Finding planets with microlensing
Article by Y. Tsapras
Gravitational microlensing, or simply microlensing, occurs any time two stars pass within ~1 milli-arcsecond of each other on the plane of the sky. The gravitational field of the lens star causes light rays from the background source star to be deflected, resulting in a temporary increase in the brightness of the source star, as seen from the Earth. The simplified geometry of a single-lens, single-source microlensing event is illustrated in Fig. 1. For all practical cases of interest, the images produced by galactic stellar microlensing are unresolvable by telescopes, and only variations in the brightness of the source star are observed.
The figure above shows a face-on view of the geometry of a single-lens microlensing event. Two images (red contours) of the source star appear around the Einstein ring of the lens (black dot). The path of the source is indicated by the blue line. Four more source trajectories are shown with different colored lines. b) Total magnification as a function of time for the trajectories shown in panel a. The filled blue circle marks the instantaneous magnification when the source is at the corresponding position (filled blue circle) in panel a.
The relative motions between the stars in the Galaxy produce microlensing events that typically last for a few weeks to a few months. Surveys of the Galactic bulge identify about 2000 new microlensing events each year. The majority of these are due to single lenses, typically low-mass K or M-dwarf stars, the most common stellar types in the Galaxy. However, the lens can also be a binary system consisting of a star and a planet. In this case, if the planet passes close to one of the images generated by the lensing event,it can cause pronounced but short-lived deviations (anomalies) in an otherwise symmetric light-curve (Fig. 2).
Fig. 2 displays the light curve of planetary microlensing event OGLE-2015-BLG-0966 showing the observations from 10 different telescopes in different colours. The planetary anomaly is due to a cold Neptune planet with mass ~20 𝑀⊕, which orbits a 0.38 𝑀⊙ M-dwarf host star lying 2.5–3.3 kpc toward the Galactic centre. The Spitzer observations from space (blue) are shifted with respect to the ground-based ones because the lensing geometry of the event looks different from space. Combining space and ground-based data allows the microlensing parallax 𝜋𝐸 to be well constrained, leading to tight limits on the mass of the planet. (Figure from Street et al. 2016).
To first order, the mass of the planet does not affect the magnitude of these deviations, but it does influence their duration. A Jupiter-mass planet would produce deviations that might last for a day or two, while an Earth-mass planet would only reveal itself for a few hours (Beaulieu et al. 2006, Street et al. 2018, Tsapras et al. 2018). This sets the minimum observing cadence required to detect planetary signals in microlensing events.
What ultimately determines the degree of success in identifying and characterising planetary signals in microlensing events is the timeliness, quantity and quality of the observations. Because microlensing events do not repeat, it is essential that anomalies are identified in real time and as early as possible, in order to initiate high-cadence observations over the affected part of the light curve. If the anomalous feature is not sampled frequently enough, it becomes difficult to interpret the event through modelling and the physical parameters cannot be well constrained, leading to degenerate solutions (Dominik et al. 2009).
Microlensing is an efficient and cost-effective method for discovering exoplanets beyond the H2O snow line - particularly at distances between 1 to 10 au - as it can be conducted using small telescopes and does not require observations over a significant portion of the orbital period (Fig. 3). Instead, it relies on detecting the photometric signature of gravitational perturbations to the light from a background source star, which only lasts for a few days in the case of planets.
Planet-finding techniques are complementary. In Fig.3, the semi-major axis has been scaled to the approximate location of the snow-line of the planet-hosting star (assuming 𝑎𝑠𝑛𝑜𝑤≈2.85𝑀∗3/2AU). The Transit and radial velocity methods are exceptionally good at finding “Hot” planets closer to their host stars, whereas microlensing and direct imaging are more efficient in discovering “cold” planets. The solar system planets are also indicated as large coloured circles and marked by their initials. (Data from the NASA exoplanet archive)
In addition, microlensing is also uniquely sensitive to planetary systems located several kiloparsecs away from the Solar system, while other methods can only detect exoplanets within a radius of a few hundred parsecs. This is significant because there is a proposed correlation between stellar metallicity and planet formation rate (Wang & Fischer 2015, Adibekyan 2019), suggesting that metal-rich environments closer to the centre of the Galaxy are associated with higher efficiency in planet formation. This could potentially result in a different statistical distribution of exoplanets compared to those observed in planet-hosting systems closer to the Solar neighbourhood. In this respect, microlensing is the only method that can offer an unbiased view of the full Galactic population of planets (Tsapras 2018).
To improve our understanding of planetary system formation and evolution, it is crucial to extend the census of exoplanets to include terrestrial-mass objects beyond the H2O snow-line and to also consider stars far from the Sun’s immediate neighbourhood. In the coming years, new microlensing discoveries will gradually provide a statistically significant exoplanet sample in other regions of the Galaxy, allowing for direct comparisons with theoretical predictions of different formation scenarios and the improvement of models of the underlying physical processes.
