In the optical spectrum of some bright nearby stars, spectral lines are observed which have not formed by absorption in the stellar atmosphere, but which arose by the interception of the starlight by interstellar matter. These interstellar absorption lines appear to occur at wavelengths which differ from those at which the cor¬responding atoms in the laboratory absorb radiation. This is due to the Doppler effect: we must conclude from these absorption lines that there exist interstellar clouds that move through the Galaxy. Comparison of the interstellar lines of stars close together in the sky shows that different clouds often have approximately the same velocities: apparently there is a systematic (that is, well-organized) motion in the interstellar gas. As we have seen, optical observations in the galactic plane are limited by observation to distances of a few kiloparsecs, but fortunately spectral lines also occur at radio wavelengths. The strongest of these lines are emission lines of atomic neutral hydrogen. The most extensively used to date is the line at 21-cm wavelength, due to a hyperfine transition in the hydrogen atom at 1421 MHz, theoretically predicted in 1946 and first observed in 1951. The radio spectral lines also show the Doppler effect, and since they can be seen right across and throughout the Galaxy it is possible to study the state of motion of the galactic gas on a very large scale (tens of kiloparsecs).

The mass distribution and the total mass of the Galaxy are closely connected with the shape of the GALACTIC ROTATION CURVE. Therefore, in order to determine these extremely important properties of our island in the Universe, it is crucial firstly to obtain the rotation curve. Radio astronomers have succeeded in doing this by observing the neutral hydrogen in a hypothetical circle drawn about a point half-way between the Sun and the galactic centre, and passing through the Sun . Let us assume that the gas moves in circular orbits about the galactic centre. Simple geometry then shows that at every point of the hypothetical circle the line of sight from the Sun makes a tangent to one particular circular orbit in the galactic plane. Therefore, all orbital velocities of matter which happen to pass across this SUBCENTRAL CIRCLE point directly towards the observer. This fact makes the subcentral circle very special, for on this circle the observed radial velocities are the highest attained along any chosen line of sight! In principle, it is possible to dream up odd-looking rotation curves for which this is not true, but the Galaxy could not stay very long in such a peculiar state of motion. Thus all of the above gives us the following recipe to determine the galactic rotation curve.

Firstly, observe the neutral hydrogen in a number of directions between longitudes 0° and 90°. Secondly, from the observed 21-cm line profile and the Doppler formula, find the velocity of the fastest-moving cloud along every line of sight. Thirdly, find out where these lines of sight intersect the subcentral circle. Fourthly, because the maximum velocities must lie on these intersections, we know what the velocity of rotation is on every circular orbit between the Sun and the galactic centre! However, as this recipe show, the rotation curve can only be found between the Sun and the galactic centre .

When these difficulties have been overcome, there still lies some hard work ahead to derive from the rotation curve the distribution of mass in the Galaxy. In order to see how such a MASS MODEL IS arrived at. consider again. It was mentioned there; that any object moving in a circular orbit about the galactic centre feels a net attraction only from the material within its orbit. Outbid this orbit, the attractive forces on the moving body all cancel each other exactly, because of the symmetrical distribution of the mat¬ter. Therefore, we reach the important conclusion that the difference of the velocities on two orbits (say orbits 2 and 3 )It depends exclusively on the difference in the amount of mass encompassed by these orbits (this difference is equal to the mass in region II . Building a mass modal, then, means constructing a series of nested shells of galactic matter, adjusted in such a way that the rotation curve of the model equals the rotation curve of the Galaxy. The adjustment is achieved by varying the shape and the density of the layers of this galactic onion. The number of mass shells taken is very large, so that the model appears smooth, for in reality the Galaxy is continuous instead of layered. Unfortunately, the adjustment in shape and in density leaves us too much freedom: many mass models are possible for one and the same rotation curve, because we have no information about the velocities everywhere in the Galaxy, especially at large distances from the plane and outside the solar orbit. The adjustment in shape must occur between two extreme models, namely the one in which the Galaxy is supposed to be entirely flat, and the one in which it is supposedly spherical. For both extreme cases, and for these only, it can be proven that there is a simple recipe to calculate the mass distribution. If the Galaxy is supposed to be perfectly flat, the mass within a certain radius is proportional to the square of the orbital velocity at that radius. U it is fully spherical, the mass is proportional to the radius times the square of the velocity. In between these extremes, everything & possible . Our Galaxy lies probably closer to the first extreme.

Once the rotation curve is determined, we have at our disposal a relationship between velocity and distance. If all interstellar gas moved accordingly, it would be possible to obtain the distance to every cloud by a simple measurement of its velocity. As an analogy, consider the Solar System, where the velocity-distance correlation is expressed in Kepler’s third law. Imagine that the planets are replaced by thin rings of neutral hydrogen gas. At a given geocentric longitude (the longitude measured from Earth) in the plane of the ecliptic, each imaginary ring of hydrogen which is cut by the line of sight gives an emission line at a certain velocity. When the observations at all longitudes are completed, the height of each hydrogen emission line is plotted against its longitude and its velocity. Each imaginary ring-shaped mock planet shows up as a ridge in this diagram. In observed longitude-velocity diagrams for interstellar gas ridges are clearly seen, so there appear to be structures in the disc which are roughly ring-shaped. Closer inspection reveals that these features are probably sections of spiral arms . However, there are many possible reconstructions of the lost third dimension, unless one assumes strictly that the gas clouds in the Galaxy all move in circular orbits. This appears unlikely, especially in the central regions. Therefore there is severe ambiguity in the interpretation of the 21-cm observations of the Galaxy: a line profile observed in a certain direction can be due to masses with radically different velocities and distributions in space.

Uncertainties of this kind have led to controversy over the distribution and dynamics of gas in the Galaxy. Especially near the centre of the system (within 5 kpc from the nucleus, say) problems are severe, because the longitude-velocity diagram of that region is very complicated. The most remarkable aspect of these observations is the presence of gas with non-zero velocities at zero longitude. As , this should not happen if galactic rotation were purely circular. Apparently radial motions in the central region occur systematically over distances of many kiloparsecs. Analysis shows that cloud collisions would destroy these motions well within the lifetime of the Galaxy. Therefore, there must be some agent which has thrown vast amounts of galactic gas out of its regular circular orbit in the plane. Probably, an explosion occurred in the galactic nucleus some 12 million years ago, hurling gaseous clouds of a million solar masses in two opposite directions inclined about 30° out of the plane. Thin traversed the relatively empty regions of the lower halo and fell back into the plane at about 3.5kpc from the centre, where it caused the radial motions which we observe today. If not all of the gas has yet fallen down, we expect to see gas with radial velocities outside the plane. Such motions are observed, in support of the notion that the nucleus was recently the scene of violent activity.

The overall strength of the 21-cm signal in the central part of the Galaxy is smaller than elsewhere in the disc. This does not necessarily mean that the centre is empty of gas, because the 21-cm line is only emitted under favourable circumstances. If the temperature is too high (1000K and higher), not enough atoms are in the correct state to emit the line. If the temperature is too low (below 100K), most atoms form H2 molecules and thereby lose the ability to emit the 21-cm line. In hot regions, such as the ionized regions near the galactic nucleus, it becomes feasible to use the radio recombination lines instead of the 21-cm line, with the same type of analysis as described above. In cold regions, the H2 molecule is of no avail, for it is a reluctant emitter. The carbon monoxide molecule, CO, is relatively abundant in cold regions and readily emits a radio spectral line (at 2.6mm wavelength); these properties make it well suited as a probe for cold clouds, and the spectral lines can be analysed as above.

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