1 Introduction

Rotation curves are a major tool for determining mass distribution in spiral galaxies. Assuming spherical mass distribution, the galactic mass M within a galactocentric radius R is estimated by

 

M = R V² / G, (1)

where V and G stand for a circular velocity and gravitational constant.

Rotation curves in their outer regions are generally flat (Rubin et al. 1980, 1982, 1985), indicating massive dark halos surrounding their optical disks (Kent 1987). In their central regions, many rotation curves rise steeply from the centers, reaching the high velocity seen in the outer flat rotation curves: typically 100-300 ${\rm ~ km ~ s^{-1}}$ within a central $100\pc$ radius (Sofue 1996; Sofue et al. 1999). These high velocities may indicate central massive cores of about $10^9~M_{\odot}$ within a central $100\pc$ radius (Sofue 1996; Sofue et al. 1999; Takamiya & Sofue 2000).

However, the gas in galactic disks does not necessarily show pure circular rotation, especially in the central regions. Bar-like distortions of the stellar system can drive non-circular (elliptical) motions for the gas. As a result, the apparent rotation curves do not represent the correct mass distribution. For example, if the elliptical orbits were aligned by chance with the line-of-sight, we would overestimate the mass (Sakamoto et al. 1999). The effect of non-circular motion on position-velocity diagrams has been intensively studied in theoretical calculations (Bureau & Athanassoula 1999; Athanassoula & Bureau 1999).

In this paper, we quantitatively study the errors in estimating the mass from rotation curves in galaxies with a weak bar, and calculate the probability that the observed mass suffers from such errors. Even if the bar-like distortion of the gravitational potential is very weak, the gas velocity-field can be non-axisymmetric (Wada 1994). In order to obtain the velocity-field of the gas in a weak bar potential, we performed Smoothed Particle Hydrodynamics (SPH) simulations (Sect. 2). Using the numerical results, we estimate the probability of overestimating the central galactic mass (Sect. 3). We discuss the implications of our results in Sect. 4.