Close-in super-Earths having radii 1–4 R _ { \oplus } may possess hydrogen atmospheres comprising a few percent by mass of their rocky cores .
We determine the conditions under which such atmospheres can be accreted by cores from their parent circumstellar disks .
Accretion from the nebula is problematic because it is too efficient : we find that 10 M _ { \oplus } cores embedded in solar metallicity disks tend to undergo runaway gas accretion and explode into Jupiters , irrespective of orbital location .
The threat of runaway is especially dire at \sim 0.1 AU , where solids may coagulate on timescales orders of magnitude shorter than gas clearing times ; thus nascent atmospheres on close-in orbits are unlikely to be supported against collapse by planetesimal accretion .
The time to runaway accretion is well approximated by the cooling time of the atmosphere ’ s innermost convective zone , whose extent is controlled by where H _ { 2 } dissociates .
Insofar as the temperatures characterizing H _ { 2 } dissociation are universal , timescales for core instability tend not to vary with orbital distance — and to be alarmingly short for 10 M _ { \oplus } cores .
Nevertheless , in the thicket of parameter space , we identify two scenarios , not mutually exclusive , that can reproduce the preponderance of percent-by-mass atmospheres for super-Earths at \sim 0.1 AU , while still ensuring the formation of Jupiters at \gtrsim 1 AU .
Scenario ( a ) : planets form in disks with dust-to-gas ratios that range from \sim 20 \times solar at 0.1 AU to \sim 2 \times solar at 5 AU .
Scenario ( b ) : the final assembly of super-Earth cores from mergers of proto-cores — a process that completes quickly at \sim 0.1 AU once begun — is delayed by gas dynamical friction until just before disk gas dissipates completely .
Both scenarios predict that the occurrence rate for super-Earths vs. orbital distance , and the corresponding rate for Jupiters , should trend in opposite directions , as the former population is transformed into the latter : as gas giants become more frequent from \sim 1 to 10 AU , super-Earths should become more rare .