4.3. Mass Discrepancy on the Periphery of Galaxies
The second problem encountered in the modelling of M31 was the rotation and density distribution on the periphery. If the rotation data were taken at face value, then it was impossible to represent the rotational velocity with the sum of gravitational attractions by known stellar populations. The local value of M / L increases toward the periphery of M31 very rapidly if the mass distribution is calculated directly from the rotation velocity. All known old metal-poor halo-type stellar populations have a low M / L 1; in contrast, on the basis of rotation data we got M / L > 1000 on the periphery of the galaxy, near the last point with a measured rotational velocity.
There were two possibilities to solve this controversy: to accept the presence of a new population with a very high M / L (a very uncommon property for an old stellar population), or to assume that on the periphery of galaxies there exist non-circular motions. We found that the first alternative had several serious difficulties. If the hypothetical population is of stellar origin, it must be formed much earlier than conventional populations, because all known stellar populations form a continuous sequence of kinematical and physical properties (Oort 1958, Rootsmäe 1961, Einasto 1974a), and there is no place where to include this new population in this sequence. Secondly, the star formation rate is proportional to the square of the local density (Schmidt 1959, Einasto 1972), thus stars of this population should have been formed during the contraction phase of the formation of the population near its central more dense regions (where the density is largest), and later expanded to the present distance. The only source of energy for expansion is the contraction of other stellar populations. The estimated total mass of the new population exceeded the summed mass of all previously known populations. Estimates of the energy needed for the expansion demonstrated that the mass of the new population is so large that even the contraction of all other stellar populations to a zero radius would not be sufficient to expand the new population to its present size. And, finally, it is known that star formation is not an efficient process (usually in a contracting gas cloud only about 1 % of the mass is converted to stars); thus we have a problem how to convert, in an early stage of the evolution of the Universe, a large fraction of primordial gas into this population of stars. Taking into account all these difficulties I accepted the second alternative - the presence on non-circular motions (Einasto 1969b), similar to many other astronomers (see Materne & Tammann 1976). As I soon realised, this was a wrong decision.