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Bayesian re-analysis of the radial velocities of Gliese 581. Evidence in favour of only four planetary companions  [PDF]
Mikko Tuomi
Physics , 2011, DOI: 10.1051/0004-6361/201015995
Abstract: The Gliese 581 planetary system has received attention because it has been proposed to host a low-mass planet in its habitable zone. We re-analyse the radial velocity measurements reported to contain six planetary signals to see whether these conclusions remain valid when the analyses are made using Bayesian tools instead of the common periodogram analyses. We analyse the combined radial velocity data set obtained using the HARPS and HIRES spectrographs using posterior sampling techniques and computation of the posterior probabilities of models with differing numbers of Keplerian signals. We do not fix the orbital eccentricities and stellar jitter to certain values but treat these as free parameters of our statistical models. Hence, we can take the uncertainties of these parameters into account when assessing the number of planetary signals present in the data, the point estimates of all of the model parameters, and the uncertainties of these parameters. We conclude that based on the Bayesian model probabilities and the nature of the posterior densities of the different models, there is evidence in favour of four planets orbiting GJ 581. The HARPS and HIRES data do not imply the conclusion that there are two additional companions orbiting GJ 581. We also revise the orbital parameters of the four companions in the system. Especially, according to our results, the eccentricities of all the companions in the system are consistent with zero.
Application of Bayesian model inadequacy criterion for multiple data sets to radial velocity models of exoplanet systems  [PDF]
Mikko Tuomi,David Pinfield,Hugh R. A. Jones
Physics , 2011, DOI: 10.1051/0004-6361/201117278
Abstract: We present a simple mathematical criterion for determining whether a given statistical model does not describe several independent sets of measurements, or data modes, adequately. We derive this criterion for two data sets and generalise it to several sets by using the Bayesian updating of the posterior probability density. To demonstrate the usage of the criterion, we apply it to observations of exoplanet host stars by re-analysing the radial velocities of HD 217107, Gliese 581, and \u{psion} Andromedae and show that the currently used models are not necessarily adequate in describing the properties of these measurements. We show that while the two data sets of Gliese 581 can be modelled reasonably well, the noise model of HD 217107 needs to be revised. We also reveal some biases in the radial velocities of \u{psion} Andromedae and report updated orbital parameters for the recently proposed 4-planet model. Because of the generality of our criterion, no assumptions are needed on the nature of the measurements, models, or model parameters. The method we propose can be applied to any astronomical problems, as well as outside the field of astronomy, because it is a simple consequence of the Bayes' rule of conditional probabilities.
Gliese 581d is the first discovered terrestrial-mass exoplanet in the habitable zone  [PDF]
Robin Wordsworth,Fran?ois Forget,Franck Selsis,Ehouarn Millour,Benjamin Charnay,Jean-Baptiste Madeleine
Physics , 2011, DOI: 10.1088/2041-8205/733/2/L48
Abstract: It has been suggested that the recently discovered exoplanet GJ581d might be able to support liquid water due to its relatively low mass and orbital distance. However, GJ581d receives 35% less stellar energy than Mars and is probably locked in tidal resonance, with extremely low insolation at the poles and possibly a permanent night side. Under such conditions, it is unknown whether any habitable climate on the planet would be able to withstand global glaciation and / or atmospheric collapse. Here we present three-dimensional climate simulations that demonstrate GJ581d will have a stable atmosphere and surface liquid water for a wide range of plausible cases, making it the first confirmed super-Earth (exoplanet of 2-10 Earth masses) in the habitable zone. We find that atmospheres with over 10 bar CO2 and varying amounts of background gas (e.g., N2) yield global mean temperatures above 0 degrees Celsius for both land and ocean-covered surfaces. Based on the emitted IR radiation calculated by the model, we propose observational tests that will allow these cases to be distinguished from other possible scenarios in the future.
Additional Keplerian Signals in the HARPS data for Gliese 667C from a Bayesian Re-analysis  [PDF]
Philip C. Gregory
Physics , 2012,
Abstract: A re-analysis of Gliese 667C HARPS precision radial velocity data was carried out with a Bayesian multi-planet Kepler periodogram (from 0 to 7 planets) based on a fusion Markov chain Monte Carlo algorithm. The most probable number of signals detected is 6 with a Bayesian false alarm probability of 0.012. The residuals are shown to be consistent with white noise. The 6 signals detected include two previously reported with periods of 7.198 (b) and 28.14 (c) days, plus additional periods of 30.82 (d), 38.82 (e), 53.22, and 91.3 (f) days. The 53 day signal is probably the second harmonic of the stellar rotation period and is likely the result of surface activity. The existence of the additonal Keplerian signals suggest the possibilty of further planets, two of which (d and e) could join Gl 667Cc in the central region of the habitable zone. N-body simulations are required to determine which of these signals are consistent with a stable planetary system. $M \sin i$ values corresponding to signals b, c, d, e, and f are $\sim$ 5.4, 4.8, 3.1, 2.4, and 5.4 M$_{\earth}$, respectively.
The Lick-Carnegie Exoplanet Survey: A 3.1 M_Earth Planet in the Habitable Zone of the Nearby M3V Star Gliese 581  [PDF]
Steven S. Vogt,R. Paul Butler,Eugenio J. Rivera,Nader Haghighipour,Gregory W. Henry,Michael H. Williamson
Physics , 2010, DOI: 10.1088/0004-637X/723/1/954
Abstract: We present 11 years of HIRES precision radial velocities (RV) of the nearby M3V star Gliese 581, combining our data set of 122 precision RVs with an existing published 4.3-year set of 119 HARPS precision RVs. The velocity set now indicates 6 companions in Keplerian motion around this star. Differential photometry indicates a likely stellar rotation period of ~94 days and reveals no significant periodic variability at any of the Keplerian periods, supporting planetary orbital motion as the cause of all the radial velocity variations. The combined data set strongly confirms the 5.37-day, 12.9-day, 3.15-day, and 67-day planets previously announced by Bonfils et al. (2005), Udry et al. (2007), and Mayor et al (2009). The observations also indicate a 5th planet in the system, GJ 581f, a minimum-mass 7.0 M_Earth planet orbiting in a 0.758 AU orbit of period 433 days and a 6th planet, GJ 581g, a minimum-mass 3.1 M_Earth planet orbiting at 0.146 AU with a period of 36.6 days. The estimated equilibrium temperature of GJ 581g is 228 K, placing it squarely in the middle of the habitable zone of the star and offering a very compelling case for a potentially habitable planet around a very nearby star. That a system harboring a potentially habitable planet has been found this nearby, and this soon in the relatively early history of precision RV surveys, indicates that eta_Earth, the fraction of stars with potentially habitable planets, is likely to be substantial. This detection, coupled with statistics of the incompleteness of present-day precision RV surveys for volume-limited samples of stars in the immediate solar neighborhood suggests that eta_Earth could well be on the order of a few tens of percent. If the local stellar neighborhood is a representative sample of the galaxy as a whole, our Milky Way could be teeming with potentially habitable planets.
Gliese 581g as a scaled-up version of Earth: atmospheric circulation simulations  [PDF]
Kevin Heng,Steven S. Vogt
Physics , 2010, DOI: 10.1111/j.1365-2966.2011.18853.x
Abstract: We use three-dimensional simulations to study the atmospheric circulation on the first Earth-sized exoplanet discovered in the habitable zone of an M star. We treat Gliese 581g as a scaled-up version of Earth by considering increased values for the exoplanetary radius and surface gravity, while retaining terrestrial values for parameters which are unconstrained by current observations. We examine the long-term, global temperature and wind maps near the surface of the exoplanet --- the climate. The specific locations for habitability on Gliese 581g depend on whether the exoplanet is tidally-locked and how fast radiative cooling occurs on a global scale. Independent of whether the existence of Gliese 581g is confirmed, our study highlights the use of general circulation models to quantify the atmospheric circulation on potentially habitable, Earth-sized exoplanets, which will be the prime targets of exoplanet discovery and characterization campaigns in the next decade.
Atmospheric studies of habitability in the Gliese 581 system  [PDF]
P. von Paris,S. Gebauer,M. Godolt,H. Rauer,B. Stracke
Physics , 2011, DOI: 10.1051/0004-6361/201016058
Abstract: The M-type star Gliese 581 is orbited by at least one terrestrial planet candidate in the habitable zone, i.e. GL 581 d. Orbital simulations have shown that additional planets inside the habitable zone of GL 581 would be dynamically stable. Recently, two further planet candidates have been claimed, one of them in the habitable zone. In view of the ongoing search for planets around M stars which is expected to result in numerous detections of potentially habitable Super-Earths, we take the GL 581 system as an example to investigate such planets. In contrast to previous studies of habitability in the GL 581 system, we use a consistent atmospheric model to assess surface conditions and habitability. Furthermore, we perform detailed atmospheric simulations for a much larger subset of potential planetary and atmospheric scenarios than previously considered. A 1D radiative-convective atmosphere model is used to calculate temperature and pressure profiles of model atmospheres, which we assumed to be composed of molecular nitrogen, water, and carbon dioxide. In these calculations, key parameters such as surface pressure and CO2 concentration as well as orbital distance and planetary mass are varied. Results imply that surface temperatures above freezing could be obtained, independent of the here considered atmospheric scenarios, at an orbital distance of 0.117 AU. For an orbital distance of 0.146 AU, CO2 concentrations as low as 10 times the present Earth's value are sufficient to warm the surface above the freezing point of water. At 0.175 AU, only scenarios with CO2 concentrations of 5% and 95% were found to be habitable. Hence, an additional Super-Earth planet in the GL 581 system in the previously determined dynamical stability range would be considered a potentially habitable planet.
Dynamical stability of the Gliese 581 exoplanetary system  [PDF]
Zsuzsanna Tóth,Imre Nagy
Physics , 2013, DOI: 10.1093/mnras/stu849
Abstract: Using numerical methods we investigate the dynamical stability of the Gliese 581 exoplanetary system. The system is known to harbour four planets (b-e). The existence of another planet (g) in the liquid water habitable zone of the star is debated after the latest analyses of the radial velocity (RV) measurements. We integrated the 4 and 5-planet model of Vogt et al. (AN 333, 561-575, 2012) with initial circular orbits. To characterize stability, the maximum eccentricity was used that the planets reached over the time of the integrations and the LCI and RLI to identify chaotic motion. Since circular orbits in the RV fits seem to be a too strong restriction and the true orbits might be elliptic, we investigated the stability of the planets as a function of their eccentricity. The integration of the circular 4-planet model shows that it is stable on a longer timescale for even an inclination i = 5{\deg}. A fifth planetary body in the 4-planet model could have a stable orbit between the two super-Earth sized planets c and d, and beyond the orbit of planet d, although another planet would likely only be stable on circular or near-circular orbit in the habitable zone of the star. Gliese 581 g in the 5-planet model would have a dynamically stable orbit, even for a wider range of orbital parameters, but its stability is strongly dependent on the eccentricity of planet d. The low-mass planet e, which quickly became unstable in eccentric models, remains stable in the circular 4-planet model, but the stable region around its initial semi-major axis and eccentricity is rather small. The stability of the inner planets e and c is dependent on the eccentricity of the Neptune-size planet b. The outermost planet d is far away from the adjacent planet c to considerably influence its stability, however, the existence of a planet between the two super-Earth planets c and d constrains its eccentricity.
Stellar Activity Masquerading as Planets in the Habitable Zone of the M dwarf Gliese 581  [PDF]
Paul Robertson,Suvrath Mahadevan,Michael Endl,Arpita Roy
Physics , 2014, DOI: 10.1126/science.1253253
Abstract: The M dwarf Gliese 581 is believed to host four planets, including one (GJ 581d) near the habitable zone that could possibly support liquid water on its surface if it is a rocky planet. The detection of another habitable-zone planet--GJ 581g--is disputed, as its significance depends on the eccentricity assumed for d. Analyzing stellar activity using the H-alpha line, we measure a stellar rotation period of 130+/-2 days and a correlation for H-alpha modulation with radial velocity. Correcting for activity greatly diminishes the signal of GJ 581d (to 1.5 sigma), while significantly boosting the signals of the other known super-Earth planets. GJ 581d does not exist, but is an artifact of stellar activity which, when incompletely corrected, causes the false detection of planet g.
Response to Comment on "Stellar activity masquerading as planets in the habitable zone of the M dwarf Gliese 581"  [PDF]
Paul Robertson,Suvrath Mahadevan,Michael Endl,Arpita Roy
Physics , 2015, DOI: 10.1126/science.1260974
Abstract: Anglada-Escud\'e and Tuomi question the statistical rigor of our analysis while ignoring the stellar activity aspects that we present. Although we agree that improvements in multiparametric radial velocity (RV) modeling are necessary for the detection of Earth-mass planets, the key physical points we raised were not challenged. We maintain that activity on Gliese 581 induces RV shifts that were interpreted as exoplanets.
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