Hadronic gamma-rays from RX J1713.7-3946?
MMon. Not. R. Astron. Soc. , 1–4 (2002) Printed 15 October 2018 (MN L A TEX style file v2.2)
Hadronic gamma–rays from RX J1713.7-3946?
S. Gabici (cid:63) and F. A. Aharonian , APC, Univ Paris Diderot, CNRS/IN2P3, CEA/Irfu, Obs de Paris, Sorbonne Paris Cit´e, France Dublin Institute for Advanced Studies, 31 Fitzwilliam Place, Dublin 2, Ireland Max-Planck-Institut f¨ur Kernphysik, Postfach 103980, D-69029 Heidelberg, GERMANY
Accepted 1988 December 15. Received 1988 December 14; in original form 1988 October 11
ABSTRACT
RX J1713.7-3946 is a key object to check the supernova remnant paradigm of theorigin of Galactic cosmic rays. While the origin of its gamma–ray emission (hadronicversus leptonic) is still debated, the hard spectrum at GeV energies reported by the
Fermi collaboration is generally interpreted as a strong argument in favor of a leptonicscenario. On the contrary, we show that hadronic interactions can naturally explainthe gamma–ray spectrum if gas clumps are present in the supernova remnant shell.The absence of thermal X–rays from the remnant fits well within this scenario.
Key words: cosmic rays – ISM: supernova remnants – gamma rays: ISM.
SuperNova Remnants (SNRs) are believed to be the sourcesof Galactic Cosmic Rays (CRs). This hypothesis, still un-proven, received further support after the detection of sev-eral SNRs in TeV gamma rays. Such emission was indeedexpected, as the result of the decay of neutral pions pro-duced in the interactions between the accelerated CRs andthe ambient gas (Drury et al. 1994). However, the relativecontribution of protons and electron (via inverse Comptonscattering) to the gamma–ray emission remains uncertain,being very sensitive to model parameters such as gas den-sity and magnetic field strength, which are often unknown(e.g. Cristofari et al. 2013). In most cases, this prevents theunambiguous identification of CR protons.RX J1713.7-3946 is the best studied TeV SNR (Aha-ronian et al. 2007). After an initial debate on the hadronicversus leptonic origin of its gamma–ray emission (Berezhko& V¨olk 2008; Morlino et al. 2009; Zirakashvili & Aharonian2010), it was detected by
Fermi (Abdo et al. 2011). Thehard spectrum revealed in the GeV domain seemed incom-patible with that expected from shock accelerated protonsand leptonic models became favored over hadronic ones (El-lison et al. 2010; Yuan et al. 2011; Finke & Dermer 2012).Moreover, the large gas density required by hadronic modelswould imply an intense thermal X–ray line emission (Katz& Waxman 2008; Ellison et al. 2010), which is not observed(Tanaka et al. 2008). However, the leptonic interpretation isnot exempt from problems. In fact, it is known that one–zone leptonic models, when normalized to fit the TeV data,fail to reproduce the GeV flux (e.g. Aharonian 2013).As suggested by Zirakashvili & Aharonian (2010), the (cid:63)
E-mail: [email protected] interpretation of the gamma–ray observations changes dra-matically if the SNR expands in a clumpy medium. Thisis indeed expected if the SNR progenitor is a massive starin a molecular cloud. The densest clumps can survive, un-shocked, the shock passage, and remain inside the SNR (In-oue et al. 2012). Then, the CRs accelerated at the SNR diffu-sively penetrate the clumps. Since the diffusion coefficient isan increasing function of particle energy, higher energy par-ticles penetrate more effectively, and the spectrum of theCRs inside the clumps might well be significantly harderthan the one accelerated at the shock (Aharonian & Atoyan1996; Gabici et al. 2007). Thus, if clumps make the domi-nant contribution to the mass in the SNR, hadronic emissioncan naturally explain the hard spectrum observed by
Fermi .Moreover, the fact that clumps remain unshocked impliesthat most of the gas in the shell is at low temperature. Thiswould explain the lack of X–ray lines in the spectrum.Here, we develop a model to describe this scenario, anddemonstrate that it provides an excellent fit to data.
We assume here that the progenitor of the SNR RX J1713.7-3946 is a massive star embedded in a molecular cloud. Thisscenario is supported by a number of observational evidences(Slane et al. 1999; Moriguchi et al. 2005; Fukui et al. 2012;Maxted et al. 2012). The stellar wind from the progenitorstrongly affects the properties of the local environment byinflating a large cavity of hot and rarefied gas (Weaver et al.1977). Molecular clouds are highly inhomogeneous, clumpystructures, and the densest clumps survive the wind and re-main intact in the cavity (Inoue et al. 2012). In this scenario,the SNR shock propagates in the low density gas, which oc- c (cid:13) a r X i v : . [ a s t r o - ph . H E ] J un S. Gabici and F. A. Aharonian cupies most of the volume, and interacts with dense clumpscharacterized by a very small volume filling factor.The temporal evolution of the SNR shock radius R s and velocity u s = d R s / d t can be computed by adopting thethin–shell approximation (e.g. Ostriker & McKee 1988). Theequation of momentum conservation then reads:d( Mu )d t = 4 π R s P th (1)where u = (3 / u s and P th are the gas velocity and ther-mal pressure behind the shock, respectively. The pressureof the ambient medium is neglected in Eq. 1 because SNRshocks are strong. The pressure P th can be derived from theconservation of the explosion energy E tot = 10 E erg: E tot = E th + (1 / Mu (2)where E th is the thermal energy inside the SNR, and M isthe mass of the gas in the SNR shell, which is the sum of themass of the supernova ejecta M ej and of the ambient gas ofdensity (cid:37) swept up by the shock: M sw = 4 π (cid:82) R s d r r (cid:37) ( r ).The swept up mass is obtained by recalling that the SNRshock expands first in the progenitor’s wind, with densityprofile (cid:37) ∝ r − , and then in the hot and tenuous gas that fillsthe cavity, of Hydrogen density n h = 10 − n h, − cm − andtemperature T h = 10 T h, K. The density profile of the windis n w = ˙ M/ (4 πm a u w r ), where ˙ M = 10 − ˙ M − M (cid:12) / yr is thewind mass loss rate, u w = 10 u w, cm/s is the wind speed,and m a = 1 . m p is the mean mass of interstellar nuclei perHydrogen nucleus for 10% Helium abundance. The positionof the wind termination shock is determined by imposingequilibrium between the wind ram pressure n w m a u w andthe thermal pressure in the cavity 2 . n h k B T h , the factor 2.3indicating the number of particles per Hydrogen atom.Eqns. 1 and 2 can be solved for the case of RX J1713.7-3946. To reproduce the measured radius of the shock R s, ≈
10 pc at the SNR age of ≈ M ej = 2 . M (cid:12) , n h, − = 2, and E = ˙ M − = u w, = T h, = 1 For sucha choice of the parameters, the mass of the swept up gasis M sw ∼ . M (cid:12) , which is comparable to the mass of theejecta. This implies that the SNR is still in the transitionbetween the ejecta–dominated and the Sedov phase, andthat the shock speed is still quite large. Our calculations give u s, ∼ . × km/s, in agreement with the observationalconstrain given in Uchiyama et al. (2007).The clumps that survive the stellar wind and re-main embedded in the cavity are characterized by a sub–parsec size, L c = 0 . L c, − pc, and a large density, n c (cid:38) n c, cm − (see the simulations by Inoue et al. 2012 andthe observations by Fukui et al. 2012 and Sano et al. 2013).The main parameter that regulates the interaction be-tween a clump and the shock is the density contrast be-tween the clump and the diffuse medium, χ = n c /n h =10 n c, /n h, − (Klein et al. 1994). When the SNR shock en-counters a clump, it drives a shock into it, with a velocity u c ≈ u s /χ / . The time it takes the clump to be shocked, t cc ≡ L c /u c , is called cloud crushing time . Klein et al. (1994)showed that the typical time scale for the development ofKelvin–Helmholtz and Rayleigh–Taylor plasma instabilitiesthat might disrupt the clump are of the same order of t cc .The value of the cloud crushing time for RX J1713.7-3946 is t cc ≈ × L c, − ( n c, /n h, − ) / ( u s /u s, ) − yr. This time is significantly longer than the SNR age, which means thatthe clumps survive against plasma instabilities. This facthas been confirmed by numerical simulations, which showthat shocks are stalled into dense clumps, which survive,unshocked, in the SNR interior (Inoue et al. 2012). Clumpevaporation due to thermal conduction is neglected here,being strongly suppressed by the turbulent magnetic fielddownstream of the SNR shock (Chandran & Cowley 1998).Another consequence of the long cloud crushing time isthe fact that the clumps remain virtually at rest (in the labframe) after the shock passage. The large difference betweenthe velocity of the clump and that of the shocked mediumgenerates a velocity shear which is in turn responsible forthe amplification of the magnetic field in a boundary layeraround the clump. The magnetic field grows very quickly(tens of years) to large values of the order of (cid:38) µ G, withpeak values up to ∼ L tr ∼ .
05 pc (Inoue et al. 2012). The magnetic field in thewhole SNR shell is also amplified to tens of microGauss dueto the vorticity induced downstream by the deformation ofthe shock surface. Such deformations can be produced bythe interaction of the shock with dense clumps (Giacalone& Jokipii 2007). Another amplification mechanism has to beconsidered if the SNR shock accelerates effectively CRs, i.e.the CR current driven instability, which predicts a magneticfield pressure downstream of the shock at the percent levelof the shock ram pressure, B d ∼ × − n / h, − ( u s /u s, ) µ G(Bell et al. 2013), which is of the same order of the fieldamplified by the shock–induced vorticity.In the following we assume that the gas is clumpy insidethe SNR shell, with a magnetic field of few tens of micro-Gauss in the diffuse gas, and of (cid:38) µ G in a thin transitionregion surrounding the clumps.
The SNR shock is expected to accelerate CRs. For a strongshock, the test–particle prediction from shock accelerationtheory gives an universal power law spectrum of acceleratedparticles Q CR ( E ) ∝ E − α with α = 2 (e.g. Drury 1983).The particle spectra inferred from gamma–ray observationsof SNRs are somewhat steeper than that, and several mod-ifications to the shock acceleration mechanism have beenproposed to explain the discrepancy (Zirakashvili & Pruskin2008; Caprioli 2011). In the following we assume α = 2 . η is defined as the frac-tion of the kinetic energy flux across the shock which isconverted into CRs: q CR = (cid:90) E max m p c d E E Q CR ( E ) = η (cid:37)u s (4 πR s ) . (3)The maximum energy of accelerated particles E max is com-puted by equating the CR diffusion length D B /u s , D B be-ing the Bohm diffusion coefficient, to some fraction χ ofthe shock radius (e.g. Gabici 2011). This gives E max ∼ R s /R s, )( u s /u s, )( χ/ . B up, − TeV, where B up =10 B up, − µ G is the magnetic field upstream of the shock.Once accelerated, CRs are advected downstream of theshock where they suffer adiabatic energy losses due to theexpansion of the SNR at a rate ˙ E = E ( u s /R s ). The time c (cid:13)000
The SNR shock is expected to accelerate CRs. For a strongshock, the test–particle prediction from shock accelerationtheory gives an universal power law spectrum of acceleratedparticles Q CR ( E ) ∝ E − α with α = 2 (e.g. Drury 1983).The particle spectra inferred from gamma–ray observationsof SNRs are somewhat steeper than that, and several mod-ifications to the shock acceleration mechanism have beenproposed to explain the discrepancy (Zirakashvili & Pruskin2008; Caprioli 2011). In the following we assume α = 2 . η is defined as the frac-tion of the kinetic energy flux across the shock which isconverted into CRs: q CR = (cid:90) E max m p c d E E Q CR ( E ) = η (cid:37)u s (4 πR s ) . (3)The maximum energy of accelerated particles E max is com-puted by equating the CR diffusion length D B /u s , D B be-ing the Bohm diffusion coefficient, to some fraction χ ofthe shock radius (e.g. Gabici 2011). This gives E max ∼ R s /R s, )( u s /u s, )( χ/ . B up, − TeV, where B up =10 B up, − µ G is the magnetic field upstream of the shock.Once accelerated, CRs are advected downstream of theshock where they suffer adiabatic energy losses due to theexpansion of the SNR at a rate ˙ E = E ( u s /R s ). The time c (cid:13)000 , 1–4 adronic gamma–rays from RX J1713 evolution of the total number of CRs inside the SNR shell N CR ( E ) is described by the equation: ∂N CR ( E ) ∂t = ∂∂E (cid:104) ˙ EN CR ( E ) (cid:105) + Q CR ( E ) . (4)Consider now a clump entering the SNR shock at a time t c . Once downstream of the shock, the clump is bombardedby the CRs accelerated at the SNR shock and accumulatedin the SNR shell. The diffusion of CRs in the highly turbu-lent region that surrounds the clump is expected to occur atthe Bohm rate. Thus, the time needed for a CR to diffusivelypenetrate into the clump is τ d ≈ L tr / D B which gives: τ d ≈ × L tr, − . B − E − yr (5)where B = 100 B − µ G is the magnetic field in the turbulentlayer, L tr = 0 . L tr, − . pc its thickness, and E = E TeVthe particle energy. For a given clump, the minimum energyof the particles that can penetrate is given by the equation τ d = t age − t c . A significantly faster CR diffusion is expectedoutside of the transition region, both inside the clump, whereion-neutral friction is expected to heavily damp magneticturbulence, and in the SNR shell, where the magnetic fieldstrength and turbulent level are significantly smaller.The equation that regulates the time evolution of thetotal number of CRs inside a clump N cl ( E ) is then: ∂N cl ( E ) ∂t = ( V cl /V sh ) N CR ( E ) − N cl ( E ) τ d (6)where V cl = (4 π/ L c and V sh are the volumes of the clumpand of the SNR shell, respectively. The total volume of theclumps is taken to be much smaller than V sh , to insure thevalidity of Eq. 4. Moreover, V cl is assumed to be constant intime (i.e. no CR adiabatic energy losses) and proton–protoninteraction energy losses are neglected since they operateon a time t pp ∼ × n − c, yr, longer than the age of theSNR. Finally, the volume V sh filled by CRs is taken to bethe shell encompassed between the SNR forward shock andthe contact discontinuity. The exact position of the contactdiscontinuity depends on several physical parameters (e.g.Orlando et al 2012), and is typically of the order of ≈ . R s .The dotted line in Fig. 1 represents the current CRdensity in the SNR shell as a function of the particle en-ergy. It has been computed from Eq. 4 after assuming aCR acceleration efficiency of η = 0 . B − = 1 .
2. An exponential cutoffat E max = 150 TeV has been multiplied to the solution ofEq. 4 to mimic the escape of the highest energy CRs fromthe shock. The CR density inside clumps is derived fromEq. 6 and plotted with solid lines. Lines 1, 2, and 3 refer toa clump that entered the SNR shock 1400, 1500, and 1550yr after the supernova explosion, respectively. Clumps thatentered the SNR at t c ≈ ≈
10 TeV. At energies largerthan that of the peak, the spectra of the CRs in the clumpsand in the SNR shell coincide. This is because at large en-ergies diffusion becomes important over times smaller than
Figure 1.
Spectrum of CRs in the SNR shell (dotted line) andinside a clump that entered the shock at t c = 1400, 1500, and1550 yr (solid line 1, 2, and 3 respectively). the residence time of clumps in the shell, allowing for a rapidequilibration of CR densities. On the other hand, CRs withenergies smaller than that of the peak diffuse too slowly toeffectively penetrate the clumps. This explains the deficit ofCRs with energies below ≈
10 TeV in the clumps. The veryhard spectral slope found below the peak is an effect of thesteep energy dependence of the Bohm diffusion coefficient.The position of the peak moves towards larger energies forclumps that enter later the SNR shock, as it can be inferredby Eq. 5 and the discussion that follows it.The hadronic gamma–ray emission from all the denseclumps in the shell is plotted as a solid line in Fig. 2. The gasdensity within clumps is n c, = 1 and the density of clumpsis 3 pc − , which implies a total mass in the clumps withinthe SNR shell of 550 M (cid:12) and a clump volume filling factor of ≈ .
01. The distance to the SNR is 1 kpc. The prediction isin agreement with
FERMI and
HESS data. The gamma–rayemission from CR interactions in the low density diffuse gasswept up by the SNR is plotted as a dashed line, and shownto be subdominant. The contribution from inverse Comptonscattering from electrons accelerated at the SNR is expectedto be negligible, if the magnetic filed is (cid:38) µ G.Secondary electrons are also produced in proton–protoninteractions in the dense clumps. Their production spectrumis similar in shape to that of gamma–rays (Fig. 2), with anormalization smaller by a factor of ≈ ≈ ∼
200 yr (Eq. 5), which isshorter than both synchrotron and Bremmstrahlung energyloss time ( ∼
450 and 3 . × yr, respectively, for the param-eters considered here). Thus, no contribution from secondaryelectrons has to be expected to the gamma–ray emission.At the present time, the CRs inside RX J1713.7-3946amounts to ≈ c (cid:13) , 1–4 S. Gabici and F. A. Aharonian
Figure 2.
Gamma–rays from RX J1713.7-3946. The emissionfrom the clumps is shown as a solid line, while the dashed linerefers to the emission from the diffuse gas in the shell. Data pointsrefer to
FERMI and
HESS observations.
SNR is of the same order of the istantaneous CR accelerationefficiency η (e.g. Gabici 2011). The value η = 0 . We have shown that the gamma–ray emission fromRX J1713.7-3946 can be naturally explained by the decay ofneutral pions produced in hadronic CR interactions with adense, clumpy gas embedded in the SNR shell. The clumpsare expected to be surrounded by a turbulent layer charac-terized by an average magnetic field of ≈ µ G, which insome cases can reach values as large as ≈ n h, − = 5 (a factor 2.5 larger than the one adoptedhere). They found that the expected emission is subdomi-nant with respect to the X–ray synchrotron emission fromthe SNR, as it is indeed observed (Tanaka et al. 2008).As noticed in the introduction, multi–zone leptonicmodels might also provide a satisfactory fit to the observedmulti–wavelength spectrum of RX J1713.7-3946. Thus, fur-ther observational evidences are needed in order to dis-criminate between the hadronic and leptonic origin of thegamma-ray emission. A conclusive proof of the validity of thehadronic scenario would come from the detection of neutri-nos. This test is feasible, since in this scenario the expectedneutrino flux from RX J1713.7-3946 is within the reach ofkm –scale detectors (e.g. Vissani & Aharonian 2012). ACKNOWLEDGMENTS
We thank S. Casanova, Y. Fukui, S. Orlando, Y. Uchiyama,J. Vink, and V. Zirakashvili for helpful discussions. SG ac-knowledges support from the UnivEarthS Labex program atSorbonne Paris Cit´e (ANR-10-LABX-0023/ANR-11-IDEX-0005-02), and API and GRAPPA Institutes at the Univer-sity of Amsterdam for kind hospitality.
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