  Analysis of SOHO/LASCO C3 data reveals a discontinuity, interpreted as a
shock wave, in plasma density radial profiles in a restricted region ahead of
each of ten selected coronal mass ejections (CME) along their travel
directions. In various events, shock wave velocity $V\approx$ 800-2500 km
s$^{-1}$. Comparing the dependence of Alfv\'{e}n Mach number $M_A$ on shock
wave strength $\rho_2/\rho_1$, measured at $R > 10R_\odot$ from the center of
the Sun, to ideal MHD calculations suggests that the effective adiabatic index
$\gamma$, characterizing the processes inside the shock front, is largely
between 2 and 5/3. This corresponds to the effective number of degrees of
freedom of motion 2 to 3. A similar dependence, $M_A(\rho_2/\rho_1)$, was
derived for the Earth's bow shock and interplanetary collisionless shock waves.
All this supports the assumption that the discontinuities in front of CMEs are
collisionless shock waves.
