Spatial and Temporal Variations of the Diffuse Iron 6.4 keV Line in the Galactic Center Region
D. O. Chernyshov, V. A. Dogiel, M. Nobukawa, T. G. Tsuru, K. Koyama, H. Uchiyama, H. Matsumoto
aa r X i v : . [ a s t r o - ph . GA ] S e p Spatial and Temporal Variations of the Diffuse Iron 6.4 keV Linein the Galactic Center Region
Dmitrii C
HERNYSHOV , , , Vladimir D OGIEL I.E.Tamm Theoretical Physics Division of P.N.Lebedev Institute of Physics, Leninskii pr. 53, 119991,Moscow, Russia Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China Institute of Astronomy, National Central University, Jhongli 320, [email protected]
Masayoshi N
OBUKAWA , Takeshi G O T SURU , Katsuji K
OYAMA
Department of Physics, Graduate school of Science, Kyoto University, Oiwake-cho, Kitashirakawa, Kyoto606-8502
Hideki U
CHIYAMA
Department of Physics, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 andHironori M
ATSUMOTO
Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University,Furo-cho, Chikusa-ku, Nagoya, 464-8602 (Received ; accepted )
Abstract
We analyze the diffuse Fe I K α line generated in the diffuse interstellar molecularhydrogen by primary photons or subrelativistic protons injected by Sagittarius (Sgr) A ∗ .We showed that unlike emission from compact molecular clouds, this emission can bepermanently observed in the directions of the Galactic center. We conclude that the diffuseemission of 6.4 keV line observed at present is probably due to Fe I K α vacancy productionby primary photons if the X-ray luminosity of Sgr A ∗ was about L X ∼ − erg s − .In principle these data can also be described in the framework of the model when the 6.4keV line emission is generated by subrelativistic protons generated by accretion onto thecentral black hole but in this case extreme parameters of this model are necessary. Key words:
Galaxy: center — X-rays: ISM — cosmic-rays1 . Introduction
Detection of the Fe I K α (6.4 keV) line from molecular clouds in the Galactic center (GC) isone of the most remarkable events in the high energy astrophysics of the last decades. The story hadstarted from 1993 when Sunyaev et al. (1993) found a diffuse X-ray emission from compact sourcesin the GC. They interpreted this emission as due to reflection of photons by dense molecular clouds(Compton echo) which were irradiated by a nearby X-ray source. In addition, they predicted a brightfluorescent K α line in the scattered spectrum of the clouds due to the K-absorption of photons withenergies E > . keV. This line was indeed discovered soon afterwards by Koyama et al. (1996). Thebrightest region of the 6.4 keV emission was located over the giant molecular cloud Sgr B2. Later onthe 6.4 keV emission was discovered also in other molecular clouds of the GC (see Murakami et al.2001; Nobukawa et al. 2008; Bamba et al. 2009). Koyama et al. (1996) (see also Murakami et al. 2000) speculated that the 6.4 keV flux fromSgr B2 is due to the past activity of the the Galactic nucleus Sgr A ∗ which had been bright severalhundred years ago but is currently dim. From the observed flux of 6.4 keV photons from the cloud, F . ∼ − ph cm − s − , and the gas column density of the cloud the differential spectrum of primaryphotons dn ( E x ) /dE x can be estimated from the equation (see e.g. Tatischeff 2003) F . ∼ c πR ⊙ Z V SgrB d r Z E x > . keV n H ( r ) dn ( E x , r ) dE x dE x ε ( E x , r ) dE x (1)where V SgrB is the volume of the cloud, ε ( E x ,r ) is the emissivity of 6.4 keV photons at the coordinate r inside the cloud and R ⊙ is the distance to Earth. The spectrum of primary photons can be derivedfrom the observed continuum emission from Sgr B2 which in the case of the XRN scenario is thesame as the spectrum of primary photons. Murakami et al. (2000) showed that these spectrum was apower-law with the spectral index of − in the energy range 2–10 keV (see also Koyama et al. 2009) dn ( E x ) dE x ∝ E − x . (2)The 2–10 keV luminosity of primary photons from Sgr A ∗ necessary to produce the observed 6.4 keVemission from Sgr B2 was estimated by Murakami et al. (2000), L − keV ∼ × d pc ! erg s − (3)where d is the distance between Sgr A ∗ and Sgr B2.The most direct evidence to favor the photoionization by an X-ray flash of the central sourcewould be a time variability of the 6.4 keV line emission from molecular clouds because of a relativelyshort time in which a photon crosses them. This idea about the Sgr A ∗ past activity as the origin of6.4 keV emission from Sgr B2 was confirmed recently. Observations found a steady decrease of theX-ray flux from Sgr B2 for the period < ∼ years. Time variations of the emission are expected in the2RN model and interpreted as photoionization of iron atoms by a flux of primary X-rays emitted bythe central source Sgr A ∗ due to an X-ray flare occurred there about 100–300 years ago (Koyama etal. 2008; Inui et al. 2009; Terrier et al. 2010; Nobukawa et al. 2011). In principle a flux of the 6.4 keV line can also be generated by collisions of subrelativisticcharged particles with the molecular gas in the GC. Thus, Yusef-Zadeh et al. (2002) accounted theimpact of subrelativistic electrons with energies 10 – 100 keV from local sources with diffuse neutralgas producing both nonthermal bremsstrahlung X-ray continuum emission and diffuse 6.4 keV lineemission. Dogiel et al. (2009a) suggested a scenario for the 6.4 keV line emission from molecularclouds which was excited by a flux of subrelativistic protons produced by star accretion onto thecentral black hole. Below these two scenarios are denoted as the low energy cosmic-ray electronmodel (LECRe) and the low energy cosmic-ray proton model (LECRp). We note that because ofrelatively long life time of protons in comparison with the average time of star capture the LECRpcomponent of 6.4 keV line emission in the GC is quasi-stationary.Generation of the 6.4 keV line is accompanied by a continuum X-ray emission produced bythe Thomson scattering for the XRN scenario and by bremsstrahlung for the LECRe and LECRpmodels. Therefore the origin of 6.4 keV line flux from the clouds can be defined from the analysisof the equivalent width eW of the iron line in the spectrum which is the ratio of the line flux to thecontinuum intensity at E x = 6 . keV, eW = F . F x ( E x = 6 . keV ) . (4)The width is a function of the iron abundance η in the clouds.From estimations of eW for the cloud Sgr B2 Nobukawa et al. (2010) concluded that thephotoionization interpretation seemed to be more attractive in comparison with the electron impactscenario. The required abundance of iron in the cloud was estimated by Nobukawa et al. (2011)by the value η = 1 . solar. However, Capelli et al. (2011) might find the iron line emission whichwas produced by subrelativistic particles. They presented results of eight years of XMM-Newtonobservations of the region surrounding the Arches cluster in the Galactic Center. They analyzedspatial distribution and temporal behavior of the 6.4 keV line emission and concluded that the origin ofthis emission might be of the photoionization origin, although excitation by cosmic-ray particles wasnot excluded. Moreover, they concluded that for the three clouds nearest to the Arches cluster, whichshowed a constant flux over the 8-year observation, the origin of the line as photoionization by photonsfrom Sgr A ∗ seemed to be at best tentative, and the hardness of the nonthermal component associatedwith the 6.4-keV line emission might be best explained in terms of bombardment by cosmic-rayparticles.Recent Suzaku observations might also find the iron line emission which was produced bysubrelativistic particles (Fukuoka et al. 2009; Tsuru et al. 2010). For the clumps G 0.174 − W ≃ eV they concluded that the XRN scenario was favored. On the other hand, for the clumpG 0.162 − eW ≃ eV they assumed that the emission from there was due to low energycosmic-ray electron (LECRe). They found also that the eW of the 6.4 keV emission line detected inthe X-ray faint region (non galactic molecular cloud region) was significantly lower than one expectedin the XRN scenario but higher than that of the LECRe model.Dogiel et al. (2011) showed that estimates of eW alone did not allow to distinguish firmlybetween the XRN and LECR scenarios because in the latter case the value of eW depended stronglyon a spectral index of ionizing charged particles, especially if they were subrelativistic protons. In thecase of ionization by charged particles spatial characteristics of 6.4 keV line are expected quite dif-ferent for electrons and protons. While for electrons we expect rather local ionization of the mediumbecause of their relatively short lifetime, protons can fill an extended region around the GC. If pro-tons generate 6.4 keV line in the GC then at least two components of 6.4 keV line emission fromthe molecular clouds and the diffuse molecular gas can be generated there. The first one is a timevariable component generated by a flare of primary X-rays emitted by Sgr A ∗ , and the second is aquasi-stationary component produced by subrelativistic protons interacting with the gas.Observations of the 6.4 keV flux from Sgr B2 have not found up to now any evident stationarycomponent for the GC molecular clouds, though as predicted by Ponti et al. (2010) a fast decreaseof 6.4 keV emission observed with XMM-Newton for several molecular clouds suggested that theemission generated by low energy cosmic-rays, if present, might become dominant in several years.A component of another than that of the XRN origin may also be seen in the X-ray spectrum of faintmolecular regions in the GC as follows from Fukuoka et al. (2009). Below we derive parameters ofthe diffuse 6.4 keV line emission in the framework of the XRN and LECRp models in attempts todefine the origin of the observed diffuse line flux from the GC.
2. Diffuse Emission of the 6.4 keV Line from the GC
The intensity of the diffuse 6.4 keV line from the GC depends on parameters of the intercloudmolecular gas there. The inner bulge (200–300 pc central region) contains (7 − × M ⊙ ofhydrogen gas. In spite of relatively small radius this region contains about 10% of the Galaxy’smolecular mass. Half of the molecular gas is contained in very compact clouds of mass − M ⊙ ,average densities of which is ≥ cm − with a volume filling factor of only a few per cent, thenthe cloud radius is in the range 1–40 pc. The other half forms the molecular intercloud gas with thedensities of at least n H > − cm − (see Morris & Serabyn 1996). Launhardt et al. (2002)estimated for the inner ∼ pc region the averaged molecular hydrogen density n H to be 140 cm − assuming homogeneous matter distribution, and for a thin intercloud medium n H ∼ cm − .Recently Koyama et al. (2009) provided careful analysis with high energy resolution and lowbackground of the diffuse 6.4 keV emission and of the hard X-ray continuum associated with thisline in the GC region. From the Suzaku data they estimated the continuum X-ray emission which isproportional to the intensity of diffuse 6.4 keV line.4ore recently Uchiyama et al. (2011) provided a careful analysis of 6.4 keV emission fromthe region around the GC. Their spatial distribution of 6.4 keV line in the GC is shown in figure 1where spikes of this emission correspond to directions to molecular clouds. Fig. 1.
Longitude (along b = − . ◦ ) and latitude ( l = − . ◦ ) distributions of the 6.4 keV line in the GC asobserved by Suzaku. The data-points taken from Uchiyama et al. (2011) We expect that characteristics of the 6.4 keV emission produced by subrelativistic cosmic-raysand by a flux of primary X-ray photons are quite different. Below we reproduce spatial distributionsof the 6.4 keV line in the framework of XRN and LECRp models.
3. Spatial Distribution of the Diffuse 6.4 keV Line Emission in the XRN Model
It is assumed in the XRN model that Sgr A ∗ was active for about T years in the past as anemitter of primary X-ray photons with the energy E x . The average luminosity of this source duringthe active period is L fl ≃ erg s − (5)for the range 2–10 keV. The source activity is supposed to cease T years ago.For the observed spectrum (2) we define the total density of primary photons on the divergentfront of primary photons, which is at the distance r from Sgr A ∗ , as n ph = L fl πcr E minx ln( E maxx /E minx ) (6)where E minx and E maxx are the minimum and maximum energies of the spectrum of primary photons.Then the differential spectrum of primary photons dn ( E x ) /dE x for the total photon density (6) wepresent as dn ( E x ) dE x = n ph F x ( E x ) (7)whith the normalization condition for F x ( E x ) maxx Z E minx F x ( E x ) dE x = 1 (8)Therefore for the spectrum (2) we have F x ( E x ) = E minx E maxx ( E maxx − E minx ) E − x θ ( E x − E min ) θ ( E max − E x ) ≃≃ E minx E − x θ ( E x − E min ) θ ( E max − E x ) , for E max >> E min (9)Here θ ( y ) is the Heaviside step function.These primary photons ionize iron atoms. The cross-section of photoionization σ K has a form σ K ( E x ) = σ (cid:18) E x E (cid:19) − θ ( E x − E ) (10)where E = 7 . keV and σ ∼ × − cm (see Tatischeff 2003).Then the emissivity of the 6.4 keV line is ǫ . ( r ) = cηω K n H n ph E max Z E σ x ( E x ) F x ( E x ) dE x == cηω K σ n H n ph E minx E − E E max ! ≃ ηω K σ n H L fl πr ln( E maxx /E minx ) 14 E , (11)where ω K is the fluorescence yield of X-ray photon emission, which is about 0.3 for iron. The averagedensity of the diffuse molecular gas was defined as n H . Below we take everywhere for calculations n H = 10 cm − and assume a uniform density distribution of the molecular gas in the GC that givesan upper limit of diffuse 6.4 keV emission from the GC. The iron abundance η is supposed to equaltwice solar, η = 2 η ⊙ ≃ × − .For the delay time T we can observe at present an irradiate emission of the diffuse gas whichis on surface of the parabola (see e.g. Sunyaev & Churazov 1998) zc = 12 T " T − (cid:18) xc (cid:19) , (12)where the coordinates x and z are shown in figure 2.Unlike the line emission from compact molecular clouds which can be observed for a relativelyshort period of time when the X-ray front is crossing a cloud ( ∼ years), the diffuse 6.4 keV emissionproduced by primary X-ray photons should be permanently observed from the GC as the front ofprimary X-ray photons is propagating though the diffuse molecular gas in the GC.The region emitting the 6.4 keV line by the diffuse gas – X-ray photon interactions is enclosedbetween the two surfaces determined by the time τ = T and τ = T + T (see Eq. (12)) whosethickness is ∆ z between z corresponding t = τ and z corresponding t = τ . We showed the geometryof the emitting region in figure 2The radial distance from Sgr A ∗ is r = x + z . For the galactic plane (galactic latitude b = 0 o )the coordinate x ≃ R ⊙ ϑ for small values of the galactic latitudes l = ϑ where R ⊙ = 8 . kpc is the6 ig. 2. Geometry of the GC reflection process. The source Sgr A ∗ in the coordinate center. Two parables shown bysolid lines denote the reflection positions of emission emitted in the time interval { τ ,τ } which can be observed byan observer at present. Two circles (thin lines) denote a schematic position of the front of primary X-ray photonsemitted by Sgr A ∗ for the period T which stopped its activity T years ago. The dashed line is the line of view ofthe observer. Two thin arrow lines show the path of a primary photon before and after reflection. distance between the GC and Earth.Then the intensity of the diffuse 6.4 keV emission in the latitude direction ϑ is I . ( x, t ) = 14 π z Z z ǫ . ( r, t ) dz = ηω K σ n H L fl (4 π ) ln( E maxx /E minx ) 14 E z Z z dzx + z , (13)If the central source was active for the period between time momenta τ and τ , then the limits ofintegration are z = 12 " cτ − x cτ (14)and z = 12 " cτ − x cτ (15)Below we define E minx = 2 keV and E maxx = 10 keV that correspond to the value of L fl whichwas derived for this energy range, then 7 . ( x, t ) = 4 . × ph s − cm − sq.min − x ×× η η ⊙ ! (cid:18) n H
10 cm − (cid:19) L fl erg s − ! ×× (cid:20) arctan (cid:18) (cid:20) cτ x − xcτ (cid:21)(cid:19) − arctan (cid:18) (cid:20) cτ x − xcτ (cid:21)(cid:19)(cid:21) . (16)As an example we show in figure 3 the spatial and time variations of 6.4 keV line intensity inthe direction of the Galactic latitude ϑ ( x = R ⊙ ϑ ) calculated from (16) when a central sources startsits activity at t = 0 and this activity drops to zero at t = 300 yr. −2 −1.5 −1 −0.5 0 0.5 1 1.5 2−9−8−7−6−5−4−3 φ (deg)t (yr) Log I ( ph / s / s q . m i n ) Fig. 3.
Spatial and time variations of 6.4 keV line intensity in XRN model for the SGR A ∗ luminosity L fl = 1 . × erg s − and the gas density n H = 10 cm − . From this figure one can see that unlike emission from molecular clouds, which can be ob-served for short periods of their irradiation ( ∼ years), the diffuse emission of 6.4 keV line from theGC can be permanently seen for ∼ − year even when a period of X-ray protons injection bySgr A ∗ is quite short.Ponti et al. (2010) estimated the following parameters of the primary flare: T = 100 yr and T = 300 yr. The expected distribution of the diffuse X-ray emission in the XRN model is shown infigure 4 by the solid line. To reproduce the observed intensity distribution of the diffuse 6.4 keV linein the GC, the power of the central source of primary photons should be L fl = 1 . × × (cid:18) n H cm − (cid:19) − η η ⊙ ! − erg s − (17)that is compatible with L fl derived for the case of Sgr B2 by Murakami et al. (2000).We notice, however, that the X-ray flare duration from Sgr A ∗ may be much shorter that esti-mated by Ponti et al. (2010). Thus, from 6.4 keV flux variations in the direction of Sgr B2 presented8 ig. 4. Expected distribution of the diffuse 6.4 keV line along the longitude as observed from Earth calculated inthe framework of XRN model for the parameters: T = 10 yr, T = 100 yr, L fl = 2 . × erg s − (dashed line);and T = 300 yr, T = 100 yr, L fl = 1 . × erg s − (solid line). in Inui et al. (2009) the total duration of the flare may be about T ∼ years only (see also in thisrespect Yu et al. 2011). In figure 4 the emission distribution for this duration of the flare is shown bythe dashed line. The required luminosity of the flare in this case should be about L fl ∼ . × ergs − that is still compatible with the estimate of Murakami et al. (2000) because the real distance fromSgr A ∗ to Sgr B2 may be longer than the projection distance of 100 pc. If, however, the flare of SgrA ∗ occurred 300 yr ago, then the required luminosity is L fl ∼ . × erg s − .As it was shown in Nobukawa et al. (2010) and Dogiel et al. (2011) the equivalent width of theiron line provided information about the line origin since the continuum and line X-ray emission weregenerated by the same primary particles (photons or subrelativistic charged particles). The continuumemission in XRN model is caused by Thomson scattering of primary photons and it should correlatewith the 6.4 keV line emission. The continuum emission due to the Compton echo from molecularclouds was analysed in details by Sunyaev & Churazov (1998). The intensity of photons due to theCompton scattering of primary photons on the diffuse molecular gas can be estimated as ( dI/dE ) c ( x ) = n H n ph z Z z F x σ T ( φ ) dz = 0 . n H r e L fl πE x ln( E maxx /E minx ) z Z z (1 + cos φ ) dzx + z , (18)here σ T is the Thomson cross-section, r e is the classical radius of electron and φ is the scatteringangle. Taking into account that cos φ = z/r we obtain that ( dI/dE ) c ( x ) = n H r e L fl πE x ln( E maxx /E minx ) " x (arctan z x − arctan z x ) + z x + z − z x + z .(19)The distribution of the equivalent width along the Galactic longitude expected in the frame-work of XRN model is shown in figure 5. Spatial variations of eW for the XRN model are due to thecross-section dependence on the angle scattering. We notice, however, it is not easy to compare this9 ig. 5. Expected distribution of the equivalent width of the diffuse 6.4 keV line along the longitude as observed fromEarth for the gas density n H = 10 cm − . Solid line is the XRN model ( T = 300 yr, T = 100 yr, L fl = 1 . × erg s − ), dashed line is the LECRp model ( D = 10 cm s − , T c = 10 yr, N k = 6 × pr). distribution of eW with that derived from observations because it is not easy to subtract a componentof diffuse X-ray emission produced by the Compton scattering from the total flux of X-ray in thedirection of GC: a significant contribution of thermal emission is expected from there. Therefore, aspecial procedure to subtract a Compton component of continuum emission is necessary, as it wasdone e.g. in Koyama et al. (2009).
4. Spatial Distribution of the 6.4 keV Line in the LECRp Model
Another mechanism which can generate a diffuse component of 6.4 keV emission in the GCis bombardment of the interstellar molecular gas by subrelativistic protons whose lifetime is longenough to fill an extended region around the GC. As follows from Dogiel et al. (2009a); Dogiel etal. (2011) these protons may be generated by accretion processes onto the central black hole. Thetime-dependent spectrum of subrelativistic protons, N ( r , E, t ) can be calculated from the equation(see for details Dogiel et al. 2009b; Dogiel et al. 2009d) ∂N∂t − ∇ D ∇ N + ∂∂E ( b ( E ) N ) = Q ( E, r , t ) , (20)where D is the spatial diffusion coefficient of cosmic-ray protons, dE/dt ≡ b ( E ) is the rate of protonenergy losses, and Q ( E, t ) is the rate of proton production by accretion, which can be presented inthe form Q ( E, r , t ) = X k =0 Q k ( E ) δ ( t − t k ) δ ( r ) , (21)where t k is the injection time. The average time of star capture in the Galaxy was taken to be T ≃ t k = k × T , where k is the number of a capture event.The energy distribution of erupted nuclei Q k ( E ) is taken as a simple Gaussian Q k ( E ) = N k σ √ π exp " − ( E − E esc ) σ , (22)where we take the width σ = 0 . E esc with E esc ≃ MeV, and N k is total amount of particlesejected by each event of stellar capture.In the nonrelativistic case the rate of energy losses of protons due to Coulomb collisions canbe approximated as (see e.g. Hayakawa 1969) dEdt ! i ≃ πn H e ln Λ m e v ≃ a √ E , (23)where ln Λ is the Coulomb logarithm, v is the proton velocity, m e is the electron rest mass and a is aconstant if we neglect a weak dependence of the Coulomb logarithm on the particle kinetic energy E .Then the solution of Eq. (20) is N ( r , E, t ) = X k =0 N k √ Eσ √ πY / k exp − (cid:16) E esc − Y / k (cid:17) σ − r D ( t − t k ) (4 πD ( t − t k )) / , (24)where Y k ( t, E ) = (cid:20) a t − t k ) + E / (cid:21) . (25)and N k is the total number of subrelativistic protons emitted in each star capture event, and T is theaverage time of star capture.The intensity I of 6.4 keV line emission in any direction s produced by subrelativistic protonsis calculated in the same way as in Dogiel et al. (2009b) I . ( s ) = ω K ηn H Z s ds Z E N ( E, r ) vσ K dE (26)where the integration is along the line of sight s . Here the cross-section σ K for subrelativistic protonswas taken from Tatischeff (2003).The result of calculation for the LECRp model for the average gas density n H = 10 cm − is shown in figure 6 for different values of the diffusion coefficient in the GC. For calculations weused the following extreme parameters of the proton injection: each star capture ejects N k = 6 × subrelativistic protons, the capture frequency is T c = 10 yr (see Dogiel et al. 2009d). From the figure6 one can see that the LECRp model can also reproduce the observed diffuse 6.4 keV emission in theGC for this set of the parameters.In figure 7 we show expected time variations of the 6.4 keV line emission in the XRN modeland the quasi-stationary component of 6.4 keV emission produced by subrelativistic protons. For theboth cases the gas density was taken as n H = 10 cm − . From the figure we see that the 6.4 keVemission produced by protons may exceed that of primary XRN photons from Sgr A ∗ in 100 years11 ig. 6. Expected distribution of the diffuse 6.4 keV line along the longitude as observed from Earth calculatedin the framework of the LECRp model for different values of the diffusion coefficient in the GC ( T c = 10 yr, N k = 6 × pr). from now if the parameters of these models were chosen correctly. In this case it is highly improbableto observe the stationary component of this line produced by the protons from the diffuse moleculargas in the foreseeable future.However, we notice that if parameters of the XRN model like the energy flux of primaryphotons from Sgr A ∗ , L fl ∼ − × erg s − and the delay time T ∼ − yr and theflare duration T ∼ − yr for Sgr B2 are more or less correctly estimated that makes derivedvalues of 6.4 keV emission from the GC generated by primary photons relatively reliable, parametersof the LECRp model are highly uncertain. We do not know exactly which sort of stars and whenwas captured by the central black hole, how many protons escape into the GC medium, what is thediffusion coefficient there etc.The continuum emission in LECRp model is caused by the inverse bremsstrahlung process(see Hayakawa 1969). Its intensity is ( dI/dE ) c ( s ) = ω K ηn H Z s ds Z E N ( E, r ) v dσ IB dE dE (27)where dσ IB dE = 83 Z e ¯ hc (cid:18) emc (cid:19) mc E ′ E x ln ( √ E ′ + √ E ′ − E x ) E x (28)is the cross-section of the inverse bremsstrahlung process, E is the energy of proton, E ′ = mM E , m is the mass of the electron and M is the mass of the proton. The corresponding equivalent width inframe of LECRp model is shown in figure 5 by the dashed line.12 −1 Galactic longitude (deg) O b s e r v ed F e I K α i n t en s i t y ( − ph / s / c m / a r c m i n ) +100 yrcurrent+200 yr+300 yr Fig. 7.
Expected distribution of the diffuse 6.4 keV line along the longitude in the future. Solid lines correspond toXRN model, dashed line is LECRp model. Parameters of these models are the same as in Fig. 5
5. Discussion and Conclusion
The diffuse emission of the 6.4 keV line in the GC region was recently observed with Suzaku.Only two components can generate ionization of the molecular gas in this extended region, namely,hard X-ray photons or subrelativistic protons with energies about 100 MeV. Because of their longlifetime hard X-ray photons and subrelativistic protons can propagate over large distances.Temporal characteristics of the diffuse line emission differ from that of compact clouds.Emission produced by photoionization in the clouds shows temporal variations with the character-istic time about several years that corresponds to the time in which a photon crosses the cloud. Onthe other hand, the diffuse emission generated by photionization changes with the characteristic timeabout < ∼ yr. Protons in both cases generate a stationary flux of the line emission.We conclude that the diffuse emission of 6.4 keV line observed at present is probably due to6.4 keV vacancy production by primary photons. This model describes nicely the observed intensityand spatial distribution of the 6.4 keV line emission around the GC. We notice, however, that theluminosity of Sgr A ∗ required to produce the intensity of the observed diffuse emission dependsstrongly on the duration of Sgr A ∗ X-ray flare. For the delay time T ∼ yr and the flare duration T from 10 to 300 yr this luminosity is about L X ∼ − erg s − that is compatible with the valuederived by Murakami et al. (2000) from the observed 6.4 keV flux from the cloud Sgr B2. If howeverthe duration is about T ∼ yr and the delay time T ∼ yr, then the required luminosity shouldbe as high as ∼ erg s − that exceeds significantly the estimate of Murakami et al. (2000) derivedfrom the Sgr B2 data.In principle these emission can also be described in the framework of LECRp model when the13ontinuum and line emission is generated by protons but in this case extreme parameters of the LECRpmodel are necessary. The main problem of LECRp model is that we don’t know reliable estimates ofprotons injection by accretion processes, the proton spectrum, characteristics of proton propagationin the central region (diffusion coefficient) etc. With all these uncertainties we can conclude that atpresent the XRN model seems to be more attractive for interpretation of the diffuse line emission inthe GC than the LECRp model though we cannot exclude that protons may contribute a significantpart of the diffuse flux.We hope that more reliable conclusions can be obtained in the near future. The first keyresults would be if observations find a stationary component of 6.4 keV line emission from molecularclouds. In this case the density of subrelativistic photons and a flux of diffuse line emission generatedby protons can be estimated for the GC region.Another very important parameter of the emission can be obtained with the planned Astro-Hmission. The point is that the width of the 6.4 keV line produced by protons is about several tensof eV, which is about one order of magnitude wider than the width expected from that generated byX-ray reflection. Future observations by Astro-H SXS, whose energy resolution is supposed to beonly 7 eV (see Takahashi et al. 2010) will be able to measure this parameter.The authors are grateful to the unknown referee for careful reading of the manuscript anduseful corrections. DOC and VAD are partly supported by the NSC-RFBR Joint Research ProjectRP09N04 and 09-02-92000-HHC-a. This work is supported by Grant-in-Aids from the Ministry ofEducation, Culture, Sports, Science and Technology (MEXT) of Japan, Scientific Research A, No.18204015 (KK), and Scientific Research B, No. 20340043 (TT). This work was also supported by theGrant-in-Aid for the Global COE Program ”The Next Generation of Physics, Spun from Universalityand Emergence” from the Ministry of Education, Culture, Sports, Science and Technology (MEXT)of Japan. References
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