PP100 AKs out-of-position. tough turn spot

[bingledork]

No read on villian. In hindsight I'd describe him as a good player. Help me with my line please.

Party Poker No-Limit Hold'em, $1 BB (6 max, 5 handed) converter

MP ($104.75)
Button ($81.01)
SB ($76.76)
Hero ($97)
UTG ($33.42)

Preflop: Hero is BB with A[img]/images/graemlins/diamond.gif[/img], K[img]/images/graemlins/diamond.gif[/img]. SB posts a blind of $0.50.
<font color="#CC3333">UTG raises to $2</font>, MP calls $2, Button calls $2, <font color="#666666">1 fold</font>, <font color="#CC3333">Hero raises to $10</font>, UTG folds, MP folds, Button calls $8.

Flop: ($24.50) 7[img]/images/graemlins/club.gif[/img], Q[img]/images/graemlins/diamond.gif[/img], Q[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, Button checks.

Turn: ($24.50) T[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets $20</font>, Button bets $71 (All-in). Hero ...

How many outs do I have here?