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early investigations of black hole accretion flows indicated that tenuous flows can develop a two - temperature structure , with proton temperature sufficient to produce a significant @xmath0-ray luminosity above 10 mev through @xmath9 production ( e.g.  dahlbacka , chapline & weaver 1974 ) . the two - temperature structure is an essential feature of the optically - thin , advection dominated accretion flow ( adaf ) model , which has been extensively studied and successfully applied to a variety of black hole systems ( see , e.g. , reviews in yuan 2007 , narayan & mcclintock 2008 , yuan & narayan 2013 ) over the past two decades , following the work of narayan & yi ( 1994 ) . mahadevan , narayan & krolik ( 1997 ; hereafter m97 ) pointed out that @xmath0-ray emission resulting from proton - proton collisions in adafs may be a signature allowing to test their fundamental nature . the model of m97 relied on a non - relativistic adaf model and their computations were improved by oka & manmoto ( 2003 ; hereafter om03 ) who used a fully general relativistic ( gr ) model of the flow . however , both m97 and om03 neglected the doppler and gravitational shifts of energy as well as gravitational focusing and capturing by the black hole , which is a major deficiency because the @xmath0-ray emission is produced very close to the black hole s horizon . furthermore , both works neglected the internal absorption of @xmath0-ray photons to pair creation , which effect should be important in more luminous systems . adafs are supposed to power low - luminosity agns , like fanaroff - riley type i ( fr i ) radio galaxies or low - luminosity seyfert galaxies , and a measurement , or even upper limits on their @xmath0-ray emission , may put interesting constraints on the properties of the source of high - energy radiation in such objects . m97 and om03 considered only the _ cgro_/egret source in the direction of the galactic center for such an analysis . significant progress in exploration of the @xmath0-ray activity of agns which has been made after their works , thanks to the _ fermi _ mission , motivates us to develop a more accurate model of the hadronic @xmath0-ray emission from adafs . detections of @xmath0-ray emission from objects with misaligned jets ( e.g.  abdo et al . 2010b ) are most relevant for our study . their @xmath0-ray radiation is usually explained as a jet emission ; we show that emission from an accretion flow may be a reasonable alternative , at least in some fr is . we focus on modelling of radiation in 100 mev  10 gev energy range , relevant for the _ fermi_-lat measurements of the fr i radio galaxies ( abdo et al . 2010b ) and over which the upper limits in seyfert galaxies are derived ( ackermann et al . 2012 ) . the dependence of the @xmath0-ray luminosity on the black hole spin parameter makes a particularly interesting context for such an investigation . already a rough estimate by shapiro , lightman & eardley ( 1976 ) indicated a strong dependence of the @xmath0-ray luminosity from a two - temperature flow on the spin of the black hole and , then , they suggested that this effect may serve as a means to measure the spin value ( see also eilek & kafatos 1983 and colpi , maraschi & treves 1986 ) . om03 , who made gr calculations for the modern adaf model , found a dramatic dependence of the @xmath0-ray luminosity on the spin value in models with thermal distribution of proton energies , however , they concluded that the dependence is weak if protons have a nonthermal distribution . in this work we extend the analysis of this issue and clarify some related properties . we find global solutions of the hydrodynamical adaf model , which follows manmoto ( 2000 ) , and use them to compute the @xmath0-ray emission . similarly to m97 and om03 we take into account emission resulting from thermal and nonthermal distribution of proton energies ; we use similar phenomenological models , with some modifications which allow to illustrate separately effects due to local distribution of proton energies and to radial profile of @xmath0-ray emissivity . we also use our recently developed model of global comptonization ( niedwiecki , xie & zdziarski 2012 ; hereafter n12 , see also xie et al . 2010 ) to compute the x - ray emission , which allows to investigate the internal absorption of @xmath0-ray photons to pair creation in the flow .    in our computations we assume a rather weak magnetic field , with the magnetic pressure of 1/10th of the total pressure , supported by results of the magnetohydrodynamic ( mhd ) simulations in which amplification of magnetic fields by the magneto - rotational instability typically saturates at such a ratio of the magnetic to the total pressure ( e.g.  machida , nakamura & matsumoto 2004 , hirose et al . 2004 , hawley & krolik 2001 ) . we investigate the dependence on the poorly understood parameter in adaf theory , @xmath10 , describing the fraction of the turbulent dissipation that directly heats electrons in the flow . we take into account only one value of the accretion rate , but the considered ranges of the spin and @xmath10 parameters yield a rather large range of bolometric luminosities of @xmath11 to @xmath12 of the eddington luminosity . in our paper we present both the spectra affected by @xmath13 absorption and those neglecting the absorption effect ; the latter may be easily scaled to smaller accretion rates , for which the @xmath13 absorption becomes unimportant . we consider a black hole , characterised by its mass , @xmath14 , and angular momentum , @xmath15 , surrounded by a geometrically thick accretion flow with an accretion rate , @xmath16 . we define the following dimensionless parameters : @xmath17 , @xmath18 , @xmath19 , where @xmath20 , @xmath21 is the gravitational radius and @xmath22 is the eddington luminosity . most results presented in this work correspond to @xmath23 , in fig [ fig:6]a we present also results for @xmath24 . we consider @xmath25 and three values of the spin parameter , @xmath26 , 0.95 and 0.998 . the inclination angle of the line of sight to the symmetry axis is given by @xmath27 . we assume that the density distribution is given by @xmath28 , where @xmath29 is the scale height at @xmath30 . we assume the viscosity parameter of @xmath31 and the ratio of the gas pressure ( electron and ion ) to the total pressure of @xmath32 . the fraction of the dissipated energy which heats directly electrons is denoted by @xmath10 . our calculations of hadronic processes are based on global solutions of the fully gr hydrodynamical model of two - temperature adafs , described in n12 , which follows closely the model of manmoto ( 2000 ) . here we recall only the ion energy equation , which is most important for the present study : @xmath33 where @xmath34 is the coulomb rate , the compressive heating and the advection of the internal energy of ions , respectively , are given by @xmath35 and the viscous dissipation rate , per unit area , is given by @xmath36 where @xmath37 , @xmath38 is the ion pressure , @xmath39 is the electron pressure , @xmath40 is the ion adiabatic index , @xmath41 is the angular velocity of the flow , @xmath42 is the lorentz factor of the azimuthal motion and @xmath43 . the form of the energy equation given in equation ( [ eq : ions ] ) is standard in adafs theory , although actually it should include an additional term describing the direct cooling of protons to pion production , @xmath44 . in our calculation of hadronic processes we find that @xmath44 is approximately equal to @xmath34 at @xmath45 . at @xmath46 , considered in this work , both @xmath44 and @xmath34 are much smaller , by over 3 orders of magnitude , than the effective heating @xmath47 and the heating is fully balanced by the advective term , @xmath48 . this justifies our neglect of the direct hadronic cooling . the only difference between our gr model and that of manmoto ( 2000 ) involves the simplifying assumption of @xmath49 adopted in the latter ; we do not follow this simplification and an exact @xmath50 profile is considered in all our hydrodynamic equations . we note that the simplification has a considerable effect in the central part of the flow , e.g.  it results in an underestimation of the proton temperature by a factor of @xmath51 within the innermost @xmath52 . applying the above simplifying assumption we get exactly the same flow parameters as manmoto ( 2000 ) ; note , however , that manmoto ( 2000 ) assumed an equipartition between the gas and plasma pressures , with @xmath53 , which in general gives a smaller proton temperature than @xmath54 assumed here . in particular , for @xmath26 and @xmath55 , models with @xmath54 give the proton temperature larger by a factor of @xmath56 , close to the horizon , than models with @xmath53 . this underlies also the differences in the @xmath0-ray luminosity levels between the thermal models of oka & manmoto ( 2003 ) and ours , as discussed in section 3 .    to obtain global transonic solutions we have to adjust the specific angular momentum per unit mass accreted by the black hole , for which the accretion flow passes smoothly through the sonic point , @xmath57 . we note that this condition permits for two kinds of solutions , below referred to as a standard and a superhot solution . the latter ( superhot ) has much larger proton temperature and density , furthermore , the sound speed is large and the sonic point located in the immediate vicinity of the event horizon , e.g.  @xmath58 for @xmath59 . in the standard solutions the sonic point is located at larger distances , @xmath60 . taking into account rather extreme properties of the superhot solutions ( specifically , a very large magnitude of @xmath61 illustrated in fig . [ fig:1](a ) and discussed in section [ sec : diss ] ) we neglect them in this work and for all values of @xmath8 we consider only the standard solutions which are consistent with solutions of the model investigated in several previous studies ( e.g.  manmoto 2000 , yuan et al  2009 , li et al . note , however , that in our previous works ( n12 , niedwiecki , xie & beckmann 2012 ) we considered the superhot solution with @xmath59 , then , the results for @xmath59 discussed in those works correspond to flows with larger proton temperature and density ( both by a factor of @xmath62 ) than these considered in the present study . [ fig:1 ] shows the dependence on the black hole spin of some parameters from our solutions which are crucial for the hadronic @xmath0-ray production . rotation of the black hole stabilizes the circular motion of the flow which yields a higher density ( through the continuity equation ) . furthermore , the stabilized rotation of the flow results in a stronger dissipative heating giving a larger proton temperature for larger @xmath8 . all these differences are significant only within the innermost @xmath63 . the hydrodynamical solutions set the proton density , @xmath64 , and temperature , @xmath65 , as a function of radius . in principle , this should allow to determine the @xmath0-ray emissivity , resulting from neutral pion production in proton - proton collisions and their subsequent decay into @xmath0-ray photons , in the rest frame of the flow . however , details of this process are subject to an uncertainty related to the distribution of proton energies , which is unlikely to be thermal in optically thin flows ( see discussion in section [ sec : protons ] ) . following m97 and om03 we assume that the temperature from the global solution functions as a parameter specifying the average energy of protons in the plasma which , however , does not have to have a thermal distribution . we consider several phenomenological models which must satisfy the obvious requirements that at each radius ( 1 ) the number density of protons equals @xmath66 , determined by the global adaf solution and ( 2 ) the average energy of protons equals the average energy @xmath67 of the maxwellian proton gas with temperature , @xmath68 , determined by the global adaf solution , where @xmath69 and we use the simplified ( cf . gammie & popham 1998 ) relativistic form of @xmath70 . we consider models involving various combinations of thermal @xmath71 ,   \label{eq : thdist}\ ] ] and power - law @xmath72 distributions of proton energies , where @xmath73 and @xmath74 are the local densities of these two populations . the thermal model ( model t ) assuming a purely maxwellian distribution of protons and the nonthermal model ( model n , same to nonthermal models of m97 and om03 ) , assuming that the total energy is stored in the power - law distribution of a small fraction of protons , allow us to estimate the _ minimum _ and _ maximum _ level of @xmath0-ray luminosity , respectively , for a given set of ( @xmath14 , @xmath75 , @xmath8 , @xmath76 , @xmath77 , @xmath10 ) . mahadevan ( 1999 ) and om03 considered the model involving the mixture of the thermal and power - law distributions , with the radius - independent parameter characterizing the fraction of energy that goes into the two distributions . deviations of such a model from model n are trivial , with the @xmath0-ray luminosity linearly proportional to the fraction of energy going to the power - law distribution . in this work we consider a different hybrid model ( model h ) with the radius dependent normalization between the power - law and the thermal distribution , which allows us to illustrate some additional effects . the detailed assumptions on the parameters of these models are as follows ( @xmath66 and @xmath68 denote values given by the global adaf solution ) :    * model t * assumes a purely maxwellian distribution of protons , equation ( [ eq : thdist ] ) , with @xmath78 and @xmath79 . * assumes that a fraction @xmath80 of protons form the power - law distribution , equation ( [ eq : pldist ] ) , with the radius - independent index @xmath81 and @xmath82 , and the remaining protons are cold , with the lorentz factor @xmath83 ( @xmath84 is assumed in the computations ) . the radius - dependent fraction @xmath80 is determined by @xmath85 . \label{psi1}\ ] ]    * model h * assumes that an efficient nonthermal acceleration operates only within the central @xmath86 , where the average proton energies resulting from the adaf solutions become relativistic . specifically , we assume that at each radius at @xmath87 a fraction of protons form a thermal distribution at a subrelativistic temperature of @xmath88 k ( @xmath89 ) , and the remaining form a power - law distribution ( equation [ eq : pldist ] ) with a constant ( i.e.  radius - independent ) index @xmath81 and @xmath82 . the relative normalization of these two distributions is determined by @xmath90 , \label{psi2}\ ] ] ( where the factor @xmath91 results from equation ( [ eq : uth ] ) with @xmath92 ) . at @xmath93 , where @xmath94 k , there are no non - thermal protons in this model , which then results in a negligible pion production at such distances , similar as in model t. the chosen value of @xmath88 k gives a smooth transition between a purely thermal and a hybrid plasma at @xmath95 , however , radiative properties of model h are roughly independent of the specific value of the temperature of the subrelativistic thermal component . we remark also that @xmath96 k is close to the limiting temperature above which the pion production prevents thermalization of protons ( see stepney 1983 , dermer 1986b )    the efficiency of pion production by protons with the power - law distribution increases with the decrease of the power - law index @xmath81 . on the other hand , the fraction @xmath80 decreases with decreasing @xmath81 , roughly as @xmath97 . these two effects balance each other yielding the largest luminosity in 0.110 gev range , @xmath98 , for @xmath99 . for @xmath100 , the dependence of @xmath98 on @xmath81 is weak ; for @xmath101 , @xmath98 is by a factor of @xmath102 smaller than for @xmath103 . to estimate the maximum value of @xmath98 that can be produced in a flow with given parameters , in our computations for models n and h we use @xmath103 . for all values of @xmath8 , @xmath104 , and also @xmath105 in models h and n with @xmath103 , within the innermost several @xmath106 .    in our solutions of the flow structure we assume that protons are thermal and we use the thermal form of the gas pressure . then , our models n and h with non - thermal proton distributions are not strictly self - consistent , as their pressure may deviate from the thermal prescription . however , this is a rather small effect , e.g.  the pressure of the purely non - thermal distribution ( model n ) differs by 2030 per cent from the pressure of a thermal gas with the same internal energy .    for a given distribution of proton energies we determine the @xmath0-ray spectra in the flow rest frame , strictly following dermer ( 1986a,1986b ) , in a manner similar to m97 and om03 ; however , we do not apply the following simplification underlying their nonthermal model . as argued in m97 , the fraction of nonthermal protons should be small , @xmath107 , and , therefore , interactions of nonthermal protons with other nonthermal protons may be neglected ; hence , only interaction of nonthermal protons with cold protons are taken into account in their computations . we remark that such an approach underestimates the @xmath0-ray luminosity , e.g.  by a factor of @xmath102 in model n with @xmath108 and @xmath103 ( for which @xmath109 in the innermost region ) . in all our models we take into account interaction of protons with all other protons .    to compute the @xmath0-ray luminosity and spectra received by distant observers we use a monte carlo method similar to that described in niedwiecki ( 2005 ) . we generate @xmath0-ray photons isotropically in the plasma frame , make a lorentz transformation from the flow rest frame to the locally non rotating ( lnr ) frame and then we compute the transfer of @xmath0-ray photons in curved space - time ; see , e.g. , bardeen et al . ( 1972 ) for the definition of lnr frames and the equations of motion in the kerr metric .    the dashed lines in fig .  [ fig:7 ] show the radial profiles of the vertically - integrated @xmath0-ray emissivity , @xmath44 ( @xmath44 gives the energy emitted from the unit area per unit time ) for models t , h and n with @xmath108 . the solid lines in fig .  [ fig:7 ] show the radial profiles of the vertically - integrated local luminosity ( the energy per unit time reaching infinity from the unit area at a given @xmath30 ) . the local luminosity profiles shown by the solid lines neglect the @xmath13 absorption , so the difference between the dashed and solid lines is only due to the relativistic transfer effects . [ fig:3 ] shows the corresponding @xmath0-ray spectra and compares them with the spectra for @xmath26 . at @xmath45 both models n and h are characterised by similar values of @xmath80 and produce similar amounts of @xmath0-rays . in both models t and h the contribution from @xmath110 is very weak ; in model n the radial emissivity is much flatter despite @xmath80 being small , e.g.  @xmath111 at @xmath112 . comparing models t and h we can see the effect of the local proton distribution function and by comparing models h and n we can see the effect of the radial emissivity .    for the thermal distribution of protons , the rest - frame photon spectra are symmetrical , in the logarithmic scale , around @xmath113 mev but in @xmath114 units they peak around 200 mev ; the position of the maximum in the spectra observed by distant observes is slightly redshifted . note that the difference of @xmath0-ray luminosities , @xmath115 , between @xmath26 and 0.95 in our model t is much smaller than that derived by om03 , whose thermal models with @xmath26 and 0.95 give @xmath115 differing by approximately three orders of magnitude . the difference is due to different values of @xmath116 assumed here and by om03 , which result in different @xmath117 , as discussed in section [ sec : flow ] . the dependence of @xmath115 on @xmath117 changes around @xmath118 ( see , e.g. , fig .  3 in dermer 1986b ) . at lower temperatures , @xmath115 is extremely sensitive to @xmath117 , with the increase of @xmath117 by a factor of 2 yielding the increase of @xmath115 by over two orders of magnitude . at @xmath104 , the dependence is more modest , e.g.  the increase of @xmath117 from 0.2 to 0.4 results in the increase of @xmath115 by only a factor of @xmath102 . for @xmath54 assumed in this work , @xmath119 at small @xmath30 for all values of @xmath8 , making the @xmath0-ray luminosity much less dependent on the black hole spin . for @xmath53 , assumed by om03 , the proton temperature is small , with the maximum value of @xmath120 for @xmath26 , which leads to the strong dependence of @xmath115 on @xmath8 . -ray spectra , respectively , for model t ( ab ) and model h with @xmath103 ( cd ) . dotted ( red ) and dot - dashed ( magenta ) lines in ( cd ) show the rest frame and the observed @xmath0-ray spectra , respectively , for model n with @xmath103 . all spectra are for @xmath55 ; panels ( a ) and ( c ) are for @xmath26 , panels ( b ) and ( d ) are for @xmath108 . in this figure , the observed spectra neglect @xmath13 absorption , so they are effected only by gr effects . , title="fig:",height=120 ] -ray spectra , respectively , for model t ( ab ) and model h with @xmath103 ( cd ) . dotted ( red ) and dot - dashed ( magenta ) lines in ( cd ) show the rest frame and the observed @xmath0-ray spectra , respectively , for model n with @xmath103 . all spectra are for @xmath55 ; panels ( a ) and ( c ) are for @xmath26 , panels ( b ) and ( d ) are for @xmath108 . in this figure , the observed spectra neglect @xmath13 absorption , so they are effected only by gr effects . , title="fig:",height=120 ]    -ray spectra , respectively , for model t ( ab ) and model h with @xmath103 ( cd ) . dotted ( red ) and dot - dashed ( magenta ) lines in ( cd ) show the rest frame and the observed @xmath0-ray spectra , respectively , for model n with @xmath103 . all spectra are for @xmath55 ; panels ( a ) and ( c ) are for @xmath26 , panels ( b ) and ( d ) are for @xmath108 . in this figure , the observed spectra neglect @xmath13 absorption , so they are effected only by gr effects . , title="fig:",height=132 ] -ray spectra , respectively , for model t ( ab ) and model h with @xmath103 ( cd ) . dotted ( red ) and dot - dashed ( magenta ) lines in ( cd ) show the rest frame and the observed @xmath0-ray spectra , respectively , for model n with @xmath103 . all spectra are for @xmath55 ; panels ( a ) and ( c ) are for @xmath26 , panels ( b ) and ( d ) are for @xmath108 . in this figure , the observed spectra neglect @xmath13 absorption , so they are effected only by gr effects . , title="fig:",height=132 ]    for both model h and n , the spectrum at @xmath121 gev has the same slope as the power - law distribution of proton energies . for model h with @xmath103 , @xmath115 is by a factor of 3 larger than in model t. rather small difference between @xmath115 in our thermal and nonthermal models is again due to our assumption of a weak magnetic field . at smaller @xmath116 , resulting in smaller @xmath117 , the presence of even a small fraction of non - thermal electrons leads to the increase of @xmath122 by orders of magnitude , as can be seen by comparing the emissivities of our models n and t at @xmath110 ( see also m97 ) . -ray spectra taking into account and neglecting the @xmath13 absorption for model h with @xmath103 ; @xmath59 ( a ) and @xmath26 ( b ) . the dot - dashed ( red ) and dashed ( blue ) lines show the spectra observed at @xmath123 , with and without absorption , and the solid ( magenta ) and dotted ( black ) lines show the spectra observed at @xmath124 , with and without absorption , respectively . , title="fig:",height=132 ] -ray spectra taking into account and neglecting the @xmath13 absorption for model h with @xmath103 ; @xmath59 ( a ) and @xmath26 ( b ) . the dot - dashed ( red ) and dashed ( blue ) lines show the spectra observed at @xmath123 , with and without absorption , and the solid ( magenta ) and dotted ( black ) lines show the spectra observed at @xmath124 , with and without absorption , respectively . , title="fig:",height=132 ]    for models t and h the bulk of the @xmath0-ray emission comes from @xmath125 ( fig . [ fig:7]ab ) and the gr transfer effects reduce the detected @xmath0-ray flux by approximately an order of magnitude . in model n the magnitude of the gr effects on the total flux is reduced due to strong contribution from @xmath126 ( which is weakly affected by gr ) . also in model n , the contribution from @xmath126 , which for @xmath26 approximately equals the contribution from @xmath45 , reduces the difference between the @xmath0-ray fluxes observed for @xmath26 and @xmath108 to only a factor of @xmath102 , see fig . [ fig:3](cd ) . the viewing - angle dependent spectra for model h , which would be observed ( if unabsorbed ) by distant observers , are shown by the dashed and dotted lines in fig . [ fig:8 ] . the flows considered in this work are quasi - spherical and optically thin and hence their appearance depends on the viewing angle primarily due to the relativistic transfer effects . most importantly , trajectories of photons emitted close to a rapidly rotating black hole are bent toward its equatorial plane . therefore , the @xmath0-ray radiation has a significant intrinsic anisotropy in models with large @xmath8 , with edge - on directions corresponding to larger @xmath0-ray fluxes . the absorption of @xmath0-rays in the radiation field of the flow has been calculated in a fully gr model by li et al . ( 2009 ) . here we use a similar approach with the major difference involving the computation of target photon density . li et al .  ( 2009 ) considered the propagation of photons with energies of 10 tev , which are absorbed mostly in interactions with infra - red photons . those low energy photons are produced primarily by the synchrotron emission which can be simply modelled using its local emissivity . in turn , photons with energies in 0.110 gev range , considered in this work , are mostly absorbed by the uv and soft x - ray photons , which are produced by comptonization . then , an exact computation of the angular- , energy- and location - dependent distribution of the target photon field requires the precise modelling of the comptonization taking into account its global nature . in our model we apply the monte carlo ( mc ) method , described in detail in n12 , with seed photons for comptonization from synchrotron and bremsstrahlung emission . we find self - consistent electron temperature distributions using the procedure described in n12 ; we iterate between the solutions of the electron energy equation ( analogous to equations [ eq : ions][eq : qdiss ] ; note that here we include the direct electron heating , while n12 assumes @xmath127 ) and the gr mc comptonization simulations until we find mutually consistent solutions . in fig . [ fig:6 ] we show the resulting spectra . fig . [ fig:4 ] shows the radial profiles of the radiative cooling of electrons ( strongly dominated by comptonization ) , @xmath128 , for @xmath55 and compares them with the @xmath0-ray emissivity , @xmath44 , for model t. note that @xmath44 is much steeper than @xmath128 so the gr effects are more important for the @xmath0-ray than for the x - ray emission .    as we can see in fig . [ fig:4 ] and also in the corresponding spectra in fig . [ fig:6]a , for @xmath129 the black hole spin negligibly affects the comptonized radiation ; this property results from a large magnitude of the compression work , which is roughly independent of @xmath8 and dominates the heating of electrons for small values of @xmath10 ( cf . n12 ) .    for @xmath130 the direct heating contributes significantly to the heating of electrons and for @xmath131 it dominates over other heating processes at @xmath132 for all values of @xmath8 . then , the dependence of @xmath61 on @xmath8 results in a noticeable dependence of the comptonized radiation on @xmath8 for @xmath130 ( see also xie & yuan 2012 for a recent study of the dependence of x - ray luminosity on @xmath10 ) . the radiative efficiency increases from @xmath133 for all values of @xmath8 at @xmath55 to @xmath134 for @xmath26 , @xmath135 for @xmath108 and @xmath136 for @xmath59 at @xmath131 . despite considering only one value of accretion rate , our solutions span a range of bolometric luminosities , from @xmath137 ( for @xmath55 ) to @xmath138 ( for @xmath131 and @xmath139 ) . the corresponding x - ray spectral slopes harden from @xmath140 to @xmath141 with the increase of @xmath4 . note that these values correspond to the range of parameters close to the turning point in the @xmath4@xmath142 correlation observed in agns ( e.g.  gu & cao 2009 ) . then , we likely consider here the range of the largest luminosities of the flows in which synchrotron emission is the dominant source of seed photons for comptonization ( see discussion and references in n12 ) . having found the self - consistent solutions , described above , we apply our mc model to tabulate the distribution of all photons propagating in the central region ( up to @xmath143 ) , @xmath144 ( in photons @xmath145 ev@xmath146 sr@xmath146 ) , where @xmath147 and @xmath148 are the boyer - lindquist coordinates , @xmath149 is the photon energy in the lnr frame and @xmath150 is the solid angle element in the lnr frame .    to compute the optical depth to pair creation , @xmath151 , we closely follow the method for determining an optical depth to compton scattering in the kerr metric , see niedwiecki ( 2005 ) and niedwiecki & zdziarski ( 2006 ) , however , here we calculate the probability of pair creation in the lnr frame whereas for the compton effect an additional boost to the flow rest frame is applied . while compton scattering is most conveniently described in the plasma rest frame , pair production can be simply modelled in the lnr frame and , thus , the transformation to the flow rest frame is not necessary here . we solve equations of the photon motion in the kerr metric and we determine the increase of the optical depth along the photon trajectory from @xmath152 where @xmath153 is the length element in the lnr frame , @xmath154 is the pair production cross section ( e.g. , gould & schreder 1967 ) , @xmath155 is the energy of the @xmath0-ray photon in the lnr frame and @xmath156 is the angle between the interacting photons in the lnr frame . -ray emissivity , @xmath44 ( for model t ) , and the comptonization rate @xmath128 , for @xmath59 ( dashed , red ) , 0.95 ( solid , black ) and 0 ( dotted , blue ) in models with @xmath55 . @xmath157 denotes the vertically integrated rates . , width=226 ]    gr affects the @xmath13 opacity through ( 1 ) bending the trajectories of both the @xmath0-ray photon and target photons and ( 2 ) changing energies of both the @xmath0-ray photon and target photons . as an example , the neglect of the gravitational shift of the @xmath0-ray photon energy , by using @xmath158 ( where @xmath159 is the energy at infinity ) instead of @xmath154 in equation ( [ eq : sgg ] ) , underestimates @xmath151 by a factor of @xmath1603 for photons emitted from the innermost region .    in fig . [ fig:5 ] we show values of the total optical depth , @xmath161 , integrated along the outward radial direction in the equatorial plane from the emission point at the radial coordinate @xmath30 to the outer boundary at @xmath162 . as we can see , the @xmath13 opacity is a strong function of both the @xmath0-ray energy and the location in the flow . the dotted lines in fig . [ fig:7 ] show how the @xmath13 absorption attenuates @xmath0-rays observed from a given @xmath30 . -ray photons with @xmath163 mev , 1 gev and 10 gev from bottom to top , as a function of the radial distance of their point of emission for @xmath108 and @xmath55 are shown by the solid ( black ) lines . the dotted ( blue ) and dashed ( red ) lines are for @xmath108 and 0 in models @xmath131 ; in these models @xmath151 is shown only for @xmath164 gev for clarity . , width=226 ]         it is apparent that around @xmath165 flows undergo transition from being fully transparent to mostly opaque to @xmath0-rays . in our models with the eddington ratio @xmath166 , the flow is fully transparent to photons with energies @xmath167 mev ; at higher energies the absorption leads to moderate attenuation , with the increase of the photon index at @xmath121 gev by @xmath168 , see fig . [ fig:8 ] . the size of the @xmath0-ray photosphere ( the surface of @xmath169 ) increases with increasing @xmath4 and for @xmath170 the gev photons can not escape from @xmath45 . at such @xmath4 , our model h gives spectra with a clear cut - off around 1 gev ( see the solid line in fig . [ fig:6]b ) which could be measured by _ fermi_. in other cases absorption leads to a smooth softening of the spectra .    in terms of the 2 - 10 kev luminosity , @xmath171 , flows with @xmath172 should be fully transparent to mev / gev photons . flows with @xmath173 can emit significant amounts of unabsorbed @xmath0-rays only if their @xmath0-ray emissivities are strong at large @xmath30 . e.g.  in our model n , the luminosity of the flow at @xmath174 , which region would be outside the photosphere of 1 gev photons even at much larger @xmath175 , is @xmath176 erg / s . then , the @xmath0-ray luminosity exceeding @xmath177 erg / s can be expected at @xmath178 if the @xmath0-ray emitting flow extends out to several tens of @xmath106 , which property is , however , unclear as objects with high luminosities often show signs of a cold disc extending to rather small radii ( so the transition between the hot and cold flow may occur within the @xmath0-ray photosphere ) . note that for such a scenario , with @xmath0-ray emission from a hot flow at large @xmath4 , we expect a small luminosity ratio of @xmath179 regardless of the value of @xmath8 . in fig .  [ fig:9 ] we summarize our results regarding the relation between the x - ray and @xmath0-ray luminosities . the range of expected @xmath98 is constrained from below by values indicated in fig . [ fig:9]a for model t , and from above by values in fig . [ fig:9]b for model n. as we can see , the models give the luminosity ratios @xmath180 between @xmath181 and 0.2 .    in model t , @xmath182 for @xmath26 and @xmath59 differ by a factor of several ; the unabsorbed luminosities differ by over an order of magnitude but for @xmath4 close to @xmath183 the @xmath13 absorption reduces the difference to a factor of @xmath184 . in model n , @xmath182 for @xmath26 and @xmath59 differ by only a factor of @xmath102 ; as noted before , the difference is reduced here due to contribution from large @xmath30 . model n for @xmath26 gives similar @xmath182 as model t with large @xmath8 ; larger density and average energy for large @xmath8 is approximately compensated by a larger fraction of protons above the pion production threshold for model n. note , however , that - despite similar luminosities - the spectra for these two regimes differ significantly , see fig . [ fig:3 ] .    in model h , @xmath182 has a similar dependence on @xmath8 as in model t , with a large difference between small and high values of @xmath8 . we conclude that it is the radial distribution of @xmath0-ray emissivity , rather than the local proton distribution function , which reduces the dependence on @xmath8 . this is even more hindering for attempts of assessing the spin value basing on the @xmath0-ray luminosity level . the proton energy distribution function is reflected in the produced spectral shape and , therefore , it could be constrained observationally and taken into account in this kind of analysis . on the other hand , one can not expect to derive information on the radial emissivity profile from observations , so an investigation of black hole spin values using the @xmath0-ray luminosity should be subject to significant uncertainty .    in models with a dominant contribution from the central @xmath63 , intrinsic @xmath0-ray luminosities of flows around submaximally ( @xmath108 ) and maximally ( @xmath59 ) rotating black holes differ by a factor of @xmath102 . for the latter , the flow extends to smaller radii and hence a larger proton temperature and density are achieved , see fig . [ fig:1 ] . however , a strong contribution from @xmath110 as well as @xmath13 absorption make the difference between the observed luminosities insignificant . regarding the dependence on @xmath10 , we notice a somewhat surprising property of models with @xmath131 , which predict a larger @xmath0-ray luminosity than models with smaller @xmath10 ( the effect is more pronounced for larger values of @xmath8 ) . the physical reason is that for @xmath131 , the slight decrease of proton temperature is outweighed by the increase of density ( through the decrease of both the radial velocity and the scale height with decreasing temperature ) , cf . manmoto ( 2000 ) , which leads to the increase of @xmath185 . at smaller values of @xmath10 , the intrinsic @xmath122 depends negligibly on @xmath10 , in agreement with the results of om03 for @xmath26 and @xmath186 in their nonthermal model . the scaling of density with @xmath75 and @xmath14 in our global gr solutions only weakly differs from that of self - similar adaf model , i.e.  @xmath187 ( e.g.  mahadevan 1997 ) . then , the intrinsic @xmath0-ray luminosity can be estimated as @xmath188 erg / s , where @xmath189 is the unabsorbed luminosity shown by the open symbols in fig . [ fig:9](ab ) . this gives also the observed luminosity at @xmath190 , when the absorption effects are unimportant . obviously , the above scaling with @xmath75 is not relevant for @xmath191 , for which the increase of @xmath75 results in the decrease of the observed @xmath98 due to @xmath13 absorption . on the other hand , the linear scaling of the @xmath0-ray luminosity with @xmath14 holds even when the @xmath13 absorption is important . the spectral distribution of comptonized radiation changes slightly with the black hole mass ( due to the change of the synchrotron emission , which affects the position of comptonization bumps , see fig 5a ) , however , the effect is insignificant for the @xmath13 opacity and we have checked that it negligibly affects the observed @xmath0-ray spectra . the form of the dissipation rate and the proton distribution function are two major uncertainties for predicting the @xmath0-luminosity . we briefly discuss here the related effects in accretion flows . the form of the viscous dissipation rate given by equation ( [ eq : ions ] ) results from the usual assumption that the viscous stress is proportional to the total pressure , with the proportionality coefficient @xmath76 . we use this form of the viscous stress for computational simplicity , however , as we discuss in n12 , this may be an oversimplified approach ( although it has support in mhd simulations , see below ) . below we briefly compare the dissipation rate in our models with that predicted by the classical novikov & thorne ( 1973 ) model . we define @xmath61 integrated over the whole body of the flow as the total dissipation rate , @xmath192 , in our solutions and compare it to the dissipation rate in a keplerian disc for the corresponding value of @xmath8 , @xmath193 , given by the novikov & thorne model . obviously , @xmath192 does not need to match @xmath193 closely . the latter value is calculated under the assumption that the shear stress vanishes at the radius of the innermost stable circular orbit ( isco ) , which condition is not applicable to geometrically thick adafs and its release should lead to stronger dissipation . on the other hand , adafs are sub - keplerian which property decreases the dissipation rate . our @xmath192 does not differ significantly from @xmath193 , however , the efficiency of dissipation in our model comparatively increases with increasing @xmath8 . specifically , @xmath194 for @xmath26 , @xmath195 for @xmath108 and @xmath196 for @xmath59 . note that in an adaf with a large value of @xmath8 most of the dissipation occurs very deep in the potential , where relativistic effects strongly reduce the energy escaping to infinity , whereas in a keplerian disc the dissipation is less centrally concentrated and its radiation is subject to less severe reduction . for example , the gravitational redshift alone ( neglecting , e.g. , the photon capture under the event horizon ) would give similar luminosities received by distant observers ( @xmath197 ) both in our adaf and in novikov & thorne models with @xmath59 , if all of the dissipated energy were converted into radiation . obviously , in optically thin adafs only a small part of the dissipated energy is radiated away and most of it is accreted by the black hole , so the radiative efficiency is much smaller than 0.3 .    as we mentioned in section [ sec : flow ] , the model formally allows for two solutions and the above values of @xmath192 correspond to the standard solution , considered in previous sections . the superhot solution has an extreme dissipation , with @xmath198@xmath199 . this is not necessarily an unphysical property ( note that @xmath192 is defined in the rest frame of the flow ) , as the observed luminosity of such flows does not exceed the accretion rate of the rest mass energy . nevertheless , the magnitude of @xmath61 suggests that the underlying assumption of @xmath200 breaks down at very large @xmath201 . the issue of the proper description of the @xmath61 term could be partially resolved by comparing analytic models such as our , aiming at a precise calculation of the produced radiation , with mhd simulations . the latter currently neglect radiative cooling , or use very approximate descriptions for it , in turn , they provide more accurate accounts of the dissipation physics . such mhd simulations support some properties of our model , e.g.  the @xmath200 prescription of viscous heating ( ohsuga et al . furthermore , the gr mhd simulations have shown that flows cross the isco without any evidence that the shear stress goes to zero , which leads to the increase of the radiative efficiency , and the deviations from novikov & thorne model increase with increasing @xmath202 ratio ( e.g.  noble , krolik & hawley 2009 , penna et al . we could not , however , quantitatively compare our models with such simulations , as the published results have a much smaller aspect ratio than our solutions ( @xmath203 ) . lastly , we remark that gammie & popham ( 1998 ) and popham & gammie ( 1998 ) present a model similar to ours but with a more elaborate description of the shear stress ( in turn , they neglect radiative processes ) . we note that their results indicate a similar in magnitude stabilizing effect of the rotation of black hole . as pointed out by mahadevan & quataert ( 1998 ) , coulomb collisions are too inefficient to thermalize protons in optically thin flows and the proton distribution function is determined by the viscous heating mechanism , which is poorly understood . our solutions , with @xmath23 and @xmath46 , give the accretion time - scale , @xmath204 , much shorter than the proton relaxation time - scale , @xmath205 ; e.g.  at @xmath206 , @xmath207 hours and @xmath208 hours . clearly , the protons can not redistribute their energy through coulomb collisions .    in solar flares , the best observationally studied example of particle acceleration / heating in a magnetised plasma , a significant fraction of the released energy is carried by non - thermal , high energy particles ( e.g.  aschwanden 2002 ) , which strongly motivates for considering the nonthermal distribution of protons , as originally proposed in m97 . applying the generic description of particle acceleration , see e.g.  section 3 in zdziarski , malzac & bednarek ( 2009 ) , we check whether the conditions in adafs allow for proton acceleration to ultrarelativistic energies , as assumed in our computations for the power - law distributions . the magnetic field strength in our adaf solutions is @xmath209 g , 100 g and 1000 g at @xmath210 , 10 and 2 , respectively . assuming an acceleration rate @xmath211 , where @xmath212 is the elementary charge and @xmath213 is the acceleration efficiency ( @xmath214 ) , we find that the maximum lorentz factor limited by the synchrotron energy loss is @xmath215 , depending on @xmath30 . another condition , of the larmor radius being smaller than the acceleration site size , @xmath216 , gives @xmath217 at @xmath218 , and larger values of @xmath219 at smaller @xmath30 , even if we safely assume @xmath220 ( @xmath221 cm ) . we conclude that the central region of a hot accretion flow may be a site of the acceleration of protons to energies which easily allow hadronic emission of photons even in the tev range . this conclusion remains valid for the whole relevant range of accretion rates and masses of supermassive black holes , as the strength of the magnetic field scales as @xmath222 . considering processes which could compete with proton - proton interactions , we note that proton - photon interactions are much less efficient in the central region of the flow . namely , the number density of @xmath0-ray photons , which can effectively interact with protons in photomeson production , is by a factor of @xmath223 smaller than the number density of protons within the innermost few @xmath106 ; the number density of hard x - ray photons , which can interact with protons in photopair production , is similar to @xmath64 . the cross - section for both channels of proton - photon interactions is by over two orders of magnitude smaller than the cross - section for proton - proton interaction , making the photo - hadronic production of secondary particles negligible . we briefly compare here predictions of our model with @xmath0-ray observations of objects which may be powered by adafs . we note , however , that for a more detailed comparison additional physical processes , related to charged pion production ( cf . mahadevan 1999 ) , should be taken into account . in particular , relativistic electrons produced by the pion decay should be important in modelling the emission in the mev range . we also tentatively discuss the origin in the accretion flow of the very high energy radiation detected from m87 and sgr a@xmath224 , for the latter under assumption that the contributions from two separate sources dominate above 100 gev ( sgr a@xmath224 ) and at lower energies ( diffuse emission ) in the radiation observed from the galactic center region . however , we note that the opacity at very high energies may be affected by the nonthermal synchrotron emission of the relativistic electrons . the work on the model implementing the effects of charged pions is currently in progress . the misaligned agns detected by the _ fermi_-lat include seven fr i radio galaxies and four fr iis ( abdo et al . the low - power fr i galaxies are supposed to be powered by radiatively inefficient accretion flows ( e.g.  balmaverde , baldi & capetti 2008 ) and , thus , are more relevant for application of our results . interestingly , wu , cao & wang ( 2011 ) assess that supermassive black holes in fr is rotate rapidly , with @xmath225 . the x - ray emission of more luminous fr is is supposed to come from an accretion flow ( e.g.  wu , yuan & cao 2007 ) , but their @xmath0-ray emission tends to be interpreted in terms of jet emission ( e.g.  abdo et al . 2009 , 2010ab ) . fr is are supposed to be the parent population of bl lac objects , however , the lorentz factors required by a jet model are much lower than typical values found in models of bl lac objects ( see , e.g. , abdo et al .  2010b ) . therefore , the radiation observed in fr is and bl lacs must have a different origin , which adds some complexity to the jet model for fr is . at least two fr i galaxies reported in abdo et al . ( 2010b ) , m87 and centaurus a , are detected because of their proximity rather than a small inclination angle of their jets and , then , they are interesting targets for searching for the @xmath0-ray emission from accretion flows .    in niedwiecki et al .  ( 2012a ) we roughly compared preliminary results of our model with the x/@xmath0-ray observational data of centaurus a from _ integral _ and _ fermi_-lat . we found that the adaf model , which matches the x - ray emission in this object , predicts the @xmath0-ray emission significantly weaker than measured by _ fermi _ if the value of the spin parameter @xmath8 is small . we should emend , however , that this conclusion is valid only for models assuming a significant @xmath0-ray emission only from the central @xmath226 , such as our models t and h. regardless of the values of @xmath8 and @xmath10 , our model n with @xmath103 predicts the absorbed @xmath98 approximately consistent with @xmath227 erg / s measured in cen a by _ fermi _ ( abdo et al . also regardless of the value of @xmath8 , our models with @xmath55 predict the 2 - 10 kev flux as well as the x - ray spectral index consistent with that observed in cen a ; for @xmath228 the model overpredicts the flux and hardness of the x - ray radiation . in the above we assumed the black hole mass of @xmath229 ( e.g.  marconi et al . 2001 ) , which is also within the range allowed by the recent measurement of gnerucci et al . ( 2011 ) . the central core of the accretion system in m87 has been considered as the @xmath0-ray emitting region e.g.  by neronov & aharonian ( 2007 ) in their model with particle acceleration in the black hole magnetosphere . the accretion rate assessed from the high - resolution observations of the nucleus of m87 by _ chandra _ , and used to model the multiwavelength spectrum of the nucleus by emission from an adaf , by di matteo et al . ( 2003 ; note that their definition of @xmath75 differs from ours by a factor of 10 ) , @xmath230/year , corresponds to @xmath231 for a black hole with @xmath232 . at such @xmath75 the central region should be transparent to @xmath0-ray photons . then , we compare the unabsorbed luminosities from our nonthermal models with @xmath233 ( approximately consistent with the slope of the _ fermi _ data above 200 mev ; abdo et al .  2009 ) and @xmath232 with the @xmath0-ray measurements of m87 . we find that the luminosity derived in the 0.2 - 10 gev range by _ fermi _ ( abdo et al . 2009 ) , and above 100 gev by ground - based telescopes ( e.g.  aleksi et al . 2012 ) in the low state of m87 , can be reproduced by our model with @xmath139 and @xmath234/year ( for @xmath235 ) . the required accretion rate , larger by 40 per cent than the face value of the estimate in di matteo et al . ( 2003 ) , is allowed by the precision of the estimation of the accretion rate using bondi accretion theory . we conclude that hadronic processes in adaf can contribute significantly to the @xmath0-ray emission observed in m87 in the low state , or even explain these observations entirely . however , such a model requires that all the available material forms the innermost flow , i.e.  it does not allow a strong reduction the accretion rate in the central region by outflows ( assumed in models of sgr a@xmath224 , see below ) . the value of @xmath75 in the central region is the major issue for applications of adaf models to the supermassive black hole in the galactic center . the bondi accretion rate corresponds to @xmath236 for @xmath237 and early models used such @xmath75 to explain the broad - band spectra of sgr a@xmath224 ( e.g.  narayan et al . the measurement of the millimetre / submillimetre polarization of sgr a@xmath224 is often assumed to limit the accretion rate to @xmath238 ( e.g.  marrone et al . 2007 ) , but counterarguments are presented , e.g. , by mocibrodzka , das & czerny ( 2006 ) and ballantyne , zel & psaltis ( 2007 ) . an updated adaf model to sgr a@xmath224 , with @xmath239 and strong electron heating , is presented in yuan , quataert & narayan ( 2003 ) . an alternative to adaf model , proposed by mocibrodzka et al . ( 2006 ) and recently applied by okuda & molteni ( 2012 ) , with the low angular momentum flow , assumes @xmath240 . the low angular momentum flow has a similar density in the innermost region as an adaf with the same @xmath75 , but much smaller proton temperature @xmath241 k. then , the magnitude of hadronic processes could be used to distinguish the two classes of models ; however , the low @xmath242 may be an artificial effect resulting from the neglect of viscosity in the former ( low angular momentum ) class . the _ cgro_/egret source , 3eg j1746 - 2851 , was initially considered as a possible @xmath0-ray counterpart of sgr a@xmath224 ; narayan et al . ( 1998 ) and om03 found that their adaf models underpredicted the @xmath0-ray luminosity implied by the egret measurement . however , improved analyses ( e.g.  pohl 2005 ) subsequently indicated that 3eg j1746 - 2851 is displaced from the exact galactic center and excluded sgr a@xmath224 , as well as the tev source observed with hess which may be directly related with sgr a@xmath224 , as its possible counterparts . recently , chernyakova et al .  ( 2011 ) analysed the _ fermi_-lat observations of the galactic center and combined them with the hess observational data of the point - like source ( aharonian et al . the spectrum of the source seen in the mev / gev band by _ fermi _ is consistent with a @xmath9-decay spectrum . the hess data indicate flattening of the spectrum above 100 gev , suggesting that at the highest energies a different spectral component dominates , with rather hard spectrum , @xmath243 . in the @xmath244 plot , the normalization of the hess source is an order of magnitude larger than the quiescent x - ray emission of sgr a@xmath224 . to explain these observations , chernyakova et al . ( 2011 ) discuss a model , following previous works ( e.g.  atoyan & dermer 2004 ) , with protons accelerated in the accretion flow and then diffusing outwards to interact with dense gas at distances of @xmath245 pc . the emission at energies below 100 gev may be explained by interactions of protons injected into the interstellar medium during a strong flare of sgr a@xmath224 that occurred 300 years ago , as protons generating photons with such energies are still diffusively trapped in the @xmath0-ray production region . on the other hand , most of the higher energy protons have already escaped and hence an additional , persistent injection of high - energy protons has to be assumed to account for the hess observations , with the required rate of @xmath246 erg / s implying a very high efficiency of the conversion of the accreting rest mass energy into the proton energy . we remark that alternatively the spectral component above 100 gev can be explained by proton - proton interactions in an accretion flow around a rapidly rotating black hole . our model with @xmath59 , @xmath233 and edge - on viewing direction predict the flux consistent with the hess detection for @xmath247 . the scenario with the @xmath0-ray emission produced in the accretion flow may be tested over the following years , if the fall of the gas cloud into the accretion zone of sgr a@xmath224 ( gillessen et al . 2012 ) results in the increase of the mass accretion rate . spectral properties of the seyfert galaxy , ngc 4151 , are consistent with the model of an inner hot flow surrounded by an outer cold disc ( e.g.  lubiski et al . 2010 ) , however , its rather large luminosity , @xmath248 indicates that a potential @xmath0-ray emission from innermost region would be strongly absorbed . the constraint of @xmath249 derived for this object in ackermann et al . ( 2012 ) can still give interesting information if the spectral model constrains the parameters of the inner hot / outer cold accretion system ( in particular , the distance of transition between the two modes of accretion ) . the constraint of @xmath250 , or even @xmath251 for some objects , found for other seyfert galaxies by ackermann et al . ( 2012 ) is not strongly constraining for the spin value , as can be seen in fig . [ fig:9 ] ( note that @xmath252 is by a factor of a few , depending on @xmath253 , larger than @xmath171 ) , especially for large x - ray luminosities ( and hence strong @xmath13 absorption ) characterising most of objects analysed in that paper . we have studied the @xmath0-ray emission resulting from proton - proton interactions in two - temperature adafs . our model relies on the global solutions of the gr hydrodynamical model , same as om03 , but we improve their computations by taking into account the relativistic transfer effects as well as the @xmath13 absorption and by properly describing the global comptonization process . we have found that the spin value is reflected in the properties of @xmath0-ray emission , but the effect is not thrilling . the speed of the black hole rotation strongly affects the @xmath0-ray emission produced within the innermost @xmath52 . if emission from that region dominates , the observed @xmath0-ray radiation depends on the spin parameter noticeably ; the intrinsic @xmath0-ray luminosities of flows around rapidly - rotating and non - rotating black holes differ by over a factor of @xmath1 . however , if the @xmath0-ray emitting region extends to larger distances , the dependence is reduced . in the most extreme case with protons efficiently accelerated to relativistic energies in the whole body of the flow , the regions within and beyond @xmath52 give comparable contributions to the total emission , reducing the difference of @xmath0-ray luminosities between high and low values of @xmath8 to only a factor of @xmath102 . the radial emissivity profile of @xmath0-rays is very uncertain ( as the acceleration efficiency may change with radius ) , then , the level of the @xmath0-ray luminosity can not be regarded as a very sensitive probe of the spin value . still , it may be possible to assess a slow rotation in a low luminosity object by putting an upper limit on the @xmath0-ray luminosity at the level of @xmath254 of the x - ray luminosity . the presence of nonthermal protons may be easily assessed from the @xmath0-ray spectrum as for a purely thermal plasma the total @xmath0-ray emission would be observed only at energies lower than 1 gev . we have considered the accretion rate of @xmath46 , for which our model gives the bolometric luminosities between @xmath255 and @xmath256 . such @xmath75 , with the corresponding range of @xmath257 , seems to be favoured for investigation of the hadronic @xmath0-ray emission , with the related effects of the space - time metric , because the internal @xmath0-ray emission is large and its attenuation by @xmath13 absorption is weak . flows with @xmath258 can produce observable @xmath0-ray radiation only if the emitting region extends out to a rather large distance of several tens of @xmath106 . we have found the x - ray to @xmath0-ray luminosities ratio as a function of the black hole spin and the efficiency of the direct heating of electrons . the @xmath180 ratios reaching @xmath259 , with the corresponding levels of the @xmath0-ray luminosities which may be probed in nearby agns at the current sensitivity of _ fermi_-lat surveys , encourage to consider contribution from an accretion flow to the @xmath0-ray emission observed in low - luminosity objects . we point out that such a contribution should be strong at least in cen a.    the @xmath0-ray luminosity decreases rapidly ( @xmath260 ) with decreasing @xmath75 . m87 and sgr a@xmath224 are the obvious , however possibly also unique , objects for which the @xmath0-ray emission from the flow can be searched at @xmath261 . obviously , contribution from other @xmath0-ray emitting sites should be properly subtracted to establish the luminosity of an accretion flow , which may be particularly difficult in sgr a@xmath224 . the adaf model with a hard ( acceleration index @xmath262 ) nonthermal proton distribution can explain the @xmath0-ray detections of both sgr a@xmath224 ( above 100 gev ) and m87 , however , it does not allow for strong reduction of the accretion rate by outflows . nevertheless , it seems intriguing that in both nearby , low accretion - rate objects , in which the @xmath0-ray radiation is not suppressed by @xmath13 absorption , observations reveal very high energy components , consistent with predictions of such a model . in both objects the model requires a large black hole spin . the luminosity ratio should decrease rather slowly ( @xmath263 , as the radiative efficiency of hot flows varies as @xmath264 at small @xmath75 ; cf . xie & yuan 2012 ) with decreasing @xmath75 . the presence of the @xmath0-ray signal in low - luminosity agns is often considered as the evidence for the origin of their radiation in a jet ( see , e.g. , takami 2011 ) . we note that such a diagnostic is not valid because accretion flows may produce a similarly strong @xmath0-ray emission as jets in such objects . we are grateful to wodek bednarek for helpful discussions and to the referee for a very careful review and comments which helped us to improve the presentation of the results . this research has been supported in part by the polish ncn grant n n203 582240 . fgx has been supported in part by the nsfc ( grants 11103059 , 11121062 , 11133005 , and 11203057 ) , the nbrpc ( 973 program 2009cb824800 ) , and shao key project no .
we present a model of @xmath0-ray emission through neutral pion production and decay in two - temperature accretion flows around supermassive black holes . 
 we refine previous studies of such a hadronic @xmath0-ray emission by taking into account ( 1 ) relativistic effects in the photon transfer and ( 2 ) absorption of @xmath0-ray photons in the radiation field of the flow . 
 we use a fully general relativistic description of both the radiative and hydrodynamic processes , which allows us to study the dependence on the black hole spin . 
 the spin value strongly affects the @xmath0-ray emissivity within @xmath1 gravitational radii . 
 the central regions of flows with the total luminosities @xmath2 of the eddington luminosity ( @xmath3 ) are mostly transparent to photons with energies below 10 gev , permitting investigation of the effects of space - time metric . for such @xmath4 , an observational upper limit on the @xmath0-ray ( 0.1  10 gev ) to x - ray ( 2  10 kev ) luminosity ratio of @xmath5 can rule out rapid rotation of the black hole ; on the other hand , a measurement of @xmath6 can not be regarded as the evidence of rapid rotation , as such a ratio can also result from a flat radial profile of @xmath0-ray emissivity ( which would occur for nonthermal acceleration of protons in the whole body of the flow ) . at @xmath7 , the @xmath0-ray emission from the innermost region 
 is strongly absorbed and the observed @xmath0-rays do not carry information on the value of @xmath8 . 
 we note that if the x - ray emission observed in centaurus a comes from an accretion flow , the hadronic @xmath0-ray emission from the flow should contribute significantly to the mev / gev emission observed from the core of this object , unless it contains a slowly rotating black hole and protons in the flow are thermal . 
 [ firstpage ]    accretion , accretion discs  black hole physics 
 gamma - rays : theory