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

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

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

A systematic fitting scheme for caustic-crossing microlensing events

We outline a method for fitting binary-lens caustic-crossing microlensing events based on the alternative model parameterisation proposed and detailed in Cassan (2008). As an illustration of our methodology, we present an analysis of OGLE-2007-BLG-472, a double-peaked Galactic microlensing event with a source crossing the whole caustic structure in less than three days. In order to identify all possible models we conduct an extensive search of the parameter space, followed by a refinement of the parameters with a Markov Chain-Monte Carlo algorithm. We find a number of low-chi2 regions in the parameter space, which lead to several distinct competitive best models. We examine the parameters for each of them, and estimate their physical properties. We find that our fitting strategy locates several minima that are difficult to find with other modelling strategies and is therefore a more appropriate method to fit this type of events.Comment: 12 pages, 11 figure

Asymptotic Expansions and Amplification of a Gravitational Lens Near a Fold Caustic

We propose two methods that enable us to obtain approximate solutions of the lens equation near a fold caustic with an arbitrary degree of accuracy. We obtain "post-linear" corrections to the well-known formula in the linear caustic approximation for the total amplification of two critical images of a point source. In this case, in order to obtain the nontrivial corrections we had to go beyond the approximation orders earlier used by Keeton et al. and to take into account the Taylor expansion of the lens equation near caustic up to the fourth order. Corresponding analytical expressions are derived for the amplification in cases of the Gaussian and power-law extended source models; the amplifications depend on three additional fitting parameters. Conditions of neglecting the correction terms are analysed. The modified formula for the amplification is applied to the fitting of light curves of the Q2237+0305 gravitational lens system in a vicinity of the high amplification events (HAEs). We show that the introduction of some "post-linear" corrections reduces chi^2 by 30% in the case of known HAE on the light curve of image C (1999). These corrections can be important for a precise comparison of different source models with regard for observational data. Key words: gravitational lensing: micro - quasars: individual (Q2237+0305) - gravitational lensing: strong - methods: analyticalComment: 16 pages, 3 figure

Limb-darkening measurements for a cool red giant in microlensing event OGLE 2004-BLG-482

Aims: We present a detailed analysis of OGLE 2004-BLG-482, a relatively high-magnification single-lens microlensing event which exhibits clear extended-source effects. These events are relatively rare, but they potentially contain unique information on the stellar atmosphere properties of their source star, as shown in this study. Methods: Our dense photometric coverage of the overall light curve and a proper microlensing modelling allow us to derive measurements of the OGLE 2004-BLG-482 source star's linear limb-darkening coefficients in three bands, including standard Johnson-Cousins I and R, as well as in a broad clear filter. In particular, we discuss in detail the problems of multi-band and multi-site modelling on the expected precision of our results. We also obtained high-resolution UVES spectra as part of a ToO programme at ESO VLT from which we derive the source star's precise fundamental parameters. Results: From the high-resolution UVES spectra, we find that OGLE 2004-BLG-482's source star is a red giant of MK type a bit later than M3, with Teff = 3667 +/- 150 K, log g = 2.1 +/- 1.0 and an assumed solar metallicity. This is confirmed by an OGLE calibrated colour-magnitude diagram. We then obtain from a detailed microlensing modelling of the light curve linear limb-darkening coefficients that we compare to model-atmosphere predictions available in the literature, and find a very good agreement for the I and R bands. In addition, we perform a similar analysis using an alternative description of limb darkening based on a principal component analysis of ATLAS limb-darkening profiles, and also find a very good agreement between measurements and model predictions.Comment: Accepted in A&

RoboTAP: Target priorities for robotic microlensing observations

Context. The ability to automatically select scientifically-important transient events from an alert stream of many such events, and to conduct follow-up observations in response, will become increasingly important in astronomy. With wide-angle time domain surveys pushing to fainter limiting magnitudes, the capability to follow-up on transient alerts far exceeds our follow-up telescope resources, and effective target prioritization becomes essential. The RoboNet-II microlensing program is a pathfinder project, which has developed an automated target selection process (RoboTAP) for gravitational microlensing events, which are observed in real time using the Las Cumbres Observatory telescope network. Aims. Follow-up telescopes typically have a much smaller field of view compared to surveys, therefore the most promising microlensing events must be automatically selected at any given time from an annual sample exceeding 2000 events. The main challenge is to select between events with a high planet detection sensitivity, with the aim of detecting many planets and characterizing planetary anomalies. Methods. Our target selection algorithm is a hybrid system based on estimates of the planet detection zones around a microlens. It follows automatic anomaly alerts and respects the expected survey coverage of specific events. Results. We introduce the RoboTAP algorithm, whose purpose is to select and prioritize microlensing events with high sensitivity to planetary companions. In this work, we determine the planet sensitivity of the RoboNet follow-up program and provide a working example of how a broker can be designed for a real-life transient science program conducting follow-up observations in response to alerts; we explore the issues that will confront similar programs being developed for the Large Synoptic Survey Telescope (LSST) and other time domain surveys

Towards A Census of Earth-mass Exo-planets with Gravitational Microlensing

Thirteen exo-planets have been discovered using the gravitational microlensing technique (out of which 7 have been published). These planets already demonstrate that super-Earths (with mass up to ~10 Earth masses) beyond the snow line are common and multiple planet systems are not rare. In this White Paper we introduce the basic concepts of the gravitational microlensing technique, summarise the current mode of discovery and outline future steps towards a complete census of planets including Earth-mass planets. In the near-term (over the next 5 years) we advocate a strategy of automated follow-up with existing and upgraded telescopes which will significantly increase the current planet detection efficiency. In the medium 5-10 year term, we envision an international network of wide-field 2m class telescopes to discover Earth-mass and free-floating exo-planets. In the long (10-15 year) term, we strongly advocate a space microlensing telescope which, when combined with Kepler, will provide a complete census of planets down to Earth mass at almost all separations. Such a survey could be undertaken as a science programme on Euclid, a dark energy probe with a wide-field imager which has been proposed to ESA's Cosmic Vision Programme.Comment: 10 pages. White Paper submission to the ESA Exo-Planet Roadmap Advisory Team. See also "Inferring statistics of planet populations by means of automated microlensing searches" by M. Dominik et al. (arXiv:0808.0004

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 Near Infrared Spectrometer and Photometer (NISP)-H-band imager, with ∼90 per cent 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-min 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 m-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 characterized 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