Determination of the relative inclination and the viewing angle of an interacting pair of galaxies using convolutional neural networks

Constructing dynamical models for interacting pair of galaxies as constrained by their observed structure and kinematics crucially depends on the correct choice of the values of the relative inclination ($i$) between their galactic planes as well as the viewing angle ($\theta$), the angle between the line of sight and the normal to the plane of their orbital motion. We construct Deep Convolutional Neural Network (DCNN) models to determine the relative inclination ($i$) and the viewing angle ($\theta$) of interacting galaxy pairs, using N-body $+$ Smoothed Particle Hydrodynamics (SPH) simulation data from the GALMER database for training the same. In order to classify galaxy pairs based on their $i$ values only, we first construct DCNN models for a (a) 2-class ( $i$ = 0 $^{\circ}$, 45$^{\circ}$ ) and (b) 3-class ($i = 0^{\circ}, 45^{\circ} \text{ and } 90^{\circ}$) classification, obtaining $F_1$ scores of 99% and 98% respectively. Further, for a classification based on both $i$ and $\theta$ values, we develop a DCNN model for a 9-class classification ($(i,\theta) \sim (0^{\circ},15^{\circ}) ,(0^{\circ},45^{\circ}), (0^{\circ},90^{\circ}), (45^{\circ},15^{\circ}), (45^{\circ}, 45^{\circ}), (45^{\circ}, 90^{\circ}), (90^{\circ}, 15^{\circ}), (90^{\circ}, 45^{\circ}), (90^{\circ},90^{\circ})$), and the $F_1$ score was 97$\%$. Finally, we tested our 2-class model on real data of interacting galaxy pairs from the Sloan Digital Sky Survey (SDSS) DR15, and achieve an $F_1$ score of 78%. Our DCNN models could be further extended to determine additional parameters needed to model dynamics of interacting galaxy pairs, which is currently accomplished by trial and error method.