= &  \dot\rho_0 \left[(1 + z)^{{a}{\eta} } + \left(\frac{1 + z}{B}\right)^{{b}{\eta}} + \left(\frac{1 + z}{C}\right)^{{c}{\eta} } \, \right]^{1/\eta}
\label{fit}\end{aligned}$$ where $a = 3.4$, $b = -0.3$, and $c = -2$, with breaks at $z_1= 1$ and $z_2 = 4$ corresponding to $B = (1 + z_1)^{1-a/b} \simeq 5100$ and $C =(1 + z_1)^{(b-a)/c} (1 + z_2)^{1-b/c}\simeq 14$, which reflect the updated high-$z$ data from @Kistler09, and we use $\eta \simeq -10$ to smooth the transitions. The normalization is $\dot{\rho}_{0} = 0.014 \,M_\odot$ yr$^{-1}$ Mpc$^{-3}$, which we have scaled down by a factor of 0.7 from the Salpeter IMF normalization of @Hopkins:2006bw to be in better agreement with the galactic mass estimates in the previous Sections. In Eq. (\[eq:rate\]), we set $t_0\sim 0.4$ Gyr corresponding to $z\approx 10$.[^1]

Since we must consider the shortest possible delay times in constructing the cosmic rate from the SFH, we again assume a power law DTD with a cutoff at $t_c=50$ Myr. We note that the results of @Umeda:1998ij (see also @Siess2007 [@Meng:2007ni]) suggest a maximum CO WD mass of $\sim 1.1\,M_\odot$ that is nearly independent of metallicity. Since the effect of decreasing the metallicity is similar to increasing the stellar mass, we take this 