Theoretical models of planetary system formation: mass vs. semi-major axis

Kepler-419 is a planetary system discovered by the Kepler photometry which is known to harbour two massive giant planets: an inner 3 MJ transiting planet with a 69.8-day period, highly eccentric orbit, and an outer 7.5 MJ non-transiting planet predicted from the transit-timing variations (TTVs) of the inner planet b to have a 675-day period, moderately eccentric orbit. Here we present new radial velocity (RV) measurements secured over more than two years with the SOPHIE spectrograph, where both planets are clearly detected. The RV data is modelled together with the Kepler photometry using a photodynamical model. The inclusion of velocity information breaks the MR−3 degeneracy inherent in timing data alone, allowing us to measure the absolute stellar and planetary radii and masses. With uncertainties of 12 and 13% for the stellar and inner planet radii, and 35, 24, and 35% for the masses of the star, planet b, and planet c, respectively, these measurements are the most precise to date for a single host star system using this technique. The transiting planet mass is determined at better precision than the star mass. This shows that modelling the radial velocities and the light curve together in systems of dynamically interacting planets provides a way of characterising both the star and the planets without being limited by knowledge of the star. On the other hand, the period ratio and eccentricities place the Kepler-419 system in a sweet spot; had around twice as many transits been observed, the mass of the transiting planet could have been measured using its own TTVs. Finally, the origin of the Kepler-419 system is discussed. We show that the system is near a coplanar high-eccentricity secular fixed point, related to the alignment of the orbits, which has prevented the inner orbit from circularising. For most other relative apsidal orientations, planet b’s orbit would be circular with a semi-major axis of 0.03 au. This suggests a mechanism for forming hot Jupiters in multiplanetary systems without the need of high mutual inclinations.

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HD 83443: a system with two Saturns

Symposium - International Astronomical Union ◽

10.1017/s0074180900217543 ◽

2004 ◽

Vol 202 ◽

pp. 84-86 ◽

Cited By ~ 2

Author(s):

M. Mayor ◽

D. Naef ◽

F. Pepe ◽

D. Queloz ◽

N. C. Santos ◽

...

Keyword(s):

Planetary System ◽

Major Axis ◽

Giant Planets ◽

Outer Planet ◽

Semi Major Axis ◽

Dynamical Study ◽

Low Mass ◽

The Stability ◽

Extrasolar Planetary System

We report the discovery of an extrasolar planetary system with two Saturnian planets around the star HD 83443. The new planetary system is unusual by more than one aspect, as it contains two very low–mass gaseous giant planets, both on very tight orbits. Among the planets detected so far, the inner planet has the smallest semi–major axis (0.038 AU) and period (2.985 days) whereas the outer planet is the lightest one with m2 sin i = 0.53 MSat. A preliminary dynamical study confirms the stability of the system.

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MCMCI: A code to fully characterise an exoplanetary system

Astronomy and Astrophysics ◽

10.1051/0004-6361/201936326 ◽

2020 ◽

Vol 635 ◽

pp. A6 ◽

Cited By ~ 3

Author(s):

A. Bonfanti ◽

M. Gillon

Keyword(s):

Time Series ◽

Light Curve ◽

Radial Velocity ◽

Global Analysis ◽

Major Axis ◽

Theoretical Models ◽

Integrated Analysis ◽

Physical Parameters ◽

Light Curve Analysis ◽

Semi Major Axis

Context. Useful information can be retrieved by analysing the transit light curve of a planet-hosting star or induced radial velocity oscillations. However, inferring the physical parameters of the planet, such as mass, size, and semi-major axis, requires preliminary knowledge of some parameters of the host star, especially its mass or radius, which are generally inferred through theoretical evolutionary models. Aims. We seek to present and test a whole algorithm devoted to the complete characterisation of an exoplanetary system thanks to the global analysis of photometric or radial velocity time series combined with observational stellar parameters derived either from spectroscopy or photometry. Methods. We developed an integrated tool called MCMCI. This tool combines the Markov chain Monte Carlo (MCMC) approach of analysing photometric or radial velocity time series with a proper interpolation within stellar evolutionary isochrones and tracks, known as isochrone placement, to be performed at each chain step, to retrieve stellar theoretical parameters such as age, mass, and radius. Results. We tested the MCMCI on the HD 219134 multi-planetary system hosting two transiting rocky super Earths and on WASP-4, which hosts a bloated hot Jupiter. Even considering different input approaches, a final convergence was reached within the code, we found good agreement with the results already stated in the literature and we obtained more precise output parameters, especially concerning planetary masses. Conclusions. The MCMCI tool offers the opportunity to perform an integrated analysis of an exoplanetary system without splitting it into the preliminary stellar characterisation through theoretical models. Rather this approach favours a close interaction between light curve analysis and isochrones, so that the parameters recovered at each step of the MCMC enter as inputs for purposes of isochrone placement.

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Theoretical models of planetary system formation

Astronomy and Astrophysics ◽

10.1051/0004-6361/201424295 ◽

2015 ◽

Vol 579 ◽

pp. A37 ◽

Cited By ~ 17

Author(s):

S. Pfyffer ◽

Y. Alibert ◽

W. Benz ◽

D. Swoboda

Keyword(s):

Planetary System ◽

Theoretical Models ◽

System Formation

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How planet–planet scattering can create high-inclination as well as long-period orbits

Proceedings of the International Astronomical Union ◽

10.1017/s1743921311020229 ◽

2010 ◽

Vol 6 (S276) ◽

pp. 225-229 ◽

Cited By ~ 2

Author(s):

Sourav Chatterjee ◽

Eric B. Ford ◽

Frederic A. Rasio

Keyword(s):

Major Axis ◽

Theoretical Models ◽

Giant Planets ◽

Direct Imaging ◽

Semi Major Axis ◽

Hot Jupiters ◽

Long Period ◽

Outer Disk ◽

Planetary Orbits ◽

Core Accretion

AbstractRecent observations have revealed two new classes of planetary orbits. Rossiter-Mclaughlin (RM) measurements have revealed hot Jupiters in high-obliquity orbits. In addition, direct-imaging has discovered giant planets at large (~ 100 AU) separations via direct-imaging technique. Simple-minded disk-migration scenarios are inconsistent with the high-inclination (and even retrograde) orbits as seen in recent RM measurements. Furthermore, forming giant planets at large semi-major axis (a) may be challenging in the core-accretion paradigm. We perform many N-body simulations to explore the two above-mentioned orbital architectures. Planet–planet scattering in a multi-planet system can naturally excite orbital inclinations. Planets can also get scattered to large distances. Large-a planetary orbits created from planet–planet scattering are expected to have high eccentricities (e). Theoretical models predict that the observed long-period planets, such as Fomalhaut-b have moderate e ≈ 0.3. Interestingly, these are also in systems with disks. We find that if a massive-enough outer disk is present, a scattered planet may be circularized at large a via dynamical friction from the disk and repeated scattering of the disk particles.

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Detection and Characterization of earth-like Planets

International Astronomical Union Colloquium ◽

10.1017/s0252921100014810 ◽

1997 ◽

Vol 161 ◽

pp. 299-311 ◽

Cited By ~ 22

Author(s):

Jean Marie Mariotti ◽

Alain Léger ◽

Bertrand Mennesson ◽

Marc Ollivier

Keyword(s):

Direct Detection ◽

Contrast Ratio ◽

Angular Size ◽

Physical Nature ◽

Major Axis ◽

Infrared Emission ◽

Space Technology ◽

Semi Major Axis ◽

Earth Like Planets ◽

Visible Wavelengths

AbstractIndirect methods of detection of exo-planets (by radial velocity, astrometry, occultations,...) have revealed recently the first cases of exo-planets, and will in the near future expand our knowledge of these systems. They will provide statistical informations on the dynamical parameters: semi-major axis, eccentricities, inclinations,... But the physical nature of these planets will remain mostly unknown. Only for the larger ones (exo-Jupiters), an estimate of the mass will be accessible. To characterize in more details Earth-like exo-planets, direct detection (i.e., direct observation of photons from the planet) is required. This is a much more challenging observational program. The exo-planets are extremely faint with respect to their star: the contrast ratio is about 10−10at visible wavelengths. Also the angular size of the apparent orbit is small, typically 0.1 second of arc. While the first point calls for observations in the infrared (where the contrast goes up to 10−7) and with a coronograph, the latter implies using an interferometer. Several space projects combining these techniques have been recently proposed. They aim at surveying a few hundreds of nearby single solar-like stars in search for Earth-like planets, and at performing a low resolution spectroscopic analysis of their infrared emission in order to reveal the presence in the atmosphere of the planet of CO H2O and O3. The latter is a good tracer of the presence of oxygen which could be, like on our Earth, released by biological activity. Although extremely ambitious, these projects could be realized using space technology either already available or in development for others missions. They could be built and launched during the first decades on the next century.

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Brightest cluster galaxies: the centre can(not?) hold

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa3286 ◽

2020 ◽

Vol 500 (1) ◽

pp. 310-318

Author(s):

Roberto De Propris ◽

Michael J West ◽

Felipe Andrade-Santos ◽

Cinthia Ragone-Figueroa ◽

Elena Rasia ◽

...

Keyword(s):

Dark Matter ◽

Local Environment ◽

Major Axis ◽

Theoretical Models ◽

Dark Matter Halo ◽

Gas Distribution ◽

X Ray ◽

Cluster Galaxies ◽

Peculiar Velocities ◽

Brightest Cluster Galaxies

ABSTRACT We explore the persistence of the alignment of brightest cluster galaxies (BCGs) with their local environment. We find that a significant fraction of BCGs do not coincide with the centroid of the X-ray gas distribution and/or show peculiar velocities (they are not at rest with respect to the cluster mean). Despite this, we find that BCGs are generally aligned with the cluster mass distribution even when they have significant offsets from the X-ray centre and significant peculiar velocities. The large offsets are not consistent with simple theoretical models. To account for these observations BCGs must undergo mergers preferentially along their major axis, the main infall direction. Such BCGs may be oscillating within the cluster potential after having been displaced by mergers or collisions, or the dark matter halo itself may not yet be relaxed.

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Some Special Types of Orbits around Jupiter

Aerospace ◽

10.3390/aerospace8070183 ◽

2021 ◽

Vol 8 (7) ◽

pp. 183

Author(s):

Yongjie Liu ◽

Yu Jiang ◽

Hengnian Li ◽

Hui Zhang

Keyword(s):

Gravity Model ◽

Small Perturbation ◽

Equilibrium Points ◽

Major Axis ◽

Semi Major Axis ◽

Ground Track ◽

The Earth ◽

Degenerate Equilibrium ◽

The Mean ◽

Element Theory

This paper intends to show some special types of orbits around Jupiter based on the mean element theory, including stationary orbits, sun-synchronous orbits, orbits at the critical inclination, and repeating ground track orbits. A gravity model concerning only the perturbations of J2 and J4 terms is used here. Compared with special orbits around the Earth, the orbit dynamics differ greatly: (1) There do not exist longitude drifts on stationary orbits due to non-spherical gravity since only J2 and J4 terms are taken into account in the gravity model. All points on stationary orbits are degenerate equilibrium points. Moreover, the satellite will oscillate in the radial and North-South directions after a sufficiently small perturbation of stationary orbits. (2) The inclinations of sun-synchronous orbits are always bigger than 90 degrees, but smaller than those for satellites around the Earth. (3) The critical inclinations are no-longer independent of the semi-major axis and eccentricity of the orbits. The results show that if the eccentricity is small, the critical inclinations will decrease as the altitudes of orbits increase; if the eccentricity is larger, the critical inclinations will increase as the altitudes of orbits increase. (4) The inclinations of repeating ground track orbits are monotonically increasing rapidly with respect to the altitudes of orbits.

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Dynamical properties of the Molniya satellite constellation: long-term evolution of the semi-major axis

Nonlinear Dynamics ◽

10.1007/s11071-021-06708-5 ◽

2021 ◽

Author(s):

Jérôme Daquin ◽

Elisa Maria Alessi ◽

Joseph O’Leary ◽

Anne Lemaitre ◽

Alberto Buzzoni

Keyword(s):

Major Axis ◽

Long Term Evolution ◽

Semi Major Axis ◽

Satellite Constellation ◽

Term Evolution ◽

Dynamical Properties

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Creation/destruction of ultra-wide binaries in tidal streams

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa3700 ◽

2020 ◽

Author(s):

Jorge Peñarrubia

Keyword(s):

Globular Clusters ◽

Galactic Halo ◽

Local Density ◽

Formation Rate ◽

Semimajor Axis ◽

Major Axis ◽

Binding Energies ◽

Semi Major Axis ◽

The Mean ◽

Tidal Streams

Abstract This paper uses statistical and N-body methods to explore a new mechanism to form binary stars with extremely large separations (≳ 0.1 pc), whose origin is poorly understood. Here, ultra-wide binaries arise via chance entrapment of unrelated stars in tidal streams of disrupting clusters. It is shown that (i) the formation of ultra-wide binaries is not limited to the lifetime of a cluster, but continues after the progenitor is fully disrupted, (ii) the formation rate is proportional to the local phase-space density of the tidal tails, (iii) the semimajor axis distribution scales as p(a)da ∼ a1/2da at a ≪ D, where D is the mean interstellar distance, and (vi) the eccentricity distribution is close to thermal, p(e)de = 2ede. Owing to their low binding energies, ultra-wide binaries can be disrupted by both the smooth tidal field and passing substructures. The time-scale on which tidal fluctuations dominate over the mean field is inversely proportional to the local density of compact substructures. Monte-Carlo experiments show that binaries subject to tidal evaporation follow p(a)da ∼ a−1da at a ≳ apeak, known as Öpik’s law, with a peak semi-major axis that contracts with time as apeak ∼ t−3/4. In contrast, a smooth Galactic potential introduces a sharp truncation at the tidal radius, p(a) ∼ 0 at a ≳ rt. The scaling relations of young clusters suggest that most ultra-wide binaries arise from the disruption of low-mass systems. Streams of globular clusters may be the birthplace of hundreds of ultra-wide binaries, making them ideal laboratories to probe clumpiness in the Galactic halo.

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