Safronov Number Research Articles

Fate of a remnant solid disk around an eccentric giant planet

The composition of giant planets' atmospheres is an important tracer of their formation history. While many theoretical studies investigate the heavy-element accretion within a gaseous protoplanetary disk, the possibility of solid accretion after disk dissipation has not been explored. Here, we focus on the case of a gas giant planet excited to an eccentric orbit and assess the likelihood of solid accretion after disk dissipation. We follow the orbital evolution of the surrounding solid materials and investigate the scattering and accretion of heavy elements in the remnant solid disks. We perform N-body simulations of planetesimals and embryos around an eccentric giant planet. We consider various sizes and orbits for the eccentric planet and determine the fate of planetesimals and embryos. We find that the orbital evolution of solids, such as planetesimals and embryos, is regulated by weak encounters with the eccentric planet rather than strong close encounters. Even in the region where the Safronov number is smaller than unity, most solid materials fall onto the central star or are ejected from the planetary system. We also develop an analytical model of the solid accretion along the orbital evolution of a giant planet, where the accretion probability is obtained as a function of the planetary mass, radius, semi-major axis, eccentricity, inclination, and solid disk thickness. Our model predicts that sim 0.01-0.1 $M_ of solids is accreted onto an eccentric planet orbiting in the outer disk ($ The accreted heavy-element mass increases (decreases) with the eccentricity (inclination) of the planet. We also discuss the possibility of collisions of terrestrial planets and find that $ of the hot Jupiters formed via high-eccentric migration collide with a planet of $10M_ However, we find that solid accretion and collisions with terrestrial planets are minor events for planets in the inner orbit, and a different accretion process is required to enrich eccentric giant planets with heavy elements.

Morphology and Mach Number Dependence of Subsonic Bondi–Hoyle Accretion

Abstract We carry out three-dimensional computations of the accretion rate onto an object (of size R sink and mass m) as it moves through a uniform medium at a subsonic speed v ∞. The object is treated as a fully absorbing boundary (e.g., a black hole). In contrast to early conjectures, we show that for an accretor with R sink ≪ R A = 2 Gm / v ∞ 2 in a gaseous medium with adiabatic index γ = 5/3, the accretion rate is independent of Mach number and is determined only by m and the gas entropy. Our numerical simulations are conducted using two different numerical schemes via the Athena++ and Arepo hydrodynamics solvers, which reach nearly identical steady-state solutions. We find that pressure gradients generated by the isentropic compression of the flow near the accretor are sufficient to suspend much of the surrounding gas in a near-hydrostatic equilibrium, just as predicted from the spherical Bondi–Hoyle calculation. Indeed, the accretion rates for steady flow match the Bondi–Hoyle rate, and are indicative of isentropic flow for subsonic motion where no shocks occur. We also find that the accretion drag may be predicted using the Safronov number, Θ = R A /R sink, and is much less than the dynamical friction for sufficiently small accretors (R sink ≪ R A ).

Capture of interstellar objects – I. The capture cross-section

ABSTRACT We study the capture of interstellar objects (ISOs) by a planet–star binary with mass ratio q ≪ 1, semimajor axis ap, orbital speed vc, and eccentricity ep. Very close (slingshot) and wide encounters with the planet are amenable to analytical treatment, while numerically obtained capture cross-sections σ closely follow the analytical results even in the intermediate regime. Wide interactions can only generate energy changes $\Delta E\lesssim q{v}_{\mathrm{c}}^2$, when $\sigma \propto v_\infty ^{-2} |\ln \Delta E|^{2/3}$ (with v∞ the ISO’s incoming speed far away from the binary), which is slightly enhanced for ep > 0. Energy changes $\Delta E\gtrsim q{v}_{\mathrm{c}}^2$, on the other hand, require close interactions when σ ∝ (v∞ΔE)−2 hardly depending on ep. Finally, at $\Delta E\gtrsim {v}_{\mathrm{c}}^2$, the cross-section drops to zero, depending on the planet’s radius Rp through the Safronov number Θ = qap/Rp. We also derive the cross-sections for collisions of ISOs with planets or moons.

New photometric analysis of hot Jupiter: WASP-135b

We report photometric follow-up observations of WASP-135b obtained using the 1.23-m telescope at Calar Alto Observatory and 1.00-m telescope at TÜBİTAK National Observatory during the 2017 and 2018 observational seasons. Eight new transit light curves of WASP-135b were analyzed with jktebop code. The ratio of the planet radius to radius of host star, fractional radius of host star, and orbital inclination of WASP-135b were found to be 0.138 ± 0.002, 0.181 ± 0.008 and 82.44 ± 0.64 degrees, respectively. Planetary radius of WASP-135b was derived from transit parameters to be 1.075 ± 0.150 RJ. The transit ephemeris of WASP-135b was also updated using the maximum likelihood method (MLM). 165 well-known hot Jupiters (HJs) were selected from the Exoplanet Data Explorer database and the classification of these HJs together with WASP-135b, based on their equilibrium temperatures and Safronov numbers, is discussed.

The refined physical properties of the transiting exoplanetary system WASP‐41

AbstractWe present the first follow‐up study of the transiting system WASP‐41 after its discovery in 2011. The main goal of this paper is to refine the physical parameters of the system and search for possible signs of transit timing variations. The observations used for analysis were taken from the public archive of the Exoplanet Transit Database (ETD). Assuming three different limb darkening laws, we found the best‐fitting model and redetermined parameters of the system. Although system parameters obtained in this study were found to be in good agreement with the discovery study, the planetary radius determined here is notably smaller, namely 1.12+0.06 –0.07 RJup. The Safronov number Θ = 0.071 ± 0.002 and equilibrium temperature Teq = 1271 ± 50 K were also determined. Both values indicate that the planet WASP‐41b belongs to Class I of transiting planets. No significant transit timing variations were detected. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Homogeneous studies of transiting extrasolar planets - III. Additional planets and stellar models

I derive the physical properties of 30 transiting extrasolar planetary systems using a homogeneous analysis of published data. The light curves are modelled with the JKTEBOP code, with attention paid to limb darkening and eccentricity. The light from some systems is contaminated by faint nearby stars, which if ignored will systematically bias the results. I show that this must be accounted for using external measurements of the amount of contaminating light. A contamination of 5% is enough to make the measurement of a planetary radius 2% too low. The physical properties of the 30 transiting systems are obtained by interpolating in stellar model predictions to find the best match to their measured quantities. The error budgets are used to compile a list of systems which would benefit from additional observations. The systematic errors arising from the inclusion of stellar models are assessed by using five different theoretical models. This model dependence sets a lower limit on the accuracy of measurements of the system properties, and at worst is 1% for the stellar mass. The correlations of planetary surface gravity and mass with orbital period have significance levels of only 3.1 sigma and 2.3 sigma. The division of planets into two classes based on Safronov number is increasingly blurred. Most of the objects studied here would benefit from more photometry and/or spectroscopy, as well as a better understanding of low-mass stars.

INDEPENDENT CONFIRMATION AND REFINED PARAMETERS OF THE HOT JUPITER XO-5b

We present HATNet observations of XO-5b, confirming its planetary nature based on evidence beyond that described in the announcement of Burke et al. (2008), namely, the lack of significant correlation between spectral bisector variations and orbital phase. In addition, using extensive spectroscopic measurements spanning multiple seasons, we investigate the relatively large scatter in the spectral line bisectors. We also examine possible blended stellar configurations (hierarchical triples, chance alignments) that can mimic the planet signals, and we are able to show that none are consistent with the sum of all the data. The analysis of the S activity index shows no significant stellar activity. Our results for the planet parameters are consistent with values in Burke et al. (2008), and we refine both the stellar and planetary parameters using our data. XO-5b orbits a slightly evolved, late G type star with mass M_s = 0.88 +/- 0.03, radius R_s = 1.08 +/- 0.04, and metallicity close to solar. The planetary mass and radius are M_p = 1.059 +/- 0.028 M_Jup and R_p = 1.109 +/- 0.050 R_Jup, respectively, corresponding to a mean density of 0.96 -0.11 +0.14 g/cm^3. The ephemeris for the orbit is P = 4.187757 +/- 0.000011, E= 2454552.67168 +/- 0.00029 (BJD) with transit duration of 0.1307 +/- 0.0013 d. By measuring four individual transit centers, we found no signs for transit timing variations. The planet XO-5b is notable for its anomalously high Safronov number, and has a high surface gravity when compared to other transiting exoplanets with similar period.

Interpreting the yield of transit surveys: are there groups in the known transiting planets population?

Each transiting planet discovered is characterized by 7 measurable quantities, that may or may not be linked together (planet mass, radius, orbital period, and star mass, radius, effective temperature, and metallicity). Correlations between planet mass and period, surface gravity and period, planet radius and star temperature have been previously observed among the known transiting giant planets. Two classes of planets have been previously identified based on their Safronov number. We use the CoRoTlux code to compare simulated events to the sample of discovered planets and test the statistical significance of these correlations. We first generate a stellar field with planetary companions based on radial velocity discoveries and a planetary evolution model, then apply a detection criterion that includes both statistical and red noise sources. We compare the yield of our simulated survey with the ensemble of 31 well-characterized giant transiting planets, using a multivariate logistic analysis to assess whether the simulated distribution matches the known transiting planets. Our multivariate analysis shows that our simulated sample and observations are consistent to 76%. The mass vs. period correlation for giant planets first observed with radial velocity holds with transiting planets. Our model naturally explains the correlation between planet surface gravity and period and the one between planet radius and stellar effective temperature. Finally, we are also able to reproduce the previously observed apparent bimodal distribution of Safronov numbers in 10% of our simulated cases, although our model predicts a continuous distribution. This shows that the evidence for the existence of two groups of planets with different intrinsic properties is not statistically significant.

HAT-P-10b: A LIGHT AND MODERATELY HOT JUPITER TRANSITING A K DWARF

We report on the discovery of HAT-P-10b, the lowest mass (0.46 +/- 0.03 MJ) transiting extrasolar planet (TEP) discovered to date by transit searches. HAT-P-10b orbits the moderately bright V=11.89 K dwarf GSC 02340-01714, with a period P = 3.7224690 +/- 0.0000067 d, transit epoch Tc = 2454729.90631 +/- 0.00030 (BJD) and duration 0.1100 +/- 0.0015 d. HAT-P-10b has a radius of 1.05 +(0.05)-(0.03) RJ yielding a mean density of 0.498+/-0.064 g cm^-3 . Comparing these observations with recent theoretical models we find that HAT-P-10 is consistent with a ~4.5 Gyr, coreless, pure hydrogen and helium gas giant planet. With an equilibrium temperature of Teq = 1030 +(26)-(19)K, HAT-P-10b is one of the coldest TEPs. Curiously, its Safronov number Theta = 0.047 +/- 0.003 falls close to the dividing line between the two suggested TEP populations.

Homogeneous studies of transiting extrasolar planets - II. Physical properties

I present an homogeneous determination of the physical properties of 14 transiting extrasolar planetary systems for which good photometric and spectroscopic data are available. The input quantities for each system are the results of the light-curve analyses presented in Paper I, and published measurements of the stellar velocity amplitude, effective temperature and metal abundance. The physical properties are determined by interpolating within tabulated predictions from stellar theory to find the optimal match to these input data. Statistical uncertainties are found using a perturbation algorithm, which gives a detailed error budget for every output quantity. Systematic uncertainties are assessed for each quantity by comparing the values found using several independent sets of stellar models. As a theory-free alternative, physical properties are also calculated using an empirical mass–radius relation constructed from high-precision studies of low-mass eclipsing binary stars. I find that the properties of the planets depend mostly on parameters measured from the light and radial velocity curves, and have a relatively minor sensitivity to theoretical predictions. In contrast, the orbital semimajor axes and stellar masses have a strong dependence on theoretical predictions, and their systematic uncertainties can be substantially larger than the statistical ones. Using the empirical mass–radius relation instead, the semimajor axes and stellar masses are smaller by up to 15 per cent. Thus, our understanding of extrasolar planets is currently limited by our lack of understanding of low-mass stars. Using the properties of all known transiting extrasolar planets, I find that correlations between their orbital periods, masses and surface gravities are significant at the 2σ –3σ level. However, the separation of the known planets into two classes according to their Safronov number is weaker than previously found, and may not be statistically significant. Three systems, HAT-P-2, WASP-14 and XO-3, form their own little group of outliers, with eccentric orbits, massive planets and stars with masses ∼1.3 M� . The detailed error budgets calculated for each system show where further observations are needed. XO-1 and WASP-1 could do with new transit light curves. TrES-2 and WASP-2 would benefit from more precise stellar temperature and abundance measurements. Velocity measurements of the parent stars are vital for determining the planetary masses: TrES-1, XO-1, WASP-1, WASP-2 and the OGLEs need additional data. The homogeneous analysis presented here is a step towards large-scale statistical studies of transiting extrasolar planetary systems, in preparation for the expected deluge of new detections from CoRoT and Kepler.

Improved Parameters for Extrasolar Transiting Planets

We present refined values for the physical parameters of transiting exoplanets, based on a self-consistent and uniform analysis of transit light curves and the observable properties of the host stars. Previously it has been difficult to interpret the ensemble properties of transiting exoplanets because of the widely different methodologies that have been applied in individual cases. Furthermore, previous studies often ignored an important constraint on the mean stellar density that can be derived directly from the light curve. The main contributions of this work are (1) a critical compilation and error assessment of all reported values for the effective temperature and metallicity of the host stars, (2) the application of a consistent methodology and treatment of errors in modeling the transit light curves, and (3) more accurate estimates of the stellar mass and radius based on stellar evolution models, incorporating the photometric constraint on the stellar density. We use our results to revisit some previously proposed patterns and correlations within the ensemble. We confirm the mass-period correlation and find evidence for a new pattern within the scatter about this correlation: planets around metal-poor stars are more massive than those around metal-rich stars at a given orbital period. Likewise, we confirm the proposed dichotomy of planets according to their Safronov number, and we find evidence that the systems with small Safronov numbers are more metal-rich on average. Finally, we confirm the trend that led to the suggestion that higher metallicity stars harbor planets with a greater heavy-element content.

Two Classes of Hot Jupiters

We identify two classes of transiting planet, based on their equilibrium temperatures and Safronov numbers. We examine various possible explanations for the dichotomy. It may reflect the influence of planet or planetesimal scattering in determining when planetary migration stops. Another possibility is that some planets lose more mass to evaporation than others. If this evaporation process preferentially removes Helium from the planet, the consequent reduction in the mean molecular weight may explain why some planets have anomalously large radii.

Stirring of a planetesimal swarm: The role of distant encounters

Planetesimals have random velocities (eccentric and inclined orbits) induced by their mutual gravitational perturbations. The viscous stirring algorithm of Stewart and Wetherill (1988, Icarus 74, 542–553) includes only scattering by close encounters of bodies in crossing orbits. A completetreatment should also include the effect of more distant bodies in noncrossing orbits. This paper presents expressions for the stirring rate due to distant encounters, derived with three-body formalism. The stirring rate has the same mass dependence as that for close encounters; the relative importance of the two mechanisms depends on the Safronov number θ. For small θ, close encounters dominate the stirring rate, but distant encounters may dominate for θ ≳ 10 2. Perturbations by a planetary embryo in scenarios involving “runaway growth” may affect the evolution of planetesimals in noncrossing orbits.

Accumulation of planetesimals in the solar nebula

Characteristic time scales relevant to the accumulation of planetesimals in a gaseous nebula are examined and the accumulation toward the planets is simulated by numerically solving a growth equation for a mass distribution function. The eccentricity and inclination of planetesimals are assumed to be determined by a balance between excitation due to mutual gravitational scattering and dissipation due to gas drag. Two kinds of mass motion in the radial direction, i.e., diffusion due to mutual scattering and inward flow due to gas drag, are both taken into account. The diffusion is shown to be effective in later stages with a result of accelerating the accumulation. As to the coalescent collision cross section, the usual formula for a binary encounter in a free space is used but the effect of tidal disruption which increases substantially the cross section is taken into account. Numerical results show that the gravitational enhancement factor (i.e., the so-called “Safronov number”), contained in the cross section formula, always takes a value of the order of unity but the accumulation proceeds relatively rapidly owing to the effects of radial diffusion and tidal disruption. That is, a proto-Earth, a proto-Jupiter, and a proto-Saturn with masses of 1×10 27 g are formed in 5×10 6, 1×10 7, and 1.6×10 8 years, respectively. Also, a tentative numerical computation for the Neptune formation shows that a proto-Neptune with the same mass requires a long accumulation time, 4.6×10 9 years. Finally, the other effects which are expected to reduce the above growth times further are discussed.