The Observed Galactic Annihilation Line. Possible Signature of the Cluster for Accreting Small Mass Black Holes Lev Titarchuk1,3 and Pascal Chardonnet2 5 ABSTRACT 0 0 2 Compton Gamma Ray Observatory, OSSE, SMM, TGRS, balloon and recent v INTEGRAL data reveal a feature of the 0.511 MeV annihilation radiation of o N the Galactic Center with a flux of approximately 5× 10−4 0.511 MeV photons 0 cm−2s−1. We argue that e+e− pairs can be generated when the X-ray radiation 1 photons and ∼ 10 − 30 MeV photons interact with each other in the compact 1 region in the proximity of the Galactic Center black hole. In fact, disks formed v near blackholesof1017 gmass shouldemit the∼ 10MeVtemperature blackbody 3 3 radiation. If positron (e+) sources are producing about 1042 e+s−1 near the 3 1 Galactic Center they would annihilate on the way out and result in 0.511 MeV 1 emission. We suggest that the annihilation radiation can be an observational 5 0 consequence of the interaction of the accretion disk radiation of the SMall Mass / h Black Holes (SMMBHs) with X-ray radiation in the Galactic Center. This is p probably the only way to identify and observe these SMMBHs. - o r t s Subjectheadings: accretion,accretiondisks—blackholephysics—radiationmech- a : anisms: nonthermal—physical data and processes—Galaxy:center v i X r a 1. Introduction The Galactic Center (GC) of our Galaxy found in 1974 as a strong radio source called Sgr A∗ is the site a supermassive black hole weighing 2.6 millions solar mass is present (e.g. Melia and Falcke 2001). Morever the total mass of stars enclosing the inner 20 pc of 1George Mason University/Center for Earth Observing and Space Research, Fairfax, VA 22030; and US Naval Research Laboratory,Code 7655, Washington, DC 20375-5352;[email protected] 2Universit´e de Savoie/ LAPTH /LAPP, 9 Chemin de; Bellevue, BP110 74941 Annecy-le-Vieux Cedex FRANCE; [email protected] 3NASA/ Goddard Space Flight Center/USRA, code 660, Greenbelt MD 20771; [email protected] – 2 – the Galaxy is ∼ 108 M , or ∼ 0.1% of the Galactic stellar mass (Baganoff et al. 2003). ⊙ Therefore, the X-ray observations of the Galactic Center can potentially reveal accreting black holes and neutron stars. During five years of Chandra observations, Baganoff et al. identified seven X-ray transients located within 20 pc of Sgr A∗. Remarkably four of these transients lie within only 1 pc of Sgr A∗ (Muno et al. 2005). This implies that, compared to the numbers of similar systems located between 1 and 20 pc, transients are over-abundant by a factor of ∼ 20 per unit stellar mass within 1 pc of Sgr A∗. It is also now a subject of intense activity due to the possible presence of a dark matter cusp inside the Galactic Center. Numerous space missions have observed the center of our Galaxy in radio, infrared, X and γ rays. Thanks to these measurements we have a more precise picture of this region. The center of our Galaxy presents the characteristic that there is a strong activity both in X and γ rays. A recent HESS (High Energy Stereoscopic System) experiment reports a detection of very high energy gamma rays from the Galactic center within 1′ of Sgr A∗. The flux above 165 GeV is order of 1.8 × 10−7 m−2 s−1 and consistent with a luminosity of 1035 ergs s−1 (Aharonian, et al. 2004). The most intense line of our Galaxy is coming also from GC: the 511 keV annihilation line. Balloon flight observations reported in 1972 showed first evidence for the existence of an annihilation line from the Galactic Center region (Johnson, Harnden & Haymes 1972; see also Johnson & Haymes, 1973). Since that time the Galactic Center has been the object of intense observations from space missions and balloon experiments (Leventhal, MacCallum & Stang 1978; Purcell et al. 1993; Ramaty, Skibo & Lingenfelter 1994; Purcell et al. 1997; and Cheng et al. 1997; Share et al. 1990; Teegarden et al. 1996; Gehrels et al. 1991; Leventhal et al. 1993; Niel et al. 1990; Chapuis et al. 1991). The observed emission of the brightest gamma-ray line in our Galaxy is due to two separate sources: a diffuse one and a point source near the Galactic Center. For the point source we use the value given by INTEGRAL from recent observations (Churazov et al. 2005). The point source line flux is : 9.9×10−4 ph cm−2 s−1, for which the corresponding luminosity of the line emission is about 6 × 1036 ergs s−1 for the distance of about 8 kpc. Then the positron sources are produced at a rate given by: ∼ 1042d2 s−1, where d is the 8 8 distanceexpressed inunitof8kpc. Thisobservationisinagoodagreementwiththeprevious measurements and is well fitted by a gaussian with the full width at half maximum of ∼ 10 degrees, with a 2 σ confidence interval of 6-18 degrees. The INTEGRAL measurement providing the line width of ∼ 2.4 keV exlcudes velocity v of the interstellar medium (ISM) greater than ∼ 800 km s−1, i.e. β = v/c ≤ 2×10−3. Several possible sources of the observed line related to the positron sources have been proposed. For example, Dermer & Skibo (1997) suggest that these sources could be as- – 3 – sociated with galactic fountains of radioactive elements ejected from supernova activity in the Galactic Center. Boehm, Fayet & Silk (2004) offer an alternative explanation that the observed annihilation line could be related to the annihilation of dark light matter particles into e+e−. In fact, Guessoum, Jean & Gillard (2005) present the list of the main processes that led to the positron production. They are: (i). the β+ decay of a radioactive nucleous which is widespread in the explosive and/or hydrostatic nucleosynthesis enviroments of no- vae, supernovae, Wolf-Rayet, and Asymptotic Giant Branch stars, (ii). π+ decay into µ+ and gives off a positron taking place where the pion is produced in collisions of highly energetic (E > 200 MeV) cosmic rays with interstellar material, (iii). pair production by interaction of an electron with a strong magnetic field and (iv) the process of the photon-photon pair production which requires photons of high energies occuring in the enviroment of luminous compact objects, black holes, active nuclei (AGN) an etc. Thus one cannot exclude that pair production is a result of the interaction of X-ray and γ− emission in the very compact shell near Galactic Center. X-ray observations of the Galactic Center have been made with several instruments (Watson et al. 1981; Skinner et al. 1987; Kawai et al. 1988; Takeshima et al. 1991; Sunyaev et al. 1993; Markevitch et al. 1993; Pavlinsky et al. 1993; Preddehl, & Trumper 1994). High-sensitivity imaging observations with the Einstein Observatory (Watson et al.) and ROSAT (Preddehl, & Trumper) resolved several discrete sources within 10′ of Galactic Center. One of the ROSAT sources, RXJ 1745.6-2900 (Preddehl & Trumper), is within 10′′ coincident of the nonthermal radio source Sgr A ∗, which is believed to be the dynamical center of our Galaxy. The Japanese satellite GINGA having detected Kα lines from highly ionized iron, found a large amount of hot plasma which is strongly concentrated towards the Galactic Center (Koyama et al. 1989; Yamauchi et al. 1990). The ASCA image (Tanaka et al. 1995) has revealed extended diffuse emission over the Galactic Center region. The observed spectrum shows the K lines from highly-ionized ions of silicon, sulphur, argon, calcium, in addition to α the high-ionization iron lines. This gives firm evidence for the presence of high-temperature (kT ≈ 10 keV) plasma. A large energy generation rate of ∼ 1041−42 ergs s−1 is required to producetheobserved plasma. Infact, Koyamaetal. (1996)argueforasourceattheGalactic Center. The luminosity required to account for the 6.6-keV line from Sgr B2 (the prominent molecular cloud) is 2 × 1039 ergs s−1 (in 2-10 keV band). While the Sgr A region has an X-rayluminosity of ∼ 1036 ergs s−1 at present, it could have been much moreluminous ∼ 300 yr ago. The distinctly bright region inside the Sgr A shell is probably due to this recent activity and the X-ray luminosity may have been as high as several ×1039 ergs s−1. Koyama et al. conclude that the ASCA results suggest the presence of an active galactic nucleus and together form the evidence for a large mass concentration at the Galactic Center and – 4 – transient activities due to sporadic mass accretion rate. Muno et al. (2004a) also presented the study of the spectrum of diffuse emission in 17′ ×17′ field around Sgr A∗ during 625 ks of Chandra observations. They confirmed and extended the results of the previous study (see e.g. Koyama et al.). In particular, they showed that the contiuum and line spectra are consistent with an origin in a two-temperature plasma. As the cooler, kT ≈ 0.8 keV plasma differs in the surface brightness, the hotter, kT ≈ 8 keV component is more spatially uniform. Recently Revnivtsev et al. (2004) have published INTEGRAL data on giant molecular cloud Sgr B2’s (IGR J17475-2822) fluorescence. They have constructed the broad band (3- 200 keV) spectrum from the ASCA-GRANAT-INTEGRAL data. It appears that the X-ray irradiating spectrum of the cloud is, in fact, not free-free, (as early proposed irradiating spectrum, see above) and it is rather quite hard, extending to over 100 keV and probably a power law with photon index 1.8. Revnivtsev et al. concluded that 300-400 years ago Sgr A∗ was a low luminosity (of ∼ 2×1039 ergs s−1 at 2-200 keV) AGN with characteristic hard X-ray Comptonization spectrum with photon index of about 1.8 and plasma temperature is about 50 keV. The γ− emission between 1 MeV and 30 Mev has been measured by COMPTEL. Using the COMPTEL data points (Hunter et al. 1997) one can calculate that the luminosity in 1-30 MeV energy band is about 4×1038 ergs s−1 with an assumption that the distance to the Galactic Center is about 8 kpc. In this Paper, we study a possibility of pair creation due to X-ray and γ− photon interaction inside the compact Galactic Center shell (the SGR A shell) and we discuss a possibility of annihilation line formation when these pairs propagate through the Galaxy from the Galactic Center region. In §2 we present a pair creation model. In §3 we compare ourtheoreticalpredictionsforthepairandannihilationphotonproductionwithobservations. We determine the size of the pair production area using the observable fluxes in X-ray and γ−ray energy ranges. In §4 we investigate the outward propagation of positrons from the Galactic Center region. In §5 we present arguments for the origin of the ∼ 10 MeV emission near Galactic Center. We discuss our results in §6 and we make our final conclusions in §7. 2. Pair creation model We assume that the photon density of X-ray photons emitted by the inner shell near the central BH within 103 R (Schwarzschild radii) is described by the following distribution S – 5 – over radius r (see Fig. 1 for the geometrical description of the model) L X n = (1) X 4πr2E c X where L is X-ray luminosity of the central source per keV (X-ray energy spectrum), E is X X the energy of X-ray photon and c is the speed of light. Also we consider that the spherical shell between the inner radius R and R (R ≤ r ≤ R and R ≫ R ) is uniformly filled by c c c γ−radiation sources where photon density production P is γ L γ P = (2) γ E 4πR3/3 γ where L is the γ-radiation luminosity of the spherical shell per keV (γ-ray energy spectrum) γ and E is the energy of the γ-ray photon. Then the pair production by the photons (for γ which the pair production condition E E > (m c2)2 is satisfied) is X γ e R PX,γ = 4π r2P dr T (r,ϕ,θ)dΩ (3) e−e+ Z γ Z X,γ Rc Ω where T (r,ϕ,θ) is the optical path for γ-ray photon propagating in the X-ray background X,γ and incoming at radius r at given direction Ω. The multiple integral in equation (3) can be calculated analytically. In fact, T (r,ϕ,θ)dΩ = {2πσ }× X,γ X,γ Z Ω 1 ∞ r 0 ∞ ′ ′ ′ dµ n(r )ds+ n(r )ds + dµ n(r )ds (4) (cid:26)Z (cid:20)Z Z (cid:21) Z Z (cid:27) 0 r(1−µ2)1/2 r(1−µ2)1/2 −1 r where n r′dr′ ′ 0 n(r )ds = (5) r′2[r′2 −r2(1−µ2)]1/2 and n = L /4πE c; where σ (E ,E ) is a pair creation cross section given by (Dirac, 0 X X X,γ X γ 1930, Heitler, 1954) πR2 1+b σ (E ,E ) = 0(1−b2) 2b(b2 −2)+(3−b4)ln (6) X,γ X γ 2 (cid:20) (cid:18)1−b(cid:19)(cid:21) and b = [1 − (m c2)2/E E ]1/2, and where the classical electron radius R = e2/m c2 = e X γ 0 e 2.818×10−13 cm. The analytical integration of n(r′)ds R dr′ n r 1−µ2 ′ 0 n(r )ds = n = arccos +C (7) Z 0Z r′ r′2 −r2(1−µ2) r 1−µ2 p r′ p p – 6 – allows us to calculate the second integral of n(r′)ds over µ: R L 3π2 X T (r,ϕ,θ)dΩ = 2πσ . (8) X,γ X,γ Z 4πE c 4r Ω X Finally, the expression for the Green’s function PX,γ can be written as e−e+ 9π2 σ L L PX,γ = X,γ X γ. (9) e−e+ 16cR E E X γ In order to obtain the total pair production rate Pe−e+ one should integrate PeX−,eγ+ over X-ray and γ− energies, namely 9π2 ∞ ∞ σ L L X,γ X γ Pe−e+ = dEX dEγ. (10) 16cR Z Z E E 0 (mec2)2/EX X γ 3. Results of calculations To compute the positron flux one needs the X and γ ray energy spectra, L and L X γ respectively. We will use for the total X-ray and γ luminosities of the inner GC region, L ∼ 2×1039 ergss−1 andL ∼ 4×1038 ergss−1 respectively (seeareviewoftheobservations X γ in the Introduction). We assume that the γ− radiation emanates from a optically thick medium and conse- quently the emergent spectrum has a blackbody like shape that color temperature T = 10 γ MeV (see Fig. 1). Then for a normalization constant C we have an equation as follows γ ∞ ∞ y3 L = L (E )dE = C dy (11) γ γ γ γ γ Z Z exp(y)−1 0 0 where y = E /kT . For the X-ray photons, we assume a power law with an exponential γ γ cutoff ∞ ∞ L = L (E )dE = C x−αexp(−x)dx (12) X X X X X Z Z 0 0 where x = E /kT , kT = 100 keV, the spectral index α = Γ − 1 = 0.8 and C is the X X X X normalization constant. From the previous section we saw that the process of pair creation is driven by thecross section given by equation(6). The energy dependence, represented by the parameter b can be expressed using the dimesionless energies x = E /kT and y = E /kT , X X γ γ namely b = [1−(m c2)2/E E ]1/2 = [1−3.26/xy]1/2. Then the formula for the pair flux e X γ 9π2 ∞ ∞ σ (E ,E )L (E )L (E ) X,γ X γ γ γ X X Pe−e+ = dEX dEγ (13) 16cR Z Z E E 0 (mec2)2/EX X γ – 7 – can be modified using the variables x and y as follows 9π2 ∞ ∞ σ (x,y)L (y)L (x) Pe−e+ = dx EX,Eγ γ X dy. (14) 16cR Z Z xy 0 3.26/x We compute this double integral and obtain the following result: 3.2×1056 Pe−e+ = cm−1 s−1. (15) R To reproduce the value of 1042s−1 for the positrons rate, one needs a value of the radius R, given by: 3.2×1056 3.2×1056 R = = = 3.2×1014 cm. (16) Pe−e+ 1042 It is worth noting that the intrinsic pair flux ∼ 1036 s−1, formed as a result of γ + γ interaction (to calculate this flux one should replace L by L in formula 14) in this X γ γ−emission region of size 3.2 × 1014 cm, is six orders of magnitude less than the pair flux ∼ 1042 s−1 required to reproduce the observed annihilation line strength. 4. Outward propagation of positrons from the Galactic Center region A positron, e+ may collide with an electron e−, to produce two gamma ray photons according to the reaction e+ +e− → γ +γ. Before decaying, the positron in the free space interacts with an electron and forms the positronium, a bound state with lifetime of order of 10−10 s. Then particles annihilate into two or three photons. One photon will have a high energy and ,if the electron is at rest; the other photon will have an energy of the order m c2 = 511 keV. In our calculations we assume that most of the produced positrons are e thermalized in the surrounding thermal plasma and thus we can consider the annihilation of thermal positrons at a temperature of order 107 K , i.e. β =< v > /c ∼ 10−3, where < v > is the thermal velocity of electrons. In fact, the recent INTEGRAL observations of 511 keV annihilation line (Churazov et al. 2005) exclude velocity of the interstellar medium greater than 10−3c. For β ≪ 1, the cross-section σ, for positron annihilation with a free electron at rest is given by Dirac (1930) σ ≈ πr2/β. (17) 0 Murphy, Dermer & Ramaty (1987) showed that the fraction of e+ that annihilites in flight prior to thermalizing usually amounts to less that 10 %, and that these positrons do not contribute to the 511 keV line emission. After entering the thermal pool, the positron annihilate in a fully ionized thermal plasma through direct annihilation. The problem of – 8 – the positron thermalization and annihilation photon production in the interstellar medium has been recently studied in details by Guessoum, Jean, & Gillard (2005) (see for a review of this subject). They reexamine in the utmost detail the various processes undergone by positron annihilation using most recent interaction cross section with atomic and molecular hydrogen, as well as helium. Putting all the new calculations together, they constructed annihilation spectra of ISM. The fair question is how far the positrons of energy about one MeV can travel from the Galactic central region to be annihilated. In order to answer to this question one has to compare the diffusion (travel) time with the energy loss (thermalization) time with taking into the main energy loss mechanisms. In general terms, the particle diffusion is related to escape of a magnetized turbulent plasma. Jean et al. (2005) present a spectral analyzis of the e+e− annihilation emission from the GC region based on the first year of measurements made with the spectrometer SPI of the INTEGRAL mission. They also analyze the positron diffusion propagation in the GC region in detail. The quasilinear diffusion coefficient the diffusion coefficient D (Melrose ql 1980) can be expressed as: 1−δ r D = D L η−1 (18) ql B (cid:18)λ (cid:19) max with D = (1/3)vr the Bohm diffusion coefficient, λ is the maximum scale of the B L max turbulence, δ = 5/3 for a Kolmogorov turbulent spectrum, η = δB2/ < B2 > is relative perturbationofthemagneticfieldpressure whichisoftenapproximatedto1, v isthepositron velocity and r is the Larmor radius (gyroradius) L m cγv e r = , (19) L qB q is the positron (electron) charge, B is the magnetic field strength, γ = [1 − (v/c)2]−1/2. The maximum scale λ was estimated to be ∼ 100 pc from the measurements of ISM max turbulence (Armstrong et al. 1995). Recently the (mean) magnetic field strength in the GC region was measured by La Rosa et al. (2005), hereafter LaR05, to be ∼ 10 µG. LaR05 have used the Very Large Array in all four configurations to image the GC region at 74 MHz. The resulting image of large scale (6o ×2o) of nonthermal synchrotron emission presented in LaR05 has a resolution of 125′′. At distance of 8 kpc the angular scales of 6o × 2o corresponds to region 840 pc × 280 pc and that of 125′′ corresponds to 0.09 pc. It has be noted that in the past several authors (see Morris & Serabyn et al. 1996 and references therein) estimated magnetic fields values of ∼ mG in the GC region. This is 2 orders of magnitude larger than the value (∼ 10 µG) obtained by LaR05. – 9 – Thus for the mean B of 10 µG and for 1 MeV positrons D ∼ 2.6×1026 cm2s−1. The ql low limit time scale for 1 MeV positrons to thermalize in a the B ∼ 10 µG, and ∼ 1 cm −3 density region due to ionization, bremsstrahlung, synchrotron and other processes is τ>105 ∼ years. Then the distance travelled by diffusion in a time of τ ∼ 107 years (slowing down d time plus annihilation time in the standard grain model) is d = D τ = 3 kpc (20) ql ql d p which is much greater than typical half-size of the hot GC region. The volume filling factor of the hot GC region 0.72 is highest among all phases of the Galactic bulge (see more details of these estimates in Jean et al. 2005). Using the spectral data and positron propagation analysis Jean et al. (2005) come to conclusion that the sources of annihilation emission are diffusively distributed over the Galaxy. They also explain that the lack of annihilation emission from the GC hot gas is due to its low density, which allows positrons to escape this phase. It is worth noting Liu, Petrosian & Melia (2004) find that an outflow of low energy electrons of order 1 MeV are distributed over a spatially larger scale than that of the BH inner region (see more discussion of their work in section 6.2). Namely, the escape time of these electrons is more than a factor of 2 shorter than the time scales for acceleration and losses. On the hand one can argue that the positrons can be diffusely trapped, thermalized and annihilated in the region that size L is of order a few parsec and where the magnetic field can be much higher than ∼ 10 µG. Melia & Falcke (2001) suggest that out to ∼ 2 − 3 pc (essentially inside the cavity surrounded by the circumnuclear disk), the field is turbulent (matching the turbulent plasma generated by wind-wind interactions from the Wolf-Rayet and O/B stars in this region), can be as high as ∼ 0.2−1 mG. So theproblem isthatthegyroradiusoftheelectrons andpositronsproduced ingamma- gamma interactions, will be far smaller than the region over which the positrons are believed to be annihilating. Consequently, the pairs should be radiating profusely via synchrotron, bremsstrahlung, and inverse Compton. The photon energy density in this region is about 1 eV cm−3. To obtain this number we assume that the bolometric luminosity of the source in the Galactic Center is of order 1038 erg s−1 (see e.g. Narayan et al. 1998). Thus the derived magnetic strength B using bol equipartition between photons and magnetic field energies is about 10 µG. For such a low magnetic field we have already demonstrated that the positrons can escape from the GC region. In fact, Longair (1994) derived the minimum magnetic energy requirement for a given – 10 – luminosity L and photon volume V per unit time (in our case V = 4πL2c). He shows that ν B ∝ (L /V)2/7 which value is higher than that obtained using relation L /(4πL2c) = min ν ν B2 /8π. But the ratio of B /B is not orders of magnitude. The difference of the bol min bol indicies of ratio L /V is 2/7 vs 1/2. Furthermore Longair found that the magnetic field ν strength, B , corresponds to approximate equality of the energies in the particles and min magnetic field. LaR05 confirm this conclusion. They show that the mean magnetic field in the GC region 10 µG inferred from their observations is consistent with the particle energy density of 1.2 eV found in cosmic-ray data. The turbulent diffusion time scale τ = L2/D is not determined by the magnetic field ql only. In fact for δ = 5/3 the diffusion coefficient D is proportional to B−1/3 (see Eq.18). ql Even if the magnetic field is about 1 mG the diffusion coefficient D decreases by factor 4.6 ql only, namely D ∼ 5.5 × 1025 cm2s−1. The related difussion time through this region τ is ql about 5 × 104 years which is much less than the thermalization and annihilation time 107 years. 5. γ-Emission as the disk emission in small mass black holes One of the possible origins for MeV-emission is a disk emission from mass accretion by SMall Mass Black Holes (SMMBHs). The BH mass can be evaluated using the color disk temperature T . Using formula (5) in Shrader & Titarchuk (1999), hereafter ShT99, we col obtain that a black hole mass in solar units (m = M /M ) bh ⊙ (1/7)34T4 m = m˙ h (21) (T )4[(7/6)2r ]3 max in where m˙ = M˙ /M˙ is the dimensionless mass accretion rate in units of M˙ = L /c2, Edd Edd Edd related to the Eddington luminosty L , T ≈ 1.2T is the maximum temperature Edd max col in the disk in keV, T = T /T is a disk color factor and r is the inner disk radius h col eff in calculated in Schwarzchild units. Analyzing quite a few BH sources, ShT99 and Borozdin et al. (1999), hereafter BRT99, established that in the soft state the inner disk radius is very close to the last stable Keplerian orbit, namely r ≈ 3. The disk color factor T ≈ 2.6 in h was calculated by BRT99 using the known contraints on BH mass and the distance to the source for GRO J1655-40. This value of the disk color factor T ≈ 2.6 obtained for GRO h J1655-40 was recently confirmed for other Galatic black hole candidates sources. Shrader & Titarchuk (2003) have made use of improved Galactic black hole binary dynamical mass determinations to derive, in effect, an empirical calibration of this factor. In the soft state the mass accretion rate in the disk m˙ = M˙ /M˙ is in the order of Edd