Conjecture on the maximum dichromatic number of oriented triangle-free graphs

For each positive integer $n$, let $\vec t(n)$ be the maximum dichromatic number of an oriented triangle-free graph of order $n$. Maximum dichromatic number conjecture.

$$\vec t(n)=\Theta\!\left(\sqrt{\frac{n}{\log n}}\right).$$

This conjecture is implied by the conjectured asymptotic order of the minimum acyclic number $\vec a(n)$ and would determine the maximum dichromatic number up to constant factors.