  We examine the possibility that icy super-Earth mass planets, formed over
long time scales (0.1--1~Gyr) at large distances ($\sim$ 200--1000~AU) from
their host stars, will develop massive H-rich atmospheres. Within the interior
of these planets, high pressure converts CH$_4$ into ethane, butane, or diamond
and releases H$_2$. Using simplified models which capture the basic physics of
the internal structure, we show that the physical properties of the atmosphere
depend on the outflux of H$_2$ from the mantle. When this outflux is $\lesssim
10^{10}$ [molec cm$^{-2}$ s$^{-1}$], the outgassed atmosphere has base pressure
$\lesssim$ 1 bar. Larger outflows result in a substantial atmosphere where the
base pressure may approach $10^3 - 10^4$ bar. For any pressure, the mean
density of these planets, 2.4--3 [g cm$^{-3}$], is much larger than the mean
density of Uranus and Neptune, 1.3--1.6 [g cm$^{-3}$]. Thus, observations can
distinguish between a Planet Nine with a primordial H/He-rich atmosphere
accreted from the protosolar nebula and one with an atmosphere outgassed from
the core.
