Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA study of the stability regions in the planetary system HD 74156 - Can it host earthlike planets in habitable zones?
37
0
0.0
(
0
)
Authors
R. Dvorak
Ask ChatGPT about the research
No Arabic abstract
Using numerical methods we thoroughly investigate the dynamical stability in the region between the two planets found in HD 74156. The two planets with minimum masses 1.56 M_JUP (HD 74156b) and 7.5 M_JUP (HD 74156c), semimajor axes 0.276 AU and 3.47 AU move on quite eccentric orbits (e=0.649 and 0.395). There is a region between 0.7 and 1.4 AU which may host additional planets which we checked via numerical integrations using different dynamical models. Besides the orbital evolution of several thousands of massless regarded planets in a three-dimensional restricted 4-body problem (host star, two planets + massless bodies) we also have undertaken test computation for the orbital evolution for fictive planets with masses of 0.1, 0.3 and 1 M_JUP in the region between HD74156b and HD74156c. For direct numerical integrations up to 10^7 years we used the Lie-integrator, a method with adaptive stepsize; additionally we used the Fast Lyapunov Indicators as tool for detecting chaotic motion in this region. We emphasize the important role of the inner resonances (with the outer planet) and the outer resonances (with the inner planet) with test bodies located inside the resonances. In these two resonance regions almost no orbits survive. The region between the 1:5 outer resonance (0.8 AU) and the 5:1 inner resonance (1.3 AU), just in the right position for habitability, is also very unstable probably due to three-body-resonances acting there. Our results do not strictly forbid planets to move there, but the existence of a planet on a stable orbit between 0.8 and 1.3 AU is unlikely.
rate research
Read More
The recently discovered planetary system in the binary GamCep was studied concerning its dynamical evolution. We confirm that the orbital parameters found by the observers are in a stable configuration. The primary aim of this study was to find stable planetary orbits in a habitable region in this system, which consists of a double star (a=21.36 AU) and a relatively close (a=2.15 AU) massive (1.7 Mjup sin i) planet. We did straightforward numerical integrations of the equations of motion in different dynamical models and determined the stability regions for a fictitious massless planet in the interval of the semimajor axis 0.5 AU < a < 1.85 AU around the more massive primary. To confirm the results we used the Fast Lyapunov Indicators (FLI) in separate computations, which are a common tool for determining the chaoticity of an orbit. Both results are in good agreement and unveiled a small island of stable motions close to 1 AU up to an inclination of about 15 deg (which corresponds to the 3:1 mean motion resonance between the two planets). Additionally we computed the orbits of earthlike planets (up to 90 earthmasses) in the small stable island and found out, that there exists a small window of stable orbits on the inner edge of the habitable zone in GamCep even for massive planets.
We perform numerical simulations to study the Habitable zones (HZs) and dynamical structure for Earth-mass planets in multiple planetary systems. For example, in the HD 69830 system, we extensively explore the planetary configuration of three Neptune-mass companions with one massive terrestrial planet residing in 0.07 AU $leq a leq$ 1.20 AU, to examine the asteroid structure in this system. We underline that there are stable zones of at least $10^5$ yr for low-mass terrestrial planets locating between 0.3 and 0.5 AU, and 0.8 and 1.2 AU with final eccentricities of $e < 0.20$. Moreover, we also find that the accumulation or depletion of the asteroid belt are also shaped by orbital resonances of the outer planets, for example, the asteroidal gaps at 2:1 and 3:2 mean motion resonances (MMRs) with Planet C, and 5:2 and 1:2 MMRs with Planet D. In a dynamical sense, the proper candidate regions for the existence of the potential terrestrial planets or HZs are 0.35 AU $< a < $ 0.50 AU, and 0.80 AU $< a < $ 1.00 AU for relatively low eccentricities, which makes sense to have the possible asteroidal structure in this system.
The presented work investigates the possible formation of terrestrial planets in the habitable zone (HZ) of the exoplanetary system HD 141399. In this system the HZ is located approximately between the planets c (a = 0.7 au) and d (a = 2.1 au). Extensive numerical integrations of the equations of motion in the pure Newtonian framework of small bodies with different initial conditions in the HZ are performed. Our investigations included several steps starting with 500 massless bodies distributed between planets c and d in order to model the development of the disk of small bodies. It turns out that after some 10^6 years a belt-like structure analogue to the main belt inside Jupiter in our Solar System appears. We then proceed with giving the small bodies masses (Moon-mass) and take into account the gravitational interaction between these planetesimal-like objects. The growing of the objects - with certain percentage of water - due to collisions is computed in order to look for the formation of terrestrial planets. We observe that planets form in regions connected to mean motion resonances (MMR). So far there is no observational evidence of terrestrial planets in the system of HD 141399 but from our results we can conclude that the formation of terrestrial planets - even with an appropriate amount of water necessary for being habitable - in the HZ would have been possible.
We perform numerical simulations to study the secular orbital evolution and dynamical structure in the quintuplet planetary system 55 Cancri with the self-consistent orbital solutions by Fischer and coworkers (2008). In the simulations, we show that this system can be stable at least for $10^{8}$ yr. In addition, we extensively investigate the planetary configuration of four outer companions with one terrestrial planet in the wide region of 0.790 AU $leq a leq $ 5.900 AU to examine the existence of potential asteroid structure and Habitable Zones (HZs). We show that there are unstable regions for the orbits about 4:1, 3:1 and 5:2 mean motion resonances (MMRs) with the outermost planet in the system, and several stable orbits can remain at 3:2 and 1:1 MMRs, which is resemblance to the asteroidal belt in solar system. In a dynamical point, the proper candidate HZs for the existence of more potential terrestrial planets reside in the wide area between 1.0 AU and 2.3 AU for relatively low eccentricities.
We have undertaken a thorough dynamical investigation of five extrasolar planetary systems using extensive numerical experiments. The systems Gl 777 A, HD 72659, Gl 614, 47 Uma and HD 4208 were examined concerning the question of whether they could host terrestrial like planets in their habitable zones (=HZ). First we investigated the mean motion resonances between fictitious terrestrial planets and the existing gas giants in these five extrasolar systems. Then a fine grid of initial conditions for a potential terrestrial planet within the HZ was chosen for each system, from which the stability of orbits was then assessed by direct integrations over a time interval of 1 million years. The computations were carried out using a Lie-series integration method with an adaptive step size control. This integration method achieves machine precision accuracy in a highly efficient and robust way, requiring no special adjustments when the orbits have large eccentricities. The stability of orbits was examined with a determination of the Renyi entropy, estimated from recurrence plots, and with a more straight forward method based on the maximum eccentricity achieved by the planet over the 1 million year integration. Additionally, the eccentricity is an indication of the habitability of a terrestrial planet in the HZ; any value of e>0.2 produces a significant temperature difference on a planets surface between apoapse and periapse. The results for possible stable orbits for terrestrial planets in habitable zones for the five systems are summarized as follows: for Gl 777 A nearly the entire HZ is stable, for 47 Uma, HD 72659 and HD 4208 terrestrial planets can survive for a sufficiently long time, while for Gl 614 our results exclude terrestrial planets moving in stable orbits within the HZ.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
