The Modified Weighted Slab Technique: Models and Results

Context. Cosmic ray electrons (CREs) are a crucial part of the interstellar medium and are observed via synchrotron emission. While much modelling has been carried out on the CRE distribution and propagation of the Milky Way, little has been done on normal external star-forming galaxies. Recent spectral data from a new generation of radio telescopes enable us to find more robust estimations of the CRE propagation. Aims. To model the synchrotron spectral index of M 51 using the diffusion energy-loss equation and to compare the model results with the observed spectral index determined from recent low-frequency observations with LOFAR. Methods. We solve the time-dependent diffusion energy-loss equation for CREs in M 51. This is the first time that this model for CRE propagation has been solved for a realistic distribution of CRE sources, which we derive from the observed star formation rate, in an external galaxy. The radial variation of the synchrotron spectral index and scale-length produced by the model are compared to recent LOFAR and older VLA observational data and also to new observations of M 51 at 325 MHz obtained with the GMRT. Results. We find that propagation of CREs by diffusion alone is sufficient to reproduce the observed spectral index distribution in M 51. An isotropic diffusion coefficient with a value of 6.6 ± 0.2 × 10 28 cm 2 s −1 is found to fit best and is similar to what is seen in the Milky Way. We estimate an escape time of 11 Myr from the central galaxy to 88 Myr in the extended disk. It is found that an energy dependence of the diffusion coefficient is not important for CRE energies in the range 0.01 GeV-3 GeV. We are able to reproduce the dependence of the observed synchrotron scale-lengths on frequency, with l ∝ ν −1/4 in the outer disk and l ∝ ν −1/8 in the inner disk.

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“…secondary-to-primary ratios like boron to carbon) within the solar neighbourhood (Jones et al 2001;Moskalenko et al 2002).…”

Section: Introductionmentioning

confidence: 99%

Modelling the cosmic ray electron propagation in M 51

Mulcahy

Fletcher

Beck

et al. 2016

A&A

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“…It is assumed that supernova remnants are the main cosmicray sources in the Galaxy (Berezinskii et al 1984;Erlykin & Wolfendale 2000;Ginzburg & Syrovatskii 1963;Jonis et al 2001;Strong & Moskalenko 1998;Tsao et al 2001). The cosmic rays are accelerated in pulsar magnetospheres and supernova shocks.…”

Section: Energy Losses Of Cosmic Rays In the Galaxymentioning

confidence: 99%

“…Those studies took into account only the nuclear interactions of the particles with the homogeneous interstellar gas. Later, more realistic models were proposed (Erlykin & Wolfendale 2001;Jonis et al 2001;Houston et al 1983;Li et al 1983;Strong & Moskalenko 1998;Tsao et al 2001), which considered cosmic ray diffusion in the heterogeneous Galactic magnetic fields and in the inhomogeneous neutral and ionized hydrogen in the Galaxy. Honda (1987) considered cosmic-ray propagation in Galactic magnetic fields (assumed to consist of the average field strength ∼3 µG, extending to ∼1 kpc above and below the Galactic plane, with irregularities in the magnetic field strength of ∼1.5 µG).…”

Section: Introductionmentioning

confidence: 99%

Formation of the cosmic-ray spectrum due to its propagation in the Galaxy

Kryvdyk

2003

A&A

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Abstract.A model of cosmic ray propagation is proposed to explain the knee of the cosmic ray energy spectrum in the energy range E ∼ 10 14 −10 17 eV. The numerous stellar winds (SW), ionized hydrogen regions (H-II) and supernova remnants (SNR) in the Galaxy are taken into account in this model. The gas density and the magnetic field in these regions are different from the interstellar gas density and the interstellar magnetic field. Therefore they act as scattering centres and magnetic traps for cosmic rays. It is shown that these regions influence cosmic ray propagation in the Galaxy. Our results show that the collision time between cosmic rays and the SNR, SW, and H-II regions is much less than the cosmic ray lifetime in standard models (Berezinskii et al. 1984;Ginzburg & Syrovatskii 1963), in which only the nuclear interaction of the particles with interstellar gas is taken into account. Cosmic ray energies, and thus the cosmic ray spectrum, change due to interactions with these regions. Cosmic ray energy losses in these regions due to adiabatic cooling are comparable to the losses due to nuclear interaction with interstellar gas. It is therefore necessary to take these into account in galactic cosmic ray propagation models.

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“…x ∼ rct Ӎ 12 cr CRs in the Galaxy, which is determined from the CR chemical composition near Earth (Ferrando et al 1991;Jones et al 2001). Below we will show that this expression is also valid for strongly nonuniform cases.…”

Section: ϫ2mentioning

confidence: 99%

The Cosmic-Ray Luminosity of the Galaxy

Dogiel¹,

Schönfelder²,

Strong³

2002

The Astrophysical Journal

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The total cosmic-ray luminosity of the Galaxy is one of the main parameters that strongly constrain possible models of the origin of cosmic rays. Recently, Dar & De Rújula suggested a luminosity that is 2 orders of magnitude larger than the standard estimate. If this estimate were correct, it would completely change our conception of the origin of cosmic rays. From a number of different arguments, however, we show that the estimate of Dar & Rújula is too high. Subject heading: cosmic rays One of the central questions concerning the astrophysics of cosmic rays (CRs) is their origin. It took almost a hundred years after the discovery of CRs by V. Hess to prove finally ("Ginzburg's test"; see Ginzburg 1972) that the bulk of CRs are emitted by Galactic sources. Measurements with the EGRET telescope (Sreekumar et al. 1993) show that the density of CRs inside the Small Magellanic Cloud is several times less than in our Galaxy, which is incompatible with the extragalactic origin of CRs. Of course, there can be no question of a complete picture if the issue of the nature and relative importance of different classes of sources is not clarified. This question was discussed in detail by Berezinskii et al. (1990). There it was shown that supernovae, based on their energy output of the order of 10 41 -10 42 ergs s , Their estimate of the total CR luminosity in the Galaxy is almost 2 orders of magnitude larger than the standard estimate. If this were correct, then it would rule out the supernova origin of CRs. This would be a dramatic result since no evident sources with this luminosity have been found in the Galaxy. We try to repeat the estimates presented in DR and show that their value is apparently mistaken.At the beginning of their paper, DR refer to the monograph of Berezinskii et al. (1990) and remark that the luminosity estimate of ergs s presented there was ob-40 Ϫ1

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The Modified Weighted Slab Technique: Models and Results

Cited by 184 publications

References 28 publications

Modelling the cosmic ray electron propagation in M 51

Modelling the cosmic ray electron propagation in M 51

Formation of the cosmic-ray spectrum due to its propagation in the Galaxy

The Cosmic-Ray Luminosity of the Galaxy

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