ORBITAL MONITORING OF THE ASTRALUX LARGE M-DWARF MULTIPLICITY SAMPLE^*

Improvements in instrumentations and techniques for high-resolution imaging as well as other detection methods have benefitted the efficient study of large samples of stars with high sensitivity. This has led to a significant amount of multiplicity studies in recent years, spanning a wide range of stellar masses (e.g., Burgasser et al. 2007; Raghavan et al. 2010; Kraus et al. 2011; Janson et al. 2013; De Rosa et al. 2014). One such technique that has become available over the past decade thanks to developments of visible light detectors with high-speed readout and low read noise is so-called Lucky Imaging (e.g., Tubbs et al. 2002; Law et al. 2006). Lucky Imaging takes advantage of the fact that the wavefront distortion pattern of the atmosphere varies on timescales of the order of 10 ms, and that in some instances, the severity of this distortion is significantly smaller than in others. By acquiring a long series of very short exposures, and selecting only those frames in which the measured wavefront is relatively pristine, spatial resolution can be gained (at the cost of sensitivity), as a nearly diffraction-limited point-spread function (PSF) is reached. Previously, we have used this technique for an extensive high-resolution imaging survey of multiplicity in ∼700 early-to-mid M-dwarf stars (Bergfors et al. 2010; Janson et al. 2012), with a recent extension to late-type M-dwarfs (Janson et al. 2014). These studies, along with other recent studies in the same spectral-type range (e.g., Law et al. 2008; Dhital et al. 2010; Dieterich et al. 2012; Jódar et al. 2013), significantly expand the samples of previous surveys (e.g., Fischer & Marcy 1992; Reid & Gizis 1997; Delfosse et al. 2004) and help to constrain the statistical distributions in M-dwarf multiplicity (for a recent summary, see Duchêne & Kraus 2013).

However, these surveys do not only provide results on multiplicity statistics. The M-dwarfs multiples provided by the surveys can also be used as laboratories for constraining low-mass stellar properties. Since targets of the Janson et al. (2012) study were chosen from the Riaz et al. (2006) sample of X-ray-selected nearby M-dwarfs, many of them are quite young. Indeed, many (∼150) of the targets have been identified as probable members of young moving groups (YMGs) in recent detailed studies (e.g., Schlieder et al. 2012; Malo et al. 2013, 2014). Young M-dwarf binaries for which dynamical masses can be determined are excellent for calibrating evolutionary models of M-dwarfs (e.g., Burrows et al. 1997; Baraffe et al. 1998), particularly if the age is known. Conversely, to the extent that the evolutionary relationships are known, absolute ages can be determined isochronally in young M-dwarf binaries (e.g., Janson et al. 2007). Even regardless of theoretical models, M-dwarf binaries can give useful constraints on ages. For instance, a population of M-dwarf binaries with dynamically determined masses in YMGs can be used to construct empirical isochrones, where relative ages between moving groups can be determined, and co-evality within groups can be stringently assessed. While extensive orbital monitoring campaigns have been performed among binaries in the M-type range (e.g., Ségransan et al. 2000; Dupuy et al. 2010), some of which are young, and while dedicated studies have been performed for some individual known YMG members (e.g., Bonnefoy et al. 2009; Konopacky et al. 2007; Köhler et al. 2013), the sample of young, low-mass binaries with well-characterized orbits remains small. Hence, it is of considerable importance to identify more such binaries for which an orbit can be closed over a reasonable time frame.

In this paper, we perform astrometric follow-up of binaries detected or confirmed in Bergfors et al. (2010) and Janson et al. (2012) in order to confirm common proper motion (CPM) in those cases where this has not yet been accomplished, and to better constrain their orbital properties. We also cross-check these binaries against identifications of members in YMGs in order to determine which systems are most promising for rigorously determining dynamical masses in the near future, and thus provide strong age constraints and/or model constraints for both the binaries themselves and the broader range of members in moving groups with which they may be associated. The paper is structured as follows. In Section 2, we describe the observations that have been performed as part of this study, as well as the data reduction procedures. We then discuss the astrometric analysis in Section 3, followed by the corresponding orbital analysis in Section 4, where we examine both the general sample as well as some particularly interesting individual cases. Finally, we summarize our results and conclusions in Section 5.

This work is based primarily on observations acquired over several years with the AstraLux Norte camera (Hormuth et al. 2008) on the 2.2 m telescope at Calar Alto in Spain, and the AstraLux Sur camera (Hippler et al. 2009) on the European Southern Observatory/New Technology Telescope 3.5 m telescope at La Silla in Chile. The observations acquired specifically within the context of this program (orbital monitoring of M-dwarf binaries) were taken in 2011 November, 2012 January, and 2012 August with AstraLux Norte, and 2010 October (ESO program ID 086.C-0869(A)) and 2012 January (088.C-0753(A)) with AstraLux Sur. Additionally, some data taken for the purpose of our late-type M-dwarf sample (Janson et al. 2014) had a few targets overlapping with targets in this program, and so the astrometry from those data are included here as well. In some cases, both i' and z' images were acquired and in some case only z' images, but here we will consistently only concern ourselves with the higher-quality z' data for the astrometric analysis.

The observations used the same settings as are normally employed for AstraLux multiplicity observations (e.g., Hormuth et al. 2007; Daemgen et al. 2009; Bergfors et al. 2013), with 15–30 ms individual readouts, adding up to 300 s of total integration time. For two of the 2010 October AstraLux Sur nights, the Barlow lens that was normally included in the light path was taken out. This led to a 2.8 times coarser pixel scale than normal, which has been taken into account in the astrometric calibration (see the next section). Under normal circumstances, the full frame field of view of AstraLux Norte is a ∼24 arcsec², and of AstraLux Sur is a ∼16 arcsec², although subarray readouts are often employed to minimize readout times.

All in all, including both science and calibration observations, this study represents ∼500 new AstraLux observations of ∼10 minutes of telescope time each. In Janson et al. (2012), we presented 242 companion candidates, of which 219 were considered as probable real companions and 23 were probable background contaminants. Including the original observations, data published elsewhere in the literature, and the additional observations presented here, there are now 2 or more epochs of observation for 221 of these 242 candidates. Of these, 132 have 3 or more epochs of observations, 77 have 4 or more epochs, and 21 have 5 or more epochs. For a few of the targets, we have also recovered archival data that have not been previously published, these are discussed for those individual targets.

Data reduction was performed with the pipeline described in Hormuth et al. (2008), to produce four collapsed frames per observation with the best 1%, 2.5%, 5%, and 10% of the individual frames, respectively. In this study, we consistently use the 10% selection for all targets. An example image from the campaign is shown in Figure 1.

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Astrometric measurements for the new data were acquired in different ways depending on the properties of the binary: for wide binaries, where the individual PSFs of the component stars were well separated, Gaussian centroiding was used to calculate relative astrometry in detector coordinates. For closer systems, the iterative PSF fitting scheme described in Bergfors et al. (2010) was used. In many cases of binaries with components of nearly equal brightness, the well-known false triple effect that commonly occurs in Lucky Imaging data was evident (see, e.g., Law 2006; Bergfors et al. 2010), such that three PSF components had to be fit simultaneously. All PSF fitting was done with three different reference star PSFs in order to evaluate the uncertainty of the procedure and the impact of PSF variability.

For astrometric calibration, we observed Trapezium whenever it was visible, and M15 otherwise. Reference astrometry was acquired from McCaughrean et al. (1994) in the case of Trapezium and van der Marel et al. (2002) for M15. We measured Gaussian centroids for five of the brightest stars in each astrometric field and referenced their relative separations and position angles to the literature values, and also compared the results to the IRAF geomap procedure used in previous work (e.g., Köhler et al. 2008; Bergfors et al. 2010). It was found that the pixel scale could vary by up to 1% depending on the choice of reference stars and methods, hence this is consistently used as the error in pixel scale. The uncertainty in field rotation was found to be 03. In this way, we determined the pixel scale and angle of true north of AstraLux Sur as 15.18 mas pixel⁻¹ and 149 for 2010 October with the Barlow lens in the beam; 42.83 mas pixel⁻¹ and 209 for 2010 October without the Barlow lens; and 15.16 mas pixel⁻¹ and 236 for 2012 January. In order to acquire a consistently calibrated astrometry over all epochs, we also re-calculate the astrometric calibration of the 2008 November epoch as 15.17 mas pixel⁻¹ and 190, and of the 2010 January epoch as 15.18 mas pixel⁻¹ and 251. For AstraLux Norte, the corresponding values are 23.56 mas pixel⁻¹ and 166 for 2011 November; 23.58 mas pixel⁻¹ and 172 for 2012 January; and 22.59 mas pixel⁻¹ and 183 for 2012 August. Here, the angle of true north is defined as the counterclockwise orientation of true north with respect to the y-axis—in other words, in calculating a true position angle in sky coordinates, a positive angle of true north is subtracted from the position angle measured in detector coordinates.

We also carried out an analysis of potential higher order geometric distortions of the AstraLux cameras by comparing AstraLux Norte observations of M13 with Hubble Space Telescope (HST) images. The HST images were processed by the standard HST pipeline, including corrections for geometric distortions. The analysis used 25 single and relatively isolated stars in common between AstraLux and HST observations, distributed over the AstraLux field of view. After correction for difference in the image scales and instrumental position angles, no systematic residuals could be identified. AstraLux image scales in the x- and y-coordinate directions are identical within the measurement uncertainties. For AstraLux Norte, the rms values for the positional residuals of the stars are of the order of 10–15 mas over the full 24'' × 24'' field of view. These residuals amount to about one-twentieth of the FWHM of the PSF for data that were obtained in a night with 16 seeing, which is a typical PSF centroiding accuracy under such circumstances. Over these scales, the errors in pixel scale and orientation derived above amount to 60–120 mas, hence these latter factors dominate the error budget, rendering higher-order geometric distortions negligible.

CPM was tested for all targets observed in multiple epochs, by extracting proper motions from the NOMAD catalog,⁶ or when unavailable there, from the PPMXL catalog (Röser et al. 2010). The expected background trajectory was calculated for each of these systems using these proper motions along with estimations of the system parallax. For this purpose, we used measured trigonometric parallaxes whenever available, and estimated parallaxes from the photometric distances otherwise. In order for a companion candidate to be considered as having a demonstrated CPM, it had to deviate from the background trajectory by at least 3σ in at least one epoch. To further count as showing significant signs of orbital motion, it had to also deviate from its original relative astrometry by at least 3σ. This method is robust for confirming CPM and thus validating physical companion candidates, but it is not strictly robust for rejecting CPM, since orbital motion can in principle mimic non-CPM (i.e., the orbital motion brings the companion close to the background trajectory by chance). We discussed some limit cases in Janson et al. (2012), and continually mark such cases with "U" for "unclear" in the CPM assessment, along with cases for which the errors are simply too large with respect to the system proper motion for any significant evaluation to be performed. In many cases, we have been able to confirm CPM and orbital motion that were not yet confirmed in Janson et al. (2012), though in several cases these properties remain undetermined due to slow proper motion or orbital motion. In a few cases (e.g., J13015919+4241160 and J14430789+1720463), it is even the case that a CPM that was previously regarded as significant is now deemed unclear; this is, however, simply due to the fact that we adopt more conservative astrometric calibration errors in this study. Our CPM results confirm the notion that the vast majority of binary candidates in Janson et al. (2012) are indeed physical companions. The astrometric values from this study as well as from the literature for the full set of multi-epoch targets are listed in Table 1.