M-dwarf binaries as tracers of star and brown dwarf formation
Michael Marks, Markus Janson, Pavel Kroupa, Nathan Leigh, Ingo Thies
aa r X i v : . [ a s t r o - ph . GA ] J un Mon. Not. R. Astron. Soc. , 1–13 (2014) Printed 28 September 2018 (MN L A TEX style file v2.2)
M-dwarf binaries as tracers of star and brown dwarfformation
Michael Marks, , ⋆ , Markus Janson , Pavel Kroupa , Nathan Leigh , and Ingo Thies Helmholtz-Institut f¨ur Strahlen- und Kernphysik, University of Bonn, Nussallee 14-16, D-53115 Bonn Clara-Fey-Gymnasium, Rheinallee 5, D-53173 Bonn Department of Astronomy, Stockholm University, AlbaNova University Center, SE-106 91 Stockholm Department of Astrophysics, American Museum of Natural History, Central Park West and 79th Street, NY 10024, USA Department of Physics, University of Alberta, CCIS 4-183, Edmonton, AB, T6G 2E1, Canada
Accepted ????. Received ?????; in original form ?????
ABSTRACT
The separation distribution for M-dwarf binaries in the
AstraLux survey is narrowerand peaking at smaller separations than the distribution for solar-type binaries. Thisis often interpreted to mean that M-dwarfs constitute a continuous transition frombrown dwarfs (BDs) to stars. Here a prediction for the M-dwarf separation distributionis presented, using a dynamical population synthesis (DPS) model in which “star-like” binaries with late-type primaries ( . . M ⊙ ) follow universal initial distributionfunctions and are dynamically processed in their birth embedded clusters. A separate“BD-like” population has both its own distribution functions for binaries and initialmass function (IMF), which overlaps in mass with the IMF for stars. Combining thesetwo formation modes results in a peak on top of a wider separation distribution for lateM-dwarfs consistent with the late AstraLux sample. The DPS separation distributionfor early M-dwarfs shows no such peak and is in agreement with the M-dwarfs inMultiples (
MinMS ) data. We note that the latter survey is potentially in tension withthe early
AstraLux data. Concluding, the
AstraLux and
MinMS data are unableto unambiguously distinguish whether or not BDs are a continuous extension of thestellar IMF. Future observational efforts are needed to fully answer this interestingquestion. The DPS model predicts that binaries outside the sensitivity range of the
AstraLux survey remain to be detected. For application to future data, we present ameans to observationally measure the overlap of the putative BD-like branch and thestellar branch. We discuss the meaning of universal star formation and distributionfunctions.
Key words: binaries: general – stars: low-mass – stars: late-type – stars: formation– stars: kinematics and dynamics.
Binaries are a dominant channel of star formation(Goodwin & Kroupa 2005; Duchˆene & Kraus 2013;Reipurth et al. 2014) which is a result of the angular-momentum problem in star formation. The distributionof their orbital separations are commonly described bybell-shaped distributions that depend on the spectral-typeof the primary.The pioneering work of Duquennoy & Mayor (1991)showed a wide distribution peaking at about ≈
30 AU, anda binary fraction of 58 ±
10% for G-dwarf binaries in the ⋆ e-mail: [email protected] (MM) Galactic field. More recent analyses largely confirmed theirfindings (Raghavan et al. 2010; Tokovinin 2014) but suggesta somewhat lower binary fraction of ≈ ± ≈ ± ≈
15% to be lower than that forstars (Close et al. 2003; Bouy et al. 2003). This has led tothe suggestion that BDs are a population separate from thehydrogen-burning stars. c (cid:13) M. Marks et. al.
Due to the different behaviour of stars and BDs in termsof their pairing characteristics, Thies & Kroupa (2007, 2008)suggested an IMF which has a discontinuity around thehydrogen-burning mass limit, but with a non-negligible over-lap of both populations, i.e. some BDs may form “star-like”while some very low-mass (VLM) stars form “BD-like”, i.ein a fragmenting circumstellar disc. In this model both pop-ulations pair their objects among each other to form bina-ries but do not mix in pairing. The two-component IMFobtained after correcting the star counts for unseen com-panions is consistent with observations (Thies & Kroupa2008) and smoothed particle hydrodynamical (SPH) compu-tations which produce BDs from encounter-triggered pertu-bations in circumstellar discs (Thies et al. 2010). The mod-els of Thies & Kroupa furthermore support an observedBD desert (McCarthy et al. 2003; Grether & Lineweaver2006; Dieterich et al. 2012). Additionally, Thies et al. (2015)recently demonstrated that assuming BDs to be a con-tinuous extension to the hydrogen-burning stars leads toan overestimation of the numbers of BDs when com-pared with actual observations, confirming the deductionsof Kroupa & Bouvier (2003). Li et al. (2015) recently inves-tigated the outcome of a similar disc fragmentation mode(through self-instability of the disc, though, not throughencounter-induced fragmentation). By combining SPH and
Nbody techniques, they found a narrow separation distri-bution for BD-like objects peaking between 5 and 10 AUafter 10 Myr of evolution (their fig. 11), similar to the BDGalactic field properties, and within the limits of their ini-tial conditions, their results are in good agreement with theobserved BD desert.The distinguishing characteristics of the two popu-lations are now being challenged by recent observationsof M-dwarfs in the Galactic field. The
AstraLux survey(Janson et al. 2012, 2014) suggests that the M-dwarf separa-tion distribution is significantly narrower than that of solar-type stars. It is unlikely that a solar-type separation distri-bution (Duquennoy & Mayor 1991; Raghavan et al. 2010)is a parent function for both early and late M-dwarfs.This is interpreted as evidence for continuous star forma-tion from BDs to stars, where a population’s binary frac-tion increases smoothly with increasing mass of the primarycomponent, along with the peak and width of the separa-tion distribution (Duchˆene & Kraus 2013). Parker & Meyer(2014) argue that these observations in combination with themultiplicity properties of BDs (Thies & Kroupa 2007), ofsolar-type stars (Raghavan et al. 2010) and of A-type stars(De Rosa et al. 2014) disfavour universal initial binary prop-erties throughout these spectral types. Instead they considera scenario in which the field binary population is indicativeof the primordial multiplicity conditions in the star forma-tion regions they were born in. This would violate the univer-sality hypothesis of star formation according to which theuniversality of the IMF and binary populations are stronglycoupled (Kroupa 2001; Kroupa & Petr-Gotzens 2011).The influence of a separate BD-like population super-posed onto a star-like population on the multiplicity prop- Note that the universality hypothesis of star formation refersto an environment independence and does not preclude a mass-dependence (see Sec. 5.2). f b ( l og a / A U ) / ∆ l og a semi-major axis a / AU brown dwarfs (log a Peak =0.66, σ =0.4, f b =15%)early AstraLux (log a Peak =1.2, σ =0.8, f b =25%)late AstraLux (log a Peak =0.78, σ =0.47, f b =18%)MinMS (log a Peak =0.77, σ =1.34, f b =25%)solar-type (log a Peak =1.64, σ =1.52, f b =46%) Figure 1.
Observed orbital separation distributions and Gaus-sian fits for binaries in the Galactic field. M-dwarf data fromthe
AstraLux survey (histograms and corresponding same-linetype Gaussian distributions, statistically cleaned samplesonly; Janson et al. 2012, 2014) and the
MinMS data (lower limit,Ward-Duong et al. 2015), BD data from the VLMBA archive asdescribed in Thies & Kroupa (2007), and solar-type data fromRaghavan et al. (2010). The key provides the distribution peak(log ( a Peak / AU)), the distribution width ( σ ) and the binaryfraction ( f b ) within the respective sensitivity ranges as statedby the authors. erties of M-dwarfs has hitherto not been tested. This is theaim of the present research paper. In Section 2 the charac-teristics of the here used surveys are summarized. Section 3outlines how the Galactic field population is modelled. Theresults of our analysis are given in Section 4 and discussedin Section 5. The paper closes with a summary in Section 6. In a lucky-imaging survey the
AstraLux survey in-vestigates binarity among “early” (spectral types M0-M6, Janson et al. 2012) and “late” M-dwarfs (M2-M8,Janson et al. 2014) in the Galactic field. Although the twosamples are not distinct in mass we nevertheless henceforthrefer to “early” and “late” for the sample with the smaller(Janson et al. 2012) and larger (Janson et al. 2014) medianspectral type, respectively.Constructing two samples distinct in spectral type orprimary mass would be desirable in order to amplify the ob-served mass-dependency under study. The selection criteriafor the two samples were however systematically different(aside from the different spectral type ranges). The earlysample was selected on the basis of X-ray brightness, whilethe late sample was based on more nearby stars with a cut-off in infrared brightness. This means that the completenessof the surveys are systematically different, and it also followsthat the early sample is systematically young and often pre-main sequence, while the late sample is not. This in turn c (cid:13) , 1–13 -dwarfs as tracers of star and BD formation means that the stellar masses and the spectral types thedifferent samples correspond to are systematically differentas the temperature evolves with age until the main sequence.Hence, a cut in spectral type between two sub-populationsin a combined sample would be inaccurate. The youth of theearly sample additionally implies that masses of some tar-gets are still subject to change which might further diminish,or amplify, the overall offset in primary mass. Furthermore,the majority of stars in the late sample have parallactic dis-tances while the majority of stars in the early sample donot, so adding stars from the early sample to the late sam-ple would compromise the quality of the semi-major axisdistribution determination of the latter. This is why we willfocus on the late-type sample whose separation distributionis more reliable. Our conclusions are not affected by inves-tigating the two samples individually since the DPS model(Sec. 3) takes into account the individual and overlappingmass-ranges.Janson et al. (2014) define a “statistically cleaned”(SC) sample. If the combined magnitude of the binary com-ponents exceeded the limiting survey brightness, the authorsremoved the target from their statistical analysis. Had theprimary been a single object, it would not have been se-lected. This SC sample then has 48 binaries among 268 tar-gets, corresponding to a binary fraction of 17 . within thesensitivity range , log ( a/AU ) = − . .
95, where a isthe semi-major axis. Fig. 1 shows that, in comparison to theseparation distribution for solar-type stars (Raghavan et al.2010), both early and late M-dwarf samples exhibit sepa-ration distributions which are rather narrow around theirpeak. For the two AstraLux samples in Fig. 1 we note thefollowing two points:(i) The semi-major axis distribution of late M-dwarfs isstrikingly close to that for BDs.(ii) The amplitude of the peak in the late M-dwarf semi-major axis distribution is larger than the one for early M-dwarfs.At first glance, item (i) appears to favour the continuity ofstar formation over and above the hydrogen-burning masslimit. However, it will be demonstrated that the origin ofthe observed proximity of both distributions might be thata separate BD-like population overlaps with a population ofstar-like bodies. In addition, the here devised DPS modelyields item (ii).
The 15 pc volume-limited M-dwarfs in Multiples survey(
MinMS , Ward-Duong et al. 2015) detects K7–M6 binariesover a separation range log ( a/AU ) ≈ . −
4, using aninfrared adaptive optics (AO) technique to find close com-panions ( ≈ − AU) and digitised wide-field archivalplates for wide companions (10 − AU) each coveringmultiple epochs. The targets stem from a reduced
Hippar-cos catalogue (van Leeuwen 2007) and have reliable paral-laxes. 65 co-moving stellar companions in a sample of 245late-K to mid-M dwarfs yield a companion star fraction of23 . ± . MinMS separa- d l og ( N ) / d l og ( m ) mass m / M sun B D b r an c h s t e ll a r b r an c h system IMFsingle-star IMF Figure 2.
The stellar and substellar IMF are disjoint (black his-tograms). The dotted lines indicate an underlying power-law ofthe form m − α with α = 0 . , . . ≈ tion distribution in Ward-Duong et al. (2015) suggests thatit is at least . × wider than for the early AstraLux separa-tion distribution, although the covered spectral-type rangesare comparable in both surveys. This potential tension willbe qualitatively addressed in the discussion of our results(Sec. 4).
The
AstraLux
M-dwarf (Janson et al. 2012, 2014) and
MinMS data (Ward-Duong et al. 2015) are for Galactic fieldbinaries. A model is thus needed to describe how these em-anate from their birth embedded stellar clusters. Such a DPSmodel is readily available from Marks & Kroupa (2011, Sec-tion 3.3). A separate BD-like population (Section 3.2) is hereadded to a star-like population. For the star-like population,we assume universal initial conditions for late-type stars,and then account for the subsequent dynamical processing(Section 3.1).The DPS model will provide predictions for M-dwarfbinaries in the Galactic field. These predictions do not stemfrom first principles because a theory of star formation doesnot exist which yields such information. Instead, the bi-nary orbital-parameter distributions to start with before dy-namical processing result from inverse DPS (Kroupa 1995)of the then available empirical data for solar-type stars(Duquennoy & Mayor 1991) and pre-main sequence binaries(e.g. Leinert et al. 1993). But since the involved DPS modelparameters (Tab. 1 below) have been constrained using inde-pendent samples, as explained in the forthcoming sections,the DPS model with a set of previously constrained pa- c (cid:13) , 1–13 M. Marks et. al. rameters can be tested against other observations using thesame parameters. This is done here for the
AstraLux and
MinMS data.
As a working hypothesis to address the question of the(non-)continuity of star formation the birth binary popu-lation for star-like objects in embedded star clusters is as-sumed to be the same for all late-type stars (Kroupa 2011;Kroupa & Petr-Gotzens 2011). “Star-like” refers to all bod-ies selected from the two-part IMF which extends into theBD regime (producing star-like BDs down to 0 . M ⊙ ) andoverlaps with a separate “BD-like” population (see Fig. 2and Section 3.2, Thies & Kroupa 2007, 2008).The birth binary population is built from an universalseparation distribution for late-type stars derived by Kroupa(1995) with an excess of long period (soft) binaries overthat in the Galactic field (eq. 8 in Kroupa 1995), as seen inyoung star formation regions such as Taurus Auriga (Tau;Kohler & Leinert 1998; Kraus et al. 2011) and Corona Aus-tralis (CrA, K¨ohler et al. 2008). The initial binary popula-tion is defined using random pairing of binary componentmasses for low-mass stars ( . a few M ⊙ ), which are selectedfrom a standard two-part power-law stellar IMF (Kroupa2001), along with a thermal eccentricity distribution (seealso Kroupa et al. 2013) which bends over in the course ofdynamical processing (Marks et al. 2011, their figs. 2 and 5).While random pairing does not well reproduce the rather flatmass-ratio distribution for solar-type stars and more massiveprimaries (Reggiani & Meyer 2011; Duchˆene & Kraus 2013)it is in agreement with the weakly rising q -distribution forM-dwarf binaries and also with the overall mass ratio dis-tribution of late-type stars (see fig. 5 in Marks & Kroupa2011). The results on the semi-major axis distribution pre-sented here are not affected by the chosen pairing mecha-nism since dynamical binary processing shows only a weakpreference to disrupt low- q systems first (Marks et al. 2011;Parker & Reggiani 2013). Any additional orbital parametersare calculated using Kepler’s laws. The subsequent birth bi-nary population is subjected to pre-mainsequence eigenevo-lution (Kroupa 1995) to account for gas-induced changesof orbital parameters in the circum-binary material duringthe cluster formation (see also Stahler 2010; Korntreff et al.2012). The initial population, which is prone to dynamicalprocessing inside its host environment, i.e. an embedded starcluster, is thus arrived at.In order to calculate the effects of dynamical process-ing on initially binary-dominated populations inside youngstar clusters, we apply the analytical description of thedynamical processing in Nbody computations devised byMarks et al. (2011). In terms of the resulting binary pop-ulation, the outcome should be dynamically equivalent toan initially sub-structured and dynamically cold configura-tion, as Parker et al. (2011) conclude. The initially binary-dominated population changes on a crossing-time scale, i.ethe resulting distribution after a few Myr depends only onthe initial stellar density (see Marks et al. 2011).
Given the existence of the BD desert and the apparentlydifferent binary characteristics between stars and BDs (Sec-tion 1), Thies & Kroupa (2007, 2008) quantified a stel-lar plus BD IMF which has a discontinuity around thehydrogen-burning mass limit. However, the stellar and BDparts have an overlap (Fig. 2), since the star formation pro-cess does not care about hydrogen burning and it is unclearwhy the hydrogen-burning mass limit should constitute asharp cutoff. Note that upon combining both populations anobserver would not readily see the discontinuity but rathera declining and continuous IMF around the star–BD masslimit (see Fig. 2 and Thies & Kroupa 2007).In this contribution a “BD-like” population is addedto the star-like population resulting from the Galactic fieldDPS model of Marks & Kroupa (2011, Section 3.3). A BDor late M-dwarf is called “BD-like” if it stems from the BD-like branch of the IMF (masses between 0 .
01 and 0 . M ⊙ ,Fig. 2). The exact value of the upper cut-off mass for BD-likes is not known and might vary between regions. The best-fit values in Thies & Kroupa (2007, 2008) for Tau, IC348and the Trapezium cluster in the ONC are in the range0 . − . M ⊙ , with individual uncertainties of about ± . ± .
08 (their table 3). For Tau its value might be closerto 0 . M ⊙ , and to 0 . M ⊙ for IC348 and in the ONC, buttheir values agree within their 2 σ mutual errorbars. SinceTau type aggregates cannot be dominant in contributing tothe Galactic field, given a significant soft binary componentnot present in the field (Marks & Kroupa 2012; Marks et al.2014), we here adhere to m max , BD = 0 . M ⊙ determined forIC348 whose binary population resembles the Galactic fieldat long periods more closely (Marks & Kroupa 2012). Themost massive objects forming in the discs around host starsof 0 . M ⊙ used in the analysis of Li et al. (2015) is trun-cated at ≈ . M ⊙ as well, motivated by the mass spectrumof objects emerging in circumstellar discs in SPH computa-tions of Stamatellos & Whitworth (2009). The influence ofthe choice of the BD-like cut-off mass is discussed further inSec. 5.1. Note that our chosen value must not be taken rep-resentative for any star forming region since we discuss herea BD population originating and superposed from many starforming events.The BD-like population is excluded from dynamicalprocessing in its birth cluster (as is described in Section 3.1),since we do not have good constraints on the initial BDpopulation at this time. Note that this does not imply thatwe consider this population to be dynamically inactive, i.e.we do not assume the field population to resemble the pri-mordial population. Instead the dynamical processing of theBD-like part is implicitely accounted for by constructing itsuch that upon superposing it with the dynamically pro-cessed star-like population, the BD binaries ( < . M ⊙ )added from both branches match the BD binary charac-teristics in the field. This is possible as the outcome of anydynamical model has to reproduce what is observed for BDsin the Galactic field as a constraint. This approach, however,fixes the parameters of the BD-like population and the dy-namical population synthesis parameters a priori (Tab. 1). The here used BD-like population is thus the one for theGalactic field and must not be used for population synthesisin star clusters.
The BD-like population that should act as c (cid:13) , 1–13 -dwarfs as tracers of star and BD formation the input to star cluster models could be universal, but herewe do not address this issue.To model BD-like binaries, individual masses are se-lected from the BD IMF (Fig. 2) randomly and stored inan array. From this array, masses are paired such that theobserved mass-ratio distribution for BDs in the field, whichhas a strong preference toward unit mass-ratio, is repro-duced. To do so, the biased-pairing algorithm introduced byThies et al. (2015) is used. This procedure applies a prob-ability p = q γ to each binary, where q = m /m ∈ [0 : 1]is the mass ratio and γ = 2. If another random numberis smaller than p the binary is accepted. If it is larger anew companion for the first selected object is assigned andthe procedure is repeated. This ensures that a mass-ratioclose to unity is strongly preferred for BDs. Note that a re-jected companion is not discarded. It later becomes either acomponent of a different binary or stays single. This step isimportant to maintain the shape of the BD-like branch inthe single-star IMF (Fig. 2). Note also that biased pairing isa natural outcome of the formation of BDs in fragmentingstellar accretion discs (Thies et al. 2010). Each BD-like bi-nary is given a semi-major axis selected from the observedseparation distribution of BDs in the Galactic field. Mostof the selected BD-like objects remain single to yield theobservationally constrained binary fraction of ≈
15 per centfor BDs upon combining it with the processed star-like pop-ulation. The total binary fraction for BD-like binaries in theGalactic field is then ≈ R pop = N BD − like /N star − like and chosento be 0 .
3. This reflects the empirically determined value forTaurus-Auriga and the Pleiades (Thies & Kroupa 2007), i.e.for every three star-like bodies there is one BD-like object.
The stellar and BD population in a galaxy is the resultof the addition of all populations formed in all embed-ded clusters. According to the galactic field DPS modelof Marks & Kroupa (2011), each embedded star cluster’sbinary population is processed for 3 Myr, the time atwhich the first supernovae are expected to occur and inso doing drive out the residual-gas and destroy most oftheir natal stellar aggregate (Lada & Lada 2003). Theseclusters are thus the building blocks of the stellar sin-gle and binary population of the Galactic field. Embed-ded stellar cluster masses, M ecl , are assumed to be dis-tributed according to a single power-law initial embed-ded cluster mass function (ECMF), ξ ecl ∝ M − βecl , with β ≈ See Section 5.1 for further discussion of this assumption. The results are not very sensitive to this time-span as dynamicalprocessing of initially binary dominated objects occurs rapidly ona crossing-time scale of the embedded cluster (Marks et al. 2011).
Table 1.
Parameters defining the initial star-like population inembedded clusters , the BD-like population in the Galactic field and the Dynamical Population Synthesis procedure. From top tobottom the parameters denote (for details see the text): initialbinary fraction and minimum mass for objects on the star-likebranch, field binary fraction and maximum mass for objects fromthe BD-like branch, fraction of BD-like to star-like objects andbiased pairing exponent, star formation rate in the Milky Way,power-law index of the ECMF, minimum embedded star clustermass and typical embedded cluster half-mass radius.Parameter Valuestar-like population (embedded clusters) f b ≈ m min . M ⊙ BD-like population (Galactic field) f b m max . M ⊙ R pop . γ M ⊙ yr − β . M ecl , min M ⊙ r h . model works well to simultaneously describe various orbital-parameter distributions of the Galactic field binary popula-tion with a single set of parameters , depending on spectral-type (mass) of the primary component. This notion is sup-ported by the present work and will be further substantiatedin an upcoming contribution, which uses the latest observa-tional data. In this work the DPS parameters inferred byMarks & Kroupa (2011) will be used (Tab. 1). Using a star-like formation mode only does not match therecent
AstraLux data for late M-dwarfs. Fig. 3 (left panel)however demonstrates that upon adding BD-like M-dwarfs,i.e. those late M-dwarfs which form as part of the BD branchin Fig. 2, a peak on-top of the wider star-like distribution ap-pears. This is due to, in the present formulation, the BD-likeM-dwarfs sharing their separation distribution with those forBDs in the Galactic field. The DPS model binary fractionof 21 .
5% in the range log a = − . .
95 is in reasonableagreement with the 17 .
9% observed in the late M-dwarf SCsample.For a more sophisticated analysis, we compare the dis-tribution shapes by means of a Kolmogorov-Smirnov (KS-)test. We do this by subjecting the DPS model to the com-pleteness of the survey. One thousand random realizations ofthe DPS model are generated and the median of the matchprobability is adopted. This is the same method used byJanson et al. (2014) to find a Gaussian distribution thatbest describes the data. For details see their sec. 6.2. Thetest involves the DPS model mass-ratio distribution which isdiscussed in Section 4.2. The experiment results in a matchprobability of 30 . c (cid:13) , 1–13 M. Marks et. al. f b ( l og a ) / ∆ l og a semi-major axis (a / AU) solar-type stars (Raghavan+2010)Fischer & Marcy (1992)BD model (<0.08 M sun )late M-dwarf model w/o BD-like pop. (0.1-0.5 M sun )late M-dwarf model with BD-like pop. (0.1-0.5 M sun ) f b ( l og a ) / ∆ l og a semi-major axis (a / AU) solar-type stars (Raghavan+2010)early M-dwarf model with BD-like pop. (0.2-0.5 M sun )MinMS model (0.1-0.7M sun ) Figure 3.
Comparing orbital semi-major axis distributions of the DPS model (curves) with
AstraLux and
MinMS data, respectively(histograms). For reference, the semi-major axis distribution of solar-type stars (dotted blue line) is shown in both panels. The DPSmodel binary mass ranges are chosen according to the mass estimates of the binaries in the
AstraLux and
MinMS survey. Line-typesas in Fig. 1.
Left panel:
Upon combining the star-like M-dwarfs (dashed black curve) with the BD-like M-dwarfs (0 . − . M ⊙ on theBD-like branch) in the DPS model, whose distribution resembles the one for (star-like + BD-like) model BDs (solid black curve), thelate M-dwarf DPS model results (green dashed curve). It resembles the late-type data in the observed range (green dashed histogram,SC sample). For comparison, the M-dwarf data from the pioneering study by Fischer & Marcy (1992, crosses) is shown. Right panel:
Apeak is not expected (solid yellow and dashed-dotted red curve) in the early M-dwarf data (corresponding histograms) since the BD-likebranch here extends to 0 . M ⊙ only. within ≈ σ certainty. This result is discussed further inSection 5.It is interesting to note that the now more than 20-yearold data of Fischer & Marcy (1992) shows a similar excess ofM-dwarf binaries which is located at about the peak of thefield BD and late M-dwarf separation distribution. Primarymasses in their observations were in the range ≈ . − . M ⊙ ,i.e. a contribution of BD-like M-dwarfs is expected. The hugeuncertainties did not suggest a real feature. But, retrospec-tively, as a tracer of a separate BD-like population, the peakmight have been in front of our eyes all along.For early M-dwarfs a similar peak on-top of a wider dis-tribution is not expected (Fig. 3, right panel). This is due tothe BD-like branch extending, in the present formulation, upto 0 . M ⊙ only (Fig. 2). This value compares to the lowest-mass M-dwarfs in Janson et al. (2014)’s early sample. Notehow the different height of the observed AstraLux earlyM-dwarf distribution is reasonably matched by the DPSmodel. The wings of the fitted distributions as seen in Fig. 1are not reproduced, but with the exception of the lowestseparation bin the DPS model might even compare withthe raw
AstraLux data. On the other hand, the available
MinMS data and the distribution fitted to this data in Fig. 1is in excellent agreement with the DPS model. This immediately questions how the observational dataon early M-dwarfs, which share similar properties (Sec. 2), Note that, although
MinMS targets with < . M ⊙ exist, wehave run the DPS model without a BD population since only onebinary with < . M ⊙ is part of the observed separation distribu-tion. relate to one another. While the increased frequency of bi-naries with distant companions can be readily explainedthrough the enhanced coverage of semi-major axes in the MinMS sample, the conflict remains for the closest cov-ered separations (Fig. 1). This is at the very least puz-zling since the covered spectral-type range is comparablein both surveys. If the slightly wider mass-range of the
MinMS targets is responsible, yet unknown processes couldbe at work around the M-/K-dwarf boundary. Another pos-sible caveat is the systematic age difference between the sam-ples (Sec. 2.1). However, at present it is hard to see a reasonhow and why these differences should approximately doublethe observed distribution width.Alternatively, one may ask whether the fits of Gaussiandistributions to the
AstraLux and
MinMS data are reli-able representations of the underlying parent distributions.The raw separation distributions (histograms in Fig. 3, rightpanel) appear to compare better in the separation rangewhere both studys overlap than a comparison of the fit-ted distributions suggests. Is it then possible that both dis-tributions are not distinct after all and stem from a com-mon parent distribution? In this latter case the Gaussianfits would be too simplistic. We cannot decide this on thebasis of the present study and possibly requires further ob-servations. It is noted that neither Janson et al. (2012) norWard-Duong et al. (2015) attempt to make any detailed fitinvolving thorough statistical tests but merely discuss var-ious general options. So it is as of yet not clear whether aparent distribution exists that fits both datasets simultane-ously at acceptable confidence limits. A wider distributionfor early M-dwarfs as in the
MinMS data compares bet-ter with some previously obtained results (Fischer & Marcy c (cid:13) , 1–13 -dwarfs as tracers of star and BD formation f b ( q ) / ∆ q mass-ratio q=m / m BD-like population (<0.08 M sun )M-dwarf model w/o BD-like pop. (0.1-0.5 M sun )M-dwarf model with BD-like pop. (0.1-0.5 M sun ) Figure 4.
Oberserved and DPS model mass-ratio distributionsfor binaries in the semi-major axis range log ( a/AU ) = − . .
95, as in the observations. Combining star-like (dashed greyline) and BD-like M-dwarfs (solid grey line) as in Fig. 3, thelate M-dwarf DPS model appears (solid black curve). The his-togram with Poissonian errorbars shows the late
AstraLux data(SC sample). Caution is required since mass estimates for
AstraLux targets are uncertain (Sec. 4.2).
AstraLux data is suggested as well byBergfors et al. (2010)’s study. Note that the latter two stud-ies which find a narrow distribution used the same observa-tional technique, i.e. lucky-imaging.
Masses and mass ratios are difficult to estimate for theVLM objects in the
AstraLux survey. The dominant dif-ficulty stems from the fact that the ages of the stars areonly very loosely constrained, which means that the tran-sition from a star’s brightness to its mass will be accom-panied by very large uncertainties. Furthermore, the evo-lutionary and atmospheric models (Hauschildt et al. 1999;Baraffe et al. 2003; Allard 2014) that are used to make sucha transition are themselves uncertain, since they have notbeen calibrated against observations for large sections of theparameter space. Both of these issues are particularly criti-cal for masses that approach the BD range. This is why theobserved mass-ratio distribution should not be too much re-lied on. Regardless, as already stated, the observed featuresof interest for our purposes are present in the data at a sta-tistically significant level.In the DPS model, mass ratios for BD-like objects prefervalues close to unity, as observed for BDs in the Galacticfield. The DPS model facilitates this through biased-pairing(Section 3.2). Fig. 4 demonstrates how combining this withstar-like M-dwarfs leads to a distribution that increases withincreasing q and flattens beyond q ≈ .
5, for binaries in thesemi-major axis range log ( a/AU ) = − . . s e c onda r y m a ss m / M s un primary mass m / M sun BD desert?AstraLux late-M (SC sample)AstraLux early-M (CS sample)MinMS sampleHST/NICMOS
Figure 5.
Primary vs. secondary component masses in the
AstraLux (Janson et al. 2012, 2014) and
MinMS
M-dwarf data(Ward-Duong et al. 2015), as well as the HST/NICMOS VLMstar data (squares, Dieterich et al. 2012). Color-coding as inFigs. 1 and 3. The DPS model prediction is depicted as greydots. The density of dots is a measure of the expected numbers.VLM M-dwarfs and BD binaries have a tendency toward unitmass-ratio. The upper solid triangle contains binaries from thestar-like branch, and the lower dashed triangle contains binariesfrom the BD-like branch of the IMF. Where the triangles overlap,binaries from both branches can be found. The horizontal dottedline is the hydrogen burning mass-limit which roughly marks thecompanion detection limit for the early M-dwarf surveys.
If BDs form in the same way as stars the natural expec-tation is that BDs pair in the same way with stars asstars do among each other. And if the IMF is continu-ous over the hydrogen-burning mass limit BDs should bethe most abundant companions to stars (Kroupa & Bouvier2003). However, studies of VLM objects have demon-strated that this is not the case, i.e. a BD desert is ap-parent (McCarthy et al. 2003; Grether & Lineweaver 2006;Dieterich et al. 2012). The SPH plus
Nbody approach ofLi et al. (2015) to study the BD-like formation mode, i.e.disc fragmentation, is in agreement with the observed BDdesert. Although Grether & Lineweaver (2006) suggest thata BD desert is a natural consequence of a universal com-panion mass function (CMF), Dieterich et al. (2012) show,using their
HST/NICMOS sample, that VLM stars havea tendency toward unit mass ratio, i.e. BD companions arerare if not absent. This suggests that deviations from a uni-versal CMF likely exist, at least for the BD regime (see their § § AstraLux and
MinMS data. The more the primary component mass ap-proaches the hydrogen-burning limit from above, the closerthe mass-ratio gets to unity. This is consistent with the find-ing of Dieterich et al. (2012). As the primary mass increases, c (cid:13) , 1–13 M. Marks et. al. w i de b i na r y f r a c t i on ( i n % ) M-type spectral subclasses
DPS modelDhital et al. (2010, est.)
Figure 6.
DPS model binary fractions and those observed forwide binaries in the study of Dhital et al. (2010, estimated fromtheir fig. 16). The semi-major axis range covers log ( a/AU ) = 3to 5. Beyond spectral type M5 the binary fraction is essentiallyzero, both in the study and in the DPS model. Observed binaryfractions are lower limits. the DPS model suggests that systems with low mass ratiosshould exist, but they are not seen in the late AstraLux ob-servations. This might reflect the difficulty to detect sys-tems where the brightness of the primary outshines a po-tentially present lower mass star or BD.
Thus, the DPSmodel predicts that as instrument sensitivity increases, theobserved low mass-ratio systems should become apparent forlate M-dwarfs, increasing the observed binary fraction andbringing it closer to that predicted by the DPS model.
Suchsystems have been found in the
HST/NICMOS sample(Dieterich et al. 2012, squares in Fig. 5).Whether a similar BD desert exists for this late M-dwarfsample is thus difficult to assess with the
AstraLux data. Ifa desert were to exist, it would contradict the suggestion thatthe semi-major axis distribution constructed from the verysame data (Figs. 1 and 3) is a tracer of a common, canonicalformation mode for all stars and BDs. Detailed observationalinvestigations of the BD desert for VLM stars in conjunction with their separation distributions will thus provide impor-tant insights into the issue of the (non-)continuity of starformation.
The
SLoWPoKES survey (Dhital et al. 2010) investigatesbinarity of low-mass, wide common-proper motion binariesin a catalog from the Sloan Digital Sky Survey (SDSS). InFig. 6 we compare their observationally deduced wide binaryfractions, a = 10 − AU, with the DPS model. A similardeclining trend towards later spectral types is seen for boththe DPS model and the observations. In the DPS modelcontext this is due to the easier break-up of binaries withlower mass primaries in their birth clusters since their bind-ing energy decreases and the uneven mass-ranges coveredin each spectral subclass (shrinking towards later M-dwarfs,e.g. Baraffe & Chabrier 1996). The DPS model appears tooverestimate the published binary fraction for the earliestM-dwarfs by about an order of magnitude. Dhital et al.(2010) state that their wide binary fraction is likely a lowerlimit because observational biases and incompleteness playa significant role. The excess of model binaries might be re-lated to this. If not, then this might indicate a short-coming of the DPS model. We note, however, that for M3 and laterspectral types, the DPS model and observed fraction agreebetter.At the small semi-major axis end the spectroscopicstudy by Clark et al. (2012) finds a binary fraction of2 . +0 . − . per cent for cool M-dwarfs binaries from the SDSShaving log ( a/AU ) < − . assuming a uniform prior semi-major axis distribution (unlike the rising semi-major axisdistribution of Kroupa 1995). This value is in agreementwith the DPS model fraction of 2 . − < log ( a/AU ) < − .
4. Clark et al. (2012) additionallyshow that the spectroscopic binary fraction is a continuouslyincreasing function of primary mass, from BDs to massiveO-type stars, which is an additional test of the DPS model.Since the present work is on M-dwarfs, we investigate thisdependence in a forthcoming contribution.
The sole fact that the most straight-forward strategy to com-bine star-like and BD-like objects is able to reproduce theobservations is remarkable. If one had thought of the impli-cations of a separate BD-like population on the late M-dwarfseparation distribution before the
AstraLux data becameavailable, the DPS model described in Section 3 using theparameters in Tab. 1 would have been devised in exactlythe same way.
No attempt at trying to merely reproduce theobservations has been made here.
Having said this, the DPSmodel thus post-hoc predicts both the
AstraLux late M-dwarf binary fraction and semi-major axis distribution, thepossibly different distribution amplitudes between the earlyand late M-dwarf data, and the
MinMS data for early M-dwarfs.The match probability of ≈
30% is already good. Itmight increase by relaxing the assumption that the wholeBD-like population, which includes late M-dwarfs from theBD-like branch, follows the BD separation distribution inthe Galactic field. A proper initial distribution for BD-likeobjects in embedded star clusters which has evolved along-side the star-like objects through dynamical processing isnot yet available. But since VLM M-dwarf binaries from theBD-like branch are on average more strongly bound than bi-naries with a BD primary, it is to be expected that in realityM-dwarf binaries from the BD branch with a larger separa-tion can better survive dynamical processing in embeddedclusters. Their separation distribution in the Galactic fieldwill thus likely extend to somewhat larger semi-major axesthan assumed here, and the amplitude of the peak will in-crease as well. This would, in turn, improve the consistencybetween the DPS model and the observations.The DPS model requires an overlap of the star-like andBD-like branches of the IMF (Fig. 2). For the present mod-elling the BD-like branch is assumed to extend to 0 . M ⊙ ,as empirically determined for IC 348 (Sec. 3.2), which isconsistent with the mass spectrum arising for objects form-ing through disc fragmentation in the SPH computations ofStamatellos & Whitworth (2009). If the cut-off mass for theBD-like branch is lowered to, say, ≈ . M ⊙ (the best-fitvalue for Tau) the amplitude of the peak in Fig. 3 is lowered c (cid:13) , 1–13 -dwarfs as tracers of star and BD formation as well. This is due to the smaller overlap of the BD-likebranch with the observed range of primary masses in thelate AstraLux data which extends down to ≈ . M ⊙ only.The match probability then changes to 11 . σ con-fidence. Staying within the DPS model context, the lowermatch probability using a lower cut-off mass as determinedfor Tau might simply imply that Tau-like binary formationis not dominant in contributing to the field, as is addition-ally evidenced by its super-field binary fraction for long-period binaries (Kohler & Leinert 1998; Kraus et al. 2011,see Sec. 3.2). Though this cut-off mass is probably not sig-nificantly larger, we note that the uncertainty associatedwith this empirically-determined parameter implies that asomewhat larger value is also consistent with the data (3.2),and this could improve the agreement with the DPS model.Uncertainties in the binary fraction of Galactic fieldBDs and in the peak and width of the BD separation distri-bution are not considered here. In principle, with the avail-able observations we have the freedom to vary these param-eters within the uncertainties to further improve agreementwith the data. However, we refrain here from arbitrarilyvarying these parameters to obtain a better match since thereasonable agreement with this simplest DPS model speaksfor itself. Instead the issue will be revisited once constraintsfor an initial BD-like population become available. The notion of universal binary formation is that star for-mation leads to invariant formal distribution functions dueto physical processes like energy and angular momentumconservation and the chemistry of molecular clouds, all ofwhich are the same everywhere, except perhaps in very in-tense star bursts. This implies an environment-independence of binary formation (Sec. 5.2.1), potentially similar to theidea that universal star formation leads to an invariant for-mal distribution of stellar masses, the IMF. These distribu-tion functions are parent distribution functions, from whicha particular case is discretised, or rendered. Universal bi-nary formation does not preclude, however, a dependenceon the primary component mass, e.g. different birth bi-nary distributions for BDs and stars and in different massranges (0 . − . M ⊙ , 1 . − M ⊙ , > M ⊙ ) are possi-ble (Sec. 5.2.2). The universal distribution functions canbe primary mass-dependent by, e.g., adding further forma-tion channels, like circumstellar disc fragmentation for BDs,which do not change the underlying universal physical pro-cesses. We need such functions to initialise, for example, Nbody models in order to study how young and old clus-ters evolve into the field and associations.
An environment-independence of binary formation has oftenbeen suggested but the observational data don’t appear tobe conclusive (Kroupa 2011; Kroupa & Petr-Gotzens 2011;Marks & Kroupa 2012; King et al. 2012; Marks et al. 2014;Parker 2014; Leigh et al. 2014).King et al. (2012) found the orbital-separation distri-butions in seven young star formation regions to be statis-tically indistinguishable, consisting mostly of hard binaries given the regions’ presently observed conditions. By implic-itly assuming that the regions were not denser in the pastthey concluded that the observed distributions resemble theones at birth. On the other hand, Marks & Kroupa (2012)demonstrated that these same regions are consistent withdynamically processed universal birth distributions for late-type stars (Kroupa 1995) if they were significantly denser inthe past. Marks et al. (2014) later re-visited this issue, andargued that the two competing scenarios are statistically in-distinguishable, given the low number of observed binariesin these regions. It follows that solutions to the observationsare degenerate. In order to settle the issue of whether ornot star formation in these regions was the same with largeinitial binary fractions, we need to know if these regionswere significantly denser in the past. With this in mind,Marks et al. (2014) offered several arguments to help con-strain the initial cluster densities, and concluded that sucha scenario is indeed plausible.Parker (2014) offered an intriguing suggestion to breakthis density degeneracy. It involves measuring a star form-ing region’s degree of substructure, and asking if it canresult from dense initial conditions. The author assumesthe Kroupa (1995) primary-mass independent initial separa-tion distribution for late-type stars that is evolved in dense,initially substructured and subvirial/collapsing clusters us-ing
Nbody models. The simulations produce clusters thatare too centrally concentrated, compared to actual observa-tions of star forming regions (except maybe the Orion Neb-ula Cluster, ONC). Parker (2014) finds initial density esti-mates from a comparison to the region’s observed structurethat are smaller than those constrained by Marks & Kroupa(2012) from a comparison to the region’s observed binaryseparation distributions. Unfortunately, the author does notcompare the resulting separation distribution in his interme-diate density computations – which reasonably match thepresent-day structure – to the observed distributions. Inter-estingly, fig. 1 in Parker (2014) suggests that these computa-tions produce separation distributions that lie between thoseobserved in Tau or CrA (i.e. an excess of long period bina-ries compared to the field, as in the Kroupa (1995) distri-bution) and the ONC (i.e. depleted in long-period binaries).This is where the observed separation distributions in theremaining investigated regions lie as well (Marks & Kroupa2012; Marks et al. 2014). If the binary populations in theintermediate density computations of Parker (2014) were in-deed to resemble the observed ones, as we here suggest, theyseem to support the hypothesis of environment-independentbirth distributions for late-type stars. This is because thecomputations then simultaneously reproduce the observedpresent-day structure and binary populations. This raisesthe question: Why do Marks & Kroupa (2012) and Parker(2014) find different initial cluster densities? One possi-ble contributing factor is the different initial cluster setups(spherical and virialized vs. substructured and collapsing,respectively). However, Parker et al. (2011) conclude thatthis should not make any difference as far as the dynamicalprocessing of the binary population is concerned.Leigh et al. (2014) confirm a similar density degener-acy of the primordial binary population for globular clusters(GCs). Using MOCCA computations (Giersz et al. 2013)over a Hubble time they show that solutions to reproducingsimultaneously the rather low binary fractions and an anti- c (cid:13) , 1–13 M. Marks et. al. correlation between the binary fractions and masses of GCs inside the half-mass radius are degenerate in terms of the ini-tial GC densities and initial binary fractions, quite similar tothe density degeneracy for young star forming regions. How-ever, they break this degeneracy by demonstrating that onlydense initial configurations, which match densities observedfor potential GC progenitors, in combination with large ini-tial binary fractions account for a similar anti-correlationseen outside the half-mass radius in Galactic GCs. Thus,the observations for GCs are consistent with the universal-ity hypothesis (not precluding different origins, Leigh et al.2012, 2013, 2014).
The present work suggests that primary-mass independentbirth distribution functions for late-type binaries plus dy-namical processing continues to be a valid working hypoth-esis for M-dwarf binaries. Whether the birth distributionfunctions can be primary-mass dependent for late-type bi-naries or not is being debated.In a recent contribution, Parker & Meyer (2014) findthat their
Nbody computation with fractal initial conditionsand peak densities around 1000 M ⊙ pc − do not reproduceobservations of binaries in the Galactic field, when using theKroupa (1995) distribution as input and assuming BDs asa continuation of stars with the same universal initial con-ditions . This has been done before in Kroupa et al. (2003),who show that this leads to distributions inconsistent withobservations, and in particular too many star-BD binaries.Kroupa et al. (2003) concluded that BDs need to be treatedwith their own pairing rules.More precisely, in the computations of Parker & Meyer(2014), the orbital separation distributions after 10 Myr ofdynamical processing do not match the Galactic field sepa-ration distributions for(i) brown dwarfs (Thies & Kroupa 2007),(ii) M-dwarf binaries in the AstraLux survey(Janson et al. 2012, 2014),(iii) solar-type binaries (Raghavan et al. 2010) and(iv) A-type binaries in the VAST survey (De Rosa et al.2014).Based on this, Parker & Meyer (2014) suggest that the ini-tial distributions are primary-mass dependent. Thus, com-putations with the observed distributions as input to theotherwise same cluster provided a better match to the obser-vations, although not perfectly due to the dynamical break-up of wide binaries among the G- and A-type population.They conclude that the field binary populations are indica-tive of the star formation process in clusters.The results presented in this paper are consistent with adifferent interpretation, however, which have the advantageof being predictive . In the following we address the apparentdisagreement with the four populations above:(i) a meaningful comparison of the dynamically processeduniversal semi-major axis distribution for late-type starsand the BD binary population in the Galactic field re-lies on the assumption that star formation is continuousand that the Kroupa (1995) distribution is valid for BDs(Parker & Meyer 2014). If this were not true, the compari- nu m be r orbital period P / days solar-type stars (Raghavan+2010)field G-dwarf model Figure 7.
Comparison of orbital period distributions for solar-type stars (histogram with Poisson errors, Raghavan et al. 2010)and G-dwarfs in the DPS model (thick crosses). The same param-eters (Tab. 1) used to construct the M-dwarf DPS model (Fig. 3)are employed. son would not be meaningful. As demonstrated here, requir-ing a separate BD population as in Kroupa et al. (2003) andThies & Kroupa (2007, 2008) yields agreement with the ob-served BD binary semi-major axis distribution by construc-tion. Importantly, the Kroupa (1995) distribution was notdeveloped to match the observed properties of binary BDs,but was instead developed for (originally only) solar-typestars after dynamical processing.(ii) as shown in this contribution, the universality hy-pothesis for late-type stars following the Kroupa (1995) or-bital parameter distributions, combined with dynamical pro-cessing and a separate BD-like population, can successfullyreproduce the late
AstraLux and early
MinMS
M-dwarfdata.(iii) extracting the orbital period distribution for G-dwarfs in the Galactic field from the DPS model adoptingthe same parameters used to extract the M-dwarfs (Tab. 1)shows agreement between the observed period distributionof solar-type binaries in the Galactic field (Raghavan et al.2010, including orbits in hierarchical multiples) and theDPS model (Fig. 7). This is not surprising, though, sincethe Kroupa (1995) model was designed to match the solar-type data of Duquennoy & Mayor (1991), and their sepa-ration distribution of orbits is indistinguishable from theone obtained by Raghavan et al. (2010). On the origin ofthe different conclusions reached by Parker & Meyer (2014)we can only speculate. We note that Kroupa (1995) ex-plicitly demonstrated that only certain combinations of ini-tial cluster masses and radii reproduce the observed pre-mainsequence and field binary populations simultaneously.This yields constraints on the physical conditions in corre-lated star-forming events (i.e. embedded clusters).(iv) while A-type binaries in the
VAST survey show anarrow distribution peaked around 370 au (De Rosa et al.2014), spectroscopic A-type binaries are also known to ex-ist at shorter separations (Abt 1965; Carrier et al. 2002; c (cid:13) , 1–13 -dwarfs as tracers of star and BD formation Carquillat & Prieur 2007). Even a double-peaked distribu-tion for A-type binaries is suggested (Duchˆene & Kraus2013). However, spectroscopic data is needed to comple-ment De Rosa et al. (2014)’s data for a complete picture.We will address the
VAST data in future work. However,the (initial) distributions for O and B-type binaries appearto be different from that given in Kroupa (1995). This maybe indicative of a different formation channel for O- andB-type stars, e.g. through the star-formation process at thedensity centres of proto-clusters (e.g. Bonnell & Bate 2005),analogous in some ways to a separate BD formation chan-nel. In this case, the DPS model should be extended to ac-count for observations of binaries with high-mass primaries(e.g. Sana et al. 2012), as developed by Oh et al. (2015).However, one would naively expect any change in the starformation process to be mapped onto the stellar IMF (cf.Banerjee & Kroupa 2012).The take-away message is that both a field-like for-mation scenario (“what-you-see-is-what-you-get”) and theDPS model with a separate BD-like population explain theGalactic field observations. The latter formulation, assumingone birth binary population distribution function for low-mass stars ( . . M ⊙ ) plus dynamical processing to be theorigin of all late-type stellar binaries and adding a sepa-rate BD-like population (and perhaps a separate OB pop-ulation) explains the data. This scenario is not only con-sistent with, but actually explains the large range of esti-mated global binary fractions, from .
10 per cent in ω Cen-tauri (Elson et al. 1995) to sub-field fractions in other GCs(Milone et al. 2012) to &
90 per cent in young star formingregions (Kohler & Leinert 1998; Duchˆene 1999). Observa-tions of separation distributions in the latter objects mightsupport this notion as well (Kroupa & Petr-Gotzens 2011;Marks & Kroupa 2012; Marks et al. 2014). In addition, veryyoung regions like Tau and CrA (Kohler & Leinert 1998;K¨ohler et al. 2008; Kraus et al. 2011) as well as proto-stellarbinaries (Connelley et al. 2008) exhibit a binary excess atlong periods that do not support a field-like formation sce-nario. These populations all have a significant soft compo-nent, which changes quickly through dynamical processingin intermediate to dense environments. Such observations re-sult naturally from different degrees of dynamical processingof the underlying binary populations.Thus, the dynamical modification of the Kroupa (1995)distribution combined with a separate BD-like population isnot only consistent with the data, if the initial cluster densityis high, but it also allows binary populations to be predictedin the Milky Way and other galaxies (Marks & Kroupa2011). The binary excess in the youngest and sparsest starforming regions is accounted for by the Kroupa (1995) dis-tribution used in the DPS model, and its dynamical mod-ification yields the binary populations in star clusters andstar forming regions (Marks et al. 2011; Marks & Kroupa2012; Marks et al. 2014; Leigh et al. 2014) and in galaxies(Marks & Kroupa 2011, and this contribution).We caution that taking observed distributions and us-ing them as input for computations of clusters which re-semble the presently observed state as initial conditions (oreven a moderately dense configuration) will in most cases I.e. a configuration which does not place the hard-soft boundary not change the observed binary distributions significantly,unless the observed cluster is extremely young ( ≪ Whether BDs and stars are indeed separate populationswith their own initial mass and binary distribution func-tions can be constrained with future surveys of Galacticfield M-dwarf binaries. The presence of a separate BD-likesubpopulation unmasks itself through a peak located closeto the field BD separation distribution which resides on-top of a wider distribution, as a result of the superposi-tion of the star-like and the BD-like M-dwarfs (Fig. 3, leftpanel). The DPS model predicts that M-dwarf binaries inthe field exist in significant numbers outside the sensitivityrange of the
AstraLux survey (e.g. as in Fischer & Marcy1992; Delfosse et al. 2004), i.e. the separation distribution iswider than reported by the
AstraLux data, both for early(Janson et al. 2012) and late (Janson et al. 2014) M-dwarfs.The recently published
MinMS data (Ward-Duong et al.2015) supports such a notion for the early M-dwarfs. Iftrue, the late M-dwarf data roughly reproduce the peakof the DPS model distribution, whereas the observed earlyM-dwarf data missed it slightly due to the sensitivity con-straints.Here the BD-like branch of the IMF extends up to0 . M ⊙ . All M-dwarf binaries with . . M ⊙ in the ≈ −
10 AU range are thus apriori BD-like binary candidates. Bycomparing these objects among each other, observers mightbe able to find further signatures for a BD-like formationmode, aside from the peak in the separation distribution.These signatures might be hidden, e.g., in other orbital pa-rameters such as their eccentricity. If the true BD-like M-dwarf binaries follow the Galactic field BD mass-ratio distri-bution they preferentially have a mass-ratio close to unity.The analysis of disc fragmentation in Li et al. (2015) pro-vides further clues.We expect a peak superposed on a wider distributionin M-dwarf binary populations which have primary com-ponents with masses below 0 . M ⊙ . The peak is not ex-pected if such binaries are absent, as is e.g. the case forJanson et al. (2012)’s early M-dwarfs and the MinMS sam-ple (Ward-Duong et al. 2015). Their sensitivity limits do notinclude the separation range where the peak is expected andprevents us from testing this scenario. Should a peak be seenfor early M-dwarfs in later surveys as well, the maximummass of BD-like objects needs to be shifted to larger masses.
This provides thus a means to constrain observationally how below about the maximum of the input semi-major axis distribu-tion.c (cid:13) , 1–13 M. Marks et. al. deep the separate BD-like population, if it exists, penetratesinto the star-like regime.
Our random pairing scenario of binary componentsfor star-like M-dwarfs predicts that low mass-ratio lateM-dwarfs will be detected at larger primary masses andthat these will be lacking BD companions (Fig. 5), i.e. ex-tend the BD desert. These are currently invisible due to
AstraLux instrumental sensitivity constraints.
It has been demonstrated how combining a dynamically pro-cessed, initially binary-dominated universal star-like popula-tion for late-type stars ( . . M ⊙ ) with a separate BD-likepopulation forming through circumstellar disc fragmenta-tion, which produces some VLM stars, leads to a predictionfor the semi-major axis distribution of late M-dwarfs in theGalactic field. Upon adding the two formation channels, Dy-namical Population Synthesis (Marks & Kroupa 2011) pro-duces a narrowly peaked distribution that appears on-topof a wider distribution. The simplest DPS model resemblesthe late M-dwarf data obtained in the AstraLux survey(Janson et al. 2014) and the null hypothesis that the DPSmodel provides a parent distribution for the observationsis confirmed to within 1 σ certainty. It has been discussedthat agreement between DPS model and observation couldimprove once an estimate for an initial BD-like binary pop-ulation becomes available and once it is allowed to partici-pate in dynamical processing alongside the star-like objectsin the DPS model. As a byproduct our results demonstratethat the hypothesis of primary-mass independent period, orsemi-major axis distribution functions accounts for all late-type populations in the Galactic field. The opposite conclu-sion reached by Parker & Meyer (2014) does thus not followunambigiously from the data (see Section 5.2.2 for a discus-sion).The DPS model predicts that binaries outside the sen-sitivity range of the AstraLux survey will be detected. Apeaked semi-major axis distribution superposed on a widerdistribution as for the late M-dwarfs is not expected for earlyM-dwarfs (as those in Janson et al. 2012; Ward-Duong et al.2015). Once surveys for early M-dwarfs become sensitiveto smaller separations than covered by the
AstraLux and
MinMS data this notion will provide a means to measurehow deeply the BD-like branch penetrates into the stellarregime. The DPS model separation distribution agrees ex-cellently with the early M-dwarfs in the
MinMS samplebut less well with the early
AstraLux data. It is pointedout that the observed separation distributions for early M-dwarfs found by Janson et al. (2012) and Ward-Duong et al.(2015), respectively, are potentially in tension (Sec. 4.1).Given the surveys of nearby stars, a BD desert is ex-pected to be present in the
AstraLux data. No BD compan-ion is seen in the data above a primary mass of 0 . M ⊙ butthe decreasing detection probability of a low mass-ratio sys-tem with increasing primary mass does not yet allow for anyfirm conclusions. If a BD desert in the data were confirmedit would contradict the continuous star formation scenarioinferred from the narrow observed M-dwarf separation dis-tributions. This is because it is unclear why stars and BDsshould pair differently, avoiding each other while forming in the same way (for a discussion on the observational reality ofthe BD desert see § § in a single sample could thus leadus closer to answering the question of the (non-)continuityof star formation.To summarize, the available M-dwarf data do not pro-vide unambigious evidence for star formation that is con-tinuous over and above the hydrogen-burning mass limit.This is because, as illustrated in this paper, the data arealso consistent with the here devised DPS model whichassumes separate formation modes for stars and BDs anduniversally valid birth separation distributions for late-typestars. Specifically, the DPS model is predictive and ableto reproduce both the MinMS and the
AstraLux (withpoorer agreement) data, as well as the data for otherbinary populations observed in a diverse range of envi-ronments (Marks & Kroupa 2011, 2012; Marks et al. 2014;Leigh et al. 2014).
ACKNOWLEDGEMENTS
This research was partly supported through DFG grant KR1635/40-1. The authors thank the referee for providing athorough report which improved the presentation of themanuscript.
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