Distribution of High Mass X-ray Binaries in the Milky Way
***Volume Title**ASP Conference Series, Vol. **Volume Number****Author** c (cid:13) **Copyright Year** Astronomical Society of the Pacific Distribution of High Mass X-ray Binaries in the Milky Way
Alexis Coleiro and Sylvain Chaty
Laboratoire AIM (UMR 7158 CEA / DSM - CNRS - Universit´e Paris Diderot),Irfu / Service d’Astrophysique, CEA-Saclay, 91191 Gif-sur-Yvette Cedex,France. e-mail: [email protected]; [email protected]
Abstract.
The INTEGRAL satellite, observing the sky at high energy, has quadru-pled the number of supergiant X-ray Binaries known in the Galaxy and has revealednew populations of previously hidden High Mass X-ray Binaries. These observationsraise new questions about the formation and evolution of these sources. The numberof detected sources is now high enough to allow us to carry out a statistical analysis ofthe distribution of HMXBs in the Milky Way. We derive the distance of each HMXBusing a Spectral Energy Distribution fitting procedure, and we examine the correlationwith the distribution of star forming complexes (SFCs) in the Galaxy. We show thatHMXBs are clustered with SFCs, with a typical size of 0.3 kpc and a characteristicdistance between clusters of 1.7 kpc.
1. Introduction
High Mass X-ray Binaries (HMXBs) are binary systems composed of a compact object,a neutron star or a black hole candidate, accreting matter from a massive companionstar: either a main sequence Be star or an evolved supergiant O or B star. Most of thesesources are observed in the Galactic Plane (Bird et al. 2007) as it is expected for suchyoung star systems which do not have time to move far from their birthplaces.Thanks to the dedicated observations from
RXTE and
INTEGRAL , around 200 HMXBsare currently known in the Milky Way allowing us to focus on their distribution. UsingRXTE data, Grimm et al. (2002) highlighted clear signatures of the spiral structure inthe spatial distribution of HMXBs. In the same way, Dean et al. (2005), Lutovinovet al. (2005), Bodaghee et al. (2007) and Bodaghee et al. (2011) showed that HMXBsobserved with
INTEGRAL also seem to be associated with the spiral structure of theGalaxy. However, the HMXB positions, mostly derived from their X-ray luminosity,are not well constrained and highly uncertain due to direct accretion as in HMXB.In order to overcome this caveat we present a novel approach allowing us to derive allHMXB positions. We build the Spectral Energy Distribution (SED) of each HMXB andfit it with a black-body model to compute the distance of each source. Finally, we studythis distribution and the correlation with Star Forming Complexes (SFCs) observed inthe Galaxy. 1 a r X i v : . [ a s t r o - ph . H E ] J u l Alexis Coleiro and Sylvain Chaty
2. Deriving the HMXB location within the Galaxy
In order to compute the HMXB distances, we gathered a set of HMXBs for which atleast 4 optical and / or NIR magnitudes are known, and for each source its SED was builtand fit with a blackbody model. This enables us to evaluate the distance of the sourcealong with its associated errors. There are currently more than 200 HMXBs detected in the Milky Way. Using an up-dated version of the Liu et al. (2006) catalogue , we retrieved the optical, NIR magni-tudes, the spectral type and the luminosity class of each source. For each HMXB, fourmagnitudes are required to compute the fitting procedure. Indeed, according to the χ computation, the condition N − n ≥ N the number of observed magnitudes and n the number of parameters left free (in our study, n =
2, cf. section 2.2), needs to bemet. Finally, we selected around 70 sources meeting these conditions.
Our fitting procedure is based on the Levenberg-Marquardt least-square algorithm im-plemented in Python. For each HMXB, we build the SED in optical and NIR from amaximum of 8 magnitude points (U, B, V, R, I, J, H, Ks) and, as we underlined before,a minimum of 4 magnitudes are required by the fitting. This SED is then fit (see figure1) by a black-body model given by the relation: λ F λ = π hc λ × − . A λ ( R / D ) exp (cid:16) hc λ k B T (cid:17) (1)where λ is the wavelength in µ m, F λ the flux density in W.m − . µ m − , h the Planckconstant, k B the Botzmann constant, c the speed of light, A λ the extinction at the wave-length λ , R / D the stellar radius over distance ratio and T the temperature of the star.From the spectral type and the luminosity class, we derive the radius and the tempera-ture of the companion star which dominates the optical and NIR flux (Morton & Adams1968; Panagia 1973; Searle et al. 2008). Two parameters are left free: the extinction inV band A V and the ratio R / D whereas the extinction A λ is derived from Cardelli et al.(1989) at each wavelength assuming R V = . R of the companion star (see Morton & Adams 1968, Panagia 1973) , we calculate thedistance D in kpc.The least square function given by the formula χ = (cid:88) i (cid:34) X i , obs − X i , model σ i (cid:35) (2)(with X i , obs the observed flux value for the filter i , X i , model , the theoretical flux inthe i th filter derived from the black-body model and σ i , the flux error in the same filter)is then minimized by the Levenberg-Marquardt algorithm. see IGR Sources web page maintained by J. Rodriguez & A. Bodaghee (http: // irfu.cea.fr / Sap / IGR-Sources / ) lexis Coleiro and Sylvain Chaty d = 8.8 kpcAv = 5.2 Figure 1. Result of the fitting for one source with distance D and extinction in Vband, A V . The magnitude uncertainties are retrieved from the literature. For the sources for whichno error is given, we use a systematic error of 0.1 magnitude. The flux uncertaintiesare then derived from these magnitude errors. Otherwise, we assume the spectral typegiven in the literature as the real spectral type of the companion star. Simulations werecarried out and enabled us to constrain the spectral type error that appears to be lessimportant for supergiant stars than for Zero-Age Main Sequence ones.Degeneracy between several parameters values (based on the fitting procedure)needs to be taken into account. Indeed, solely relying on a single best fit does notcapture the full phenomenology associated with SED fitting because extinction A V anddistance D are degenerated in this approach. In order to produce the most likely setof fits and to determine the dispersion on distance and extinction we carried out 500Monte-Carlo simulations for each observed source by varying the photometry withinthe uncertainties. Hence, we generate a random number from a normal distribution (as-suming the photometric errors to be Gaussian) contained within the error bars for eachphotometric point so that we build 500 new SEDs derived from the original one. These500 new SEDs are subject to the same χ statistic computation as the one describedabove. Then, we have an entire set of best fits of parameters ( A V , D ) and, we are ableto plot the distribution in the parameters space, showing the distribution of propertiesderived from these Monte-Carlo simulations and especially showing the dispersion ondistance and extinction. This dispersion value is taken as the error coming from thefitting procedure and the median value of dispersion on distance determination (for allthe HMXBs under study) is 0.75 kpc.There are other sources of uncertainties, particularly the infrared excess of Bestars due to their circumstellar envelope generating free-free radiation. According toDougherty et al. (1994), this excess should not exceed a mean 0.1 magnitude in J band,0.15 magnitude in H band and 0.25 magnitude in K band. However, this value corre-sponds to absolute magnitude and therefore can be smaller for sources located far awayand higher for close ones. To take this e ff ect into account, an estimate of the distanceand extinction A V is needed. Since these two values are derived from the fitting pro-cedure, we are only able to consider as a distance and absorption estimate the valuesobtained without taking this IR excess into account. This approach is finally equiva- Alexis Coleiro and Sylvain Chaty lent to adding a conservative excess of 0.1, 0.15 and 0.25 magnitude to the apparentmagnitude in the J, H and Ks bands respectively. The results are presented on figure2.1. N o r m a C r ux C a r i n a S c u t u m P e r s e u s C y g nu s S a g i tt . Figure 2. 1) Green circles represent the initial positions of Be stars whereas bluestars represent the source positions taking into account the IR excess. 2) Distributionof HMXBs (blue stars) and distribution of SFCs (green circles). Circle radius repre-sent the di ff erent excitation parameter values. The spiral arms model from Russeil(2003) is also plotted and the red star (at X = =
3. Results: distribution of HMXBs and correlation with Star Forming Com-plexes distribution
We present hereafter the distribution of HMXBs in the Galaxy, obtained with our novelapproach. The spiral arms model given by Russeil (2003) is also presented (see figure2.2). We want to assess the question whether there is a correlation between this distribu-tion of HMXBs and, in a first time, the distribution of Star Forming Complexes (SFCs)in the Milky Way (given by Russeil 2003), as it is expected from the short HMXB life-time.The first approach we adopt is to carry out a Kolmogorov-Smirnov test (KS-test)in each axis in order to quantify the fact that the two samples are drawn or not from thesame probability distribution. We got a value of 0.15 for the X axis, a value of 0.25 forthe Y axis and a value of 0.31 for the galactic longitude. Even if these values are notnegligible, suggesting that a correlation between the two samples is likely established,part of the information is lost because of the projection on the two axis. To overcomethis caveat, we propose another method described hereafter.We suppose that each HMXB (blue stars on figure 3.1) is clustered with severalSFCs (green circles on the same figure). Hence, we can define two characteristic scales:a typical cluster size and a typical distance between clusters. Around each HMXB, wedefine several circles with di ff erent radius (red circles on figure 3.1) and we finallycount the number of HMXBs for which at least one SFC is within the specified radius.The number of HMXBs for which at least one SFC is within the specified radiusversus the circle radius is plotted as the blue curve on figure 3.2. The green curve is thatexpected from chance correlations assuming the HMXBs are evenly distributed across lexis Coleiro and Sylvain Chaty Cluster size D i s t a n c e b e t w ee n c l u s t e r s HMXBs Random Difference
Figure 3. 1) Description of the method used to evaluate the correlation. 2) Resultof the correlation determination in 2D. the sky. The dashed line represents the di ff erence between the two previous curves. Thisdi ff erence, being non equal to zero, allows us to state that a strong correlation existsbetween the HMXB and the SFC positions in the Milky Way. Moreover, we computethe two characteristic scales exposed before: the typical cluster size of 0.3 kpc and thetypical distance between clusters of 1.7 kpc, which is larger than the median error onHMXB distances. If we take into account the uncertainties in the HMXB positions(obtained via the Monte-Carlo simulations) and in the SFC positions (given in Russeil2003, median error of 0.25 kpc), the correlation still exists with the same cluster sizeand the same distance between clusters. These results, while obtained with a di ff erentmethod, are consistent with those reached by Bodaghee et al. (2011). Finally, we testour correlation code using a sample of globular clusters (Bica et al. 2006), principallylocated in the Galactic bulge. Therefore, figure 4.1 shows the two distributions in theMilky Way whereas figure 4.2 shows the result of correlation test. Clearly, as expected,no correlation is revealed. HMXBs Random Difference
Figure 4. 1) Distribution of HMXBs and globular clusters. 2) Result of the corre-lation determination with globular clusters.
Alexis Coleiro and Sylvain Chaty
4. Conclusion
Evaluation of HMXB distribution is now of major interest in order to study in depth theformation of these high energy sources. However, HMXB locations are usually poorlyconstrained and largely dependent on the determination method. We propose here todetermine the location of a whole set of sources using the same approach: a SED fittingof the distance of HMXBs. This method, based on a least-square minimization, enablesus to reveal a consistent picture of the HMXB distribution, showing them to follow thespiral arm structure of the Galaxy. The consideration of uncertainties leads to a smallerror on the source locations and allows us to tackle the study of the correlation withSFC distribution. This study shows that HMXBs are clustered with SFCs and enablesfor the first time to quantitatively define the cluster size (0.3 kpc) and the distance be-tween clusters (1.7 kpc). The challenge is now to quantify this correlation by takinginto account the o ff set between current spiral density wave position and HMXB posi-tions expected due to the fact that the matter rotation velocity is di ff erent to the spiralarm rotation speed. Acknowledgments.
We acknowledge A. Bodaghee for his help and discussionsabout this project. We acknowledge P.A. Charles, C. Knigge, J. A. Zurita Heras,P. A. Curran and F. Rahoui for useful discussions and advice. This work was sup-ported by the Centre National d’Etudes Spatiales (CNES), based on observations ob-tained with MINE – the Multi-wavelength INTEGRAL NEtwork –. This researchhas made use of the IGR Sources page maintained by J. Rodriguez & A. Bodaghee(http: // irfu.cea.fr / Sap / IGR-Sources / ), of data products from the Two Micron All SkySurvey, which is a joint project of the University of Massachusetts and the InfraredProcessing and Analysis Center / California Institute of Technology, funded by the Na-tional Aeronautics and Space Administration and the National Science Foundation andof the SIMBAD database and the VizieR catalogue access tool, operated at CDS, Stras-bourg, France.
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