On the Galactic Evolution of $D$ and $^3He$

The determined abundances of primordial $^4He$ and $^7Li$ provide a basis with which to test the standard model of big bang nucleosynthesis in conjunction with the other two light element isotopes $D$ and $^3He$, also produced in the big bang. Overall, consistency in the standard big bang nucleosynthesis model is best achieved for a baryon-to-photon ratio of typically $3 \times 10^{-10}$ for which the primordial value of $D$ is five times greater than the present observed abundance and about three times greater than the pre-solar value. We consider various models for the chemical evolution of the Galaxy to test the feasibility for the destruction of D without the overproduction of $^3He$ and overall metallicity. Models which are capable of achieving this goal include ones with a star formation rate proportional to the gas mass fraction or an exponentially decreasing star formation rate. We discuss the effect of parameters that govern the initial mass function and of surviving fractions of $^3He$ in stars between one and three solar masses.