Annu. Rev. Astron. Astrophys. 1979. 17: 135-87
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2.1 The Solar Neighborhood, a Benchmark in M/L

Because most of the mass resides in intrinsically faint stars, the stellar mass density can be directly determined only in the immediate neighborhood of the sun. In practice this is accomplished by combining the luminosity function, Phi (M), with the mass-luminosity relationship for each stellar group to find the stellar density, rho. The faint-star luminosity function now appears to be well determined for MV ltapprox +15 (Wielen 1974, Luyten 1968, 1974). From Gliese's (1969) data, Wielen derives rhos = 0.046 Msun pc-3 while Luyten (1968) gives rhos = 0.064 Msun pc-3.

The greatest uncertainty in rhos arises from the difficulty of properly applying the mass-luminosity relationship to the observed sample. The mass-luminosity relation (Veeder 1974) and observational data (van de Kamp 1971) are most reliable for main sequence stars, which Wielen finds amount to 0.038 Msun pc-3. Sources of error include confusion between low-mass stars and more massive, cooled degenerate stars (e.g. Hintzen & Strittmatter 1974) and the interpretation of the drop in Phi (M) for MV gtapprox +15. This could be due to a real absence of very low-mass objects. On the other hand, stars with M ltapprox 0.08 Msun are not able to support stable H burning (Graboske & Grossman 1971, Straka 1971) and so might cool sufficiently rapidly to produce an apparent deficiency of low-luminosity stars (Kumar 1969, Greenstein et al. 1970, Hoxie 1970). Joeveer & Einasto (1976) have estimated that this effect requires increasing the contribution of low-mass stars by about 0.02 Msun pc-3.

The other major mass contribution resides in white dwarfs. Luyten (1975) finds nWD appeq 0.006 pc-3, while Sion & Liebert (1977) obtain nWD gtapprox 0.01 pc-3. For a mean white dwarf mass of 0.7 Msun (Wegner 1974, Greenstein et al. 1977), rhoWD 0.004-0.007 Msun pc-3, compared to the theoretical prediction of 0.012-0.03 Msun pc-3 (Hills 1978), which depends on the age of the disk (Hills took 1.2 x 1010 yr). Hills also shows that the mass in neutron stars is probably negligible.

The stellar mass density near the sun thus most likely lies in the range 0.05 < rhos < 0.09 Msun pc-3. To this must be added the mass in interstellar matter, which from Savage et al.'s (1977) measurement of the mean density of hydrogen is rhoISM 0.03 Msun pc-3. The total density, rho, then lies between 0.08 and 0.12 Msun pc-3, consistent with the estimate of 0.09±0.02 Msun pc-3 found by Joeveer & Einasto (1976).

The local mass density can also be measured by observing the z density and velocity dispersion for a homogeneous stellar population (Oort 1965). Although straightforward in principle, the accurate measurement of the galactic acceleration gradient perpendicular to the plane has proved elusive. Different determinations are in conflict with each other and in some cases yield nonphysical results (Dessureau & Upgren 1975, Joeveer & Einasto 1976, King 1977). The most likely value of the density found by this method, rhodyn appeq 0.14 Msun pc-3 (Jones 1976), must be considered uncertain. Thus at present there is no compelling evidence for significant undiscovered mass in the immediate solar vicinity. This result is consistent with a model mass-distribution for the galaxy computed by Ostriker & Caldwell (1979); the model has much unseen mass in an extended halo but very little in the neighborhood of the sun.

To compute the local mass-to-light ratio, we need the local luminosity density, curlyL. This quantity follows directly from Phi (M), which must now be based on a large volume since rare stars make a significant contribution to the luminosity. The Phi (M) of Starikova (1960) and McCuskey (1966, Table 8) respectively give curlyLV = 0.049 and curlyLV = 0.063 Lsun pc-3. A recent study by F. Malagnini (private communication) suggests that the results of Starikova may be preferable, so we adopt curlyLV = 0.055±0.01 Lsun pc-3. Since Malagnini finds B - V = 0.62 for the solar neighborhood, curlyLV appeq curlyLB . For rho = 0.09±0.02, M / LB = 1.1-2.4. Using rhodyn = 0.15, we find M / LB = 2.3-3.3. If the light contribution from younger stars (spectral type earlier than G2 on the main sequence) were removed, then the local M / L would be approximately doubled.

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