Origin of Nonthermal Emission from the Fermi Bubbles and Mechanisms of Particle Acceleration There
aa r X i v : . [ a s t r o - ph . H E ] N ov The Galactic Center: IAU 303: Feeding and Feedback in a NormalGalactic NucleusProceedings IAU Symposium No. 303, 2013A.C. Editor, B.D. Editor & C.E. Editor, eds. c (cid:13) Origin of Nonthermal Emission from theFermi Bubbles and Mechanisms of ParticleAcceleration There
V. A. Dogiel † , K.-S. Cheng ‡ , D. O. Chernyshov & C.-M. Ko P.N.Lebedev Institute of Physics, Leninskii pr. 53, 119991 Moscow, Russiaemail: [email protected], [email protected] Department of Physics, University of Hong Kong, Pokfulam Road, Hong Kong, Chinaemail: [email protected] Institute of Astronomy, National Central University, Chung-Li 32054, Taiwanemail: [email protected]
Introduction.
The discovery of the two giant gamma-ray lobes (Fermi Bubbles) in theGalactic Center (see Dobler et al. 2010 and Su et al. 2010) was one of the most impressiveevents of the last few years in astrophysics. However, some indications on giant structuresin the GC were observed several years before by WMAP in the radio frequency rangebetween 23 and 33 MHz (Finkbeiner 2004) , and by ROSAT in hard X-rays (Bland-Hawthorn & Cohen 2003). Recent observations performed by the Planck Collaboration(Ade et al. 2012) found also lobes in the microwave range which spatially coincided theFermi Bubbles that indicated on the common origin of these phenomena.Parameters of emission from the Fermi bubbles have several remarkable distinction:( a ) The structures are symmetrically elongated in the direction perpendicular to theGalactic Plane;( b ) Spectra nonthermal emission from the Bubbles are harder than anywhere in theGalaxy;( c ) The spatial distribution of emission in the Bubbles shows sharp edges of the Bub-bles;( d ) The surface emissivity is almost uniform inside the Bubbles although findings ofHooper & Slatyer (2013) might indicate on features of the gamma-ray spectrum at lati-tudes b ◦ which they interpreted as a contribution from the dark matter annihilationnearby the GC.The origin of the Bubbles is actively discussed in the literature. Thus, Crocker & Aharonian(2011)and Zubovas & Nayakshin (2012) suggested the hadronic origin of gamma-ray emissionfrom the Bubbles, when gamma-ray photons are produced by collisions of relativisticprotons with that of the background gas. Alternatively, these gamma-rays can be pro-duced by the inverse Compton scattering of relativistic electrons on background photons(leptonic model) and the same electrons generate radio and microwave emission from theBubbles via synchrotron (see e.g. Su et al. 2010). There may be several sources (processes)which generate electrons in the Bubbles: • In-situ stochastic acceleration by MHD-turbulence nearby the Bubble surface (Mertsch& Sarkar 2011); • Acceleration by shocks which result from periodical star accretion onto the centralblack hole (Cheng et al. 2011); † V.A.Dogiel thanks for grants from the IAU and RFFI (grant 12-02-00005) that gave himan opportunity to participate in the IAU303 Symposium. ‡ KSC is supported by a GRF grant under HKU 701013. • Acceleration within jets near the GC about ∼ yr ago, and subsequent electrontransfer into the bubble by convective flows (Guo et al. 2012 and Yang et al. 2013).Below we discuss some of these models. Stochastic acceleration from the background plasma.
In order to reproduce the spatialdistribution of gamma-ray emissivity in the bubble Mertsch & Sarkar (2011) assumedarbitrarily that: a) the acceleration is nonuniformly distributed inside the Bubbles and itsefficiency increases near the shock which excited the MHD-turbulence inside the bubble;b) the maximum energy of electrons is a function of the distance to the shock.There are no other evident sources for electrons accelerated in the halo except elec-trons from the background plasma and electrons injected by supernova remnants (SNRs)or jets. Estimates of acceleration efficiency in the case of stochastic (Fermi) accelerationfrom the background plasma is not trivial. As Wolfe & Melia (2006) and Petrosian &East (2008) showed, the energy supplied by sources of stochastic acceleration is quicklydumped into the thermal plasma because of ionization/Coulomb energy losses of acceler-ated particles. As a result this acceleration is accompanied by plasma overheating whilea tail of nonthermal particles is not formed, i.e. the effect of stochastic acceleration isnegligible.However, latter Chernyshov et al. (2012) concluded that the efficiency of stochasticacceleration depended strongly on parameters of acceleration and prominent tails ofnonthermal particles can be generated by the acceleration although the conclusions ofWolfe & Melia (2006) and Petrosian & East (2008) are correct for some conditions.To define whether the stochastic mechanism is able to produce enough acceleratedelectrons needed for the observed flux of gamma-rays we take the following parameters ofthe background plasma in the Bubbles: the density n = 10 − cm − and the temperature T = 2 keV (see Su et al. 2010).The kinetic equation for the distribution function electrons, f ( p, t ), when processes ofspatial propagation are neglected, has the form ∂f∂t + 1 p ∂∂p p (cid:20)(cid:18) dpdt (cid:19) C f − { D C + D F ( p ) } ∂f∂p (cid:21) = 0 , (0.1)( dp/dt ) C and D C ( p ) describe particle energy losses and diffusion in the momentum spacedue to Coulomb collisions. The stochastic (Fermi) acceleration is described as diffusionin the momentum space with the coefficient D F ( p ), which we take in the form: D F ( p ) = αp ς θ ( p − p ) where α , ς and p are arbitrary parameters.Parameters of this model can be restricted from the three conditions:( a ) The energy of electrons emitting gamma-rays by inverse Compton is restricted bythe value ∼ eV (Su et al. 2010 and Cheng et al. 2011);( b ) The total gamma-ray flux at energies E > F γ ≃ × erg s − thatrestricts the number of accelerated electrons (Su et al. 2010);( c ) Mechanism of particle acceleration should effectively generate nonthermal particlesi.e . no plasma overheating (Chernyshov et al. 2012).From the results of numerical calculations shown in Fig. 1 we conclude that the stochasticacceleration from background plasma may provide the density and the spectrum of accel-erated electrons needed for the observed gamma-ray and radio emission from the Bubblesif the parameters of the model are: ζ = 2 . α = 3 . × − s − , p = (0 . − . mc . Therequired power supplied by sources of acceleration is about 10 erg s − that does notexceed the upper limit of the rate of energy release expected in the GC which is in therange from 10 (Crocker & Aharonian 2011) to 10 erg s − (Cheng et al. 2011). Stochastic re-acceleration of relativistic electrons emitted by SNRs in the Galactic Disk.D 6. High Energy and Magnetic Processes.... in the Galactic Center Ζ -14.8-14.6-14.4-14.2-14 Log @ Α DH s - L p / m e c τ ( y r) T = 2 keV, n = 10 −2 cm −3 , ς = 2.2 Figure 1.
Left panel:
The functions of α ( ζ ) as derived from the conditions: a) - dashed dot-ted line; b) - solid line. Right panel:
The timescales of temperature variations (solid line) andacceleration (dashed line) for different values of p (condition c). In this case the kinetic equation has the form − ∇ [ D ( r, z, p ) ∇ f − u ( r, z ) f ] + 1 p ∂∂p p (cid:20)(cid:18) dpdt − ∇ u p (cid:19) f − κ ( r, z, p ) ∂f∂p (cid:21) = Q ( p, r ) δ ( z ) , (0.2)where r is the galactocentric radius, z is the altitude above the Galactic plane, p is themomentum of electrons, u is the velocity of the Galactic wind, D and κ are the spatialand momentum (stochastic acceleration) diffusion coefficients, dp/dt describes the rateof electron energy losses, and Q describes the spatial distribution of CR sources in theGalactic plane ( z = 0) and their injection spectrum.As it follows from our hydrodynamic numerical simulations the process of re-accelerationof electrons is supposed to take place high above the Galactic plane in regions where therequired MHD-turbulence is excited. Therefore because of the synchrotron and inverseCompton energy losses only relatively low energy electrons ejected by SNRs can reachthis region. The thickness of re-acceleration region is defined from the intensity of theobserved gamma-ray and radio emission.In the simplest case the number of electrons reaching the re-acceleration region can becalculated in the framework of the diffusion model of CR propagation (see Berezinskii etal. 1990) when the convection terms are neglected ( u = 0). For calculations we used themodel parameters from Ackermann et al. (2012).Our numerical calculations show that too many high energy electrons are produced inthe re-acceleration region and, thus, the condition b) can no be satisfied in the modelif the electron spectrum is formed by the acceleration processes only. Formally we canassume that processes of particle escape from the acceleration region are essential enoughto make the spectrum steeper and thus to decrease the number of emitting electrons.Indeed, the momentum spectrum of accelerated particles is power-law, f ( p ) ∝ p − δ , withthe spectral index δ equaled δ = 32 + r
94 + τ acc τ esc , (0.3)where the acceleration time τ acc ≈ α − and escape time is τ esc ≈ ∆ r b / D . Here ∆ r b isthe thickness of re-acceleration region and D is the spatial diffusion coefficient equaled D ( p ) = 4 v a p / (6 κ ( p )). Here v a is the Alfven velocity which is about 35 km/s in theGalactic halo (see Ackermann et al. 2012). The numerical calculations showed that themodel reproduces the gamma-ray spectrum if α ∼ − s − , ∆ r b ∼
10 pc, and δ ∼
4. We V. A. Dogiel et al.notice, however, that the pure diffusion model of CR propagation has serious restrictions.In particular, the effect of convective transfer (Galactic wind) may be essential in theGalaxy as it follows from observations (see e.g. Carretti et al. 2013) as well as fromtheoretical treatments (Bloemen et al. 1993 and Breitschwerdt et al. 2002). The influenceof the wind might decrease the density of SNR electrons in the halo significantly thatpossibly makes the effect of re-acceleration negligible.
Acceleration by shocks generated by processes of tidal disruption.
We discussed thismodel in details in Cheng et al. (2011). In principle, this model describes quite reason-ably the spectra of gamma-ray and radio emission from the Fermi Bubbles and it explainsthe shape of the Bubbles because shocks propagate in the exponential atmosphere per-pendicular to the galactic plane (see Kompaneets 1960). However, serious simplificationswere used for our calculations, e.g. we used the electron spectrum obtained in a station-ary approximation although the situation of shock propagation in the halo is essentiallynon-stationary, we did not take into account shock evolution in the halo etc. However, wesuppose that the shock model of the Bubbles does not have serious objections up to now.The energy release from processes of star capture by the central black hole may release ahuge energy up to 10 erg. A part of this energy is transformed into a flux of hard X-rayemission. Very recently Swift detected to giant X-ray flares in normal galaxies whoseluminosity was about 10 − erg/s (see e.g. Bloom et al. 2011). Such a huge fluxof hard X-rays from Sgr A* may provide an observational effect in the Galactic molec-ular clouds seen at present in the form of ”Compton echo” (see Cramphorn & Sunyaev2002). Besides, some results of observations have been already interpreted as traces ofpast activity of Sgr A* with a very high energy release (see Bland-Hawthornet al. 2013and Nakashima et al. 2013) that is in favor of our model. References
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