Codino, A

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29th International Cosmic Ray Conference Pune (2005) 6, 317320The energy at which the intensities of the extragalactic and galacticcosmic rays equalizeAntonio Codino (a) Dipartimento di Fisica dell’Universita’ degli Studi di Perugia e INFN, Via A. Pascoli, 06123 Perugia, ItalyPresenter: Antonio Codino (antonio.codino@pg.infn.it), ita-codino-A-abs1-he13-oralA variety of observational data suggest that cosmic rays below the knee energy are accelerated in the Galaxywhile those beyond the ankle outside. The extragalactic and galactic components of cosmic rays are inter-mixed in the solar cavity, by quite different amounts, depending on the energy. The purpose of this study is todetermine that particular energy where the two components become equal. Using undisputed, reliable, obser-vational facts regarding the galactic magnetic field, the position of the solar cavity in the Galaxy, the size ofthe disk and halo, the interstellar matter density, and the inelastic nuclear cross sections, properly blended insimple algorithms, the equalization energy of the two components is calculated. The equalization of the twocomponents for Helium takes place around the energy of	. When the intervals of the parametersmentioned above are allowed to vary within the experimental limits, the above value shifts to a minimum of	and to a maximum of 	ﬀ. The equalization energy of heavier cosmic rays is close tothese figures.1. IntroductionThe intensity of cosmic rays arriving at the solar cavity, ﬁ , may be subdivided in two components dependingon the position of their sources. Denoting the galactic and the extragalactic sources by ﬁﬂ and ﬁﬃ , respectively,one can write:ﬁ !ﬁ"ﬂ$#%ﬁ&ﬃGalactic cosmic rays dominate the energy spectrum below the knee energy, while extragalactic cosmic raysdominate the spectrum at energies higher than the ankle energy. Traditionally the knee energy is at '%	(ﬀ)and the ankle energy at about*	ﬀ+,. In order to determine the energy of cosmic rays wherethe extragalactic component becomes equal to the galactic component, let us identify two comfortable energyintervals in the differential energy spectrum of the cosmic rays , where the dominance of one componentis well established. The extragalactic component is believed to be negligible at energies below the knee.The dominance of the galactic component at low energy is based on - rays intensities measured by manyexperiments in the energy interval	./-	102[1,2]. From these is derived a spatial gradient along thegalactocentric radius 3 , which indicates that cosmic-ray intensity is higher in the core of the Galaxy and lowerin its periphery though this gradient differs significantly from that of supernovae [3]. These findings stronglysuggest that the sources of the cosmic rays are in the Galaxy and not outside. Moreover, the detection of theelectron component in many spiral galaxies by radiotelescopes also suggests the origin of low energy cosmicrays in the Galaxy [4] along with the measurements of the residence times of cosmic rays by radioactive clocks.The extragalactic component should dominate at those energies where the field strength of the Galaxy is notsufficient to retain cosmic rays for long time. This certainly takes place at energies beyond	ﬀ45but detailedcalculations, like those reported here, demonstrate that the extragalactic component is robust and dominant evenat lower energies, down to	ﬀ6. From these observational facts it follows that there should be an energywhere the two components ﬁ ﬂ and ﬁ ﬃ join together and exchange the role, from dominant to marginal, and798;:73=<> .318 A. Codinogalactic sourcesextragalactic sourcesrelative intensityE (eV)Figure 1. Computed intensity of galactic (thick line) and extragalactic (thin line) cosmic rays observable in the localgalactic zone versus energy. The galactic component is normalized at ?A@9BDCFE&G and the extragalactic one at ?"@HBJIFE&G asexplained in the text.2. Some relevant parameters of the calculationThere are four basic parameters used in the calculation. The size of the Milky Way, the matter density in theinterstellar space, the galactic magnetic field, and the inelastic nuclear cross sections. All these parameters arebased on numerous observational data, more than adequate for the accuracy of this calculation. Cylindricalcoordinates 3 , K with the origin in the galactic center are used. The gaseous disk has a radius of 15 kpc, halfthickness of 120 L : up to 9.5 ML : , then enlarges linearly with 3 to the value of 375 L : at 15 kpc. Interstellarmatter consists only of hydrogen; its density in the galactic midplane reaches a maximum of 2.4 atoms per :"NPOat the radial distance of 4.6 kpc, decreasing to the value of 1.3 at 8.5 ML : and down to 0.11 at 15 ML : . There is anexponential decrease of the density along K . The configuration of the galactic magnetic field incorporated in thealgorithms is described elsewhere [5,6]. Cosmic rays are studied using the method of the trajectories utilized inprevious works (see for example [5,6,7], upgraded by new algorithms appropriate for ultrahigh energy cosmicrays, as reported in another paper of this conference [8].The energy at which the intensities of the extragalactic and galactic cosmic rays equalize 3193. Results of the calculationIn order to calculate QRﬂ cosmic-ray trajectories are propagated in the galactic disk and those intercepting arecording instrument at Earth are counted. A small sphere, 50 L : in diameter is used to count the number ofcosmic rays, QSﬂ . Note that both QRﬂ and QTﬃ are proportional to ﬁUﬂ and ﬁﬃ , respectively. Galactic sources aredistributed in space as supernove remnants. In figure 1 is given Q ﬂ versus energy (thick line) . The fall ofQ ﬃ above	reflects the inefficiency of the magnetic field to retain cosmic rays as the energy increases.Figure 2 shows the grammage encountered by the galactic cosmic rays traversing the Galaxy for the disk andthe halo, separately. Above the energy of,V	ﬀ6Wmanifests itself the inefficiency of the magnetic field tobend particles and above 'P	ﬀ+Wthe grammage attains its asymptotic limit.In principle the intensity of the extragalactic component at Earth, Q5ﬃ , can be calculated by injecting cosmic raysfrom the halo frontier, reconstructing and counting cosmic-ray trajectories intercepting an appropriate instru-ment at Earth. This direct method has severe computational drawbacks and it is not used here. A more efficientmethod takes advantage of the reversilibility of the trajectories in a magnetic field as explained elsewhere [9].In order to determine QXﬃ all cosmic rays are injected from the Earth into the galactic volume and only thosereaching the halo frontier counted by QXﬃ . The halo frontier is an ellipsoid: K = ( >Y - ZUY3Y )ﬀ[Y where > =	\	and Z = 11.11	.]Y^ML:Y . The number Q ﬃ versus energy, for helium nuclei, is reported in figure 1 as a thin line.4. Interpretation of the results and conclusionsIn the following it is analyzed the logical chain to establish the equalization energy, _ ﬃ for Helium at Earth. Letus summarize the hypothesis : ( ` ) there are two energy regions where the galactic and extragalactic componentseparately dominate. In another paper [10] it is postulated that a universal acceleration mechanism operateseverywhere, inside galaxies and in the intergalactic space, at least within 30 abL : from the Milky Way, shapingand setting the spectral index of cosmic rays at the approximate value of 3. This postulate is anchored to somebasic observations regarding the differential energy spectrum, the arrival directions of cosmic rays beyondcb	9ﬀ4dand others. Out of all possible modes, the extragalactic and galactic components might havejoined together between	eand	9ﬀ+$, as a matter of fact, the differential energy spectrum measured bymany experiments unmistakably indicate a smooth, regular transition. Profound dips, spikes or undulationsin the energy spectrum are not observed. Let us translate all that in a form (hypothesis ( f )) useful here : thecomponents ﬁ ﬂ and ﬁ ﬃ join together approximately with the same spectral index. In the present context, withoutthe hypothesis ( f ), the determination of _ ﬃ is not possible because Q ﬃ and Q ﬂ versus energy are unmeasured andunknown at Earth and they might differ by orders of magnitudes in a given galactic location for a given energy.Adopting the hypothesis ( f ), the curves Q ﬂ and Q ﬃ versus energy in figure 1 are normalized to their maximumvalues in the those regions where QXﬃ and QSﬂ separately dominate. The equalization energy is obtained byoverlapping the curves in figure 1. From the results in figure 1 the equalization energy for Helium results. ,P	.The results shown in figure 1 and their interpretation silently assume that the energy spectrum at the galacticsources, in the full energy range, e. g. from	.;gto	Yg, has a constant spectral index; this index isbelieved to be lower than 3 below '	)because of the propagation effects in the Galaxy. According tomany authors the acceleration mechanisms in the Galaxy become highly inefficient as the energy increases, inthe interval	eto	9ﬀ6h. Hence, Q ﬂ versus energy in figure 1 delimits the maximum intensity of galacticcosmic rays at Earth. In this circumstance the equalization energy for Helium have to shifted to a value lowerthan,P	6and accordingly _ ﬃ given above is overestimated.320 A. Codinodiskgalactic halogrammage (g/cm2 )E (eV)Figure 2. Gas column (grammage) versus energy encountered by galactic cosmic rays with sources distributed as super-novae remnants in the galactic disk (thick line) and in the halo (thin line).References[1] C. L. Bhat, J. Phys. G., Nucle. Phys., 12, 1087, (1986)[2] J. Szabelski et al., Advances in Space Research, Vol.9, N 12 (1989).[3] A. W. Strong and I. V. Moskalenko, ApJ, 509, 212 (1998).[4] I. Lerche and R. Schlickeiser, Proc. 17th ICRC, 2, 244 (1981). Dati sperimentali[5] M.T. Brunetti and A. Codino, ApJ 528, 789, (2000).[6] A. Codino, Conference proceeding, Vulcano Workshop, pp 439-453, (1998)[7] M. T. Brunetti and A.Codino, Proc. 25th ICRC, Vol. 4, 273, (1997).[8] A. Codino, Prompt extragalactic cosmic rays from Andromeda, Proceedings of 29th ICRC, Pune (2005).[9] A. Codino and F. Plouin, The extension and shape of the collecting zones of galactic cosmic rays fromHelium to Iron, to appear in ApJ this year.[10] A. Codino, Ultrahigh energy cosmic rays are accelerated in the space between galaxies, Proceedings of29th ICRC, Pune (2005).

The energy at which the intensities of the extragalactic and galactic cosmic rays equalize

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