scholarly journals A numerical method for computing optimum radii of host stars and orbits of planets, with application to Kepler-11, Kepler-90, Kepler-215, HD 10180, HD 34445 and TRAPPIST-1

2020 ◽  
pp. 2150028
Author(s):  
V. S. Geroyannis
Keyword(s):  
Numerical Method ◽  
Planetary System ◽  
Hydrostatic Equilibrium ◽  
Polytropic Index ◽  
Spherical Shells ◽  
Polytropic Model ◽  
Emden Equation ◽  
Exoplanetary Systems ◽  
Planetary Orbits ◽  
Host Stars

In the so-called “global polytropic model”, we assume planetary systems in hydrostatic equilibrium and solve the Lane–Emden equation in the complex plane. We thus find polytropic spherical shells providing accommodation to planetary orbits. On the basis of this model, we develop a numerical method which can compute optimum values for the polytropic index of the global polytropic model that simulates the planetary system, for the orbits of the planets, and for the host star radius. We apply our method to the exoplanetary systems Kepler-11, Kepler-90, Kepler-215, HD 10180, HD 34445 and TRAPPIST-1.

scholarly journals Host-star and exoplanet compositions: a pilot study using a wide binary with a polluted white dwarf

2021 ◽  
Vol 503 (2) ◽  
pp. 1877-1883
Author(s):  
Amy Bonsor ◽  
Paula Jofré ◽  
Oliver Shorttle ◽  
Laura K Rogers ◽  
Siyi Xu(许偲艺) ◽  
...  
Keyword(s):  
White Dwarf ◽  
Planetary System ◽  
Kuiper Belt ◽  
Wide Binary ◽  
Elemental Abundances ◽  
Exoplanetary Systems ◽  
Planetary Bodies ◽  
Refractory Composition ◽  
Observational Errors ◽  
Host Stars

ABSTRACT Planets and stars ultimately form out of the collapse of the same cloud of gas. Whilst planets, and planetary bodies, readily loose volatiles, a common hypothesis is that they retain the same refractory composition as their host star. This is true within the Solar system. The refractory composition of chondritic meteorites, Earth, and other rocky planetary bodies are consistent with solar, within the observational errors. This work aims to investigate whether this hypothesis holds for exoplanetary systems. If true, the internal structure of observed rocky exoplanets can be better constrained using their host star abundances. In this paper, we analyse the abundances of the K-dwarf, G200-40, and compare them to its polluted white dwarf companion, WD 1425+540. The white dwarf has accreted planetary material, most probably a Kuiper belt-like object, from an outer planetary system surviving the star’s evolution to the white dwarf phase. Given that binary pairs are chemically homogeneous, we use the binary companion, G200-40, as a proxy for the composition of the progenitor to WD 1425+540. We show that the elemental abundances of the companion star and the planetary material accreted by WD 1425+540 are consistent with the hypothesis that planet and host-stars have the same true abundances, taking into account the observational errors.

scholarly journals Stellar Structure in a Newtonian Theory with Variable G

Physics ◽  
2021 ◽  
Vol 3 (4) ◽  
pp. 1123-1132
Author(s):  
Júlio C. Fabris ◽  
Túlio Ottoni ◽  
Júnior D. Toniato ◽  
Hermano Velten
Keyword(s):  
Spatial Dependence ◽  
Equilibrium Structure ◽  
Hydrostatic Equilibrium ◽  
Stellar Structure ◽  
Polytropic Index ◽  
Gravitational Coupling ◽  
Matter Distribution ◽  
Newtonian Theory ◽  
Emden Equation ◽  
Variable G

A Newtonian-like theory inspired by the Brans–Dicke gravitational Lagrangian has been recently proposed by us. For static configurations, the gravitational coupling acquires an intrinsic spatial dependence within the matter distribution. Therefore, the interior of astrophysical configurations may provide a testable environment for this approach as long as no screening mechanism is evoked. In this work, we focus on the stellar hydrostatic equilibrium structure in such a varying Newtonian gravitational coupling G scenario. A modified Lane–Emden equation is presented and its solutions for various values of the polytropic index are discussed. The role played by the theory parameter ω, the analogue of the Brans–Dicke parameter, in the physical properties of stars is discussed.

scholarly journals Stable mass ranges of ν Andromedae planetary system

2004 ◽  
Vol 202 ◽  
pp. 193-195
Author(s):  
Takashi Ito ◽  
Shoken M. Miyama
Keyword(s):  
Radial Velocity ◽  
Extrasolar Planets ◽  
Planetary System ◽  
Initial Conditions ◽  
Line Of Sight ◽  
Upper Limit ◽  
Doppler Observation ◽  
Planetary Orbits ◽  
Lower Limits ◽  
Host Stars

Doppler observation of extrasolar planets through the radial velocity displacement of their host stars can only determine lower limits of planetary masses. We numerically integrate ν Andromedae planetary orbits with various initial conditions of masses and angle variables to investigate which initial configuration produces stable orbits during the timescale of host star's age. According to our preliminary results starting from Lick dataset, ν Andromedae planetary system seems to remain stable over the timescale of its host star's age if sin i > 0.7 where i is the unknown line-of-sight inclination of planetary orbits. In this case we may estimate that the upper limit masses of ν Andromedae planets in our model is about 1/0.7 ∽ 1.43 times larger than its minimum.

scholarly journals Emden’s Polytropes: Gas Globes In Hydrostatic Equilibrium

2013 ◽  
Vol 12 (1) ◽  
pp. 99-127
Author(s):  
M N Anandaram
Keyword(s):  
Mass Distribution ◽  
Equilibrium Structure ◽  
Review Article ◽  
Hydrostatic Equilibrium ◽  
Graphical Form ◽  
Polytropic Index ◽  
Tabular Form ◽  
Program Code ◽  
Emden Equation ◽  
Python Script

The theory of polytropes dealing with the hydrostatic equilibrium structure of gas globes had its origin in Emden’s publication, Gaskugeln a century ago (1907). This review article has been written for students of physics and astrophysics not only to understand the theory of polytropes as the simplest of stellar models but also computationally solve the Lane-Emden equation for polytropes. Anyone can easily obtain values of normalized temperature, density, pressure and mass distribution as a function of the normalized radius or mass in any polytrope model in tabular form as well as in graphical form using the program code. Explanation of the algorithm to write a code is provided (python script on request). A graphical description of how the polytropic index determines the structure of the polytrope is also given.

scholarly journals On the alignment of debris discs and their host stars’ rotation axis - implications for spin-orbit misalignment in exoplanetary systems

2011 ◽  
Vol 413 (1) ◽  
pp. L71-L75 ◽  
Author(s):  
C. A. Watson ◽  
S. P. Littlefair ◽  
C. Diamond ◽  
A. Collier Cameron ◽  
A. Fitzsimmons ◽  
...  
Keyword(s):  
Rotation Axis ◽  
Spin Orbit ◽  
Exoplanetary Systems ◽  
Host Stars

A numerical method for analysis of free vibration of spherical shells.

AIAA Journal ◽  
1967 ◽  
Vol 5 (7) ◽  
pp. 1256-1261 ◽  
Author(s):  
M. S. ZARGHAMEE ◽  
A. R. ROBINSON
Keyword(s):  
Free Vibration ◽  
Numerical Method ◽  
Spherical Shells

scholarly journals Planetary architectures in interacting stellar environments

2020 ◽  
Vol 496 (2) ◽  
pp. 1453-1470 ◽  
Author(s):  
Yi-Han Wang ◽  
Rosalba Perna ◽  
Nathan W C Leigh
Keyword(s):  
High Resolution ◽  
Cross Section ◽  
Cross Sections ◽  
Velocity Dispersion ◽  
Planetary System ◽  
Star Clusters ◽  
Exoplanetary Systems ◽  
The Cross ◽  
Star Binary ◽  
Strong Scattering

ABSTRACT The discovery of exoplanetary systems has challenged some of the theories of planet formation, which assume unperturbed evolution of the host star and its planets. However, in star clusters the interactions with fly-by stars and binaries may be relatively common during the lifetime of a planetary system. Here, via high-resolution N-body simulations of star–planet systems perturbed by interlopers (stars and binaries), we explore the reconfiguration to the planetary system due to the encounters. In particular, via an exploration focused on the strong scattering regime, we derive the fraction of encounters that result in planet ejections, planet transfers, and collisions by the interloper star/binary, as a function of the characteristics of the environment (density, velocity dispersion), and for different masses of the fly-by star/binary. We find that binary interlopers can significantly increase the cross-section of planet ejections and collisions, while they only slightly change the cross-section for planet transfers. Therefore, in environments with high binary fractions, floating planets are expected to be relatively common, while in environments with low binary fractions, where the cross-sections of planet ejection and transfer are comparable, the rate of planet exchanges between two stars will be comparable to the rate of production of free-floating planets.

scholarly journals Different types of star-planet interactions

2019 ◽  
Vol 15 (S354) ◽  
pp. 259-267
Author(s):  
A. A. Vidotto
Keyword(s):  
Physical Characteristics ◽  
Electromagnetic Spectrum ◽  
Exoplanetary Systems ◽  
Different Types ◽  
Host Stars

AbstractStars and their exoplanets evolve together. Depending on the physical characteristics of these systems, such as age, orbital distance and activity of the host stars, certain types of star-exoplanet interactions can dominate during given phases of the evolution. Identifying observable signatures of such interactions can provide additional avenues for characterising exoplanetary systems. Here, I review some recent works on star-planet interactions and discuss their observability at different wavelengths across the electromagnetic spectrum.

Stability analysis of the polytropic solar wind

2014 ◽  
Vol 92 (11) ◽  
pp. 1419-1424 ◽  
Author(s):  
P.K. Karmakar ◽  
M. Gohain ◽  
U. Deka
Keyword(s):  
Growth Rate ◽  
Solar Wind ◽  
Stability Analysis ◽  
Dispersion Relation ◽  
Dynamic Equilibrium ◽  
Nonlinear Function ◽  
Linear Growth Rate ◽  
Polytropic Index ◽  
Solar Plasma ◽  
Polytropic Model

A linear stability analysis of a simple polytropic model for the solar wind dynamics within the framework of a magnetohydrodynamic equilibrium configuration is theoretically proposed. The simplistic analysis is based on the model developed based on the data available from the Advanced Composition Explorer (ACE) spacecraft mission. A unique form of dispersion relation is derived by coupling the adiabatic and polytropic processes in the limit of ideal gas approximation for the solar wind gas in accordance with the standard Fourier technique. Applying usual variable-separation methodology on the dispersion relation, we obtain the linear growth rate of the fluctuations. It is seen that the growth rate is an explicitly nonlinear function of the variable polytropic index (α) and radial position (r) with respect to the considered center of the Sun. Numerical analyses are carried out to understand the physical insight of the growth profiles of the fluctuations. It is shown that the growth is maximized near the solar corona, where α ∼ 1, relative to that observed elsewhere in the entire solar plasma system. The source for this growth may be attributed to the free flow of energy coming from the dynamic equilibrium of the solar plasma itself. As compared with existing model predictions, our results are qualitatively capable of reproducing the average behavior of the solar wind fluctuation and stability behaviors on the astrophysical scales of space and time.

scholarly journals The effects of stellar winds and magnetic fields on exoplanets

2013 ◽  
Vol 9 (S302) ◽  
pp. 228-236 ◽  
Author(s):  
A. A. Vidotto
Keyword(s):  
Solar System ◽  
Interplanetary Medium ◽  
Great Majority ◽  
Stellar Winds ◽  
Stellar Rotation ◽  
Low Mass Stars ◽  
Exoplanetary Systems ◽  
Cool Stars ◽  
Low Mass ◽  
Host Stars

AbstractThe great majority of exoplanets discovered so far are orbiting cool, low-mass stars whose properties are relatively similar to the Sun. However, the stellar magnetism of these stars can be significantly different from the solar one, both in topology and intensity. In addition, due to the present-day technology used in exoplanetary searches, most of the currently known exoplanets are found orbiting at extremely close distances to their host stars (< 0.1 au). The dramatic differences in stellar magnetism and orbital radius can make the interplanetary medium of exoplanetary systems remarkably distinct from that of the Solar System. To constrain interactions between exoplanets and their host-star's magnetised winds and to characterise the interplanetary medium that surrounds exoplanets, more realistic stellar wind models, which account for factors such as stellar rotation and the complex stellar magnetic field configurations of cool stars, must be employed. Here, I briefly review the latest progress made in data-driven modelling of magnetised stellar winds. I also show that the interaction of the stellar winds with exoplanets can lead to several observable signatures, some of which that are absent in our own Solar System.

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