Evidence of Systematic Errors in $Spitzer$ Microlens Parallax Measurements

Naoki Koshimoto, David Bennett

Published 2019-05-14Version 1

The microlensing parallax campaign with the $Spitzer$ space telescope aims to measure masses and distances of microlensing planetary events seen towards the Galactic bulge. The hope is to measure how the distribution of planets depends on position within the Galaxy. In this paper, we compare 50 microlens parallax measurements from 2015 $Spitzer$ campaign to three different Galactic models commonly used in microlensing analyses, and we find that $\geq 80\,$\% of these events have microlensing parallax values higher than the medians predicted by Galactic models. We use the Anderson-Darling (AD) and Kolmogorov-Smirnov (KS) tests on the distributions of the prior probability that the each of the $Spitzer$ parallax measurements is at least as large as the observed microlensing parallax values. These tests indicate probabilities of $p_{\rm AD} < 3.0 \times 10^{-8}$ and $p_{\rm KS} < 4.1 \times 10^{-6}$ that the data are consistent with these Galactic models from the AD and KS tests respectively. Given that many $Spitzer$ light curves show evidence of large correlated errors, we conclude that this discrepancy is probably due to systematic errors in the $Spitzer$ photometry. We consider a simple scheme to correct for this problem by multiplying the reported error bars on the $Spitzer$ microlensing parallax measurements by a constant factor, and we find that an error bar renormalization factor of 3.4 provides reasonable agreement with all three Galactic models. We expect, however, that corrections to the uncertainties in the $Spitzer$ photometry itself are likely to be a more effective way to address the systematic errors. We also argue that is important to include the ${\bm \pi_{\rm E}}$ prior distributions when analyzing events with large uncertainties or degeneracies in ${\bm \pi_{\rm E}}$ measurements.