Population of persistent high mass X-ray binaries in the Milky Way
aa r X i v : . [ a s t r o - ph . H E ] F e b Mon. Not. R. Astron. Soc. , 1–17 (2013) Printed 5 February 2013 (MN L A TEX style file v2.2)
Population of persistent high mass X-ray binaries in theMilky Way
A.A. Lutovinov ⋆ , M.G. Revnivtsev , S.S. Tsygankov , , , R.A. Krivonos , Space Research Institute, Russian Academy of Sciences, Profsoyuznaya 84/32, 117997 Moscow, Russia Finnish Centre for Astronomy with ESO (FINCA), University of Turku, V¨ais¨al¨antie 20, FI-21500 Piikki¨o, Finland Astronomy Division, Department of Physics, FI-90014 University of Oulu, Finland Space Sciences Laboratory, 7 Gauss Way, University of California, Berkeley, CA 94720, USA
ABSTRACT
We present results of the study of persistent high mass X-ray binaries (HMXBs) in theMilky Way, obtained from the deep INTEGRAL Galactic plane survey. This surveyprovides us a new insight into the population of high mass X-ray binaries becausealmost half of the whole sample consists of sources discovered with INTEGRAL. It isdemonstrated for the first time that the majority of persistent HMXBs have super-giant companions and their luminosity function steepens somewhere around ∼ × erg s − . We show that the spatial density distribution of HMXBs correlates well withthe star formation rate distribution in the Galaxy. The vertical distribution of HMXBshas a scale-height h ≃
85 pc, that is somewhat larger than the distribution of youngstars in the Galaxy. We propose a simple toy model, which adequately describes gen-eral properties of HMXBs in which neutron stars accrete a matter from the wind ofthe its companion (wind-fed NS-HMXBs population). Using the elaborated model weargue that a flaring activity of so-called supergiant fast X-ray transients, the recentlyrecognized sub-sample of HMXBs, is likely related with the magnetic arrest of theiraccretion.
Key words:
Galaxy: general – X-rays: binaries – X-rays: stars – Galaxy: stellarcontent
A formation and evolution of stars and binary systems arevery slow processes (typical timescales of > yr) and cannot be directly traced. The only way to understand themis to study populations of sources. Properties of an ensem-ble of sources at different stages of their evolution do havecharacteristics which can be measured and compared withpredictions of different models.X-ray sources in our Galaxy were discovered quitelong ago (Giacconi et al. 1962, 1971) and studied inten-sively in different ways during ∼
40 years. Advances ina sensitivity and angular resolution of current X-ray tele-scopes allow now to detect and count such objects in avariety of outer galaxies (see e.g. Trinchieri & Fabbiano1991; Primini, Forman, & Jones 1993; Gilfanov 2004;Kim & Fabbiano 2004).In spite of this observational progress the properties ofpopulations of different types of X-ray sources are not fullyunderstood yet. The main reason for this is a scarce informa- ⋆ E-mail:[email protected] tion about physical properties of large samples of HMXBs.Objects in outer galaxies can be counted and their X-rayappearances measured, but physical properties of detectedsources (first of all, types and ages of their stellar compo-nents, orbital periods, etc.), which can help to understandtheir formation and evolution, rarely can be obtained (typ-ically from optical or infrared instruments) due to their ex-treme faintness.On the other hand – physical properties of stellar bi-naries in our Galaxy can often be well measured, but theuniform highly sensitive surveys of such objects were absentuntil recently. A strong absorption of soft X-rays ( < Lutovinov et al. whole Galaxy, have typically a poor angular resolutionand thus are affected by a source confusion in theGalactic plane (e.g., UHURU, Forman et al. 1978; RXTE,Markwardt et al. 2000; Revnivtsev et al. 2004). Samples ofsources, collected over all history of X-ray astronomy (e.g.,Liu, van Paradijs, & van den Heuvel 2007) can not to betaken as a representative for statistical and physical studiesof populations due to their non-uniformity respect to theflux, detection criteria, etc.A systematic survey of the Galaxy in 2003-2011 with theINTEGRAL observatory (Winkler et al. 2003) in the hardX-ray energy range ( >
17 keV) with the moderate angularresolution ( ∼ ′ ) allowed us for the first time to overcomeall these difficulties and to perform virtually unbiased searchfor X-ray binaries in the Milky Way with an unprecedentedsensitivity (Krivonos et al. 2012).Previous observations of galactic sources with the IN-TEGRAL observatory have proved to be fruitful in a va-riety of fields: for explanation of the origin of the Galac-tic Ridge X-ray emission in hard X-rays (Krivonos et al.2007); for systematic discoveries of strongly photoabsorbedhigh mass X-ray binaries and study of their distribution inthe Galaxy (see e.g. Courvoisier et al. 2003; Lutovinov et al.2005; Bodaghee et al. 2007; Lutovinov et al. 2007; Chaty2008; Coleiro & Chaty 2011; Bodaghee et al. 2012); for con-firmation of the presence of the break in the luminosity func-tion of low mass X-ray binaries (Revnivtsev et al. 2008a),which is likely related with changes of the evolutionary typeof stellar companions in these systems (Revnivtsev et al.2011).In this paper we present the most sensitive unbiasedflux-limited sample of non-transient high mass X-ray bina-ries in our Galaxy. Our main goal is to establish and under-stand general properties of this population. This knowledgeis a very important for different reasons: for understandingof properties of compact objects, their formation and evolu-tion; for explanation of the observed behaviour of differenttypes of HMXBs (in particular, supergiant fast X-ray tran-sients); for interpretation of observations of variety of galax-ies, which are now became possible with new generation ofX-ray telescopes (in particular, to calculate a contributionof HMXBs to observed luminosities), etc. In our study we use results from the INTEGRAL Galacticplane survey, presented in Krivonos et al. (2012). The sen-sitivity of this survey is typically 10 − erg s − cm − inthe 17-60 keV energy band, which ensures the detection ofsources with luminosities > ∼ erg s − within a half of theGalaxy ( < ∼ > ∼ × erg s − overthe whole Galaxy ( < ∼
20 kpc from the Sun).One of advantages of the INTEGRAL Galactic planesurvey is the multiple coverage of virtually all galacticsources. During the period of operation all parts of theGalaxy were observed tens of times, that allow us to quan-tify a long term behaviour of a majority of sources. Thisis important because the goal of our work is to understandproperties of the population of high mass X-ray binaries,which are typically registered (or can be registered) in ex-
Figure 1.
Three upper panels.
Examples of light curves ofthree sources of different types: persistent (GX 301-2), super-giant fast X-ray transient (IGR J17391-3021) and Be-transient(4U 0115+63).
Bottom panel.
Normalized distribution of valuesof fluxes, measured for these three sources in single revolutions(with the duration of about 3 days) of the INTEGRAL spacecraft(histograms). Dashed lines indicate median fluxes registered fromsources, dashed-dotted lines – mean flux values. Red color corre-sponds to the source GX 301-2, black one – to IGR J17391-3021,green one – to 4U 0115+63. isting and future surveys both our Galaxy and distant galax-ies.
Therefore in our work we concentrate only on persistentsources . Transiently appearing HMXBs typically have smallduty cycles and thus they should be a minority among thepopulation of HMXBs detected in snapshot observations ofgalaxies.As a first step, among sources detected on the averagemap of the Galactic plane we exclude all sources which areknown to be not high mass X-ray binaries. The remaining opulation of HMXBs in the Milky Way Figure 2.
Sensitivity of the INTEGRAL survey (at the 4 . σ levelin the 17-60 keV energy band) over the whole Galaxy (solid line).Coordinates and fluxes of 26 non-identified persistent sources areshown by circles. Uncertainties correspond to 1 σ . Dashed linedenotes the survey flux limit (see text for details). objects are either HMXBs or unidentified sources. In to-tal, 75 HMXBs with a confirmed nature and 33 sources ofan unknown origin (including HMXB candidates) at lati-tudes | b | < ◦ were detected during the INTEGRAL Galac-tic plane survey (Krivonos et al. 2012).Then we exclude transient sources from our sample.There is no firmly established concept of a transiency, there-fore this is a non-trivial task. To illustrate it, some examplesof a different long term behaviour of sources are shown inFig.1, where one can see light curves (upper panels) anddistributions of fluxes (bottom panel) of three sources, rep-resenting three big families of high mass X-ray binaries:(quasi-)persistent sources, Be-transients and supergiant fastX-ray transients (SFXTs). We quantify the ”persistency”of a source via a ratio of two flux values: the median fluxvalue F median and the mean flux value h F i . For our mainsource sample we accept only sources which have the ratio F median / h F i > .
5. This resulted in 54 confirmed HMXBsand 26 unidentified sources. It is necessary to note, that sev-eral SFXTs or candidates, which are named ”trantients”,still passed the selection criteria. It can be connected with ahigh duty cycle for some sources (like IGR J16479-4514) ordue to a luminosity dynamic range not particularly high forsome sources in the INTEGRAL energy band (this could bethe case of the so called intermediate SFXTs IGR J17354-3255, IGR J16418-4532, AX J1845.0-0433).In order to further increase the identification complete-ness of our sample we raise the flux limit of the survey, asvirtually all non-identified sources are faint. The sensitivityof the survey is shown as a function of the galactic longi-tude in Fig.2. It was calculated as the average value of theINTEGRAL/IBIS/ISGRI sensitivity over Galactic latitudes − ◦ < b < ◦ for each longitude direction. Circles denotefluxes of non-identified sources with their uncertainties. Twoimportant facts are clearly seen from this figure: 1) the sur-vey sensitivity is not uniform over the Galaxy and is muchbetter in its inner part (directions with | l | < ∼ ◦ ); 2) allnon-identified sources are faint. Thus, if we increase the sur-vey flux limit up to 0 . − erg s − cm − in the17 −
60 keV energy band) over the Galactic longitude range − ◦ < l < ◦ and 1 . γ -loud HMXBs).The list of selected persistent HMXBs (and non-identified) sources with their main parameters is presentedin Table 1; its contents are described below. Column (1) “Name” – source name.
Columns (2,3) “ l , b ” – source galactic coordinates, lon-gitude and latitude, respectively. Column (4) “Luminosity” – time-averaged source lumi-nosity in the 17 −
60 keV energy band. For sources withunknown distances the flux in mCrabs in this energy bandis mentioned.
Column (5) ”Distance” – distance to the source in kpc.
Column (6) ” P orb ” – orbital period of the system. Column (7) ”Class” – optical class of the normal com-panion in the binary system. In some cases two possible typeare indicated.
Column (8) “References, notes” – references andalternative source names. References correspond to thedistance, class and orbital period measurements.The spatial distribution of HMXBs from Table 1 areshown in Fig.3.
In our Galaxy there are (and it can be seen from the Ta-ble1) several types of persistent X-ray binaries with massivecompanions. The most numerous population of them is bi-naries, in which the neutron star accrete a matter from thestellar wind of the massive companion (wind-fed systems).Other types of persistent X-ray binaries with massive starsinclude: • binaries in which neutron stars accrete matter due tothe Roche lobe overflow of the giant companion star (likelyCen X-3, see e.g. Lamers, van den Heuvel, & Petterson1976); • binaries with accreting black holes (Cyg X-1, likelyCyg X-3); • binaries with a super-Eddington regime of accretion, inwhich the central engine is obscured by the accretion diskand only jet is visible in X-rays (e.g., SS 433, Fabrika 2004; • binaries where an X-ray (and gamma-ray) emissionoriginates as a result of a non-thermal emission of particlesaccelerated in colliding winds of components (PSR B1259-63, LS 5039, LSI +61 303, Eta Carinae, etc.).These classes of sources have only a few representativesin our Galaxy, which makes a study of their statistics im-possible. Therefore we will concentrate in this paper only onbinary systems with the wind-fed accreting neutron stars.
A distribution of HMXBs over their luminosities (lumi-nosity function, LF) is the simplest, but still an informativecharacteristic, which can be calculated from the sample of
Lutovinov et al.
Table 1.
List of persistent galactic high-mass X-ray binaries detected by the INTEGRAL observatoryHMXBs with fluxes > − erg s − cm − and known distancesName l , b , L X, − keV , Distance, P orb , Class Referencesdeg deg 10 erg s − kpc daysVela X-1 -96.93 3.93 5 . ± .
003 1.4 8.96 B0.5Ib 1, 2, 33U 1022-55 -74.64 1.49 0 . ± .
033 5.0 B0III-Ve 4, 5Cen X-3 -67.90 0.33 24 . ± .
041 5.7 2.09 O6-7II-III 6, 7, 8IGR J11305-6256 -66.05 -1.48 0 . ± .
012 3.0 B0IIIe 9, 10IGR J11435-6109 -65.12 0.68 3 . ± .
097 8.6 52.46 B2III or B0V 11, 12A 1145.1-6141 -64.50 -0.02 20 . ± .
095 8.5 14.4 B2Iae 13, 14X 1145-619 -64.38 -0.24 0 . ± .
012 3.1 187.5 B1Vne 15, 5, 161ES 1210-646 -61.13 -2.31 0 . ± .
011 2.8 B2V 11GX 301-2 -59.90 -0.03 31 . ± .
016 3.5 41.5 B1Ia+ 17, 18, 191RXP J130159.6-635806 -55.91 -1.12 0 . ± .
041 5.5 O9V or B1III 20, 94U 1416-62 -46.98 -1.57 0 . ± .
048 6.0 42.12 B1Ve 21, 5, 224U 1538-522 -32.58 2.16 5 . ± .
024 4.5 3.73 B0.2Ia 23, 24, 25IGR J16207-5129 -27.54 -1.05 1 . ± .
041 6.1 9.73 O7.5 26, 27, 28B1Ia 26IGR J16195-4945 -26.44 0.33 0 . ± .
022 4.5 B1sg 29, 27IGR J16318-4848 -24.38 -0.44 0 . ± .
002 1.6 sgB[e] 27IGR J16320-4751 -23.67 0.16 2 . ± .
013 3.5 8.96 O8I 27, 30AX J163904-4642 -21.99 0.07 7 . ± .
125 10.6 BIV-V 31IGR J16418-4532 -20.81 0.49 9 . ± .
191 13.0 3.75 O8.5(sg?) 31, 27, 32IGR J16465-4507 -19.94 0.13 1 . ± .
100 9.4 30.32 B0.5I 27, 33O9.5Ia 26IGR J16479-4514 -19.84 -0.12 0 . ± .
009 2.8 3.32 O8.5I 26, 27, 34O9.5Iab 26IGR J16493-4348 -18.62 0.57 6 . ± .
260 15.0 6.78 B0.5Ib 35, 36, 37OAO 1657-415 -15.63 0.32 48 . ± .
058 7.1 10.4 B0-6sg 38, 39, 404U 1700-377 -12.24 2.17 12 . ± .
004 2.12 3.41 O6.5Iaf+ 41, 42, 43EXO 1722-363 -8.50 -0.35 3 . ± .
032 6.1 9.74 B0-B1 Ia 27, 44, 45AX J1749.1-2733 1.58 0.06 3 . ± .
128 13.5 B1-3 46AX J1749.2-2725 1.70 0.11 2 . ± .
137 14.0 B3 46IGR J18027-2016 9.43 1.03 10 . ± .
140 12.4 4.6 B1b 47, 48IGR J18214-1318 17.67 0.48 1 . ± .
076 8.0 B0V-O9I 49AX J1845.0-0433 28.14 -0.66 0 . ± .
015 3.6 O9.5I 50XTE J1855-026 31.07 -2.09 14 . ± .
114 10.0 6.07 B0Iaep 51, 52, 53X 1908+075 41.89 -0.81 9 . ± .
047 7.0 4.4 O7.5-9.5sg 54, 554U 1907+097 43.74 0.47 4 . ± .
024 5.0 8.38 O8-9Ia 56, 56, 57IGR J19140+0951 44.29 -0.46 1 . ± .
012 3.6 13.56 B1I 47, 27, 58B0.5I 26SWIFT J2000.6+3210 68.98 1.13 2 . ± .
092 8.0 early BV or mid BIII 594U 2206+543 100.60 -1.10 0 . ± .
010 2.6 9.57 O9.5V 60, 611A 0114+650 125.71 2.55 6 . ± .
063 7.2 11.6 B1Ia 62, 63RX J0146.9+6121 129.52 -0.80 0 . ± .
010 2.5 B1Ve 64, 5HMXBs and candidates to HMXBs with fluxes > − erg s − cm − and unknown distancesIGR J10100-5655 -77.76 -0.67 0 . ± . a early giant 70AX J1700.2-4220 -16.23 -0.03 1 . ± . a . ± . a HMXB 70IGR J17354-3255 -4.54 -0.26 0 . ± . a . ± . a HMXB 74HMXBs with fluxes < − erg s − cm − IGR J00370+6122 121.21 -1.42 0 . ± .
010 3.0 15.665 BN0.5II-IIIb 68, 69IGR J14331-6112 -45.15 -0.76 1 . ± .
135 10.0 BIII or BV 59IGR J16283-4838 -24.66 0.08 3 . ± .
339 17.6 OBsg 65IGR J17544-2619 3.24 -0.32 0 . ± .
010 3.6 4.93 O9Ib 27, 66, 67IGR J18410-0535 26.78 -0.23 0 . ± .
011 3.2 B1Ib 26IGR J22534+6243 109.87 2.88 0 . ± . a HMXB 75 opulation of HMXBs in the Milky Way Table 1. (continue)HMXBs with black holesName l , b , L X, − keV , Distance, P orb , Class Referencesdeg deg 10 erg s − kpc daysSS 433 39.69 -2.24 3 . ± .
030 5.5 13.1 Asg 76, 77Cyg X-1 71.34 3.07 38 . ± .
005 1.86 5.6 O9.7Iab 78, 79, 80Cyg X-3 79.85 0.70 101 . ± .
057 7.2 0.2 WR 81, 82, 83 γ -loud HMXBsPSR B1259-63 -55.82 -0.99 0 . ± .
010 2.3 1236.7 B2e 84, 85, 86LS 5039 16.87 -1.29 0 . ± .
007 2.9 3.906 O6.5Vf 87, 88, 89LSI 61 +303 135.67 1.07 0 . ± .
013 2.0 26.496 B0Ve 90, 91, 92 a flux in the 17-60 keV energy band, in mCrabs References: (1) Chevalier & Ilovaisky (1998), (2) Hiltner, Werner, & Osmer (1972), (3) Boynton et al. (1984), (4) Motch et al. (1997), (5) Reig (2011), (6)Thompson & Rothschild (2009), (7) Ash et al. (1999), (8) Schreier et al. (1972), (9) Masetti et al. (2006), (10) Tomsick et al. (2008), (11) Masetti et al. (2009), (12)Corbet & Remillard (2005), (13) Ray & Chakrabarty (2002), (14) Densham & Charles (1982), (15) Stevens et al. (1997), (16) Hutchings, Crampton, & Cowley (1981),(17) Kaper, van der Meer, & Najarro (2006), (18) Koh et al. (1997), (19) Sato et al. (1986), (20) Bodaghee et al. (2007), (21) Grindlay, Petro, & McClintock (1984),(22) Finger, Wilson, & Chakrabarty (1996), (23) Clark (2004), (24) Parkes, Murdin, & Mason (1978), (25) Clark (2000), (26) Nespoli, Fabregat, & Mennickent (2008),(27) Rahoui et al. (2008), (28) Jain, Paul, & Maitra (2011), (29) Sidoli et al. (2005), (30) Corbet et al. (2005), (31) Chaty et al. (2008), (32) Corbet et al. (2006), (33)Clark et al. (2010), (34) Jain, Paul, & Dutta (2009), (35) Nespoli, Fabregat, & Mennickent (2010), (36) Nespoli, Fabregat, & Mennickent (2008), (37) Cusumano et al.(2010), (38) Audley et al. (2006), (39) Chakrabarty et al. (2002), (40) Chakrabarty et al. (1993), (41) Megier et al. (2009), (42) Clark et al. (2002), (43) Jones & Liller(1973), (44) Mason et al. (2009), (45) Markwardt & Swank (2003), (46) Karasev, Lutovinov, & Burenin (2010), (47) Torrej´on et al. (2010), (48) Augello et al. (2003),(49) Butler et al. (2009), (50) Coe et al. (1996), (51) Corbet et al. (1999), (52) Negueruela et al. (2008), (53) Corbet & Mukai (2002), (54) Morel & Grosdidier(2005), (55) Wen, Remillard, & Bradt (2000), (56) Cox, Kaper, & Mokiem (2005), (57) Marshall & Ricketts (1980), (58) Corbet, Hannikainen, & Remillard (2004), (59)Masetti et al. (2008), (60) Blay et al. (2006), (61) Corbet & Peele (2001), (62) Reig et al. (1996), (63) Crampton, Hutchings, & Cowley (1985), (64) Tapia et al. (1991),(65) Pellizza, Chaty, & Chisari (2011), (66) Pellizza, Chaty, & Negueruela (2006), (67) Clark et al. (2009), (68) Negueruela & Reig (2004), (69) den Hartog et al.(2004), (70) Masetti et al. (2006), (71) Markwardt et al. (2010), (72) Tomsick (2009), (73) D’A`ı et al. (2011), (74) Tomsick et al. (2009), (75) Masetti et al. (2012), (76)Gies, Huang, & McSwain (2002), (77) Margon (1984), (78) Reid et al. (2011), (79) Walborn (1973), (80) Pooley, Fender, & Brocksopp (1999), (81) Ling, Zhang, & Tang(2009), (82) van Kerkwijk et al. (1992), (83) Canizares et al. (1973), (84) Negueruela et al. (2011), (85) Johnston et al. (1994), (86) Wang, Johnston, & Manchester(2004), (87) Mold´on et al. (2012), (88) Clark et al. (2001), (89) Casares et al. (2005), (90) Frail & Hjellming (1991), (91) Casares et al. (2005), (92) Gregory (2002). sources. It can be easily done for outer galaxies, but in thecase of the Milky Way, while calculating the HMXBs LF,we should make an appropriate correction for an incompletecoverage of the Galaxy at different X-ray luminosities. Inother words – we should correct for the fact that sourceswith given luminosities are detectable for the INTEGRALsurvey only within some distance limits.The simplest way to do such a correction was adoptedby Grimm, Gilfanov, & Sunyaev (2002) and Voss & Ajello(2010), where authors assumed some particular volume den-sity distribution of HMXBs over the Galaxy. In the formerwork it was assumed that the HMXBs volume density dis-tribution has a disk shape with certain parameters, in thelatter paper authors suggested that HMXBs are distributedsimilar to the stellar mass in the Galaxy.In this work we want to measure the HMXBs densitydistribution over the Galaxy rather then assume it. There-fore we have adopted here a different approach.
As a first step we divided the whole available luminosityrange of HMXBs into two intervals – above the luminosity2 × erg s − (taking into account the adopted flux limitof our survey 10 − erg s − cm − this sample is complete upto ≃
13 kpc from the Sun) and above the luminosity 2 × erg s − (complete up to ≃ . < . .
6, which is a re-normalization, calculated fromthe measured density distribution of HMXBs (see below).This plot provides us an indication that the luminosityfunction of HMXBs in the whole luminosity range (10 − erg s − ) is not following a single power law, but ratheris curved at luminosities around (0 . − × erg s − . Themaximum likelihood approximation of the LF with simplepower law functions at L > × erg s − and L > × erg s − gives the best fit values of their slopes γ faint =1 . ± .
21 (34 . < log L x < .
5) and γ bright = 2 . ± . . < log L x < . ∼ σ significant.It is important to emphasize that distances to sources(Table 1) are known with a limited accuracy due to differentreasons. In general, it is reasonable to assume that they havean average accuracy not worse than ∼ ∼
40% for the known average flux values. To estimatea possible influence of these uncertainties on our results wehave performed simple simulations. We have varied distancesaround values, presented in Table 1, assuming a Gaussiandistribution with σ =20% of the source distance. Systematicuncertainties for the LF slopes calculated by this way are:∆ γ faint ≈ .
06, ∆ γ bright ≈ .
1, respectively, i.e. well withinthe statistical uncertainties.
In order to calculate the luminosity function of the wholesample of HMXBs we should take into account the fact thatsources with given luminosities are detectable for the INTE-GRAL survey only within some distance limits. In order todo this we need to determine their surface density distribu-tion.Given the limited accuracy of distances to sources in
Lutovinov et al.
Figure 3.
Maps of the inner part of the Galactic plane, obtained with INTEGRAL/IBIS in the 17-60 keV energy band. All persistentsources from Table 1 are marked with circles and names. opulation of HMXBs in the Milky Way Figure 4.
Luminosity functions of the wind fed accreting HMXBsin the Galaxy. Two black solid histograms represent luminosityfunctions within volume limited samples (see text for details).Dotted histogram is the original number-luminosity function ofthe volume limited sample of sources within d < . .
6, calculated fromdensities of HMXBs in different galactocentric annuli. Red solidhistogram is a luminosity function of the whole sample (normal-ized to the number of HMXBs over the whole Galaxy), calculatedtaking into account luminosity dependent corrections (due to lim-ited sensitivity of the survey), dashed red curve – the best fitmodel of the luminosity function with parameters from Table 2.Hatched area shows the number-luminosity function of all classesof HMXBs in our Galaxy from Grimm, Gilfanov, & Sunyaev(2002). our sample we have limited ourself by an axially symmetricdistribution of HMXBs in the Galaxy. We have divided theGalaxy into annuli with radii R g < − − −
11 kpc, 11 −
14 kpc from the center (the distancefrom the Sun to the Galactic center is expected to be 8.5kpc).We assume that: • the surface density of HMXBs (src/kpc − ) is constantwithin each annulus; • shape of the luminosity function and its parameters arethe same for all annuli.In our flux limited survey the sources with different lu-minosities can be detected within different galactic areas.In order to take this effect into account we have adoptedmethod 1 /V max (Schmidt 1968). For estimation of parame-ters of the HMXBs luminosity function φ ( L ) = dN/dL weused the Cash-statistics (Cash 1979) as follows: C = 2 X j Z φ ( L ) S max ,j ( L ) dL − N j X i =1 ln [ φ ( L i,j ) S max ,j ( L i,j )] ! (1)Here, a summation j goes over the set of annuli and Table 2.
Best fit parameters of the luminosity function ofHMXBs and their spatial density distributionParameter Value and 1 σ error α . ± . ± . α > . L ∗ , erg s − . +2 . − . (stat.) ± . R g , kpc N ( L > erg s − ) kpc − . ± . . +0 . − . (stat.) ± . . +0 . − . (stat.) ± . . +2 . − . ) × − (stat.) ± . × − (syst.)11-14 (6 . +7 . − . ) × − (stat.) ± . × − (syst.) a summation i goes over N j sources within each annulus. S max ,j is the maximum area of annulus j , within which asource with the luminosity L i,j can be detected.A minimization of the C -statistics gives us best fit pa-rameters of the luminosity function and its normalizationin each annulus. We have adopted a simple broken powerlaw shape of the luminosity function with slopes α and α below and above the break at the luminosity L ∗ : dNdL = (cid:26) A j ( L/L ∗ ) − α if L < L ∗ A j ( L/L ∗ ) − α if L > L ∗ (2)where A j – normalization of the luminosity function in eachannulus j . Best fit parameters of this model with uncertain-ties are presented in Table 2. Statistical uncertainties corre-spond to a 1 σ level; the systematical ones were calculatedby variations of distances to sources as it was described inSection 3.1.The shape of the LF of wind-fed HMXBs demonstratesa break, or at least a curvature. From a purely statisti-cal point of view the statistical significance of the breakis ∼ ∼ σ (∆ C ≈ . The HMXBs surface densities (averaged over correspondingannuli) are presented in Table 2 and Fig. 5,6. It can be seenthat the overall distribution of surface density of HMXBs inthe Galaxy has a peak at galactocentric radii 2 − Lutovinov et al.
Figure 5.
An illustrative view of the surface density of HMXBsin the Galaxy (the darker color of the annulus correspondsto the higher surface density of HMXBs). Black dotted anddashed curves show areas of the Galaxy, within which the IN-TEGRAL Galactic survey detects all sources with luminosities > . erg s − and > erg s − , respectively. Red dottedand dashed circles show distances, till which we detect all sourceswith luminosities higher than 10 erg s − and 2 × erg s − according to the adopted flux limit 0.7 mCrab in the inner partof the Galaxy − ◦ < l < ◦ . Blue points indicate positionsof HMXBs from our sample. All distances are in kpc. Grimm, Gilfanov, & Sunyaev 2002; Lutovinov et al. 2005,2007; Bodaghee et al. 2012) supports this general conclu-sion, but various incompleteness of previously available sam-ples of HMXBs precluded accurate estimates of their globaldensity distribution.A comparison of the obtained HMXBs surface densitieswith the star formation surface densities taken from papersof Guesten & Mezger (1982); Lyne, Manchester, & Taylor(1985); Chiappini, Matteucci, & Romano (2001)shows their very good correlation: N ( HMXB, L x > erg s − )/kpc ≈ . × − SF R/SF R ⊙ (see Fig.6),here SF R ⊙ is the surface density of the star formation ratenear the Sun.It is necessary to note, that on the average map,obtained with the INTEGRAL observatory, there are 5HMXBs with fluxes > . ∼ We have fitted a vertical distribution of HMXBs in two com-monly used ways: 1) with a simple exponential model of theirvolume density ρ = ρ exp( − z/h ) and 2) with a model of aself-gravitating isothermal disk ρ = ρ sech ( z/ √ h ). The Figure 6.
Dependence of the HMXBs surface density (histogram,right axis) and star formation rate surface density (left axis)on the galactocentric distance. Star formation rates are pre-sented by their upper and lower bounds (solid curves) from worksGuesten & Mezger (1982); Lyne, Manchester, & Taylor (1985);Chiappini, Matteucci, & Romano (2001). Error bars on the his-togram represent statistical (larger error bars) and systematic(smaller error bars) uncertainties. Systematic uncertainties areestimated by variations of distances to sources. former model gives the best fit height h = 85 +23 − pc, thelatter one h = 90 ±
15 pc. The systematic uncertainty ofthe scale-height due to a limited accuracy of distances tosources is smaller than the statistical one. This scale-heightof the HMXBs distribution is somewhat smaller than thatpresented in papers of Grimm, Gilfanov, & Sunyaev (2002);Dean et al. (2005); Bodaghee et al. (2007), likely due to thehigher completeness and uniformity of our sample.It is important to note that the scale-height of theHMXBs distribution is larger than the one of the distri-bution of massive stars in the Galaxy, e.g., the sample ofWR stars has a scale of ∼
45 pc (Conti & Vacca 1990),OB star formation regions ∼
30 pc (Bronfman et al. 2000),open clusters ∼
50 pc (Pandey, Bhatt, & Mahra 1988; Joshi2005). This indicates that HMXBs should have traveled afinite distance from their birth sites. If we will assume thatHMXBs receive their systemic velocity during supernova ex-plosions, we can make a rough estimate of the kinematic ageof HMXBs after the supernova explosion (see, e.g., similarestimates in Brandt & Podsiadlowski 1995).Adopting the value ∼ s − of the systemic ve-locity as a typical value for HMXBs (see e.g. Kaper et al.1997; Huthoff & Kaper 2002) we can estimate their kine-matic age, τ ≃
50 pc/(50 −
90) km s − ≃ . − . − × erg/sec might have smaller ages. opulation of HMXBs in the Milky Way Having collected the statistically clear sample of wind-fedbinaries with accreting neutron stars, we now can try tounderstand physical parameters which determine their pop-ulation.
The simplest picture of neutron stars accreting from a stellarwind was developed in classical works of Hoyle & Lyttleton(1940); Bondi & Hoyle (1944); Davidson & Ostriker (1973).In this framework the luminosity of the accreting neutronstar simply depends on the mass flow, intercepted by itsgravitational field. Masses of neutron stars lie in the narrowrange of values ( ∼ . − . M ⊙ ), therefore they do not in-fluence strongly on the HMXBs accretion luminosity. Themass ˙ M , intercepted by a neutron star from the stellar windof the companion mainly depends on three parameters: 1)the stellar wind mass loss rate ˙ M w , 2) the distance betweencomponents in the binary system a and 3) the stellar windvelocity v w (here we adopt that the wind velocity is muchlarger than the velocity of the orbital motion of binary stars;such an assumption is valid for the fast wind of young mas-sive stars of our sample). Roughly it can be expressed as˙ M ∝ ˙ M w v − a − . (3)The orbital separation in the binary system depends onits orbital period. For a fixed distance between componentsin HMXBs the X-ray luminosity of the neutron star willbe a function of the mass loss rate and the wind velocityof the optical star. Speaking very generally, for some fixeddistance between companions in the binary system its X-rayluminosity (the accretion powered luminosity of the neutronstar) should depend mainly on the mass of the normal star.The larger mass of the optical star should lead to the higherX-ray luminosity of the binary. Lets compare these simplearguments with properties of the real sample.In Fig.7 we present the cumulative luminosity functionof the wind-fed HMXBs within a limited range of orbitalperiods from 4 to 10 days (the latter restricts somehow thedistance between binary components).From this figure it is clearly seen three main propertiesof this sub-sample: • persistent HMXBs with orbital periods 4-10 days haveluminosities in the range from 10 erg s − to 2 × erg s − and their luminosity function can be approximated by apower law dN/dL ∝ L − . (dashed line); • there is a tentative trend that masses of optical stars(in cases where we can find them in the literature) decreasetowards the lower X-ray luminosities; • the lowest luminosity of the HMXB in this small sampleis L x ∼ . × erg s − .The power law shape of the X-ray luminosity function ofHMXBs with fixed orbital periods was explained by Postnov(2003) by properties of the mass distribution of secondariesin the binary, and scalings of their stellar wind mass lossrate.An additional important hint from this plot is that for a Figure 7.
Cumulative luminosity function of wind-fed NS-HMXBs from our sample with orbital periods in the range of4 −
10 days. Dashed curve demonstrates a model prediction cal-culated from a simple analytical formula dN/dL ∝ L − . in theluminosity range 2 . × < L x < × erg s − . The compan-ion star masses in some binaries are written along the histogram.They were taken from papers of Tomsick & Muterspaugh (2010)for XTE J1855-026, Mason et al. (2011) for IGR J18027-2016,Levine et al. (2004) for X 1908+075, Quaintrell et al. (2003)for Vela X-1, Cox, Kaper, & Mokiem (2005) for 4U 1907+097,Mason et al. (2010) for EXO 1722-363. Dotted line shows an ap-proximate value of the X-ray luminosity of the HMXB with M ∼ − M ⊙ (see text for details). given orbital period, it seems that there should be a minimalX-ray luminosity of the wind-fed HMXB.This conclusion is not absolutely robust from the ob-servational point of view because at luminosities below L x ∼ (2 − × erg s − our sample have a low complete-ness with the respect to orbital periods of binaries. Never-theless, usually there are no significant observational prob-lems to determine orbital periods in the range of 4-10 days,therefore we do not expect that this incompleteness is large.From the theoretical point of view this lower bound-ary of the X-ray luminosity of the wind-fed HMXB can beeasily understood. Let’s consider the accretion onto the non-magnetic neutron star, i.e. without an additional ’accretionflow–neutron star magnetosphere’ interaction, which can in-hibit the accretion and thus significantly diminish the timeaverage X-ray luminosity of such a binary system. If we willfix the orbital period of the binary system (that approxi-mately corresponds to the fixed distance between compan-ions), it will have the minimal X-ray luminosity if the opti-cal star has the lowest mass. We can expect that the lowestmasses in HMXBs should be approximately 8 − M ⊙ . Ifwe will use the ’X-ray luminosity – mass of the optical com-panion’ scaling from work of Postnov (2003) L x ∝ M . , wecan estimate the minimal X-ray luminosity of the HMXB inthis small sub-sample. The resulted minimal X-ray luminos- Lutovinov et al.
Figure 8.
Orbital periods and mean X-ray luminosities ofHMXBs from the flux limited sample (open circles). Gray filledcircles denote positions of known supergiant fast X-ray transients,which still passed our selection criteria for the ”persistency” dueto their faintness. In addition to sources in the Milky Way wealso demonstrate positions of two HMXBs in Magellanic Clouds,which accrete via the Roche lobe overflow of the optical star. Dot-ted horizontal line shows the level above which we know orbitalperiods for more than 90% of sources from our sample. Dashedline shows an approximate lower boundary of the ”allowed” areafor wind-fed accreting sources (see text). ity will be in a range of (0 . − × erg s − , that wellagrees with the distribution, presented in Fig.7. In this section we will try to simulate the global prop-erties of the population of NS-HMXBs, incorporatingmain ingredients from works of Hoyle & Lyttleton(1940); Bondi & Hoyle (1944); Davidson & Ostriker(1973); Lamers, van den Heuvel, & Petterson (1976);Iben, Tutukov, & Yungelson (1995); Postnov (2003);Bhadkamkar & Ghosh (2012).The main simplification in the modeling of the HMXBspopulation comes from the fact that their lifetimes are small.Thus, it can be securely adopted that properties of thesesystems depend only on their current parameters and arenot significantly influenced by the previous history. In oursimple toy model we will use this fact explicitly.As it was mentioned in Section 4.1 the X-ray luminosityof the neutron star fed by a fast stellar wind of a massive staris determined by: 1) the stellar wind density at the positionof the compact object, and 2) the wind velocity.The mass loss rate in the stellar wind ˙ M w is mainly afunction of the mass of the optical star M and the windvelocity v w (e.g. Castor, Abbott, & Klein 1975). ˙ M w ≈ ǫ L v w c , (4)where L is the luminosity of the optical star, which by-turn is connected with its mass M , ǫ a dimensionless effi-ciency parameter. It depends on the type and temperatureof the optical star (Lamers, van den Heuvel, & Petterson1976) and can be varied in the range of ǫ ≃ . − . ǫ ≃ . M ≈ ˙ M w (cid:18) GM ns v , ns a (cid:19) , (5)where v w , ns – the wind velocity at the position of the neutronstar v w , ns ≈ v w (1 − R /a ) / (Castor, Abbott, & Klein 1975;Vink 2000), which might be significantly lower than the windvelocity at infinity v w if the neutron star is not far from theoptical star, R is its radius.For the mass-radius relation for optical stars inthe binary system we adopt R /R ⊙ ≃ . M /M ⊙ ,which was calculated for sources in our sample. Itapproximately true in general (but with a largescatter due to evolutionary effects). For the mass-luminosity relation we adopt L /L ⊙ = 19( M /M ⊙ ) . (Vitrichenko, Nadyozhin, & Razinkova 2007).Combining above formulas with the assumed mass toenergy conversion during the neutron star accretion L x =0 . M c , we can simply estimate that the X-ray luminosityof the wind-fed neutron star is: L x ≈ . k × (cid:18) M M ⊙ (cid:19) . ×× (cid:18) a R ⊙ (cid:19) − (cid:18) v w [1 − R /a ] / s − (cid:19) − (6)where coefficient k incorporates all uncertainties in the ap-proach used for the hard X-ray luminosity estimation. Todescribe the observed population of HMXBs (see Fig.8,9) inthe best way this coefficient should be around ≃ . − . P orb − L x (see Fig.8).Indeed, at any given orbital period P orb (which can be trans-lated into the orbital separation) there should be a lowerlimit on the HMXB X-ray luminosity, corresponding (withinthe framework of our simple consideration) to the binarywith the smallest masses of the companion star and thus tothe lowest values of the mass loss rate. This lower boundshould have a functional form L x ∝ a − ∝ P − / at largeorbital periods and, roughly speaking, divide the P orb − L x diagram into two areas – ”allowed” for wind-fed neutronstars and ”forbidden” for them. It is remarkable that we dosee this lower boundary on the diagram P orb − L x , shown on opulation of HMXBs in the Milky Way Figure 9.
Luminosity function of persistent HMXBs in the MilkyWay as seen by INTEGRAL (crosses) along with the model ofthe simulated HMXBs population (solid line). Long-dashed andshort-dashed lines show best fit models of the HMXBs LF ob-tained by Voss & Ajello (2010) and Grimm, Gilfanov, & Sunyaev(2002), respectively. The former one was calculated in the 15 − −
60 keV energy band. There-fore the corresponding LF is presented in its respective luminos-ity interval. The LF in the paper of Grimm, Gilfanov, & Sunyaev(2002) was calculated in the 2 −
10 keV energy band. Therefore, torecalculate it to the 17 −
60 keV energy band we used an approxi-mate ratio between fluxes F − /F − ≃ .
5, which wasderived from the analysis of broadband spectra of typical HMXBswith neutron stars (see, e.g., Filippova et al. 2005).
Fig.8 (dashed line). This provides a significant support forour simple approach.
In order to simulate the population of HMXBs with neu-tron stars we need to assume some distribution of massesof secondaries and orbital periods of these systems. Postnov(2003) suggested that secondary stars in HMXBs have aninitial (Salpeter) mass distribution ignoring a possible evo-lution of this distribution before the beginning of an activeHMXB phase. Bhadkamkar & Ghosh (2012) recently ana-lyzed this evolution and showed that really the overall powerlaw slope of this distribution does not change significantly inthe mass interval 15 − M ⊙ . Therefore, for our subsequentmodelling we adopt the mass distribution of secondaries inthe form dN/dM ∝ M − . in the mass interval 10-60 M ⊙ .For logarithm of orbital periods we assume a flat dis-tribution (see e.g. ¨Opik 1924; Masevich & Tutukov 1988),but restrict this distribution by the interval 1 . < log P (days) < . • we adopt some specific mass-radius relation for opticalstars; this assumption led to the fact that the wind velocityat the infinity v w is the same for all stars in the simulatedpopulation; an evolution of young massive stars can lead toa spread (at least) in this value; • we do not take into account that an X-ray illumina-tion of the wind matter from the accreting neutron star canlead to a deviation of the wind flow from a simple analyticformula (4); • we do not take into account that some part of the persis-tent NS-HMXBs population can accrete a matter from thedense equatorial wind of Be stars (i.e. X Per or X 1145-619);it will raise their X-ray luminosities above what might beexpected for a binary system with a spherically symmetricstellar wind; • we do not take into account that depending on the mag-netic field and spin period of the accreting neutron star theaccretion flow might be stopped by a propeller mechanism(Illarionov & Sunyaev 1975); it should lead to a disappear-ance of binaries from different parts of our P orb − L x diagramand can distort the shape of the luminosity function.Nevertheless, below we show that in spite of these limi-tations our toy model reasonably well describe observationalappearances of HMXBs.A comparison of the luminosity function of the simu-lated wind-fed HMXBs population with that measured forsuch systems in our Galaxy is presented in Fig.9. It is clearlyseen that in spite of our simplistic approach to the simu-lation of the HMXBs population their luminosity functionclosely follows the observed LF of wind-fed NS-HMXBs inthe Milky Way. At the same time, the measured luminos-ity function of HMXBs is somehow different from thoseof Grimm, Gilfanov, & Sunyaev (2002) and Voss & Ajello(2010) (dotted and dashed lines, respectively). The origin ofthis difference can be connected with the absence of blackhole accretors, Roche-lobe filling systems and transients inour sample, and another way of the correction for the in-completeness.The main properties of the luminosity function of theHMXBs population are the steep cutoff at luminositiesabove ∼ erg s − and its flattening at luminositiesbelow ∼ − . erg s − . According to our simple pop-ulation model it is likely that wind-fed HMXBs are lim-ited by a hard X-ray luminosity ∼ × erg s − .This conclusion is not new and was mentioned already bye.g. Lamers, van den Heuvel, & Petterson (1976). More lu-minous HMXBs should have a different nature. For exam-ple, they can harbor WR stars with more powerful winds,can accrete from Roche lobe overflowing massive giants(which can provide a mass accretion rate as high as 10 − M ⊙ yr − or more), can have black holes as primaries, etc. Inour Galaxy we know only a few such sources (e.g., CygX-1, Cyg X-3), which, being taken together with wind-fed NS-HMXBs, will make the bright part of the HMXBsLF flatter than we see it on Fig.9. This fact could be areason why the luminosity function of HMXBs in galax- Lutovinov et al.
Figure 10.
Density of sources, produced with our toy model ofthe wind-fed NS-HMXBs population (gray scale) along with thedistribution of known galactic sources on the plane P orb − L x (same as Fig.8). ies with high star formation rates continues with a powerlaw d log N/d log L x ∼ − . ∼ erg s − ) is a con-sequence of a log-constant distribution of orbital periods ofbinary systems. But, it is necessary to note, that at thepresent level of the survey sensitivity this flattening is notvery significant.The corresponding distribution of the simulatedHMXBs population on the P orb − L x diagram is shown inFig.10 by a gray scale. It is clearly seen that it forms the”allowed” region on the diagram, where most of persistentHMXBs are located. Monitoring observations of the Galaxy with the INTEGRALobservatory have revealed a new pattern of a variability ofmore than dozen of high mass X-ray binaries – short brightflares with long periods of quiescence (Smith et al. 1998;Sunyaev et al. 2003; Sguera et al. 2005; Negueruela et al.2006; Sidoli 2011). These sources rapidly have grown up tobe a special subpopulation of HMXBs – supergiant fast X-ray transients (SFXTs, virtually all of them shown to becontaining early type supergiant companions).An origin of such flares is not yet fully understood.Proposed models can be separated roughly in two mainbranches: a) flares occurring due to an occasional ac-cretion of blobs of the matter from the clumpy stellarwind of a supergiant (see, e.g., Walter & Zurita Heras 2007;Oskinova, Feldmeier, & Kretschmar 2012), and b) magneticarrest of the accretion due to a rotating neutron starmagnetosphere and its occasional breakthrough (see, e.g., ✸(cid:0)
Figure 11.
Positions of supergiant fast X-ray transients (SFXTs)on the P orb − L x diagram. Here all sources are shown by twovalues – using the median and maximal fluxes, measured by theINTEGRAL observatory (solid circles). Dashed circle denotes themeasurements of the minimal flux for IGR J16418-4532 based onthe XMM-Newton data (Sidoli 2012) and recalculated to the 17-60 keV energy band. Grebenev & Sunyaev 2007; Bozzo, Falanga, & Stella 2008;Postnov et al. 2008; Shakura et al. 2012). Some combina-tion of these two types of models was considered byDucci, Sidoli, & Paizis (2010).In order to reveal a true nature of the SFXTs phe-nomenon it is very informative to put these sources in acontext of the outlined toy model of the wind-fed HMXBspopulation.A sub-sample of SFXTs (and SFXT candidates) withknown distances and orbital periods is presented in Table 3and shown in Fig.11. Now every source has two values of itsluminosity – the most probable (median) value, calculatedusing all INTEGRAL measurements, and the peak luminos-ity value. The last ones were extracted from correspondinglight curves of sources binned into ∼ It explicitlymeans that most of the time the accretion in SFXTs is in-hibited by some mechanism.
The only one source, whichmedian value lies in the allowed area – IGR J16465-4507 –sometimes classified as an ”intermediate” SFXT, and its fluxvariability is largely related with the orbital modulation ofthe accretion flow (Clark et al. 2010). Somewhat a similarsituation is emerging for IGR J16418-4532, which is firmlyestablished SFXT, but located near the border between al-lowed and forbidden areas. It happen only because we werelimiting ourself with data of INTEGRAL/IBIS, which are opulation of HMXBs in the Milky Way Table 3.
Luminosities of some Supergiant Fast X-ray Transients. a Name L X,med , b L X,peak , c Distance, P orb , References d erg s − erg s − kpc daysIGR J16418-4532 9.8 334.2 13.0 3.75 1, 2IGR J16465-4507 1.4 74.6 9.4 30.32 3, 4IGR J16479-4514 0.31 35.8 2.8 3.32 3, 5IGR J17391-3021 0.04 29.1 2.7 51.47 3, 6IGR J17544-2619 0.09 29.4 3.6 4.93 7, 8SAX J1818.6-1703 0.024 17.1 2.1 30.0 9, 10IGR J18483-0311 0.22 16.1 2.8 18.55 9, 11 a in the 17–60 keV energy band b most probable (median) luminosity c maximum luminosity, averaged over ∼ d references correspond to the distance and orbital period measurements References: (1) Chaty et al. (2008), (2) Corbet et al. (2006), (3) Rahoui et al. (2008), (4) Clark et al. (2010), (5) Jain, Paul, & Dutta (2009), (6) Drave et al. (2010),(7) Pellizza, Chaty, & Negueruela (2006), (8) Clark et al. (2009), (9) Torrej´on et al. (2010), (10) Zurita Heras & Chaty (2009), (11) Sguera et al. (2007). significantly worse that those of focusing X-ray telescopes. Ifwe instead use the results of Sidoli (2012), obtained with theXRT/Swift telescope, the median luminosity of the sourcein the quiescent state will be ∼ × erg s − , that is ∼ A general understanding of the luminosity function ofHMXBs and their Galaxy-wide distribution provides us apossibility to make predictions of a number of persistentsources at fainter fluxes.Using the real sensitivity of the INTEGRAL Galacticplane survey instead of our adopted value 0.7 mCrab (seeFig.2) we can predict that in total we should detect up to ∼
54 persistent HMXBs (here we have taken into accountthat surface densities, calculated in Section 3.2, do not in-clude 5 HMXBs with unknown distances and thus the truesurface densities of HMXBs might be ∼
14% higher than itis presented in Table 2). Forty two of them were alreadyobserved with the adopted flux limit 0.7 mCrab. Below thislimit there should be only ∼
12 persistent HMXBs among allunidentified INTEGRAL sources. Six of them were alreadydetected in the survey (see Table 1). Judging from estimatesof surface densities of different types of sources on the sky wecan anticipate that the majority of the remaining galacticsources will be cataclysmic variables (CVs).This conclusion follows from Fig.12, where the expectednumber of HMXBs in flux limited surveys of the Galactiplane is shown in line with ones for active galactic nuclei(AGNs) and CVs. A number-flux function of AGNs wastaken from Krivonos et al. (2010), a number-flux function ofcataclysmic variables was calculated using the parametriza-tion from Revnivtsev et al. (2008b). It is clear that the num-ber of CVs and AGNs begin to dominate over HMXBs atfluxes below ∼ − erg s − cm − , which will be achievedwith the new generation of hard X-ray telescopes like NuS-TAR (Harrison et al. 2010) and Astro-H (Takahashi et al.2010). Small fields of view of these instruments will limitthe detection rate of HMXBs. In order to increase the num-ber of known persistent HMXBs in the Galaxy (mainly dueto low luminosity sources) one need to use large survey mis-sions like Spectrum-RG (Pavlinsky et al. 2009). Lutovinov et al.
Figure 12.
Surface density of HMXBs in the direction to theNorma (345 ◦ < l < ◦ ) and Scutum regions (15 ◦ < l < ◦ ) inthe Galactic plane (gray areas). Lines show predictions of num-bers of different types of sources in these areas: AGNs (dashedline), CVs (dotted line) and HMXBs (solid lines). Predictions ofa number of HMXBs at faint fluxes were done using two types oftheir LF with different slopes d log N/d log at luminosities below10 erg s − (at higher luminosities the LF was taken as mea-sured, see Table 2): 1) an upper solid curve – the slope is fixed atthe value − .
4, as measured at 10 erg s − < L x < erg s −
2) a lower solid curve – the slope of the LF is fixed at the value −
1, as predicted from our toy model (see Fig.9).
We have constructed for the first time a well defined sampleof non-transient High Mass X-ray Binaries in our Galaxyusing the flux limited 9-years long survey of the INTEGRALobservatory. Our results can be summarized as follows: • The majority of persistent HMXBs accrete matter fromthe stellar wind of their supergiant/giant companions; • The luminosity function of wind-fed persistent HMXBswith accreting neutron stars can be described by a brokenpower law with the break around ∼ × erg s − ; at highluminosities the power law slope of the differential luminos-ity function is γ bright > .
2, at low luminosities γ faint ≈ . • Using this luminosity function we have showed that thepredicted number of HMXBs will be significantly lower thannumber of CVs and AGNs in future surveys with the bettersensitivity (NuSTAR, Astro-H); • The spatial density distribution of wind-fed NS-HMXBsover the Galaxy have been measured. We have divided theGalaxy into several annuli and showed that the HMXBs sur-face density has a maximum on galactocentric distances 2-8kpc. Such a distribution correlates well with the distribu-tion of the surface density of the star formation rate in theGalaxy. • We have constructed a simple toy model of the wind-fedNS-HMXBs population and showed that it can adequatelydescribe properties of the observed population. The modelclearly shows that wind-fed HMXBs should disappear at lu- minosities higher than ∼ × erg s − and their LF shouldflatten at L x < erg s − . The overall shape of the lumi-nosity function of the simulated population agrees with themeasured one; • We argued that for wind-fed NS-HMXBs there is an”allowed” region on the P orb − L x diagram due to generalproperties of the wind accretion. We demonstrated that allpersistent wind-fed HMXB lies in this allowed area. • All supergiant fast X-ray transients (SFXTs) in theirquiescent state lie in the ”forbidden” area of the P orb − L x diagram and only during flares they ”jump” into the ”al-lowed” region. This strongly supports the idea that theirtransient behavior is caused by some kind of (possible mag-netic) inhibition of the accretion onto the neutron star. ACKNOWLEDGEMENTS
Authors are grateful to Jerome Rodriguez and ArashBodaghee for their efforts to support the web-site dedicatedto IGR sources (http://irfu.cea.fr/Sap/IGR-Sources/). ALand MR thank Marat Gilfanov, Sergey Sazonov and ArashBodaghee for valuable discussions of methods and results.Authors also thanks to the anonymous referee for the care-ful reading of the manuscript and useful comments. Wewould like to thank E.M. Churazov for developing the IBISdata analysis algorithms and providing the software. Thiswork was supported by the grants of President of RussianFederation (RF) MD-1832.2011.2, NSh-5603.2012.2, grantsRFBR 10-02-00492, 12-02-01265, programs P21 and OFN17of Russian Academy of Sciences (RAS), State contract14.740.11.0611 and grants 8701 and 8629 from Ministry ofScience and Education of RF.
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