Galactic center at very high-energies
M. Chernyakova, D. Malyshev, F.A. Aharonian, R. M. Crocker, D. I. Jones
aa r X i v : . [ a s t r o - ph . H E ] S e p D RAFT VERSION N OVEMBER
13, 2018
Preprint typeset using L A TEX style emulateapj v. 8/13/10
GALACTIC CENTER AT VERY HIGH-ENERGIES. C HERNYAKOVA , M. , M ALYSHEV , D. , A HARONIAN , F. A. , , C ROCKER , R. M. , J ONES , D I. Dublin Institute for Advanced Study, Astronomy & Astrophysics Section, 31 Fitzwilliam Place, Dublin, 2 Ireland and Max Planck Institut f¨ur Kernphysik, Postfach 103980, 69029 Heidelberg, Germany
Draft version November 13, 2018
ABSTRACTEmploying data collected during the first 25 months’ observations by the Fermi -LAT, we describe andsubsequently seek to model the very high energy ( > MeV) emission from the central few parsecs of ourGalaxy. We analyse, in particular, the morphological, spectral and temporal characteristics of the central source,1FGL J1745.6-2900. Remarkably, the data show a clear, statistically significant signal at energies above 10GeV, where the Fermi -LAT has an excellent angular resolution comparable to the angular resolution of HESSat TeV energies. This not only reduces dramatically the contamination both from the diffuse background andthe nearby gamma-ray sources, but also makes meaningful the joint analysis of the Fermi and HESS data.Our analysis does not show statistically significant variability of 1FGL J1745.6-2900. Using the combinationof Fermi data on 1FGL J1745.6-2900 and HESS data on the coincident, TeV source HESS J1745-290, weshow that the spectrum of the central γ -ray source is inflected with a relatively steep spectral region matchingbetween the flatter spectrum found at both low and high energies. We seek to model the gamma-ray productionin the inner 10 pc of the Galaxy and examine, in particular, cosmic ray (CR) proton propagation scenariosthat reproduce the observed spectrum of the central source. We show that a model that instantiates a transitionfrom diffusive propagation of the CR protons at low energy to almost rectilinear propagation at high energies(given a reasonable energy-dependence of the assumed diffusion coefficient) can well explain the spectralphenomenology. In general, however, we find considerable degeneracy between different parameter choiceswhich will only be broken with the addition of morphological information that γ -ray telescopes cannot delivergiven current angular resolution limits. We argue that a future analysis done in combination with higher-resolution radio continuum data holds out the promise of breaking this degeneracy. Subject headings:
Galaxy: center — synchrotron radiation: cosmic rays — molecular clouds: general INTRODUCTION
Over the past decade-and-a-half since the discovery byEGRET of a very high energy (VHE) gamma-ray source nearthe Galactic center (GC), there has been intense speculationas to what mechanism(s) are producing the observed emis-sion. The subsequent discovery of TeV gamma-ray emissionfrom the Sgr A* region by the ground-based gamma-ray in-struments, in particular by the HESS array of atmosphericCherenkov telescopes (Aharonian et al. 2004), has generatedfurther theoretical activity. Of general interest and import –given the GC constitutes the nearest example of a galactic nu-cleus – is the question concerning the sites and mechanism(s)by which particles are accelerated to TeV energies and beyondin the dynamical center of our Galaxy.Despite the fact that the GC TeV gamma-ray source isa point-like object for HESS, the . ◦ PSF of the instru-ment and the extremely crowded and complex nature ofthe region (as evidenced by the complex radio morphology(Law et al. 2008)) do not allow the unambiguous identifi-cation of the source(s) of gamma-ray emission. With thelatest data, however, it is possible to place the center-of-gravity of the TeV point source within the central ∼ ′′ ofthe Galaxy (Acero et al. 2010), leaving only a handful ofpossible sources. These include the central black hole it-self, Sgr A* (Aharonian & Neronov 2005a; Liu et al. 2006);a plerion discovered within the central few arcseconds ofthe Galaxy (Wang et al. 2006; Hinton & Aharonian 2007), aputative ”black hole plerion” produced by the wind fromSgr A* (Atoyan & Dermer 2004), and the diffuse ≤ pc [email protected] region surrounding Sgr A* (Aharonian & Neronov 2005b;Ballantyne et al. 2007, 2010).Given the above background, we consider here the furtherinsights now possible in light of the Fermi -LAT observationsof the GC region. In particular, since the PSF of Fermi above ∼ GeV is similar to that of HESS, it is possible to explorea quite broad energy interval of relativistic particles localizedin this region.First 11 months of Fermi observations of the GC were pre-sented by J.Cohen-Tanugi on behalf of Fermi LAT collabo-ration during the 2009 Fermi Symposium. In this work, theauthors argued that the Fermi source 1FGL J1745.6-2900 andthe HESS source J1745-290 are spatially coincident. Also,they derived an energy spectrum of the Fermi source till 100GeV and concluded that to match the HESS spectrum either ahigh-energy break or a cut-off is required.In this work we analyze 25 months of Fermi LAT data. Inaddition to the central GeV source and other reported sources,our analysis reveals four new sources of GeV gamma-rays lo-cated in this region. With the spectral information from bothFermi and HESS in hand, we model below the production ofgamma-rays from the inner GC due to hadronic interactionsof protons accelerated within the central black hole and dif-fusing into the surrounding interstellar medium.In section 2, we describe the reduction and analysis of theFermi data. We present the details of our model in section 3.In section 4 we discuss the implications of the obtained resultsand summarize the main conclusions in section 5. DATA ANALYSIS AND RESULTS.
Chernyakova et al.
TABLE 1C
OORDINATES AND TS OF THE NEW SOURCES DISCOVERED DURINGTHE ANALYSIS .RA Dec TS(J2000.0) (J2000.0)264.906 -28.555 331266.210 -30.360 424270.060 -30.091 189270.697 -30.626 192
The large area telescope (LAT) on board the Fermi satelliteis a pair-conversion gamma-ray detector operating between20 MeV and 300 GeV. The LAT has a wide field of view of ∼ ∼ ∼
565 km; full detailsof the instrumentation are given in Atwood et al. (2009)). Thedata used for our analysis are based on the first 25 months ofobservations (August 4, 2008 – August 18, 2010).The data analysis was performed using the LAT Sci-ence Tools package with the
P6 V3 post-launch instru-ment response function (Rando & et al. 2009). The standardevent selection for source analysis, resulting in the strongestbackground-rejection power (diffuse event class) was applied.In addition, photons coming from zenith angles larger than ◦ were rejected to reduce the background from gammarays produced in the atmosphere of the Earth. The analysiswas further restricted to the energy range above 100 MeV,because below this energy effective area becomes very smalland the residual uncertainty in the instrumental response issignificant.In order to take into account the broad point spread func-tion (PSF) at low ( ∼ MeV) energies, we constructed asequence of test statistic (TS) images of the ◦ × ◦ re-gion around the Sgr A*. In producing TS images, we used the gttsmap tool with a tolerance parameter of f tol = 10 − and a bin size in each map of . ◦ . Finally, after subtract-ing the 19 known sources from the one year Fermi cata-logue (1FGL) which happen to be within the selected region,we found four new sources, which are listed in the Table 1,in the residual images. One of these sources (indicated asJ1744.8-3021) – shown in magenta in Figure 1 – lie withinthe . ◦ × ◦ area around the GC. This source coincides spa-tially with known HESS source HESS J1745-303 and EGRETsource 3EGJ1744-3011.In order to construct a light-curve for 1FGL J1745.6-2900,we used a spectral method by selecting data in 300 MeV–100 GeV energy range and fitting all known sources, selectedas above, with a single power law model. Afterwards, we splitthe whole time interval into 25 equal time bins and fit sourcespectra by fixing their slopes to the best-fit value obtained overthe entire time period, leaving the source normalization as afree parameter. The normalization of the Galactic and extra-galactic background was also left as a free parameter. Theresulting light-curve is shown in Figure 2 and is relativelystable and does not show any statistically significant varia-tion. The averaged flux is equal to (324 . ± . × − counts cm − s − , with a reduced χ = 1 . for 24 degrees offreedom.Spectral fitting was performed within 100 MeV–300 GeVenergy range with the gtlike tool. The spectrum in100 MeV–300 GeV energy range can be fitted by a powerlaw with a slope of Γ = 2 . ± . and a flux normal-ization of F = (1 . ± . × − cm − s − MeV − at100 MeV. We also attempted to split the spectrum into two different energy bands, and found that the fitted slope is equalto Γ = 2 . ± . in 300 MeV–5 GeV energy range, and Γ = 2 . ± . in 5 – 100 GeV energy range. The errorsgiven above are statistical errors and represent the 1 σ devi-ation. Thus the slope of the Fermi spectrum above severalGeV is significantly steeper than the spectrum reported bythe HESS collaboration at TeV energies ( F HESS ∼ E − . ,(Aharonian et al. 2009). Note that at low energies, Fermi hasa very broad PSF, rapidly moving from 4 ◦ at 100 MeV to 2 ◦ at 300 MeV. Thus, taking into account the possible sourceconfusion in the region, one should treat the first point in thespectrum (100–300 MeV) with caution. MODELING
As proposed in Aharonian & Neronov (2005b), a signifi-cant fraction of the protons accelerated near the black holemay enter the surrounding gaseous environment and initiateVHE gamma-ray emission through neutral pion productionand subsequent decay. The efficiency of the process, and theenergy spectrum of resulting gamma-rays depends not onlyon the protons’ injection rate and the ambient gas density,but also on the speed of proton transport into the surround-ing medium (Aharonian & Neronov 2005b; Ballantyne et al.2007, 2010). To explain the gamma-ray spectrum reportedby the HESS collaboration, Aharonian & Neronov (2005b)assumed that relativistic protons with a power-law spectrumpossessing a spectral index of Γ ∼ are injected into thedense gaseous environment surrounding the central blackhole. The diffusion coefficient, D , was assumed to havea power-law dependence on energy of the form D ( E ) =10 ( E/ GeV ) β κ cm s − . For the cosmic ray diffusionin the Galactic disk κ ∼ and β ∼ , but of course thediffusion coefficient in the GC could be quite different. InAharonian & Neronov (2005b) the parameter β was assumedto be in the range of 0.5–1. In the model of Ballantyne et al.(2007, 2010) the propagation is treated using the ray-tracingtechnique. They found that in order to reproduce in theirmodel the reported energy distribution of TeV gamma-rays,the spectrum of protons should be hard with a spectral index ∼ . . Such an exceptionally hard injection spectrum of pro-tons implies a very strong energy dependence of the characterof propagation of protons which, within the formalism of dif-fusion, would require a diffusion coefficient with β ∼ . .Given that the VHE emission detected by HESS and Fermican be localized to within the central several arcminutes then,for a GC distance of d ∼ n H = 1000 cm − at 1 pc radius, with either constant or /r radial de-pendence. The inner and outer radii of this shell are pa-rameters in our model. Another relevant parameter is thetime evolution of the proton injection. Although one cantreat it as a quasi-stationary process, in fact the proton in-jection can be dominated by one or several flares that oc-curred in the past in Sgr A*. In this context, one should men-tion the morphological interpretation of the diffuse gamma-ray emission observed by HESS from the central 200 pc re-gion of GC, which relates the positive detections of gamma-rays from giant molecular clouds in GC to a putative ”proton”alactic center at very high-energies 3 F IG . 1.— TS maps of the central part ( . ◦ × . ◦ ) of the Galaxy center as seen by Fermi in 300 MeV – 3GeV, 3GeV–30 GeV and 30GeV–300 GeV energyranges (left to right). Positions of new sources are marked with magenta circles. Green ellipses correspond to the positions of the sources from the 1 year Fermicatalogue. Note that linear colour scheme has different maximum value in all cases varying from 5500 in the less energetic left picture to 140 in the most energeticright one. Source significance can be approximately estimated as a square root of TS.F IG . 2.— Lightcurve of the 1FGL J1745.6-2900 in 300 MeV – 100 GeVenergy range. The average flux is shown with a dashed line. flare that occurred in Sgr A* in the past, 10,000 years ago orso (Aharonian et al. 2006). The detection of reflected X-rayemission from the Sgr B2 cloud is another, more direct pieceof evidence about the short flaring activity of Sgr A* a fewhundred years ago (Sunyaev et al. 1993; Koyama et al. 1996,2008; Revnivtsev et al. 2004; Terrier et al. 2010). In the standard diffusion approximation the propaga-tion of particles is described by the diffusion equation(Ginzburg & Syrovatskii 1964) which, in the spherically sym-metric case, reduces to the form: ∂n∂t = Dr ∂∂r r ∂n∂r + ∂∂E ( bn ) + Q, (1)where n ( r, t, E ) is the space density of relativistic particleswith energy E , at instant t being a distance r from the source; b ( e ) = − dE/dt is the continuous energy loss rate; Q ( E, t ) is the injection rate; and D ( E ) is the energy-dependent dif-fusion coefficient. We have assumed here, for simplicity, that D is independent of r and has a power-law dependence onenergy as stated above. The solution of equation (1) can bewritten as (Syrovatskii 1959): n ( E, r, t ) = Z t P ( E, r, t − x ) Q ( E, x ) dx, (2)where the propagator, P ( E, r, t ) , is defined as: P ( E, r, t ) = 1[4 πλ ( E, t )] / exp (cid:20) − r λ ( E, t ) (cid:21) , (3) Chernyakova et al.and λ ( E, t ) = − Z EE g ( t ) dx D ( x ) b ( x ) . (4)In equation (4) E g is the energy that a cooled particle has attime t , if its initial energy was E .Formally, the diffusion equation does not contain infor-mation on how fast a particle may propagate. Since Eq.(1)does not prevent an artificial ”superluminal motion” ( v =2 D ( E ) /r & c ), we follow the phenomenological approachproposed by Aloisio et al. (2009) who introduced a propaga-tor, P ( E, r, t ) in the form: P ( E, r, t ) = θ (1 − ξ )4 π ( ct ) − ξ ) α ( E, ξ ) K [ α ( E, ξ )] exp " − α ( E, ξ ) p − ξ , (5)where θ ( x ) is the Heaviside step function, ξ ( t ) = r/ct , K ( x ) is modified Bessel function of the second kind, and α ( E, t ) isdefined as: α ( E, t ) = c t λ ( E, t ) . (6)In the low-energy regime (i.e., E ≪ E c ), the propagatorgiven by Eq.(5) reproduces the standard treatment of diffu-sion, whilst in the high-energy regime ( E & E c ) it describesparticles that move in a rectilinear fashion. Here E c is theenergy at which Eq. (1) allows diffusion with the speed oflight E c = (cid:18) cR D (cid:19) /β GeV. (7)Due to the energy dependence of the diffusion coefficient,proton propagation will be quite different at low as comparedto high energies. We have explored how this plays out inthe GC environment. The result presented in Figure 3 showsthe change of the radial distribution of protons as a func-tion of energy. We have determined the proton distributionafter 300 years of continuous injection into the interstellarmedium of density n H = 10 cm − within a region of ra-dius R = 3 pc. The initial spectrum of protons was assumedto have a power-law distribution with an exponential cutoff, Q ( E ) ∝ E − exp( − E/ TeV ) .It can be clearly seen from Figure 3 that, whilst at 10 TeVthe particles pass through the region in an almost rectilinearfashion, at lower energies, protons propagate diffusively. Anexplanation for the lack of low-energy protons at high radiican be found in the fact that these particles have too low anescape velocity to travel that far in a given time.The spectrum of the protons integrated over the gamma-rayproduction region (see Figure 3) is shown in Figure 4. Pho-tons produced by the interaction of relativistic protons withsuch an energy distribution fit both Fermi and HESS data well.At low (GeV) energies, the diffusion radius is smaller than theregion so that protons are accumulated within the region and,given the almost energy-independent pp cross-section, mirrorthe spectrum of the injected protons. On the other hand, atTeV energies protons begin to propagate in a rectilinear modeand will have again the form of the injected spectrum, albeit ata lower flux level. Protons with an intermediate energy have amuch steeper, diffusion-processed spectrum representing thetransition between the two extremes. The spectral shape of thehighest energy gamma-rays is not affected by the propagationeffects. Therefore in order to match the spectrum at highest F IG . 3.— The fluxes of protons as a function of radius at different energiesshown as marked. For ease of comparison each energy was multiplied bya factor of 900 (for 10 GeV), 8000 (100 GeV), × (1TeV) and × (10 TeV). The flux at each energy have been multiplied by R , so thatrectilinear propagation corresponds to a horizontal line.F IG . 4.— The energy distribution of protons averaged over 3pc of gamma-ray production region, as reconstructed from Fermi and HESS data.F IG . 5.— Spectral energy distribution of gamma-rays expected from a re-gion filled with relativistic and non-relativistic protons within different as-sumptions concerning the injection, diffusion and the region geometry (seetext for a discussion of parameters for each specific model). The data pointshave been derived from the Fermi and HESS data energies reported by HESS (Aharonian et al. 2009), we as-sumed an exponential cut-off in the proton spectrum and fixits position at 100 TeV.alactic center at very high-energies 5Below, we fit parameters which represent the particle in-jection spectrum, the propagation of the injected protons, andthe geometry of the interstellar medium. It is instructive tosystematically examine the influence of these model param-eters on the resulting spectrum. To do this we begin with years of injection of relativistic protons with a spectrumof the form Q ( E ) ∝ E − . exp( − E/ TeV ) into a 3 pcradius region filled by an interstellar gas of constant den-sity, n H = 10 cm − . The injection rate was taken equalto Q = 3 . × erg/sec. The diffusion parameters werechosen as β = 0 . , κ = 0 . in order to reproduce the com-bined Fermi and HESS spectrum. The photon spectrum re-sulting from this parameter set (model A) is shown in Figure5. The other curves in Figure 5 illustrate the effect of changeof a single parameter, while all others are fixed to the valuesused in model A.Figure 5 corresponds to the case of a source active for only300 years (model B). This change does not affect high energyparticles, traveling rectilinearly, because their escape time is t esc = R/c ∼ years, much shorter then the injection time.These particles fully fill the region and their density is thesame as in the case of model A. The diffusion time at lowenergies ( E < E c ∼ t diff = R / D ∼ years at 1GeV). Thus,300 years will be not enough for low-energy particles to travelto the outer regions of the shell, and the total spectrum is ex-pected to be harder with respect to model A. Thus, in thisparameter set, whilst the radiation does not differ from ourheuristic case at high energies, at lower energies there are nec-essarily fewer gamma-rays.Models C and D in Figure 5 show what occurs when thediffusion parameters κ and β are changed. If one increasesthe diffusion coefficient by a factor of 10, then by the samefactor, the diffusion time of the low-energy particles is de-creased, leading to a corresponding reduction in the intensityof the gamma-ray emission. If one changes the energy de-pendence of the diffusion by decreasing β by a factor of two,then the transition of the particles propagation from diffusionto rectilinear propagation occurs at much higher energies ( E c has /β dependance, see equation (7), and reaches PeV en-ergy in this case). Thus the emission increases at all energiesand the spectral form changes due to a larger influence of highenergy particles.Models E and F in Figure 5 show the change of the photonspectrum due to the change of the geometry of the region. Thecorresponding curve in figure corresponds to a shell geometrywith an outer radius of R = 10 pc (as compared to the 3 pc ra-dius considered in the other models). Using this particular ge-ometry causes the overall normalization of the resulting spec-trum to increase (a factor of 0.25 was applied to this spectrumfor easier comparison in the production of Figure 5) due tothe increase in size of the gamma-ray production region. Ad-ditionally, the ‘bump’ at lower energies becomes wider, sincethe energy at which particles transition from the diffuse to therectilinear propagation regimes increases as R /β , and thusthe larger the radius, the larger the number of ’intermediate’,GeV, energy particles that can be accumulated.The effect of the shell volume is clearly seen in the casewhen the value of the inner radius of the disk is changed.Model F in Figure 5 is for a shell with inner radius R min =2 pc and outer radius R max = 3 pc. In this case the overallnormalization of the resulting spectrum decreases (in Figure5 a factor of 3.3 has been applied to this spectrum in order F IG . 6.— Brightness profile of the GC in 100MeV - 1GeV (solid lines) and1GeV – 10GeV (dashed lines) energy ranges. See Table 2 for the descriptionof the models. 25 ′′ corresponds to 1pc.TABLE 2P ARAMETERS OF DIFFERENT MODELS USED FOR F IGURE
6. T
HEMEDIUM DENSITY AT
R=1
PC WAS ASSUMED TO BE EQUAL TO n H = 10 CM − . Q AND Q f CORRESPOND TO THE INJECTION RATESOF THE CONSTANT SOURCE AND A FLARE CORRESPONDINGLY .model n H κ β Q R min Q f erg/s pc 10 erg/sconst const 0.02 0.95 6 0 0 /r /r to more easily aid the comparison to other models), but thelow-energy bump is still wider than in the case of a shell withno hole (i.e. an oblate spheroid). This is due to the fact thatremoving the inner part of the shell mostly diminishes the softphoton emission, effectively increasing the relative number ofmore energetic ones.Finally note that the sharp drop of gamma-ray spectra below1 GeV is the result of the kinematics of pion production at p-p interactions, and therefore does not depend on the modelparameters.The radial distribution of photons is also highly dependenton the model parameters. Figure 6 shows the brightness pro-file of the inner 3 pc after years of the constant injec-tion at energies between 100 MeV–1 GeV (solid lines) and1 GeV–10 GeV (dashed lines). For all models the constantsource was active for 10 years. The initial spectrum of pro-tons is assumed to be a power-law with an exponential cutoff, Q ( E ) ∝ E − exp( − E/ TeV ) . The medium density atR=1pc was assumed to be equal to n H = 10 cm − .At higherenergies particles pass through the region almost rectilinearlyand the region will appear as a point-like source of gamma-rays to Fermi . As labeled in Figure 6, different curves corre-spond to different model parameter sets in terms of the ambi-ent matter distribution and injection. For all models in Figure6, parameters, given in Table 2, were chosen so that the result-ing integrated emission accurately reproduces the Fermi andHESS data, and the resulted profiles were normalized to themaximum value to aid comparison.Geometrically, the solid line represents the case of constantdensity and exhibits a broader profile at higher energies (line).If instead, one models the region with a density falling off Chernyakova et al.proportional to a n H ∝ /r profile, the resulting profilesare thinner and are represented by the red solid and dashedlines, which almost coincide on the figure. The profile is morecentrally peaked in the latter case, since the matter is moreconcentrated in the center and so the photon flux will originatemostly from this region.The green solid and dashed lines show the profile created if,in addition to a constant source, there was also a flare whichoccurred 300 years ago (the injection rate in the Table 2 cor-responds to a flare of length 10 years). In order to match ob-servational data in this case, a larger diffusion coefficient hadto be assumed, which inevitability leads to a larger diffusionradius and – correspondingly – to a wider profile. Finally inFigure 6 we show the brightness profiles corresponding to ashell geometry. In this case the profile has a maximum at aradius of the inner shell. DISCUSSION
The spectral properties of the very high energy emissionfrom the GC differs considerably from that at lower energies:whilst the GC is known to be variable at X-rays and near-IRwavelengths, no variability has been detected either by HESS,or by Fermi. This seeming duality has a natural explanation ifthe low energy emission is generated very close to the centralblack hole, while the gamma-ray emission originates from amuch larger region and is emitted during the diffusion of therelativistic protons through the interstellar medium surround-ing the central black hole. In such a case, the very high energyemission would only reflect (with a delay) major flares orig-inating from the central source. As remarked above, one in-terpretation of the distribution of the diffuse, TeV γ -ray emis-sion relative to the molecular clouds in the central ∼ pcof our Galaxy, is that a central CR proton source flared about years ago (Aharonian et al. 2006). In the previous sec-tion we showed that our model is able to reconstruct dataif we assume a constant injection of relativistic protons for . × years (see Figure 5). This time is higher than thediffusion time for the used set of parameters and thus the ob-tained photon energy spectrum is effectively steady state.The observations of reflected X-radiation from the cloudSgr B2 located at a distance of 100 pc from Sgr A* suggeststhat a few hundred years ago there was an increase of X-ray luminosity of Sgr A* (Sunyaev et al. 1993; Koyama et al.1996, 2008; Revnivtsev et al. 2004; Terrier et al. 2010). In ourmodeling, we checked that we are able to explain the data asa result of a constant injection of protons over three hundredsyears. We found that if one assumes an injection rate of pro-tons of × erg/s, and takes β = 0 . , κ = 0 . (theresulting radial distribution of protons for this model is shownin Figure 3), then the resulting emission is in good agreementwith the observations. Our model is able to self-consistentlyexplain different spectral indices at GeV and TeV energies bythe different effective escape velocities of the protons. Whilehigh energy protons, producing TeV photons, escape quasi-rectilinearly without spectral deformation, as, indeed, do theparticles fully trapped at the lowest energies, the particles withintermediate energies are affected by diffusion, but not fullytrapped and their spectrum becomes much steeper providingthe transition between two extreme cases.Recent monitoring of the Sgr B2 cloud with X-ray in-struments shows flux variability on time scales of 10 years(Terrier et al. 2010). This variability can be naturally inter-preted as a measure of the flare duration. Although the X-rayluminosity and proton acceleration in Sgr A* should not nec- F IG . 7.— Combined Fermi (green points) and HESS (blue points) explainedby superposition (black solid line) of a proton flare of 10 years durationhappened 300 years ago (magenta dashed line) and a constant source thatswitched on years ago (red dotted line). See Section 4 for model param-eters. essarily correlate, it is interesting to explore also the scenariowhen we deal with a flare of proton acceleration and injectioninto the interstellar medium on timescales of years.In Figure 7 we compare the spectra of gamma-ray emissionresulting from realization of three different scenarios: (i) aproton flare of 10 years duration that occurred 300 years ago,(ii) a constant source that switched on years ago, and (iii)a proton flare on top of the constant source, namely the super-position of (i) and (ii). To fit the data, we took the size of thegamma-ray emission region to be R = 8 pc, parameters ofthe diffusion coefficient β = 0 . , κ = 1 , and initial protonspectrum of Q ( E ) ∝ E − exp( − E/ TeV ) , with the pro-ton injection rate of . × erg/s for the constant sourceand . × erg/s for the flare.For this parameter set, the 300 year old flare cannot havea strong impact on the observed TeV spectrum at this pointin time, since most of the high energy protons from the flarehave already escaped. On the other hand, the emission at GeVenergies is produced by protons from the flare which are stilltrapped by diffusion in the gamma-ray production region. Toexplain the TeV data we need much slower diffusion or a freshinjection of protons, for example contributed from a very re-cent flare, or by the quasi-steady component of protons. Ac-tually the form of TeV emission doesn’t depend on the age ofthe source if it exceeds t esc = R/c ∼ years. The case ofsuperposition (solid line) of the flare (dashed line) and persis-tent (dotted line) components of protons is shown in Figure 7.For the chosen parameters, the GeV energy range of gamma-rays is dominated by the flare component of protons, whilethe TeV gamma-rays are contributed mainly by protons fromthe persistent component.Thus, we are able to reproduce the observed broad-bandspectrum of gamma-rays in different ways. In all cases therequired injection rate is well below the Eddington limit ofthe × M J black hole in GC, L Edd = πGMm p cσ T ≃ × erg/s. The total energy required in relativistic protonscurrently trapped in the gamma-ray production region variesfrom to erg for different models. This energy canbe injected in very different ways: in reality there has proba-bly been a series of flares with different energetic signaturesoccurring throughout the life-time of the central source.The observed spectral and temporal properties of the GC atvarious wavebands are not enough to constraint all the param-alactic center at very high-energies 7eters in our model. Additional information can be extracted,in principle, from the gamma-ray morphology of the innerarcminute region: above, we showed that different set of pa-rameters describing the observed spectral properties result invery different radial profiles (e.g., Figure 6). However, withthe angular resolutions of the current space- and ground-baseddetectors, we cannot distinguish between the different radialprofiles. Fortunately, such information can be recovered byobservations of synchrotron emission of secondary electronsfrom decays of charged pions, accompanying the productionof gamma-rays from decays of neutral muons. Since throughthis channel the electrons and gamma-rays are produced withsimilar energy distributions, we can connect directly the fre-quency of synchrotron photons of secondary electrons withthe energy of the “genetically” connected gamma-rays: ǫ ≃ (cid:18) B − G (cid:19) (cid:18) E γ (cid:19) MHz , (8)where the magnetic field is normalized to the probable mini-mum value expected in the region (Crocker et al. 2010).Thus, in the first approximation, the morphology of the syn-chrotron radiation of ”hadronic” origin should be similar tothe morphology of GeV gamma-rays. While at sub-GHz fre-quencies, GC radio photons are attenuated by free-free ab-sorption in dense H II regions between the GC and the Earth(see Crocker et al. 2010), the synchrotron emission at ∼ GHzfrequencies arrives without significant attenuation. The emis-sivity of synchrotron radiation of secondary electrons in theinner few pc of the Galaxy has been studied by Crocker et al.(2007) , based on a model where the interactions of pro-tons, diffusing away from an assumed central source, supplythe observed, point-like TeV signal (Ballantyne et al. 2007).They then compared the predicted synchrotron emission tothe GHz radio frequency spectrum, and found that essentiallyall the diffuse non-thermal GHz radio emission from the cen-tral parsecs of the Galaxy could be explained as due to emis-sion of secondary electrons (and positrons). Therefore we an-ticipate that the new Fermi data combined with available ra-dio measurements, should allow us to constrain significantlythe parameter space of models positing that the GeV and TeVgamma-ray emission of the GC is due to hadronic interactionsin the central few parsecs of GC. Analysis of the morphologyof radio emission holds out particular promise here. The re-sults of such an analysis are beyond the scope of this paperand will be presented elsewhere.It should be noted that cosmic ray electrons produce pho-tons not only in the radio domain; their bremsstrahlung emis-sion can be an important source of high energy gamma-rays. Comparing the synchrotron and bremsstrahlung coolingtimes: t synch ≃ × (cid:18) B − G (cid:19) − (cid:18) E e TeV (cid:19) − s (9) t bremms ≃ . × (cid:16) n H cm − (cid:17) − s , (10)we conclude that bremsstrahlung losses dominates at energies below: E e . (cid:16) n H cm − (cid:17) (cid:18) − G B (cid:19) GeV . (11)This suggests that bremsstrahlung will dominate at energiesless than ∼ GeV for fiducial n H and B values.The relative importance of electron bremsstrahlung in pro-ducing the observed gamma-ray emission, is characterized bythe ratio of cooling times of electrons and protons associatedwith the bremsstrahlung and neutral pion production, respec-tively: q brγ /q π γ ≃ (3 t pp /t br ) f ≃ f , where f = n e /n p isthe electron to proton energy density ratio (Aharonian 2004).Hence, if the ratio of protons to electrons is ≫ , then π -decay gamma-rays dominate over bremsstrahlung. The con-tribution of electron bremsstrahlung to TeV gamma-rays isquite limited because of the severe energy losses of very highenergy electrons due to the synchrotron and IC losses.Finally, we note that the Fermi data presented here can notbe explained by IC models proposed by Atoyan & Dermer(2004) and Hinton & Aharonian (2007). While these mod-els are in a good agreement with HESS data, they predict thatthe energy flux in the GeV part of the spectrum should besmaller than in TeV range, apparently contrary to the Fermiobservations. SUMMARY
We have analyzed 25 months of Fermi data on the GC re-gion. The Fermi LAT source 1FGL J1745.6-2900 lies withinthe error box of HESS source J1745-290. We found that,while below 5 GeV, the spectrum of 1FGL J1745.6-2900 hasa photon spectral index similar to the HESS source, the spec-trum at higher energies is better described by a steeper spec-tral index. We have formulated a model which producesa photon spectrum that can naturally explain the observedbroad-band gamma-ray emission. This model considers thehadronic interactions of relativistic protons which, having dif-fused away from a central source, presumably the centralblack hole, fill the inner few parsecs of our Galaxy. We haveexplored the parameter space of our model, in terms of thegeometry, characteristics of the diffusion coefficient, and in-jection rate history.We have shown that the available spectral information canbe well described with different sets of model parameters andthat additional information is required to distinguish modelscenarios. Such information could be obtained from the spa-tial distribution of the observed gamma-ray emission; how-ever, the required arc-second resolution cannot be reached bygamma-ray telescopes. Luckily, synchrotron emission fromthe secondary electrons and positrons expected in our modelmay be detected by radio telescopes which possess an angu-lar resolution high enough for the purposes of distinguishingbetween model parameters.The authors are grateful to Venya Berezinsky for the dis-cussions on the transition from diffusion to rectlinear regime.The authors wish to acknowledge the SFI/HEA Irish Centrefor High-End Computing (ICHEC) for the provision of com-putational facilities and support. The work of D.M. was sup-ported by grant 07/RFP/PHYF761 from Science FoundationIreland (SFI) under its Research Frontiers Programme.
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