▪ Abstract Rotation curves of spiral galaxies are the major tool for determining the distribution of mass in spiral galaxies. They provide fundamental information for understanding the dynamics, evolution, and formation of spiral galaxies. We describe various methods to derive rotation curves and review the results obtained. We discuss the basic characteristics of observed rotation curves in relation to various galaxy properties, such as Hubble type, structure, activity, and environment.

We present a unified rotation curve of the Galaxy re-constructed from existing data by re-calculating the distances and velocities for a set of Galactic constants, $R_0$$=$ 8 kpc and $V_0$$=$ 200 km s$^{-1}$. We decomposed it into a bulge with de Vaucouleurs-law profile of half-mass scale radius 0.5 kpc and mass 1.8 $\times$ 10$^{10}M_\odot$, an exponential disk of scale radius 3.5 kpc and 6.5 $\times$ 10$^{10}M_\odot$, and an isothermal dark halo of terminal velocity 200 km s$^{-1}$. A $r^{1/4}$-law fit was obtained for the first time for the Milky Way’s rotation curve. After fitting by these fundamental structures, two local minima, or dips, of the rotation velocity are prominent at radii 3 and 9 kpc. The 3-kpc dip is consistent with the observed bar. It is alternatively explained by a massive ring with the density maximum at a radius of 4 kpc. The 9-kpc dip is clearly exhibited as the most peculiar feature in the Galactic rotation curve. We explain it by a massive ring of amplitude as large as 0.3 to 0.4-times the disk density with the density peak at a radius of 11 kpc. This great ring may be related to the Perseus arm, while no peculiar feature of HI-gas is associated.

Analyzing high-resolution longitude–velocity (LV) diagrams of the Galactic Center observed with the Nobeyama 45-m telescope in the CO and CS line emissions, we obtained a central rotation curve of the Milky Way. We combined it with data for the outer disk, and constructed a logarithmic rotation curve of the entire Galaxy. The new rotation curve covers a wide range of radius from r ∽ 1 pc to several hundred kpc without a gap of data points. It links, for the first time, the kinematical characteristics of the Galaxy from the central black hole to the bulge, disk and dark halo. Using this grand rotation curve, we calculated the radial distribution of the surface mass density in the entire Galaxy, where the radius and derived mass densities vary over a dynamical range with several orders of magnitudes. We show that the galactic bulge is deconvolved into two components: the inner (core) and main bulges. Both of the two bulge components are represented by exponential density profiles, but the de Vaucouleurs law was found to fail to represent the mass profile of the galactic bulge.

We review the current status of the study of rotation curve (RC) of the Milky Way, and present a unified RC from the Galactic Center to the galacto-centric distance of about 100 kpc. The RC is used to directly calculate the distribution of the surface mass density (SMD). We then propose a method to derive the distribution of dark matter (DM) density in the in the Milky Way using the SMD distribution. The best-fit dark halo profile yielded a local DM density of ${\rho }_{\odot }=0.36\pm 0.02$ GeV cm ${}^{-3}$ . We also review the estimations of the local DM density in the last decade, and show that the value is converging to a value at ${\rho }_{\odot }=0.39\pm 0.09$ GeV cm ${}^{-3}$ .

Grand rotation curves (GRC) within ∼ 400 kpc of M 31 and the Milky Way were constructed by combining disk rotation velocities and radial velocities of satellite galaxies and globular clusters. The GRC for the Milky Way was revised using the most recent solar rotation velocity. The derived GRCs were deconvolved into a de Vaucouleurs bulge, exponential disk, and a dark halo with a Navarro–Frenk–White (NFW) density profile by least-χ² fitting. Comparison of the best-fitting parameters revealed similarities between the disks and bulges of the two galaxies, whereas the dark-halo mass of M 31 was found to be twice that of the Galaxy. We show that the NFW model may be a realistic approximation of the observed dark halos in these two giant spirals.

Rotation curves are the basic tool for deriving the distribution of mass in spiral galaxies. In this review, we describe various methods to measure rotation curves in the Milky Way and spiral galaxies. We then describe two major methods to calculate the mass distribution using the rotation curve. By the direct method, the mass is calculated from rotation velocities without employing mass models. By the decomposition method, the rotation curve is deconvolved into multiple mass components by model fitting assuming a black hole, bulge, exponential disk, and dark halo. The decomposition is useful for statistical correlation analyses among the dynamical parameters of the mass components. We also review recent observations and derived results.