Giant planet formation by core accretion requires a core that is sufficiently massive to trigger runaway gas accretion in less that the typical lifetime of protoplanetary disks .
We explore how the minimum required core mass , M _ { crit } , depends on a non-ideal equation of state and on opacity changes due to grain growth , across a range of stellocentric distances from 5-100 AU .
This minimum M _ { crit } applies when planetesimal accretion does not substantially heat the atmosphere .
Compared to an ideal gas polytrope , the inclusion of molecular hydrogen ( H _ { 2 } ) dissociation and variable occupation of H _ { 2 } rotational states increases M _ { crit } .
Specifically , M _ { crit } increases by a factor of \sim 2 if the H _ { 2 } spin isomers , ortho- and parahydrogen , are in thermal equilibrium , and by a factor of \sim 2 - 4 if the ortho-to-para ratio is fixed at 3:1 .
Lower opacities due to grain growth reduce M _ { crit } .
For a standard disk model around a Solar mass star , we calculate M _ { crit } \sim 8 M _ { \oplus } at 5 AU , decreasing to \sim 5 M _ { \oplus } at 100 AU , for a realistic EOS with an equilibrium ortho-to-para ratio and for grain growth to cm-sizes .
If grain coagulation is taken into account , M _ { crit } may further reduce by up to one order of magnitude .
These results for the minimum critical core mass are useful for the interpretation of surveys that find exoplanets at a range of orbital distances .