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The formation and evolution of binary systems. III. Low-mass binaries in the Praesepe clust


arXiv:astro-ph/0106493v1 27 Jun 2001

Abstract. With the aim of investigating the binary population of the 700 Myr old Praesepe cluster, we have observed 149 G and K-type cluster members using adaptive optics. We detected 26 binary systems with an angular separation ranging from less than 0.08 to 3.3 arcsec (15– 600 AU). After correcting for detection biases, we derive a binary frequency (BF) in the log P (days) range from 4.4 to 6.9 of 25.3±5.4%, which is similar to that of ?eld G-type dwarfs (23.8%, Duquennoy & Mayor 1991). This result, complemented by similar ones obtained for the 2 Myr old star forming cluster IC 348 (Paper II) and the 120 Myr old Pleiades open cluster (Paper I), indicates that the fraction of long-period binaries does not signi?cantly evolve over the lifetime of galactic open clusters. We compare the distribution of cluster binaries to the binary populations of star forming regions, most notably Orion and Taurus, to critically review current ideas regarding the binary formation process. We conclude that it is still unclear whether the lower binary fraction observed in young clusters compared to T associations is purely the result of the early dynamical disruption of primordial binaries in dense clusters or whether it re?ects intrinsically di?erent modes of star formation in clusters and associations. We also note that if Taurus binaries result from the dynamical decay of small-N protostellar aggregates, one would predict the existence of a yet to be found dispersed population of mostly single substellar objects in the Taurus cloud. Key words: Stars: binaries: close; Stars: formation; Stars: low-mass, brown dwarfs; Galaxy: open clusters and associations: individual: Praesepe, M44

A&A manuscript no. (will be inserted by hand later) Your thesaurus codes are: missing; you have not inserted them


The formation and evolution of binary systems. III. Low-mass binaries in the Praesepe cluster.?
J. Bouvier1 , G. Duch?ne1,2 , J.-C. Mermilliod3, and T. Simon4 e

2 3 4

Laboratoire d’Astrophysique, Observatoire de Grenoble, Universit? Joseph Fourier, B.P. 53, 38041 Grenoble Cedex 9, France e http://www-laog.obs.ujf-grenoble.fr/ UCLA Division of Astronomy and Astrophysics, Los Angeles, CA 90095-1562, USA Institut d’Astronomie de l’Universit? de Lausanne, CH-1290 Chavannes-des-Bois, Switzerland e Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA

Received / Accepted

1. Introduction Binary and multiple systems provide a fossil record of the star formation process. In the last decade, studies of various galactic populations (?eld stars, open clusters, star forming regions) have led to the conclusion that most solar-type stars occur in binary systems rather than in isolation (e.g., Duquennoy & Mayor 1991, Mathieu et al. 2000). Hence, the most common output of protostellar collapse appears to be the formation of multiple systems. Beyond this indisputable observational result, the way stellar systems form remains an important issue (Bodenheimer et al. 2000), and so a robust determination of the detailed properties of binary stars, e.g., the distributions in their orbital periods, mass-ratios, and orbital eccentricities, is critically needed to guide theoretical models (Clarke et al. 2001, Ghez 2001). Equally important in order to get clues to the star formation process is to determine whether the properties of binaries depend upon the environment in which they form, and whether these properties evolve over time or, to the contrary, remain stable during pre-main sequence and main sequence evolution: that is, are the statistical properties of binary populations universal and do they unambiguously re?ect the processes which gave them birth, or do they vary both over time and from place to place in the solar neighbourhood? In order to address these issues, multiple systems have to be sampled and characterized in various types of environments and in stellar populations that have reached di?erent stages of evolution. A number of studies have been devoted to these issues. Large scale searches for binaries have been completed among low-mass ?eld dwarfs (Duquennoy & Mayor 1991, Fisher & Marcy 1992, Tokovinin 1992), T Tauri stars in young stellar associations (e.g., Leinert et al. 1993, Ghez et
Send o?print requests to: J. Bouvier ? Based on observations obtained at the Canada-FranceHawaii Telescope Correspondence to: jbouvier@laog.obs.ujf-grenoble.fr

al. 1993, Simon et al. 1995) and low-mass stars in young clusters (e.g., Bouvier et al. 1997, Duch?ne et al. 1998, e Patience et al. 1998, Mermilliod & Mayor 1999). The results indicate that in most surveyed regions the low-mass stars exhibit a similar fraction of close visual binaries with semi-major axes between a few tens to about 1000 AU (see Duch?ne 1999 for a summary). There are, however, e two notable exceptions. First, the Taurus star-forming association appears to contain about twice as many binaries as are present in the ?eld (Leinert et al. 1993, Ghez et al. 1993). Second, there is a marked de?cit of wide binaries, with semi-major axes in the range from 1000 to 5000 AU, in the Orion cluster as compared to the ?eld binary population (Scally et al. 1999). One of the di?culties in interpreting these results is that the various studies were performed with di?erent techniques, thus introducing di?erent observing biases (see Duch?ne 1999). Motivated by the need to obtain hoe mogeneous data sets for close visual binaries, especially in cluster environments whose study has been somewhat neglected compared to star forming regions and ?eld populations, we have started high angular resolution surveys of low-mass stars in nearby young clusters. For this project, we have selected a number of clusters having ages in the range from 2 Myr to 700 Myr, in order to investigate any evolution of the binary content with time. The ?rst 2 papers of this series reported on the results obtained for the ?100 Myr Pleiades cluster (Bouvier et al. 1997, Paper I), the ?2 Myr IC 348 cluster (Duch?ne et al. 1999, Paper e II), while preliminary results for the ?80 Myr Alpha Per cluster have been reported by Eisl¨?el et al. (2001). o We report here the results obtained on the binary population of the 700 Myr old Praesepe cluster from high angular resolution observations of 149 low mass cluster members. Section 2 describes our data aquisition and analysis techniques, which are similar to those used in Papers I and II. The binary frequency among the low-mass stars in Praesepe and the binary properties of the cluster are derived in Section 3. Combining these data with those

J. Bouvier et al.: Praesepe low-mass binaries


available in the literature for other young clusters, star forming associations, and the ?eld, we discuss in Section 4 the implications of the trends (or lack of) observed in binary frequency as a function of time and environmental conditions for the binary formation process. 2. Observations and data analysis The sample was primarily drawn from the proper motion study of Praesepe candidate members by Jones & Stauffer (1991, hereafter JS91). From this catalogue, we ?rst selected 70 candidates in a B-V range between 0.52 and 1.4 which had a proper motion membership probability larger than 90%. These candidates were observed in February and December, 1997. For another observing session in January 1998, 53 additional candidates were selected from JS91 in the same B-V range, which had a proper motion membership probability larger than 75% and visual photometry consistent with membership in a (V,B-V) color-magnitude diagram. We completed our sample with 26 additional candidates having both radial velocities and photometry consistent with Praesepe membership, which were selected from Mermilliod’s Open Clusters Database (WEBDA, Mermilliod 1999) and amongst Praesepe halo candidates (Mermilliod et al., 1990). A total of 149 Praesepe G and K dwarfs were thus observed in 1997 and 1998 at the Canada-France-Hawaii Telescope with the adaptive optics system PUEO (Rigaut et al. 1998). The IR camera was MONICA (Nadeau et al. 1994) in Feb. 1997 and KIR (Doyon et al. 1998) in Dec. 1997 and Jan. 1998, which provide a ?eld of view of 9′′ and 36′′ , respectively. We used the same aquisition procedure for all runs. The targets were observed successively in four quadrants of the camera, for a total integration time of typically 60s; the 4 exposures were subsequently registered and added to produce a ?nal image that was properly sky subtracted and ?at-?eld corrected. The primaries were ?rst observed in either the H or K band, depending on the atmospheric turbulence conditions, in order to optimize the adaptive correction. Whenever a binary was detected in real-time, it was observed in at least one other ?lter in order to subsequently check the membership of the companion in a color-magnitude diagram. During each run, the images produced by the adaptive optics system were di?raction-limited in the H and K bands, providing a spatial resolution of 0.09′′ and 0.13′′ FWHM, respectively. Aperture photometry was performed using IRAF/APPHOT and calibrated using several UKIRT Faint Standards observed during the 3 runs. The photometric accuracy is of order of 0.05 magnitudes in the JHK bands. Table 1 lists the near infrared magnitudes of non resolved primaries while those of Praesepe binaries are listed in Table 2. For the binaries, di?erential photometry was obtained by ?tting a template PSF simultaneously to the primary and the companion within IRAF/DAOPHOT. The PSF was provided by unresolved

Praesepe stars that were observed just before and/or just after the exposure on the binary. Several PSF templates were used for each binary, thus providing an estimate of the photometric error. Typically, the di?erential photometry is accurate to within 0.02 magnitudes, but the error may be larger for binaries with a separation close to the resolution limit or for companions close to the detection limit. The magnitude di?erence between the companion and the primary was combined with the aperture photometry of the system to provide the magnitude of each component. The separation and position angle were derived from the photocenter of the components in the image as provided by the PSF ?tting algorithm. The plate scale and orientation of the detector were calibrated by observing IDS astrometric standards (Van Dessel & Sinachopoulos, 1993) during each run. The rms error is typically 5 mas on the separation and 0.1? on the position angle. 3. Results We detected 26 binaries and one triple system having separations less than 7′′ among 149 Praesepe G and K dwarfs. Table 2 provides their names and cross-identi?cations, visual photometry, and indicates whether they were previously known as either photometric or spectroscopic binaries. 3.1. Comparison with previous work Of the 26 binaries reported here, eight were previously known as spectroscopic binary (SB) systems (Mermilliod & Mayor 1999): three long-period SBs (BDA 297, 322, 533) are resolved here with a projected separation of 23 AU or less, while three others have too short a period to be resolved (BDA 287, 540, 1184) and so the companion reported here makes them triple systems. The two remaining systems, BDA 365 and BDA 495, are known to be spectroscopic triples (Mermilliod et al. 1994). They both consist of a long-period binary with one of the components itself being a short-period binary. Both objects are spatially resolved here, and, given their angular separations and spectroscopic orbits, it is likely that we resolved the widest binary pair of these systems. Figure 1 shows a (V, B-V) color-magnitude diagram (CMD) for the whole sample of G and K Praesepe members observed in this survey. The di?erent symbols indicate previously known spectroscopic binaries, visual binaries detected here by adaptive optics, and “single” stars. Not surprisingly, the sample contains a number of (presumably short-period) SBs located on the main and binary sequences of the cluster that are not resolved by adaptive optics. More interestingly, about 15 objects that are not detected as binaries, either from spectroscopy or adaptive optics, lie more than 0.5 mag above the main sequence of the cluster and must therefore be nearly equal-mass bi-


J. Bouvier et al.: Praesepe low-mass binaries

Table 1. Photometry of non resolved Praesepe primaries1
BDA 9 49 141 ... 1 Table Filt Mag K 9.51 H 9.27 H 10.27 ... ... 1 is available Run BDA jan98 23 jan98 58 dec97 162 ... ... electronically in Filt Mag Run BDA K 9.64 feb97 30 K 9.64 feb97 70 H 9.15 feb97 172 ... ... ... ... extenso at CDS, Starsbourg Filt K H K ... Mag 9.75 10.08 10.34 ... Run jan98 dec97 jan98 ... BDA 48 127 181 ... Filt K H H ... Mag 10.17 9.41 9.04 ... Run jan98 jan98 jan98 ...

Table 2. Astrometric and photometric properties of Praesepe binaries
BDA KWa VLb JSc V B-V sep








q 0.64 0.75 0.11 0.42 0.47 1.0 0.15 0.83 0.8 0.77 0.79 0.43 0.10 0.26 0.17 0.99 0.93 0.11 0.66 0.92 0.48 0.38 0.73 0.23 0.22 0.32 0.85 0.97

Notes 1 1

79 79 572 211 12.10 0.91 0.174 73.5 10.40 9.98 9.83 1.40 1.58 90 90 598 222 10.89 0.70 0.184 27.4 9.20 9.14 0.90 1.02 100 100 621 228 10.55 0.58 1.03 97.3 9.53 9.22 9.25 6.20 5.70 164 164 789 279 11.31 0.70 0.256 18.4 9.60 2.76 198 198 870 306 12.62 0.97 1.153 354.48 10.82 10.37 10.25 2.64 2.50 2.35 275 275 993 9.96 0.58 0.21 90.4? 8.83 8.60 8.54 0.03 -0.02 0.02 287 287 1014 10.37 0.59 1.798 24.84 9.46 9.07 9.15 5.63 5.31 5.13 297 297 1033 362 11.64 0.86 0.126 188.3 9.49 9.40 0.61 0.56 322 322 1070 375 10.87 0.68 <0.09 ?150 9.20 9.14 ?0.5 334 334 1091 387 11.01 0.72 0.091 44.9 9.56 9.20 1.14 0.85 365 365 1142 407 10.18 0.65 0.373 109.27 8.86 8.52 0.87 0.83 401AB 401 1214 436 12.97 1.00 1.688 239.56 10.77 10.23 10.15 2.51 2.41 2.30 401AC? 401 1214 436 12.97 1.00 1.776 286.69 10.77 10.23 10.15 6.1 5.4 466?? 466 1345 486 10.99 0.65 2.184 304.97 9.71 4.48 4.12 3.87 488 488 1399 509 11.43 0.73 1.263 198.1 9.76 9.73 4.91 4.65 495 495 1416 515 9.97 0.66 0.072 159.3? 9.66 9.35 0.03 533 533 237 122 11.59 0.90 0.124 16.2 9.54 0.25 540 540 387 167 11.03 0.69 3.35 233.59 9.69 9.33 9.29 6.12 5.88 5.67 809 194 13.04 1.13 1.737 325.96 10.99 10.44 10.32 1.62 1.49 1.35 901 354 13.82 1.39§ 2.428 191.7 10.66 10.52 0.34 0.31 1184 184 102 11.85 0.79 1.285 151.95 9.85 9.73 2.50 2.43 1452 452 186 13.87 1.32§ 0.390 130.9 10.80 10.68 2.78 2.62 1995 995 350 12.97 1.21 0.337 289.49 10.71 10.11 10.01 0.18 0.11 0.18 2029 1029 359 12.90 1.04 0.520 204.9 10.46 10.38 3.94 3.78 2085 1085 383 12.89 1.10§ 0.642 186.9 10.54 10.44 4.00 3.79 2418 1418 516 13.67 1.18 0.394 221.5 10.84 10.65 3.1 3.16 2692 1692 588 10.92 0.72 0.405 234.6 9.17 9.13 0.50 0.61 3231 231 13.31 1.39§ 0.168 172.0? 10.26 10.16 0.13 0.09 a b c Klein-Wassink 1927, Vanderlinden 1933, Jones & Stau?er 1991 § Photographic magnitudes. ? Within 3σ photometric errors, the P.A. could be 180? away from the listed value. ? BDA 401C is a probably a ?eld object. ?? Due to non-photometric conditions, only di?erential photometry was obtained in the H and K bands. Notes: 1 Photometric binary; 2 SB1, P=7635d; 3 SB1, long period; 4 SB1, P>10000d; 5 Triple, A: SB1O, B:single; single, B: SB2; 7 SB2, long period; 8 SB1, P=1149d; 9 SB1, P=1.23d.

1 2 3 4 1 5

6 7 8



Triple, A:

nary systems. In order to have escaped detection, these systems must have an orbital period in the range from about 3 103 to 3 104 days, i.e., a semi-major axis in the range from about 4 to 15 AU. Finally, although many of the binaries that are resolved in the present study are displaced above the main sequence as expected, about a third of them are located on the cluster main sequence and were not previously detected as binaries through photometry. BDA 1184 (the triangle at V = 11.85, B-V = 0.79) is the

most extreme case: it appears to be a single star but is in fact a triple system, a short-period spectroscopic bi′′ nary and a wider companion at 1. 28. This simply means that many faint and red companions are hidden in visible light and are too light-weight to show up in radial-velocity observations. A (K, V-K) CMD, also shown in Figure 1, is more appropriate to detect very red companions photometrically. In this diagram, BDA 1184 shows a vertical displacement

J. Bouvier et al.: Praesepe low-mass binaries


Fig. 1. Color-magnitude diagrams (CMD) for low-mass Praesepe members. The (V, B-V) CMD (left panel) contains the whole sample observed with PUEO, while the (K, V-K) one (right panel) contains only a subset of it since some primaries were not observed in the K-band. Symbols are as follows: ?lled squares: binary systems resolved with PUEO, ?lled dots: known spectroscopic binaries, ?lled triangles: triple systems resolved by PUEO, open circles: “single stars”, crosses: suspected non members. Several systems resolved in the near-infrared appear to be single in the visible. of 0.42 mag. Another example, BDA 2418, which lies right on the single star sequence in the (V, B-V) plane, already shows a displacement of 0.15 mag in (I, V-I) and 0.35 mag in (K, V-K). However, the star BDA 287, another triple system, is still located on the single star sequence even in (K, V-K), because the K magnitude di?erence is 5.13. To conclude this section, the common use of (V, BV) colour-magnitude diagram to study binarity in open clusters from photometric data is not a good choice or strategy. (I, V-I) planes are certainly better and JHK observations provide still much more information on faint red companions. Observations through the BV IK ?lters would therefore permit the detection of a wealth of new binary candidates, which would raise the binary frequency to values that are probably more realistic. However, direct observations are still needed to detect systems with large magnitude di?erences or with a multiplicity of order higher than 2. 3.2. Binary frequency and orbital period distribution Table 2 also lists the astrometric and infrared properties of the systems and their components. Although BDA 322 is clearly elongated on the images, its separation is too small for deriving precise astrometric and photometric properties, and so we list only approximate values in Table 2. The masses of the individual binary components and the resulting mass ratios, q = M2 /M1 , were derived from the JHK photometry of the components using the mass-magnitude relationships from Bara?e et al. (1998) models, assuming an age of 0.7 Gyr and a distance modulus for Praesepe of (m ? M ) = 6.28 (d = 180pc, Robichon et al. 1999). For the primaries or secondaries that are themselves unresolved spectroscopic binaries, this method would overestimate their mass by up to about 20% for equal-brightness components. In order to ascertain photometric membership, we plotted the primaries and secondaries in various JHK color-magnitude diagrams, comparing their location in these diagrams with the 700 Myr isochrone from Bara?e et al. (1998). The primaries and secondaries are all consistent with being Praesepe members within the photometric errors. However, the third component of the BDA 401 system, BDA 401C, lies far away from the isochrone and is probably a ?eld object. We therefore ignore it in the following discussion and consider BDA 401 to be a double. Finally, a few binaries were observed at only one wave-


J. Bouvier et al.: Praesepe low-mass binaries

Table 3. Binary frequency (see text)
log Porb Semi-major axis Sep. range ?mmax qmin Ndetect. [qmin , 1.0] Nundetect. [0.1, qmin ] Ntot B.F. Praesepe (rms) B.F ?eld G dwarfs log Porb =4.4-6.9 4.4-4.9 4.9-5.4 18-39 39-86 0.08-0.17 0.17-0.38 2.2 3.0 0.50 0.40 4 6 6.4 5.4 10.4 11.4 7.0 (3.5) 7.7 (3.1) 5.4 5.3 B.F. Praesepe: 25.3 5.4-5.9 86-183 0.38-0.81 4.5 0.20 5 0.95 5.95 4.0 (1.8) 5.0 ± 5.4% 5.9-6.4 6.4-6.9 183-394 394-852 0.81-1.74 1.74-3.76 6.7 7.2 <0.1 <0.1 6 4 0 0 6 4 4.0 (1.6) 2.6 (1.3) 4.5 3.9 B.F. ?eld: 23.8% days AU


% %

length, but these systems are so tight that their binary nature is not in serious doubt.

Fig. 2. Limit of detection for faint companions. The location of resolved Praesepe binaries in this diagram is indicated (crosses: ?J, ?lled dots: ?H, ?lled triangles: ?K). The curve indicates the maximum magnitude di?erence detectable on AO images at any distance from the center of the primary. It was derived by computing the 5σ noise level on radial pro?les of unresolved Praesepe primaries. By adding arti?cial companions to the primaries on the images, we empirically veri?ed that this curve corresponds to the limit of detectability of faint and/or close companions. That we ?nd only one chance projection at a distance of less than 7′′ in a sample of 149 stars is consistent with the 2MASS Point Source Catalogue Statistics, which predict about 1200 objects per square degree down to a magnitude of K=15 in the direction of Praesepe. This translates into ?0.015 objects within a 7′′ radius and leads to an estimate of 2 chance projections in the present sample.

Fig. 3. Distribution of orbital periods for Praesepe binaries (histogram). The error bars represent Poisson noise (see text). The dashed curve is the orbital period distribution of ?eld G dwarf binaries as derived by DM91. In order to estimate the binary frequency among the Praesepe G and K dwarfs, a correction factor has to be applied to the number of systems actually detected to account for the detection limit of our survey. The largest magnitude di?erence we are able to detect between the secondary and the primary is shown in Figure 2 as a function of angular separation. At separations close to the di?raction limit, the detection of faint companions is limited by the constrast against the bright primary while, at large separations, the detection is background limited. We therefore proceed to derive a correction factor in various separation bins as follows. In each bin, we convert the maximum reachable contrast between the secondary and the primary, ?mmax , into a minimum mass ratio qmin using the mass-magnitude relationship from the Bara?e et al. (1998) models. We assume that the mass-ratio distribution of the Praesepe bi-

J. Bouvier et al.: Praesepe low-mass binaries


naries is the same as that of the ?eld G dwarfs derived by Duquennoy & Mayor (1991, DM91). This assumption is consistent with the mass ratio distribution derived for our binary sample. While the overall q–distribution is rather ?at (see Table 2), restricting the analysis to the separation range where we can detect all companions down to q = 0.1 (sep≥0.8′′ , see Table 3) so that we can compare to DM91, we count 10 companions. Mass ratios in this small subsample range from 0.11 to 0.92, with a mean of 0.38. In DM91 survey, for binaries with periods longer than 104 days, the average mass ratio is 0.40. Both results are very similar, though ours admitedly relies on only a few systems. The fraction of missed companions is then found by integrating DM91’s mass-ratio distribution between q=0.1 and q=qmin . We ?nally apply this correction factor to the number of detected binaries to obtain the total number of systems with mass-ratios larger than 0.1 in this separation range. The 1σ uncertainties on BF in each log P bin √ correspond to Poisson noise, i.e., σ = Nd × (1 + Nu /Nd ), where Nd and Nu are the number of detected and missed systems, respectively (see Table 3). In order to establish the distribution of orbital periods, i.e., the frequency of binary systems in each log P bin, we convert the intervals of projected separation into bins of orbital periods. Angular separations ρ are statistically corrected for projection e?ects to yield the semi-major axis according to: log a = log(ρ × d) + 0.1 (DM91), where d = 180 pc is the distance to the Praesepe cluster. Kepler’s 3rd law with an average mass of 1.3 M⊙ for the system yields the corresponding range of orbital periods (see Table 3). The last lines of Table 3 list and also Figure 3 illustrates the derived frequency of Praesepe low-mass binaries in each log P bin between 4.4 and 6.9 (P in days), as compared to the frequency of G dwarf binaries over the same separation range1 . Even though the statistical uncertainties in each bin are somewhat large, especially at the shortest orbital periods where the incompleteness correction is signi?cant, the overall binary frequency appears to be very similar among the solar-type Praesepe stars and the ?eld G dwarfs, amounting to 25.3±5.5% and 23.8%, respectively, for the 4.4-6.9 range in log P . Restricting the comparison to the range of orbital periods not a?ected by detection biases (log P from 5.4 to 6.9), the BF amounts to 10.7±2.6% for Praesepe stars compared to 13.4% for ?eld dwarfs. We thus conclude that the frequency of long period binaries among Praesepe G and K stars is indistinguishable from that measured among the G ?eld dwarfs by DM91. This conclusion seems to apply to short-period systems as well (log P ≤ 4.0) as Mermilliod’s & Mayor’s (1999) investigation of spectroscopic binaries in the Prae1 As in our previous paper on the Pleiades (Bouvier et al. 1997), we de?ne the binary frequency, B.F., as the number of binary orbits divided by the number of primaries in the sample. This is equivalent to the companion star fraction, csf = (B + 2T )/(S + B + T ), where S, B, and T are single, binary, and triple systems, respectively.

sepe cluster yields BF= 25 ± 5%, as compared to 21% for ?eld dwarfs. Praesepe has nearly the same age as the Hyades cluster. Unfortunately, comparison of the BF between the two clusters is limited by the fact that there is only a slight overlap in the separation ranges covered by Patience et al.’s (1998) survey in the Hyades and ours in Praesepe. In the 15–50 AU common range of semi-major axes, we detect 8 companions, i.e. an observed companion fraction of 5.3±1.9%. In the same separation range, Patience et al. (1998) detected 9 companions, out of which 3 would not have been detected in our survey given their ?ux ratios. This amounts to a companion star fraction of 3.7±1.5%, less than 1σ lower than our Praesepe estimate. Within this restricted range of orbital periods, we thus do not ?nd any signi?cant di?erence between Hyades and Praesepe binary fraction, though this conclusion is obviously based on small number statistics. 4. Discussion In this section, we ?rst brie?y review current observational results on the statistics of binary frequency in young clusters and associations, including results from both this and previous papers of this series and other published work. The comparative analysis of the properties of binary populations in di?erent environments and at various evolutionary stages provides constraints on binary formation models, which are discussed below with the emphasis on the di?culties that are encountered by the various formation scenarios. The discussion is restricted to visual (a ? 20-1000 AU), low-mass binaries (? 0.5-1.1 M⊙ ) that are resolved by high angular resolution techniques. 4.1. Binary statistics in clusters and associations The three young clusters we surveyed for low-mass binaries, IC 348 (?2 Myr, Duch?ne et al. 1999), the Pleiades e (120 Myr, Bouvier et al. 1997), and Praesepe (700 Myr), have been observed with the same instrumentation, thus resulting in similar detection biases. Moreover, the results have been analyzed in a consistent way, in particular with regard to the incompleteness corrections. The three clusters are found to exhibit identical binary frequencies over the log P range ?4.5-7.0, <BF> ? 0.25 ± 0.05, which is also consistent with the BF measured for solar-type ?eld dwarfs in the same range of orbital periods (BF ? 0.24, DM91). Similar results have been obtained for other clusters, Orion (?2 Myr, Prosser et al. 1994, Petr et al. 1998, Simon et al. 1999), Alpha Persei (? 80 Myr, Eisl¨?el o et al. 1999), and the Hyades (?600 Myr, Patience et al. 1998) — all of which exhibit a low-mass BF in a restricted log P range that is consistent with the ?eld dwarf BF when the results are analyzed in a uniform way (see Duch?ne e 1999).


J. Bouvier et al.: Praesepe low-mass binaries

Since the ages of these clusters cover a huge range from 2 to 700 Myr, the results suggest that low-mass binaries are formed at a very early stage of cluster evolution (at an age ≤ 1 Myr) and that the binary fraction does not evolve much thereafter until the cluster eventually dissolves into the ?eld (? 1 Gyr). The lack of a signi?cant evolution of the binary population during the secular dynamical evolution of a cluster is consistent with recent numerical simulations (e.g. Kroupa 2000). Note, however, that this conclusion may not hold for more massive and/or spectroscopic binaries. Abt & Willmarth (1999) have reported marginal evidence for a BF that increases with a cluster’s age, from the Orion Nebula Cluster to Praesepe, for spectroscopic binaries with A-type primaries. They interpret this trend as the possible signature of binary formation by capture in evolving clusters and/or preferential escape of single stars during the secular dynamical evolution of clusters (de la Fuente Marcos 1997). No such trend is seen for low-mass wide binaries. Another general result is that pairs of nearly coeval clusters (e.g., IC348 and Orion, Alpha Persei and the Pleiades, Praesepe and the Hyades) not only exhibit similar fractions of low-mass visual binaries over the separation range probed by adaptive optics and speckle techniques (?20-1000 AU), but the distribution of orbital periods is consistent as well, with admittedly large uncertainties in the shape of the log P distribution (see Fig. 3). These similarities suggest that either all these clusters were formed under very similar conditions and have evolved in the same way, or else the binary content of clusters and their properties depend only weakly on initial conditions. In marked contrast with the results obtained for cluster binaries, the binary frequency in low-density star forming associations, most notably the Taurus-Auriga cloud, is higher by a factor of about 2 than that observed in both clusters and ?eld solar-type stars (Leinert et al. 1993, Ghez et al. 1993). Ghez (2001) also reported a signi?cant di?erence between the log P distributions of binaries in clusters and those in associations, the latter harbouring a larger fraction of wider binaries than the former. The di?erent properties of binary populations in clusters and associations can be a signature of di?erent formation mechanisms in these environments (e.g., Durisen & Sterzik 1995). Alternatively, if one assumes a universal formation mechanism that yields the same initial BF in clusters and associations, the observed di?erences could re?ect dynamical processes acting very early-on, such as the rapid disruption of wide primordial binaries in clusters through gravitational encounters (e.g. Kroupa et al. 1995). We discuss these two possibilities in turn below.

4.2. A universal mechanism for binary formation? Among the various possible ways of forming low-mass binaries, tidal capture has been shown to be ine?cient even in the densest protostellar clusters (Clarke & Pringle 1991, Kroupa 1995, Clarke 2001) and ?ssion of massive protostars or protostellar disks, which could conceivably yield the tightest binaries, seems to be prevented by the development of bar-like instabilities (Durisen et al. 1986, Bate 1998). Therefore, multiple fragmentation during protostellar collapse appears today to be the most promising mechanism for creating wide multiple systems (Bodenheimer 2001). Recent collapse calculations indicate that the likely output of multiple fragmentation is the formation of smallN protostellar aggregates, where N? 3-10 (e.g., Burkert, Bate & Bodenheimer 1997, Klessen & Burkert 2000). These aggregates experience rapid dynamical decay and eventually leave a bound binary system, while other fragments are dynamically ejected mostly as single remnants (e.g., McDonald & Clarke 1993, 1995; Sterzik & Durisen 1998). Since few-body interactions occur on a small scale within protostellar aggregates (r ? a few 100 AU) and on a very short time scale (? 104 yr), the resulting primordial binary fraction is not expected to depend strongly upon the global properties of the star forming region. The fraction of primordial binaries that results from the dynamical decay of protostellar aggregates is usually identi?ed with the high BF observed in loose associations like Taurus. Then, the lower BF measured in clusters is thought to result from the rapid disruption of primordial binaries, through destructive gravitational encounters that occur on a time scale of less than 1 Myr (e.g., Kroupa, Petr, & MacCaughrean 1999). Since the rate of gravitational encounters scales with the local stellar density, this scenario conceivably accounts for the observed trend of lower binary fractions in denser star forming regions (Patience & Duch?ne 2001), and it is further supported by e the paucity of wide binaries observed in the ONC (Scally et al. 1999) and, more generally, in young open clusters (Ghez 2001). This mode of binary formation is not exempt from dif?culties, however. One issue is whether the Taurus binaries can be regarded as representative of a universal population of primordial binaries. The frequency of primordial binaries that is expected from the decay of small-N aggregates is of order of BFp ? 1 / (N-1), i.e., at most 50% for N=3. This is signi?cantly lower than the BF measured in the Taurus association, which amounts to ≥80% for stars in the mass range ? 0.3 ? 1.2 M⊙ , with little dependence on the primary mass (Leinert et al. 1993). This discrepancy could be solved if single fragments that were dynamically ejected from protostellar aggregates had escaped from their birth place. With typical ejection velocities of 3-4 km s?1 (Sterzik & Durisen 1995), they would be located a few parsecs away from their birth site at an

J. Bouvier et al.: Praesepe low-mass binaries


age of 2 Myr, i.e., a few degrees away from the Taurus stellar groups (Gomez et al. 1995). A widely distributed population of X-ray emitting T Tauri stars has been detected with ROSAT over the Taurus cloud (Wichmann et al. 1996, 2000, Frink et al. 1997), but these stars do not seem to be preferentially single (K¨hler & Leinert 1998), o as would be expected if they were escapers. An intriguing possibility is that the ejected fragments are very low mass, indeed substellar, objects (Sterzik & Durisen 1999, Clarke & Reipurth 2001) that might so far have escaped detection in the Taurus cloud. Although the search for brown dwarfs in Taurus has been somewhat disappointing (Luhman 2000), it has only concentrated on very limited areas centered on the small Taurus stellar groups. A widely distributed population of (single) substellar objects over the Taurus cloud could reconcile the high BF frequency measured for Taurus stars with the lower BF expected from the decay of small-N aggregates, which includes both stellar and substellar fragments. In support of this hypothesis, we note that current determinations of the substellar IMF do indicate that isolated brown dwarfs are numerous in clusters (e.g. Luhman et al. 2000, Moraux et al. 2001) and appear to be preferentially single objects (Mart? et al. 1999). If originally ?n ejected from small-N aggregates, substellar fragments may be more easily retained in the deep potential well of dense clusters than in loose associations (de la Fuente Marcos & de la Fuente Marcos 2000), which might explain why they have not been found in the central regions of Taurus. Another aspect of the models that is challenged by the observations is whether the lower BF of clusters compared to associations can be understood as the mere result of the disruption of primordial binaries. Models that describe the dynamical evolution of primordial binaries in young clusters, starting from an initial distribution similar to the one observed in Taurus, show that the destruction rate of wide primordial binaries (log P ?5-7) is a sensitive function of the initial stellar density (e.g., Kroupa 1995; Kroupa, Aarseth & Hurley 2000). Yet, all clusters studied so far appear to harbour the same BF to within a few percent in this log P range. The lack of dispersion in the BF measured for clusters is then surprising, given that it is unlikely all clusters surveyed so far have formed with precisely similar densities. For instance, the stellar density in the Trapezium cluster is of order of 5 104 pc?3 (McCaughrean & Stau?er 1994) whereas, at a similar age, it is about 5 103 pc?3 in IC 348 (Herbig 1998). If gravitational encounters leading to the disruption of primordial binaries are the dominant mechanism that yields a lower BF in clusters, one would expect to observe somewhat di?erent binary fractions between clusters themselves. Hence, while scenarios of binary formation and evolution that assume an initially large fraction of primordial binaries in all star forming regions, followed by a rapid erosion of the binary population in dense clusters, have re-

cently become quite popular, it remains to be seen whether the di?culties outlined above can be solved. 4.3. Do local conditions impact on the binary formation process? As an alternative to a universal formation mechanism, it is probably too early yet to rule out binary and, indeed, single star formation as the direct outcome of cloud collapse and fragmentation, without going through the transient episode of small-N protostellar aggregates. Unfortunately, the theory and simulations of fragmentation are not yet predictive enough, and the ?nal product of protostellar collapse can depend sensitively on initial conditions (see Bodenheimer et al. 2000 for a review), e.g., the radial density pro?le of the parental cloud (Burkert et al. 1997), its temperature (Sterzik and Durisen 1995), turbulence (Klein 2001), the magnetic ?eld (Boss 2001), etc. The large scale environment, such as cloud-cloud collisions, or other external impulsive processes, such as supernova blasts, may also impact on the fragmentation process (Whitworth 2001). Hence, one might expect that di?erent initial conditions in star forming regions lead to signi?cant variations in the properties of the young stellar populations they harbour. Since the initial conditions that led to star formation in a given molecular cloud are usually poorly known, it is somewhat di?cult to constrain this alternative mode of binary and single stars formation with current observations. As noted above, however, one of the striking results of the recent binary surveys is the quasi-universality of the BF in clusters, which all appear to harbour the same fraction of solar-type, wide (sep ≥ 20 AU) binaries to within the statistical uncertainties. This suggests that the fragmentation process, if directly responsible for the formation of binary systems, might not be as sensitive to local conditions as numerical simulations tend to indicate. On the other hand, while the results for cluster binaries are homogeneous and similar to those obtained for the ?eld binary population, the much larger BF observed in the Taurus cloud would seem to suggest that gross variations in the local conditions do impact on the fragmentation process. In this respect, it is interesting to note that binary frequency is not the only di?erence that exists between the stellar populations of the Orion cluster and Taurus association. Signi?cant di?erences have also been found in the distribution of stellar angular momentum among their low-mass T Tauri stars (Clarke & Bouvier 2000), and in the distribution of their stellar masses, with Taurus harbouring apparently both fewer high-mass stars and fewer very-low mass objects than Orion (Hartmann& Kenyon 1995, Luhman 2000). It is tempting to think that the di?erences observed in the fundamental properties (mass and angular momentum distributions, binary frequency) of the Orion and Taurus populations are causally related and point to a common origin that re?ects intrinsically


J. Bouvier et al.: Praesepe low-mass binaries

di?erent modes of star formation in clusters and in associations (e.g., Myers 1998, Williams et al. 2000, Motte & Andr? 2001). e 5. Conclusion From an adaptive optics imaging survey of 149 G and K-type primaries of the Praesepe cluster, we ?nd that solar-type cluster members harbour the same proportion of close visual binaries as do G-type ?eld dwarfs. Long lived open clusters, such as Praesepe, probably started their evolution as extremely dense protostellar clusters. Yet, only about 10% of the ?eld population is thought to result from the dissipation of such rich clusters. At the other extreme, Taurus-like regions of distributed star formation have very low star forming e?ciencies. Hence, as recently advocated by Adams & Myers (2001), most ?eld stars must have been born in stellar groups which dissipate in a few million years, corresponding to initial conditions somewhat intermediate between dense protostellar clusters destined to become young open clusters and loose associations. The very similar binary fraction measured for solar-type stars in young open clusters (Praesepe, Pleiades, Alpha Per) and in the ?eld thus suggest that the formation and evolution of low-mass binaries is not very sensitive to local conditions. The main limitation of studies like the present one which aim at constraining the star formation process through the investigation of young binaries is that they have been mostly concerned with low-mass systems so far and somewhat neglected higher mass binaries (see, however, Preibisch et al. 1999, Garc` & Mermilliod 2001, ?a Duch?ne et al. 2001). If multiple fragmentation of cole lapsing clouds is the dominant mode for the formation of multiple stellar systems, the mass distribution of fragments in small protostellar groups may largely determine the resulting binary frequency for a given primary mass. For instance, we argued above that the high BF observed for T Tauri stars in Taurus might merely be the result of neglecting a putative population of single brown dwarfs distributed over the cloud. In regions where high mass stars are formed, such as in Orion, more single ejected fragments would be of solar mass or so, thus resulting in a lower binary fraction among low mass stars. The investigation of such causal relationships between the fundamental properties of young stars, e.g., between binary fraction and the mass function, requires the consideration of the whole stellar population of the star forming region with a complete census of multiple systems at all primary masses, which is not available today for any star forming region. A promising new way to better understand the formation of multiple systems is to investigate, in di?erent environments, extremely young stellar objects still embedded in their natal cloud at the end of the protostellar collapse. The high degree of multiplicity of such Class 0 and Class I “protostellar” sources starts to be revealed from high an-

gular resolution studies in the millimeter range (Looney, Mundy & Welch 2000). The advent of adaptive optics systems equipped with near-IR wavefront sensors on large telescopes will now open the way to large scale surveys of embedded protobinaries with a tenfold increase in angular resolution compared to current millimeter studies, reaching separations as small as a few astronomical units. Such studies will provide unprecedented details on the fragmentation process at a very early stage of evolution of young systems, before any signi?cant dynamical evolution of protostellar systems has occurred.
Acknowledgements. We thank Jean-Luc Beuzit and Olivier Lai for reobserving in Nov.-Dec. 1999 some suspected binaries with the same instrumentation and Isabelle Bara?e for computing and providing a 700 Myr isochrone from her models of low mass stars. We acknowledge useful discussions with Cathie Clarke and Pavel Kroupa on cluster dynamics and with Fr?d?rique e e Motte on prestellar cores.

Abt H.A., Wilmarth D.W. 2000, ApJ 521, 682 Adams F.C., Myers P.C. 2001, ApJ in press, astro-ph/0102039 Bara?e I., Chabrier G., Allard F., Hauschildt P.H. 1998, AA 337, 403 Bate M.R. 1998, ApJ 508, L95 Bodenheimer P. 2001, in: The Formation of Binary Stars, ASP Conf. Ser., Vol.200, eds Zinnecker & Mathieu, in press Bodenheimer P., Burkert A., Klein R.I., Boss A.P. 2000, in: Protostars & Planets IV, eds. Mannings et al., p.675 Boss A.P. 2001, in: The Formation of Binary Stars, ASP Conf. Ser., Vol.200, eds Zinnecker & Mathieu, in press Bouvier J., Rigaut F., Nadeau D. 1997, AA 323, 139 Burkert A., Bate M.R., Bodenheimer P. 1997, MNRAS 289, 497 Clarke C.J. 2001, in: The Formation of Binary Stars, ASP Conf. Ser., Vol.200, eds Zinnecker & Mathieu, in press Clarke C.J., Bouvier J. 2000, MNRAS 319, 457 Clarke C.J., Pringle J.E. 1991, MNRAS 249, 584 Clarke C.J., Reipurth B. 2001, in press de la Fuente Marcos R. 1997, AA 322, 764 de la Fuente Marcos R., de la Fuente Marcos C. 2000, ApSS 271, 127 Doyon R., Nadeau D., Vallee P., et al. 1998, in: Fowler A.M. (ed.), SPIE Proc. 3354, Infrared Astronomical Instrumentation Duch?ne G. 1999, AA 341, 547 e Duch?ne G., Bouvier J., Simon T. 1999, AA 343, 831 e Duch?ne G., Eisl¨?el J., Simon T., Bouvier J., 2001, AA, sube o mitted Duquennoy A., Mayor M. 1991, AA 248, 485 (DM91) Durisen R.H., Sterzik M.F. 1994, AA 286, 84 Durisen R.H., Gingold R.A., Tohline J.E., Boss A.p. 1986, ApJ 305, 281 Eisl¨?el J., Simon T., Close L., Bouvier J. 2001, 11th Camo bridge workshop on Cool Stars, Stellar Systems and the Sun, ASP Conf. Ser., eds Garcia Lopez et al., Vol. 223, in press Fischer D.A., Marcy G.W. 1992, ApJ 396, 178

J. Bouvier et al.: Praesepe low-mass binaries Frink S., R¨ser S., Neuha¨ser R., Sterzik M.F. 1997, AA 325, o u 613 Garc` B., Mermilliod J.-C. 2001, AA 368, 122 ?a Ghez A.M. 2001, in: The Formation of Binary Stars, ASP Conf. Ser., Vol.200, eds Zinnecker & Mathieu, in press Ghez A., Neugebauer G., Matthews K. 1993, AJ 106, 2005 Gomez M., Hartmann L., Kenyon S.J., Hewett R. 1993, AJ 105, 1927 Herbig G.H. 1998, ApJ 497, 736 Jones B.F., Stau?er J.R. 1991, AJ 102, 1080 Kenyon S.J., Hartmann L.W. 1995, ApJS 101, 117 Klein-Wassink W.J. 1927, Publ. Kapteyn Astr. Lab. no 41 Klein R.I., Fisher R., McKee C.F. 2001, in: The Formation of Binary Stars, ASP Conf. Ser., Vol.200, eds Zinnecker & Mathieu, in press Klessen R.S., Burkert A. 2000, ApJS 128, 287 K¨hler R., Leinert Ch. 1998, AA 331, 977 o Kroupa P. 1995, MNRAS 277, 1507 Kroupa P. 2000, in: Massive Stellar Clusters, ASP Conf. Ser. 211, eds Lan?on & Boily, p.233 c Kroupa P., Aaserth P., Hurley S.J. 2001, MNRAS 321, 699 Kroupa P., Petr M.G, McCaughrean M.J. 1999, New Astron. 4, 495 Leinert Ch., Zinnecker H., Weitzel N. et al. 1993, AA 278, 129 Looney L.W., Mundy L.G., Welsch W.J. 2000, ApJ 529, 477 Luhman K.L. 2000, ApJ 544, 1044 Luhman K.L., Rieke G.H., Young E.T., et al. 2000, ApJ 540, 1016 McCaughrean M.J., Stau?er J.R. 1994, AJ 108, 1382 McDonald J.M., Clarke C.J. 1993, MNRAS 262, 800 McDonald J.M., Clarke C.J. 1995, MNRAS 275, 671 Mart? E.L., Brandner W., Bouvier J., et al. 2000, ApJ 543, ?n 299 Mathieu R.D, Ghez A.M., Jensen E.L.N., Simon M. 2000, in: Protostars & Planets IV, eds. Mannings et al., p.703 Mermilliod J.-C. 1999, Webda: http://obswww.unige.ch/ webda/webda.html Mermilliod J.-C., Mayor M. 1999, AA 352, 479 Mermilliod J.-C., Duquennoy A., Mayor M. 1994, AA 283, 515 Mermilliod J.-C., Weis E.W., Duquennoy A., Mayor M. 1990, AA 235, 214 Moraux E., Bouvier J., Stau?er J.R. 2001, AA 367, 211 Motte F., Andr? P. 2001, AA 365, 440 e Myers P.C. 1998, ApJ 496, L109 Nadeau D., Murphy D.C., Doyon R., Rowlands N. 1994, PASP 106, 909 Patience J., Duch?ne G. 2001, in: The Formation of Binary e Stars, ASP Conf. Ser., Vol.200, eds Zinnecker & Mathieu, in press Patience J., Ghez A., Reid I., Weinberger A., Matthews K. 1998, AJ 115, 1972 Petr M., Coud? du Foresto V., Beckwith S., Richichi A., Mce Caughrean M. 1998, ApJ 500, 825 Preibisch T., Balega Y., Hofmann K.-H., Weigelt G., Zinnecker H. 1999, NewA 4, 531 Prosser C.F., Stau?er J.R., Hartmann L.W., et al. 1994, ApJ 421, 517 Rigaut F., Salmon D., Arsenault R., et al. 1998, PASP 110, 152 Robichon N., Arenou F., Mermilliod J.-C., Turon C. 1999, AA 345, 471


Robin A., Haywood M., Cr?z? M., Ojha D.K., Bienaym? O. e e e 1996, AA 305, 125 Scally A., Clarke C., McCaughrean M.J., 1999, MNRAS 306, 253 Simon M., Close L.M., Beck T.L. 1999, AJ 117, 1375 Simon M., Ghez A., Leinert Ch. et al. 1995, ApJ 443, 625 Sterzik M.F., Durisen R.H. 1995, AA 304, L9 Sterzik M.F., Durisen R.H.1998, AA 339, 95 Sterzik M.F., Durisen R.H. 1999, in: Star Formation 1999, ed. T. Nakamoto, p.387 Tokovinin A. 1992, AA 256, 121 Vanderlinden H.L. 1933, Etude de l’amas de Praesepe, Duculot Editeur (Gembloux) Van Dessel A., Sinachopoulos D. 1993, AAS 100, 517 Whitworth A.P. 2001, in: The Formation of Binary Stars, ASP Conf. Ser., Vol.200, eds Zinnecker & Mathieu, in press Wichmann R., Krautter J., Schmitt J.H.M.M., et al. 1996, AA 312, 439 Wichmann R., Torres G., Melo C.H.F., et al. 2000, AA 359, 181 Williams J.P., Blitz L., McKee C.F. 2000, in: Protostars & Planets IV, eds. Mannings et al., p.97

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