Structure of the Galaxy

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    STRUCTURE OF THE GALAXY,

    MATTER-ANTIMATTER ANNIHILATION,

    AND ORIGIN OF THE COSMIC RAYS.

    Maurice LALOUM(CNRS/ IN2P3 Paris, LPNHE)

    Abstract.

    Various outstanding paradoxes in the mechanical balance of 

    the Galaxy are highlighted. There outmost relevance must needs a

    coherent and likely explanation. We propose a unique and synthetic

    interpretation, including a cosmological theory of the origin of the

    observed cosmic rays, especially at the highest energies known. t

    involves matter!antimatter annihilation in the median plane of the

    "ilky Way. #ccordingly, we discuss the structure and equilibrium of 

    the Galaxy, seen as made of two parallel disks of matter versus

    antimatter dominance, opposed through the repulsion of an

    annihilation gas, settled in the equator disk. The admitted

    suppression of antimatter in the $niverse, after the %big!bang&, is

    questioned. Various tests performed, indeed, tend to confirm our 

    theory' in particular, the now classical power!law energy behaviour 

    of the incident flux of energetic cosmic rays is easily derived, quite

    with expected exponents of !(.) and *+ main dependence, including

    the first knee-. $ltra!high energies, further, are easily attainable, with

    no necessary restriction of the %G/& kind, for instance. 0eyond

    1220 

    eV, rather, a new break is still made possible.

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    E! "OR#S 3 4tructure, galaxy, matter, antimatter, annihilation, origin,

    cosmic rays, flux, energy, ultra!high, disk, gas, equator,

    sources, power!law, knee, ankle, big!bang, globular 

    clusters, logarithmic slope, gamma ray bursts, dark mass.

    (I)  IN$RO#UC$ION%

     (a) #AR MASS

      # series of important paradoxical facts, of mechanical nature,

    salient from the very stuff of our Galaxy, still remain unexplained.

      5or instance, it is fully established now, from the mere aspect and

     behaviour of the old spiral arms, that their kinematics of gravitation

    requires an enormous rate of unknown extra mass, the so!called %dark

    mass&, in order to guarantee the overall balance in motion.

      The point, however, is not 3 what is the mysterious nature of this

    elusive %dark mass&, however remote or invisible it may be ' but what is

    the cosmological origin and associated productive mechanism 6 #t first,

    merely from definitions, such %dark mass& should essentially be exotic '

     but on another side, however, being deeply rooted in the very wheels of

    the Galaxy, it belongs to it and, thus, cannot either be exotic at all 7 This

    self!contradicting assessment, set as it is in the fundaments, unavoidably

    constitutes a paradox of its own, requiring intelligible answer.

    (b) &ALA'! S$RUC$URE

      The dynamical structure displayed by the "ilky Way, on another

    side, is by itself blatantly paradoxical to the highest degree. t is rarely

    MECHANICAL PARA#O'ES

    SALIEN$ IN $HE &ALA'! 

    (

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     pointed out, indeed, that it displays laterally a three!layer form, in a kind

    of %sa*ic+ s+ai-&, being made of two brilliant disks, parallel and

    opposite, but separated by another disk, this one dark and broad, settled

    in the equatorial region, seemingly almost deprived of luminous stars '

    with a similar width, of the order of 1222 ly light!years-, at least see

    5ig. 1a-. 4uch a reconstituted shape is by no way exceptional 3 indeed,

    quite a lot of galaxies, probably spiral as seen edge!on, in profile, display

    such a sandwich structure in real observation, through the lengthy side

    ex. 3 "128 , 94:)12 , ;G< =>?@ ?A1 @ 821+ @ 8)=) @ )?==@ >?18 B-

    C5ig. 1b, 1cD . 9ven the distorted lengthy galaxy ;G< +>1?, probably

    also a spiral one as seen in profile, undergoing gravitational attractions,

    accordingly displays a similarly distorted median dark stripe. t may be

    emphasiEed that such an effect can be observed as well for small!bulb

    galaxies, as for an huge!bulb galaxy like "128, the famous %4ombrero&.

    9ven the elliptical radio!galaxy ;G< )1(? displays such an equatorial

    stripe, very broad and dark. Fowever, when seen frontally upon a face,spiral galaxies manifest no obvious sign of equatorial obscurity.

      The point about it is more that of dark stability, than of primaeval

    genesis. :bviously, merely from gravitational attraction, the upper and

    lower parts of the Galaxy should have reoined long ago, in the long run,

    and the repelling gas seen settled in the equatorial region should therefore

    have been displaced, -raua suusi-, permeating the brilliant disks.

    There is absolutely no sign of such distortion and shift 7

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    maintenance mechanism, as a paramount mystery, remain unexplained.

    (c) &LOULAR CLUS$ERS

      The globular clusters, with some apparent %stability& or meta!

    stability-, concentrate an enormous amount of stars in quite a restricted

    field of space, whereas gravitational attraction in the gathering process,

    obviously, should have induced an enormous perturbative kinetic energy

    among the stars and so, ipso facto, an extreme mechanical instability,

    unavoidably, with patent effects in the long run for such old, type!,

     populations- 7 5or instance, %8> Toucan& is quite an old cluster, > billion

    years of age, gathering a regular set of some ( or + million stars, within

    (22 ly 3 being observed in extreme detail, almost star by star, it reveals no

    sign of instability in its core, not even the least %black hole&, as expected7

      Generally so, globular clusters present a phenomenon of kinetic

    stability and steady regularity, perfectly paradoxical on its own, requiringa fully mysterious evacuation of the primordial gravitational energy from

    gathering, through no obvious standard mechanism, a priori 7

    n the general frame of astrophysics and cosmology, repetitive

    observations of the kind stand unexplained, as a fundamental paradox.

    () 4UASARS 

    The extreme luminosity of some %H$#4#I4& may occasionally

    exceed a thousand times the brightest galaxies, from a core of tiny siEe

    less than 1 ly , a hundred thousand times smaller than a standard galaxy.

    t raises thus the problem of a prodigious density of radiative energy, if

    not of mass density. t stands quiEEical on its own, requiring a minimum

    of rational interpretation. t may be contrasted with the phenomenon of

    %bac5 +1es&, from which conectural strong radiative emissions should

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     be re!examined, as utterly paradoxical, if not self!contradicting for the

    name

    C1+D.

    (II)

      The observation of the extremely high energies reached by some

    cosmic rays 6 7027 eV-, indeed, suggests the existence of a powerful

    hidden phenomenon of appropriate creation, actually both intense and

    uniform in the Galaxy, at energies very much superior to those usually

    occurring in production mechanisms. :ne has thus to contemplate some

     process of likely cataclysmic genesis, extended through cosmic space,

    and still leading to an immense spectrum of effective energies, between

    6 7070 and 6 7027 eV 3 a flux variation curve almost perfectly smooth,

    apart from a few casual breaks as duly observed two small %knees&, one

    %ankle& etc.- ' and analytically accounted for, in first approximation, by a

    simple power!law in E82.9 , versus energy, of sheer decrease C1D.

    #mong the interpretative theories propounded, the eruptive

    one through a SUPERNO:A, at first sight, is thus natural and

     particularly commanding attention. t stands as an ancient proposal,

     by the way, tracing back to 5ritE wicky in 1A+?, to 9nrico 5ermi in

    1A8?, to 9vry 4chatEman in 1A==B, to "arcowith in (22= C(,+D.

     ;evertheless, beyond all technical refinements successively set

    forth in its various versions, this theory is harshly impeded by

    fundamental obections in principles and enormous obstacles in

    facts, actually rather numerous. :ther origins propounded 3 from

    %H$#4#I4& C8D, %J$K4#I4& C)D, %4$J9I!0$00K94& C1(DB

    are still, likewise, questionable.- %Gamma Iay 0ursts& GI0Ls- maystill be connected phenomena CAD.

    $HE PARA#O' O; A S$ALE ;LU' O;

    COSMIC RA!S A$ UL$RA8HI&H ENER&!.

    )

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    #nd indeed, humanity has not registered more than about ten

    quite certified 4$J9I;:V#9, on the whole, within the last (222

    years. There is, however, now a current opinion that 4$J9I;:V#9

    should genuinely be much more numerous, perhaps ) or 12 times 7

    0ut, obviously, most of them, being extra!galactic, cannot noticeably

    contribute for instance, 4;1A?>#, recently certified 4$J9I;:V#,

    from the Karge "agellanic

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    easily be estimated, for instance, for any standard solar!type system

    same result exactly with a J$K4#I, at large distance, even starting

    with some 12@ Tesla at ≈ 122 km-. #s mean distance between stars

    is obviously much larger, as we know, the average magnetic field, in

     between, should thus be much less than the 70870 Tesla postulated,

    and so quite insufficient to ensure such a galactic confinement.

    "oreover, to be effective, the confining magnetic field must

    stay roughly, but uniformly, ereicuar t1 t+e &aa ae '

     but, actually, there is no compelling reason for it 3 star fields should

    rather be more or less ra1 i irecti1, a priori, thus resulting

    in reduced if not nearly Eero- average magnetic field, in the Galaxy.

      There are still two fundamental hitches for this mechanism 3

    first, only electrically charged emission is meant in magnetic capture,

     but we perfectly know that eutra c11ets, such as neutrinos,

     photons B if not molecules and neutral atoms-, must be lost with a

     paramount fraction of the 4$J9I;:V# energy radiated. 0esides,

    such magnetic capture is fully effective only for horiEontal emission,

    i. e., essentially within the plane of the Galaxy 3 since 4$J9I;:V#

    explosion should be is1tr1ic, radiating in every direction, obviously

    emission must be mostly transversal and, thus, 1st 1r c1ieet.

    :n the whole, this old theoretical vision, in many respects,

    should thus appear exceedingly unrealistic, if not irrational, to stay aconvincing one. We shall however maintain the essentials, namely

    the requirement of a vast cataclysmic mechanism, much more

     powerful if possible than the mere 4$J9I;:V# above M 707< eV-

    and, particularly, with much more steady and regular emission,

    involving the galactic plane in a much more natural way, both

    >

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    geometrically and dynamically, and no neglect of the obviously

     paramount neutral emissions  L s, B s B-.

    #ll these preliminary conditions, on the basis of observations,

    look quite compulsory to establish the fundaments of an acceptable

    and c1+eret t+e1r of astrophysics.

    ?

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    (III) MA$$ER 8 AN$IMA$$ER E4UILIRIUM

    AN# S$RUC$URE O; $HE UNI:ERSE.

    t is accordingly convenient to go back to the farthest roots of our

     physical concepts and, thereby, to the nature, nay to the general structure,

    of the $niverse.

    We know that, originally, at the precise %0G!0#;G& time, the total

     baryonic number of the $niverse should have been Eero. 0ut now, it is

    too easily admitted that, ust immediately after, a paradoxical unbalance

    occurred and should have depressed, and even almost suppressed, anti!

     baryonic- #;T"#TT9I versus baryonic- "#TT9I, mysteriously,

    throughout an essential drastic asymmetry, to such a point that, now, we

    could almost only perceive the latter one, in practice. The total baryonic

    number of the $niverse, accordingly, would henceforth be made largely

     positive, forever.0ut now, another possible assumption is still possible 3 namely, that

    hidden matter and antimatter, in similar if not identical proportions, should

    actually be well balanced throughout the $niverse, if not locally, without

    manifesting it clearly, as a consequence of some primordial separation.

    t is uneasily believable that pure matter galaxies, in opposition to

     pure antimatter galaxies, might distinctly exist, indeed. The reason is that

    their formal separation, in itself, with condensation a long time after the

    %0G!0#;G&, would mean no solution to the genuine problem, and look

    artificial or even unthinkable in the absence of any patent repulsive

    mechanism, a priori at stance. That is not, however, rigorously impossible.

    4o, it is much more natural to suppose that matter and antimatter,

    actually, do cohabit inside the galaxies. ;ow, they should unavoidably

    annihilate mutually, then, by contact or by coalescence, which might be at

    A

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    the origin of phenomena in astronomy as quiEEical as the mysteriously

    intensely radiating %H$#4#I4&, that basic astrophysics can uneasily

    interpret through usual frames.

    That might be, as well, at the origin of the elusive %ar5 eer-&, if

    not of the unaccountable %ar5 ass&, according to the dedicated terms,

    which should constitute the most part of the cosmic world, by far, in spite

    of their lack of any direct visibility. The challenge in corpuscular physics,

    as a matter of fact, has not yet been surmounted in any convincing way.-

    9ven the %usars& raise a problem3 it is fully admitted, indeed, that

    they are neutron stars and, so, somewhat gravitational prisons close to the

    so!called %bac5 +1es&-, paradoxically occasioning massive energetic

    local emissions of theirs. The point is not that rotating usars with high

    magnetic fields ≈ 12@ Tesla - could not engender sufficient accelerating

    electric field the effect being spatially restricted to the strict vicinity of

    the magnetic poles- ' but that there is nearly nothing to accelerate from a

    neutron star 7-. f there was, through unlikely ionisation of neutron matter,the acceleration energy produced would still be heavily diminished by the

     paramount gravitational energy, in extraction from the pulsar.

      n that spirit, however, according to some theoretical proposals still,

    there exists a clear assumption that such emitting usars might constitute

    a source for ultra!high!energy cosmic rays C)D 7

    5urthemore, the so!called %bac5 +1es& are sometimes similarlyregarded as intensely radiating sources ust like %*+ite *es&-, through

    some axiomatic arguments 3 we might, more naturally, connect them to

    some cosmic regions of matter and antimatter, possibly undergoing violent

    gravitational attraction, at first, and eventually thus annihilating C=D.

    n an associated paper, however, we try to give some classical

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     ustification, through a cosmological solution implying %ubiDuit1us

    r1babiit *aes&, at the frontier of Huantum "echanics C1+D.-

    (I:)

      We shall surmise that the median disk is constituted by an abnormal

    amount of some sort of complex %gas&, under very high pressure whatever

    may be its composition 3 atoms, molecules, ions, dust, meteorites B of any

    siEes-. t would result from massive annihilation, be it primordial or not, of

    stars and %anti!stars& or, more generally, of any coalescing antimatter and

    matter, following the 0G ! 0#;G. This repulsive gas, casually renewed

    still by annihilation, should thus suffice to ensure the gravitational balance

    of the whole 3 giving poise, in attraction, to the two opposite brilliant disks,

    one of them being essentially made up, supposedly, of positively baryonic

    matter and containing our solar system-, and the parallel, remote one, of

    anti!baryonic- antimatter, respectively.

     ;ow, let us specify things quantitatively. This conecture can be

    deeply probed, indeed, through various fundamental tests.

    a) $ES$ O; $HE ;LU' SPEC$RUM LA".

    0eing almost perfectly regular between ≈ 12? and ≈ 1227  eV , the

    spectrum behaviour suggests a common origin for energetic cosmic rays,

    differences being essentially mathematical and hardly physical.

      4ince, actually, genuine products and precise mechanisms implied

    in the annihilations probably quite unusual ones-, are properly unknown,

    &ENESIS O; COSMIC RA!S ;ROMMA$$ER8AN$IMA$$ER ANNIHILA$ION

    11

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    we shall adopt a purely phenomenological attitude.

      To start, let us suppose, at first guess, that the annihilation matter is

    a perfect gas in adiabatic expansion, and that still non!relativistic equations

    formally apply with proper constants-.

    n usual notations3  pVγ  

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    to 1.8 O >@) and to 1.+++ O ?@= , respectively, for such an effective theory.

    Jower!law spectrum shapes are thus quite naturally resulting in

     perfect agreement, at first order, as expected, with the observational flux 3

    namely, in E82.= and in E83, respectively, C>D the former term prevailing

     before the %knee& 121) eV-, and the latter term above from M 121) eV to

    M 12(2 eV-. #bove 12(2 eV, the genuine behaviour is still experimentally

    controversial C5ig. (, +a, +bD.

      #ll these derivations and results were made straightforward, indeed,

    without any kind of analytic adustment or any forcible approximation.-

    4uch a heuristic analysis, quantifying ust through integer numbers,

    already appears in excellent agreement with the observation data, enabling

    one to account even for the first %knee&. Well, it may still easily be refined

    much further, in depth to account for new details of the spectrum, such as

    extra %knees&, %ankles&, %toes&B-, merely through addition of some extra

    S contributions ' but this would imply no great improvement basically, at

    the level of principles C5ig.(,+D.

    Jointedly, such a kind of formal behaviour might be quite general 3

    for instance, non*thermal U cosmic rays still appear to display an E82 

     behaviour, quite analogous and characteristic, corresponding to the value 3

    S O 1.) O =@8 , as another structure constant, possibly,.

    Rear5.

    Therefore, all S terms are symptomatically observed to present the

     purely heuristic analytical form3

    J ( 2) /  , with integer n ' namely, J < , = ,

      The resulting 9 exponent3 7/ G7   is , accordingly, equal to

    ( / 2) J 2 , 2.= , 3  

    1+

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      4uch integers might effectively reflect some unknown relativistic

    structure constants, at stance. With upper n O >,? B, we should still expect

    S O *+.), * 8 B ' and so, possibly, a new steep break above 12(2 eV , not

    incompatible with some recent controversial data C+,?D.

    18

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    b)  $ES$ O; &RA:I$A$IONAL ALANCE.

      PLANAR S$AILI$! J

      The second test is connected with the internal galactic balance.

      :ur sun, for instance, is attracted by the lower galactic disk, merely

    in agreement with the law of universal attraction.

    Fowever, the total impulse received by the sun per time unit is meant

    as the sum of all impulses accordingly received from cosmic rays through

    space, coming from the gaseous medium, settled in the equator disk of the

    Galaxy-, in the south galactic hemisphere3 this makes up the repulsive force

    acting upon the sun, eventually.

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    the highest energies between M 1212 and M 12(1 eV, and more particularly

    from above 121) eV-, appear almost negligible, when compared to lowest!

    energy contributions below M 1212 eV-, on account of the drastic power* 

    law decrease of the flux spectrum versus energy-.

      &LOULAR CLUS$ERS S$AILI$!     

      The overall mechanical stability of globular clusters, in the suburbs

    or our galaxy, a priori appears quite paradoxical, since their primordial

    gathering through gravitational attraction should have inherently involved

    quite an enormous, destabilising, dynamical energy ' the disappearance of

    such a fundamental energy cannot be explained merely through elementary

    celestial mechanics. 0ut it should get, now, quite clear and natural through

    %E:APORA$ION A;$ER ANNIHILA$IONQ, from old primary stages.

    c) $ES$ O; NOR$H SOU$HQ &ALAC$IC

    AS!MME$R! O; $HE ;LU'.

    :bviously, from all previous stances, the flux of the high!energy

    cosmic rays should mainly originate from the galactic plane and, therefore,

    display quite a characteristic downright asymmetry, being oriented from the

    southern equatorial region to the %;:ITF&, in Galactic coordinates,

      #nd that is precisely what is observed 3 the cosmic flux, indeed, is

    isotropic at intermediate energies, while clearly oriented from %4:$TF& to

    %;:ITF& at highest energies. 4uch a test would be almost incompatible,

    for instance, with an extra!galactic origin of the radiation, or even with any

    uniform emission from our own galactic halo.

    1=

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      5rom previous considerations, it should be obvious that the opposition

    of disks of matter and antimatter being generally pointless for most eitica

    -aaies, confused and compact as they appear, the above studied mechanism

    of annihilation, abundantly producing %dark matter& and cosmic rays of the

    highest energy, as hypothesised, should ust rarely occur in such instances.

      n conclusion, scarcit or %eart+& is predictable 1r ar5 atterQ,

    according to expectations, for most big elliptical galaxies, as a paradox.

      #nd precisely, this amaEing fact has been observed on a large scale

    and ust recently notified, in physical astronomy, indeed, t provides another

    confirmation of our general theory of galactic cosmogenesis, as a fourth test.

    (:) CONCLUSION

     

    We have shown that many mechanical mysteries are at stance in the

    Galaxy, and deserve a righteous unique, synthetic and likely, interpretation.

      #ccordingly, we have proposed an astrophysical theory of atter8

    atiatter ai+iati1, which should answer any such issues and, most

     particularly, account for the analytical behaviour of ultra!high energies of

    cosmic rays, and the very possibility of their existence above 127< eV.

      The origin, if not the exotic nature, of massively dominant %#I/

    "#TT9I&, tightly attached to our Galaxy, in regulation of its mechanics,

    then receives a natural interpretation.

    ()

      #EAR$H T

    O; #AR MA$$ER 

    IN ELLIP$ICAL &ALA'IES

    1>

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      0y the way, we thus give general phenomenological indications, in

    furtherance, for a heuristic theory of utra8reatiistic t+er1aics of 

    cosmic rays and so, possibly, of such galactic dominant dark matter.

      n an associated paper about neutrino oscillation in vacuum, we

    give extra evidence for it as a necessary +ie et+er eiu C1+D.

    The dark broad stripe which, pointedly, appears in the equator of the

    "ilky Way, as well as of many other spiral galaxies, indeed, resulting from

    annihilation of opposite luminous disks, when in contact, and thus ensuring

    their poise by constant repulsion, should then, actually, undergo a

     permanent renewal, compensating the unavoidable gas evaporation slow

    enough, not to smear the brilliant regions-.

      4imilarly, the meta!stability of the old globular clusters, otherwise

    mechanically puEEling, is now quite understood, as well as the prodigious

    radiation density observed from some H$#4#I4.

    n the same spirit, we can add that promptly varying emissions from

    many H$#4#I4 sensed over several months, nay a few days-, have beennoted, suggesting violent internal activity. 5or some ones still , relativistic

    expansion velocities CAD duly observed testify in the same way.

    The amaEing opposition of age between usually very young radio

    J$K4#I4 settled in the equatorial realm, and very old J$K4#I4 outside

    uniformly scattered all throughout the Galaxy, as it seems-, now, receives

    clear ustification. The fact that, generally, the former ones are isolated,

    while the latter get binary, goes in the same sense all these features being

    meant through violently perturbative phenomena, of course, in agreement

    with our framing conecture of massive cosmological annihilation, within

    the galactic plane.-

    These general considerations could be extended to various other

    mysteries in astrophysics.

    1?

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      Jarticularly, on such account, the sudden irruption of enormous

    antimatter meteorites into our solar system is highly improbable and, thus,

    should rarely be occurring, but still remains always possible. t might still

    explain, accordingly, some strange phenomena happened through the solar

    system, such as the probably sudden disintegration of a fifth planet, located

     between "ars and Xupiter, four times as big as the 9arth, and from which

    gigantic fragments still remain nowadays among the famous %asteroids&,

    gravitating on elliptical traectories, with half maor axes close to (.?

    astronomical units, exactly as expected from the Titius!0ode formula-.

    4uch a natural interpretation had been completely abandoned, in

    the past, actually, as being unlikely with ust a common matter meteorite

    onto such a huge planet.

     ;ow, the disintegration hypothesis can be regularly restored, as

     being quite natural with impinging real antimatter.

    The dilapidated present state of "ars, as well as the somewhat

    uncertain evolution of Jluto might be related to such phenomena.#t least in some occurrences, what is sometimes qualified as a

    %0K#

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    F:K94&. We can, accordingly, hope for concrete results in that spirit, in

    some close future.

      #nyhow, the usual hypothesis of absolute matter dominance is

     ust of pragmatic origin, and theory is forcibly only adusted to our biased

    current observation. n a sense, somewhat, it deeply contradicts the rooted

     principles of cosmogenesis, of a primordial native equilibrium ' for which

    the immediate rupture, to the point of almost complete cancellation of some

    species in favour of the symmetric almost equivalent- one, far from being

    obvious, might even seem artificial, axiomatically far!fetched or contrived.

      ndeed, merely because we cannot see antimatter where we live,

    we still suppose that it must be nearly absent from the whole remnant of the

    $niverse. 0ut actually, if we cannot see it, hereby, it is simply because it

    should soon disintegrate, through contacts with prevailing present matter.

      The fundamental

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    RE;ERENCES

    C1D I. 9ngel, ;ucl. Jhys.  Jroc. 4uppl.- 7=7,8+> (22=-'

    #.V. :linto, 4cience 37=, =? (22>-.

    C(D T. /obayashi, et al., arUiv3 astro!ph@2+2?8>2 (22+-'

    #. "arcowith et al., #stron. #strophys.,

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    C11D #. Yamamoto, et al., (?th nt.

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    ;I&URE CAP$IONS

    ;i-. 7

    a- Jrofile classical view of our Galaxy, from numerical simulations,

    and data, by X.;. 0ahcall nstitute for #dvanced 4tudy-.

     

    ;i-. 2

    Whole flux spectrum of high!energy cosmic rays, from 12@ to 1227 eV,

    from cumulated data 3 extended over 1+ orders of magnitude in energy,

    and ++ orders of magnitude in cosmic!ray flux. The curve is almost

     perfectly regular, with a few remarkable details however, in disturbance 3

    a former %knee& set at ). 127= eV ' a second %knee& at +. 1279 eV, is

    hardly distinguishable' an %ankle& set at +. 127@ eV ' a questionable

    %G/ cut& above ?. 127? eV, in contradiction with controversial data.

    ;i-. 3a, b

    The flux for check is multiplied by an 93 factor, to account for the 983 

    dependence, with cumulated data. The curve obtained is flat, indeed, ust

     between the two knees.

    (+

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    5G. (

    (8

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