The word 'abstractedly' is correct and can be used in written English.
It means to be in a state of being absent-minded or lost in thought. Example: She sat at her desk, staring out the window, her mind wandering abstractedly as she thought about her future plans.
As Arlen started to improvise, according to Lawrence Stewart, Ira "moves to a cat-clawed green armchair nearer the piano, where he sits with Calliope, the Siamese, on his lap and pets her abstractedly as he smokes a cigar.
His right eye opened like a blue crack of sky, and his other hand pushed flat against the metal wall — and then, impossibly, he was standing up, staring abstractedly at Louis, half his face a sputtering blank.
Whenever he faces a vexing story problem, he pulls abstractedly at his forelock, twisting it into a kind of tusk that, if he lowered his head and charged, would deal the problem a mortal blow.
He looked across the room abstractedly.
("Art-vertising?" proposed one male acquaintance, leafing abstractedly through the pages — medieval-scale compendiums of semi-naked women tending to attract crowds).
"Because mathematics is so central to how we think about the world, physicists often are speaking a different language than biologists, asking different questions," said Dr. Bialek, his impish, abstractedly cerebral face and full, free-wheeling beard giving him something of a jolly professor manner.
I like to imagine Bean in a silk dressing gown and a cravat, abstractedly puffing on a Balkan Sobranie in a long cigarette holder, asking the director in the clipped tones of Noel Coward: "How was that for you, heart-face?
She felt nothing and he had his crisis all too quickly, leaving her to achieve her own by rubbing herself abstractedly against him.
They are abstractedly suicidal, stoically damaged, darkly amused; in the case of Isserley, sent across the galaxy to the Scottish highlands to harvest hitchhikers for upmarket otherworldly delis in Faber's first novel, Under the Skin, quite literally alienated.
I will say this, though: at the point where Charlton Heston wanders abstractedly away when the questioning gets too hot, with Moore in angry pursuit, the ageing actor suddenly wears an expression of weary, wounded blankness very similar to Ronald Reagan's when he was being questioned about the Iran-Contra scandal.
An unabashed freeloader ("Someone was always there to take Melinda out to dinner"), equally in her element lunching at the Berkeley Hotel or attending blue movie screenings in Chelsea, her fatal attraction is ascribed to a trick of cupping her chin in her hands and staring abstractedly into the distance to create "an air of elusiveness that men found irresistible".
