Modeling the Impact of Unresolved Stellar Companions on Detection Sensitivity in Kepler's Small Planet Occurrence Rates

TL;DR

This study quantifies how unresolved stellar companions bias Kepler-derived small-planet occurrence rates by altering transit depths and detection sensitivity. It builds a Palomar adaptive optics imaging program to characterize both observed and undetected companions and integrates those corrections into a Bergsten2022-style occurrence model via extensive MCMC across four host-scenario treatments. The authors find that accounting for companions increases the inferred occurrence of small, close-in planets by roughly 1.08–1.19 and raises the habitable-zone Earth-like occurrence rate by factors of about 1.18–1.46, depending on the assumed companion rate. The work provides bounds on multiplicity-induced biases, highlights the importance of multiplicity-aware completeness corrections for exoplanet demographics, and informs planning for future missions targeting Earth-like planets (e.g., LUVOIR/HabEx) by clarifying how undetected companions can inflate yield expectations.

Abstract

Unresolved stellar companions can cause both under-estimations in the radii of transiting planets and over-estimations of their detectability, affecting our ability to reliably measure planet occurrence rates. To quantify the latter, we identified a control sample of 198 Kepler stars with sensitivity to Earth-like planets if they were single stars, and imaged them with adaptive optics. In 20% of systems, we detected stellar companions that were close enough to go unresolved in Kepler observations. We calculated the distribution of planet radius correction factors needed to adjust for these observed companions, along with simulations of undetected companions to which our observations were not sensitive. We then used these correction factors to optimize an occurrence rate model for small close-in planets while correcting Kepler's detection efficiency for the presence of unresolved companions, and quantified how this correction affects occurrence estimates. Median occurrence rates for small planets between $2-100$ days increased by an average factor of $1.08-1.19$ (depending on statistical treatments), with the largest differences found for smaller planets at larger orbital periods. We found that the frequency of Earth-sized planets in the habitable zone ($η_\oplus$) increased by a factor of ${1.18}_{-0.66}^{+0.43}-{1.46}_{-0.83}^{+0.53}$ when accounting for the effect of unresolved companions on Kepler's detection sensitivity.

Figures (7)

• Figure 1: The sample of Kepler FGK dwarf stars around which a 1 R$_\oplus$ planet receiving the same insolation as Earth could have been detected. The full set of 2,136 stars are shown in gray circles, using the stellar effective temperatures and (log) surface gravities available in Berger2020. The randomly selected subset of 198 Sun-like control stars we observed are shown in color: the set of control stars for which we found companions are shown in orange squares, while the control stars we did not detect companions around are shown in blue circles. Side panels show the corresponding histograms for the top: stellar effective temperature and right: surface gravity distributions.
• Figure 2: Example AO adaptive image and sensitivity curve for KIC 5961302 -- a V=13.7mag K4V Kepler target in our control sample. The resolution of the image is 0.109$^{\prime\prime}$ (FWHM of the PSF). The black points represent the measured sensitivity relative to the brightness of the target in FWHM radial steps from the target. The purple represents the azimuthal rms dispersion of the sensitivity measurements. The inset image is a 4$^{\prime\prime}$ zoom in on the target from the final fully mosaiced image which was approximately $17\hbox{$^{\prime\prime}$}\times17\hbox{$^{\prime\prime}$}$ in size.
• Figure 3: Imaged companions in our Kepler control sample, showing magnitude differences in the Kepler band as functions of projected left: on-sky or right: physical separations (measured with respect to the primary). Circle markers are colored and sized by the RUWE values of the primary star; black square markers indicate systems that did not have RUWE values available in Gaia DR3. The cut-off for on-sky separations to be included in our sample was roughly twice the Kepler pixel size ($\sim$8″).
• Figure 4: The probability distribution of planet radius correction factors from our Kepler control sample, assuming planets orbit left: the primary or right: the second-brightest star. Blue circles represent the distribution measured from the observed companions, orange squares represent the distribution measured from the simulated, undetected companions, while the black histogram represents a blend of those two distributions averaged in each bin.
• Figure 5: Modifications to the Kepler survey completeness for our sample, based on the simulated presence of stellar companions using left: the properties of our observed companion sample at their observed rate of 20% or right: a combination of properties from our observed and simulated undetected companions at the field rate of 45%. Top: the colormap denotes the original (i.e., Scenario 1) Kepler average survey completeness, with black solid contours at the 0.1, 1, and $10\%$ levels. Other contours represent the average completeness maps from scenarios where some stars are assigned companions, shifting their completeness grids vertically upwards. These shifts depend on radius correction factors drawn assuming planets orbit the primary (dotted, Scenario 2), secondary (dashed, Scenario 3), or a mix of the two (dot-dashed, Scenario 4). Bottom: the colormap denotes the ratio of average completeness maps with and without companions (Scenario 4 / Scenario 1). Contours show where the Scenario 4 map equals either 75, 80, or $90\%$ of the original Scenario 1 map.