Indication of a mass-dependent anisotropy above $10^{18.7}\,$eV in the hybrid data of the Pierre Auger Observatory

We test the hypothesis of an anisotropy laying along the galactic plane which depends on the mass of primary cosmic-rays. The sensitivity to primary mass is provided by the depth of shower maximum, $X_\text{max}$, from hybrid events measured at the Pierre Auger Observatory. The 14 years of available data are split into on- and off-plane regions using the galactic latitude of each event to form two distributions in $X_\text{max}$, which are compared using the Anderson-Darling 2-samples test. A scan over a subset of the data is used to select an optimal threshold energy of $10^{18.7}$ eV and a galactic latitude splitting at $|b| = 30^\circ$, which are then set as a prescription for the remaining data. With these thresholds, the distribution of $X_\text{max}$ from the on-plane region is found to have a $9.1 \pm 1.6^{+2.1}_{-2.2}$ g/cm$^{2}$ shallower mean and a $5.9\pm2.1^{+3.5}_{-2.5}$ g/cm$^{2}$ narrower width than that of the off-plane region. These differences are as such to indicate that the mean mass of primary particles arriving from the on-plane region is greater than that of those coming from the off-plane region. Monte-Carlo studies yield a $4.4\,\sigma$ post-penalization statistical significance for the independent data. Including the scanned data results in a $4.9^{+1.4}_{-1.5}\,\sigma$ post-penalization statistical significance, where the uncertainties are of systematic origin. Accounting for systematic uncertainties leads to an indication for anisotropy in mass composition above $10^{18.7}$ eV at a confidence level of $3.3\,\sigma$. The anisotropy is observed independently at each of the four fluorescence telescope sites. Interpretations of possible causes of the observed effect are discussed.