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2011, Monthly Notices of the Royal Astronomical Society
With planets orbiting stars, a planetary mass function should not be seen as a low-mass extension of the stellar mass function, but a proper formalism needs to take care of the fact that the statistical properties of planet populations are linked to the properties of their respective host stars. This can be accounted for by describing planet populations by means of a differential planetary mass-radius-orbit function, which together with the fraction of stars with given properties that are orbited by planets and the stellar mass function allows to derive all statistics for any considered sample. These fundamental functions provide a framework for comparing statistics that result from different observing techniques and campaigns which all have their very specific selection procedures and detection efficiencies. Moreover, recent results both from gravitational microlensing campaigns and radial-velocity surveys of stars indicate that planets tend to cluster in systems rather than being the lonely child of their respective parent star. While planetary multiplicity in an observed system becomes obvious with the detection of several planets, its quantitative assessment however comes with the challenge to exclude the presence of further planets. Current exoplanet samples begin to give us first hints at the population statistics, whereas pictures of planet parameter space in its full complexity call for samples that are 2-4 orders of magnitude larger. In order to derive meaningful statistics however, planet detection campaigns need to be designed in such a way that well-defined fully-deterministic target selection, monitoring, and detection criteria are applied. The probabilistic nature of gravitational microlensing makes this technique an illustrative example of all the encountered challenges and uncertainties.
The Astrophysical Journal, 2014
Motivated by the order-of-magnitude difference in the frequency of giant planets orbiting M dwarfs inferred by microlensing and radial velocity (RV) surveys, we present a method for comparing the statistical constraints on exoplanet demographics inferred from these methods. We first derive the mapping from the observable parameters of a microlensing-detected planet to those of an analogous planet orbiting an RV-monitored star. Using this mapping, we predict the distribution of RV observables for the planet population inferred from microlensing surveys, taking care to adopt reasonable priors for, and properly marginalize over, the unknown physical parameters of microlensing-detected systems. Finally, we use simple estimates of the detection limits for a fiducial RV survey to predict the number and properties of analogs of the microlensing planet population such an RV survey should detect. We find that RV and microlensing surveys have some overlap, specifically for super-Jupiter mass planets (m p 1 M Jup ) with periods between ∼ 3 − 10 years. However, the steeply falling planetary mass function inferred from microlensing implies that, in this region of overlap, RV surveys should infer a much smaller frequency than the overall giant planet frequency (m p 0.1 M Jup ) inferred by microlensing. Our analysis demonstrates that it is possible to statistically compare and synthesize data sets from multiple exoplanet detection techniques in order to infer exoplanet demographics over wider regions of parameter space than are accessible to individual methods. In a companion paper, we apply our methodology to several representative microlensing and RV surveys to derive the frequency of planets around M dwarfs with orbits of 30 years.
General Relativity and Gravitation, 2010
The 'most curious' effect of the bending of light by the gravity of stars has evolved into a successful technique unlike any other for studying planets within the Milky Way and even other galaxies. With a sensitivity to cool planets around low-mass stars even below the mass of Earth, gravitational microlensing fits in between other planet search techniques to form a complete picture of planet parameter space, which is required to understand their origin in general, that of habitable planets more particularly, and that of planet Earth especially. Current campaigns need to evolve from first detections to obtaining a sample with well-understood selection bias that allows to draw firm conclusions about the planet populations. With planetary signals being a transient phenomenon, gravitational microlensing is a driver for new technologies in scheduling and management of non-proprietary heterogeneous telescope networks, and can serve to demonstrate forefront science live to the general public.
2008
The study of other worlds is key to understanding our own, and by addressing formation and habitability of planets, one not only investigates the origin of our civilization, but also looks into its future. With a bunch of extraordinary characteristics, gravitational microlensing is quite a distinct technique for detecting and studying extra-solar planets. Rather than in identifying nearby systems and learning about their individual properties, its main value is in obtaining the statistics of planetary populations within the Milky Way and beyond. Only the complementarity of different techniques currently employed promises to yield a complete picture of planet formation that has sufficient predictive power to let us understand how habitable worlds like ours evolve, and how abundant such systems are in the Universe. A cooperative three-step strategy of survey, follow-up, and anomaly monitoring of microlensing targets, realized by means of an automated expert system and a network of ground-based telescopes is ready right now to be used to obtain a first census of cool planets with masses reaching even below that of Earth orbiting K and M dwarfs in two distinct stellar populations, namely the Galactic bulge and disk. In order to keep track with the vast data volume that needs to be dealt with in real time in order to fulfill the science goals, and to allow the proper extraction of the planet population statistics, fully-automated systems are to replace human operations and decisions, so that the hunt for extra-solar planets thereby acts as a principal science driver for time-domain astronomy with robotic-telescope networks adopting fully-automated strategies. Several initiatives, both into facilities as well as into advanced software and strategies, are supposed to see the capabilities of gravitational microlensing programmes step-wise increasing over the next 10 years. New opportunities will show up with high-precision astrometry becoming available and studying the abundance of planets around stars in neighbouring galaxies becoming possible. Finally, with the detection of extra-solar planets (not only by gravitational microlensing) and the search for extra-terrestrial life being quite popular topics already, we should not miss out on sharing the vision with the general public, and make its realization to profit not only the scientists but all the wider society.
Publications of the Astronomical Society of the Pacific, 2008
We analyze 8 years of precise radial velocity measurements from the Keck Planet Search, characterizing the detection threshold, selection effects, and completeness of the survey. We first carry out a systematic search for planets, by assessing the false alarm probability associated with Keplerian orbit fits to the data. This allows us to understand the detection threshold for each star in terms of the number and time baseline of the observations, and the underlying "noise" from measurement errors, intrinsic stellar jitter, or additional low mass planets. We show that all planets with orbital periods P < 2000 days, velocity amplitudes K > 20 m s −1 , and eccentricities e 0.6 have been announced, and we summarize the candidates at lower amplitudes and longer orbital periods. For the remaining stars, we calculate upper limits on the velocity amplitude of a companion. For orbital periods less than the duration of the observations, these are typically 10 m s −1 , and increase ∝ P 2 for longer periods. We then use the non-detections to derive completeness corrections at low amplitudes and long orbital periods, and discuss the resulting distribution of minimum mass and orbital period. We give the fraction of stars with a planet as a function of planet mass and orbital period, and extrapolate to long period orbits and low planet masses. A power law fit for planet masses > 0.3 M J and periods < 2000 days gives a mass-period distribution dN = C M α P β d ln Md ln P with α = −0.31 ± 0.2, β = 0.26 ± 0.1, and the normalization constant C such that 10.5% of solar type stars have a planet with mass in the range 0.3-10 M J and orbital period 2-2000 days. The orbital period distribution shows an increase in the planet fraction by a factor of ≈ 5 for orbital periods 300 days. Extrapolation gives 17-20% of stars having gas giant planets within 20 AU. Finally, we constrain the occurrence rate of planets orbiting M dwarfs compared to FGK dwarfs, taking into account differences in detectability.
Icarus, 2020
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Optical, Infrared, and Millimeter Space Telescopes, 2004
The Microlensing Planet Finder (MPF) is a proposed Discovery mission that will complete the first census of extrasolar planets with sensitivity to planets like those in our own solar system. MPF will employ a 1.1m aperture telescope, which images a 1.3 sq. deg. field-of-view in the near-IR, in order to detect extrasolar planets with the gravitational microlensing effect. MPF's sensitivity extends down to planets of 0.1 Earth masses, and MPF can detect Earth-like planets at all separations from 0.7AU to infinity. MPF's extrasolar planet census will provide critical information needed to understand the formation and frequency of extrasolar planetary systems similar to our own.
Universe
As of February 2022, over 4900 exoplanets have been confirmed. In this study, we conducted statistical analyses on both the exoplanets and their host stars’ parameters. Our findings suggest that the radius and true mass distribution of the exoplanets remain largely unchanged compared to prior research. However, we observed a correlation between the average eccentricity and the number of planets in a system, and fluctuations in the “size” of the planets may contribute to such variation. Moreover, we discovered that, among planets with precise measurements of radius, true mass, and semi-major axis, the true mass-radius relationship follows a power–law distribution. Interestingly, the power–law index tends to decrease from super-Earths to cold Jupiters, potentially due to atmospheric composition. We also revised the radius valley, and determined that M-type host stars with low mass and metal abundance exhibit high planetary ownership rates or harbor large-mass planets, suggesting a dif...
Monthly Notices of the Royal Astronomical Society, 2002
We investigate the distribution of mass M and orbital period P of extrasolar planets, taking account of selection effects caused by the limited velocity precision and duration of existing surveys. We fit the data on 72 planets to a power-law distribution of the form dn = C M −α P −β (dM/M)(dP/P), and find α = 0.11 ± 0.10, β = −0.27 ± 0.06 for M 10 M J , where M J is the mass of Jupiter. The correlation coefficient between these two exponents is −0.31, indicating that uncertainties in the two distributions are coupled. We estimate that 4 per cent of solar-type stars have companions in the range 1 M J < M < 10 M J , 2 d < P < 10 yr.
2002
We present an analysis of precision radial velocity measurements for 580 stars from the Keck survey. We first discuss the detection threshold of the survey, and then describe a Bayesian approach to constrain the distribution of extrasolar planet orbital parameters using both detections and upper limits.
1999
Among various techniques to search for extrasolar planets, microlensing has some unique characteristics. Contrary to all other methods which favour nearby objects, microlensing is sensitive to planets around stars at distances of several kpc. These stars act as gravitational lenses leading to a brightening of observed luminous source stars. The lens stars that are tested for the presence of planets are not generally seen themselves. The largest sensitivity is obtained for planets at orbital separations of 1-10 AU offering the view on an extremely interesting range with regard to our own solar system and in particular to the position of Jupiter. The microlensing signal of a jupiter-mass planet lasts typically a few days. This means that a planet reveals its existence by producing a short signal at its quasi-instantaneous position, so that planets can be detected without the need to observe a significant fraction of the orbital period. Relying on the microlensing alerts issued by several survey groups that observe ∼ 10 7 stars in the Galactic bulge, PLANET (Probing Lensing Anomalies NETwork) performs precise and frequent measurements on ongoing microlensing events in order to detect deviations from a light curve produced by a single point-like object. These measurements allow constraints to be put on the abundance of planets. From 42 well-sampled events between 1995 and 1999, we infer that less than 1/3 of M-dwarfs in the Galactic bulge have jupiter-mass companions at separations between 1 and 4 AU from their parent star, and that less than 45 % have 3-jupiter-mass companions between 1 and 7 AU.
Solar System Research, 2019
To build the mass distribution of exoplanets discovered with the method of measuring the radial velocities, it is necessary to take into consideration the observational selection factors. We propose the detectability-window method to form homogeneous series of exoplanets. In addition, the errors in determining the masses are taken into account. The mass distributions of the transiting planets and the planets discovered with the radial-velocity method are compared in a range of 0.5 to 13 Jupiter masses.
Astronomische Nachrichten, 2010
The dates of receipt and acceptance should be inserted later Within less than 15 years, the count of known planets orbiting stars other than the Sun has risen from none to more than 400 with detections arising from four successfully applied techniques: Doppler-wobbles, planetary transits, gravitational microlensing, and direct imaging. While the hunt for twin Earths is on, a statistically well-defined sample of the population of planets in all their variety is required for probing models of planet formation and orbital evolution so that the origin of planets that harbour life, like and including ours, can be understood. Given the different characteristics of the detection techniques, a complete picture can only arise from a combination of their respective results. Microlensing observations are well-suited to reveal statistical properties of the population of planets orbiting stars in either the Galactic disk or bulge from microlensing observations, but a mandatory requirement is the adoption of strictly-deterministic criteria for selecting targets and identifying signals. Here, we describe a fully-deterministic strategy realised by means of the ARTEMiS (Automated Robotic Terrestrial Exoplanet Microlensing Search) system at the Danish 1.54m telescope at ESO La Silla between June and August 2008 as part of the MiNDSTEp (Microlensing Network for the Detection of Small Terrestrial Exoplanets) campaign, making use of immediate feedback on suspected anomalies recognized by the SIGNALMEN anomaly detector. We demonstrate for the first time the feasibility of such an approach, and thereby the readiness for studying planet populations down to Earth mass and even below, with ground-based observations. While the quality of the real-time photometry is a crucial factor on the efficiency of the campaign, an impairment of the target selection by data of bad quality can be successfully avoided. With a smaller slew time, smaller dead time, and higher through-put, modern robotic telescopes could significantly outperform the 1.54m Danish, whereas lucky-imaging cameras could set new standards for high-precision follow-up monitoring of microlensing events.
Arxiv preprint arXiv: …, 2010
SPIE Proceedings, 2004
The Microlensing Planet Finder (MPF) is a proposed Discovery mission that will complete the first census of extrasolar planets with sensitivity to planets like those in our own solar system. MPF will employ a 1.1m aperture telescope, which images a 1.3 sq. deg. field-of-view in the near-IR, in order to detect extrasolar planets with the gravitational microlensing effect. MPF's sensitivity extends down to planets of 0.1 Earth masses, and MPF can detect Earth-like planets at all separations from 0.7AU to infinity. MPF's extrasolar planet census will provide critical information needed to understand the formation and frequency of extrasolar planetary systems similar to our own.
Astrophys J, 2010
Radial-velocity planet search campaigns are now beginning to detect low-mass "Super-Earth" planets, with minimum masses M sin ilsim 10 M ⊕. Using two independently developed methods, we have derived detection limits from nearly four years of the highest-precision data on 24 bright, stable stars from the Anglo-Australian Planet Search. Both methods are more conservative than a human analyzing an individual observed data set, as is demonstrated by the fact that both techniques would detect the radial-velocity signals announced as exoplanets for the 61 Vir system in 50% of trials. There are modest differences between the methods which can be recognized as arising from particular criteria that they adopt. What both processes deliver is a quantitative selection process such that one can use them to draw quantitative conclusions about planetary frequency and orbital parameter distribution from a given data set. Averaging over all 24 stars, in the period range P< 300 days and the eccentricity range 0.0 < e < 0.6, we could detect 99% of planets with velocity amplitudes Kgsim 7.1 m s-1. For the best stars in the sample, we are able to detect or exclude planets with Kgsim 3 m s-1, corresponding to minimum masses of 8 M ⊕ (P = 5 days) or 17 M ⊕ (P = 50 days). Our results indicate that the observed "period valley," a lack of giant planets (M > 100 M ⊕) with periods between 10 and 100 days, is indeed real. However, for planets in the mass range 10-100 M ⊕, our results suggest that the deficit of such planets may be a result of selection effects.
The Astrophysical Journal, 2014
We extend the statistical analysis of Lissauer et al. (2012, ApJ 750, 112), which demonstrates that the overwhelming majority of Kepler candidate multiple transiting systems (multis) represent true transiting planets, and develop therefrom a procedure to validate large numbers of planet candidates in multis as bona fide exoplanets. We show that this statistical framework correctly estimates the abundance of false positives already identified around Kepler targets with multiple sets of transit-like signatures based on their abundance around targets with single sets of transit-like signatures. We estimate the number of multis that represent split systems of one or more planets orbiting each component of a binary star system. We use the high reliability rate for multis to validate more than one dozen particularly interesting multi-planet systems herein. Hundreds of additional multi-planet systems are validated in a companion paper by Rowe et al. (2014, ApJ). We note that few very short period (P < 1.6 days) planets orbit within multiple transiting planet systems and discuss possible reasons for their absence. There also appears to be a shortage of planets with periods exceeding a few months in multis.
The first step in discovering the extent of life in our galaxy is to determine the number of terrestrial planets in circumstellar habitable zones (HZ). The Kepler Mission is designed around a 0.95 m aperture Schmidt-type telescope with an array of 42 CCDs. The photometer is designed to continuously monitor the brightness of 100,000 solar-like stars to detect the transits of Earthsize and larger planets. It is scheduled to be launched into a heliocentric orbit in 2007. Measurements of the depth and repetition time of transits provide the size of the planet relative to the star and its orbital period. When combined with ground-based spectroscopy of these stars to fix the stellar parameters, the true planet radius and orbit, semi-major axis, hence the position relative to the HZ, are determined. The spectra are also used to discover the relationships between the characteristics of planets and the stars that they orbit. In particular, the association of planetary size and occurrence frequency with stellar mass and metallicity will be investigated. At the end of the four year mission, hundreds of terrestrial planets should be discovered in and near the HZ of their stars if such planets are 428 Borucki et al. common. Extending the mission to six years doubles the expected number of Earth-size planets in the HZ. A null result would imply that terrestrial planets in the HZ occur in less than 1% of the stars and that habitable planets might be quite rare. Based on the results of the current Doppler velocity discoveries, detection of the reflected light from several hundred short-period giant planets is also expected. Information on the albedos and densities of those giants showing transits will be obtained.
Arxiv preprint arXiv: …, 2008
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