2. Let $F_{1}$ and $F_{2}$ be the two foci of the hyperbola $\Gamma: x^{2}-\frac{y^{2}}{3}=1$, $O$ be the origin, and point $P$ be on $\Gamma$ such that $|O P|=2$. Then the area of $\triangle P F_{1} F_{2}$ is $\qquad$ .
2.3.

Given that $P$ is a point on the hyperbola $\Gamma$ and combining this with $|O P|=2$, we can find the absolute value of the y-coordinate of point $P$.