Both the dog and the cat are in a state of pure bliss. It takes an incredibly long period of time to trust someone with your entire being. Now that the two of them have been through that phase, they can finally relax. This is how friendships are forged, when you overcome that initial phase of insecurity, selfishness and skepticism. Merely looking at their peaceful and content faces is enough to induce deep slumber, so don't stare for too long.
It does help that the dog has a coat of heavy fur which serves as the perfect cushion for the cat. This is her blanket, her mattress and her bed. When the owner gives them a morsel of food, they both eat from it. When the owner takes them out to hike, they both walk outside with each other.