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*Astron. Astrophys. 339, 405-408 (1998)*
## 3. Discussion and conclusions
The four surveys have led to number density estimates of brown
dwarfs of 0.46 pc^{-3}, 0.076 pc^{-3}, 0.069
pc^{-3}, and 0.15 pc^{-3} respectively. Assuming again
a typical mass of a brown dwarf of 0.065 this
corresponds to mass densities of 0.03
pc^{-3}, 0.0049 pc^{-3}, 0.0045
pc^{-3} and 0.01
pc^{-3}, respectively. We note, however, that despite the
large differences the estimates are still statistically consistent
within two standard deviations. This can be shown by integrating the
Poisson probability function with respect to the mean value at a given
number of N realizations. The range of mean values
(, ) of Poisson
distributions from which the N realizations have been drawn with a
probability of 95%, for instance, is then given by
If N=1, (, ) = (0.24,
5.6) and in the case of N=3 (,
) = (1.1, 8.8). This shows immediately that the
statistical uncertainties of the density estimates of brown dwarfs
overlap at two standard deviations.
The high estimate of the space density of Kelu-1 type objects,
leads us to ask if they would be detectable in deep star count data
taken with the Space Telescope (HST). We first consider star counts in
the Hubble Deep Field (HDF) (Flynn et al. 1996). No very red
stars, i.e. stars which appeared only in the I-band images and
not in the V-band images, were detected in the HDF to a limiting
magnitude of I=26.3. The number density implied by Kelu-1 itself is
0.1 pc^{-3}, while figuring in the older brown dwarfs
associated with Kelu-1 raises the estimated number density to 0.4
pc^{-3}. Taking the absolute magnitude of Kelu-1 like other
brown dwarfs as and their local density to be
0.4 pc^{-3} and assuming an exponential scale height of 300
pc, we estimate that 6 Kelu-1 type objects would have appeared in the
4.4 square arcminute HDF, which is marginally inconsistent with none
being observed, while only 0.5 would be expected if they have an
exponential scale height of 100 pc, which is consistent with none
observed. Stronger limits can be obtained using faint HST star counts
in the Groth Strip (Gould et al. 1997), which covers 114.0 square
arcminutes to a limiting I-band magnitude of .
In this field we would expect 5 Kelu-1 type objects for a scale height
of 100 pc and 15 for a scale height of 300 pc, whereas only 1 very red
object (V-I5.0) was detected. However, this
assumes that all of the 0.4 pc^{-3} local space density of
Kelu-type brown dwarfs would be as bright as Kelu-1 itself, whereas
most will be older and fainter. For example, in a two-component toy
model, containing a young component with a space density of 0.1
pc^{-3}, scale height 100 pc and and an
old component with a space density of 0.3 pc^{-3}, scale
height 300 pc and we would expect circa 1 star
from each component in the Groth strip, consistent with 1 observed red
star. We conclude that faint star counts in HDF and the Groth strip
are unable to rule out the high space density of Kelu-1 type objects
measured by Ruiz et al. (1997).
These density estimates can be compared with measurements of the
densities of the other constituents of the galactic disk.
Jahreiß & Wielen (1997) derive from a discussion of the most
recent data of nearby stars that the mass density of luminous stars in
the solar neighbourhood is 0.039
pc^{-3}. Thus, if the mass density estimate of brown dwarfs
based on the Calan-ESO survey is correct, brown dwarfs contribute
almost as much to the local mass budget as the luminous stars. The
mass density estimates of brown dwarfs can be also compared with
dynamically determined local mass densities. Such measurements include
all gravitating matter. Fuchs & Wielen (1993) and Flynn &
Fuchs (1994) have used samples of K dwarfs and K giants, respectively,
to measure the local slope of the force law.
Both measurements have led to a total local mass densities of 0.1
pc^{-3} with an estimated uncertainty of
20%.A repetition of the measurement using improved data of K giants
indicates a total local mass density at the lower end of this range
(Flynn & Fuchs, in preparation). Crézé et
al. (1997) have used recently Hipparcos observations of A stars
and determine a value of the total local mass density of 0.076
0.015 pc^{-3}.
The local surface density of interstellar gas in the form of cold HI
and is 6 pc^{-2}
(Dame 1993). If corrected for the presence of heavier elements and
folded with a vertical scale height of 100 pc, this implies a local
mass density of interstellar gas of 0.037
pc^{-3}. The mass density of warm HI and ionized interstellar
gas is more difficult to assess, but is probably only 0.003
pc^{-3} (Kuijken & Gilmore 1984). We
conclude from this discussion that there is evidence for a local mass
density of brown dwarfs of the order of 0.01
pc^{-3}, which would seem to fill the gap between dynamical
mass determinations and the mass density of so far identified stellar
and interstellar matter, whereas the mass density estimate by Ruiz et
al. (1997) (1997) seems to be on the high side. Hopefully,
further discoveries of brown dwarfs, such as announced by the 2MASS
survey (Kirkpatrick et al. 1998), will clarify this issue.
© European Southern Observatory (ESO) 1998
Online publication: October 21, 1998
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