Orientation of orbital planes of planetary systems detected in microlensing campaigns

Abstract

Galactic microlensing has the capability to determine the position angle of the detected planets in a sky reference frame. By a broad enough statistics, it is possible to investigate possible anisotropies in the distribution of the orbital planes of the planetary systems. We select 66 published microlensing planets suitable for such study and test the hypothesis that such orientations are randomly distributed against the possibility that the orbital planes follow some preferential alignment. The whole sample seems to be overall isotropically distributed, but by re-binning according to the distance along the line of sight, we find some local anisotropy peaks. Excluding those coming from very poor statistics or possible systematics, the anisotropy at 3 kpc may suggest a preferential alignment of planetary orbits in the Scutum-Centaurus spiral arm of the Milky Way with the Galactic plane. Special orientations of the orbital planes may be reminiscent of the specific conditions that triggered and drove the star formation processes and how these are related to local and global Galactic kinematics. Using the method proposed here, the future Roman microlensing survey will be able to identify and quantify preferential orientations in all structures from the Sun to the bulge with high confidence and accuracy.

Figures (10)

• Figure 1: Geometric determination of the planet position angle $PA$ in a microlensing event. The angle $\alpha$ between the host-planet direction and the proper motion $\mathbf{\mu}_{rel}$ of the lens relative to the source is very precisely constrained from the modeling of the microlensing light curve. The North-East components of the proper motion are determined by the parallax effect or by high-resolution imaging. The blue axes represent the North and East directions, while the green axes represent the directions for increasing Galactic latitude $b$ and longitude $l$.
• Figure 2: Relative position in the sky of the microlensing planets with respect to their hosts. Different colors distinguish planets in different distance intervals from the Solar System; the best models are shown with full color, while alternative disfavored models, when present, are shown in a more transparent color. The directions of increasing Galactic latitude $b$ and longitude $l$ are marked, together with the ecliptic plane. The dashed colorful line marks the preferential plane we find for planets in the $2-4$ kpc range (blue). Circles mark projected separations from the host in units of au.
• Figure 3: Assumed distributions for the orbital angular momenta of individual planets with respect to the reference direction $\hat{R}$ for different values of $q$: $q=0$ corresponds to an isotropic distribution. For visualization purposes, distributions have been normalized to one at $\cos i=1$.
• Figure 4: Normalized probability distribution for the position angle $PA'$ of planets with respect to the reference direction $\hat{R}$ for different values of the anisotropy parameters $q$.
• Figure 5: Example of microlensing efficiency for planet detection as a function of the angle $\alpha$ between the planet-lens axis and the relative proper motion between lens and source. This plot is calculated for $s=0.8$