![]() | Annu. Rev. Astron. Astrophys. 1979. 17:
135-87 Copyright © 1979 by Annual Reviews. All rights reserved |
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,
(M), with the mass-luminosity relationship
for each stellar group to find the stellar density,
. The faint-star
luminosity function now appears to be well determined for
MV
+15
(Wielen 1974,
Luyten 1968,
1974).
From Gliese's (1969)
data, Wielen
derives
s
= 0.046 M
pc-3 while
Luyten (1968)
gives
s = 0.064 M
pc-3.
The greatest uncertainty in s 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 M
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
(M) for
MV
+15. This could be due to a real absence of very
low-mass objects. On the other hand, stars with M
0.08 M
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 M
pc-3.
The other major mass contribution resides in white dwarfs.
Luyten (1975)
finds nWD 0.006 pc-3, while
Sion & Liebert (1977)
obtain nWD
0.01 pc-3. For a mean white dwarf mass of 0.7
M
(Wegner 1974,
Greenstein et
al. 1977),
WD 0.004-0.007 M
pc-3, compared to the
theoretical prediction of 0.012-0.03 M
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 < s < 0.09 M
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
ISM 0.03 M
pc-3. The total density,
, then lies between
0.08 and 0.12 M
pc-3, consistent with the
estimate of 0.09±0.02 M
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, dyn
0.14 M
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, . This
quantity follows directly from
(M), which
must now be based on a large volume since rare stars make a
significant contribution to the luminosity. The
(M) of
Starikova (1960)
and McCuskey (1966,
Table 8) respectively give
V = 0.049 and
V = 0.063
L
pc-3. A recent study by F. Malagnini (private
communication) suggests that the results of Starikova may be
preferable, so we adopt
V = 0.055±0.01 L
pc-3. Since Malagnini finds
B - V = 0.62 for the solar neighborhood,
V
B . For
= 0.09±0.02, M / LB
= 1.1-2.4. Using
dyn = 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.