# Circumnuclear rings and Lindblad resonances in spiral galaxies

## TL;DR

This study investigates the relationship between circumnuclear rings and Lindblad resonances in spiral galaxies by analyzing spectral data and constructing rotation curves, confirming that rings are located near these resonances.

## Contribution

The paper provides new observational evidence linking circumnuclear rings to inner Lindblad resonances using spectral analysis and resonance modeling in spiral galaxies.

## Key findings

- CNRs are located between inner and outer ILRs or between the center and ILR.
- The angular velocity pattern ranges from 26 to 47 km s$^{-1}$ kpc$^{-1}$.
- The ratio R$_{CR}$/R$_{bar}$ is between 1.1 and 1.6, consistent with previous studies.

## Abstract

In order to study the location of circumnuclear rings (CNR) and their possible relation with the inner Lindblad resonances (ILR), we investigate a sample of spiral galaxies. For this purpose, we have obtained and analyzed medium resolution spectra of 5 spiral galaxies in the range 6200 \AA \ to 6900 \AA.\, Through the H$\alpha$ emission line, we constructed the radial velocity curves, and then the rotation curves. By fitting them, considering two or three components of an axisymetric Miyamoto$-$Nagai gravitational potential, we constructed the angular velocity and Lindblad curves. In addition, we determined the CNR radius by using the 2D spectra and generating the H$\alpha$ spatial emission radial profiles. We determined the position of the resonances and we calculated the angular velocity pattern, which are in the range of 26 $-$ 47 km s$^{-1}$ kpc$^{-1}$ for the galaxies of the sample. According to our results, the CNRs are located between the inner ILR (iILR) and the outer ILR (oILR), or between the center of the galaxy and the ILR, when the object has only one of such resonance; in agreement with previous results. In addition, we calculated the dimensionless parameter defined as $\mathcal{R}=$ R$_{CR}$ / R$_{bar}$, being in the range 1.1 $-$ 1.6, in agreement with previous results found in the literature.