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The primordial binary population II: Recovering the binary population for intermediate mass stars in Sco OB2

M. B. N. Kouwenhoven, A. G. A. Brown, S. F. Portegies Zwart, L. Kaper

arXiv:0707.2746v1astro-ph

TL;DR

The paper addresses how to recover Sco OB2’s intrinsic binary population from observations biased by survey selection effects. It simulates observations of modeled associations and finds a very high binary fraction, with orbital-size distributions favoring Öpik’s law while the Duquennoy–Mayor period distribution underpredicts spectroscopic binaries.

  • Problem

    Sco OB2’s binary population cannot be observed directly because target selection and instrumental limits bias the observable parameter ranges.

  • Method

    The study compares observations from major visual, spectroscopic, and astrometric surveys with simulated observations of association models incorporating their selection effects.

  • Results

    Sco OB2 has a binary fraction of at least 70% at 3σ confidence, with observations consistent with Öpik’s law but showing that the Duquennoy–Mayor period distribution underpredicts spectroscopic binaries.

  • Takeaways & Limitations

    Practically all intermediate-mass stars in Sco OB2 are part of binary or multiple systems, making multiplicity a fundamental parameter in star formation.

  • Takeaways & Limitations

    The analysis focuses on intermediate-mass binaries because systematic low-mass binarity surveys are unavailable, and it omits close-binary interactions.

Abstract

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We characterize the binary population in the young and nearby OB association Scorpius OB2 using available observations of visual, spectroscopic, and astrometric binaries with intermediate-mass primaries. We take into account observational biases by comparing the observations with simulated observations of model associations. The available data indicate a large binary fraction (> 70% with 3sigma confidence), with a large probability that all intermediate mass stars in Sco OB2 are part of a binary system. The binary systems have a mass ratio distribution of the form f(q) ~ q^-0.4. Sco OB2 has a semi-major axis distribution of the form f(log a) ~ constant (Opik's law), in the range 5-5e6 Rsun. The log-normal period distribution of Duquennoy & Mayor results in too few spectroscopic binaries, even if the model binary fraction is 100%. Sco OB2 is a young association with a low stellar density; its current population is expected to be very similar to the primordial population. The fact that practically all stars in Sco OB2 are part of a binary (or multiple) system demonstrates that multiplicity is a fundamental factor in the star formation process, at least for intermediate mass stars.

1. Introduction

The paper seeks to recover Sco OB2’s primordial binary population despite strongly biased observations. Its youth, proximity, and low density make Sco OB2 a suitable test case, while simulated surveys provide constraints on the underlying population.

  • 1. Introduction: Multiplicity is central to characterizing the outcome of star formation and helps explain diverse astrophysical phenomena.The paper links binaries to supernovae, gamma-ray bursts, runaway stars, compact remnants, and cluster dynamics.
  • 1. Introduction: The primordial binary population is defined just after gas removal, when stars can no longer accrete from their surroundings.After gas removal, binary evolution is governed by stellar evolution and pure N-body dynamics.
  • 1. Introduction: OB associations are useful laboratories because their young ages and low stellar densities limit dynamical alteration of their binary populations.Associations younger than about 20 Myr generally have experienced little stellar evolution, and their densities are below 0.1 M⊙pc^-3.
  • 1. Introduction: Sco OB2 is especially suitable because it lies 118–145 pc away, is 5–20 Myr old, and has a well-studied membership and binary population.Its youth is expected to preserve the population close to the state established after gas removal.
  • 1. Introduction: Selection effects prevent direct observation of Sco OB2’s binary population across semi-major axis, period, eccentricity, and mass ratio.The paper addresses this by modeling six major binarity surveys and comparing simulated observations with the actual data.

2. Method and terminology

The paper recovers Sco OB2’s intrinsic binary properties by simulating associations with varied populations and applying survey selection effects. The models restrict multiplicity and assume independence among several binary parameters to keep the inference tractable.

  • 2. Method and terminology: The recovery method simulates observations of modeled stellar populations to infer Sco OB2’s underlying binary population.The approach is designed to account for observational selection effects rather than directly correcting observed distributions.
  • 2. Method and terminology: Each association model is compared with simulated observations for every major binarity survey, identifying models consistent with the observed data.When parameter space is fully searched and selection effects are well modeled, the method also estimates uncertainties.
  • 2. Method and terminology: The models include only single stars and binary systems, excluding higher-order multiples.The paper later considers consequences of this assumption.
  • 2. Method and terminology: The models assume binary parameters are independent, including semi-major axis and eccentricity, while close-binary interactions are omitted.Roche-lobe overflow and common-envelope evolution are excluded; any present close evolved systems could slightly lower the inferred binary fraction.
  • 2. Method and terminology: Binary populations may be parameterized by semi-major axis or orbital period, alongside masses and orbital elements.The formulation includes primary and companion masses, eccentricity, inclination, periastron argument, node position angle, and mean anomaly.
  • 2. Method and terminology: The overall binary fraction is modeled as independent of primary mass because the study covers a narrow intermediate-mass range.The paper notes that binary fraction may increase with primary mass, but lacks a quantitative prescription for that dependence.

3. The Sco OB2 association

Sco OB2 comprises three young subgroups whose observed membership and stellar distributions define the association model. The analysis focuses on intermediate-mass binaries and calibrates Hipparcos completeness against TYCHO-2 data.

  • 3. The Sco OB2 association: Sco OB2 consists of Upper Scorpius, Upper Centaurus Lupus, and Lower Centaurus Crux, which are likely products of triggered star formation.The paper lists subgroup distances, radii, ages, extinction, memberships, and observed multiplicity properties.
  • 3. The Sco OB2 association: The adopted stellar mass distribution is piecewise, with slopes −0.6±0.1, −0.9±0.2, −2.8±0.5, and −2.6±0.5 across successive mass ranges.The prescription is roughly consistent with Kroupa’s distribution and slightly steeper than Salpeter in the intermediate-mass regime.
  • 3. The Sco OB2 association: The study focuses on intermediate-mass binaries because systematic low-mass binarity surveys in Sco OB2 are unavailable.Consequently, the exact low-mass limits of the mass distribution are largely irrelevant unless both binary components are independently drawn from it.
  • 3. The Sco OB2 association: The association models use STARLAB, a 20 pc projected half-mass-radius Plummer model, and an assumed distance of 130 pc and age of 5 Myr.The models are not evolved over time, so the assumptions of virial equilibrium and the adopted structure do not affect the reported results.
  • 3. The Sco OB2 association: Hipparcos membership is based on position, proper motion, and parallax, but the catalogue’s completeness is complicated by its crowding limit and selected target lists.The study calibrates completeness in the Sco OB2 region using the Hipparcos-to-TYCHO-2 proportion as a function of V magnitude.

4. Observations of binary systems in Sco OB2

The paper assembles visual, spectroscopic, astrometric, eclipsing, and literature data for confirmed Sco OB2 members, while modeling survey-specific selection effects. The observed sample includes substantial multiplicity but is incomplete and potentially contaminated by spurious companions.

  • 266 known companions among 521 confirmed Sco OB2 members imply an observed multiplicity fraction of at least 40%.This count includes known binary and multiple systems, assuming proposed companions are physical.
  • Observed parameter distributions are not intrinsic because selection effects limit detection across separation, period, eccentricity, and mass ratio.Potentially spurious companions, including bright background stars, further complicate interpretation.
  • The analysis combines the KO5, KO6, SHT, LEV, BRV, and HIP datasets covering visual, spectroscopic, and astrometric binarity.The datasets partially overlap, and the combined analysis accounts for that overlap.
  • The KO5 dataset used here contains 199 targets and 60 companion stars after applying membership and multiplicity-selection rules.At most one companion per target is retained when studying multiple systems.
  • The modeled selection effects distinguish sample bias from instrument bias across the major surveys.Sample bias includes observer choice and brightness constraints; instrument bias includes telescope, detector, atmospheric, and background-confusion effects.

4.2. KO6 — Kouwenhoven et al. (2007) observations

KO6 uses multi-colour adaptive-optics follow-up to reassess ambiguous KO5 secondaries and models detection through contrast, Strehl ratio, field of view, and angular position. Its non-random target selection limits direct comparison with randomly sampled simulations.

  • Multi-colour JHKS observations place secondaries on a colour-magnitude diagram to distinguish likely Sco OB2 companions from background stars.Companions are expected near the subgroup isochrone, whereas background stars are generally farther from it.
  • 22 of 199 KO5 targets received KO6 NACO follow-up, yielding 62 secondaries classified as 18 confirmed companions, 11 possible companions, and 33 background stars.The follow-up subset favored faint and close background stars, secondaries near KS ≈12 mag, and newly discovered candidates.
  • The analysis uses 15 confirmed and 5 candidate companions from KO6, with special handling for double companions and higher-order systems.For several multiple systems, only the inner companion or a combined companion representation is retained.
  • Because only 11% of KO5 targets were followed up and the real subset was non-random, simulated KO6 observations cannot be directly compared with the observed KO6 results.They remain useful for estimating expected companion counts under the modeled selection process.
  • KO6 detection modeling uses a 50% contrast limit parameterized by angular separation and Strehl ratio.For simulations, Strehl ratios are drawn from an observed distribution approximated with mean 24% and standard deviation 7%.
  • The KO6 14′′ × 14′′ field of view makes detection depend on both angular separation and position angle.The field-of-view probability is modeled for random binary orientations using the linear size LN = 14′′.

4.3. SHT — Shatsky & Tokovinin (2002) observations

SHT surveyed B-type stars with adaptive optics and identified physical companions among confirmed Sco OB2 members. The analysis models brightness, contrast, coronagraphic and non-coronagraphic coverage, field-of-view geometry, and background-star classification.

  • SHT surveyed 115 B-type stars, including 87 confirmed Sco OB2 members.The observations used the ADONIS near-infrared adaptive-optics instrument at the ESO 3.6-meter telescope.
  • Among the 87 confirmed members, SHT found 80 secondaries, of which 19 were likely physical companions and 61 likely optical companions.The analysis uses 17 of the 19 likely physical companions after excluding selected components.
  • The final SHT dataset contains 87 targets and 23 physical companions.It includes selected non-observed targets whose companions were incorporated according to detectability under the SHT strategy.
  • SHT selection modeling imposes a minimum target mass of 3.5 M⊙ and minimum target brightness of V = 7 mag.All targets are required to be confirmed Hipparcos members of Sco OB2.
  • For non-coronagraphic observations, detection probability depends on separation and square-detector field-of-view geometry.The model uses detector size L = 12.76′′ and diagonal translation K = 8.5′′, with angular resolution ρlim,S = 0.1′′.
  • SHT detects companions through either coronagraphic or non-coronagraphic observations, combining the two modes.The coronagraph provides deeper observations, while the non-coronagraphic mode covers a larger angular-separation range.
  • SHT classifies likely background stars using J > 13 mag, KS > 12 mag, or J − KS > 1.7 mag unless the secondary is already a known companion.These magnitude and colour limits are applied to simulated observations.

4.4. LEV — Levato et al. (1987) observations

The LEV dataset combines radial-velocity observations with simulated sampling and detection criteria to estimate spectroscopic binarity in Sco OB2. The confirmed-member sample contains 39 detected binary systems among 53 targets.

  • Observed LEV sample: 30% is the minimum observed spectroscopic binary fraction, rising to 74% if all radial-velocity variables are binaries.The lower bound assumes all radial-velocity variables are spurious; the upper bound treats them as genuine binaries.
  • Sample selection: The simulations restrict the comparison to 53 confirmed Hipparcos members and remove systems fainter than V = 8.1 mag.This models the membership and magnitude selection of the LEV sample.
  • Observed LEV sample: 39 of 53 confirmed-member targets are detected as binary systems in the LEV dataset.The detections comprise 16 SB1/SB2 systems and 23 radial-velocity variables.
  • Bias modeling: The LEV observational bias is modeled with windowed radial-velocity sampling over T = 2.74 year at intervals ΔT = 0.38 year.The assumed radial-velocity accuracy is ǫRV = 3.1 km s−1.
  • Binary classification: Targets with p ≤ 0.0027 from the χ2 test are classified as binaries, while higher-p targets are classified as single stars.The threshold corresponds to the 3σ confidence level for rejecting constant radial velocity.

4.6. HIP — Hipparcos observations

The Hipparcos analysis identifies candidate astrometric and visual binaries among confirmed Sco OB2 members and models their catalogue-selection biases. Suspected non-single stars are treated separately because their binary nature is uncertain.

  • Observed Hipparcos categories: 46 of 521 confirmed Sco OB2 members are candidate or confirmed astrometric binaries, while 79 additional members are classified as visual binaries.The astrometric count includes the X, O, G, and S categories; the visual count refers to C binaries.
  • Binary classification: The analysis counts X, O, G, and C targets as binaries and compares results with and without S-category targets.The S category is excluded from the primary count because its binarity is uncertain.
  • Table structure: Table 5 reports subgroup membership counts, Hipparcos binary categories, astrometric fractions with and without S binaries, and the visual fraction for C binaries.V binaries are absent from Sco OB2.
  • Bias modeling: C binaries are modeled as resolved visual systems without detected orbital motion, whereas X, O, and G systems are modeled as astrometric binaries.The two groups are compared with observations using separate Hipparcos-bias prescriptions.
  • Limitations: The model excludes V-flagged systems because stellar variability is not included and excludes S-flagged systems because their classification depends on Hipparcos reduction comparisons.The simplified treatment also cannot accurately predict the individual X, O, and G categories.

5. Recovering the pairing function and mass ratio distribution

The paper tests pairing functions and mass-ratio distributions against visual and spectroscopic observations of Sco OB2 using simulated observations. The data favor PCP pairing with fq(q) ∝ q^γq and γq ≈ −0.4, alongside an intrinsic binary fraction above approximately 95%.

  • Pairing functions: Random pairing (RP) and primary-constrained random pairing (PCRP) predict too few high-mass-ratio systems and are excluded with strong confidence.Under their most favorable parameters, simulations give QRP ≈ QPCRP ≈ 0.004%, versus the observed KO5 value of Q̃KO5 = 5.0 ± 1.6%.
  • Pairing functions: PCP is consistent with the observations, while PCP-I, PCP-II, and PCP-III cannot be distinguished using the available intermediate- and high-mass data.Their mass-ratio distributions and binary fractions are effectively the same for the targets studied.
  • Mass-ratio distribution: γq ≈ −0.4 is the adopted best-fitting slope for the mass-ratio distribution fq(q) ∝ q^γq.Models outside approximately −0.6 < γq < −0.3 can be rejected at 1σ confidence.
  • Binary fraction constraints: Models with FM < 95% can be excluded at 2σ confidence or more for γq < 0.2 when compared with the observed visual binary fraction.Small γq values place most companions at low mass ratios, reducing visual detectability.
  • Binary fraction constraints: For γq ≳ −0.6, models with FM ≈ 100% best match the observed spectroscopic binary fraction, although they still predict relatively few spectroscopic detections.The spectroscopic comparison uses observed lower and upper limits rather than a single goodness-of-fit value.
  • Combined constraints: Combining the mass-ratio and binary-fraction comparisons favors γq ≈ −0.4 and an intrinsic binary fraction larger than approximately 95% at 1σ confidence.The combined slope depends somewhat on the relative weighting assigned to the visual and mass-ratio fits.

6. Recovering the semi-major axis distribution, the period distribution and the binary fraction

The observations favor an approximately Öpik-law semi-major-axis distribution and a very high intrinsic binary fraction, while the Duquennoy–Mayor period distribution underpredicts spectroscopic binaries.

  • The maximum semi-major axis and period: 2×10^6 R⊙ ≲ amax ≲ 8.9×10^6 R⊙, corresponding to 0.15 Myr ≲ Pmax ≲ 4 Myr, constrains the widest systems.The widest binaries are difficult to characterize because of confusion with background stars.
  • A power-law semi-major axis distribution?: γa ≈ −1.0 best describes the semi-major-axis distribution, consistent with Öpik’s law.Models with −1.15 ≲ γa ≲ −0.90 reproduce the observed angular-separation distribution well.
  • A power-law semi-major axis distribution?: The observed visual and spectroscopic binary fractions require an intrinsic binary fraction close to 100%.Models reproduce the observed visual fraction only near 100% intrinsic binarity, and the combined comparison gives the same requirement.
  • A log-normal period distribution?: The Duquennoy–Mayor distribution with µ = 4.8 and σ = 2.3 fits angular separations and visual fractions but underpredicts spectroscopic binaries even at 100% binarity.Broader log-normal period distributions are more consistent with the observations.
  • Conclusions on fa(a), fP(P) and FM: 2.3 < σ < ∞ gives the best description of Sco OB2, although both Öpik’s law and the Duquennoy–Mayor distribution cannot be excluded.The adopted combination γa ≈ −1.0 and γq ≈ −0.4 remains among the best-fitting joint solutions.

7. Recovering the eccentricity distribution

The eccentricity analysis favors flat or thermal distributions over a single eccentricity value, but its conclusions are limited mainly to short-period intermediate-mass binaries.

  • Scope and limitations: The inferred eccentricity properties apply only to short-period systems, approximately P ≲ 14 days and a ≲ 40 R⊙.The analysis does not fully recover the eccentricity distribution because of limited measurements, complex selection effects, and possible e–P correlation.
  • Candidate eccentricity distributions: e0 = 0.27 is ruled out with ∼3σ confidence for a single-valued eccentricity distribution.Measurement errors are about 0.05, and the observed distribution is broader than a single intrinsic value.
  • Candidate eccentricity distributions: The observed eccentricity distribution agrees better with the thermal and flat distributions than with a single-valued distribution.In the LEV sample, 14 of 16 systems with measured orbital elements have e < 0.5.
  • Selection effects: Highly eccentric systems are harder to detect because they spend much of their orbit near apastron.Selection effects can therefore partly explain the apparent excess of low-eccentricity systems.
  • Comparison with spectroscopic observations: The log-normal period and thermal-eccentricity models underpredict low-eccentricity spectroscopic binaries even with a 100% binary fraction.Öpik’s law with a flat eccentricity distribution matches the observations only if most RVV candidates are spectroscopically single.

8. The binary fraction in Sco OB2

The inferred binary fraction among intermediate-mass stars in Sco OB2 is very high, with models near 100% most consistent with the observations. The comparison also favors broad orbital-size distributions over the Duquennoy & Mayor period distribution for spectroscopic binaries.

  • The observed spectroscopic fraction is 30 ± 6% to 74 ± 6%, depending on whether radial-velocity variables are spurious or binaries.The lower and upper limits correspond to all or none of the radial-velocity variables being genuine binaries.
  • The Duquennoy & Mayor log-normal period distribution underpredicts spectroscopic binaries even at 100% intrinsic binary fraction.If 50% or 100% of the radial-velocity variables are binaries, it can be excluded at 4σ or 5σ, respectively, under the other assumptions.
  • ≈70% is the lower 3σ bound on the binary fraction, while models with 100% are most consistent with the observations.The corresponding 2σ lower bound is approximately 85%.
  • The inferred orbital-size and period-related distributions are insensitive to the adopted tightest and widest orbit limits, although the inferred binary fraction depends on those limits.Uncertainties in the limits contribute approximately 2% to the visual fraction and about 2–5% to the spectroscopic fraction.
  • 100% intrinsic binary fraction models are used when comparing predicted visual and spectroscopic detection fractions across surveys.The predicted fractions scale with the adopted intrinsic binary fraction.

9. The primordial binary population in Sco OB2

Sco OB2 is young and diffuse enough that stellar evolution has changed few binaries, while dynamical processing remains more difficult to quantify. The analysis therefore supports a current population close to the primordial one, subject to uncertainties in past conditions and higher-order systems.

  • 5–20 Myr ages and ∼0.1 M⊙pc−3 density imply only mild alteration of the binary population by stellar and dynamical evolution.The association’s crossing times are at least approximately 10 Myr.
  • Changes from stellar evolution can be neglected for the relevant population, except that evolved massive binaries may contain compact objects and altered companions.Supernova kicks can also produce runaway systems.
  • Hard–soft classification depends on binary binding energy and the properties of the surrounding association, because binaries interact more frequently than single stars.The hard–soft boundary uses the average field-object mass and the association’s three-dimensional velocity dispersion.
  • 72 ± 5% of binaries above 1.4 M⊙ are hard and 28 ± 5% are soft if Öpik’s law holds.Under the Duquennoy & Mayor period distribution, the corresponding fractions are 77 ± 3% and 24 ± 3%.
  • The current binary population is likely similar to the primordial population, but unknown initial density and other conditions require expanding-association N-body simulations.This uncertainty limits how tightly the primordial population can be constrained.

10. Discussion

The discussion examines modeling assumptions and observational contaminants affecting the recovered Sco OB2 binary population. It also considers mass-dependent multiplicity and concludes that the high intermediate-mass binary fraction is robust within the studied scope.

  • Triple and higher-order systems are omitted from the analysis, although they may partially explain the modeled underabundance of spectroscopic binaries.Quantifying spectroscopic subsystems requires prior knowledge of the triple population.
  • The mass-ratio distribution is modeled as fq(q) ∝ q^γq, using the LEV sample’s mean mass ratio of approximately 0.27 as context.The paper’s adopted fit has γq = −0.4.
  • Background stars are modeled by magnitude, position, pointing, and angular separation to reproduce contamination in visual-binary surveys.The expected number of bright background stars is small in the KO5 and SHT samples.
  • Approximately 1–4 bright background stars are expected among 199 KO5 targets, and about 1 among 87 confirmed SHT members.The KO6 magnitude criterion correctly classifies companions and background stars in about 85% of cases.
  • Binary fraction, semi-major axis, eccentricity, and mass-ratio dependencies on primary mass are ignored, but are expected to have little effect over the narrow studied mass range.The derived distributions fa(a), fP(P), and fq(q) are practically independent of the adopted FM(M1).

11. Summary and outlook

Monte Carlo comparisons of visual, spectroscopic, and astrometric surveys recover a high binary fraction and characteristic mass-ratio and orbital-size distributions for intermediate-mass stars in Sco OB2. The current population is expected to resemble the primordial population, although several modeling and scope limitations remain.

  • Summary and outlook: Monte Carlo simulations compare modeled associations with visual, spectroscopic, and astrometric surveys to recover Sco OB2’s primordial binary population.The analysis accounts for observational selection effects by comparing simulated observations with survey results.
  • Summary and outlook: 70% is the lower limit for the current binary fraction among A and B stars at 3σ confidence, with 100% providing the best agreement.The observations favor models in which all intermediate-mass stars are in binary systems.
  • Summary and outlook: γ_a ≈ −1.0 is consistent with Öpik’s law, f_a(a) ∝ a^γa, corresponding to a period distribution f_P(P) ∝ P^-1.The best-fitting period distributions have width σ_P > 2.3; the Duquennoy–Mayor log-normal distribution underpredicts spectroscopic binaries.
  • Summary and outlook: γ_q ≈ −0.4 describes the mass-ratio distribution, f_q(q) ∝ q^γq, while random and primary-constrained random pairing are excluded with high confidence.The recovered pairing function is specific to intermediate-mass binaries in Sco OB2.
  • Summary and outlook: The current Sco OB2 binary population is expected to be very similar to the primordial population because stellar and dynamical evolution have only mildly affected it.This conclusion depends on the association having formed at low density; substantial expansion could have made dynamical evolution more prominent.
  • Summary and outlook: Practically all intermediate-mass stars in Sco OB2 are part of a binary or multiple system, making multiplicity a fundamental parameter in star formation.This conclusion extends the high observed binary fraction to the broader role of multiplicity in the formation process.
  • Summary and outlook: The study includes six major surveys but omits smaller surveys and individual discoveries, while neglecting triple and higher-order systems because their selection effects are difficult to model.The authors expect the included surveys to contain the large majority of known Sco OB2 binaries.
  • Summary and outlook: The recovery assumes independent binary parameters, and improved modeling of spectroscopic and astrometric selection effects is needed for direct comparison of parameter distributions.Properties of the low-mass binary population also remain difficult to derive because relatively few low-mass members have known binaries.

Appendix A: Datasets used

The appendix documents the visual and spectroscopic datasets used to analyze binaries in Sco OB2. Tables describe candidate companions and survey classifications, with some targets handled specially to limit binarity bias.

  • Appendix A: Datasets used: Tables A.1 and A.2 list properties of the KO5 and KO6 datasets, considering only single stars and binary systems in the analysis.Known double companions for HIP68532 and HIP69113 are treated as single companions.
  • Appendix A: Datasets used: Six SHT targets unsuitable for wavefront sensing because of known close companions were included to avoid bias toward low binarity.The SHT tables do not list all candidate companions.
  • Appendix A: Datasets used: The LEV dataset contains 16 spectroscopic binaries with orbital elements and 23 radial-velocity variables without orbital elements.LEV observed 53 confirmed Sco OB2 members, including 8 SB1s, 8 SB2s, 23 RVVs, and 14 constant-velocity targets.
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