Fast computation of quadrupole and hexadecapole approximations in microlensing with a single point-source evaluation

The exoplanet detection rate from gravitational microlensing has grown significantly in recent years thanks to a great enhancement of resources and improved observational strategy. Current observatories include ground-based wide-field and/or robotic world-wide networks of telescopes, as well as space-based observatories such as satellites Spitzer or Kepler/K2. This results in a large quantity of data to be processed and analyzed, which is a challenge for modeling codes because of the complexity of the parameter space to be explored, and the intensive computations required to evaluate the models. In this work, I present a method that allows to compute the quadrupole and hexadecapole approximation of the finite-source magnification with more efficiency that previously available codes, with routines about x6 and x4 faster respectively. The quadrupole takes just about twice the time of a point-source evaluation, which advocates for generalizing its use to large portion of the light curves. The corresponding routines are available as open-source python codes.Comment: Published in MNRAS (7 pages, 2 figures, 1 table). Open source codes available on GitHub (cf. reference in the paper

Bayesian analysis of caustic-crossing microlensing events

Aims: Caustic-crossing binary-lens microlensing events are important anomalous events because they are capable of detecting an extrasolar planet companion orbiting the lens star. Fast and robust modelling methods are thus of prime interest in helping to decide whether a planet is detected by an event. Cassan (2008) introduced a new set of parameters to model binary-lens events, which are closely related to properties of the light curve. In this work, we explain how Bayesian priors can be added to this framework, and investigate on interesting options. Methods: We develop a mathematical formulation that allows us to compute analytically the priors on the new parameters, given some previous knowledge about other physical quantities. We explicitly compute the priors for a number of interesting cases, and show how this can be implemented in a fully Bayesian, Markov chain Monte Carlo algorithm. Results: Using Bayesian priors can accelerate microlens fitting codes by reducing the time spent considering physically implausible models, and helps us to discriminate between alternative models based on the physical plausibility of their parameters.Comment: Accepted in A&A - 7 pages, 4 figure

Interferometric visibility of single-lens models: the thin-arcs approximation

Long baseline interferometry of microlensing events can resolve the individual images of the source produced by the lens, which combined with the modelling of the microlensing light curve, leads to the exact lens mass and distance. Interferometric observations thus offer a unique opportunity to constrain the mass of exoplanets detected by microlensing, and to precisely measure the mass of distant isolated objects such as stars and brown dwarfs, and of stellar remnants such as white dwarfs, neutron stars, and stellar black holes. Having accurate models and reliable numerical methods is of particular importance as the number of targets is expected to increase significantly in the near future. In this work we discuss the different approaches to calculating the fringe complex visibility for the important case of a single lens. We propose a robust integration scheme to calculate the exact visibility, and introduce a novel approximation, which we call the `thin-arcs approximation', which can be applied over a wide range of lens--source separations. We find that this approximation runs six to ten times faster than the exact calculation, depending of the characteristics of the event and the required accuracy. This approximation provides accurate results for microlensing events of medium to high magnification observed around the peak (i.e. a large fraction of potential observational targets).Comment: Same as published versio

One or more bound planets per Milky Way star from microlensing observations

Most known extrasolar planets (exoplanets) have been discovered using the radial velocity or transit methods. Both are biased towards planets that are relatively close to their parent stars, and studies find that around 17–30% of solar-like stars host a planet. Gravitational microlensing on the other hand, probes planets that are further away from their stars. Recently, a population of planets that are unbound or very far from their stars was discovered by microlensing. These planets are at least as numerous as the stars in the Milky Way. Here we report a statistical analysis of microlensing data (gathered in 2002–07) that reveals the fraction of bound planets 0.5–10 au (Sun–Earth distance) from their stars. We find that 17^(+16)_(-9)% of stars host Jupiter-mass planets (0.3–10 M_J, where M_J = 318 M_⊕ plus and M_⊕ plus is Earth’s mass). Cool Neptunes (10–30 M_⊕ plus) and super-Earths (5–10 M_⊕ plus) are even more common: their respective abundances per star are 52^(+22)_(-29)% and 62^(+35)_(-73)% . We conclude that stars are orbited by planets as a rule, rather than the exception

A Bayesian algorithm for model selection applied to caustic-crossing binary-lens microlensing events

We present a full Bayesian algorithm designed to perform automated searches of the parameter space of caustic-crossing binary-lens microlensing events. This builds on previous work implementing priors derived from Galactic models and geometrical considerations. The geometrical structure of the priors divides the parameter space into well-defined boxes that we explore with multiple Monte Carlo Markov Chains. We outline our Bayesian framework and test our automated search scheme using two data sets: a synthetic lightcurve, and the observations of OGLE-2007-BLG-472 that we analysed in previous work. For the synthetic data, we recover the input parameters. For OGLE-2007-BLG-472 we find that while \chi^2 is minimised for a planetary mass-ratio model with extremely long timescale, the introduction of priors and minimisation of BIC, rather than \chi^2, favours a more plausible lens model, a binary star with components of 0.78 and 0.11 M_Sun at a distance of 6.3 kpc, compared to our previous result of 1.50 and 0.12 M_Sun at a distance of 1 kpc.Comment: 13 pages, 9 figures, 3 tables, MNRAS in pres

Genetic map construction and quantitative trait loci (QTL) mapping for nitrogen use efficiency and its relationship with productivity and quality of the biennial crop Belgian endive (Cichorium intybus L.)

A genetic study of the biennial crop Belgian endive (Cichorium intybus) was carried out to examine the effect of nitrogen nutrition during the vegetative phase in the control of the productivity and quality of the chicon (etiolated bud), a crop that grows during the second phase of development (forcing process). A population of 302 recombinant inbred lines (RIL) was obtained from the cross between contrasting lines "NS1" and "NR2". A genetic map was constructed and QTLs of several physiological and agronomical traits were mapped under two levels of nitrogen fertilization during the vegetative phase (N- and N+). The agronomical traits showed high broad sense heritability, whereas the physiological traits were characterized by low broad sense heritability. Nitrogen reserves mobilization during the forcing process was negatively correlated with nitrogen reserves content of the tuberized root and common QTLs were detected for these traits. The chicon productivity and quality were not correlated, but showed one common QTL. This study revealed that chicon productivity and quality were genetically associated with nitrogen reserves mobilization that exerts opposite effects on both traits. Chicon productivity was positively correlated with N reserves mobilization under N- and N+ and a common QTL with the same additive effects was detected for both traits. Chicon quality was negatively correlated with N reserves mobilization under N- and N+ and a common QTL with opposite additive effects was detected for both traits. These results lead to the conclusion that N reserves mobilization is a more effective trait than N reserves content in predicting chicon productivity and quality. Finally, this study revealed agronomical and physiological QTLs utilizable by breeders via marker-assisted selection to aid the optimization of chicon quality under adapted N fertilization

Composition of Ices in Low-Mass Extrasolar Planets

We study the formation conditions of icy planetesimals in protoplanetary disks in order to determine the composition of ices in small and cold extrasolar planets. Assuming that ices are formed from hydrates, clathrates, and pure condensates, we calculate their mass fractions with respect to the total quantity of ices included in planetesimals, for a grid of disk models. We find that the composition of ices weakly depends on the adopted disk thermodynamic conditions, and is rather influenced by the initial composition of the gas phase. The use of a plausible range of molecular abundance ratios and the variation of the relative elemental carbon over oxygen ratio in the gas phase of protoplanetary disks, allow us to apply our model to a wide range of planetary systems. Our results can thus be used to constrain the icy/volatile phase composition of cold planets evidenced by microlensing surveys, hypothetical ocean-planets and carbon planets, which could be detected by Corot or Kepler.Comment: Accepted for publication in The Astrophysical Journa

ExELS: an exoplanet legacy science proposal for the ESA Euclid mission. II. Hot exoplanets and sub-stellar systems

The Exoplanet Euclid Legacy Survey (ExELS) proposes to determine the frequency of cold exoplanets down to Earth mass from host separations of ~1 AU out to the free-floating regime by detecting microlensing events in Galactic Bulge. We show that ExELS can also detect large numbers of hot, transiting exoplanets in the same population. The combined microlensing+transit survey would allow the first self-consistent estimate of the relative frequencies of hot and cold sub-stellar companions, reducing biases in comparing "near-field" radial velocity and transiting exoplanets with "far-field" microlensing exoplanets. The age of the Bulge and its spread in metallicity further allows ExELS to better constrain both the variation of companion frequency with metallicity and statistically explore the strength of star-planet tides. We conservatively estimate that ExELS will detect ~4100 sub-stellar objects, with sensitivity typically reaching down to Neptune-mass planets. Of these, ~600 will be detectable in both Euclid's VIS (optical) channel and NISP H-band imager, with ~90% of detections being hot Jupiters. Likely scenarios predict a range of 2900-7000 for VIS and 400-1600 for H-band. Twice as many can be expected in VIS if the cadence can be increased to match the 20-minute H-band cadence. The separation of planets from brown dwarfs via Doppler boosting or ellipsoidal variability will be possible in a handful of cases. Radial velocity confirmation should be possible in some cases, using 30-metre-class telescopes. We expect secondary eclipses, and reflection and emission from planets to be detectable in up to ~100 systems in both VIS and NISP-H. Transits of ~500 planetary-radius companions will be characterised with two-colour photometry and ~40 with four-colour photometry (VIS,YJH), and the albedo of (and emission from) a large sample of hot Jupiters in the H-band can be explored statistically.Comment: 18 pages, 16 figures, accepted MNRA

ExELS: an exoplanet legacy science proposal for the ESA Euclid mission. II. Hot exoplanets and sub-stellar systems

The Exoplanet Euclid Legacy Survey (ExELS) proposes to determine the frequency of cold exoplanets down to Earth mass from host separations of ~1 AU out to the free-floating regime by detecting microlensing events in Galactic Bulge. We show that ExELS can also detect large numbers of hot, transiting exoplanets in the same population. The combined microlensing+transit survey would allow the first self-consistent estimate of the relative frequencies of hot and cold sub-stellar companions, reducing biases in comparing "near-field" radial velocity and transiting exoplanets with "far-field" microlensing exoplanets. The age of the Bulge and its spread in metallicity further allows ExELS to better constrain both the variation of companion frequency with metallicity and statistically explore the strength of star-planet tides. We conservatively estimate that ExELS will detect ~4100 sub-stellar objects, with sensitivity typically reaching down to Neptune-mass planets. Of these, ~600 will be detectable in both Euclid's VIS (optical) channel and NISP H-band imager, with ~90% of detections being hot Jupiters. Likely scenarios predict a range of 2900-7000 for VIS and 400-1600 for H-band. Twice as many can be expected in VIS if the cadence can be increased to match the 20-minute H-band cadence. The separation of planets from brown dwarfs via Doppler boosting or ellipsoidal variability will be possible in a handful of cases. Radial velocity confirmation should be possible in some cases, using 30-metre-class telescopes. We expect secondary eclipses, and reflection and emission from planets to be detectable in up to ~100 systems in both VIS and NISP-H. Transits of ~500 planetary-radius companions will be characterised with two-colour photometry and ~40 with four-colour photometry (VIS,YJH), and the albedo of (and emission from) a large sample of hot Jupiters in the H-band can be explored statistically.Comment: 18 pages, 16 figures, accepted MNRA