The acceleration of cosmic rays in shock fronts - I
Open accessAbstract
It is shown that charged particles can be accelerated to high energies in astrophysical shock fronts. Fast particles are prevented from streaming away upstream of a shock front by scattering off Alfvén waves which they themselves generate. This scattering confines the particles to the region around the shock and results in first-order Fermi acceleration due to the particles crossing the shock many times. The consequent energy spectrum is a power law with an index close to that observed for galactic cosmic rays. The discussion relates to particles which are already relativistic, and their initial acceleration from thermal energies is not considered.
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A strong shock with Mach ≳5 is required to produce cosmic rays with a spectral index of p≈2.1 following diffusive shock acceleration.
“One, however, requires a strong shock with Mach, M ≳ 5 to produce CR with a spectral index of p ≈ 2 . 1, following a diffusive shock acceleration mechanism where ( p ≈ ( χ + 2) / ( χ -1), with χ as the density compression ratio; Bell 1978; Drury 1983; Blandford & Eichler 1987; Fujita et al. 2013, 2014).”
From The Fermi/eROSITA bubbles: a look into the nuclear outflow from the Milky Way (2024) · cites this paper as Bell 1978
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Crocker, R. M., Bicknell, G. V., Taylor, A. M., & Carretti, E. (2015) · The Astrophysical Journal · doi:10.1088/0004-637x/808/2/107 · Cited by 120 · see citing works
THE FERMI BUBBLES AS A SCALED-UP VERSION OF SUPERNOVA REMNANTS
Fujita, Y., Ohira, Y., & Yamazaki, R. (2013) · The Astrophysical Journal · doi:10.1088/2041-8205/775/1/l20 · Cited by 47 · see citing works
“…the wave growth is given by ∂ψ ∂t = 4π 3 vAp 4v UM |∇f |, (8) where ψ(r, p, t) is the energy density of Alfvén waves per unit logarithmic bandwidth (which are resonant with particles of momentum p) relative to the ambient magnetic energy density UM (Bell 1978), and v is the particle velocity.”
MethodThe Fermi/eROSITA bubbles: a look into the nuclear outflow from the Milky Way
Sarkar, K. C. (2024) · The Astronomy and Astrophysics Review · doi:10.1007/s00159-024-00152-1 · Cited by 34 · see citing works
“1, following a di ff usive shock acceleration mechanism where ( p ≈ ( χ + 2) / ( χ − 1), with χ as the density compression ratio; Bell 1978; Drury 1983; Blandford & Eich-ler 1987; Fujita et al. 2013, 2014).”
BackgroundMethod
- Authors
- Bell, A. R.
- Affiliations
- University of Cambridge (GB)
- Corresponding author
- Bell, A. R.
- Venue
- Monthly Notices of the Royal Astronomical Society
- Publisher
- Oxford University Press (OUP)
- Published
- 1978-02-01
- Volume
- 182
- Issue
- 2
- Pages
- 147-156
- ISSN
- 0035-8711 (ISSN-L)
- 1365-2966
- OpenAlex
- W1989756559
- Cited by
- 2,679
- References
- 0
- Citations by year
- 2026: 78 · 2025: 125 · 2024: 113 · 2023: 115 · 2022: 116 · 2021: 143 · 2020: 122 · 2019: 163 · 2018: 113 · 2017: 113 · 2016: 106 · 2015: 85 · 2014: 98 · 2013: 119 · 2012: 104
- FWCI
- 6.07
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Monthly Notices of the Royal Astronomical Society (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Astrophysics and Cosmic Phenomena
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Solar and Space Plasma Dynamics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Gamma-ray bursts and supernovae
- Keywords
- cosmic ray acceleration, astrophysical shocks, diffusive shock acceleration, Alfvén waves, charged particle scattering, relativistic particles, power-law energy spectrum, galactic cosmic rays, shock front
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