No Sub-Saturn-mass Planet Desert in the CORALIE/HARPS Radial-velocity Sample

We analyze the CORALIE/HARPS sample of exoplanets found by the Doppler radial-velocity method for signs of the predicted gap or “desert” at 10–100 M ⊕ caused by runaway gas accretion at semimajor axes of <3 au. We find that these data are not consistent with this prediction. This result is similar to the finding by the MOA gravitational microlensing survey that found no desert in the exoplanet distribution for exoplanets in slightly longer period orbits and somewhat lower host masses (Suzuki et al. 2018). Together, these results imply that the runaway gas accretion scenario of the core accretion theory does not have a large influence on the final mass and semimajor axis distribution of exoplanets.

Modelling of Planetary Gravitational Microlensing Events

<p>This thesis describes and develops procedures for the generation of theoretical lightcurves that can be used to model gravitational microlensing events that involve multiple lenses. Of particular interest are the cases involving a single lens star with one or more orbiting planets, as this has proven to be an effective way of detecting extrasolar planets. Although there is an analytical expression for microlensing lightcurves produced by single lensing body, the generation of model lightcurves for more than one lensing body requires the use of numerical techniques. The method developed here, known as the semi-analytic method, involves the analytical rearrangement of the relatively simple ‘lens equation’ to produce a high-order complex lens polynomial. Root-finding algorithms are then used to obtain the roots of this ‘lens polynomial’ in order to locate the positions of the images and calculate their magnifications. By running example microlensing events through the root-finding algorithms, both the speed and accuracy of the Laguerre and Jenkins-Traub algorithms were investigated. It was discovered that, in order to correctly identify the image positions, a method involving solutions of several ‘lens polynomials’ corresponding to different coordinate origins needed to be invoked. Multipole and polygon approximations were also developed to include finite source and limb darkening effects. The semi-analytical method and the appropriate numerical techniques were incorporated into a C++ modelling code at VUW (Victoria University of Wellington) known as mlens2. The effectiveness of the semi-analytic method was demonstrated using mlens2 to generate theoretical lightcurves for the microlensing events MOA-2009-BLG-319 and OGLE-2006-BLG-109. By comparing these theoretical lightcurves with the observed photometric data and the published models, it was demonstrated that the semi-analytic method described in this thesis is a robust and efficient method for discovering extrasolar planets.</p>

Modelling of Planetary Gravitational Microlensing Events

<p>This thesis describes and develops procedures for the generation of theoretical lightcurves that can be used to model gravitational microlensing events that involve multiple lenses. Of particular interest are the cases involving a single lens star with one or more orbiting planets, as this has proven to be an effective way of detecting extrasolar planets. Although there is an analytical expression for microlensing lightcurves produced by single lensing body, the generation of model lightcurves for more than one lensing body requires the use of numerical techniques. The method developed here, known as the semi-analytic method, involves the analytical rearrangement of the relatively simple ‘lens equation’ to produce a high-order complex lens polynomial. Root-finding algorithms are then used to obtain the roots of this ‘lens polynomial’ in order to locate the positions of the images and calculate their magnifications. By running example microlensing events through the root-finding algorithms, both the speed and accuracy of the Laguerre and Jenkins-Traub algorithms were investigated. It was discovered that, in order to correctly identify the image positions, a method involving solutions of several ‘lens polynomials’ corresponding to different coordinate origins needed to be invoked. Multipole and polygon approximations were also developed to include finite source and limb darkening effects. The semi-analytical method and the appropriate numerical techniques were incorporated into a C++ modelling code at VUW (Victoria University of Wellington) known as mlens2. The effectiveness of the semi-analytic method was demonstrated using mlens2 to generate theoretical lightcurves for the microlensing events MOA-2009-BLG-319 and OGLE-2006-BLG-109. By comparing these theoretical lightcurves with the observed photometric data and the published models, it was demonstrated that the semi-analytic method described in this thesis is a robust and efficient method for discovering extrasolar planets.</p>

A Semi-Analytical Model for Gravitational Microlensing

<p>This thesis describes the theory and implementation of a semi-analytical model for gravitational microlensing. Gravitational microlensing is observed when a distant background `source' star comes into close alignment with an intermediate `lens' star. The gravitational eld of the lens de ects the paths of light emitted from the source, which causes an increase in its observed brightness. As the alignment of the two stars changes with time, the apparent magni cation of the source follows a well de ned `lightcurve'. A companion body (such as a planet) orbiting the lens star can introduce large deviations from the standard lightcurve, which can be modelled to determine a mass ratio and separation for the companion(s). This provides a means to detect extrasolar planets orbiting the lens star. We show, from basic principles, the development of the standard model of a mi- crolensing event, including the e ect of multiple lens masses and orbital motion. We discuss the two, distinctly di erent, numerical approaches that are used to calculate theoretical lightcurves using this model. The `ray shooting' approaches are discussed with reference to the previously developed modelling code (MLENS), which implemented them. This is followed by a comprehensive description of the `semi-analytical' approaches used in the new software (mlens2) developed during this thesis programme; a key feature of these techniques is the determination of the source magni cation from the roots of a high order polynomial. We also discuss the process of nding the best- t model for an observed microlensing event, with respect to the mlens2 software package. Finally, we demonstrate the capabilities of our semi-analytical model by generating theoretical lightcurves for the microlensing events OGLE-2005-BLG-390 and OGLE-2006-BLG-109 and comparing them to the observational data and published models.</p>

A Semi-Analytical Model for Gravitational Microlensing

<p>This thesis describes the theory and implementation of a semi-analytical model for gravitational microlensing. Gravitational microlensing is observed when a distant background `source' star comes into close alignment with an intermediate `lens' star. The gravitational eld of the lens de ects the paths of light emitted from the source, which causes an increase in its observed brightness. As the alignment of the two stars changes with time, the apparent magni cation of the source follows a well de ned `lightcurve'. A companion body (such as a planet) orbiting the lens star can introduce large deviations from the standard lightcurve, which can be modelled to determine a mass ratio and separation for the companion(s). This provides a means to detect extrasolar planets orbiting the lens star. We show, from basic principles, the development of the standard model of a mi- crolensing event, including the e ect of multiple lens masses and orbital motion. We discuss the two, distinctly di erent, numerical approaches that are used to calculate theoretical lightcurves using this model. The `ray shooting' approaches are discussed with reference to the previously developed modelling code (MLENS), which implemented them. This is followed by a comprehensive description of the `semi-analytical' approaches used in the new software (mlens2) developed during this thesis programme; a key feature of these techniques is the determination of the source magni cation from the roots of a high order polynomial. We also discuss the process of nding the best- t model for an observed microlensing event, with respect to the mlens2 software package. Finally, we demonstrate the capabilities of our semi-analytical model by generating theoretical lightcurves for the microlensing events OGLE-2005-BLG-390 and OGLE-2006-BLG-109 and comparing them to the observational data and published models.</p>

Detecting isolated stellar-mass black holes in the absence of microlensing parallax effect

ABSTRACT Gravitational microlensing can detect isolated stellar-mass black holes (BHs), which are believed to be the dominant form of Galactic BHs according to population synthesis models. Previous searches for BH events in microlensing data focused on long time-scale events with significant microlensing parallax detections. Here we show that, although BH events preferentially have long time-scales, the microlensing parallax amplitudes are so small that in most cases the parallax signals cannot be detected statistically significantly. We then identify OGLE-2006-BLG-044 to be a candidate BH event because of its long time-scale and small microlensing parallax. Our findings have implications to future BH searches in microlensing data.