Toward Complete Statistics of Massive Binary Stars: Penultimate Results from the Cygnus OB2 Radial Velocity Survey
Henry A. Kobulnicky, Daniel C. Kiminki, Michael J. Lundquist, Jamison Burke, James Chapman, Erica Keller, Kathryn Lester, Emily K. Rolen, Eric Topel, Anirban Bhattacharjee, Rachel A. Smullen, Carlos A. Vargas Alvarez, Jessie C. Runnoe, Daniel A. Dale, Michael M. Brotherton
aa r X i v : . [ a s t r o - ph . S R ] J un Accepted for Publication in ApJ
TOWARD COMPLETE STATISTICS OF MASSIVE BINARYSTARS: PENULTIMATE RESULTS FROM THE CYGNUS OB2RADIAL VELOCITY SURVEY
Henry A. Kobulnicky , Daniel C. Kiminki , Michael J. Lundquist , Jamison Burke , ,James Chapman , , Erica Keller , , Kathryn Lester , , Emily K. Rolen , , Eric Topel , ,Anirban Bhattacharjee , Rachel A. Smullen , Carlos A. Vargas A´lvarez , Jessie C.Runnoe , , Daniel A. Dale , Michael M. Brotherton ABSTRACT
We analyze orbital solutions for 48 massive multiple-star systems in theCygnus OB2 Association, 23 of which are newly presented here, to find thatthe observed distribution of orbital periods is approximately uniform in log P for P <
45 d, but it is not scale-free. Inflections in the cumulative distributionnear 6 d, 14, d, and 45 d, suggest key physical scales of ≃ ≃ ≃ Dept. of Physics & Astronomy, University of Wyoming, Laramie, WY 82070, [email protected] Dept. of Astronomy, University of Arizona, Tucson, AZ 85721, USA Department of Physics and Astronomy, Swarthmore College, Swarthmore, PA 19081, [email protected] Massachusetts College of Liberal Arts, 375 Church St., North Adams, MA 01247, [email protected] Department of Astronomy, Mt. Holyoke College, 50 College Street, South Hadley, MA 01075, [email protected] Department of Physics, Lehigh University, 16 Memorial Drive East, Bethlehem, PA 18015, [email protected] Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235, [email protected] Department of Physics, 1520 St. Olaf Avenue, Northfield, MN 55057, [email protected] Department of Physics, Department of Astronomy & Astrophysics, The Pennsylvania State University,525 Davey Lab, University Park, PA 16802, USA β ≃ − .
22 provides a crude approximationover P =1.4 – 2000 d, as does a piece-wise linear function with a break near 45 d.The cumulative period distribution flattens at P >
45 d, even after correction forcompleteness, indicating either a lower binary fraction or a shift toward low-masscompanions. A high degree of similarity (91% likelihood) between the Cyg OB2period distribution and that of other surveys suggests that the binary propertiesat P .
25 d are determined by local physics of disk/clump fragmentation and arerelatively insensitive to environmental and evolutionary factors. Fully 30% of theunbiased parent sample is a binary with period
P <
45 d. Completeness correc-tions imply a binary fraction near 55% for
P < . < q < . < e < . e ≃ ∼
30 km s − attributed to atmospheric fluctuations. Subject headings:
Stars: massive — (Stars:) binaries: spectroscopic — (Stars:)binaries: general — (Stars:) binaries:(including multiple): close — (Stars:) early-type — Stars: kinematics and dynamics — Techniques: radial velocities
1. Introduction
Massive stars (M > ⊙ ) earlier than about B2.5V dominate the cosmic production ofionizing photons and stellar wind momentum before terminating in nature’s most energeticexplosive events, leaving behind neutron stars and black holes. Formation scenarios for theseexplosions and subsequent compact stellar remnants require the existence of a close stellarcompanion. In X-ray binaries the massive star becomes a neutron star accreting from anevolved star. Mergers of compact objects (neutron star-neutron star or black hole-neutronstar) produce gravitational waves (GW) that should be detected by the immanent gener-ation of GW experiments (Dominik et al. 2013). “Runaway” or “high-velocity stars alsoowe their extreme kinematics to hard interactions with massive binary systems (Blaauw1961; Gies & Bolton 1986; Hoogerwerf et al. 2001). In particular, stars in the range 8–25M ⊙ that have close companions may become the progenitors of Type Ibc supernovae whenthe H envelope of the more massive star is stripped during a phase of common envelopeevolution (Nomoto et al. 1995; Smartt et al. 2009; Eldridge et al. 2013; Smith 2014). Closebinaries may even produce all type Ibc supernova if single H-poor Wolf-Rayet stars collapse to 3 –become black holes without producing a supernova (Fryer et al. 2007). Furthermore, super-novae of type Ic and γ -ray bursts appear to happen simultaneously, suggesting a connectionbetween the two types of events that may have their origins in massive binary progenitors(Woosley & Bloom 2006). Close massive binaries also produce the population of low-massX-ray binary systems through evolution of the more massive star to a supernova, produc-tion of a neutron star or black hole, and then the subsequent evolution of the lower-masscompanion that becomes the mass donor (van den Heuvel 1983).The Cygnus OB2 Radial Velocity Survey (Kiminki et al. 2007) is an optical spectro-scopic survey of 128 photometrically selected O and early-B stars comprising an unbiased(with respect to binarity) sample within the core region of the nearby Cygnus OB2 Asso-ciation ( ∼ ∼ B2.5V are included in the Survey because they areexpected to dominate the population of supernova progenitors, given typical initial massfunctions. Other large studies of binarity among massive stars include the spectroscopicsurveys of Garmany et al. (1980), Sana et al. (2012), and Chini et al. (2012) as well as theimaging surveys of Kouwenhoven et al. (2007) and Mason et al. (2009).In this contribution we report the observations (Section 2) and orbital solutions for 22new single-lined spectroscopic binaries and one new double-lined binary (Section 3). Thesedata contribute to the growing census of massive binary statistics in a complete sampleof massive stars defined in Paper I. This increasingly complete compilation of orbital peri-ods, eccentricities, and mass ratios provides a rich dataset to constrain our understandingof massive star formation, evolution through binary channels, and massive star end states.Section 3 also contains a list of 16 stars that show minimal velocity variations after exten-sive observation and six stars—all supergiants—that exhibit irregular variations presumedto originate from atmospheric pulsations. An appendix provides an update on orbital so-lutions for six stars from Papers II and III for consistency with the most recent Cyg OB2 4 –analyses. We conclude by tabulating orbital parameters for the 48 known binary (and severaltriple) systems and conducting a high-level analysis of the distribution of orbital parameters(Section 4). Nomenclature of objects discussed herein follows the MT91
2. Spectroscopic Observations, Reductions, and Radial Velocity Measurement
Observational methodologies and data reduction procedures closely follow those de-scribed in Kobulnicky et al. (2012) and earlier papers. Paper I describes instrumental se-tups and dates of observation for observing runs using Keck+HIRES spectrograph (1999–2001), Lick+Hamilton echelle spectrograph (1999–2000), and WIYN+Hydra spectrograph(2001–2008). Results presented here principally use spectra obtained at the Wyoming In-frared Observatory (WIRO) 2.3 meter telescope+Longslit optical spectrograph using a 2000l mm − grating in first order during the 2011–2013 observing seasons, with a small numberof observations obtained in 2014 May. Resolutions of R ≈ . ′′ − grating in second order oran 1800 l mm − grating in first order to achieve spectral resolutions of R ≈ I − so that the interstellar Na II λλ II lines so thesespectra potentially have systematic velocity zero point differences compared to the WIROdata. However, our analysis of constant-velocity stars in the Survey shows good agreement,at the level of 3–6 km s − , between the velocities obtained from Keck, WIYN, and WIROspectra. Nevertheless, solutions are obtained solely from WIRO data, where possible. Whennecessary, data from Keck and/or WIYN are included in the solutions. Data from Lick weregenerally of lower quality and are not used.Radial velocities were measured by fitting Gaussian profiles to the He I I − ) between velocities from the various telescopes and instruments,lending confidence to the solutions that involve all three sources of data. Our fitting code fixes the Gaussian width and depth to be the mean determined from all the spectra, afterrejecting outliers, and it solves for the best-fitting line center and its uncertainty. Sincethe primary goal of the Cygnus OB2 radial velocity survey is to obtain orbital parametersfor massive binaries, a goal that requires good relative radial velocities, we did not observeradial velocity standard stars, and consequently the absolute space velocities reported arelikely to be accurate to ∼ − . Nevertheless, there is good agreement between themean velocities of our Cyg OB2 OB star sample ( V ave =-15.6 km s − ; σ V =8.2 km s − ) andresults from other workers ( V ave ≃ -18 km s − ; N. Wright, private communication).Table 1 records the heliocentric Julian Date, orbital phase, the heliocentric radial ve-locity, the velocity uncertainty, and the observed-minus-computed (O-C) velocity for eachmeasurement based on the orbital solutions that follow. All systems, with the exception ofMT91 646, are single-lined spectroscopic binaries so that only one velocity is reported foreach epoch. MT91 268 is a probable triple system exhibiting two periodicities, so both ve-locity components appear in Table 1. Figure 1 shows a three-color view of the Cygnus OB2region with 4.5, 8.0, and 24 µ m mosaic images from the Spitzer Cygnus-X Legacy Survey (Hora et al. 2007) in blue, green, and red, respectively. White points depict massive stars inthe Cygnus OB2 Radial Velocity Survey parent sample, while magenta points mark knownbinary or higher-order systems. The 5 pc bar at lower left marks the linear scale at theadopted distance of 1.4 kpc. Binaries are apparently distributed across the face of the As-sociation without preference for radial distance from center.
3. Orbital Solutions
We analyzed the radial velocity power spectrum for each object to select likely periodsand then examined the folded velocity curve for periods corresponding to the strongest peaks.In most cases the strongest peak yielded a clear, unambiguous period and a convincing phasedvelocity curve. Secondary peaks and possible aliases could be eliminated by visual inspectionowing to the much larger dispersion in the data at any given phase. We used the binaryorbital solution package “BINARY” by D. Gudehus with these initial period estimatesand the radial velocity data to solve for the full suite of orbital parameters and associateduncertainties. Tables 2 through 6 compile these best-fitting parameters and uncertainties for We use the robust curve-fitting algorithm MPFIT as implemented in IDL (Markwardt 2009). ∼ gudehus/binary.html P ), eccentricity of the orbit ( e ),longitude of periastron in degrees ( ω ), systemic radial velocity ( γ ), epoch of periastron ( T ),primary velocity semi-amplitude ( K ) and (if applicable) secondary velocity semi-amplitude( K ), spectral classifications from this survey (S.C. & S.C. , if available), estimates of theinclination ( i ), the adopted primary stellar mass ( M ) and (if applicable) secondary mass( M ), mass ratio ( q ), semi-major axis ( a ), and reduced chi squared values of the best fittingsolution. Tables 2 through 6 list orbital parameters for 22 new systems reported in this work.Masses for OB stars are taken from Martins et al. (2005) for O stars and Hunter et al. (2008)for early B stars. Upper and lower limits on the inclinations are obtained, in most cases, byadopting 90 ◦ and the lowest inclination compatible with the absence of secondary spectralfeatures (i.e., where the mass of the secondary approaches that of the primary). MT91 021—
Kiminki et al. (2007) classified the MT91 021 primary (V=13.74; Massey & Thompson1991) as a probable single-lined binary system on the basis of four data points. Using a com-bination of three WIYN spectra we revise the spectral type to B1.5V by comparison in theWalborn & Fitzpatrick (1990) spectral atlas. Table 1 lists the 14 radial velocity measure-ments from WIRO spanning 2010 August – 2013 September. Figure 2 shows the best-fittingorbital solution (solid curve) and folded velocity data (points with error bars). Table 2 sum-marizes the full suite of orbital parameters. If we adopt a mass of 12 M ⊙ for the primary(MT91 021a), an inclination of i =85 ◦ implies a secondary (MT91 021b) mass of 2.2 M ⊙ ,while i =15 ◦ requires the secondary (MT91 021b) mass to approach that of the primary.This system is interesting for having such a high eccentricity despite its short period. How-ever, the eccentricity is strongly dependent on just a few data points, and a solution withfixed eccentricity of zero still yields a similar χ value.Finally, we note that the reduced χ of the fit (3.2) is large. The O-C residuals appear toshow evidence for periodic variation at ∼ − , suggest-ing the possibility of this being a triple system. This would make the tertiary, MT91 021c,a probable solar mass star with a minimum mass of 0.5 M ⊙ . Additional measurements willbe needed to confirm the periodicity and amplitude of a second velocity component in thissingle-lined system. Inclusion of older (but less precise) WIYN (2 spectra) and Keck (2spectra) measurements strengthen the evidence for more than one velocity component inMT91 021. MT91 187—
The B1 V primary of this V=13.24 system was not initially detected asa probable binary on the basis of five measurements (Kiminki et al. 2007). The present 7 –dataset consisting of two Keck spectra, four WIYN spectra, and 19 WIRO spectra spanning1999–2013 (Table 1) reveals this systems to be a P =13.531 ± K =6.5 ± − . Figure 3 shows the best-fitting orbital solution (solid line) and folded velocity curvedata (points with error bars). This is one of the lowest amplitude systems yet detected in theSurvey. The velocity variability is consistent with a binary (reduced χ =0.82 for 12 degreesof freedom) but not a constant-velocity system (reduced χ =1.8 for 19 degrees of freedom,yielding a probability of < e =0.51 ± P ≃ ⊙ for the B1V primary, an inclination of i =85 ◦ implies a secondary (MT91 187b) mass of0.43 M ⊙ , while i =3 ◦ allows a secondary mass approaching that of the primary. Given theprobable low-mass secondary and extreme mass ratio, this system is a candidate for being aprogenitor of a low-mass X-ray binary system if the system remains bound once the primaryreaches its end-state as a neutron star. MT91 202—
This V =14.40 binary is listed as an SB1 by Kiminki et al. (2007) on thebasis of five data points, and they type the primary as B2V. We find an orbital period of P =43.07 ± K =19.7 ± − using17 measurements from WIRO. The eccentricity is e =0.23 ± ⊙ for theprimary yields M =2.0 M ⊙ if i =90 ◦ . The lack of known eclipses does not provide usefulconstraints on the inclination given the relatively long period. The mass of the secondary(MT91 202b) approaches that of the primary if i =15 ◦ . These rough mass constraints meanthat the secondary spectral type probably lies in the range A to mid-B, assuming a main-sequence star. Although there are hints of line width variations that may suggest a double-lined system, the low SNR of our spectra on this faint star coupled with the broad linewidthand small velocity amplitude means that no attempt was made to separate components.Figure 4 shows the best-fitting orbital solution and folded velocity data. MT91 234—
This V=13.25 system is dominated by its B1.5V (revised from B2V inPaper I) primary star that exhibits long-term radial velocity variations. The solution re-quired a combination of data spanning the whole range of the Cygnus OB2 Radial VelocitySurvey from 1999 October using Keck+HIRES (two measurements) through 2001 August–2008 June using WIYN+Hydra (10 measurements), and 2011–2013 October using WIRO(14 measurements).Figure 5 shows the best-fitting orbital solution and folded velocity data. Symbol typesdesignate data from Keck (triangles), WIYN (diamonds), and WIRO (squares). The pe-riod of 13.6 ± ± K =17.1 ± − is large for such a long-period system and implies a fairly massivecompanion. Adopting a primary mass of 12 M ⊙ yields a minimum secondary (MT91 234b)mass of 11 M ⊙ for i = 90 ◦ . This suggests that the system is seen nearly edge-on and thatthe secondary is also a B star. MT91 241—
A B1.5V (revised here from B2V in Paper I) primary star, the 11 WIROdata combined with three Keck and five WIYN measurements show that MT91 241a hasa period of 671 ± ± − with eccentricity of0.45 ± ⊙ , the implied secondary mass (MT91 241b) is 5.2 M ⊙ for i =90 ◦ .The very narrow He I lines show no sign of a second component, so it seems likely that thesecondary star mass is closer to this lower limit than to the primary mass, implying a massratio in the range 0.42 < q . MT91 268—
A B2V (revised from B2.5V in Paper I), this single-lined shows unambigu-ous evidence for being a triple system. The initial single-component solution at a periodnear 33.2 d displayed systematic residuals with a period near 5.0 days. We used these ini-tial guesses to fit a joint orbital solution for two velocity components using two data fromKeck, five data from WIYN, and 15 data from WIRO between 1999 and 2013. Our best-fitting solution consists of the first component having P =33.327 ± e =0.41 ± K − comp =33.0 ± − , and the second component having P =5.082 ± e =0.48 ± K − comp =17.4 ± − . Figures 7 and 8 display the orbital solution and folded ve-locity data for each component. The existence of several outlier measurements in both plotsis consistent with the hypothesis of this being a quadruple system.Adopting 11 M ⊙ for the mass of the primary star MT91 268a, the implied mini-mum masses for the unseen companions are M ≥ ⊙ for the 33.2-day component 1(MT91 268b) and M ≥ ⊙ for the 5.08-day component 2 (MT91 268c). This allowsthat the companions are probable A–mid-B and G–B dwarfs, respectively. Given the mod-erate eccentricity, short period, and extreme mass ratio, this may be a dynamically unstablesystem. MT91 292—
With a period of 14.811 ± K = 25.3 ± − is well-defined by the combination of 1 Keck data point, six WIYNmeasurements, and 13 WIRO measurements spanning nearly the entire length of the 2000–2013 survey period. Adopting a primary mass of 11 M ⊙ , an inclination of i =90 ◦ implies aminimal secondary mass for MT292b of M =1.6 M ⊙ . The secondary mass approaches thatof the primary if i ≃ ◦ . Figure 9 shows the best-fitting orbital solution and folded velocity 9 –data. MT91 295—
Fourteen measurements from WIRO during 2012 and 2013 indicate thatthis B1.5V (revised from B2V in Paper I) has P =2.4628 ± e =0.30 ± K =9.2 ± − issmall but detectable given the typical uncertainty of 3.9 km s − . The power spectrum hasmultiple peaks consistent with this being a triple system having components with periodsof 4.67 d and 1.68 d and velocity semi-amplitudes near 4–6 km s − . The two-componentsolution provides a somewhat better fit, but the number of free parameters approaches thenumber of data points. In either case, this is a short-period multiple system. Figure 10shows the best-fitting single-component orbital solution and folded velocity data. Adopting12 M ⊙ for the mass of the primary, the implied lower limit on the secondary (MT91 295b)mass is M =0.3 M ⊙ . The inclination is unconstrained, as M approaches M for i =3 ◦ . MT91 336—
This narrow-lined B2V (revised slightly from B3III in Paper I) has oneobservation from Keck, seven from WIYN, and four from WIRO spanning 1999 – 2014. Thetwelve data points yield a period of 2.04087 ± K =8.8 ± − and eccentricity of e =0.21 ± ⊙ for the mass ofthe primary, the implied lower limit on the secondary (MT91 336b) mass is M =0.3 M ⊙ .The inclination is unconstrained, as M approaches M for i =3 ◦ . MT91 339—
With a velocity amplitude of just K =3.4 ± − this O8V primaryhas one of the smallest amplitudes of any in our survey. The narrow, deep He lines allowfor a high level of precision, leading to typical velocity uncertainties of ∼ − on the 34WIRO spectra spanning 2008–2013. The orbital period is P =37.86 ± ± ⊙ to 21M ⊙ . MT91 378—
The V=13.49 B0V primary shows a velocity amplitude of K =36.3 ± − and a period of 29.41 ± ⊙ , an inclination of i =90 ◦ yields M =4.1 M ⊙ . The secondary mass approaches the 10 –primary mass if i =17 ◦ . Hence, the secondary (MT91 378b) is limited to be a B spectraltype, assuming it is on the main sequence. MT91 390—
With a velocity amplitude of K =5.4 ± − , this O8V primary isamong the lowest-amplitude systems observed in the survey. The period of P =4.625 ± i =90 ◦ the implied secondary massis M =0.32 M ⊙ , while for i =2 ◦ the secondary (MT91 390b) mass approaches that of theprimary. Figure 14 shows the best-fitting orbital solution and folded velocity data. MT91 403—
This B1V primary exhibits a velocity semi-amplitude of K =49.8 ± − and a period of P =16.638 ± ⊙ leads to a secondary mass of M =4.1 M ⊙ for i =90 ◦ and M =14 M ⊙ for i =23 ◦ . These limitsdictate that the secondary (MT91 403b) is a probable B star. Figure 15 shows the best-fittingorbital solution and folded velocity curve. MT91 417B (Schulte
MT91 417 is a visual double consisting of MT91 417A(O3I; the northwest component) and MT91 417B (O6V; the southeast component) at aseparation of 1 . ′′ ∼ ≃ ◦ . We obtained14 spectra of MT91 417B at WIRO in good seeing conditions between 2013 August 6 and2014 May 26 with the 1 . ′′ P =38.0 ± K =9.5 ± − . Figure 16 shows the best-fitting orbitalsolution and folded velocity curve. The implied secondary (MT91 417B-b) minimum massis 1.8 M ⊙ for i =90 ◦ . The secondary mass approaches that of the primary for i =5 ◦ . Thevelocity curve is not well-sampled at all phases so the derived parameters are particularlyuncertain. MT91 448—
A period of P =3.1704 ± ± − and a low eccentricity of e =0.10 ± i =90 ◦ yields a minimum secondary (MT91 448b) mass M =2.1 M ⊙ , while the secondary mass approaches that of the primary for i =6 ◦ . Figure 17shows the best-fitting orbital solution and folded velocity curve data. MT91 473—
This O8.5V has three measurements from Keck (1999–2000), nine fromWIYN (2000–2008) and 24 from WIRO (2010–2013). The power spectrum is complex,showing multiple peaks on timescales of 2000 d to 1.9 d. The dominant peak at 1700 d 11 –yields a folded velocity curve that appear consistent with the long-term trends observed inan unphased velocity curve. The WIRO data alone suggest a period in this same vicinity. AMonte Carlo simulation wherein the Julian dates are shuffled randomly among the observedvelocities shows that in only 1.3% of the iterations does the peak in the power spectrumexceed the observed one. We conclude that the observed periodicity is highly likely tobe real. Our best-fitting orbital solution gives a period of P =1687 ±
51 d and amplitude K =7.5 ± − . Figure 18 shows the best-fitting orbital solution and folded velocitydata.Smaller peaks in the power spectrum suggest the possibility of short-period variationson the ∼ I λ I λ ◦ , such that the line splitting doesnot exceed the observed values. MT91 473c is the unseen companion responsible for theradial velocity curve shown in Figure 18. Adopting masses of 19 M ⊙ for each of componentsa and b implies a mass of 5.0 M ⊙ for i =90 ◦ , meaning that the secondary must be at least amid-B star. For inclinations as small as 11 ◦ the mass of component c could approach thatof a+b. MT91 485—
MT91 485 is an O8V showing long-term radial velocity variations with P =4066 ±
45 d and semi-amplitude K =15.0 ± − based on two Keck measurements,nine WIYN measurements, and 17 WIRO measurements covering the period 2001 Augustthrough 2013 October. We found it necessary to fix the eccentricity during fitting to avoidextremely large values. We estimate e =0.75 ± ⊙ for the primary mass, theinclination of i =90 ◦ leads to a secondary mass of M =11.4 M ⊙ . M approaches M for i =40 ◦ .The secondary, MT91 485b, must be more massive than an early-B dwarf star. MT91 485is an example of a highly eccentric system that could easily be missed in a radial velocitysurvey if it were not for fortuitous phase coverage. 12 – MT91 555—
One of the long-term radial velocity variables in the survey, MT91 555(O8V) has a period P =1279.5 ± K =20.4 ± − .Figure 20 shows the best-fitting orbital solution and folded velocity data using 1 datumfrom Keck, 7 from WIYN, and 20 from WIRO. Adopting a primary mass of 21 M ⊙ yieldsa minimum secondary mass M =10.3 M ⊙ , meaning that the secondary (MT91 555b) isconstrained to be about B2V or earlier. For i =34 ◦ the secondary mass approaches that ofthe primary. MT91 561—
A B2V, the primary star of MT91 561 shows a period of P =40.09 ± ± − using 17 WIRO data points between 2007and 2013. Figure 21 shows the best-fitting orbital solution and folded velocity curve. For anadopted primary mass of 11 M ⊙ , the secondary mass is M =3.3 M ⊙ if i =90 ◦ . M approaches M when i =23 ◦ . This constrains the secondary (MT91 561b) to be a least as massive as alate B main sequence star, and the mass ratio lies in the range q =0.30–1. MT91 588—
This B0V has a moderately eccentric orbit with P =245.1 ± e =0.51 ± ± − using one measurement from Keck, fourfrom WIYN, and 16 from WIRO over the period 1999–2013. Figure 22 shows the best-fittingorbital solution and folded velocity data. Adopting a primary mass of 18 M ⊙ yields a mini-mum secondary mass M =3.2 M ⊙ , meaning that the secondary (MT91 588b) is constrainedto be an early A star or earlier. For i =15 ◦ the secondary mass approaches that of the pri-mary. The sampling of the velocity curve is such that aliases of 34.9 d, 69.8 d, 104 d, 174 dare possible but less likely. MT91 601—
The two Keck, one WIYN and 28 WIRO data of this O9.5III reveal a periodof 510.2 ± K =12.8 ± − . Owing to the incomplete phase coverage, wefound it necessary to fix the eccentricity (at 0.67) to avoid extremely large eccentricities thattended to result during the fitting process. Manual experimentation suggests an eccentricityuncertainty of ∼ ⊙ yields a minimum secondary mass M =4.1 M ⊙ ,meaning that the secondary (MT91 601b) is likely a B or O main sequence star. The reduced χ of the fit is unusually large, at 3.4. We examined the O-C residuals for signs of periodicity,but no strong peaks were seen. We conclude that this evolved primary star exhibits irregularphotospheric variations in addition to the identified periodic modulation. MT91 646—
Classified as B1.5V in both Massey & Thompson (1991) and Kiminki et al.(2007), spectra of this system reveal a variable line width indicating an SB2. In several ofour 19 WIRO spectra the lines are sufficiently separated to see that the line depths andwidths are similar, having a FWHM near 2.9 ˚A. We fit the most deblended of the 19 WIROspectra with two-component fixed-width Gaussian profiles to measure velocities for each 13 –component. The solution yields a period of P =49.8 ± K =61.6 ± − and K =79.6 ± − . This implies a mass ratio of q =0.77 ± ⊙ , consistent with a B1V and B1.5V seen at a highinclination. As such, MT91 646 is one of the most “twinlike” systems among the Cyg OB2sample. MT91 745—
This O7V has two observations from Keck, eight from WIYN, and 22 fromWIRO over 1999–2013, yielding a period P =151.2 ± K =17.5 ± − , and eccentricity e =0.49 ± ⊙ , the implied lower limit to thesecondary mass is M =4.0 M ⊙ for i =90 ◦ . M approaches M for i =15 ◦ . Thus, the secondary(MT91 745b) is at least the mass of a B dwarf star. Garmany et al. (1980) noted that some of their O-star sample exhibited irregular ratherthan periodic velocity variations. This phenomenon is quite common in massive stars, espe-cially evolved stars, and has been attributed to line profile variations caused by non-radialpulsations or clumps in the stellar winds (Vogt & Penrod 1983; Fullerton et al. 1996). Wenote here six objects that have more than 18 data measurements where significant velocityvariations at the level of 25–30 km s − are observed, but no strong periodicity is evident.Table 7 lists the Heliocentric Julian dates, velocities, and velocity uncertainties of each mea-surement. MT91 138—
The two Keck data, eight WIYN data, and 22 WIRO data between 1999 and2008 show that this O8I displays a low level of irregular variability. A long-term, eccentricbinary cannot be ruled out.
MT91 417A (Schulte
This O3If shows variations at the level of about 25 km s − on the basis of 20 WIRO data from 2008 and 2014. Our lack of long-term data prevents usfrom ruling out the possibility of longer term orbital variations. We can only say that theobserved variations appear random on the basis of the data presented in Table 7. Becauseof the very weak He I lines in this very hot star, velocities are measured from He II λ I should not be present in such a hot star, butlight from the PSF wings of MT91 417B may contaminate some of our spectra given theclose 2 ′′ separation. MT91 457—
One Keck, four WIYN, and 11 WIRO data on this O3If during 1999–2008 14 –show that this star exhibits non-periodic variations at the level of ∼
25 km s − . MT91 483—
This O5I/III shows low-amplitude (15 km s − ) variations but exhibits poweron many scales from days to months using three data from Keck, three from WIYN, and 25data from WIRO over 1999 - 2013. We show, using a Monte Carlo analysis which randomlyshuffles the dates of observation among the observed velocities, that the peaks near 124 daysand five days have at least a 0.32 probability of occurring by chance. Because of the weakHe I lines in this very hot star, velocities are measured from He II λ MT91 556—
MT91 556 was observed 40 times between 2008 and 2013 at WIRO withan average velocity uncertainty of 4 km s − and variations of up to 20 km s − . Althoughvelocity variations are observed in this B1I, there is no dominant periodicity and they areconsistent with random atmospheric fluctuations. MT91 632—
MT691 32 was observed 30 times between 2008 and 2011 at WIRO with anaverage velocity uncertainty of 3 km s − . Although velocity variations are observed in thisO9I at the level of 25 km s − , there is no dominant periodicity and they are consistent withrandom atmospheric fluctuations. We report here 16 stars having at least 12 velocity measurements spanning at least fiveyears that show no evidence for velocity variations. These stars are candidates for singlestars, stars with very low-mass companions, or systems seen at very low inclination angles.Among this list there may be undetected binaries with long periods and/or highly eccentricorbits. Additionally, systems with periods near multiples of one year undergoing periastronduring December–April when Cygnus is minimally observable have a low probability of beingdetected in this survey. For each non-variable system we report the mean velocity, the rmsvelocity dispersion, and the mean velocity uncertainty.
MT91 005—
This O6V was observed twice at Keck, three times at WIYN, and ten timeswith WIRO over the period 1999–2013. The radial velocities have a mean systemic velocityof − − , an rms of 2.1 km s − and mean uncertainties of 2.5 km s − . The very narrowlines (1.9 ˚A FWHM) suggest that the rotational axis may be nearly parallel to the line ofsight. MT91 020—
Twelve measurements at WIRO, four from Keck, and two from WIYNspanning 1999–2011 show no evidence for variability, with a mean velocity of − − , 15 –an rms of 4.3 km s − , and mean uncertainties of 4.2 km s − . MT91 083—
With 22 measurements at three observatories spanning 1999–2008, this B1Istar shows no evidence for variability. The mean systemic velocity is − − , with anrms of 1.7 km s − and mean uncertainties of 2.4 km s − in the nine WIRO data, one Keckdatum, and 7 WIYN data. MT91 217—
Having two measurements from Keck, seven from WIYN, and 17 fromWIRO spanning 1999–2011, this O9V star shows no evidence for variability. The meansystemic velocity is − − , with an rms of 2.4 km s − and mean uncertainties of 3.0km s − . MT91 227—
Two data from Keck, six from WIYN, and 26 from WIRO over the period1999–2011, are remarkably constant for this O9V. The mean velocity is − − withan rms of 5.5 km s − and mean uncertainties of 5.1 km s − . MT91 259—
One Keck, six WIYN, and seven WIRO data over the period 1999–2011show a mean velocity of − − with an rms of 1.3 km s − and mean uncertainties of2.1 km s − . MT91 299—
This O7V has two data from Keck, six from WIYN, and 37 from WIRObetween 1999 and 2013. The mean velocity is − − with an rms of 6.0 km s − and atypical velocity uncertainty of 5.5 km s − . This object shows some evidence for a periodicitynear 405 days, but the amplitude is low compared to the observational uncertainties, and aconvincing orbital solution was not obtained. MT91 317—
This O8V has two data from Keck and 11 from WIYN between 1999 and2007. The mean velocity is − − with an rms of 4.4 km s − and a typical velocityuncertainty of 5.5 km s − . This object shows some evidence for a periodicity near 405 days,but the amplitude is low compared to the observational uncertainties, and a convincingorbital solution was not obtained. MT91 376—
On the basis of two Keck and 10 WIYN data over the period 1999–2006this O8V shows a mean velocity of − − and rms of 6.2 km s − for a mean velocityuncertainty of 7.5 km s − . MT91 455—
This O8V has two data from Keck, 3 from WIYN, and 20 from WIRObetween 1999 and 2013. The mean velocity is -12.2 km s − with and rms of 3.3 km s − anda mean velocity uncertainty of 3.6 km s − . MT91 462—
This O7III has 12 data from from WIRO between 2008 and 2014. Themean velocity is -11.9 km s − with and rms of 2.8 km s − and a mean velocity uncertainty 16 –of 4.1 km s − . MT91 470—
Two measurements from Keck, five from WIYN, and nine from WIRO overthe the period 1999–2013 show no evidence for velocity variations beyond the uncertainties.The mean velocity is − − with an rms of 6.9 km s − and a mean velocity uncertaintyof 5.2 km s − . MT91 480—
We measured both He I and He II velocities for this broad-lined O7V using4 WIYN and 14 WIRO data between 2001 and 2013, finding no compelling evidence forvelocity variations. The line profiles are broad and appear to vary without evidence ofperiodicity. The mean velocity is − − with an rms of 13.3 km s − and a meanvelocity uncertainty of 11.7 km s − . MT91 507—
Two Keck, two WIYN, and 14 WIRO data between 1999 and 2013 yield amean velocity of − − with an rms of 5.1 km s − and a mean velocity uncertainty of6.5 km s − for this O9V star. MT91 534—
Three Keck, two WIYN, and 14 WIRO data between 1999 and 2013 yielda mean velocity of − − with an rms of 3.8 km s − and a mean velocity uncertaintyof 3.1 km s − for this O8.5V star. MT91 611—
Two Keck and 14 WIYN data between 1999 and 2008 yield a mean velocityof − − with an rms of 3.7 km s − and a mean velocity uncertainty of 3.9 km s − for this O7V. The Cygnus OB2 Radial Velocity Survey was designed to produce a complete cen-sus of massive binaries drawn from a photometrically selected sample, namely that ofMassey & Thompson (1991). The parent sample contained 150 stars—the 146 listed inTable 1 of Paper I plus MT91 267 (inadvertently excluded initially but reported as a binaryin Paper VI), MT91 417B (not initially recognized as a close companion to MT91 417A),Schulte
We estimated the completeness of the Survey as a function of orbital period using aMonte Carlo analysis identical to that described in Kiminki & Kobulnicky (2012). Our codegenerates populations of binary systems with periods 1 – 5000 days having mass ratios andeccentricities described by power laws: Prob( q ) ∝ q α , and Prob( e ) ∝ e γ . The nominal power-law exponents are α ≃ γ ≃
0, as inferred, in part, by Kiminki & Kobulnicky (2012)and strengthened by the additional data in this work. A random inclination is assigned toeach system before being sampled at the actual dates and times of the Survey observations.A nominal detection threshold of 7 km s − is used to determine whether the system wouldbe observed as a binary in the Survey. This is lower than the more conservative value of15 km s − used in Kiminki & Kobulnicky (2012), but it better represents the sensitivity ofthe data to radial velocity variability given the typical resolutions of R ≃ − FWHM) achieved in the majority of WIRO spectra. Velocity precisions of better than 0.1 ofthe spectral FWHM are typically attained by centroiding on the strong He I λ − in some objects where rotation broadens the line profile. Uponcareful examination, the detection threshold is really a complex function of the signal-to-noise ratio of the spectra, the spectral type of the star, and the breadth of the spectralfeatures (i.e., rotational velocity); nevertheless, the adopted value of 7 km s − is generallyapplicable as a Survey average, while 15 km s − is a conservative value.Figure 26 displays the completeness as a function of orbital period, where completeness 18 –is defined as the ratio of detected binaries to all binaries of the same period in the synthesizedpopulation. Different line styles depict different values for the power law exponent γ anddifferent choices for the detection velocity threshold. Completeness exceeds 80% for systemswith P <
100 days in the case of a 7 km s − detection threshold and is only ∼
10% lower forthe conservative threshold of 15 km s − . At P =1000 d we find that 40–60% of binaries arestill detected. The smooth decline in completeness with orbital period reflects the difficultyin detecting wide, long-period systems. While the completeness estimates are only as valid asthe input power-law assumptions for the mass ratio and period distributions, the conclusionthat the vast majority of systems with periods less than a few hundred days have beendetected is a robust one. Completeness estimates beyond about 2000 d should be regardedas highly uncertain.
4. Discussion and Analysis of the Orbital Parameters from Cyg OB24.1. Summary of Binaries
Table 8 summarizes the spectroscopic binary type (SB1/SB2), spectral types for thecomponents, orbital period, primary semi-amplitude, eccentricity, and mass ratio constraintsfor all 48 massive multiple systems now known in Cygnus OB2. Twenty three are new resultsfrom this work, twenty are reported in previous papers in this series, and five stem from otherpublished works. The final two columns provide references to published orbital solutions andadditional notes on each system. The table contains six stars not initially included in Table 1of Kiminki et al. (2007) among the unbiased list survey targets. MT91 267 and MT91 417B,explained in Section 3.4 constitute two of these. The double-lined system CPR2002 B17 wasreported and analyzed by Stroud et al. (2010). Schulte
Figure 28 shows the observed distribution of orbital eccentricities for the full sample of48 Cyg OB2 binaries. The left-hand y-axis labels and the plotted points shows the cumu-lative fraction. The right-hand y-axis and plotted histogram shows the number of objectsin each eccentricity bin. The distribution is approximately uniform (Prob( e ) ∝ e ) between e = 0 and e ≃ . < e < .
6. We also employed the Anderson-Darling (A-D) two-sample statistic which ismore sensitive to differences between two populations when differences in the the cumulativedistributions are both positive and negative across the sample range, or when these differ-ences occur near the ends of the distributions. The A-D statistic concurs that the probabilityof the eccentricities being drawn from a uniform distribution between 0 . < e < . e < . − γ , the power law exponent describing the eccentricity distribution. Completenessis shown to be insensitive to γ . Nevertheless, a few long-period, high-eccentricity systems The Anderson-Darling statistic and its advantages over the K-S statistic are described in more de-tail at Feigelson & Babu (2012). We use the code in the Python scipy.stats package to compute the A-Dprobabilities.
20 –have likely evaded detection with the current dataset. Unless there are an disproportionatenumber of high- e systems in Cyg OB2, the e distribution can be described as approximatelyuniform out to periods of ∼ The distribution of mass ratios among our sample can be recovered, statistically, usingMonte Carlo methods, by assigning randomly chosen inclinations on the unit sphere. In mostcases an upper limit on the inclination is estimated by either the observed eclipse profile orthe lack of observed eclipses; for long-period systems the upper limit on the inclination iseffectively 90 ◦ . A lower limit on the inclination is obtained by letting the mass of the sec-ondary approach that of the primary; the lack of observed spectral features from a secondarystar is a weak constraint on this lower bound. For each system we use the measured orbitalperiod, adopted primary mass, observed velocity amplitude, and a random inclination be-tween the observationally imposed limits to solve for the mass of the secondary star. Themean value of q is then computed after 1000 such iterations for each system. Figure 29shows the resulting histogram of mass ratios. The overall distribution is approximately uni-form. However, incompleteness appreciably affects the bins at q . .
2, so the true numberof binaries in these bins is highly uncertain. Given the large uncertainties on any individualmass ratio value, we elect not to pursue a statistical analysis of these data. In principle wecould estimate the completeness factor at q < . Figure 30 displays the observed cumulative distribution of orbital periods (in log P )for the full sample of 48 massive (B3 and earlier) systems in Cyg OB2 (filled circles), Ostars from six Galactic open clusters (Sana et al. 2012, plusses), and bright O stars drawnfrom the general Galactic population from Garmany et al. (1980, open squares). Fiducialmarks near the top of the plot indicate the period in days. Other annotations mark thecorresponding semi-major axis for the given period, assuming a total system mass of 30 M ⊙ . 21 –The Garmany et al. (1980) sample has been normalized by a factor of 1.5 to allow bettercomparison with the other two surveys in the short-period limit where all three are highlycomplete. Both the Sana et al. (2012) sample and the Cyg OB2 sample are reasonablycomplete to periods of several hundred days, while the Garmany et al. (1980) sample lackssuch longer-period systems—a consequence of the limited observing campaign. A constantslope in this plot corresponds to a uniform distribution in log P . A steeper slope means alarger number of detected binaries per log P interval than a shallower slope.The observed cumulative period distributions for the three samples appear remarkablysimilar at short periods, rising rapidly with similar slope from a short-period limit of about1.4 days to near 7 days. An A-D test shows that the Cyg OB2 and Sana et al. (2012)observed distributions have a 91% chance of being drawn from the same parent populationsin this range, increasing to 97% if the complete instead of the unbiased Cyg OB2 sampleis used. All three samples show an abundance of short-period binaries, noted previouslyby Kiminki & Kobulnicky (2012); Sana et al. (2012); Zinnecker & Yorke (2007). All threesamples also show a flattening of the slope beginning at about 6 days. The Cyg OB2 sampleexhibits the most pronounced flattening between 6 and 14 days, indicating a paucity ofsystems in this range, as noted previously by Kiminki & Kobulnicky (2012). There is thenan upturn between 14 and ∼
45 days, with a slope approximately matching that of thevery short-period systems. The Sana et al. (2012) and Garmany et al. (1980) samples, bycontrast, show lesser degrees of flattening longward of six days, with the former being steeperthan the latter. The limited number of data points precludes any strong statement regardingthe similarity of the three samples in this restricted range, or the reality of the change inslope near six days.Both the Cyg OB2 and the Sana et al. (2012) samples flatten or exhibit a break near 45d. The Garmany et al. (1980) sample has become considerably incomplete at these periodsand is not considered further. Both samples exhibit similar slopes out to periods of sev-eral thousand days where both become significantly incomplete. Sana & Evans (2011) andSana et al. (2012) considered the possibility that period distribution could be characterizedby a double- ¨Opik (i.e., uniform in log P ; ¨Opik 1924) distribution with a break near 10 days,however they found that such a description did not provide a better fit to the data. Correc-tions for observational bias (i.e., incompleteness) become important at periods greater thanseveral hundred days, and we address these in the context of the Cyg OB2 sample below. 22 – A two-sample Anderson-Darling test shows that the Cyg OB2 and the Sana et al.(2012) observed cumulative distributions are individually consistent with uniform (in logP given by β = 0) between 1.4 and 45 days at the 42% and 45% levels, respectively; theCyg OB2 and Sana et al. (2012) samples becomes consistent with uniform at the 86% and62% level for periods <
25 days. The Cyg OB2 and Sana et al. (2012) samples are consistentwith each other at the 91% levels for
P <
25 d but only 19% for
P <
45 d. The Cyg OB2and the Garmany et al. (1980) samples are consistent with each other at the 40% and 5%levels for upper period limits of 25 d and 45 d, respectively. Taken together, these statisticsindicate that the period distributions in the Cyg OB2 and Sana et al. (2012) surveys areprobably consistent with each other
P <
25 d, but not at
P >
25 d and are not consistentwith a uniform distribution even at the shortest periods.When all three surveys are combined, the probability that the combined sample isconsistent with uniform drops to 14% and 21% for upper period limits of 25 d and 45 d,respectively. We interpret this to be evidence for structure in the period distribution thatbecomes apparent with sufficiently large numbers. Thus, the period distribution does notappear to be scale-free; it is suggestive of features imposed by physical phenomena occurringduring the formation and/or evolution of massive systems.The most obvious feature in the period distribution at
P <
45 d is the flattening of theslope near 6 days seen in all three datasets. Kiminki & Kobulnicky (2012) characterized thisstructure as a possible excess of 3–6 d systems accompanied by a deficit of 7–14 d systems,observed here as a flattening of the slope of the cumulative distribution over that range inall three samples. This possible feature seen in the Cyg OB2 distribution is not as obviousin the other two data sets. Incompleteness in Garmany et al. (1980) sample, though notexplicitly quantified in that work, probably begins in the 15–30 d range and could easilymask such a signal if it were present. By contrast, the completeness of the Cyg OB2 surveyis >
90% for
P <
10 d. The reality of such a signal in the Sana et al. (2012) sample is uncertainowing to the small number of points between 6 d and 45 d (10 systems), even though thesample is likely to be similarly complete. We conclude that the Cyg OB2 period data is notconvincingly consistent with uniform (a single power law of slope zero) at
P <
45 d. There is We use the Anderson-Darling statistic exclusively hereafter in lieu of the more popular but more prob-lematic Kolmogorov-Smirnov statistic. We find that the K-S statistic yields similar probabilities to theA-D statistic when when the cumulative distributions are smooth; the A-D statistic yields lower probabil-ities of the null hypothesis that the two distributions are drawn from the same parent population whenthe cumulative distributions show multiple points of inflection. This is consistent with the discussion inFeigelson & Babu (2012).
23 –evidence for structure in the form of a 3–6 d period ”excess” and the 6–14 d period “deficit”that becomes more pronounced when the three samples are combined.In the period range 60 – 4000 d the Cyg OB2 and Sana et al. (2012) samples, as observed,are consistent with uniform at the 94% and 55% levels. The two samples are consistent witheach other at the 99% level. By contrast, over the full period range 1.4 – 5000 days, bothsamples are inconsistent with uniform, having a < β = 0 power law is a poor description of the observed perioddistribution over the full range, but observational biases against detection of long-periodsystems must be considered before strong conclusions may be drawn. Figure 31 (lower panel) shows the observed cumulative period distribution for the unbi-ased sample of 45 systems as observed (filled symbols) and after correction for completeness(open symbols) as described by completeness curve in Figure 26 using the solid line repre-senting the 15 km s − (most conservative) detection threshold. The y-axis is now scaled toindicate the fraction of the total number of stars in the unbiased Cyg OB2 sample. Thecorrection from observed to underlying period distribution is performed by tabulating thecumulative incompleteness (1-completeness) at the location of each observed system, N,starting from the shortest periods, and inserting an additional “system” when the cumula-tive incompleteness reaches an integer value; systems are added at periods halfway betweenthe period of system N and N-1. This can result in the appearance of two or more systemsplotted at the same orbital period when the completeness is low (i.e., for long periods).Open symbols in Figure 31 trace a curve similar to the filled symbols until the correctionfor completeness becomes a large factor beyond about 2000 days. The difference betweenthe filled and open symbols is small for periods less than a few hundred days but approaches20% at the 5000-day limit of the Survey. The open symbols display an apparent change inslope near 45 days, indicating that the putative break in the cumulative distribution is notlikely to be caused by observational biases. Under the adopted prescriptions for the massratio distribution (i.e., uniform) and the eccentricity distribution (i.e., uniform) adopted inthe Monte Carlo modeling, this figure shows that the binary fraction reaches 30% by P =45d. Fifty-five percent of the systems are binaries with periods less than 5000 days. This isnearly identical to the binary fraction of 51% computed for O stars in the Large MagellanicCloud (Sana et al. 2013) and may indicate that the binarity characteristics of massive starsare insensitive to metallicity. An extrapolation of the quasi-linear trend defined by systemswith P >
100 days would suggest a binary fraction near 70% for systems with periods less 24 –than 10 days. On the other hand, a naive extrapolation of the much steeper slope at P < days.We used the A-D test to quantify the probability of a change in slope of the completeness-corrected cumulative period distribution by comparing it to a hypothetical uniform (i.e.,linear) distribution in a moving window of encompassing seven observed systems. Windowwidths of five to nine do not appreciably change the results. Figure 31 (upper panel) plots theprobability that the completeness-corrected period distribution is consistent with uniform.The probability drops below 1% (2.6 σ , shown by the dotted horizontal line) in the vicinity ofthe hypothesized 45-day break. The low probability near six days and 14 days supports thehypothesis of a change slope near these locations as well. The similarity of the Cyg OB2 andthe Sana et al. (2012) observed cumulative distribution slopes above 45 days in Figure 30 isnoteworthy as is the apparent flattening near 45 days ( ≃ > β = − . β ≃ − .
22 power law is not anunreasonable approximation over 3.3 orders of magnitude in period (1.4 days to 2000 days),even if it does not describe the fine details of the distribution at a statistically compellinglevel of significance.We conclude by noting that the agreement between the observed orbital period dis-tributions of the Cyg OB2 sample, where OB stars formed across an extent of nearly 50pc, compared to the Sana et al. (2012) sample from several young Galactic clusters, sug-gests that the large-scale physical environment does not determine the orbital parametersof massive binaries formed therein. This stands in contrast to suggestions that the binaryfraction depends on local stellar density, being lower in the densest regions (Sana et al.2008; Zinnecker & Yorke 2007). Rather, the small-scale physics of cloud collapse and frag-mentation on the sub-A.U. scale appear more important in establishing the high fraction of 25 –binaries among massive stars and their mass ratio distribution which clearly shows that mas-sive stars preferentially have massive companions. The results of the massive star surveysstand in stark contrast to those from radial velocity surveys of solar-type stars where thedistribution of periods is log-normal with a mean of 180 years (Duquennoy & Mayor 1991).The inflections in the cumulative period distribution near 0.2 A.U. and near 0.9 A.U. aresuggestive of key physical size scales beyond which the formation of close massive binariesbecomes less efficient.
5. Conclusions
The addition of 23 new massive binary orbital solutions presented herein raises the totalnumber known in the Cygnus OB2 Association to 48. This is the largest collection of com-plete solutions obtained within a single environment and constitutes a substantial fractionof all early type orbits published to date. At least 35% of massive systems in Cyg OB2 arebinary or higher-order multiples, with several more long-period or highly eccentric systemsexpected to be discovered. The number of unobserved high-inclination or extreme-mass-ratiosystems has been modeled statistically. These computations suggests that the true binaryfractions are near 55% for periods P ≤ P < d.The distribution of orbital periods is described as approximately uniform in log P between the short-period limit of 1.2 d and ≃
45 d, but there is evidence for structure inthis distribution, with an excess of 3–6 d systems and a possible dearth of 7–14 d systems,along with a break near 45 days. Between 45 d and the long-period survey limit of ∼ β = − .
22 also provides a rough description ofthe cumulative period distribution between 1.4 and ∼ γ -ray bursts. It is our hope that suchmodels may now be grounded more solidly in the data. This compilation may also provehelpful in guiding models of massive star formation and evolution by providing observationalconstraints on the binary frequency and distribution of periods and mass ratios among early-type systems. We expect that there are several more discoverable binary (and multiple)systems among the Survey targets, but this present compilation likely contains the vastmajority of systems discoverable using radial velocity techniques.Insightful comments from an expert anonymous referee greatly improved this manuscript.We thank our long-term collaborator Chris Fryer for continued encouragement, in particularfor a timely conversation after a colloquium at UC Santa Cruz in 1998 that launched theCygnus OB2 Radial Velocity Survey. We acknowledge continued support from the NationalScience Foundation through Research Experience for Undergraduates (REU) program grantAST 10-63146, through grant AST 03-07778, and grant AST 09-08239. The Wyoming NASASpace Grant Consortium provided student support through grant Facilities:
WIRO (), WIYN (), Keck:I ()
REFERENCES
Blaauw, A. 1961, BAN, 15, 265Chini, R., Hoffmeister, V. H., Nasseri, A., Stahl, O., & Zinnecker, H. 2012, MNRAS, 424,1925 27 –Comer´on, F., Pasquali, A., Rodighiero, G., et al. 2002, A&A, 389, 874Contreras, M. E., Rodriguez, L. F., Tapia, M., Cardini, D., Emanuele, A., Badiali, M., &Persi, P. 1997, ApJ, 488, 153De Becker, M., Rauw, G., & Manfroid, J. 2004, A&A, 424, L39Dominik, M., Belczynski, K., Fryer, C., HOlz, D. E., Berti, E., Bulik, T., Mandel, I., &O’Shaughnessy, R. 2013, arXiv:1308.1546Drilling, J. S., & Landolt, A. U. 2000, in Astrophysical Quantities, ed. A. N. Cox (4th ed.;New York; Springer), 381Duquennoy, A., & Mayor, M. 1991, A&A, 248, 485Eldridge, J. J., Fraser, M., Smartt, S. J., Maund, J. R., & Crockett, R. M. 2013, MNRAS,436, 774Feigelson, E. D. & Babu, G. J., 2012, “Modern Statistical Methods for Astronomy with RApplications”, Cambridge Univ Press (Chpt 3)Fullerton, A. W., Gies, D. R., & Bolton, C. T. 1996, ApJS, 103, 475Fryer, C. L., Mazzali, P. A., Prochaska, J., et al. 2007, PASP, 119, 1211Garmany, C. D., Conti, P. S., & Massey, P. 1980, ApJ, 242, 1063Gies, D. R., & Bolton, C. T. 1986, ApJS, 61, 419Gonz´alez, J. F., & Levato, H. 2006, A&A, 448, 283Hall, D. S. 1974, AcA, 24, 69Hanson, M. M. 2003, ApJ, 597, 957Hoogerwerf, R., de Bruijne, J. H. J., & de Zeeuw, P. T. 2001, A&A, 365, 49Hora, J., Adams, J., Allen, L., et al. 2007, Spitzer Proposal, 40184Hubeny, I., & Lanz, T. 1995, ApJ, 439, 875Hunter, I., Lennon, D. J., Dufton, P. L., et al. 2008, A&A, 479, 541Kiminki, D. C. 2010, Ph.D. Thesis, University of WyomingKiminki, D. C., et al. 2007, ApJ, 664, 1120 (Paper I) 28 –Kiminki, D. C., McSwain, M. V., & Kobulnicky, H. A. 2008, ApJ, 679, 1478 (Paper II)Kiminki, D. C., Kobulnicky, H. A., Gilbert, I., Bird, S., Chunev, G. 2009, AJ, 137, 4608(Paper III)Kiminki, D. C., Kobulnicky, H. A., Ewing, I., et al. 2012, ApJ, 747, 41 (Paper IV)Kiminki, D. C., & Kobulnicky, H. A. 2012, ApJ, 751, 4 (Paper V)Kobulnicky, H. A., & Fryer, C. L. 2007, ApJ, 670, 747Kobulnicky, H. A., Smullen, R. A., Kiminki, D. C., et al. 2012, ApJ, 756, 50 (Paper VI)Kobulnicky, H. A., Kiminki, D. C., et al. 2014, ApJ, in prepKouwenhoven, M. B. N., Brown, A. G. A., Portegies Zwart, S. F., & Kaper, L. 2007, A&A,474, 77Lanz, T., & Hubeny, I. 2003, ApJS, 146, 417Markwardt, C. B. 2009, Astronomical Data Analysis Software and Systems XVIII, 411, 251Martins, F., Schaerer, D., & Hillier, D. J. 2005, A&A, 436, 1049Mason, B. D., Hartkopf, W. I., Gies, D. R., Henry, T. J., & Helsel, J. W. 2009, AJ, 137,3358Massey, P., & Thompson, A. B. 1991, AJ, 101, 1408Miczaika, G. R. 1953, PASP, 65, 141Naz´e, Y., De Becker, M., Rauw, G., & Barbieri, C. 2008, A&A, 483, 543Naz´e, Y., Mahy, L., Damerdji, Y., et al. 2012, A&A, 546, A37Nomoto, K. I., Iwamoto, K., & Suzuki, T. 1995, Phys. Rep., 256, 173¨Opik, E. J. 1924, Tartu Obs. Publ., 25Otero, S. 2008a, Open European Journal on Variable Stars, 83, 1Otero, S. 2008b, Open European Journal on Variable Stars, 91, 1Pigulski, A., & Kolaczkowski, Z. 1998, MNRAS, 298, 753Rauw, G., Vreux, J. M., & Bohannan, B. 1999, ApJ 517, 416 29 –Rios, L. Y., & DeGioia-Eastwood, K. 2004, BAAS, 205, No. 09.05Romano, G. 1969, MmSAI, 40, 375Sana, H., & Evans, C. J. 2011, IAU Symposium, 272, 474Sana, H., Gosset, E., Naz´e Y., Rauw, G., & Linder, N. 2008, MNRAS, 386, 447Sana, H., de Mink, S. E., de Koter, A., et al. 2012, Science, 337, 444Scappini, F., Cecchi-Pestellini, C., Casu, S., & Olberg, M. 2007, A&A, 466, 243Sana, H., de Koter, A., de Mink, S. E., et al. 2013, A&A, 550, A107Schulte, D. H. 1958, AJ, 128, 41Smartt, S. J., Eldridge, J. J., Crockett, R. M., & Maund, J. R. 2009, MNRAS, 395, 1409Smith, R. J., Longmore, S., & Bonnell, I. 2009, MNRAS, 400, 1775Smith, N. 2014, arxiv.org/abs/1402.1237Stroud, V. E., Clark, J.S., Negueruela, I. , Roche, P., & Norton, A.J. 2009, A&A, 511, 84van den Heuvel, E. P. J. 1983, Accretion-Driven Stellar X-ray Sources, 303Vogt, S. S., & Penrod, G. D. 1983, ApJ, 275, 661Walborn, N. R. 1973, ApJ, 180, L35Walborn, N. R. & Fitzpatrick, E. L. 1990, PASP 102, 379Wilson, O. C. 1948, PASP, 60, 385Wilson, O. C., & Abt, A. 1951, ApJ, 144, 477Woosley, S. E., & Bloom, J. S. 2006, ARA&A, 44, 507Wozniak, P. R., et al. 2004, AJ, 127, 2436, Northern Sky Variability Survey: Public DataReleaseZinnecker, H., Yorke, H. W. 2007, ARA&A, 45, 481
This preprint was prepared with the AAS L A TEX macros v5.2.
30 –
A. Re-analysis of Orbital Solutions for Systems from Papers II and III
In this Appendix we briefly re-analyze systems originally presented in Papers II and IIIfor purposes of self-consistency, using the methods employed in this work and incorporatingany new spectra, when available. Most of the solutions are essentially unchanged, but resultsare presented in a manner consistent with the solutions reported in Papers IV, VI, and inthis contribution. In three cases (MT91 252, S 73, CPR2002 A45), additional data allowedus to discover that the original solutions were aliases and to present a better solution.In this work, we disentangled the component spectra of double-lined binaries using themethod of Gonz´alez & Levato (2006). One of the strengths of this method is that the radialvelocities can be refined via cross correlation after each iteration (i.e, cross-correlating thethe residual spectra with the resultant component spectrum as the template). The cross-correlated velocities generally have smaller uncertainties and utilize more lines, leading to abetter measurement of the true stellar velocity and the binary systemic velocity.
MT91 059—
Table 9 lists the updated ephemeris and Table 10 provides refined orbitalelements for the single-lined binary MT91 059 originally presented in Paper II. Figure 32displays the best-fitting solution and folded velocity data. The original period of 4.85 d ischanged only slightly, but we note here the large reduced chi of 4.3 that indicates either anadditional velocity component or photosspheric variability. Attempts to identify periodicitiesin the observed-minus-computed velocities in Table 9 did not yield convincing evidence for anadditional velocity component. Hints of emission in the cores of the He I λ ∼ MT91 145—
Table 9 lists the updated ephemeris and Table 10 provides refined orbitalelements for this single-lined O9II star originally presented in Paper III. The orbital elementsare only slightly revised from the original published estimate. Figure 33 displays the best-fitting solution and folded velocity data.
MT91 252—
We identified this system as an SB2 in Paper II but could only performa limited analysis owing to the small number of spectra and low SNR of the data. Us-ing the technique described in this paper, we included 17 epochs of WIRO spectra and aKECK+HIRES spectrum to compute the solution listed in Table 11. The previously esti-mated period of 18–19 days has been revised to 9 . ± .
001 days. The power spectra forboth components showed an alias at ∼ ⊙ for the B1–2V components, the period and velocity amplitudes imply an inclination 31 –between 30 and 40 degrees. MT91 258—
Originally presented as an SB1 in Paper II, the updated ephemeris for this14.658 d O8V appears in Table 9 and the orbital parameters appear in Table 10. Figure 35displays the best-fitting solution and folded velocity curve. We attribute the unusually highreduced χ value to velocity zero point differences between data from different observatoriesused in the solution. MT91 372—
Identified as a 2.2 d binary in Paper III, this eclipsing double-lined systemis analyzed in greater detail in conjunction with the eclipsing binary distance to Cygnus OB2in a forthcoming work (Kobulnicky et al. 2014).
MT91 696—
An updated ephemeris for this eclipsing O9.5+B0V+B? triple system fromPaper IV will be presented in (Kobulnicky et al. 2014).
Schulte
An updated ephemeris for this eclipsing O6IV: + O9III system from PaperII will be presented in (Kobulnicky et al. 2014).
Schulte
This system was identified as a 17.28 day SB2 in Paper III. Velocitiesremeasured with the technique described in Papers IV, VI, and this work were used as theinitial guesses for the Gonz´alez & Levato (2006) method of spectral deconvolution and crosscorrelation for all WIRO data. Owing to the limited phase coverage of the WIYN+Hydraspectra, we did not apply the Gonz´alez & Levato (2006) method to these data. However,since the He I I ∼
10 days, ∼
17 days, ∼
57 days, and ∼
67 days. However, these were ruledout based on the large scatter in the corresponding folded velocity curves. The updatedsolution is provided in Table 11 and shown in Figure 36. We slightly revise the spectralclassifications, based on equivalent width ratios of He II I ∼ ◦ . CPR2002 A36—
An updated ephemeris for this eclipsing B0Ib + B0III system fromPaper III will be presented in (Kobulnicky et al. 2014).
CPR2002 A45—
Also identified as an SB2 in Paper III, this system was previouslylisted with a period of 2.884 days and an uncharacteristically high eccentricity of 0.273.Using the Gonz´alez & Levato (2006) spectral deconvolution method and some additionalobservations from WIRO, the revised radial velocities indicate a period near half the originalsolution. Both components’ power spectra show a singular strong signal at 1.5020 days. The 32 –final combined solution yields a period of 1 . ± . . ± .
02. The revised solution is listed in Table 11 and shown in Figure 37.We retain the primary spectral classification of B0.5V, but owing to the new, higher massratio of 0.72 ∼ ◦ . 33 –Table 1. Ephemerides for New Binary Systems V r σ V O − C Date (HJD-2,400,000) φ (km s − ) (km s − ) (km s − )MT91 02155418.648 0.367 -37.9 18.0 -0.2055489.731 0.695 1.9 17.9 -4.7755780.694 0.691 11.6 6.4 5.4755791.720 0.828 20.8 4.2 -1.3455805.681 0.267 -41.1 6.1 7.0956209.582 0.906 18.7 5.3 -1.9456215.552 0.522 -27.4 5.4 -9.8356446.902 0.372 -38.0 8.7 -1.0256461.683 0.896 48.6 10.6 26.7756463.804 0.115 -51.8 6.9 -4.2256466.758 0.419 -29.4 10.1 1.7756470.764 0.832 8.8 6.2 -13.6356472.721 0.034 -21.3 8.7 2.2556566.728 0.726 32.1 7.3 21.15MT91 18751467.858 0.166 -11.7 2.1 -0.8551805.908 0.149 -8.8 4.1 1.5552146.686 0.333 -17.3 4.1 -4.5052162.651 0.513 -14.6 2.9 -1.9653338.617 0.419 -15.7 5.0 -2.8353989.652 0.532 -13.4 4.2 -0.8454696.894 0.799 -8.3 2.3 0.8955791.858 0.720 -14.7 2.3 -3.8555805.801 0.750 -11.8 3.3 -1.5455836.692 0.033 -1.7 3.6 0.8756211.700 0.747 -8.6 3.2 1.7356215.635 0.038 -4.0 3.3 -0.9756494.713 0.662 -9.6 3.0 1.9656446.784 0.120 -8.0 4.3 1.2856459.737 0.077 -7.6 1.9 -0.9156462.891 0.311 -12.9 2.2 -0.1756463.903 0.385 -14.2 5.4 -1.3256470.884 0.901 -6.5 2.4 -1.4356472.752 0.039 -2.1 2.8 1.1456490.729 0.368 -5.9 3.2 7.0056493.744 0.591 -11.9 3.3 0.2656494.745 0.665 -9.6 3.0 1.9456495.752 0.739 -5.1 6.2 5.4456496.901 0.824 -8.7 4.2 -0.2056497.906 0.898 -2.9 2.8 2.32
34 –Table 1—Continued V r σ V O − C Date (HJD-2,400,000) φ (km s − ) (km s − ) (km s − )MT91 20254696.928 0.880 -15.9 16.5 -0.1354697.883 0.902 -18.9 15.4 0.5155781.847 0.065 -33.9 8.8 -0.9055836.786 0.340 12.1 21.8 16.1256247.641 0.878 -7.7 11.0 7.7356251.586 0.969 -32.8 8.9 -3.1756446.855 0.502 -6.2 15.2 -10.4556461.717 0.847 -21.2 11.2 -10.4256464.770 0.918 -23.3 15.6 -1.2856469.713 0.033 -25.5 16.2 8.3756489.726 0.497 7.2 12.4 3.1256491.691 0.543 7.1 19.8 2.0256504.789 0.847 -7.4 11.8 3.3956533.762 0.520 4.4 13.4 -0.2456566.612 0.282 -6.8 14.2 2.3556588.593 0.792 0.3 16.9 4.3556607.643 0.235 -18.7 11.9 -4.63MT91 23451467.855 0.288 -16.8 6.4 -2.7451805.911 0.356 -33.8 7.4 -13.4152146.686 0.424 -20.5 5.5 5.3052161.793 0.427 -22.3 4.8 3.7152162.851 0.427 -24.3 5.3 1.7353338.617 0.663 -40.0 5.3 -7.7553340.576 0.663 -33.9 4.1 -1.6653989.652 0.793 -13.4 4.7 11.0453990.848 0.793 -18.3 8.4 6.1254286.904 0.852 -28.5 5.3 -10.5354628.880 0.921 -15.5 7.1 -6.0654630.852 0.921 -5.4 4.9 3.9955713.928 0.138 -12.0 10.6 -11.1855717.858 0.139 -0.8 3.9 0.0255737.828 0.143 -3.6 5.7 -2.5055741.587 0.144 -1.3 5.5 -0.1255766.847 0.149 1.8 3.6 3.2755781.912 0.152 -3.3 8.3 -1.6255782.854 0.152 -0.2 4.7 1.4855795.453 0.154 -4.1 4.0 -2.2356118.661 0.219 -8.5 4.5 -1.2456166.369 0.229 -6.5 5.2 1.70
35 –Table 1—Continued V r σ V O − C Date (HJD-2,400,000) φ (km s − ) (km s − ) (km s − )56178.604 0.231 -8.2 5.8 0.2156460.868 0.287 -13.7 5.7 0.3356464.894 0.288 -19.4 4.8 -5.2956468.901 0.289 -12.8 5.8 1.34MT91 24151364.067 0.035 10.0 2.1 0.7251466.739 0.188 -12.0 1.4 -0.7151806.950 0.695 -26.7 4.1 0.6652161.793 0.224 -7.3 4.9 7.1653340.576 0.980 3.0 3.3 -1.7053989.774 0.948 -4.4 5.6 -0.7354286.901 0.390 -19.9 9.1 3.4254628.748 0.900 4.0 7.8 18.2256107.562 0.103 -0.4 2.6 0.0156240.279 0.301 -22.4 2.2 -2.9356258.544 0.328 -18.9 2.0 1.9556445.897 0.607 -27.1 2.2 0.4756463.763 0.634 -28.7 2.6 -1.0456471.705 0.646 -27.7 2.5 -0.0756472.675 0.647 -25.5 4.2 2.1656475.891 0.652 -26.8 2.6 0.7956555.611 0.771 -29.1 2.8 -3.4156590.618 0.823 -22.8 1.8 0.1956608.615 0.850 -21.4 2.2 -0.65MT91 268-component151364.087 0.872 -68.0 3.1 -4.4151466.729 0.952 -73.0 4.1 -11.7552146.829 0.359 -10.8 8.1 -9.0352161.650 0.803 -63.7 6.1 -9.5952162.828 0.839 -46.9 8.1 12.3954628.880 0.835 -38.8 10.1 20.0354630.852 0.895 -67.3 14.1 -1.6556107.937 0.216 25.0 5.1 13.9956178.806 0.343 10.7 3.8 10.8256445.758 0.353 -9.3 6.5 -8.1456469.761 0.073 -2.3 5.5 -7.4156470.718 0.102 -0.3 4.4 -11.6556490.802 0.704 -46.9 4.6 -6.7956491.810 0.735 -43.8 5.1 0.4256493.854 0.796 -26.7 5.0 26.3256494.745 0.823 -43.1 5.6 13.94
36 –Table 1—Continued V r σ V O − C Date (HJD-2,400,000) φ (km s − ) (km s − ) (km s − )56505.868 0.156 2.0 5.5 -11.9356533.824 0.995 -36.5 5.4 2.8956552.632 0.560 -32.3 4.2 -9.7656574.679 0.221 23.9 4.0 13.2656589.679 0.671 -30.8 4.3 4.9756608.547 0.237 -25.3 7.2 -34.73MT91 268-component251364.087 0.658 -13.5 3.1 -2.5451466.729 0.857 -14.8 4.1 0.4852146.829 0.690 -7.9 8.1 4.0952161.650 0.606 -16.6 6.1 -7.4852162.828 0.838 4.4 8.1 19.8454628.880 0.119 13.8 10.1 -2.9354630.852 0.507 -9.2 14.1 -3.8756107.937 0.175 19.3 5.1 6.8856178.806 0.121 14.1 3.8 -2.5156445.758 0.653 -4.8 6.5 5.9256469.761 0.376 0.0 5.5 -0.2956470.718 0.564 -4.0 4.4 3.5456490.802 0.517 -8.4 4.6 -2.6556491.810 0.715 -1.8 5.1 11.0256493.854 0.117 22.6 5.0 5.6956494.745 0.293 9.4 5.6 4.7456505.868 0.481 -5.3 5.5 -0.9456533.824 0.983 0.7 5.4 -2.5556552.632 0.684 -9.0 4.2 2.7656574.679 0.022 18.7 4.0 3.4556589.679 0.974 4.1 4.3 3.7156608.547 0.687 -29.6 7.2 -17.70MT91 29251805.904 0.838 -35.0 4.1 -7.1152146.686 0.847 -23.0 8.1 6.3852161.793 0.867 -25.2 10.1 7.7352162.651 0.925 -35.9 9.9 10.2453340.576 0.458 -10.5 12.8 -3.2453989.774 0.291 -11.0 12.1 -1.5954403.777 0.244 -24.8 10.6 -13.1954409.683 0.643 -12.2 5.3 -0.8256118.870 0.046 -48.0 5.4 -1.6256219.688 0.853 -27.6 3.7 2.7856443.749 0.982 -55.0 6.3 2.47
37 –Table 1—Continued V r σ V O − C Date (HJD-2,400,000) φ (km s − ) (km s − ) (km s − )56464.729 0.398 21.7 18.6 28.9956496.764 0.561 -11.0 6.6 -2.2756497.801 0.631 -14.1 5.7 -3.1956500.729 0.829 -25.0 3.9 1.5656502.770 0.967 -62.6 8.5 -6.8256504.743 0.100 -26.3 5.3 4.1556505.810 0.172 -19.6 6.4 -1.7856555.657 0.538 -6.4 3.3 1.8456560.782 0.884 -40.9 4.7 -4.68MT91 29556118.832 0.998 -28.9 3.3 -0.1756240.645 0.458 -17.9 3.3 -1.3856447.807 0.574 -6.5 4.7 7.5556465.847 0.899 -18.9 4.5 0.5256471.784 0.309 -18.3 3.6 3.0356489.874 0.655 -10.3 4.4 2.8356496.690 0.422 -20.4 3.9 -2.9156502.730 0.875 -18.4 4.8 -0.7256504.830 0.727 -14.7 4.7 -1.5556555.786 0.417 -13.2 4.3 4.3956589.731 0.200 -28.0 4.0 -1.6856590.565 0.539 -19.5 3.2 -4.7956599.638 0.223 -24.9 3.8 0.3156623.557 0.935 -23.4 4.4 -0.67MT91 33651364.116 0.849 -20.6 ( 2.2) 0.9552146.820 0.362 -1.6 ( 4.8) 4.6252161.650 0.629 -13.3 ( 4.6) -1.6752162.820 0.202 -8.2 ( 4.7) 0.9854629.860 0.017 -18.0 ( 4.6) 3.1054630.740 0.448 -9.6 ( 2.5) -2.7154632.740 0.428 -1.2 ( 4.5) 5.4354633.850 0.972 -23.2 ( 4.6) -0.1156623.601 0.922 -25.6 ( 2.3) -2.0456798.913 0.822 -16.2 ( 6.2) 4.1756799.837 0.275 -7.4 ( 2.7) -0.4156804.884 0.748 -15.1 ( 4.7) 1.68MT91 33954641.903 0.475 -10.7 1.2 1.10
38 –Table 1—Continued V r σ V O − C Date (HJD-2,400,000) φ (km s − ) (km s − ) (km s − )54642.890 0.501 -14.0 4.1 -1.9054643.757 0.524 -14.7 4.0 -2.2254644.826 0.552 -14.0 3.7 -1.1054647.860 0.632 -16.3 3.0 -2.2854669.803 0.212 -10.0 2.0 -0.1754671.884 0.267 -9.6 1.9 0.3054672.834 0.292 -10.9 1.3 -0.9354673.889 0.320 -10.1 1.5 0.0154674.914 0.347 -10.4 1.9 -0.0156118.932 0.483 -12.5 1.9 -0.6156179.923 0.093 -10.9 2.5 0.5356209.798 0.882 -15.6 1.2 0.9956211.649 0.931 -18.0 1.7 -1.9656438.789 0.930 -16.8 5.6 -0.6656443.890 0.065 -13.6 2.8 -1.3756444.745 0.087 -9.3 2.9 2.3156445.742 0.114 -10.0 2.7 0.9656446.934 0.145 -9.6 2.3 0.8356447.930 0.171 -11.2 2.5 -1.1156457.798 0.432 -11.2 2.1 0.0456458.700 0.456 -10.4 2.5 1.1856475.835 0.908 -15.2 2.0 1.2256486.814 0.198 -11.8 2.9 -1.9056491.785 0.330 -9.5 2.8 0.7656493.726 0.381 -11.5 2.6 -0.8656494.672 0.406 -10.5 2.4 0.4656559.699 0.123 -11.0 2.2 -0.2456566.758 0.310 -10.0 2.4 0.1156567.769 0.336 -6.8 3.6 3.4956574.633 0.518 -13.3 2.0 -0.9456585.607 0.807 -16.9 3.2 -0.5156588.682 0.889 -18.3 2.2 -1.7256590.548 0.938 -15.8 2.0 0.17MT91 37855424.755 0.861 -38.2 31.8 -16.8055491.691 0.138 22.4 27.3 -17.5155779.871 0.938 -12.5 10.2 -12.3655790.594 0.303 14.1 5.6 -2.9255866.476 0.883 -9.9 6.8 6.6456076.633 0.030 33.2 7.0 2.7056080.493 0.162 36.2 7.3 -1.8256092.490 0.570 -23.3 7.2 -2.0756093.492 0.604 -24.1 9.2 0.51
39 –Table 1—Continued V r σ V O − C Date (HJD-2,400,000) φ (km s − ) (km s − ) (km s − )56097.520 0.741 -32.1 5.8 -0.1256463.835 0.198 36.2 7.5 2.4956465.733 0.263 25.3 7.1 1.6156469.682 0.397 10.0 8.0 8.3056470.827 0.436 -4.8 6.2 -0.6356472.788 0.503 -16.5 6.1 -3.2056489.839 0.082 37.2 8.4 -2.2256491.859 0.151 34.1 7.3 -4.8956518.751 0.066 40.4 7.1 2.8756519.753 0.100 46.1 8.7 5.62MT91 39055715.888 0.670 -18.7 5.2 0.7355718.899 0.321 -13.5 2.7 -0.9755768.806 0.111 -16.2 3.7 -0.5055782.732 0.122 -17.8 4.8 -2.4855796.785 0.160 -14.6 5.9 -0.5355805.923 0.136 -13.3 6.3 1.5856211.817 0.893 -23.0 4.5 0.0856212.744 0.093 -14.5 3.4 1.9656240.753 0.149 -14.2 4.4 0.2056251.637 0.502 -16.5 2.8 -1.3756494.867 0.090 -17.9 3.7 -1.3156496.807 0.510 -14.0 6.7 1.3256497.841 0.733 -21.1 3.9 -0.0856502.855 0.817 -29.3 9.0 -6.4856504.902 0.260 -10.9 4.1 1.6056505.702 0.433 -11.2 4.4 2.6456533.900 0.530 -15.0 4.8 0.75MT91 40355714.893 0.479 -8.1 4.7 -2.8755717.890 0.659 -33.6 4.0 4.4555727.901 0.261 30.0 5.0 0.5955738.896 0.922 -62.0 4.2 -5.7655740.551 0.021 -2.9 3.5 4.5955756.824 0.999 -19.6 5.4 0.9455796.877 0.407 2.1 10.4 -5.2655832.549 0.551 -18.7 4.2 -0.6355855.693 0.942 -46.5 4.2 3.2755857.646 0.059 7.7 3.8 -4.6055906.555 0.999 -22.6 3.4 -1.7355911.533 0.298 28.4 3.8 3.85
40 –Table 1—Continued V r σ V O − C Date (HJD-2,400,000) φ (km s − ) (km s − ) (km s − )56076.514 0.214 33.7 6.5 -0.2556080.524 0.455 -6.4 5.4 -5.4356092.534 0.177 35.4 6.0 0.0556093.552 0.238 33.3 6.1 1.4356179.471 0.402 5.0 5.8 -3.2356205.353 0.958 -41.8 5.2 1.25MT91 417B54672.823 0.194 -10.1 ( 7.8) 2.4156511.750 0.528 -19.9 ( 6.8) -1.8756512.762 0.554 -18.9 ( 3.6) 0.2356519.663 0.736 -31.2 ( 4.9) -4.3956533.734 0.106 -17.8 ( 5.1) -1.2956534.756 0.132 -13.4 ( 5.3) 1.4756556.732 0.710 -25.0 ( 3.8) 0.7356574.608 0.180 -10.8 ( 4.0) 2.0756582.586 0.390 -15.3 ( 4.4) -1.6556589.552 0.573 -19.1 ( 4.0) 0.6956590.676 0.602 -22.8 ( 4.0) -1.7256606.553 0.020 -20.9 ( 3.8) 2.9756626.550 0.545 -22.7 ( 3.9) -3.9456795.922 0.997 -23.4 ( 10.0) 2.3756804.923 0.233 -12.6 ( 6.1) -0.71MT91 44855766.875 0.552 -33.9 6.1 0.0855781.721 0.235 -8.0 5.6 4.2555832.632 0.293 -11.6 10.8 9.8055834.666 0.935 16.8 6.6 -0.4955847.701 0.046 17.2 5.8 -0.4455876.617 0.167 -6.9 6.2 -6.8856077.852 0.640 -29.6 4.1 -2.5156080.797 0.569 -28.5 5.4 4.5656092.806 0.356 -30.3 6.2 -1.3256093.840 0.683 -12.3 6.8 9.5956097.807 0.934 18.3 4.7 1.0756179.749 0.780 -9.5 5.4 -3.0656446.824 0.020 17.2 6.2 -2.1356447.900 0.359 -26.2 5.7 3.0756458.767 0.787 -10.2 6.6 -5.0056463.867 0.396 -43.0 8.8 -10.7256469.840 0.280 -20.1 4.6 -0.6456470.796 0.581 -29.9 5.3 2.40
41 –Table 1—Continued V r σ V O − C Date (HJD-2,400,000) φ (km s − ) (km s − ) (km s − )MT91 47351365.110 0.925 -10.1 5.1 3.5151467.882 0.986 -12.1 5.1 0.6951805.789 0.186 -4.1 5.1 -4.2952161.793 0.397 -3.0 5.1 -0.7153340.576 0.095 3.0 7.1 2.6853989.770 0.480 -8.0 7.1 -4.6454286.904 0.656 -12.0 7.1 -6.0254628.748 0.859 -4.0 8.1 6.9554629.860 0.860 -14.0 9.1 -3.0354630.739 0.860 -14.0 5.1 -3.0154631.850 0.861 -10.0 6.1 1.0154633.850 0.862 -7.0 8.1 4.0655420.926 0.328 1.8 10.4 3.3055461.790 0.353 7.4 10.3 9.1155490.761 0.370 -2.5 10.6 -0.5655717.919 0.504 -0.9 5.9 2.7455740.894 0.518 -0.3 5.8 3.5455790.919 0.548 -4.8 7.0 -0.4855794.758 0.550 -11.4 9.4 -7.0955834.790 0.574 -3.7 3.8 0.9955847.762 0.581 -2.6 4.2 2.2255855.760 0.586 -5.3 4.1 -0.4255856.545 0.587 -10.8 5.3 -5.9255866.778 0.593 6.2 6.3 11.1556128.911 0.748 -9.8 6.1 -2.0556190.867 0.785 -9.0 5.4 -0.3356205.661 0.794 -14.7 5.7 -5.8156457.907 0.943 -16.0 4.7 -1.7756472.825 0.952 -7.6 5.7 6.8756486.779 0.960 -28.3 7.4 -13.8756489.822 0.962 -13.3 6.7 1.1556490.852 0.963 -18.2 5.2 -3.8156491.892 0.963 -13.2 6.0 1.2656493.777 0.964 -8.7 5.8 5.6756494.689 0.965 -14.7 5.3 -0.2956495.909 0.966 -15.2 7.5 -0.89MT91 48551467.878 0.813 -23.1 4.0 -8.2651805.804 0.896 -17.2 4.2 -4.8252146.829 0.980 2.5 5.2 -1.17
42 –Table 1—Continued V r σ V O − C Date (HJD-2,400,000) φ (km s − ) (km s − ) (km s − )52161.650 0.983 5.5 5.5 -0.2652162.820 0.984 8.5 5.1 2.5753339.570 0.273 -12.3 4.7 1.9353989.870 0.433 -12.2 5.0 3.3554285.920 0.506 -23.3 4.8 -7.4754628.700 0.590 -16.2 7.4 -0.2454630.739 0.590 -17.8 5.4 -1.8454631.850 0.591 -12.2 5.6 3.7655714.847 0.857 -9.5 3.8 4.3855715.919 0.857 -16.7 3.5 -2.8155718.762 0.858 -12.8 2.7 1.1255738.873 0.863 -11.6 3.8 2.1655740.574 0.863 -13.4 2.8 0.3255757.764 0.868 -13.0 2.9 0.5655768.894 0.870 -11.5 4.2 2.0255781.819 0.874 -11.6 2.9 1.7255834.836 0.887 -12.2 2.4 0.6655866.756 0.894 -10.5 3.6 1.9656076.828 0.946 -7.9 4.5 -0.4956080.853 0.947 -8.1 4.1 -0.9156092.861 0.950 -7.9 3.9 -1.2056097.882 0.951 -7.1 4.1 -0.6456460.731 0.040 -0.2 4.0 -0.0356471.928 0.043 -1.5 3.7 -0.6156590.763 0.072 -5.9 4.3 0.29MT91 55551805.820 0.775 -21.0 4.1 -2.3752146.686 0.042 6.3 10.1 -2.9252161.793 0.053 4.4 13.1 -1.5852162.651 0.054 16.2 16.1 10.4153338.617 0.973 21.9 9.1 8.9553340.576 0.975 16.7 9.1 3.4153989.652 0.482 -25.2 12.1 -0.7254628.880 0.981 -4.5 14.1 -19.1355718.875 0.833 -11.1 5.1 3.1355740.870 0.851 -10.5 4.6 1.9855768.789 0.872 -9.7 4.4 -0.0655782.825 0.883 -2.9 5.0 5.0955791.940 0.890 -7.2 4.3 -0.4355794.842 0.893 -12.1 6.3 -5.6955847.678 0.934 3.4 5.1 0.7456118.744 0.146 -12.4 6.2 -0.3056179.888 0.194 -22.6 6.5 -6.02
43 –Table 1—Continued V r σ V O − C Date (HJD-2,400,000) φ (km s − ) (km s − ) (km s − )56191.831 0.203 -12.3 6.4 5.0256460.777 0.413 -23.4 6.7 0.6456465.764 0.417 -22.7 6.2 1.4156468.815 0.419 -30.8 7.0 -6.6456518.789 0.459 -7.9 9.1 16.4956552.756 0.485 -31.0 5.4 -6.4756566.807 0.496 -7.5 8.3 16.9856567.714 0.497 -20.1 12.1 4.3856574.804 0.502 -21.2 5.6 3.2856588.656 0.513 -22.5 5.4 1.9656608.668 0.529 -23.9 4.4 0.56MT91 56154403.790 0.752 -31.7 9.2 -1.6154406.679 0.824 -15.5 8.5 0.2755377.898 0.050 41.5 21.3 15.0855426.768 0.269 12.5 21.6 6.3555457.652 0.039 72.0 25.9 46.3555470.731 0.365 -4.2 25.5 9.7055758.813 0.551 -37.6 7.4 3.1955790.941 0.353 -15.3 6.8 -4.0956166.884 0.730 -29.2 9.7 4.3356179.680 0.049 6.5 10.7 -19.8256445.866 0.689 -48.3 11.2 -9.7556461.898 0.089 32.6 9.3 4.9256465.792 0.186 20.9 9.2 0.3656469.808 0.286 4.9 10.8 2.2156475.715 0.433 -27.3 9.7 -0.6856490.877 0.811 -16.1 10.3 2.4756494.909 0.912 7.1 11.8 2.61MT91 58851805.819 0.648 -11.3 5.0 8.1652146.686 0.038 -18.9 5.7 -2.0052162.651 0.103 4.3 5.5 12.3153989.652 0.558 -19.1 5.1 -2.8553990.848 0.562 -16.3 10.1 0.1256165.921 0.437 -13.3 6.1 -0.6656218.697 0.652 -24.2 6.0 -4.5556258.636 0.815 -31.2 6.8 -3.4656460.754 0.640 -18.1 5.2 1.0956464.704 0.656 -21.3 5.4 -1.5256534.801 0.942 -35.8 5.8 -0.03
44 –Table 1—Continued V r σ V O − C Date (HJD-2,400,000) φ (km s − ) (km s − ) (km s − )56556.854 0.032 -12.9 5.2 5.7156559.742 0.043 -15.8 4.1 -0.1456560.699 0.047 -17.5 4.3 -2.7356566.830 0.072 -17.1 4.4 -6.4356574.574 0.104 -4.6 3.9 3.3956582.616 0.137 -6.5 4.2 0.4656587.554 0.157 -2.2 5.8 4.5856588.566 0.161 -10.0 3.5 -3.2556590.729 0.170 -9.7 3.9 -2.9156607.576 0.239 -7.5 4.8 0.25MT91 60151467.916 0.681 -10.8 3.1 1.8151805.746 0.343 -11.0 3.1 6.7052146.686 0.012 -1.0 3.8 0.4854643.857 0.906 0.2 4.7 2.8454644.926 0.908 -0.4 5.1 1.9554647.882 0.914 1.6 4.6 3.3854669.940 0.957 4.7 2.4 0.7454672.765 0.963 -0.3 2.1 -5.1654673.770 0.965 4.4 2.2 -0.7554674.896 0.967 11.1 2.1 5.6956076.678 0.715 -5.6 2.7 6.2456080.915 0.723 -11.8 2.5 -0.2456092.907 0.746 -8.5 2.5 2.4456098.779 0.758 -17.4 2.2 -6.8256110.915 0.782 -11.8 2.5 -2.0456118.713 0.797 -9.0 3.1 0.1956128.951 0.817 -3.0 3.0 5.4056166.976 0.892 -2.7 4.0 1.2056179.913 0.917 -5.6 2.4 -4.1156212.580 0.981 6.7 2.2 0.0156222.715 0.001 2.6 1.8 -0.6856440.951 0.429 -18.8 2.9 -2.0456460.688 0.467 -26.9 2.8 -10.7056462.832 0.471 -25.2 2.5 -9.0256491.924 0.528 -13.9 3.4 1.4756497.897 0.540 -15.2 2.8 -0.0356552.875 0.648 -12.0 2.3 1.2856559.771 0.661 -8.3 2.5 4.7756590.754 0.722 -9.8 2.5 1.8156622.557 0.784 -5.6 2.2 4.0956795.895 0.124 2.8 2.2 21.40
45 –Table 1—Continued V r σ V O − C Date (HJD-2,400,000) φ (km s − ) (km s − ) (km s − )MT91 646a56191.706 0.278 -72.7 ( 4.8) 0.856461.866 0.701 6.4 ( 3.7) -6.756464.862 0.761 31.1 ( 4.3) 5.056467.795 0.820 42.4 (10.2) 5.956469.872 0.862 56.6 ( 6.1) 16.456495.871 0.383 -65.1 ( 8.9) -10.356496.732 0.401 -64.6 ( 5.2) -13.256500.887 0.485 -44.4 (14.1) -9.956504.870 0.564 2.7 ( 7.1) 20.056505.735 0.582 0.6 ( 4.4) 14.156552.682 0.524 -56.9 (10.5) -30.956556.801 0.607 12.4 ( 5.2) 20.556560.740 0.686 12.1 ( 8.3) 2.456566.777 0.807 33.9 ( 3.0) -0.756574.649 0.965 11.9 ( 2.1) -1.256582.648 0.126 -62.3 ( 5.2) 16.556589.771 0.269 -71.5 ( 2.9) 3.456590.695 0.287 -70.7 ( 4.0) 1.456599.736 0.469 -57.7 ( 7.6) -19.9MT91 646b56191.706 0.278 39.3 (5.9) 0.456461.866 0.701 -65.8 (4.6) 7.256464.862 0.761 -81.5 (5.4) 8.356467.795 0.820 -96.2 (12.7) 7.056469.872 0.862 -98.8 (7.6) 9.256495.871 0.383 14.7 (11.1) -0.156496.732 0.401 22.7 (6.5) 12.256500.887 0.485 13.9 (17.7) 25.456504.870 0.564 -55.0 (8.9) -21.456505.735 0.582 -61.6 (5.4) -23.156552.682 0.524 1.7 (13.1) 24.056556.801 0.607 -60.2 (6.5) -14.556560.740 0.686 -74.9 (10.4) -6.356566.777 0.807 -105.4 (3.7) -4.656574.649 0.965 -77.6 (2.6) -4.656582.648 0.126 50.1 (6.5) 4.256589.771 0.269 30.9 (3.6) -9.856590.695 0.287 36.1 (5.0) -1.056599.736 0.469 5.5 (9.5) 12.7MT91 745
46 –Table 1—Continued V r σ V O − C Date (HJD-2,400,000) φ (km s − ) (km s − ) (km s − )56166.691 0.507 -16.7 7.2 0.6756211.440 0.803 -12.5 3.7 -2.5256218.487 0.849 -14.1 5.8 -7.2756457.883 0.432 -16.1 12.3 1.8056460.712 0.451 -21.6 5.2 -3.8256462.843 0.465 -20.3 3.8 -2.5656475.700 0.550 -20.5 5.3 -3.6056500.921 0.717 -8.3 5.0 5.2956504.690 0.742 -10.8 5.6 1.9856505.680 0.749 -13.7 4.9 -1.1856511.662 0.788 -13.0 5.1 -2.2156518.815 0.835 -10.1 4.9 -2.2756552.859 0.061 -6.0 4.6 -3.3156556.872 0.087 -3.3 4.1 4.6156559.781 0.106 -11.0 3.8 -0.5056560.621 0.112 -12.0 3.9 -0.9556571.604 0.185 -17.2 5.2 -1.5256585.544 0.277 -15.7 4.5 1.8756588.724 0.298 -15.6 3.8 2.2356599.768 0.371 -20.8 3.9 -2.7356606.580 0.416 -14.0 3.7 4.0056608.599 0.429 -15.2 4.3 2.6951467.889 0.430 -21.4 4.5 -3.4751805.782 0.665 -14.6 4.7 0.3852146.829 0.920 4.5 5.4 2.2552161.650 0.018 11.3 3.7 -0.2052162.828 0.026 1.3 6.0 -7.3253339.572 0.809 -7.1 4.6 2.5553340.576 0.815 -1.8 4.6 7.4553989.774 0.109 -9.3 4.7 1.4854285.779 0.067 -12.9 6.0 -8.8254286.904 0.074 -9.5 9.1 -3.85
47 –Table 2. Orbital Elements of New Binaries
Element MT91 021 MT91 187 MT91 202 MT91 234 MT91 241 P (days) 9.70 ± ± ± ±
330 671 ± e ± ± ± ± ± ω (deg) 81 ±
31 15 ±
19 160 ±
40 328 ±
54 338 ± γ (km s − ) -16.2 ± ± ± ± ± T (HJD-2,400,000) 56336.58 ± ± ± ±
722 125161 ± K (km s − ) 37.8 ± ± ± ± ± K (km s − ) · · · · · · · · · · · · · · · S. C. B1.5V B1V B2V B1.5V B1.5VS. C. mid-late B? ... B,A B? early B i (degrees) 16–85 3–85 15–90 ∼ ∼ M (adopted; M ⊙ ) 12 14 11 12 12 M (M ⊙ ) 11–2 14 – 0.43 11 – 2 17: 11–4.6 q a (AU) ∼ ∼ . ∼ ∼ ∼ χ red
48 –Table 3. Orbital Elements of New Binaries
Element MT91 268-c1 MT91 268-c2 MT91 292 MT91 295 MT91 236 P (days) 33.327 ± ± ± ± ± e ± ± ± ± ± ω (deg) 256 ±
13 294 ±
28 191 ±
13 137 ±
46 216 ± γ (km s − ) -22.5 ± ± ± ± ± T (HJD-2,400,000) 56667.7 ± ± ± ± ± K (km s − ) 33.0 ± ± ± ± ± K (km s − ) · · · · · · · · · · · · · · · S. C. B2V B2V B2V B2V B2VS. C. B–A B–G B–F B–K B–M i (degrees) 33–90 33–90 12–90 3–90 3–90 M (adopted; M ⊙ ) 9 9 11 11 11 M (M ⊙ ) 9–3.9 9–3.9 11–1.6 11-0.3 11–6 q a (AU) ∼ ∼ ∼ ∼ ∼ χ red
49 –Table 4. Orbital Elements of New Binaries
Element MT91 339 MT91 378 MT91 390 MT91 403 MT91 417B P (days) 44.63 ± ± ± ± ± e ± ± ± ± ± ω (deg) 251 ±
32 299 ±
14 240 ±
52 260 ± ± γ (km s − ) -13.0 ± ± ± ± ± T (HJD-2,400,000) 55229.7 ± ± ± ± ± K (km s − ) 3.4 ± ± ± ± ± K (km s − ) · · · · · · · · · · · · · · · S. C. B0V O8V B1V O6VS. C. O–K B: O–K B: O6V-A i (degrees) 2–90 19–90 2–90 23–90 5–90 M (adopted; M ⊙ ) 21 18 21 14 31 M (M ⊙ ) 21–0.5 17–4.1 21–0.32 14 –4.0 31–1.8 q a (AU) ∼ ∼ ∼ ∼ ∼ χ red
50 –Table 5. Orbital Elements of New Binaries
Element MT91 448 MT91 473 MT91 485 MT91 555 MT91 561 P (days) 3.1704 ± ± a ±
45 1278.7 ± ± e ± ± ± ± ω (deg) 3 ±
34 255 ±
28 352 ± ±
13 325 ± γ (km s − ) -10.6 ± ± ± ± ± T (HJD-2,400,000) 55971.2 ± ±
438 52229 ±
29 57208 ±
49 55977 ± K (km s − ) 27.7 ± ± ± ± ± K (km s − ) · · · · · · · · · · · · · · · S. C. O6V O8.5V+O9V: O8V O8V B2VS. C. O6V-A O–B O–B O–B2 O-A1 i (degrees) 6–90 12–90 40–90 34–90 24–90 M (adopted; M ⊙ ) 31 19+19 21 21 11 M (M ⊙ ) 31–2.0 39–5 21–11 21–10 11–3.3 q a (AU) ∼ ∼ ∼ ∼ ∼ χ red a Probable triple system; described here are the parameters for the combined ∼ Table 6. Orbital Elements of New Binaries
Element MT91 588 MT91 601 MT91 646 MT91 745 P (days) 245.1 ± ± ± ± e ± ± ± ω (deg) 242 ±
16 41 ±
20 260 ± ± γ (km s − ) -17.8 ± ± ± ± T (HJD-2,400,000) 56549.1 ± ± ± ± K (km s − ) 14.5 ± ± ± ± K (km s − ) · · · · · · ± · · · S. C. B0V O9.5III B1V O7VS. C. B–A O–B B1.5V A–B i (degrees) 15–90 18–90 75–90 15–90 M (adopted; M ⊙ ) 18 21 14 25 M (M ⊙ ) 18–3.2 21–4.1 ∼
12 25–4.0 q ± a (AU) ∼ ∼ ∼ ∼ χ red
51 –Table 7. Velocities of Stars Showing Aperiodic Variations V Helio σ V Date (HJD-2,400,000) (km s − ) (km s − )MT91 13852146.686 -14.1 5.252161.793 -8.8 3.552162.651 -5.2 6.653338.617 -31.6 9.153989.652 -6.6 5.353990.848 -1.6 4.154285.925 -23.4 4.854286.904 -19.6 3.954341.887 -17.1 3.554342.777 -16.5 3.754343.746 -15.6 3.654344.775 -22.4 4.254345.790 -17.1 3.554347.789 -21.9 4.454348.812 -20.6 3.754399.696 -24.8 8.154401.649 -22.4 7.954402.719 -21.0 3.454641.844 -22.2 1.854643.718 -22.5 5.454644.789 -16.4 3.954647.828 -19.5 4.354669.831 -19.6 2.754747.682 -23.4 3.654748.641 -22.8 2.354753.648 -37.1 3.154754.717 -22.4 1.754755.763 -23.1 2.154756.690 -22.4 4.054757.747 -29.3 3.9MT91 417A a
52 –Table 7—Continued V Helio σ V Date (HJD-2,400,000) (km s − ) (km s − )56556.722 -28.8 3.156574.599 -12.3 5.456582.571 -12.5 5.556588.703 -21.2 11.056589.54 -18.0 6.556590.665 -24.2 3.356599.693 -21.9 7.456607.561 -22.4 6.656626.536 -3.8 8.156798.871 14.6 11.556804.946 -7 8.9MT91 45751381.776 -9.2 2.551382.947 -11.4 2.451411.719 -12.9 2.451412.762 -19.1 2.051736.792 -18.2 2.651737.871 -7.9 1.352146.829 -12.0 2.052161.650 -12.5 3.052162.828 -9.6 2.953339.572 -14.7 3.054642.776 -23.0 4.354643.792 -12.5 3.054644.736 -10.0 3.254645.779 -1.2 3.654646.755 -15.7 3.054647.726 -12.9 1.654648.830 -10.7 3.154669.770 -26.4 5.254672.734 -23.6 2.854673.738 -11.8 2.354674.770 -16.3 5.8MT91 483 a
53 –Table 7—Continued V Helio σ V Date (HJD-2,400,000) (km s − ) (km s − )54642.793 -7.3 3.154644.721 6.2 3.754647.873 -3.9 2.754669.894 -7.3 2.854672.673 -5.5 4.254673.819 -6.5 3.654674.704 0.4 3.556438.944 -11.0 2.056457.720 -21.4 2.456460.945 -5.3 3.856462.751 -6.0 2.156466.921 -15.5 2.556486.860 -4.1 3.856493.800 0.8 2.456494.899 -1.8 3.256495.706 -9.0 4.056496.680 -4.3 2.856520.906 -2.3 4.556533.953 -3.9 3.156556.883 -18.0 4.156561.636 -15.8 3.356571.636 -4.1 7.356574.827 -4.7 2.8MT91 55654643.850 2.5 5.254644.908 -12.5 5.754645.874 -12.3 5.454647.792 -12.0 5.054671.914 -3.7 4.554672.755 -3.8 4.854673.759 -5.1 4.454674.829 9.9 4.854747.789 -17.4 3.354748.685 -9.6 3.554749.582 -7.8 3.554753.624 -11.2 3.054754.754 4.1 4.354755.655 1.7 5.854756.677 -8.2 3.555726.901 -7.8 2.755738.919 17.8 5.155741.732 -4.9 6.155779.962 -13.2 3.0
54 –Table 7—Continued V Helio σ V Date (HJD-2,400,000) (km s − ) (km s − )55791.962 -6.3 3.655794.878 -4.2 7.555834.592 -17.6 4.155847.807 -27.4 2.755855.665 -7.8 10.855866.534 -0.3 2.555901.662 -1.2 3.256118.721 -2.9 3.256205.506 -10.8 4.256209.837 -16.3 3.856212.651 -3.6 3.456219.824 -17.9 3.156444.745 -11.9 4.256445.936 3.0 3.856457.688 1.8 3.356460.696 -8.9 3.456462.768 -12.5 4.256464.925 -10.9 4.556465.927 -11.1 6.256468.880 -6.0 3.656470.917 -10.6 3.056472.889 -10.8 3.356475.750 2.6 2.9MT91 63254642.809 -8.4 4.854643.873 -8.1 3.954644.713 -6.4 4.754645.759 2.0 4.054646.738 -17.3 3.754647.709 -10.6 3.254648.810 -14.1 3.554669.956 -11.2 3.454671.710 -14.6 3.254672.654 -8.1 1.754673.787 -3.6 2.654674.666 -10.0 2.654675.777 -0.6 2.854746.768 17.9 2.754747.630 4.7 2.654748.617 -19.5 2.054748.805 -15.5 1.954749.573 -8.0 2.954753.599 1.8 2.1
55 –Table 7—Continued V Helio σ V Date (HJD-2,400,000) (km s − ) (km s − )54754.602 -8.5 2.354755.642 -0.0 2.654756.662 3.8 2.154757.639 -9.4 2.354758.702 -9.2 2.455010.732 -12.2 1.655011.632 8.7 1.655012.637 -2.5 2.455013.635 -10.1 2.256212.561 -0.0 3.556258.623 -10.8 3.9 a Velocities measured from He II λ
56 –Table 8. OB Binaries in Cyg OB2
P K Star Type S.C. (days) (km s − ) e q Ref. NotesMT91 021 SB1 B1.5V + B + ? 9.70 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
330 17.1 ± ± ± ± ± pm ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± · · · · · · ∼ ± ±
15 0.38 ± ± ± ± ± ± ± ± ± ± ± ±
51 7.5 ± ± ±
45 15.0 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
10 0 (fixed) 0.802 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
57 –Table 8—Continued
P K Star Type S.C. (days) (km s − ) e q Ref. Notes(+ B0V:) 138.8 ± · · · ± ± ± ± ± ± ± ± ± ± ± ± ± ± P < β Lyr type (ellipsoidal;
P >
58 –Table 9. Reanalyzed Ephemerides for Systems from Paper II and Paper III V r σ V O − C Date (HJD-2,400,000) φ (km s − ) (km s − ) (km s − )MT91 05951467.913 0.294 37.0 5.2 5.5251805.750 0.918 -124.7 5.4 -16.8552146.697 0.182 7.5 5.1 3.3652162.650 0.470 27.7 5.3 7.6353338.617 0.819 -87.0 4.2 7.5953570.693 0.646 -16.0 9.7 16.0853573.675 0.261 27.7 11.8 0.9853633.634 0.618 -34.6 4.3 -12.8453634.676 0.832 -82.8 9.4 15.3853636.753 0.260 31.7 6.8 5.0853657.660 0.569 10.8 4.1 16.5053903.839 0.303 9.8 14.5 -22.4253904.708 0.482 -28.7 9.3 -46.1553905.821 0.711 -65.2 6.5 -8.5153906.717 0.896 -118.0 11.7 -9.9853907.769 0.113 -34.3 16.6 -5.9853907.864 0.132 -33.3 8.9 -15.2053932.831 0.278 39.7 9.2 10.2853932.839 0.279 46.5 20.2 16.8553935.775 0.885 -97.4 16.5 9.9053987.695 0.584 -25.2 14.1 -14.6353988.695 0.791 -97.2 9.1 -11.4353989.652 0.988 -87.2 4.3 5.4053990.848 0.234 15.2 5.0 -5.7354285.925 0.045 -55.4 7.0 10.35MT91 14551381.906 0.869 10.7 2.1 1.1651383.775 0.943 -16.6 2.5 0.4851467.903 0.291 -29.0 1.1 0.2051736.897 0.997 -47.9 2.9 -0.1451737.961 0.039 -64.9 3.9 -0.6152146.686 0.306 -27.1 1.8 -0.4952161.793 0.908 -2.8 1.6 -1.4952162.650 0.942 -17.1 3.2 -0.7253338.617 0.744 16.1 2.0 -1.6253340.576 0.822 10.1 1.6 -5.7953570.879 0.988 -46.4 4.2 -3.5353632.836 0.454 -8.4 3.5 -2.7453633.714 0.489 -14.1 4.2 -12.5053636.865 0.614 13.6 5.3 3.07
59 –Table 9—Continued V r σ V O − C Date (HJD-2,400,000) φ (km s − ) (km s − ) (km s − )53657.691 0.443 -4.7 8.0 2.2753987.694 0.577 6.8 2.1 -0.5353988.740 0.619 11.9 1.9 1.0253989.651 0.655 15.5 1.8 1.9453990.848 0.703 20.5 2.7 4.1954285.925 0.446 -2.6 3.2 3.9754286.655 0.475 -3.3 2.5 -0.1754287.721 0.518 6.0 2.9 4.4654397.705 0.895 6.6 1.5 3.7854399.685 0.974 -36.7 1.6 -2.0554401.662 0.053 -66.2 1.2 0.3854402.711 0.094 -66.7 1.2 -0.36MT91 252a51365.058 0.607 -63.3 1.4 -0.654341.855 0.038 74.4 3.7 -0.454342.841 0.141 60.7 4.4 4.454343.789 0.240 17.4 3.3 0.454345.845 0.455 -43.1 4.4 1.254346.880 0.563 -56.1 4.7 3.654348.783 0.762 -49.6 3.8 3.254410.722 0.242 18.8 4.1 2.854696.705 0.162 44.5 4.0 -3.754697.690 0.265 14.9 3.1 7.254698.826 0.384 -30.7 5.1 -2.054700.838 0.594 -55.8 4.1 6.254701.798 0.695 -55.0 4.1 7.054747.741 0.501 -62.1 5.5 -10.054748.781 0.610 -62.0 4.3 0.854755.716 0.335 -27.3 3.5 -11.754757.701 0.543 -57.7 5.0 -0.155866.304 0.524 -61.2 5.8 -5.9MT91 252b51365.058 0.607 55.0 2.3 0.954341.855 0.038 -120.7 6.2 -15.654342.841 0.141 -61.5 7.4 22.454343.789 0.240 -42.1 5.6 -3.954345.845 0.455 27.8 7.3 -5.154346.880 0.563 52.2 7.9 1.654348.783 0.762 48.6 6.4 6.054410.722 0.242 -40.7 7.0 -3.654696.705 0.162 -60.2 6.5 14.1
60 –Table 9—Continued V r σ V O − C Date (HJD-2,400,000) φ (km s − ) (km s − ) (km s − )54697.690 0.265 -41.0 5.1 -13.554700.838 0.594 49.8 6.9 -3.554701.798 0.695 50.6 6.8 -2.854747.741 0.501 34.2 9.4 -7.754748.781 0.610 50.1 7.1 -4.254757.701 0.543 47.4 8.2 -0.8MT91 25851467.915 0.647 2.1 2.8 16.4851805.748 0.694 -10.0 1.7 -5.4652146.686 0.953 21.4 6.6 -6.2252161.793 0.983 24.5 3.8 1.6352162.651 0.042 8.3 4.1 0.3853338.617 0.266 -47.1 3.5 -0.8953340.576 0.400 -49.6 2.8 -1.2853987.695 0.547 -37.2 4.6 -4.7453988.741 0.618 -15.8 4.7 4.2153989.652 0.680 -10.3 4.7 -2.8953989.774 0.689 -2.5 4.1 3.1453990.848 0.762 10.1 5.1 -0.0054342.873 0.777 6.4 3.5 -6.8554343.759 0.838 31.9 2.6 7.8154345.811 0.978 17.9 3.8 -6.0454347.802 0.113 -14.6 2.6 0.0154285.925 0.892 28.3 3.7 -1.2554286.656 0.942 32.8 9.1 4.1254287.721 0.015 14.6 8.9 -1.03Schulte
61 –Table 9—Continued V r σ V O − C Date (HJD-2,400,000) φ (km s − ) (km s − ) (km s − )54697.841 0.972 -55.6 9.1 -8.354697.913 0.974 -40.9 4.4 9.254698.705 0.996 -75.0 4.3 4.054698.905 0.002 -86.7 4.6 -1.554699.713 0.025 -102.0 5.5 1.954699.923 0.031 -108.2 5.5 -1.654700.713 0.054 -108.6 4.1 1.554701.718 0.083 -104.6 5.1 -1.554701.934 0.089 -100.6 7.1 0.154724.680 0.741 61.6 4.9 4.354724.800 0.744 63.9 6.3 6.554725.685 0.770 60.0 4.5 2.654725.794 0.773 58.3 4.4 0.954726.694 0.799 56.1 4.3 0.054726.817 0.802 56.6 4.5 0.854729.653 0.884 34.9 5.3 -0.654729.834 0.889 36.4 4.7 3.6Schulte
62 –Table 9—Continued V r σ V O − C Date (HJD-2,400,000) φ (km s − ) (km s − ) (km s − )54726.694 0.799 -61.3 3.6 -2.154726.817 0.802 -56.7 4.5 2.154729.653 0.884 -36.3 5.3 2.354729.834 0.889 -33.2 3.7 2.8CPR2002 A45a54403.658 0.437 127.7 5.6 -4.654403.738 0.491 139.8 7.8 -4.154405.714 0.806 -60.0 9.1 -5.054405.737 0.822 -67.5 8.0 -1.354406.642 0.424 112.5 10.3 -14.354406.652 0.431 106.3 10.2 -23.554406.770 0.509 156.0 10.7 12.454409.739 0.486 130.1 10.1 -13.554410.675 0.110 -104.7 5.4 -0.854641.836 0.031 -133.5 6.6 -4.054642.901 0.740 -2.2 7.3 -1.354643.707 0.277 6.9 8.1 -11.954647.805 0.005 -150.0 5.5 -18.154672.895 0.712 9.5 4.7 -14.254724.704 0.210 -16.2 5.9 21.954724.776 0.258 1.2 4.7 -0.854725.713 0.881 -89.0 4.7 13.554729.700 0.536 149.5 5.6 10.554746.635 0.813 -46.5 8.1 13.254747.583 0.444 132.0 6.4 -2.754748.591 0.115 -108.8 7.9 -7.654754.767 0.227 -25.0 6.2 -1.4CPR2002 A45b54403.658 0.437 -194.2 9.8 -7.954403.738 0.491 -185.2 10.9 17.354406.642 0.424 -195.4 17.3 -16.754406.652 0.431 -202.9 16.9 -20.254406.770 0.509 -179.1 16.1 22.954409.739 0.486 -220.0 15.8 -17.954410.675 0.110 143.1 9.7 -1.154641.836 0.031 196.2 12.8 16.354642.901 0.740 -5.9 12.3 -5.954643.707 0.277 4.4 16.4 31.954647.805 0.005 178.3 15.9 -5.054672.895 0.712 1.8 10.4 36.154724.704 0.210 29.1 11.3 -23.1
63 –Table 9—Continued V r σ V O − C Date (HJD-2,400,000) φ (km s − ) (km s − ) (km s − )54724.776 0.258 15.2 10.0 19.254725.713 0.881 145.1 9.6 2.854726.719 0.551 -188.6 10.4 0.954726.791 0.599 -162.1 13.9 -4.754729.700 0.536 -192.7 12.0 3.154746.635 0.813 68.3 14.5 -14.154747.583 0.444 -191.9 11.3 -2.254748.591 0.115 161.1 17.6 20.754754.767 0.227 11.1 13.8 -20.8
64 –Table 10. Updated Orbital Elements for SB1 Systems from Prior Papers
Element MT91 059 MT91 145 MT91 258 P (Days) 4.8523 ± ± ± e ± ± ± ω (deg) 225 ±
22 125 ± ± γ (km s − ) -30.1 ± ± ± T (HJD-2,400,000) 56338.2 ± ± ± K (km s − ) 71.0 ± ± ± K (km s − ) · · · · · · · · · S. C.
08V O9III O8VS. C. O–midB O–midB O–B i (degrees) 19–90 19–90 15–90 M (adopted; M ⊙ ) 21 23 21 M (M ⊙ ) 21–5 23–5.3 21–3.9 q a (AU) ∼ ∼ ∼ χ red I λ I λ Table 11. Updated Orbital Elements for SB2 Systems from Prior Papers
Element MT91 252 Schulte P (Days) 9.558 ± ± ± e ± ± ± ω (deg) 326 ± ± ± γ (km s − ) -9 ± ± ± T (HJD-2,400,000) 54704.7 ± ± ± K (km s − ) 70 ± ± ± K (km s − ) 81 ± ± ± B1–2V O8.5III: B0.5VS. C. B1–2V O9.0III: B1–2V i (degrees) 30–40 ∼
40 40–45 M /mathrmsin i (M ⊙ ) 1.6 ± ± ± M /mathrmsin i (M ⊙ ) 1.4 ± ± ± q ± ± ± a (/rsun) 0.127 ∼ ∼ ± χ red
65 –Fig. 1.— Three-color image of the Cygnus OB2 region with the
Spitzer µ m, 8.0 µ m,and 24 µ m images in blue/green/red. White symbols denote O- and early B massive starswhile larger magenta symbols mark the 48 known binary/multiple systems. The early-B SB2system CPR2002 A45 lies just off the field of view to the upper right. The bar at lower leftshows a linear scale of 5 pc at a distance of 1.4 kpc. 66 –Fig. 2.— Folded radial velocity curve and best-fitting solution for MT91 021. The largereduced χ of 3.2 suggests the presence of an additional velocity component in this single-lined, potentially triple system. 67 –Fig. 3.— Folded radial velocity data and best-fitting solution for MT91 187. 68 –Fig. 4.— Folded radial velocity data and best-fitting solution for MT91 202. 69 –Fig. 5.— Folded radial velocity data and best-fitting solution for MT91 234. 70 –Fig. 6.— Folded radial velocity data and best-fitting solution for MT91 241. 71 –Fig. 7.— Folded radial velocity data and best-fitting solution for the single-lined triplesystem MT91 268, Component 1. 72 –Fig. 8.— Folded radial velocity data and best-fitting solution for the single-lined triplesystem MT91 268, Component 2. 73 –Fig. 9.— Folded radial velocity data and best-fitting solution for MT91 292. 74 –Fig. 10.— Folded radial velocity data and best-fitting solution for MT91 295. 75 –Fig. 11.— Folded radial velocity data and best-fitting solution for MT91 336. 76 –Fig. 12.— Folded radial velocity data and best-fitting solution for MT91 339. 77 –Fig. 13.— Folded radial velocity data and best-fitting solution for MT91 378. 78 –Fig. 14.— Folded radial velocity data and best-fitting solution for MT91 390. 79 –Fig. 15.— Folded radial velocity data and best-fitting solution for MT91 403. 80 –Fig. 16.— Folded radial velocity data and best-fitting solution for MT91 417B (Schulte e = 0 and e ≃ filledcircles ), the Sana et al. (2012) sample of O stars in Galactic open clusters ( pluses ), and Ostars from Garmany et al. (1980) ( open squares ). 95 –Fig. 31.— (Lower panel) Observed cumulative distribution of orbital periods in the unbiasedCyg OB2 sample as a fraction of the entire sample ( filled circles ) and the the inferred truedistribution of orbital periods ( open circles ) using the completeness corrections shown inFigure 26 and assumptions for the underlying distribution of eccentricities and mass ratios,as described in the text. The solid curve is a power law with slope β = − .
22. (Upper panel)Probability that the observed distribution is consistent with uniform in a moving window ofwidth seven observed systems. Probable changes in slope near 6 days, 14 days, and 45 daysappear as dips in the probability curve. 96 –Fig. 32.— Folded radial velocity data and best-fitting solution for MT91 059, re-analyzedand updated slightly from Paper II. The large reduced χ2