Galactic Centre as an efficient source of cosmic rays
aa r X i v : . [ a s t r o - ph . H E ] J un Galactic Centre as an efficient source of cosmic rays
Rita. C. Anjos
1, 2, ∗ and Fernando Catalani † Department of Astronomy, Harvard University, 60 Garden Street, Cambridge, MA 02138, USA Departamento de Engenharias e Ciˆencias Exatas, Universidade Federal do Paran´a (UFPR),Pioneiro, 2153, 85950-000 Palotina, PR, Brazil. Escola de Engenharia de Lorena, Universidade de S˜ao Paulo,´Area I - Estrada Municipal do Campinho, S/N, 12602-810 Lorena, SP, Brazil.
After the discovery of Fermi Bubbles and the excess of gamma-ray emission, the Galactic Centrehas received increasing attention with the aim to understand its role in the origin and accelerationof primary cosmic rays (CRs). Based on a diffusion/re-acceleration model, we use the GALPROPsoftware to solve the diffusion equation for the cosmic rays and compare the results with the CRsspectrum, motivated by relationship between several energetic sources at the Galactic Centre andthe generated diffuse GeV-TeV gamma-rays. We calculate the cosmic ray distribution, gamma-rayflux from Galactic Centre and explore its contribution on the spectrum and chemical compositionof cosmic rays observed at Earth. We also discuss the effects of nuclei interactions with differentinterstellar gas models.
I. INTRODUCTION
The origin of cosmic rays with energies up to 10 eV are commonly attributed to supernova remnants (SNR) in ourGalaxy [1]. However, with a supermassive black hole, millisecond pulsars, transient radio and X-ray sources locatedaround the Galactic Centre (GC), it has become an excellent scenario for the study of astrophysical phenomena,indicating a correlation between past activities in the GC region and observational evidence [2–5]. Historically, themodels for the sources radial distributions consider that the density vanishes at the GC. Since our Galaxy is a spiralone, the population of SNR is distributed over the entire galactic disk, leaving the parametrizations for the densityof sources zero at r = 0 [6, 7]. However, recent observations with remarkable sensitivity were able to detect activitiesin the GC [8, 9], with the discoveries of the 511 keV emission line and Fermi Bubbles (FB) [2–5].Much effort has been devoted to the study and observation of the GC since it is one of the most appealing regionsobserved from radio to gamma ray. The observations of the GC confirm the presence of a Supermassive black hole(Sagittarius A*) with an intense activity in the past. Outstanding recent discoveries indicate that Sgr A* can bea source of PeV galactic cosmic rays [9], that could have been accelerated from relativistic outflows. Based on thisscenario, Cheng et al [2] propose that Fermi Bubbles can act as a acceleration site for some of the CR particlesoriginally accelerated in SNR located at galactic disk. In their model, the origin of the Bubbles is explained by theperiodic capture and tidal disruption of stars by the Black Hole at the Galactic Centre. These gargantuan eventscreate periodic energy releases in the Halo in the form of multiple shock waves, with larger length scales and lifetimethan those found in SNR, allowing the stochastic acceleration of particles inside the Bubbles at energies higher than10 eV. Very recently, the Atacama Large Millimeter/sub-millimeter Array (ALMA) and measurements of stellarorbits around Galactic Centre reported indications of new candidates in the central region of our Galaxy besides SgrA*. These discoveries can indicate much more activity in the past which could explain the TeV γ -ray observations[10, 11].The CRs interact with the molecular gas via nuclear reactions in the galaxy and generate diffuse GeV-TeV gamma-rays. Many scenarios have been proposed to explain the GC excess of gamma ray emission at GeV energies up to ∼ ◦ from the GC generated by interactions in the galaxy. Detailed discussions of these interpretations can be foundin [2, 3, 6, 12, 13]. In addition, the GC excess energy spectrum is also consistent with a possible scenario of gammarays emitted from a galactic halo of dark matter [14, 15]. However, no indication of the flux from Milky Way dwarfgalaxies, expected to be dark matter dominated, has been detected [16].Hadronic and leptonic models are two distinct interpretations suggested to explain the gamma-ray production fromactivities related to the GC [2, 5, 17]. In the hadronic models, gamma rays are produced by decay of neutral pionsproduced in inelastic collisions between relativistic protons and the thermal nuclei. On the other hand, in the leptonicreactions, gamma rays are generated by inverse-Compton scattering of background interstellar radiation by cosmic-ray ∗ Electronic address: [email protected] † Electronic address: [email protected] electrons and positrons [3, 17]. In [18] is suggested a connection between leptonic and hadronic anomalies with theobjective of modeling the diffusive gamma rays emission in other parts of the Galaxy, taking into account old SNRcontribution to the GeV-TeV spectrum.In this paper, based on recent cosmic rays and gamma ray observations [12, 19], we calculate the contributions ofcosmic rays nuclei spectra and gamma rays spectra with a numerical implementation of models of the GC region [20–23]. We extend the treatment of the case given in [20] using GALPROP [24]. We consider two classes of CRs sourcesrepresented by a source at the centre of the Galaxy (Model GC) and sources modeled by a spherical power-law densityprofile around Galactic Centre (Model FB) [25]. This paper is organized as follows: in Section II we describe our CRspropagation calculations. In particular we detail the numerical implementation of our model and the methodologyadopted for the determination of the key parameters. In Section III we present our results for the models and discussthe gamma-rays from the GC and the conclusions are summarized in Section IV.
II. DESCRIPTION OF THE MODEL
We use the numerical code GALPROP v56 to simulate the distribution of CRs in the Galaxy [24]. GALPROP solvesthe transport equation for a given source distribution and boundary conditions using the second-order Crank-Nicolsonmethod. The equation includes energy losses, nuclear fragmentation and decay, source distributions, convection(galactic wind), diffusive and re-acceleration processes. We adopt the diffusion/re-acceleration model, which describeswell the secondary-to-primary ratios and the effects of convection. A detailed description of the GALPROP model isgiven in [24, 26–28] and Web Site [29]. The GALPROP software has been used in previous studies of Galactic Centre[6, 30, 31] and in this work we extended the code in order to analyze the contribution of CRs sources at the centre ofthe Galaxy.Our simulations assume cylindrical geometry in the galaxy with a diffusion halo with radius R = 20 kpc and haloheight z = 10 kpc with z = 0 located at the galactic plane, which are suggested by previous studies [32]. Sincethe Fermi Bubbles (FB) extend up to 9 kpc north and south from the GC and the halo size has influence on theCRs fluxes, the variations related to the geometry are important to the final cosmic rays and gamma-rays spectra.Using a smaller halo height for the Galactic Centre region as observed by the WMAP haze [33], a very large injectionpower will be needed to describe the CRs data [20]. Taking into account the diffusion and re-acceleration model, thetransport equation for cosmic-rays nuclei in the Galaxy can be written as [29]: ∂N∂t = Q ( x , p ) + ~ ∇ . ( D xx ~ ∇ N − ~vN ) + ∂∂p p D pp ∂∂p p N − ∂∂p ( ˙ pN − p ~ ∇ .~v ) N ) − X i =1 Nτ i (1)where N ( x, p ) is the cosmic rays density per unit of total particle momentum and Q is a cosmic rays injection sourceterm including secondary production of cosmic-rays. In our model, D xx is the spatial diffusion coefficient, ~v is theconvection velocity, the time scales for fragmentation and radioactive decay are τ and τ , respectively [24].The diffusion coefficient is assumed as a scalar function, homogeneous and isotropic throughout the Galaxy, depend-ing on the particle rigidity via a power law with an index δ : D xx = βD ( ρ/ρ ) δ , where ρ = 3 GV, D is a diffusionconstant, β is the velocity in unit of light speed. Cosmic-ray propagation models commonly assume an isotropic diffu-sion coefficient to account for the random deflection of cosmic rays by the interstellar magnetic field. In our model weconsider a spatial diffusion inversely proportional to the magnetic field turbulent component D ( ρ, z ) = D xx exp( | z | z t ),where z t is a characteristic scale (halo size ∼ z t ) [34]. However, an inhomogeneous anisotropic diffusion coefficient isessential in future models to interpret recent measurements of large scale anisotropy of TeV cosmic rays and gamma-raydiffuse emissions [35].The convection velocity ~v ( z ) = dv/dz × z (in z-direction only) is assumed to increase linearly with distance z fromthe plane to halo. The cosmic rays propagation is diffusive-convective in one zone | z | > ∼ D pp , which is related to the spacial coefficient D xx via D pp ∝ p v a /D xx , where v a isthe Alfv´en speed, ˙ p ≡ dp/dt is the momentum loss rate and the Kolmogorov spectrum of turbulence is considered.The parameters of the diffusion coefficient and Alfv´en speed are determined by B/C ratio [24, 34].Our model of the galactic magnetic field has a cylindrical symmetry and is chosen to provide a description of thesynchrotron emission of the Galaxy: B ( r, z ) = B e ( R ⊙ − r ) /R B e −| z | /z B [27], where R ⊙ = 8 . B = 5 µ G and R B = 6 kpc and z B = 2 kpc are the radial and vertical scale-lengths [24]. This model framework onlyconsiders the random magnetic field distribution, since it is associated to diffusive properties of cosmic rays [34, 35].However, the strong magnetic fields are insufficiently constrained near the galactic centre [30] and are beyond thescope of the present model.The source function Q ( x , p ) is described as n ( x ) q ( p ), where n ( x ) is the spatial distribution and q ( p ) is the injectionenergy spectrum of cosmic rays. We adopt a differential injection spectrum which follows a power law in momentum dq ( p ) /dp ∝ p − α , with index α = 2 . yr. In our models, the CRs injection power is in the range ∼ × erg.s − , power needed for the luminosityof CRs in our galaxy.The High Altitude Water Cherenkov (HAWC) gamma-ray observatory reported upper limits above 1 TeV in theNorthern Fermi Bubble region [38]. In the hadronic models, the upper limit on the integral flux of GeV-TeV gamma-rays of a given source can lead to the upper limit on the total CRs luminosity [39, 40]. Motivated by this correlation,to model the spatial distribution of the sources at the FB, we adopt the distribution of the galactic gas halo in whichFB expands [25, 41]: n ( r ) ∝ [1 + ( rr c ) ] − ξ/ , where r is the distance to the GC, r c = 0 .
35 kpc is the core radius and ξ = 0 .
71. On the other hand, the Model GC injects CRs following a δ -function centered at the centre of the Galaxy. III. RESULTS AND DISCUSSION
Considering that the purpose of this paper is to investigate the interplay of galactic cosmic-rays and GC gamma-rays, we compare the measured data at low energies with the energy spectra of Model GC and Model FB for differentelements (proton, helium, carbon, oxygen, silicon and iron) in figure 1. The parameter values that reproduce themeasured data at low energies are listed in table I. The halo half-thickness z = 10 kpc was determined by fittingthe B/C ratio at high energy [42], see figure 3a. The parameters of the Model GC are in agreement with those in[20]. It shows that the CRs flux for lower energies is comparable to that from the SNR and suggests that one singlepowerful source at the GC centre could provide enough CRs that are detected on Earth. Small variations on thevalues of re-acceleration and convection does not change significantly our results. As is clear from fig. 1, the modelFB reproduces well the observed data up to ∼ TeV. This indicates the effect of halo size on the resulting energyspectrum of CRs [24].The CRs injected by sources located at the GC can contribute to the spectrum up to knee [2]. Consequently, theCRs spectrum is a combination of the SNR contribution from the galactic disk and the CRs acceleration in the FB.Similarly, in [3], based on a diffusion-halo model, Sagittarius A* can contribute as a Pevatron to the galactic CRsnear the knee. Our model GC added to the SNR and SgR A* contributions to the proton spectrum is shown in figure2. The total proton spectrum is consistent with the measured data and shows that the contribution of the GC canexplain the observed primary CRs from GeV up to PeV.The measurements of the secondary-to-primary ratio is a tool to understand cosmic rays propagation in the Galaxy.In particular, boron to carbon flux ratio measures the average quantity of interstellar matter traversed by cosmic rays.While boron nuclei are produced by the interactions of heavy nuclei, carbon nuclei are principally produced in thesources. In figure 3, both propagation models provide good fit for
B/C ratio as a function of kinetic energy pernucleon. This figure combines data from TRACER [43], PAMELA [44], ATIC2 [45], CREAM [46], AMS-02 [47] andDAMPE [48], with their statistical uncertainties. The spectra was modulated to 300 MV, appropriate to these data.The Solar modulation is important below a few GeV. At the highest energies ( K ≥ MeV), all results are based onfew events indicating that the primary cosmic rays suffer less spallation and the correction for atmospheric productionof boron may become considerable [49, 50]. The agreement with the data at high energy is less accurate, which maybe improved considering SNR also as sources and CRs acceleration at the same time.In figure 4-(a,b) we show the gamma spectrum from inverse Compton scattering, pion decay and bremsstrahlungthat we have calculated using the gas distribution adopted by the Fermi-LAT collaboration [51] - 4a and by the new2D gas distribution galactic ensemble component [52] - 4b. GALPROP produces a projected map of the gamma rayflux as a product of the cosmic-ray protons propagation taking into account the gas model.The interstellar gas consists essentially of hydrogen and helium, while heavier elements represent a minor fraction ofthe total gas mass. The figure 4-(a,b) shows that dominant processes for gamma ray production are inverse Comptonscattering and decay of neutral pions. Also, the figure 4b shows that at high energy ∼ γ br /γ π ∼ R ∼ . Parameters Units Model GC Model FBSource − GC Fermi Bubbles D cm s − . × . × δ − kpc kpc v a km s − dv/dz km s − kpc − α − IV. CONCLUSIONS
There is a general consensus that the origin and acceleration of the galactic cosmic rays of energy up to the kneeare related to the distribution of supernova remnants in the galactic disk. However, with the increasing number ofstudies of high energy phenomena at the Galactic Centre it is becoming clear that this region can not be neglected.The aim of this work was to study the contribution of the Galactic Centre as a source of galactic CRs based onthe GC gamma-ray observations. We have shown that a single source at the GC can describe the low-energy cosmicrays spectra and the observed cosmic-ray ratio
B/C . We have also carried out simulations of the emission processesof gamma rays using a new 2D galactic distribution gas [52], demonstrating the necessity to include the contributionof the gas in these processes.The results here obtained can be extended to scenarios beyond the knee allowing different contributions of the SNR.For instance, a two-component SNR model: one old SNR component, which would dominate the flux below ∼ B/C ratio. Another possibility is to applyour description in the two-halo model: CRs propagation taking place in two regions characterized by different energydependencies of the diffusion coefficient [54].The simulations presented in this paper enable a better interpretation of CRs and gamma rays data from GCand FB, demonstrating that the GC cosmic rays can contribute significantly to the CRs spectrum. In addition,mechanisms of CRs acceleration at supermassive black hole Sagittarius A* and millisecond pulsars located aroundthe GC can contribute as Pevatrons to the galactic CRs around the knee [3, 4]. We expect that, in the near future,neutrino and TeV gamma-ray detectors, such as CTA [55], with its improved resolution and sensitivity, will be ableto reveal the very nature of the Galactic Centre gamma ray source.
Acknowledgments
The research of RCA is supported by the CAPES-HARVARD Program (Junior Visiting Professor Award) undergrant 88881.162283/2017-01, CNPq grant numbers 307750/2017-5 and 401634/2018-3, and Serrapilheira Institutegrant number Serra-1708-15022. RCA also thanks to Avi Loeb for very fruitful discussions about the Galactic Centreand the Harvard-Smithsonian Center for Astrophysics for hospitality. The authors acknowledge FAPESP Project2015/15897-1 and also gratefully the National Laboratory for Scientific Computing (LNCC/MCTI, Brazil) for pro-viding HPC resources of the SDumont supercomputer, which have contributed to the research results reported withinthis paper. URL:http://sdumont.lncc.br. The authors thank Daniel Supanitsky for helpful comments and the use ofthe software package GALPROP v56 [29]. [1] S. P. Reynolds, Supernova Remnants at High Energy, Annual Review of Astronomy and Astrophysics. , 89 (2008).[2] K. S. 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Taillet, CRDB: a database of charged cosmic rays, Astron. Astrophys. , A32 (2014). E [MeV] −2 −1 E J ( E )[ M e V c m − − r − ] Proton flux
Model GCPamela 2011 AMS02 2013Model FB (a) Proton E [MeV] −3 −2 −1 E J ( E )[ M e V c m − s − s − ] Helium flux
Model GCPamela 2011 AMS02 2017Model FB (b) Helium E [MeV] −3 −2 −1 E J ( E )[ M e V c m − − r − ] Carbon flux
Model GCPamela 2011 AMS02 2017Model FB (c) Carbon E [MeV] −3 −2 −1 E J ( E )[ M e V c m − s − s r − ] Oxygen flux
M del GCAMS02 2017ATIC2 2009 CREAMM del FB (d) Oxygen E [MeV] −4 −3 −2 −1 E J ( E )[ M e V c m − s − s − ] Silicon flux
Model GCATIC2 2009 CREAMModel FB (e) Silicon E [MeV] −4 −3 −2 −1 E J ( E )[ M e V c m − s − s − ] Iron flux
Model GCATIC2 2009 CREAMModel FB (f) Iron
FIG. 1: Energy spectra for six elements: proton, helium, carbon, oxygen, silicon and iron. The spectra aremultiplied by E . The models calculations are shown in comparison with the data using different modulationparameter values for elements, respectively: Φ = 0 . , . , . , . , . . , . , . , . , . E [MeV] −3 −2 −1 E J ( E )[ M e V c − s − s r − ] CR flux
SNRSgr A*Cheng 2012Model GCTotal
FIG. 2: Contribution of GC - SNR - SgR A* to the proton spectrum. The red line represents the observations andtotal contribution. The model GC is the CRs flux calculated in this paper. The Cheng model 2012 [2] describes there-acceleration of the CRs in the Fermi Bubbles producing CRs beyond the knee. These CRs are produced by SNRin the galactic disk. The lines black and magenta represent the contribution of CRs from SNR and spectrum of CRsinjected by Sgr A*, respectively [3]. E k [MeV/nuc] B / C Model GCModel FB AMS-02PAMELA ATIC2DAMPE TRACERCREAM I (a) Boron to Carbon ratio E k [MeV/nuc] B / C Model GCModel FB
AMS-02ATIC2
DAMPETRACER
CREAM I (b) Boron to Carbon ratio at high energy ( K ≥ MeV)
FIG. 3:
B/C ratio as function of kinetic energy per nucleon for the models GC and FB. E [MeV] E J ( E )[ M e V c m s s r ] T)−al m) elPi)( ecayI(verse C)mp−)(Bremss−rahlu(gBubble N)r−h Bubble S)u−hBubblesGC e0cess - Calore (2015)Diffuse emission - H.E.S.S (a) E [MeV] E J ( E )[ M e V c m s s r ] T)−al m) elPi)( ecayI(verse C)mp−)(Bremss−rahlu(gBubble N)r−h Bubble S)u−hBubblesGC e0cess - Calore (2015)Diffuse emission - H.E.S.S (b)
FIG. 4: Inner Galaxy spectra of diffuse gamma-ray emission components. Model GC with a) gas distribution [51]and b) new 2D gas distribution [52], respectively. The data are extracted from the CRDB database [56].0 (a) Bremss (b) Bremss (c) Fractional residual - bremsstrahlungintensity(d) Inverse Compton (e) Inverse Compton (f) Fractional residual - IC intensity(g) Pion decay (h) Pion decay (i) Fractional residual - π -decay intensity FIG. 5: Model of diffuse galactic gamma rays from the Milky Way at 2.5 GeV [51]. Left: Model GC with centralproton source. Middle: Model FB with proton source. Right: Fractional residual maps comparing the models. Thetotal gamma-ray emission is composed of hadronic cosmic-ray interactions with gas and leptonic interactions withthe gas (bremsstrahlung) and inverse Compton scattering. Maps are in galactic coordinates with ( l, b ) = (0 ,
0) at thecenter of the map.1 (a) Bremss (b) Bremss (c) Fractional residual - bremsstrahlungintensity(d) Inverse Compton (e) Inverse Compton (f) Fractional residual - IC intensity(g) Pion decay (h) Pion decay (i) Fractional residual - π -decay intensity FIG. 6: Model of diffuse galactic gamma rays from the Milky Way at 2.5 GeV with 2D gas distribution galacticensemble component [52]. Left: Model GC with central proton source. Middle: Model FB with proton source.Right: Fractional residual maps comparing the models. The total gamma-ray emission is composed of hadroniccosmic-ray interactions with gas and leptonic interactions with the gas (bremsstrahlung) and inverse Comptonscattering. Maps are in galactic coordinates with ( l, b ) = (0 ,,