Multiplying the initial mass function - the number of stars per unit mass - by mass, and normalising that function by the total mass of stars formed, gives S(M). This function describes the fraction of the total star-forming mass of a given molecular cloud which becomes bound up in stars of a given mass, providing a measurement of the relative efficiency of the star-formation process. In the case of the field-star IMF, S(M) a M0 for 0.1 < M/M0 < 1; that is, mass is equally divided among stars in this mass range. Integrating ^(M), stars with masses between the hydrogen-burning limit and 1 M0 account for ^48% of the total star-forming mass. Most of the residual mass is in 1-10 M0 stars, with (intrinsically rare) higher mass stars adding only ~1% of the total. Brown dwarfs are extremely numerous, but regardless of which mass function is adopted, they contribute only 2-3% of the star-forming mass budget.
Integrating ^(M) also allows an upper limit to be set on the contribution made by stars to the local mass density, p0. Subsolar-mass stars contribute ^0.036 M0 pc-3, with half of the mass density in M dwarfs. A straightforward integration of ^(M) for higher-mass (1-100 M0) stars would indicate that those stars make a similar total contribution. However, the calculation fails to take into account the fact that most of those stars have evolved off the main sequence, and have recycled much of their material to the interstellar medium. As a result, highmass stars make a relatively small contribution to p0 at any given time. In the local inter-arm region, 1-10 M0 stars contribute only ^0.004 M0 pc-3 to the total mass density. Stellar remnants make a similarly small contribution, amounting to ^0.005M0 pc-3, giving a total stellar mass density of 0.045M0 pc-3.
As discussed in Section 8.3, one of the main stimulants in the surge of interest in M dwarfs in the 1970s was the discrepancy between the Oort dynamical mass density and the summed contribution from known constituents of the Solar Neighbourhood: the hypothesis of 'missing mass' in the Galactic Disk. How do matters stand at the turn of the century? The observed mass density remains largely unchanged: interstellar gas and dust contributes pism ~ 0.03 to 0.05 M0/pc3 which, combined with the stellar mass density, gives pobs ~ 0.075 to 0.095M0/pc3. Dynamical estimates, however, have changed. The most recent, based on Hipparcos data, derives a mass density of pdyn ~ 0.076 ± 0.015 M0/pc3 [C2], significantly lower than Oort's 0.15 M0/pc3, and consistent with the observed value. Thus, there is no longer a need to invoke significant quantities of dark matter within the Galactic Disk.
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