Mon.Not.R.Astron.Soc.000,1–19(2010) Printed9January2012 (MNLATEXstylefilev2.2) Testing the universality of star formation - I. Multiplicity in nearby star-forming regions Robert R. King1⋆, Richard J. Parker2,3, Jenny Patience1, and Simon P. Goodwin3 1Astrophysics Group, College of Engineering Mathematics and Physical Sciences, University of Exeter, Stocker Road, Exeter EX4 4QL, UK 2 2Institute of Astronomy, ETH Zu¨rich, Wolfgang-Pauli-Strasse 27, 8093 Zu¨rich, Switzerland 1 3Department of Physics and Astronomy, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield, S3 7RH, UK 0 2 n Accepted????.Received???? a J 5 ABSTRACT ] We have collated multiplicity data for five clusters (Taurus, Chamaeleon I, Ophi- R uchus, IC348, and the Orion Nebula Cluster). We have applied the same mass ratio S (flux ratios of ∆K ≤2.5) and primary mass cuts (∼0.1–3.0M ) to each cluster and ⊙ h. therefore have directly comparable binary statistics for all five clusters in the sepa- p ration range 62–620 au, and for Taurus, Chamaeleon I, and Ophiuchus in the range - 18–830 au. We find that the trend of decreasing binary fraction with cluster density o is solely due to the high binary fraction of Taurus, the other clusters show no obvious r t trend over a factor of nearly 20 in density. s With N-body simulations we attempt to find a set of initial conditions that are a [ able to reproduce the density, morphology and binary fractions of all five clusters. Only an initially clumpy (fractal) distribution with an initial total binary fraction 1 of 73 per cent (17 per cent in the range 62–620 au) is able to reproduce all of the v observations (albeit not very satisfactorily). Therefore, if star formation is universal 1 the initial conditions must be clumpy and with a high (but not 100 per cent) binary 1 fraction. This could suggest that most stars, including M-dwarfs, form in binaries. 3 1 Key words: stars: binaries – formation – kinematics – galaxy: open clusters and . 1 associations - methods: numerical 0 2 1 : v 1 INTRODUCTION duce very different binary populations then this suggests i thatstarformationwasdifferentbetweentheseregions(see X Star formation is one of the outstanding problems in astro- Duchˆene et al. 2004; Goodwin 2010). r physics.Howstarsformisextremelyinterestinginitself,but a also has huge implications for understanding galaxy forma- Indeed, differences between the binary populations of tion and evolution, and planet formation. different clusters have been observed. Most famously, the One of the major unsolved problems in star formation binaryfractionofTaurus(Leinertetal.1993)issignificantly is the universality of the process: is the difference between higherthanthebinaryfractionoftheOrionNebulaCluster small,localstarformingregionssuchasTaurus(∼102M⊙), (hereafterONC,Prosseretal.1994;Petretal.1998;Ko¨hler and massive starburst clusters like 30 Doradus (∼ 105M⊙) et al. 2006; Reipurth et al. 2007) and approximately twice merely one of the level of star formation, or is there some- thatseeninthefield(Duquennoy&Mayor1991;Fischer& thing fundamentally different between these two extremes? Marcy 1992; Raghavan et al. 2010). There is no evidence that the initial mass function (IMF) of stars varies systematically between different en- However,weknowthatdenseregionswillprocesstheir vironments (see e.g., Luhman et al. 2003; Bastian et al. primordialbinarypopulationsandwhatweseeatlatertimes 2010). Such a result is rather surprising and interesting, may not reflect the primordial population. In a dense envi- but it means that determinations of the IMF are unable ronment encounters are common and binaries will tend to to probe the universality, or otherwise, of star formation. be destroyed (Heggie 1975; Hills 1975). Kroupa (1995a,b) A more promising route might be to search for differences showed that it is possible to process a Taurus-like primor- betweenprimordialbinarypopulations–iftworegionspro- dialbinarypopulationintoanOrion-likeevolvedpopulation very quickly. However, Parker, Goodwin & Allison (2011) suggestthatevenwithdynamicalprocessingtheprimordial ⋆ E-mail:[email protected] binary populations of Taurus and the ONC were probably ©2010RAS 2 Robert R. King et al. different(seealsoKroupa&Petr-Gotzens2011;Marksetal. Table 1.Asummaryofthenumberofstarsanddensitiescalcu- 2011). latedforeachregion. The problem is that it is difficult to ‘reverse engineer’ the current binary population of a cluster to determine the Region #ofStellar StellarDensity(starspc−3) primordialpopulation(reversepopulationsynthesis,Kroupa Members r r<0.25pc r<0.10pc 1/2 1995b).Amajoraspectofthisproblemisthatitisdifficult to compare the observed binary populations of different re- ChamI 200 5.7±0.7 275±65 1190±530 gions due to differences in the separation range probed and Taurus 215 — 6.0±1.2 — Oph 295 236±27 610±180 1910±955 the sensitivity to lower-mass companions between different IC348 265 326±73 1115±140 3820±1110 surveys. ONC ∼1700 425±33 4700±290 22600±1200 In this paper we approach the problem of examining differences between primordial binary populations with a Note: ThedensityreportedhereforTaurusiscalculatedwithin two-fold approach. Firstly, we construct (in as much as is aradiusof1pcfromthecentreofL1495;thenumberofstellar possible) a uniform comparison of binary fractions in the membersfortheONCisextrapolatedfromthenumberof COUPsourceswithinthehalf-numberradius(r )defined same separation ranges for five different regions (Taurus, 1/2 usingtheHillenbrand(1997)survey;andthenumberofstellar Oph/L1688, Cham I, IC348, and the ONC). Secondly, we membersforTaurusisfortheNorthernfilamentonly. attempt to simulate their dynamical evolution and binary destructionasrealisticallyaspossiblewithbothsmoothand the most recent determinations of the stellar membership. clumpy initial conditions. With these data we form a rough estimate of the stellar This paper is organised as follows. In Section 2 we de- densities.Notethattoensureconsistencyweexcludebrown scribetheobservationsofbinaritythatwehaveusedinour dwarfs from the density calculation and focus on the more fivedifferentregions.InSection3weconstructasfairacom- easily identified stellar population. parisonaspossiblebetweentheregions.Wesummarisethese We measure the number of stars within the half- resultsanddiscussthestructureofeachclusterinSection4. number, 0.1 pc and 0.25 pc radii from a cluster ‘centre’ de- InSection5weintroduceourN-bodysimulationsandcom- terminedfromtheaverage(‘centreofmass’)positionsofall pare these with the observational results. In Section 6 we the stars. We then assume that the third dimension is the discuss our findings, finally concluding in Section 7. sameallowingusabasicestimateofthestellarvolumeden- sities in each region as shown in Table 1. The uncertainties onthedensitiesareestimatedbyaccountingforthePoisson 2 CLUSTER MEMBERSHIPS AND BINARITY errors on the stars within each volume and the uncertainty on the distance to each region. As we will see later in Sec- Wehavechosentocomparebinarysurveysofyoungstarsin tion 4.2, several of these regions are far from spherical and fivewell-studiedregions:theChamaeleonIcloud(Lafreni`ere lack a proper ‘centre’. However, we feel that these approxi- etal.2008),Taurus(Leinertetal.1993),L1688inOphuichus matedensitiesgiveabroadpictureoftherelativedensities. (Ratzka et al. 2005), IC348 (Duchˆene et al. 1999) and the OrionNebulaCluster(Reipurthetal.2007).Thefirstfourof thesesurveysallinvolvednear-IRobservations(3K-band,1 2.1 Chamaeleon I H-band)and soaremosteasily compared. Thefifthsurvey 2.1.1 Membership (oftheONC)wasselectedbecauseitisthemostcomprehen- sivesurveyofthisimportant,massivestar-formationregion. ToestimatethedensityoftheyoungstellarclusterChamI, These regions provide as broad a range in density as pos- we have used the compilation of known members presented sible within the confines of the Solar Neighbourhood which by Luhman (2008). This member list was constructed from allows us to probe down to separations of a few tens of au. the results of many past studies including surveys for Hα Aftersummarisingthemostimportantpaststudiesfor emission, X-ray emission, photometric variability and IR- each region, we identify the most comprehensive binary excessemission.TherehavealsobeenChamImembersiden- studies with which we will make a comparison between the tifiedusingopticalandnear-IRimaging,duetothemoder- different regions. For each region we report the multiplicity ateopticalextinction,andthesubsequentcolour-magnitude fraction (MF) and the corresponding companion star frac- diagrampositionofmembersrelativetothecontamination. tion (CSF) defined as The known members include brown dwarfs with spec- traltypesaslateasM9.5.Attheclusterageof∼2Myr(Luh- man 2004, 2007), the sub-stellar limit occurs at an approx- B+T +Q MF = (1) imate spectral type of M6. From the total of 237 known S+B+T +Q members of Cham I, we are left with 201 stellar members after removing those with spectral types later than M6 (as B+2T +3Q CSF = (2) reported by Luhman (2008)) S+B+T +Q At an age of 2Myr, a 0.1M star is expected to have ⊙ where S is the number of single stars, B, T and Q are anapparentmagnitudeofKS≃11atthedistanceofChamI. thenumbersofbinary,tripleandquadruplesystems,respec- Giventhe2MASS10-σdetectionlimit(KS ≃14.3),wewould tively.OurN-bodysimulationsdonotproducesystemswith expect 2MASS to have detected all stars through AV<30, morethantwocomponents,sointhiscasetheMFandCSF much larger than the estimated maximum extinction in are equal to the binary fraction. Cham I of AV =5–10. Additionally, from a very sensitive For each of the five star-forming regions we also report X-rayobservationofthenorthernclusterofChamI,Feigel- ©2010RAS,MNRAS000,1–19 Testing the universality of star formation 3 Table 2.Asummaryoftheseparationranges,contrastsandderivedmultiplicityfractionsfromeachbinarysurveyused. Region SeparationRange Contrast MultiplicityFraction Reference (arcsec) (au) Taurus 0.13–13. 18–1820 ∆K≤2.5 42±8% Leinertetal.(1993) Oph/L1688 0.13–6.4 17–830 ∆K≤2.5 31±6% Ratzkaetal.(2005) ChamI 0.10–6.0 16–960 ∆K≤3.1 27±5% Lafreni`ereetal.(2008) 4 IC348 0.10–8.0 32–2530 ∆H≤6.5 20±5% Duchˆeneetal.(1999) ONC 0.15–1.5 62–620 ∆Hα≤5.0 8.5±1.0% Reipurthetal.(2007) son&Lawson(2004)foundnoevidenceforpreviouslyunre- above the substellar limit in this ∼1–2Myr old cluster. Af- portedmemberssuggestingtheknownmembersinthatfield ter removing the brown dwarfs, we are left with a stellar arecompleteto0.1M .Wethereforeconsiderthemember- membership of 265 objects from the 288 known members. ⊙ ship list of Luhman (2008) to be essentially complete down to 0.1M . ⊙ 2.1.2 Stellar density 2.2.2 Stellar density TheChamIclustercomprisesanorthernandsoutherncom- Althoughsubclusteringisevidentonspatialscalesof∼0.1pc ponentwithnoobviousoverallcentre.Forthenortherncom- (Lada & Lada 1995), IC348 shows a relatively symmetric ponent (centre α = 167.47○, δ = −76.515○) we determined radial profile. From a cluster centre of 56.160○,+32.166○, we a half-number radius of 0.85○ or 2.37pc at a distance of have determined a half-number radius of 303′′, or ∼0.464pc 160pc(seeLuhman2008,fordiscussion)and0.59○or1.65pc at the cluster distance of 316±22pc (Luhman et al. 2003; forthesoutherncomponent(centre167.06○,-77.567○).This Strom et al. 1974), which gives a stellar density in excess gives half-number radius densities of ∼2 and ∼5 stars/pc3, of 300 stars/pc3- a determination which is well-matched by respectively. Within radii of 0.25pc and 0.10pc the densi- those of Lada & Lada (1995) and Herbig (1998). Within ties for the southern component are 275±65 stars/pc3 and radii of 0.25pc and 0.10pc, IC348 has stellar densities of 1190±530 stars/pc3 (with little difference for the northern 1115±138 stars/pc3 and 3819±1111 stars/pc3, respectively. component). 2.1.3 Stellar binarity Anumberofstudieshaveprobedthebinarityofthisyoung 2.2.3 Stellar binarity cluster (e.g., Reipurth & Zinnecker 1993; Ghez et al. 1997), In the first binary survey of IC348, Duchˆene et al. (1999) but here we make use of the Lafreni`ere et al. (2008) study reported the detection of 12 binary systems (and no higher which acquired adaptive optics imaging of more than 50% ordersystems)fromasampleof66targetssystemsusingthe of the known population. Lafreni`ere et al. (2008) found 30 surveyofHerbig(1998)todefineclustermembership.They binary systems and 6 tertiary systems in a sample of 126 were sensitive to binaries with separations down to 0.1′′, or Cham I members with separations in the range 0.1–6.0′′, ∼32au at a distance of 316pc, and their maximum separa- correspondingto16–960auatadistanceof160pc.Theyre- tionof8.0′′waschosentorestricttheconfusionbetweenreal portamultiplicityfractionof27±5%(CSF=32±6%)within 4 5 binarysystemsandbackgroundalignments.However,three this range, including only companions where the flux ratio apparent binaries were removed from the sample as they isabovetheir90%completenesslimits.Twoapparentcom- were identified as likely background stars due to their large panions were discounted due to a low probability of being separationsandmagnitudedifferencescomparedtotherest bound to the primary and follow-up spectroscopic obser- of the observed binary systems. vations which were inconsistent with the young age of the Duchˆene et al. (1999) then use the known mass ratio region (i.e., they were likely distant background stars). distribution of the solar neighbourhood from Duquennoy & Mayor (1991) to estimate the number of undetected binary systems. They apply this small correction to determine the 2.2 IC348 likelynumberoftotalbinariesinIC348andsoderiveatotal multiplicityfractionof19±5%(CSF=19±5%,sincenon>2 2.2.1 Membership systemswerefound)withinaseparationrangeof0.1–8.0′′,or To estimate the stellar density in IC348, we have used the 32–2530auatadistanceof316pc.Afteraccountingforstars results of Luhman et al. (2003) who used optical and near- rejected as non-members, but which appear in the more re- IRsurveys,alongwithspectroscopicfollow-up,toconstruct centLuhmanetal.(2003)compilation,wedeterminedthat a census which is complete well into the substellar regime. the Duchˆene et al. (1999) study detected 14 binaries from Forconsistency,wehaveconsideredonlythoseobjectswith 71 targets systems, giving a multiplicity fraction of 20±5% spectral types of M6 or earlier, corresponding to sources over a separation range of 32–2530au. ©2010RAS,MNRAS000,1–19 4 Robert R. King et al. 2.3 The ONC 2.4 Ophiuchus 2.3.1 Membership 2.4.1 Membership Although a very well-studied region, there is no published Due to the large and dispersed nature of the ρ Ophiuchi listofconfirmedstellarmembersdowntothesubstellarlimit complexwehavechosentofocusonthemaincloud,L1688. which covers more than the centre of this rich star cluster. A census of the known members of this core was presented Therefore, to estimate the stellar density of the ONC, we byWilkingetal.(2008)whichtheybelievetobe‘essentially have used the complementary membership lists of Hillen- complete’ for class II and III objects. This is supported by brand (1997) (hereafter H97) and the Chandra Orion Ul- theircomparisonoftheX-rayluminosityfunctionsofL1688 tradeep Project (COUP, Getman et al. 2005). The H97 ob- tothatoftheONCfromthedeepCOUPstudyofFeigelson servations cover a large area (∼0.5×0.5○), but do not probe etal.(2005).Forconsistencywiththeotherregionsstudied down to the substellar limit, while the COUP list is rela- here,wehaveusedtheWilkingetal.(2008)listofcandidate tively complete to below ∼0.1M , but covers only the cen- browndwarfstoremovethosefromthememberlist,leaving ⊙ tral ∼17′×17′. 295 known stellar members in L1688. 2.4.2 Stellar density WhilethestellardensityoftheOphiuchusassociationtaken 2.3.2 Stellar density as a whole is relatively low, the density of the L1688 The ONC shows a slightly north-south elongated struc- core is approximately an order of magnitude higher. The ture, but is centrally concentrated with a dense core. We L1688 core shows significant sub-clustering with no obvi- therefore used the H97 list to determine a half-number ra- ous overdensity at the centre. Wilking et al. (2008) sum- dius of 390′′ centred on 83.8185○, -5.3875○, corresponding marise the various distance estimates for the ρ Ophiuchus to ∼0.78pc at a distance of 414±7pc (Menten et al. 2007). cloud (120–145pc) and so, similarly, we adopt a distance From this we extrapolate that the ONC has a stellar pop- of 130pc to L1688. Using a cluster centre of 246.727○, ulation of ∼1700 stars and within the half-number radius −24.44○,wehavedeterminedahalf-numberradiusof0.234○, has a stellar density of 425±33 stars/pc3. This increases to or ∼0.5pc at the distance of L1688, which results in an 4700±290 stars/pc3 within 0.25pc of the cluster centre and mean density of 236±27 stars/pc3. Within radii of 0.25pc to 22,600±1200 stars/pc3 in the inner 0.1pc. and0.10pc,L1688hasstellardensitiesof611±183 stars/pc3 and 1910±955 stars/pc3, respectively. 2.4.3 Stellar binarity 2.3.3 Stellar binarity In a lunar occultation and direct imaging search for binary There have been several studies of the binarity of stars in stars, Simon et al. (1995) targeted 35 pre-main-sequence thisnearbymassivestar-formingregion.Prosseretal.(1994) starsinOphiuchus,butthesmallsamplesizefrustratedtheir reported an estimated binary fraction of ∼11% in the range attemptstocomparewithsurveysofTaurus.Morerecently, 0.1–1.0′′ (42–420au). Petr et al. (1998) then used high an- Ratzkaetal.(2005)presentedabinarysurveyof158young gular resolution near-IR imaging to probe ONC binaries stellar systems in the ρ Ophiuchus molecular clouds, cen- and reported a binary fraction of 5.9±4.0% in the separa- tred on the dark cloud L1688. They reported a multiplicity tion range 0.14–0.5′′(58–207au), but they were hampered fractionof29.1±4.3%withinaseparationrangeof0.13–6.4′′ by very low numbers (only four binaries were detected). (corresponding to 17–830au at 130pc) where their obser- Toprovidethemostcomprehensivesampleforcompar- vations were fully sensitive to flux ratios ≥0.1, but with a ison with other regions, we have chosen to use the more significant number of companions with higher flux ratios. recentandwider-fieldHSTsurveyofReipurthetal.(2007) However, if we consider only those systems which have which imaged over 1000 stars, of which 781 have a high beenidentifiedasmembersofChamIintherecentWilking membership probability. They found 78 multiple systems et al. (2008) census, then we are left with 106 systems, of withseparationsintherange0.1–1.5′′ (42–620au)andfrom which 32 are binaries and 3 tertiary systems. Ratzka et al. the density of stars they estimated that 9 of their observed (2005) also analysed the contribution of the background to binaries were a result of projection effects. Reipurth et al. theobservednumberofcompanionsanddeterminedthatfor (2007) report a background-corrected multiplicity fraction their sample there should be three unidentified non-bound of8.5%±1.0%(CSF=8.8%±1.1%)intherange0.15–1.5′′,or systems. Similarly, for our reduced sample, there should be 62–620au1 This includes companions with flux ratios of up two systems where the apparent companion is not bound, to ∆Hα∼6m. resultingin amultiplicityfractionof 31±6%(CSF=34±6%) within a separation range of 17–830au. 2.5 Taurus 1 Theseparationrangequotedhereisdifferenttothatgivenby 2.5.1 Membership Reipurthetal.(2007)asweusetheanewerdistancefromMenten et al. (2007), supported by Jeffries (2007) and Mayne & Naylor A census of the known stellar and substellar pre-main se- (2008). quencemembersoftheTaurus-Aurigaassociationwascom- ©2010RAS,MNRAS000,1–19 Testing the universality of star formation 5 piledbyKenyonetal.(2008)andupdatedbyLuhmanetal. 0 IC348 (H) (2009).Thecompletenessofthissamplewasinvestigatedby 4 Luhmanetal.(2009)whoreportedthattheregionscovered 0 by the XEST survey (Gu¨del et al. 2007, where complimen- Cha I (K) tary optical and IR surveys exist) are complete for class ce 4 n I and II stars and complete down to 0.02M⊙ for class II ere 0 brown dwarfs. Deep, wide-field, optical, near-IR (Bricen˜o e Diff 4 Oph (K) et al. 2002; Luhman 2004; Guieu et al. 2006) and Spitzer d u 0 imaging surveys (Luhman et al. 2010) of Taurus provide a gnit Taurus (K) high level of completeness into the substellar regime across Ma 4 theregion.Therefore,toprovideanessentiallycompletestel- 0 ONC (H alpha) lar membership list we have removed objects with spectral 4 typeslaterthanM6,correspondingtosourcesabovethesub- stellar limit in this ∼1–2Myr old cluster, leaving 292 stars. 1 10 100 1000 Separation (AU) Figure 1. The contrast of each multiple system found in the five surveys shown as a function of separation. The filled lines demarcate the completeness of each survey. The labels identify 2.5.2 Stellar density theclustersandthefilterusedintheobservations. Due to the dispersed nature of the young stars in the ∼1– 2Myr Taurus-Auriga association, it is not useful to define densitieswithinahalfnumberradiusorwithinradiiassmall 3 COMPARISON OF OBSERVED STELLAR as 0.25pc. We therefore report the average surface density BINARITY of∼0.4±0.1stars/pc2forthenorthernfilament(definedhere as 62○< α < 72○, 22○< δ < 31○) and the volume density of 3.1 Contrast sensitivities 6.0±1.2 stars/pc3 within a radius of 1pc from the centre of To enable a fair comparison of the various binary surveys the densest core (L1495, centre 64.6○,+28.40○) using a dis- we must determine the contrast ratio to which each survey tanceof140±14pc(Wichmannetal.1998;Ko¨hler&Leinert was sensitive. Table2 lists the maximum contrast ratio for 1998). each survey in the passband employed while Fig.1 shows how these vary with physical projected distance from the primary star. For simplicity, we aimed to use only surveys carried out in the K-band, but this was not possible for IC348andwouldhaveseverelyrestrictedthesampleforthe 2.5.3 Stellar binarity ONC,whichusedanH-bandandtheNICMOSF658Nfilter Although a number of authors have reported binary statis- respectively. For the surveys carried out in the K-band, a tics for young stars in Taurus (Ghez et al. 1993; Duchˆene common contrast cut of ∆K=2.5 was chosen. et al. 2004), in some cases probing down to below 1au (Si- TodetermineaconversionofthecontrastintheH and monetal.1992,1995),herewemakeuseofthebinarysurvey F658N filters to the K-band, we have used the theoretical ofTauruspresentedbyLeinertetal.(1993)whichsurveyed modelsofSiessetal.(2000).Byconsideringprimarystarsat over100stellarmembers.WedonotusethesurveyofK¨ohler 1Myr with masses in the range 0.1–3.0M and mass ratios ⊙ & Leinert (1998) as the weak-lined T Tauri stars identified of 0.1–1, we were able to predict the range of magnitude thoughtheirX-rayemissionaremorewidespreadacrossthe differences expected. Figure2 shows the relation between regionthanthemajorityoftheconfirmedTaurusmembers, modelmagnitudedifferencesintheH andK-bandsforthis suggesting that they may be a separate population. That sample of possible systems. This clear linear relation allows said, Ko¨hler & Leinert (1998) find no significant difference us to convert our chosen common K-band contrast limit to in binarity between the weak-lined and classical T Tauri an H-band contrast limit. stars in the two samples. Leinert et al. (1993) reported a For the F658N filter, the situation is complicated by multiplicity fraction of 42±6% for their observations which the lack of reported magnitudes in that filter for the theo- weresensitivetosystemswithafluxratioofupto∆K=2.5 retical models. However, comparisons with the IPHAS Hα, overaseparationrangeof0.13–13.0′′,correspondingto18– r′ and Cousins R-band indicate that there is a near linear 1820au. The contribution of the background was examined relation between magnitudes in these bands. We therefore andtwoapparentcompanionswerediscountedastheirlarge compare the magnitude differences in the R and K bands separationsandcoloursidentifiedthemasbackgroundstars. to determine the appropriate contrast cut for the Reipurth Nootherprojectedcompanionswereexpectedintheirsam- etal.(2007)surveyoftheONC.Figure3showstherelation ple. betweenmodelmagnitudedifferencesintheRandK-bands If we consider only the targets within the area of the fortheprimarymassesandmassratiosdescribedabove.Al- northernfilament(asdescribedabove),Leinertetal.(1993) thoughthestructureobserveddoesnotprovidesuchaclear find 27 binary, 2 triple and 1 quadruple system from a to- correlationasfortheHandK-bands,our∆Klimitof2.5al- tal of 72 surveyed systems, giving a multiplicity fraction lowsmostofthisstructuretobeignoredandgivesacontrast of 42±8% (CSF=47±8%) within a separation range of 18– ofF658N≃5.WealsonotethatthemajorityoftheReipurth 1820au. et al. (2007) binaries have contrasts of ∆R<3.0. This then ©2010RAS,MNRAS000,1–19 6 Robert R. King et al. 3 4 2.5 2 3 K K 1.5 (cid:54) (cid:54) 2 1 1 0.5 0 0 0 0.5 1 1.5 2 2.5 3 0 0.2 0.4 0.6 0.8 1 (cid:54)H Mass Ratio Figure 2. The magnitude difference in the H and K bands be- Figure 4. The K-band magnitude difference as a function of tween primary and secondary stars using the predicted bright- massratioforsystemswithprimaryandsecondarymassesinthe nesses from the 1Myr Siess et al. (2000) evolutionary model for range0.1–3.0M⊙ fromthe1MyrSiessetal.(2000)evolutionary primary masses in the range 0.1–3.0M⊙ and mass ratios of 0.1– model. 1.0. binarysurveypapersforthesurveytargetstosetupperand 3 lower mass limits (Hillenbrand 1997; Lafreni`ere et al. 2008; Luhman & Rieke 1999; Luhman et al. 2003, 2009). Using 2.5 thespectraltyperange ofG5–M5.5commonto allfive sur- veys,wehavelimitedourcomparisontoprimarystarswith massesof∼0.1–3.0M assuminganageof1Myr(Siessetal. 2 ⊙ 2000). K While,foroursurveycomparison,weneednotexplicitly 1.5 (cid:54) set limits on the range of mass ratios probed, we can use the theoretical models of Siess et al. (2000) to estimate the 1 massratiosgiventhecontrastlimitof∆K=2.5.Asshownin Fig.4, the contrast limit we have adopted is approximately 0.5 equivalent to a mass ratio of 0.1 for 0.1–3.0M⊙ primary stars at an age of ∼1Myr. We note however, that there will beasmallbiasduetodifferinglevelsofcompletenessinthe 0 0 1 2 3 4 5 6 binary surveys (assuming a variation with primary mass), (cid:54)R i.e.,onesurveymayhavesurveyedalargerfractionoflower massstarsthananotherandsomayfindaslightlydecreased Figure 3. The magnitude difference in the R and K bands be- binarity. tween primary and secondary stars using the predicted bright- nesses from the 1Myr Siess et al. (2000) evolutionary model for primary masses in the range 0.1–3.0M⊙ and mass ratios of 0.1– 3.3 Separation sensitivities 1.0. The final cuts necessary to compare the binary surveys are to the separation ranges probed. As the ONC is the far- allowsustoapplyaconsistentcontrastlimitacrossthefive thestanddensestofourregions,itsetsalimitontheupper surveys (∆K=2.5 => ∆H=2.7, ∆F658N=5). and lower separation probed by all five surveys. However, applying this to all five surveys would severely restrict the number of binary systems. We therefore present a compari- 3.2 Primary mass and mass ratio sonofthefivesurveyswiththreedifferentseparationrange In the field the binarity of stars appears to decrease with cuts.Cut1(18–830au)allowsustocomparethewidestpos- primarymass(Duquennoy&Mayor1991;Fischer&Marcy sible separation range for Cham I, Ophiuchus and Taurus; 1992; Lada 2006). Simulations suggest that dynamical de- cut2(32–830au)alsoincludesIC348;andcut3(62–620au) struction is relatively insensitive to primary mass (at least allows a comparison of all five regions. from M-dwarfs to G-dwarfs), and so this mass-dependence may reflect a primordial mass-binarity relationship (see Parker&Goodwin2011).Therefore,inadditiontomatching 4 OBSERVATIONAL RESULTS contrastratiosbetweendifferentsurveys,wemustensurewe cover the same masses of stars to avoid introducing a pos- InTable3weshowthecomparablemultiplicityfractionsfor sible bias in the observed binarity. To do this we have used the five regions in the three separation ranges. For each re- the spectral type reported in the various membership and gionthecompanionsandtargetsofthebinarysurveyshave ©2010RAS,MNRAS000,1–19 Testing the universality of star formation 7 50 50 40 40 %) %) n ( n ( ctio 30 ctio 30 a a Fr Fr y y cit 20 cit 20 pli pli ulti ulti M M 10 10 0 0 1 10 100 1000 10000 1 10 100 1000 10000 Number Density (Stars/pc3) Number Density (Stars/pc3) Figure 5. The stellar multiplicity fractions of Taurus, Cham I Figure 6. The stellar multiplicity fractions of all five regions andOphiuchusagainststellardensitywhenweconsiderthesame against stellar density when we consider the same contrast cuts, contrastcuts,stellarmassesandaseparationrangeof18–830au. stellarmassesandaseparationrangeof62–620au.Thedensities Thedensitiesarecalculatedwithinaprojecteddistanceof0.25pc arecalculatedasforFig.5. from the cluster centre, except in the case of Taurus where a radiusof1pcisused. Table3.Stellardensitiesandmultiplicityfractionsforthethree separationranges. been removed where the spectral types are not within the rangeG5–M5.5andwherethemagnitudedifferenceexceeds Region StellarDensity Multiplicityfraction 2.5m.InthecaseoftheONC,thespectraltypeinformation (starpc−3) (percent) was not available so no mass cuts have been made to the sample. This is likely to mean the binarity is higher than Separation=18–830au it should be for this comparison due to the (postulated) in- Taurus 6.0±1.2 34.7±6.9 creasingbinaritywithstellarmass(see,e.g.,Raghavanetal. ChamI 275±65 25.4±4.7 2010; Parker & Goodwin 2011). Ophiuchus/L1688 610±180 22.7±4.8 For comparison, a log-normal field G-dwarf-like distri- Separation=32–830au bution (µ =1.57, σ =1.53, with a 60 per cent total log a log a binaryfraction)wouldhaveabinaryfractionof24percent Taurus 6.0±1.2 29.2±6.4 intherange18−830au,20percentintherange32−830au, ChamI 275±65 17.5±3.9 and 14 per cent in the range 62−620 au. Similarly, for an Ophiuchus/L1688 610±180 14.4±3.9 M-dwarf-like distribution with a total binary fraction of 40 IC348 1115±140 11.7±4.4 per cent (and the same log-normal parameters) the binary Separation=62–620au fractions would be 16, 13, and 9 per cent respectively. As moststarsinoursamplesareM-dwarfsthemostreasonable Taurus 6.0±1.2 16.7±4.8 comparison is to the M-dwarf-like field distribution. ChamI 275±65 11.4±3.2 Ophiuchus/L1688 610±180 6.2±2.5 Inthe18−830aurangeallclustersareover-abundantin IC348 1115±140 10.0±4.1 binariescomparedtotheM-dwarf-likefielddistribution,and ONC 4700±290 8.5±1.0 Taurus very significantly so. In the 32−830 au range only TaurusandChamIareover-abundant,andinthe62−620au range only Taurus has a significant excess. We will return Thereisarelationshipbetweenbinaryfractionandden- to this in the discussion. sity, but this relationship is driven almost entirely by Tau- rus.InFig.6inparticular,therelationshipwithoutTaurus isweakatbest.Thisisratherunexpectedasthefourclusters 4.1 Binarity variations with stellar density (without Taurus) span more than a decade in density. Giventhatbinaryfractionsarethoughttoevolveduetothe dynamicaldestructionofbinariesitisusuallyassumedthat 4.2 Observed morphologies thereshouldbeadecreaseinthebinaryfractionwithstellar density(Kroupa1995a,b;Parkeretal.2009).Thisrelation- We have used the stellar density of clusters detailed above, ship is thought to be seen in the significant differences in but there are problems associated with the determination the binary fractions of Taurus and the ONC (∼17 per cent (or meaning) of an average density in at least two of our versus ∼8.5 per cent respectively). clusters(TaurusandChamI).Insmoothdistributionstak- In Figs. 5 and 6 we show the binary fractions against ing a typical stellar density as a measure of the proximity density for the range 18–820 au (for Taurus, Cham I, and ofstarsandthelikelihoodofencountersisperfectlyreason- Ophiuchus),and62–620au(forallfiveclusters).Inallcases able.However,atleasttwooftheclustersweareexamining thedensityiscalculatedwithinaprojectedradiusof0.25pc, arefarfromsmoothanditisquestionabletowhatextenta except Taurus which is within a 1 pc projected radius. ‘stellar density’ is a meaningful concept. ©2010RAS,MNRAS000,1–19 8 Robert R. King et al. 10 1.2 1 5 0.8 0.6 0.4 0 c) c) 0.2 p p y ( y ( 0 (cid:239)5 (cid:239)0.2 (cid:239)0.4 (cid:239)10 (cid:239)0.6 (cid:239)0.8 (cid:239)15 (cid:239)1 (cid:239)20 (cid:239)15 (cid:239)10 (cid:239)5 0 5 10 (cid:239)2 (cid:239)1.5 (cid:239)1 (cid:239)0.5 0 0.5 1 1.5 x (pc) x (pc) Figure 7.Thelocationsofeachofthemembersofthenorthern Figure 10.ThelocationsofeachofthemembersofIC348with filamentofthe Taurus MolecularCloud (asdescribedin Sect.2) physicalprojectedseparationsassumingadistanceof316pc. withphysicalprojectedseparationsassumingadistanceof140pc. 2 9 1.5 8 7 1 6 0.5 5 c) pc) 4 y (p 0 y ( 3 (cid:239)0.5 2 (cid:239)1 1 0 (cid:239)1.5 (cid:239)1 (cid:239)2 (cid:239)2 (cid:239)2.5 (cid:239)2 (cid:239)1.5 (cid:239)1 (cid:239)0.5 0 0.5 1 1.5 2 (cid:239)20 (cid:239)15 (cid:239)10 (cid:239)5 0 5 10 15 20 x (pc) x (pc) Figure 11. The locations of each of the members of the Orion Figure 8. The locations of each of the members of the Cham I Nebula Cluster from Hillenbrand (1997) with physical projected cluster with physical projected separations assuming a distance separations assuming a distance of 414pc. These observations of160pc. clearly miss some of the cluster members farthest from the cen- tre and do not extend down to the stellar/substellar limit (see Sect.2.3).Theabsorptionfeatureassociatedwiththe‘lip’ofthe 1.5 emission nebula is seen as an under-density of sources in a strip acrossthemap(seeHillenbrand1997). 1 0.5 In Figs.7 to 11 we show the (two-dimensional) stellar 0 distributions in each of our regions. Ophiuchus, IC348 and c) the ONC (Figs. 9, 10, and 11) are fair examples of clas- y (p (cid:239)0.5 sic ‘clusters’: centrally concentrated with density declining with radius. However, Taurus and Cham I (Figs. 7 and 8) (cid:239)1 are clearly very sub-structured and far from smooth. De- (cid:239)1.5 spite our earlier attempt to define a ‘stellar density’, it is very unclear from these figures if a global ‘density’ has any (cid:239)2 meaning whatsoever. We address this question in the next section and in the discussion. (cid:239)2.5 (cid:239)1.5 (cid:239)1 (cid:239)0.5 0 0.5 1 1.5 x (pc) 5 SIMULATIONS OF BINARY DESTRUCTION Figure 9. The locations of each of the members of the L1688 core in Ophiuchus with physical projected separations assuming Inthissectionweattempttousetheobservationsoftheclus- adistanceof130pc. ter morphologies and multiplicity fractions to construct N- bodymodelsofstarclustersto‘reverseengineer’thecurrent ©2010RAS,MNRAS000,1–19 Testing the universality of star formation 9 state to determine the primordial binary fractions (Kroupa andaprimordialbinaryfractionof100percentcontains150 1995b). stellar systems, all of which are binaries; a similar cluster It is well-known that many binaries are destroyed in withafield-likebinaryfraction(∼45percent)contains200 denseenvironments(Heggie1975;Hills1975),andmuchthe- systems, 100 of which are binaries. We note that this may oreticalworkhasgoneintomodellingtheevolutionofstellar underestimatethenumberofstarsineachcluster,asbinary binary properties in different clustered environments. The systems outside of the observable separation ranges would first comprehensive simulations were performed by Kroupa be either unresolved or seen as two independent stars. (1995a,b,c), who showed that a primordial binary separa- tion distribution similar to that observed in Taurus–Auriga (Leinertetal.1993)canevolveintoafield-like(Duquennoy 5.2 Stellar systems &Mayor1991)separationdistributioniftheclusterisdense To create a stellar system, the mass of the primary star is enough. chosen randomly from a Kroupa (2002) IMF of the form Kroupa (1995a,b) and Kroupa & Petr-Gotzens (2011) deriveauniversalpre-mainsequenceseparationdistribution N(M)∝{ M−1.3 m0<M/M⊙≤m1, (3) basedonthesesimulations,whichischaracterisedbyanini- M−2.3 m1<M/M⊙≤m2, tial binary fraction and an excess of binaries with separa- tions a > 103au, compared to the Galactic field. Recently, wherem0 =0.1M⊙,m1 =0.5M⊙,andm2 =50M⊙.Wedo not include brown dwarfs in the simulations as these have Marks, Kroupa & Oh (2011) have developed an analytical been removed from the observational samples. operator, which, depending on the cluster’s initial density, We then assign a secondary component to the system canbeusedtopredicttheeffectsofdynamicalevolutionon depending on the binary fraction associated with the pri- the binary separation distribution in any star forming en- mary mass: field-like, 73 per cent, and 100 per cent. vironment, if the primordial binary population is described For a field-like binary fraction we divide primaries by the (Kroupa 1995a) distribution. This operator assumes that the cluster is roughly spherical and relaxed at birth. into four groups. Primary masses in the range 0.1 ≤ However, the assumption that clusters are roughly mp/M⊙ < 0.47 are M-dwarfs, with a binary fraction of 0.42 (Fischer & Marcy 1992). K-dwarfs have masses in the spherical and relaxed at birth is almost certainly not a rea- sonable assumption (see the distributions of Taurus and range 0.47 ≤ mp/M⊙ < 0.84 with a binary fraction of 0.45 (Mayor et al. 1992), and G-dwarfs have masses from ChamIinFigs.7and8above).Also,althoughL1688(Oph), IC348 and the ONC appear fairly smooth now, they may 0.84≤ mp/M⊙ <1.2withabinaryfractionof0.57(Duquen- noy & Mayor 1991; Raghavan et al. 2010). All stars more well have formed in a clumpy, complex distribution with massive than 1.2M are grouped together and assigned a their current smooth appearance due to dynamical evolu- ⊙ binaryfractionofunity,asmassivestarshaveamuchlarger tion(seeAllisonetal.2009,2010;Parkeretal.2011).Parker binary fraction than low-mass stars (e.g. Abt et al. 1990; et al. (2011) show that there can be significant binary pro- Masonetal.1998;Kouwenhovenetal.2005,2007;Pfalzner cessingeveninlow-densityclustersiftheyareinitiallysub- & Olczak 2007; Mason et al. 2009, and references therein). structured. This is because the local density can be high For the 100 per cent binary fractions all stars are in enough to destroy binaries even if the average global den- binaries. For the 73 per cent binary fractions, 73 per cent sity is very low. After a crossing time the initial substruc- of all stars (regardless of mass) are in binary systems. This ture is erased and the cluster is roughly spherical and re- sounds like a rather arbitrary number, but as we will de- laxed. Therefore two clusters that are almost identical at scribebelowitisthisbinaryfractionthatprovidesthebest 1–2Myr old can have a very different past dynamical his- fit to all of the clusters. tory and therefore very different processing of their initial Secondary masses are drawn from a flat mass ratio binary populations. distribution; recent work by Reggiani & Meyer (2011) has In this section we will simulate the evolution of clus- shown the mass ratio of field binaries to be consistent with ters starting from clumpy and smooth initial distributions being drawn from a flat distribution, rather than random with sizes and densities chosen to roughly match our five pairing from the IMF. observed clusters. We model the initial binary populations We draw the periods of the binary systems from the in the simulations as a Duquennoy & Mayor-like wide log- log -normal fit to the G-dwarfs in the field by Duquennoy normal with either a 45, 73 or 100 per cent initial binary 10 & Mayor (1991) – see also Raghavan et al. (2010), which fraction. has also been extrapolated to fit the period distributions of the K- and M-dwarfs (Mayor et al. 1992; Fischer & Marcy 5.1 Cluster membership 1992): Ibnleo,rwdeerusteoampaptrcohxitmheatoeblysetrhveedsacmluestneurmsbasercsloosfeslytaarssipnoossuir- f(log10P)∝exp⎧⎪⎪⎨⎪⎪−(log120σP2−log10P)2⎫⎪⎪⎬⎪⎪, (4) simulations of each cluster as are observed. Therefore, our ⎩ log10P ⎭ clustersdesignedtomimicChamIcontain200stars,IC348- likeclusterscontain260stars,theONC-likeclusterscontain where log10P =4.8, σlog10P =2.3 and P is in days. We con- verttheperiodstosemi-majoraxesusingthemassesofthe 1500stars;andtheOphiuchus-andTaurus-likeclusterscon- binary components. tain 300 stars. Theeccentricitiesofbinarystarsaredrawnfromather- Wekeepthenumberofstarsfixed;however,fordifferent mal distribution (Heggie 1975; Kroupa 2008) of the form primordialbinaryfractionsthisresultsindifferentnumbers ofsystems.Forexample,aTaurus-likeclusterwith300stars fe(e)=2e. (5) ©2010RAS,MNRAS000,1–19 10 Robert R. King et al. InthesampleofDuquennoy&Mayor(1991),closebinaries and measure the volume density from that star, adopting a (with periods less than 10 days) are almost exclusively on radius of 0.25 pc for Cham I and 1 pc for Taurus. tidallycircularisedorbits.Weaccountforthisbyreselecting theeccentricityofasystemifitexceedsthefollowingperiod- dependent value (Parker & Goodwin 2011): 5.5 Cluster set-up and morphologies 1 We assume two different morphologies for the initial con- etid= 2[0.95+tanh(0.6log10P −1.7)]. (6) ditions of our clusters. Firstly, we model clusters as radi- We combine the primary and secondary masses of the ally smooth Plummer spheres (Plummer 1911), which are binarieswiththeirsemi-majoraxesandeccentricitiestode- usedextensivelyinmodellingthedynamicalevolutionofstar termine the relative velocity and radial components of the clusters(e.g.Kroupaetal.1999;Morauxetal.2007;Parker stars in each system. The binaries are then placed at the etal.2009).Secondly,weadoptafractaldistributionsothat centre of mass and velocity for each system in a fractal or our clusters contain substructure initially (e.g. Goodwin & Plummer sphere (see below). Whitworth 2004; Allison et al. 2010; Parker et al. 2011). In two dimensions these model set-ups reproduce, to first or- der, the entire range of observed morphologies described in 5.3 Numerical parameters Section 5, although we note that other set-ups, such as the Kingprofile(e.g.King1966)can,andhavebeenusedtofit The simulations are run for 10Myr using the kira integra- several of the observed clusters (e.g. the ONC Hillenbrand torintheStarlabpackage(e.g.PortegiesZwartetal.1999, & Hartmann 1998). 2001)andthebinaryfractionsanddensitiesaredetermined Ouraimistoproduceclustersthathavethesamemor- after 1Myr. We do not include stellar evolution in the sim- phology, density, and binary fractions as the observed clus- ulations. As no systems of higher order than n = 2 form, ters at the age of the observed clusters. thebinaryfractionisequivalenttothemultiplicityfraction. Details of each simulation are presented in Table 4. We determine whether a star is in a bound binary 5.5.1 Plummer spheres system using the nearest neighbour algorithm outlined in Parker et al. (2009) and Kouwenhoven et al. (2010). If two Plummerspheres(andfractals,seebelow)areusedasinitial starsarecloserthantheaveragelocalstellarseparation,are conditions for the clusters that are observed to be roughly alsomutualnearestneighbours,andhaveanegativebinding spherical, namely the ONC, Ophiuchus and IC348. Due to energy, then they are in a bound binary system. their obviously substructured nature we do not attempt to In principle, this differs from an observer’s definition model Cham I or Taurus with Plummer spheres as initial of a visual binary, which could include chance associations conditions. We set up Plummer spheres according to the along the line of sight. However, numerical experiments in- prescription in Aarseth, Henon & Wielen (1974), and we dicate that the total number that could merely be chance assumethattheyareinvirialequilibriumatthestartofthe associations is negligible. simulations. Weassumethreedifferenthalf-massradiiforthesimu- lated clusters; 0.1, 0.4 and 0.8pc. For an ONC-like cluster, 5.4 ‘Observing’ simulations ahalf-massradiusof0.1pccorrespondstoaninitialdensity of ∼104M pc−3, which is significantly higher than the ob- ⊙ Weanalysethebinaryfractionsofclustersinawayasclose servedvalue.However,Parkeretal.(2009)showthatsucha as possible to the observations. We only ‘observe’ binaries clusterexpandsduringthefirst1Myrofevolutionandmay in the separation ranges matched by the real observations, have a similar density to the ONC after this time. A half- takingcloserbinariestobesingleunresolvedstars,andwider massradiusof0.8pccorrespondstothehalf-massradiusof binariestobetwoseparatestars.Weonly‘observe’systems the ONC today (Hillenbrand & Hartmann 1998). with primary masses in the range 0.1M⊙ ≤ mp < 3.0M⊙, WeshowexamplesofPlummerspheremorphologiesfor and with mass ratios q=ms/mp≥0.1. simulations of three of the observed clusters (details of the Todeterminethestellardensitiesoftheclustersweuse cluster set-up are given in Table 4). In Fig. 12 we show a the same method as applied to the real clusters, determin- Plummer sphere with 1500 stars, and a half-mass radius2 ing the volume densities within 0.25 pc from a 2D centroid of 0.4pc (simulation ID = 2 in Table 4, before dynamical fittothecentreoftheclusterforourmodelsfortheONC-, evolution(Fig.12(a))andat1Myr(Fig.12(b)).Thiscorre- Ophiuchus- and IC348-like clusters. As with the observa- spondstoanONC-likecluster,iftheclusterformedwithout tions,suchadeterminationisproblematicforsub-structured substructure. distributions,butweuseitintheabsenceofanythingbetter. We also show Plummer sphere morphologies for our For our Cham I-like and Taurus-like clusters, we mea- IC348- and Ophiuchus-like clusters. In Fig. 13 we show a sure the stellar surface density for each star, according to Plummer sphere with 260 stars, and a half-mass radius of the prescription of Casertano & Hut (1985): 0.4pc(IC348,simulationID=7inTable4),andinFig.14 N−1 we show a Plummer sphere with 300 stars, and a half-mass Σ= πD2 , (7) radiusof0.8pc(Ophiuchus,simulationID=13inTable4). N where N is the Nth nearest neighbour (we choose N = 7) andDN istheprojecteddistancetothatnearestneighbour. 2 Weassumethatthereisnoprimordialmasssegregation,sothis Wethendeterminethestarwiththehighestsurfacedensity alsocorrespondstothehalf-numberradius. ©2010RAS,MNRAS000,1–19