# Accounting for Incompleteness due to Transit Multiplicity in Kepler Planet Occurrence Rates

## TL;DR

This study examines how detection order affects Kepler planet detection efficiency, revealing a significant bias in observed multiplicity and providing a refined model for planet occurrence rates that accounts for detection incompleteness.

## Contribution

It introduces a method to account for detection order effects in Kepler data, improving estimates of planet occurrence and multiplicity distributions.

## Key findings

- Detection efficiency drops by 5.5% for periods <200 days and 15.9% for >200 days due to detection order.
- Only about 4% of GK dwarfs host a planet, lower than previous estimates.
- Average planets per GK dwarf are estimated at approximately 5.86 within Kepler's parameter space.

## Abstract

We investigate the role that planet detection order plays in the Kepler planet detection pipeline. The Kepler pipeline typically detects planets in order of descending signal strength (MES). We find that the detectability of transits experiences an additional $5.5\%$ and $15.9\%$ efficiency loss, for periods $<200$ days and $>200$ days respectively, when detected after the strongest signal transit in a multiple-planet system. We provide a method for determining the transit probability for multiple-planet systems by marginalizing over the empirical Kepler dataset. Furthermore, because detection efficiency appears to be a function of detection order, we discuss the sorting statistics that affect the radius and period distributions of each detection order. Our occurrence rate dataset includes radius measurement updates from the California Kepler Survey (CKS), Gaia DR2, and asteroseismology. Our population model is consistent with the results of Burke et al. (2015), but now includes an improved estimate of the multiplicity distribution. From our obtained model parameters, we find that only $4.0\pm4.6\%$ of solar-like GK dwarfs harbor one planet. This excess is smaller than prior studies and can be well modeled with a modified Poisson distribution, suggesting that the Kepler Dichotomy can be accounted for by including the effects of multiplicity on detection efficiency. Using our modified Poisson model we expect the average number of planets is $5.86\pm0.18$ planets per GK dwarf within the radius and period parameter space of Kepler.