One of the main motivations for measuring the binary fraction of stars is to better understand the process of star formation. In particular, VLM binary formation environments and processes are not well understood. The current sample of known VLM binaries is only on the order of 50. A larger sample would greatly help to further constrain these systems' abundances and properties. Once resolved, binaries can then be targeted by dynamical mass, spectral and other programmes.
We have surveyed at high angular resolution a sample of nearby (<40 pc) and red (V-K > 6) stars to assess their binarity. LuckyCam, a novel imaging system designed and built by our group, was used for all observations. We imaged 48 targets in both SDSS i' and z' filters at a median FWHM resolution of ~0.12", in 8 hours of observing during the nights of 3-6 June 2005 on the 2.56m Nordic Optical Telescope (NOT). One star (GJ 1245ABC) has been previously resolved into a close binary; all others have not to our knowledge been previously imaged at high resolution.
The V-K colour distribution and approximate spectral class range of our sample 48 nearby M dwarfs is shown above. Lucky Imaging allows us to observe targets in the visible that were previously only in reach of near-infrared Adaptive Optics (AO) systems. All 48 targets were imaged in a total of only 8 hours on the 2.5m Nordic Optical Telescope. Exposure times were 2 minutes in each of the i' and z' bands, and seeings ranged from 0.5 arcseconds to 1.2 arcseconds. For comparison we show the 36 star sample of Siegler et al. (2005, ApJ 621:1023-1032), observed with Gemini North, VLT, Keck II and Subaru.
The recorded frames are ranked on the basis of their Strehl ratios and a fraction (dependent on the resolution / signal requirements) are selected. The selected frames are then aligned, resampled and co-added using the Drizzle algorithm (Fruchter & Hook 2002). These 7 close binaries are shown with 10% of the 3000 frames in 100 second exposures in both the SDSS i' and the z' filter. Each scale bar denotes 1 arcsecond. The top first and last binaries are not triple systems. If the binary's components have similar brightnesses photon shotnoise can cause the reduction software to mistakenly lock onto the secondary star in some frames. This leads to a faint image of the primary opposite to that of the secondary.
Very close binaries with similar component brightnesses will switch the frame shift lock between the two components randomly, leading to a very elongated PSF. A 0.15" binary is shown upper left-hand pair, resolved into a very elongated PSF in poor seeing. When reobserved in good seeing (image to the right) the secondary is well resolved. The two pairs of images lower down have very clearly elongated PSFs in comparison to reference PSFs taken just before and just after these stars - and so are also likely to be very (< 0.15 arcseconds) close binaries.
One binary had a large contrast ratio, necessitating PSF subtraction for confirmation. In this case a 1-sigma clipped average radial profile was subtracted from the PSF, although another star's PSF could also be used. We have yet to do this for all our data and so may find further higher contrast binaries.
Lucky Imaging offers a particularly elegant and uncomplicated solution to the smearing effects of atmospheric turbulence. Amongst the rapid turbulent fluctuations of the atmosphere moments of relatively quiet air appear, lasting a few tens of milliseconds. Sampling at high frame rates with LuckyCam allows us to follow rapid seeing variations and select those times with very much better images - effectively integrating only during periods of truly superb seeing. LuckyCam is an L3CCD camera system developed by our group, which can read out at rates of up to 100 frames per second (12 FPS full-frame) with negligible readout noise. Faint (<1 photon / pixel / frame) targets can be observed in a photon counting mode at standard CCD quantum efficiencies. A typical Lucky Imaging point spread function (PSF) consists of a diffraction-limited core surrounded by a halo (which is smaller than the seeing-limited PSF), as is expected for the form of a partially compensated turbulence degraded image.
We have found that our system can correct images in the visible to close to the diffraction limit of the NOT in good seeing over a much wider field of view than adaptive optics, using reference stars as faint as I=16.0. Even in poor seeing Lucky image selection strategies deliver an improvement in image resolution of as much as a factor of four.
The results of 44 separate 160 second runs - a small sample from 4 separate observing runs in 2001- 2004. Lucky Imaging reliably improves the resolution by large factors in all encountered conditions. Blue squares are data taken at 12Hz; red circles at 18Hz and green diamonds at 36Hz. We slightly undersample a diffraction limited PSF for the NOT in I-band; an effectively diffraction limited image would have a measured FWHM of ~0.1".
In a sample of 48 late-M stars we have detected 11 companions, giving a binary fraction of 23 %, uncorrected for biases. Although we are sensitive to very faint companions (i'=20 magn. at 1 arcsec, Dm=8), none of the detected companions are much fainter than the primary (Dm > 2 mags).
As an example, for a 1 Gyr 0.2 Msol primary at 20 pc we can detect a 0.075Msol brown dwarf companion (q = 0.4) at 0.5 arcseconds separation. A 0.05 brown dwarf (q = 0.25) could be imaged at 1.0 arcseconds.
In all 48 20x20" full fields only one red background object was detected. Limiting our binary search to 2 arcseconds radius from each target star, we would thus expect only 0.03 spurious associations in our dataset
The distribution of orbital radii is consistent with that found in previous work, with a peak at around 4 AU and no companions found at larger radii than 40AU. We also note that two of our new binaries fall near a previous single detection at about 35 AU.
The closest binaries in our sample, with orbital radii of ~4AU, have orbital periods of 10s of years and would be very interesting targets for dynamical-mass followup observations, allowing verification of the mass-luminosity relation for very low mass stars.
One of our targets, GJ 1245AC, has previous HST imaging (above, logarithmically scaled). The orbital motion of both components B & C is clearly evident on the (linearly scaled) LuckyCam image taken ~8 years later. With the addition of an objective prism LuckyCam can also acquire high spatial resolution spectra (the image below has ~30nm spectral resolution).
Poster paper presented at the IAC-TNG Workshop on Ultralow-mass star formation and evolution workshop La Palma June 28 -July 1 2005