2. The left and right foci of a hyperbola are $F_{1}, F_{2}$, respectively. A line passing through $F_{2}$ intersects the right branch of the hyperbola at points $A, B$. If $\triangle F_{1} A B$ is an equilateral triangle, then the eccentricity of the hyperbola is $\qquad$.
2. $\sqrt{3}$.

Let the equation of the hyperbola be $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1(a>0, b>0)$, with the semi-focal distance being $c$, then $c^{2}=a^{2}+b^{2}$. From
$$
\left|F_{1} A\right|-\left|F_{2} A\right|=\left|F_{1} B\right|-\left|F_{2} B\right|=2 a, \quad\left|F_{1} A\right|=\left|F_{2} A\right|+\left|F_{2} B\right|=\left|F_{1} B\right|,
$$

we solve to get $\left|F_{2} A\right|=\left|F_{2} B\right|=2 a$. This indicates that $A B \perp x$ axis, and it is easy to see that at this time $\left|F_{2} A\right|=\left|F_{2} B\right|=\frac{b^{2}}{a}$, combining with $c^{2}=a^{2}+b^{2}$, we solve to get the eccentricity of the hyperbola $e=\frac{c}{a}=\sqrt{3}$.