RHIC $\sqrt{s_{NN}}=200$ GeV hadron yields and the isospin dependent equation of state

The statistical hadronization model has been successful in extracting information at chemical freeze-out in heavy-ion collisions. At RHIC, with a collision energy of $\sqrt{s_{NN}}=200$ GeV, many different ion species have been used for $A$+$A$ collisions. This allows for a scan across the charge fraction $Y_Q=Z/A$, where $Z$ is the proton number and $A$ is the baryon number. We first make predictions for $A$+$A$ collisions that do not yet have published experimental data on hadron yield ratios (O+O, Ru+Ru, Zr+Zr). We then use both the experimental and predicted yield ratios to perform thermal fits across $Y_Q$, enabling us to extract $s/n_B$ and other thermodynamic information at chemical freeze-out. Using the relation between $s/n_B$ and $Y_Q$, we can calculate a new constraint on the finite temperature equation of state at finite densities. We discuss implications of this constraint and propose future runs that can help connect to the equation of state relevant for neutron star mergers.