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radio galaxies exhibit several extended components on the kpc scale , namely : jets , hotspots and lobes . the lobes are double structures extended over large scales , roughly symmetrical and ellipsoidal lying on both sides of the active nuclei of radio galaxies . it was first noticed by fanaroff & riley ( 1974 ) that the relative positions of regions of high and low surface brightness in the extended components of extragalactic radio sources are correlated with their radio luminosity . it was found that nearly all sources with luminosity @xmath5 @xmath6 2 @xmath7 10@xmath8 @xmath9 w hz@xmath10 str@xmath10 were of class i ( i.e. , fri ) while the brighter sources were nearly all of class ii ( i.e. , frii ) . fris have a surface brightness which is larger toward their cores while friis have it larger toward their edges . the morphology of radio galaxies turns out to reflect the method of energy transport in the radio source . fri radio galaxies typically have bright jets in the center , while friis have faint jets but bright hotspots at the ends of their lobes ( e.g. , baum et al . 1995 ) . the radio emission arising from the lobes is widely interpret as due to synchrotron radiation , while the high - energy radiation has been successfully described as inverse compton emission off the cosmic microwave background ( ic / cmb ) . moreover , because of the low electron densities in the large lobe volumes the synchrotron self compton ( ssc ) mechanism produces a negligible contribution both at x - ray and at @xmath0-rays ( e.g. , hardcastle et al . 2002 , croston et al . 2005 , hereafter c05 ) . the radio lobes extension is typically @xmath3 100 kpc implying a timescale for their growth spanning from tens to hundreds of millions of years ( blundell & rawlings 2000 , mullin et al . if relativistic particles in the lobes are not continuously accelerated , considering the synchrotron cooling time @xmath11 @xmath3 16.4 @xmath12 @xmath13 @xmath14(g ) yr , relativistic electrons with lorentz factor @xmath0 @xmath15 10@xmath2 in magnetic fields of @xmath3 10@xmath16 - 10@xmath17 g do not emit on epochs longer than @xmath3 1 myr , which is shorter than the age of radio lobes ( van der laan & perola 1969 ) . a population of energetic electrons is required to interpret the radio / millimeter observations of radio galaxy lobes ( e.g. , hardcastle & looney 2008 ) , and recently , the _ wilkinson microwave anisotropy probe _ ( wmap ) and _ fermi _  observations of the centaurus a lobes ( hardcastle et al . 2009 : abdo et al . in addition , the _ chandra _ , _ xmm - newton _   and _ suzaku _  observations of radio galaxy lobes ( isobe et al . 2002 , 2005 , 2009 , kataoka et al . 2003 , c05 ) show that their ic / cmb spectral energy distribution ( sed ) is rising in the x - rays and consequently a significant fraction of their high - energy emission is expected to be radiated in the hard x - rays and at low energy @xmath0-rays . following the idea of bergamini et al . ( 1967 ) , the ic / cmb process of extended structures in radio galaxies could provide a significant contribution to the diffuse extragalactic @xmath0 ray background ( egb ) in the kev to mev energy range . the contribution to the egb of kpc - scale jets in the case of fris , from ic scattering of starlight photons by the ultrarelativistic electrons , has been estimated by stawarz et al . these estimates show that this emission contributes @xmath3 1% of the egb at gev energies , and it is less relevant at mev energies , where the contribution of the ic / cmb emission peaks .    in this letter , we adopt a statistical acceleration scenario for the lobes in friis , due to turbulent magnetic fields , that balances the radiative cooling and keeps electron energies up to @xmath0 @xmath3 10@xmath4 - 10@xmath2 ( e.g. , pacholczyk & scott 1976 , eilek & shore 1989 ) , in agreement with the recent _ fermi _  observations . a similar mechanism has been proposed by hardcastle et al . ( 2009 ) and osullivan et al . ( 2009 ) to identify radio galaxy lobes as possible accelerators for the ultra high - energy cosmic rays ( e.g. , hillas 1984 ) . finally , we consider a template sed of the emission from the friis lobes to estimate their contribution to the egb . we use cgs units and a flat cosmology with @xmath18 km s@xmath10 mpc@xmath10 , @xmath19 and @xmath20 ( dunkley et al . 2009 ) . the relativistic electrons in radio galaxy lobes are subject to two main radiative loss processes : the synchrotron radiation and the ic / cmb . the first mechanism is responsible for the lobe radio emission , while the latter describes their observed high - energy emission in the x - rays , and recently , also in the @xmath0-rays as in the nearby case of centaurus a ( abdo et al . 2010a ) .    to clarify these radiative processes it is interesting to consider the case of a single relativistic electron of lorentz factor @xmath0 . the total power emitted via synchrotron and ic / cmb radiation is : @xmath21 where @xmath22 is the lobe magnetic field while @xmath23 = 3.26 @xmath12 10@xmath17@xmath24 g , the value of the magnetic field that has the same energy density as the cmb at redshift @xmath25 ( e.g. , murgia et al . the @xmath26 ratio identifies which emission process , synchrotron or ic / cmb , is more relevant for the electron radiative cooling . ratio ( upper panel ) for the friis lobes in the sample of c05 . the dashed red line indicates the case @xmath26 = 1 , when synchrotron and ic / cmb losses have the same relevance . b ) the equivalent spherical radius of the lobe volume , @xmath27 , as a function of redshift estimated for the same sample.,width=332,height=283 ]    in figure 1(a ) , we report the @xmath26 ratio and @xmath27 , the equivalent spherical radius of the lobe volume , with respect to @xmath25 , for the sample of frii lobes detected in the x - rays ( c05 ) , where @xmath22 has been estimated by fitting the radio - to - x - ray lobe seds . we note that the ratio @xmath26 is of order a few , in particular for the sources with larger @xmath27 at low redshift ( i.e. @xmath280.5 ) , for which the cmb energy density exceeds the estimate of the magnetic field energy density ( figure 1(b ) ) . seventy - five percent of the considered frii lobes have @xmath26 in the range 0.72 ( figure 1a ) , suggesting that in these sources the radiative losses for synchrotron and for ic / cmb have similar importance . this strongly suggests that the luminosity ratio of the two sed components @xmath29 is @xmath3 1 .    however , these estimates of the @xmath26 ratio for radio galaxy lobes are dependent on the choice of the particle energy distribution ( ped ) adopted . the restricted energy ranges , where lobe emission is detected , do not allow us to estimate the ped shape and to constrain the @xmath29 accurately , introducing uncertainties in the estimates of the @xmath26 . another relevant process for particle energy losses in lobes is adiabatic expansion . these losses could play a significant role during the evolution of radio lobes ( e.g. , longair et al . assuming a self similar expansion scenario ( e.g. , matthews & scheuer 1990 , kaiser & alexander 1997 ) , the adiabatic losses are relevant in the initial phase of the lobe evolution , as in the case of young , compact radio galaxies .    during the final phase of the lobe expansion , when the lobe pressure is in equilibrium with that of the external medium , losses are dominated by radiative processes , e.g. , via ic / cmb or synchrotron emission ( if @xmath26 is still @xmath30 1 ) . friis , with lobe size @xmath15 30 - 50 kpc , can be considered at the end of their evolution , when the adiabatic expansion losses are negligible ( e.g. , pacholczyk & scott 1976 ) . acceleration by turbulent magnetic fields ( due to electron scattering with magnetized plasma irregularities ) via second order _ fermi _ mechanisms , could be considered as a possible mechanism to compensate both the synchrotron and the ic radiative losses ( e.g. , eilek & shore 1989 , osullivan et al . 2009 , hardcastle 2010 ) .    adopting this scenario , the acceleration timescale via statistical mechanism can be written as @xmath31 @xmath32 @xmath33 , where @xmath34 is the characteristic length scale of the magnetic field inhomogeneities ( i.e. , the mean free path of the electrons between collisions ) and @xmath35 = @xmath36 is the ratio of the alfvn velocity @xmath37 and the speed of light @xmath38 . consequently , according to kardashev ( 1962 ) , the energy gain by systematic statistical acceleration , for a single relativistic electron in a turbulent magnetic field @xmath22 is : @xmath39 where @xmath40 is the energy density of the turbulent magnetic field , @xmath41 is the plasma density and @xmath42 and @xmath43 the electron and the proton mass , respectively ( e.g. , tsytovich 1966 , eilek & shore 1989 ) . we can estimate the maximum lorentz factor of the electrons in the lobes , balancing the acceleration energy gain ( equation ( 2 ) ) with the radiative losses ( equation ( 1 ) ) : @xmath44 that is only dependent on the length scale , @xmath34 , on the plasma density , @xmath45 , and on the @xmath26 ratio . lobes are usually assumed to be close to the equipartition condition between magnetic field and electrons , implying @xmath46 @xmath47 @xmath3 10@xmath16 g ( e.g. , hardcastle et al . 2002 ) . however , the recent case of pictor a ( migliori et al . 2007 ) or similar friis ( e.g. , brunetti et al . 2002 , isobe et al . 2005 , c05 ) suggest that this requirement is not very tight indicating that for a lobe with @xmath25 between 0.5 and 1 , as the majority of frii lobes are detected in x - rays , @xmath26 is of the order of unity ( see figure 1a ) . the mean free path , until an electron collides with a magnetic inhomogeneity in a turbulent plasma , must be smaller than the source size and it has been estimated to be of the order of @xmath3 1 kpc ( e.g. , lacombe 1977 ) . consequently , substituting @xmath34 @xmath3 10@xmath48@xmath27 @xmath32 10@xmath49 cm into equation ( 3 ) , and assuming @xmath26 @xmath3 1 , @xmath50 is of the order of 10@xmath4 - 10@xmath2 , as required to interpret the @xmath0-ray emission of centaurus a lobes as ic / cmb and in agreement with the estimate of osullivan et al . this is consistent the radio / millimeter observations of radio galaxies ( e.g. , hardcastle & looney 2008 ) , that imply the presence of a population of high - energy electrons in their lobes ( i.e. , @xmath51 10@xmath4 - 10@xmath2 ) . our scenario is also in agreement with that proposed by pacholczyk & scott ( 1976 ) for the in situ re - acceleration of extended structures in radio galaxies . we note that electrons with energies @xmath0 @xmath3 10@xmath52 - 10@xmath53 have synchrotron cooling times @xmath11 @xmath3 10@xmath54 - 10@xmath55 yr and are not expected to be present in radio lobes at the epochs of about few myrs ( which is the typical lobe age ) . this is in agreement with the non - detection of lobes at ir and optical frequencies ( i.e. , @xmath56 @xmath3 10@xmath57hz ) , where the synchrotron emission in a magnetic field of about @xmath58 - @xmath59 g of electrons with @xmath0 @xmath3 10@xmath52 - 10@xmath53 should be seen .    [ sec : egb].,width=328,height=283 ] the cmb is a blackbody exhibiting the peak frequency of the sed at @xmath60 @xmath3 1.6 @xmath12 10@xmath61 hz ( adopting the wien law ) . consequently , the expected peak frequency of the ic emission in thomson regime is @xmath62 . low energy electrons at @xmath63 radiate via ic / cmb in the x - ray band , while electrons with @xmath1 - 10@xmath2 emit in the mev - gev energy range . the emission arising from highest energy electrons produces the tail of the ic / cmb sed component and as such its intensity is not expected to be extremely large making the source undetectable by _ fermi _ , unless the radio galaxy lies at very low redshift . as previously anticipated this high - energy radiation could contribute to the diffuse egb . to take this contribution into account , we built a template sed of the lobe emission from the radio to @xmath0-rays . the template has been evaluated assuming a smooth log - normal ped : @xmath64 , ( massaro et al . this distribution has been suggested as intrinsic shape of lobe and hotspots ( e.g. , katz - stone & rudnick 1994 ) . the parameters considered to calculate our sed template are reported in table 1 and it is shown in figure 2a . llcc parameter & symbol & units & template + redshift & z &  & 0.2 + ped curvature & r &  & 0.7 + ped energy peak & @xmath65 &  & 7@xmath1210@xmath54 + ped min energy & @xmath66 &  & 10@xmath67 + ped max energy & @xmath50 &  & @xmath68 + ped density & n & @xmath69 & 10@xmath70 + luminosity ratio & @xmath29 &  & 1 + equivalent lobe radius & @xmath27 & kpc & 45 +     +    we did not assume that the ic / cmb emission is beamed , since there is no evidence of relativistic bulk motion in lobes . we chose the value of @xmath27 to be consistent with the typical value of the c05 sample ( see figure 1(b ) ) , and @xmath65 to have the peak of the synchrotron emission in the radio band at @xmath71 ghz . this is justified by the case of 3c 219 at @xmath25 = 0.1744 ( comastri et al . 2003 ) , for which high frequency radio observations are available . the predicted ir flux of the template at 3.6@xmath72 m is @xmath32 7 @xmath7 10@xmath73 ergs@xmath10cm@xmath48 , in agreement with the non - detected emission at infrared and optical frequencies . the template is in agreement with the observed radio - to - x - ray luminosities measured in the lobe sample of c05 ( see figure 2(b ) and with the models adopted for the x - ray detected lobes of other friis ( e.g. , 3c 219 , comastri et al . 2003 , 3c  207 , brunetti et al . 2002 , 3c  452 , 3c  98 , 3c  326 isobe et al . 2002 , 2005 , 2009 , pictor a , migliori et al . 2007 ) . we calculate the sed template with the luminosity ratio between the synchrotron and the ic / cmb component @xmath29 of the order of unity ( figure 2a ) . this corresponds to the assumption that the energy losses for the radiative processes considered are equivalent , similar condition of @xmath26 @xmath3 1 , in agreement with the observations of friis ( see sect . 2 ) . in addition , the x - ray spectral index is consistent with the typical slope observed for the few lobes for which a detailed spectral analysis exists ( hardcastle et al . 2002 , c05 , isobe et al . 2002 , 2005 , 2009 ) . the estimate of the total diffuse flux arising from the frii radio galaxy population can be evaluated adopting the following relation , as reported in ajello et al . ( 2008 , 2009 ) :    @xmath75    where @xmath76 is the diffuse flux in units of photons cm@xmath48 s@xmath10 sr@xmath10 mev@xmath10 , @xmath77 is the luminosity function ( lf ) , @xmath78 is derived from our sed template of the lobes in the observer s frame at energy @xmath79 and @xmath80 is the comoving volume element per unit redshift and unit solid angle ( hogg 1999 ) . the knowledge of the source lf is crucial to estimate correctly this contribution . indeed , it gives the space density of objects with luminosity @xmath81 at redshift @xmath25 . we adopt the frii radio galaxy lf at 15ghz ( cara & lister 2008 ) . the sed template used in equation ( 4 ) is renormalized such that at a given redshift @xmath25 the luminosity in the native radio band of the lf is @xmath81 . moreover , the ic component is multiplied by an additional factor @xmath82 to account for the fact that the energy density of the cmb scales like @xmath83 . the luminosity of the lf of cara & lister ( 2008 ) refers to the luminosity of the frii core while our sed template applies to the lobe emission . to convert the core luminosity into a proxy for the lobe luminosity at 15ghz we have used the available observations of frii ( c05 ) we have found that rescaling the core luminosity by a factor @xmath84 ( and re - normalizing the sed template as described above ) produces seds that reproduce well the available data on friis for the range of source luminosities and redshifts reported in c05 . we randomly extracted sources from our model and selected only those with flux at 1kev @xmath15 10@xmath85erg cm@xmath48 s@xmath10 and @xmath86 . as shown in figure ( 2 ) our lf model is able to reproduce successfully the range of radio and x - ray luminosities of the c05 sample ( see figure 2(b ) ) . moreover , we performed an additional test integrating the lf coupled to our sed model over luminosity and redshift and we counted how many objects would be detectable in an all - sky survey above a flux of 10@xmath85erg cm@xmath48 s@xmath10 in the x - ray band . the number of detectable sources is @xmath3100 and they display a typical ( average ) x - ray luminosity of @xmath87erg cm@xmath48 s@xmath10 . these numbers appear to be consistent with the _ chandra _  and _ xmm - newton _   observations ( e.g. , c05 ) . as an example , adopting a value for @xmath88 of 10@xmath10 or 10@xmath89 would produce @xmath34000 or @xmath31 observable sources in the entire sky . both these scenarios seem very unlikely given the observations described above . we estimated the uncertainties on @xmath88 adopting the following approach . to set a lower limit on k , we required that the number of detectable lobes all - sky ( estimated through equation ( 4 ) ) at 1kev , with flux @xmath15 10@xmath85erg cm@xmath48 s@xmath10 matches ( within 1@xmath90 ) the number of sources in the c05 sample . this condition is satisfied for @xmath91 . then , to set the upper limit , we request that the density of sources observable at x - rays ( same criteria as above ) matches the frii density at 178mhz in the complete sample of mullin et al . this condition is satisfied for @xmath92 . 3 shows the contribution to the diffuse egb emission arising from the extended structures of frii lobes and its uncertainty . it is apparent that lobes give a significant , @xmath310% contribution to the egb in the mev energy range . in this letter , we adopted a statistical acceleration scenario based on turbulent magnetic fields to show that balancing the particle energy gain with the radiative losses , the expected lorentz factor is of the order of @xmath0 @xmath3 10@xmath4 - 10@xmath2 for electrons in the frii lobes , in agreement with the radio / millimeter observations of lobes in radio galaxies ( e.g. , hardcastle & looney 2008 ) . this has been estimated assuming that the acceleration length scale is comparable to the mean free path in the lobe not far from the equipartition condition , supported by the recent x - ray analyses of c05 . the above scenario is able to justify the presence of high - energy electrons responsible for the @xmath0-ray emission arising from the radio galaxy lobes , via ic / cmb , as the _ fermi _  observations of the nearby centaurus a ( abdo et al . 2010a ) . considering the ic / cmb scattering as the main radiative process for the emission in the mev energy range , we estimated the contribution of the friis to the diffuse egb . we found that the peak of this diffuse emission lies at @xmath3 1  mev and the radiation arising from lobes could contribute @xmath3 10% of the egb close to this energy . so far , the lobes in radio galaxies were only observable at radio frequencies and at high energies in the x - rays . this implies that the shape of the emitting ped is uncertain . consequently , the estimates of the lobe magnetic field and the possibility of identifying which is the most relevant radiative process , synchrotron or ic emission are not well constrained . however , current models adopted to describe the sed of lobes in friis assume the presence of high - energy electrons up to @xmath51 10@xmath4 - 10@xmath2 ( e.g. , c05 ) .    to test this hypothesis , very deep infrared and/or hard x - ray observations , with sufficient spatial resolution are necessary . if _ fermi _  will detect @xmath0-ray emission arising from nearby frii radio galaxies , these observations will be crucial to confirm the presence of high - energy electrons in radio lobes and to constrain their sed . we thank the anonymous referee for the constructive suggestions that have improved and strengthened the manuscript . we are grateful to m. murgia , d. harris and a. cavaliere for fruitful suggestions and to j. finke , l. stawarz and t. cheung for their comments . f.  massaro acknowledges the foundation blanceflor boncompagni - ludovisi , nee bildt for the grant awarded him in 2010 . the work at sao is supported by the nasa grant nnx10ad50 g . m.  ajello acknowledges support by nasa grant nnh09zda001n . adbo a. a. et al . 2010a sci , 328 , 725 adbo a. a. et al . 2010b apj , 720 , 435 ajello , m. et al . 2008 apj , 689 , 666 ajello , m. et al . 2009 apj , 699 , 603 baum , stefi a. , zirbel , esther l. , odea , christopher p. 1995 , apj , 451 , 88 bergamini , r. , londrillo , p. , setti , g. 1967 ncimb , 52 , 495 blundell , k. m. & rawlings , s. 2000 aj , 119 , 1111 brunetti , g. , bondi , m. , comastri , a. , setti , g. 2002 a&a , 381 , 795 cara , m. & lister , m. l. 2008 apj , 674 , 111 comastri , a. , brunetti , g. , dallacasa , d. , bondi , m. , pedani , m. , setti , g. 2003 mnras , 340l , 52 croston , j. h. , hardcastle , m. j. , harris , d. e. , belsole , e. , birkinshaw , m. , worrall , d. m. 2005 apj , 626 , 733 dunkley , j. et al . 2009 apj , 701 , 1804 eilek j. a. & shore , s. n.1989 apj , 342 , 187 fanaroff , b.l . & riley j.m . 1974 , mnras , 167 , 31 fukada , y. et al . 1975 , nature , 254 , 398 hillas , a. m. 1984 ara&a , 22 , 425 hardcastle , m. j. , birkinshaw , m. , cameron , r. a. , harris , d. e. , looney , l. w. , worrall , d. m. 2002 apj , 581 , 948 hardcastle , m. j. & looney l. w. 2008 mnras , 388 , 176 hardcastle , m. j. , cheung , c. c. , feain , i. j. , stawarz , l. 2009 mnras , 393 , 1041 hardcastle , m. j. 2010 mnras , 405 , 2810 hogg , d. w. 1999 , arxiv : astroph/9905116v4 isobe , n. , tashiro , m. , makishima , k. , iyomoto , n. , suzuki , m. , murakami , m. m. , mori , m. , abe , k. 2002 apj , 580 , l111 isobe , n. , makishima , k. , tashiro , m. , hong , s. 2005 apj , 632 , 781 isobe , n. , tashiro , m. s. , gandhi , p. , hayato , a. , nagai , h. , hada , k. , seta , h. , matsuta , k. 2009 apj , 706 , 454 kaiser , c. r. & alexander , p. 1997 mnras , 286 , 215 kardashev , n. s. 1962 sva , 6 , 317 kataoka , j. , leahy , j. p. , edwards , p. g. , kino , m. , takahara , f. , serino , y. , kawai , n. , martel , a. r. 2003 a&a , 410 , 833 katz - 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the recent discovery of the @xmath0-ray emission from the lobes of the closest radio galaxy centaurus a by _ fermi _  implies the presence of high - energy electrons at least up to @xmath1 - 10@xmath2 . 
 these high - energy electrons are required to interpret the observed @xmath0-ray radiation in terms of inverse compton emission off the cosmic microwave background ( ic / cmb ) ; the widely accepted scenario to describe the x - ray emission of radio galaxy lobes . in this letter , we consider the giant radio lobes of fr ii radio galaxies showing that it is possible to maintain electrons at energies @xmath0 @xmath3 10@xmath4 - 10@xmath2 , assuming an acceleration scenario ( driven by turbulent magnetic fields ) that compensates the radiative losses . 
 in addition , we consider the contribution to the diffuse extragalactic @xmath0-ray background due to the ic / cmb emission of friis lobes showing its relevance in the kev to mev energy range .