My binary terrestrial planets are roughly the size of earth and they are tidally locked with one another. They are 12,000 miles (19,312 km) apart. That distance is based off of this article, http://phys.org/news/2014-12-binary-terrestrial-planets.html, which suggests a likely distance of only three planet radii.
No axial tilt. The atmosphere is similar to Earth. I know the gravitational pull would cause these planets to bulge toward one another. My question is: how much, if any, water on these planets would remain at the poles?
At 12,000 miles, this first reminded me of another question about two colliding planets (not sure how to link to related questions) and the effects on atmosphere and surface gravity. If we accept that these two bodies would orbit one another relatively stably, http://www.calctool.org/CALC/phys/astronomy/planet_orbit showed me that they would orbit one another once every 111 minutes. I went to http://keisan.casio.com/exec/system/1360312100 and plugged in a few combinations of masses and distances, with the following results:
If our moon were moved in to a distance of 12,000 miles, the tide force would be more than 7,000 times as powerful as it is now.
If the mass of the object at 12,000 miles were increased to that of the Earth, the tide force would be over 600,000 times as powerful as it is now.
Would there be any water left at the poles? It seems as though any liquid water would be piled up into Interstellar-level tides at the near and far sides of the planets. If we can imagine frozen water at the poles remaining through the "kissing" event that established this orbit (I can't imagine that - it sounds deeply apocalyptic) then it might remain frozen at the poles for a very brief time until tidal heating melted it all and it made its way to the party.