Origin of X-ray and gamma-ray emission from the Galactic central region D. O. Chernyshov1,2,3, K.-S. Cheng2, V. A. Dogiel1,2,4, C. M. Ko3,5 January 11, 2017 7 1 0 ABSTRACT 2 n a We study a possible connection between different non-thermal emissions from the J inner few parsecs of the Galaxy. We analyze the origin of the gamma-ray source 2FGL 0 1 J1745.6−2858 (or 3FGL J1745.6−2859c) in the Galactic Center (GC) and the diffuse hard X-ray component recently found by NuSTAR, as well as the radio emission and ] E processes of hydrogen ionization from this area. We assume that a source in the GC H injected energetic particles with power-law spectrum into the surrounding medium in . h the past or continues to inject until now. The energetic particles may be protons, p electrons or a combination of both. These particles diffuse to the surrounding medium - o and interact with gas, magnetic field and background photons to produce non-thermal r t emissions. We study the spectral and spatial features of the hard X-ray emission and s a gamma-ray emission by the particles from the central source. Our goal is to examine [ whether the hard X-ray and gamma-ray emissions have a common origin. 1 v Our estimations show that in the case of pure hadronic models the expected flux of 8 hard X-ray emission is too low. Despite protons can produce a non-zero contribution 8 4 in gamma-ray emission, it is unlikely that they and their secondary electrons can make 2 a significant contribution in hard X-ray flux. In the case of pure leptonic models it is 0 . possible to reproduce both X-ray and gamma-ray emissions for both transient and con- 1 0 tinuous supply models. However, in the case of continuous supply model the ionization 7 rate of molecular hydrogen may significantly exceed the observed value. 1 : v i Subject headings: Galaxy: center - cosmic rays - gamma rays: general - X-ray: ISM X r a 1I.E.Tamm Theoretical Physics Division of P.N.Lebedev Institute of Physics, Leninskii pr. 53, 119991 Moscow, Russia; [email protected] 2Department of Physics, University of Hong Kong, Pokfulam Road, Hong Kong, China 3Instituteof Astronomy,National Central University,Jhongli, Taoyuan, Taiwan, R.O.C. 4Moscow Instituteof Physics and Technology, 141700 Moscow Region, Dolgoprudnii, Russia 5DepartmentofPhysicsandCenterforComplexSystems,NationalCentralUniversity,Jhongli,Taoyuan,Taiwan, R.O.C.; [email protected] – 2 – 1. Introduction The interstellar medium of several pc around Sgr A∗ in the center of our Galaxy is charac- terized by a number of peculiar parameters (see, e.g., Ferri`ere et al. 2007; Ferri`ere 2012). The central supermassive black hole is surrounded by a circumnuclear disk (CND) whose total mass was estimated by Christopher et al. (2005) to be 106 M⊙. The analysis of Ferri`ere (2012) gave a slightly lower value of mass about 2×105 M⊙ for the region of radius Rc = 3 ∼ 5 pc with average gas density in the CND of about 4 × 105 cm−3. Unlike other regions of the Galaxy the central region shows prominent emissions in a very broad range of electromagnetic waves, from radio to gamma-ray. • The Very Energetic Radiation Imaging Telescope Array System (VERITAS) (Archer et al. 2016)andTheHighEnergyStereoscopicSystem(H.E.S.S.)(Aharonian et al.2009)detecteda prominentgamma-rayfluxintheTeVenergyrange. RecentobservationsofH.E.S.S. (Abramowski et al. 2016) with the angular resolution 0.01◦ provided some new information about this GC area. These observations found a point-like source in the center and a diffuse emission around the source that is correlated with the gas distribution which may mean a hadronic origin of this emission. Therecovered cosmic ray density decreases as 1/r (wherer is the distance from the source) that can be interpreted as a stationary ejection of relativistic protons by the source. • TheLargeAreaTelescope(FermiLAT)ofFermialsodetectedagamma-raysourceintheGeV region(seeNolan et al.2012;Acero et al.2015). InthesecondFermiLAT sourcecatalog,this source was identified as the source 2FGL J1745.6−2858. The estimated gamma-ray flux from this source for E > 2 GeV is I = 1.08×10−10 erg cm−2 s−1 with a spectral index γ = 2.68 obs (see Chernyakova et al. 2011). This corresponds to a luminosity about 8×1035 erg s−1. The positional error circle of 2FGL J1745.6−2858 overlaps with Sgr A∗. This is compatible with the picture that its emission originates within the CND or within the central cavity. It is reasonabletoassumethatthisemissionisprovidedeitherbyCRsprotons(Chernyakova et al. 2011; Linden et al. 2012), or by CR electrons (Kusunose & Takahara 2012; Malyshev et al. 2015), or by both protons and electrons (Guo et al. 2013) produced in the vicinity of Sgr A∗. IndependentanalysisoftheFermiLAT databyChernyakova et al.(2011)andMalyshev et al. (2015) indicated that recovered by them spectra are compatible with 2FGL J1745.6−2858 data at GeV energies yet significantly softer in the sub-GeV range. In the Fermi LAT 4-Year Point Source Catalog (3FGL) (Acero et al. 2015), this source was identified as 3FGL J1745.6−2859c. However the gamma-ray spectrum of this source is significantly softer below 1 GeV in comparison to 2FGL J1745.6−2858. The discrepancy may be due to another bright source 3FGL J1745.3−2903c in this area, which was not identified in the second catalog. Since there is a flag “c” in the name of the source the reliability of the derived spectrum of 3FGL J1745.6−2859c is not very high dueto the contamination from the nearbybrightsource. Inthispaperwedonotjudgewhichanalysisismoreappropriate,instead wepresentourmodelfittingsforboth3FGLdataanddataobtainedbyMalyshev et al.(2015). – 3 – • Large scale diffuse radio emission from this region is known as radio halo. It has a spherical shape with radius of about 8 pc. At frequencies about tens of GHz the emission have a clear synchrotron nature and thus confirms the presence of high-energy electrons in this area (Pedlar et al. 1989). • The Nuclear Spectroscopic Telescope Array (NuSTAR) found a flux of non-thermal hard X- ray emission in the direction of the central few parsecs region of the Galaxy (Perez et al. 2015). Total luminosity in the energy range 20-40 keV was estimated as 2.4×1034 erg s−1, which corresponds to an energy flux at the Earth of 3.3×10−12 erg cm−2 s−1. Spatial profile of the emission has an elliptical shape with a major axis 8 pc and a minor axis 4 pc. It is larger than gas structures in the GC like the central cavity (1.2 pc in diameter) and CND (6 pc in diameter) (Ferri`ere 2012). It also does not spatially coincide with Sgr A East. However it looks similar to the Nuclear Star Cluster (8 pc by 5.6 pc, Scho¨del et al. 2014). Therefore it was concluded that this emission was produced by unresolved point like sources. This idea was further developed by Hailey et al. (2016) who concluded that the X-ray emission can be produced by intermediate polars (a type of cataclysmic variables) with masses of about 0.9 solar masses. Despitethefactthatpoint-likesourcespotentiallyplayamajorroleinthehardX-rayemission we suppose that there is still room for a diffuse component of X-rays generated by CRs. Indeed as we mentioned earlier the presence of high-energy protons or electrons is confirmed by gamma-ray and radio observations. It is perceivable that these energetic particles also contribute to the total hard X-ray flux from the GC. Inprinciple,hardX-rayphotonsmaybegeneratedbysynchrotronemissionofsecondaryhigh- energy electrons produced by collisions of TeV protons with the background gas in the GC region. RecentobservationsofTeVgamma-raypoint-likesourcedetectedaclearcut-offinthe gamma-ray spectrum (Archer et al. 2016) at around 12 TeV. This gives the maximum energy ofprimaryprotonsatabout12/0.075 = 160TeV.Themaximumenergyofsecondaryelectrons is thus about 12×0.039/0.075 = 6.24 TeV (see Atoyan 1992). Therefore, in order to produce a non-thermal emission with power-law spectrum up to 40 keV by secondary electrons, the magnetic field strength there should be about 16 mG. This value is significantly higher than the 1 ∼ 3 mG obtained by Killeen et al. (1992); Yusef-Zadeh et al. (1996); Eatough et al. (2013). Hence we must conclude that synchrotron origin of this X-rays is doubtful. Ifhoweverthecut-offinthespectrumofthissourceisduetoabsorptionofthegamma-raypho- tonsbytheirinteractionswithbackgroundinfra-redemissionassuggestedbyAbramowski et al. (2016), the spectrum of primary protons may be power-law up to energies higher than 140 TeV. In this case synchrotron emission can produce up to 10%-20% of the flux detected by NuSTAR dependingon the magnetic field strength. We note however that the density of the infra-red photons does not appear to be high enough to produce the observed cut-off in the gamma-ray spectrum by photon-photon (γγ) collisions (see, e.g., Kistler 2015). Alternatively, X-rays can be generated by electron bremsstrahlung or inverse Compton ef- – 4 – fect (or both). This model was developed in Chernyshov et al. (2014). They assumed that the gamma-ray flux of the source 2FGL J1745.6−2858 is generated by relativistic protons in CND. The secondary electrons produce a flux of hard X-rays by bremsstrahlung in CND and by inverse Compton effect in the region surrounding CND. Then the X-ray halo around CND could be more extended than the gas distribution as observed by NuSTAR. However, Chernyshov et al.(2014)consideredaspherically symmetricmodelwhichis unabletoexplain the observed asymmetry of the hard X-ray emission. Besides, the hard X-ray flux predicted in that work turned out to be significantly lower than the observed value. Therefore, modifi- cation of the model is required if this interpretation is correct. Thus, these observations indicate a high efficiency CR production in the GC. Additional evi- dence supporting high density of CRs in the GC came from the measured ionization rate in the 1 pc region of CND by Goto et al. (2013, 2014). They obtained a value ζ ≃ 1.2×10−15 s−1, which is one order of magnitude higher than in other parts of the Galaxy. This ionization is most likely produced by subrelativistic CRs with a density higher than those outside the GC region. The estimated source luminosity of these subrelativistic CRs in the GC is about 1038 ∼ 1039 erg s−1 (see, e.g., Dogiel et al. 2013, 2014; Yusef-Zadeh et al. 2013). The goal of our present investigation is to explain simultaneously all phenomena mentioned above except TeV gamma-ray emission in the framework of a single model where CRs are injected from the central source. This source may be stationary (Macias et al. 2015; Abramowski et al. 2016) or transient (Macias et al. 2015). Both possibilities will be discussed. We will estimate the required parameters of this source. We analyze two types of models of the source: • Hadronic model. The central source injects mainly high energy protons. Most of the non- thermal electrons is produced by interactions of these protons with background medium. Gamma-rays are generated by proton-proton (pp) collisions. X-rays are produced by protons via inverse bremsstrahlung and by secondary electrons through bremsstrahlung and inverse Comptonscattering. Radioemissionisproducedbysynchrotronlossesofsecondaryelectrons. • Leptonic model. Thecentralsourceinjectsprimaryhighenergyelectrons. Inthiscasegamma- ray andhardX-ray emission aremainlyproducedby their bremsstrahlungandinverseComp- ton scattering. Radio flux is produced by their synchrotron emission. Unlike previous investigations our goal is to explain all types of non-thermal emissions using thesameinjectionofparticles(protonsorelectrons). Theultimategoalistoreproducetheobserved hard X-ray spectrum and the spatial distribution of hard X-rays using the observed gamma-ray spectrum as a reference point to determine the injection and propagation parameters. Also we examinewhethertheestimated gamma-ray fluxinthemodelsiscompatiblewithotherobservations there, such as the radio emission and the ionization rate of molecular hydrogen. Below we take into – 5 – account the non-spherical shape of the gas distribution in the central few parsecs. The parameters of the gas distribution in the CND region are taken from Ferri`ere (2012). In this investigation we assume that TeV gamma-ray emission discovered by H.E.S.S. and VERITAS, and GeV gamma-ray emission discovered by Fermi LAT are produced by two different sources. Indeed the overall gamma-ray spectrum indicates an “ankle-like” break at the transition from GeV to TeV energies. This break can be described naturally by a combination of two com- ponents with different spectral indices. Since TeV component exhibits much harder spectrum, its contribution to X-rays, radio emission and ionization should be much lower in comparison to GeV component. Therefore we restrict our analysis to GeV gamma-rays only. 2. Model description We use a cylindrically symmetric model to study the evolution of proton and electron distri- bution functions f (t,r,z,E) and f (t,r,z,E) with time. The z = 0 plane corresponds to the CND p e plane of symmetry, and the origin (r,z) =(0,0) corresponds to the center of the CND with Sgr A∗ as the source. Equation for the distribution functions is ∂f ∂ ∂f 1 ∂ ∂f ∂ dE p,e p,e p,e − D − rD + f = Q (t,r,z,E). (1) p,e p,e p,e p,e ∂t ∂z ∂z r∂r ∂r ∂E dt (cid:18) (cid:19) (cid:18) (cid:19) "(cid:18) (cid:19)p,e # Here we assume that the diffusion is isotropic and the diffusion coefficient D = D (E,r,z) has p,e p,e different values inside and outside the molecular cloud. The diffusion coefficient is a function of particle rigidity, ς p D (E,r,z) = D (r,z)β , (2) p,e 0 p (cid:18) 0(cid:19) where the value of D is the same for protons and electrons, p is the particle momentum, β is 0 the particle velocity in the units of c, p = 4 GeV/c, and the spectral index ς is determined by 0 the spectrum of MHD-turbulence for non-magnetized particles or by a structure of magnetic field lines for magnetized particles. Outside the cloud we assume that the diffusion is mainly due to energetic particle scattering bytheinterstellar turbulencewithKolmogorov spectrumandtherefore ςinter = 0.33 (Ackermann et al. 2012). Inside the molecular cloud, however, the situation is quite different due to the very efficient damping of MHD waves by ion-neutral friction. In this case diffusion is due to tangled magnetic field. Therefore the mean-free path of charged particles is determined by the characteristic corre- lation length of the intracloud magnetic field. As a result the diffusion coefficient does not depend on particle rigidity and ςcloud = 0 (see, e.g., Dogiel et al. 2015). The parameter D in the GC center region and inside the CND is unknown. For some regions 0 of the Galaxy, it can be estimated from observational data. Ackermann et al. (2012) gave a value – 6 – of Dinter = 5 ∼ 10 × 1028 cm2 s−1 as an average over the Galaxy diffusion coefficient. As for 0 intracloud, diffusion estimations for cloud such as Sgr B2 gave a value of about Dcloud = 1028 cm2 0 s−1 (Dogiel et al. 2015). However, the inner few parsec of the Galaxy are located in a special region characterized by processes of effective energy release in different forms. Therefore, it is reasonable to assume that the diffusion coefficient there is significantly smaller than in the other part of the GC region. We estimate this parameter from the spatial and spectral properties of the emissions. Theenergyloss termdE/dt inEquation(1)consistof Coulomblosses andproton-protonlosses for protons (Mannheim & Schlickeiser 1994), and of Coulomb, bremsstrahlung, inverse-Compton and synchrotron losses for electrons (Blumenthal & Gould 1970). The source term Q (t,r,z,E) p,e are model-dependent and we derive them later (see sections 3 and 4). We adopt the ambient density distribution from Ferri`ere (2012). We divide the space into the following regions: (1) central cavity with density of 103 cm−3, (2) outer layer of CND with density of 3.2×104 cm−3, (3) CND with density of 4.4×105 cm−3, and (4) radio halo with density of 210 cm−3 (see Figure 1). Fig. 1.— Gaseous structure in the Galactic Center region (Ferri`ere 2012). Inordertoestimatetheelectronenergylossandtheiremissionweneedtoknowthedistribution of softphotons. Wetake into accountthefollowing components(assumingtheyall haveblack-body spectrum): (1) optical emission from the central cluster (T = 3×104 K), (2) mid-infrared emission from the central cluster (T = 170 K), (3) dust emission from CND (T = 70 K), and (4) optical emission from the nuclear star cluster (T = 3500 K). Details on the estimation of soft photon density can be found in Appendix A. – 7 – From equation (1) we derive the evolution of the distribution functions f and f and the p e gamma-ray emission produced by these CRs I (t,E )= dV dE f (t,r,z,E)n(r,z)v dσ(E,Eγ) γ γ p dEγ pp Z (cid:20) (cid:16) (cid:17) +R dE f (t,r,z,E)w(r,z)v dσ(E,Eγ) e dEγ IC (cid:16) (cid:17) + RdE f (t,r,z,E)n(r,z)v dσ(E,Eγ) , (3) e dEγ br (cid:16) (cid:17) i R where v is particles velocity, n(r,z) and w(r,z) are the density distributions of ambient gas and soft photons, respectively. Proton-proton cross-section (dσ/dE ) is taken from Kamae et al. γ pp (2006), bremsstrahlung(dσ/dE ) and inverse-Compton cross-sections (dσ/dE ) are taken from γ br γ IC Blumenthal & Gould (1970). We adjust the initial parameters to make sure that gamma-ray spectrum I (E ) matches the γ γ observed one by Fermi LAT. With these parameters X-ray emissivity can be estimated as ǫ(t,r,z,E ) = dE f (t,r,z,E)n(r,z)v dσ(E,Ex) x p dEx ib (cid:16) (cid:17) +R dE f (t,r,z,E)w(r,z)v dσ(E,Ex) e dEx IC (cid:16) (cid:17) +RdE f (t,r,z,E)n(r,z)v dσ(E,Ex) , (4) e dEx br (cid:16) (cid:17) R where(dσ(E,E )/dE ) isthecross-sectionoftheinverse-bremsstrahlungprocess(Hayakawa1964; x x ib Tatischeff 2003). To obtain the spatial distribution of X-rays across the sky, the emissivity should be integrated along the line-of-sight. We take into account the fact that CND is inclined to the Galactic plane by 20◦ (see Figure 1). Ionization rate of molecular hydrogen is computed from ζ = dE σ vf + dE σ vf , (5) Hp p He e Z Z where σ and σ are the cross-sections of hydrogen ionization by proton and electron impact, Hp He respectively (Tatischeff 2003). We combine Equation (5) with the approach of Dalgarno et al. (1999) to take into account of the influence low-energy electrons. Equations (3), (4) and (5) are applicable to both hadronic and leptonic models. Obviously, in the case of leptonic model we assume f ≡ 0 and ignore all terms related to protons. p – 8 – 3. Hadronic models We start from injection spectrum of primary protons. Energetic electrons are considered as secondaries and their source function is dσ(E ,E) p Q (t,r,z,E) = n(r,z) dE f (t,r,z,E )v , (6) e p p p dE Z (cid:18) (cid:19)se where the cross-section (dσ/dE) of electron production includes proton-proton collision term se (Kamae et al. 2006) and the knock-on term (Hayakawa 1964). The source function of protons is model-dependent. We adopt the following form, δ(r) Q (t,r,z,E) = A(E)T(t)δ(z) , (7) p 2πr where δ(z) and δ(r) are Dirac delta-functions of z and r, respectively. A(E) is the spectrum of the injected particles and T(t) describes the temporal variations of the injection. The injected particle spectrum is assumed to be a power-law in momentum space, i.e., dN(> p) ∝ p−α, (8) dp where p is the momentum of the particle, α is a spectral index of of the injection spectrum and N(> p)istotalnumberofparticleswithmomentahigherthanp. Oneshouldnotethatamomentum power-law distribution of particles is expected inside of accelerator while the injected spectrum of particles maybemodifiedbyenergy lossesorescapewhichwillpotentially develop aspectralbreak. Thisis really importantsince we performcalculations in awideenergy range -from non-relativistic to ultra-relativistic energies. However in the particular case of the hadronic model we would like to maximize potential X-ray emission so we assume that particles are injected with power-law spectrum without any breaks. After re-expressing Equation (8) in terms of kinetic energy E, we obtain the spectrum A(E) in Equation (7) A(E) = A (E+Mc2)(E2 +2Mc2E)−(α+1)/2, (9) 0 where E and M are the kinetic energy and mass of the particle, respectively. In the present section we take M = m , the mass of proton. p Thenormalization constantA andthespectralindexαofEquation (9)can beestimated from 0 the gamma-ray data. Their values should be adjusted to fit the observed gamma-ray spectrum. With these parameters one can estimate the intensity of hard X-rays and radio emission. Radio emission depends strongly on the magnetic field strength whose value has not been well established. Hence radio emission cannot be considered as a strong indicator for the validity of the model. The same is true for the ionization rate whose value is known only up to an order of magnitude. Therefore, we consider that these two observations play a supplementary role in our discussion, and we mainly concentrate on hard X-ray emission to examine whether the model is compatible with observations or not. – 9 – 3.1. Single-burst hadronic model In the framework of this model, we assume that the injection happened some time ago in the form of a short burst. The temporal term of the injection function in Equation (7) is expressed as T(t) =δ(t). The observed spectrum of Malyshev et al. (2015) can be reproduced by assuming α = 2.5 in Equation (9), andα = 2.3 forthe 3FGL data(Acero et al. 2015)(see theleft panelof Figure2). As one can see from the figure the fit of the data is not very good. It was indicated by Malyshev et al. (2015) that the low-energy part of the spectrum cannot be explained in the framework of pure hadronic model, and the situation is worse in the case of 3FGL data. Gamma-ray spectrum depends weakly on time t and the diffusion coefficients. However the intensity of hard X-ray emission is more sensitive to these parameters. Its value increases as the diffusion coefficients decrease. To maximize the intensity of X-rays we used the following propagation parameters: inside the cloud Dcloud = 1026 cm2 s−1 while outside the cloud Dinter = 0 0 1027 cm2 s−1 (see Equation 2). The evolution of the hard X-ray intensity with time is presented in the right panel of Figure 2. Fig. 2.— Left: Gamma-ray spectrum in the case of single-burst hadronic model. Black crosses with tick mark are data points taken from Malyshev et al. (2015) and gray crosses from 3FGL (Acero et al. 2015). Right: Evolution of the hard X-ray intensity in the case of single-burst hadronic model. In both panels, theoretical curves corresponding to Malyshev et al. (2015) and 3FGL (Acero et al. 2015) are black and gray, respectively. The resulting X-ray intensity in the model is significantly less than the value of 3.3×10−12 erg cm−2 s−2 observed by NuSTAR. This conclusion agrees with Chernyshov et al. (2014). Although the curves in right panel of Figure 2 show a tendency to increase with time, an unreasonably long time and unreasonably high energy of the initial burst are needed to reach the observed value. Therefore,weconcludethatsingle-bursthadronicmodelisunabletoreproducetheobservedhardX- ray emission from the GC. However, relativistic protons may produce a non-negligible contribution – 10 – Fig. 3.— The same as Figure 2 except for the case of continuous supply hadronic model. to the gamma-ray emission. Thetotalenergybudgettoproducegamma-rayemissiondependsonhowlongagotheinjection of protons took place. Since protons escape from the region with dense gas, the longer the time from the injection, the higher the energy is required. For characteristic time about 2000 ∼ 7000 yrs, the total energy required is within (0.15 ∼ 1)×1050 erg. One can see that a single supernova explosion can supply enough energy assuming 10% acceleration efficiency. 3.2. Continuous supply hadronic model In this case the temporal term of the injection function in Equation (7) is expressed as T(t)= Θ(t), where Θ(t) is the Heaviside step function. The results are shown in Figure 3. The total power required is about 5×1037 erg/s. Both gamma-ray and X-ray results do not differ strongly from that of the single-burst hadronic model except that theX-ray emission is even lower. Therefore, the conclusion is not in favor of continuous supply (or stationary) model also. 4. Leptonic models In this section we assume that the central source injects relativistic electrons. The source function of electrons in Equation (1) is similar to that used in Section 3 (see Equation (7)), δ(r) Q (t,r,z,E) = A(E)Θ(E −E)T(t)δ(z) , (10) e max 2πr where the energy part A(E) is described by Equation (9) with M = m , the electron mass. We e introduced a cut-off energy E (the Heaviside step-function in Equation (10)) to reproduce a max