I often see Vega in the Heston model specified as: \begin{align*} \nu & = \frac{\partial C}{\partial v} = \frac{\partial C}{\partial v_0} 2 \sqrt{v_0} \end{align*} where $v = \sqrt{v_0}$. Why are we setting $v = \sqrt{v_0}$? Where is the square-root and "2" coming from?

Thank you!

I often see Vega in the Heston model specified as: \begin{align*} \nu & = \frac{\partial C}{\partial v} = \frac{\partial C}{\partial v_0} 2 \sqrt{v_0} \end{align*} where $v = \sqrt{v_0}$. 

Why are we setting $v = \sqrt{v_0}$? 

Where is the square-root and "$2$" coming from?