SUB-STELLAR COMPANIONS AND STELLAR MULTIPLICITY IN THE TAURUS STAR-FORMING REGION

The target sample was originally constructed by picking 10–15 targets in each of five equal logarithmic mass bins over the 0.15–3.0 M_☉ range, originating from a compilation of 275 stars in Taurus with known spectral types and magnitudes R ⩽ 13 mag (Leinert et al. 1993; Ghez et al. 1993; Simon et al. 1995; Köhler & Leinert 1998; Hartmann et al. 2005; Luhman 2006; Luhman et al. 2006; Guieu et al. 2006). A total of 72 stars were observed between fall 2011 and 2012 with a few follow-up observations in 2013 to confirm common-proper motion of the newly-found companion candidates (Section 4.2 for details). A significant fraction of the targeted stars have been part of previous binary surveys. Since one of our goals is an unbiased view on the multiplicity properties of Taurus stars, we do not exclude them from the sample.

The magnitude cut at R < 13 mag results from the fact that we use adaptive optics to observe the sample. At a distance of ∼140 pc and an age of 2 Myr, this corresponds to a lower mass cut at 0.17 M_☉, assuming negligible extinction. As described in Section 2.2, in addition to a young population, we evoke a subpopulation with an estimated age of ∼20 Myr. At this age, the magnitude limit translates to masses ≳0.75 M_☉, making this sub-sample on average more massive than the younger sample. The results in this paper are independent of this skew since singles and binaries will be affected in the same way. However, the deduced statistics as a function of mass will be less precise for the lowest-mass objects because fewer targets enter the lowest-mass bins. At the very faintest end, applying a magnitude limit may introduce a bias for the inclusion of binaries. The inferred multiplicity frequency might accordingly be biased toward higher fractions in the lowest mass bin under consideration. This is further discussed in Section 5.2.

A detailed analysis of the membership of our target stars in the Taurus cloud is presented in Appendix A, while a summary of it is given here. To be able to draw conclusions that apply to the Taurus population as a whole and to its very young stars in particular, we thoroughly consider evidence for both membership and youth, for all targets of this study. This results in a necessary split of the sample into young Taurus members with ages ∼2 Myr and an extended sample that appears to be co-moving with Taurus, i.e., formed within the same association of clouds, but that lacks conclusive evidence for extreme youth. Membership in the young category is indicated by the presence of accretion or strong infrared excess originating from a disk in addition to strong Lithium absorption, which indicates an age ≪10 Myr (e.g., Hernández et al. 2008). Stars in the extended category are likely part of a population with an age ∼20 Myr, as indicated by their lithium absorption which appears comparable to or stronger than that of the weakest Li signature found in members of Lower Centaurus Crux/Upper Centaurus Lupus (∼16–17 Myr) for a given effective temperature (Song et al. 2012). We take this and other evidence (for the full analysis see Appendix A) as indication that a burst of star formation about ∼20 Myr ago created this group of stars which was followed by another star formation burst 1–2 Myr ago.

We find 36 stars to be classified as young members, while another 29 belong to the extended sample. A total of eight stars in the original sample lack evidence for youth and/or membership in the Taurus association. We present their measurements for completeness reasons but do not include them in the analysis. The resulting sub-samples together with basic stellar parameters and the applied membership criteria are listed in Table 1. In the course of the paper, the entirety of all Taurus members of this study, i.e., the extended sample together with the young members sample, is referred to as the combined sample.

All observations were obtained at the Gemini North telescope with the NIRI instrument (Hodapp et al. 2003) in K_s band (1.95–2.30 μm). The ALTAIR adaptive optics (AO) system (Herriot et al. 2000) was used to obtain diffraction-limited images on NIRI's 1024×1024 Aladdin InSb detector array. The f/32 camera provides a sampling of ∼21.9 mas/pixel and a field of view of ∼22''×22''.

The observing strategy was similar to the one described by Lafrenière et al. (2008). For sky subtraction and bad pixel correction, each target was observed at five dither positions. At each dither position, one non-saturated short exposure (divided into many coadds) was acquired in high-readnoise mode, followed immediately by a longer (typically 10 s/dither) saturated exposure in low-readnoise mode. Using the low-readnoise mode for the latter exposure allows us to reach the sky background limit; otherwise, the contrast would be limited by the high readnoise. This strategy results in a high observing efficiency, and a large dynamic range providing sensitivity at both small and large angular separations. With typical Strehl ratios between 15% and 25%, the observations were sensitive to companions as faint as K ∼ 18 mag (5σ) at large separations ≳2'' from the central star.

We followed standard procedures for data reduction. A sky frame was constructed by taking the median of the dithered images (masking the regions dominated by the target's signal). The individual images were then sky subtracted and divided by a normalized flat field, and the bad pixels were replaced by a median over their good neighbors. For all images, field distortion was corrected as described in Lafrenière et al. (2014). Their analysis shows residual systematic uncertainties of 15 mas, 25 mas, and 50 mas at radii of 4'', 8'', and 12'' from the center, respectively, and a systematic uncertainty of the position angle of 015. These uncertainties do not affect our relative astrometric measurements with NIRI, but may result in systematic separation offsets for wide companions when compared to observations with other instruments (Section 4.2). Figure 1 shows fully reduced, unsaturated images of three discovered close-in bona fide companions.

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We identified a total of 74 companion candidates through visual inspection of the individual shallow and deep exposures of the targeted 64 Taurus members. Our attempts to remove the static speckle pattern by subtracting a point-spread function (PSF) from a different exposure taken close in time did not reveal any additional companion candidates. The companions' positions and magnitudes relative to the target stars were determined with simultaneous PSF photometry using the IRAF task daophot. The required reference PSFs were constructed from the target stars themselves, within a radius of 150 pixels. If one or more of the companions appeared within this radius, they were removed by replacing the contaminated section with a copy of the equivalent region on the other side of the reference star's PSF, rotated by 180°. We confirmed that this procedure introduces negligible photometric and astrometric uncertainties by comparing the resulting photometry of an uncontaminated PSF with and without substitution.

Whenever possible, the individual shallow images were used for photometry/astrometry. If the companion was too faint to be reliably detected in the shallow images, a combination of the deep and shallow exposures, which restores the natural PSF shape in the central saturated core of the central star in the deep exposures, was used. This combination replaces the innermost 8–10 pix with the unsaturated PSF core from a shallow exposure of the same star, scaled to the same exposure time. The introduced uncertainties are ∼0.05 pixels for the measured separations and 0.1 mag for the relative photometry.

We determined astrometric and photometric uncertainties from the statistical fluctuations between the individual dither images, the residual flux after PSF subtraction (typically <5%), and the deep+shallow combination noise. The typical FWHM of the measured PSFs was ∼008 assuming a pixel scale of 0.0219 arcsec/pixel of NIRI. The resulting photometry is listed in Table 2.

The photometry and astrometry of the components of RX J0444.9+2717 required a special routine considering that the central object is a close binary with significantly different component magnitudes and the wide companion is not bright enough to reliably serve as a PSF reference (see Figure 1). We used aperture photometry of the isolated wide and the combined close components, respectively. The resolved component photometry was inferred from the peak flux at the position of the individual components (after correction for the contribution of the other PSF wings), using a power law fit to the correlation between peak and total flux. The relative positions were measured from the centroids of the individual peaks. The location of the faint peak in the wing of the central object is not expected to be strongly biased, since two individual peaks can be identified at a separation larger than the FWHM of the PSF.

The 5σ sensitivity limits for the detection of companions to all targeted stars are tabulated in Appendix C and are shown in Figure 2. They are derived from our companion-free exposures (see Section 3.1). To obtain the curves, the noise in 5×5 pixel regions is measured around every pixel in the image, multiplied by a factor of five, and averaged in annuli of width w = 1 × FWHM around the central star. Since all companions are detected in all five dither images of an observation, the displayed effective sensitivity is a factor of $1/\sqrt{5}$ (≈0.87 mag) better than that of the individual exposures. The separation and brightness distribution of the discovered binary companions relative to our sensitivity limits (Figure 2) suggest that observations are better than 90% complete for binary companions at separations >10 and brighter than ΔK ≈ 8 mag. For reference, Figure 2 shows all literature binary companions detected in the Taurus region within the same separation limits 005–12'' (Harris et al. 2012; Dahm & Lyke 2011; Kraus et al. 2011; Duchêne 2010; Luhman et al. 2010; Rebull et al. 2010; Todorov et al. 2010; Kraus & Hillenbrand 2009a, 2009b, 2007; Itoh et al. 2008; Correia et al. 2006; Duchêne et al. 2004; Cutri et al. 2003; White & Ghez 2001; Woitas et al. 2001; Koresko 2000; Köhler & Leinert 1998; Leinert et al. 1997, 1993; Ghez et al. 1997, 1993, 1991; Simon et al. 1996; Thiebaut et al. 1995; Hartigan et al. 1994; Moneti & Zinnecker 1991).

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Since none of the presently available pre-main sequence evolution models cover the large range of spectral types of the binary components in Taurus, masses are estimated from a combination of model isochrones (T_eff < 2700 K: DUSTY, Chabrier et al. 2000; 2700 K ⩽ T_eff < 3400 K: BCAH98, Baraffe et al. 1998; T_eff ⩾ 3400 K: Siess et al. 2000). Ages assumed for the individual subsamples were 2 Myr for the confirmed young members sample and 20 Myr for the extended sample. Since we cannot exclude the possibility that a few targets of the extended sample are actually very young ≪10 Myr (see Appendix A), part of the inferred masses may be overestimated, because the dependence of spectral type depends only weakly on effective temperature which itself is higher at young ages for a star of the same mass.

Primary masses were derived directly from their effective temperatures, which were inferred from spectral types according to the transformations in Luhman et al. (2003; SpT later than M0) and Schmidt-Kaler (1982; earlier SpT). If no individual component spectral types were known, system spectral types were assigned to the primary assuming that the most massive component dominates the system luminosity. Following the scheme in Lafrenière et al. (2008), secondary masses were derived from the model magnitude of the respective primary according to its assumed spectral type and the magnitude difference between the primary and the secondary, if known. Under the assumption that extinctions are similar for both components of a binary, this is expected to return an extinction-independent model magnitude that can be converted to mass, again with the same isochrones. It has been shown that the inferred mass ratios q = M_B/M_A do not depend strongly on the used pre-main sequence models (Correia et al. 2013), suggesting that the derived values are reliable. Calculated primary and secondary masses are listed in Table 2.

In a sample of 64 observed Taurus members, we found a total of 74 companion candidates (28 in the young and 46 in the extended sample) to 40 stars in the separation range of ∼006 to 12'' and within the sensitivity limits shown in Figure 2. Of the detected companion candidates, 40 were previously known and 34 are new discoveries. Since we have no photometry in other filters and second epoch observations for only a fraction of the new companion candidates (see Section 4.2), we evaluate the probability that a particular companion candidate is physically bound from the density of background stars in the Taurus region. The procedure closely follows the analysis presented in Lafrenière et al. (2014), who use the number of expected chance alignments with unrelated background stars E_det to quantify whether a source is likely bound or not. E_det is calculated as the sum over all target stars of the number of expected background sources that are as bright or brighter and within the separation of the detected companion. The number of background stars is estimated from the density of objects in the Two Micron All Sky Survey (2MASS) point source catalog (Cutri et al. 2003) within 15' from each star using Poisson statistics. Since many of our detections are fainter than the limiting magnitude of the 2MASS catalog of K ≈ 15 mag, we extrapolate the almost linear increase of sources with magnitudes between K = 7 and K = 14 to fainter magnitudes. This approach is validated by the fact that the number N_det of actual detections of similar sources in all our images is always of the same order as E_det. Both values are presented in Table 2.

We consider all sources with E_det ⩽ 0.05 as bound, which equals to a probability of 95% that they are indeed bound, according to Poisson statistics. Similarly, we classify all sources with E_det ⩾ 3 as background with 95% probability that this is true. The status of sources with 0.03 < E_det < 3 cannot be decided statistically and follow-up observations are required (see Section 4.2). The statistically classified number of sources in each category bound:unbound:inconclusive is 22:36:16.

Figure 2 illustrates that most detections with ΔK ≳ 5 mag have low probabilities of being bound. A few of these (a total of 10 companions to DI Tau, HD 283572, LkCa 19, RX J0409.8+2446, RX J0420.8+3009) were previously observed with deep H-band AO imaging by Itoh et al. (2008) and both relative proper motion and color information can be used to assess their nature. Furthermore, 10 target stars were re-observed with a time lapse of ∼1 or 2 yr as part of our survey. If the companions are found to be co-moving with their parent stars, physical association can be assumed. Proper motion checks for all companion candidates with multiple-epoch observations are shown in Appendix B, and the comparison with data from Itoh et al. in Figure 3.

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We find that almost half of the companion candidates with second epoch observations are likely real companions. These are mostly bright close-in companions that also exhibit a high probability of being bound according to their E_det value. Some of these show evidence for orbital motion. We detect four companion candidates to be consistent with being background objects. The rest are inconclusive, either because the uncertainties of the measurements are larger than the proper motion (e.g., DQ Tau), or because they are neither consistent with being background nor co-moving. This suggests significant motion relative to both the background and the respective target star, which can be the case if the faint source is a foreground star or a high-relative-motion member of the Taurus cloud.

The mostly inconclusive results in Figure 3, when combining the observations from this survey with H-band adaptive optics and Hubble Space Telescope (HST) observations from Itoh et al. (2008) lead us to suspect that systematic offsets of relative position angles and/or separations wash out possible signatures. These may be partly caused by the insufficiently constrained distortion correction of NIRI. An attempt to support the proper motion measurements with H−K colors failed due to large systematic uncertainties originating from possible extinction through an edge-on disk, foreground nebulosity, or photometric variability. Additional attempts to use the near-infrared colors of widely-separated companions that have been cataloged by the UKIDSS (Lawrence et al. 2007) and SDSS⁶ surveys did not provide further indications for or against physical association of the companion candidates. Since both the currently available astrometric and photometric measurements suffer from significant systematic uncertainties, new simultaneous observations in different NIR bands will be required to confirm physical association of the faint companion candidates.

Taking into account all of the available evidence, we find that 25 of the 74 companion candidates are likely physically bound to their primaries—confirmed either by proper motion or E_det ⩽ 0.05—while 45 other candidates still need confirmation through future measurements. The remaining four could be ruled out as likely background objects (Appendix B). Two of the confirmed targets are likely of sub-stellar nature. The interesting faint, co-moving sub-stellar companion at a separation of ∼37 from HD 284149 is described in detail in a separate publication (Bonavita et al. 2014). Companion candidate RX J0444.9+2717/cc4 will be part of further investigations.

We find 25 companions with a high chance of being bound around 21 of our 64 observed Taurus members. This is equivalent to a raw multiplicity fraction of ${\rm MF}_\mathrm{raw} = 32.8^{+6.3}_{-5.2}$%. The sensitivity for the detection of faint companions, however, is variable between the stars due to different target brightnesses and variable quality of the AO correction. More meaningful quantities can be derived using only those companions between 10 and 1500 AU that could have been detected around 90% of the stars and taking into account only those stars whose sensitivity curve is equal to or better than that of 90% of the targets. We further base our statistics only on those companions with either statistical or other evidence that they are bound. The resulting multiplicity fractions are lower limits, as it is likely that some of the inconclusive companion candidates may eventually turn out to be real companions.

Among 57 stars meeting the above criteria, we find 14 binaries and 1 triple system with a high probability of being physically bound. This is equivalent to a multiplicity fraction of ${\rm MF}=({\mathrm{B}+\mathrm{T}+\dots }/{\mathrm{S}+\mathrm{B}+\mathrm{T}+\dots })=26.3^{+6.6}_{-4.9}$% assuming binomial uncertainties and stating 68% confidence intervals. The companion star fraction is ${\rm CSF}=({\mathrm{B}+2\mathrm{T}+3\mathrm{Q}+\dots }/{\mathrm{S}+\mathrm{B}+\mathrm{T}+\dots })=28.1^{+6.0}_{-5.3}$% assuming Poisson statistics. When separating into the young and extended subsamples, multiplicity fractions are ${\rm MF}(\mathrm{young})=16.1^{+8.7}_{-4.5}$%, ${\rm MF}(\mathrm{extended})=38.5^{+10.0}_{-8.4}$%. The difference between the two subsamples is consistent with the fact that the extended sample has a significantly larger fraction of stars with masses >1 M_☉ ($(N_{\!M>1M_\odot }$/$N_{\!M<1M_\odot })_{\mathrm{extended}}=3$) than the sample of young stars ($(N_{\!M>1M_\odot }$/$N_{\!M<1M_\odot })_{\mathrm{young}}=0.6$) and that we detect a positive correlation between multiplicity fraction and mass (Section 5.2).

4.3.1. The Frequency of Triples and Higher Order Multiples

Figure 4 demonstrates that our data are compatible with the same binary parameter distributions as field stars, i.e., a flat mass ratio distribution and a log-normal separation distribution (Raghavan et al. 2010). While Kolmogorov–Smirnov (K-S) tests suggest that the assumed and measured distributions cannot be distinguished (P_ρ = 98.1%, P_q > 99.99%), we caution that a log-normal separation distribution as seen in the field might not accurately represent young stars because dynamical evolution can change separations on timescales of up to 100 Myr (Reipurth & Mikkola 2012). An alternatively suggested log-flat separation distribution of companions in Taurus (Kraus et al. 2011; Kraus & Hillenbrand 2012) cannot be ruled out by our data. We find, however, a comparably low K-S probability of P_ρ = 0.46 for this scenario. Since the Kraus et al. results were derived from shallower photometric data and with a different binary separation coverage, a direct comparison is not straight-forward and reanalysis of their data is beyond the scope of this study. Accordingly we will assume in the following a log-normal separation distribution like the one observed for the field, as it appears statistically more likely and in general more physical than a log-flat distribution.

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The young age and low stellar density of the Taurus region imply that it is in a dynamically young state and its binary population is closer to being primordial than denser regions like the Orion Nebula Cluster (ONC) or the dynamically strongly processed population of field stars. Thus, measuring binary parameters in Taurus can shed light on the binary population as it is generated during the embedded star-formation phases before external influences become significant or even wash out the primordial distribution altogether.

The derived multiplicity frequency of ${\rm MF}=26.3^{+6.6}_{-4.9}\%$ is in line with previous multiplicity studies which consistently find that Taurus has a larger binary population than the field and other star-forming regions (Leinert et al. 1993; Petr et al. 1998; Duchêne et al. 1999; Kraus et al. 2011). This can be seen when comparing with the large survey of Solar-type field stars by Raghavan et al. (2010). When limiting their catalog to companions between 10 and 1500 AU, we find a multiplicity fraction of 27% ± 2% for field stars with masses between 0.7 and 1.4 M_☉. This is a factor of 1.63 ± 0.10 smaller than the overall field-star MF 44% ± 2% in the full separation range between ∼0.01 AU and ∼10⁵ AU covered by the survey. We use this factor as a completeness correction for our Taurus sample, under the assumption that field-like mass ratio and separation distributions apply (Section 4.4). In the identical mass and separation range, we find that 38$^{+9}_{-8}$% of all stars in our Taurus sample are multiples, ∼1σ larger than in the field. This corrects to a completeness-corrected multiplicity fraction of ∼62% ± 14% for Taurus stars between 0.7 and 1.4 M_☉.

This indicates that the total multiplicity fraction of Taurus is larger than that of field stars in the same mass and separation range. This is likely due to dynamical processing in dense clusters and agrees well with the proposal that most field stars were born in dense regions like the ONC (Lada & Lada 2003). Our findings are in agreement with previous surveys by, e.g., Kraus et al. (2011), who find a multiplicity frequency of 2/3–3/4. The fact that our deeper observations return a similar multiplicity frequency is due to two factors. On one hand, we could not yet confirm the physical nature of a large number of our candidate sub-stellar companions. On the other, the abundance of low-mass companions is very small, as further discussed in Section 5.3.

In the process of star formation, not only binaries form frequently but a significant fraction of the emergent systems consists of three or more components. While there exists no good theory of how many triples, quadruples, etc., must form as a result of core fragmentation, observations of field binaries show that multiples with n (=2, 3, 4, 5,...) components are on average four to five times as abundant as multiples of the next higher level n + 1 (Eggleton & Tokovinin 2008). With respect to this finding, the present observations of Taurus show a relatively low abundance of triple stars of f₃ = T/B = 1/14 = $0.07_{-0.02}^{+0.13}$. Rather than pointing to a physical property of Taurus' multiples, this value is likely a consequence of the hierarchical nature of stable multiple systems: since all detected stellar companions must have separations within the survey's sensitivity limits, and most stable configurations require a ratio of semi-major axes of at least 3–4 (Harrington 1972), there is a significant chance that either the close pair or wide tertiary remain undetected. This conclusion is supported by the fact that the frequency of triples and higher-order multiples among field stars of ∼11% (Raghavan et al. 2010) reduces to 2.6% ± 0.8% when limiting separations to 10–1500 AU, equivalent to a reduction of f₃ from $0.27^{+3.8}_{-3.2}$ to $0.10^{+3.6}_{-2.1}$. We accordingly find no significant difference between the abundance of triple stars in Taurus and the field.

Previous observations of the multiplicity fraction of stars on, e.g., the Main Sequence, often revealed a small number of binaries with low-mass primaries compared to higher-mass systems (Raghavan et al. 2010; Janson et al. 2012). If mostly due to dynamical processing, this signature should be less pronounced in Taurus with its short lifetime compared to dynamical timescales and low stellar density.

The top panel in Figure 5 shows the multiplicity fraction divided into three equal logarithmic primary mass bins between 0.2 and 3 M_☉. Fitting a linear correlation to the data points we find a slope of α = 0.26 ± 0.19, i.e., ∼1σ evidence for a positive correlation of multiplicity frequency with primary mass. A positive slope is particularly evident (∼3σ) for the extended subsample with α = 0.73 ± 0.24 while young Taurus members show no such correlation (α = −0.12 ± 0.12). The positive slope for the slightly older systems in Taurus agrees with the correlation of multiplicity frequency with mass seen in previous observations of the field (Duchêne & Kraus 2013) and cluster formation simulations (Bate 2012; Krumholz et al. 2012). For example, field stars show an increase of multiplicity from about 20%–30% close to the brown dwarf boundary to >50%–60% at 2–10 M_☉ (Duchêne & Kraus 2013) which is consistent with a slope α_field ≈ 0.37 between 0.1 and 2.7 M_☉. It is accordingly possible that we see an indication for evolution from a flatter distribution at young ages ≪10 Myr to a steeper curve at older ages which would be in agreement with dynamical evolution destroying preferably low-mass binaries due to their lower binding energy. A comparison between the current study and previous results in the field must, however, be regarded with caution as it is possible that binaries with separations outside our sensitivity range follow a different multiplicity–mass relation.

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Nevertheless, no strong biases should exist when comparing our young and extended samples. The possibility that our lowest mass bin may be biased toward a higher multiplicity frequency in this magnitude-limited survey does not significantly change the slope difference even if all tentative companion candidates turn out to be physically bound. It thus appears that we see significant evolution of binary characteristics during the first 20 Myr of stellar evolution. This can be caused by the evolution of either the multiplicity frequency through, e.g., ejection of stellar companions, or the separation distribution. Evidence for changes of the latter can neither be detected nor excluded with confidence in our sample: Gaussian fits to the log-separation histograms of young versus extended binaries find a shift of the peak from −0.34 ± 1.93 to −0.04 ± 1.93 between the samples and a KS-test returns an insignificant probability of P = 0.34 that the two distributions are different. The third possibility, significant evolution of mass ratios, is unlikely at this late evolutionary stage where the mass accretion rates from a circumstellar disk are low, typically ∼10⁻¹⁰–10⁻⁷ M_☉ yr⁻¹, and disk lifetimes are limited to a few more Myr (Natta et al. 2006; Jayawardhana et al. 2006).

We perform a quantitative comparison of the multiplicity frequency as a function of mass with other surveys of young star-forming regions by applying uniform sensitivity limits. In the bottom panel of Figure 5 we compare our results to observations in the 5 Myr-old Upper Scorpius star-forming region. The MF versus primary mass distribution in both regions is qualitatively similar, but with a slightly smaller (≲1σ significance) multiplicity fraction of Taurus stars in each mass bin. Log-linear slopes in the three populated mass bins are not significantly different (α_USco = 0.06 ± 0.17, α_Tau = 0.25 ± 0.17). Lafrenière et al. (2014) further find that their Upper Scorpius data are consistent with a previous study of stars in the 2–3 Myr-old Chamaeleon I star-forming region (Lafrenière et al. 2008). The fact that these distributions of young stars appear relatively flat—within the current sensitivity limits—might thus be a universal feature of star formation.

Interestingly, only very few companion candidates were detected with magnitude differences with respect to the primary of 5 mag < K < 8 mag at separations <6''. This magnitude range deserves particular attention, because it is roughly consistent with the sub-stellar mass range between the deuterium and hydrogen burning limit at young ages. Since the magnitude limits of our survey are for the most part significantly fainter than the faintest observed companions at separations >02, this void is apparently a real feature of the binary population.⁷

With two candidate brown dwarfs discovered with a high chance of being bound, we calculate a frequency of brown dwarf companions of MF(BD) = 3.5$^{+4.3}_{-1.1}$% within our 90% sensitivity limits between effectively ∼20–70 and 1500 AU. As there are a three additional companion candidates with currently unclear status (0.05 ⩽ E_det ⩽ 3), an upper limit of 8.8$^{+5.2}_{-2.5}$% can be estimated when assuming all of these turned out to be true companions. This result is consistent with previous estimates in Taurus (>3.9$^{+2.6}_{-1.2}$% between 5 and 5000 AU; Kraus et al. 2011) as well as young stars in Upper Scorpius with frequencies of 1.8% and ≲4.0$^{+3.0}_{-1.2}$% for sub-stellar companions at separations of 50–250 AU and 250–1000 AU respectively (Lafrenière et al. 2014). Furthermore, Metchev & Hillenbrand (2009) find a brown dwarf companion frequency of ∼3.6% to solar-type field stars between 28 and 1590 AU. Thus, brown dwarf companions with separations of up to several hundred AU appear with frequencies of a few percent at all evolutionary stages.

We want to know whether the low density of brown dwarf and planetary companions is consistent with being drawn from common separation and mass ratio distributions between the stellar and sub-stellar mass regime. We test this by determining whether the observed number of brown dwarf companions can be reproduced with the observed separation and mass ratio distributions (Figure 4), which are based on an almost entirely stellar (except one brown dwarf) companion population. We simulated and analyzed 10,000 sets of synthetic observations. These were used to determine the frequency of cases where the supposedly underdense region harbors at most one companion. The individual data sets are generated according to the following algorithm. (1) Draw a random mass from our observed sample (Table 2). (2) Create a companion with a separation to the host star randomly drawn from the log-normal separation distribution in Figure 4. (3) Assign a companion mass assuming a linear-flat mass–ratio distribution and the primary star's mass. (4) Repeat 57 times (= the original binary sample size). We find that in 68% of the cases, the examined region has at most as many stars as were observed here. Accordingly, the observed density is highly compatible with the assumed distributions.

The implications are two-fold. On one hand, we do not find evidence for an extension of the so-called brown-dwarf desert at wide separations, i.e., a dearth brown dwarf companions below what is expected from extrapolation of the distribution functions of higher-mass companions. The term brown dwarf desert was originally coined to describe the significant lack of close-in (≲ 10 AU) brown dwarf companions around solar-type stars in radial velocity surveys (Marcy & Butler 2000) and was suspected to possibly also hold for wider companions. On the other hand, the observed low frequency of brown dwarf companions is consistent with being the low-mass tail of the stellar companion mass distribution. Accordingly their properties require neither a discontinuity of the mass distribution (e.g., a "break mass") nor of the underlying dominant formation mechanism of stellar and brown dwarf companions. These results for a young star-forming region such as Taurus appear to be in line with results from the study of much older stars by Metchev & Hillenbrand (2009) who reach similar conclusions from their analysis of solar-type stars in the field.