Missing Primaries

First, it is important to discuss the density of the nearby stellar system population, as defined by the primary stars. Population density diagrams provide a gauge of the uniformity of systems within a volume stretching to 25 pc, as shown in Figure 8.1, whereMV, a proxy for

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Figure 8.1 Population density plot for the entire 25 pc sample. Illustrated is the constant stellar density to 25 pc for brighter and more massive objects in the solar neighborhood from

MV = 0 − 8.8. The horizontal lines outline the M dwarf region at MV = 8.8 − 20.

mass, is plotted versus distance in eight equal volume shells. It is evident that the density of the more massive (MV = 0 − 8.8 mags) stellar members of the solar neighborhood is constant to 25 pc. Thus, a constant density for the M dwarfs can be assumed as well.

With the expectation that the nearby M dwarf population should be uniformly distributed to 25 pc, we can turn our attention to the state of the current census. Figures 8.2 (a) and (b) are population density diagrams for the M dwarf sample within 25 pc, where mass is plotted versus distance in eight equal volume shells to 25 pc for the primaries alone (a) and all M dwarfs (b) in the multiplicity project. Primaries have been noted in red, the companions in

Figure 8.2 Population density diagrams. (a) A population density diagram for the 1122 M dwarf primaries in the multiplicity sample with masses estimated from deblended photome- try. (b) A population density diagram for the 1431 M dwarf components in the multiplicity sample with masses estimated from deblended photometry. Primaries are plotted in red; companions in blue, suspected new companions in green. The horizontal lines divide the sample into subsamples that span factors of two in mass.

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blue, and the suspected companions in green. The horizontal lines indicate the subsamples of M dwarfs at masses 0.075 − 0.15 M⊙, 0.15 − 0.30 M⊙, and 0.30 − 0.60 M⊙ (divisions

by factors of two in mass) that have been analyzed. It is evident that the closer primaries are more uniformly distributed, but that beyond ∼15 pc, the density drops, indicating that both primaries, particularly those in the lowest mass regions, and secondaries are missing at further distances. The missing secondaries were revealed previously in the cumulative multiplicity fraction (Figure 6.2).

Next, we can analyze the collection of M dwarfs by mass subset to determine which of the subsamples are most incomplete and at what distances their numbers begin to diverge from expected values. Figure 8.3 illustrates cumulative curves of the numbers of M dwarf primaries in each mass bin (1048 with masses less than 0.6 M⊙) currently found within

25 pc as a function of increasing distance. Mass estimates are calculated from deblended photometry. The solid curves represent the numbers of actual red dwarf primaries in each mass bin. The dashed lines are the expected numbers of primaries, based on the number found either within (a) 5 pc or (b) 10 pc and extrapolated to 25 pc. The dotted lines are the Poisson error limits calculated from the number of objects either within (a) 5 pc or (b) 10 pc. Orange indicates the bin of the largest mass objects (0.30−0.60 M⊙), red shows the

mid-mass bin (0.15− 0.30 M⊙), and brown is for the lowest mass bin (0.075− 0.15 M⊙).

Let us consider Figure 8.3(b) first. The curves of known stars and predicted stars appear to be the same up to distances of 15, 13, and 11 pc, respectively for the large, medium, and small mass bins. The sample of most massive stars (the orange curve) appears most

Figure 8.3 Cumulative censuses of M dwarf primaries in the multiplicity study. Masses have been estimated from the deblended photometry of M dwarf primaries. The solid lines represent the cumulative known numbers of M dwarf primaries in each mass bin. The dashed lines indicate the expected number of primaries in each mass bin extrapolated to 25 pc from the number known to lie within (a) 5 pc or (b) 10 pc, and assuming a constant stellar density. The dotted lines are the upper and lower Poisson error limits.

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complete, while the sample of least massive stars (the brown curve) is the most incomplete at 25 pc, which is expected. The errors on the extrapolated values are satisfyingly small, due to a reasonable number of objects within the three mass bins at 10 pc (65, 59, and 61 for the largest, medium, and lowest mass bins, respectively). But these numbers are all very similar, and an impression is given that each bin therefore makes up an equal percentage of the M dwarf population. But this is not what is expected, judging from the trend presented in Table 8.2 of increasing numbers of objects with decreasing mass. There is no reason to expect that the situation would change suddenly in the M dwarf regime. We expect that the lowest mass bin of M dwarfs will be the most populous, hinting that more objects in the mid- and lowest mass bins remain to be found even within 10 pc.

Let us now inspect Figure 8.3(a). For now, we assume that we know all stars within 5 pc, even though the number of objects found in each mass bin is small: 12, 7, and 16 for the large, medium, and small subsamples, respectively. Admittedly these are very small numbers of stars. Surprisingly, the medium mass bin appears complete to∼13 pc, while the curves for the largest and lowest mass objects already diverge from the expected curves at

∼6 pc. But the expected incompleteness of the lowest mass subsample is revealed. All of the curves we expect to shift upward to larger percentages of the sample once more M dwarfs are discovered and/or have parallaxes measured.