tokens: of the two mini-BAL outflows in our sample. The Si iv trough is quite narrow and the S iv trough is unblended with other absorptions. In this case, the excellent template fit of the S iv trough is evident by the value f ( χ 2 ) = 0.4%. The S iv * absorption trough is heavily contaminated by a strong, likely Ly α , absorption trough from an intervening system. SDSS J0941+1331 has a multicomponent Si iv absorption trough. Following the procedure outlined in Section 4.2 , we use only the marked velocity interval as the template (see Figure 2 ). The Si iv template fits the S iv and S iv * absorption troughs well with f ( χ 2 ) = 6.8% in our survey. In order to account for possible systematic differences due to the Ly α forest, we compare the derived N ion from template fittings to the pure AOD extractions that includes the Ly α absorption features. In Figure 3 , we show the comparison of the observed S iv 1062.66 Å and S iv * 1072.97 Å absorption troughs. The AOD column densities integrated within the vertical dotted lines are N(S iv ) AOD = 1620 and N(S iv *) AOD = 740 (hereafter, all N ion are in units of 10 12 cm −2 ), while the template fitting results integrated over the same velocity range are N(S iv ) tmpl = 1450 and N(S iv *) tmpl = 540. Note that the AOD method overestimates the N ion because it includes the contributions from Ly α forest absorptions. These values yield a density sensitive ratio, N(S iv *)/N(S iv ), of 0.46 and 0.37 for the AOD method and the template fitting method, respectively. Using the same methodology described in Section 4.2 , the AOD method leads to a decrease of R by 25%. This difference is similar to our errors for the determined R value in Table 4 . Therefore, possible Ly α forest contaminations affect our derived R only moderately. Figure 3. Comparison of the normalized flux of S iv 1062.66 Å(blue) and S iv * 1072.97 Å(red) absorption troughs for SDSS J0941+1331 in velocity space. The vertical dotted lines are the range of Si iv template corresponding to Figure 2 . For SDSS J1135+1615, the Si iv absorption troughs are saturated and rather flat. We choose the two strongest local maxima to construct the Si iv template (see Figure 2 ). Fitting the S iv and S iv * absorption troughs with this template shows that the S iv * absorption trough is deeper than that of S iv . Including the many narrow Ly α troughs in the N ion extractions increase the N(S iv ) and N(S iv *) by 16% and 14%, respectively, and only marginally affects the derived R (6%). 5. Photoionization Analysis In order to derive the physical conditions of the outflow, we run the spectral synthesis code Cloudy (version c17.00, Ferland et al. 2017 ) to generate a grid of photoionization simulations. Cloudy self-consistently solves the photoionization and thermal equations necessary to model the physical conditions in the gas. The absorbers are modeled as plane-parallel, thin slabs of constant density gas with solar metallicity. They are irradiated by
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