Abstract

We study the velocity ellipsoids in an N-body + SPH (smooth particle hydrodynamics) simulation of a barred galaxy which forms a bar with a BP bulge. We focus on the 2D kinematics, and quantify the velocity ellipses by the anisotropy, βij , the correlation, ρij , and the v erte x deviation, l v . We e xplore the variations in these quantities based on stellar age within the bulge and compare these results with the Milky Way's bulge using data from APOGEE (Apache Point Observatory Galactic Evolution Experiment) DR16 and Gaia DR3. We first explore the variation of the model's velocity ellipses in galactocentric velocities, v R and v φ, for two bulge populations, a (relatively) young one and an old one. The bar imprints quadrupoles on the distribution of ellipse properties, which are stronger in the young population, as expected from their stronger bar. The quadrupoles are distorted if we use heliocentric velocities v r and v l . We then project these kinematics along the line of sight onto the (l, b)-plane. Along the minor axis βrl changes from positive at low | b| to ne gativ e at large | b| , crossing o v er at lower | b| in the young stars. Consequently, the v erte x deviation peaks at lower | b| in the young population, but reaches similar peak values in the old. The ρβrl is much stronger in the young stars, and traces the bar strength. The APOGEE stars split by the median [Fe / H] follow the same trends. Lastly, we explore the velocity ellipses across the entire bulge region in ( l, b) space, finding good qualitative agreement between the model and observations. © 2025 2025 The Author(s).