Cosmic Ray Acceleration Inside Molecular Clouds

1
Cosmic Ray Acceleration Inside Molecular Clouds

• Magnetic field fluctuations in molecular clouds
• Charged particle interaction with these
  fluctuations
• Spectra of relativistic electrons and protons on
  the clouds
• Fluxes of radio and gamma-ray emission from the
  clouds

2
Parameters of Molecular Clouds

• Total mass of the gas up to
• Gas density
• Temperature
• Size
• Ionization degree
• Energy of turbulent motions

3
Neutral Gas Turbulence

• Von Hoerner (1951) spectrum of turbulent
  velocities in Orion Nebula
• Spectra of turbulent motions in molecular clouds
  
  Larson (1981) and Myers (1983) CO and NH3
  lines (see also Dame et al.(1986), Solomon et
  al.(1987)
• Kolmogorov-type spectrum

4
Kolmogorov Spectrum

• Spectrum in the inertial range L0LLmin is
  independent of forcing and dissipative
  processes.
• The steady state energy cascade in this range is
  constant that gives
• MHD turbulence Kolmogorov-type spectrum

5
Magnetic Fluctuations in Quasi-Neutral Gas
(Dogiel et al. 1987)
6
Spectrum of Magnetic Fluctuations
For Fourier transformation
we assume simple correlation properties of
neutral turbulence
and for the correlator of magnetic fluctuations
we have a nonlinear equation for Q(k,t)
where
7
Stationary State
8
Particle Propagation and Acceleration
From the drift equations of particles propagation
and the Boltzmann equation we can derive an
equation for average distribution function of
particles for magnetized and
nonmagnetized particles
where
where
9
Particle Propagation and Acceleration
From the drift equations of particles propagation
and the Boltzmann equation we can derive an
equation for average distribution function of
particles for magnetized and
nonmagnetized particles
where
where
10
Particle Production in Molecular Clouds(Dogiel
and Sharov, 1990)
For parameters of the Galactic molecular clouds

Particle Sources

• Cosmic rays penetrating from outside
• Particles sources near or inside molecular clouds
• Secondary particles produced inside the clouds
• Acceleration from background pool

11
Density of CR Protons in the Clouds
12
Secondary and Primary Electrons in the Clouds
13
Gamma-Ray Emissivity of the Clouds
14
Relative Gamma-Ray Emissivity
15
Radio Emission from Molecular Clouds
16
CR Positrons Ejected by the Clouds
Dogiel Sharov, 1990
Coutu et al., 1999, DuVernois et al. 2001
17
Conclusion

• Turbulence of neutral gas excites fluctuations of
  electromagnetic fields inside molecular clouds.
• Chaotic electromagnetic fields accelerate charged
  particles inside molecular clouds up to 10 GeV.
• Characteristic time of acceleration is about
  10 11s that is less than the time of spatial
  diffusion from a cloud.
• This excess of relativistic electrons and protons
  gives rise to a relatively high gamma-ray
  emissivity from the clouds.
• The gamma-ray and the radio fluxes produced by
  accelerated protons and electrons are strongly
  depended on cloud size
• In principle some of giant molecular clouds could
  be unidentified gamma-ray sources due to
  acceleration excited by turbulence of neutral gas