  We study the gravitational instability (GI) of small solids in a gas disk as
a mechanism to form planetesimals. Dissipation from gas drag introduces secular
GI, which proceeds even when standard GI criteria for a critical density or
Toomre's $Q$ predict stability. We include the stabilizing effects of turbulent
diffusion, which suppresses small scale GI. The radially wide rings that do
collapse contain up to $\sim 0.1$ Earth masses of solids. Subsequent
fragmentation of the ring (not modeled here) would produce a clan of chemically
homogenous planetesimals. Particle radial drift time scales (and, to a lesser
extent, disk lifetimes and sizes) restrict the viability of secular GI to disks
with weak turbulent diffusion, characterized by $\alpha \lesssim 10^{-4}$. Thus
midplane dead zones are a preferred environment. Large solids with radii
$\gtrsim 10$ cm collapse most rapidly because they partially decouple from the
gas disk. Smaller solids, even below $\sim$ mm-sizes could collapse if
particle-driven turbulence is weakened by either localized pressure maxima or
super-Solar metallicity. Comparison with simulations that include particle
clumping by the streaming instability shows that our linear model underpredicts
rapid, small scale gravitational collapse. Thus the inclusion of more detailed
gas dynamics promotes the formation of planetesimals. We discuss relevant
constraints from Solar System and accretion disk observations.
