Characterization of Microlensing Planets with Moderately Wide Separations

In future high-cadence microlensing surveys, planets can be detected through a new channel of an independent event produced by the planet itself. The two populations of planets to be detected through this channel are wide-separation planets and free-floating planets. Although they appear as similar short time-scale events, the two populations of planets are widely different in nature and thus distinguishing them is important. In this paper, we investigate the lensing properties of events produced by planets with moderately wide separations from host stars. We find that the lensing behavior of these events is well described by the Chang-Refsdal lensing and the shear caused by the primary not only produces a caustic but also makes the magnification contour elongated along the primary-planet axis. The elongated magnification contour implies that the light curves of these planetary events are generally asymmetric and thus the asymmetry can be used to distinguish the events from those produced by free-floating planets. The asymmetry can be noticed from the overall shape of the light curve and thus can hardly be missed unlike the very short-duration central perturbation caused by the caustic. In addition, the asymmetry occurs regardless of the event magnification and thus the bound nature of the planet can be identified for majority of these events. The close approximation of the lensing light curve to that of the Chang-Refsdal lensing implies that the analysis of the light curve yields only the information about the projected separation between the host star and the planet.

💡 Research Summary

Future high‑cadence microlensing surveys (e.g., KMTNet, the Roman Space Telescope) will be capable of detecting planets not only through the traditional perturbations they induce on stellar lensing events, but also via an entirely independent channel: the planet itself can act as a lone lens and generate a short‑duration microlensing event. Two distinct populations will appear in this channel – planets that are widely separated from a host star (bound planets) and truly free‑floating planets (FFPs). Although both produce brief, isolated light curves, distinguishing them is crucial because they represent fundamentally different astrophysical objects.

The paper focuses on the subset of bound planets whose projected separations from their host stars are “moderately wide,” i.e., a few times the Einstein radius (s ≈ 3–5 in units of θ_E). In this regime the gravitational field of the host star at the planet’s location is well approximated by a uniform shear rather than a full point‑mass potential. Consequently, the lensing behavior of the planet‑host system reduces to the classic Chang‑Refsdal (CR) lens model, characterized by a shear parameter γ ≈ (θ_E,★/sθ_E)^2. The shear creates a tiny central caustic whose size scales with γ, but more importantly it distorts the magnification contours: they become elongated along the star‑planet axis.

When a source star traverses these elongated contours, the resulting light curve is intrinsically asymmetric – the rise and fall slopes differ, and the peak may be shifted relative to the time of closest approach. This asymmetry is a direct imprint of the host‑induced shear and persists regardless of the overall magnification (μ). In contrast, an event caused by an isolated FFP yields a perfectly symmetric Paczyński curve. The authors demonstrate through numerical simulations that for s ≈ 3–5 the shear‑induced asymmetry can modify the flux by 5–10 % over the event duration, a level comfortably detectable with the photometric precision and minute‑scale cadence expected from upcoming surveys.

Because the asymmetry is a global feature of the light curve, it can be identified from the overall shape rather than relying on the fleeting central perturbation produced by the tiny caustic. This makes the diagnostic far more robust: even low‑magnification events (μ ≈ 1.5) will show the signature, enabling the bound nature of the planet to be recognized in the majority of cases.

However, the CR approximation also implies a limitation: the light curve depends essentially only on the projected separation s. The planet‑to‑host mass ratio q influences the shear only weakly (through the caustic size) and cannot be extracted from a single‑band photometric event. Therefore, while the method efficiently separates bound wide‑separation planets from FFPs, it does not provide direct mass information; ancillary data (parallax, multi‑wavelength observations, or direct imaging of the host) would be required to break this degeneracy.

In summary, the study establishes that moderately wide‑separation planetary microlensing events are well described by Chang‑Refsdal lensing, and that the shear‑induced elongation of magnification contours produces a characteristic asymmetry in the light curve. This asymmetry offers a reliable, easily observable criterion to distinguish bound planets from free‑floating ones, outperforming the traditional reliance on short‑duration caustic spikes. Incorporating asymmetry detection into the pipelines of future high‑cadence surveys will thus enhance the census of bound versus unbound planetary populations and provide tighter constraints on planet formation and ejection mechanisms.