uuid:3d336b31-dff1-4c34-b1f1-69040a60efda
xmp.did:51EB6E41DC08E0118CD1A1379105AB9F
adobe:docid:indd:55b2be19-d352-11de-a31b-ffe24ab5dd96
proof:pdf
xmp.iid:50EB6E41DC08E0118CD1A1379105AB9F
xmp.did:8DE6A8628006E0118C14D5A210D33D03
adobe:docid:indd:55b2be19-d352-11de-a31b-ffe24ab5dd96
default
saved
xmp.iid:DF4F1135F500DF1183D4C400F4FDAB2A
2010-01-14T12:11:40+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:E04F1135F500DF1183D4C400F4FDAB2A
2010-01-14T12:11:40+02:00
Adobe InDesign 6.0
/metadata
saved
xmp.iid:E14F1135F500DF1183D4C400F4FDAB2A
2010-01-14T12:57:47+02:00
Adobe InDesign 6.0
/metadata
saved
xmp.iid:E24F1135F500DF1183D4C400F4FDAB2A
2010-01-14T12:57:47+02:00
Adobe InDesign 6.0
/;/metadata
saved
xmp.iid:E34F1135F500DF1183D4C400F4FDAB2A
2010-01-14T13:05:54+02:00
Adobe InDesign 6.0
/metadata
saved
xmp.iid:E44F1135F500DF1183D4C400F4FDAB2A
2010-01-14T13:05:54+02:00
Adobe InDesign 6.0
/;/metadata
saved
xmp.iid:E54F1135F500DF1183D4C400F4FDAB2A
2010-01-14T13:06:32+02:00
Adobe InDesign 6.0
/metadata
saved
xmp.iid:E64F1135F500DF1183D4C400F4FDAB2A
2010-01-14T13:06:32+02:00
Adobe InDesign 6.0
/;/metadata
saved
xmp.iid:8B8F7935800ADF1196F4F0D3B5D1C75F
2010-01-26T15:39:21+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:EB908C55810ADF119871DD04D56AB754
2010-01-26T15:47:24+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:A7846867300FDF11BF5AA4F055A5AD9D
2010-02-01T14:50:41+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:B057E256CA0FDF119599DE52A871FFD0
2010-02-02T09:12:35+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:3825F28ACA0FDF119EBECC396F3E9DAD
2010-02-02T09:14:03+02:00
Adobe InDesign 6.0
/metadata
saved
xmp.iid:3925F28ACA0FDF119EBECC396F3E9DAD
2010-02-02T09:14:03+02:00
Adobe InDesign 6.0
/;/metadata
saved
xmp.iid:3A25F28ACA0FDF119EBECC396F3E9DAD
2010-02-02T09:15:25+02:00
Adobe InDesign 6.0
/metadata
saved
xmp.iid:3B25F28ACA0FDF119EBECC396F3E9DAD
2010-02-02T09:15:25+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:750D6B85D60FDF1188BCB36B58452661
2010-02-02T10:39:48+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:31194067DE0FDF11A5B2A403972F4363
2010-02-02T11:36:13+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:07ECB50BEE0FDF11BBB4F6BC3B9209ED
2010-02-02T13:28:11+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:AD4FC578CB10DF118A8CA43869F3300B
2010-02-03T16:25:54+02:00
Adobe InDesign 6.0
/metadata
saved
xmp.iid:AE4FC578CB10DF118A8CA43869F3300B
2010-02-03T16:25:54+02:00
Adobe InDesign 6.0
/;/metadata
saved
xmp.iid:E17C070C2C12DF11B142D80DAF079995
2010-02-05T11:11:41+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:9FE1915B7B14DF11A14BB0E9A56DDE1E
2010-02-08T08:29:51+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:867F6D139614DF11848FA3FFF101FBD9
2010-02-08T11:41:04+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:897F6D139614DF11848FA3FFF101FBD9
2010-02-08T12:15:11+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:32753A1AB714DF118E28FDBAA5305E60
2010-02-08T15:37:29+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:176951A1BB17DF118887886E4ABEDC0E
2010-02-12T13:23+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:CF46D29CBB1BDF11B4B8FDDE6A3F4A4C
2010-02-17T14:00:48+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:A3827179AE38DF1189E6F2A4962AD137
2010-03-26T10:06:25+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:3477E364B243DF1186869D4BEEF890CA
2010-04-09T10:55:53+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:AD3170A1C343DF11BE778C82F63CB51F
2010-04-09T12:48:45+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:AE3170A1C343DF11BE778C82F63CB51F
2010-04-09T15:13:08+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:6ECB6C039247DF1195BFCCF10E897A16
2010-04-14T08:50:29+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:12FCE54E724CDF1199E8951AD8227FCF
2010-04-20T14:12:15+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:AF3853F2DF58DF11A4F6F892A2F259B1
2010-05-06T12:17:44+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:0DFFBACC0359DF11A4F6F892A2F259B1
2010-05-06T13:37:49+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:CF57CA045462DF11B6D2C7DCD6C7E964
2010-05-18T10:04:44+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:D057CA045462DF11B6D2C7DCD6C7E964
2010-05-18T11:13:41+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:FACCD3D48062DF11B59BA25A0A8354F6
2010-05-18T15:25:31+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:FBCCD3D48062DF11B59BA25A0A8354F6
2010-05-18T15:26:18+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:FCCCD3D48062DF11B59BA25A0A8354F6
2010-05-18T15:26:23+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:88D17199AA7ADF11BCBDBB26D015DE34
2010-06-18T09:45:10+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:918620765683DF11BC59B35A780499F7
2010-06-29T13:01:10+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:DDA394163E88DF119F88D8B0E8A3931B
2010-07-05T16:03:29+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:6F485926118FDF11837EA4CEF60DBE4A
2010-07-14T08:32:18+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:A8A10BA7AF90DF11B12C9778406FCB23
2010-07-16T11:10:26+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:AC8CD32B9094DF11895AA966BA2EADDB
2010-07-21T08:21:17+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:AF8CD32B9094DF11895AA966BA2EADDB
2010-07-21T08:36:03+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:D0C753EAFEBEDF11BFC0D36D35EC0202
2010-09-13T08:19:50+02:00
Adobe InDesign 6.0
/metadata
saved
xmp.iid:D1C753EAFEBEDF11BFC0D36D35EC0202
2010-09-13T08:19:50+02:00
Adobe InDesign 6.0
/;/metadata
saved
xmp.iid:566B6F5D37BFDF119FFF87DEABBE45F2
2010-09-13T15:03:55+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:596B6F5D37BFDF119FFF87DEABBE45F2
2010-09-13T16:12:18+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:5A6B6F5D37BFDF119FFF87DEABBE45F2
2010-09-13T16:16:04+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:25E0390ADABFDF11AB1DF20C369C5409
2010-09-14T10:32:04+02:00
Adobe InDesign 6.0
/metadata
saved
xmp.iid:26E0390ADABFDF11AB1DF20C369C5409
2010-09-14T10:32:04+02:00
Adobe InDesign 6.0
/;/metadata
saved
xmp.iid:27E0390ADABFDF11AB1DF20C369C5409
2010-09-14T10:32:43+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:36F4E256E2C6DF11AAA5A68FD48543AC
2010-09-23T09:15:26+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:BE76034298E1DF1194F6A7BDBDCC45F2
2010-10-27T09:09:23+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:BF76034298E1DF1194F6A7BDBDCC45F2
2010-10-27T09:43:20+02:00
Adobe InDesign 6.0
/metadata
saved
xmp.iid:C076034298E1DF1194F6A7BDBDCC45F2
2010-10-27T09:43:20+02:00
Adobe InDesign 6.0
/;/metadata
saved
xmp.iid:C176034298E1DF1194F6A7BDBDCC45F2
2010-10-27T09:47:41+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:2385C26927E3DF11A1D7FFCAE040767D
2010-10-29T09:19:09+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:6499BD5F92E5DF1197EEB0EDBA0D5BC0
2010-11-01T10:44:50+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:6A99BD5F92E5DF1197EEB0EDBA0D5BC0
2010-11-01T11:18:43+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:BE8C5D71A7E5DF118CB4CE6078BBF9DE
2010-11-01T13:16:48+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:6105172EB1E8DF11A753B641A055A129
2010-11-05T10:44:52+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:0C428AE8C0E8DF11A753B641A055A129
2010-11-05T11:42:52+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:A73217627AEDDF1191AD98825A3C6EE7
2010-11-11T15:42:21+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:CCC640551AF6DF11BF4EA173CF16F835
2010-11-22T12:14:46+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:EB8A314D94F7DF1194E2943A804C7025
2010-11-24T08:30:16+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:F5EFADB442FDDF11A13A8150ECA8BBCD
2010-12-01T14:01:18+02:00
Adobe InDesign 6.0
/metadata
saved
xmp.iid:F6EFADB442FDDF11A13A8150ECA8BBCD
2010-12-01T14:01:18+02:00
Adobe InDesign 6.0
/;/metadata
saved
xmp.iid:F7EFADB442FDDF11A13A8150ECA8BBCD
2010-12-01T14:14:53+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:F8EFADB442FDDF11A13A8150ECA8BBCD
2010-12-01T14:57:15+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:FAEFADB442FDDF11A13A8150ECA8BBCD
2010-12-01T15:49:52+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:C629F8C7E1FDDF118687865BA3BAC07F
2010-12-02T09:00+02:00
Adobe InDesign 6.0
/metadata
saved
xmp.iid:C729F8C7E1FDDF118687865BA3BAC07F
2010-12-02T09:00+02:00
Adobe InDesign 6.0
/;/metadata
saved
xmp.iid:C829F8C7E1FDDF118687865BA3BAC07F
2010-12-02T09:20:22+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:B6E1B3880BFEDF118687865BA3BAC07F
2010-12-02T13:58:53+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:F805677AD6FEDF11B6BEB0C1DC3146AA
2010-12-03T14:11:37+02:00
Adobe InDesign 6.0
/metadata
saved
xmp.iid:F905677AD6FEDF11B6BEB0C1DC3146AA
2010-12-03T14:11:37+02:00
Adobe InDesign 6.0
/;/metadata
saved
xmp.iid:FA05677AD6FEDF11B6BEB0C1DC3146AA
2010-12-03T14:14:19+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:FB05677AD6FEDF11B6BEB0C1DC3146AA
2010-12-03T14:49:32+02:00
Adobe InDesign 6.0
/metadata
saved
xmp.iid:FC05677AD6FEDF11B6BEB0C1DC3146AA
2010-12-03T14:49:32+02:00
Adobe InDesign 6.0
/;/metadata
saved
xmp.iid:FD05677AD6FEDF11B6BEB0C1DC3146AA
2010-12-03T14:53:28+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:FE05677AD6FEDF11B6BEB0C1DC3146AA
2010-12-03T14:54:15+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:7855DA44E3FEDF11B6BEB0C1DC3146AA
2010-12-03T15:59:22+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:7955DA44E3FEDF11B6BEB0C1DC3146AA
2010-12-03T16:00:42+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:03C098EC0501E0118DFD956056236FB5
2010-12-06T08:56:17+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:BDCB8E6CD501E0118139ABDD0BD95C31
2010-12-07T11:48:58+02:00
Adobe InDesign 6.0
/metadata
saved
xmp.iid:BECB8E6CD501E0118139ABDD0BD95C31
2010-12-07T11:48:58+02:00
Adobe InDesign 6.0
/;/metadata
saved
xmp.iid:BFCB8E6CD501E0118139ABDD0BD95C31
2010-12-07T11:54:21+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:C0CB8E6CD501E0118139ABDD0BD95C31
2010-12-07T14:41:54+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:C1CB8E6CD501E0118139ABDD0BD95C31
2010-12-07T15:09+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:C2CB8E6CD501E0118139ABDD0BD95C31
2010-12-07T16:21:05+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:3883D97A8703E011BBCFDCB9638408AB
2010-12-09T13:28:43+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:8CE6A8628006E0118C14D5A210D33D03
2010-12-13T08:23:18+02:00
Adobe InDesign 6.0
/metadata
saved
xmp.iid:8DE6A8628006E0118C14D5A210D33D03
2010-12-13T08:23:18+02:00
Adobe InDesign 6.0
/;/metadata
saved
xmp.iid:4BEB6E41DC08E0118CD1A1379105AB9F
2010-12-16T08:55:58+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:4CEB6E41DC08E0118CD1A1379105AB9F
2010-12-16T08:58:07+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:4DEB6E41DC08E0118CD1A1379105AB9F
2010-12-16T08:58:55+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:4EEB6E41DC08E0118CD1A1379105AB9F
2010-12-16T09:00:22+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:4FEB6E41DC08E0118CD1A1379105AB9F
2010-12-16T09:02+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:50EB6E41DC08E0118CD1A1379105AB9F
2010-12-16T10:16:18+02:00
Adobe InDesign 6.0
/metadata
saved
xmp.iid:51EB6E41DC08E0118CD1A1379105AB9F
2010-12-16T10:16:18+02:00
Adobe InDesign 6.0
/;/metadata
saved
xmp.iid:28CE8C89A809E011A2A1AC44D3365C34
2010-12-17T13:34:48+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:00735F4CD209E011A2A1AC44D3365C34
2010-12-17T13:39:25+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:6E5FFCDD1C0CE0118576AB1D4175C7EC
2010-12-20T11:48:11+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:705FFCDD1C0CE0118576AB1D4175C7EC
2010-12-20T12:20+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:3BD41987B51CE011AF50FF63199158A7
2011-01-10T14:58:23+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:41BADD46531DE011A620D959CC994409
2011-01-11T12:28:47+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:0BB1C0296E1DE011A620D959CC994409
2011-01-11T14:51:58+02:00
Adobe InDesign 6.0
/
saved
xmp.iid:92F09223DD1EE011B519B4BDFEEC40C9
2011-01-13T08:19:55+02:00
Adobe InDesign 6.0
/
2011-01-17T12:03:56+02:00
2011-01-17T12:03:57+02:00
2011-01-17T12:03:57+02:00
Adobe InDesign CS4 (6.0)
JPEG
256
256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7652
xml
Adobe PDF Library 9.0
False
Cosmic ray propagation in a fractal galactic medium
Authors:
Hamid A. Kermani1
Jalileldin Fatemi1
Affiliation:
1Department of Physics, Faculty of Science, University of Kerman,
Islamic Republic of Iran
Correspondence to:
Hamid Kermani
email:
ham_arjomand@yahoo.com
Postal address:
Department of Physics, Faculty of Science, University of Kerman,
22 Bahman Avenue, Kerman, Islamic Republic of Iran
Dates:
Received: 13 May 2010
Accepted: 21 Sept. 2010
Published: [To be released]
How to cite this article:
Kermani HA, Fatemi J. Cosmic ray propagation in a fractal galactic medium. S Afr J Sci. 2011;107(1/2), Art. #275, 4 pages. DOI: 0.4102/sajs.v107i1/2.275
© 2011. The Authors.
Licensee: OpenJournals
Publishing. This work
is licensed under the
Creative Commons
Attribution License.
Simple cosmic ray diffusion in magnetic fields is often discussed in terms of a characteristic scattering mean free path or equivalent diffusion coefficient. This assumes very simple properties of the structure of astrophysical magnetic fields. A better approximation is to assume that the magnetic structure has fractal properties and there is then the possibility of including very short and very long interaction lengths when modelling the propagation. Results of modelling such propagation in a fractal medium are discussed. Values of the propagation parameter (α) less than 2 were obtained and confirm the plausibility of the hypothesis that supernova are the origin of galactic cosmic rays in the energy range below the knee in the spectrum.
Introduction
It is thought that supernova remnants are the most probable origins of galactic cosmic rays below 0.1 PeV (1014 eV)1 and that these are possible sources of energies up to 100 PeV, above which extragalactic sources are believed to dominate. Even if only 10% of the supernova explosion energy (1051 erg) goes into cosmic rays, they are energetically capable of delivering the requisite cosmic ray power of 1042 erg/s into the interstellar medium. They may well be the only class of object within our galaxy with this capability. The acceleration mechanism of cosmic ray particles is most probably diffusive shock acceleration, which can produce the appropriate power and satisfy the requirement of a power law energy spectrum.
However, supernova acceleration models, such as those of Axford2, Berezhko et al.3 and others, confront many problems. For example, none of the existing supernova models can demonstrably provide the necessary acceleration efficiency up to the observed energies (greater than 1 PeV) of galactic cosmic rays. Also, in such models, the total energy of particles extracted from the shock energy is found to be greater than 10%. This is much higher than required to provide the observed energy which is needed to fit the observed flux at Earth using the conventional galactic propagation models.
The problems with a supernova model can be approached in two ways. The first is to look for modifications to the model for the origin of the galactic cosmic rays. The second is to look for a different model for the propagation of particles in the interstellar medium of the galaxy, such that the relationship between the observed energy density and the total source energies is changed.
In this paper, we discuss the second approach and examine whether particle density as a function of the galactic radius has the required features within a model for the diffusion of cosmic rays in an interstellar medium with fractal structure.
It is known that the distribution of matter and magnetic fields in the galaxy is highly non-homogeneous on different spatial scales. Gaseous clouds with very different densities, temperatures and degrees of ionisation move through space in a highly turbulent way. Galactic structures such as shells, clouds and filaments are widely spread in the interstellar medium. We can say that the galaxy has a multi-scale structure or even a multi-scale length structure.4 Therefore we wish to consider the consequences of cosmic ray propagation in a multi-scale turbulent medium.
Cosmic ray propagation has usually been assumed to be in a form of normal diffusion, resulting in a Gaussian spatial distribution of particles around a source. We will now assume that, (1) cosmic rays with energies below the knee of the cosmic ray spectrum at 3 PeV (1 PeV = 1015 eV) are of supernova origin and that, (2) based on a recent suggestion by Lagutin and colleagues5, the propagation of such particles in an interstellar medium with a fractal structure is described by a different diffusion equation to that usually assumed.
The result we obtained differs from those usually found, because the cosmic rays now propagate in a non-homogeneous interstellar medium.
Super-diffusion
On the basis of the assumption that the interstellar medium has a fractal structure, Lagutin et al.5 have formulated and solved analytically the equation for anomalous diffusion in a fractal medium for different input conditions. The super-diffusion equation formulated in Lagutin’s work has the general form:
∂N (r, E, t) = – D (E, α)(-∆)α/2 N (r, E, t) + S(r, E, t)
∂t [Eqn 1]
Where N(r,E,t) is the number of cosmic ray particles with the energy of E at the distance r from the source, D is the anomalous diffusion coefficient, (-∆)a/2 is the fractional Laplacian called the ‘Riss’ operator and S(r,E,t) is the function describing the density distribution of sources.
To obtain the number of particles at a distance r from a supernova (assumed to be a point source with an inverse power spectrum), we followed the suggestion of Lagutin et al.5, and used the steady-state diffusion equation:
D (-∆)α/2 N (r, E) = S (r, E) [Eqn 2]
Finally, we find the solution of the steady-state case of the diffusion equation as:
N (r, E) = 2-α S0Γ (3 - α) E-P-δ
π D0r3-αΓ( α ) [Eqn 3]
Where E-p is the energy spectrum of source (p is related to the effect of source) and α = 2δ is the intrinsic property of the interstellar medium. The details of the solutions to [Eqn 1] and [Eqn 2] are given by Lagutin et al.5,6
Lagutin et al.5 suggested the investigation of such a super-propagation regime and calculated the propagation parameter (α) range, specific to such a medium 0.6 < α < 2. In this work, it is assumed that all cosmic rays in the mentioned energy range, are of supernova origin. The spatial distribution of supernovae is given by [Eqn 4]:
F (R, Z) = ( R )a exp (-b ( R -1 ) - Z )
R0 R0 Hz [Eqn 4]
Actually, the intensity of cosmic rays (I), in every energy range is proportional to N(r,E) F(R,Z). The intensity in terms of R for different α, is shown in Figure 1.
Radial distribution of supernovae in the galactic disk with cylindrical symmetry is calculated using [Eqn 4]. Where
a = 1.69 ± 0.22, b = 3.33 ± 0.37, R0 = 8.5 kpc (distance of the sun from the galactic centre), Hz = 0.2 kpc7 (the vertical scale parameter of the galaxy) and Z is the vertical distance from the galactic disk. And we know that the producing rate of supernovae (Type П) in the galaxy is 10-2 per year.
We present the results of a Monte Carlo simulation using a diffusion equation appropriate to a non-homogeneous medium. As we noted above, the assumption of normal diffusion, resulting in a Gaussian spatial distribution of particles, does not easily reproduce observed cosmic ray fluxes. We will now examine the suggestion by Lagutin et al.5 and consider an interstellar medium with scales described by a fractal structure, resulting in an ‘anomalous’ diffusion equation.
By assuming a Kolmogrov-type spectrum for the galactic magnetic field strength, a trajectory and relative galactic containment times of cosmic rays for conventional and super-diffusion propagations are simulated.
Parameterising the diffusion
The parameter α, given in Lagutin et al.5,6, is the basic parameter for describing the propagation of cosmic rays in an anomalous interstellar medium. Its magnitude is related to the spectrum of magnetic irregularities of the medium. The standard diffusion model (for particles in a homogenous turbulent medium), which leads to the Gaussian distribution of particle densities, is found when α = 2. On the other hand,
α < 2 is related to the anomalous super-diffusion regime.5,6 We will see the detailed role of parameter α below. Our results will show the usefulness of assuming that the interstellar medium has a fractal structure with α < 2.5 This assumption, which is consistent with our physical picture of galactic magnetic fields, will reduce the discrepancy between expectation and observation for cosmic ray fluxes in supernova models, noted above, through changes to the galactic propagation characteristics of cosmic rays originating in supernovae.
Super-diffusion and galactic containment times
Because the interstellar medium has a multi-phase character and is non-homogenous, the turbulence level is high and the ratio of the mean amplitude irregular magnetic field in the galaxy determined by the turbulence of the regular field undoubtedly varies from place to place, depending on the proximity of stars of various types and shocks of a wide range of strengths. The way to advance on the simple homogenous diffusion approximation is by using the so-called anomalous diffusion scenario.8 Here there are two regimes, (1) sub-diffusion, in which there are relatively small spatial displacements and (2) super-diffusion, where there are large displacements (the so-called levy flights). For a random walk leading to super-diffusion (levy flights), the step length l is chosen from a probability distribution that decays as P(l) = l-µ for large l, where µ < 3; for normal diffusion, the step-size distribution has a decay exponent of µ > 3.
Super-diffusion has the effect of applying a diffusion mean free path which is variable within the limits set by its being drawn from a fixed statistical distribution. Unlike more conventional diffusion, this has the effect of occasionally allowing the diffusing particle to travel an unexpectedly large distance between interactions. On the other hand, there may also be many more short distances between interactions (Figure 2).
When considering the containment time for cosmic ray particles of the same composition within a galactic magnetic field, it is the former effect which is most important. A cosmic ray will occasionally travel a large distance between interactions and this may be sufficient for it to leave the galactic magnetic field unexpectedly quickly. The effect of this process is to reduce the overall containment time (and hence the predicted energy density of cosmic rays) at energies where containment is usually effective, that is, the range of energies between the knee and the ankle of the cosmic ray energy spectrum. This is shown in Figure 3, in which calculations for cosmic ray propagation in turbulent galactic magnetic fields give a greater galactic residence time for conventionally diffusing particles compared to super-diffusion particles at energies below about 100 PeV (1017 eV).
Super-diffusion to derive an appropriate galactic cosmic ray energy density
We modelled the super-diffusive propagation of cosmic rays in galactic magnetic fields. We assume that supernovae are the nuclei cosmic ray sources, but for cosmic ray electrons other sources with different acceleration efficiency also can contribute.9 In the case of supernovae, they are distributed within the galactic plane with a scale height from the plane of 0.2 kpc. We assume a supernova radial distribution that is normalised to one supernova in the galaxy, as is shown in Figure 4.
We calculated the energy density of cosmic rays from a single supernova and then extended this to supernovae distributed throughout the galactic volume. This allowed us to determine a radial gradient of the galactic cosmic ray density and a local value for the cosmic ray energy density. Figure 5 shows the radial gradient results and the spread in acceptable values of α to be derived from the gradient (shown in Figure 5 as the solid line). Also using the standard deviation method, we find that for every α the error is 0.02 (shown in Figure 5 as the dashed lines above and below the full line). Furthermore, the experimental region of the radial gradient range, between 0.03 kpc-1 and 0.06 kpc-1,10,11 is consistent with our result.
Assuming a Type II supernova rate of 1/100 per year, we can use super-diffusion ideas to calculate the cosmic ray energy density distribution throughout the galactic disk. Such modelling has the super-diffusion parameter α as a free parameter (remembering that α = 2 gives conventional diffusion). We can then use the known cosmic ray spectrum and radial gradient in the vicinity of the solar system to define an energy density at that radial distance for comparison with the modelling results. The result of this comparison is that the best fit for the value of α is about 1.65. Possible fits range from 1.6 − 1.9, but no acceptable fit is found for α = 2, which would correspond to conventional diffusion. This confirms our original expectation that conventional diffusion is unable to fit the measured cosmic ray energy density at the galactic radial distance of the solar system.
Summary
Our calculations show that the interstellar medium within which galactic cosmic rays produced by supernovae propagate, may have a fractal and non-homogenous structure. If our results are compared with the experimental values of the radial gradient of cosmic rays (in the range of 0.03 kpc-1 − 0.06 kpc-1)10,11 and also the simulated values of energy density of cosmic rays with the expected ones
(1.8 x 10-4 eV/cm3), values of α less than 2 are obtained for the super-diffusion equation suggested by Lagutin et al5. This does not fit the normal diffusion of particles in a homogenous medium with a Gaussian spatial distribution, which would result if α = 2. As a result, this work confirms the plausibility of the hypothesis that supernovae are the likely origin for galactic cosmic rays in the energy range below the knee in the spectrum (~1 PeV), providing that the propagation of particles is in a fractal interstellar medium (α < 2).
Acknowledgements
The authors wish to acknowledge Dr Roger Clay (the University of Adelaide, Australia) for his essential contribution to our data acquisition and many stimulating discussions.
References
1. Protheroe RJ, Clay RW. Ultra high energy cosmic rays. Publication of the Astronomical Society of Australia. 2004;21:1–22.
2. Axford WI. The modulation of galactic cosmic rays in interplanetary medium. Planet Space Sci. 1965;13:115–130.
3. Berezhko EG, Elshin VK, Ksenfontov LT. [Cosmic ray acceleration in supernova remnants.] Zh Eksp Teor Fiz. 1996;109:3 [IETP (English translation);109:1]. Russian.
4. Elmegreen BG, Kim S, Staveley-Smith L. A fractal analysis of the HI emission from the Large Magellanic Cloud. Astrophys J. 2001;548:749.
5. Lagutin AA, Makrov VV, Tyumentsev AG. Anomalous diffusion of the cosmic rays: Steady state solution. Paper presented at: ICRC 2001. Proceedings of the 27th International Cosmic Ray Conference; 2001 Aug 7–15; Hamburg, Germany. Berlin: Copernicus GmbH; 2001. p. 1889.
6. Lagutin AA, Uchaikin VV. Fractional diffusion of cosmic rays. Paper presented at: ICRC 2001. Proceedings of the 27th International Cosmic Ray Conference; 2001 Aug 7–15; Hamburg, Germany. Berlin: Copernicus GmbH; 2001. p. 1900.
7. Erlykin AD, Lagutin AA, Wolfendale AW. Properties of the interstellar medium and the propagation of cosmic rays in the galaxy. Astropart Phys. 2003;19:351–362.
8. Bouchaud JP, Georges A. Anomalous diffusion in disordered media: Statistical mechanics, models and physical applications. Phys Rep. 1990;195:127.
9. Buesching OC, Jager DE, Potgieter MS, Venter C. A cosmic ray positron anisotropy due to two middle-aged, nearby pulsars. Astrophys J. 2008;678:L39–L42.
10. Erlykin AD, Wolfendale AW. The origin of cosmic rays. Europhysics News. 2001;32:1–10.
11. Erlykin AD, Wolfendale AW. A single source of cosmic rays in the range 1015 _ 1016 eV. J Phys G: Nucl Part Phys. 1997;23:976–989.
N(r, t)
x 106
Alpha = 1.75
9
8
7
6
5
4
3
2
1
0
Alpha = 1.5
Alpha = 1.25
Alpha = 0.75
Alpha = 0.5
2 4 6 8 10 12 14
Radius
FIGURE 1: Intensity of cosmic rays produced by supernovae in the fractal interstellar medium for different values of alpha, α.
2
3
–
2
2
Note: Distance scales are in units of kpc.
FIGURE 2: A cosmic ray trajectory in a 1 µG turbulent magnetic field as might be found in our galaxy. This track is modelled by following a 10 PeV proton through Kolmogorov turbulence (equivalent to a conventional diffusion model). Super-diffusion models have occasional long straighter paths between major changes of direction.
log (increase in residence time)
log(E/100PeV)
FIGURE 3: Relative galactic cosmic ray containment times for conventional and super-diffusion propagation.
F(r) (normalised to one supernova)
Galactic radius (kpc)
FIGURE 4: Assumed radial distribution of supernovae normalised to one supernova in the galaxy.
Average slope
Experimental region of radial gradient of the galactic cosmic rays
Alpha
Note: The experimentally observed range is indicated by the box.
FIGURE 5: Modelling results showing the calculated relationship between the cosmic ray radial gradient (fraction/kpc) in the galaxy and the propagation parameter alpha, α.