Cosmic Ray (Stochastic) Acceleration from a Background Plasma

0.23 MB·

by  V. A. Dogiel

Nuclearand
ParticlePhysics
Proceedings
NuclearandParticlePhysicsProceedings00(2017)1–8
Cosmic Ray (Stochastic) Acceleration from a Background Plasma
V.A.Dogiel1a,b,e, K.S.Chengb, D.O.Chernyshova,b,A.D.Erlykina,c,C.-M.Kod,andA.W.Wolfendalec
aP.N.LebedevPhysicalInstitute,Moscow,Russia
bDepartmentofPhysics,UniversityofHongKong,HongKong,China
7
cDepartmentofPhysics,DurhamUniversity,Durham,UK
1
dNationalCentralUniversity,ZhongliDist.,TaoyuanCity,Taiwan(R.O.C.)
0
eMoscowInstituteofPhysicsandTechnology(StateUniversity),Dolgoprudny,141707,Russia
2

n
a
J

9
Abstract
1
WegiveashortreviewofprocessesofstochasticaccelerationintheGalaxy. Wediscuss: howtoestimatecorrectly

]
thenumberofacceleratedparticles, andatwhichconditionthestochasticmechanismisabletogeneratepower-law
E
nonthermal spectra. We present an analysis of stochastic acceleration in the Galactic halo and discuss whether this
H
mechanismcanberesponsibleforproductionofhighenergyelectronsthere,whichemitgamma-rayandmicrowave
.
h emissionfromthegiantFermibubbles. Lastly,wediscusswhethertheeffectsofstochasticaccelerationcanexplain
p theCRdistributionintheGalacticdisk(CRgradient).
-
o
Keywords:
r
t
s
a
[ 1. Introduction whereuisthevelocityofmagneticfluctuationsandLis

theaveragedistancebetweenfluctuations.
1
v ThetheoryofCRoriginstartedfromthekeypapers Anadvantageofthismodelwasthatthismechanism
1 of Baade and Zwicky [1] and Fermi [2, 3]. In the first generates power-law spectra of accelerated particles,
8 paper the authors assumed that the bulk of CRs ob- justasneededfortheobservedCRpower-lawspectrum.
4 served near Earth are produced by supernovae explo- However,spectraintheFermimodelweremuchharder
5
sionsintheMetagalaxy.Theyexcludedthatsupernovae (∝ E−1inthelimitcase)thantheobservedforCRspec-
0
. in our Galaxy were sources of CRs because, accord- trum. Besides, tooaverytimewasnecessarytoaccel-
1 ing to their estimates, their energy density had to be erateparticlesuptothehighenergiesneeded.
0
too high. An alternative explanation was suggested by
7 In1964GinzburgandSyrovatskii[4]suggestedtheir
Fermi. He assumed that CRs were of the Galactic ori-
1 theory of CR origin. Using the observed CR chemical
: gin and the whole volume of the Galaxy was a source composition they estimated the CR luminosity, which
v
i of CRs. CR acceleration is in this case due to regular was about 1040 erg s−1, and concluded that probably
X collisionsofchargedparticleswithchaoticallymoving
Galactic supernovae are the sources of CRs, because
r magneticfluctuations. Theaccelerationisduetothein- only 10% of supernovae shocks energy was needed to
a
ducedelectricfieldE
generatetheGalacticCRflux. Theydevelopedalsothe
1dH diffusionmodelofCRpropagationintheGalaxywhere
curlE=− (1)
c dt particlescatteringbymagneticfluctuationsintheinter-
stellarmediumwasdescribedasspatialdiffusion.
excitedbyatime-varyingmagneticfieldH.
The next important mile-stone was connected with
Asaresulttheenergyofparticles,E,increasesas
the papers of Krymskii and Bell [5, 6] who suggested
dE (cid:18)u(cid:19)2 E thetheoryofCRaccelerationbysupernovaeshocks. In
∼ =α E (2)
dt c L/c 0 principle, this model is a modification of the classical
/NuclearandParticlePhysicsProceedings00(2017)1–8 2
model of Fermi, because the important component of The solution of this equation is the equilibrium
theaccelerationprocessisthatofparticlesscatteringon Maxwelliandistribution:
moving magnetic fluctuations but the new component (cid:114)
2 (cid:18) E (cid:19)
of the model is a velocity ”jump” on the shock front f (p)= n exp − (5)
that changes the acceleration process drastically. First, M π 0 kT
this acceleration generates steeper spectra of particles wheren isthedensityofbackgroundplasmaand E is
0
(∝ E−2)justasneededtoexplaintheobservedCRspec- theparticleenergy.
trum. Secondly the rate of acceleration is proportional Ifbackgroundparticlesareundertheinfluenceofany
tothefirstdegreeofu/c acceleration, (dE/dt) = α E, (see Eqs. (2) and (3))
ac 0
dE u thentherateofenergyvariationsis
∝ E (3)
dt c (cid:32) (cid:33) (cid:32) (cid:33)
dE dE dE
thatmakestheshockaccelerationmuchmoreeffective dt = dt − dt (6)
ac C
thanthatofFermi. Hereuistheshockvelocity. Since
then the theory of shock acceleration in the interstellar where(dE/dt)C istherateofionizationlossesinagas
mediumhasbeendevelopedfervently,andforthemod- with the density n, which can be presented as (see e.g.
erntheoryofthisprocessreadersarereferredtothetalk [12])
byDamianoCaprioliatthisconference. (cid:32)dE(cid:33) (cid:18) E (cid:19)−3/2
We notice, nevertheless, that the classical stochastic =ν E (7)
Fermi acceleration may also be effective in an astro- dt C 0 kT
physicalplasma. Stochasticaccelerationmaybeeffec-
where
tive near shocks of supernovae where magnetic turbu-
lence is generated by the Rayleigh-Taylor and Kelvin- ν = 4πn0e4m1p/2Λ (8)
Helmholtzinstabilities,seee.g.[7].Anotherexampleis 0 (kT)3/2m
e
thediscoveryoffreshlyacceleratedCRsintheCygnus
is the frequency of Coulomb collisions of thermal par-
Superbubble[8]. Itwasassumed,thatCRsareacceler-
ticles, Λ is the Coulomb logarithm, m and m are the
atedtherebythecollectiveactionofshocksinthisarea. e p
restmassesofelectronsandprotons.
Thetheoryofstochastic(multi-shock)accelerationbya
ThenEq. (6)hastheform
supersonicturbulencewasdevelopedin[9,10].
dE (cid:18) E (cid:19)−3/2
=α E−ν E (9)
2. Theory of In-Situ Acceleration from a Back- dt 0 0 kT
groundPlasma. TheNumberofAcceleratedPar-
FromEq.(9)wecaderivethethresholdenergy,ε
thr
ticles
(cid:32)ν (cid:33)2/3
Oneoftheimportantquestions,whichmodelsofac- ε (n ,α )(cid:39)kT 0 (10)
thr 0 0 α
celerationshouldsolve,is: howmanyhighenergypar- 0
ticlescanbeproducedbytheseprocesses? Thereareno
whichdefinestheenergyrangeofacceleratedparticles
other sources of particles for acceleration except those withE >ε .
thr
fromabackgroundplasmaorhighenergyparticlespre-
Thestochasticaccelerationformsapower-lawspec-
acceleratedbyothersorces. Westartfromacceleration
trumofnonthermalparticles
fromabackgroundplasma.
The spectrum of background plasma, f , is formed f = Kp−γ (11)
M nth
byCoulombcollisionsandisdescribedbytheequation
Thesimplestwaytoestimatethenumberofacceler-
(see[11])
atedparticles(constantK)isjusttomatchthermal(Eq.
(cid:34)(cid:32) (cid:33) (cid:35)
1 d p2 dp f +D dfM =0 (4) (5))andnonthermal(Eq. (11))componentsofthetotal
p2dp dt M C dp spectrumattheenergyE =ε thatgives
C thr
where pistheparticlemomentum,(dp/dt)C istherate (cid:114)2 (cid:18) ε (cid:19)
of Coulomb losses, D = (dp/dt) mkT/p is the coef- K = n exp − thr (12)
C C π 0 kT
ficient of momentum diffusion due to Coulomb colli-
sions,misthemassoftheacceleratedparticles,kisthe However,asGurevichnoticed(see[13]),theparticle
BoltzmannconstantandT istheplasmatemperature. distributionbecomesnon-equilibriumandtime-varying
/NuclearandParticlePhysicsProceedings00(2017)1–8 3
inthiscase,andaproperestimateofthenumberofac- clusterandshowedthatforreasonableparameters,this
celeratedparticlescanbeobtainedintheframeworkof stochastic acceleration is able to produce enough high
equationwhichincludesthetermofstochasticacceler- energyparticlesneededtoexplaintheComaX-rayex-
ation (described by another momentum diffusion with cess.
the coefficient DF) and the terms describing Coulomb However, in [13] a linear equation of acceleration
collisions, which form the Maxwellian distribution of was analysed with a constant temperature of plasma,
thermalparticles. Thetotalequationhastheform T = const, which did not take into account a back re-
(cid:34)(cid:32) (cid:33) (cid:35) actionofacceleratedparticlesontotheparameterofthe
∂f 1 d dp df
− p2 f +(D +D ) =0(13) thermal pool. This was done by Wolfe and Melia[16]
∂t p2dp dt C F dp
C andPetrosianandEast[17], whoshowedfromnumeri-
that gives the solution for the distribution function of calcalculationsofasystemofnon-linearequationsthat
particleswithe.g. D =α p2as this mechanism of in-situ acceleration did not work at
F 0
allbecausetheenergysuppliedbytheaccelerationwas
  
N(p¯)= (cid:114)π2n0exp−(cid:90)p¯ 1+(αud0/uνo)p¯5 ismulmtinegdieaffteelyctaobfsoacrbceedlerbaytiothnewthaesrmapallapsomoal,oavnedrhtehaetirneg-
insteadofapower-lawspectraofnon-thermalparticles.
0
 
−exp−(cid:90)∞ 1+(αud0/uνo)p¯5 (14) tteumrLeavotaefrrei,aqCtuihoaentrison.ynTsshhdoeevyscesrthiaoblwi.n[e1gd8a]tchacanetaltlehyresaetrideosanunlatoninndlgitneeeffmaerpcsetyroasf--
0
√ in-situaccelerationfrombackgroundplasmadepended
wherethedimensionlessmomentum p¯ = p/ 2mkT. strongly on its parameters. If the momentum diffusion
coefficienthasacut-offatlowenergies,e.g. intheform
1 D(p) = αpζθ(p− p ) the situation depends drastically
0
on the relation between the cut-off momentum, p and
√ 0
10-3 theinjectionmomentum, p = 2mε . If p < p
inj thr 0 inj
the effect of acceleration is similar to [16, 17], i.e. the
Np()10-6 plasmaisoverheated. Asurpisinglydifferentresultwas
obtainedforthecaseof p > p . Inthiscaseacceler-
0 inj
10-9 ationsubtractsfromthethermalpoolonlyhighenergy
particlesoftheMaxwelliandistribution. Asaresultthe
1 10 100 plasmacoolsdown(analoguetoMaxwelldemon),and
p the power-law ”tail” is formed by the acceleration. As
a restriction of this model we should mention that the
larger is the value of p , the smaller is the number
Figure1: Illustrativepicturewhichshowsthesolutionofcorrectki- inj
neticequation(14)(solidline)andsimplematchingofthermaland of accelerated particles. On the other hand, for high
nonthermal(power-law)compon√ents(dottedline). Here p¯ isthedi- enough pinj theMaxwellianspectrummatchesdirectly
mensionlessmomentump¯=p/ 2mkT.
withthepower-lawtailat p insteadof p asassumed
0 inj
inEq. (12).
The total spectrum of particles is shown in Fig. 1.
The question is what could be the reason for the ac-
Two important conclusions follow from this solution.
celerationcut-offatrelativelylowmomenta. Thiscould
The first one is that in the case of stochastic accelera-
be due to absorption of MHD waves by CRs of rela-
tiontheMaxwellianandpower-lawcomponentsdonot
tivelylowenergy[19]. Inthestationarycasetheequa-
matchwitheachotherasassumedinEq. (12). Thereis
tionforspectrumofMHD-waves,W(k,t)canbewritten
an extended region of a distorted Maxwellian distribu-
as[20]
tionformedbyCoulombcollisions,whichtriestocom-
pensate the flux of particles running-away into the re-
gionofacceleration. Secondly,asonecanseefromFig. dΠ(W,k,t)
=−2Γ W+Φδ(k−k ), (15)
1, thesimpleestimate(12)underestimatesstronglythe dk cr 0
numberofacceleratedparticles.
Dogieletal.[14,15]appliedthismodelofparticleac- where k is the wave-number, Π(W,k,t) decribes the
celerationfromabackgroundplasmaforinterpretation non-linearcascadeofwaves,Φisenergyfromexternal
of the hard X-ray excess in the spectrum of the Coma sourcesatk=k ,andΓ isthedecrementofabsorption
0 cr
/NuclearandParticlePhysicsProceedings00(2017)1–8 4
byCRs,see[21] Analysis of this acceleration for both situations was
providedin[22,27]. Inthefirstcase,thekineticequa-
πZ2e2V2 (cid:90)∞ dp tion for the distribution function is similar to Eq. (13)
Γ (k)= A F(p), (16)
cr 2kc2 p but it includes also synchrotron and inverse Compton
pres(k) energylossesforelectrons. Thenumberofaccelerated
where p (k) = ZeH/ck, F(p)istheCRspectrumand electrons depends strongly on the value of cut-off mo-
res mentum p . Itcannotbetoosmallbecauseoftheeffect
Histhemagneticfieldstrength. 0
Thederivedcoefficientofthemomentumdiffusionis ofplasmaoverheating, andtoolargebecausethenum-
ber of accelerated particle is smaller than needed for
(see[22])
theobservedgamma-rayfluxfromthebubbles. In[22]
D(p)=α (p)J (ξ) (17) it was shown that stochastic acceleration from a back-
0 2
ground is able to explain the observed emission from
whereα (p)isapower-lawfunctionandJ istheBessel
0 2 theFermibubblesbutforanexceptionallynarrowrange
function,whereξisacomplicatedfunctionofp(seefor
oftheaccelerationparameters,whichmakesthismodel
detailsofcalculationsAppendixin[22]). Thediffusion
doubtful.
coefficienthasacut-off D(p) = 0at J = 0,thatcorre-
2 The analysis of the second case [27] showed that it
spondstoξ = 5.14or p0 = 0.2mcforparametersofthe is more effective for production of electrons than the
Galactichalo.
accelerationfromabackgroundplasma,becauseinthe
caseofSNRelectronre-accelerationtheirenergyshould
3. Stochastic Acceleration in the Galactic Halo. be increased by three orders of magnitude only while
ModelsoftheFermiBubbles foraccelerationfrombackgroundpoolelectronsareac-
celerated from their temperatures (about several keV).
Recent Fermi-LAT observations found new sources Thekineticequationinthiscasehasamorecomplicated
of CRs in the Galaxy whose origin is enigmatic. First formthan(13)becauseitincludesalsotermsofparticle
of all, we mention mysterious giant gamma-ray fea- propagation,
turesinthecentralpartoftheGalaxy(FermiBubbles)
elongated perpendicular to the Galactic plane[23, 24]. −∇·(cid:2)κ(r,z,p)∇f −u(r,z)f(cid:3)+
(cid:34)(cid:32) (cid:33) (cid:35)
Severalmodelsweresuggestedtoexplaintheoriginof 1 ∂ dp ∇·u ∂f
p2 − p f −D(r,z,p) =
the bubbles which include phenomenological assump- p2∂p dt 3 ∂p
tionsabouttheprocessesofparticleaccelerationthere. Q(p,r)δ(z), (18)
Thus,Chengetal. [25]assumedthatgamma-rayemis-
sion is generated by high energy electrons accelerated where r is the galactocentric radius, z is the altitude
inthehalobygiantshocksresultingfromtidaldisrup- abovetheGalacticplane, p = E/cisthemomentumof
tion of stars captured by the central black hole. Al- electrons, u is the velocity of the Galactic wind, κ and
ternatively, Mertsch and Sarkar[26] assumed that this D are the spatial and momentum (stochastic accelera-
emissionisproducedbyelectronsin-situacceleratedby tion)diffusioncoefficients,c(dp/dt) = dE/dtdescribes
MHD-turbulence behind the shock. In this paper the the rate of electron energy losses, and Q describes the
authorstriedtoreproducespectralcharacteristicsofthe spatial distribution of cosmic ray (CR) sources in the
emission from the Fermi bubbles but did not estimate Galacticplane(z=0)andtheirinjectionspectrum.
whether this mechanism could provide enough elec- The problem of the second model is that the spec-
trons needed for the observed nonthermal fluxes from trum of re-accelerated electrons is too steep to repro-
thebubbles. ducethemicrowaveemissionfromthebubblesasmea-
As we mentioned above there are no other evident sured by Planck [28]. Thus, both models of stochastic
sources ofelectrons foracceleration exceptthose from accelerationofelectronsinthebubbleshaveproblems,
the background plasma or those injected by supernova andinthatsensethemodelofelectronaccelerationby
remnants. In the first case electrons are injected with shocks [25] seems to be more attractive. We do not
energies close to their background temperature in the discuss here the hadronic model of Fermi bubbles (see
halo(i.e. aboutkeV).Inthesecondcase,onlyelectrons e.g. [29, 30, 31, 33]), whose problems were presented
withenergies E ≤ 1GeVcanreachthealtitudesofthe in[34]
Fermi bubbles. In both case further re-acceleration up Ontheotherhand,thestochasticaccelerationofpro-
toenergiesabout1012eVisneededtogenerategamma- tonsintheFermibubblesmayexplaintheoriginofCRs
raysfromtheFBs. with energies above the ”knee” (> 1015 eV) as shown
/NuclearandParticlePhysicsProceedings00(2017)1–8 5
by Cheng et al. in [35]. We presented, however, these self-generated turbulence. In their model they investi-
results in details at the last San-Vito conference which gatedasystemofequationsforCRpropagation(aone-
werepublishedin[36]. dimensional version of Eq. (18) for propagation in the
directionperpendiculartotheGalacticplane)andequa-
tionsforMHD-waveexcitationbytheCRstreamingin-
4. Stochastic Acceleration in the Galaxy and the
stabilityandtheirdamping. Inthismodelofnon-linear
problemsOfCRGradient
CRtransportthegradientandthespectralshapeofCRs
The main questions of the theory of CR origin atdifferentgalactocentricradiiwerereproduced.
are where CRs are generated and how they propa- If we return to models of CR acceleration we no-
gate through the Galaxy. Necessary information can tice that at some conditions the injection energy of
be obtained from investigations of the diffuse Galac- stochastic acceleration is a function of plasma temper-
tic gamma-ray emission. First investigations of this ature. This may also be true for shock wave accelera-
emission showed that the derived distribution of CRs tion because in some models of particle injection into
in the Galactic disk was flatter than the radial distribu- shocks the temperature of the ambient ISM has rele-
tion of their potential sources: SNRs and pulsars (see vance[48,49,50]. Itisknownthatthereisaradialin-
e.g. [37, 38]). The first attempts to interpret this dif- creaseoftemperatureinHIIregionsfromabout6600K
ference were performed in terms of CR propagation in atR = 2kpctoabout10000KatR = 14kpc[51]. Re-
the Galactic halo. In [39, 40, 41] it was assumed that cently,Erlykinetal. [52]examinedhowmanyparticles
an effective mixture of CRs in the Galactic halo due can be acclerated from background plasma depending
toCRscatteringdiffusionmadetheirdistributioninthe onitstemperature.
Galaxymoreorlessuniform. However,numericalcal- For simple estimates of the fraction of background
culations showed that even in the most favorable case particles accelerated by Fermi mechanism we take Eq.
of an extended halo the diffusion is unable to remove (14), and for the shock acceleration from background
thesignatureoftheobservationallyinferredSNRsource plasmawetaketheequationfrom[48],whichis
distribution. The problem is even more aggravated for (cid:32) (cid:33)
∂ ∂f 1du 1 ∂
thesharperSNRdistributionofGreen[42]. u(x)f −D =− (p2f) (19)
∂x ∂x 3dx p2∂p
Recent analysis of the Fermi-LAT gamma-ray data
[43,44]ingeneralconfirmedaflatterCRdistributionin where the coordinate x is perpendicular to the shock
the outer part of the Galaxy, although showed a sharp front, Disthecoefficientofparticlespatialdiffusion,u
drop of CR density near the GC. Interpretation of the istheparticlefluidvelocityandthevelocityjumpatthe
last result is beyond the scope of our analysis. If con- shock (x = 0) is u−/u+ = 4 for strong shocks with the
firmed, it may be due to specific processes in the GC. Machnumber M >> 1. Fromthisequationthenumber
Interpretation of the flat CR distribution in the outer ofacceleratedparticlescanbeestimatedas
Galaxy can be obtained in two different ways. One of
(cid:32) (cid:33)
n p m
themwassuggestedby[39,45]whoassumedthatthisis nth (cid:39) T e δ1/3×
aneffectof”unseen”SNRsatlargegalactocentricradii. n0 pthr mp
[s4e6rTv]headenoCdtRhRerdeciwsctahryiibawuetaitosanslu.ingg[t4eh7set]eGdwabhlayocBtiincrteedirtipsscrkehtwiendetredthrtmeestoaoblf-. exp−δ1/21+ 21ln(cid:32)mmei(cid:33)231δ (20)
convectivetransport(galacticwind). In[46]theauthors where m and m are the electron and proton mass re-
e p
concludedfromanalysesofasystemofhydrodynamic spectively,m isthemassoftheacceleratedparticles,
i
and kinetic equations that the wind velocity is propor-
(cid:112)
tional to the CR pressure PCR which in turn is propor- pT = 2kTmi
(cid:114)
tionaltothedensityofCRsources QCR. Fromanalyti- p = p mpδ1/3
calandnumericalcalculationsofthethree-dimensional thr T m
e
equationsofCRpropagationsimilartoEq. (18),where
Dν¯
the wind velocity is a function of coordinates and the δ=
u2
sourcedensity,u(r,z,Q),theyshowedthatCRsescaped
2πn e4m2
faster from regions of higher source density. Just this ν¯ = 0 pΛ
effectexplainsinthemodelflatterCRdistribution. mep¯3
(cid:114)
In[47]theauthorsanalysedanon-linearmodelofCR 2kT
p¯ =m
propagation,inwhichtheirtransportisdeterminedbya p m
e
/NuclearandParticlePhysicsProceedings00(2017)1–8 6
Coulombcollisionstrytocompensateafluxofpar-
1.×10-2
ticles running-away from a background pool into
5.×10-3
the acceleration region. Therefore, a very broad
n01.×10-3 transfer region is formed by Coulomb collisions
n/nth between thermal and non-thermal components of
the total spectrum. In order to estimate the num-
1.×10-4 ber of accelerated particles one should analyse a
kinetic equation which includes both the term of
6000 7000 8000 9000 10000 11000 12000 Coulomb collisions, which forms the Maxwellian
T(K)
distribution of thermal particles, and the term of
stochastic acceleration, which forms a nonlinear
Figure2:Illustrativepictureofthefractionofacceleratedparticlesfor powerlowspectrumofnon-thermalparticles.
stochastic(solidline)andshockwave(dottedline)accelerationasa
functionoftemperatureTofbackgroundplasma.
• Ifthestochasticaccelerationinteractswithallpar-
ticles of the Maxwellian spectrum, then it does
Asonecanseeinbothcasestheinjectionefficiencyin- not form power-law ”tails” of accelerated parti-
creaseswiththetemperatureT. InFig. 2wepresented cles. The energy supplied by acceleration is ab-
the fraction of accelerated particles as it follows from sorbed immediately by the thermal pool through
Eqs. (14)and(20). ionization losses of accelerated particles. The re-
Asitfollowsfromtheradiodata,thedensityofSNRs sulting effect of stochastic acceleration is plasma
dropsby30timesfromtheradiusR = 2kpctoR = 14 overheating.
kpc[42],whilethedensityofCRsdropsby2timesonly
fortheseradii. However,asweseeinFig. 2,themodel • If the stochastic acceleration interacts with a high
efficiencyofparticleaccelerationrisesin20-100times
energy fraction of the Maxwellian distribution
forthesedistancesfromtheGCbecauseofthetempera-
only, then power-law spectra of particles are gen-
turevariations. Thus,theefficiencyofaccelerationmay
erated,andthenumberofacceleratedparticlesde-
compensatepartiallythedropofsupernovadensityand
pends strongly on the position of acceleration the
with this effect the observed CR density can be repro- low momentum cutoff of the stochastic accelera-
duced in the ”temperature” model. Erlykin et al. [52]
tionprocess.
derivedfromtheMaxwell-Boltzmandistributionatdif-
ferent temperatures the necessary value of ε , which
thr • Weanalysedwhetherthestochasticaccelerationin
shouldbeabout2.5eVfortheobservedCRdenstyvari-
the Galactic halo can produce there enough num-
ations. Thisanalysisgivesareasonablecoincidenceof
ber of high energy electrons needed to explain
the”temperature”modelwithvariationsofCRdensity
the gamma-ray and microwave emission from the
intheGalacticdiskalthoughthereareanumberofun-
enigmaticFermibubblesintheGalacticcentralre-
certaintieswhichrequirefurtherinvestigations.
gion. Weanalysedtwocasesofelectronaccelera-
We notice, however, that this estimates presented in
tion:a)in-situaccelerationofelectronsfromback-
Fig. 2, are mainly illustrative and give qualitative im-
ground plasma, and b) re-acceleration in the halo
pressionabouttheinjectionprocesses. Thus,shocksin
ofelectronsgeneratedbySNRsinthedisk,which
theGalaxyarecollisionless,andparticleinjectionisde-
reachthealtitudesoftheFermibubbleedges. We
terminedbyinteractionswithmagneticfluctuations(not
showed that there are problems in both cases, but
byCoulombcollisions, seethetalkofDamianoCapri-
the needed number of electrons can be provided
oli).
underspecificconditions.
5. Conclusion • We discussed whether the CR gradient in the
Galactic disk can be explained in terms of the
model of stochastic acceleration. We showed that
Wegiveashortreviewofprocessstochasticaccelera-
ifthenumberofacceleratedparticlesisafunction
tionintheGalaxy. Theconclusionsareitemizedbelow:
ofthetemperatureofbackgroundplasmathenthis
• Inthecaseofstochasticaccelerationfromaback- effectmayexplaintheobservedradialvariationof
ground plasma the distribution is nonequilibrium. theCRdensityintheGalacticdisk.
/NuclearandParticlePhysicsProceedings00(2017)1–8 7
Acknowledegments onInterstellarTurbulenceandCosmic-RayTransport,ApJ642
(2006)902
V.A.D. and D.O.C. acknowledge a partial support [20] C.A.Norman,A.Ferrara,TheTurbulentInterstellarMedium:
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