Stellar cosmic rays as an important source of ionisation in
  protoplanetary disks: a disk mass dependent process
  We assess the ionising effect of low energy protostellar cosmic rays in
protoplanetary disks around a young solar mass star for a wide range of disk
parameters. We assume a source of low energy cosmic rays located close to the
young star which travel diffusively through the protoplanetary disk. We use
observationally inferred values from nearby star-forming regions for the total
disk mass and the radial density profile. We investigate the influence of
varying the disk mass within the observed scatter for a solar mass star. We
find that for a large range of disk masses and density profiles that
protoplanetary disks are "optically thin" to low energy ($\sim$3 GeV) cosmic
rays. At $R\sim10$au, for all of the disks that we consider
($M_\mathrm{disk}=6.0\times10^{-4} - 2.4\times 10^{-2}M_\odot$), the ionisation
rate due to low energy stellar cosmic rays is larger than that expected from
unmodulated galactic cosmic rays. This is in contrast to our previous results
which assumed a much denser disk which may be appropriate for a more embedded
source. At $R\sim70$au, the ionisation rate due to stellar cosmic rays
dominates in $\sim$50% of the disks. These are the less massive disks with less
steep density profiles. At this radius there is at least an order of magnitude
difference in the ionisation rate between the least and most massive disk that
we consider. Our results indicate, for a wide range of disk masses, that low
energy stellar cosmic rays provide an important source of ionisation at the
disk midplane at large radii ($\sim$70au).
