Assuming the Axiom of Determinacy (abbreviated AD), Martin showed how to derive a rather strong partition on $\omega_1$, namely that $\omega_1\rightarrow(\omega_1)^{\omega_1}$. In "Infinitary Combinatorics and the Axiom of Determinateness", Kleinberg goes through Martin's proof that $\omega_1\rightarrow(\omega_1)^{\omega_1}$ under AD, and from there he goes on to prove much about the large cardinal structure of ZF+AD below $\aleph_\omega$. In fact, he does this directly from the partition relation. In particular, Kleinberg shows that $\aleph_1$ and $\aleph_2$ are measurable, for each $n>2, \aleph_n$ has cofinality $\aleph_2$ and is Jonsson, and that $\aleph_\omega$ is Rowbottom.

We see that the existence of such a partition relation is inconsistent with choice. In fact, the following is a theorem of Erdos and Rado:

For all infinite $\tau$, there is no $\kappa$ such that $\kappa\rightarrow(\tau)^\tau$

However, I am curious about the following:

How much is known about the amount of determinacy one can derive from ZF + DC + $\omega_1\rightarrow(\omega_1)^{\omega_1}$?

In particular, any references would be greatly appreciated.

Edit:

I elaborated on the nature of the question in a comment to an answer. For sake of visibility, I'm pasting the relevant portion here:

To elaborate on the question, it's interesting that one can derive so much about the large cardinal structure of ZF + AD directly from the strong partition relation on $\omega_1$. As far as I know, "$\omega_1$ is measurable" and "$\omega_2$ is measurable" alone allow us a fragment of determinacy. I was curious as to what is known beyond what can be derived from these measures, as $\omega_1\rightarrow(\omega_1)^{\omega_1}$ gives us these measures.