Clustering between high-mass X-ray binaries and OB associations in the Milky Way
Arash Bodaghee, John A. Tomsick, Jerome Rodriguez, J. Berian James
aa r X i v : . [ a s t r o - ph . H E ] S e p Clustering between high-mass X-ray binariesand OB associations in the Milky Way
A. Bodaghee and J. A. Tomsick
Space Sciences Laboratory, 7 Gauss Way, University of California, Berkeley, CA 94720, USA [email protected] and
J. Rodriguez
Laboratoire AIM, CEA/IRFU - Universit´e Paris Diderot - CNRS/INSU,CEA DSM/IRFU/SAp, Centre de Saclay, F-91191 Gif-sur-Yvette, France and
J. B. James
Dark Cosmology Centre, University of Copenhagen, Juliane Maries Vej 30, 2100 Copenhagen, DenmarkAstronomy Department, University of California, Berkeley, CA 94720, USA
ABSTRACT
We present the first direct measurement of the spatial cross-correlation function of high-mass X-raybinaries (HMXBs) and active OB star-forming complexes in the Milky Way. This result relied on asample containing 79 hard X-ray selected HMXBs and 458 OB associations. Clustering between the twopopulations is detected with a significance above 7 σ for distances < ± ±
50 km s − . The characteristic scale of thecorrelation function suggests an average kinematical age (since the supernova phase) of ∼ Subject headings:
Galaxy: evolution, open clusters and associations, stellar content, structure ; Stars: emission-line,Be, neutron, supergiants ; X-rays: binaries
1. Introduction
High-mass X-ray binaries (HMXBs) are systemsin which a compact object (usually a neutron star, butsometimes a black hole candidate) accretes from amassive stellar companion ( M & M ⊙ ). The mass-age relation in stellar evolution predicts that ∼ yrelapses between starbirth and supernova in high-massstars (Schaller et al. 1992). Thus, HMXBs are rela-tively young systems which are not expected to mi-grate far from their birthplaces: sites with a recent history of massive star formation, i.e., the OB as-sociations that trace the Galactic spiral arms (e.g.Brown et al. 1999).Observational evidence linking Galactic HMXBsand OB associations has been demonstrated in indi-vidual cases in which the connection is attested byother factors: i.e., consistent proper motions and dis-tances, the position of the HMXB donor star with re-spect to the main sequence (MS) of the OB associa-tion on color-magnitude diagrams, etc. On a Galacticscale, however, the evidence is limited to comparing1istributions of Galactic longitudes ( l ) or galactocen-tric distances ( R ) (e.g., Grimm et al. 2002; Dean et al.2005; Lutovinov et al. 2005; Bodaghee et al. 2007;Lutovinov et al. 2008). Both HMXBs and OB as-sociations show maxima around Galactic longitude l ∼ ◦ which corresponds roughly to the directionof the Norma and Inner Perseus Arms (upper panelof Fig. 1). Moderate peaks are found towards the Ca-rina, Scutum, and Sagittarius Arms. This suggeststhat HMXBs are spatially correlated with active sitesof massive-star formation. This correlation is furtherexemplified by the similarity in the distributions ofgalactocentric distances of HMXBs and OB associa-tions: both distributions can be approximated by Gaus-sians centered on the galactocentric distance of the Sun(lower panel of Fig. 1).Recent efforts to describe the Galactic distribu-tion of HMXBs raised the intriguing possibility ofan offset between the peak in the HMXB longitu-dinal distribution with respect to the tangent to theNorma Arm (Lutovinov et al. 2005; Dean et al. 2005;Bodaghee et al. 2007; Lutovinov et al. 2008). This di-rection features the highest formation rate of massivestars (Bronfman et al. 2000). An offset would im-ply that we are witnessing the systematic delay ( ≡ kinematical age) between the epoch of star formationand the moment when these massive binaries becameX-ray emitters. Figure 2 presents the population ofHMXBs and OB associations in the Milky Way as itwould appear to an observer situated above the Galac-tic Plane. Thanks to an increase in HMXB statistics,and by using a recent Galactic spiral arm model (Vall´ee2008), we can now attribute the apparent offset, at leastpartly, to foreground sources that are unrelated to theNorma Arm, and to sources located towards the tan-gent to the Inner Perseus Arm. The extension of thelatter arm into the Inner Galaxy was not considered inprevious spiral arm models (see also Hou et al. 2009).Clearly, a precise study of the spatial relation ofmassive star-forming regions and the HMXBs theyspawn can offer valuable insight into stellar and Galac-tic evolution. The drawback with longitudinal orgalactocentric distance distributions is that these his-tograms consider only a single dimension at a time. Ineffect, they project an entire spatial component ( R inthe case of a longitudinal distribution, and l in the caseof a galactocentric distance distribution) onto the othercomponent. Precious information about the true prox-imity of objects in the two populations is lost. Hence,these methods can not accurately assess the spatial Fig. 1.— Distribution of Galactic longitudes andgalactocentric distances (when known) of HMXBs(shaded histogram) and OB associations from Russeil(2003) (thick curve: divided by 5). The locations ofthe spiral arm tangents are shown. The distributions ofHMXBs in these projected spatial directions are com-patible with those of OB associations.relation, restricting their ability to provide the char-acteristic scales that would help us understand howHMXBs are distributed in the Milky Way.A better approach is to consider the spatial (orcross-) correlation function ξ (or SCF). This functionprovides a statistical measure of the clustering of pointsources in multi-dimensional maps of the sky. It is fre-quently used to relate active galactic nuclei with clus-ters of galaxies (e.g. Peebles 1980; Landy & Szalay1993). In Section 3, we adapt the methods described inthese papers to suit the study of HMXBs on a Galacticscale, and we assess biases in Section 4. Our findingsare discussed in the context of stellar and Galactic evo-lution in Section 5.
2. Data
We selected all sources from Bodaghee et al. (2007)which are confirmed or strongly suspected of beingHMXBs. This catalog contains hard X-ray detectedsources ( &
20 keV), meaning that their detection doesnot depend on the photoelectric absorption that blocks2ig. 2.— Galactic distribution of HMXBs whose distances are known (79, filled triangles) and the locations of OBassociations from Russeil (2003) (458, circles). The symbol size of the latter is proportional to the amount of activityin the association ( ≡ amount of ionizing photons as determined from the radio continuum flux). The spiral arm modelof Vall´ee (2008) is overlaid with the Sun situated at 7.6 kpc from the Galactic Center (GC). HMXBs whose distancesare not known have been placed at 7.6 kpc (23, empty triangles), i.e., the Sun-GC distance assumed in Vall´ee (2008);note that these sources are not included in the cross-correlation analysis. The shaded histogram represents the numberof HMXBs in each 15 ◦ bin of galactic longitude as viewed from the Sun.soft X-rays ( . . The date of April 1, 2011, representsthe cut-off after which we no longer considered new http://irfu.cea.fr/Sap/IGR-Sources
3. The Spatial Correlation Function
For a given HMXB in a volume element δ V , theprobability δ P (in excess of Poisson) of finding an OBassociation in a volume element δ V separated by adistance r (in kpc) is: δ P = n n (cid:2) + ξ ( r ) (cid:3) δ V δ V (1)The mean number densities are given by n and n where the subscripts refer to the two populations:HMXBs (1) and OB associations (2). These are youngobjects that remain within 45 ±
20 pc of the GalacticPlane (Reed 2000), so we assume that the displace-ment along the z -axis is negligible, and surface (ratherthan volume) elements are used.Rings of 1-kpc thickness (from 0 to 20 kpc) are con-structed around each HMXB. In each ring, we countthe number of observed OB associations, and we keepa separate tally of the number of OB associations Fig. 3.— Spatial correlation functions ξ ( r ), where r represents the distance from a given HMXB (in kpc),are presented for both estimators. Three random dis-tributions were considered: a Gaussian ring centeredat 7.6 kpc with σ z = . ≤ r ≤
16 kpc; and a uniform disk with a hole at 2 kpcfrom the GC. The curves are slightly shifted horizon-tally in order to allow the 1- σ error bars to be clearlydistinguished. At short distances from a given HMXB, ξ >
1. This suggests that the closest neighbors ofan HMXB tend to be observed OB associations ratherthan OB associations drawn from a random distribu-tion.drawn from a random distribution. An HMXB-OBpair is referred to as a DD -pair (for data-data pair),while an HMXB-random OB pair is labelled DR (fordata-random). In this way, we construct ξ for each ra-dius according to the definition of Peebles (1980): ξ ( r ) = n R DD n D DR − ξ =
0, which implies that each ring contains asmany DD -pairs as DR -pairs, then Eq. 1 is simply a uni-form Poissonian probability. However, if ξ >
0, thenthere is a higher chance of an HMXB having a neigh-bor that is an observed (rather than a randomized) OBassociation. Landy & Szalay (1993) propose a morerobust estimator for ξ in which the variance is nearlyPoissonian:4ig. 4.— Distributions of distances between pairsof HMXBs and observed OB associations (redshaded histogram), and between pairs of HMXBsand Gaussian-randomized OB associations (divided by10 , blue histogram). A KS-test (lower panel) yields aprobability < − of statistical compatibility. ξ ( r ) = DD − DR − DR + RR RR (3)Three random distributions were considered: a diskmodel in which the OB associations were uniformlydistributed between 0 an 16 kpc from the GC; a diskmodel with a hole, i.e., a uniform distribution from2 kpc to 16 kpc from the GC; and a Gaussian distri-bution centered at 7.6 kpc from the GC with σ z = . n D and n R are equal. One thousand trials were performedwith each randomization model. The average ξ , alongwith its 1- σ uncertainties, are shown in Fig. 3.All three randomization models and both estimatorsof ξ lead to the same result: near an HMXB, the prob-ability of finding a known OB association is higherthan expected from Poisson statistics. In other words,HMXBs and OB associations are clustered together. Our measured value of ξ ( r < = . ± . xDD ∼ DR (where x ∼ . ∼ ξ ∼ r < σ in excess of Poisson (up to17 σ for the Landy & Szalay (1993) estimator). Theobserved and random surface-density distributions arestatistically compatible only at large radii (i.e. r & ξ ( r < > ξ (2 ≤ r < ξ decreases as wemove away from an HMXB (up to a certain limit).This is simply a consequence of the increase in thesurface areas, and hence the number of possible pairs,with increasing radius.Of the three models, the Gaussian distribution pro-vides the best approximation since its ξ deviates theleast from Poisson statistics at short distances. Thedisk distributions (with and without a central hole) areno longer considered.
4. Statistical and Systematic Biases
Observational biases affect the correlation functionof the objects in the survey. This is not trivial as thedistribution of HMXBs and OB associations are, a pri-ori , not well understood. The type of random dis-tribution that one chooses leads to a systematic bias.This is readily apparent from Fig. 4 where the dis-tances between pairs of HMXBs and observed OB as-sociations are compared with the distances betweenpairs of HMXBs and Gaussian-randomized OB associ-ations. Despite the fact that the distributions have sim-ilar mean and variance values, the higher moments ofthe distributions (skewness and kurtosis) disagree. AKolmogorov-Smirnov test yields a probability of lessthan 10 − of statistical compatibility between the twodistributions.Selection bias is also important. An HMXB sit-uated far from the Sun needs to be correspondinglymore luminous in order to be detected in the X-rays.Large distances also make the optical classification asan HMXB more difficult: line spectroscopy of thedonor star is hindered by reddening and absorptionfrom interstellar material in the Galactic Disk. Thisleads to a preponderance of HMXBs (as well as ob-5ig. 5.— Same as Fig. 3 but restricted to objects within8 kpc from the Sun. The random catalog assumesa Gaussian-ring distribution. Clustering between 54HMXBs and 361 OB associations persists with a sta-tistical significance of 7 σ .served OB associations) close to the Sun, and a paucityof such objects situated behind the GC and its bar: a re-gion referred to as the “zona Galactica incognita” (e.g.,Vall´ee 2002). The random distributions of HMXBsand OB associations that we generated did not con-sider this observational sampling bias.It is reasonable to expect symmetry in the distribu-tion of HMXBs and OB associations around the Galac-tic Disk. However, the fact that there are less HMXBsdetected (with distances measured) in the zona incog-nita will surely affect the SCF. Therefore, we gener-ated the SCF for a restricted boundary correspondingto a circle of 8-kpc radius around the Sun—a perime-ter inside of which most HMXBs and OB associationsshould be detectable and their distances known withreasonable accuracy. When only pair counts of objects(54 HMXBs and 361 OB associations) in the Solarneighborhood are considered, the clustering signal atsmall radii persists with a statistical significance of 7 σ for r < Top : Three-sigmaboundaries (gray shaded region) from multiple SCFsgenerated by randomly shuffling (according to a Gaus-sian distribution) the line-of-sight distance to eachHMXB within its distance uncertainty. The blue dottedline and data points represent the non-perturbed (i.e.,observed) SCF as presented in Fig. 3.
Bottom : The dis-tribution of the clustering significance from all reshuf-fling trials where significance is defined as ξ ( r ) /σ .From left to right, the panels present the distributionsfor ξ ( r < ξ (1 ≤ r < ξ (2 ≤ r < ξ for each of the 100 randomly-shuffled HMXB distributions. Keep in mind that theOB distribution is itself randomized 10 times per trial,which means that the total number of different HMXB-OB configurations that we tested is actually 10 .Even when the HMXBs are perturbed within theirline-of-sight uncertainties, the clustering signal re-mains above 7 σ in all trials for r < ξ ≥ ξ value that is above thiscutoff at the 3- σ level. Based on the >
99% confidenceinterval displayed in Fig. 6, we estimate a systematicuncertainty of 5% on ξ .Potential differences in the scale heights of the twopopulations has thus far been ignored. A few HMXBspresent high velocities tangential to the Galactic Plane(e.g., 4U 1907 +
09, Gvaramadze et al. 2011). Byprojecting this velocity component onto the GalacticPlane, we can expect to underestimate the true offsetbetween an HMXB and a nearby OB association. Thiswill lead to samples that are more correlated than theyshould be. Therefore, we calculated the Galactic scaleheight for members of our HMXB and OB samples.The average scale heights are in good agreement at0.1 kpc for both samples with standard deviations of Fig. 8.— The SCF is presented for the case in whicha randomized (Gaussian ring) HMXB catalog is takenas the observed set and is then compared with the OBassociations.0.1 and 0.4 for HMXBs and OBs, respectively. Thissuggests that at the 3- σ level, HMXBs are located atmost 0.4 kpc above or below the Plane. This valueis consistent with the characteristic scale and averageminimum offset that are discussed in Section 5. Ninetypercent of the HMXBs (70/79) are within 0.25 kpcof the Plane with no HMXBs located further than0.55 kpc from the Plane. Therefore, we are justifiedin using the 2-D distribution since any increase in thecorrelation significance caused by this projection ef-fect will be negligible given that these offsets are lessthan the 1-kpc width of each ring in our correlationanalysis.We tested the correlation between HMXBs and OBassociations against the spiral arm model of Russeil(2003) whose equations represent the best-fitting four-arm logarithmic spiral to the locations of the star-forming complexes shown as blue circles in Fig. 2.Here, we adopted the Sun-GC distance of 8.5 kpc as-sumed in the model. This model yields an overdensityof points describing an arm in the inner Galaxy com-pared with the same arm in the outer Galaxy (i.e., asone loops through the range of angles that trace an armfrom the inner to the outer Galaxy, the actual distanceseparating successive points becomes larger). Thus, in7ig. 9.— The SCF compares HMXBs with 133 glob-ular clusters from Bica et al. (2006) that are locatedwithin 20 kpc of the GC. The random catalog of glob-ular clusters assumes an exponential decay law. TheSCF is consistent with Poisson statistics at close radii,which means that the neighbors of HMXBs are just aslikely to be drawn from the observed distribution asthey are from a random one: i.e., there is no clusteringbetween HMXBs and globular clusters.order to reduce this bias, we extracted 115 points cho-sen at random along each of the four arms (460 total:i.e. equivalent in number to the 458 observed OB as-sociations). We performed a visual check and verifiedthat the spiral pattern was easily discernible with nomajor gaps ( > ξ ( r ) ∼ r (i.e., DD ∼ DR for all r ). Similarly,we found no significant clustering between HMXBsand the points representing the spiral arms. Restrict-ing the analysis to objects in the Solar vicinity (i.e.,within 8 kpc of the Sun) leads to similar conclusions,so we can rule out an apparent lack of distant OB as-sociations (or HMXBs) skewing the results. In otherwords, around any given OB association (or HMXB),one tends to find as many neighbors drawn from arandomized Gaussian ring distribution, as neighborsrepresenting the spiral arms. These comparisons ofour observed stellar samples with the Galactic mod- els allow us to conclude, as acknowledged by Russeil(2003), that such spiral arm models are an overly sim-plistic representation of the real picture.In another test, we randomized the HMXB distri-bution (using the Gaussian ring approximation) andwe assumed that this sample was the observed HMXBset. The ξ relating randomized HMXBs and OB as-sociations is presented in Fig. 8. There is a moder-ate deviation from Poisson statistics at short radii forthe Peebles (1980) estimator (whose values are > observed HMXBdistribution that is clustered with the OB associations.Clustering between HMXBs and OB associations isexpected. How would ξ react if HMXBs were com-pared to a population of sources for which no spa-tial correlation is expected? We tested the correlationfunctions of HMXBs against a set of 133 globular clus-ters from Bica et al. (2006) that are located less than20 kpc from the GC. Globular clusters contain olderpopulations such as cool KM dwarf stars and low-mass X-ray binaries (LMXBs). Unlike HMXBs, glob-ular clusters (and LMXBs) are densely packed in theGalactic Bulge and their numbers drop exponentiallywith increasing radius from the GC (Bodaghee et al.2007). The random distribution of globular clusterswas thus modeled as an exponential decay law ad-justed to be consistent with the observed distribution.Figure 9 shows that ξ between HMXBs and globularclusters is consistent with 0 for r < − in the forward ( + ) and reverse ( − ) directions of time.The continuous curve represents the values for ξ ( r < ξ (1 ≤ r < ξ (2 ≤ r <
5. Discussion
There are several questions that we seek to addressusing the SCF. What is the characteristic scale of theclustering between HMXBs and OB associations? Canthis scale be used to constrain the amount of migra-tion due to the effects of Galactic rotation (see, e.g.,Ramachandran & Deshpande 1994), and perhaps dueto the primordial “kick” velocity imparted to the sys-tem during the formation of the compact object? Over-all, what can this scale tell us about the evolutionaryhistory of HMXBs?
According to the density-wave theory of spiralgalaxies (Lin & Shu 1964; Lin et al. 1969), the veloc-ity of the spiral pattern is only half that of the materialmoving in and out of the arms. These arms appear sta-tionary to an observer in a non-inertial reference framethat is rotating at the pattern speed, while the motionsof individual objects within the Galaxy are not. As material encounters the quasistatic density waves, it isshocked and compressed which allows the Jeans crite-rion to be satisfied locally, triggering fragmentation ofthe cloud, and ultimately star formation.Massive stars in binary systems have a main se-quence (MS) lifetime of around 5 × yr (Schaller et al.1992). The exact age depends strongly on the stellarmass and spectral type. In addition, there is a system-atic delay of ∼ × yr between the supernova phaseand the X-ray emission phase (van den Heuvel 1983).The X-ray phase lasts only 10 yr (Iben et al. 1995)which is negligible on these timescales. In 10 Myr,a combination of global (Galactic rotation) and localeffects (e.g., supernova kicks, cluster outflows, anddynamical ejections) will cause newly-formed O andB stars to eventually migrate away from the densegaseous regions in which they were born. In principle,each spiral arm includes three components (Lin et al.1969): a dusty strip in which the gas concentrationand OB star formation rate are highest; a lane of lumi-nous and recently-formed OB stars that have ionizedlarge regions of gas (H II); and a wider lane of post-MS, red, or dying supergiant stars with smaller H IIregions. The HMXBs should be found among therecently-formed OB stars and the post-MS stars.Outside of the inner Galaxy (i.e., galactocen-tric radius R & ∼
200 km s − (e.g., Merrifield1992; Brand & Blitz 1993; Glushkova et al. 1999;Sofue et al. 2009). Thus, a star at the Solar galacto-centric radius (7.6 kpc) will have moved 6 . × km(200 pc) in 1 Myr (defined as the migration timescaleor τ ), assuming a circular orbit. In this manner, werotated the HMXBs in space along their galactocen-tric orbits corresponding to τ = + ) andreverse ( − ) directions of time (clockwise and counter-clockwise, respectively, in Fig. 2). Figure 10 presentsthe values of the SCF resulting from these shifts forsmall radii ( r < ∼ ξ is compatible with Pois-sonian statistics, and so these curves are omitted forclarity.Certain shifts increase the amplitude of the clus-tering signal. Increases in the amplitude of ξ are di-rectly related to an increase in the number of observedOB associations contained within the specified radiusaround the shifted HMXBs. This is because the ran-domized OB distribution is axisymmetric with respectto the GC, and so the number of random OB associa-9ions inside the radius remains relatively constant un-der shifts in either direction. Given that these shiftsare small ( . ξ diminishes withincreasing distance from an HMXB, as illustrated bythe trend towards flatter curves for ξ (1 ≤ r < ξ (2 ≤ r < ξ ( r < ξ maximized for migration timescales around −
10 Myr. Instead, we find that the amplitude of ξ is maximized for migration timescales between − − ξ is a good indicator of the averageproximity of HMXBs to the OB associations that tracethese arms, we should see an asymmetry in its distri-bution with higher values of ξ at negative timescalesthan at positive timescales.Indeed, there is a slight preference for migration to-wards the leading edge of spiral arms as hinted at bythe asymmetric distribution and the downward trendin ξ for − . τ . + ξ isgreater for negative migration timescales ( τ ∼ − τ = ξ for small positive migration timescales (i.e., + . τ . + Galactic rotation can not fully explain the be-havior of ξ under different migration timescales.One mechanism suspected of giving an HMXB asignificant velocity is the primordial kick inheritedby the binary during the supernova event that cre-ated the compact object. This runaway velocity(with respect to its OB association) can be pro-duced by asymmetric supernovae (Shklovskii 1970),or from recoil due to anisotropic mass loss fromthe primary to the secondary (Blaauw 1961). Fac-tors external to the binary can also allow it to es-cape from its parent association: e.g,, dynamicalejection and cluster outflows (Poveda et al. 1967;Pflamm-Altenburg & Kroupa 2010).Theoretical estimates for post-SN kick veloci-ties are v k ∼ − (Brandt & Podsiadlowski1995), assuming a non-eccentric, 1–25-d orbital pe-riod binary system composed of a 5 M ⊙ star that ex-plodes in an asymmetric supernova leaving behind a1.4 M ⊙ NS that tugs its hefty 15 M ⊙ donor star. Ve-locities typical of isolated pulsars (200 km s − or even350 km s − ) have been suggested depending on the ini-tial conditions in the binary (Portegies Zwart 1995;van Bever & Vanbeveren 1997). van den Heuvel et al.(2000) distinguish between kick velocities in SGXBsystems from those of BEXBs: ∼
40 and ∼
15 km s − ,respectively. Selecting only the 38 SGXBs or onlythe 35 BEXBs from the HMXB sample yield consis-tent results: both populations show & σ clusteringwith OB associations with no statistically significantdifferences between SGXBs and BEXBs.In certain cases, the value of the kick velocitycan be derived from the the radial velocity or propermotion when the identity of its parent OB associa-tion and the line-of-sight distances are known. TheHMXB can then be traced back to its birthplace lead-ing to an estimation of its kinematical age. Obser-vations of the SGXB LS 5039 set v ∼
150 km s − which constrains the time since its supernova towithin 1.1 Myr (Rib´o et al. 2002). Another BEXB,LS I + ◦ v =
27 km s − and experienced itssupernova 1 . ± . −
377 shows v =
75 km s − withits supernova 2 . ± . v =
90 km s − with 2 ± +
09 was measured at ∼
160 km s − r min = ± r min ,and with ξ maximized at τ ∼ − ±
50 km s − for theHMXBs in our sample. This is consistent with mea-surements of the kick velocities in individual objects(see Table 2 and, e.g., Gunn & Ostriker 1970; Stone1979).Alternatively, with r min = . ± . v =
100 km s − , this translates to a migrationtimescale of 4 ± ξ whose value is maximized between − − ξ between + + Myr (which we wouldexpect for kicks in random directions) is consistentwith the effects of Galactic rotation, and is supportedby Carney et al. (2005) who found a significant defi-ciency in the number of objects moving in retrogradeGalactic orbits, at least for metal-poor binary stars inthe Solar neighborhood. The range of shifts that in-crease the correlation amplitude is wide reflecting thebroad parameter space of velocities and kinematicalages represented within the HMXB class. Dynamicalejection from the cluster prior to the supernova phasecan lead to runaway velocities of the order of 150–200 km s − (Poveda et al. 1967; Gies & Bolton 1986;Pflamm-Altenburg & Kroupa 2010). This would makeit difficult to retrace the trajectory of the HMXB backto its parent association, and the migration distancewould be larger than expected from a kick alone. Thisis another factor contributing to the wide range in theshifts that increase the amplitude of ξ .Thus, the observed distribution of HMXBs in the Milky Way is consistent with the view that these sys-tems have high velocities, on average. Chevalier & Ilovaisky(1998) arrived at the same conclusion by deriving thepeculiar velocities of 17 HMXBs using HIPPARCOS observations (see also van den Heuvel et al. (2000)concerning unreliable distance estimates for thesesources). This feature is not unique to the Milky Waysince HMXBs in the Small Magellanic Cloud alsopossess large velocities, on average (Coe 2005).Minimum separation distances can provide cluesto the HMXB-OB connection in specific cases (e.g.,van den Heuvel et al. 2000). For example, thereare 8 HMXBs in our sample for which the uncer-tainty on the line-of-sight distance is smaller thanthe distance separating it from its nearest OB asso-ciation: 1H 1249 − + − − + ∼ ± − −
2, GX 304 −
1, H 1145 − + + + − − . +
634 which has an uncertainty of ±
6. Summary & Conclusions
This is the first time that the clustering of HMXBsand OB associations in the Milky Way has beendemonstrated statistically. Since the correlation func-tion relates objects in Cartesian space (adding a thirddimension is trivial), this is a more robust spatial rela-tion than those derived in prior studies which focusedon the distribution of a single dimension such as lon-gitudes or galactocentric radii.Not only does the correlation function confirm theexpected view that HMXBs and OB associations areclustered together, the characteristic scale of the cor-relation contains the vestiges of stellar and Galacticevolution. Migration due to the kick velocity gainedby the binary after the supernova can be constrained toa few hundred parsecs. This translates to kinematicalages (time spanning the supernova and HMXB phases)of ∼ Chandra survey of the NormaArm will help locate dozens of new HMXBs whichwill allow us to examine the clustering of HMXBs andOB associations within a specific arm. The structure of these spiral arms should come into sharper focus withthe
Gaia mission (Perryman et al. 2001). The nexthard X-ray surveyor,
NuSTAR (Harrison et al. 2010),will provide unprecedented sensitivity at these ener-gies in the hunt for HMXBs. An increase in the dis-covery space of HMXB populations should allow us toprobe deeper into the evolutionary history of massivestars and compact objects. This will permit a betterunderstanding of the stellar content and its distributionin the Galaxy.The authors warmly thank the referee for usefuldiscussions that led to an improved manuscript. ABthanks Prof. I.F. Mirabel for discussions on the natureof HMXBs, and Dr. N. Barri`ere for help with IDL.AB and JT acknowledge partial support from
Chan-dra award number G08-9055X issued by the
Chan-dra
X-ray Observatory Center, which is operated bythe Smithsonian Astrophysical Observatory for and onbehalf of the National Aeronautics and Space Admin-istration (NASA), under contract NAS8-03060. Thisresearch has made use of: data obtained from the HighEnergy Astrophysics Science Archive Research Cen-ter (HEASARC) provided by NASA’s Goddard SpaceFlight Center; the SIMBAD database operated at CDS,Strasbourg, France; NASA’s Astrophysics Data Sys-tem Bibliographic Services; and the IGR Sources page( http://irfu.cea.fr/Sap/IGR-Sources ). REFERENCES
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This 2-column preprint was prepared with the AAS L A TEX macrosv5.2.
ABLE ISTANCES REPORTED FOR THE HIGH - MASS X- RAY BINARIES USED IN THIS ANALYSIS
Name l b distance [kpc] classification reference1A 0535 +
262 181.445 − + . − . BEXB (P, QPO, C, T) Steele et al. (1998)1A 1118 −
615 292.500 − ± − − . ± . −
637 301.958 − . ± .
055 BEXB (P?) Megier et al. (2009)3A 0114 +
650 125.710 + . ± . −
072 220.128 − . ± . −
024 30.421 − +
543 100.603 − . −
56 285.350 + −
377 347.754 + . ± .
343 SGXB Megier et al. (2009)4U 1909 +
07 41.896 − ± − + . ± . + ± + . ± .
25 SGXB (BHC, muQSO) Zi´ołkowski (2005)Cyg X-3 79.845 + . + . − . SGXB (BHC, muQSO, QPO) Ling et al. (2009)EXO 0331 +
530 146.052 − . ± . +
375 77.152 − . ± . − . ± .
012 BEXB Megier et al. (2009)Ginga 1843 +
009 33.038 + . ± . −
57 283.000 − +
610 135.675 + . − − . ± . − + . ± . +
634 125.924 + ± −
619 295.611 − . ± . −
624 313.021 − ± −
522 327.419 + . +
097 43.744 + + − + + + + ± . + + − + . − − . − + . − − − + . − − . ± . − − − + . ± . − − . + . − . SGXB (E?) Nespoli et al. (2008)
ABLE Continued
Name l b distance [kpc] classification referenceIGR J16318 − − . − + . − − − − ± − + . − + − + . + . − . SFXT (P, E?) Nespoli et al. (2008)IGR J16479 − − . + . − . SFXT (E, P?) Nespoli et al. (2008)IGR J17252 − − + . − SGXB (P, E) Mason et al. (2009)IGR J17391 − + . − − . − − . ± − + . ± . − + ± − − . − − . + − . SFXT (P) Nespoli et al. (2008)IGR J18450 − − . − − . ± .
05 SFXT (P) Torrej´on et al. (2010)IGR J19113 + + . + − . ± .
04 SGXB (NS?) Torrej´on et al. (2010)IGR J21347 + − . +
300 66.099 + . ± . −
415 344.369 + . ± . −
63 304.165 − . + . − . BEXB (P, VHE) Cordes & Lazio (2002)RX J0146.9 + − . ± . + − . ± . − − . ± . − − . ± . + − . ± . − . ± . + + + . ± . − . ± .
138 BEXB (P, C) Megier et al. (2009)XTE J1543 −
568 324.955 − −
189 11.362 + . −
098 21.697 + −
026 31.076 − +
274 63.207 + . ± . OTE .—BEXB=Be X-ray binary; BHC=black hole candidate; C=cyclotron; E=eclipsing; HMXB=high-mass X-ray binary;muQSO=microquasar; NS=neutron star; P=pulsations; QPO=quasi-periodic oscillations; SFXT=supergiant fast X-ray transient;sgB[e]=supergiant B-emission line star; SGXB=supergiant X-ray binary; T=transient; VHE=very high energy
ABLE ICK VELOCITIES AND KINEMATICAL AGES REPORTED FOR A FEW WELL - KNOWN
HMXB S name velocity [km s − ] kinematical age [Myr] migration distance [kpc] reference4U 1700 −
377 75 2.0 0.2 Ankay et al. (2001)LS 5039 150 1.1 0.2 Rib´o et al. (2002)LS I + ◦
303 27 1.7 0.05 Mirabel et al. (2004)Vela X-1 160 0.1 0.02 Gvaramadze et al. (2011)T
ABLE INIMUM SEPARATION DISTANCES BETWEEN
HMXB
S AND OB ASSOCIATIONS IN SELECTED CASES name HMXB distance uncertainty [kpc] distance to nearest OB assoc. [kpc]HMXB distance uncertainty < distance to nearest OB assoc.1H 1249 −
637 0.06 0.1Cyg X-3 0.5 0.7EXO 2030 +
375 0.2 0.6gam Cas 0.02 0.08IGR J18027 − − + ≥ distance to nearest OB assoc.4U 1700 −
377 0.5 0.2Cyg X-1 0.25 0.2GX 301 − − −
619 0.5 0.2IGR J01583 + + + − −−