The Binary Fraction in Different Star Forming Regions

Observations of different star forming regions have been performed with the adaptative optics system (PUEO) at CHFT in order to detect binaries around low-mass stars ( $M<1.5M_\odot$ ). Companion star fraction are determined in the Pleiades and in a very young cluster, IC 348. Preliminary estimations are also presented for Præsepe and $\alpha$ Per. All clusters show overall fractions and period distributions similar to the expectations from main sequence figures. We argue that the difference between these star forming regions and other young associations, like Taurus and Chameleon, are probably not due to time evolution, but that the formation initial conditions may have an impact on the final binary fraction, with the loosest associations forming more wide binaries (separations $\gt\sim 10$ AU).

Introduction

More recently, several studies have tackled the question of the number of binaries in young pre-main sequence (PMS) stars. The variety of the findings shows that the formation of binaries is probably not as simple and universal as one might believe. For example, while the Orion Trapezium shows the same binary fraction as the MS population (Prosser et al. 1994, Petr et al. 1998), binaries are much more common in Taurus, where almost all stars are in multiple systems, if the period distribution is the same as on the MS (e.g., Leinert et al. 1993).

According to some authors, the difference between the PMS and MS populations is due to evolutionary effects (e.g., binaries would be disrupted in gravitational encounters). In this picture, the Trapezium would be an exception with its unusually low binary fraction. Another possibility could be a tight link between initial physical conditions and binary population (either the overall fraction or the period distribution).

To get insight into these differences, we started a long-term project aiming at the determination of the numbers of binaries in different star forming regions, with different stellar densities and at different evolutionary stages. In order to get meaningful results, we need:

All these constraints have led us to the use of CFHT, with its large diameter and efficient adaptative optics system. The first run on this programme (September 96, see Sect.2) was performed with the MONtreal Infrared CAmera, and the last two (December 97 and January 98, Sect.3 and 4) with KIR. Implications and future research are presented in Sect.5.

The Pleiades Survey

The Pleiades cluster is a well-known zero-age main sequence (ZAMS) cluster, with an age of about 120 Myr. It is therefore well suited to investigate the gap between very young PMS stars and the much older MS population. Also, it is relatively nearby (130 pc), allowing the detection of binaries with projected separations as close as 10-12 AU, sampling the peak of the separation distribution (30 AU for a 1 $M_\odot$ system mass).

We observed 144 G- and K-type members in K. All systems which turned out to be binaries were also observed in J and H. A total of 22 binaries and 3 triple systems were found, with separations between 0.08'' and 7'' (the largest separation is dictated by the field-of-view of the detector). To eliminate projected background companions, we used a J-(J-K) diagram; 5 out of the 7 companions with $\Delta K \gt 4$ mag are not real companions.

Figure 3 in Bouvier et al. (1997) shows the detection limit as calculated from 3 $\sigma$ r.m.s. noise in the wings of the PSF. Although we can find very faint companions at large separations (down to $\Delta K \sim 6.5$ mag), it is obvious that we have missed companions in the central 0.5'' from the stars. In order to correct for this bias, we make two assumptions:

Then, the binaries were binned into intervals of separation where the detectability of companions is roughly constant. The maximum detectable flux ratio is converted into a minimum mass ratio q_min (with the mass-luminosity relation and assuming a mean primary mass of 0.8 $M_\odot$ , the median mass of our binary sample). Finally, the number of missed companions is estimated by integrating the mass ratio distribution from 0.1 to the estimated q_min. With this correction, we estimate another 13 binaries leading to a total of 41 companions and a companion star fraction of $28\pm6$ % (number of companions per primary, which could be greater than 100% if many systems were triples).

We compare the binary fraction observed for the Pleiades with the fraction expected from the field star MS distribution. The number of MS companions lying between 14 and 1150 AU is estimated by integrating the period distribution from Duquennoy & Mayor (1991). Here again, there are two (less critical) assumptions: our median value of the total system mass (1.3 $M_\odot$ ) is typical for the whole sample, and projected and real separations are linked by a statistical relation assuming random inclinations ( $<\log a\gt=<\log \rho\gt+0.1$ , see Duquennoy & Mayor). In this range of separation, the MS companion star fraction is $27\pm3$ %, so that there is no excess in the Pleiades binarity. From Bouvier et al. Figure 4 , we also see that the binary fraction is not only similar to the MS for visual binaries, but also for spectroscopic binaries (Mermilliod et al. 1992). Actually, the whole Pleiades period distribution is in good agreement with that of the main sequence.

IC 348

The cluster is about 300 pc away, so that we are only able to resolve companions with projected separations larger than 30 AU, which provides a large enough separation range to reach significant results. Herbigic (1998) estimated ages for about 100 low-mass stars, out of which we surveyed 69 for close companions (the other ones are too faint, below the $R\sim15.5$ limit for the adaptative optics guiding). Our estimation of the limiting magnitude of companions in each bin of separation (solid histogram in Figure 1) is estimated by adding faint stars with a similar PSF close to a primary and checking visually the images to see if we could find them. It roughly corresponds to a 5 $\sigma$ detection.

**Figure 1:** Completeness limit for the IC 348 survey. The two lower curves are 3 $\sigma$ noise level for two different primaries, while the solid histogram was derived experimentally (see text). Filled symbols are companions around known members, while empty circles denote background companion or primaries with unknown status (*i.e.,* probably non-members).
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In Figure 1, only three ``companions'' are found above $\Delta K =2.5$ , and they all have $\Delta K \gt 5$ . For the widest one, we have JH photometry, and this allows us to access that it is a background chance projection companion. With only H photometry for the other two (the fainter one was missed during the observations, and the other was too close to the chip edges), we can only assume that they are also background stars. We thus end with 11 companions for 69 targets.

Since mass-luminosity relations are much steeper for the MS than for very young PMS (we used the results from Baraffe et al. 1998 for 2 Myr), it is much easier to detect very low mass secondaries in IC 348 than in the Pleiades: a q=0.1 mass ratio corresponds to $\Delta K=3$ mag for 2 Myr-old stars and to 6 mag on the MS. Therefore, the completeness correction is much smaller in this case than it was in the first survey. Actually, we estimate that we have missed about half a companion, yielding to a total companion star fraction of $17\pm5$ % in the range 40-2820 AU.

The corresponding G-type MS binary fraction is $23\pm3$ %, indicating that there is no binary excess in IC 348. The slighty smaller binary fraction for IC 348 could be due to the fact that most of the stars with known spectral type have masses smaller than 0.8 $M_\odot$ and thus should be compared with K-M dwarfs, for which the binary fraction in this range of separation is about 18%. Also, to be sure that the contribution by chance projection binaries is small, we can cut the distribution at 2'', which leads to similar results. The fact that our conclusion does not depend on the cut-off is an indication that we have well corrected for background contamination.

**Figure 2:** Distribution of orbital periods in IC 348 binaries (solid histogram), compared to MS equivalent curves for G-type (dotted curve) and M-type dwarfs (dashed curve).
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Figure 2 shows the comparison of orbital period distributions in our sample, and in G-type and M-type MS dwarfs. The two probable background stars have been removed. As in the Pleiades, the distributions do not look different, but, on the whole, IC 348 seems closer to M dwarfs, in agreement with the masses derived in this cluster by Herbig (1998). It is also noteworthy that no very low mass companions have been found, although they would have been detectable. This could reveal a change in the IMF slope below 0.3-0.5 $M_\odot$ , since it appears that very low-mass stars are not numerous enough to form binaries with mass ratios $q<\sim0.25$ .

We have also used the large age spread in the cluster to search for a time evolution of the binary fraction. Although we are dealing with small sample sizes, we do not find any evolution of the binary fraction with primary's age. This suggests that the rate of binary formation has remain constant over the last 10 Myr. It also means that the ages derived by Herbig are not systematically biased by binarity (if it was the case, we would find a lot of young binaries, the age distributions of single and binaries, however, are similar).

Other Clusters

We also obtained a large set of data concerning the $\alpha$ Per cluster, which has been observed on the UH 88'' with the UH adaptative optics system. 33 systems were found multiples (with three triples) out of 160 targets. Again, the distance to this cluster is about 150 AU, and due to its age (only 50-70 Myr, i.e., slightly pre-main sequence), the completeness correction will be smaller than that of the Pleiades or Præsepe. This again suggests a binary fraction for $\alpha$ Per similar to that of the MS dwarfs.

Implications for Binary Formation

The binary fraction in different star forming regions

We can now address the two scenarios mentionned in Sect.1 to account for the binary excess observed in Taurus compared to other SFRs and clusters: a time evolution of the binary fraction, or the influence of the stellar formation physical conditions on the binary fraction.

Star forming regions with MS binary fraction are found at all ages (from 1 Myr up to the MS). This is evidence for the absence of a time evolution of the binary frequency; if any, evolution of the binary fraction should be completed within the first Myr.

**Figure 3:** Evolution of the binary fraction with age. The vertical axis is the ratio of the observed binary fraction to the value for MS in the same separation range. ``Southern SFR'' is an average over Ophiuchus, Chameleon and Lupus stars. Details of the calculation are presented in Duchêne (1998).
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Since time evolution cannot explain the difference between Taurus and Trapezium, for instance, we investigate the possibility of the dependency of binary fraction upon cluster density. We do not know the exact cluster densities (it depends on the cell size used for the estimation), but we have orders of magnitude estimates for this parameter: the stellar aggregates in Taurus have a few stars per pc³, as well as Chameleon. Ophiuchus is one or two orders of magnitude denser. IC 348 and NGC 2024 have about 1000 stars per pc³, and Trapezium is denser by a factor of barely 10. Figure 4 shows a possible trend for the loosest associations to have more binaries, although this is not highly significant due to large arror bars (related to small samples). Taurus has a 2.6 $\sigma$ excess, while the other associations have only poorly significant excesses. In the following, we assume that these effects are real, although we acknowledge that deeper studies are still required to improve their statistical significance.

**Figure 4:** Tentative evolution of the binary fraction with cluster density. The horizontal axis is more or less arbitrary, but the different star forming regions have been grouped by the order of magnitude of their density.
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The main assumption in this study is that the binary separation distribution is a universal feature. We are aware, however, of the possibility of a change in the orbital period distribution, as has recently been proposed by Brandner & Köhler (1998). Unfortunately, the young dense clusters already studied are more remote than the Taurus-like associations ( $\alpha$ Per, the Pleiades or Præsepe, which all lie at distances $\sim140$ pc, are older and we cannot exclude that the period distribution changes on a timesacle of a few 10⁷ Myr). The useful separation range is thus narrower, and it is impossible to estimate the binary fraction within similar ranges. In Taurus and Ophiuchus, however, where three orders of magnitude in separations have been sampled, the period distribution is very similar to that of the MS: if the overall binary fractions are identical in Taurus and MS populations, then there must be an important lack of close binaries in the former (with separations smaller than a few AU), but the spectroscopic binary fraction in Taurus is at least equivalent to the main sequence value (Mathieu 1994).

Different implications can be drawn from these results. First, since dense cluster members and field stars have the same binary fraction, it suggets that most of the solar neighbourhood field stars were formed in dense SFRs rather than in loose associations. Thus the star formation rate in loose associations must be much smaller than in dense protostellar clusters. Comparison of the binary fraction between clusters and at different ages indicate that the binary fraction is already set at 1 Myr, implying that binary disruption after 1 Myr is rare.

The most important result of this study is that all star forming regions with possible binary excess are loose associations: more wide binaries (separation $\gt\sim 10$ AU) form in Taurus-like regions than in clusters. Reipurth & Zinnecker (1993) have already proposed such a trend, although with lower confidence level and less star forming regions involved. It seems that the binary formation mechanism has different outputs, depending on the cluster density or another parameter governing the latter (i.e., gas temperature, physical process initiating fragmentation).

Future developments

To increase the confidence level of the ``density trend'', it would be very interesting to observe additional very loose star forming regions, to see whether they also show an important binary excess. Observations of clusters with large age spreads and larger populations than IC 348 are also needed to confirm that the binary fraction and the orbital period distribution do not change on a timescale of $\sim$ 10 Myr.

We also plan to extend this study to higher mass Herbig Ae/Be stars. A survey of isolated Herbig stars has been done to search for binaries (Corporon 1998), and it would be interesting to see whether or not the binary fraction in this population is smaller in clusters as it is for low-mass stars.

$\begin{references} % latex2html id marker 143 \reference{isa} Baraffe, Chabrier,... ..., 517 \reference{rz} Reipurth~\& Zinnecker, 1993, \aap, 278, 81\end{references}$