THE ASTRALUX MULTIPLICITY SURVEY: EXTENSION TO LATE M-DWARFS^*

The multiplicity properties of stars hold clues to their formation and early evolution (e.g., Goodwin & Kroupa 2005; Marks & Kroupa 2011; Bate 2012), and binarity is of fundamental importance for a range of astrophysical applications, such as determination of physical properties and target selection for exoplanet studies. Consequently, detailed multiplicity studies have been performed over a wide range of stellar masses and ages (see, e.g., Duchêne & Kraus 2013; Reipurth et al. 2014, for recent summaries). While multiplicity at the low-mass end—in the M-dwarf regime—has been a subject of study for a long time (e.g., Fischer & Marcy 1992; Delfosse et al. 2004; Law et al. 2008), there have recently emerged reasons to revisit this subject. The main reason for this is that the nearby M-dwarf population is becoming increasingly well characterized. Recent studies have greatly increased our sample of securely identified M-dwarf stars in the solar neighborhood (e.g., Riaz et al. 2006; Reid et al. 2007; Lépine & Gaidos 2011). Furthermore, while distances for this class of objects have previously been scarce due to the fact that they are generally too faint to have been observed by Hipparcos (Perryman et al. 1997), recent parallax studies have started to become increasingly complete to the lowest-mass stars (e.g., Henry et al. 2006; Dittmann et al. 2014; Reidel et al. 2014). Hence, larger well-defined statistical samples can be studied than has been possible before, and a greater accuracy is achievable in the characterization of their properties.

The AstraLux Norte (Hormuth 2007; Hormuth et al. 2008) and Sur (Hippler et al. 2009) cameras are well suited for multiplicity studies by use of high-resolution imaging (e.g., Hormuth et al. 2007; Daemgen et al. 2009; Peter et al. 2012; Bergfors et al. 2013), with a resolving power of approximately 100 mas. AstraLux is a high speed and low read noise camera used for the purpose of so-called Lucky Imaging (e.g., Tubbs et al. 2002; Law et al. 2006). Previously, we have used this instrument for the study of multiplicity in primarily early-type M-dwarfs (Bergfors et al. 2010; Janson et al. 2012). In the summary study of 2012 (Janson et al. 2012), we found that the multiplicity properties of these stars were largely consistent with being continuously intermediate between the Sun-like (Raghavan et al. 2010) and brown dwarf (Burgasser et al. 2007) populations, though possibly with the exception of the mass ratio distribution (see also Reggiani & Meyer 2013; Goodwin 2013). The apparent continuities and discontinuities motivate further study of a later-type sample, bridging the gap between early/mid M-dwarfs in Janson et al. (2012) and very low mass (VLM) stars and brown dwarfs in Burgasser et al. (2007). The sample presented in Lépine & Gaidos (2011) provides an excellent basis for this purpose. Here we will present a study of multiplicity in mid/late M-type stars (primarily M3 and later, down to M8), which overlaps with both the previous M-dwarf and VLM studies.

In the following, we will first discuss the sample properties in Section 2, and then the observations and data reductions in Section 3. This will be followed by a summary of the results in Section 5 and a description of the statistical properties of the sample in Section 6. Finally, we will discuss the implications of this study in the context of multiplicity across all stellar masses in Section 8 and summarize the conclusions in Section 9.

2.1. Observational Properties

2.2. Physical Properties

All observations in this program were acquired with the AstraLux Norte camera on the 2.2 m telescope at Calar Alto in Spain. The 2.2 m telescope is on an equatorial mount. AstraLux uses an Andor DV887-UVB camera head equipped with a thinned, back-illuminated, electron-multiplying 512 × 512 pixel monolithic CCD. The CCD is equipped with two readout registers, one for conventional readout, and one 536 stage electron multiplication register. Each of the two registers comes with its own output amplifier. All Lucky Imaging data were obtained using the electron multiplication mode, and the associated output amplifier. The camera allows to select electron multiplication gains of up to 2500. For astronomical observations, the gain values are typically selected such that the ADU counts in the brightest pixel do not exceed 50% of the linearity limit of the camera. It has been verified in lab experiments that charge transfer efficiency does not have any impact on the astrometric accuracy. Typical observations are made using a 256 by 256 pixel window readout, which facilitates shorter single frame integration times. The window also allows to avoid column 244 of the detector, which is subject to a charge trap that traps a few electron per clock cycle. Apart from column 244, the CCD has very good cosmetics without any clusters of bad pixels. The raw pixel scale (before oversampling; see below) is approximately 46 mas pixel⁻¹ on average.

The observations were carried out in six separate runs: on 2011 November 8–9, on 2012 January 5–8, on 2012 June 6–7, on 2012 August 27–29, on 2012 September 3, and on 2012 November 22–24. Each target was observed in both the i' band and the z' band, and a large fraction of the targets, including the singles, were observed in two or more separate epochs. In total, excluding calibration observations, approximately 940 observations were acquired for the purpose of this survey, covering the 286 individual targets. As per usual, observing conditions varied during the runs, but since so many targets were observed several times, there is in general at least one frame of acceptable quality per star. The typical full width at half-maximum (FWHM) is close to 100 mas, which is an appropriate measure for the resolving power of this instrument. For the purpose of astrometric calibration, we observed either the Trapezium or M15, depending on the season during which the observations were performed. The astrometric calibration is described in more detail in Section 4.

Although the field of view of AstraLux Norte can be as large as 23'' across with the full frame in use, many of the images were taken with a subarray readout and the target was not always centered perfectly in the frame, so the fully complete region has a radius of 5'' around each star. We will thus only consider companions inside of 5'' for statistical purposes in this study.

The basic data reduction makes use of the pipeline developed specifically for the purpose, described in Hormuth et al. (2008). The pipeline performs flat fielding and bias correction of the data, followed by a drizzle algorithm to oversample the image by a factor of two, for a final pixel scale of approximately 23 mas pixel⁻¹. Individual frames are then aligned based on the brightest pixel in the oversampled image, and the re-aligned images are subsequently recombined into collapsed images. By default, the pipeline produces four different reduced frames per full observation, corresponding to different cut-offs for the selection of frames used. In this study, we consistently used the selection in which the 10% best frames were included in the collapsed frame. Individual frame exposure times were typically 30 ms, with minor variations depending on observing conditions and target brightness. The total number of frames was always selected so that the total integration time would add up to 300 s. Hence, the typical number of frames acquired was 10,000, leading to a 10% selection of 1000 frames, adding up to 30 s of "useful" integration time.

Astrometry was first calculated in detector coordinates, and subsequently translated into sky coordinates using the calibration observations of the Trapezium or M15. For the calibration data, we chose five of the brightest stars in the field, determined their relative positions using Gaussian centroiding, and compared to the relative locations of these stars in van der Marel et al. (2002) for M15 and McCaughrean et al. (1994) for Trapezium. We also compared the results with a calibration based on the IRAF geomap procedure (see, e.g., Köhler et al. 2008), and found that calibration within a given observing run was consistent to within 1% in pixel scale and 03 in position angle, regardless of choice of calibration method and selection of stars within the method. In this way, it was found that the pixel scale and orientation of true north in the respective runs were: 23.57 mas pixel⁻¹ and 166 in 2011 November, 23.58 mas pixel⁻¹ and 172 in 2012 January, 23.67 mas pixel⁻¹ and 190 in 2012 June, 22.59 mas pixel⁻¹ and 183 in 2012 August, 22.69 mas pixel⁻¹ and 196 in 2012 September, and 22.67 mas pixel⁻¹ and 185 in 2012 November. The calibration errors are dominated by the 1% uncertainty in pixel scale and the 03 uncertainty in position angle mentioned above, which we adopt as the formal error bars in each case.

As in previous runs, astrometry for wide binaries in the sample was determined using Gaussian centroiding, and astrometry for close binaries was determined using PSF fitting (Bergfors et al. 2010). Three point-spread functions (PSFs) were used in each case, to provide a well-defined mean and scatter in the PSF fitting. The PSFs were chosen among single stars in the survey to represent a broad range in observing conditions. In principle, one might tailor the PSF templates to each given target, such that only PSFs acquired under similar conditions are used in the fitting scheme. However, given the complex multi-modal variations of the PSF and the rapidly varying conditions during the observing nights, this is impractical, and our experience implies that no significant gain is achieved through such a procedure. Even if an apparent improvement were achieved, it would also be dubious whether the resulting implied precision could be trusted, given the aforementioned PSF complexity. We therefore consider it a better strategy to reflect a representative range of instrumental PSF realizations in the fitting, so that the derived error bars robustly encompass these variations. While the FWHM does not change much between different PSFs, since this measure is dominated by the diffraction-limited PSF core, beyond the core there can be quite a bit of variation in the PSF, sometimes showing diffraction rings and other times just a smooth halo. Astrometric values for the various systems are provided in Table 2. Relative photometry was determined simultaneously with the astrometry, by measuring aperture photometry in the case of wide binaries, and the relative brightness of the PSFs fit to each component for close binaries. In the case of the so-called "false triple" effect, which often occurs in Lucky Imaging shift-and-add analysis when a binary with components of about equal brightness is observed and produces a tertiary ghost feature (at the same separation from the primary as the secondary but on the opposite side), we fit for all three components in the PSF fitting procedure. The photometry of the individual components was then calculated in the same way as in Janson et al. (2012), as first implemented by Law (2006).

With the age estimates from Section 2 in hand and the photometry derived here, upper and lower bounds for the individual component masses in each candidate multiple system are determined in the following way: given a certain age estimate (an upper or lower bound for given target), a grid of model values for each of Δi', Δz', and total M_J are calculated for every combination of possible primary and secondary masses covered by the parameter space of the theoretical atmospheric and evolutionary models.⁶ These model values are then compared to the actual measured values (with their measured error bars) for every real binary pair. The matching that provides the minimum χ² then determines the masses that are assigned to the pair. For each star, we generate four different mass estimates, and for each binary pair we separately generate four different mass ratio estimates. The four estimates correspond to all possible combinations of the two age extremes and the two model sets (NextGen and BT-Settl with associated evolutionary models, see Hauschildt et al. 1999; Baraffe et al. 1998, 2003; Allard 2014). The final values and errors are then taken as the mean and the standard deviation of these four values for each star and each pair. In this way, both age and model uncertainties are considered in the estimations. The age uncertainty is the dominant one, due to the wide adopted ranges in this quantity. It is important to note that while the uncertainties in the individual stellar masses are large, the uncertainties in their mass ratios (q = m_B/m_A) are substantially smaller. This is due to the fact that any error in the age or model affects the estimated mass of the primary and secondary in a very similar way. As a result, while the median uncertainties in the primary and secondary masses are 23% and 22%, respectively, the median error in the mass ratio is only 8%. Table 3 includes the masses and mass ratios that have been derived with this procedure.

Several both new and previously known companion candidates were detected in this survey, and many of them could be confirmed to share a common proper motion with the primary, confirming physical companionship. In total, 66 of the 286 systems were found to be either probable or confirmed multiples within the complete range of 5'' separation, 41 of which were new discoveries. Of all systems, most were binaries and only two were triple systems, one of which was previously known. However, as noted in the individual notes, some of the systems are higher-order multiples when considering known companions outside of the AstraLux detectability range. Indeed, the system I08316+1932 is in reality a quintuple system, which is described in more detail in the individual notes. Several of the companions are probable brown dwarfs. A few examples of detected multiples are shown in Figure 1.

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For the candidates that were either observed twice with AstraLux or were already reported in previous imaging surveys, it was possible to test for common proper motion. Since these targets are very nearby and therefore have large proper motions in general, such a determination is possible even over rather short baselines. Our test followed the same structure as in Janson et al. (2012)—based on the location of a given candidate in one epoch relative to the primary star (in terms of separation and position angle), we made a prediction based on its proper motion and parallax of where it would occur in the second epoch if it were a static background object, and compared it to the actual measured position in the second epoch. If the locations were more than 3σ discrepant, common proper motion was considered as confirmed. For candidates that passed this test, we also made a test for measureable orbital motion by testing if the first and second epoch positions differed from each other by more than 3σ. If so, we considered orbital motion as confirmed as well. These evaluations were based on the motion between the first and last listed data points for each given target listed in Table 2, since this maximizes the observational baseline. After applying both tests, 37 candidates could be confirmed as bona fide companions, of which 33 also showed significant orbital motion. Three candidates could be discarded as background objects.

A color test was applied to all 37 single-epoch candidates, in which it was checked whether the Δi' and Δz' yielded consistent results for an expected secondary. The same test was applied to one candidate for which two epochs of data exist, but where the baseline is insufficient for a conclusive proper motion test to be made. In this way, 33 candidates were found to have colors consistent with real companions. Five candidates were too blue to be low-mass stellar companions (Δz' − Δi' > 0, which would imply that the secondary is bluer than the primary), and thus discarded as likely background contaminants, although astrometric follow-up in the future will still be valuable for such candidates, in order to test whether there could be white dwarf companions among them. Even for many of the candidates that have only been observed or detected in one epoch, it is possible to draw conclusions about common proper motion. The targets move rapidly across the sky (from ∼100 mas yr⁻¹ to several hundreds of mas yr⁻¹), and have been observed in previous all-sky surveys spanning decades backward in time. Hence, any background contaminant that happens to end up close to the primary star at the AstraLux epoch should be separated from it by up to several arcseconds in those previous epochs of data. Hence, they are often detectable there, despite the much worse spatial resolution of wide-field surveys, and so from their presence or absence in the archival data, it can be determined whether or not they share a common proper motion with the primary. We have used archival data from primarily two surveys for this purpose: the Two Micron All Sky Survey (2MASS, see Skrutskie et al. 2006) and the first Palomar Observatory Sky Survey (POSS). Since 2MASS was performed in the late nineties up across the millennial shift, it provides up to a 15 yr baseline, and a quite reasonable spatial resolution for a wide-field survey. However, while POSS has a slightly worse spatial resolution, it is the most useful survey for this purpose. This is due to the fact that it was performed largely in the early 1950s, providing a 60 yr baseline for the vast majority of the targets. Since the candidates are bright, sensitivity is not a limiting issue for these purposes, but the most important issue is how far a background contaminant would have traveled relative to the primary since the archival epoch, hence why a large baseline is preferred. By examining these archival data sets, we were able to conclude for 24 targets that if the candidate were a background contaminant, it would have been clearly visible in the images. Since they are not there, we can infer that the candidates are physical companions that share a common proper motion with the primary. In most of the nine remaining cases (which are generally the targets that have the slowest proper motions and/or the faintest companions), a background contaminant would have been marginally detectable, but for any such limit case, we count common proper motion as not having been proven yet.

The vast majority (and probably all) of these nine remaining cases are expected to be real companions. Aside from the high confirmation rate in the candidates for which a proper motion test has been performed, this can also be deduced from the fact that the distribution of the candidates in projected separation is strongly slanted toward small separations, while the opposite would be true in a sample dominated by background contaminants. They also all pass the color test mentioned above, matching the expectation for physical companions, which would be rare for background contaminants, since the blackbody flux peak sweeps across the i' − z' wavelength range in the M-dwarf regime. In total, we thus consider 68 candidates in 66 systems to be either probable or confirmed physical companions.

The detections are plotted in Figure 2, and the binary properties are summarized in Tables 2 and 3.

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6.1. Multiplicity Fraction

6.2. Semi-major Axis Distribution

Given that a significant fraction of the stars in our sample have trigonometric parallaxes, we can establish good projected physical separations in general, which benefits the purpose of determining a well-constrained semi-major axis distribution. For translating between projected physical separation and semi-major axis, we use the same conversion factor of close to one as in Janson et al. (2013), based on the derivation of Brandeker et al. (2006) for a typical eccentricity distribution of f(e) ∼ 2e. Our procedure for determining the semi-major axis distribution is based on generating a simulated population with a certain distribution, subjecting it to the sensitivity limits of AstraLux, and testing how well the resulting sample matches the actual body of detections, using a Kolmogorov–Smirnov test.

To begin with, we will assume that the sample has a uniform mass distribution, but later on we will discuss how changing the mass ratio distribution affects these results. As input distributions for the semi-major axes (in units of AU here), we choose log-normal functions, both since this is the usual choice in this type of study (e.g., Duquennoy & Mayor 1991; Raghavan et al. 2010; Janson et al. 2012) and since it a priori appears to potentially provide a good fit to the observed distribution (see Figure 3). We then vary the σ_a and μ_a parameters of the distribution in steps of 0.01 and see how the choices in these parameters affect the quality of the fit to the observed distribution. The steps are performed in a grid where both the σ_a and μ_a values are varied simultaneously, in order to find the global maximum in fit quality. This is important since there is some covariance in these parameters, where, e.g., a smaller σ_a can potentially be partly compensated for through a larger μ_a, and vice versa.

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The outer boundary of the AstraLux sensitivity range is set by the 5'' completeness radius. The inner boundary is set by the resolving power of approximately 100 mas. In between, the detectability of a candidate is set by the brightness contrast of the candidate relative to the contrast curve of the instrument. Contrast curves are calculated in the same way as is typically done in imaging surveys for faint companions (e.g., Lafrenière et al. 2007; Janson et al. 2011), by taking the standard deviation in a series of annuli centered on the star with different radii to represent the σ at various separations from the star, and relating them to the measured flux of the star for representing the limiting contrast of detectability. A 5σ criterion is chosen as the basis for the contrast curves. Since the resulting contrast curve varies a bit with the brightness of the primary, we have divided the target stars into faint (9–10 mag), intermediate (8–9 mag) and bright (<8 mag). Representative contrast curves are then derived by taking the median of the contrast curves for all single stars in the survey in each brightness category. The simulated populations are set to have the same brightness distribution as the full real sample, and so the detectability of companions around a given simulated star is evaluated based on the representative contrast curve for its particular brightness category. Any companion in the simulation that ends up inside of these completeness boundaries is counted as being detected, and any companion that does not is counted as a non-detection.

Finally, the separation distribution of "detected" simulated companions is compared to the distribution of the actual detected sample. Every test is done 1000 times, and the median of the match probability of the 1000 tests is adopted (Babu & Feigelson 2006). For the log-normal distribution of the semi-major axis a in units of AU, we find that μ_a = 0.78 and σ_a = 0.47 gives the best match to the observed distribution, with a match probability of 92.4%. As we mentioned previously, this is under the assumption of a uniform mass ratio distribution. If we instead choose a linearly increasing mass ratio distribution, the best-fit values become μ_a = 0.80 and σ_a = 0.48 with a match probability of 92.5%. Hence, the result is not heavily dependent on the mass ratio distribution. The match probabilities as function of μ_a and σ_a for cross-sections in the parameter grid with values of ±0.15 around the best-fit values are shown in Figure 4, for both the cases of a uniform and a linearly increasing underlying mass ratio distribution.

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As has been mentioned previously, the mass ratio distribution is very challenging to constrain. This is due to several reasons. (1) It is difficult to assign reliable masses to late M-type stars due to uncertainties in age and evolutionary models, although as we have seen in Section 2, this has a relatively small impact on the mass ratio. (2) The survey is incomplete for the smallest mass ratios, meaning that the distribution cannot be well constrained there. (3) There appears to be a bias avoiding near-equal brightnesses in close systems that are subject to the false triplet effect (see Janson et al. 2012). This affects the mass ratio distribution in a way that is difficult to quantify. In order to mitigate the third issue, we only consider binaries outside of 1'' separation (see Figure 5). This completely avoids the bias, but also leaves us with a smaller sample, such that less stringent conclusions can be drawn about the mass ratio distribution than the semi-major axis distribution.

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The procedure for determining the distribution is the same as in the previous section, apart from that we consider 1'' instead of 100 mas as the effective inner working angle, and obviously that we compare the mass ratio distributions of the real and simulated samples instead of the semi-major axis distribution. We test three cases of mass ratio distributions: a uniform distribution (f ∼ q⁰), a linearly increasing distribution (f ∼ q¹), and a uniform distribution but with a cut-off at some minimum mass ratio q_min, for which we test a range of values. These different cases are illustrated in Figure 6. As a semi-major axis distribution, we simply choose μ_a = 0.78 and σ_a = 0.47 here—as with the reverse case, the specific choice of semi-major axis distribution does not affect the results in any significant way. The uncertainties in the measured mass ratios are represented by assigning Gaussian distributed random errors given by the estimated values listed in Table 3 to the mean mass ratios, with a different random seed for each simulation.

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We find that a uniform distribution provides a match probability of 58.0%, which is an entirely reasonable fit to the data. However, the distribution is unconstrained at small mass ratios. For instance, a uniform distribution with a cut-off at q_min = 0.3 gives a match probability 84.1%, which is an even better fit. We therefore step through q_min in steps of 0.01 in order to test when it becomes marginally inconsistent with the data, which we count here as a match probability of less than ∼33%, i.e., equivalent to a typical 1σ rejection. This occurs at a q_min of 0.39. A linearly increasing mass ratio gives a match probability of 53.0%. This is almost equally consistent with the data as the fully uniform distribution, underlining the fact that the mass ratio distribution is largely unconstrained.

The range of q_min that fit the data (∼0.0–0.39) give a range of possible detectable fractions, which feeds back into the multiplicity fraction discussed in Section 6.1. The lowest q_min (fully uniform distribution) gives a detectable fraction of 66.6%, and the highest gives a fraction of 85.4%.

As we have seen, the mass ratio distribution is one of the main contributors to uncertainty in the total multiplicity fraction. Aside from the caveats already mentioned in the mass ratio determination, it could also be the case that the mass ratio distribution has a dependence on semi-major axis. Such a dependence has been hinted at in several other multiplicity studies (e.g., Janson et al. 2013; Lafrenière et al. 2014). If so, the mass ratio distribution determined at >1'' may not be representative for the <1'' region where the majority of binaries reside. Nonetheless, it appears that values of ∼21%–27% appropriately bracket the most plausible total multiplicity fraction range. This range is fully consistent with a smoothly decreasing multiplicity fraction as function of primary mass, as arrived at in many previous studies (e.g., Kouwenhoven et al. 2007; Raghavan et al. 2010; Janson et al. 2012). In Figure 7, we show a comparison between the multiplicity fraction of our full sample and the multiplicity as a function of spectral type from Janson et al. (2012). Our derived multiplicity is well consistent with this previous study. The two studies imply a smooth evolution across the M-type range, with no evidence for any sudden jumps, which has been suggested in some scenarios that consider star and brown dwarf formation as separate processes (e.g., Thies & Kroupa 2007).

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It is currently not possible to distinguish stringently whether the mass ratio distribution remains close to uniform toward small mass ratios, or whether it starts to decrease somewhere below q = 0.4. It is in any case clear that there is no sharp cut-off below a q of ∼0.8, as has been reported for the yet lower-mass sample of VLM stars and brown dwarfs (e.g., Burgasser et al. 2007). There could however in principle be such a cut-off in the q < 0.4 range, as our analysis with q_min in Section 7 demonstrates. If so, the necessarily lower threshold of our sample could imply that there would be some characteristic secondary mass for which companions become less frequent. However, this should obviously be taken as mere speculation at this point, given the incompleteness issues, in addition to the difficulties in the mass ratio determinations.

The semi-major axis distribution, on the other hand, is well constrained by the data, since the AstraLux sensitivity range covers the majority of the range of where the binaries reside, encompassing both sides of a distribution that is well represented by a Gaussian function. As derived in Section 6.2 and shown in Figure 3, a Gaussian distribution with μ_a = 0.78 and σ_a = 0.47 matches the data at >90% probability. By contrast, a Sun-like distribution with μ_a = 1.64 and σ_a = 1.52 (Raghavan et al. 2010) only has a <0.03% probability of matching the data and can be firmly excluded. Thus, the result fits the trend of a semi-major axis that gets continuously narrower and closer in with decreasing primary mass (e.g., Burgasser et al. 2007; Janson et al. 2012), with an opposite trend toward higher masses (e.g., Kouwenhoven et al. 2007; Janson et al. 2013).

Most trends observed here and in other studies of low-mass stars are consistent with a smooth transition from the highest-mass stars to the lowest mass brown dwarfs in the field (e.g., Luhman et al. 2005a; Bourke et al. 2006), possibly implying a universal formation scenario for this whole range of objects. The main remaining mystery in this regard is the mass ratio distribution, which appears to be markedly different between stars and brown dwarfs (e.g., Goodwin 2013). Given the many difficulties in assigning reliable masses to low-mass objects, however, it would be valuable to further study the mass ratios of both our systems and systems of yet lower mass. We are currently looking into ways in which this could be done. A high-resolution spectrograph with adaptive optics capacity, such as CRIRES at the Very Large Telescope (Käufl et al. 2004), could measure the individual radial velocities of the components of binaries discovered here, and thus could directly measure model-independent mass ratios over a relatively short timeframe. This would greatly assist studies of multiplicity properties of low-mass stars and brown dwarfs, by aiding in both mass ratio distribution and multiplicity fraction determinations.

We have presented observations of 286 mid/late M-dwarfs using the AstraLux Norte camera at Calar Alto in Spain. We resolved 66 probable or confirmed multiple systems, of which 41 were new discoveries. The majority of binary candidates were observed twice or more, and could be confirmed as bona fide companions.

Based on these discoveries and evaluations of the sensitivity range of AstraLux Norte, we deduced a multiplicity fraction inside of the AstraLux sensitivity range of 17.9%, corresponding to a total multiplicity fraction of 21%–27%. The mass ratio distribution is consistent with being uniform down to q = 0.4, but cannot be stringently constrained below this value. The semi-major axis distribution is well represented by a Gaussian function with μ_a = 0.78 and σ_a = 0.47—a function which is significantly narrower and peaked at smaller separations than the corresponding distribution of Sun-like stars.

Most observables point to continuous distributions and a common formation scenario for stars and brown dwarfs, but some discrepancies persist, most notably in the mass ratio distribution. This is however also one of the most uncertain distributions, and more work will be required in the future to more robustly assess mass ratios at the low-mass tail of the stellar population.

We thank all the staff at the Calar Alto observatory for their support. This study made use of the CDS services SIMBAD, VizieR, and CDS Portal, as well as the SAO/NASA ADS service. Some of the archival study was based on photographic data of the National Geographic Society–Palomar Observatory Sky Survey (NGS-POSS) obtained using the Oschin Telescope on Palomar Mountain. The NGS-POSS was funded by a grant from the National Geographic Society to the California Institute of Technology. The plates were processed into the present compressed digital form with their permission. The Digitized Sky Survey was produced at the Space Telescope Science Institute under US Government grant NAG W-2166. Other parts of the archival study make use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation.

In this section, we list special remarks on individual targets, where relevant.

I00235+7711 (GJ 1010). As noted in the Washington Double Star (WDS) catalog (e.g., Mason et al. 2001), this star is a member of an 11'' binary. Both components are visible in full-frame AstraLux images, but since the separation is larger than the region of completeness, I00235+7711 counts as a single star within this range.

I00395+1454N (G 32-37 B). As implied by its identifier, I00395+1454N has a wide binary companion toward the south at a separation of 17'' according to the WDS, which is not included in the AstraLux field of view. Given the new detection of a closer companion with AstraLux, it is probable that the system is in reality at least a triple system.

I00413+5550W (GJ 1015 A). I00413+5550W has a 10'' companion to the east that is noted in WDS. It is visible in the AstraLux image but outside of its completeness range, and thus the star counts as single for statistical purposes.

I01028+4703 (G 172-35). This target is a component of a 15'' binary noted in WDS, which is visible in the AstraLux images, but outside of the completeness range.

I01076+2257E (GJ 9040 B). As its name implies, I01076+2257E is a secondary component in a 10'' binary noted in WDS, which can be seen in the AstraLux images, but does not count in our analysis due to its >5'' separation.

I02027+1334 (GJ 3129). This target has been noted as a double-lined spectroscopic binary with an estimated maximum semi-major axis of 0.13 AU (Shkolnik et al. 2010). As expected, it is therefore not detected in AstraLux imaging. There are no other companions seen with AstraLux, and it thus counts as single in the statistics.

I03325+2843 (J03323578+2843554). This triple system has been observed in several epochs, as reported in Janson et al. (2012). We will discuss it in more detail in a near-future study (M. Janson et al., in preparation) that analyzes systems observed in multiple epochs with AstraLux. The BC pair does not count as a separate pair in the statistical analysis, since its separation is just below 100 mas in the epoch considered here. The measured brightness differences between the B and C components are Δz' = 0.58 ± 0.12 mag and Δi' = 1.03 ± 0.08 mag.

I03372+6910 (GJ 3236). The I03372+6910 system is a known double-lined spectroscopic binary (Shkolnik et al. 2010), which is also eclipsing (Irwin et al. 2009), and thus is of significant use for calibration of low-mass stellar properties. The companion is at a <0.1 AU separation and thus beyond the AstraLux sensitivity range, where we find no additional companions.

I03392+5632 (G 175-2). In addition to the companion discovered in this study, there is a known wide (24'') common proper motion companion noted in WDS, hence the system is at least triple in reality.

I04123+1615 (LP 414-117). There is a spectroscopic binary companion to this star with an orbital period of ∼128 days (Bender & Simon 2008). It is too close to be spatially resolved with AstraLux, and there are no other companions within the sensitivity range of our study.

I04129+5236 (LHS 1642). I04129+5236 is a known close binary system with a well-determined orbit (Pravdo et al. 2004; Martinache et al. 2009). Its separation is smaller than 100 mas at all times, and it therefore remains unresolved by AstraLux. We do detect one other point source in the field of view, but it is a suspected background contaminant based on its blue color, with Δz' = 5.8 ± 0.1 mag and Δi' = 5.3 ± 0.1 mag.

I04247-0647 (J04244260-0647313). This is a target that overlaps with our previous study in Janson et al. (2012). As we already noted there, it is single in the AstraLux field of view, but it is a triple-lined spectroscopic multiple system further in Shkolnik et al. (2010).

I04308-0849S (Koenigstuhl 2 B). Another target that overlaps with Janson et al. (2012), this star is single in the AstraLux field but has a known wide common proper motion companion at 17'' separation (Caballero 2007).

I04388+2147 (G 8-48). In addition to the companion discovered here, there is a wide binary companion at 15'' separation noted in the WDS, hence it is likely that the system is at least a triple.

I04425+2027 (J04423029+2027115). This is a double-lined spectroscopic binary with a period of a few days (Mochnacki et al. 2002), which is far too close to be resolved with AstraLux. It is single in our sensitivity range.

I05030+2122 (LP 359-186). For binaries with a small brightness difference between the components, one should always be wary of potential 180^o phase shifts between different astrometric epochs. For this system, such a shift in the Law et al. (2008) data point with respect to our two epochs seems highly probable, given the consistency in apparent orbital motion when such a shift is considered (∼1^o yr⁻¹ in each case with the shift included, versus a sudden change from ∼30^o to ∼1^o yr⁻¹ when it is not). The quoted value in Table 2 therefore includes such a shift.

I06171+0507 (NLTT 16333). I06171+0507 is a close binary that has been previously resolved in several epochs by Pravdo et al. (2006), and which we re-detect with AstraLux. The pair is itself part of a higher-order multiple system with the bright star HR 2251 at a 103'' separation.

I06579+6219 (GJ 3417, LHS 1885). If taken at face value, the body of astrometric points that exists for this target does not make sense. Three epochs of astrometry exists: one from Henry et al. (1997) taken in 1996 (ρ = 20 and θ = 220^o), one from Law et al. (2008) taken in 2005 (ρ = 15 and θ = 320^o), and our data point taken in 2012 (ρ = 14 and θ = 240^o). Given that background objects can be firmly excluded, this would imply an enormously fast orbital motion since the binary would move from 220^o to 320^o and then back to 240^o within 16 yr, which is impossible for such a low-mass binary with a ∼17 AU semi-major axis. However, the astrometry becomes entirely sensible in an orbital motion framework if we impose a 90^o phase shift on the Law et al. (2008) position angle such that it is 230^o instead, giving a continuous motion of 20^o in 16 yr. In Janson et al. (2012), we suggested an equal phase shift for similar reasons for the Law et al. (2008) data point in the J15553178+3512028 binary system. We thus include such a shift in Table 2.

I07111+4329 (J07111138+4329590). I07111+4329 is a known binary that has been observed previously over several epochs (e.g., Dupuy et al. 2010). There is also a background star in the field of view, with Δz' = 5.7 ± 0.1 mag and Δi' = 4.2 ± 0.1 mag.

I07307+4811 (LHS 229). Although this star looks single in the AstraLux images, it is in fact part of a quadruple system (Harrington et al. 1981). I07307+4811 itself is a close binary M-dwarf pair with a separation of ∼50 mas, too close to be resolved here. In addition, at a 103'' separation far beyond the AstraLux field of view, there is a pair of white dwarfs that are physically bound to this system.

I07320+1719W (G 88-35). As implied by its identifier, I07320+1719W is part of a wide binary system registered in WDS with an 11'' separation. It is visible in the AstraLux images, but beyond the completeness range of the instrument.

I08119+0846 (LHS 35). There is a relatively strong linear trend noted in the radial velocity analysis for the target in Bonfils et al. (2013). Such trends can be signs of stellar companions, but in this case we detect no companions in the AstraLux data.

I08316+1923 (CU Cnc and CV Cnc). This is a known quintuple system, as reported in, e.g., Delfosse et al. (1999) and Beuzit et al. (2004). Four of the components are resolved in two separate pairs (AaAb and BaBb) by AstraLux. The two pairs themselves (CU Cnc and CV Cnc) are too far separated for the AstraLux completeness range, and so they count as two separate binary pairs for statistical purposes. The fifth component is unresolved in the images; this is an eclipsing binary companion to the Aa component.

I08589+0828 (G 41-14). I08589+0828 is a triple system with a close spectroscopic pair on a 7.6 day orbit, and one wider component which is reported at a separation of 620 mas in Delfosse et al. (1999). Subsequently, an orbit has been determined for the wider pair (Hartkopf et al. 2012), with a period of 5.66 yr and a 424 mas angular semi-major axis. Using the estimated orbital elements to predict the location of the wider component in 2012 January when the AstraLux image was taken, the predicted separation is ∼100 mas. This is in excellent agreement with what is seen in the AstraLux image, where the PSF is substantially extended, but not quite sufficiently to get a satisfactory binary fit. Since the fit does not converge, the star counts as single within the AstraLux sensitivity range.

I10497+3532 (GJ 1138). I10497+3532 has been previously reported as a 300 mas binary Beuzit et al. (2004). The fact that it looks single in our AstraLux images despite the excellent quality of those observations implies that it must have undergone substantial orbital motion, bringing it to a much smaller (<100 mas) projected separation in June of 2012. The non-detectability in AstraLux images means that it counts as a single system for the purpose of the multiplicity analysis performed here.

I13143+1320 (NLTT 33370). Recently, Schlieder et al. (2014) reported I13143+1320 as a binary. In NACO images that are approximately coincident with the AstraLux images, the projected separation of the binary is ∼75 mas, which is consistent with the fact that the binary is unresolved in the AstraLux images. It counts as a single system in the analysis performed here.

I15474+4507 (G 179-55). This star is a known eclipsing and double-lined spectroscopic binary with a period of 3.55 days (Hartman et al. 2011). The separation is far too small to be resolved with AstraLux, and we detect no other companions within the AstraLux field of view.

I16555-0823 (GJ 644 C). While the star I16555-0823 (also known as VB 8) itself is single in the AstraLux sensitivity range, it is part of a higher-order multiple (at least triple, possibly quintuple) as a known 1500 AU companion to GJ 644, which was discussed in our Janson et al. (2012) study.

I18180+3846W (LHS 461). I18180+3846W has a 10'' companion to the east registered in WDS. It is visible in the AstraLux images, but outside of the completeness range. There are no other candidates observed in the field.

I18427+1354 (GJ 4071). There is a point source at 37 separation from I18427+1354. The system has only been observed in one epoch, but based on the colors of the candidate (Δz' = 5.8 ± 0.1 mag and Δi' = 5.7 ± 0.1 mag), it counts as a probable background contaminant in our analysis.

I19312+3607 (G 125-15). While I19312+3607 has no candidates visible in the AstraLux images, it is actually a triple system. I19312+3607 itself is noted as a very close (<0.01 AU) double-lined spectroscopic binary in Shkolnik et al. (2010). Additionally, there is a wide common proper motion companion at 46'' (Caballero 2010).

I20298+0941 (HU Del). The I20298+0941 system is a well-known astrometric binary (e.g., Benedict et al. 2000), but to our knowledge, the AstraLux images represent the first instance in which the binary has been spatially resolved.

I20433+5520 (GJ 802 A). I20433+5520 is a well-studied close triple system (e.g., Ireland et al. 2008). It consists of a spectroscopic pair with a period of only 19 h, and a brown dwarf at a separation of ∼90 mas. Both are too close to be resolved with AstraLux, and there are no other candidates in the field of view.

I21000+4004E (GJ 815 A). In addition to the component that we resolve with AstraLux, which was previously known and has been studied over a long timescale (e.g., Lippincott 1975), the primary component of the resolved pair is a 3.3 day spectroscopic binary (Pourbaix 2000),

I21109+4657S (G 212-27). Both of the point sources in the AstraLux field of view are consistent with static background objects that do not share a common proper motion with the primary star, hence they are contaminants rather than physical companions. Their colors (Δz' = 4.0 ± 0.3 mag and Δi' = 3.3 ± 0.5 mag for the closer point source and Δz' = 4.8 ± 0.3 mag and Δi' = 4.3 ± 0.1 mag for the farther one) verify this conclusion.

I21160+2951E (GJ 4185 A). Although I21160+2951E is single within the AstraLux field of view, it has a wide companion at 26'' separation. It also appears that I21160+2951E is itself a close binary pair; this is implied in Shkolnik et al. (2012), but an as of yet unpublished paper is referred to for the specific properties of this pair. Since a general comment is made that separations down to 40 mas are being probed, it is presumably the case that the third component of the system is simply too close in to be resolved with AstraLux.

I21376+0137 (J21374019+0137137). This newly discovered binary candidate is a probable member of the β Pic moving group according to the Schlieder et al. (2012b) study. Its relatively small projected separation of ∼4.5 AU implies that its orbit could be dynamically constrained in a reasonable timeframe, which makes it a potential benchmark binary in the future.

I23318+1956E (EQ Peg B). This wide binary used to have a separation that would have kept it inside of the completeness range of AstraLux (e.g., 35 separation in 1941 according to WDS), but at the AstraLux epoch it is just outside of this range, at 54. It therefore counts as being outside of this range.