On the Possibility of Habitable Trojan Planets in Binary Star Systems

Abstract

Abstr actApproximately 60 percent of all stars in the solar neighbourhood (up to 80 percent in our Milky Way) are members of binary or multiple star systems. This fact led to the speculations that many more planets may exist in binary systems than are currently known. To estimate the habitability of exoplanetary systems, we have to define the so-called habitable zone (HZ). The HZ is defined as a region around a star where a planet would receive enough radiation to maintain liquid water on its surface and to be able to build a stable atmosphere. We search for new dynamical configurations -where planets may stay in stable orbits -to increase the probability to find a planet like the Earth. Therefore we investigated five candidates and found that two systems (HD 41004 and HD 196885) which have small stable regions. Intr oductionToday we know about 3000 exoplanets thereof 100 exoplanets are found in binary star systems and approximately 20 exoplanets in multiple (triple) star systems. The data and statistics of all planets are collected in the Exoplanet-catalogue maintained by J. Schneider 1 at (see Schneider et al. 2011) whereas the binary-and multiple-star systems can be found at binary catalogue of exoplanets maintained by R. Schwarz 2 1 (see Schwarz et al. 2016).http://exoplanet.eu 2 http://www.univie.ac.at/adg/schwarz/multiple.html When we speak about the possibility of habitable Trojan planets in binary star systems we have to answer two questions:• Why do we sear ch for exoplanets in binar ies? Because many stars in the solar Neighbourhood are members of binary or multiple star systems. This fact leads to the conclusion that the knowledge of the dynamics of exoplanets in binary systems will be important in the future.• Why do we sear ch for Tr ojan planets? Because we are searching for new dynamical configurations where planets may stay in stable orbits. The more planets we will find the higher the possibility will be, to find a planet like the EARTH! Fig. 1 Dependence of the secondary star mass m2 on the mass ratio μ and the mass of the primary star m1 (main sequence stars between 0.5 < Msun < 3).Jupiter's Trojan asteroids are in a 1:1 mean motion resonance with Jupiter, librating around the L 4 or L 5 points of the Sun-Jupiter system, preceding (L 4 ) or following (L 5 ) Jupiter at about 60°. Today we know approximately 5100 Jovian, 8 Neptunian and 5 Martian Trojans, but also one Uranus Trojan (2011QF99) and one Earth Trojan (2010TK7) were found.It is known that in the planar, circular restricted three-body problem the equilibrium points L 4 or L 5 are stable for mass ratios up to μ = 0.04; this stability limit is marked in Fig.1 as dashed vertical line. The mass ratio μ is defined as μ = m 2 / (m 1 + m 2 ) at which m 1 and m 2 being the masses of the primary and secondary bodies. So it seems that binaries may not have a population of Trojan asteroids or a Trojan planet, because the masses of the stars involved are comparable. However in a former study (Schwarz et al. 2009) we could show that binaries can ...

Celestial mechanics and polarization optics of the Kordylewski dust cloud in the Earth–Moon Lagrange point L5 – I. Three-dimensional celestial mechanical modelling of dust cloud formation

“…Astronomers found a large number of minor celestial bodies around these points of the planets of our Solar System and the Sun. The most well-known are the Greek and Trojan minor planets around the L4 and L5 points of the Sun-Jupiter system (Schwarz et al 2015, Schwarz & Dvorak 2012. Minor planets have also been found around the triangular Lagrange points of the Sun-Earth (John et al 2015), Sun-Mars (Christou 2017) and Sun-Neptune systems (Sheppard &Trujillo 2006).…”

The structure of the co-orbital stable regions as a function of the mass ratio

“…However, previous works have shown that it is possible to exist stability in the co-orbital region of systems with much greater mass ratio values than those we have studied, such as trojan planets in binary star systems (e.g. Schwarz et al 2015).…”

“…As these bodies were being discovered, many important works were made to study the co-orbital systems. There are studies on the dynamics in a restricted three-body problem (Danby 1964;Dermott & Murray 1981a;Lohinger & Dvorak 1993;Mittal et al 2020), on the stable regions around Lagrangian points (Deprit & Deprit-Bartholomé 1967;Marchal 1991;Érdi & Sándor 2005;Érdi et al 2007;Zhou et al 2009;Ćuk et al 2012), studies on the co-orbital regions of Solar System's planets (Mikkola & Innanen 1992;Nesvornỳ & Dones 2002;Scholl et al 2005;Tabachnik & Evans 2000), dynamics of some known co-orbital satellites (Dermott & Murray 1981b;Yoder et al 1983;Treffenstädt et al 2015), on stability and formation of the Solar System's trojans (Izidoro et al 2010;Donnison & Williams 1985;Chanut et al 2008;Mourão et al 2006;Pitjeva & Pitjev 2019;Zhou et al 2011Zhou et al , 2019Zhou et al , 2020Dvorak, R. et al 2012;Mikkola & Innanen 1990;Lykawka et al 2009Lykawka et al , 2011Marzari & Scholl 2013), and even hypothetical coorbital exoplanets (Schwarz et al 2009(Schwarz et al , 2012(Schwarz et al , 2015Beaugé et al 2007;.…”

Investigating Exoplanet Orbital Evolution Around Binary Star Systems with Mass Loss

“…Supported by observations, many exoplanets are orbiting binary star systems, with nearly 70 exoplanets found in binary stellar systems (Schwarz et al 2015). This work studied the effects of stellar mass loss from one star in the inner binary system on its companion planetary orbit.…”