  Analysis of a database of solar coronal mass ejections (CMEs) and associated
flares over the period 1996-2007 finds well-behaved power law relationships
between the 1-8 AA flare X-ray fluence and CME mass and kinetic energy. We
extrapolate these relationships to lower and higher flare energies to estimate
the mass and energy loss due to CMEs from stellar coronae, assuming that the
observed X-ray emission of the latter is dominated by flares with a frequency
as a function of energy dn/dE=kE^-alpha. For solar-like stars at saturated
levels of X-ray activity, the implied losses depend fairly weakly on the
assumed value of alpha and are very large: M_dot ~ 5x10^-10 M_sun/yr and E_dot
~ 0.1L_sun. In order to avoid such large energy requirements, either the
relationships between CME mass and speed and flare energy must flatten for
X-ray fluence >~ 10^31 erg, or the flare-CME association must drop
significantly below 1 for more energetic events. If active coronae are
dominated by flares, then the total coronal energy budget is likely to be up to
an order of magnitude larger than the canonical 10^-3 L_bol X-ray saturation
threshold. This raises the question of what is the maximum energy a magnetic
dynamo can extract from a star? For an energy budget of 1% of L_bol, the CME
mass loss rate is about 5x10^-11 M_sun/yr.
