Low-Mass Binaries and the Stellar Luminosity Function

We present a new investigation of the influence of unresolved binaries on the form deduced for the stellar luminosity function from photometric parallax surveys. We have compiled a catalogue of photometry and binary statistics for stars known to be north of -30° declination and within 8 parsecs of the Sun, and have used these stars as a reference sample for our multiplicity analysis. M-dwarfs comprise almost eighty percent of the sample. The overall multiplicity fraction amongst the 106 systems (and 151 stars) in this sample is only 35%. Transforming the local luminosity function to a mass function, we find relatively good agreement amongst most of the currently-available mass-luminosity relations. The mass function is best-represented as a power-law, Ψ(M)∝M-1.05 for masses between 1 and 0.10 Msun, with a steeper slope at higher masses and a sharp decline in numbers below 0.1 Msun. While incompleteness in the 8-parsec sample may contribute to some extent to the decrease in number density at the lowest masses, the 5.2-parsec sample shows the same behavior, suggesting that the mass function turns over before reaching the hydrogen-burning limit. We have combined images taken with the Planetary Camera on the Hubble Space Telescope with previously-obtained wide-field Schmidt plate data to search for wide (>10 a.u. separation) binaries amongst a sample of mid-type M-dwarfs which have been employed in photometric parallax analyses of the stellar luminosity function. Six of the 41 stars observed are binary, while a further two are triple with the number of resolved companions expected from moving the local sample to a comparable distance. We have determined the mass-ratio distribution for the nearby-star sample, and find that it is incompatible with the hypothesis of both components being drawn independently from the same power-law mass function. Rather, there is clear evidence for preferred formation (or survival) of systems with components of nearly equal mass. We also find no strong evidence for a correlation between mass-ratio and the orbital semi-major axis. Based on these results, we have constructed starcount models to investigate how unresolved binary systems influence the form of the luminosity function derived using photometric parallax methods. Our conclusion is that the results are only weakly dependent on the binary fraction, and that low-mass binaries cannot bring these photometric studies into agreement with the luminosity function derived by counting the nearest stars. However, previous photometric analyses have failed to take into account the change in the slope in the (Mv, V-I) relation at (V-I) ∼2.9 magnitudes- close to the peak in the luminosity function. Once the data are analyzed using a more appropriate color-magnitude relation, we find (statistically) good agreement between the local luminosity function and the results of the photometric parallax analyses of more distant stars.