摘要：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
× 1028 cm2 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.
关键词：cosmic rays;galaxies: individual: M 51;galaxies: ISM;galaxies: magnetic fields;polarization;radio continuum: galaxies
