Nuclear Energy Generation and Dissipation in Galaxies

The amount of helium in our galaxy as a whole is hard to estimate. There is considerable uncertainty in the H/He ratio in young stars and planetary nebulae, where it can directly be measured; a mean value of 10 (in numbers of atoms) may not be unreasonable. However, if we accept the idea that all of the helium has been produced by the burning of hydrogen in stars, it is probable that this value is not representative of the Galaxy as a whole but is too high, since a large part of the mass is tied up in old small-mass stars that have processed only a very minute fraction of their hydrogen. Thus a lower and therefore more conservative estimate is that 10% of the total mass of all of the Galaxy has been converted to helium. The energy released by this fusion process would amount to 8.7 X 1061 ergs. Now the luminosity of the Galaxy is not known, but it cannot be very different from that of M 31 which has Mvg = -19.95. The most luminous galaxies known do not exceed absolute magnitudes of 20 or so. This corresponds to a rate of radiation of 5 X 1043 ergs/sec. Thus if all of the thermonuclear energy released in transmuting hydrogen to helium had been radiated by stars in the Galaxy, it would have taken about 1011 years, whereas it is generally believed that the Galaxy is only about 1010 years old. This paradox cannot be avoided by supposing that a large part of the energy goes into the generation of motions in the interstellar gas, if this kinetic energy has remained at a constant level. The total energy contained in this gas amounts to some 1055 to 1056 ergs and none of the dissipation mechanisms, such as collisions in the gas, magnetic dissipation, or generation of cosmic rays, is so powerful at the present time that renewal of this energy every 104 years as would be required to remove the discrepancy is to be expected. We are forced to conclude, therefore, that unless there is some large-scale radiation continuously being emitted in wavelength