Constraining the Low-Energy Cosmic Ray Spectrum

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Constraining the Low-Energy Cosmic Ray Spectrum

• Nick Indriolo, Brian D. Fields, Benjamin J. McCall

University of Illinois at Urbana-Champaign
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Cosmic Ray Basics

• Charged particles (e-, e, p, a, etc.)
  with high energy (103-1019 eV)
• Galactic cosmic rays are primarily accelerated in
  supernovae remnants

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Background

• Cosmic rays have several impacts on the
  interstellar medium, all of which produce some
  observables
• Ionization molecules
• CR H2 ? H2 e- CR
• H2 H2 ? H3 H
• Spallation light element isotopes
• p, a C, N, O ? 6Li, 7Li, 9Be, 10B, 11B
• Nuclear excitation gamma rays
• p, a C, O ? C, O ? ? (4.4, 6.13 MeV)

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Motivations

• Many astrochemical processes depend on ionization
• Cosmic rays are the primary source of ionization
  in cold interstellar clouds
• Low-energy cosmic rays (2-10 MeV) are the most
  efficient at ionization
• The cosmic ray spectrum below 1 GeV cannot be
  directly measured at Earth

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Example Cosmic Ray Spectra
1 - Nath, B. B., Biermann, P. L. 1994, MNRAS,
267, 447 2 - Hayakawa,
S., Nishimura, S., Takayanagi, T. 1961, PASJ,
13, 184 3 - Valle, G., Ferrini, F., Galli,
D., Shore, S. N. 2002, ApJ, 566, 252
4 - Kneller, J. P., Phillips, J. R., Walker, T.
P. 2003, ApJ, 589, 217 5 - Spitzer,
L., Jr., Tomasko, M. G. 1968, ApJ, 152, 971
6 - this study
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Motivations

• Recent results from H3 give an ionization rate
  of ?2410-16 s-1
• Given a cosmic ray spectrum and cross section,
  the ionization rate can be calculated
  theoretically

Indriolo, N., Geballe, T. R., Oka, T., McCall,
B. J. 2007, ApJ, 671, 1736
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Cross Sections
Bethe, H. 1933, Hdb. d Phys. (Berlin J.
Springer), 24, Pt. 1, 491 Read, S. M., Viola,
V. E. 1984, Atomic Data Nucl. Data, 31, 359
Meneguzzi, M. Reeves, H. 1975, AA, 40, 91
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Leaky Box Model
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Leaky Box Model

• Broken power law in momentum
• Produces an ionization rate of 110-17 s-1, much
  lower than the value inferred from H3
• Try a spectrum with more flux at low energies by
  changing power law index below 200 MeV

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Matching Observations

• Float the spectral index to match inferred ?2
• Choose a low energy cutoff (2 MeV)
• We find a relationship of p-2.0 is required to
  produce an ionization rate of 3.610-16 s-1
• This gives 8.610-17 s-1 assuming a 10 MeV cutoff
  (dense cloud)

Cravens, T. E., Dalgarno, A. 1978, ApJ, 219, 750
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Effects on Light Elements
Lemoine, M., Vangioni-Flam, E., Cassé, M.
1998, ApJ, 499, 735
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Effects on Gamma Rays

• Interstellar gamma ray lines at 4.4 MeV 6.13
  MeV have not been observed
• We predict a diffuse Galactic flux of 610-8
  cm-2 s-1 deg-2 for both lines
• This is below the detection limit of current
  gamma ray telescopes such as Integral

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Energy Requirements

• We can also calculate the rate at which all of
  the particles in our spectrum lose energy
• The result is 0.151051 ergs century-1
• The standard supernova energy is 1051 ergs, and
  the standard supernova rate is 3 per century in
  the Galaxy, so this energy requirement is well
  within the Galactic budget

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Conclusions

• Leaky box propagated spectrum is unable to
  account for ionization rate
• Possible to generate an ionization rate of about
  410-16 s-1 given the correct power law index
  (p-2) at low energies
• This spectrum is in rough agreement with light
  element abundances, and is not inconsistent with
  gamma ray observations
• Required input energy is available from supernovae

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Future Work

• Use more advanced cosmic ray models including
  re-acceleration effects
• Consider variation of the cosmic ray spectrum in
  space and time
• Continue observations to put better constraints
  on the ionization rate in various environments

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Acknowledgments