Ice Lines in Circumbinary Protoplanetary Disks

I find the location of the ice line in circumbinary disks heated by steady mass accretion and stellar irradiation, comparing the position with the minimum stable semimajor axis, interior to which planetary orbits are unstable. I show that there is a critical binary separation for which binaries with separations larger than this critical value have ice lines that lie interior to the boundary of stability. The critical separation for an equal-mass binary of 1 M_⊙ stars is ~ 1.04 AU, scaling weakly with mass accretion rate and Rosseland mean opacity of the disk. For a steady mass accretion rate of Ṁ ~ 10^-8 M_⊙ yr^-1 and a Rosseland mean opacity of κ_R ~ 1 cm² g^-1, I show that >~ 80% of all binary systems with component masses M _☆ <~ 2.0 M_⊙ have ice lines interior to the boundary of stability. This suggests that rocky planets should not be common in these systems. Searching for planets around binaries with separations larger than the critical separation with Kepler or microlensing will provide a test of this prediction.