Chapter 7
The LuckyCam Survey for VLM Binaries
II. M4.5-M6.0 Targets

This chapter discusses the second of two LuckyCam VLM Binary surveys, carried out in June and November 2005. The survey is designed to further increase the number of known VLM binaries by observing targets that were not accessible to the June 2005 survey. The target sample is also more constrained and has slightly more massive targets than that of chapter 6, being a magnitude-limited survey of M-dwarfs between V-K = 6 (~M4.5) and V-K = 7 (~M6). As an additional investigation, the sample is further divided into X-ray emitting and non-emitting stars.

In this survey, a further 14 new VLM binaries were discovered using LuckyCam, in 78 targets imaged in only 11 hours on-sky.

7.1 The Sample

As in chapter 6, I selected a magnitude and colour limited sample of nearby late M-dwarfs from the LSPM-North High Proper motion catalogue (Lépine & Shara, 2005). The LSPM-North catalogue is a survey of the Northern sky for stars with annual proper motions larger than 0.15”/year. Most stars in the catalogue are listed with both 2MASS IR photometry and V-band magnitudes estimated from the photographic B_J and R_F bands.

The LSPM-North high proper motion cut ensures that all stars are relatively nearby, and thus removes contaminating distant giant stars from the sample. I cut the LSPM catalogue to include only stars with V-K colour ≥6, and K-magnitude brighter than 10. The colour cut selects approximately M5 and later stars; its effectiveness is confirmed in section 7.3.2, and also discussed in chapter 6.

Figure 7.1: The 2MASS K-magnitude, V-K colour and distance distributions of the X-ray-active and non-X-ray-active samples. Distances are estimated from the LSPM V-K colours of the samples and the V-K photometric absolute magnitude relations detailed in Leggett (1992). The distances are accurate to approximately 30%, and assume that all targets are single stars.

Table 7.1: The observed non-X-ray-emitting sample. The quoted V & K magnitudes are taken from the LSPM catalogue. K magnitudes are based on 2MASS photometry; the LSPM-North V-band photometry is estimated from photographic BJ and RF magnitudes and is thus approximate only, but is sufficient for spectral type estimation – see section 7.3.2. Spectral types and distances are estimated from the V & K photometry (compared to SIMBAD spectral types) and the young-disk photometric parallax relations described in Leggett (1992). Spectral types are accurate to approximately 0.5 spectral classes and distances to ~30%.

Table 7.2: The observed X-ray emitting sample. The star properties are estimated as described in the caption to table 7.1. ST is the estimated spectral type; the ROSAT flux is given in units of counts per second.

7.1.1 X-ray selection

After the colour and magnitude cuts, the sample contains 231 late M-dwarfs. I then divide the late M-dwarfs into two target lists on the basis of X-ray activity. Since this is a large sample of VLM stars, we decided that interesting extra investigations would be enabled by ensuring that the observed sample contained a statistically-significant number of X-ray bright targets.

It has been demonstrated that increased magnetic activity indicators (including X-ray fluxes) correlate with increased stellar rotation rate (eg. Simon (1990); Soderblom et al. (1993)) – the so-called rotation-activity paradigm. The stellar rotation rate and therefore X-ray activity evolves with age (eg. Scholz & Eislöffel (2004)), depending on the stellar environment (for a review on the evolution of angular momentum, see Herbst & Mundt (2005)). Any correlations found between X-ray emission and the number and properties of discovered companions may then give insight into the formation environments of multiple stars.

Makarov (2002) found that field stars (mostly F & G spectral types) detected in the ROSAT Bright Source Catalogue are 2.4 times more likely to be members of wide (> 0.3 arcsec) multiple systems than those not detected in X-Rays. They suggest two hypotheses to explain the bias: 1/ The X-ray sample selects younger stars which may have higher binarity and 2/ the wide binaries have a different angular momentum evolution from single stars.

A goal of the X-ray sample selection in this chapter is to test for a correlation between X-ray emission and binarity among our sample of much later-type stars. Such a bias, if present, would be both useful and interesting. Firstly, the search for VLM binaries (and presumably higher-order systems) could be sped up by the addition of X-ray selection into target samples. Secondly, constraints on the dynamical evolution of 1AU+ radius VLM binary systems could be set by appealing to the rotation-activity paradigm.

In this chapter, I mark a star as X-ray active if the target star has a ROSAT All-Sky Survey detection from the Faint Source Catalogue (Voges et al., 2000) or the Bright Source catalogue (Voges et al., 1999) within 1.5× the 1σ uncertainty in the X-ray position. Known or high-probability non-stellar X-Ray associations noted in the QORG catalogue of radio/X-ray sources (Flesch & Hardcastle, 2004) are removed. Finally, I manually checked the Digitized Sky Survey (DSS) field around each star, and removed those stars which did not show an unambiguous association with the position of the X-ray detection. The completeness and biases of the X-Ray selection are discussed in section 7.4.2.

It should be noted that the fraction of stars which show magnetic activity (as measured in Hα) reaches nearly 100% at a spectral type of M7, and the X-ray selection here only picks especially active stars (Gizis et al., 2000; Schmitt & Liefke, 2004). For convenience, in the remainder of the chapter the sample of stars without evidence for X-Ray activity are called non-X-ray active.

One star in the remaining sample, LSPM J0336+3118, is listed as a T-Tauri in the SIMBAD database, and was therefore removed. I note that in the case of the newly detected binary LSPM J0610+2234, which is ~0.7σ away from the ROSAT X-Ray source I associate with it, there is another bright star at 1.5σ distance which may be the source of the X-Ray emission.

7.1.2 Target distributions

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Table 7.3: The previously known binaries in this survey which are re-detected by LuckyCam.

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These cuts left 51 X-ray active stars and 179 stars without evidence for X-Ray activity. I drew roughly equal numbers of stars at random from these both these lists to form the final observing target set of 37 X-Ray active stars and 41 non-X-ray active stars described in tables 7.1 and 7.2. 4 of the X-Ray active stars and 3 of the non-X-ray stars are previously known to be binary systems (detailed in table 7.3), but we reimaged them with LuckyCam to ensure a uniform survey sensitivity in both angular resolution and detectable contrast ratio.

Figure 7.1 shows the survey targets’ distributions in K magnitude, V-K colour and photometrically estimated distance. Figure 7.2 compares the targets to the rest of the stars in the LSPM catalogue. The X-ray and non-X-ray samples are very similar, although the non-X-ray sample has a slightly higher median distance, at 15.4pc rather than 12.2pc (the errors on the distance determination are about 30%).

7.2 Observations

All 78 targets were imaged in approximately 11 hours of on-sky time in November 2005, using LuckyCam on the 2.56m Nordic Optical Telescope. Each target was observed for 100 seconds in both the SDSS i’ and the z’ filters.

The observations were performed though varying cloud cover with a median extinction on the order of three magnitudes. This did not significantly affect the imaging performance, as all these stars are 3-4 magnitudes brighter than the LuckyCam guide star requirements, but the sensitivity to faint objects was reduced. No calibrated photometry was attempted because of the rapid variations in cloud transmission, although I did perform relative photometry of the components of the detected binaries. As discussed in later sections, good constraints can be set on the orbital radii and spectral types of the systems solely on the basis of their measured separations and catalogued unresolved V-K colours.

7.2.1 Binary detection and photometry

Companions were detected according to the criteria described in detail in chapter 6. We required 10σ detections above both photon and speckle noise; the detections must appear in both SDSS i’ and z’ images. Detection is confirmed by comparison with point spread function (PSF) reference stars imaged before and after each target; in this case, because the observed binary fraction is only ~30%, other survey sample stars serve as PSF references.

I measured resolved photometry of each binary system by the fitting and subtraction of two identical PSFs to each image, modelled as Moffat functions with an additional diffraction-limited core (see chapter 5) . In some cases, where the target binary is faint and its components are of nearly equal brightness, photon noise can cause the Lucky Imaging software to occasionally align the images on the basis of the wrong star. This leads to an image showing three equally spaced stars in a line; in those cases, as described in chapter 5, I fit three identical PSFs and use the two flux ratios to solve for the true binary flux ratio.

7.2.2 Sensitivity

The sensitivity of the survey was limited by the cloud cover. Because of the difficulty of flux calibration under very variable extinction conditions I do not give an overall survey sensitivity. However, a minimum sensitivity can be estimated. LuckyCam requires an i’=+15.5m guide star to provide good correction; all stars in this survey must be at least that bright^* . The sensitivity of the survey around a i=+15.5m star is calculated in chapter 6 and the sensitivity as a function of companion separation is discussed in section 7.4.4.

As noted in chapter 6, the survey is also sensitive to white dwarf companions around all stars in the sample. However, until calibrated resolved photometry is obtained for the systems it is not possible to distinguish between the M-dwarf and white-dwarf companions. Since a large sample of very close M-dwarf companions to white dwarf primaries have been found spectroscopically (for example, Delfosse et al. (1999); Raymond et al. (2003)), but few have been resolved, it will be of interest to further constrain the incidence of these systems.

7.3 Results & Analysis

14 new low mass and very low mass binaries were found, as well at two possible detections. The binaries are shown in figure 7.3 and the observed properties of the systems are detailed in table 7.4. In addition to the new discoveries, we confirmed seven previously known binaries, also detailed in table 7.4.

GJ 376B is known to be a common-proper-motion companion to the G star GJ 376, located at a distance of 134 arcsec (Gizis et al., 2000). Since the separation is very much greater than can detected in the LuckyCam survey, I treat it as a single star in the following analysis.

G 256-25 and GJ3971 both show PSF elongation indicative of binarity but are not fully resolved; the elongation is not present in stars taken before or after those targets. Both targets were taken at high zenith angle without an ADC, and so their elongation may be the result of atmospheric dispersion. For that reason, I do not include the two stars as confirmed binary detections, and followup observations of the targets are required.

Figure 7.3: The newly discovered binaries. All images are orientated with North up and East to the left. The images are the results of a Lucky Imaging selection of the best 10% of the frames taken in SDSS i’, with the following exceptions: LSPM J0409+0546, LSPM J0610+2234 and LSPM J0859+2918 are presented in the z’ band, as the cloud extinction was very large during their i’ observations. The image of LSPM J0738+4925 uses the best 2% of the frames taken and LSPM J0115+4702S uses the best 1%, to improve the light concentration of the secondary. LSPM J2023+6710 was observed through more than 5 magnitudes of cloud extinction, and was thus too faint for Lucky Imaging; a summed image with each frame centroid-centred is presented here, showing clear binarity.

Table 7.4: The observed properties of the detected binaries. The top group are stars with newly detected companions; the bottom group are the previously known systems. LSPM J0409+0546 and LSPM J0610+2234 were observed though thick cloud and in poor seeing, and so only upper limits on the contrast ratio are given. LSPM J2023+6710 was not observed in z’, and cloud prevented useful z’ observations of LSPM J0035+0233.

7.3.1 Confirmation of the binaries

In the entire LuckyCam VLM binary survey, covering a total area of (22′′× 14.4′′) × 122 fields, there are 10 objects which would have been detected as companions if they had happened to be close to the target star. One of the detected objects is a known wide common proper motion companion; others are due to random alignments. For the purposes of this section, I assume that all detected widely separated objects are not physically associated with the target stars.

Limiting the detection radius to 2 arcsec around the target star (I confirm wider binaries by testing for common proper motion against DSS images) 0.026 random alignments would be expected in our dataset. This corresponds to a probability of only 2.5 per cent that one or more of the apparent binaries detected here is a chance alignment of the stars. I thus conclude that all the detected binaries are physically associated systems.

8 of the newly discovered binaries have moved more than one DSS PSF-radius between the acquisition of DSS images and these observations (table 7.5). With a limiting magnitude of i_N ~ +20.3m (Gal et al., 2004), the DSS images are deep enough for clear detection of all the companions found here, should they actually be stationary background objects. None of the DSS images show an object at the present position of the detected proposed companion, confirming the common proper motions of these companions with their primaries.

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Table 7.5: The newly discovered binaries which have moved far enough since DSS observations to allow confirmation of the common proper motion of their companions.

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7.3.2 The nature of the target stars

Because of the cloudy conditions during most of the observations, calibrated resolved photometry is not available for the components of 12 of the 14 new systems, and thus individual estimates of the spectral types and masses of the components are difficult to obtain. However, unresolved V & K-band photometry listed in the LSPM survey allows useful constraints on the nature of these targets. Because the LSPM V-band magnitudes are only approximate estimates from photographic magnitudes, it is necessary to check their accuracy and precision for spectral type determination.

The MK spectral type of approximately one third of the stars in our sample is listed in the SIMBAD database, based on spatially unresolved spectroscopy from Jaschek (1978). Plotting the LSPM V-K colour against the spectroscopic spectral type (figure 7.4) we find that all survey targets are M3 and later. Stars with 6.0 < V-K < 6.5 have an average spectral type of M4.5, with a 1σ range of 0.5 spectral types, while those with redder V-K colours are all later than M5.

The estimated spectral type of the unresolved system is dominated by the primary’s spectral type, as shown in table 7.6. Unresolved V & K-band photometry thus allows a reasonably precise determination of the primary component’s spectral type. The secondary’s spectral type can then be constrained on the basis of the contrast ratio of the binary.

To ensure that all binaries are measured on the same spectral type system, I list spectral types derived in the above way for all systems, notwithstanding if a spectroscopic spectral type is available in the literature.

Table 7.6: The apparent V-K colour of an unresolved binary system, calculated from the V-K vs. spectral type and absolute magnitude relations detailed in Leggett (1992). Each cell of the table corresponds to a different combination of stellar spectral types; the V-K based spectral type that would be estimated for the system is given in brackets. In all cases, because of the rapid falloff in luminosity with later spectral types, the estimated spectral type from unresolved V & K-band photometry is the same as that of the most massive (earliest type) component of the binary. The uncertainties in each V-K colour are approximately 0.35 mags.

7.3.3 Distances

The measurement of the distances to the stars is a vital step in the determination of the orbital radii of the systems. None of the newly discovered binaries presented here has a measured parallax (although four^{* *} G 132-25 (NLTT 2511) is listed in Reid & Cruz (2002) and the SIMBAD database as having a trigonometric parallax of 14.7 ±4.0 mas, based on the Yale General Catalogue of Trigonometric Stellar Parallaxes (van Altena et al., 2001). However, this appears to be a misidentification, as the star is not listed in the Yale catalogue. The closest star listed, which does have the parallax stated for G 132-25 in Reid & Cruz (2002), is LP 294-2 (NLTT 2532). This star has a very different proper motion speed and direction to G 132-25 (0.886 arcsec/yr vs. 0.258 arcsec/yr in the LSPM catalogue & SIMBAD). In addition, the G 132-25 LSPM V and K photometry is inconsistent with an M-dwarf at a distance of 68pc. I thus do not use the stated parallax for G 132-25. of the previously known systems do) and calibrated resolved SDSS i’ and z’ photometry is not available for almost all the systems. I therefore calculate distances to the newly discovered systems using the V-K colour-absolute magnitude relations described in Leggett (1992). Calculation of the distances in this manner requires care, as the V and K-band photometry is unresolved, and so two luminous bodies contribute to the observed colours and magnitudes.

The estimated distances to the systems, and the resulting orbital separations, are given in table 7.7. The stated 1σ distance ranges include the following contributions:

• A 0.6 magnitude Gaussian-distributed uncertainty in the V-K colour of the system (a combination of the colour uncertainty noted in the LSPM catalogue and the maximum change in the V-K colour of the primary induced by a close companion, as discussed in section 7.3.2).
• A 0.3 magnitude Gaussian-distributed uncertainty in the absolute K-band magnitude of the system, from the uncertainty in the colour-absolute magnitude relations
• A 0.75 magnitude flat-distributed uncertainty in the absolute K-band magnitude of the system, to account for the unknown K-band contrast ratio of the binary system (which can be between equal magnitude and almost all the light coming from the primary).

The resulting distances have 1σ errors of approximately 35%, with a tail towards larger distances due to the K-band contrast ratio uncertainties. The photometrically-estimated distances to three of the four systems with astrometric parallaxes match to within one sigma. The fourth (LP 325-15) differs by ~1.5σ. Although parallax-based measurements of the distance to these systems would be ideal, distances based on resolved i and z photometry for each component of the multiple systems produces only 10-15% distance uncertainties (chapter 6). We are planning photometric followup of these systems to improve the distance estimates.

Table 7.7: The derived properties of the binary systems. The top group are stars with newly detected companions; the bottom group are the previously known binaries. All parallaxes are from the Yale General Catalogue of Trigonometric Stellar Parallaxes (van Altena et al., 2001). Distances and orbital radii are estimated as noted in the text; the stated errors are 1-σ. The binary contrast ratio is the magnitude of the companion minus the magnitude of the primary. Spectral types of the primaries are derived from the V-K colour of the unresolved system and the relations in Leggett (1992). The secondaries’ spectral types are derived by: 1/ assuming the estimated primary spectral type to be the true value and 2/ using the spectral type vs. i’ and z’ absolute magnitude relations in Hawley et al. (2002) to estimate the difference in spectral types between the primary and secondary. The primaries’ spectral types have a 1σ uncertainty of ~0.5 subtypes (section 7.3.2); the difference in spectral types is accurate to ~0.5 spectral subtypes.

7.3.4 Notes on some individual systems

Two of the detected systems benefit from detailed discussion.

NLTT 14406 – A Triple System

NLTT 14406 is identified with LP 359-186 in the NLTT catalogue (Luyten, 1995), although it is not listed in the revised NLTT catalogue (Salim & Gould, 2003). LP 359-186 is a component of the common-proper-motion (CPM) binary LDS 6160 (the Luyten Double Star catalogue; Luyten (1997)), with the primary being LP 359-216 (NLTT 14412), 167 arcsec distant and listed in the SIMBAD database as a M2.5 dwarf.

The identification of these high proper motion stars can be occasionally problematic when working over long time baselines. As a confirmatory check, the LSPM-listed proper motion speeds and directions of these candidate CPM stars agree to within 1σ (using the stated LSPM proper motion errors). In the LSPM catalogue, the two stars are separated by 166.3 arcsec at the J2000.0 epoch. I thus identify the newly discovered M6, 4.4AU companion to NLTT 14406 as a member of a triple system with an M2.5 primary located at 2280_-420¹⁰⁸⁰AU.

The Orbit of GJ 1245AC

The astrometric binary GJ 1245AC was first resolved by McCarthy et al. (1988), using one-dimensional speckle interferometry. Schroeder et al. (2000) used HST to obtain the first direct resolved image of the system. Figure 7.5 shows a comparison of the LuckyCam imaging and the HST Wide Field Planetary Camera 2 (WFPC2) observations.

(a) HST WFPC2, 1.02μm, Oct. 1997 (b) LuckyCam, 0.77μm, June 2005 (c) Seeing-limited, 0.77μm, June 2005 Figure 7.5: Imaging of the triple system GJ1245AC. The HST WFPC2 image is reproduced from Schroeder et al. (2000), and the seeing-limited image is simulated from the LuckyCam data. All the images are on a logarithmic scale, and are orientated with North up and East to the left. The orbital motion of both the C and B components is clearly evident.

Harrington (1990) quotes an astrometrically derived orbit for GJ 1245AC. As a test of the capability of the LuckyCam VLM binary survey to calculate orbits for close binaries, I compared the predicted position of the companion star to the calculated position from the stated orbit (figure 7.6(a)). To increase the number of data points available, I supplemented the LuckyCam positions with the two positions listed in Schroeder et al. (2000). I also retrieved two epochs of archival HST observations of the system and measured the centroided position of the companion for those dates.

(a) The orbit of GJ 1245AC orbit from Harrington (1990).   (b) A re-fit orbit using LuckyCam and HST observations. Figure 7.6: The orbit of GJ 1245AC. The year markers around the orbit show the predicted position of the the secondary. The filled circles are measured positions (the leftmost is from LuckyCam; all others are from HST archival data or Schroeder et al. (2000)). The open circles mark the predicted position of the secondary at the epoch of each of the measured positions. The parameters of the two orbits are noted on the figures; α is the orbital semi-major axis in arcsecs, P is the period in years, T is the periastron time, e is the eccentricity, i is the inclination in degrees, ω is the periastron argument in degrees and is the position angle of the node in degrees.

As also found by Schroeder et al. (2000) from two measured positions, the measured orbit falls behind the calculated positions, by 18 months for the Schroeder et al. (2000) epoch and about two years for the LuckyCam measurement. The strong agreement in the direction and timing of the orbit discrepancy between the several HST measurements and the LuckyCam measurements indicates that the Harrington (1990) orbit is in error in at least one of its parameters.

In figure 7.6(b) I show a re-fit to the orbit of GJ 1245AC using the LuckyCam and HST data points. The orbit calculation follows that described in Argyle (2004); I used a simulated-annealing minimisation routine (Press et al., 1988) to fit the orbital parameters to the data. The resulting parameters are listed in figure 7.6(b); the main alteration from the Harrington (1990) orbit is an increase in orbital period, from 15.22 years to 17.65 years, and a 4% increase in the orbital radius.

Kepler’s Third Law relates the orbital period and radius to the total system mass:

(7.1)

where P is the orbital period, a is the orbital radius, M is the primary mass and m is the secondary mass. The total system mass was estimated to be 0.205M_⊙ in Harrington (1990); with the new orbit the total system mass is decreased by 20% to 0.17M_⊙. On the basis of the previous orbit, Henry et al. (1999) find that the companion straddles the stellar-brown dwarf border with a mass of 0.074M_⊙ ; the lowering of the total system mass pushes the companion well into the brown dwarf regime. This test illustrates that LuckyCam can perform these orbit-tracking programmes very easily.

7.4 Discussion

7.4.1 The binary frequency of stars in this survey

14 new binaries are present in a sample of 78 VLM stars, as well as a further 7 previously known binaries. This corresponds to a binary fraction of 26.9_-4.4^+5.5%, assuming Poisson errors. However, as in chapter 6, this value does not take into account the larger volume of space occupied by the binary stars in our sample, compared to the single stars. Binaries appear to be brighter for a given colour because there are two luminous bodies, and so for a given distance appear closer than the single stars in our sample. Correcting for this, assuming a range of contrast ratio distributions between all binaries being equal magnitude and all constrast ratios being equally likely (Burgasser et al., 2003), I find a distance-corrected binary fraction of 13.5_-4 ^+6.5 %.

Because the binaries are more distant on average than the single stars in this survey, they also have a lower average proper motion. This implies that the LSPM proper motion cut will preferentially remove binaries from a sample which is purely selected on magnitude and colour. The above correction factor for the increase magnitude of binary systems does not include this effect, and so will overestimate the number of binaries selected in the survey.

A detailed examination of these and other biases (for sensitivity to faint companions, for example) would require a Monte-Carlo simulation of the survey. The simulation would generate a sample of several hundred thousand M-dwarfs, with velocities and masses following the ranges found in the solar neighbourhood. Companions would then be randomly assigned to the stars, and a simulation of the sensitivity of the LuckyCam imaging system applied. Comparison with the observed results would then allow the confidence ranges of the population parameters (binarity, companion mass, etc) to be determined. This procedure may be undertaken in future work.

7.4.2 Biases in the X-ray sample

Before testing for correlations between X-ray emission and binary parameters, it is important to assess the biases introduced in the selection of the X-ray sample.

The X-ray flux assignment criteria described in section 7.1.1 are conservative. To reduce false associations, the X-ray source must appear within 1.5σ of the candidate star, which implies that ~13% of true associations are rejected. The requirement for an unambiguous association will also reject some fraction of actual X-ray emitters (~10% of the candidate emitting systems were rejected on this basis). The non-X-ray emitting sample will thus contain some systems that do actually meet the X-ray flux-emitting limit.

The X-ray source detection itself, which cuts only on the detection limit in the ROSAT Faint Source catalogue, is biased both towards some sky regions (the ROSAT All-Sky Survey does not have uniform exposure time (Voges et al., 1999) and towards closer stars. However, these biases have only a small effect: all but three of the target stars fall within the relatively constant-exposure area of the ROSAT survey, where the brightness-cutoff is constant to within about 50%. The samples also do not show a large bias in distance – the X-ray stars’ median distance is only about 10% smaller than that of the non-X-ray sample (figure 7.1).

The X-Ray active stars also represent a different stellar population from the non-active sample. In particular, the X-ray active stars are more likely to be young (eg. Jeffries (1999) and references therein). It may thus be difficult to disentangle the biases introduced by selecting young stars from those intrinsic to the population of X-ray emitting older stars.

The latter bias is very important, as it introduces uncertainty into the nature of the target sample. For this reason, although I compare the X-ray and non-X-ray samples in a number of parameters in the following sections (and do not find significant correlations), follow-up observations to determine the detailed nature of the X-ray emitters are required.

Finally, it could be thought that the binaries in the sample are more likely to be detected in X-Rays, as there are two emitting bodies. However, for the same reason, the binary stars are selected by the magnitude cut when the primary components are fainter or at larger distances than the single stars, reducing the importance of this effect. A useful test, however, must remove this effect of binarity – in the next section I use the fraction of light of each target emitted in X-rays, searching for a correlation with binarity.

7.4.3 Is X-ray activity an indicator of binarity?

11 of the 21 detected binaries are X-ray active. The non-distance-corrected binary fraction of X-Ray active targets in our survey is thus 30_-6⁺⁸%, and that of non-X-ray-active targets is 24_-5⁺⁸%. I thus do not find that X-Ray activity is a indicator of binarity, with the binary fractions differing at less than the 1σ level – although this determination may be corrupted by the effects discussed in section 7.4.2.

The fraction of the X-ray target’s bolometric luminosity which is in the X-Ray emission (L_x∕F_bol) is shown in figure 7.7, and again no correlation with binarity is found. The two targets with very large L_x ∕F_bol (GJ 376B and LSPM J1832+2030) are listed as flaring sources in Fuhrmeister & Schmitt (2003) (a survey of variability in the ROSAT all-sky survey) and thus were probably observed during flare events (although Gizis et al. (2000) argues that GJ 376B is simply very active).

This contrasts with the 2.4 times higher binarity among the similarly-selected sample of F & G type X-ray active stars in Makarov (2002). However, the binary fractions themselves are very similar, with a 31% binary fraction among X-ray active F & G stars, compared with 13% for X-ray mute F & G stars. Since the fraction of stars showing X-Ray activity increases towards later types, it is possible that the Makarov sample preferentially selects systems containing an X-ray emitting late M-dwarf. However, most of the stellar components detected in Makarov (2002) are F & G types, so it is unclear if the discrepancy can be explained in that way.

7.4.4 Contrast ratios

Figure 7.8 compares the contrast ratios of the detected systems to the instrumental sensitivity, derived from the tests presented in chapter 6. In common with previous surveys, all but two of the detected systems have contrast ratios lying between 0 and 1.7 mags. This is well above the survey sensitivity limits, as illustrated by the two binaries detected at much larger contrast ratios. Although those two systems are at larger radii, they would have been detected around most targets in the survey at as close as 0.2-0.3 arcsec (for example, see the faint companion to Ross 530 detected at 0.15 arcsec in chapter 6).

It is difficult to obtain good constraints on the mass contrast ratio for these systems because of the lack of calibrated photometry, and so I leave the determination of the individual component masses for future work (although some progress could be made with the contrast ratios in the current data). However, an interesting feature of the sample is that no binaries with contrast ratios consistent with equal mass stars are detected (one such binary was detected in chapter 6).

There is no obvious correlation between the orbital radius and the i-band contrast ratios, nor between X-ray emission and the contrast ratios (figure 7.9).

7.4.5 The distribution of orbital radii

Previous VLM surveys have found a peak in the VLM binary orbital radius distribution at around 4AU. The orbital radius distribution derived in this survey (figure 7.10) replicates this peak, but 9 of the 21 systems are at a nominal radius of more than 10 AU (this chapter’s surveyed primary stellar masses range from 0.089M_⊙ to 0.11M_⊙ using the models in Baraffe et al. (1998)). In the 36 M6-M7.5 M-dwarf sample of Siegler et al. (2005), 5 binaries are detected but none are found to be wider than 10AU. Note in most of these systems (as for the LuckyCam surveys) the projected separation at a particular epoch is measured, rather than the system’s semi-major axis.

Looking at all known VLM systems^{* *}Collated by Nick Siegler at http://paperclip.as.arizona.edu/~nsiegler/VLM_binaries/; VLM there is defined at the slightly lower value of total system mass of < 0.2M_⊙ , only 13 out of 77 known binaries are wider than 10AU.

Early M-dwarfs and G-dwarfs binaries have a broad orbital radius peak of around 30AU (Fischer & Marcy, 1992; Duquennoy & Mayor, 1991). Is it possible that the wider orbital radius binaries detected here are drawn from a population that has the same orbital radius distribution as higher mass stars? If so, a colour bias would be expected in the orbital radius distribution, with the redder objects having smaller orbital radii. Plotting system separation against V-K colour (figure 7.11), all but one of the systems with orbital radii larger than 10AU have V-K < 6.5, while the systems with < 10AU orbital radius are evenly distributed between V-K = 6 and V-K = 7. However, a Kolmogorov-Smirnov (K-S) test does not find a significant difference between the two distributions, with a 29% probability that the orbital radius distributions are consistent.

To decrease the uncertainty in the comparison of distributions, I supplemented the V-K > 6.5 systems from the LuckyCam sample with the known VLM binaries from the Siegler collection (which, due to a different mass cut, all have a lower system mass than the LuckyCam sample). To reduce selection effects from the instrumental resolution cut-offs, I only considered VLM binaries with orbital radius > 3.0 AU. The resulting cumulative probability distributions are shown in figure 7.12. There is a clear deficit in wider systems in the V-K > 6.5 sample compared to the earlier type systems. A K-S test between the two orbital radius distributions gives an 8% probability that they are derived from the same underlying distribution. Although the test would benefit from the more massive systems having a larger sample, there may be a sharp cut-off in the incidence of systems with orbital radii > 10AU, at around the M5-M5.5 spectral type. Note that the K-S test is here used to find the significance of an anomaly already noticed by eye in the data; the cutoff at V-K=6.5 is arbitrary for example. A more rigorous test would be to re-observe a similar sample of targets and find if the same cutoff is also significant for that sample.

7.5 Conclusions from the LuckyCam Surveys

What can we conclude about the nature of the VLM star formation processes from the LuckyCam surveys? The current picture of VLM star formation is usually modelled as fragmentation of the initial molecular cloud core followed by ejection of the low mass stellar embryos before mass accretion has completed - the ejection hypothesis (Reipurth & Clarke, 2001).

Multiple systems formed by fragmentation are limited to be no smaller than 10AU by the opacity limit (eg. Boss (1988)), although closer binaries can be formed by dynamical interactions and orbital decay (Bate et al., 2002).

The ejection hypothesis predicted binary frequency is about 8% (Bate & Bonnell, 2005); few very close (< 3AU) binaries are expected (Umbreit et al., 2005) without appealing to orbital decay. Few wide binaries with low binding energies are expected to survive the ejection, although recent models produce some systems wider than 20AU when two stars are ejected simultaneously in the same direction (Bate & Bonnell, 2005). The stardard ejecton hypothesis orbital radius distribution is thus rather tight and centered at about 3-5 AU, although its width can be enlarged by appealing to the above additional effects.

The LuckyCam surveys found several wide binary systems, with 11 of the 24 detected systems at more than 10 AU orbital radius and 3 at more than 20 AU. With the latest models, the ejection hypothesis cannot be ruled out by these observations, and indeed (as suggested in Bate & Bonnell (2005)) the frequency of wider systems will be very useful for constraining later models capable of predicting the frequency in detail. The observed distance-bias-corrected binary frequency in the LuckyCam survey is consistent with the ejection hypothesis models, but may be inconsistent when the number of very close binaries undetected in the surveys is taken into account (Maxted & Jeffries, 2005; Jeffries & Maxted, 2005).

For fragmentation to reproduce the observed orbital radius distribution, including the likely number of very close systems, dynamical interactions and orbital decay must be very important processes. However, SPH models also predict very low numbers of close binaries. An alternate mechanism for the production of the closest binaries is thus required (Jeffries & Maxted, 2005), as well as modelling constraints to test against the observed numbers of wider binaries. Combining the LuckyCam surveys with radial velocity tests for much closer systems would offer a very useful insight into the full orbital radius distribution that must be reproduced by the models.

7.5.1 Extensions to the LuckyCam VLM Binary Surveys

The LuckyCam VLM binary surveys offer a wealth of targets suitable for followup.

Firstly, the binaries discovered in this chapter require follow-up LuckyCam observations, to obtain calibrated resolved photometry for the components. As in chapter 6, this will allow modelling of the component masses of the systems as well as improved constraints on their spectral types.

Secondly, the binaries which are barely resolved require higher-resolution imaging – this includes the < 0.15 arcsec binaries presented in this chapter, and the possible substellar triple system in chapter 6. Some of these systems will be observed using LuckyCam on the 3.6m New Technology Telescope in June 2006; the increased mirror size increases the diffraction-limited resolution but at the cost of a lower probability of obtaining a good frame. Since these targets are known to be binaries, however, longer integration times can be assigned, allowing smaller numbers of frames to be selected to obtain the highest resolutions.

The new binaries (especially the more exotic systems) will also be studied intensively with other instruments. Resolved near-infrared imaging of the systems will be especially useful to determine the properties of the later-type companions. Such imaging would require (in many cases) laser guide star adaptive optics systems, as the targets are faint. If possible, resolved spectroscopy of the systems would be the best method for the accurate determination of the temperatures and spectral types of the stars.

Radial velocity observations of the samples presented here would determine the number of very close binaries. These systems probably make up a substantial fraction of VLM binaries (Jeffries & Maxted, 2005), and so searches for very close companions are required for a complete census of the binarity in the samples.

In the longer term, I would like to follow the orbits of these binaries astrometrically (and with radial velocity measurements). Many of the systems presented here have short enough orbital periods to allow a full orbital solution in a relatively short time: for example, with a total system mass of 0.2M_⊙ (typical for the binaries presented in this chapter) and an orbital radius of 2.3AU (the closest new binary in this chapter), the full orbital period is only 16 years (from equation 7.1). The orbital period of the possible substellar companion presented in chapter 6 is estimated to be 15-30 years. Since the orbit may be fit before the completion of a full orbital period, many of these systems will allow an accurate mass calibration of these object types over a reasonably short timescale.

I also plan to extend the LuckyCam VLM binary survey to cover many more targets. The June 2006 run on the NTT is planned to extend the survey by several hundred Southern targets (weather permitting). This will both very significantly increase the known number of VLM binaries (by up to 100% in total) and offer the possibility of the discovery of more exotic systems, such as substellar companions or higher-order multiple systems.

7.6 Summary

• I found 21 very low mass binary systems in a 78 star sample, including one binary which is a companion in a 2300 AU wide triple system. 14 of the binary systems are new discoveries.
• All of the new systems are significantly fainter than the previously known close systems in the sample, demonstrating LuckyCam’s faint-guide-star capability.
• I demonstrated the use of LuckyCam for binary orbit determination, and found that the previously known mass for the GJ1245AC system is in error by ~20%.
• The distance-corrected binary fraction is 13.5_-4^+6.5%, in agreement with previous results, and there is no detectable correlation between X-Ray emission and binarity.
• The orbital radius distribution of the binaries appears to show characteristics of both the late and early M-dwarf distributions, with 9 systems having an orbital radius of more than 10 AU.
• The orbital radius distribution of the binaries with V-K < 6.5 in this survey is not consistent with that of lower-mass objects, suggesting a possible sharp cutoff in the number of binaries wider than 10 AU at about the M5 spectral type.