A&A 468, 721-729 (2007)
DOI: 10.1051/0004-6361:20066671

The frequency of planets in multiple systems[*]

M. Bonavita1,2 - S. Desidera1


1 - INAF - Osservatorio Astronomico di Padova, Vicolo dell'Osservatorio 5, 35122 Padova, Italy
2 - Dipartimento di Astronomia, Università di Padova, Italy

Received 31 October 2006 / Accepted 5 March 2007

Abstract
Context. The frequency of planets in binaries is an important issue in the field of extrasolar planet studies, because of its relevance in estimating of the global planet population of our Galaxy and the clues it can give to our understanding of planet formation and evolution. However, only preliminary estimates are available in the literature.
Aims. We analyze and compare the frequency of planets in multiple systems to the frequency of planets orbiting single stars. We also try to highlight possible connections between the frequency of planets and the orbital parameters of the binaries (such as the periastron and mass ratio.)
Methods. A literature search was performed for binaries and multiple systems among the stars of the sample with uniform planet detectability defined by Fischer & Valenti (2005, ApJ, 622, 1102), and 202 of the 850 stars of the sample turned out to be binaries, allowing a statistical comparison of the frequency of planets in binaries and single stars and a study of the run of the planet frequency as a function of the binary separation.
Results. We found that the global frequency of planets in the binaries of the sample is not statistically different from that of planets in single stars. Even conservatively taking the probable incompleteness of binary detection in our sample into account, we estimate that the frequency of planets in binaries can be no more than a factor of three lower than that of planets in single stars. There is no significant dependence of planet frequency on the binary separation, except for a lower value of frequency for close binaries. However, this is probably not as low as required to explain the presence of planets in close binaries only as the result of modifications of the binary orbit after the planet formation.

Key words: stars: planetary systems - stars: binaries: general

   
1 Introduction

The increasing number of extra-solar planets discovered in binary or multiple stellar systems (Eggenberger et al. 2004; Raghavan et al. 2006; Desidera & Barbieri 2007) suggests that planets can form and survive in a variety of stellar environments. Determining the frequency of planets in binaries is an important issue in the field of extrasolar planets studies, because of its relevance in estimating the global planet population of our Galaxy (more than half of the solar type stars are in binary or multiple systems as reported in Duquennoy & Mayor 1991) and because of the clues it can give to our understanding of planet formation and evolution. The study of the properties of planets in binaries, as well as any difference to those of the planets orbiting single stars, could shed light on the effects from the presence of the companions.

A recent study by Desidera & Barbieri (2007) shows that the mass distribution of short period planets in relatively tight binaries (separation $\le $150-200 AU) is significantly different from that of planets orbiting the components of wide binaries and single stars. There are also other possible peculiar features of planets in tight binaries compared to planets orbiting single stars, such as a lack of long-period planets and multiple planets, that need confirmation. The properties of exoplanets orbiting the components of wide binaries are instead compatible with those of planets orbiting single stars, except for a possible greater abundance of high-eccentricity planets.

This result implies that the formation and/or migration and/or dynamical evolution processes acting in the presence of a sufficiently close external perturber are modified with respect to single stars. Several scenarios can be devised to explain it, such as a different formation mechanism for planets in tight binaries (e.g. disk instability induced by dynamical perturbations, as proposed by Boss 2006), and enhanced migration and accumulation rate in the presence of a stellar companions (Kley 2000), and dynamical interactions after planet formation (Pfahl & Muterspaugh 2006).

However, to better understand the cause of these anomalies and the origin itself of the planets in very close binaries (a challenge for current planet formation models) a key piece of information is missing: the frequency of planets in binaries as a function of the binary separation and compared to that of planets orbiting single stars. Determining the planet frequency in binaries is made difficult by the biases against binaries in most of the ongoing planet search surveys and by the incompleteness of binary and planet detections in these samples.

A first step in this direction has been made by Eggenberger et al. (2006), performing an adaptive-optics search for companions around stars with and without planets and without previously known stellar companions from the Coralie survey. This guarantees a fairly homogeneous binary detectability in their sample. However, the small number of objects (and the lack of confirmation of the physical association in a few cases at the time of the presentation of their preliminary results) did not allow them to make clear inferences on the planet frequency and in particular on possible differences as a function of the binary separations.

A much wider sample (850 stars vs the 110 stars studied by Eggenberger et al. 2006) that might be used for a study of planet frequency is the "Uniform Detectability'' (hereafter UD) sample collected by Fischer & Valenti (2005) (hereafter FV05). This sample is complete for detecting planets with radial velocity (hereafter RV) semi-amplitude >30 m/s and period <4 yr. However, the binarity of stars in the UD sample has not been considered up to now.

Despite some incompleteness and biases concerning binarity, this sample can be considered valid to draw an independent measurement of the frequency of planets in binary stars, thanks to the completeness of planet detection and the large sample size. Thus, the binarity of the stars with uniform detectability was investigated in this work by searching some stellar catalogs listing stellar companions (Sect. 3). The result is a sub-sample of UD binaries, separated according to their different values of periastron and critical semimajor axis for dynamical stability of planetary orbits (see Holman & Wiegert 1999) (Sect. 3.2). In this way it has been possible to compare the values of the frequency of planets in the two sub-samples (single stars and binary stars) and to verify a possible dependence of the frequency on critical semimajor axis and periastron (Sect. 4). The biases against binaries in the original selection sample, the completeness of the binary detection for stars with and without planets and their impact on the results are discussed in Sect. 4.1. The results are discussed further in Sect. 5, and in Sect. 6 we summarize our conclusions and offer future perspectives.

   
2 The uniform detectability sample

The uniform Detectability sample has been built by considering that, despite the detectability of the planets' changes from star to the next and from a survey to the other because of the different time span of the observations and different levels of RV errors, we can consider it complete for companions with velocity amplitudes K>30 m/s and orbital periods shorter than 4 years. Then, beginning from the initial target list, which included 1330 stars observed by the Lick, Keck, and Anglo Australian Surveys, FV05 selected a subsample of 850 stars that satisfy these entries provided that at least 10 observations spanning four years were available. Stars that were added after a planet was discovered by other groups were not included in the sample. However, stars independently present in one of these surveys were considered even if a planet was detected first by another group. Only planets with K> 30 m/s and orbital periods shorter than 4-years were considered for the study of planet frequency. This corresponds to Saturn-mass planets for the shortest periods and Jupiter-mass planets for 4 year orbits.

   
2.1 Changes in the UD sample

During the analysis made for our work, we made some changes to the original UD sample, such as:

The modified UD sample that is the result of those changes was then searched for companions, in order to build a sample of UD binaries.

   
3 Searching for UD binaries

In order to identify known or claimed companions for the stars included in the UD sample, we checked available sources listing stellar companions. Some of the most important sources are listed below:

We also consider additional references for individual objects (see Table 8 and Appendix A).

   
3.1 Selection criteria

After this search, we excluded from our UD binary sample the stars with non confirmed companions and with companions listed in CCDM but with inconsistent proper motions (and without other indication of binarity found in literature), and considered those stars as singles. Stars with long-term RV and/or astrometric trends were included in the binary sample, on the basis of the dynamical evidence of a companion. The RV trends we included (from Nidever et al. 2002) cause an overall RMS of RV faster than 100 m/s that cannot be due to planetary companions. We also included stars with brown dwarf companions in the sample of binaries. At small separation, the existence of the brown dwarf desert (see Butler et al. 2006) guarantees little ambiguity in the classification of an object as a massive planet or a brown dwarf (a couple of individual cases are listed in Appendix A). At large separations, where brown dwarfs companions are probably more frequent (Gizis et al. 2001), this ambiguity should be taken into account but is again limited to a few individual cases, e.g. HD 206860, which has a T dwarf companion of mass $0.021 \pm 0.09~M_{\odot}$ according to Luhman et al. (2007), smaller than the mass limit for planetary companions adopted by Butler et al. (2006). The small number of brown dwarf companions makes this issue irrelevant for the global results.

   
3.2 The sub-sample of UD binaries

The properties of the UD binaries, selected from the modified UD sample, are listed in Table 8. The stars with both components included in the UD sample are listed twice, otherwise only the star under planet scrutiny is listed. If more than one companion is known, we report only the closer one, because of its stronger influence on planetary formation/stability. For hierarchical triple (or higher-order multiplicity) systems, for which the isolated star is included in the UD sample, we sum the mass of the closest pair to consider its effective dynamical influence. The minimum mass is listed for single-lined spectroscopic binaries.

For each object we report:

We chose $a_{\rm crit}$ as a reference value, because it is a physical quantity that represents, better than the semi-major axis or the projected separation, the dynamical effects of the presence of the companion first on the circumstellar region and then on planet formation and stability. This feature, in fact, includes both the orbital parameters and the mass ratio, and represents the maximum value of the semimajor axis for stable planetary orbits around the planet hosts. The value of $a_{\rm crit}$ is higher than the limit of the region in which the encounter velocities of planetesimal is small enough to allow the accretion of kilometer-sized planetesimals ( $a_{\rm cross}$, Thébault et al. 2006). The radius of tidal truncation of the circumstellar disk $a_{\rm tid}$ (Pfahl & Muterspaugh 2006; Pichardo et al. 2005) is intermediate between $a_{\rm crit}$ and $a_{\rm cross}$. Figure 1 shows the values of $a_{\rm crit}$ (solid line), $a_{\rm cross}$, and $a_{\rm tid}$, versus binary semimajor axis, for fixed values of eccentricity and masses (e=0.3, $M_{\rm com}=0.5~M_{\odot}$, and $M_{\rm obj}=1~M_{\odot}$).


  \begin{figure}
\par\resizebox{7.8cm}{!}{\includegraphics[height=6.5cm]{6671fig1.ps}}\end{figure} Figure 1: Values of $a_{\rm crit}$ (solid line) and $a_{\rm cross}$ (dashed line) and $a_{\rm tid}$ (dotted line), versus binary semimajor axis, for e=0.31, $M_{\rm com}=0.5~M_{\odot}$, and $M_{\rm obj}=1~M_{\odot}$.
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4 Results and selection effects

The result of this search for companions of the UD stars is a sub-sample of 202 objects, 15 of those having planets, so the global frequency of planets in the UD binary sample is 7.4%. The frequency of planets in the UD single stars sub-sample is 5.3% (see Table 1). The two frequencies are compatible within their errors[*], and the slightly higher value of the global frequency in the binary sub-sample is probably due to some incompleteness in the sample, which is discussed in Sect. 4.1.

The rather large sample size allows us to divide stars in some sub-samples according to different values of critical semimajor axis for dynamical stability of planets (hereafter $a_{\rm crit}$; see Eq. (1)). All the stars with RV and/or astrometric trend and without direct imaging identification or full orbit characterization (37 objects) were included in the closest bin, as it is likely that the companion responsible for the trend has a small separation.

We also binned the UD binary sample according with the periastron because this allowed us to make a direct comparison with theoretical expectations, such as those of Pfahl & Muterspaugh (2006). The resulting values of the frequency are listed in Tables 1 and 2, together with the characteristics of each sample. In Table 1 we also show the values of frequency for the complete UD binary sample and for the UD single sub-sample. Figures 2-3 show $a_{\rm crit}$ and periastron vs mass ratios for the binaries of the sample with and without planets.

These figures suggest that the binary components hosting planets usually have low-mass secondaries, for both low and high separation values. This item is confirmed by Fig. 4 which shows the histogram of the mass-ratio values for the two populations. In order to better investigate the dependence of the planet frequency on the binary mass-ratio, we performed a Kolmogorov Smirnov Test (hereafter KST) on the two populations. The resulting value for the KST probability is $\sim$11% for the entire sample (excluding objects with trends, for which the value of the secondary mass is unknown) and $\sim$10% for the stars with $a_{\rm crit}> 20$ AU. The difference between the distributions is not significant enough to allow us to confirm or reject the hypothesis that the presence of planets is favored in binaries with a low value of the mass ratio. This feature, as discussed in Sect. 4.1.2, could also be due to how the stars hosting planets are preferentially searched for low-mass companions, and this is probably one of the causes of their lower observed values of the mass ratio. On the other hand, the lack of planet detections up to now in the ongoing RV planet search using SARG at TNG (Desidera et al. 2006), which targets only binaries with similar components and with a typical separation between 100 to 400 AU, suggests that the mass ratio might be an important parameter for the occurrence of planets. Therefore, the possible role of the mass ratio on the frequency of planets remains an open point that requires further investigations.


  \begin{figure}
\par\resizebox{8cm}{!}{\includegraphics[height=6.5cm]{6671fig2.ps}}\end{figure} Figure 2: Critical semimajor axis (from Holman & Wiegert 1999) vs. mass-ratio for the binaries with planets (filled circles) and without planets (open circles) in the UD sample.
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  \begin{figure}
\par\resizebox{7.8cm}{!}{\includegraphics[height=6.5cm]{6671fig3.ps}}\end{figure} Figure 3: Periastron vs. mass-ratio for the binaries with planets (filled circles) and without planets (open circles) in the UD sample.
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  \begin{figure}
\par\subfigure[]{\includegraphics[height=5.5cm]{6671fg4a.ps} }
\par\subfigure[]{\includegraphics[height=5.5cm]{6671fg4b.ps} }
\end{figure} Figure 4: Distribution of mass-ratio values for star with (solid line) and without (dashed line) planets. Panel  a) shows the histogram and panel  b) the cumulative distribution.
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Table 1: Frequency of planets in binaries with different values of $a_{\rm crit}$.

Table 2: Frequency of planets in binaries with different values of periastron.

   
4.1 Completeness and selection effects

These results suggest that the planet frequency in binaries and single stars is similar. However, selection effects concerning binaries in the original definitions of the Lick, Keck, and AAT samples and possible incompleteness of binary detection might alter the results; we discuss them here in order to better estimate the frequency of planets in binaries.

   
4.1.1 Estimate of the missing binaries

The first issue to consider is the completeness of the binary census in the sample. We can derive an upper limit to the incompleteness by assuming that the stars in the UD sample have the same binary frequency as in Duquennoy & Mayor (1991) (57%). The number of missing binaries in the sample would then be $\sim$296[*].

To derive a lower limit to the frequency of planets in binaries, we assume that all the "missing" binaries are without planets. We then obtain $f_{\rm bin}=3.09 \pm 0.94 \%$ and $f_{\sin}=9.31 \pm 0.69 \%$; i.e. the frequency of planets in binaries cannot be less than one third of that of planets orbiting single stars. We stress that this is a very conservative lower limit on the frequency of planets in binaries (an upper limit on the incompleteness of the binary detection in the sample), because the UD sample has selection biases against binarity. In fact the input target lists exclude spectroscopic binaries and binaries with separations less than 2 arcsec known at the time of the target selection (see Wright et al. 2004; Marcy et al. 2005; Jones et al. 2002). Therefore we expect that the absolute binary frequency in the UD sample is significantly lower than the unbiased one derived by Duquennoy & Mayor (1991); the distribution of the orbital parameters and mass ratio of the binaries in the UD sample should also be different with respect to unbiased samples.

To take this selection bias in account, we did a Monte Carlo simulation making an estimate of the fraction of binaries with $\rho < 2''$ expected on the basis of the period and mass-ratio distribution assumed by Duquennoy & Mayor (1991)[*]. In this way we found that $\sim$45.7% of the binaries predicted by Duquennoy & Mayor (1991) have $\rho < 2''$for the distance distribution of the stars of the UD sample, so we expect that a significant fraction of the "missing'' binaries are given by stars excluded at the time of the target selection because of their small separation.

Combining these features, we find that the total number of binaries expected in the UD sample with a separation >2 arcsec is 221. Our census yields 138 binaries (120 without considering wide companions orbiting close pairs with a separation <2 arcsec) so there should be 83 missing binaries (95 without considering wide companions in triple systems) with separations >2 arcsec.

These numbers are expected to hold if there are no biases besides the exclusion of binaries with separations smaller than 2 arcsec in the UD sample. However, it is possible that the stars that were added later to the samples for specific reasons (e.g. high metallicity, Butler et al. 2000; Tinney et al. 2003) have different selection criteria concerning binarity. In some individual cases, the inclusion in the input target lists of certain types of systems is favored: a few binary systems with similar components were probably included in the sample after dedicated studies of chemical abundances differences between the components (Martín et al. 2002; Gratton et al. 2001). Unfortunately, we do not have enough information about the details of the building of the sample. We do expect that this only plays a minor role in the global binary statistics.

   
4.1.2 Completeness of the binarity of planet hosts vs. non planet hosts

The role of completeness in binary detection would be minor for our purposes if the completeness itself were independent of the occurrence of planets. Unfortunately, this is not the case. Planet hosts are systematically searched for companions after planet discoveries. Therefore, the completeness of the binarity of planet hosts is certainly greater than that of stars without planets. This bias could cause a spurious increase in planet frequency in binaries and should be carefully addressed. We proceeded as follows. We considered the binarity of planet hosts in the UD sample (including those with K<30 m/s and/or P>4 yr; 21 objects overall). If the binarity was found on the basis of dedicated studies after planet discoveries, the star was classified as single; if instead the binarity was known independently of the planet discovery (e.g. inclusion in WDS, CCDM, Hipparcos, detection of astrometric and RV trends, etc.), the star was kept as a binary. This results in a change in binary status for 7 stars (4 with UD planets and 3 with non-UD planets). In this way we obtained a binary sample that is less complete than the original one but without biases favoring the binarity of planet hosts. The revised frequency of planets in binaries then becomes 11/195=0.056 and the corresponding for single stars 38/654=0.058 (the results for all the $a_{\rm crit}$ bins are reported in Table 3). The difference with respect to the full sample indicates that indeed the dedicated searches for companions around planet hosts somewhat alters the results but the frequencies of planets in binaries and in single stars remain similar.

Table 3: Frequency of planets in binaries with different values of $a_{\rm crit}$, without considering as a binary the planet-host whose companions were discovered thanks to dedicated follow up after planet detection.

4.1.3 Dependence on separation

The completeness of binarity in this sample is probably a function of the separation. At small separations, the inclusion of stars with RV and an astrometric trend probably allows a fairly high completeness level. In fact, most of the binaries recently discovered by means of deep adaptive optics imaging (e.g. HD 13445; HD 161797, HD 190406, HD 196885; see App. A for references) would have been included as binaries in this study thanks to their dynamical signatures, even without the direct imaging identification. Pairs with a small magnitude difference in separation between 0.2 to 10 arcsec should have been detected by Hipparcos (Quist & Lindegren 2000). Wide binaries ( $\rho> 5 {-} 10$ arcsec) are more easily discovered and then included in CCDM and WDS even for larger magnitude differences. Intermediate values of separation (e.g. 1 to 5 arcsec) are probably the most incomplete ones, as the detection of a low-mass companion requires dedicated high-resolution imaging that is not available for all the stars, and the companions are not expected to produce detectable RV or astrometric signatures.

4.1.4 Effects of incomplete information on orbit and masses of the companions

The determination of $a_{\rm crit}$ requires the availability of the full binary orbit and an estimate of the mass the companion. All these quantities are unknown for the 37 stars with astrometric and/or RV trends . In any case, we included these objects in the binary statistic because of the significance high level of the trends as resulting from the original works by Makarov & Kaplan (2005) and Nidever et al. (2002). Furthermore, several objects present both the astrometric and RV signatures, which further confirms their nature as multiple objects. From the timescales of the detected orbital motion, we can reasonably infer a period short enough to allow the inclusion of these stars in our closest bin ( $a_{\rm crit}< 20$ AU). However, any more detail on the separation distribution of these companions cannot be determined, which representing a major limitation for studying of the details run of planet frequency vs. $a_{\rm crit}$ at small separations.

For the stars where only the projected separation is available, we have considered an approximate values for the semimajor axis and eccentricity values from the adopted statistical relations. Even if for individual objects this approximation could be quite different from the real value, we expect that statistically it would give a realistic representation of the true semimajor axis and periastron distributions.

   
4.2 The volume-limited sample

As a further investigation of the role of the biases mentioned in Sect. 4.1 in our results, we have selected a volume-limited sample (hereafter VLUD), including the stars within a distance of 18 pc from the Sun, analogous with FV05. The selection effects considered in Sect. 4.1 are expected to be smaller for the VLUD sample. In fact, the census of companions around stars in this sample is expected to be more complete than that of the global sample because the closest stars were in general more carefully searched for stellar companions, and at close distance the 2 arcsec limit corresponds to a smaller physical separation (36 AU at 18 pc). The small distance also favors overlap between different detection techniques. Indeed, only 1 star with astrometric trend and without direct imaging identification is included in the VLUD sample.

The volume-limited UD sample includes 129 stars, of which 44 are known binaries. The fraction of stars with planets in the VLUD sub-sample is 9.1% for binaries and 9.4% for single stars. We selected some bins in $a_{\rm crit}$ and periastron also for the VLUD sample but, because of the small number of stars included in this sample, we considered only 2 ranges of values. Tables 4 and 5 show the frequency values obtained for the VLUD sub-samples. Statistical error bars are larger for the VLUD sample because of the small number of objects but the frequency of planets in single stars and in binaries is again similar.

Table 4: Frequency of planets in binaries with different values of $a_{\rm crit}$ for the volume-limited sample.

Table 5: Frequency of planets in binaries with different values of periastron for the volume limited sample.

A possibly interesting difference with respect to the full UD sample is that the frequency of planets in tight binaries ( $a_{\rm crit}< 20$ AU) is not lower than in wide binaries and single stars. This might be explained looking at Fig. 5. The panels show the distribution of $a_{\rm crit}$ for the lowest bin in $a_{\rm crit}$ for the complete UD sample (upper panel) and for the VLUD sample (lower panel). In both panels, the first column on the left contains the stars included as binaries only because of the long-term RV or astrometric trends (i.e. mass and separation of the companions not known). From these histograms we can easily see that the percentage of the stars without definite orbital characteristics (thus included only on the basis of dynamical signatures) is much larger in the complete UD sample (37/89, $\sim$42%) with respect to the VLUD sample in which just one object, HD 120780, is included only thanks to its astrometric trend. At the same time, for the systems for which $a_{\rm crit}$ can be derived, the distribution of the $a_{\rm crit}$ values for the VLUD sample is centered on the second bin ( $2.5 < a_{\rm crit} < 5.0$ AU), while in the complete sample there is a relatively large number of binaries (at least 20, excluding those with only RV or astrometric trends) for which $a_{\rm crit}$ is smaller than $\sim$2.5 AU, the separation limit corresponding to P=4 yr for solar-type systems. Therefore a lower frequency for planets in these systems is expected, as only a part of the separation range considered here can host planets on stable orbits.


  \begin{figure}
\par\subfigure[]{\includegraphics[height=5.5cm]{6671fg5a.ps} }
\par\subfigure[]{\includegraphics[height=5.5cm]{6671fg5b.ps} }
\end{figure} Figure 5: Distribution of $a_{\rm crit}< 20$ AU for the complete UD binary sample a) and for the VLUD sample b). In both panels, the light grey column contains the stars with-long term RV or astrometric trends, arbitrarily placed at $a_{\rm crit}<0$ for display purposes. The dark grey column represents the contribute of spectroscopic binaries.
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5 Discussion

5.1 Global estimate of frequency of planets in binary stars

Using a sample made of binaries with uniform planet detectability, we compared the frequency of planets in binaries to that of planets orbiting single stars. Looking at the whole binary sample we can conclude that the frequency of planets in binaries is not statistically different from planets orbiting single stars. With very conservative assumptions on the incompleteness of binary detection, we find that the frequency of planets in the binaries of the sample cannot be lower by more than a factor of three compared to planets orbiting single stars. When considering samples that are less affected by selection biases such as the VLUD sample, or excluding only the binaries detected thanks to dedicated follow-up after planet discoveries, that cause a spurious increase of the binary fraction of planet hosts, we found that the two frequencies are indeed very similar. This is qualitatively consistent with the preliminary results of Eggenberger et al. (2006).

An important point to consider is that this conclusion applies to the kind of binaries that are included in UD sample, i.e. with a separation distribution biased against close binaries, and cannot be directly applied to samples with unbiased binary distribution. Furthermore, it applies to the kind of planets fulfilling the requirements for inclusion in the UD sample, i.e. P<4 yr and K>30 m/s. It is possible that e.g. the effects of binarity on planets in wider orbits are stronger.

   
5.2 Dependence on the binary separation

The size of our sample allowed us to divide it into some sub-groups according to the value of the critical semimajor axis for the dynamical stability. In this way we can argue that there is no significant dependence of the frequency on $a_{\rm crit}$ (and on the periastron) except for companions with $a_{\rm crit}$ less than 20 AU (that corresponds to a separation <50-100 AU, depending on the mass ratio of the components). This result makes stronger the conclusion by Desidera & Barbieri (2007), who reported that the presence of distant companions (separation >300-500 AU) does not significantly affect the process of planet formation, as the mass and period distribution of planets in such wide binaries are similar to those of planets orbiting single stars (Desidera & Barbieri 2007), and the frequency of planets is also similar (this work).

What happens at small separations is more crucial to understanding the role of companions in planet formation. Desidera & Barbieri (2007) found that the properties of planets in close binaries, in particular the mass distribution, are different from those orbiting single stars and components of wide binaries[*]. We showed in this study indication for a lower frequency of planets in tight binaries.

The frequency of planets in close binaries can be used to further investigate how these planets formed and the origin of their anomalous properties. Indeed, Pfahl & Muterspaugh (2006) shows that knowing the value of the frequency of planets in close binaries[*] should allow two alternative formation scenarios to be distinguished. A low frequency (about 0.1% but with an uncertainty of about one order of magnitude, so we can consider 1% as a limit-value) would be compatible with dynamical interactions that cause the formation of the tight binary after planet formation.

Table 6: Probability of observing 2 binaries with planets in a sample of 89 (resp. 21) binaries in the UD (resp. VLUD) sample with $a_{\rm crit}< 20$ AU, for different planet frequencies.

Table 7: Probability of observing 2 binaries with planets in a sample of 81 (resp. 19) binaries in the UD (resp. VLUD) sample with periastron <50 AU, for different planet frequencies.

We tested the probability of obtaining the observed number of close binaries with planets in the UD and VLUD samples for different frequencies of planets using the binomial distribution. This leads to being able to confidently exclude (99%, see Tables 6 and 7) the preferred value in Pfahl & Muterspaugh (2006). The observed frequency is marginally compatible only with the upper limit on planet frequency by Pfahl & Muterspaugh (2006) ( $f \sim 1\%$) for the UD sample, and hardly compatible for the VLUD sample. The nominal probabilities derived here should be taken with some caution because of the possible incompleteness in binary detection at small separations (anyway estimated to be small, in particular for the VLUD sample, see above) and because the separation distribution is different than the unbiased samples. Nevertheless, our relatively high frequency of planets in close binaries suggests that the dynamical interaction after planet formation is not the unique channel for creating this kind of systems. Instead, we can infer that giant planets might form in binaries that have a small separation at the time of planet formation, possibly in a different way from planets around single stars (and around components of wide binaries).

The run of planet frequency at small separations might shed more light on the formation mechanism(s) of planets in binaries. Desidera & Barbieri (2007) noted a possible paucity of planets in binaries with a critical semimajor axis for dynamical stability in the range 10-30 AU; only one planet was found in this range, while there are 5 planets with $a_{\rm crit}$ less than 10 AU and 4 planets with $30 < a_{\rm crit} < 50$ AU. A bimodal distribution of planet frequency, with a secondary maximum at $a_{\rm crit} \sim 3{-}5$ AU, is suggested by these data, and it would explain the different characteristics of planets in tight binaries as the result of a different formation mechanism. However, our work is not able to confirm or reject the reality of such a feature, as only 1 star in the UD sample has $10 <a_{\rm crit} < 20$ AU and 11 have $20 < a_{\rm crit} < 30$ AU (none of them with planets), making the lack of planet detections insignificant. Furthermore, the closest bin ( $a_{\rm crit}< 20$ AU or periastron <50 AU) includes several stars (37 out of 89) for which a direct detection of the companion is missing and which are included only on the basis of the astrometric and/or RV trends. Without a determination of the physical parameters of these companions, the study of the run of planet frequency at small separations is not possible.

   
6 Conclusions

After a detailed search for binarity for all stars in the UD sample collected by Fischer & Valenti (2005), we compared the frequency of planets in binaries and single stars. It turns out that the two frequencies of planets are fairly similar. Even taking possible incompleteness in the binary detection into account in a very conservative way, the frequency of planets in the binaries of the sample cannot be more than a factor of three lower than that of planets orbiting single stars.

For moderately wide binaries, the frequency of planets is independent on separation. Considering the similar mass and period distributions of planets orbiting single stars and components of wide binaries, we then concluded that a wide companion plays a marginal role in the formation and evolution of giant planets.

On the other hand, we found a lower frequency of planets in close binaries than in single stars and components of wide binaries. However, this is probably not as low as required to explain the occurrence of planets in close binaries only as the result of modifications in the binary orbit after planet formation. This, together with the differences in the properties of planets in tight binaries (Desidera & Barbieri 2007), suggests that planets do form in tight binaries in spite of the unfavorable conditions, possibly in a different way than for planets around single stars. However, crucial issues still need clarification. In fact, it is not yet clear if the run of the planet frequency when moving to smaller separations is characterized by a continuous decrease, by a sharp cut off at which the differences on planet frequency characteristics suddenly onset, or by a bimodal distribution, with a minimum between $10 < a_{\rm crit} < 30$ AU, a relative maximum at $a_{\rm crit} \sim 3{-}5$ AU, a further decrease to zero at extremely small separations, as the zone for dynamical stability of planets vanishes.

These open points might be clarified by a detailed characterization of the binaries in current samples of RV surveys (completeness of binary detection and, when possible, full determination of the orbital elements) and by the completion of dedicated surveys searching for planets in binaries (Eggenberger et al. 2006; Desidera et al. 2006; Konacki 2005).

Acknowledgements
This research has made use of the SIMBAD database, operated at the CDS, Strasbourg, France, of the Washington Double Star Catalog maintained at the US Naval Observatory, and of data products from the Two Micron All Sky Survey. We warmly thank D. Fischer for kindly providing information on the UD sample and S. Lepine for providing the complete tables of his work before publication. We thank the anonymous referee for comments that allowed us to improve the content and the presentation of the paper. We thank R. Gratton for his comments and suggestions. This work was funded by COFIN 2004 "From stars to planets: accretion, disk evolution and planet formation'' by the Ministero Univ. e Ricerca Scientifica Italy and by PRIN 2006 "From disk to planetary systems: understanding the origin and demographics of solar and extrasolar planetary systems'' by INAF.

References

 

  
Online Material

Table 8: Properties of binaries found in the UD sample: projected separation (arcsec), eccentricity and semimajor axis (when available), masses of the object and the companion, and critical semimajor axis for dynamical stability of planets (Holman & Wiegert 1999). For systems for which only the projected separation was available (empty spaces in eccentricity column) the semimajor axis was derived from the projected separation using the relation a(AU) = 1.31$\rho $(arcsec)d(pc) (see Fischer et al. 2002; Duquennoy & Mayor 1991). The asterisk in the last column marks systems discussed individually in Appendix A. The mass flag indicates the source for the companion mass: a: $M_{\rm comp}$ from VF06; b: $M_{\rm comp}$ from Delfosse et al. (2000); Reid & Gizis (1997); c: $M_{\rm comp}$ from individual papers (see Reference below).

   
Appendix A: Comments on individual objects

   
A.1 List of included binaries

   
A.2 Unconfirmed binaries



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