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Physics & Astronomy International Journal

Review Article Volume 2 Issue 2

Anomalous cosmic ray fluxes in diffusive shock acceleration processes in the heliosphere and in planetary and WR–nebulae

Ararat Yeghikyan

Byurakan Astrophysical Observatory (BAO), Armenia

Correspondence: Ararat Yeghikyan, Byurakan Astrophysical Observatory (BAO), Byurakan, 0213, Aragatzotn Province, Armenia, Tel 374?93?62?12?98

Received: December 28, 2017 | Published: April 23, 2018

Citation: Yeghikyan A. Anomalous cosmic ray fluxes in diffusive shock acceleration processes in the heliosphere and in planetary and WR–nebulae. Phys Astron Int J. 2018;2(2):149-153. DOI: 10.15406/paij.2018.02.00077

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Abstract

Based on the analogy between interacting stellar winds of planetary nebulae and WR–nebulae, on the one hand, and the heliosphere and the expanding envelopes of supernovae, on the other, an attempt is made to calculate the differential intensity of the energetic protons accelerated to energies of 100 MeV by the shock wave. The proposed one–parameter formula for estimating the intensity at 1–100 MeV, when applied to the heliosphere, shows good agreement with the Voyager–1 data, to within a factor of less than 2. The same estimate for planetary (and WR–) nebulae yield a value 7–8 (3–4) orders of magnitude higher than the mean galactic intensity value. The obtained estimate of the intensity of energetic protons in mentioned kinds of nebulae was used to estimate the doses of irradiation of certain substances, in order to show that such accelerated particles play an important role in radiation–chemical transformations in such nebulae.

Keywords: heliosphere, planetary, WR–nebulae, accelerated particles, dominance, hydrogenated amorphous carbon

Introduction

Flows of fast stellar winds interacting with the surrounding circumstellar medium form structures with (two) shock waves, where it is possible to accelerate protons and alpha particles at least up to energies about 1–100 MeV. These are usual scenario for expanding supernovae remnants,1 the heliosphere moving relative to the interstellar medium,2 expanding planetary (PN) and Wolf–Rayet nebulae (WRN) interacting with matter of previous more slow winds3–6 and references therein). After conversion of the intense slow stellar wind of the precursor AGB star of the nucleus of the planetary nebula (PN) into a fast, but less intense wind in a time of the order of several hundred years, a structure, formally analogous to the heliosphere is established–i.e. regions of the interaction of the solar wind with the surrounding interstellar space.3,7 The same result is true and for massive WR stars with stellar winds by 2–3 orders of magnitude larger mass loss rates and corresponding timescales.6 I first consider an approximate formula of accelerated particle fluxes in the heliosphere which is suitable for direct use in the considered scenario of interacting winds in PN and WRN and then apply such a formula to calculate the intensities of energetic particles in the heliosphere and in PN and WRN (Sections 2–3). Some applications of the obtained energetic spectra are discussed in Section 4 and the conclusion is given in Section 5.

Anomalous cosmic rays generated directly in the region of the heliospheric inner shock front from incoming suprathermal particles and their analogs in PN and WRN

There is a large number of analytical and numerical models of the intensity of energetic particles accelerated at the heliospheric shock, taking into account the whole variety of process features, such as the formation of a spectrum of energetic particles, the orientation of the magnetic field vector with respect to the normal of the shock front, the sources of suprathermal particles undergoing acceleration by Fermi–1 and transforming to energetic anomalous cosmic rays, shock compession ratio, etc.2,8–11 These theories give reasonable values and are consistent in the heliospheric case with direct observational data of the space probes Voyager 1 and 2.3 On the other hand such theories are too complicated and demand on careful consideration of shock conditions, magnetic fields configurations, diffusion and acceleration characteristic timescales, maximal possible energies to be reached, etc.2,9,10,12,13 On the other hand one may propose an approximate simple formula to connect a fraction of the flow kinetic energy to be converted to accelerated particles energy fluxes in the range of 1–100 MeV. Such a formula first proposed by Yeghikyan et al.4,5 for heliospheric conditions is used here to describe particle acceleration under conditions of steady–state interacting stellar winds in PN and WRN.

The point is that with the expansion of the PN (WRN) due to the increase of the PN (WRN) internal border ri its ability to form energetic particles decreases, as follows from Equation 1,4,5

η 1 4π M ˙ f V f 2 4π r i 2 = E 1 E max J E ( E )dE MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaeq4TdGwcfa4aaSaaaOWdaeaajugib8qa caaIXaaak8aabaqcLbsapeGaaGinaiabec8aWbaajuaGdaWcaaGcpa qaaKqzGeWdbiqad2eagaGaaKqbaoaaBaaajuaibaqcLbmacaWGMbaa juaGbeaajugibiaadAfal8aadaqhaaqcKfaG=haajugWa8qacaWGMb aajqwaa+=daeaajugWa8qacaaIYaaaaaGcpaqaaKqzGeWdbiaaisda cqaHapaCcaWGYbWcpaWaa0baaKazba4=baqcLbmapeGaamyAaaqcKf aG==aabaqcLbmapeGaaGOmaaaaaaqcLbsacqGH9aqpjuaGdaWdXbqa aKqzGeGaamOsaKqba+aadaWgaaqcKvaq=haajugWa8qacaWGfbaaju aGpaqabaWdbmaabmaapaqaaKqzGeWdbiaadweaaKqbakaawIcacaGL PaaajugibiaadsgacaWGfbaajqwba9FaaKqzadGaamyraSWdamaaBa aajqwba9FaaKqzadWdbiaaigdaaKazfa0=paqabaaapeqaaKqzadGa amyraSWdamaaBaaajqwba9FaaKqzadWdbiaad2gacaWGHbGaamiEaa qcKvaq==aabeaaaKqzGeWdbiabgUIiYdaaaa@80B5@ , (1)

Where M ˙ f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGabmytayaacaqcfa4aaSbaaKqbGeaajugW aiaadAgaaKqbagqaaaaa@3DCD@ –the fast stellar wind mass loss rate (g/s), V f MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOvaSWdamaaBaaajeaibaqcLbmapeGa amOzaaqcbaYdaeqaaaaa@3D11@ –the fast wind velocity (cm/s), J E ( E ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOsaSWdamaaBaaajeaibaqcLbmapeGa amyraaqcbaYdaeqaaKqba+qadaqadaGcpaqaaKqzGeWdbiaadweaaO GaayjkaiaawMcaaaaa@4097@ –differential intensity of accelerated particles (erg cm–2s–1sr–1MeV–1) and η MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaeq4TdGgaaa@3B1B@ –the fraction of fast wind kinetic energy converted into energetic particle energy E 1 E E max MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamyraSWdamaaBaaajeaibaqcLbmapeGa aGymaaqcbaYdaeqaamrr1ngBPrwtHrhAYaqeguuDJXwAKbstHrhAGq 1DVbacgaqcLbsapeGae8xFQqOaamyraiab=1NkekaadweajuaGpaWa aSbaaKqaGeaajugWa8qacaWGTbGaamyyaiaadIhaaSWdaeqaaaaa@511C@ after acceleration by the shock. By the way, according to the standard theory of the galactic cosmic ray origin under supernovae expanding shell conditions, usually η=0.10.3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaeq4TdGMaeyypa0JaaGimaiaac6cacaaI XaGaai4eGiaaicdacaGGUaGaaG4maaaa@4127@ ,1 but according to the exact numerical calculations and comparison with observations this values may be as large as η=0.5 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaeq4TdGMaeyypa0JaaGimaiaac6cacaaI 1aaaaa@3E4B@ .12,13

Now let’s check the estimate (1) from data for the solar wind, comparing the calculated values with the measurements of the Voyager 1 probe.14 Assuming

J E ( E )= J E ( E 1 ) ( E 1 /E ) γ , J p ( E )= J E ( E )/ E 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOsaSWdamaaBaaajeaibaqcLbmapeGa amyraaqcbaYdaeqaaKqba+qadaqadaGcpaqaaKqzGeWdbiaadweaaO GaayjkaiaawMcaaKqzGeGaeyypa0JaamOsaSWdamaaBaaajeaibaqc LbmapeGaamyraaqcbaYdaeqaaKqba+qadaqadaGcpaqaaKqzGeWdbi aadweal8aadaWgaaqcbasaaKqzadWdbiaaigdaaKqaG8aabeaaaOWd biaawIcacaGLPaaajugibiabgwSixNqbaoaabmaak8aabaqcLbsape GaamyraSWdamaaBaaajeaibaqcLbmapeGaaGymaaqcbaYdaeqaaKqz GeWdbiaac+cacaWGfbaakiaawIcacaGLPaaal8aadaahaaqcbasabe aajugWa8qacqaHZoWzaaqcLbsacaGGSaGaamOsaSWdamaaBaaajeai baqcLbmapeGaamiCaaqcbaYdaeqaaKqba+qadaqadaGcpaqaaKqzGe WdbiaadweaaOGaayjkaiaawMcaaKqzGeGaeyypa0JaamOsaSWdamaa BaaajeaibaqcLbmapeGaamyraaqcbaYdaeqaaKqba+qadaqadaGcpa qaaKqzGeWdbiaadweaaOGaayjkaiaawMcaaKqzGeGaai4laiaadwea l8aadaWgaaqcbasaaKqzadWdbiaaigdaaKqaG8aabeaaaaa@7067@ , (2)

Where E 1 =1 MeV MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamyraSWdamaaBaaajeaibaqcLbmapeGa aGymaaqcbaYdaeqaaKqzGeWdbiabg2da9iaaigdacaGGGcGaaeytai aabwgacaqGwbaaaa@42E5@ , γ=24 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaeq4SdCMaeyypa0JaaGOmaiabgkHiTiaa isdaaaa@3E83@ for the particles differential intensity at E= E 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamyraiabg2da9iaadweal8aadaWgaaqc KfaG=haajugWa8qacaaIXaaajqwaa+=daeqaaaaa@4226@ (in units particles cm–2s–1sr–1MeV–1),

J p ( E 1 )= J E ( E 1 ) E 1 = γ1 E 1 2 η 1 4π M ˙ f V f 2 4π r i 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOsaSWdamaaBaaajeaibaqcLbmapeGa amiCaaqcbaYdaeqaaKqba+qadaqadaGcpaqaaKqzGeWdbiaadweal8 aadaWgaaqcbasaaKqzadWdbiaaigdaaKqaG8aabeaaaOWdbiaawIca caGLPaaajugibiabg2da9Kqbaoaalaaak8aabaqcLbsapeGaamOsaK qba+aadaWgaaqcbasaaKqzadWdbiaadweaaSWdaeqaaKqba+qadaqa daGcpaqaaKqzGeWdbiaadweal8aadaWgaaqcbasaaKqzadWdbiaaig daaKqaG8aabeaaaOWdbiaawIcacaGLPaaaa8aabaqcLbsapeGaamyr aSWdamaaBaaajeaibaqcLbmapeGaaGymaaqcbaYdaeqaaaaajugib8 qacqGH9aqpjuaGdaWcaaGcpaqaaKqzGeWdbiabeo7aNjabgkHiTiaa igdaaOWdaeaajugib8qacaWGfbWcpaWaa0baaKqaGeaajugWa8qaca aIXaaajeaipaqaaKqzadWdbiaaikdaaaaaaKqzGeGaeq4TdGwcfa4a aSaaaOWdaeaajugib8qacaaIXaaak8aabaqcLbsapeGaaGinaiabec 8aWbaajuaGdaWcaaGcpaqaaKqzGeWdbiqad2eagaGaaSWaaSbaaKqa GeaajugWaiaadAgaaKqaGeqaaKqzGeGaamOvaSWdamaaDaaajeaiba qcLbmapeGaamOzaaqcbaYdaeaajugWa8qacaaIYaaaaaGcpaqaaKqz GeWdbiaaisdacqaHapaCcaWGYbWcpaWaa0baaKqaGeaajugWa8qaca WGPbaajeaipaqaaKqzadWdbiaaikdaaaaaaaaa@7C58@ (3)

Taking M ˙ f =2 10 -14 M /yr MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGabmytayaacaWcdaWgaaqcKfaG=haajugW aiaadAgaaKazba4=beaajugibiabg2da9iaaikdacqGHflY1caaIXa GaaGimaSWdamaaCaaajeaibeqaamXvP5wqSX2qVrwzqf2zLnharyGq HrxyUDgaiyGajugWa8qacaWFTaGaaGymaiaaisdaaaqcLbsacaWGnb qcfa4damaaBaaajeaibaqcLbmapeGaeSyMIugal8aabeaajugib8qa caGGVaGaaeyEaiaabkhaaaa@5B12@ , V f =400km/s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOvaSWdamaaBaaajeaibaqcLbmapeGa amOzaaqcbaYdaeqaaKqzGeWdbiabg2da9iaaisdacaaIWaGaaGimai aadUgacaWGTbGaai4laiaadohaaaa@4475@ , r i =100au MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOCaSWdamaaBaaajeaibaqcLbmapeGa amyAaaqcbaYdaeqaaKqzGeWdbiabg2da9iaaigdacaaIWaGaaGimai aadggacaWG1baaaa@42E4@ , η=0.1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaeq4TdGMaeyypa0JaaGimaiaac6cacaaI Xaaaaa@3E48@ , at γ = 2, 3, 4 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaeq4SdCMaaeiiaiabg2da9iaabccacaaI YaGaaiilaiaabccacaaIZaGaaiilaiaabccacaaI0aaaaa@423E@ gives J p ( E 1 ) 0.8, 1.6, 2.4 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOsaKqba+aadaWgaaqcbasaaKqzadWd biaadchaaSWdaeqaaKqba+qadaqadaGcpaqaaKqzGeWdbiaadweal8 aadaWgaaqcbasaaKqzadWdbiaaigdaaKqaG8aabeaaaOWdbiaawIca caGLPaaajugibiabloKi7iaacckacaaIWaGaaiOlaiaaiIdacaGGSa GaaeiiaiaaigdacaGGUaGaaGOnaiaacYcacaqGGaGaaGOmaiaac6ca caaI0aaaaa@4FDE@ particles cm–2s–1sr –1MeV–1, correspondingly, which with the accuracy of the factor 2 is coincident with Voyager 1 data of 1.4 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaeyisISRaaGymaiaac6cacaaI0aaaaa@3D4A@ .14,15 Of course, in a rigorous theory it is necessary to calculate the characteristic acceleration time depending on the compression parameters in the shock wave and compare it with the characteristic diffusion time, for which it is necessary to have independently calculated values of the diffusion coefficients as functions of the energy. Corresponding estimates and discussion are given in Yeghikyan et al.3,5,6 and may be summarized as follows: for a characteristic dynamical time in PN of 1000 years only a soft part of the spectrum (1–10 MeV) is formed, while in 100000 years, characteristic for WRN the complete spectrum in the range of 1–100 MeV is resulted. Because of very steep spectra in both cases the most importa 10 23 10 24   cm 2 / s MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaaGymaiaaicdal8aadaahaaqcKfaG=hqa baqcLbmapeGaaGOmaiaaiodaaaqcLbsacqGHsislcaaIXaGaaGimaS WdamaaCaaajqwaa+FabeaajugWa8qacaaIYaGaaGinaaaajugibiaa cckacaqGJbGaaeyBaSWdamaaCaaajqwaa+FabeaajugWa8qacaaIYa aaaKqzGeGaai4laiaabohaaaa@5179@ nt contribution into irradiation processes is related with the flux values near 1 MeV, At last but not least corresponding diffusion coefficient values are not larger than for energies of 1–100 MeV.16

Energetic particle intensities in the PN and WRN

Now let’s calculate differential intensities of energetic protons under conditions of young PN. Taking M ˙ f =4 10 -9 M /yr MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGabmytayaacaqcfa4aaSbaaKazba4=baqc LbmacaWGMbaajeaibeaajugibiabg2da9iaaisdacqGHflY1caaIXa GaaGimaKqba+aadaahaaqcKfaG=hqabaWexLMBbXgBd9gzLbvyNv2C aeHbcfgDH52zaGGbcKqzadWdbiaa=1cacaaI5aaaaKqzGeGaamytaK qba+aadaWgaaqcKfaG=haajugWa8qacqWIzkszaKazba4=paqabaqc LbsapeGaai4laiaabMhacaqGYbaaaa@5F08@ , V f =1000km/s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOvaKqba+aadaWgaaqcbasaaKqzadWd biaadAgaaSWdaeqaaKqzGeWdbiabg2da9iaaigdacaaIWaGaaGimai aaicdacaWGRbGaamyBaiaac+cacaWGZbaaaa@4590@ , r i = 10 16 cm MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOCaSWdamaaBaaajeaibaqcLbmapeGa amyAaaqcbaYdaeqaaKqzGeWdbiabg2da9iaaigdacaaIWaWcpaWaaW baaKqaGeqabaqcLbmapeGaaGymaiaaiAdaaaqcLbsacaWGJbGaamyB aaaa@45D2@ , η=0.1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaeq4TdGMaeyypa0JaaGimaiaac6cacaaI Xaaaaa@3E48@ ,17 then the equation (1) is used where already the concentration of fast wind near the shock wave is determined by the ratio n 1 = M ˙ f /( 4π r i 2 V f m p ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOBaSWdamaaBaaajeaibaqcLbmapeGa aGymaaqcbaYdaeqaaKqzGeWdbiabg2da9iqad2eapaGbaiaalmaaBa aajeaibaqcLbmapeGaamOzaaqcbaYdaeqaaKqzGeWdbiaac+cajuaG daqadaGcpaqaaKqzGeWdbiaaisdacqaHapaCcaWGYbWcpaWaa0baaK qaGeaajugWa8qacaWGPbaajeaipaqaaKqzadWdbiaaikdaaaqcLbsa caWGwbWcpaWaaSbaaKqaGeaajugWa8qacaWGMbaajeaipaqabaqcLb sapeGaamyBaSWdamaaBaaajeaibaqcLbmapeGaamiCaaqcbaYdaeqa aaGcpeGaayjkaiaawMcaaaaa@5745@ . Resulted values would be typical for young PN. According to the evolutionary models of PN18 in the earlier time the fast wind should be slower and the mass loss rate higher, so with corresponding input of the data M ˙ f =4 10 -7 M /yr MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGabmyta8aagaGaaSWaaSbaaKazba4=baqc LbmapeGaamOzaaqcKfaG==aabeaajugib8qacqGH9aqpcaaI0aGaey yXICTaaGymaiaaicdal8aadaahaaqcbasabeaatCvAUfeBSn0BKvgu HDwzZbqegiuy0fMBNbacgiqcLbmapeGaa8xlaiaaiEdaaaqcLbsaca WGnbWcpaWaaSbaaKqaGeaajugWa8qacqWIzkszaKqaG8aabeaajugi b8qacaGGVaGaaeyEaiaabkhaaaa@5A36@  and V f =100km/s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOvaSWdamaaBaaajeaibaqcLbmapeGa amOzaaqcbaYdaeqaaKqzGeWdbiabg2da9iaaigdacaaIWaGaaGimai aadUgacaWGTbGaai4laiaadohaaaa@4472@ results would be the same.

It should be stressed here that the average galactic value of J p ( E ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOsaSWdamaaBaaajqwaa+FaaKqzadWd biaadchaaKazba4=paqabaqcfa4dbmaabmaak8aabaqcLbsapeGaam yraaGccaGLOaGaayzkaaaaaa@4448@ at E = 1 MeV, is about of 2·10–4 particles·cm–2·s–1·sr–1·MeV–1,15 which means that at the inner border of young PN the estimated intensities of energetic particles are more than 7 orders of magnitude higher than the average galactic intensity. It is not surprising because, for example, at the heliosphere caused by the much less intense solar wind one can seе such dominance by more than 3 orders of magnitude.15 So, the young PN are locally intense sources of soft energetic particles and it is interesting to speculate about their probable observational consequences in PN.

We now turn to the calculation of the differential intensity of the energetic protons under the conditions of the WRN. We take M ˙ f = 10 5   M /yr MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGabmyta8aagaGaaSWaaSbaaKqaGeaajugW a8qacaWGMbaajeaipaqabaqcLbsapeGaeyypa0JaaGymaiaaicdal8 aadaahaaqcbasabeaajugWa8qacqGHsislcaaI1aaaaKqzGeGaaiiO aiaad2ealmaaBaaajeaibaqcLbmacqWIzkszaKqaGeqaaKqzGeGaai 4laiaabMhacaqGYbaaaa@4C91@ , V f =1500km/s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOvaSWdamaaBaaajeaibaqcLbmapeGa amOzaaqcbaYdaeqaaKqzGeWdbiabg2da9iaaigdacaaI1aGaaGimai aaicdacaWGRbGaamyBaiaac+cacaWGZbaaaa@4531@ , r i =3 10 18 cm MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOCaKqba+aadaWgaaqcbasaaKqzadWd biaadMgaaSWdaeqaaKqzGeWdbiabg2da9iaaiodacqGHflY1caaIXa GaaGimaSWdamaaCaaajeaibeqaaKqzadWdbiaaigdacaaI4aaaaKqz GeGaam4yaiaad2gaaaa@493F@ , η= 0.1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaeq4TdGMaeyypa0JaaeiiaiaaicdacaGG UaGaaGymaaaa@3EEA@ .19 On the inner boundary of the nebula (1 or 10 pc), the intensity of the energetic particles ( 1000 or 10, particles cm 2 s 1 sr 1 MeV 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaaGymaiaaicdacaaIWaGaaGimaiaabcca caWGVbGaamOCaiaabccacaaIXaGaaGimaiaacYcacaqGGaGaamiCai aadggacaWGYbGaamiDaiaadMgacaWGJbGaamiBaiaadwgacaWGZbGa eyyXICTaae4yaiaab2gal8aadaahaaqcbasabeaajugWa8qacqGHsi slcaaIYaaaaKqzGeGaeyyXICTaae4CaSWdamaaCaaajeaibeqaaKqz adWdbiabgkHiTiaaigdaaaqcLbsacqGHflY1caqGZbGaaeOCaSWdam aaCaaajeaibeqaaKqzadWdbiabgkHiTiaaigdaaaqcLbsacqGHflY1 caqGnbGaaeyzaiaabAfal8aadaahaaqcbasabeaajugWa8qacqGHsi slcaaIXaaaaaaa@6A13@ respectively) by more than several orders of magnitude, (7 or 5) exceeds the mid–galactic one. Thus, WRN also can be a powerful local source of energetic particles (with not very high energies) and it would be interesting to investigate their possible observational manifestations in the nebula itself.

Dust processing in PN and WRN by energetic particles

A point which may be discussed concerning the high fluxes of energetic particles in PN and WRN is connected with irradiation of complex chemical species, like water, fullerenes etc. Molecules of water are observed in PN both in the gas phase (water "fountain" and related masers in young PN)20–22 and in the solid phase (emission from crystal water ice).23–25

Here one may be only concerned with a simple estimation of the flux F( E ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOraKqbaoaabmaak8aabaqcLbsapeGa amyraaGccaGLOaGaayzkaaaaaa@3DDD@ of accelerated particles in the range of 1–100 MeV, dominant in the ionization of molecular hydrogen. Assuming r i = 10 16 cm MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOCaSWdamaaBaaajeaibaqcLbmapeGa amyAaaqcbaYdaeqaaKqzGeWdbiabg2da9iaaigdacaaIWaWcpaWaaW baaKqaGeqabaqcLbmapeGaaGymaiaaiAdaaaqcLbsacaqGJbGaaeyB aaaa@45CE@ , M ˙ f =1 10 -9 M /yr MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGabmytayaacaWcdaWgaaqcfasaaKqzadGa amOzaaqcfasabaqcLbsacqGH9aqpcaaIXaGaeyyXICTaaGymaiaaic dal8aadaahaaqcbasabeaatCvAUfeBSn0BKvguHDwzZbqegiuy0fMB NbacgiqcLbmapeGaa8xlaiaaiMdaaaqcLbsacaWGnbWcpaWaaSbaaK qaGeaajugWa8qacqWIzkszaKqaG8aabeaajugib8qacaGGVaGaaeyE aiaabkhaaaa@5679@ , V f =2000km/s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOvaSWdamaaBaaajeaibaqcLbmapeGa amOzaaqcbaYdaeqaaKqzGeWdbiabg2da9iaaikdacaaIWaGaaGimai aaicdacaqGRbGaaeyBaiaac+cacaqGZbaaaa@4527@ , one can write for the intensity J( E=1MeV )=1.0 10 4  particles cm 2 s 1 sr 1 MeV 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOsaKqbaoaabmaak8aabaqcLbsapeGa amyraiabg2da9iaaigdacaqGnbGaaeyzaiaabAfaaOGaayjkaiaawM caaKqzGeGaeyypa0JaaGymaiaac6cacaaIWaGaeyyXICTaaGymaiaa icdal8aadaahaaqcbasabeaajugWa8qacaaI0aaaaKqzGeGaaeiOai aabchacaqGHbGaaeOCaiaabshacaqGPbGaae4yaiaabYgacaqGLbGa ae4CaiabgwSixlaabogacaqGTbWcpaWaaWbaaKqaGeqabaqcLbmape GaeyOeI0IaaGOmaaaajugibiabgwSixlaabohal8aadaahaaqcbasa beaajugWa8qacqGHsislcaaIXaaaaKqzGeGaeyyXICTaae4Caiaabk hal8aadaahaaqcbasabeaajugWa8qacqGHsislcaaIXaaaaKqzGeGa eyyXICTaaeytaiaabwgacaqGwbWcpaWaaWbaaKqaGeqabaqcLbmape GaeyOeI0IaaGymaaaaaaa@7572@ , at dE=1 MeV MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamizaiaadweacqGH9aqpcaaIXaGaaiiO aiaab2eacaqGLbGaaeOvaaaa@4098@ .4,5 Thus, even with a conservative choice of fast wind parameters M ˙ f MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibiqad2eagaGaaSWaaSbaaKqaGeaajugWaiaadAgaaKqaGeqa aaaa@3CC3@ and V f MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOvaSWdamaaBaaajeaibaqcLbmapeGa amOzaaqcbaYdaeqaaaaa@3D11@ the obtained estimate of the intensity at the inner radius of the young PN is about 7–8 orders of magnitude greater than an average value in the ISM J( E=1 MeV )=2.0 10 4  particles cm 2 s 1 sr 1 MeV 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOsaKqbaoaabmaak8aabaqcLbsapeGa amyraiabg2da9iaaigdacaGGGcGaaeytaiaabwgacaqGwbaakiaawI cacaGLPaaajugibiabg2da9iaaikdacaGGUaGaaGimaiabgwSixlaa igdacaaIWaWcpaWaaWbaaKqaGeqabaqcLbmapeGaeyOeI0IaaGinaa aajugibiaabckacaqGWbGaaeyyaiaabkhacaqG0bGaaeyAaiaaboga caqGSbGaaeyzaiaabohacqGHflY1caqGJbGaaeyBaSWdamaaCaaaje aibeqaaKqzadWdbiabgkHiTiaaikdaaaqcLbsacqGHflY1caqGZbWc paWaaWbaaKqaGeqabaqcLbmapeGaeyOeI0IaaGymaaaajugibiabgw SixlaabohacaqGYbWcpaWaaWbaaKqaGeqabaqcLbmapeGaeyOeI0Ia aGymaaaajugibiabgwSixlaab2eacaqGLbGaaeOvaSWdamaaCaaaje aibeqaaKqzadWdbiabgkHiTiaaigdaaaaaaa@7784@ .15

Because the flux of H 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake Gabaa+nKqzGeaeaaaaaaaaa8qacaqGibWcpaWaaSbaaKqaGeaajugW a8qacaaIYaaajeaipaqabaaaaa@3DDA@ ionizing energetic protons, the ionization rate ζ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaeqOTdOhaaa@3B2C@ and the cross–section σ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaeq4Wdmhaaa@3B32@ of the interaction at a given value of energy E MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamyraaaa@3A39@ are connected with the evident relation F( E )dE=ζ/σ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaamOraKqbaoaabmaak8aabaqcLbsapeGa amyraaGccaGLOaGaayzkaaqcLbsacaWGKbGaamyraiabg2da9iabeA 7a6jaac+cacqaHdpWCaaa@4558@ ,26 it is clear that the ionization rate at such PN, ζ( PN ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaeqOTdOxcfa4aaeWaaOWdaeaajugib8qa caWGqbGaamOtaaGccaGLOaGaayzkaaaaaa@3FAD@ should be larger as well, than ζ( GCR ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaeqOTdOxcfa4aaeWaaOWdaeaajugib8qa caWGhbGaam4qaiaadkfaaOGaayjkaiaawMcaaaaa@4070@ –the average for the ISM, so ζ( PN )=5 10 7 ζ( GCR ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacqaH2oGEjuaGdaqadaGcpaqaaKqz GeWdbiaadcfacaWGobaakiaawIcacaGLPaaajugibiabg2da9iaaiw dacqGHflY1caaIXaGaaGimaSWdamaaCaaajeaibeqaaKqzadWdbiaa iEdaaaqcLbsacqGHflY1cqaH2oGEjuaGdaqadaGcpaqaaKqzGeWdbi aadEeacaWGdbGaamOuaaGccaGLOaGaayzkaaaaaa@52C8@ . The radius of a molecular part of the young PN envelope should be at least a few of r i = 10 16 cm MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaWGYbWcpaWaaSbaaKqaGeaajugW a8qacaWGPbaajeaipaqabaqcLbsapeGaeyypa0JaaGymaiaaicdal8 aadaahaaqcbasabeaajugWa8qacaaIXaGaaGOnaaaajugibiaaboga caqGTbaaaa@4697@ with a number density of n 10 6 cm 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaWGUbGaeyipI4NaaGymaiaaicda l8aadaahaaqcbasabeaajugWa8qacaaI2aaaaKqzGeGaae4yaiaab2 gal8aadaahaaqcbasabeaajugWa8qacqGHsislcaaIZaaaaaaa@461F@ .17 This corresponds to the column density of nebular matter of about 10 22 cm 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaaIXaGaaGimaSWdamaaCaaajeai beqaaKqzadWdbiaaikdacaaIYaaaaKqzGeGaae4yaiaab2gal8aada ahaaqcbasabeaajugWa8qacqGHsislcaaIYaaaaaaa@447B@ , and the flux of energetic protons may be decreased, by 1 order of magnitude due to ionization energy losses27,28 and reflection from magnetic irregularities, depending on the magnetic field strength ( 110 μG MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaaIXaGaai4eGiaaigdacaaIWaGa aeiiaiabeY7aTjaadEeaaaa@4043@ ), by 1–2 orders29,30 and, additionally by 1 order because of r 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaWGYbWcpaWaaWbaaKqaGeqabaqc LbmapeGaeyOeI0IaaGOmaaaaaaa@3E7C@ behavior in the postshock region.15 Thus at the outer part of the (young) PN the differential intensity of energetic particles may be J( E=1 MeV )=110 particles cm 2 s 1 sr 1 MeV 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaWGkbqcfa4aaeWaaOWdaeaajugi b8qacaWGfbGaeyypa0JaaGymaiaacckacaqGnbGaaeyzaiaabAfaaO GaayjkaiaawMcaaKqzGeGaeyypa0JaaGymaiabgkHiTiaaigdacaaI WaGaaiiOaiaabchacaqGHbGaaeOCaiaabshacaqGPbGaae4yaiaabY gacaqGLbGaae4CaiabgwSixlaabogacaqGTbWcpaWaaWbaaKqaGeqa baqcLbmapeGaeyOeI0IaaGOmaaaajugibiabgwSixlaabohal8aada ahaaqcbasabeaajugWa8qacqGHsislcaaIXaaaaKqzGeGaeyyXICTa ae4Caiaabkhal8aadaahaaqcbasabeaajugWa8qacqGHsislcaaIXa aaaKqzGeGaeyyXICTaaeytaiaabwgacaqGwbWcpaWaaWbaaKqaGeqa baqcLbmapeGaeyOeI0IaaGymaaaaaaa@71A6@ which will be used below.

It is also interesting to recall that a 0.8 MeV proton beam irradiation of a mixture of H 2 O: C 2 H 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaqGibWcpaWaaSbaaKqaGeaajugW a8qacaaIYaaajeaipaqabaqcLbsapeGaae4taiaacQdacaqGdbWcpa WaaSbaaKqaGeaajugWa8qacaaIYaaajeaipaqabaqcLbsapeGaaeis aSWdamaaBaaajeaibaqcLbmapeGaaGOmaaqcbaYdaeqaaaaa@472A@ ices at doses of 5–25 eV/18 amu (0.28–1.4 eV/amu) leads to the formation of CH 2 =CH( OH ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaqGdbGaaeisaKqba+aadaWgaaqc basaaKqzadWdbiaaikdaaSWdaeqaaKqzGeWdbiabg2da9iaaboeaca qGibqcfa4aaeWaaOWdaeaajugib8qacaqGpbGaaeisaaGccaGLOaGa ayzkaaaaaa@4671@ –vinyl alcohol, and a saturation occurs already at a dose of 0.22 eV/amu.31 One can estimate the irradiation dose of water ice by energetic protons on the basis of a simple relation:27

( nM( n ) )d D p /dt= E 1 E 2 F( E )S( E )dE, D p =( d D p /dt )t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqbacbaaaaaaaaapeWaaeWaaOWdaeaajugib8qacaWGUbGa eyyXICTaamytaKqbaoaabmaak8aabaqcLbsapeGaamOBaaGccaGLOa GaayzkaaaacaGLOaGaayzkaaqcLbsacqGHflY1caWGKbGaamiraKqb a+aadaWgaaqcbasaaKqzadWdbiaadchaaSWdaeqaaKqzGeWdbiaac+ cacaWGKbGaamiDaiabg2da9KqbaoaawahakeqajeaipaqaaKqzadWd biaadweajuaGpaWaaSbaaKGaGeaajugWa8qacaaIXaaajiaipaqaba aajeaibaqcLbmapeGaamyraKqba+aadaWgaaqccasaaKqzadWdbiaa ikdaaKGaG8aabeaaa0qaaKqzGeWdbiabgUIiYdaacaWGgbqcfa4aae WaaOWdaeaajugib8qacaWGfbaakiaawIcacaGLPaaajugibiabgwSi xlaadofajuaGdaqadaGcpaqaaKqzGeWdbiaadweaaOGaayjkaiaawM caaKqzGeGaeyyXICTaamizaiaadweacaGGSaGaamiraKqba+aadaWg aaqcbasaaKqzadWdbiaadchaaKqaG8aabeaajugib8qacqGH9aqpju aGdaqadaGcpaqaaKqzGeWdbiaadsgacaWGebqcfa4damaaBaaajeai baqcLbmapeGaamiCaaqcbaYdaeqaaKqzGeWdbiaac+cacaWGKbGaam iDaaGccaGLOaGaayzkaaqcLbsacqGHflY1caWG0baaaa@843A@ , (4)

Where F( E )=4π J p ( E ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaWGgbqcfa4aaeWaaOWdaeaajugi b8qacaWGfbaakiaawIcacaGLPaaajugibiabg2da9iaaisdacqaHap aCcaWGkbWcpaWaaSbaaKqaGeaajugWa8qacaWGWbaajeaipaqabaqc fa4dbmaabmaak8aabaqcLbsapeGaamyraaGccaGLOaGaayzkaaaaaa@4A09@ , S( E )=dE/dx MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaWGtbqcfa4aaeWaaOWdaeaajugi b8qacaWGfbaakiaawIcacaGLPaaajugibiabg2da9iaadsgacaWGfb Gaai4laiaadsgacaWG4baaaa@4494@ –energy losses of particles in the path x MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaWG4baaaa@3B35@ (in units keV/μ), and ρ=nM( n )1 amu MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacqaHbpGCcqGH9aqpcaWGUbGaeyyX ICTaamytaKqbaoaabmaajaaypaqaaKqzGeWdbiaad6gaaKaaGjaawI cacaGLPaaajugibiabgwSixlaaigdacaGGGcGaaeyyaiaab2gacaqG 1baaaa@4D1B@ . For energies E 1 =1 MeV MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaWGfbWcpaWaaSbaaKqaGeaajugW a8qacaaIXaaajeaipaqabaqcLbsacqGH9aqppeGaaGymaiaabccaca WGnbGaamyzaiaadAfaaaa@4333@ , E 2 =100 MeV  S( E ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaWGfbWcpaWaaSbaaKqaGeaajugW a8qacaaIYaaajeaipaqabaqcLbsacqGH9aqppeGaaGymaiaaicdaca aIWaGaaeiiaiaad2eacaWGLbGaamOvaiaacckacaGGGcGaam4uaKqb aoaabmaajaaypaqaaKqzGeWdbiaadweaaKaaGjaawIcacaGLPaaaaa a@4C29@ can be calculated by the SRIM computer program,32 for example, S( E=1 MeV )=26keV/μ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaWGtbqcfa4aaeWaaOWdaeaajugi b8qacaWGfbGaeyypa0JaaGymaiaabckacaqGnbGaaeyzaiaabAfaaO GaayjkaiaawMcaaKqzGeGaeyypa0JaaGOmaiaaiAdacaqGRbGaaeyz aiaabAfacaGGVaGaaeiVdaaa@4BDD@ for water ice. Water is observed in young PN in the solid phase.23-25 Assuming that water ice is present in ice mantles of dust particles coming with the cold AGB wind, adopting in the maximum ice concentration region behind the photo dissociation front ζ= 10 12 10 13 s 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacqaH2oGEcqGH9aqpcaaIXaGaaGim aSWdamaaCaaajeaibeqaaKqzadWdbiabgkHiTiaaigdacaaIYaaaaK qzGeGaeyOeI0IaaGymaiaaicdal8aadaahaaqcbasabeaajugWa8qa cqGHsislcaaIXaGaaG4maaaajugibiaadohal8aadaahaaqcbasabe aajugWa8qacqGHsislcaaIXaaaaaaa@4E45@ and choosing a conservative case F( E )=F( E=1 MeV ) E 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaWGgbqcfa4aaeWaaOWdaeaajugi b8qacaWGfbaakiaawIcacaGLPaaajugibiabg2da9iaadAeajuaGda qadaqcaa2daeaajugib8qacaWGfbGaeyypa0JaaGymaiaacckacaqG nbGaaeyzaiaabAfaaKaaGjaawIcacaGLPaaajugibiabgwSixlaadw eal8aadaahaaqcKfaG=hqabaqcLbmapeGaeyOeI0IaaGOmaaaaaaa@5390@ one finally obtains D p =0.141.4eV/amu MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaWGebWcpaWaaSbaaKqaGeaajugW a8qacaWGWbaajeaipaqabaqcLbsapeGaeyypa0JaaGimaiaac6caca aIXaGaaGinaiabgkHiTiaaigdacaGGUaGaaGinaiaabwgacaqGwbGa ai4laiaabggacaqGTbGaaeyDaaaa@4AB4@ for 1000 years. Here the contribution of α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacqaHXoqyaaa@3BD6@ –particles was taken into account by multiplying the approximate dose of protons by 2, since the loss of α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacqaHXoqyaaa@3BD6@ –particles is on the order of magnitude greater,33 while the abundance is on the order of magnitude smaller. In a hydrogen–deficient case the estimates would be, of course, different. With this caveat, one should note that the dose of energetic particles is at about the threshold of radiation–chemical transformations of ices. Thus, some chemical species under PN conditions practically have time to form from ice mixtures with dominant water ice.

At last, but not least, it is interesting the radiation chemical transformation of more complex systems already formed in the AGB wind, for example, the HAC (hydrogenated amorphous carbon) on the surface of dust grains, or PAH (polycyclic aromatic hydrocarbons), sometimes mentioned as possible sources of the observed fullerene. In short, the infrared observations of recent years registered PAH, and even fullerenes C 60 , C 70 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaqGdbWcpaWaaSbaaKqaGeaajugW a8qacaaI2aGaaGimaaqcbaYdaeqaaKqzGeWdbiaacYcacaqGdbWcpa WaaSbaaKqaGeaajugWa8qacaaI3aGaaGimaaqcbaYdaeqaaaaa@43C0@ in the spectra of several PN, including 11 out of 338 observed by Spitzer.34 These authors interpret the observations as follows: the most likely places of formation of such compounds are the outflows of cold carbon stars in the AGB phase transition to the PN, but little details are known. In particular, it is unclear whether they are present initially in AGB winds, but not observed, due to the lack of appropriate sources of excitation, or they form during the process of transition to a PN phase. There is a point of view that fullerenes are formed by the UV destruction of hydrogenated amorphous carbon (HAC) and/or the dehydrogenation of large PAH molecules in the early PN stages, when there is the intense UV irradiation.34-36 We would like to note that similar transformations are known also under corpuscular irradiation26 and one should now just estimate a dose needed.

First of all, one can recall the well–known laboratory data on the stability of C 60 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaae4qaSWdamaaBaaajeaibaqcLbmapeGa aGOnaiaaicdaaKqaG8aabeaaaaa@3D8B@ and C 70 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaae4qaSWdamaaBaaajeaibaqcLbmapeGa aG4naiaaicdaaKqaG8aabeaaaaa@3D8C@ . It is known that the oligomerization of molecular crystals with a dominant concentration of C 60 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aajugibabaaaaaaaaapeGaae4qaSWdamaaBaaajeaibaqcLbmapeGa aGOnaiaaicdaaKqaG8aabeaaaaa@3D8B@ (fullerite, the density of 2 g/cm3) starts with an irradiation dose of ionizing radiation ( γ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacqaHZoWzaaa@3BDE@ –rays or α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacqaHXoqyaaa@3BD6@ –particles) equal to 2.6 MGy =2.6 10 10 erg/g=20eV/amu MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaWGnbGaam4raiaadMhacaqGGaGa eyypa0JaaGOmaiaac6cacaaI2aGaeyyXICTaaGymaiaaicdal8aada ahaaqcKfaG=hqabaqcLbmapeGaaGymaiaaicdaaaqcLbsacaqGLbGa aeOCaiaabEgacaGGVaGaae4zaiabg2da9iaaikdacaaIWaGaaeyzai aabAfacaGGVaGaaeyyaiaab2gacaqG1baaaa@55F4@ , while the amorphization begins with 250 MGy ( 2000eV/amu MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaaIYaGaaGimaiaaicdacaaIWaGa aeyzaiaabAfacaGGVaGaaeyyaiaab2gacaqG1baaaa@4262@ ), i.e. approximately at 100 times greater values.37 On the other hand, unlike the above scheme with ices, there is no need now to link the region of their maximum concentration close to the outer radius, where, as is already mentioned, the possible maximum value of ζ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacqaH2oGEaaa@3BF5@ do not exceed ζ 10 12 s 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacqaH2oGEcqWIdjYocaaIXaGaaGim aSWdamaaCaaajeaibeqaaKqzadWdbiabgkHiTiaaigdacaaIYaaaaK qzGeGaam4CaSWdamaaCaaajeaibeqaaKqzadWdbiabgkHiTiaaigda aaaaaa@4776@ . On the contrary, the processes of decomposition of HAC covered dust systems and/or the PAH defragmentation with the formation of fullerenes can be considered, starting from the inner radius, where the rate may be as large as ζ 10 9 s 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacqaH2oGEcqWIdjYocaaIXaGaaGim aSWdamaaCaaajeaibeqaaKqzadWdbiabgkHiTiaaiMdaaaqcLbsaca WGZbWcpaWaaWbaaKqaGeqabaqcLbmapeGaeyOeI0IaaGymaaaaaaa@46C2@ . Energy losses in the case of fullerite should be less than or comparable to the losses in the graphite (the density is 2.26 g/cm3), and 2 times more than in a water ice while the particles flux may be 3 orders of magnitude larger, so that the possible maximum dose will be D p =21.4 10 3 =2800eV/amu MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaWGebWcpaWaaSbaaKqaGeaajugW a8qacaWGWbaajeaipaqabaqcLbsapeGaeyypa0JaaGOmaiabgwSixl aaigdacaGGUaGaaGinaiabgwSixlaaigdacaaIWaWcpaWaaWbaaKqa GeqabaqcLbmapeGaaG4maaaajugibiabg2da9iaaikdacaaI4aGaaG imaiaaicdacaqGLbGaaeOvaiaac+cacaqGHbGaaeyBaiaabwhaaaa@548F@ in 1000 years, that is larger than the amorphization dose. The dose of HAC decomposition and/or PAH dehydrogenation is most likely less. Thus, in general, the dose can be expected in the range of 20–2800 eV/amu over a considerable part of the PN volume. Of course, these qualitative assessments could not substitute for a rigorous theory, necessary for the simulation of the real abundance of fullerenes in the given PN. For that it is necessary, as already mentioned, to adequately describe the transfer of energetic particles in the medium (probably, with a magnetic field) of known geometry, and enable the time–and spatial dependent ζ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacqaH2oGEaaa@3BF4@ incorporation in physical–chemical models of PN. Also it is necessary the correct description of HAC and PAH complexes transformations. Thus, in the models of physical–chemical plasma calculation in PN in general, and in the fullerene formation problem under PN conditions in particular, it appears mandatory to consider the factor of high fluxes of energetic particles, causing significant radiation–induced chemical transformations. It is also necessary to experimentally confirm the similarity mechanisms of the fullerene–type systems origin both under the UV and corpuscular irradiation of potential targets, but better, at their joint impact.

Because of the high values of the fluxes of energetic particles in the WRN, it is interesting also to estimate the radiation doses of certain substances in such nebulae. For the flux of accelerated particles we have expressions (1), in the energy range 1–100 MeV, which is important in the irradiation of substances, as well as in the ionization of molecular hydrogen. Assuming M ˙ f = 10 5 M /yr  MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qaceWGnbWdayaacaWcdaWgaaqcbasa aKqzadWdbiaadAgaaKqaG8aabeaajugib8qacqGH9aqpcaaIXaGaaG imaSWdamaaCaaajeaibeqaaKqzadWdbiabgkHiTiaaiwdaaaqcLbsa caWGnbWcpaWaaSbaaKqaGeaajugWa8qacqWIzkszaKqaG8aabeaaju gib8qacaGGVaGaaeyEaiaabkhacaGGGcaaaa@4D98@ , V f =1500km/s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaWGwbWcpaWaaSbaaKqaGeaajugW a8qacaWGMbaajeaipaqabaqcLbsapeGaeyypa0JaaGymaiaaiwdaca aIWaGaaGimaiaadUgacaWGTbGaai4laiaadohaaaa@45FA@ , for the differential intensity of the energy protons at E 1 =1 MeV MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaWGfbWcpaWaaSbaaKqaGeaajugW a8qacaaIXaaajeaipaqabaqcLbsapeGaeyypa0JaaGymaiaabccaca WGnbGaamyzaiaadAfaaaa@4333@ , one can write for two values of the internal radius r i =110 pc MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaWGYbWcpaWaaSbaaKqaGeaajugW a8qacaWGPbaajeaipaqabaqcLbsapeGaeyypa0JaaGymaiabgkHiTi aaigdacaaIWaGaaiiOaiaabchacaqGJbaaaa@45B8@ :

J p ( E 1 )=10.0 10 3   particles cm 2 ssrMeV MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaWGkbWcpaWaaSbaaKqaGeaajugW a8qacaWGWbaajeaipaqabaqcfa4dbmaabmaak8aabaqcLbsapeGaam yraSWdamaaBaaajeaibaqcLbmapeGaaGymaaqcbaYdaeqaaaGcpeGa ayjkaiaawMcaaKqzGeGaeyypa0JaaGymaiaaicdacaGGUaGaaGimai abgkHiTiaaigdacaaIWaWcpaWaaWbaaKqaGeqabaqcLbmapeGaaG4m aaaajugibiaacckajuaGdaWcaaGcpaqaaKqzGeWdbiaabchacaqGHb GaaeOCaiaabshacaqGPbGaae4yaiaabYgacaqGLbGaae4CaaGcpaqa aKqzGeWdbiaabogacaqGTbWcpaWaaWbaaKqaGeqabaqcLbmapeGaaG OmaaaajugibiabgwSixlaabohacqGHflY1caqGZbGaaeOCaiabgwSi xlaab2eacaqGLbGaaeOvaaaaaaa@6AA3@ . (5)

Thus, for standard values of the WR parameters of nebulae, the obtained intensity estimates on the inner boundary of the nebula are 5–7 orders of magnitude greater than the mid–galactic one:15

J p ( E 1 )=1.0 10 4   particles cm 2 ssrMeV MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaWGkbWcpaWaaSbaaKqaGeaajugW a8qacaWGWbaajeaipaqabaqcfa4dbmaabmaak8aabaqcLbsapeGaam yraSWdamaaBaaajeaibaqcLbmapeGaaGymaaqcbaYdaeqaaaGcpeGa ayjkaiaawMcaaKqzGeGaeyypa0JaaGymaiaac6cacaaIWaGaeyyXIC TaaGymaiaaicdal8aadaahaaqcbasabeaajugWa8qacqGHsislcaaI 0aaaaKqzGeGaaiiOaKqbaoaalaaak8aabaqcLbsapeGaaeiCaiaabg gacaqGYbGaaeiDaiaabMgacaqGJbGaaeiBaiaabwgacaqGZbaak8aa baqcLbsapeGaae4yaiaab2gal8aadaahaaqcbasabeaajugWa8qaca aIYaaaaKqzGeGaeyyXICTaae4CaiabgwSixlaabohacaqGYbGaeyyX ICTaaeytaiaabwgacaqGwbaaaaaa@6C34@  . (6)

Further, ζ( WR )= 10 5 10 7 ζ( GCR ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacqaH2oGEjuaGdaqadaGcpaqaaKqz GeWdbiaadEfacaWGsbaakiaawIcacaGLPaaajugibiabg2da9iaaig dacaaIWaWcpaWaaWbaaKqaGeqabaqcLbmapeGaaGynaaaajugibiab gkHiTiaaigdacaaIWaWcpaWaaWbaaKqaGeqabaqcLbmapeGaaG4naa aajugibiabeA7a6Lqbaoaabmaak8aabaqcLbsapeGaam4raiaadoea caWGsbaakiaawIcacaGLPaaaaaa@52D4@ . It is clear that such estimates are meaningful only when the WRN itself contains a molecular gas or is close enough to some molecular cloud, such as WR 7 (NGC 2359).38,39 In particular, for this nebula, the column density is of the order of 10 20 с м 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GabaaWgKqzGeaeaaaaaaaaa8qacaaIXaGaaGimaSWdamaaCaaajeai beqaaKqzadWdbiaaikdacaaIWaaaaKqzGeGaamyqeiaadYdbl8aada ahaaqcbasabeaajugWa8qacqGHsislcaaIYaaaaaaa@4432@ (ibid), whence it follows that protons with energies of 1 MeV and more practically do not lose energy for this path,27,28 and the flow decreases because of the divergence according to the law r 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaWGYbWcpaWaaWbaaKqaGeqa baqcLbmapeGaeyOeI0IaaGOmaaaaaaa@3F31@ .15 The effect of the magnetic field (if present) can be twofold: on the one hand, the protons can be reflected from the magnetic inhomogeneities, and, depending on the strength and geometry of the magnetic field ( 110μG MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaaIXaGaai4eGiaaigdacaaI WaGaeqiVd0Maam4raaaa@4055@ ), the flux can decrease by 1–2 orders of magnitude.29,30 On the other hand, nonthermal protons of relatively low energies can possibly be accelerated to 1–10 MeV in the presence of magneto hydrodynamic turbulence with a certain spectrum (the Fermi–2 process).40 Thus, in this case, the actual particle flux at the outer boundary of the nebula can be reduced, at most, by 2–3 orders of magnitude, to the value

J p ( E=1 MeV )=0.110  particles cm 2 ssrMeV MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaWGkbWcpaWaaSbaaKqaGeaa jugWa8qacaWGWbaajeaipaqabaqcfa4dbmaabmaak8aabaqcLbsape Gaamyraiabg2da9iaaigdacaGGGcGaaeytaiaabwgacaqGwbaakiaa wIcacaGLPaaajugibiabg2da9iaaicdacaGGUaGaaGymaiabgkHiTi aaigdacaaIWaGaaiiOaKqbaoaalaaak8aabaqcLbsapeGaaeiCaiaa bggacaqGYbGaaeiDaiaabMgacaqGJbGaaeiBaiaabwgacaqGZbaak8 aabaqcLbsapeGaae4yaiaab2gal8aadaahaaqcbasabeaajugWa8qa caaIYaaaaKqzGeGaeyyXICTaae4CaiabgwSixlaabohacaqGYbGaey yXICTaaeytaiaabwgacaqGwbaaaaaa@6A7C@ .

It is known that in many WR nebulae dust is observed, the origin of which is still discussed,19,41-43 but most likely dust is formed in the conditions of colliding winds of massive pairs.44

It is possible to calculate the radiation dose of dust D p MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaWGebWcpaWaaSbaaKqaGeaa jugWa8qacaWGWbaajeaipaqabaaaaa@3E87@ by energy protons in WRN in time t by means of (4), where again F( E )=4π J p ( E ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaWGgbqcfa4aaeWaaOWdaeaa jugib8qacaWGfbaakiaawIcacaGLPaaajugibiabg2da9iaaisdacq aHapaCcaWGkbqcfa4damaaBaaajeaibaqcLbmapeGaamiCaaWcpaqa baqcfa4dbmaabmaak8aabaqcLbsapeGaamyraaGccaGLOaGaayzkaa aaaa@4B22@ and S( E )=dE/dx MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaWGtbqcfa4aaeWaaOWdaeaa jugib8qacaWGfbaakiaawIcacaGLPaaajugibiabg2da9iabgkHiTi aadsgacaWGfbGaai4laiaadsgacaWG4baaaa@4636@ is the energy loss of the particle passing the path dx MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaWGKbGaamiEaaaa@3CD3@ (in keV/μ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaqGRbGaaeyzaiaabAfacaGG VaGaaeiVdaaa@3F91@ ) in a dust particle with a concentration n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaWGUbaaaa@3BE0@ and a molecular weight M( n ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaWGnbqcfa4aaeWaaOWdaeaa jugib8qacaWGUbaakiaawIcacaGLPaaaaaa@3F8B@ (accordingly, the amount of energy dE MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaWGKbGaamyraaaa@3CA0@ absorbed by the dust particle is positive). S( E ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaWGtbqcfa4aaeWaaOWdaeaa jugib8qacaWGfbaakiaawIcacaGLPaaaaaa@3F68@ in the energy range 1–100 MeV can be easily calculated using the Bethe–Bloch formula, for example, using the computer program SRIM,32 in particular, S( E=1 MeV )=52 keV/μ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaWGtbqcfa4aaeWaaOWdaeaa jugib8qacaWGfbGaeyypa0JaaGymaiaacckacaqGnbGaaeyzaiaabA faaOGaayjkaiaawMcaaKqzGeGaeyypa0JaaGynaiaaikdacaGGGcGa ae4AaiaabwgacaqGwbGaai4laiaabY7aaaa@4DB6@ for graphite with a density of 2.26 g/cm3 ( 1.13 10 23 atom/ cm 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaaIXaGaaiOlaiaaigdacaaI ZaGaeyyXICTaaGymaiaaicdal8aadaahaaqcbasabeaajugWa8qaca aIYaGaaG4maaaajugibiaabggacaqG0bGaae4Baiaab2gacaGGVaGa ae4yaiaab2gal8aadaahaaqcbasabeaajugWa8qacaaIZaaaaaaa@4DE4@ ), and S( E=10 MeV )=9.3 keV/μ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaWGtbqcfa4aaeWaaOWdaeaa jugib8qacaWGfbGaeyypa0JaaGymaiaaicdacaGGGcGaaeytaiaabw gacaqGwbaakiaawIcacaGLPaaajugibiabg2da9iaaiMdacaGGUaGa aG4maiaacckacaqGRbGaaeyzaiaabAfacaGGVaGaaeiVdaaa@4F27@ , S( E=50 MeV )=2.5 keV/μ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaWGtbqcfa4aaeWaaOWdaeaa jugib8qacaWGfbGaeyypa0JaaGynaiaaicdacaGGGcGaaeytaiaabw gacaqGwbaakiaawIcacaGLPaaajugibiabg2da9iaaikdacaGGUaGa aGynaiaacckacaqGRbGaaeyzaiaabAfacaGGVaGaeqiVd0gaaa@4F9A@ . For hydrogenated amorphous carbon (a: C–H) with a density of up to 2.4 g/cm3),45 the energy loss is approximately 1.06 times greater, S( E=1 MeV )=55.1 keV/μ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaWGtbqcfa4aaeWaaOWdaeaa jugib8qacaWGfbGaeyypa0JaaGymaiaacckacaqGnbGaaeyzaiaabA faaOGaayjkaiaawMcaaKqzGeGaeyypa0JaaGynaiaaiwdacaGGUaGa aGymaiaacckacaqGRbGaaeyzaiaabAfacaGGVaGaaeiVdaaa@4F26@ . Then, choosing the not very steep type of the spectrum, F( E )=F( E= E 1 =1 MeV ) ( E/ E 1 ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaWGgbqcfa4aaeWaaOWdaeaa jugib8qacaWGfbaakiaawIcacaGLPaaajugibiabg2da9iaadAeaju aGdaqadaGcpaqaaKqzGeWdbiaadweacqGH9aqpcaWGfbqcfa4damaa BaaajeaibaqcLbmapeGaaGymaaWcpaqabaqcLbsapeGaeyypa0JaaG ymaiaacckacaqGnbGaaeyzaiaabAfaaOGaayjkaiaawMcaaKqzGeGa eyyXICDcfa4aaeWaaKaaG9aabaqcLbsapeGaamyraiaac+cacaWGfb WcpaWaaSbaaKazba4=baqcLbmapeGaaGymaaqcKfaG==aabeaaaKaa G9qacaGLOaGaayzkaaWcpaWaaWbaaKazba4=beqaaKqzadWdbiabgk HiTiaaikdaaaaaaa@6432@ one can get D p =1.5150eV/amu MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaWGebWcpaWaaSbaaKqaGeaa jugWa8qacaWGWbaajeaipaqabaqcLbsapeGaeyypa0JaaGymaiaac6 cacaaI1aGaeyOeI0IaaGymaiaaiwdacaaIWaGaamyzaiaadAfacaGG VaGaamyyaiaad2gacaWG1baaaa@4AC3@ for the values ​​of the inner boundary of WRN r i =10 и 1 pc MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaWGYbWcpaWaaSbaaKqaGfaa jugWa8qacaWGPbaajeaypaqabaqcLbsapeGaeyypa0JaaGymaiaaic dacaGGGcGaamioeiaacckacaaIXaGaaiiOaiaabchacaqGJbaaaa@4909@ , respectively, and for a characteristic time interval of 100000 years. If there is a hydrogen deficit in the stellar wind, that is, with predominating helium the value obtained should be multiplied by 10, since the energy losses of the α particles are an order of magnitude larger,32 and the doses will be of 15–1500 eV/amu.

In some cases, characteristic PAH emission lines are also observed with dust.46 There is a point of view that further UV irradiation of PAH followed by dehydrogenation can even lead to the formation of fullerenes,34-36 which are observed in different (but WR–radiation–like) objects, for example, in PN.36 Therefore, we also estimate the radiation dose for such systems (HAC, fullerenes) under WRN conditions, since, as a rule, in radiation–chemical transformations of complex compounds, electromagnetic and corpuscular irradiation are equivalent, and this fact must be taken into account.26 From the standpoint of irradiation of fullerenes, laboratory data on the stability of C 60 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaqGdbWcpaWaaSbaaKqaGeaa jugWa8qacaaI2aGaaGimaaqcbaYdaeqaaaaa@3F09@ and C 70 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaqGdbWcpaWaaSbaaKqaGeaa jugWa8qacaaI3aGaaGimaaqcbaYdaeqaaaaa@3F0A@ are interesting: oligomerization of molecular crystals with a dominant content of C 60 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaqGdbWcpaWaaSbaaKqaGeaa jugWa8qacaaI2aGaaGimaaqcbaYdaeqaaaaa@3F09@ (fullerite, density 1.7 g/cm3) begins with radiation doses ( γ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacqaHZoWzaaa@3C93@ –rays or α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacqaHXoqyaaa@3C8B@ –particles) of the order of 2.6 MGy=2.6 10 10  erg/g=20 eV/amu MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIj xAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake GacaaTaaaWgKqzGeaeaaaaaaaaa8qacaWGnbGaam4raiaadMhacqGH 9aqpcaaIYaGaaiOlaiaaiAdacqGHflY1caaIXaGaaGimaKqba+aada ahaaqcbawabKazba4=baqcLbmapeGaaGymaiaaicdaaaqcLbsacaGG GcGaaeyzaiaabkhacaqGNbGaai4laiaabEgacqGH9aqpcaaIYaGaaG imaiaacckacaqGLbGaaeOvaiaac+cacaqGHbGaaeyBaiaabwhaaaa@593B@ , whereas for amorphization a large dose of 250 MGy (2000 eV/ amu) is needed approximately 100 times larger.37 Thus, the dose of fullerite irradiation in WRN (at the inner boundary) is comparable with the dose for graphite (1.5–150 eV / amu for 100000 years), and for HAC it is somewhat larger. The dose of HAC decomposition and defragmentation of PAH is obviously less than the laboratory values ​​of the doses of amorphization of fullerene and are comparable to the real values ​​of the doses obtained in WRN on the inner boundary in which, as already noted, doses in the range of 1.5–150 eV/amu can be expected (15–1500 eV/amu in case of hydrogen deficiency). Thus, in the nebulae, not only dust, but also PAH (which are observed in some cases), and even fullerenes, whose manifestations are worth searching in the observed spectra, can form. A detailed analysis of the described phenomena based on the kinetics of processes is beyond the scope of this article and will be given elsewhere.

Conclusion

In this paper the differential intensities of protons accelerated to energies of 1–100 MeV under the conditions of shock waves of interacting stellar winds forming PN and WRN were calculated. The estimates were based on the formula (1), which relates the fraction of the kinetic energy of the expanding shell converted to the energy of accelerated particles. It is interesting to note that under the conditions of the heliosphere, estimates coincide with the Voyager 1 data at 1 MeV14 to within a factor of less than 2, if a flow kinetic energy conversion factoris chosen in Equation 1. Because of the steepness of the spectrum, the exponent does not have a special significance when calculating radiation doses, because the contribution of more energetic particles is usually small. In addition, for the characteristic time of a young PN for about 1000 years, only the soft part of the spectrum, 1–10 MeV, will be formed. Estimated fluxes of energetic particles in PN are more than 7 orders of magnitude larger than an average ISM value at 1 MeV. This may cause serious consequences concerning dust processing by energetic particles. An important example is the value of the doses of irradiation of water ice and fullerite, exceeding the known laboratory data on destructive threshold of the dose values. In conclusion, the importance of taking energetic particles into account in the physico–chemical modeling of PN is emphasized, because the local hydrogen ionization rate is 7–8 orders of magnitude higher than the mean galactic rate. In particular, it is shown, that under high flux irradiation by energetic particles complex species may be formed from ice mixtures with dominant water abundance during characteristic time of young PN of 1000 years. Besides, irradiation by such particles should be taken into account when modeling of fullerene–like systems in PN.

The accelerated particle fluxes at the inner boundary of the WRN exceed the mean galactic value at 1 MeV by more than 4 orders of magnitude. This may have interesting consequences in assessing the effects of particle dust irradiation in WRN. Important examples relate to the irradiation of systems such as graphite and / or HAC and PAH, with possible decomposition and defragmentation, as well as fullerite, with calculated doses being of the same order as laboratory ones, causing important radiation–chemical transformations. In conclusion, we emphasize that increased fluxes of energetic particles must necessarily be taken into account in physical–chemical modeling of WRN nebulae.

Acknowledgements

The author acknowledges with thanks a support by the Alexander von Humboldt Foundation (Germany) for a 3 months visit to the Argelander Institute for Astronomy at the University of Bonn, and a support by the RA MES State Committee of Science (Armenia) in the frames of the research project № 15T–1C081. The author is grateful to H. Fahr and Argelander Institute of Astronomy at the University of Bonn for hospitality and useful discussions.

Conflict of interest

Author declares there is no conflict of interest.

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