The rotation curve of the Galaxy: results
We can thus derive the circular velocity by measuring
the largest velocity where emission from HI is observed for each longitude.
The results of this study are shown in Fig.2 (Fig.2.19
from Sparke & Gallagher)
Note that the variation of V(R) is not completely smooth. This is due to
the presence of spiral arms whose gravitational pull on the HI gas can induce
velocity changes of the order of 10-20 km/s. Thus if the tangent point is
located close to a spiral arm, the velocity measured will differ from the
average speed of a circular orbit at that radius.
The determination of the circular velocity in the outer Galaxy is more difficult
(since the distance to the gas is unknown). It is possible to use distances
to cepheids, young stellar associations (obtained from spectroscopic or
photometric parallax methods, etc.), and measure their radial velocity from
the emission lines of cold or hot gas around the stars. Such distances are
sufficiently accurate to show without doubt that the rotation speed V(R) does
not decline much in the outer Galaxy, and even that it may be rising.
We shall see later that the
circular velocity at a given radius V(R) is related to the mass interior to
that radius M(<R) by
M(< R) = R V2/G
Since V(R) does not decline, this means that the mass of the Milky Way
must increase almost linearly with radius, even in the outer Galaxy where
there are much fewer stars observed.
This discrepancy between the light and the mass is a common phenomenon
in spiral galaxies. Galaxies presumably contain a large amount of matter
that does not emit any light: this is the dark-matter.