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Register a new userDetectability of quasi-circular co-orbital planets. Application to the radial velocity technique
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Several celestial bodies in co-orbital configurations exist in the solar system. However, co-orbital exoplanets have not yet been discovered. This lack may result from a degeneracy between the signal induced by co-orbital planets and other orbital configurations. Here we determine a criterion for the detectability of quasi-circular co-orbital planets and develop a demodulation method to bring out their signature from the observational data. We show that the precision required to identify a pair of co-orbital planets depends only on the libration amplitude and on the planets mass ratio. We apply our method to synthetic radial velocity data, and show that for tadpole orbits we are able to determine the inclination of the system to the line of sight. Our method is also valid for planets detected through the transit and astrometry techniques.
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Co-orbital planets have not yet been discovered, although they constitute a frequent by-product of planetary formation and evolution models. This lack may be due to observational biases, since the main detection methods are unable to spot co-orbital companions when they are small or near the Lagrangian equilibrium points. However, for a system with one known transiting planet (with mass $m_1$), we can detect a co-orbital companion (with mass $m_2$) by combining the time of mid-transit with the radial-velocity data of the star. Here, we propose a simple method that allows the detection of co-orbital companions, valid for eccentric orbits, that relies on a single parameter $alpha$, which is proportional to the mass ratio $m_2/m_1$. Therefore, when $alpha$ is statistically different from zero, we have a strong candidate to harbour a co-orbital companion. We also discuss the relevance of false positives generated by different planetary configurations.
The detection of Earth-like planets, exocomets or Kuiper belts show that the different components found in the solar system should also be present in other planetary systems. Trojans are one of these components and can be considered fossils of the first stages in the life of planetary systems. Their detection in extrasolar systems would open a new scientific window to investigate formation and migration processes. In this context, the main goal of the TROY project is to detect exotrojans for the first time and to measure their occurrence rate (eta-Trojan). In this first paper, we describe the goals and methodology of the project. Additionally, we used archival radial velocity data of 46 planetary systems to place upper limits on the mass of possible trojans and investigate the presence of co-orbital planets down to several tens of Earth masses. We used archival radial velocity data of 46 close-in (P<5 days) transiting planets (without detected companions) with information from high-precision radial velocity instruments. We took advantage of the time of mid-transit and secondary eclipses (when available) to constrain the possible presence of additional objects co-orbiting the star along with the planet. This, together with a good phase coverage, breaks the degeneracy between a trojan planet signature and signals coming from additional planets or underestimated eccentricity. We identify nine systems for which the archival data provide 1-sigma evidence for a mass imbalance between L4 and L5. Two of these systems provide 2-sigma detection, but no significant detection is found among our sample. We also report upper limits to the masses at L4/L5 in all studied systems and discuss the results in the context of previous findings.
We present observations with the planet finder SPHERE of a selected sample of the most promising radial velocity (RV) companions for high-contrast imaging. Using a Monte Carlo simulation to explore all the possible inclinations of the orbit of wide RV companions, we identified the systems with companions that could potentially be detected with SPHERE. We found the most favorable RV systems to observe are : HD,142, GJ,676, HD,39091, HIP,70849, and HD,30177 and carried out observations of these systems during SPHERE Guaranteed Time Observing (GTO). To reduce the intensity of the starlight and reveal faint companions, we used Principle Component Analysis (PCA) algorithms alongside angular and spectral differential imaging. We injected synthetic planets with known flux to evaluate the self-subtraction caused by our data reduction and to determine the 5$sigma$ contrast in the J band $vs$ separation for our reduced images. We estimated the upper limit on detectable companion mass around the selected stars from the contrast plot obtained from our data reduction. Although our observations enabled contrasts larger than 15 mag at a few tenths of arcsec from the host stars, we detected no planets. However, we were able to set upper mass limits around the stars using AMES-COND evolutionary models. We can exclude the presence of companions more massive than 25-28 MJup around these stars, confirming the substellar nature of these RV companions.
A number of giant planet pairs discovered by the radial velocity method with period ratios $lesssim 2$ may reside in mean motion resonances. Convergent orbital migration and resonant capture at the time of formation would naturally explain the present-day resonant orbital configurations of these systems. Planets that experience smooth migration and eccentricity damping forces due to a proto-planetary disk should not only capture into mean motion resonances but also end up in a specific dynamical configuration within the resonance, sometimes referred to as apsidal corotation resonance (ACR). Here we develop a method for testing the hypothesis that a planet pair resides in an ACR by directly fitting radial velocity data. The ACR hypothesis strongly restricts the number of free parameters describing the radial velocity signal and we compare fits using this highly restricted model to fits using a more conventional two-planet RV model by using nested sampling simulations. We apply our method to HD 45364 and HD 33844, two systems hosting giant planet pairs in 3:2 and 5:3 resonances, respectively. We demonstrate that the observations of both systems support an ACR configuration and we use the results of our ACR model fits to constrain possible migration histories of these systems.
We study the stability regions and families of periodic orbits of two planets locked in a co-orbital configuration. We consider different ratios of planetary masses and orbital eccentricities, also we assume that both planets share the same orbital plane. Initially we perform numerical simulations over a grid of osculating initial conditions to map the regions of stable/chaotic motion and identify equilibrium solutions. These results are later analyzed in more detail using a semi-analytical model. Apart from the well known quasi-satellite (QS) orbits and the classical equilibrium Lagrangian points L4 and L5, we also find a new regime of asymmetric periodic solutions. For low eccentricities these are located at $(sigma,Deltaomega) = (pm 60deg, mp 120deg)$, where sigma is the difference in mean longitudes and Deltaomega is the difference in longitudes of pericenter. The position of these Anti-Lagrangian solutions changes with the mass ratio and the orbital eccentricities, and are found for eccentricities as high as ~ 0.7. Finally, we also applied a slow mass variation to one of the planets, and analyzed its effect on an initially asymmetric periodic orbit. We found that the resonant solution is preserved as long as the mass variation is adiabatic, with practically no change in the equilibrium values of the angles.
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