# Models of Bars I: Flattish Profiles for Early-Type Galaxies

## TL;DR

This paper introduces a new family of barred galaxy models with flat rotation curves and flattish density profiles, revealing novel orbital structures and stability features relevant to early-type galaxies.

## Contribution

The paper presents a simple, analytically constructed barred galaxy model with flat rotation curves and unique orbital dynamics, differing from previous elliptical models.

## Key findings

- Models exhibit highly triaxial inner regions and spheroidal outer parts.
- Orbital analysis reveals additional Lagrange points and off-centered trapped orbits.
- Bar strength influences orbital stability and the presence of $x_1$ and $x_4$ orbit families.

## Abstract

We introduce a simple family of barred galaxy models with flat rotation curves. They are built by convolving the axisymmetric logarithmic model with a needle density. The density contours in the bar region are highly triaxial and elongated, but become spheroidal in the outer parts. The mass distribution differs markedly from the elliptical shape assumed in other analytical models, like Ferrers or Freeman bars. The surface density profile along the bar major axis is flattish, as befits models for bars in early-type galaxies (SB0, SBa). The two-dimensional orbital structure of the models is analysed with surfaces of section and characteristic diagrams and it reveals qualitatively new features. For some pattern speeds, additional Lagrange points can exist along the major axis, and give rise to off-centered, trapped orbits. When the bar is weak, the orbital structure is very simple, comprising just prograde, aligned $x_1$ orbits and retrograde anti-aligned $x_4$ orbits. As the bar strength increases, the $x_1$ family becomes unstable and vanishes, with propeller orbits dominating the characteristic diagram.