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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