Mass Distribution of Spiral Galaxies in a Thin Disk Model with Velocity Curve Extrapolation

TL;DR

This paper presents a simplified thin disk model to derive mass distributions of spiral galaxies directly from their rotational velocity curves, including extrapolation techniques, and applies it to multiple galaxies to infer dark matter presence.

Contribution

It introduces a streamlined method for calculating galaxy mass density from velocity curves with extrapolation, tested on known models and applied to real galaxies.

Findings

Mass density can be reconstructed accurately with sufficient velocity data.

Total galaxy mass correlates with the extent of the flat velocity curve.

High light-to-mass ratios indicate dark matter presence.

Abstract

We model a spiral galaxy by a thin axially symmetric disk that includes both visible and dark matter. The surface mass density of the disk is calculated directly from the rotational velocity curve without extra assumptions. We simplify the standard application of the model. Since most velocity curves are known out to some radius, r_{max}, we extrapolate them by attaching a Keplerian tail. The numerical procedure and the extrapolation are tested with a known toy mass density and shown to reconstruct it with a good precision if r_{max} includes a sufficient part of the velocity curve. Mass density curves are calculated for Milky Way and NGC 3198. We vary the extent of the flat part of the velocity curves from 30 kpc to 200 kpc and show that does not affect appreciably the calculated mass density inside r_{max}=30 kpc. The reconstructed masses for Milky Way are 15 x 10^10 solar masses inside the visible disk and 23 x 10^10 solar masses inside 30 kpc. For NGC 3198, the reconstructed mass inside the visible disk is 6.5 x 10^10 solar masses and 11 x 10^10 solar masses inside 30 kpc. The total galactic masses are roughly proportional to the extent of the flat part of the velocity curves which is currently unknown. The high light-to-mass ratios obtained for the visible disks of the galaxies - 11 solar units for Milky way and 9.3 for NGC 3198 - suggest presence of dark matter. The method is also applied to NGC 3031 - a spiral galaxy with a declining velocity curve in which case it is able to reconstruct both the mass density curve and the total mass (14 x 10^10 solar masses).