I examine the position of the ice line in circumbinary disks heated by steady mass accretion and stellar irradiation and compare with the critical semi-major axis , interior to which planetary orbits are unstable .
There is a critical binary separation , dependent on the binary parameters and disk properties , for which the ice line lies within the critical semi-major axis for a given binary system .
For an equal mass binary comprised of 1 ~ { } { M _ { \odot } } components , this critical separation is \approx 1.04 ~ { } AU , and scales weakly with mass accretion rate and Rosseland mean opacity ( \propto [ \dot { M } \kappa _ { R } ] ^ { 2 / 9 } ) .
Assuming a steady mass accretion rate of \dot { M } \sim 10 ^ { -8 } ~ { } { M _ { \odot } ~ { } yr ^ { -1 } } and a Rosseland mean opacity of \kappa _ { R } \sim 1 ~ { } { cm ^ { 2 } ~ { } g ^ { -1 } } , I show that \gtrsim 80 \% of all binary systems with total masses M _ { tot } \lesssim 4.0 ~ { } { M _ { \odot } } have ice lines that lie interior to the critical semi-major axis .
This suggests that rocky planets should not form in these systems , a prediction which can be tested by looking for planets around binaries with separations larger than the critical separation with Kepler ( difficult ) and with microlensing .