Richard Schwarz | University of Vienna (original) (raw)

Papers by Richard Schwarz

The dynamical stability of extrasolar planets in the habitable zones (HZs) of compact planetary s... more The dynamical stability of extrasolar planets in the habitable zones (HZs) of compact planetary systems around M stars, e.g. Proxima Centauri, has been investigated by performing extensive numerical simulations. The estimated HZs for these systems range between 0.190 0.483 AU for M0 stars and 0.014 0.039 AU for M9 stars, respectively. Within these regions, we placed fictitious Earth-sized planets according to Hill’s criteria so that the innermost planet is located at the inner limit of the HZ and all other fictitious planets are lined up to the outer limit of the HZ. The main goal of our investigation is to determine the maximum number of possible terrestrial planets within the HZ. Numerical simulations with different initial conditions and integration times up to 10 years showed that long-time stable motion is possible for up to 4 Earth-sized bodies in the Proxima Centauri system. In addition, we present several investigations around M star systems and we show the differences in th...

Planetary and Space Science, 2009

Approximately 60 percent of all stars in the solar neighbourhood (up to 80 percent in our Milky W... more Approximately 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.

This paper is devoted to study the circumstances favourable to detect circumstellar and circumbin... more This paper is devoted to study the circumstances favourable to detect circumstellar and circumbinary planets in well detached binary-star-systems using eclipse timing variations (ETVs). We investigated the dynamics of well detached binary star systems with a star separation from 0.5 to 3~AU, to determine the probability of the detection of such variations with ground based telescopes and space telescopes (like former missions CoRoT and Kepler and future space missions Plato, Tess and Cheops). For the chosen star separations both dynamical configurations (circumstellar and circumbinary) may be observable. We performed numerical simulations by using the full three-body problem as dynamical model. The dynamical stability and the ETVs are investigated by computing ETV maps for different masses of the secondary star and the exoplanet (Earth, Neptune and Jupiter size). In addition we changed the planet's and binary's eccentricities. We conclude that many amplitudes of ETVs are lar...

This paper is devoted to study the circumstances favourable to detect Trojan planets in close bin... more This paper is devoted to study the circumstances favourable to detect Trojan planets in close binary-star-systems by the help of eclipse timing variations (ETVs). To determine the probability of the detection of such variations with ground based telescopes and space telescopes (like former missions CoRoT and Kepler and future space missions like Plato, Tess and Cheops), we investigated the dynamics of binary star systems with a planet in tadpole motion. We did numerical simulations by using the full three-body problem as dynamical model. The stability and the ETVs are investigated by computing stability/ETV maps for different masses of the secondary star and the Trojan planet. In addition we changed the eccentricity of the possible Trojan planet. By the help of the libration amplitude σ we could show whether or not all stable objects are moving in tadpole orbits. We can conclude that many amplitudes of ETVs are large enough to detect Earth-like Trojan planets in binary star systems....

In close eclipsing binaries, measurements of the variations in binary's eclipse timing may be... more In close eclipsing binaries, measurements of the variations in binary's eclipse timing may be used to infer information about the existence of circumbinary objects. To determine the possibility of the detection of such variations with CoRoT and Kepler space telescopes, we have carried out an extensive study of the dynamics of a binary star system with a circumbinary planet, and calculated its eclipse timing variations (ETV) for different values of the mass-ratio and orbital elements of the binary and the perturbing body. Here, we present the results of our study and assess the detectability of the planet by comparing the resulting values of ETVs with the temporal sensitivity of CoRoT and Kepler. Results point to extended regions in the parameter-space where the perturbation of a planet may become large enough to create measurable variations in the eclipse timing of the secondary star. Many of these variations point to potentially detectable ETVs and the possible existence of Jov...

Here we compute for a two-body system (two spherical bodies) the dependency of the annual insolat... more Here we compute for a two-body system (two spherical bodies) the dependency of the annual insolation on the ellipticity of the orbit of the celestial planetary body. This will be the basis for a simple Python progam which demonstrates the insolation as function of orbital ellipticity. This text might also be introductory for undergraduate students. This study is mostly based on the work of A.Berger [2a]

Monthly Notices of the Royal Astronomical Society

The scenario and efficiency of water transport by icy asteroids and comets are still amongst the ... more The scenario and efficiency of water transport by icy asteroids and comets are still amongst the most important unresolved questions of planetary systems. A better understanding of cometary dynamics in extrasolar systems shall provide information about cometary reservoirs and give an insight into water transport especially to planets in the habitable zone. The detection of Proxima Centauri b (PCb), which moves in the habitable zone of this system, triggered a debate whether or not this planet can be habitable. In this work, we focus on the stability of an additional planet in the system and on water transport by minor bodies. We perform numerous N-body simulations with PCb and an outer Oort cloud-like reservoir of comets. We investigate close encounters and collisions with the planet, which are important for the transport of water. Observers found hints for a second planet with a period longer than 60 d. Our dynamical studies show that two planets in this system are stable even for a more massive second planet (∼12 Earth masses). Furthermore, we perform simulations including exocomets, a second planet, and the influence of the binary Alpha Centauri. The studies on the dynamics of exocomets reveal that the outer limit for water transport is around 200 au. In addition, we show that water transport would be possible from a close-in planetesimal cloud (1-4 au). From our simulations, based on typical M-star protoplanetary discs, we estimate the water mass delivered to the planets to be between the extremes 0 and 51 Earth oceans.

Astronomy and Astrophysics, 2007

Monthly Notices of the Royal Astronomical Society, 2015

This paper is devoted to study the circumstances favourable to detect Trojan planets in close bin... more This paper is devoted to study the circumstances favourable to detect Trojan planets in close binary-star-systems by the help of eclipse timing variations (ETVs). To determine the probability of the detection of such variations with ground based telescopes and space telescopes (like former missions CoRoT and Kepler and future space missions like Plato, Tess and Cheops), we investigated the dynamics of binary star systems with a planet in tadpole motion. We did numerical simulations by using the full threebody problem as dynamical model. The stability and the ETVs are investigated by computing stability/ETV maps for different masses of the secondary star and the Trojan planet. In addition we changed the eccentricity of the possible Trojan planet. By the help of the libration amplitude σ we could show whether or not all stable objects are moving in tadpole orbits. We can conclude that many amplitudes of ETVs are large enough to detect Earth-like Trojan planets in binary star systems. As an application, we prepared a list of possible candidates.

We investigate the dynamical stability of planetary systems in the CoRoT discovery space. The aim... more We investigate the dynamical stability of planetary systems in the CoRoT discovery space. The aim was to check whether they are stable within the habitable zone around M main-sequence stars. We place the first fictitious planet at a distance of 0.01 AU from its host-star and fill-up the CoRoT discovery space with planets so that they are tightly packed according to the Hill criterion supplying the initial minimum relative distances between the fictitious planets. The habitable zone of M-stars covers the region between 0.02 - 0.5 AU which is partly inside the CoRoT discovery space. Additionally we include a gas giant which perturbs the close-in planets, and compare the different results.

From the nearly 190 planets that have been discovered so far we can distinguish the following typ... more From the nearly 190 planets that have been discovered so far we can distinguish the following types of HZs from the dynamicals point of view: 1) The solar-system type (SST) - where the HZ is between the host-star and the detected giant planet. 2) The hot-Jupiter type (HJT) for a close-in giant planet, the HZ is outside its orbit. 3) The giant planet type (GPT) - when the detected planet moves in the HZ. In this case we can only expect "habitable moons" or "habitable trojan-like planets". 4) Furthermore in multi-planet systems there will be combinations of these 3 types. But even if a planet will be detected in the HZ, it has to be verified if it can be considered as habitable planet. An important contribution from the dynamical point of view is to examine the long-term dynamical behavior of the orbital motion in this region, which obviously depends on the motion of the giant planets in the systems. Motivated by the fact, that in some of the discovered multi-plane...

Monthly Notices of the Royal Astronomical Society, 2014

This paper is devoted to the study of secondary resonances and the stability of the Lagrangian po... more This paper is devoted to the study of secondary resonances and the stability of the Lagrangian point L 4 in the spatial restricted three-body problem for moderate mass ratios µ, meaning that µ 0.0045. However, we concentrated our investigations on small mass ratios µ 0.001, which represent the mass ratios for stable configurations of tadpole orbits in the Solar system. The stability is investigated by numerical methods, computing stability maps in different parameter planes. We started investigating the mass of the secondary; from Earth-mass bodies up to Jupiter-mass bodies. In addition we changed the orbital elements (eccentricity and inclination) of the secondary and Trojan body. For this parameter space we found high order secondary resonances, which are present for various inclinations. To determine secondary resonances we used Rabe's equation and the frequency analysis. In addition we investigated the stability in and around these secondary resonances.

Origins of Life and Evolution of Biospheres, 2015

Approximately 60 percent of all stars in the solar neighbourhood (up to 80 percent in our Milky W... more Approximately 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 oduction Today 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).

Proceedings of the International Astronomical Union, 2011

Up to now, more than 500 extra-solar planets have been discovered. Many of these extrasolar syste... more Up to now, more than 500 extra-solar planets have been discovered. Many of these extrasolar systems consist of one star and only one giant planet. However, recently more and more different types of systems have become known, including also extrasolar planets in binaries. In our study, we will concentrate on such systems, since a large percentage of all G-M stars are expected to be part of binary or multiple stellar systems. Therefore, these kinds of systems are worthy of investigation in detail. In particular, we will concentrate on planets in P-Type motion, where the planet orbits around both stars. During the last few years, four such systems (NN Ser, HW Vir, HU Aqr and DP Leo) have been discovered. In our study, we performed dynamical studies for three multi-planetary systems in binaries (NN Ser, HW Vir, HU Aqr), and compared simulated eclipse timing variations (ETV) to current observational data.

Proceedings of the International Astronomical Union, 2011

In close eclipsing binaries, measurements of the variations in the binary's eclipse timing ma... more In close eclipsing binaries, measurements of the variations in the binary's eclipse timing may be used to infer information about the existence of planets in P-Type motion. To study the possibility of detecting such planets with CoRoT and Kepler, we calculated eclipse timing variations (ETV) for different values of the mass and orbital elements of the perturbing planet. These investigations are a continuation of the work of Schwarz et al. (2011).

Proceedings of the International Astronomical Union, 2007

In this article we examine the motion of fictitious Trojan planets close to the equilateral Lagra... more In this article we examine the motion of fictitious Trojan planets close to the equilateral Lagrangean equilibrium points in extrasolar planetary systems. Whether there exist stable motion in this area or not depends on the massratio of the primariy bodies in the restricted three body problem, namely the host star and the gasgiant. Taking into account also the eccentricity of the primaries we show via results of extensive numerical integrations that Trojan planets may survive only fore< 0.25. We also show first results of a mapping in the 1:1 resonance with a gas giant on an eccentric orbit which is applied to the extrasolar planetary systems HD 17051. We furthermore study the influence of an additional outer planet which perturbs the motion of the gasgiant as well as the Trojan cloud around itsL4Lagrangean point.

The dynamical stability of extrasolar planets in the habitable zones (HZs) of compact planetary s... more The dynamical stability of extrasolar planets in the habitable zones (HZs) of compact planetary systems around M stars, e.g. Proxima Centauri, has been investigated by performing extensive numerical simulations. The estimated HZs for these systems range between 0.190 0.483 AU for M0 stars and 0.014 0.039 AU for M9 stars, respectively. Within these regions, we placed fictitious Earth-sized planets according to Hill’s criteria so that the innermost planet is located at the inner limit of the HZ and all other fictitious planets are lined up to the outer limit of the HZ. The main goal of our investigation is to determine the maximum number of possible terrestrial planets within the HZ. Numerical simulations with different initial conditions and integration times up to 10 years showed that long-time stable motion is possible for up to 4 Earth-sized bodies in the Proxima Centauri system. In addition, we present several investigations around M star systems and we show the differences in th...

Planetary and Space Science, 2009

Approximately 60 percent of all stars in the solar neighbourhood (up to 80 percent in our Milky W... more Approximately 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.

This paper is devoted to study the circumstances favourable to detect circumstellar and circumbin... more This paper is devoted to study the circumstances favourable to detect circumstellar and circumbinary planets in well detached binary-star-systems using eclipse timing variations (ETVs). We investigated the dynamics of well detached binary star systems with a star separation from 0.5 to 3~AU, to determine the probability of the detection of such variations with ground based telescopes and space telescopes (like former missions CoRoT and Kepler and future space missions Plato, Tess and Cheops). For the chosen star separations both dynamical configurations (circumstellar and circumbinary) may be observable. We performed numerical simulations by using the full three-body problem as dynamical model. The dynamical stability and the ETVs are investigated by computing ETV maps for different masses of the secondary star and the exoplanet (Earth, Neptune and Jupiter size). In addition we changed the planet's and binary's eccentricities. We conclude that many amplitudes of ETVs are lar...

This paper is devoted to study the circumstances favourable to detect Trojan planets in close bin... more This paper is devoted to study the circumstances favourable to detect Trojan planets in close binary-star-systems by the help of eclipse timing variations (ETVs). To determine the probability of the detection of such variations with ground based telescopes and space telescopes (like former missions CoRoT and Kepler and future space missions like Plato, Tess and Cheops), we investigated the dynamics of binary star systems with a planet in tadpole motion. We did numerical simulations by using the full three-body problem as dynamical model. The stability and the ETVs are investigated by computing stability/ETV maps for different masses of the secondary star and the Trojan planet. In addition we changed the eccentricity of the possible Trojan planet. By the help of the libration amplitude σ we could show whether or not all stable objects are moving in tadpole orbits. We can conclude that many amplitudes of ETVs are large enough to detect Earth-like Trojan planets in binary star systems....

In close eclipsing binaries, measurements of the variations in binary's eclipse timing may be... more In close eclipsing binaries, measurements of the variations in binary's eclipse timing may be used to infer information about the existence of circumbinary objects. To determine the possibility of the detection of such variations with CoRoT and Kepler space telescopes, we have carried out an extensive study of the dynamics of a binary star system with a circumbinary planet, and calculated its eclipse timing variations (ETV) for different values of the mass-ratio and orbital elements of the binary and the perturbing body. Here, we present the results of our study and assess the detectability of the planet by comparing the resulting values of ETVs with the temporal sensitivity of CoRoT and Kepler. Results point to extended regions in the parameter-space where the perturbation of a planet may become large enough to create measurable variations in the eclipse timing of the secondary star. Many of these variations point to potentially detectable ETVs and the possible existence of Jov...

Here we compute for a two-body system (two spherical bodies) the dependency of the annual insolat... more Here we compute for a two-body system (two spherical bodies) the dependency of the annual insolation on the ellipticity of the orbit of the celestial planetary body. This will be the basis for a simple Python progam which demonstrates the insolation as function of orbital ellipticity. This text might also be introductory for undergraduate students. This study is mostly based on the work of A.Berger [2a]

Monthly Notices of the Royal Astronomical Society

The scenario and efficiency of water transport by icy asteroids and comets are still amongst the ... more The scenario and efficiency of water transport by icy asteroids and comets are still amongst the most important unresolved questions of planetary systems. A better understanding of cometary dynamics in extrasolar systems shall provide information about cometary reservoirs and give an insight into water transport especially to planets in the habitable zone. The detection of Proxima Centauri b (PCb), which moves in the habitable zone of this system, triggered a debate whether or not this planet can be habitable. In this work, we focus on the stability of an additional planet in the system and on water transport by minor bodies. We perform numerous N-body simulations with PCb and an outer Oort cloud-like reservoir of comets. We investigate close encounters and collisions with the planet, which are important for the transport of water. Observers found hints for a second planet with a period longer than 60 d. Our dynamical studies show that two planets in this system are stable even for a more massive second planet (∼12 Earth masses). Furthermore, we perform simulations including exocomets, a second planet, and the influence of the binary Alpha Centauri. The studies on the dynamics of exocomets reveal that the outer limit for water transport is around 200 au. In addition, we show that water transport would be possible from a close-in planetesimal cloud (1-4 au). From our simulations, based on typical M-star protoplanetary discs, we estimate the water mass delivered to the planets to be between the extremes 0 and 51 Earth oceans.

Astronomy and Astrophysics, 2007

Monthly Notices of the Royal Astronomical Society, 2015

This paper is devoted to study the circumstances favourable to detect Trojan planets in close bin... more This paper is devoted to study the circumstances favourable to detect Trojan planets in close binary-star-systems by the help of eclipse timing variations (ETVs). To determine the probability of the detection of such variations with ground based telescopes and space telescopes (like former missions CoRoT and Kepler and future space missions like Plato, Tess and Cheops), we investigated the dynamics of binary star systems with a planet in tadpole motion. We did numerical simulations by using the full threebody problem as dynamical model. The stability and the ETVs are investigated by computing stability/ETV maps for different masses of the secondary star and the Trojan planet. In addition we changed the eccentricity of the possible Trojan planet. By the help of the libration amplitude σ we could show whether or not all stable objects are moving in tadpole orbits. We can conclude that many amplitudes of ETVs are large enough to detect Earth-like Trojan planets in binary star systems. As an application, we prepared a list of possible candidates.

We investigate the dynamical stability of planetary systems in the CoRoT discovery space. The aim... more We investigate the dynamical stability of planetary systems in the CoRoT discovery space. The aim was to check whether they are stable within the habitable zone around M main-sequence stars. We place the first fictitious planet at a distance of 0.01 AU from its host-star and fill-up the CoRoT discovery space with planets so that they are tightly packed according to the Hill criterion supplying the initial minimum relative distances between the fictitious planets. The habitable zone of M-stars covers the region between 0.02 - 0.5 AU which is partly inside the CoRoT discovery space. Additionally we include a gas giant which perturbs the close-in planets, and compare the different results.

From the nearly 190 planets that have been discovered so far we can distinguish the following typ... more From the nearly 190 planets that have been discovered so far we can distinguish the following types of HZs from the dynamicals point of view: 1) The solar-system type (SST) - where the HZ is between the host-star and the detected giant planet. 2) The hot-Jupiter type (HJT) for a close-in giant planet, the HZ is outside its orbit. 3) The giant planet type (GPT) - when the detected planet moves in the HZ. In this case we can only expect "habitable moons" or "habitable trojan-like planets". 4) Furthermore in multi-planet systems there will be combinations of these 3 types. But even if a planet will be detected in the HZ, it has to be verified if it can be considered as habitable planet. An important contribution from the dynamical point of view is to examine the long-term dynamical behavior of the orbital motion in this region, which obviously depends on the motion of the giant planets in the systems. Motivated by the fact, that in some of the discovered multi-plane...

Monthly Notices of the Royal Astronomical Society, 2014

This paper is devoted to the study of secondary resonances and the stability of the Lagrangian po... more This paper is devoted to the study of secondary resonances and the stability of the Lagrangian point L 4 in the spatial restricted three-body problem for moderate mass ratios µ, meaning that µ 0.0045. However, we concentrated our investigations on small mass ratios µ 0.001, which represent the mass ratios for stable configurations of tadpole orbits in the Solar system. The stability is investigated by numerical methods, computing stability maps in different parameter planes. We started investigating the mass of the secondary; from Earth-mass bodies up to Jupiter-mass bodies. In addition we changed the orbital elements (eccentricity and inclination) of the secondary and Trojan body. For this parameter space we found high order secondary resonances, which are present for various inclinations. To determine secondary resonances we used Rabe's equation and the frequency analysis. In addition we investigated the stability in and around these secondary resonances.

Origins of Life and Evolution of Biospheres, 2015

Approximately 60 percent of all stars in the solar neighbourhood (up to 80 percent in our Milky W... more Approximately 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 oduction Today 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).

Proceedings of the International Astronomical Union, 2011

Up to now, more than 500 extra-solar planets have been discovered. Many of these extrasolar syste... more Up to now, more than 500 extra-solar planets have been discovered. Many of these extrasolar systems consist of one star and only one giant planet. However, recently more and more different types of systems have become known, including also extrasolar planets in binaries. In our study, we will concentrate on such systems, since a large percentage of all G-M stars are expected to be part of binary or multiple stellar systems. Therefore, these kinds of systems are worthy of investigation in detail. In particular, we will concentrate on planets in P-Type motion, where the planet orbits around both stars. During the last few years, four such systems (NN Ser, HW Vir, HU Aqr and DP Leo) have been discovered. In our study, we performed dynamical studies for three multi-planetary systems in binaries (NN Ser, HW Vir, HU Aqr), and compared simulated eclipse timing variations (ETV) to current observational data.

Proceedings of the International Astronomical Union, 2011

In close eclipsing binaries, measurements of the variations in the binary's eclipse timing ma... more In close eclipsing binaries, measurements of the variations in the binary's eclipse timing may be used to infer information about the existence of planets in P-Type motion. To study the possibility of detecting such planets with CoRoT and Kepler, we calculated eclipse timing variations (ETV) for different values of the mass and orbital elements of the perturbing planet. These investigations are a continuation of the work of Schwarz et al. (2011).

Proceedings of the International Astronomical Union, 2007

In this article we examine the motion of fictitious Trojan planets close to the equilateral Lagra... more In this article we examine the motion of fictitious Trojan planets close to the equilateral Lagrangean equilibrium points in extrasolar planetary systems. Whether there exist stable motion in this area or not depends on the massratio of the primariy bodies in the restricted three body problem, namely the host star and the gasgiant. Taking into account also the eccentricity of the primaries we show via results of extensive numerical integrations that Trojan planets may survive only fore< 0.25. We also show first results of a mapping in the 1:1 resonance with a gas giant on an eccentric orbit which is applied to the extrasolar planetary systems HD 17051. We furthermore study the influence of an additional outer planet which perturbs the motion of the gasgiant as well as the Trojan cloud around itsL4Lagrangean point.