The effect of Compton scattering on gamma-ray spectra of the 2005 January 20 flare

Research in AstronAstrophys2012 Vo112 No10，14391450 http：wwwraa-journa1org http：wwwioporgjournalsraa Researchin Astronomyand Astrophysics The effect of Compton scattering on gamma-ray spectra of the 2005 January 20 flare Wei Chen and WeiQun Gan Key Laboratory of Dark Matter and Space Astronomy，Purple Mountain Observatory，Chinese Academy of Sciences，Nanjing 210008，China；wchenpmoac Received 2012 March 23；accepted 2012 April 1 1 Abstract Gammaray spectroscopy provides a wealth of information about acceler- ated particles in solar flares，as well as the ambient medium with which these energetic particles interactThe neutron capture line(2223 MeV)，the strongest in the solar gammaray spectrum，forN1s in the deep atmosphereThe energy of these photons call be reduced via Compton scatteringWith the fully relativistic GEANT4 toolkit，we have carried out Monte Carlo simulations of the transport of a neutron capture line in solar flaresand applied them to the flare that occurred on 2005 January 20(X712B)， one of the most powerful gamma-ray flares observed bv R丑E SI during the 23rd solar cycleBy comparing the fitting results of different models with and without Compton scattering of the neutron capture 1ine，we find that when including the Compton scat- tering for the neutron capture linethe observed gammaray spectrum can be repro- duced by a population of accelerated particles with a very hard spectrum(s 23) The Compton effect of a 2223 MeV line on the spectra is therefore proven to be sig nificant，which influences the time evolution of the neutron capture line flux as wel1 The study also suggests that the mean vertical depth for neutron cal：lture in hydrogen forthis eventis about 8 g cm_。 Key words：Sun：flares-Sun：gamma-rays-scattering：Compton scattering 1 INTRoDUCTIoN In solar flares，both ions and electrons are accelerated to high energies；the interactions between them and ambient nuclei produce gammarays，positrons，neutrons，and mesons(eg，Chupp& Ryan 2009)Observations of gammaray emission give information about the nature of accelerated ions(see Kiener et a12006；Murphy et a12007)and about the physical properties of the ambient medium fGall 2005)The first observation(Chupp et a11973)of gamma-ray spectra firmly estab lished gammaray spectroscopy as a tool to study the active Sun(for example Ramaty et a11977； Murphy et a119871991) Gawlmaray line emissions in solar flares cover the energy band ranging from 04 to 8 MeV including lines from deexcitation of nuclei，the 2223 MeV line from neutron capture in hydrogen， and the 05 ll MeV line from positronannihilationNarrow de-excitation lines are produced by Suppoaed by the National Natural Science Foundation of China 1440 、 Chen QGan accelerated protons，alpha particles r口)，and 0He jnteracting with ambient heavier nuclei，while broad lines result from interactions of accelerated C，N，O and other heavier nuclei with the ambient H and HeThere are also many unresolvedlines that are blended with the gammaray continua Detailed theoretical calculatioas of a neutron caDture line(HuaLingenfelter 1987；Hua et a1 2002)and gammaray lines(Ramaty et a11979；Ramaty&Murphy 19871 produced by interac tions with accelerated ions were carried out beforeRecently，Murphy et a1(2009)extended the gammaray line production model by incorporating the cross sections computed from the TALYS code(KoningDuijvestijn 2006)This code was introduced into astrophysical calculations of nu- clear reaction rates fGoriely et a12008；Spyrou et a12008)and radioactive nuclei yields in solar flares(Tatischeff et al。2006) The traditional method used for studying the spectrum of accelerated ions in solar flares is to estimate the fluence ratio ofthe 4-7 MeV band to the neutron capture line(Murphy&Ramaty 1984； HHa&Lingenfelter 1987；Murphy et a12007)Gan(1998)developed a method which uses the time profilesof4-7MeVandtheneutroncapturelinetodeducethe spectralevolutionofacceleratedions Howeverwe should point out that the approach taken in our work is differentFirst and foremost， the whole solar deexcitation line spectrum was calculated under the assumption of various solar atmosphere abundances and accelerated ion compositions for a set of spectral indices of accelerated ionsThen by use of these template spectra，we fit the observed spectrum to determine the best parameters of the accelerated ion spectrum Compton scattering has been studied by severa1 authors fBaiRamaty 1978；Kontar et a1 2006)，who showed that this process can significantly modify the bremsstrahlung spectraHowever, these initial studies focused on subMeV energiesKotoku et a1(2007)，Oil the other hand，studied the Compton scattering of gammarays produced by energetic electrons via the bremsstrahlung process In the present work，we foCUS on the propagation of high energy photons experiencing a sexes of Compton scatteringsFor this purpose，we employed a Monte Carlo simulation toolkit named GEANT4which is widely used in experimental highenergy physics，to simulate the effect of Compton scattering on photons in a solar atmosphereIn Section 2 we present the calculations of the Comptonscattered continuum of the 2223 MeV neutron capture line as a function of depthIn Section 3we apply these results in RHESSI observations to see whether the Compton scattering on the 2223 MeV line has a significant effect on the gammaray spectraWe also present time pro- files of the neutron caDture depth and the corrected neutron capture line fluxW_e summarize our conclusions in Section 4 2 S玎 ULATIoN oF CoMPToN SCA1TERING It is well known that nuclear deexcitation lines are produced in optically thin regions，where the attenuation in the transpoprocess is negligibleHowever,the 2223 MeV neutron capture line is mostly produced in the deeper chromosphere or even me photosphere(Hua&Lingenfelter 1 987)， and the Compton scattering can modify the resulting emission characteristics The GEometry ANd Tracking version 4 fGEANT4)Monte Carlo simulation toolkit(Agostinelli et a12003)is a platform for simulations of the passage of particles through matterDeveloped at CERN bv expefimenthighenergy physicists，GEANT4 has the following important features： firstly,it allows a very flexible construction of the“geometry”in which particles interact；secondly, it can“trackan individual particle while monitoring its physical quantities，such as the energy， momentum，position，and time lag；thirdly，it allows us to incorporate the desked interactions，in me present caseincluding multiple scattering and capture of neutrons，and Compton scattering of photonsThe pair-production is neglected because at 2223 MeV in hydrogen plasma，the total pair- production CROSS section is approximately three orders of magnitude smaller than the total Compton cross sectionThe photoelectric effect is also neglected because it is only dominant at lower energy f100keV) The Effect of Compton Scattering on Gammaray Spectra 1441 Using the GEANT4 toolkit，we simulated the effects of Compton scattering on isotropic 2223 MeV photons passing through a spherical shel1 of the solar atmosphere with a series of depths， and recorded the escaping photonsenergies to determine the expected speca1 hen we compared these results with observations to constrain the depth or neutron capture processes The dependence of the Compton effect on the depth of neutron capture photon production was examined by carrying out a series of simulations in which 2223 MeV line photons were released at specific atmospheric depths with the HeH ratio of 01 Figure 1 shows the Compton scattered speca of the 2223 MeV line for different depths ranging from 10 to 500 g cm_。We can see that the Compton effect of the 2223 MeV line decreases sharply with decreasing neutron capture depthMoreover，the Comptonscattered continuum has a relatively flat spectrum at energies between the 2223 MeV line and 1 MeV and becomes steep below一1 MeV As a measure of the relative strength of the Compton scattered spectrum for VarlOUS depths，we assume that the Comptonscattered continuum 1s a uniform spectrum whlch extends from 0 to 2223 MeV Also we consider the average number of photons per keV of the scattered component at the l一2_22 MeV band as that of the whole Comptonscattered continuumHere we neglect the slope of the continuum below the 1 MeV band because positronannihilation photons and bremsstrahlung photons tend to dominate the counting rates at these energles in Hare spectra One can then define the Compton Efficiency as the ratio of the Compton-scattered continuum in- tensity to the intensity of the 2223 MeV lineWe have approximated these results by the expression D=1453CE+062 (1) Here CE= is Compton Efficiency， is the 2223 MeV line intensity and厶is the Compton scattered continuum intensityThis equation can be used to estimate the depth of production of the neutron capture 1ineFor flare analysis，it should be noted that D in Equation(1)is the lineof-sight depth in units of g cm一2Since the height and size of a flare is typically smal1 when compared to the solar radius，the transformation of the line of-sight depth to the vertical depth is just multiplied by a cosine of heliocentric angleAn accurate calculation must take into account the dependence of depth on the density of the solar atmosphere since it has a song updown asymmetryHowever，the preliminary simulation shows that there is no significant difference among scattered spectra resulting from backscattering at different depths，except a small effect that lowers the energy of the scattered spectrum Vestrand(1 990)developed a Monte Carlo code for photon transportation to simulate the neu- tron capture photons in a semiinfinite planeparallel atmosphereThe calculation indicated that the relative strength of the Compton tai1 increased with the depth of photon productionBased on the ad vanced Monte Carlo simulation code，GEANT4，we obtained similar resultsThe relmive strengths Of the scattered continuum are quantitatively consistent with each otherBy incorporating the depth and Compton efficiency into Equation(1)，it is easier to determine the neutron capture depth 3 APPLICATIoN AND DISCUSS10N To investigate the role of Compton scattering in the gammaray spectra、we study in detail the X712B event on 2005 January 20which occurred in active region 10720 at coordinates N14 W61 rwith a heliocentric angle of一65。1This flare was well observed by R The light curves are displayed in Figure 2The background subtraction was done with the same method as Smith et a1 (2003)taking 15 orbits before and after the flareThe temporal evolution of the flare 1ooks simple， with only one dominant Deak in gammaray energY bandsThe light curves in this period consist of three phases：risepeakand decayW_e have chosen the time interval 06：43：10-07：00：10 UT as our period of interestand divided this period into 16 intervals for later calculations RHESSI observations with a high spectra1 resolution in gammaray enable us to analyze its con tinuum and line profilesA fu11 count spectrum from 250 keV to l 6 MeV(the upper limit of energy The Effect of Compton Scattering on Gammaray Spectra 1443 fChen&Gan 2012)The abundances of both accelerated particles and ambient elements are coronal (Reames 1 995)except for the ambient HeH ratio of 01 and the accelerated p ratio ranging from 00 tO 10A11 nuclear cross sections are calculated from the TALYS code，which has been verified by many authorsWle have two assumptions in our calculationFirst，we assume a downwardisotropic angular distribution of the accelerated ionsShare et a1(2003)showed that an isotropic distribution in the downward direction is better than a simple downward beamSecond，considering the effect of both angular distribution of ions and diversification of the nuclear reactions，we assume the isotropic gammaray emissions are in the excited nucler rest flameIn addition，we consider the effect of the flare 1ocation on the de excitation line spectrumSince the flare location is a known quantity of measurement，the deexcitation gammaray spectrum，therefore，depends on the spectral index of accelerated ions and the alpha to proton ratio(oLP)The continuous emission in the gamma-ray band is mainly from electron bremsstrahlung and 7rdecayBecanse the shape of 7rdecay emission approximates a power-law distribution at energies below 1 6 MeV we assume the broken power-law shape represents the continuous emission which blends the electron bremsstrahlung emission and 丌一decay emission The fitting was done by using the SPEX package fSchwartz et a12002)with different models W did not consider the Compton scattering of the 2223 MeV line in our first fitting mode1The bestfitting result of the time interval 06：43：10-07：00：10 UT for this event is shown in Figure 3。 in which the green curve represents the continuous emission component with a broken power-law shapethe yellow curve and the pink curve represent the positronannihilation 1ine(05 l1 MeV) and the neutron capture line(2223 MeV)respectively，and the cVan curve re，resents the total de excitation lines which include the narrow lines and the continuaThe sum of all these contributions is presented by the red curve The Compton scattering of the 2223 MeV line was introduced in our second fitting model with an extra parameter of Comptonscattered continuum intensity Figure 4 shows the bestfit resultIn this casewe can see a large contribution in the lower energy spectrum resulting from the Comptonscattered continuum of the 2223 MeV line rpurple curve) Comparing both the bestfit results without and with Compton scattering in Figures 3 and 4 respectivelywe note that the shape and intensity of the 05 1 1 MeV line has hardly changed in both casesA similar situation is presented in the 2223 MeV lineHowever,the accelerated ion spectrum of the latter fitting model is much flatter than that of the formerTo determine the quality of fit，we use the statistic x。=(ct一zt) 。 (2) as defined in Murphy et a1(1990)，where c is the number of observed counts in channel i，mi is the number of counts predicted by the model and o- is the uncertainty of the measurement in channel iThe minimum values are 1291 and 1237 for these two models，respectivelyWe then plot a AX (AX =)( 一)(m2 in)contour map in the bottom right panel of Figures 3 and 4 which can be used to estimate the spectra1 index of ions and the alphatoproton ratioBy using a Monte Carlo simulation，the estimated A values with 1盯uncertainty are 89 and 10 for these two cases， respectivelyIn addition the residuals of fitting results are also improved with a smaller chisquare value in the second mode1especially near 2 MeV Both sets of evidence imply that the second model is betterMoreover,since the neutron capture photons are emitted at a vertical depth corresponding to a column density of about 10 一10 H cm一 (Hua&Lingenfelter l987)the Compton effect of 2223 MeV photons is naturally expected from a physical point of viewA11 results support that the second model is more reasonable in this eventThe corresponding Compton eficiency is about 14 for the best fitting result of the second mode1W_e thus infer from Equation f l 1 that the 1ineof-sight depth D is about 20 g cm DHe to the off-diagonal response from the neu仃on capture line being significant for the RHESSI,we then estimated that the intensity of the Compton scattered continuum has changed by about 20for an uncertainty of instrumental response changing 1 0in magnitude So the vertical depth for neutron capture on hydrogen in this event is 85土03土191 g cmzHere 1446 量 10 藏 毯 4， i i i j 1- 5 Chen& QGan Photon Energy(MeV) 0 2 4 6 8 Photon Energy(MeV) Fig5 Calculated deexcitation gammaray spectra versus the accelerated ion power-law indexThe left panel shows the spectrum from accelerated ions with power-law index s=20The right panel shows the spectrum from accelerated ions with powerlaw index s=50The solid curves show total deexcitation gammaray spectra of the solar flare at a heliocentric angle of 60。，while the dashed curve and the dotted curve show the broad lines and the unresolved components，respectively J。J。 ： ： uh Iinenu H：二二二 J。_。-。_ 。 。 。-。 Btr hlu gnu at25。k 一 Nude n砒I。nlinen唧 H _ L ： T T s 一o。 I I I 06：44 ： 06 ： ；仉 麟01 3 z 差 2 - 3 1- 5 J ：二： ut e nenu 1 。 。“： Annih nIim ： 二工_J 一 ： Bremsstrahlungflat 250keV一- 二二_ 二 pIctralind ： 06：48 06：52 06：56 07：呻06：44 Start Time(20-Jan05 06：43：10) 06：48 06：52 06：56 07：00 Start Time(20-Jan05 06：43：10) Fig6 Time evolution of the neutron capture line(2223 MeV)flux，positronannihilation line (05 1 1 MeV)flux，bremsstrahlung flux at 250 ke nuclear deexcitation line flux，and power-law index of accelerated ion spectrumThe starting time of the figure is 06：43：10 UTThe teft and right sides are bestfitting results without and with Compton scattering，respectively Besides the time profiles of line flux and spectral index，we also derive the time evolution of the Compton scattered componentIn Figure 7 we show the time profiles of the neutroncapture line flux，the Comptonscattered continuum intensity，and the Compton efficiency for the flareAs can be seen，there is a strong correlation between neutron capture line flux and the Comptonscattered 目0l0qd 5 4 j 2 蛊1 0 The Effect of Compton Scattering on Gammaray Spectra 一 f 。“：。nn“u-l“tensity 一 eC二omr。pntocn Eff：irceie。nec ytlh Start Time(2O-Jan05 06：43：10) Fig7 Time profiles of the neutron capture line flux(top pane1)，the Comptonscattered continuum intensity(middle pane1)，and the Compton efficiency and the neutron capture depth(bottom pane1) for the flareThe diamond symbol in the top panel represents the corrected neutron capture line flux 1447 continuum intensity of the 2223 MeV line during some time periodHowever,the latter rises faster and lasts only several minutesThe Compton effect looks important，at least around the peak of the flare Wle can also see from Figure 7 that the Compton e伯ciency rises rapidly at the early phaseand then declines graduallyCombining the