Variations related to stellar activity and correlated noise can prevent the detections of low-amplitude signals in radial velocity data if not accounted for. This can be seen as the greatest obstacle in detecting Earth-like planets orbiting nearby st
ars with Doppler spectroscopy regardless of developments in instrumentation and rapidly accumulating amounts of data. We use a statistical model that is not sensitive to aperiodic and/or quasiperiodic variability of stellar origin. We demonstrate the performance of our model by re-analysing the radial velocities of the moderately active star CoRoT-7 ($log R_{rm HK} = -4.61$) with a transiting planet whose Doppler signal has proven rather difficult to detect. We find that the signal of the transiting planet can be robustly detected together with signals of two other planet candidates. Our results suggest that rotation periods of moderately active stars can be filtered out of the radial velocity noise, which enables the detections of low-mass planets orbiting such stars.
Due to their higher planet-star mass-ratios, M dwarfs are the easiest targets for detection of low-mass planets orbiting nearby stars using Doppler spectroscopy. Furthermore, because of their low masses and luminosities, Doppler measurements enable t
he detection of low-mass planets in their habitable zones that correspond to closer orbits than for Solar-type stars. We re-analyse literature UVES radial velocities of 41 nearby M dwarfs in a combination with new velocities obtained from publicly available spectra from the HARPS-ESO spectrograph of these stars in an attempt to constrain any low-amplitude Keplerian signals. We apply Bayesian signal detection criteria, together with posterior sampling techniques, in combination with noise models that take into account correlations in the data and obtain estimates for the number of planet candidates in the sample. More generally, we use the estimated detection probability function to calculate the occurrence rate of low-mass planets around nearby M dwarfs. We report eight new planet candidates in the sample (orbiting GJ 27.1, GJ 160.2, GJ 180, GJ 229, GJ 422, and GJ 682), including two new multiplanet systems, and confirm two previously known candidates in the GJ 433 system based on detections of Keplerian signals in the combined UVES and HARPS radial velocity data that cannot be explained by periodic and/or quasiperiodic phenomena related to stellar activities. Finally, we use the estimated detection probability function to calculate the occurrence rate of low-mass planets around nearby M dwarfs. According to our results, M dwarfs are hosts to an abundance of low-mass planets and the occurrence rate of planets less massive than 10 M$_{oplus}$ is of the order of one planet per star, possibly even greater. ...
We re-analyse the recently published HARPS and PFS velocities of the nearby K dwarf GJ 221 that have been reported to contain the signatures of two planets orbiting the star. Our goal is to see whether the earlier studies discussing the system fell v
ictims of false negative detections. We perform the analyses by using an independent statistical method based on posterior samplings and model comparisons in the Bayesian framework that is known to be more sensitive to weak signals of low-mass planets. According to our analyses, we find strong evidence in favour of a third candidate planet in the system corresponding to a cold sub-Saturnian planet with an orbital period of 500 days and a minimum mass of 29 $M_{oplus}$. Application of sub-optimal signal detection methods can leave low-amplitude signals undetected in radial velocity time-series. Our results suggest that the estimated statistical properties of low-mass planets can thus be biased because several signals corresponding to low-mass candidate planets may have gone unnoticed. This also suggests that the occurrence rates of such planets based on radial velocity surveys might be underestimated.
Exoplanet Doppler surveys are currently the most efficient means to detect low-mass companions to nearby stars. Among these stars, the light M dwarfs provide the highest sensitivity to detect low-mass exoplanet candidates. Evidence is accumulating th
at a substantial fraction of these low-mass planets are found in high-multiplicity planetary systems. GJ 163 is a nearby inactive M dwarf with abundant public observations obtained using the HARPS spectrograph. We obtain and analyse radial velocities from the HARPS public spectra of GJ 163 and investigate the presence of a planetary companions orbiting it. The number of planet candidates detected might depend on some prior assumptions. Since the impact of prior choice has not been investigated throughly previously, we study the effects of different prior densities on the detectability of planet candidates around GJ 163. We use Bayesian tools, i.e. posterior samplings and model comparisons, when analysing the GJ 163 velocities. We consider models accounting for the possible correlations of subsequent measurements. We also search for activity-related counterparts of the signals we observe and test the dynamical stability of the planetary systems corresponding to our solutions using direct numerical integrations of the orbits. We find that there are at least three planet candidates orbiting GJ 163. The existence of a fourth planet is supported by the data but the evidence in favor of the corresponding model is not yet conclusive. The second innermost planet candidate in the system with an orbital period of 25.6 days and a minimum mass of 8.7 Me is inside the liquid-water habitable zone of the star.
Bayesian data analysis techniques, together with suitable statistical models, can be used to obtain much more information from noisy data than the traditional frequentist methods. For instance, when searching for periodic signals in noisy data, the B
ayesian techniques can be used to define exact detection criteria for low-amplitude signals - the most interesting signals that might correspond to habitable planets. We present an overview of Bayesian techniques and present detailed analyses of the HARPS-TERRA velocities of HD 40307, a nearby star observed to host a candidate habitable planet, to demonstrate in practice the applicability of Bayes rule to astronomical data.
The abilities of radial velocity exoplanet surveys to detect the lowest-mass extra-solar planets are currently limited by a combination of instrument precision, lack of data, and jitter. Jitter is a general term for any unknown features in the noise,
and reflects a lack of detailed knowledge of stellar physics (asteroseismology, starspots, magnetic cycles, granulation, and other stellar surface phenomena), as well as the possible underestimation of instrument noise. We study an extensive set of radial velocities for the star HD 10700 ($tau$ Ceti) to determine the properties of the jitter arising from stellar surface inhomogeneities, activity, and telescope-instrument systems, and perform a comprehensive search for planetary signals in the radial velocities. We perform Bayesian comparisons of statistical models describing the radial velocity data to quantify the number of significant signals and the magnitude and properties of the excess noise in the data. We reach our goal by adding artificial signals to the flat radial velocity data of HD 10700 and by seeing which one of our statistical noise models receives the greatest posterior probabilities while still being able to extract the artificial signals correctly from the data. We utilise various noise components to assess properties of the noise in the data and analyse the HARPS, AAPS, and HIRES data for HD 10700 to quantify these properties and search for previously unknown low-amplitude Keplerian signals. ...
The K2.5 dwarf HD 40307 has been reported to host three super-Earths. The system lacks massive planets and is therefore a potential candidate for having additional low-mass planetary companions. We re-derive Doppler measurements from public HARPS spe
ctra of HD 40307 to confirm the significance of the reported signals using independent data analysis methods. We also investigate these measurements for additional low-amplitude signals. We used Bayesian analysis of our radial velocities to estimate the probability densities of different model parameters. We also estimated the relative probabilities of models with differing numbers of Keplerian signals and verified their significance using periodogram analyses. We investigated the relation of the detected signals with the chromospheric emission of the star. As previously reported for other objects, we found that radial velocity signals correlated with the S-index are strongly wavelength dependent. We identify two additional clear signals with periods of 34 and 51 days, both corresponding to planet candidates with minimum masses a few times that of the Earth. An additional sixth candidate is initially found at a period of 320 days. However, this signal correlates strongly with the chromospheric emission from the star and is also strongly wavelength dependent. When analysing the red half of the spectra only, the five putative planetary signals are recovered together with a very significant periodicity at about 200 days. This signal has a similar amplitude as the other new signals reported in the current work and corresponds to a planet candidate with M sin i = 7 Me (HD 40307 g). ...
The four-planet system around GJ 581 has received attention because it has been claimed that there are possibly two additional low-mass companions as well - one of them being a planet in the middle of the stellar habitable zone. We re-analyse the ava
ilable HARPS and HIRES Doppler data in an attempt to determine the false positive rate of our Bayesian data analysis techniques and to count the number of Keplerian signals in the GJ 581 data. We apply the common Lomb-Scargle periodograms and posterior sampling techniques in the Bayesian framework to estimate the number of signals in the radial velocities. We also analyse the HARPS velocities sequentially after each full observing period to compare the sensitivities and false positive rates of the two signal detection techniques. By relaxing the assumption that the radial velocity noise is white, we also demonstrate the consequences that noise correlations have on the obtained results and the significances of the signals. According to our analyses, the number of Keplerian signals favoured by the publicly available HARPS and HIRES radial velocity data of GJ 581 is four. This result relies on the sensitivity of the Bayesian statistical analysis techniques but also depends on the assumed noise model. We also show that the radial velocity noise is actually not white and that this feature has to be accounted for when analysing radial velocities in a search for low-amplitude signals corresponding to low-mass planets. ...
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 severa
l 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.
