Abstract
An accurate computational method is presented for determining the mass distribution in a mature spiral galaxy from a given rotation curve by applying Newtonian dynamics for an axisymmetrically rotating thin disk of finite size with or without a central spherical bulge. The governing integral equation for mass distribution is transformed via a boundary-element method into a linear algebra matrix equation that can be solved numerically for rotation curves with a wide range of shapes. To illustrate the effectiveness of this computational method, mass distributions in several mature spiral galaxies are determined from their measured rotation curves. All the surface mass density profiles predicted by our model exhibit approximately a common exponential law of decay, quantitatively consistent with the observed surface brightness distributions. When a central spherical bulge is present, the mass distribution in the galaxy is altered in such a way that the periphery mass density is reduced, while more mass appears toward the galactic center. By extending the computational domain beyond the galactic edge, we can determine the rotation velocity outside the cut-off radius, which appears to continuously decrease and to gradually approach the Keplerian rotation velocity out over twice the cut-off radius. An examination of circular orbit stability suggests that galaxies with flat or rising rotation velocities are more stable than those with declining rotation velocities especially in the region near the galactic edge. Our results demonstrate the fact that Newtonian dynamics can be adequate for describing the observed rotation behavior of mature spiral galaxies.
Highlights
Without direct means for accurate measurement, mass distribution in galaxies—gravitationally bound assemblies of (105 –1012 ) stars—can only be inferred from the observable information according to the known physical laws
While Feng and Gallo [12] focused mainly on illustrating the computational method with a few idealized rotation curves, we apply this method to the in-depth evaluation of the realistic rotation curves available in the open literature We extend our method to including the spherical central core and bulge, to further applications, such as for determining rotation velocity beyond the cut-off radius, and so on and so forth
With the computational method presented here, mass distributions in mature spiral galaxies corresponding to various types of measured rotation curves can be accurately determined by solving a linear algebra matrix equation, which clarifies the uniqueness of the solution when it exists
Summary
Without direct means for accurate measurement, mass distribution in galaxies—gravitationally bound assemblies of (105 –1012 ) stars—can only be inferred from the observable information according to the known physical laws. The observable information is usually carried by electromagnetic radiation—the light—emitted from the visible objects. The light can be analyzed to provide information about the emitting objects, such as their material constituents, surface temperature, distance, moving velocity, etc. The speed of the circular motion of objects in galaxies can be determined from the Doppler shift of light, and its plot against the galactocentric distance is called the rotation curve or circular speed curve. The measured rotation curve has been considered to provide the most reliable information for deriving the mass distribution in thin-disk galaxies [2,3]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
