattering of the comet-like tail pointed toward a dust size of ∼0.1 μ m for silicate compositions. These small particles would produce a much deeper optical transit depth than near-infrared transit depth. We measure a transmission spectrum for KIC 12557548b using the SpeX spectrograph (covering 0.8–2.4 μ m) simultaneously with the MORIS imager taking r ′ (0.63 μ m) photometry on the Infrared Telescope Facility for eight nights and one night in H band (1.63 μ m) using the Wide-field IR Camera at the Palomar 200 inch telescope. The infrared spectra are plagued by systematic errors, but we argue that sufficient precision is obtained when using differential spectroscopic calibration when combining multiple nights. The average differential transmission spectrum is flat, supporting findings that KIC 12557548b’s debris is likely composed of larger particles ≳0.5 μ m for pyroxene and olivine and ≳0.2 μ m for iron and corundum. The r ′ photometric transit depths are all below the average Kepler value, suggesting that the observations occurred during a weak period or that the mechanisms producing optical broadband transit depths are suppressed.

79 ASTRONOMY AND ASTROPHYSICS↗

K2 DISCOVERS A BUSY BEE: AN UNUSUAL TRANSITING NEPTUNE FOUND IN THE BEEHIVE CLUSTER

Open clusters have been the focus of several exoplanet surveys, but only a few planets have so far been discovered. The Kepler spacecraft revealed an abundance of small planets around small cool stars, therefore, such cluster members are prime targets for exoplanet transit searches. Kepler's new mission, K2, is targeting several open clusters and star-forming regions around the ecliptic to search for transiting planets around their low-mass constituents. Here, we report the discovery of the first transiting planet in the intermediate-age (800 Myr) Beehive cluster (Praesepe). K2-95 is a faint (Kp=15.5 mag) M3.0±0.5 dwarf from K2's Campaign 5 with an effective temperature of 3471±124 K, approximately solar metallicity and a radius of 0.402±0.050 R ⊙ . We detected a transiting planet with a radius of 3.47 -0.53 +0.78 R ⊕ and an orbital period of 10.134 days. We combined photometry, medium/high-resolution spectroscopy, adaptive optics/speckle imaging, and archival survey images to rule out any false-positive detection scenarios, validate the planet, and further characterize the system. The planet’s radius is very unusual as M-dwarf field stars rarely have Neptune-sized transiting planets. The comparatively large radius of K2-95b is consistent with the other recently discovered cluster planets K2-25b (Hyades) and K2-33b (Upper Scorpius), indicating systematic differences in their evolutionary states or formation. These discoveries from K2 provide a snapshot of planet formation and evolution in cluster environments and thus make excellent laboratories to test differences between field-star and cluster planet populations.

79 ASTRONOMY AND ASTROPHYSICS↗