Using optical lines to study particle acceleration at supernova remnants
aa r X i v : . [ a s t r o - ph . H E ] S e p Nuclear Physics B Proceedings Supplement 00 (2018) 1–9
NuclearPhysics BProceed-ingsSupple-ment
Using optical lines to study particle acceleration at supernovaremnants
Giovanni Morlino a,b a APC, AstroParticule et Cosmologie, Universit´e Paris Diderot, CNRS / IN2P3, CEA / Irfu, Observatoire de Paris, Sorbonne Paris Cit´e, 10, rue AliceDomon et L´eonie Duquet, F-75205 Paris Cedex 13, France. b Department of Physics & Astronomy, Purdue University, 525 Northwestern Avenue, West Lafayette, IN 47907-2036, USA.
Abstract
The shocks of several young supernova remnants (SNR) are often associated with very thin optical filaments dominated by Balmeremission resulting from charge-exchange and collisional excitation between neutral Hydrogen from the interstellar medium andshocked protons and electrons. Optical lines are a direct probe of the conditions at the shock, in particular the width of the narrowand broad components reflect the temperature upstream and downstream of the shock, respectively. When the shock acceleratee ffi ciently non-thermal particles, the shock structure changes producing anomalous Balmer lines and it is possible to use their lineshape and their spatial profile to check the e ffi ciency of SNR shocks in accelerating cosmic rays. Here we illustrate the kinetictheory of shock acceleration in presence of neutrals with some applications to young SNRs. We show that in three cases (RCW 86,SNR 0509-67.5 and Tycho) anomalous Balmer lines can be explained assuming that a fraction of ∼
10% of the total shock kineticenergy is converted into not thermal particles, while in one single case, the northwestern part of SN 1006, there is no evidence ofe ffi cient acceleration. Keywords: cosmic-rays, particle acceleration, supernova remnants, Balmer lines
1. Introduction
In the context of supernova remnant (SNR) paradigmfor the origin of cosmic rays (CR), particle accelera-tion takes place at shocks associated with the super-nova explosion, and it is described by the non lineartheory of di ff usive shock acceleration (see [1] for a re-view). Energy and momentum conservation at the shockin the presence of accelerated particles leads to twostraightforward conclusions: 1) since part of the energyis channeled into particle acceleration, the thermal en-ergy (hence the temperature) of the downstream gas isexpected to be lower than in the absence of CRs; 2)the dynamical reaction of CRs induces the formationof a precursor upstream of the shock, which results ina deviation of the CR spectrum from a simple power-law behavior. Optical spectra observed from so calledBalmer dominated shocks can be used to test these pre-dictions. In fact some young SNR shocks emit opticallines mainly consisting of Balmer H α emission. The first detection of bright H α filaments around theremnants of Kepler, Tycho and the Cygnus Loop was re-ported by [2]. A peculiarity of this emission is the weak-ness of forbidden metal lines which implies an hightemperature of the emitting region so that radiative cool-ing and recombination are unimportant. The interpreta-tion of such optical emission remained a mystery up tothe seminal works of [3, 4] who proposed that it canbe produced by shocks propagating thorough a partiallyneutral gas. Their model was able to explain the inten-sity, spectrum and width of the filaments observed inTycho’s SNR, including the weakness of the forbiddenmetal lines. A peculiarity of Balmer dominated shocks,firstly reported by [4] for the Tycho’s SNR, is that theH α line is formed by two distinct components, a narrowline with a FWHM of few tens km / s and a broad linewith a FWHM of the order of the shock speed. Sim-ilar optical profiles are now observed from a bunch ofyoung SNRs both in the Galaxy and in the Large Mag-1 . Morlino / Nuclear Physics B Proceedings Supplement 00 (2018) 1–9 ellanic Cloud (for a review see [5]).SNR shocks are collisionless and when they propa-gates in partially ionized medium, only ions are heatedup and slowed down, while neutral atoms are una ff ectedto first approximation. However, when a velocity dif-ference is established between ions and neutrals in thedownstream of the shock, the processes of charge ex-change (CE) and ionization are activated and this ex-plain the existence of two distinct lines: the narrowline is emitted by direct excitation of neutral hydro-gen after entering the shock front while the broad lineresults from the excitation of hot hydrogen populationproduced by CE of cold hydrogen with hot shocked pro-tons. As a consequence, optical lines are a direct probeof the conditions at the shock, in particular the widthof the narrow and broad components reflect the temper-ature upstream and downstream of the shock, respec-tively. Now, as already pointed out, if the shock accel-erate particles e ffi ciently, the shock’s structure will bemodified, altering the plasma temperature and inducingthe formation of a CR precursor. Hence, Balmer emis-sion could be used to provide an indirect measurementof the CR acceleration e ffi ciency and even to gather in-formation on the CR induced precursor.The first clue that Balmer emission could provideevidence for the presence of accelerated particles wasput forward as a possible way to explain the anoma-lous width of narrow Balmer lines reported for the firsttime by [6] and [7]: FWHM ranging from 30 to 50 kms − was detected for four SNRs in the LMC and for theCygnus Loop, implying a pre-shock temperature around25,000-50,000 K. Values in the same range have beenreported afterwards for other SNRs (see, e.g.[8]). If thiswere the ISM equilibrium temperature there would beno atomic hydrogen, implying that the pre-shock hy-drogen is heated by some form of shock precursor in aregion that is su ffi ciently thin so that collisional ioniza-tion equilibrium cannot be established before the shock.Several explanations for this anomaly were proposedbut only two of them was considered realistic: 1) theneutral-induced precursor and 2) the CR-induced pre-cursor.Let us comment the former possibility first. Whenfast, cold neutrals undergo CE interactions with theslower hot ions downstream of the shock, some frac-tion of the resulting hot neutrals can cross the shockand move upstream. The relative velocity between thesehot neutrals and the upstream ions triggers the onsetof CE and ionization interactions that lead to the heat-ing and slowing down of the ionized component of theupstream fluid. The system then tends to develop a neutral-induced shock precursor, in which the fluid ve- locity gradually decreases, and even more important, thetemperature of ions increases as a result of the energyand momentum deposition of returning neutrals. A firstattempt at investigating the broadening of the narrowline component induced by the neutral precursor wasmade by [9], using a simplified Boltzmann equation forneutrals, but their calculation does not show any appre-ciable change of the narrow line width. This conclu-sion was confirmed by [10, 11], using a fully kinetic ap-proach able to describe the interaction between neutralsand ions in a more accurate way. The physical reason isthat the ionization length-scale of returning hot neutralsin the upstream is always smaller than the CE length-scale of incoming cold neutrals. Interestingly enough,[11] showed that the neutral precursor could produce adi ff erent signature, namely the presence of a third inter-mediate Balmer line due to hydrogen atoms that under-gone charge exchange with warm protons in the neutralprecursor.The second and more promising possibilities to ex-plain the anomalous width of narrow lines requires ef-ficient particle acceleration which leads to the forma-tion of a CR-induced precursor, where ionized plasmais heated before crossing the shock. If the precursoris large enough, CE can occur upstream leading to abroader narrow Balmer line. The first attempt to modelthis scenario was done by [12] using a two-fluid ap-proach to treat ions and CRs but neglecting the dynam-ical role of neutrals. A di ff erent model was proposedby [13] where momentum and energy transfer betweenions and neutrals is included, but the profile of the CR-precursor is assumed a-priori . Both works concludedthat the observed width of 30-50 km s − can be ex-plained using a low CR acceleration e ffi ciency.From the theoretical point of view, the main di ffi -culty in describing the structure of a collisionless shockpropagating in a partially ionized medium is that neu-trals have no time to reach thermalization and cannot betreated as a fluid. Steps forward in relaxing the fluidassumption have been made by [14] and [15], even ifthese works neglect the modification induced by neu-trals upstream of the shock. A more reliable interpreta-tion of Balmer line profile requires an accurate descrip-tion of the CR acceleration process where the mutualinterplay between CRs, neutrals, ionized plasma andmagnetic turbulence is simultaneously taken into ac-count. Such an approach has been developed by [16]using a semi-analytical technique. This work showedthat the main physical e ff ect able to broaden the nar-row line is the damping of magnetic turbulence in theCR precursor while the adiabatic compression alone isine ff ective. Hence the observed widths are compatible2 . Morlino / Nuclear Physics B Proceedings Supplement 00 (2018) 1–9 also with large acceleration e ffi ciency provided the rightlevel of magnetic damping.E ffi cient CR acceleration can also a ff ect the width ofbroad lines. In fact, when a sizable fraction of the rampressure is channeled into non-thermal particles, theplasma temperature behind the shock is expected to belower, and this should reflect in a narrower width of thebroad H α line. Remarkably, there are clues of this phe-nomenon in two di ff erent remnants, RCW 86 [17, 18],and SNR 0509-67.5 in the LMC [19, 20]. In both casesthe measured FWHM of the broad lines is compatiblewith theoretical predictions only assuming fast electron-proton equilibration downstream of the shock, a con-clusion which seems to be at odds with both theoreticalmodels and observations [21].
2. The kinetic approach
Here we summarize the kinetic model for shock par-ticle acceleration in presence of neutrals developed in[10, 11, 16]. We consider a stationary system with aplane-parallel shock wave propagating in a partially ion-ized proton-electron plasma with velocity V sh along the z direction. The fraction of neutral hydrogen is fixed atupstream infinity where ions and neutrals are assumedto be in thermal equilibrium with each other. The shockstructure is determined by the interaction of CRs andneutrals with the background plasma. Both CRs andneutrals profoundly change the shock structure, espe-cially upstream where both create a precursor: the CR-induced precursor reflects the di ff usion properties of ac-celerated particles and has a typical spatial scale of theorder of the di ff usion length of the highest energy parti-cles. The neutral-induced precursor develops on a spa-tial scale comparable with a few interaction lengths ofthe dominant process between CE and ionization. Thedownstream region is also a ff ected by the presence ofboth CRs and neutrals and the velocity gradients thatarise from ionization have a direct influence on the spec-trum of accelerated particles. A self consistent descrip-tion of shock particle acceleration in presence of neutralHydrogen, requires to consider four mutually interact-ing components: thermal particles (protons and elec-trons), neutrals (hydrogen), accelerated protons (CRs)and turbulent magnetic field. We neglect the presenceof helium and heavier chemical elements. The interac-tion terms make the system highly non linear and thesolution is found using a iterative scheme similar to theone we introduced in some previous works [22, 23, 10].Let us start with the description of neutrals. The maindi ffi culty arises from the fact that neutrals cannot be de-scribed as a fluid, because in the downstream the colli- sional ionization length is smaller than the equilibrationlength. Hence neutrals are described kinetically, usingthe stationary Boltzmann equation to calculate the evo-lution of the velocity distribution function, f N ( ~ v , z ), v z ∂ f N ( ~ v , z ) ∂ z = β N f i ( ~ v , z ) − (cid:2) β i + β e (cid:3) f N ( ~ v , z ) , (1)where z is the distance from the shock (which is locatedat the origin), v z is the velocity component along the z axis and the electron and proton distribution functions, f i ( ~ v , z ) and f e ( ~ v , z ), are assumed to be Maxwellian ateach position. The collisional terms, β k f l , describe theinteraction (due to CE and / or ionization) between thespecies k and l . The interaction rate β k is formally writ-ten as β k ( ~ v , z ) = Z d w v rel σ ( ~ v rel ) f k ( ~ w , z ) , (2)where v rel = | ~ v − ~ w | and σ is the cross section for therelevant interaction process. More precisely, β N is therate of CE of an ion that becomes a neutral, β i is the rateof CE plus ionization of a neutral due to collisions withprotons, while β e is the ionization rate of neutrals due tocollisions with electrons. A full description of the crosssections used in the calculations can be found in [11].The isotropic distribution function of CRs satisfiesthe following transport equation in the reference frameof the shock: ∂∂ z " D ( z , p ) ∂ f ∂ z − u ∂ f ∂ z + dudz p ∂ f ∂ p + Q ( z , p ) = . (3)The z -axis is oriented from upstream infinity ( z = −∞ )to downstream infinity ( z = + ∞ ) with the shock locatedat z =
0. We assume that the injection occurs only at theshock position and is monoenergetic at p = p inj . Thedi ff usion properties of particles are described by the dif-fusion coe ffi cient D ( z , p ). We assume Bohm di ff usion inthe local amplified magnetic field: D ( z , p ) = cr L [ δ B ( z )] , (4)where r L ( δ B ) = pc / [ e δ B ( z )] is the Larmor radius in theamplified magnetic field. The calculation of δ B is de-scribed assuming that the only turbulence which scat-ters particles is the one self-generated by the particlesthemselves through the resonant streaming instability.These waves are also damped due to several processes.In particular, when the plasma is not fully ionized, thepresence of neutrals can damp Alfv`en waves via ion-neutral damping. The equation for transport of wavescan be written as: ∂ z F w = u ( z ) ∂ z P w + P w [ σ CR ( k , z ) − Γ TH ( k , z )] , (5)3 . Morlino / Nuclear Physics B Proceedings Supplement 00 (2018) 1–9 where F w ( k , z ) and P w ( k , z ) are, respectively, the energyflux and the pressure per unit logarithmic bandwidth ofwaves with wavenumber k . σ is the growth rate of mag-netic turbulence, while Γ TH is the damping rate. Forresonant wave amplification the growth rate of Alfv´enwaves is: σ CR ( k , x ) = π v A ( x ) P w ( k , x ) " p v ( p ) ∂ f ∂ x p = ¯ p ( k ) , (6)where p = ¯ p ( k ) = eB / km p c is the resonant momen-tum. The damping of the waves is mainly due to non-linear Landau damping and ion-neutral damping. Forthe sake of simplicity here we adopt a phenomenologi-cal approach in which the damping results in a genericturbulent heating (TH) at a rate Γ TH = η TH σ CR . Thisexpression assumes that a fraction η TH of the power inamplified waves is locally damped and results in heatingof the background plasma.Finally we need to describe the dynamics of the back-ground plasma which is a ff ected by the presence of ac-celerated particles and by CE and ionization of neu-trals. Protons and electrons in the plasma are assumedto share the same local density, ρ i ( z ) = ρ e ( z ), but notnecessarily the same temperature, i.e., T i ( z ) may be dif-ferent from T e ( z ). The equations describing the conser-vation of mass, momentum and energy taking into ac-count the interactions of the plasma fluid with CRs are: ∂∂ z (cid:2) ρ i u i + µ N (cid:3) = , (7) ∂∂ z h ρ i u i + P g + P c + P w + P N i = , (8) ∂∂ z " ρ i u i + γ g P g u i γ g − + F w + F N = − u i ∂ P c ∂ z +Γ P w . (9)Here µ N = m H R d vv k f N , P N = m H R d vv k f N and F N = m H / R d vv k ( v k + v ⊥ ) f N are respectively thefluxes of mass, momentum and energy of neutrals alongthe z direction (labelled as k ). They can be easily com-puted once the neutral distribution function is known. P w and F w are the pressure and energy flux of waves,while P c is the CR pressure computed from the CR dis-tribution function: P c ( z ) = π Z d p p v ( p ) f ( z , p ) . (10)The dynamical role of electrons in the conservationequations is usually neglected due to their small mass.However, collective plasma processes could contributeto equilibrate electron and proton temperatures, at least partially. If the equilibration occurs in a very e ffi cientmanner, the electron pressure cannot be neglected andthe total gas pressure needs to include both the protonand electron contributions, namely P g = P i + P e = P i (1 + β ), where β ( z ) ≡ T e / T i is the electron to protontemperature ratio and is taken here as a free parameter.While it is well established that electron-ion equilibra-tion in the downstream might be only partial [24, 25], inthe presence of a precursor (either induced by the CRsor by the neutrals), also upstream of the shock the levelof equilibration becomes an unknown.In order to solve the set of non-linear equations in-volving neutrals, ions, CRs and magnetic field, we adoptan iterative method that is fully described in [16]. Theinput quantities are the values of the shock velocity andall environmental quantities at upstream infinity, wherethe distribution function of neutrals is assumed to beMaxwellian at the same temperature as that of ions. Atthe end the calculation provides the distribution functionof neutrals as well as the spatial and velocity profile ofBalmer emission.
3. CR-precursor vs. neutral-precursor
The formalism presented above represents the firsttheory of particle acceleration at collisionless shocks inthe presence of neutral atoms and allows us to calculatethe shock structure, the spectrum of accelerated parti-cles and the Balmer emission from the shock region.A good way to visualize the modification induced onthe shock by the presence of both neutrals and CRs isto look at the temperature profile of ions in the shockregion. In the top panel of Fig. 1 we compare the tem-perature profile for a case with and without CRs. Wechose a test case with values of parameters typical ofa SNR expanding in the cold ISM, at the beginning ofthe Sedof-Taylor phase, i.e. V sh = − , totalISM density of 0.1 cm − with 50% of ionization fractionand temperature T ISM = K. The black-tick solid lineshows the temperature profile without CRs: the temper-ature increase produced ahead of the shock, on the scaleof ∼ cm is entirely due to the return flux of neu-trals which deposit upstream a fraction of energy sub-tracted from the downstream. Indeed the length-scalecorresponds to the collisional ionization length of re-turning neutrals with upstream ions. The remaining thincurves show the case when CR acceleration is turnedon. For all these curves we assume the same accelera-tion e ffi ciency of 40% (determined by the injection pa-rameter ξ inj = .
5) and the same maximum proton en-ergy of 50 TeV, but we change the damping e ffi ciencyof magnetic turbulence. When the damping is absent,4 . Morlino / Nuclear Physics B Proceedings Supplement 00 (2018) 1–9 V sh = − , n = . − , h N = . B = µ G. When CRacceleration is turned on, we assume ξ inj = . p max =
50 TeV / c.The thick solid (black) line refers to the case with no CRs. The thin(red) solid line refers to the case with CRs but no damping of magneticturbulence (i.e. η TH = ). The remaining thin curves are calculated forincreasing values of η TH , as labelled. The dashed and dotted rectan-gles mark the CR and the neutral-induced precursor, respectively. the temperature profile is only slightly di ff erent fromthe case without CRs, the di ff erence being due to theadiabatic compression produced by the CR pressure,while, when the damping is turned on, the temperatureincreases in the whole CR-precursor in a way propor-tional to the amount of damping. Notice that the typicalCR-precursor length is D ( p max ) / V sh ≈ × δ B − µ G cm,where δ B is the amplitude of Alfv´en waves which res-onate with particles at p = p max . We further notice thatall cases with e ffi cient CR acceleration have a tempera-ture in the downstream smaller than ∼
40% with respectto the case without CRs.The shape of the spatially-integrated Balmer lineemission is plotted in the top panel of Fig. 2, while thebottom panel shows a zoom in the region of the narrowBalmer lines. The curves refer to the same cases as inFig. 1, labelled as indicated. The width of the broadcomponent of the Balmer line is appreciably reducedwhen CR acceleration is turned on, but the results arenot sensitive to the amount of TH. On the other hand, thenarrow Balmer line becomes broader when CR accel-eration is e ffi cient; the e ff ect is more pronounced whennon-negligible TH is taken into account. Hence, the dis-tribution function of neutrals becomes broader mainlybecause of the scattering with a warmer ion distributionin the far precursor (i.e., where TH is more e ff ective),rather than because of the neutral return flux, which op-erates only within a few CE interaction lengths from thesub-shock. -4 -3 -2 -1 -2000 -1000 0 1000 2000 H α e m i ss i v i t y v x [km/s]V sh = 4000 km/sn = 0.1 cm -3 p max = 50 TeV/c no CR ξ inj = 3.5; η TH = 0.00.20.50.810 -2 -1 -100 -50 0 50 100 H α e m i ss i v i t y v x [km/s]V sh = 4000 km/sn = 0.1 cm -3 p max = 50 TeV/c no CR ξ inj= 3.5; η TH = 0.00.20.50.8 Figure 2. Volume-integrated line profile of Balmer emission for thesame cases shown in Fig. 1. The lower panel shows a zoom in of thenarrow line region, showed with a shadow box in the top panel. Thethick solid line shows the case without CRs, while di ff erent thin linesare calculated at fixed ξ inj = . ff erent values of the THe ffi ciency as labelled.
4. Application to young SNRs
In this paragraph we compare the results of the ki-netic theory for Balmer dominated shocks with few no-ticeable cases of young SNRs. We concentrate only onthe two more direct observables from Balmer emission,namely the width of the spatially-integrated broad andnarrow lines. Other possible observables, like the spa-tial profile, the intermediate line or the narrow-to-broadintensity ratio could also be used but, in order to con-straint the model, we need more accurate data that theones available in the literature up to know. In the followwe analyze the broad Balmer emission from three rem-nants, SN 1006, RCW 86 and SNR 0509-65.7, whilefor the narrow line we show only one single case, theTycho’s remnant.The width of the broad Balmer line is probably themost powerful tool to infer the presence of non-thermal5 . Morlino / Nuclear Physics B Proceedings Supplement 00 (2018) 1–9
500 1000 1500 2000 2500 3000 3500 4000 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 F W H M b r oad li ne [ k m / s ] V sh [km/s] SNR 0509-67.5 (SW)SN1006 (NW)RCW86 (E) T e /T p = 0.010.10.51 Figure 3. Measured FWHM of the broad Balmer line as a function ofthe shock speed for three di ff erent remnant: RCW 86 (three di ff erentlocations, one in the northeast (open circle) and two location in thesoutheast (filled square), data from [17] assuming a distance from theremnant of 2.5 kpc); northwest rim of SN 1006 [27]; southwest rim ofSNR 0509-67.5 (the FWHM is taken from [19] while the uncertaintyon V sh is taken from the theoretical model in [20]). Lines show thetheoretical prediction without CR acceleration for di ff erent values ofelectron to proton temperature ratio in the downstream [16]. particles. If the velocity of the shock is known, thewidth of the broad line depends mainly on two factor:the electron-to-proton temperature ratio, and the CR ac-celeration e ffi ciency, while it does not depend on thetotal ISM density and has a weak dependence on theionization fraction. In Fig. 3 we show the theoreticalprediction of the FWHM of the broad lines as a functionof the shock speed and for di ff erent value of T e / T p , inthe absence of CRs. The plot also shows the data for thethree SNRs mentioned above. When measured data liebetween the top and the bottom lines, they are in prin-ciple compatible with the absence of CRs, unless one isable to measure the electron temperature, breaking thedegeneracy between di ff erent lines. In the following wediscuss separately each single remnant. The remnant of SN 1006 is a special case in that itpresents hints of e ffi cient particle acceleration only inthe northeastern (NE) and in the southwestern (SW) re-gions. Here non-thermal X-ray have been detected, con-centrated in thin filaments. As extensively discussedin literature, the thickness of X-ray filaments is inter-preted as due to rapid synchrotron losses of electronsin a strong magnetic field ( ∼ µ G), which could beproduced by CR-induced amplification (if the CR ac-celeration is e ffi cient). Moreover the same regions havebeen detected in γ -rays emission [26]. A further indi- rect indication supporting e ffi cient CR acceleration isthe distance between the contact discontinuity and theforward shock, which is smaller in the NE and SW withrespect to the rest of the remnant. In fact, when a nonnegligible fraction of the shock kinetic energy is con-verted into CRs, the downstream plasma become morecompressible and a reduced distance is expected.Now, data for the FWHM of the broad Blamer lineshown in Fig. 3 (shaded box) are taken from the NW re-gion [27] where none of the above signatures have beendetected. Remarkably enough, the detected FWHM isfully compatible with theoretical expectation withoutCRs and assuming a low level of electron-proton equi-libration ( T e / T p < . − [8], corresponding toan ISM temperature of 10 K, compatible with absenceof a CR precursor. It would be extremely interestingto measure the width of Balmer lines also from the NEand the SW, but the emission in those regions is so faintthat tens of hours of observation are needed to reach therequired signal to noise ratio.
RCW 86 is a shell like SNR and a γ -ray source, de-tected both in GeV range by FermiLAT and in the TeVrange by HESS. The NE part also shows non-thermal X-rays, suggesting a possible e ffi cient production of CRs.The remnant presents many Balmer filaments aroundthe external shell and, recently, the proper motion andthe line width of these filaments have been measured[17]. Here we summarize the results presented in [18],where the analysis has been concentrated on the east-ern part of the remnant because this is the region show-ing the highest shock speed, hence the one with a largerprobability to accelerate CRs. Because the proper mo-tion is known, the results depends on the assumed dis-tance from us, which is very uncertain, but generallybound between 2 and 3 kpc. The most quoted value inliterature is 2.5 kpc, which will be used in the followingdiscussion. The three data points shown in Fig. 4 repre-sent the FWHM measured in three di ff erent regions ofthe eastern part of the remnant by [28]. The error bars inthe shock speed reflect the error in the measured propermotion. The three point seem to be marginally compati-ble with absence of CR acceleration if we assume a fullelectron-proton equilibration. On the other hand this as-sumption is at odd with the results by [28], where, usingthe thermal X-ray emission, the authors were able to in-fer the electron temperature in the same regions wherethe Balmer lines have been detected. These values can6 . Morlino / Nuclear Physics B Proceedings Supplement 00 (2018) 1–9 ff erent regions of the easternpart of RCW 86 by [28] (see their Fig. 3). Lines show the theoreticalprediction without CRs as in Fig. 3. The filled circles show the valuethat the FWHM should have in these three locations if one accountfor the measured electron temperature and if no e ffi cient accelerationwere present. be used as upper limits for the electron temperature be-hind the shock, because they are obtained integratingonto a large region in the downstream where Coulombcollisions can enhance the electron temperature. Thisinformation allows us to fix an upper limit to the valueof T e / T p and to break the degeneracy between di ff erenttheoretical curves. We get T e / T p . . ∼ d = < − , hence we do not expect particles accelerated up tovery high energies. Moreover, if the neutral fraction is > ff ect the acceleration in thedirection to make the spectrum steeper, to the point thatthe non-thermal energy is dominated by particles witha momentum close to the injection momentum. If thiswere the case, the γ -ray spectrum observed by Fermi-LAT and HESS could not be explained by hadronic in-teraction, but is more probably due to electron inverse-Compton, has suggested in [29] on the basis of the hardspectrum measured by FermiLAT. The Balmer emission from SNR 0509-67.5 has beenstudied in [20]. SNR 0509-67.5 is located in the LMC,so that its distance from the Sun is known to be 50 ± ± ffi -ciency. If the shock moves faster than ∼ − ,one can conclude that particle acceleration must be tak-ing place with an e ffi ciency of several tens of percent.For lower shock velocity the evidence of particle accel-eration becomes less clear because of the uncertaintyin the electron-ion equilibrium downstream. We canspeculate that if T e / T p is as low as the value inferredin SN 1006, than the acceleration e ffi ciency of the SWrim should be & ff erent techniques, which point towards an inverserelation between the electron-to-ion temperature ratioand the shock speed [21]. On the other hand none ofthese measurement has been done for SNR 0509-67.5up to now. The Tycho’s SNR is the best known candidate whereto look for e ffi cient CR acceleration mainly because theobserved γ -ray spectrum is very steep and is di ffi cultto explain it using leptonic processes, while pion decayproduced in hadronic collisions can fit the observationsvery well, assuming a CR acceleration e ffi ciency ∼ ffi ciency (namelyRadio and X-ray spectrum, radio end X-ray morphol-ogy, distance between contact discontinuity and forwardshock). Unfortunately the Balmer emission in Tycho isfaint even if it is present all over around the remnant. Inspite of this there is a small region of the shock, called knot-g where the Balmer emission is enhanced, proba-bly due to a larger ISM density in that region. These re-gion has been analyzed by several authors and presentstwo interesting anomalies which could be related to ef-ficient acceleration.7 . Morlino / Nuclear Physics B Proceedings Supplement 00 (2018) 1–9
1) A gradual increase of H α intensity has been mea-sured just ahead of the shock front [31]. This has beeninterpreted as emission from the thin shock precursor( ∼ ′′ which implies a thickness of ∼ × cm for adistance of 3 kpc) likely due to CRs. If confirmed, thisdetection would represent the first direct proof of theexistence of a CR precursor. On the other, hand Balmeremission from the upstream can be produced also bythe neutral-induced precursor, as showed in [11], and,in order to distinguish between these two possibilities,a careful modeling of the shock is required, taking intoaccount the the complex interaction between the CR andthe neutral induced precursor. At the moment the mostpromising technique seems to be the kinetic theory de-veloped in [16].2) The FWHM of the narrow component has beenmeasured to be 44 ± − [8]. Such values imply-ing a pre-shock temperature between 36,000 and 52,000K. If this were the ISM equilibrium temperature therewould be no atomic hydrogen, implying that the pre-shock hydrogen is heated by some form of shock precur-sor in a region that is su ffi ciently thin so as to make col-lisional ionization equilibrium before the shock unfeasi-ble. The CR precursor is the most plausible candidate toexplain such a broadening of the narrow line width. Tosupport this statement in Fig. 5 we compare the valuemeasured from the knot-g in Tycho with the theoreti-cal expectation calculated using the kinetic theory. TheFWHM of the narrow Balmer line is plotted as a func-tion of the maximum momentum p max and for three dif-ferent value od the turbulent heating η TH = . , . ξ inj = . , . , .
8, which ap-proximately correspond to ǫ CR = . , . V sh = − and n = . − . The maxi-mum momentum, p max determines the spatial extent ofthe CR-induced precursor. Larger values of p max im-ply that there is more time (space) for depositing heat inthe upstream, and the width of the narrow Balmer linebroadens correspondingly. The e ff ect becomes morepronounced for larger values of the parameter η TH . Thenumber of free parameters is too large and the FWHMof the narrow line alone cannot be used to constrainnone of them. Nevertheless, the FWHM is an increasingfunction of all the three parameters, p max , η TH and ǫ CR ,hence if the shock speed, the upstream density and neu-tral fraction are known, we can put lower limit to theseparameters. Following this procedure, in the case of Ty-cho we get: p max &
40 TeV, η TH & . ǫ CR & Figure 5. FWHM of the narrow line as a function of the maxi-mum momentum of accelerated protons. The three panels refer to η TH = . , . ff erent injection parameter, ξ inj = . , . ǫ CR = . , . − , the total density 0.1 cm − with 50% of neutral fraction.The shadow band represent the FWHM measured from the knot-g inthe Tycho’s SNR.
5. Conclusions
The quest for the origin of Galactic CRs remainsopen. The search for their origin is di ffi cult and all newobservational input need to be considered very care-fully. Based mainly on the detection of gamma raysfrom several SNRs and on the morphology of the X-ray emission, which suggests strong magnetic field am-plification, SNRs are considered, now more than everbefore, as the most likely source of the bulk of CRs.Because the shocks produced by SN explosions oftenpropagate in partially ionized gas, the emission linesof neutral hydrogen have recently been recognized asa possible diagnostic tool for CRs. There are three dif-ferent signatures in the Balmer emission which couldreveal the presence of CRs: 1) a shock that is acceler-ating particles is expected to be less e ff ective in heatingthe background plasma, which is reflected in a Balmer-line emission with a smaller width than in the absenceof CR acceleration; 2) the presence of a CR precursorupstream of the shock could heat the upstream plasmaon a scale larger than the charge-exchange length but8 . Morlino / Nuclear Physics B Proceedings Supplement 00 (2018) 1–9 small than the ionization length, resulting in a largerwidth for the Balmer narrow line; 3) if the heating of theupstream plasma (especially electrons) is large enough,the collisional excitation between electrons and Hydro-gen atoms can produce Balmer emission also from theregion ahead of the shock.Remarkably all these signatures has been observedin some SNRs. Here we summarized the results ob-tained by the kinetic theory of collisionless shocks in thepresence of neutral hydrogen developed in [10, 11, 16]comparing the theoretical predictions with data on theBalmer line emission from four SNRs: SN 1006, RCW86, SNR 0509-67.5 and Tycho. While the NW regionof SN 1006 is compatible with absence of CR accelera-tion, the other three remnants presents anomalies in theBalmer lies which can be explained assuming an accel-eration e ffi ciency around ∼
10% which is remarkablythe amount of e ffi ciency required for SNRs to be themain sources of Galactic CRs. Balmer emission couldbe used also to gather information on the CR-precursorlength, on the magnetic damping in the precursor and onthe electron-to-proton temperature equilibration. Unfor-tunately the quality of data or the lack of important in-formation (like the shock proper motion) prevent a bet-ter determination of the CR acceleration e ffi ciency aswell as other parameter involved in the theory. How-ever the good news is that the amount and the quality ofthe data concerning the Balmer emission will increasesoon in the next few years. For this reason the analy-sis of Balmer emission can be regarded as one of themost powerful technique to study the process of shockacceleration and, more generally, to study the physics ofcollisionless shock. Acknowledgment
I want to thank P. Balsi, E. Amato, R. Bandiera andD. Caprioli for our long-term collaboration on this topicand on cosmic ray physics in general. I am also deeplygrateful to Nicoletta Mastroleo for her never-endingsupport and for sharing with me my doubts and uncer-tainties, solving many of them. This work has been par-tially founded through the NSF grant n.1306672, andit has been also supported by a grant from the SimonsFoundation and the hospitality of the Aspen Center forPhysics during September 2013.
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