The scientific goals of the Yakutsk array under modernization
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The scientific goals of the Yakutsk array under modernization. A . A . Ivanov for the Yakutsk array group. CR Physics Large Scale Experiments at the Second Decade of the 21st Century MSU, May 16-18 2011. Content. Introduction Main results and the present status - PowerPoint PPT Presentation
Transcript of The scientific goals of the Yakutsk array under modernization
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A.A. Ivanov for the Yakutsk array groupThe scientific goals of the Yakutsk array under modernization
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ContentIntroductionMain results and the present status of the Yakutsk array experiment Next step astrophysical goals Modernization of the arrayConclusions
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ContentIntroductionMain results and the present status of the Yakutsk array experiment Next step astrophysical goals Modernization of the arrayConclusions
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N.N. Efimov and D.D. KrasilnikovIn 1959 D.D. Krasilnikov formulated an idea of EAS array in Yakutsk.
5.09.1964: The project is approved by the Scientific Council of AS USSR.
1967: The beginning of construction of EAS-13 prototype (13 stations, D.D. Krasilnikov, I.Ye. Sleptsov).
1967-1970: Engineering stage; first showers detected.
1971-1973: the 1st stage array built up, consisting of 43 stations with 2 scintillators; Cherenkov light detectors; detectors of muons (N.N. Efimov).
The 2nd stage of the array was completed to 1991 (I.Ye. Sleptsov). The infill array of 18 stations, and the large area muon detector was added.Additional experiments have been fulfilled to measure neutrons initiated by EAS (1976-1987) and to detect radio signal from showers (1.9 MHz:1972-1973, 32 MHz: 1986-1989). S.N. Vernov, S.I. Nikolsky, G.B. Khristiansen
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IntroductionMain results and the present status of the Yakutsk array experiment Next step astrophysical goals Modernization of the arrayConclusions
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Present day arrangement of the Yakutsk array detectors. SY=8.2 km2.- Stations with 2 scintillators (49x2+10)- Cherenkov light detectors (32)Detectors of muons S=20 2 (5)Large area detector of muons S=180 2
- Pinhole detectors
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The energy spectrum of cosmic rays below E=1018 eVDifferential spectra measured with EAS arraysDifferential spectra after systematic corrections to CR intensity and energy(A.A. Ivanov, S.P. Knurenko and I.Ye. Sleptsov, NJP, 11 (2009) 065008).
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4.90901258624.634.534.434.334.234.135.00423275470.0162920260.01692710294.85383251090.00009338660.00009340674.95518792744.78728195194.9460729521
4.93763110585.01218531240.01566280220.0162488834.860016880.00008671150.00008672884.95509410394.80355579454.9559739422
4.81547797424.9934575530.01888534420.01974405824.87513570140.00015893670.00015899494.96472486794.80766235874.9658749323
4.88921561285.01744934470.02098449150.02205014074.88049938520.0002953380.0002955394.99381304744.80981269934.9658749323
4.8352936774.97854176860.02329446310.0246150894.8876772440.00021889840.00021900884.97628676734.81661655684.9757759224
4.87711642194.97507463190.0291800050.03128272154.89619224360.00030317240.00030338424.97094460824.81277861864.9757759224
4.87638597544.91677270470.03809004960.04175474814.90439489840.00037374740.00037406934.89672470334.816177334.9757759224
4.89693212474.91902171560.04009729550.04417946584.91283422270.00034399560.00034426834.86356294474.82467898450.00549747190.00556795424.9658749323
4.94939316754.83405588220.05098076270.05777121284.92226643310.00050809540.00050869054.85059359664.81653263570.00632478870.00641826194.9559739422
4.95930101894.84787328060.0579919470.06694678964.92977812880.00058728130.00058807664.84893040424.81826582130.00789648080.00804272034.9220912663
5.01176206174.7338395960.08505718620.10587573064.9365966510.00065062860.00065160474.80844278724.79817160570.00971616550.00993852254.9022892861
5.01103161524.70314052980.09775248560.12634649954.94857519820.00079468360.00079614044.79706945934.81513916270.01055018230.01081286934.8329823554
4.94647138154.78485023810.08894108330.11197375944.96295294480.00102118330.00102359024.74532041814.79617102160.01378828450.01424043914.793378395
4.89254944564.67161298980.11763949790.16185081994.97211557650.00120917340.00121254944.65366201244.73610827950.01472325680.01523996664.7834774049
4.88118070124.66365813960.10546982470.13959102454.978234820.00149670850.00150188444.65814288054.72480154070.02802872360.02996322344.72407146430.02970297030.0396039604
4.88045025474.57422595750.14748203360.22502459184.98165761530.00186372770.00187176024.62700338280.02041446480.02142160424.71020100680.02732312720.02915822874.73397245440.03960396040.0396039604
4.77333682954.72431202580.11125269920.14994883294.95970369210.00230787280.00232020264.59900253340.01966516010.02059801994.69860827950.02896369590.03103423374.55575463260.04950495050.0693069307
4.83203476184.64535237720.16814882770.27803871284.93908111890.00290499060.0029245534.56955874850.02233670920.02354812184.69469530050.04090498780.04516215884.67456651380.05940594060.0693069307
4.7293227454.90167489460.00373107520.00376340734.52433890660.02440498660.02585849874.65842957630.0579919470.06694678964.43694275140.0990099010.1089108911
4.73482918794.85809684460.00472948770.00478155964.49933702290.02530586530.02687214644.37757197540.12142216290.16914239914.47654671180.10891089110.1386138614
4.74473703934.80547041040.00606497720.00615087634.5095842170.02767142660.02955524364.79793811760.11539341870.15760785344.4963486920.11881188120.1782178218
4.70145340134.76244308530.00782533750.00796892974.40876676110.03392612050.03680264794.55575463260.13861386140.2079207921
4.6794463594.76023403430.0096506660.00987000124.40780958250.0367228070.0401172232
4.67871591254.71519926520.01239770580.01276204654.38119574980.059585690.0690809191
4.64607057244.70593212110.01524903710.01580400994.33185612090.08424275410.1046146293
4.5877472284.67166660310.01939604960.0203029589
4.58261537314.59633383680.02566396030.0272763102
4.56244381184.64340458540.02953127760.0316868176
4.53419988014.57721922940.03861804580.0423901629
4.49715313164.4808392250.05194134750.0590082605
4.4601063834.56574715370.05716496890.065846596
4.4549745284.50447415560.07349107690.0885121505
4.37977599644.41374952740.09753115770.125975956
4.4065590351
4.3827165118
4.3482356907
4.3075179802
4.2491946359
4.2121478873
4.11567276
4.110540905
4.0947707522
4.0195722206
4.0038020677
log10(E, eV)
log10(JE2.75, GeV1.75m-2s-1sr-1)
Knurenko
Original Knurenko spectrum - 05Intensity correctionEnergy correction
E0JE^3, eVdJJ-dJJ+dJlgElgJE^2.75, GeVlgElgJE^2.75, GeVJ-dJ+dlgE*RlgJE^2.75lgE+lgRlgJE^2.75
1.60E+063.50E+2415.204.99315.2044.99315.0954.95515.1174.998
2.00E+063.70E+2415.304.99315.3014.99315.1924.95515.2144.997
2.50E+064.00E+2415.405.00315.3985.00315.2894.96515.3105.007
2.90E+064.40E+2415.465.02815.4475.03215.3384.99415.3605.036
3.50E+064.50E+2415.545.01715.5565.01415.4484.97615.4695.019
4.60E+064.70E+2415.665.00615.6535.00915.5454.97115.5665.013
5.70E+064.30E+2415.764.94415.7084.95715.5994.89715.6204.939
6.30E+064.20E+2415.804.92315.7994.92315.6914.86415.7124.906
7.80E+064.30E+2415.894.91015.8924.91015.7834.85115.8054.893
9.50E+064.50E+2415.984.90915.9784.90915.8694.84915.8904.891
1.15E+074.30E+2416.064.86816.0614.86815.9524.80815.9734.851
1.40E+074.40E+2416.154.85716.1464.85716.0374.79716.0594.839
1.78E+074.10E+2416.254.80016.2304.80516.1224.74516.1434.788
2.19E+073.50E+2416.344.70916.3224.71416.2144.65416.2354.696
2.80E+073.80E+2416.454.71816.4474.71816.3384.65816.3604.701
3.50E+073.76E+241.80E+233.58E+243.94E+2416.544.6890.0210.02016.5444.6870.02142160420.020414464816.4354.62716.4574.669
4.20E+073.67E+241.70E+233.50E+243.84E+2416.624.6590.0210.02016.6234.6590.02059801990.019665160116.5154.59916.5364.641
5.10E+073.60E+241.90E+233.41E+243.79E+2416.714.6290.0240.02216.7084.6290.02354812180.022336709216.5994.57016.6204.612
6.60E+073.46E+242.00E+233.26E+243.66E+2416.824.5840.0260.02416.8204.5840.02585849870.024404986616.7114.52416.7324.567
7.90E+073.50E+242.10E+233.29E+243.71E+2416.904.5700.0270.02516.9404.5590.02687214640.025305865316.8314.49916.8524.542
1.00E+083.80E+242.50E+233.55E+244.05E+2417.004.5800.0300.02817.0414.5690.02955524360.027671426616.9334.51016.9544.552
1.58E+083.20E+242.60E+232.94E+243.46E+2417.204.4550.0370.03417.1464.4690.03680264790.033926120517.0374.40917.0594.451
1.66E+083.40E+243.00E+233.10E+243.70E+2417.224.4760.0400.03717.2554.4680.04011722320.03672280717.1474.40817.1684.450
2.00E+083.40E+245.00E+232.90E+243.90E+2417.304.4560.0690.06017.3624.4410.06908091910.0595856917.2534.38117.2744.424
3.10E+083.27E+247.00E+232.57E+243.97E+2417.494.3920.1050.08417.4914.3920.10461462930.084242754117.3834.33217.4044.374
Knee15.6020599913RlgR
1.050.0211892991
kappa1kappa2
Sigma1.672.1
0.251.09106373611.147760325
lgRJ0.03785012130.0598512083
Knurenko
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
000.02041446480.0214216042
000.01966516010.0205980199
000.02233670920.0235481218
000.02440498660.0258584987
000.02530586530.0268721464
000.02767142660.0295552436
000.03392612050.0368026479
000.0367228070.0401172232
000.059585690.0690809191
000.08424275410.1046146293
CERN
My fault
lgE15.2015.3015.4015.4515.5515.6515.7515.8515.950.0016.0516.1516.2516.3516.4516.5516.6516.7516.8516.9517.0517.1517.2517.3517.50
J0.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00
dJ0.000.000.000.000.000.000.000.000.000.00
0.020.020.020.030.030.030.040.040.070.10
lg(J*E^2.75),GeV4.984.995.014.995.034.974.935.065.07-39.034.844.874.804.744.734.714.734.754.674.714.724.324.564.594.42
0.020.020.020.020.030.030.030.040.060.08
BLANKA
BLANKA
lgE14.3514.4514.5514.6514.7514.8514.9515.0515.1515.2515.3515.4515.5515.6515.7515.8516.0016.2016.4016.6016.80
J/GeV1.21E-106.68E-113.58E-111.91E-111.03E-115.42E-122.90E-121.57E-128.18E-134.36E-132.21E-131.22E-136.20E-142.90E-141.50E-147.70E-152.90E-158.10E-162.10E-163.10E-172.30E-17
dJ4.00E-132.00E-132.00E-131.00E-131.00E-134.00E-143.00E-142.00E-141.20E-148.00E-155.00E-153.00E-152.00E-151.00E-151.00E-155.00E-162.00E-168.00E-173.00E-171.00E-177.00E-18
0.010.010.010.010.010.010.020.030.030.030.050.070.170.16
lgJE^2.754.804.814.824.824.834.824.824.834.834.834.814.824.804.754.744.724.714.714.674.394.81
0.010.010.010.010.010.010.010.030.030.030.040.060.120.12
Intensity corerction
lgE*R14.3014.4014.5014.6014.7014.8014.9015.0015.1015.2015.3015.4015.5015.6015.7015.8015.9516.1516.3516.5516.75
lgJE^2.75-lgR4.794.804.814.814.824.814.824.824.824.824.804.824.804.744.724.714.704.694.664.384.80
Energy correction
lgE+lgR14.3814.4814.5814.6814.7814.8814.9815.0815.1815.2815.3815.4815.5815.6815.7815.8816.0316.2316.4316.6316.83
lgJE^2.75+2lgR4.9456444444.96191828664.96602485084.96817519144.97497904894.97114111074.97453982214.98304147664.97489512784.97662831344.95653409784.97350165484.95453351374.89447077164.88316403284.86856349894.85697077164.85305779264.81679206844.53593446754.9563006097
Knee15.6020599913RlgR
1.20.079181246
kappa1kappa2
Sigma1.672.1
0.121.0202830411.0322614727
lgRJ0.00872066790.0137897184
Models
Erlykin from HorandellgRJ0.05
dx72.33184.006.00
dy66.00166.003.00
x445464738393102112121131141151160170179189198208218227237247256266276285295304314324
y212210208206205203201200199198197196195193193192191191189183180177173164158154149145141136
lgE13.0613.2013.3413.4713.6013.7413.8714.0014.1314.2714.4114.5414.6714.8114.9315.0715.1915.3315.4715.5915.7315.8716.0016.1316.2716.4016.5316.6616.8016.94
lg(J*E^2.5)3.703.673.643.613.593.563.533.523.503.483.473.453.443.413.413.393.383.383.353.263.213.173.112.972.882.822.742.682.622.55
lg(J*E^2.75)4.804.824.844.864.864.894.914.934.964.974.914.904.884.854.754.704.674.634.604.574.53
lgJ+lgR4.854.874.894.914.914.944.964.985.015.024.964.954.934.904.804.754.724.684.654.624.58
lgRJ0.00
Lagutin
lgE15.0015.5016.0016.5017.0017.5018.0018.5019.0019.5020.00
lgJE^36.466.626.586.556.556.576.596.476.426.456.50
lgJE^2.754.965.004.834.684.554.454.34
lgJ+lgR4.965.004.834.684.554.454.34
Tunka
Tunka - (Hamburg)
lgE14.55914.65814.75814.85714.95715.05615.15515.25515.35415.45315.55315.65215.75215.85115.95016.05016.16116.24816.36016.46016.55916.65816.75816.857
4.6614.6174.5944.6394.3394.5944.6064.5834.8174.1834.117
lgJE^2.75, GeV4.6064.6284.6394.6724.6834.6944.7174.7614.7174.7064.7724.8284.7174.6944.6834.6724.7174.4834.6614.6834.6834.9064.4174.417
4.7394.7284.7284.7944.5944.7174.7504.7614.9834.5614.594
Mifi - 04
lgE14.85414.95115.06815.16515.26215.35915.45615.55315.65015.76715.86415.96116.05816.15516.25216.35016.46616.31116.66016.75716.85416.951
4.7234.7334.5254.6444.3664.3764.3564.386
lgJE^2.75, GeV4.9704.9804.9904.9905.0005.0005.0004.9904.9804.9604.9414.8714.8324.8224.7624.7724.5944.7134.4754.5154.5354.594
4.7924.8124.6444.7724.5744.6244.6534.733
0.0400.0400.0690.0690.1090.1390.1780.208
lgJE^2.75, GeV4.9704.9804.9904.9905.0005.0005.0004.9904.9804.9604.9414.8714.8324.8224.7624.7724.5944.7134.4754.5154.5354.594
0.0300.0400.0500.0590.0990.1090.1190.139
Intensity correction
lgE-lgR14.76714.86414.98115.07815.17515.27215.36915.46615.56415.68015.77715.87415.97116.06816.16516.26316.37916.22416.57316.67016.76716.864
lgJE^2.75-lgR4.9464.9564.9664.9664.9764.9764.9764.9664.9564.9224.9024.8334.7934.7834.7244.7344.5564.6754.4374.4774.4964.556
Energy corrction
lgE+lgR14.78914.88615.00215.09915.19615.29315.39115.48815.58515.70115.79815.89515.99216.09016.18716.28416.40016.24516.59416.69216.78916.886
lgJE^2.75+2lgR4.9884.9985.0085.0085.0185.0185.0185.0084.9984.9644.9454.8754.8364.8264.7664.7764.5984.7174.4794.5194.5394.598
Knee15.6020599913RlgR
1.050.0211892991
kappa1kappa2
Sigma1.672.1
0.21.05736292311.0922065415
lgRJ0.02422407760.0383047733
FigxRJxRE
FigxRJxRE
4.634.534.434.334.234.134.99756652564.9456444444.98845155024.86445979674.97777622320.0162920260.01692710294.8710328544
4.9974727024.96191828664.99835254034.89307831644.9857287810.01566280220.0162488834.8772172235
5.0071034664.96602485085.00825353044.77092518484.96700102150.01888534420.01974405824.8923360449
5.03619164554.96817519145.00825353044.84466282344.99099281320.02098449150.02205014074.8976997287
5.01866536554.97497904895.01815452054.79074088754.95208523720.02329446310.0246150894.9048775875
5.01332320644.97114111075.01815452054.83256363254.94861810040.0291800050.03128272154.9133925871
4.93910330144.97453982215.01815452054.8318331864.89031617320.03809004960.04175474814.9215952419
4.90594154294.98304147660.00549747190.00556795425.00825353044.85237933524.89256518420.04009729550.04417946584.9300345662
4.89297219484.97489512780.00632478870.00641826194.99835254034.90484037814.80759935080.05098076270.05777121284.9394667766
4.89130900234.97662831340.00789648080.00804272034.96446986444.91474822954.82141674920.0579919470.06694678964.9469784724
4.85082138534.95653409780.00971616550.00993852254.94466788424.96720927234.70738306460.08505718620.10587573064.9537969945
4.83944805744.97350165480.01055018230.01081286934.87536095354.96647882584.67668399840.09775248560.12634649954.9657755417
4.78769901624.95453351370.01378828450.01424043914.83575699324.90191859214.75839370670.08894108330.11197375944.9801532884
4.69604061054.89447077160.01472325680.01523996664.82585600314.84799665624.64515645830.11763949790.16185081994.98931592
4.70052147864.88316403280.02802872360.02996322344.76645006250.02970297030.03960396044.83662791184.63720160810.10546982470.13959102454.9954351635
4.6693819810.02041446480.02142160424.86856349890.02732312720.02915822874.77635105260.03960396040.03960396044.83589746534.54776942610.14748203360.22502459184.9988579588
4.64138113150.01966516010.02059801994.85697077160.02896369590.03103423374.59813323080.04950495050.06930693074.72878404014.69785549430.11125269920.14994883294.9769040356
4.61193734660.02233670920.02354812184.85305779260.04090498780.04516215884.7169451120.05940594060.06930693074.78748197234.61889584570.16814882770.27803871284.9562814624
4.56671750480.02440498660.02585849874.81679206840.0579919470.06694678964.47932134960.0990099010.10891089114.68476995564.9188752381
4.5417156210.02530586530.02687214644.53593446750.12142216290.16914239914.518925310.10891089110.13861386144.69027639854.8752971881
4.55196281520.02767142660.02955524364.95630060970.11539341870.15760785344.53872729020.11881188120.17821782184.70018424984.822670754
4.45114535930.03392612050.03680264794.59813323080.13861386140.20792079214.65690061184.7796434288
4.45018818060.0367228070.04011722324.63489356964.7774343778
4.42357434790.059585690.06908091914.63416312314.7323996088
4.37423471910.08424275410.10461462934.60151778294.7231324647
4.54319443864.6888669466
4.53806258374.6135341804
4.51789102244.660604929
4.48964709074.5944195729
4.45260034214.4980395685
4.41555359364.5829474973
4.41042173864.5216744992
4.3352232074.430949871
4.3620062456
4.3381637224
4.3036829013
4.2629651908
4.2046418465
4.1675950979
4.0711199705
4.0659881156
4.0502179628
3.9750194311
3.9592492783
log10(E, eV)
log10(JE2.75, GeV1.75m-2s-1sr-1)
Fig x RJ
Fig x RJ
4.90901258624.634.534.434.334.234.135.00423275470.0162920260.01692710294.85383251090.00009338660.00009340674.95518792744.78728195194.9460729521
4.93763110585.01218531240.01566280220.0162488834.860016880.00008671150.00008672884.95509410394.80355579454.9559739422
4.81547797424.9934575530.01888534420.01974405824.87513570140.00015893670.00015899494.96472486794.80766235874.9658749323
4.88921561285.01744934470.02098449150.02205014074.88049938520.0002953380.0002955394.99381304744.80981269934.9658749323
4.8352936774.97854176860.02329446310.0246150894.8876772440.00021889840.00021900884.97628676734.81661655684.9757759224
4.87711642194.97507463190.0291800050.03128272154.89619224360.00030317240.00030338424.97094460824.81277861864.9757759224
4.87638597544.91677270470.03809004960.04175474814.90439489840.00037374740.00037406934.89672470334.816177334.9757759224
4.89693212474.91902171560.04009729550.04417946584.91283422270.00034399560.00034426834.86356294474.82467898450.00549747190.00556795424.9658749323
4.94939316754.83405588220.05098076270.05777121284.92226643310.00050809540.00050869054.85059359664.81653263570.00632478870.00641826194.9559739422
4.95930101894.84787328060.0579919470.06694678964.92977812880.00058728130.00058807664.84893040424.81826582130.00789648080.00804272034.9220912663
5.01176206174.7338395960.08505718620.10587573064.9365966510.00065062860.00065160474.80844278724.79817160570.00971616550.00993852254.9022892861
5.01103161524.70314052980.09775248560.12634649954.94857519820.00079468360.00079614044.79706945934.81513916270.01055018230.01081286934.8329823554
4.94647138154.78485023810.08894108330.11197375944.96295294480.00102118330.00102359024.74532041814.79617102160.01378828450.01424043914.793378395
4.89254944564.67161298980.11763949790.16185081994.97211557650.00120917340.00121254944.65366201244.73610827950.01472325680.01523996664.7834774049
4.88118070124.66365813960.10546982470.13959102454.978234820.00149670850.00150188444.65814288054.72480154070.02802872360.02996322344.72407146430.02970297030.0396039604
4.88045025474.57422595750.14748203360.22502459184.98165761530.00186372770.00187176024.62700338280.02041446480.02142160424.71020100680.02732312720.02915822874.73397245440.03960396040.0396039604
4.77333682954.72431202580.11125269920.14994883294.95970369210.00230787280.00232020264.59900253340.01966516010.02059801994.69860827950.02896369590.03103423374.55575463260.04950495050.0693069307
4.83203476184.64535237720.16814882770.27803871284.93908111890.00290499060.0029245534.56955874850.02233670920.02354812184.69469530050.04090498780.04516215884.67456651380.05940594060.0693069307
4.7293227454.90167489460.00373107520.00376340734.52433890660.02440498660.02585849874.65842957630.0579919470.06694678964.43694275140.0990099010.1089108911
4.73482918794.85809684460.00472948770.00478155964.49933702290.02530586530.02687214644.37757197540.12142216290.16914239914.47654671180.10891089110.1386138614
4.74473703934.80547041040.00606497720.00615087634.5095842170.02767142660.02955524364.79793811760.11539341870.15760785344.4963486920.11881188120.1782178218
4.70145340134.76244308530.00782533750.00796892974.40876676110.03392612050.03680264794.55575463260.13861386140.2079207921
4.6794463594.76023403430.0096506660.00987000124.40780958250.0367228070.0401172232
4.67871591254.71519926520.01239770580.01276204654.38119574980.059585690.0690809191
4.64607057244.70593212110.01524903710.01580400994.33185612090.08424275410.1046146293
4.5877472284.67166660310.01939604960.0203029589
4.58261537314.59633383680.02566396030.0272763102
4.56244381184.64340458540.02953127760.0316868176
4.53419988014.57721922940.03861804580.0423901629
4.49715313164.4808392250.05194134750.0590082605
4.4601063834.56574715370.05716496890.065846596
4.4549745284.50447415560.07349107690.0885121505
4.37977599644.41374952740.09753115770.125975956
4.4065590351
4.3827165118
4.3482356907
4.3075179802
4.2491946359
4.2121478873
4.11567276
4.110540905
4.0947707522
4.0195722206
4.0038020677
log10(E, eV)
log10(JE2.75, GeV1.75m-2s-1sr-1)
Fig
14.214.214.214.214.214.2
4.634.534.434.334.234.13
Fig
4.90901258624.796002619813.0645161294.96292134834.97029702974.99303804870000005.00423275470.0162920260.01692710294.85383251090.00009338660.0000934067
4.93763110584.812276462513.2027649774.99971910114.98019801984.99294422525.01218531240.01566280220.0162488834.860016880.00008671150.0000867288
4.81547797424.816383026613.34101382494.82977528094.99009900995.00257498924.9934575530.01888534420.01974405824.87513570140.00015893670.0001589949
4.88921561284.818533367213.4654377884.67780898884.99009900995.03166316875.01744934470.02098449150.02205014074.88049938520.0002953380.000295539
4.8352936774.825337224713.60368663594.552808988855.01413688864.97854176860.02329446310.0246150894.8876772440.00021889840.0002190088
4.87711642194.821499286513.74193548394.445786516955.00879472954.97507463190.0291800050.03128272154.89619224360.00030317240.0003033842
4.87638597544.824897997913.8663594474.338764044954.95657591164.91677270470.03809004960.04175474814.90439489840.00037374740.0003740693
4.89693212474.83339965240.00556795420.005497471914.004608294918.54.99009900994.9234141534.91902171560.04009729550.04417946584.91283422270.00034399560.0003442683
4.94939316754.82525330370.00641826190.006324788714.1290322581194.98019801984.91044480494.83405588220.05098076270.05777121284.92226643310.00050809540.0005086905
4.95930101894.82698648930.00804272030.00789648084.801668761319.54.96039603964.90878161254.84787328060.0579919470.06694678964.92977812880.00058728130.0005880766
5.01176206174.80689227370.00993852250.00971616554.8210794582204.94059405944.86829399554.7338395960.08505718620.10587573064.9365966510.00065062860.0006516047
5.01103161524.82385983070.01081286930.01055018234.8404901554.87128712874.85692066764.70314052980.09775248560.12634649954.94857519820.00079468360.0007961404
4.94647138154.80489168950.01424043910.01378828454.85644463064.83168316834.80517162644.78485023810.08894108330.11197375944.96295294480.00102118330.0010235902
4.89254944564.74989799790.01523996660.01472325684.86070381234.82178217824.71351322074.67161298980.11763949790.16185081994.97211557650.00120917340.0012125494
4.88118070124.73859125910.02996322340.02802872364.89180980314.76237623760.02970297030.03960396044.71799408884.66365813960.10546982470.13959102454.978234820.00149670850.0015018844
4.88045025474.72399072520.02915822870.02732312724.91122049994.77227722770.03960396040.03960396044.68685459110.02041446480.02142160424.57422595750.14748203360.22502459184.98165761530.00186372770.0018717602
4.77333682954.71239799790.03103423370.02896369594.92717497564.59405940590.04950495050.06930693074.65885374170.01966516010.02059801994.72431202580.11125269920.14994883294.95970369210.00230787280.0023202026
4.83203476184.70848501890.04516215880.04090498784.96173718754.71287128710.05940594060.06930693074.62940995670.02233670920.02354812184.64535237720.16814882770.27803871284.93908111890.00290499060.002924553
4.7293227454.67221929470.06694678960.0579919474.96599636924.47524752480.0990099010.10891089114.58419011490.02440498660.02585849874.90167489460.00373107520.0037634073
4.73482918794.39136169380.16914239910.12142216294.90619326914.51485148510.10891089110.13861386144.55918823120.02530586530.02687214644.85809684460.00472948770.0047815596
4.74473703934.8117278360.15760785340.11539341874.89530093564.53465346530.11881188120.17821782184.56943542530.02767142660.02955524364.80547041040.00606497720.0061508763
4.70145340134.88440860224.59405940590.13861386140.20792079214.46861796940.03392612050.03680264794.76244308530.00782533750.0079689297
4.6794463594.85490853234.46766079080.0367228070.04011722324.76023403430.0096506660.0098700012
4.67871591254.75310710794.4410469580.059585690.06908091914.71519926520.01239770580.0127620465
4.64607057244.6967602294.39170732920.08424275410.10461462934.70593212110.01524903710.0158040099
4.5877472284.66726015924.67166660310.01939604960.0203029589
4.58261537314.62606479544.59633383680.02566396030.0272763102
4.56244381184.59656472564.64340458540.02953127760.0316868176
4.53419988014.5705208774.57721922940.03861804580.0423901629
4.49715313164.52932551324.4808392250.05194134750.0590082605
4.4601063834.56574715370.05716496890.065846596
4.4549745284.50447415560.07349107690.0885121505
4.37977599644.41374952740.09753115770.125975956
4.4065590351
4.3827165118
4.3482356907
4.3075179802
4.2491946359
4.2121478873
4.11567276
4.110540905
4.0947707522
4.0195722206
4.0038020677
log10(E, eV)
log10(JE2.75, GeV1.75m-2s-1sr-1)
TibetIII
RlgR
1.020.01
Amenomori et al 08ApJ submittedEnergy correction
QGSJET+HDE, GeVlgE, GeVdJ/dE,m-2s-1sr-1GeV-1dJdlnJlgE, eVlgJlgJE^2.75+-lgE+lgRlgJ+2*lgR
1.1259.30.002-101.12E+055.050.000000000900.00014.05-9.034.850.0000.00014.064.8710328544
1.4155.0080.001-101.41E+055.150.000000000500.00014.15-9.304.860.0000.00014.164.8772172235
1.7852.7320.001-101.78E+055.250.000000000300.00014.25-9.564.880.0000.00014.264.8923360449
2.2451.470.001-102.24E+055.350.000000000100.00114.35-9.834.880.0000.00014.364.8976997287
2.8257.9340.004-112.82E+055.450.000000000100.00114.45-10.104.890.0000.00014.464.9048775875
3.5554.2960.003-113.55E+055.55000.00114.55-10.374.900.0000.00014.564.9133925871
4.4752.3230.002-114.47E+055.65000.00114.65-10.634.900.0000.00014.664.9215952419
5.6251.2620.001-115.62E+055.75000.00114.75-10.904.910.0000.00014.764.9300345662
7.0856.8340.008-127.08E+055.85000.00114.85-11.174.920.0010.00114.864.9394667766
8.9153.6950.005-128.91E+055.95000.00114.95-11.434.930.0010.00114.964.9469784724
1.1262.0010.003-121.12E+066.05000.00115.05-11.704.940.0010.00115.064.9537969945
1.4161.0920.002-121.41E+066.15000.00215.15-11.964.950.0010.00115.164.9657755417
1.7865.9470.014-131.78E+066.25000.00215.25-12.234.960.0010.00115.264.9801532884
2.2463.2280.009-132.24E+066.35000.00315.35-12.494.970.0010.00115.364.98931592
2.8261.7380.006-132.82E+066.45000.00315.45-12.764.980.0010.00215.464.9954351635
3.5569.3010.04-143.55E+066.55000.00415.55-13.034.980.0020.00215.564.9988579588
4.4764.6920.025-144.47E+066.65000.00515.65-13.334.960.0020.00215.664.9769040356
5.6262.3840.016-145.62E+066.75000.00715.75-13.624.940.0030.00315.764.9562814624
7.0861.1590.01-147.08E+066.85000.00915.85-13.944.900.0040.00415.864.9188752381
8.9165.5710.061-158.91E+066.95000.01115.95-14.254.860.0050.00515.964.8752971881
1.1272.6310.037-151.12E+077.05000.01416.05-14.584.810.0060.00616.064.822670754
1.4171.2650.023-151.41E+077.15000.01816.15-14.904.760.0080.00816.164.7796434288
1.7876.6310.149-161.78E+077.25000.02216.25-15.184.760.0100.01016.264.7774343778
2.2473.1770.092-162.24E+077.35000.02916.35-15.504.720.0120.01316.364.7323996088
2.8271.6510.059-162.82E+077.45000.03616.45-15.784.710.0150.01616.464.7231324647
3.5578.1010.37-173.55E+077.55000.04616.55-16.094.670.0190.02016.564.6888669466
4.4773.6140.22-174.47E+077.65000.06116.65-16.444.600.0260.02716.664.6135341804
5.6272.1460.151-175.62E+077.75000.07016.75-16.674.640.0300.03216.764.660604929
7.0879.7640.908-187.08E+077.85000.09316.85-17.014.580.0390.04216.864.5944195729
8.9174.1560.528-188.91E+077.95000.12716.95-17.384.480.0520.05916.964.4980395685
1.1282.6940.379-181.12E+088.05000.14117.05-17.574.570.0570.06617.064.5829474973
1.4181.2420.229-181.41E+088.15000.18417.15-17.914.500.0730.08917.164.5216744992
1.7885.311.337-191.78E+088.25000.25217.25-18.274.410.0980.12617.264.430949871
TibetIII
Tibet
dx159.522715
dy316.36255
x155171187203219235251267283299315331347363379395411427443
y615618621624627627629629624618614609603598591583576564553
lgE14.5514.6514.7514.8514.9515.0515.1515.2515.3515.4515.5515.6515.7515.8515.9516.0516.1516.2516.35
lg(J*E^2.75), GeV4.974.984.995.005.015.015.015.015.004.984.974.954.934.914.894.874.854.814.77
KASCADE
lgE15.0315.0815.1215.1715.2115.2615.3015.3515.4015.4415.4915.5315.5815.6315.6815.7215.7715.8115.8615.9115.9516.0016.0416.0916.1316.1816.2316.27
Venus0.030.020.030.030.040.040.050.050.060.060.070.090.10
J*E^2.75, GeV4.994.994.974.974.954.934.934.914.914.894.874.864.854.844.834.794.774.744.744.684.704.654.664.664.664.634.604.54
0.020.030.030.030.040.040.050.050.050.060.070.070.09
QGS0.020.030.030.030.050.040.050.060.060.070.07
J*E^2.755.005.004.994.994.994.984.984.974.974.974.964.954.954.944.954.934.934.894.894.864.854.834.844.804.794.834.754.77
0.030.030.030.030.030.040.050.050.050.060.07
RlgR
0.97-0.01
Energy spectra for elemental groupsAntoni et al 2005
QGSJet01m-2s-1sr-1GeV-1SIBYLL2.1m-2s-1sr-1GeV-1Energy correction
E,GeVlgE+9dJ/dElgJlgJE2.75Stat error-+Syst errordJ/dElgJlgJE2.75Stat errorSyst errorlgE+lgRlgJ+2*lgR
1.78E+0615.250-12.18442225175.004232754700.0170.0160.03800.340-12.198596294.990058716400.0300.21-0.0215.244.98
224000015.350-12.4509967385.012185312400.0160.0160.03700.210-12.46218090495.001001145500.0400.20-0.0215.344.99
282000015.450-12.74472749494.99345755300.0200.0190.04400.270-12.74472749494.99345755300.0500.21-0.0215.444.97
355000015.550-12.99567862625.017449344700.0220.0210.05000.220-135.013127970900.0500.22-0.0215.544.99
447000015.650-13.309803924.978541768600.0250.0230.05500.200-13.30891850794.979427180700.0500.21-0.0215.644.95
562000015.750-13.58670023594.975074631900.0310.0290.06900.220-13.58169870874.980076159100.0500.21-0.0215.744.95
708000015.850-13.9208187544.916772704700.0420.0380.09200.220-13.86646109164.97113036700.0700.21-0.0115.844.89
891000015.950-14.19314197054.919021715600.0440.0400.09700.210-14.20342566684.908738019300.0700.21-0.0115.944.89
1120000016.050-14.55129368014.834055882200.0580.0510.12500.210-14.4400933754.945256187400.0800.21-0.0116.044.81
1410000016.150-14.81247927924.847873280600.0670.0580.14300.210-14.82973828464.830614275200.0900.21-0.0116.144.82
1780000016.250-15.20481541034.73383959600.1060.0850.21600.220-15.12090412054.817750885800.1000.02-0.0016.244.71
2240000016.350-15.51004152064.703140529800.1260.0980.25200.210-15.39254497684.820637073600.1300.21-0.0116.344.68
2820000016.450-15.70333480974.784850238100.1120.0890.22700.220-15.72815839354.760026654400.1200.24-0.0116.444.76
3550000016.550-16.09151498114.671612989800.1620.1180.31100.240-16.05502409164.708103879300.0200.27-0.0216.544.65
4470000016.650-16.3746875494.663658139600.1400.1050.27500.270-16.43770713554.600638553100.1800.32-0.0216.644.64
5620000016.750-16.73754891034.574225957500.2250.1470.40400.430-16.64016451774.671610350200.2000.39-0.0216.744.55
7080000016.850-16.86327943284.724312025800.1500.1110.29200.390-17.0319842864.555607172600.2900.58-0.0316.844.70
8910000016.950-17.21681130894.645352377200.2780.1680.47300.660-17.23582386764.626339818500.3600.74-0.0416.944.62
KASCADE
00.0162920260.0169271029
00.01566280220.016248883
00.01888534420.0197440582
00.02098449150.0220501407
00.02329446310.024615089
00.0291800050.0312827215
00.03809004960.0417547481
00.04009729550.0441794658
00.05098076270.0577712128
00.0579919470.0669467896
00.08505718620.1058757306
00.09775248560.1263464995
00.08894108330.1119737594
00.11763949790.1618508199
00.10546982470.1395910245
00.14748203360.2250245918
00.11125269920.1499488329
00.16814882770.2780387128
Akeno
Akeno
lgE14.6814.8214.9315.0215.1115.1915.2815.3715.4615.5515.6315.7215.8115.9015.9916.0716.1616.2716.3416.4416.5316.6216.7116.8016.8816.9917.1017.2217.2917.3917.5017.6117.6917.8017.8517.9017.9418.0518.1518.2418.3518.4518.5418.64
0.040.030.020.040.050.060.06
lg(J*E^2.75), GeV4.914.944.824.894.844.884.884.904.954.965.015.014.954.894.884.884.774.834.734.734.744.704.684.684.654.594.584.564.534.504.464.454.384.414.384.354.314.254.214.124.114.094.024.00
0.040.030.030.050.050.060.06
Energy correction
lgE+lgR14.6614.8014.9115.0015.0815.1715.2615.3515.4415.5215.6115.7015.7915.8815.9616.0516.1416.2516.3216.4216.5116.6016.6916.7716.8616.9717.0717.2017.2717.3717.4817.5817.6717.7817.8317.8817.9218.0218.1318.2218.3218.4318.5218.62
lgJ+2*lgR4.864.894.774.844.794.834.834.854.904.914.974.974.904.854.844.844.734.794.684.694.704.664.634.634.604.544.544.524.494.454.424.414.344.364.344.304.264.204.174.074.074.053.983.96
RlgR
0.95-0.02
4
4.634.534.434.334.234.134.99756652564.9456444444.98845155024.86445979674.97777622320.0162920260.01692710294.8710328544
4.9974727024.96191828664.99835254034.89307831644.9857287810.01566280220.0162488834.8772172235
5.0071034664.96602485085.00825353044.77092518484.96700102150.01888534420.01974405824.8923360449
5.03619164554.96817519145.00825353044.84466282344.99099281320.02098449150.02205014074.8976997287
5.01866536554.97497904895.01815452054.79074088754.95208523720.02329446310.0246150894.9048775875
5.01332320644.97114111075.01815452054.83256363254.94861810040.0291800050.03128272154.9133925871
4.93910330144.97453982215.01815452054.8318331864.89031617320.03809004960.04175474814.9215952419
4.90594154294.98304147660.00549747190.00556795425.00825353044.85237933524.89256518420.04009729550.04417946584.9300345662
4.89297219484.97489512780.00632478870.00641826194.99835254034.90484037814.80759935080.05098076270.05777121284.9394667766
4.89130900234.97662831340.00789648080.00804272034.96446986444.91474822954.82141674920.0579919470.06694678964.9469784724
4.85082138534.95653409780.00971616550.00993852254.94466788424.96720927234.70738306460.08505718620.10587573064.9537969945
4.83944805744.97350165480.01055018230.01081286934.87536095354.96647882584.67668399840.09775248560.12634649954.9657755417
4.78769901624.95453351370.01378828450.01424043914.83575699324.90191859214.75839370670.08894108330.11197375944.9801532884
4.69604061054.89447077160.01472325680.01523996664.82585600314.84799665624.64515645830.11763949790.16185081994.98931592
4.70052147864.88316403280.02802872360.02996322344.76645006250.02970297030.03960396044.83662791184.63720160810.10546982470.13959102454.9954351635
4.6693819810.02041446480.02142160424.86856349890.02732312720.02915822874.77635105260.03960396040.03960396044.83589746534.54776942610.14748203360.22502459184.9988579588
4.64138113150.01966516010.02059801994.85697077160.02896369590.03103423374.59813323080.04950495050.06930693074.72878404014.69785549430.11125269920.14994883294.9769040356
4.61193734660.02233670920.02354812184.85305779260.04090498780.04516215884.7169451120.05940594060.06930693074.78748197234.61889584570.16814882770.27803871284.9562814624
4.56671750480.02440498660.02585849874.81679206840.0579919470.06694678964.47932134960.0990099010.10891089114.68476995564.9188752381
4.5417156210.02530586530.02687214644.53593446750.12142216290.16914239914.518925310.10891089110.13861386144.69027639854.8752971881
4.55196281520.02767142660.02955524364.95630060970.11539341870.15760785344.53872729020.11881188120.17821782184.70018424984.822670754
4.45114535930.03392612050.03680264794.59813323080.13861386140.20792079214.65690061184.7796434288
4.45018818060.0367228070.04011722324.63489356964.7774343778
4.42357434790.059585690.06908091914.63416312314.7323996088
4.37423471910.08424275410.10461462934.60151778294.7231324647
4.54319443864.6888669466
4.53806258374.6135341804
4.51789102244.660604929
4.48964709074.5944195729
4.45260034214.4980395685
4.41555359364.5829474973
4.41042173864.5216744992
4.3352232074.430949871
4.3620062456
4.3381637224
4.3036829013
4.2629651908
4.2046418465
4.1675950979
4.0711199705
4.0659881156
4.0502179628
3.9750194311
3.9592492783
log10(E, eV)
log10(JE2.75, GeV1.75m-2s-1sr-1)
Knurenko
Original Knurenko spectrum - 05Intensity correctionEnergy correction
E0JE^3, eVdJJ-dJJ+dJlgElgJE^2.75, GeVlgElgJE^2.75, GeVJ-dJ+dlgE*RlgJE^2.75lgE+lgRlgJE^2.75
1.60E+063.50E+2415.204.99315.2044.99315.0954.95515.1174.998
2.00E+063.70E+2415.304.99315.3014.99315.1924.95515.2144.997
2.50E+064.00E+2415.405.00315.3985.00315.2894.96515.3105.007
2.90E+064.40E+2415.465.02815.4475.03215.3384.99415.3605.036
3.50E+064.50E+2415.545.01715.5565.01415.4484.97615.4695.019
4.60E+064.70E+2415.665.00615.6535.00915.5454.97115.5665.013
5.70E+064.30E+2415.764.94415.7084.95715.5994.89715.6204.939
6.30E+064.20E+2415.804.92315.7994.92315.6914.86415.7124.906
7.80E+064.30E+2415.894.91015.8924.91015.7834.85115.8054.893
9.50E+064.50E+2415.984.90915.9784.90915.8694.84915.8904.891
1.15E+074.30E+2416.064.86816.0614.86815.9524.80815.9734.851
1.40E+074.40E+2416.154.85716.1464.85716.0374.79716.0594.839
1.78E+074.10E+2416.254.80016.2304.80516.1224.74516.1434.788
2.19E+073.50E+2416.344.70916.3224.71416.2144.65416.2354.696
2.80E+073.80E+2416.454.71816.4474.71816.3384.65816.3604.701
3.50E+073.76E+241.80E+233.58E+243.94E+2416.544.6890.0210.02016.5444.6870.02142160420.020414464816.4354.62716.4574.669
4.20E+073.67E+241.70E+233.50E+243.84E+2416.624.6590.0210.02016.6234.6590.02059801990.019665160116.5154.59916.5364.641
5.10E+073.60E+241.90E+233.41E+243.79E+2416.714.6290.0240.02216.7084.6290.02354812180.022336709216.5994.57016.6204.612
6.60E+073.46E+242.00E+233.26E+243.66E+2416.824.5840.0260.02416.8204.5840.02585849870.024404986616.7114.52416.7324.567
7.90E+073.50E+242.10E+233.29E+243.71E+2416.904.5700.0270.02516.9404.5590.02687214640.025305865316.8314.49916.8524.542
1.00E+083.80E+242.50E+233.55E+244.05E+2417.004.5800.0300.02817.0414.5690.02955524360.027671426616.9334.51016.9544.552
1.58E+083.20E+242.60E+232.94E+243.46E+2417.204.4550.0370.03417.1464.4690.03680264790.033926120517.0374.40917.0594.451
1.66E+083.40E+243.00E+233.10E+243.70E+2417.224.4760.0400.03717.2554.4680.04011722320.03672280717.1474.40817.1684.450
2.00E+083.40E+245.00E+232.90E+243.90E+2417.304.4560.0690.06017.3624.4410.06908091910.0595856917.2534.38117.2744.424
3.10E+083.27E+247.00E+232.57E+243.97E+2417.494.3920.1050.08417.4914.3920.10461462930.084242754117.3834.33217.4044.374
Knee15.6020599913RlgR
1.050.0211892991
kappa1kappa2
Sigma1.672.1
0.251.09106373611.147760325
lgRJ0.03785012130.0598512083
Knurenko
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
000.02041446480.0214216042
000.01966516010.0205980199
000.02233670920.0235481218
000.02440498660.0258584987
000.02530586530.0268721464
000.02767142660.0295552436
000.03392612050.0368026479
000.0367228070.0401172232
000.059585690.0690809191
000.08424275410.1046146293
CERN
My fault
lgE15.2015.3015.4015.4515.5515.6515.7515.8515.950.0016.0516.1516.2516.3516.4516.5516.6516.7516.8516.9517.0517.1517.2517.3517.50
J0.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00
dJ0.000.000.000.000.000.000.000.000.000.00
0.020.020.020.030.030.030.040.040.070.10
lg(J*E^2.75),GeV4.984.995.014.995.034.974.935.065.07-39.034.844.874.804.744.734.714.734.754.674.714.724.324.564.594.42
0.020.020.020.020.030.030.030.040.060.08
BLANKA
BLANKA
lgE14.3514.4514.5514.6514.7514.8514.9515.0515.1515.2515.3515.4515.5515.6515.7515.8516.0016.2016.4016.6016.80
J/GeV1.21E-106.68E-113.58E-111.91E-111.03E-115.42E-122.90E-121.57E-128.18E-134.36E-132.21E-131.22E-136.20E-142.90E-141.50E-147.70E-152.90E-158.10E-162.10E-163.10E-172.30E-17
dJ4.00E-132.00E-132.00E-131.00E-131.00E-134.00E-143.00E-142.00E-141.20E-148.00E-155.00E-153.00E-152.00E-151.00E-151.00E-155.00E-162.00E-168.00E-173.00E-171.00E-177.00E-18
0.010.010.010.010.010.010.020.030.030.030.050.070.170.16
lgJE^2.754.804.814.824.824.834.824.824.834.834.834.814.824.804.754.744.724.714.714.674.394.81
0.010.010.010.010.010.010.010.030.030.030.040.060.120.12
Intensity corerction
lgE*R14.3014.4014.5014.6014.7014.8014.9015.0015.1015.2015.3015.4015.5015.6015.7015.8015.9516.1516.3516.5516.75
lgJE^2.75-lgR4.794.804.814.814.824.814.824.824.824.824.804.824.804.744.724.714.704.694.664.384.80
Energy correction
lgE+lgR14.3814.4814.5814.6814.7814.8814.9815.0815.1815.2815.3815.4815.5815.6815.7815.8816.0316.2316.4316.6316.83
lgJE^2.75+2lgR4.9456444444.96191828664.96602485084.96817519144.97497904894.97114111074.97453982214.98304147664.97489512784.97662831344.95653409784.97350165484.95453351374.89447077164.88316403284.86856349894.85697077164.85305779264.81679206844.53593446754.9563006097
Knee15.6020599913RlgR
1.20.079181246
kappa1kappa2
Sigma1.672.1
0.121.0202830411.0322614727
lgRJ0.00872066790.0137897184
Models
Erlykin from HorandellgRJ0.05
dx72.33184.006.00
dy66.00166.003.00
x445464738393102112121131141151160170179189198208218227237247256266276285295304314324
y212210208206205203201200199198197196195193193192191191189183180177173164158154149145141136
lgE13.0613.2013.3413.4713.6013.7413.8714.0014.1314.2714.4114.5414.6714.8114.9315.0715.1915.3315.4715.5915.7315.8716.0016.1316.2716.4016.5316.6616.8016.94
lg(J*E^2.5)3.703.673.643.613.593.563.533.523.503.483.473.453.443.413.413.393.383.383.353.263.213.173.112.972.882.822.742.682.622.55
lg(J*E^2.75)4.804.824.844.864.864.894.914.934.964.974.914.904.884.854.754.704.674.634.604.574.53
lgJ+lgR4.854.874.894.914.914.944.964.985.015.024.964.954.934.904.804.754.724.684.654.624.58
lgRJ0.00
Lagutin
lgE15.0015.5016.0016.5017.0017.5018.0018.5019.0019.5020.00
lgJE^36.466.626.586.556.556.576.596.476.426.456.50
lgJE^2.754.965.004.834.684.554.454.34
lgJ+lgR4.965.004.834.684.554.454.34
Tunka
Tunka - (Hamburg)
lgE14.55914.65814.75814.85714.95715.05615.15515.25515.35415.45315.55315.65215.75215.85115.95016.05016.16116.24816.36016.46016.55916.65816.75816.857
4.6614.6174.5944.6394.3394.5944.6064.5834.8174.1834.117
lgJE^2.75, GeV4.6064.6284.6394.6724.6834.6944.7174.7614.7174.7064.7724.8284.7174.6944.6834.6724.7174.4834.6614.6834.6834.9064.4174.417
4.7394.7284.7284.7944.5944.7174.7504.7614.9834.5614.594
Mifi - 04
lgE14.85414.95115.06815.16515.26215.35915.45615.55315.65015.76715.86415.96116.05816.15516.25216.35016.46616.31116.66016.75716.85416.951
4.7234.7334.5254.6444.3664.3764.3564.386
lgJE^2.75, GeV4.9704.9804.9904.9905.0005.0005.0004.9904.9804.9604.9414.8714.8324.8224.7624.7724.5944.7134.4754.5154.5354.594
4.7924.8124.6444.7724.5744.6244.6534.733
0.0400.0400.0690.0690.1090.1390.1780.208
lgJE^2.75, GeV4.9704.9804.9904.9905.0005.0005.0004.9904.9804.9604.9414.8714.8324.8224.7624.7724.5944.7134.4754.5154.5354.594
0.0300.0400.0500.0590.0990.1090.1190.139
Intensity correction
lgE-lgR14.76714.86414.98115.07815.17515.27215.36915.46615.56415.68015.77715.87415.97116.06816.16516.26316.37916.22416.57316.67016.76716.864
lgJE^2.75-lgR4.9464.9564.9664.9664.9764.9764.9764.9664.9564.9224.9024.8334.7934.7834.7244.7344.5564.6754.4374.4774.4964.556
Energy corrction
lgE+lgR14.78914.88615.00215.09915.19615.29315.39115.48815.58515.70115.79815.89515.99216.09016.18716.28416.40016.24516.59416.69216.78916.886
lgJE^2.75+2lgR4.9884.9985.0085.0085.0185.0185.0185.0084.9984.9644.9454.8754.8364.8264.7664.7764.5984.7174.4794.5194.5394.598
Knee15.6020599913RlgR
1.050.0211892991
kappa1kappa2
Sigma1.672.1
0.21.05736292311.0922065415
lgRJ0.02422407760.0383047733
FigxRJxRE
FigxRJxRE
4.634.534.434.334.234.134.99756652564.9456444444.98845155024.86445979674.97777622320.0162920260.01692710294.8710328544
4.9974727024.96191828664.99835254034.89307831644.9857287810.01566280220.0162488834.8772172235
5.0071034664.96602485085.00825353044.77092518484.96700102150.01888534420.01974405824.8923360449
5.03619164554.96817519145.00825353044.84466282344.99099281320.02098449150.02205014074.8976997287
5.01866536554.97497904895.01815452054.79074088754.95208523720.02329446310.0246150894.9048775875
5.01332320644.97114111075.01815452054.83256363254.94861810040.0291800050.03128272154.9133925871
4.93910330144.97453982215.01815452054.8318331864.89031617320.03809004960.04175474814.9215952419
4.90594154294.98304147660.00549747190.00556795425.00825353044.85237933524.89256518420.04009729550.04417946584.9300345662
4.89297219484.97489512780.00632478870.00641826194.99835254034.90484037814.80759935080.05098076270.05777121284.9394667766
4.89130900234.97662831340.00789648080.00804272034.96446986444.91474822954.82141674920.0579919470.06694678964.9469784724
4.85082138534.95653409780.00971616550.00993852254.94466788424.96720927234.70738306460.08505718620.10587573064.9537969945
4.83944805744.97350165480.01055018230.01081286934.87536095354.96647882584.67668399840.09775248560.12634649954.9657755417
4.78769901624.95453351370.01378828450.01424043914.83575699324.90191859214.75839370670.08894108330.11197375944.9801532884
4.69604061054.89447077160.01472325680.01523996664.82585600314.84799665624.64515645830.11763949790.16185081994.98931592
4.70052147864.88316403280.02802872360.02996322344.76645006250.02970297030.03960396044.83662791184.63720160810.10546982470.13959102454.9954351635
4.6693819810.02041446480.02142160424.86856349890.02732312720.02915822874.77635105260.03960396040.03960396044.83589746534.54776942610.14748203360.22502459184.9988579588
4.64138113150.01966516010.02059801994.85697077160.02896369590.03103423374.59813323080.04950495050.06930693074.72878404014.69785549430.11125269920.14994883294.9769040356
4.61193734660.02233670920.02354812184.85305779260.04090498780.04516215884.7169451120.05940594060.06930693074.78748197234.61889584570.16814882770.27803871284.9562814624
4.56671750480.02440498660.02585849874.81679206840.0579919470.06694678964.47932134960.0990099010.10891089114.68476995564.9188752381
4.5417156210.02530586530.02687214644.53593446750.12142216290.16914239914.518925310.10891089110.13861386144.69027639854.8752971881
4.55196281520.02767142660.02955524364.95630060970.11539341870.15760785344.53872729020.11881188120.17821782184.70018424984.822670754
4.45114535930.03392612050.03680264794.59813323080.13861386140.20792079214.65690061184.7796434288
4.45018818060.0367228070.04011722324.63489356964.7774343778
4.42357434790.059585690.06908091914.63416312314.7323996088
4.37423471910.08424275410.10461462934.60151778294.7231324647
4.54319443864.6888669466
4.53806258374.6135341804
4.51789102244.660604929
4.48964709074.5944195729
4.45260034214.4980395685
4.41555359364.5829474973
4.41042173864.5216744992
4.3352232074.430949871
4.3620062456
4.3381637224
4.3036829013
4.2629651908
4.2046418465
4.1675950979
4.0711199705
4.0659881156
4.0502179628
3.9750194311
3.9592492783
log10(E, eV)
log10(JE2.75, GeV1.75m-2s-1sr-1)
Fig x RJ
Fig x RJ
4.90901258624.634.534.434.334.234.135.00423275470.0162920260.01692710294.85383251090.00009338660.00009340674.95518792744.78728195194.9460729521
4.93763110585.01218531240.01566280220.0162488834.860016880.00008671150.00008672884.95509410394.80355579454.9559739422
4.81547797424.9934575530.01888534420.01974405824.87513570140.00015893670.00015899494.96472486794.80766235874.9658749323
4.88921561285.01744934470.02098449150.02205014074.88049938520.0002953380.0002955394.99381304744.80981269934.9658749323
4.8352936774.97854176860.02329446310.0246150894.8876772440.00021889840.00021900884.97628676734.81661655684.9757759224
4.87711642194.97507463190.0291800050.03128272154.89619224360.00030317240.00030338424.97094460824.81277861864.9757759224
4.87638597544.91677270470.03809004960.04175474814.90439489840.00037374740.00037406934.89672470334.816177334.9757759224
4.89693212474.91902171560.04009729550.04417946584.91283422270.00034399560.00034426834.86356294474.82467898450.00549747190.00556795424.9658749323
4.94939316754.83405588220.05098076270.05777121284.92226643310.00050809540.00050869054.85059359664.81653263570.00632478870.00641826194.9559739422
4.95930101894.84787328060.0579919470.06694678964.92977812880.00058728130.00058807664.84893040424.81826582130.00789648080.00804272034.9220912663
5.01176206174.7338395960.08505718620.10587573064.9365966510.00065062860.00065160474.80844278724.79817160570.00971616550.00993852254.9022892861
5.01103161524.70314052980.09775248560.12634649954.94857519820.00079468360.00079614044.79706945934.81513916270.01055018230.01081286934.8329823554
4.94647138154.78485023810.08894108330.11197375944.96295294480.00102118330.00102359024.74532041814.79617102160.01378828450.01424043914.793378395
4.89254944564.67161298980.11763949790.16185081994.97211557650.00120917340.00121254944.65366201244.73610827950.01472325680.01523996664.7834774049
4.88118070124.66365813960.10546982470.13959102454.978234820.00149670850.00150188444.65814288054.72480154070.02802872360.02996322344.72407146430.02970297030.0396039604
4.88045025474.57422595750.14748203360.22502459184.98165761530.00186372770.00187176024.62700338280.02041446480.02142160424.71020100680.02732312720.02915822874.73397245440.03960396040.0396039604
4.77333682954.72431202580.11125269920.14994883294.95970369210.00230787280.00232020264.59900253340.01966516010.02059801994.69860827950.02896369590.03103423374.55575463260.04950495050.0693069307
4.83203476184.64535237720.16814882770.27803871284.93908111890.00290499060.0029245534.56955874850.02233670920.02354812184.69469530050.04090498780.04516215884.67456651380.05940594060.0693069307
4.7293227454.90167489460.00373107520.00376340734.52433890660.02440498660.02585849874.65842957630.0579919470.06694678964.43694275140.0990099010.1089108911
4.73482918794.85809684460.00472948770.00478155964.49933702290.02530586530.02687214644.37757197540.12142216290.16914239914.47654671180.10891089110.1386138614
4.74473703934.80547041040.00606497720.00615087634.5095842170.02767142660.02955524364.79793811760.11539341870.15760785344.4963486920.11881188120.1782178218
4.70145340134.76244308530.00782533750.00796892974.40876676110.03392612050.03680264794.55575463260.13861386140.2079207921
4.6794463594.76023403430.0096506660.00987000124.40780958250.0367228070.0401172232
4.67871591254.71519926520.01239770580.01276204654.38119574980.059585690.0690809191
4.64607057244.70593212110.01524903710.01580400994.33185612090.08424275410.1046146293
4.5877472284.67166660310.01939604960.0203029589
4.58261537314.59633383680.02566396030.0272763102
4.56244381184.64340458540.02953127760.0316868176
4.53419988014.57721922940.03861804580.0423901629
4.49715313164.4808392250.05194134750.0590082605
4.4601063834.56574715370.05716496890.065846596
4.4549745284.50447415560.07349107690.0885121505
4.37977599644.41374952740.09753115770.125975956
4.4065590351
4.3827165118
4.3482356907
4.3075179802
4.2491946359
4.2121478873
4.11567276
4.110540905
4.0947707522
4.0195722206
4.0038020677
log10(E, eV)
log10(JE2.75, GeV1.75m-2s-1sr-1)
Fig
14.214.214.214.214.214.2
4.634.534.434.334.234.13
Fig
4.90901258624.796002619813.0645161294.96292134834.97029702974.99303804870000005.00423275470.0162920260.01692710294.85383251090.00009338660.0000934067
4.93763110584.812276462513.2027649774.99971910114.98019801984.99294422525.01218531240.01566280220.0162488834.860016880.00008671150.0000867288
4.81547797424.816383026613.34101382494.82977528094.99009900995.00257498924.9934575530.01888534420.01974405824.87513570140.00015893670.0001589949
4.88921561284.818533367213.4654377884.67780898884.99009900995.03166316875.01744934470.02098449150.02205014074.88049938520.0002953380.000295539
4.8352936774.825337224713.60368663594.552808988855.01413688864.97854176860.02329446310.0246150894.8876772440.00021889840.0002190088
4.87711642194.821499286513.74193548394.445786516955.00879472954.97507463190.0291800050.03128272154.89619224360.00030317240.0003033842
4.87638597544.824897997913.8663594474.338764044954.95657591164.91677270470.03809004960.04175474814.90439489840.00037374740.0003740693
4.89693212474.83339965240.00556795420.005497471914.004608294918.54.99009900994.9234141534.91902171560.04009729550.04417946584.91283422270.00034399560.0003442683
4.94939316754.82525330370.00641826190.006324788714.1290322581194.98019801984.91044480494.83405588220.05098076270.05777121284.92226643310.00050809540.0005086905
4.95930101894.82698648930.00804272030.00789648084.801668761319.54.96039603964.90878161254.84787328060.0579919470.06694678964.92977812880.00058728130.0005880766
5.01176206174.80689227370.00993852250.00971616554.8210794582204.94059405944.86829399554.7338395960.08505718620.10587573064.9365966510.00065062860.0006516047
5.01103161524.82385983070.01081286930.01055018234.8404901554.87128712874.85692066764.70314052980.09775248560.12634649954.94857519820.00079468360.0007961404
4.94647138154.80489168950.01424043910.01378828454.85644463064.83168316834.80517162644.78485023810.08894108330.11197375944.96295294480.00102118330.0010235902
4.89254944564.74989799790.01523996660.01472325684.86070381234.82178217824.71351322074.67161298980.11763949790.16185081994.97211557650.00120917340.0012125494
4.88118070124.73859125910.02996322340.02802872364.89180980314.76237623760.02970297030.03960396044.71799408884.66365813960.10546982470.13959102454.978234820.00149670850.0015018844
4.88045025474.72399072520.02915822870.02732312724.91122049994.77227722770.03960396040.03960396044.68685459110.02041446480.02142160424.57422595750.14748203360.22502459184.98165761530.00186372770.0018717602
4.77333682954.71239799790.03103423370.02896369594.92717497564.59405940590.04950495050.06930693074.65885374170.01966516010.02059801994.72431202580.11125269920.14994883294.95970369210.00230787280.0023202026
4.83203476184.70848501890.04516215880.04090498784.96173718754.71287128710.05940594060.06930693074.62940995670.02233670920.02354812184.64535237720.16814882770.27803871284.93908111890.00290499060.002924553
4.7293227454.67221929470.06694678960.0579919474.96599636924.47524752480.0990099010.10891089114.58419011490.02440498660.02585849874.90167489460.00373107520.0037634073
4.73482918794.39136169380.16914239910.12142216294.90619326914.51485148510.10891089110.13861386144.55918823120.02530586530.02687214644.85809684460.00472948770.0047815596
4.74473703934.8117278360.15760785340.11539341874.89530093564.53465346530.11881188120.17821782184.56943542530.02767142660.02955524364.80547041040.00606497720.0061508763
4.70145340134.88440860224.59405940590.13861386140.20792079214.46861796940.03392612050.03680264794.76244308530.00782533750.0079689297
4.6794463594.85490853234.46766079080.0367228070.04011722324.76023403430.0096506660.0098700012
4.67871591254.75310710794.4410469580.059585690.06908091914.71519926520.01239770580.0127620465
4.64607057244.6967602294.39170732920.08424275410.10461462934.70593212110.01524903710.0158040099
4.5877472284.66726015924.67166660310.01939604960.0203029589
4.58261537314.62606479544.59633383680.02566396030.0272763102
4.56244381184.59656472564.64340458540.02953127760.0316868176
4.53419988014.5705208774.57721922940.03861804580.0423901629
4.49715313164.52932551324.4808392250.05194134750.0590082605
4.4601063834.56574715370.05716496890.065846596
4.4549745284.50447415560.07349107690.0885121505
4.37977599644.41374952740.09753115770.125975956
4.4065590351
4.3827165118
4.3482356907
4.3075179802
4.2491946359
4.2121478873
4.11567276
4.110540905
4.0947707522
4.0195722206
4.0038020677
log10(E, eV)
log10(JE2.75, GeV1.75m-2s-1sr-1)
TibetIII
RlgR
1.020.01
Amenomori et al 08ApJ submittedEnergy correction
QGSJET+HDE, GeVlgE, GeVdJ/dE,m-2s-1sr-1GeV-1dJdlnJlgE, eVlgJlgJE^2.75+-lgE+lgRlgJ+2*lgR
1.1259.30.002-101.12E+055.050.000000000900.00014.05-9.034.850.0000.00014.064.8710328544
1.4155.0080.001-101.41E+055.150.000000000500.00014.15-9.304.860.0000.00014.164.8772172235
1.7852.7320.001-101.78E+055.250.000000000300.00014.25-9.564.880.0000.00014.264.8923360449
2.2451.470.001-102.24E+055.350.000000000100.00114.35-9.834.880.0000.00014.364.8976997287
2.8257.9340.004-112.82E+055.450.000000000100.00114.45-10.104.890.0000.00014.464.9048775875
3.5554.2960.003-113.55E+055.55000.00114.55-10.374.900.0000.00014.564.9133925871
4.4752.3230.002-114.47E+055.65000.00114.65-10.634.900.0000.00014.664.9215952419
5.6251.2620.001-115.62E+055.75000.00114.75-10.904.910.0000.00014.764.9300345662
7.0856.8340.008-127.08E+055.85000.00114.85-11.174.920.0010.00114.864.9394667766
8.9153.6950.005-128.91E+055.95000.00114.95-11.434.930.0010.00114.964.9469784724
1.1262.0010.003-121.12E+066.05000.00115.05-11.704.940.0010.00115.064.9537969945
1.4161.0920.002-121.41E+066.15000.00215.15-11.964.950.0010.00115.164.9657755417
1.7865.9470.014-131.78E+066.25000.00215.25-12.234.960.0010.00115.264.9801532884
2.2463.2280.009-132.24E+066.35000.00315.35-12.494.970.0010.00115.364.98931592
2.8261.7380.006-132.82E+066.45000.00315.45-12.764.980.0010.00215.464.9954351635
3.5569.3010.04-143.55E+066.55000.00415.55-13.034.980.0020.00215.564.9988579588
4.4764.6920.025-144.47E+066.65000.00515.65-13.334.960.0020.00215.664.9769040356
5.6262.3840.016-145.62E+066.75000.00715.75-13.624.940.0030.00315.764.9562814624
7.0861.1590.01-147.08E+066.85000.00915.85-13.944.900.0040.00415.864.9188752381
8.9165.5710.061-158.91E+066.95000.01115.95-14.254.860.0050.00515.964.8752971881
1.1272.6310.037-151.12E+077.05000.01416.05-14.584.810.0060.00616.064.822670754
1.4171.2650.023-151.41E+077.15000.01816.15-14.904.760.0080.00816.164.7796434288
1.7876.6310.149-161.78E+077.25000.02216.25-15.184.760.0100.01016.264.7774343778
2.2473.1770.092-162.24E+077.35000.02916.35-15.504.720.0120.01316.364.7323996088
2.8271.6510.059-162.82E+077.45000.03616.45-15.784.710.0150.01616.464.7231324647
3.5578.1010.37-173.55E+077.55000.04616.55-16.094.670.0190.02016.564.6888669466
4.4773.6140.22-174.47E+077.65000.06116.65-16.444.600.0260.02716.664.6135341804
5.6272.1460.151-175.62E+077.75000.07016.75-16.674.640.0300.03216.764.660604929
7.0879.7640.908-187.08E+077.85000.09316.85-17.014.580.0390.04216.864.5944195729
8.9174.1560.528-188.91E+077.95000.12716.95-17.384.480.0520.05916.964.4980395685
1.1282.6940.379-181.12E+088.05000.14117.05-17.574.570.0570.06617.064.5829474973
1.4181.2420.229-181.41E+088.15000.18417.15-17.914.500.0730.08917.164.5216744992
1.7885.311.337-191.78E+088.25000.25217.25-18.274.410.0980.12617.264.430949871
TibetIII
Tibet
dx159.522715
dy316.36255
x155171187203219235251267283299315331347363379395411427443
y615618621624627627629629624618614609603598591583576564553
lgE14.5514.6514.7514.8514.9515.0515.1515.2515.3515.4515.5515.6515.7515.8515.9516.0516.1516.2516.35
lg(J*E^2.75), GeV4.974.984.995.005.015.015.015.015.004.984.974.954.934.914.894.874.854.814.77
KASCADE
lgE15.0315.0815.1215.1715.2115.2615.3015.3515.4015.4415.4915.5315.5815.6315.6815.7215.7715.8115.8615.9115.9516.0016.0416.0916.1316.1816.2316.27
Venus0.030.020.030.030.040.040.050.050.060.060.070.090.10
J*E^2.75, GeV4.994.994.974.974.954.934.934.914.914.894.874.864.854.844.834.794.774.744.744.684.704.654.664.664.664.634.604.54
0.020.030.030.030.040.040.050.050.050.060.070.070.09
QGS0.020.030.030.030.050.040.050.060.060.070.07
J*E^2.755.005.004.994.994.994.984.984.974.974.974.964.954.954.944.954.934.934.894.894.864.854.834.844.804.794.834.754.77
0.030.030.030.030.030.040.050.050.050.060.07
RlgR
0.97-0.01
Energy spectra for elemental groupsAntoni et al 2005
QGSJet01m-2s-1sr-1GeV-1SIBYLL2.1m-2s-1sr-1GeV-1Energy correction
E,GeVlgE+9dJ/dElgJlgJE2.75Stat error-+Syst errordJ/dElgJlgJE2.75Stat errorSyst errorlgE+lgRlgJ+2*lgR
1.78E+0615.250-12.18442225175.004232754700.0170.0160.03800.340-12.198596294.990058716400.0300.21-0.0215.244.98
224000015.350-12.4509967385.012185312400.0160.0160.03700.210-12.46218090495.001001145500.0400.20-0.0215.344.99
282000015.450-12.74472749494.99345755300.0200.0190.04400.270-12.74472749494.99345755300.0500.21-0.0215.444.97
355000015.550-12.99567862625.017449344700.0220.0210.05000.220-135.013127970900.0500.22-0.0215.544.99
447000015.650-13.309803924.978541768600.0250.0230.05500.200-13.30891850794.979427180700.0500.21-0.0215.644.95
562000015.750-13.58670023594.975074631900.0310.0290.06900.220-13.58169870874.980076159100.0500.21-0.0215.744.95
708000015.850-13.9208187544.916772704700.0420.0380.09200.220-13.86646109164.97113036700.0700.21-0.0115.844.89
891000015.950-14.19314197054.919021715600.0440.0400.09700.210-14.20342566684.908738019300.0700.21-0.0115.944.89
1120000016.050-14.55129368014.834055882200.0580.0510.12500.210-14.4400933754.945256187400.0800.21-0.0116.044.81
1410000016.150-14.81247927924.847873280600.0670.0580.14300.210-14.82973828464.830614275200.0900.21-0.0116.144.82
1780000016.250-15.20481541034.73383959600.1060.0850.21600.220-15.12090412054.817750885800.1000.02-0.0016.244.71
2240000016.350-15.51004152064.703140529800.1260.0980.25200.210-15.39254497684.820637073600.1300.21-0.0116.344.68
2820000016.450-15.70333480974.784850238100.1120.0890.22700.220-15.72815839354.760026654400.1200.24-0.0116.444.76
3550000016.550-16.09151498114.671612989800.1620.1180.31100.240-16.05502409164.708103879300.0200.27-0.0216.544.65
4470000016.650-16.3746875494.663658139600.1400.1050.27500.270-16.43770713554.600638553100.1800.32-0.0216.644.64
5620000016.750-16.73754891034.574225957500.2250.1470.40400.430-16.64016451774.671610350200.2000.39-0.0216.744.55
7080000016.850-16.86327943284.724312025800.1500.1110.29200.390-17.0319842864.555607172600.2900.58-0.0316.844.70
8910000016.950-17.21681130894.645352377200.2780.1680.47300.660-17.23582386764.626339818500.3600.74-0.0416.944.62
KASCADE
00.0162920260.0169271029
00.01566280220.016248883
00.01888534420.0197440582
00.02098449150.0220501407
00.02329446310.024615089
00.0291800050.0312827215
00.03809004960.0417547481
00.04009729550.0441794658
00.05098076270.0577712128
00.0579919470.0669467896
00.08505718620.1058757306
00.09775248560.1263464995
00.08894108330.1119737594
00.11763949790.1618508199
00.10546982470.1395910245
00.14748203360.2250245918
00.11125269920.1499488329
00.16814882770.2780387128
Akeno
Akeno
lgE14.6814.8214.9315.0215.1115.1915.2815.3715.4615.5515.6315.7215.8115.9015.9916.0716.1616.2716.3416.4416.5316.6216.7116.8016.8816.9917.1017.2217.2917.3917.5017.6117.6917.8017.8517.9017.9418.0518.1518.2418.3518.4518.5418.64
0.040.030.020.040.050.060.06
lg(J*E^2.75), GeV4.914.944.824.894.844.884.884.904.954.965.015.014.954.894.884.884.774.834.734.734.744.704.684.684.654.594.584.564.534.504.464.454.384.414.384.354.314.254.214.124.114.094.024.00
0.040.030.030.050.050.060.06
Energy correction
lgE+lgR14.6614.8014.9115.0015.0815.1715.2615.3515.4415.5215.6115.7015.7915.8815.9616.0516.1416.2516.3216.4216.5116.6016.6916.7716.8616.9717.0717.2017.2717.3717.4817.5817.6717.7817.8317.8817.9218.0218.1318.2218.3218.4318.5218.62
lgJ+2*lgR4.864.894.774.844.794.834.834.854.904.914.974.974.904.854.844.844.734.794.684.694.704.664.634.634.604.544.544.524.494.454.424.414.344.364.344.304.264.204.174.074.074.053.983.96
RlgR
0.95-0.02
-
The energy spectrum of cosmic rays above E=1018 eVEnergy spectra measured with giant arrays: AGASA, HiRes, PAO and Yakutsk.Differential spectra after systematic corrections to CR intensity and energy(A.A. Ivanov, S.P. Knurenko and I.Ye. Sleptsov, NJP, 11 (2009) 065008).Data:
PAOHiResYscYchAGASA
REAGASAHiResPAOYscYchAGASA10.750.631.050.82HiRes1.3310.851.41.08PAO1.61.211.71.3Ysc0.910.710.610.75Ych1.220.930.81.331
1
24.388851526924.478998316424.32853584750.02166997920.022808292524.459864024424.56593286110.19803298430.374410895324.64799375310.08783880160.11022880670.0750.07524.29737801790.23214305130.53260568270.0750.0750.10.124.00011511240.01172420760.011724207624.52511809020.09883720930.104651162824.2111646018
24.377279175924.469608645124.31831668230.02899705060.03107253324.467042929324.94902374880.09645659960.124184097924.59418962070.06783052670.08042150690.07510096070.075100960724.00589334010.2319292170.53136374990.07460955630.07460955630.09008284670.090082846723.9586263740.01548202810.015482028124.43209483440.05232558140.058139534924.1573919473
24.358763414324.45552413824.30785124860.04522753990.050490992324.443233405524.57852198840.09442121260.120822170424.51466627580.05380288960.06142350240.06962310080.069623100824.74505479880.09452069190.1209855160.09589451350.09589451350.0900082390.09000823923.97655459230.01948462780.019484627824.42046692740.03488372090.029069767424.1632059008
24.328675301824.436744795324.2265463090.08656917970.108233043124.427360389724.51157519880.06774374170.080299441624.56042376630.03741445990.0409441890.07494228540.074942285424.6693628470.08061633440.09907157640.06303294830.06303294830.10020905440.100209054424.01217523730.02354408050.023544080524.408839020424.2155314821
24.29627271924.413270616924.12643115610.12008623380.166545941124.403550865924.50637400510.04139268520.045757490624.42865538320.03057324340.0328896190.08083077180.08083077180.11475582150.114755821524.04549056680.02852489530.028524895324.403025066924.1515779938
24.27312801724.380406767224.41545149450.17549015930.299231672324.443233405524.54729075110.04766760820.05355204450.04009143460.040091434624.07186560070.03483665070.034836650724.385583206524.22715938910.02906976740.0348837209
24.256926725624.356932588824.47512958760.19828911240.375369210324.427360389724.53276449790.03896870970.04281310990.04989557160.049895571624.10489976180.04222003310.042220033124.344885532124.25041520310.03488372090.0406976744
24.245354374624.314679067624.39635484030.20035983380.383216751924.46704292930.03968253970.047619047624.50746536380.03056778970.03288330730.05491663960.054916639624.16339216790.04969039950.049690399524.315815764624.36669427280.04069767440.0406976744
24.240725434224.291204889224.91168044770.23446399910.546359841124.46704292930.05555555560.055555555624.51843759740.02448737450.02595101420.0451565040.04515650424.1692444220.06213697660.062136976624.310001811124.29111287750.04069767440.0465116279
24.243039904424.267730710824.5067254690.06349206350.071428571424.52560138020.01996110190.02092294240.05009799470.050097994724.18893145190.07647191130.076471911324.263490183224.23878729610.05232558140.0639534884
24.24998331524.244256532424.58609054840.07142857140.079365079424.59064085680.01495512450.01548853360.05000668060.050006680624.17710388720.09759000730.097590007324.263490183224.2969268310.06976744190.0813953488
24.26155566624.234866861124.64958261190.07936507940.095238095224.62019610030.01197643810.01231609840.04932186290.049321862924.22516068240.11624763870.116247638724.205350648324.21553148210.08720930230.0813953488
24.275442487224.234866861124.43529689760.15873015870.150793650824.59064085680.01027606210.01052511410.05118645440.051186454424.04719181680.1796053020.17960530224.170466927424.38413613330.11627906980.1162790698
24.3078450724.244256532424.53847150080.16666666670.190476190524.59596036580.00815565330.0083117450.04914327090.049143270924.03488081080.22941573390.229415733924.16465297390.02906976740.034883720924.14576404030.11046511630.1162790698
24.34256212324.33815324623.9494460110.36507936510.444444444424.62657768510.00732856610.00745435880.05018527260.050185272623.9977805920.30151134460.301511344624.14576404030.03488372090.040697674423.69614108280.18604651160.2034883721
24.374964705724.399186109924.54468410630.22222222220.24603174624.67134862280.00649106350.00658955440.05008974880.050089748823.87217287480.3779644730.37796447324.25041520310.03488372090.046511627924.05660619910.36046511630.6511627907
24.384222586524.483693152124.54468410630.29365079370.341269841324.68448163810.00648121490.00657940480.04989557160.049895571619.9424.17483380770.04651162790.052325581423.75428061770.29069767440.3372093023
24.381908116324.582284701424.76690632850.36507936510.444444444424.72503348170.00773013980.00787022820.04495599710.044955997120.0424.2736710170.05232558140.05232558140.51744186050.7093023256
24.365706824924.723129771824.71938587960.01535756060.01592060740.0398447450.03984474523.62323386181124.2852989240.04651162790.0523255814
24.34256212324.906228363420.2424.36669427280.06395348840.0639534884
24.303216129620.3424.35506636590.09883720930.0930232558
24.222209672624.36669427280.14534883720.1511627907
24.113429573323.60893178050.51744186050.5639534884
24.0185362951
23.923643017
23.8588378514
log10(E, eV)
log10(J*E3 ,m-2 s-1 sr-1 eV2)
AGASA 03
RlgRAGASA to CERNCERN to JETPRlgR
AGASA astro-ph/02094220.8474576271-0.072below dip1.10.8060.88660.82-0.086
0.8936550492-0.049above dip
0.6064281383-0.217cutoff
18.5518.6518.7518.8518.9519.0519.1519.2519.3519.4519.5519.6519.7519.8519.9520.0520.1520.35
lgE18.4318.5318.6318.7318.8318.9319.0219.1319.2219.3219.4319.5319.6319.7319.8319.9320.0320.22
d0.050.060.070.080.100.150.190.440.250.340.44
lgJ-31.12-31.44-31.76-32.08-32.40-32.67-32.97-33.25-33.53-33.79-34.02-34.25-34.77-34.97-35.69-35.40-35.70-36.06
d0.040.060.060.070.080.160.170.370.220.290.37
J*E^324.459864024424.467042929324.443233405524.427360389724.403550865924.443233405524.427360389724.467042929324.467042929324.50672546924.586090548424.649582611924.435296897624.538471500823.94944601124.544684106324.544684106324.7669063285
lgE18.33918.44018.54018.64118.74118.84218.93719.04319.13819.23919.33919.44019.54019.64119.74119.84219.94220.138
lgJE^324.28724.29524.27124.25524.23124.27124.25524.29524.29524.33424.41424.47724.26324.36623.77724.37224.37224.595
AGASA 03
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Wolfendale
dx113453113.3333333333RlgRWW to CERNCERN to JETP
dy1914042131.050.0211.50.8061.209
x113130162186202223232251262275288301318325363378395414441475
y284282279275270263258249244239234232232234254267285306336375
lgE17.0217.1717.4517.6717.8117.9918.0718.2418.3418.4518.5718.6818.8318.8919.2319.3619.5119.6819.9220.22
lgJ24.4824.4724.4624.4424.4124.3824.3624.3124.2924.2724.2424.2324.2324.2424.3424.4024.4824.5824.7224.91
Wolfendale
24.4366197183
24.4272300469
24.4131455399
24.3943661972
24.3708920188
24.338028169
24.3145539906
24.2723004695
24.2488262911
24.2253521127
24.2018779343
24.1924882629
24.1924882629
24.2018779343
24.2957746479
24.3568075117
24.441314554
24.5399061033
24.6807511737
24.8638497653
Auger
lgENJ*1e30lgJlgJ+3lgE1/sqrt(N)lgEFlgJ+3lgE+lgFlgElgJ
18.4572750.05078233-31.294287376724.05571262330.011718.3424.000115112418.45424.228001817
18.5541720.02313257-31.63577611524.0142238850.015518.4423.95862637418.55424.1865130787
18.6526340.01160100-31.935504573224.01449542680.019518.5423.976554592318.65424.2044412969
18.7518040.00631126-32.199883928224.05011607180.023518.6424.012175237318.75424.2400619419
18.8512290.00341532-32.466568598724.08343140130.028518.7424.045490566818.85424.2733772714
18.958240.00181889-32.740193564724.10980643530.034818.8424.071865600718.95424.2997523054
19.055610.00098365-33.007159403724.14284059630.042218.9424.104899761819.05424.3327864664
19.154050.00056407-33.248666997624.20133300240.049719.0424.163392167919.15424.3912788725
19.252590.00028654-33.542814743424.20718525660.062119.1424.16924442219.25424.3971311266
19.351710.00015027-33.823127713624.22687228640.076519.2424.188931451919.35424.4168181565
19.451050.00007329-34.134955278324.21504472170.097619.3424.177103887219.45424.4049905918
19.55740.00004103-34.38689848324.2631015170.116219.4424.225160682419.55424.4530473871
19.65310.00001365-34.864867348624.08513265140.179619.5424.047191816819.65424.2750785215
19.75190.00000665-35.177178354724.07282164530.229419.6424.034880810819.75424.2627675154
19.85110.00000306-35.514278573524.03572142650.301519.7423.99778059219.85424.2256672966
19.9570.00000155-35.809668301824.04033169820.378019.8423.872172874819.95424.1000595794
20.0500.00000034-36.46852108319.9420.054
20.1500.00000027-36.568636235820.0420.154
20.2510.00000011-36.958607314823.79139268521.000020.1423.623233861820.25423.8511205664
20.3500.00000017-36.769551078620.2420.354
20.4500.00000013-36.886056647720.3420.454
dE0.22Factor1/FlgFRlgR
below 18.62.31.1370.8798375419-0.0555975111.30.114
above 18.61.91.0910.9163453186-0.0379408345
above 19.641.4730.6789552903-0.1681588234
Auger
00.01172420760.01172420760
00.01548202810.01548202810
00.01948462780.01948462780
00.02354408050.02354408050
00.02852489530.02852489530
00.03483665070.03483665070
00.04222003310.04222003310
00.04969039950.04969039950
00.06213697660.06213697660
00.07647191130.07647191130
00.09759000730.09759000730
00.11624763870.11624763870
00.1796053020.1796053020
00.22941573390.22941573390
00.30151134460.30151134460
00.3779644730.3779644730
00
00
0110
00
00
Fig E normed
Fig E normed
24.388851526924.478998316424.32853584750.02166997920.022808292524.31605538790.19803298430.37441089530.10.124.39811627990.08783880160.11022880670.0750.07524.04750054470.23214305130.53260568270.0750.07524.287491729224.59196560120.10465116280.098837209324.278012112824.2280018170.01172420760.0117242076
24.377279175924.469608645124.31831668230.02899705060.03107253324.69914627550.09645659960.12418409790.09008284670.090082846724.34431214750.06783052670.08042150690.07510096070.075100960723.75601586690.2319292170.53136374990.07460955630.074609556324.294670634124.49894234540.05813953490.052325581424.224239458224.18651307870.01548202810.0154820281
24.358763414324.45552413824.30785124860.04522753990.050490992324.32864451520.09442121260.12082217040.0900082390.09000823924.26478880260.05380288960.06142350240.06962310080.069623100824.49517732560.09452069190.1209855160.09589451350.095894513524.270861110324.48731443840.02906976740.034883720924.230053411724.20444129690.01948462780.0194846278
24.328675301824.436744795324.2265463090.08656917970.108233043124.26169772560.06774374170.08029944160.10020905440.100209054424.31054629310.03741445990.0409441890.07494228540.074942285424.41948537380.08061633440.09907157640.06303294830.063032948324.254988094424.475686531424.282378993124.24006194190.02354408050.0235440805
24.29627271924.413270616924.12643115610.12008623380.166545941124.25649653190.04139268520.04575749060.11475582150.114755821524.178777910.03057324340.0328896190.08083077180.080830771824.231178570624.469872577924.21842550470.02906976740.034883720924.27337727140.02852489530.0285248953
24.27312801724.380406767224.41545149450.17549015930.299231672324.29741327790.04766760820.05355204450.04009143460.040091434624.270861110324.452430717524.29400690010.03488372090.040697674424.29975230540.03483665070.0348366507
24.256926725624.356932588824.47512958760.19828911240.375369210324.28288702470.03896870970.04281310990.04989557160.049895571624.254988094424.41173304324.31726271410.04069767440.040697674424.33278646640.04222003310.0422200331
24.245354374624.314679067624.39635484030.20035983380.383216751924.25758789060.03056778970.03288330730.05491663960.054916639624.29467063410.03968253970.047619047624.382663275624.43354178380.04069767440.046511627924.39127887250.04969039950.0496903995
24.240725434224.291204889224.91168044770.23446399910.546359841124.26856012420.02448737450.02595101420.0451565040.04515650424.29467063410.05555555560.055555555624.376849322124.35796038850.05232558140.063953488424.39713112660.06213697660.0621369766
24.243039904424.267730710824.2757239070.01996110190.02092294240.05009799470.050097994724.33435317380.06349206350.071428571424.330337694224.30563480710.06976744190.081395348824.41681815650.07647191130.0764719113
24.24998331524.244256532424.34076338360.01495512450.01548853360.05000668060.050006680624.41371825320.07142857140.079365079424.330337694224.3637743420.08720930230.081395348824.40499059180.09759000730.0975900073
24.26155566624.234866861124.37031862710.01197643810.01231609840.04932186290.049321862924.47721031670.07936507940.095238095224.272198159324.28237899310.11627906980.116279069824.45304738710.11624763870.1162476387
24.275442487224.234866861124.34076338360.01027606210.01052511410.05118645440.051186454424.26292460240.15873015870.150793650824.237314438424.45098364430.11046511630.116279069824.27507852150.1796053020.179605302
24.3078450724.244256532424.34608289250.00815565330.0083117450.04914327090.049143270924.36609920550.16666666670.190476190524.23150048490.03488372090.029069767424.21261155130.18604651160.203488372124.26276751540.22941573390.2294157339
24.34256212324.33815324624.37670021190.00732856610.00745435880.05018527260.050185272623.77707371580.36507936510.444444444424.21261155130.04069767440.034883720923.76298859380.36046511630.651162790724.22566729660.30151134460.3015113446
24.374964705724.399186109924.42147114960.00649106350.00658955440.05008974880.050089748824.3723118110.22222222220.24603174624.31726271410.04651162790.034883720924.123453710.29069767440.337209302324.10005957940.3779644730.377964473
24.384222586524.483693152124.43460416480.00648121490.00657940480.04989557160.049895571624.3723118110.29365079370.341269841324.24168131870.05232558140.046511627923.82112812860.51744186050.709302325620.0539433523
24.381908116324.582284701424.47515600850.00773013980.00787022820.04495599710.044955997124.59453403320.36507936510.444444444424.3405185280.05232558140.052325581420.1539433523
24.365706824924.723129771824.46950840640.01535756060.01592060740.0398447450.03984474524.3521464350.05232558140.046511627923.851120566411
24.34256212324.906228363424.43354178380.06395348840.063953488420.3539433523
24.303216129624.42191387680.09302325580.098837209320.4539433523
24.222209672624.43354178380.15116279070.1453488372
24.113429573323.67577929140.56395348840.5174418605
24.0185362951
23.923643017
23.8588378514
log10(E, eV)
log10(J*E3 ,m-2 s-1 sr-1 eV2)
Fig
Fig
24.388851526924.478998316424.32853584750.02166997920.022808292524.459864024424.56593286110.19803298430.374410895324.64799375310.08783880160.11022880670.0750.07524.29737801790.23214305130.53260568270.0750.0750.10.124.00011511240.01172420760.011724207624.52511809020.09883720930.104651162824.2111646018
24.377279175924.469608645124.31831668230.02899705060.03107253324.467042929324.94902374880.09645659960.124184097924.59418962070.06783052670.08042150690.07510096070.075100960724.00589334010.2319292170.53136374990.07460955630.07460955630.09008284670.090082846723.9586263740.01548202810.015482028124.43209483440.05232558140.058139534924.1573919473
24.358763414324.45552413824.30785124860.04522753990.050490992324.443233405524.57852198840.09442121260.120822170424.51466627580.05380288960.06142350240.06962310080.069623100824.74505479880.09452069190.1209855160.09589451350.09589451350.0900082390.09000823923.97655459230.01948462780.019484627824.42046692740.03488372090.029069767424.1632059008
24.328675301824.436744795324.2265463090.08656917970.108233043124.427360389724.51157519880.06774374170.080299441624.56042376630.03741445990.0409441890.07494228540.074942285424.6693628470.08061633440.09907157640.06303294830.06303294830.10020905440.100209054424.01217523730.02354408050.023544080524.408839020424.2155314821
24.29627271924.413270616924.12643115610.12008623380.166545941124.403550865924.50637400510.04139268520.045757490624.42865538320.03057324340.0328896190.08083077180.08083077180.11475582150.114755821524.04549056680.02852489530.028524895324.403025066924.1515779938
24.27312801724.380406767224.41545149450.17549015930.299231672324.443233405524.54729075110.04766760820.05355204450.04009143460.040091434624.07186560070.03483665070.034836650724.385583206524.22715938910.02906976740.0348837209
24.256926725624.356932588824.47512958760.19828911240.375369210324.427360389724.53276449790.03896870970.04281310990.04989557160.049895571624.10489976180.04222003310.042220033124.344885532124.25041520310.03488372090.0406976744
24.245354374624.314679067624.39635484030.20035983380.383216751924.46704292930.03968253970.047619047624.50746536380.03056778970.03288330730.05491663960.054916639624.16339216790.04969039950.049690399524.315815764624.36669427280.04069767440.0406976744
24.240725434224.291204889224.91168044770.23446399910.546359841124.46704292930.05555555560.055555555624.51843759740.02448737450.02595101420.0451565040.04515650424.1692444220.06213697660.062136976624.310001811124.29111287750.04069767440.0465116279
24.243039904424.267730710824.5067254690.06349206350.071428571424.52560138020.01996110190.02092294240.05009799470.050097994724.18893145190.07647191130.076471911324.263490183224.23878729610.05232558140.0639534884
24.24998331524.244256532424.58609054840.07142857140.079365079424.59064085680.01495512450.01548853360.05000668060.050006680624.17710388720.09759000730.097590007324.263490183224.2969268310.06976744190.0813953488
24.26155566624.234866861124.64958261190.07936507940.095238095224.62019610030.01197643810.01231609840.04932186290.049321862924.22516068240.11624763870.116247638724.205350648324.21553148210.08720930230.0813953488
24.275442487224.234866861124.43529689760.15873015870.150793650824.59064085680.01027606210.01052511410.05118645440.051186454424.04719181680.1796053020.17960530224.170466927424.38413613330.11627906980.1162790698
24.3078450724.244256532424.53847150080.16666666670.190476190524.59596036580.00815565330.0083117450.04914327090.049143270924.03488081080.22941573390.229415733924.16465297390.02906976740.034883720924.14576404030.11046511630.1162790698
24.34256212324.33815324623.9494460110.36507936510.444444444424.62657768510.00732856610.00745435880.05018527260.050185272623.9977805920.30151134460.301511344624.14576404030.03488372090.040697674423.69614108280.18604651160.2034883721
24.374964705724.399186109924.54468410630.22222222220.24603174624.67134862280.00649106350.00658955440.05008974880.050089748823.87217287480.3779644730.37796447324.25041520310.03488372090.046511627924.05660619910.36046511630.6511627907
24.384222586524.483693152124.54468410630.29365079370.341269841324.68448163810.00648121490.00657940480.04989557160.049895571619.9424.17483380770.04651162790.052325581423.75428061770.29069767440.3372093023
24.381908116324.582284701424.76690632850.36507936510.444444444424.72503348170.00773013980.00787022820.04495599710.044955997120.0424.2736710170.05232558140.05232558140.51744186050.7093023256
24.365706824924.723129771824.71938587960.01535756060.01592060740.0398447450.03984474523.62323386181124.2852989240.04651162790.0523255814
24.34256212324.906228363420.2424.36669427280.06395348840.0639534884
24.303216129620.3424.35506636590.09883720930.0930232558
24.222209672624.36669427280.14534883720.1511627907
24.113429573323.60893178050.51744186050.5639534884
24.0185362951
23.923643017
23.8588378514
log10(E, eV)
log10(J*E3 ,m-2 s-1 sr-1 eV2)
HiRes
dx56553124.25HiRes 07 in PRDRlgRHiRes to CERNCERN to JETPRlgR
dy147319172below dip0.9267840593-0.0331.50.8061.2091.080.033
above dip0.9487666034-0.023
cutoff0.7936507937-0.100
x88100112125137149162174187199211224236249261273286298317342367391416
y24322722522322221921220720619819818818218117619418119820021421221497
dy down225217220175169186172189191203196188
dy up260236231186182200189207208225229239186
lgJo0.55813953490.46511627910.45348837210.44186046510.43604651160.41860465120.37790697670.34883720930.34302325580.29651162790.29651162790.2383720930.20348837210.19767441860.16860465120.2732558140.19767441860.29651162790.30813953490.38953488370.37790697670.3895348837-0.2906976744
lgE17.172545271617.269124748517.365704225417.47033199217.566911468817.663490945717.768118712317.864698189117.969325955718.065905432618.162484909518.267112676118.363692152918.468319919518.564899396418.661478873218.766106639818.862686116719.015603621719.216810865219.418018108719.611177062419.8123843058
lgJ24.525118090224.432094834424.420466927424.408839020424.403025066924.385583206524.344885532124.315815764624.310001811124.263490183224.263490183224.205350648324.170466927424.164652973924.145764040324.250415203124.174833807724.27367101724.28529892424.366694272824.355066365924.366694272823.6089317805
0.10465116280.05813953490.02906976740.03488372090.04069767440.04651162790.05232558140.05232558140.05232558140.06395348840.09302325580.15116279070.5639534884
0.09883720930.05232558140.03488372090.02906976740.03488372090.03488372090.04651162790.05232558140.04651162790.06395348840.09883720930.14534883720.5174418605
lgE17.20617.30317.39917.50417.60017.69717.80217.89818.00318.09918.19618.30118.39718.50218.59818.69518.80018.89619.04919.25019.45119.64519.846
lgJ24.591965601224.498942345424.487314438424.475686531424.469872577924.452430717524.41173304324.382663275624.376849322124.330337694224.330337694224.272198159324.237314438424.231500484924.212611551324.317262714124.241681318724.34051852824.35214643524.433541783824.421913876824.433541783823.6757792914
x249
