A MULTIPLICITY CENSUS OF INTERMEDIATE-MASS STARS IN SCORPIUS–CENTAURUS^*

Our sample consists of early-type stars in the Sco–Cen region. The stars were selected among all targets identified as Sco–Cen members in de Zeeuw et al. (1999) that fulfilled two criteria: (1) they had to have a measured parallax and proper motion by Hipparcos and (2) they had to have been previously unobserved with adaptive optics (AO) instruments on large telescopes; i.e., in the surveys of Shatsky & Tokovinin (2002) or Kouwenhoven et al. (2007), or in our NIRI survey of the USco region (D. Lafrenière et al., in preparation). The Hipparcos-based requirement allowed for automatic selection of targets with well-determined kinematics and distances, which is important both for a high fidelity in selection of bona fide members, as well as being helpful for the physical interpretation of any discovered companions. Indeed, the vast majority of early-type Sco–Cen stars that were followed up in Chen et al. (2011) were confirmed as real members, whereas later-type stars had a lower confirmation rate. Likewise, all our targets that have been studied in Rizzuto et al. (2011) were assigned high membership probabilities. The visual brightness limit of Hipparcos of V ∼ 9 mag also matches well with the range of optimal performance for AO wave front sensors, and thus ensures that a good contrast can be achieved in each case (provided acceptable ambient conditions). The avoidance of Shatsky & Tokovinin (2002) and Kouwenhoven et al. (2007) targets helped both to ensure a maximal utility of our survey in terms of mapping the full multiplicity properties of Sco–Cen, and also honed in on an interesting range of planet properties—since the previous surveys focused largely on more massive stars (B- and early A-type), the remaining targets are primarily F- and late A-type (with a few cases of early G-type), which is a range that has not been covered in multiplicity studies as extensively as most other spectral type ranges thus far.

As a result of these selections, our total sample consisted of 145 stars, of which 138 were eventually observed. The sample has a median mass of 1.5 M_sun, with masses ranging from 1.0 M_sun to 4.2 M_sun (mass determinations are described in Section 3.2). While four stars have masses >5 M_sun, they were imaged with a different instrumental setting that disfavors a homogenous analysis, and by chance several of the images were also observed under rather poor conditions. Hence, these four objects have simply been excluded from any statistical analysis. The ages of the targets adopted for the analysis performed here are 5 Myr for the (relatively few) USco members and 10 Myr for the UCL and LCC members. These ages have been under discussion in the recent literature, with Pecaut et al. (2012) suggesting an older age, but we base our estimates on the Song et al. (2012) analysis, which empirically demonstrates UCL and LCC to be younger than β Pic; the authors adopt an age of 10 Myr in both cases. The USco region is not discussed in Song et al. (2012), but since it is known to be younger than UCL and LCC, we adopt the original age of 5 Myr (de Zeeuw et al. 1999). There are two scientific issues studied here that are in principle impacted by age: the detection limit estimation and the mass ratio determinations. However, as we will discuss in the following individual sections, the impact of a factor ∼2 change in age would be modest for the purposes of this study. The targets are summarized in Table 1.

The first epoch imaging was performed in the spring of 2011, using the NICI AO-assisted camera (Artigau et al. 2008) on the Gemini South telescope in Chile. Out of 145 proposed targets, 115 were observed during this period. Follow-up of 53 targets with companion candidates was executed with the same instrument one year later, during observing cycle 2012A. Furthermore, due to an unforeseen excess in available observing time with NICI, our 2011A program was re-introduced into the queue in 2012A, and an additional 23 targets were imaged, for a total of 138 targets observed in at least one epoch. Some candidates that had indications of sharing a common proper motion with the primary were followed up spectroscopically, either using Very Large Telescope/NACO (Lenzen et al. 2003; Rousset et al. 2003) during ESO period 89 for simultaneous H+K coverage with AO-assisted slit spectroscopy, or using Gemini/NIFS (McGregor et al. 2002) during 2012A for AO-assisted H-band integral field spectroscopy. Some targets were also followed up in a third astrometric epoch using excess time for the 2012A program that arose from efficient scheduling and execution of the observations. Finally, in period 2013A, we performed follow-up of those targets with candidates that had only been observed in one epoch during 2012A, in addition to acquiring another epoch of imaging for the particularly puzzling targets HIP 80130 and HIP 82569.

Our imaging observations were optimized for a high observing efficiency, and consisted of two sequential exposures per target, where the first exposure included 10 coadds of 0.38 s each; 0.38 s is the minimal individual integration time available for NICI. The second exposure consisted of a single 80 s integration. The dual-band imaging mode was employed with the 50/50 beamsplitter, using the K_s filter in the red channel and the H₂(1–0) filter in the blue channel. The H₂(1–0) filter is a narrow-band filter within the K-band range, with an almost identical pivotal wavelength (2.12 μm) to the K_s filter. In this way, we achieved a nearly simultaneous and very wide dynamic range, with the primary star being generally non-saturated in the short H₂(1–0) exposures. We also obtained good sensitivity with respect to the read noise limit for faint candidates in the long K_s exposures. Each target was subjected to a random offset of <5'' after acquisition. This allowed adjacently-observed targets to be used as sky frames for each other, in the same way as during dithering/jittering, but applied on a sequence of targets instead of on a sequence of images of a single target. The observations were generally acquired under average to good conditions (fulfilling the Gemini 70th percentile image quality condition), with a few exceptions that are marked in Table 1 and excluded from any statistical analysis.

The spectroscopic observations were mainly utilized for the analysis presented in Janson et al. (2012b), but were also useful for some of the targets presented specifically here. Summarizing the description in the previous work, the NACO spectra were taken in the H+K setting with a spectral resolution of R ∼ 550 and simultaneous coverage from 1.33 to 2.53 μm. An ABBA nodding sequence along the 172 mas wide slit was employed for background subtraction, with a nod throw of 10''. One initial AB cycle was completed with short integration times of 1 s and 12 coadds, followed by a series of 100 s exposures, structured as 3 AB cycles with 5 s by 20 coadds for the brightest candidates and 10 AB cycles with 25 s by 4 coadds for the faintest candidates. The short exposures allowed the primary to remain non-saturated such that it could be used as a reference star, and the long exposures minimized the read noise, enabling a high signal-to-noise ratio for the companion candidate. The NIFS spectra were taken in the H band with a spectral resolution of R ∼ 5000 covering a spectral range of 1.49–1.80 μm. Each sequence observation started with a dither sequence with 21 s integration times with the central star in the field of view, to obtain non-saturated spectra of the primary for the purpose of using it as a standard star. This sequence was then followed by a deeper dithering sequence with integration times of 240 s, with the companion candidate included in the field of view. If the separation of the candidate was small enough that the NIFS field of view (3'' on each side) could fit both the star and companion, then this was accommodated, otherwise the field was centered on the candidate.

Data reduction for the NICI imaging was performed using custom IDL routines, since the observational strategy was somewhat novel and thus required flexibility in the reduction procedure. For each image file, the red and blue channel images were extracted and analyzed separately. As a first step, flat fielding and bad pixel removal were applied, followed by a background subtraction, in which a median of several adjacent images were taken and subtracted from each individual image. A distortion correction was applied using the separate distortion solutions for the red and blue channels provided on the NICI homepage,⁹ with a quadratic interpolation scheme. By default, north points downward in NICI images, and the red and blue channels are mirror images of each other, with one having a right-handed and the other a left-handed orientation. Which channel is oriented which way depends on whether NICI is mounted in an up-looking or side-looking configuration. Thus, since the instrument was mounted in different configurations at different epochs, the orientation switched between the red and blue channels between images. All images were re-oriented into a common framework with north pointing up and east to the right, taking these various circumstances into account. Finally, the images were shifted using a spline interpolation, such that the primary star became centered on the central pixel. For this purpose, Gaussian centroiding was used for the H₂(1–0) images, where the star was unsaturated in the short exposures. For the K_s images, where the primary was typically saturated even in the short exposures, manual centering by eye was applied. As described in Janson et al. (2012b), this gives a smaller scatter in the background star astrometry than a range of other methods tested for the purpose, and the good consistency between the independent H₂(1–0) and K_s astrometry noted in Section 3.1 further demonstrates the validity of the method.

In the same way as for the NICI imaging, the NACO spectroscopy data reduction was also performed with a custom IDL pipeline, since we had a set of routines available from a previous observing program (Janson et al. 2010) that could be easily adapted to form part of the pipeline. The procedure started with flat fielding and bad pixel removal. Each AB set was then pairwise subtracted to remove the background. The spectral traces were (nearly) vertical on the NACO detector. Hence, for each pixel row, the photocenter of the star was determined through Gaussian centroiding. This works well not only for the non-saturated sequences, but also for the longer-exposure sequences, since the stars are only mildly saturated. A spectral trace was then fitted to the centers of the respective rows, and all the data were shifted so as to form a perfectly vertical spectral trace, with the photocenter of the star at the central pixel column, for all frames in each observational sequence. One collapsed frame of the collected non-saturated data and one of the saturated data were produced using a regular mean combination. At this point, the secondary spectra were clearly visible at their known positions in the deep exposures, and could be extracted using an interpolation between the fluxes measured directly inside and outside of the location of the secondary as an estimation of the stellar point spread function (PSF) at that location. A 162 mas aperture was used in the extraction of both the stellar and companion spectra. Wavelength calibration was performed using a combination of telluric features and intrinsic features in the stellar spectra. For flux calibration, the primary star was modeled as a single-temperature blackbody. The extracted companion spectrum was divided by the fraction of the stellar spectrum to the model blackbody, which eliminates all telluric features from the companion's spectrum. Intrinsic stellar features remain as contaminants, but as noted in Janson et al. (2012b), such features are rare and weak in these early-type stars, and do not affect the largely continuum-based analysis that they are used for.

Basic data reduction of the NIFS data was performed using the facility-provided IRAF pipeline. This executed all fundamental steps such as flat field correction, distortion correction, wavelength calibration, and data cube construction. The final steps of registering and shifting all frames to a common center, as well as extracting the spectra, were done in IDL. Each wavelength slice of each data cube was treated as an individual image, being centroided and interpolated in the same way as described above for the imaging. Extraction was performed using a 172 mas circular aperture.

As a general broad classification, the candidate companions can be divided into a bright group and a faint group. The brighter candidates generally have very small background contamination probabilities (≪1%), favorably small separations, estimated masses in the stellar regime, and are visible in both the K_s and the H₂(1–0) images. The fainter candidates, by contrast, generally have high contamination probabilities (≫1%), favorably large separations, estimated masses in the planetary regime if they would be interpreted as companions (∼5–15 M_jup), and are generally not visible in the H₂(1–0) images. There are a few intermediate cases, some of which were discussed in Janson et al. (2012b) and the rest of which will be discussed individually here, but first we discuss the separate analyses that were applied to the two distinct populations.

The brighter candidates, as mentioned, were visible in both the K_s and H₂(1–0) images, and so astrometric analysis was performed independently in the two channels for these candidates. We used Gaussian centroiding for determining the positions of the companions in both cases. The astrometry was found to have good consistency between the two bands, except for a systematic rotational shift of 117 in the H₂(1–0) data with respect to the K_s data, which switches sign between the up-looking and side-looking instrumental configurations. Hence, we interpret the blue channel as having a 117 rotational offset that is corrected for by de-rotating the images by the corresponding amount. We then evaluate errors in the astrometry on the basis of the scatter between the H₂(1–0) and the K_s astrometry. We do this separately for the very close (⩽05) and the wider (05–5'') population of candidates, and find errors of 4 mas in separation and 09 in position angle in the former case, and 8 mas and 04, respectively, in the latter.

Given that these objects have very low contamination probabilities and increase in frequency toward smaller angular separations in an opposite way from what would be expected for background stars, they are considered to be probable companions and are considered as such for the remainder of the discussion. They have not been confirmed with common proper motion, except in cases where a fainter candidate was followed up in the same system. Among the targets that were followed up for this reason, HIP 58220 B can be confirmed as a common proper motion companion. HIP 57595 B could not be accurately registered in the second epoch due to overlap with a bright sidelobe from the primary star, although by eye it does appear to share a common proper motion. HIP 75891 B and HIP 77520 B are consistent with common proper motion, but the background hypothesis cannot be rejected due to a small motion of the primary stars relative to the astrometric precision. One exception, however, is HIP 72630, where the candidate has a false alarm probability of only 0.3%, but the proper motion analysis nonetheless shows that it is a background contaminant. The candidate has the highest false alarm probability of all the targets with ≪1%, hence while its presence is relatively unlikely, it is not particularly surprising. It does however demonstrate that common proper motion testing would be an important aspect of providing final proof of companionship for the individual binaries, and to weed out any potential contaminants that could conceivably remain in the sample, e.g., HIP 58528 B (false alarm probability of 0.2%) or HIP 67428 (0.3%).

The fainter candidates are generally not visible in the H₂(1–0) images, but as noted above, the astrometry in the K_s and H₂(1–0) bands has good consistency, hence we proceed with astrometry from the K_s band alone for this population. It is known a priori that the vast majority of these candidates must be background contaminants from the calculated probabilities alone, so Common Proper Motion (CPM) analysis is certainly necessary in order to detect any real companions among them. Thus, all of the faint candidates have been followed up in at least one additional epoch. Since Sco–Cen targets move rather slowly on the sky, the confidence level of the common proper motion testing rarely reaches 3σ or higher. However, the candidates move by a median amount of 27 mas, larger than the residual scatter of 13 mas, and the median difference between the candidate motion and the expected background trajectories is only 4 mas. Hence, the typical faint candidate shows a motion that is well consistent with background motion, and is distinct from the common proper motion by just above the 2σ level.

Nonetheless, at these levels of confidence, both real companions and background contaminants can plausibly exist among the candidates that experience relatively little motion. Hence, for the targets that seemed to move the least or sometimes not at all, we performed further follow-up in a third epoch of astrometry, as well as with spectroscopy in many cases. In this way, the brown dwarfs discussed in Janson et al. (2012b) were confirmed as companions (HIP 65423 B, HIP 65517 B, and HIP 72099 B), both through the CPM and spectral analyses consistently. Similarly, most of the rest of the targets could be confirmed as background contaminants in the CPM analysis, and in cases where spectra were acquired (e.g., for the candidates around HIP 62677 and HIP 72584), a consistent result was obtained. However, there are two cases that remain puzzling in this regard. These targets—HIP 80130 and HIP 82569—will be discussed in more detail in Section 3.5.

The multi-epoch astrometry is summarized in Table 2.

In order to determine the physical properties of the binaries discovered in our sample, we first calculated their photometric properties. The secondaries in the systems are typically clearly visible and non-saturated in both the short H₂(1–0) and the short K_s exposures. The primaries, on the other hand, are typically only non-saturated in the H₂(1–0) filter. However, the pivotal wavelengths of the respective filters are almost identical (2.12 μm in both cases), which means that the [H₂ − K_s] color is essentially independent of stellar temperature. Indeed, integration of the flux in the bandpasses of the respective filters shows that the difference in this color between a 5000 K and a 10,000 K blackbody is less than 0.01 mag. This temperature range encompasses all of our primary stars as well as Vega, implying that in Vega magnitudes, the H₂(1–0) and K_s magnitudes are essentially identical. As a result, we can estimate the primary flux count in the K_s image by multiplying the measured count in the H₂(1–0) image by a uniform factor. We determined this factor by measuring the fluxes of all secondaries that are non-saturated in both images; we found a value of 14.02. Hence, we can estimate the K_s-band binary flux ratios by estimating the primary counts in this way and by measuring the secondary counts directly. In addition, we can measure the H₂(1–0)-band binary flux ratios directly in the image, and by comparing the ratios we can cross-validate the method and get an estimate of the errors associated with it. We find that the two measurements are consistent to within 0.2 mag, which we use as the photometric error. In all cases, we use a circular aperture of 72 mas diameter to determine the counts.

For calculating masses of the various components, apparent K-band magnitudes are adopted from 2MASS (Skrutskie et al. 2006), and the primary and secondary magnitudes are calculated using the flux ratios described above. The apparent magnitudes are translated into absolute magnitudes using distance moduli based on the Hipparcos parallaxes (Perryman et al. 1997). These absolute magnitudes are then used in conjunction with isochrones at the ages of the Sco–Cen sub-groups to derive masses. In our case, we use the Siess et al. (2000) isochrones, since they cover the full range of stellar masses in our sample from 0.1 M_sun to 5 M_sun. However, we also compare the results to the Baraffe et al. (1998) isochrones in the overlapping range of ⩽1.4 M_sun and find that at these ages and masses, the predicted K-band magnitudes are consistent to within 0.1 mag between the models, which is smaller then the photometric error. We also use the Baraffe et al. (1998) isochrones for one secondary with a mass of <100M_jup, i.e., outside of the range of the Siess et al. (2000) models. The magnitudes and masses of the binary components are listed in Table 3.

For evaluating the detectability of companions around any given star in the survey, and for evaluating the completeness to such companions in the survey as a whole, we must first calculate contrast curves. This is done in a very similar manner to the contrast calculation of actual binaries described in Section 3.2, i.e., by estimating the primary flux count in the deep K_s-band images from the non-saturated H₂(1–0) count and factoring in the filter translation, as well as the difference in integration times. The standard deviation is calculated in a series of annuli at different separations from the central star to acquire σ as a function of angular separation, and a 5σ criterion is used as the detection threshold. Normalizing the 5σ curves by the primary flux gives the contrast curve, and factoring in the primary magnitude and the distance modulus as in Section 3.2 gives the detectable absolute magnitude as a function of separation around each star. Since these limits correspond to planet and brown dwarf masses, we use DUSTY models (Chabrier et al. 2000) for temperatures of >1700 K and COND models (Allard et al. 2001; Baraffe et al. 2003) for <1700 K for translating magnitude limits into mass limits, given the estimated ages. The completeness of the survey as a whole can then be calculated as a 2D function of separation and mass by evaluating what fraction of the targets provide detectability for companions of any given mass and separation. We plot some contours of this function in Figure 2. There are bumps in the individual contours due to strong PSF sidelobes and similar features in the images. As an example, we find that the completeness is 70% for 10 M_jup planets outside of 12, which corresponds to 160 AU at the median distance of the sample of 132 pc.

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The detection limits quoted in terms of mass depend on the exact ages of the systems, hence given the uncertainty in age of the Sco–Cen association as discussed above, they should be treated with a certain degree of caution. However, the impact of the factor ∼2 uncertainty in age has a modest impact for the masses near our detection limits. For instance, according to the DUSTY models (Chabrier et al. 2000), a 10 M_jup object at 5 Myr has the same K-band brightness as a ∼13 M_jup object at 10 Myr. Our 70% completeness limit quoted above would thus only increase by ∼30% if the Pecaut et al. (2012) ages were applied.

Here, we will consider the statistical distributions of the binary population in our observed sample. Figure 3 displays the mass fraction versus the projected separation of the detected binaries. The most striking trend is a lack of nearly equal-mass binaries, particularly at large separations. This cannot be caused by any bias related to our detection limits, both because the completeness is very good over our whole considered separation range of 01 to 50 for masses down to our lowest-mass detected companions of ∼50 M_jup as shown in Section 3.3, and also because our sensitivity increases toward larger separations and toward larger masses, and is maximal in the range where the lack of companions is observed. The inferred masses of the individual components depend on age, but since both components evolve with time, the impact of age uncertainties on the relevant order is limited by their calculated mass ratio. For instance, according to the Baraffe et al. (1998) models, a 1 M_sun primary and 0.1 M_sun secondary at 10 Myr (the approximate UCL/LCC age according to Song et al. 2012) correspond in K-band brightness to a 1.1 M_sun primary and 0.13 M_sun secondary at 16 Myr (the corresponding Pecaut et al. 2012 age). Hence, the mass ratio only changes from 0.10 to 0.12 between the younger and older age, and the impact decreases as the mass ratio gets larger, since the evolution of the components becomes more equal. As a result, the age uncertainty has a small impact on the observed mass ratio distribution, and cannot explain the lack of near equal-mass binaries.

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We can attempt to quantify the companion mass ratio distribution with a simple power law, $f \sim q^{\alpha _q}$, where f is the frequency, q is the mass ratio (secondary to primary, i.e., between 0 and 1), and α_q is the power law index. This is done by generating simulated populations with a given distribution determined by α_q and comparing to the observed population using a Kolmogorov–Smirnov test. For each population, we generate 1000 binaries; 1000 populations are being simulated in order to verify the robustness of the results. Cases where the secondary mass is <50 M_jup are removed in order to maintain a good completeness, hence the power law fit is only valid down to secondaries of this mass. The full range of separations (01–50) is included in the comparison. The median probability among the 1000 simulations is adopted as the result of the full test, and the 5th and 95th percentiles are taken as the lower and upper bounds, respectively. This is equivalent to the procedure applied in Babu & Feigelson (2006). In this way, we can firmly exclude that the mass ratio is uniformly distributed, since simulated populations with α_q = 0 have a 1.4 ± 0.4 × 10⁻⁷ probability of matching the observed distribution. It is necessary to make α_q substantially negative (a bottom-heavy mass ratio distribution) to obtain better fits. A value of α_q = −0.4, which has been used for more massive stars (e.g., Kouwenhoven et al. 2007), is still too shallow, with a probability of 0.023$^{+0.007}_{-0.005}$%. α_q = −0.9 fits better at 17.5$^{+0.04}_{-0.03}$%. However, this form of power-law fitting does not have a promising asymptotic behavior, as it starts to drastically overshoot at small mass ratios for steep power law indices. Hence, we slightly alter the form of the distribution, and formulate it as $f \sim 1 - q^{\beta _q}$, which better fits the observations for a range of values of β_q. Note that in this framework, a higher β_q implies a more bottom-heavy mass ratio distribution, i.e., in the opposite sense to α_q. Stepping through β_q in steps of 0.5, we find that the best fit is provided by β_q = 2.5, which has a 66.6$^{+4.1}_{-3.8}$% probability of matching the observed distribution, hence we adopt this value for the remainder of this analysis.

The semimajor axis distribution is another issue of interest to address. We do this in a very similar way as above, simulating populations with given distributions and comparing them to the observed distribution using a Kolmogorov–Smirnov test. For translating from our observed projected separations into semimajor axes, we multiply the separations by a factor 1.02. This was calculated based on Brandeker et al. (2006) as the conversion factor between semimajor axis and projected separation for a sample with an assumed eccentricity distribution of f(e) ∼ 2e. For a less eccentric distribution, the conversion factor can be somewhat higher, up to a maximum of 1.27 for completely circular orbits. For instance, Fischer & Marcy (1992) calculated a factor of 1.26 for their M-dwarf sample. We have tried the same analysis as below with a 1.26 conversion factor, and found that it makes very little difference for the results and has no impact on the conclusions. Hence, in the procedure described in the following, only the factor of 1.02 is used.

Relative to the mass ratio case, a comparison of the semimajor axis distribution to other distributions in the literature is less discriminating, partly due to the fact that the binaries here cover a somewhat limited semimajor axis range relative to the extremely wide range that occurs in the universe (approximately six orders of magnitude from a few solar radii to tens of thousands of AU). For Sun-like stars, a log-normal distribution with μ_a = 1.64 and σ_a = 1.52 has been measured (Raghavan et al. 2010). Applying this relation in our simulations results in a 29.9$^{+4.5}_{-3.9}$% probability that it is drawn from the same distribution as our observed sample. For more massive stars, it has been suggested that Öpik's law (Öpik 1924) might provide a better fit than a log-normal distribution (Kouwenhoven et al. 2007). Öpik's law represents a uniform distribution in logarithmic semimajor axis space. In this sense, it can be seen as a log-normal distribution with infinite σ_a. Applied to our sample, Öpik's law results in a 39.3$^{+5.6}_{-5.4}$% matching probability. Thus, while neither of these distributions fit extremely well, neither can be more than at best marginally excluded. This is consistent with a picture in which intermediate-mass objects have an intermediate distribution between lower-mass and higher-mass stars. We note that if we adopt a log-normal distribution and simply shift the Sun-like distribution to wider separations, μ_a = 2.40 and σ_a = 1.52, then we get a 67.2% ± 5.1% probability match, hence we adopt this relation for future purposes. In all of these cases, we set lower and upper bounds on the semimajor axis of 0.023 AU and 23,000 AU, respectively (Kouwenhoven et al. 2007).

The multiplicity fraction within 01 <ρ < 50 is 27/130 = 20.8%, with 4.0% errors assuming Poissonian statistics. If we were to assume a total multiplicity fraction of 100%, then adopting the best-fit distributions in mass ratio and semimajor axis as above, and accounting for the completeness function, would result in a higher multiplicity fraction within 01 <ρ < 50 of 35.1%. Hence, these distributions imply that the actual total multiplicity should be approximately 59%, in order to reproduce the 20.8% multiplicity observed in our covered observational range. Obviously, there is significant uncertainty in this number, primarily due to the limited coverage in semimajor axis space. For instance, if we were to adopt Öpik's law instead, then the total implied multiplicity fraction would be 81%. However, since the distribution is as narrow as the Sun-like distribution in the former case, and it cannot possibly be broader than the Öpik distribution adopted in the latter case, it is probably fair to conclude that the total multiplicity fraction is bounded between 59% and 81% for any realistic distribution.

Here we provide individual notes for targets for which special information exists.

HIP 50083. HIP 50083 is one of the four stars that have a mass of >5 M_sun, and is therefore excluded from the statistical study. The data are of insufficient quality to put any stringent constraints on the presence or absence of companions.

HIP 50847. The image of HIP 50847 is of too poor quality to be scientifically useful. Nonetheless, there is a probable bright binary companion visible in the image, at a separation of ∼22 and a position angle of ∼351°. HIP 50847 is one of the four >5 M_sun stars that were omitted from any statistical analysis. Aside from the possible companion reported here, HIP 50847 (HD 90246) is a known double-lined spectroscopic binary with a period of ∼15 days (Quiroga et al. 2010), hence the system is possibly triple.

HIP 56543. There is a bright source at the edge of the field, at a separation of 992 and a position angle of 3107. Thanks to the large separation and relatively small brightness contrast, this source is visible in 2MASS (Skrutskie et al. 2006) with designation 2MASS J11353717−5043180, at a separation of 1024 and position angle of 3093 from HIP 56543. The expected motion of HIP 56543 relative to a static background object over the ∼12 yr baseline is 343 mas west and 31 mas south, fully in agreement with the observations. Hence, we can conclude that 2MASS J11353717−5043180 is a background star, physically unrelated to HIP 56543.

HIP 57238. While the PSF of HIP 57238 is extended, it is extended to the same degree and in the same direction in both the primary and the well-resolved secondary in the system. Hence, we conclude that it is likely to be a PSF artifact.

HIP 58899. This is one of the two systems in the sample that are triple within the sensitivity range of the survey. For the statistical investigations of mass ratio and semimajor axis, HIP 58899 is counted as two pairs, where the tighter AC pair is counted as a regular pair and the wider AB pair is counted as another pair but the A+C mass is used for the A component.

HIP 59481. Given its relatively low contamination probability of 1.1%, and the fact that it was the only point source in the field of view, the candidate companion to HIP 59481 was considered one of the most interesting targets for follow-up after the first epoch of imaging. However, the astrometric follow-up clearly shows that it is a background contaminant.

HIP 63962. Given a rather extended PSF, HIP 63962 may be an unresolved binary, with a separation of a few tens of mas (well under 50 mas) and a position angle of ∼40°.

HIP 64322. This star was observed under too poor conditions for the images to be scientifically useful, but a probable bright binary companion is visible at a separation of ∼23 and a position angle of ∼170°. Like all images of insufficient quality, it is omitted from the statistical analysis.

HIP 66001. Since the PSF of HIP 66001 is extended, it may be an unresolved binary. The separation would be a few tens of mas (well under 50 mas), and the position angle ∼30°.

HIP 77038. HIP 77038 is one out of the two systems in the survey that are triple systems. For statistical purposes, when counting mass ratio and semimajor axis, the system is counted as one pair in which the primary is one component, and the sum of the tight BC pair is the other component. The BC pair itself is not counted as a pair in this context, since the components are both late-type, and thus the mass of B is outside of the range of interest in primary mass.

HIP 78384. Also known as η Lup, this is one of the four >5 M_sun stars that are excluded from our statistical study. The system is known as a probable triple system (e.g., Eggleton & Tokovinin 2008), but both the secondary and tertiary components are outside of the NICI field of view.

HIP 79097. Apart from the clearly resolved companion at 08 separation, there is an additional extension in the HIP 79097 A component that is not present in the companion. This strongly implies that a third component is present in the system as a close companion to component A, with a separation of a few tens of mas (well under 50 mas) and a position angle of ∼110°.

HIP 79977. This star has a debris disk that was recently spatially resolved (Thalmann et al. 2013). The deep image in Thalmann et al. (2013) also shows two faint point sources within 5''. Our image is too shallow to detect either the disk or the point sources at a statistically significant level, although the point sources can be traced at their expected background positions with prior knowledge of where to look.

HIP 80130. The most puzzling target in the survey, HIP 80130 has a faint point source residing at 41 separation from the star, which was identified as a candidate very low-mass brown dwarf in the first epoch image, and thus was followed up in a second epoch. The second epoch showed indications of common proper motion, so it was followed up in a third (and subsequently a fourth) epoch of astrometry, and with spectroscopy. The photometry over the four epochs suggests strong variability, with ΔK = 7.1 ± 0.8 mag. The astrometry in all four epochs, spanning approximately two years, is essentially perfectly consistent with common proper motion, and is inconsistent with the expected background trajectory by a total of 10.0σ (see Figure 4). On the other hand, the spectrum of the candidate favors a different interpretation. The best-fit spectral type is in the range of ∼M3 (see Figure 5), implying a temperature of 3300 K (Slesnick et al. 2004). Using the Baraffe et al. (1998) models and an age of 5 Myr, the implied mass is ∼250 M_jup and the corresponding predicted absolute magnitude is M_K = 5.25 mag. This is wildly in conflict with the actual magnitude measured in the image (if we assume that the candidate is indeed comoving with HIP 80130) of M_K = 8.69 mag, which by itself yields a mass of ∼18 M_jup from Chabrier et al. (2000). Thus, there is a discrepancy of 3.44 mag (a factor of 24) in brightness, or equivalently a factor of 14 in mass, between the estimations based on spectral type and apparent brightness, respectively. The gap is too large to be explained by any model uncertainties or errors in, for example, distance or the variability of the source.

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A further observational constraint that underlines the peculiar nature of the source comes from the fact that HIP 80130 was covered in the UKIDSS survey (Lawrence et al. 2007) in a K-band image from epoch 2009.34. A point source is reported at a separation of 409 and a position angle of 1110, which corresponds to our identified point source. The location is considerably closer to the CPM location than the background trajectory, lending further support to the CPM hypothesis. The K-band contrast is 6.9 mag, consistent with our NICI contrast. Hence, the UKIDSS data broadly confirm the picture posed by the NICI data: that HIP 80130 is an unusual object in one way or another. The options that come most readily to mind are that the object is either a very unusual form of companion or a background star that by chance has the same proper motion as HIP 80130, both of which seem highly unlikely. Perhaps the object is a 3300 K star that is obscured to an extreme degree (for its age), for instance by an edge-on disk. This might be supported by its strong variability. However, given these uncertainties, we cautiously do not include HIP 80130 in any of the statistical analysis for the moment, and we emphasize that more data will be needed to clarify the real properties of the source.

HIP 80208. This is one of the four stars that have a mass of >5 M_sun, and is therefore excluded from the statistical study.

HIP 82569. HIP 82569 resides in a crowded field with several point sources present within the NICI field of view. Surprisingly, none of the sources appear to move with respect to the primary over four epochs of imaging spanning nearly two years. While the proper motion of HIP 82569 is among the lowest in the sample at 24.4 mas yr⁻¹, it should be significant over the two-year baseline. The normal inference for any single point source would be that it shares a common proper motion, and thus is a companion to the star. However, ∼10 point sources at similar projected separations, some of which are evidently binaries themselves, cannot be companions to the same star. Hence, we consider the proper motion of this star to be unreliable and count the point sources as probable background sources. Further analysis in the future will be required to stringently test whether single sources in the field may nonetheless share a common proper motion with HIP 82569.