Fermi LAT has discovered two extended gamma-ray bubbles above and below the
galactic plane. We propose that their origin is due to the energy release in
the Galactic center (GC) as a result of quasi-periodic star accretion onto the
central black hole. Shocks generated by these processes propagate into the
Galactic halo and accelerate particles there. We show that electrons
accelerated up to ~10 TeV may be responsible for the observed gamma-ray
emission of the bubbles as a result of inverse Compton (IC) scattering on the
relic photons. We also suggest that the Bubble could generate the flux of CR
protons at energies > 10^15 eV because the shocks in the Bubble have much
larger length scales and longer lifetimes in comparison with those in SNRs.
This may explain the the CR spectrum above the knee.Comment: 5 pages, 4 figures. Expanded version of the contribution to the 32nd
  ICRC, Beijing, #0589. To appear in the proceeding

Cheng, K. -S.

Chernyshov, D. O.

Dogiel, V. A.

Ip, W. -H.

Ko, C. M.

Wang, Y.

English

arXiv

Fermi LAT has discovered two extended gamma-ray bubbles above and below the galactic plane. We propose that their origin is due to the energy release in the Galactic center (GC) as a result of quasi-periodic star accretion onto the central black hole. Shocks generated by these processes propagate into the Galactic halo and accelerate particles there. We show that electrons accelerated up to  10 TeV may be responsible for the observed gamma-ray emission of the bubbles as a result of inverse Compton (IC) scattering on the relic photons. We also suggest that the Bubble could generate the flux of CR protons at energies > 10(15) eV because the shocks in the Bubble have much larger length scales and longer lifetimes in comparison with those in SNRs. This may explain the CR spectrum above the knee.postprintThe 32nd International Cosmic Ray Conference (ICRC2011), Beijing, China, 11-18 August 2011. In Proceedings of ICRC201

Cheng, KS

Wang, Y

Chernyshov, D

Dogel, V

Ko, CM

Ip, WH

HKU Scholars Hub

Title Particle acceleration and the origin of gamma-ray emission fromFermi BubblesAuthor(s) Chernyshov, D; Cheng, KS; Dogel, V; Ko, CM; Ip, WH; Wang, YCitation The 32nd International Cosmic Ray Conference (ICRC2011),Beijing, China, 11-18 August 2011. In Proceedings of ICRC2011Issued Date 2011URL http://hdl.handle.net/10722/145613Rights Creative Commons: Attribution 3.0 Hong Kong License32ND INTERNATIONAL COSMIC RAY CONFERENCE, BEIJING 2011Particle acceleration and the origin of gamma-ray emission from Fermi BubblesD.O. CHERNYSHOV1,2,3, K.-S. CHENG2, V.A. DOGIEL1, C.M. KO2,3, W.-H. IP3 AND Y. WANG21I.E.Tamm Theoretical Physics Division of Lebedev’s Physical Institute, Leninskii pr. 53, 119991, Moscow, Russia2Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China3Institute of Astronomy, National Central University, Jhongli 320, Taiwanchernyshov@td.lpi.ruAbstract: Fermi LAT has discovered two extended gamma-ray bubbles above and below the galactic plane. We proposethat their origin is due to the permanent energy release in the Galactic center (GC) as a result of star accretion onto thecentral black hole. Shocks generated by these processes propagate into the Galactic halo and accelerate particles there.We show that electrons accelerated up to ∼ 10 TeV may be responsible for the observed gamma-ray emission of thebubbles as a result of inverse Compton (IC) scattering on the relic photons. We suggest that the Bubble could generatethe flux of CR protons at energies > 1015 eV because the shocks in the Bubble have much larger length scales and longerlifetime in comparison with those in SNRs. This may explain the the CR spectrum above the knee.Keywords: Galaxy: halo – radiation mechanisms: non-thermal — acceleration of particles — shock waves1 IntroductionFermi bubbles are symmetric structures elongated aboveand below the Galactic plane for about 8 kpc [13]. Theirdiscovery is one of the most remarkable events in astro-physics. The origin of the bubble is still enigmatic and upto now a few models were presented in the literature. Theteam, which subtracted this structured gamma-ray emissionfrom the total diffuse galactic emission presented differentexplanations of the phenomenon though they seem to trendtowards the model of a single huge energy release in theGalactic center (GC) when about 10 million years ago ahuge cloud of gas or a star cluster was captured by the cen-tral black hole that produced the Fermi bubbles seen today.Later it was shown that electrons may be accelerated by theturbulence excited by Kelvin-Helmholtz instabilities [12].Another interpretation was presented by [8] who proposeda relatively slow energy release (∼ 1039 erg s−1) due to su-pernova explosions as a source of proton production in theGC which emitted gamma-rays there.An alternative explanation based on the assumption that theenergy for the Fermi bubbles was originated from star cap-ture events which occurred in the GC every 104−105 yearswas suggested by [7]. About one thousands of such eventsform giant shocks propagating through the central part ofthe Galactic halo and thus produce accelerated particle re-sponsible for the bubble emission. Processes of particle ac-celeration by the bubble shocks in terms of sizes of the en-velope, maximum energy of accelerated particles, etc. maydiffer significantly from those obtained for SNs that maylead to the maximum energy of accelerated particles muchlarger than can be reached in SNRs. In this respect, weassume that acceleration of protons in Fermi bubbles maycontribute to the total flux of the Galactic cosmic rays (CR)above the ’knee’ break (≥ 1015eV).2 Structure of Shocks in the Fermi BubbleAs it was assumed in [7] the central massive black holecaptures a star every τ0 ∼ 104 − 105 years and as a re-sult releases energy about E0 ∼ 1052 erg in the form ofsubrelativistic particles which heat the central ≤ 100 pcin the GC. This heating produces a shock propagating intothe surrounding medium [15]. For exponential atmospherewith plasma density profileρ(z) = ρ0 exp(−zz0), (1)an analytical solution for permanent energy injection bystar accretion was obtained by [10]. Here z is the coor-dinate perpendicular to the Galactic plane. The radius ofthe bubble as a function of the height z and the time t isr = 2z0 cos−1[12ez2z0(1−(y2z0)2+ e−zz0)], (2)wherey =t∫0(γ2 − 12λαWtV (t)ρ0)0.5dt , (3)D.CHERNYSHOV et al. PARTICLE ACCELERATION IN FERMI BUBBLESFigure 1: The bubble multi-shock structure.V is a current volume enveloped by the shockV (t) = 2pia(t)∫0r2(z, t)dz , (4)a is the position of the shock topa(t) = −2z0 ln(1−y2z0), (5)W = E0/τ0 is the average luminosity of the central source,γ is the polytropic coefficient, and α and λ are numbers [5].Depending on capture parameters one can imagine the bub-ble interior as a volume filled with many shocks of differentages (see Fig.1).For W = 3 · 1040 erg s−1, z0 = 4 kpc and n0 = 1 cm−3,the shock reaches the height a = 8 kpc for the time t ∼ 108yr. The average plasma temperature in the bubble interioris about T ∼ 1 keV, the plasma density n ∼ 10−2 cm−3and the maximum radius of the bubble rmax ' 6 kpc.3 Particle Acceleration by the BubbleShocksCorrect analysis of shock acceleration in the bubble re-quires sophisticated calculations of each stage of this pro-cess which we hope to perform later. Now we presentsimple estimates of characteristics of accelerated spectra.We analyze spectra of protons and electrons separately be-cause they are formed by completely different processesand as we later conclude their spectral characteristics dif-fer strongly from each other. We present also the spectrumof gamma-ray emission produced by inverse Compton (IC)scattering of the accelerated electrons in the bubble.3.1 Proton SpectrumBelow we analyse the spectrum of protons accelerated inthe bubble and discuss whether the bubble contributionto the total flux of CRs in the Galaxy may explain theknee steepening. We remind that the generally acceptedpoint of view is that the flux of relatively low energy CRs(< 1015eV) is generated by SNRs which ejects a power-law spectrum E−2 into the interstellar medium. This spec-trum is steepened by propagation (escape) processes inthe Galaxy in accordance with the spectrum observed nearEarth (for details see [4]). However these sources canhardly produce CRs with energies more than 1015eV (see[2, 3]). Just at this energy a steepening (the knee) in the CRspectrum is observed. We assume that the bubble may gen-erate the flux of CRs at energies above 1015eV. The originof CRs with energies above 1015eV is the goal of this sub-section. It is natural to assume that the bubble shocks mayproduce this flux considering their large scales and longlifetimes.In the framework of our model one can imagine the bubbleas a volume of the radius 6 -10 kpc filled with hundredsof shocks propagating in series one after another. The fre-quency of shock injection (star capture) is poorly knownparameter, especially for the conditions of the GC. Fromthe analysis of shock hydrodynamics we estimated the ageof outer shock by 108 yr though this value depends stronglyon parameters of the self-similar solution which is a strongsimplification of conditions in the Galaxy. The frequencyof star capture by a central black hole is estimated fromtheoretical treatments ν ∼ 10−4 − 10−5yr−1 [1]. Thus, amulti-shock structure can be produced by the capture pro-cesses with an average distance L between separate shocksgiven byL = τcapu = 30(ν × 3× 104yr)(u/108cm/s)pc. (6)On the other hand there is another spatial scale whichcharacterizes processes of particle acceleration by a singleshock which is lD ∼ D/u where D is the spatial diffu-sion coefficient near a shock and u is the shock velocity.Depending on the relation between L and lD there maybe different regimes of acceleration in the bubble. Thisproblem of particle acceleration in supersonic turbulenceor multi-shock structure was analyzed in [6]. The accelera-tion regime is characterized by a dimensionless parameterψ =LlD=uLD, (7)If ψ << 1, the diffusion length scale of a single shocklD exceeds the distance between shocks L. Therefore,particle are accelerated by interactions with many shocksthat gives the acceleration similar to the classical stochasticFermi acceleration. The critical energy E1 for this regimeof acceleration is estimated from the condition ψ ∼ 1 orl(E1) ∼ L. In the Bohm limit with the diffusion coeffi-cient D ∼ crL(E)/3 where rL(E) = E/eB is the particleLarmor, the value of E1 isE1 ∼eBLuc= 1015(B5µG)(L30pc)(u108cm/s)eV.(8)which is about of the position of the knee break.32ND INTERNATIONAL COSMIC RAY CONFERENCE, BEIJING 201110310410510610710810910101011E2 dN/dE [eV m-2 s-1 sr-1]10141015101610171018101910201021E (eV) Tibet (SIBYLL 2.1) KASCADE (QGSJET 01) KASCADE (SYBILL 2.1) KASCADE-Grande (2009) HiRes I HiRes II Auger (2010)Figure 2: The Bubble contribution to the flux of CRs. Thedata are summarized in [11].The kinetic equation for the case ψ << 1 (E >> E1) con-verges to the diffusion in the spatial and momentum spaces(Fermi stochastic acceleration) in the form∂∂zD(ρ)∂f∂z+1ρ∂∂ρD(ρ)ρ∂f∂ρ+1p2∂∂pκ(ρ, p)p2∂f∂p= 0(9)where ρ and z are the cylindrical spatial coordinates, p isthe particle momentum, D(ρ) is the spatial diffusion coef-ficient and the momentum diffusion coefficient κ isκ ∼u2cLp2 (10)The momentum dependence of f can be presented by apower-law function, f(p) ∝ p−γ , where γ should be de-termined from Eq.(9):γ '32+√94+cLD0u2H2(11)where H is the height of the Galactic halo and D =D0(E/E0)ξ is the average diffusion coefficient in theGalaxy. For H ' 10 kpc, D0 ' 1029 cm2s−1, ξ ' 0.3,E0 ' 3 GeV [14] and u = 108 cm/s, L = 100 pc wehave γ ' 5, i.e. the power-law spectrum above 1015 eV isin the form N(E) ∝ E−3 as necessary for the knee spec-trum. The contribution of protons to the flux of the Galacticcosmic rays is shown in Fig. 2.3.2 Electron Spectrum and Spatial DistributionUnlike protons relativistic electrons lose their energy effec-tively by synchrotron and inverse Compton radiation. Therate of energy loss of electrons isdEdt= −βE2 = −cσT (wH + wph)(Emec)2. (12)The maximum energy of electrons Emax can be estimatedif the spatial diffusion coefficient at the shock Dsh isknown. From Eq. (12) we haveEemax ∼u2cβDsh(13)For the Bohm diffusion coefficient we can estimate the up-per limit for Eemax which isEeBmax ∼√eHu23cβ. (14)that gives for the velocity u = 108 cm s−1, the magneticfield strength H = 10−5 G and wph = 0.25 eV cm−3 themaximum energy of accelerated electrons about EBmax ∼5 × 1013eV, i.e. for electrons E < EBmax << E1. Itfollows from this inequality that electrons are acceleratedin the regime ψ >> 1. Kinetic equations for this case werederived in [6].In the case of electrons there is one more spatial parameteressential for acceleration by shocks, namely the electronmean free path λ. Therefore we have two more dimension-less parameters which describe electron acceleration in thecase of supersonic turbulence, lsh/λ and lD/λ. Nearbyshocks electrons propagate by diffusion, and λ there is afunction of energyλD(E) ∼√DβE(15)From Eq. (13) one can see that for E < Eemax we haveλ > lD i.e. acceleration by shocks is effective.Far away from shocks electrons propagate by convectionand for the velocity u the mean free path isλV (E) ∼uβE(16)For relatively low energy electrons λ(E) > lsh, and aregime of multi-shock acceleration for electrons is realizedin this case where interactions with many shocks changeslowly the shock to E−1 (for details see [6]) which pro-duces a hard E−1 spectrum . The break position E∗ be-tween the single shock and multi-shock spectra followsfrom the equality λ(E∗) = lshE∗ ∼uβlsh(17)that gives e.g. E∗ ∼ 2.8× 1011 eV for lsh = 1021 cm.If we assume that the bubble gamma-rays are producedby IC scattering of electrons on the relic photons, then itfollows from our model that: 1. the drop of the bubblegamma-ray flux at Eγ < 1 GeV as observed by [13] is dueto a flattening of electron spectrum at E < E∗; and 2. adrop of this spectrum in the range Eγ > 100 GeV is due toa cut-off in the electron spectrum at E ∼ Eemax. The ex-pected spectrum of gamma-ray emission from the Bubbledue to IC scattering of the electrons is shown in Fig. 3.Spatial distribution of the gamma-ray emission in case ofsingle shock and in case of N uniformly spaced shocksseparated by distance L is shown in Fig. 4. For the multi-ple shocks it was assumed that they fill only the outer partof the Bubble, i.e., they are located at distances 3 kpc, 3D.CHERNYSHOV et al. PARTICLE ACCELERATION IN FERMI BUBBLESFigure 3: The spectrum of gamma-ray emission fromFermi bubble in case of multi-shock acceleration. Datapoints are taken from [13].kpc −lsh, ..., 3 kpc −N · lsh from the center of the Bub-ble. One can see that in case of single shock and in casewhen the bubble volume is uniformly filled with 30 shocks(N = 30, dash-dotted line) the fitting of the experimentaldata is not very good. The spatial distribution is reproducedwell if the number of shocks is around 15 (dashed line), i.e.,if shocks fill only the outer 1-2 kpc of the Bubble (see also[12]).4 ConclusionWe have shown that series of shocks produced by a sequen-tial stellar captures by the central black hole can further ac-celerate the protons up to energies above 1015eV . It is quitedifficult to achieve these energies in supernovae due to thelimited acceleration time and length scale of SN shocks.The predicted CR spectrum contributed by the Bubble maybe E−ν where ν ∼ 3 for 1015 eV < E < 1019 eV thatexplains the knee CR spectrum.The regime of electron acceleration in the bubble is quitedifferent from that of protons, which is a combination ofsingle and multishock accelerations. In this case we havea cut-off of the electron spectrum at E > 3 1013 eV andflattening of the spectrum at E < 100 GeV that explainsnicely the bubble gamma-ray spectrum observed by [13] ifthis emission is due to IC on the relic photonsAcknowledgementsDOC and VAD are partly supported by the NSC-RFBRJoint Research Project RP09N04 and 09-02-92000-HHC-a.KSC is supported by the GRF Grants of the Government ofthe Hong Kong SAR under HKU 7011/10P. CMK is sup-ported, in part, by the Taiwan National Science CouncilGrant NSC 98-2923-M-008-01-MY3 and NSC 99-2112-M-008-015-MY3. WHI is supported by the Taiwan Na-tional Science Council Grant NSC 97-2112-M-008-011-Figure 4: Spatial distribution of the gamma-ray emission.Data are from [13]. Top: in case of single shock. Dottedline correspond to D=1029 cm2/s, solid to D=1030 cm2/s,dashed to D=1031 cm2/s and dash-dotted D=1032 cm2/s,Bottom: in case of several uniformly spaced shocks sepa-rated by distance L = 100 pc. Dotted line corresponds toamount of shocks N = 5, solid line to N = 10, dashedline to N = 15 and dash-dotted line to N = 30.MY3 and Taiwan Ministry of Education under the Aim forTop University Program National Central University.References[1] Alexander, T., PhR, 2005, 419: 65[2] Bell, A. R., MNRAS, 2004, 353: 550[3] Berezhko, E. G. & Voelk, H. J., A&A, 2000, 357: 283[4] Berezinskii, V. S. et al, 1990, Astrophysics of CosmicRays, ed. V.L.Ginzburg, Norht-Holland, Amsterdam[5] Bisnovatyi-Kogan, G. S., Silich, S. A., RvMP, 1995,67: 661[6] Bykov, A. M. & Toptygin, I. N., Physics Uspekhi,1993, 36, 1020[7] Cheng, K.-S. et. al., ApJ, 2011, 731, L17[8] Crocker, R. M., Aharonian, F., PhRvL, 2011,106:,id.101102[9] Dogiel, V. et. al., PASJ, 2009, 61: 1099[10] Kompaneets A. S., Akademiia Nauk SSSR, Doklady(DoSSR, in Russian), 1960, 130, 5[11] Kotera, K. & Olinto, A. V., 2011, astro-ph 1101.4256[12] Mertsch, P.; Sarkar, S., 2011, astro-ph 1104.3585[13] Su, M., Slatyer, T. R., Finkbeiner, D. P., ApJ, 2010,724: 1044[14] Strong, A. W., Moskalenko, I. V., ApJ, 1998, 509, 212[15] Weaver, R., McCray, R., Castor, J., Shapiro, P.,Moore, R., ApJ, 1977, 218, 377

Particle acceleration and the origin of gamma-ray emission from Fermi Bubbles

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Particle acceleration and the origin of gamma-ray emission from Fermi
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Particle acceleration and the origin of gamma-ray emission from Fermi Bubbles

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