On the Gamma-Ray Spectrum of RX J1713.7-3946 in the GLAST era

a r X i v :0806.3303v 1 [a s t r o -p h ] 20 J u n 2008On the Gamma-Ray Spectrum of RX J1713.7−3946in the GLASTeraRyo Yamazaki 1,Kazunori Kohri 2,and Hideaki Katagiri 11Department of Physical Science,Hiroshima University,Higashi-Hiroshima,Hiroshima 739-8526,Japan2Physics Department,Lancaster University,LA14YB,UK (Dated:June 20,2008)Abstract The recently launched GLAST satellite is expected to find out if cosmic-ray (CR)protons are generated at supernova remnants,especially at RX J1713.7−3946,by observing the GeV-to-TeV γ-rays.We show,however,that if the nonlinear effects of CR acceleration are considered,it may be impossible to distinguish the evidence of the proton acceleration from leptonic one in the γ-ray spectrum.On the other hand,future km 3-class neutrino observations will find a clear evidence of the proton acceleration.PACS numbers:I.INTRODUCTIONRecently,The Gamma Ray Large Area Space Telescope(GLAST)satellite,observing GeV γ-ray photons,has been launched[1].The GeVγ-ray observations with GLAST are expected to identify the accelerators of Galactic cosmic-ray(CR)protons whose energy extends up to the“knee”energy(∼1015.5eV).At present,most probable candidate of the CR accelerator is the young supernova remnant(SNR).Since the detections of synchrotron X-rays in some SNRs give evidence for electron acceleration[2],the current unsolved issue is whether the SNRs produce high-energy protons or not.TeVγ-ray observations are important to address this problem.So far,TeVγ-rays are detected from several young SNRs[3].They arise from either leptonic(CMB photons up-scattered by high energy electrons)or hadronic(π0-decay photons generated via accelerated protons)processes,and it is generally difficult to separate these processes only in the TeV energy band.Hence the study of wide-band,GeV-to-TeV spectrum is necessary.RX J1713.7−3946(hereafter RXJ1713)is a representative SNR,from which bright TeVγ-rays have been detected.The TeV spectrum is measured by HESS experiment,and its shape is better explained by the hadronic model[4,5].Recently,time variation of synchrotron X-rays was reported by[6].If the variation timescale is determined by the synchrotron cooling of X-ray emitting electrons,the magneticfield is estimated as B∼mG.If so,leptonic one-zone emission model cannot explain the TeV-to-X-rayflux ratio,supporting the hadronic origin of TeVγ-rays.It should be noted that the amplified magneticfield is theoretically expected[7].In this case,according to the standard diffusive shock acceleration theory,the maximum energy of accelerated protons is estimated as[16]E max,p=8×103B mG t34000km s−1 2TeV,(1)which can be comparable to the knee energy.Here,B mG,v s,t3,andηg are thefield strength in units of mG,the shock velocity,the age of the SNR in units of103yr,and the gyrofactor, respectively.However,at present,there are several problems to be addressed,so that the above picture on RXJ1713is not yet proved.First of all,if B∼mG and TeV emission is hadronic,then in order to explain the measuredflux of radio synchrotron emitted by primary electrons,the electron-to-proton ratio at the SNR should be anomalously small,K ep∼10−6[8,9],which is far below the observed value at the earth and estimated values at the nearby galaxy[10].Second,hadronic scenario may be inconsistent with the molecular cloud(MC)observation [11].RXJ1713is surrounded by MCs,which suggests the collision with them and high target number density.If the TeVγ-rays are hadronic,such a region should be more brighter than observed[12].Third,if the measured width of the synchrotron X-rayfilaments at the shock front of SNRs is determined by the synchrotron cooling effect[8,13],magneticfield is independently estimated as B∼0.1mG[14],which is an order of magnitude smaller than that estimated by[6].Finally,the cutoffenergy of TeVγ-ray spectrum is small,so that in the hadronic scenario E max,p is estimated as30–100TeV[15],which is approximately two orders of magnitude smaller than the knee energy.If E max,p<100TeV and B∼1mG, then Eq.(1)tells usηg>80,implying far from the“Bohm limit”(ηg∼1)which is inferred from the X-ray observation[14,17]or expected theoretically[7].In these circumstances,GLAST will give us important information on theγ-ray emission mechanism.GeV emission is thought to be bright if the TeV emission is hadronic,while dim if leptonic.However,this argument is not so straightforward if the nonlinear model of CR acceleration is considered.In the next section,we calculate the photon spectrum using a simple semi-analytic model taking into account the nonlinear effects.Indeed,we show that in a certain case,the hadronic emission spectrum in the GeV-to-TeV band is similar to the leptonic one.II.HADRONIC GAMMA-RAYS IN THE EFFICIENT ACCELERATION CASEIf a large amount of protons are accelerated,their momentumflux is large,so that the back-reaction of them is significant and the background shock structure is modified [18].Compared with the test-particle(inefficient acceleration)case in which the back-reaction effects are neglected,the background plasma is more compressed at the shock due to the additional CR pressure,which leads harder CR spectrum.Hence the hadronic emission becomes harder.At present,there is no reliable theory to determine the acceleration efficiency,and it is not clear whether this nonlinear model is correct or not.Thus,the observations to determine the acceleration efficiency and the CR spectrum at the acceleration site are important.There are several models of nonlinear CR acceleration[19,20,21,22].Here,we adopt the one-dimensional,semi-analytic model,developed by[20].In the following,we brieflysummarize their formalism.The accelerated CR protons are described by the distribution function,f(x,p),where x is the spatial coordinate and p is the momentum of accelerated proton.We derive stationary solutions to the set of an equation for f(x,p)that describes the diffusive transport equation of accelerated protons,and equations for the background thermal plasma that is treated as afluid.The velocity,density,and thermodynamic prop-erties of thefluid can be determined by the mass and momentum conservation equations, with the inclusion of the CR pressure calculated as4πP CR(x)=10-1010-1110-1210-137 8 9 10 11 12 13 14νF ν [e r g /s /c m 2]log (h ν/ eV)FIG.1:νF ν-spectra in γ-ray band,predicted by hadronic π0-decay model in the efficient acceler-ation case (solid line)and leptonic IC model in the inefficient case (dashed line).The dot-dashed curve shows the 1year,5σsensitivity for the GLAST LAT taking into account the Galactic diffuse background [25].The observed spectrum in the TeV band is shown [5].detailed distributions of the daughter particles such as π0and π±.We have also obtained the distribution functions of emitted photons and neutrinos which are produced by subsequent decays of those mesons and muons in the same code [24].The result is shown in Fig.1.For comparison,we show,in Fig.1,the spectrum of leptonic inverse-Compton (IC)radiation via accelerated electrons.The assumed form of the electron distribution isN e (E e )∝E −s e e exp(−E e /E max ),and we adopt s e =2.0and E max =28TeV.One canfind that the π0-decay γ-ray emission in the nonlinear model coincides with the leptonic IC model.The reason is simple.Let s i be the index of the energy spectrum of accelerated par-ticles i (i =p or e ),so that N i (E i )∝E −s i i .Then,the radiation spectrum of π0-decay γ-rays is in the form νF ν∝ν2−s p ,while the spectrum of IC radiation is given by νF ν∝ν−(s e −3)/2.Hence,hadronic emission with s p =1.5and IC emission with s e =2.0give the same spectral slope.Below several hundreds of MeV,hadronic γ-ray emission is dimmer than leptonic IC emission because π0creation reaction does not occur for low-energy (<70MeV in the center-of-mass frame)protons.Unfortunately,GLAST sensitivity is not well enough to recognize this decline below ∼GeV.One canfind that both models slightly deviate from the observed spectrum.This fact is sometimes strengthened,because the leptonic one-zone IC model is unlikely[5].However, in the next section,we see that it is not serious if a two-zone model is considered.III.LEPTONIC TWO-ZONE MODELObserved correlation between TeVγ-ray and synchrotron X-rays[4]may suggest the same origin of them.Then,since synchrotron X-rays arise from accelerated electrons,one may expect that the leptonic model is likely[26].Here,we consider simple leptonic two-zone model to better explain the observed TeV spectrum[16].In our model,two independent regions are considered.The region j(j=1,2)has aexp(−E e/E(j)max),where magneticfield B(j)and the electron spectrum N(j)(E e)=A(j)E−s(j)eeA(j)is the normalization constant.We consider synchrotron emission and IC emission in which the target photon is CMB.The total emission spectrum from the SNR is simply given by the sum of the emissions from two regions.Figures2and3show the result,where we adopt B(1)=2.1µG,B(2)=10µG,s(1)e= s(2)e=2.0,E(1)max=10TeV,E(2)max=40TeV,and A(1)/A(2)=2.74.Observed spectrum, including radio and X-ray bands as well,can be explained by this model.In a similar way, hadronic two-zone model in the efficient acceleration case may also reproduce the observed TeV spectrum.Note that in the leptonic model,the magneticfield strength must be much less than observationally inferred values[6,14]in order tofit the radio and X-ray synchrotron spectrum—if the magneticfield were larger than10µG,the predicted synchrotron radiation would be much brighter than observed[16].Hence,other explanations for the observational facts of rapid time variability and thin width of synchrotronfilaments may be necessary [9,10].IV.CONCLUSIONSome other models predict relatively bright GeVγ-rays compared with those consid-ered above.If the CR back-reaction effect on the particle spectrum is small(inefficient-acceleration case),then the energy spectral index of protons is s p∼2,and theπ0-decay γ-ray emission shows roughlyflatνFν-spectrum,νFν∝ν0,in the GeV–TeV band.Predicted10-1010-1110-1210-137 8 9 10 11 12 13 14νF ν [e r g /s /c m 2]log (h ν/ eV)FIG.2:νF ν-spectra in γ-ray band,predicted by two-zone leptonic IC model (solid line).The dashed and dotted lines represent fluxes from region 1and 2,respectively.Others are the same as in Fig.1.10-910-1010-1110-1210-13-5 0 510 15νF ν [e r g /s /c m 2]log (h ν / eV)total region 1region 2FIG.3:The same as in Fig.2,but in the wide-band energy range from radio to TeV γ-rays.Radio and X-ray data are taken from [4,27].flux is marginally consistent with the EGRET upper limit,νF ν∼5×10−11erg s −1cm −2at 1–10GeV [4,28].On the other hand,if the magnetic field is moderately strong (B ∼60µG),the synchrotron cooling effect causes steepening of the electron spectrum over a wide energy range —typically s e ∼3[29].In this case,leptonic IC emission in the GeV–TeV band10-910-1010-1110-1210-1314131211νF ν [e r g /s /c m 2]log (Energy / eV)FIG.4:νF ν-spectra of TeV γ-rays (solid line)and µ-neutrinos (dashed line)calculated within hadronic model in the efficient acceleration case.The solid line is the same as in Fig.1.We have averaged the vacuum oscillation effects among neutrinos.The dotted line shows the daily averaged atmospheric neutrino flux expected in KM3NeT [31,33].shows again the nearly flat νF ν-spectrum.In summary,it may be difficult to differentiate between hadronic and leptonic emission by the spectral shape of the GeV-to-TeV γ-ray emission.As shown in this Letter,when the GeV γ-ray flux is relatively low,both efficient acceleration model with hadronic γ-ray emission and inefficient acceleration model with leptonic one may give similar spectral shapes.On the other hand,when the GeV emission is relatively bright,one may not be able to distinguish the hadronic model in the inefficient case from the leptonic one with moderately strong magnetic field [29].GLAST will surely provide us rich information on the emission 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