\chapter{Properties of Planetary Nebula Central Stars and Their Progenitors}
\addcontentsline{lof}{chapter}{\thechapter \hspace{1.5mm} Properties of Planetary Nebula Central Stars and Their Progenitors}
\addcontentsline{lot}{chapter}{\thechapter \hspace{1.5mm} Properties of Planetary Nebula Central Stars and Their Progenitors}
%\begingroup
%\fontsize{14}{16.8}\selectfont
%\textbf{Chapter 4}\\
%\endgroup
%\begingroup
%\fontsize{13}{15.6}\selectfont
%\\
%\textbf{Discussion}\\
%\\
%\endgroup
In order to constrain the central star's temperature and luminosity of each planetary nebula, Cloudy version 13.03~(\citet{fer13}) was used to generate photoionization models of each PN. For a given set of input parameters, Cloudy simultaneously solves energy and ionization equilibrium equations at specific radial points in the PN model. Three iterations for each model were carried  out to ensure that each model had converged to a solution. The assumed spectral energy distribution (SED) of the central star was taken to be either the Rauch H-Ni (example shown in Figure~\ref{rauchHNi}) or the Rauch pg1159 (example shown in Figure~\ref{rauchpg1159}) atmospheric simulations~(\citet{rau03}), depending on the known atmospheric properties of the central stars. Rauch H-Ni includes line blanketing for lines from hydrogen to nickel, whereas for Rauch pg1159, the line blanketing effects only include lines of helium, carbon, nitrogen, and oxygen. NGC 5315 was the only PN for which the Rauch pg1159 SED was employed, since its central star was observed to be hydrogen deficient by~\citet{men82}. Assumptions for each model were a spherically symmetric and static geometry without shock heating of the gas. The stellar parameters for the initial model were chosen to be the average of the most reliable values found in the literature (\citet{sha85}, \citet{sha89}, \citet{zha93}, \citet{cor03}, and \citet{fre08}) but were allowed to vary in subsequent models. Fixed angular radii for the models were measured from archival HST WFPC2 images and the values are as follows; IC 2165 r=2.67$''$, IC 3568 r=3.54$''$, NGC 2440 r=6.51$''$, NGC 3242 r=9.30$''$, NGC 5315 r=1.50$''$, NGC 5882 r=3.21$''$, and NGC 7662 r=10.71$''$. These fixed angular radii ensured that a change in the outer radius of each model resulted in a change in the assumed distance to the nebula. Lastly, the nebular properties initially were set to the values discussed in \S2 (densities in Table~\ref{emisstab1} and total abundances in Table~\ref{tab:abun1}) but also left variable.
\begin{landscape}
\begin{figure}
\caption{The Rauch H-Ni SED used in the case of NGC 3242. The r$_o$ refers to the inner radius of the nebula from the model.\newline}
\includegraphics[scale=0.44]{rauchH-Ni.png}
\label{rauchHNi}
\end{figure}
\end{landscape}
\begin{landscape}
\begin{figure}
\caption{The Rauch pg1159 SED used in the case of NGC 5315. The r$_o$ refers to the inner radius of the nebula from the model.\newline}
\includegraphics[scale=0.44]{rauchpg1159.png}
\label{rauchpg1159}
\end{figure}
\end{landscape}
The calculations for converting the internal model gas properties into model emission line strengths were made with the self-written C++ program PANIC (PlAnetary Nebula Intensity Calculator). To summarize the process, volume emissivity values as a function of radius from each Cloudy model are read into PANIC, which then calculates the model line intensities based on the geometry and other properties of the modeled gas. Specifically, PANIC calculates the volume of gas in each region's line-of-sight for each radial distance from the model, multiplies this volume by the appropriate emissivity, and adds up each contribution to determine the maximum emission strength for a particular line. Finally, this maximum emission strength is scaled by the filling factor (the ratio of the volume of gas to the total, physical volume) to get the total emission line strength. 

To weight the emission lines equally, only one\footnotemark~emission line per ion from the observations was used in the comparison to the models and only for lines having a S/N $>$ 3. A total rms value was calculated for each model from the expression $\sqrt{\frac{1}{N}\sum_{1}^{N}{(1-\frac{model}{observed})^2}}$, where \textit{N} is the total number of lines and diagnostics, \textit{model} is the value of each line or diagnostic predicted by the model, and \textit{observed} is the observed value. A similar rms value for the observations was calculated using the line's uncertainty by replacing $1-\frac{model}{observed}$ in the above expression with $\frac{uncertainty}{observed}$. This observed rms value was later used in the calculation of the uncertainties in the parameters from each model. The model that yielded the lowest rms value was chosen to be the best model. 
\footnotetext[1]{Additional lines from some ions were used in diagnostic line ratios only.}

Degeneracies between models with similar rms values were broken by employing five common diagnostics. The first, $\frac{[O\ III]\ \lambda5007+\lambda4959+[O\ II]\ \lambda3727}{H\beta}$, is used to gauge the metallicity of the nebula since oxygen is often the most abundant metal. The next two, $\frac{[O\ II]\ \lambda3727}{[O\ III]\ \lambda5007}$ and $\frac{He\ II\ \lambda4686}{He\ I\ \lambda5876}$, are sensitive to the ionization state of the nebula. The temperature of the nebular gas is probed with the fourth diagnostic, $[O\ III]\ \frac{\lambda4363}{\lambda5007}$. The final diagnostic, $\frac{C\ III]\ \lambda1909}{C\ [III]\ \lambda1907}$, is used to determine the density of the nebula.

To test the validity of the described rms method for assessing the best model, the method of~\citet{mor09} was used for NGC 3242. In their method, a quality factor, \textit{Q}, is calculated by the expression $\frac{log(\frac{model}{observed})}{log(1+RelativeError)}$ where \textit{RelativeError} is $\frac{uncertainty}{observed}$. Minimizing this \textit{Q} value instead of the rms resulted in a small difference in the best fit stellar temperature and luminosity of only 200 K and 0.011 dex, respectively.

Next, the sensitivity of the final stellar parameters on the choice of nebular density profiles was explored by testing three profiles. The first had a constant density throughout the entire gas region (constant density profile). The brightest portions of each nebula are primarily from one shell, so a constant density profile is a sensible first choice. However, the sharp cutoff of the gas at the boundaries is unphysical in nature. Therefore, the second profile replaces the constant density with a Gaussian shaped density profile (Gaussian density profile), allowing for a smoother transition to low density areas. The Gaussian density profile, however, does not take into account the less luminous, exterior shells of gas seen in most of the objects. To represent these outer shells in the third profile, a radially decreasing power-law is appended to the Gaussian density profile (Gaussian with a power-law density profile). Figures~\ref{densfig1}~\&~\ref{densfig2} shows the different profiles for each planetary nebula's Full Region.
\begin{figure}
\caption{The three different density profiles used for the full regions of IC 2165, IC 3568, NGC 2440 and NGC 3242 are shown here. The solid red lines are the constant density profiles. The blue dash lines are the Gaussian density profile. The combination of the blue dash lines and green dot-dash lines are the Gaussian with a power-law density profiles.\newline}
\includegraphics[scale=0.29]{4PNeDenShape.png}
\label{densfig1}
\end{figure}
\begin{figure}
\caption{The same as Figure~\ref{densfig1} but for NGC 5315, NGC 5882, and NGC 7662.\newline}
\includegraphics[scale=0.29]{3PNeDenShape.png}
\label{densfig2}
\end{figure}

Since each model assumes a specific value for each stellar and nebular parameter, locating the global minimum (in parameter space) or best value for each stellar parameter is critical. Two methods were used to find these minima. The first method employed a suite of constant density models spanning a wide range of stellar and nebular parameters, using resources from the OU Supercomputing Center for Education and Research at the University of Oklahoma. The benefit of this method is that local minima can be easily identified and avoided. The downside is the sheer number of models required to adequately probe each parameter. The second method determined the rms after each model run and kept parameters that reduced the rms value. This way drastically reduces the number of models required to be run but can be susceptible to stopping in local minima. Both methods were tested on NGC 3242 with negligible differences in the final stellar parameters found. Also, it was observed by inspecting the rms values from the large suite of models that local minima were not a major concern for the stellar parameters. Therefore, only the second method was used for the other six planetary nebulae. 

Describing the first method in detail, a primary grid of 81,000 constant density models was produced for NGC 3242 by varying the stellar temperature and luminosity, the inner and outer radii, and the filling factor of the gas while holding the abundances of He, C, Ne, and O constant. The range of the stellar temperature and luminosity was between 50,000-100,000K ($\bigtriangleup$T = 1000K) and (log[L/L$_{\astrosun}$])=3.0-5.0 ($\bigtriangleup$dex = 0.1), respectively. These ranges cover all published values of these stellar parameters. The filling factor was varied between 0.01 and 0.5, a range which encompasses typical values of planetary nebulae, in steps of 0.01. The inner/outer radii were varied from 0.039pc/0.0415pc to 0.041pc/0.0437pc with a step size of 10$^{-3}$pc/10$^{-4}$pc, covering values that are reasonable for the assumed distance. The nebular composition was chosen to be the full region's values from Table~\ref{tab:abun1}, since all regions had elemental abundances within error of the full region's values. Grains were chosen to be the \textit{planetary nebula} set internal to Cloudy with a fixed scaling factor of 1.0.  The density was chosen to be the full region's value of 4500~cm$^{-3}$ except for Regions 1, 2, 7, and 9.

Next, the set of observed emission line strengths for NGC 3242 were used to reduce the primary grid to a smaller group of models which were the most successful at reproducing the observations, as determined by the previously discussed rms analysis. Finally, within the refined boundaries of the previously discussed parameters, the abundances were varied within the observed errors to produce a secondary grid of over 10 million models to further reduce the model rms (9 parameters total with 6 steps in each parameter). Ultimately, the best values were found by starting with the best model from the grid, and manually adjusting each input parameter and keeping the values that lowered the model rms. An estimation of the error for each parameter was carried out by starting with the best (lowest rms) model and varying each parameter one at a time (the stellar temperature and luminosity were varied together) until the model rms was larger than the sum of the best fit model rms and observed rms\footnotemark, e.g. model rms $>$ 0.21 (0.06+0.15) for Region Full of NGC 3242. This estimation process was used only for the constant density models, due to constraints imposed by computational time requirements.
\footnotetext[1]{Admittedly, each parameter is not fully independent. However, varying the stellar parameters together takes into account more of the covariance.}

For the second method, the nebular and stellar parameters described above were used as starting values and other parameters such as the grain properties and filling factor were set to typical PN values. The constant density profile was again chosen. The density was adjusted until the carbon density diagnostic, (C~III] $\lambda$1909/[C~III] $\lambda$1907), was within roughly 1\% of the observed value. Next, the radius and overall thickness of the gas was adjusted until the line strength of H$\beta$ was within 10\% of the observed value. Finally, all other parameters (abundances, stellar properties, etc.) were adjusted as needed to get the rms down around 0.3, ensuring an average error for all lines and diagnostics near 10\%. From there, the best parameters set so far were entered into a script that varied each parameter one at a time, calculated the rms after each model run by calling PANIC, compared the new rms to the previous values, and retained the sets that resulted in a smaller rms. It continuously looped through all parameters until it failed to produce a lower rms value. To minimize convergence times, the step size for each parameter began at relatively large values (e.g. $\bigtriangleup$T=500K, log[L/L$_{\astrosun}$] $\bigtriangleup$dex=0.1, abundance $\bigtriangleup$dex=0.1), but then was reduced to smaller values (e.g. $\bigtriangleup$T=100K, log[L/L$_{\astrosun}$] $\bigtriangleup$dex=0.01, abundance $\bigtriangleup$dex=0.01) to yield the smallest rms and subsequent best parameters.

The Gaussian and Gaussian with a power-law density profiles initially assumed the best fit constant density parameters as the initial values with the inner and outer radii held fixed. Since there is less gas contained within a Gaussian profile of equal height and width relative to a constant profile, the density peak of the Gaussian profile was increased by trial and error to compensate for the decrease in the H$\beta$ line strength. However, for NGC 5315, the increase was found to be too large to keep the carbon density diagnostic within reasonable error, so the inner and outer radii were increased while keeping the peak of the Gaussian distribution located at the midpoint of the best constant density model. The slope of the power-law was chosen such that the Gaussian side of the profile was around 2000 cm$^{-3}$ and decreased to about 10 cm$^{-3}$ at the location of the outermost known shell/halo of each planetary nebula. The error estimation process was the same as what was described above in the first method.

Table~\ref{modline1} contains the ratios of the model-predicted strengths to their observed counterparts of important emission lines for each nebular region. The wavelength of each emission line is in the first column followed by the identification of the ion that produces it in the second column. The remaining columns contain the individual region's model$/$observed ratios. The majority of modeled lines for each full region fall within the respective errors shown in Table~\ref{emisstab1}. Region Full of NGC 3242 has the most lines that are outside the errors listed in Tables~\ref{emisstab1}. This is probably due to the modeling assumptions becoming less valid compared to the smaller regions and the smaller uncertainties in the line strengths. Table~\ref{nmodline1} provides the same type of comparison as Table~\ref{modline1} but for the other two density profiles and only for the full regions. IC 2165 and NGC 2440 have the largest increase in the number of lines falling outside of the observed errors for the two non-constant density profiles compared to the constant density profile. This suggests that these PN are better represented by the constant density profile.
\begin{landscape}
\begin{deluxetable}{clccccc}
\tabletypesize{\footnotesize}
\setlength{\tabcolsep}{0.07in}
\tablewidth{0in}
%\rotate
\tablecaption{Constant Density Model Emission Lines Compared to Observations\label{modline1}}
\tablehead{
\multicolumn{7}{c}{Constant Density Model Emission Lines Compared to Observations}
}
\startdata
Wave & & IC2165 Full & IC2165 1 & IC2165 2 & IC2165 3 & IC2165 4 \\ 
\cline{3-7}
(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
\tableline
1485 & N IV] 				& 1.00$\pm$0.11 & 1.00$\pm$0.15 				& 1.00$\pm$0.15 			& 1.00$\pm$0.13 			& 1.01$\pm$0.13 \\     
1907 & [C III]					& 1.01$\pm$0.11 & 0.96$\pm$0.13 				& 1.05$\pm$0.15 			& 1.03$\pm$0.13 			& 1.06$\pm$0.13 \\    
1909\tablenotemark{b} & C III]  		& 1.00$\pm$0.11 & 0.97$\pm$0.13 				& 1.04$\pm$0.15 			& 1.03$\pm$0.13 			& 1.06$\pm$0.13 \\        
3869 & [Ne III]  				& 1.00$\pm$0.07 & 1.00$\pm$0.07 				& 1.00$\pm$0.11 			& 1.00$\pm$0.12 			& 1.01$\pm$0.11 \\  
4363\tablenotemark{b} & [O III]  	& 1.01$\pm$0.11 & 0.87$\pm$0.18	 			& 1.11$\pm$0.14			& 1.04$\pm$0.20 			& 1.10$\pm$0.22 \\       
4686 & He II  				& 1.00$\pm$0.05 & 1.09$\pm$0.06\tablenotemark{a} 	& 0.81$\pm$0.06\tablenotemark{a} & 0.97$\pm$0.06			& 0.85$\pm$0.05\tablenotemark{a} \\
4861 & H$\beta$  				& 0.98$\pm$0.03 & 1.00$\pm$0.04 				& 0.95$\pm$0.05 & 0.94$\pm$0.04\tablenotemark{a} & 0.84$\pm$0.04\tablenotemark{a} \\  
4959\tablenotemark{b} & [O III]  	& 1.03$\pm$0.03 & 0.99$\pm$0.03 				& 1.04$\pm$0.04 & 1.01$\pm$0.03 			& 1.11$\pm$0.03 \\       
5007 & [O III]  				& 1.01$\pm$0.02 & 0.95$\pm$0.03\tablenotemark{a}	& 1.04$\pm$0.03\tablenotemark{a} & 1.03$\pm$0.03 			& 1.08$\pm$0.03\tablenotemark{a} \\   
5876 & He I  					& 1.00$\pm$0.14 & 1.06$\pm$0.28 				& 0.95$\pm$0.41 			& 0.98$\pm$0.32 			& 0.93$\pm$0.37 \\
7136 & [Ar III]  				& 1.00$\pm$0.14 & 1.00$\pm$0.15 				& 1.00$\pm$0.30			& 1.00$\pm$0.15 			& 1.00$\pm$0.22 \\  
9532 & [S III]  				& 1.00$\pm$0.06 & 1.00$\pm$0.12 				& 1.00$\pm$0.10 			& 1.00$\pm$0.12 			& 1.00$\pm$0.14 \\
\tableline
\\
 & & IC2165 5 & IC2165 6 & IC3568 Full & IC3568 1 & IC3568 2 \\
\cline{3-7}
  & & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
\tableline
1485 &  N IV]  				& 1.00$\pm$0.16 			& 0.97$\pm$0.56 			& \nodata 				& \nodata 				& \nodata \\   
1549 & C IV 					& \nodata 			& \nodata 			& 1.00$\pm$0.13 				& 1.00$\pm$0.19 				& 1.02$\pm$0.17 \\ 
1907 &  [C III]  				& 0.92$\pm$0.14 			& 0.91$\pm$0.33 			& 1.00$\pm$0.10 				& 1.02$\pm$0.14 				& 0.99$\pm$0.16 \\   
1909\tablenotemark{b} &  C III]  	& 0.92$\pm$0.14 			& 0.91$\pm$0.34 			& 1.01$\pm$0.11 				& 1.01$\pm$0.18 				& 1.03$\pm$0.17 \\ 
%\tableline   
% & & IC2165 5 & IC2165 6 & IC3568 Full & IC3568 1 & IC3568 2 \\
%\cline{3-7}           
% & & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
%\tableline  
3869 &  [Ne III]  				& 0.99$\pm$0.08 			& 0.99$\pm$0.18 			& 1.00$\pm$0.06 				& 1.00$\pm$0.19				& 1.01$\pm$0.06 \\ 
4363\tablenotemark{b} &  [O III]  	& 0.81$\pm$0.16\tablenotemark{a} & 0.96$\pm$0.73 		& 0.99$\pm$0.31 				& 1.01$\pm$0.21				& 0.97$\pm$0.41 \\              
4686 &  He II  				& 1.00$\pm$0.08 			& \nodata 			& \nodata 				& \nodata				& \nodata \\   
4861 &  H$\beta$  				& 1.10$\pm$0.04\tablenotemark{a} & 1.21$\pm$0.10\tablenotemark{a} 	& 0.94$\pm$0.03\tablenotemark{a} & 0.87$\pm$0.04\tablenotemark{a} & 0.96$\pm$0.04 \\ 
4959\tablenotemark{b} &  [O III]  	& 0.87$\pm$0.03\tablenotemark{a} & 0.99$\pm$0.07 			& 1.12$\pm$0.02\tablenotemark{a} & 1.18$\pm$0.03\tablenotemark{a} & 1.13$\pm$0.03\tablenotemark{a} \\              
5007 &  [O III]  				& 0.89$\pm$0.03\tablenotemark{a} & 0.87$\pm$0.07\tablenotemark{a} 	& 1.00$\pm$0.02 			& 1.07$\pm$0.03\tablenotemark{a} 	& 1.01$\pm$0.03 \\  
5876 &  He I  				& 1.03$\pm$0.14 			& 1.01$\pm$0.28 			& 1.00$\pm$0.14 				& 0.99$\pm$0.24				& 1.00$\pm$0.29 \\
7136 &  [Ar III]  				& 1.01$\pm$0.13 			& 1.00$\pm$0.24 			& 1.00$\pm$0.21 				& 1.01$\pm$0.32				& 1.00$\pm$0.31 \\ 
9532 &  [S III]  				& 0.99$\pm$0.07 			& 1.00$\pm$0.18 			& \nodata 				& \nodata				& \nodata 
%\tableline
\tablebreak
Wave & & IC3568 3 & NGC2440 Full & NGC2440 1 & NGC2440 2 & NGC2440 3 \\
\cline{3-7}
(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
\tableline
1485 &  N IV]  				& \nodata 			& 0.98$\pm$0.12 			& 0.97$\pm$0.11 				& 0.79$\pm$0.21 & 0.85$\pm$0.11\tablenotemark{a} \\ 
1907 &  [C III]  				& 1.00$\pm$0.47 			& 0.99$\pm$0.12 			& 0.95$\pm$0.10 			& 0.99$\pm$0.21 			& 0.92$\pm$0.11 \\   
1909\tablenotemark{b} &  C III]  	& 1.00$\pm$0.47 			& 0.97$\pm$0.12 			& 1.01$\pm$0.11 			& 0.96$\pm$0.21 			& 0.91$\pm$0.11 \\               
3727 & [O II] 				& \nodata 			& 0.98$\pm$0.06 			& 0.93$\pm$0.06\tablenotemark{a} 	& 1.11$\pm$0.87 			& 0.93$\pm$0.08 \\  
3869 &  [Ne III]  				& 1.00$\pm$0.29 			& 1.00$\pm$0.05 			& 0.98$\pm$0.06 			& 1.01$\pm$0.27			& 0.98$\pm$0.06 \\ 
4363\tablenotemark{b} &  [O III]  	& 0.98$\pm$0.96 			& 1.00$\pm$0.10 			& 0.70$\pm$0.08\tablenotemark{a} & 1.05$\pm$0.52 			& 0.97$\pm$0.09 \\              
4686 &  He II  				& \nodata 			& 1.03$\pm$0.04 			& 1.14$\pm$0.04\tablenotemark{a} 	& 0.89$\pm$0.07\tablenotemark{a} & 1.06$\pm$0.04\tablenotemark{a} \\ 
%Wave & & IC3568 3 & NGC2440 Full & NGC2440 1 & NGC2440 2 & NGC2440 3 \\
%\cline{3-7}
%(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
%\tableline
4861 &  H$\beta$  				& 1.02$\pm$0.14 			& 0.98$\pm$0.04 			& 0.84$\pm$0.03\tablenotemark{a} 	& 1.01$\pm$0.07 			& 1.14$\pm$0.04\tablenotemark{a} \\ 
4959\tablenotemark{b} &  [O III]  	& 1.13$\pm$0.09\tablenotemark{a} & 1.01$\pm$0.02 		& 0.84$\pm$0.02\tablenotemark{a} 	& 1.05$\pm$0.05 			& 1.02$\pm$0.02 \\              
5007 &  [O III]  				& 0.98$\pm$0.09 			& 0.99$\pm$0.02 			& 0.84$\pm$0.02\tablenotemark{a} 	& 0.94$\pm$0.04\tablenotemark{a} & 1.04$\pm$0.02\tablenotemark{a} \\  
5876 &  He I  				& 1.00$\pm$0.74 			& 1.01$\pm$0.10 			& 1.09$\pm$0.16 				& \nodata 			& 1.05$\pm$0.17 \\  
6584 & [N II] 				& \nodata 			& 1.02$\pm$0.00\tablenotemark{a} & 0.97$\pm$0.00\tablenotemark{a} 	& 1.14$\pm$0.02\tablenotemark{a} & 1.05$\pm$0.00\tablenotemark{a} \\  
7136 &  [Ar III]  				& 1.00$\pm$0.70			& 1.00$\pm$0.04 			& 1.00$\pm$0.06 				& 1.01$\pm$0.19 			& 1.01$\pm$0.04 \\ 
9532 &  [S III]  				& \nodata 			& 1.00$\pm$0.04 			& 0.99$\pm$0.09 				& 1.00$\pm$0.27 			& 1.00$\pm$0.06 \\
\tableline
%\tablebreak
\\
 & & NGC3242 Full & NGC3242 1 & NGC3242 2 & NGC3242 3 & NGC3242 4 \\
\cline{3-7}
  & & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
 \tableline
1485 & N IV] 			& 1.00$\pm$0.09 			& 1.00$\pm$0.35				& 1.00$\pm$0.17 				& 1.00$\pm$0.15 			& 1.00$\pm$0.19 \\
1907 & [C III]				& 1.05$\pm$0.03\tablenotemark{a} & 1.01$\pm$0.20 			& 1.01$\pm$0.09 				& 1.01$\pm$0.10 			& 1.01$\pm$0.13 \\
1909\tablenotemark{b} & C III] & 1.05$\pm$0.04\tablenotemark{a} & 1.01$\pm$0.20				& 1.01$\pm$0.08 				& 1.02$\pm$0.11 			& 1.00$\pm$0.14 \\
3727 & [O II] 			& 0.95$\pm$0.40 			& \nodata 				& \nodata 				& \nodata			& \nodata\\
3869 & [Ne III] 			& 1.04$\pm$0.02\tablenotemark{a} & 1.01$\pm$0.08 			& 1.00$\pm$0.07 				& 1.00$\pm$0.06 			& 1.01$\pm$0.06 \\
%3969\tablenotemark{c} & [Ne III] & 1.057\tablenotemark{a} & 1.018 & 1.054 & 1.110 & 0.982 \\
%4101\tablenotemark{c} & H$\delta$ & 0.886\tablenotemark{a} & 0.721\tablenotemark{a} & 0.880\tablenotemark{a} & 0.968 & 0.861 \\
%4340\tablenotemark{c} & H$\gamma$ & 0.939\tablenotemark{a} & 0.910 & 0.999 & 1.032 & 0.955 \\
4363\tablenotemark{b} & [O III] & 1.08$\pm$0.07\tablenotemark{a} & 0.99$\pm$0.35 			& 0.97$\pm$0.09 				& 0.93$\pm$0.17 				& 0.95$\pm$0.19 \\
4686 & He II 			& 0.94$\pm$0.02\tablenotemark{a} & 1.00$\pm$0.21 			& 0.90$\pm$0.07\tablenotemark{a} 	& 0.90$\pm$0.04\tablenotemark{a} 	& 0.99$\pm$0.11 \\
4861 & H$\beta$ 			& 0.91$\pm$0.01\tablenotemark{a} & 0.93$\pm$0.06\tablenotemark{a} 	& 0.96$\pm$0.03\tablenotemark{a} 	& 0.94$\pm$0.03\tablenotemark{a} 	& 0.98$\pm$0.04 \\
4959\tablenotemark{b} & [O III] & 1.07$\pm$0.01\tablenotemark{a} & 1.02$\pm$0.04 			& 1.01$\pm$0.02 				& 1.00$\pm$0.02 				& 0.99$\pm$0.03 \\
5007 & [O III] 			& 1.08$\pm$0.01\tablenotemark{a} & 1.03$\pm$0.04 			& 1.02$\pm$0.02 	& 1.01$\pm$0.02 				& 1.01$\pm$0.03 \\
5876 & He I 				& 0.96$\pm$0.07 			& 1.00$\pm$0.23 				& 0.95$\pm$0.19 				& 0.98$\pm$0.38 				& 1.00$\pm$0.38 \\
%6563\tablenotemark{c} & H$\alpha$ & 0.918\tablenotemark{a} & 0.943\tablenotemark{a} & 0.967\tablenotemark{a} & 0.949\tablenotemark{a} & 0.974\tablenotemark{a} \\
%6678\tablenotemark{b}\tablenotemark{c} & He I & 1.114 & \nodata & \nodata & \nodata & \nodata \\
Wave & & NGC3242 Full & NGC3242 1 & NGC3242 2 & NGC3242 3 & NGC3242 4 \\
\cline{3-7}
(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
\tableline
7136 & [Ar III] & 1.00$\pm$0.11 & \nodata & \nodata & \nodata & \nodata \\
9532 & [S III] & 1.01$\pm$0.20 & \nodata & \nodata & \nodata & \nodata \\
\tableline
\\
 & & NGC3242 5 & NGC3242 6 & NGC3242 7 & NGC3242 8 & NGC3242 9 \\
\cline{3-7}
  & & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
 \tableline
1485 & N IV] 			& 1.01$\pm$0.20 			& 1.00$\pm$0.20 				& 1.00$\pm$0.15 			& 1.00$\pm$0.14 			& 1.00$\pm$0.31 \\
1907 & [C III] 			& 1.02$\pm$0.12 			& 1.01$\pm$0.12 				& 1.02$\pm$0.13 			& 1.00$\pm$0.11 			& 0.99$\pm$0.14 \\
1909\tablenotemark{b} & C III] & 1.03$\pm$0.13 			& 1.01$\pm$0.11 				& 1.03$\pm$0.12 			& 1.00$\pm$0.11 			& 1.00$\pm$0.14 \\
3869 & [Ne III] 			& 1.01$\pm$0.06 			& 1.00$\pm$0.06 				& 1.01$\pm$0.06 			& 1.00$\pm$0.05 			& 1.00$\pm$0.06 \\
%3969\tablenotemark{b} & [Ne III] & 1.036 & 1.006 & 1.106 & 1.029 & 1.124 \\
%4101\tablenotemark{b} & H$\delta$ & 0.969 & 0.992 & 1.008 & 0.961 & 1.053 \\
%4340\tablenotemark{b} & H$\gamma$ & 0.952 & 0.976 & 1.008 & 0.953 & 1.006 \\
4363\tablenotemark{b} & [O III] & 1.07$\pm$0.25 			& 1.01$\pm$0.27 				& 1.10$\pm$0.25 			& 0.93$\pm$0.15 				& 0.99$\pm$0.14 \\
4686 & He II 			& 1.00$\pm$0.07 			& 0.99$\pm$0.09 				& 0.99$\pm$0.08 			& 0.73$\pm$0.04\tablenotemark{a} 	& 0.96$\pm$0.10 \\
4861 & H$\beta$ 			& 0.89$\pm$0.04\tablenotemark{a} & 0.95$\pm$0.03\tablenotemark{a} & 0.97$\pm$0.04			& 0.96$\pm$0.03\tablenotemark{a} 	& 0.98$\pm$0.04 \\
4959\tablenotemark{b} & [O III] & 1.07$\pm$0.02\tablenotemark{a} & 1.02$\pm$0.02 			& 1.07$\pm$0.03\tablenotemark{a} & 0.99$\pm$0.02 			& 1.02$\pm$0.03 \\
5007 & [O III] 			& 1.08$\pm$0.02\tablenotemark{a} & 1.03$\pm$0.02\tablenotemark{a} & 1.08$\pm$0.02\tablenotemark{a} & 1.01$\pm$0.02 				& 1.03$\pm$0.03 \\
5876 & He I 				& 0.99$\pm$0.31 			& 1.00$\pm$0.34 				& 0.98$\pm$0.27 			& 0.89$\pm$0.27				& 0.99$\pm$0.35 \\
%6563\tablenotemark{b} & H$\alpha$ & 0.889\tablenotemark{a} & 0.946\tablenotemark{a} & 0.976\tablenotemark{a} & 0.966\tablenotemark{a} & 0.987\tablenotemark{a}  
\tableline
\\
 & & NGC5315 Full & NGC5315 1 & NGC5315 2 & NGC5315 3 & NGC5315 4 \\
\cline{3-7}
 & & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
\tableline
1549 & C IV 					& 0.99$\pm$0.04 			& 0.99$\pm$0.11 			& 0.99$\pm$0.06 			& 1.04$\pm$0.06 			& 0.99$\pm$0.18 \\
1907 &  [C III]  				& 1.00$\pm$0.07 			& 1.00$\pm$0.23 			& 1.01$\pm$0.06 			& 0.97$\pm$0.12 			& 0.98$\pm$0.30 \\
1909\tablenotemark{b} &  C III]  	& 1.01$\pm$0.05 			& 1.00$\pm$0.25 			& 1.04$\pm$0.03\tablenotemark{a} & 1.02$\pm$0.09		& 0.98$\pm$0.25\\
3869 &  [Ne III] 				& 0.99$\pm$0.01			& 1.00$\pm$0.08 			& 1.00$\pm$0.01 			& 1.01$\pm$0.02 			& 1.01$\pm$0.09 \\
4363\tablenotemark{b} &  [O III]  	& 0.99$\pm$0.06 			& 1.02$\pm$0.36 			& 1.03$\pm$0.02\tablenotemark{a} & 1.14$\pm$0.14 & 1.09$\pm$0.66\\
4861 &  H$\beta$  				& 1.06$\pm$0.01\tablenotemark{a} & 1.00$\pm$0.03 		& 0.90$\pm$0.01\tablenotemark{a} & 0.89$\pm$0.01\tablenotemark{a} & 0.91$\pm$0.04\tablenotemark{a} \\
4959\tablenotemark{b} &  [O III]  	& 0.98$\pm$0.01\tablenotemark{a} & 1.28$\pm$0.03\tablenotemark{a} & 0.99$\pm$0.01 		& 1.13$\pm$0.01\tablenotemark{a} & 1.25$\pm$0.03\tablenotemark{a}\\
5007 &  [O III]  				& 0.98$\pm$0.00\tablenotemark{a} & 0.99$\pm$0.02 		& 1.02$\pm$0.00\tablenotemark{a} & 1.06$\pm$0.01\tablenotemark{a} & 1.04$\pm$0.03\tablenotemark{a} \\
5876 &  He I  				& 1.01$\pm$0.01 			& 0.99$\pm$0.13 			& 1.00$\pm$0.01 			& 0.96$\pm$0.01\tablenotemark{a} & 0.97$\pm$0.05 \\
%Wave & & NGC5315 Full & NGC5315 1 & NGC5315 2 & NGC5315 3 & NGC5315 4 \\
%\cline{3-7}
%(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
%\tableline
7136 &  [Ar III]  				& 0.99$\pm$0.00\tablenotemark{a} & 1.00$\pm$0.02 				& 1.00$\pm$0.00 & 1.01$\pm$0.01 & 1.01$\pm$0.04 \\
Wave &  & NGC5315 Full & NGC5315 1 & NGC5315 2 & NGC5315 3 & NGC5315 4 \\
\cline{3-7}
(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
\tableline
9532 &  [S III]  				& 0.96$\pm$0.01\tablenotemark{a} & 1.02$\pm$0.02 				& 1.02$\pm$0.00\tablenotemark{a} & 1.08$\pm$0.01\tablenotemark{a} & 1.08$\pm$0.03\tablenotemark{a} \\
\tableline
%\tablebreak
\\
 & & NGC5882 Full & NGC5882 1 & NGC5882 2 & NGC5882 3 & \\
\cline{3-6}
  &  & Model/Observed & Model/Observed & Model/Observed & Model/Observed &  \\
 \tableline
1549 & C IV 					& 1.00$\pm$0.24 			& 0.91$\pm$0.35 			& 0.91$\pm$0.19 				& 1.08$\pm$1.10 \\
1907 &  [C III]  				& 1.00$\pm$0.14 			& \nodata 			& \nodata 				& \nodata \\
1909\tablenotemark{b} &  C III]  	& 0.99$\pm$0.11 			& 1.03$\pm$0.26\tablenotemark{c} & 1.07$\pm$0.15\tablenotemark{c} 	& 0.89$\pm$0.26\tablenotemark{c} \\
3869 &  [Ne III]  				& 1.02$\pm$0.04 			& 1.02$\pm$0.05 			& 1.04$\pm$0.03\tablenotemark{a} 	& 1.02$\pm$0.09 \\
4363\tablenotemark{b} &  [O III]  	& 1.13$\pm$0.20 			& 1.22$\pm$0.35 			& 1.00$\pm$0.23 				& 0.94$\pm$0.86 \\
4686 &  He II  				& 0.98$\pm$0.24 			& 0.92$\pm$0.22 			& 0.84$\pm$0.18 				& \nodata \\
4861 &  H$\beta$  				& 0.81$\pm$0.02\tablenotemark{a} & 0.84$\pm$0.03\tablenotemark{a} & 0.77$\pm$0.01\tablenotemark{a} & 0.82$\pm$0.04\tablenotemark{a} \\
4959\tablenotemark{b} &  [O III]  	& 1.33$\pm$0.02\tablenotemark{a} & 1.40$\pm$0.02\tablenotemark{a} & 1.25$\pm$0.01\tablenotemark{a} & 1.27$\pm$0.03\tablenotemark{a} \\
5007 &  [O III]  				& 1.12$\pm$0.02\tablenotemark{a} & 1.19$\pm$0.02\tablenotemark{a} & 1.07$\pm$0.01\tablenotemark{a} & 1.06$\pm$0.03\tablenotemark{a} \\
5876 &  He I  				& 0.98$\pm$0.05 			& 0.95$\pm$0.12 			& 0.94$\pm$0.05\tablenotemark{a} 	& 1.01$\pm$0.09 \\
6584 & [N II] 				& 1.00$\pm$0.03 			& 1.00$\pm$0.02 			& 1.01$\pm$0.04 				& 1.01$\pm$0.05 \\
7136 &  [Ar III]  				& 1.00$\pm$0.05			 & 0.99$\pm$0.07			& 1.03$\pm$0.03 				& 1.01$\pm$0.09 \\
9532 &  [S III]  				& 1.02$\pm$0.03 			& 1.00$\pm$0.04 			& 1.02$\pm$0.03 				& 1.01$\pm$0.07 \\
\tableline 
\\
 & & NGC7662 Full & NGC7662 1 & NGC7662 2 & NGC7662 3 & NGC7662 4 \\
\cline{3-7} 
 & & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
\tableline
1485 &  N IV]  				& 1.07$\pm$0.06\tablenotemark{a} & 1.01$\pm$0.19 & 1.03$\pm$0.10 			& 1.00$\pm$0.14 			& 0.97$\pm$0.10 \\
1549 & C IV 					& 1.00$\pm$0.04 			& 0.96$\pm$0.09 & 0.82$\pm$0.05\tablenotemark{a} & 0.94$\pm$0.10 			& 0.97$\pm$0.07 \\
1750 & N III] 				& 0.90$\pm$0.24 			& \nodata & \nodata 			& \nodata 			& \nodata \\
1907 & [C III]  				& 0.96$\pm$0.04 			& 1.01$\pm$0.09 & 1.12$\pm$0.05\tablenotemark{a} & 1.05$\pm$0.11 			& 0.95$\pm$0.07 \\
1909\tablenotemark{b} &  C III]  	& 0.95$\pm$0.05 			& 1.00$\pm$0.10 & 1.12$\pm$0.05\tablenotemark{a} & 1.04$\pm$0.11 			& 0.96$\pm$0.07 \\
3727 & [O II] 				& 1.02$\pm$0.30 			& \nodata & \nodata 			& \nodata 			& \nodata \\
3869 &  [Ne III]  				& 0.98$\pm$0.03 			& 0.99$\pm$0.05 & 1.01$\pm$0.04 			& 1.00$\pm$0.06 			& 0.99$\pm$0.03 \\
4363\tablenotemark{b} &  [O III]  	& 0.83$\pm$0.06\tablenotemark{a} & 0.93$\pm$0.14 & 1.10$\pm$0.10 			& 1.08$\pm$0.08 & 0.93$\pm$0.04\tablenotemark{a} \\
Wave & & NGC7662 Full & NGC7662 1 & NGC7662 2 & NGC7662 3 & NGC7662 4 \\
\cline{3-7} 
(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
\tableline
4686 &  He II  				& 1.02$\pm$0.02\tablenotemark{a} & 1.06$\pm$0.05\tablenotemark{a} & 0.93$\pm$0.02\tablenotemark{a} & 0.99$\pm$0.04 			& 0.47$\pm$0.02\tablenotemark{a} \\
4861 &  H$\beta$  				& 0.99$\pm$0.01 			& 1.04$\pm$0.03\tablenotemark{a} & 0.89$\pm$0.02\tablenotemark{a} & 0.88$\pm$0.03\tablenotemark{a} & 1.08$\pm$0.02\tablenotemark{a} \\
4959\tablenotemark{b} &  [O III]  	& 1.02$\pm$0.01\tablenotemark{a} & 1.02$\pm$0.02 & 1.07$\pm$0.01\tablenotemark{a} & 1.19$\pm$0.02\tablenotemark{a} & 1.02$\pm$0.02 \\
5007 &  [O III]  				& 0.93$\pm$0.01\tablenotemark{a} & 0.93$\pm$0.02\tablenotemark{a} & 1.01$\pm$0.01 			& 1.02$\pm$0.02 & 0.93$\pm$0.02\tablenotemark{a} \\
5876 &  He I  				& 1.02$\pm$0.14 			& \nodata 			& 0.97$\pm$0.48 				& \nodata 		& 0.99$\pm$0.31 \\
7136 &  [Ar III]  				& 1.00$\pm$0.12 			& 1.00$\pm$0.14 			& 1.04$\pm$0.12 				& 1.00$\pm$0.09 		& 0.94$\pm$0.12 \\
9532 &  [S III]  				& 0.99$\pm$0.09 			& 1.00$\pm$0.16 			& 1.04$\pm$0.16 				& 1.01$\pm$0.19 		& 0.93$\pm$0.15 \\
\tableline
%\tablebreak
\\
Wave & &  NGC7662 5 & NGC7662 6 & NGC7662 7 & NGC7662 8 & \\
\cline{3-6}
(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & \\
\tableline
1485 &  N IV]  				& 1.07$\pm$0.11 			& 1.00$\pm$0.10 			& 0.97$\pm$0.12 				& 1.01$\pm$0.17 \\
1549 & C IV 					& 1.00$\pm$0.05 			& 1.01$\pm$0.04 			& 0.96$\pm$0.08 				& 0.86$\pm$0.08\tablenotemark{a} \\
1750 & N III] 				& 0.91$\pm$0.29 			& \nodata 			& \nodata 				& \nodata \\
1907 &  [C III] 				& 0.98$\pm$0.05 			& 0.97$\pm$0.04 			& 0.98$\pm$0.08 				& 0.98$\pm$0.08 \\
1909\tablenotemark{b} &  C III]  	& 0.97$\pm$0.06 			& 0.97$\pm$0.04 			& 0.99$\pm$0.08 				& 0.93$\pm$0.09 \\
3727 & [O II] 				& \nodata 			& \nodata 			& 1.06$\pm$0.30 				& \nodata \\
3869 &  [Ne III]  				& 0.96$\pm$0.03\tablenotemark{a} & 0.99$\pm$0.02 		& 1.00$\pm$0.04 				& 0.97$\pm$0.04 \\
4363\tablenotemark{b} &  [O III]  	& 0.91$\pm$0.17 			& 0.90$\pm$0.08\tablenotemark{a} & 0.86$\pm$0.08\tablenotemark{a} & 0.80$\pm$0.19\tablenotemark{a} \\
4686 &  He II  				& 0.56$\pm$0.02\tablenotemark{a} & 0.95$\pm$0.02\tablenotemark{a} & 1.11$\pm$0.04\tablenotemark{a} & 1.13$\pm$0.06\tablenotemark{a} \\
4861 &  H$\beta$  				& 1.07$\pm$0.02\tablenotemark{a} & 1.08$\pm$0.01\tablenotemark{a} & 0.91$\pm$0.03\tablenotemark{a} & 1.20$\pm$0.03\tablenotemark{a} \\
4959\tablenotemark{b} &  [O III]  	& 0.98$\pm$0.01\tablenotemark{a} & 1.01$\pm$0.01 & 1.00$\pm$0.02 			& 0.73$\pm$0.01\tablenotemark{a} \\
5007 &  [O III]  				& 0.93$\pm$0.01\tablenotemark{a} & 0.92$\pm$0.01\tablenotemark{a} & 0.87$\pm$0.02\tablenotemark{a} & 0.72$\pm$0.01\tablenotemark{a} \\
5876 &  He I  				& 0.95$\pm$0.25 			& 0.99$\pm$0.11 			& 1.03$\pm$0.23 				& \nodata \\
7136 &  [Ar III]  				& 0.97$\pm$0.18 			& 0.99$\pm$0.17 			& 0.97$\pm$0.11 				& \nodata \\
9532 &  [S III]  				& 0.97$\pm$0.14 			& 1.00$\pm$0.13 			& 0.98$\pm$0.17 				& \nodata \\
\enddata
\tablenotetext{a}{Modeled emission line intensity outside observed error bar.}
\tablenotetext{b}{This line was only included in a diagnostic for the rms calculation for reasons discussed in the text.}
\tablenotetext{c}{Blended 1907 and 1909.}
\end{deluxetable}
\end{landscape}
\begin{landscape}
\begin{deluxetable}{clcccccc}
\tabletypesize{\footnotesize}
\setlength{\tabcolsep}{0.07in}
\tablewidth{0in}
%\rotate
\tablecaption{Non-constant Density Model Emission Lines Compared to Observations For Full Regions\label{nmodline1}}
\tablehead{
\multicolumn{8}{c}{Non-constant Density Model Emission Lines Compared to Observations For Full Regions}
}
\startdata
 & & \multicolumn{2}{c}{IC2165 Full} & \multicolumn{2}{c}{IC3568 Full} & \multicolumn{2}{c}{NGC2440 Full}\\
\cline{3-8}
 & & Gaussian & Gaussian With & Gaussian & Gaussian With & Gaussian & Gaussian With\\
Wave & & & power-law & & power-law & & power-law \\ 
\cline{3-8}
(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\ 
\tableline
1485 &  N IV]  				& 1.00$\pm$0.11 			& 1.00$\pm$0.11 				& \nodata 			& \nodata 				& 0.77$\pm$0.12\tablenotemark{a} & 0.77$\pm$0.12\tablenotemark{a}\\
1549 & C IV 					& \nodata 			& \nodata 				& 1.01$\pm$0.13 			& 1.01$\pm$0.13 				& \nodata 			& \nodata \\
1907 &  [C III]  				& 1.04$\pm$0.11 			& 1.06$\pm$0.11 				& 0.99$\pm$0.10 			& 0.99$\pm$0.10 				& 1.02$\pm$0.12 			& 1.00$\pm$0.12  \\  
1909\tablenotemark{b} &  C III]  	& 1.12$\pm$0.11\tablenotemark{a} & 1.14$\pm$0.11\tablenotemark{a} & 1.08$\pm$0.11			& 1.06$\pm$0.11 				& 1.04$\pm$0.12 			& 1.02$\pm$0.12 \\
3727 &  [O II]  				& \nodata 			& \nodata 				& \nodata 			& \nodata 				& 0.83$\pm$0.06\tablenotemark{a} & 0.83$\pm$\tablenotemark{a}0.06 \\  
3869 &  [Ne III]  				& 1.00$\pm$0.07 			& 1.00$\pm$0.07 				& 0.99$\pm$0.06 			& 0.99$\pm$0.06 				& 0.99$\pm$0.05 			& 1.02$\pm$0.05\\
4363\tablenotemark{b} &  [O III]  	& 1.13$\pm$0.11\tablenotemark{a} & 1.15$\pm$0.11\tablenotemark{a} & 1.05$\pm$0.31			& 0.99$\pm$0.31 				& 1.06$\pm$0.10 			& 1.04$\pm$0.10 \\ 
4686 &  He II  				& 0.99$\pm$0.05 			& 1.00$\pm$0.05 				& \nodata 			& \nodata 				& 1.12$\pm$0.04\tablenotemark{a} & 1.10$\pm$0.04\tablenotemark{a} \\
4861 &  H$\beta$  				& 0.97$\pm$0.03			 & 0.98$\pm$0.03 			& 0.99$\pm$0.03 			& 1.02$\pm$0.03 				& 1.03$\pm$0.04 			& 1.02$\pm$0.04\\
4959\tablenotemark{b} &  [O III]  	& 1.08$\pm$0.03\tablenotemark{a} & 1.09$\pm$0.03\tablenotemark{a} & 1.19$\pm$0.02\tablenotemark{a} & 1.12$\pm$0.02\tablenotemark{a} & 1.10$\pm$0.02\tablenotemark{a} & 1.07$\pm$0.02\tablenotemark{a} \\ 
5007 &  [O III]  				& 1.06$\pm$0.02\tablenotemark{a} & 1.07$\pm$0.02\tablenotemark{a} & 1.06$\pm$0.02\tablenotemark{a} & 1.00$\pm$0.02 				& 1.08$\pm$0.02\tablenotemark{a} & 1.06$\pm$0.02\tablenotemark{a}\\ 
5876 &  He I  				& 0.98$\pm$0.14 			& 0.99$\pm$0.14 				& 0.99$\pm$0.14 			& 1.00$\pm$0.14 				& 1.03$\pm$0.10 			& 1.02$\pm$0.10 \\  
6584 &  [N II]				& \nodata 			& \nodata 				& \nodata 			& \nodata 				& 1.16$\pm$0.00\tablenotemark{a} & 1.16$\pm$0.00\tablenotemark{a} \\
7136 &  [Ar III]  				& 1.00$\pm$0.14 			& 0.99$\pm$0.14 				& 0.99$\pm$0.21 			& 1.00$\pm$0.21 				& 1.08$\pm$0.04\tablenotemark{a} & 1.07$\pm$0.04\tablenotemark{a} \\
9532 &  [S III]  				& 1.00$\pm$0.06 			& 0.99$\pm$0.06 				& \nodata 			& \nodata 				& 1.05$\pm$0.04\tablenotemark{a} & 1.04$\pm$0.04 \\ 
\tableline
\tablebreak
 & & \multicolumn{2}{c}{NGC5315 Full} & \multicolumn{2}{c}{NGC5882 Full} & \multicolumn{2}{c}{NGC3242 Full}\\
\cline{3-8}
 & & Gaussian & Gaussian With & Gaussian & Gaussian With & Gaussian & Gaussian With\\
 Wave & & & power-law & & power-law & & power-law \\ 
\cline{3-8}
(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\ 
\tableline
1485 &  N IV] 					& \nodata 			& \nodata 				& \nodata 			& \nodata 				& 1.00$\pm$0.09 			& 1.00$\pm$0.09 \\
1549 & C IV 						& 1.00$\pm$0.04 			& 0.99$\pm$0.04 				& 1.00$\pm$0.24 			& 1.16$\pm$0.24 				& \nodata 			& \nodata \\
1907 &  [C III]  					& 0.99$\pm$0.07 			& 0.99$\pm$0.07 				& 1.00$\pm$0.14 			& 1.00$\pm$0.14 				& 1.10$\pm$0.03\tablenotemark{a} & 1.11$\pm$0.03\tablenotemark{a} \\
1909\tablenotemark{b} &  C III]  		& 1.07$\pm$0.05\tablenotemark{a} & 1.07$\pm$0.05\tablenotemark{a} & 1.00$\pm$0.11 			& 0.99$\pm$0.11 				& 1.10$\pm$0.04\tablenotemark{a} & 1.11$\pm$0.04\tablenotemark{a} \\
3727 & [O II] 					& \nodata 			& \nodata 				& \nodata 			& \nodata 				& 0.95$\pm$0.40 			& 0.90$\pm$0.40 \\
3869 &  [Ne III]  					& 1.00$\pm$0.01 			& 0.99$\pm$0.01 				& 1.03$\pm$0.04 			& 1.07$\pm$0.04\tablenotemark{a} 	& 1.05$\pm$0.02\tablenotemark{a} & 1.02$\pm$0.02 \\
4363\tablenotemark{b} &  [O III]  		& 1.05$\pm$0.06 			& 1.02$\pm$0.06 				& 1.12$\pm$0.20 			& 1.14$\pm$0.20 				& 1.13$\pm$0.07\tablenotemark{a} & 1.18$\pm$0.07\tablenotemark{a} \\
4686 &  He II  					& \nodata 			& \nodata 				& 0.99$\pm$0.24 			& 0.96$\pm$0.24 				& 0.90$\pm$0.02\tablenotemark{a} & 0.93$\pm$0.02\tablenotemark{a} \\
4861 &  H$\beta$  					& 1.03$\pm$0.01\tablenotemark{a} & 1.04$\pm$0.01\tablenotemark{a} & 0.81$\pm$0.02\tablenotemark{a} & 0.86$\pm$0.02\tablenotemark{a} 	& 0.92$\pm$0.01\tablenotemark{a} & 0.94$\pm$0.01\tablenotemark{a} \\
4959\tablenotemark{b} &  [O III]  		& 1.01$\pm$0.01 & 1.00$\pm$0.01 			& 1.32$\pm$0.02\tablenotemark{a} & 1.37$\pm$0.02\tablenotemark{a} 	& 1.09$\pm$0.01\tablenotemark{a} & 1.12$\pm$0.01\tablenotemark{a}\\
5007 &  [O III]  					& 0.99$\pm$0.00\tablenotemark{a} & 0.98$\pm$0.00\tablenotemark{a} & 1.11$\pm$0.02\tablenotemark{a} & 1.16$\pm$0.02\tablenotemark{a} 	& 1.11$\pm$0.01\tablenotemark{a} & 1.13$\pm$0.01\tablenotemark{a} \\
5876 &  He I  					& 1.01$\pm$0.01 			& 1.00$\pm$0.01 				& 0.99$\pm$0.05 			& 1.05$\pm$0.05 	& 0.92$\pm$0.07\tablenotemark{a} & 0.95$\pm$0.07 \\
6584 & [N II] 					& \nodata 			& \nodata 				& 1.00$\pm$0.03 			& 0.98$\pm$0.03 				& \nodata 			& \nodata \\
7136 &  [Ar III]  					& 0.98$\pm$0.00\tablenotemark{a} & 1.00$\pm$0.00 & 1.00$\pm$0.05 			& 0.99$\pm$0.05 				& 1.00$\pm$0.11 			& 1.03$\pm$0.11 \\
% & & \multicolumn{2}{c}{NGC5315 Full} & \multicolumn{2}{c}{NGC5882 Full} & \multicolumn{2}{c}{NGC7662 Full}\\
%\cline{3-8}
% & & Gaussian & Gaussian With & Gaussian & Gaussian With & Gaussian & Gaussian With\\
%Wave & & & power-law & & power-law & & power-law \\ 
%\cline{3-8}
%(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\ 
%\tableline
9532 &  [S III]  					& 0.95$\pm$0.01\tablenotemark{a} & 0.95$\pm$0.01\tablenotemark{a} & 1.01$\pm$0.03 			& 1.01$\pm$0.03 				& 1.02$\pm$0.20 			& 1.03$\pm$0.20 \\
\tableline
\tablebreak
 & & \multicolumn{2}{c}{NGC7662 Full} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{}\\
\cline{3-8}
 & & Gaussian & Gaussian With \\
Wave  & & & power-law \\ 
\cline{3-8}
(\AA) & ID & Model/Observed & Model/Observed  \\ 
\tableline
1485 &  N IV] 				& 1.02$\pm$0.06 			& 1.02$\pm$0.06 \\
1549 & C IV 					& 0.93$\pm$0.04\tablenotemark{a} & 0.91$\pm$0.04\tablenotemark{a} \\
1750 & N III] 				& 1.00$\pm$0.24 			& 0.99$\pm$0.24 \\
1907 &  [C III]  				& 1.04$\pm$0.04 			& 1.04$\pm$0.04 \\
1909\tablenotemark{b} &  C III]  	& 1.06$\pm$0.05\tablenotemark{a} & 1.07$\pm$0.05\tablenotemark{a} \\
3727 & [O II] 				& 0.90$\pm$0.30 			& 0.90$\pm$0.30 \\
3869 &  [Ne III]  				& 1.00$\pm$0.03 			& 1.01$\pm$0.03 \\
4363\tablenotemark{b} &  [O III]  	& 0.91$\pm$0.06\tablenotemark{a} & 0.92$\pm$0.06\tablenotemark{a} \\
4686 &  He II  				& 1.04$\pm$0.02\tablenotemark{a} & 1.03$\pm$0.02\tablenotemark{a} \\
4861 &  H$\beta$  				& 0.97$\pm$0.01\tablenotemark{a} & 0.99$\pm$0.01 \\
4959\tablenotemark{b} &  [O III]  	& 1.07$\pm$0.01\tablenotemark{a} & 1.09$\pm$0.01\tablenotemark{a}\\
5007 &  [O III]  				& 0.98$\pm$0.01\tablenotemark{a} & 0.99$\pm$0.01 \\
5876 &  He I  				& 1.03$\pm$0.14 			& 1.02$\pm$0.14 \\
7136 &  [Ar III]  				& 1.00$\pm$0.12 			& 1.00$\pm$0.12 \\
% & & \multicolumn{2}{c}{NGC5315 Full} & \multicolumn{2}{c}{NGC5882 Full} & \multicolumn{2}{c}{NGC7662 Full}\\
%\cline{3-8}
% & & Gaussian & Gaussian With & Gaussian & Gaussian With & Gaussian & Gaussian With\\
%Wave & & & power-law & & power-law & & power-law \\ 
%\cline{3-8}
%(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\ 
%\tableline
9532 &  [S III]  				& 1.00$\pm$0.09 			& 1.01$\pm$0.09 \\
\enddata
\tablenotetext{a}{Modeled emission line intensity outside observed error bar.}
\tablenotetext{b}{This line was only included in a diagnostic for the rms calculation for reasons discussed in the text.}
\end{deluxetable}
\end{landscape}

Table~\ref{condenmods1} contains the best parameter values and associated errors for the constant density models.  Names of the stellar and nebular parameters that were used in the modeling are in the first column along with the values for each region in the subsequent columns. Below the modeling parameters are the nebular temperatures, densities, ionization correction factors, and rms values for each region. For most of the regions, the model rms is below the observed rms, implying a good fit. The smallest model rms of 0.0063 from the full region of IC 2165 shows that the assumed model represented that region's structure quite well. In most cases, the modeled temperatures and densities of the gas are within the observed errors. Also, the model abundances for the regions agree within error with the observed abundances in most cases. The asymmetry in the errors is due to the $1-\frac{model}{observed}$ term in the equation for the rms having a lower bound of 1. The errors in stellar temperature and luminosity and nebular abundances are inversely related to overall signal strength in the emission lines, where the larger error corresponds to overall weaker signal strength.
\begin{landscape}
\begin{deluxetable}{cccccc}
\tabletypesize{\footnotesize}
\tablewidth{0in}
%%%\rotate
\tablecaption{Constant Density Models\label{condenmods1}}
\tablehead{
\multicolumn{6}{c}{Constant Density Models}
}
\startdata
Parameter & IC2165 Full & IC2165 1 & IC2165 2 & IC2165 3 & IC2165 4 \\
\tableline
$T_{star}$ (kK) & 110.0$^{+7.0}_{-17.0}$ & 110.0 & 110.0 & 110.0& 110.0  \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & 3.17$^{+0.20}_{-0.14}$ & 3.17 & 3.17 & 3.17 & 3.17  \\
Distance (kpc) & 2.39$^{+0.36}_{-0.33}$ & 2.39 & 2.39 & 2.39 & 2.39 \\
$H_{den}$ (log[$H_{density}$]) & 3.79$^{+0.02}_{-0.03}$ & 3.75$^{+0.04}_{-0.04}$ & 4.06$^{+0.05}_{-0.07}$ & 3.70$^{+0.04}_{-0.04}$ & 3.75$^{+0.04}_{-0.05}$ \\
Inner Radius ($10^{-2}$pc) & 2.60$^{+0.06}_{-0.06}$ & 2.56$^{+0.11}_{-0.15}$ & 2.60$^{+0.05}_{-0.04}$ & 2.38$^{+0.15}_{-0.16}$ & 2.47$^{+0.13}_{-0.13}$ \\
Outer Radius ($10^{-2}$pc) & 3.09$^{+0.05}_{-0.05}$ & 3.09$^{+0.08}_{-0.07}$ & 2.73$^{+0.04}_{-0.05}$ & 3.11$^{+0.12}_{-0.11}$ & 2.96$^{+0.12}_{-0.12}$ \\
Filling Factor ($10^{-1}$) & 9.89$^{+0.11}_{-0.99}$ & 10.00$^{+0.00}_{-0.16}$ & 9.49$^{+0.51}_{-2.97}$ & 10.00$^{+0.00}_{-0.17}$ & 10.0$^{+0.00}_{-0.25}$ \\
He/H ($10^{-2}$) & 10.28$^{+1.41}_{-1.29}$ & 11.07$^{+2.58}_{-2.03}$ & 10.26$^{+4.20}_{-5.03}$ & 10.33$^{+2.55}_{-2.01}$ & 10.47$^{+3.33}_{-3.23}$ \\
C/H ($10^{-4}$) & 4.57$^{+2.41}_{-1.59}$ & 4.75$^{+5.55}_{-2.63}$ & 2.86$^{+5.15}_{-2.16}$ & 4.35$^{+4.78}_{-2.30}$ & 3.80$^{+5.97}_{-2.45}$ \\
N/H ($10^{-4}$) & 1.10$^{+0.43}_{-0.43}$ & 0.78$^{+0.56}_{-0.55}$ & 1.38$^{+1.52}_{-1.35}$ & 0.94$^{+0.34}_{-0.66}$ & 0.95$^{+0.91}_{-0.87}$ \\
O/H ($10^{-4}$) & 2.69$^{+0.91}_{-0.80}$ & 2.89$^{+1.95}_{-1.49}$ & 1.75$^{+1.80}_{-1.38}$ & 2.68$^{+1.89}_{-1.42}$ & 2.82$^{+2.43}_{-1.84}$ \\
Ne/H ($10^{-5}$) & 3.39$^{+1.32}_{-1.31}$ & 3.70$^{+2.70}_{-2.63}$ & 2.10$^{+2.14}_{-2.06}$ & 2.98$^{+2.15}_{-2.07}$ & 2.90$^{+2.72}_{-2.65}$ \\
S/H ($10^{-6}$) & 3.73$^{+1.42}_{-1.44}$ & 3.56$^{+2.53}_{-2.50}$ & 2.15$^{+2.11}_{-2.11}$ & 5.19$^{+3.72}_{-3.57}$ & 4.44$^{+4.08}_{-4.02}$ \\
Ar/H ($10^{-7}$) & 20.09$^{+7.58}_{-7.76}$ & 24.89$^{+17.77}_{-17.48}$ & 9.86$^{+9.86}_{-9.68}$ & 26.06$^{+17.6}_{-18.12}$ & 24.66$^{+22.65}_{-22.47}$ \\
\tableline
[O III] $T_{e}$ (K) & 13500 & 13900 & 14800 & 13700 & 14100 \\
\[[S II] N$_{e}$($cm^{-3}$) & 7900 & \nodata & \nodata & \nodata & \nodata \\
C III] $N_{e}$ ($cm^{-3}$) & 7200 & 6600 & 14000 & 5800 & 6700 \\
icf (O)  & 1.55 & 1.54 & 1.53 & 1.82 & 1.92 \\
icf (Ar)  & 1.30 & 1.30 & 1.25 & 1.36 & 1.37 \\
icf (Ne)  & 1.22 & 1.21 & 1.18 & 1.38 & 1.41 \\
icf (S)  & 4.30 & 4.43 & 3.30 & 6.07 & 5.98 \\
Model RMS ($10^{-2}$)  & 0.63 & 4.00 & 7.00 & 2.13 & 6.86 \\
Observed RMS ($10^{-2}$)  & 9.35 & 14.53 & 19.35 & 15.8 & 17.69\\
\tableline
\tablebreak
%\\
Parameter & IC2165 5 & IC2165 6 & IC3568 Full & IC3568 1 & IC3568 2 \\
\tableline
$T_{star}$ (kK) & 110.0 & 110.0 & 69.6$^{+15.0}_{-18.3}$ & 69.6 & 69.6 \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & 3.17 & 3.17 & 3.52$^{+0.74}_{-0.38}$ & 3.52 & 3.52 \\
Distance (kpc) & 2.39 & 2.39 & 2.29$^{+1.26}_{-0.67}$ & 2.29 & 2.29 \\
$H_{den}$ (log[$H_{density}$]) & 3.62$^{+0.03}_{-0.03}$ & 3.99$^{+0.09}_{-0.18}$ & 3.70$^{+0.05}_{-0.05}$ & 3.76$^{+0.06}_{-0.08}$ & 3.59$^{+0.06}_{-0.08}$ \\
Inner Radius ($10^{-2}$pc) & 1.80$^{+0.24}_{-0.37}$ & 3.15$^{+0.23}_{-0.91}$ & 3.55$^{+0.08}_{-0.09}$ & 3.44$^{+0.09}_{-0.09}$ & 3.97$^{+0.21}_{-0.20}$ \\
Outer Radius ($10^{-2}$pc) & 3.32$^{+0.12}_{-0.11}$ & 3.57$^{+0.06}_{-0.07}$ & 3.93$^{+0.09}_{-0.08}$ & 3.74$^{+0.10}_{-0.10}$ & 4.66$^{+0.24}_{-0.23}$ \\
Filling Factor ($10^{-1}$) & 9.92$^{+0.08}_{-1.32}$ & 9.64$^{+0.36}_{-5.54}$ & 10.00$^{+0.00}_{-2.20}$ & 9.88$^{+0.12}_{-3.03}$ & 9.96$^{+0.04}_{-3.16}$ \\
He/H ($10^{-2}$) & 9.18$^{+1.78}_{-1.42}$ & 7.59$^{+9.40}_{-7.59}$ & 9.71$^{+4.42}_{-4.46}$ & 10.89$^{+6.89}_{-7.34}$ & 8.53$^{+5.59}_{-5.58}$ \\
C/H ($10^{-4}$) & 5.85$^{+5.63}_{-2.83}$ & 38.73$^{+212.46}_{-28.25}$ & 5.47$^{+2.85}_{-2.38}$ & 2.85$^{+2.05}_{-1.73}$ & 7.08$^{+5.51}_{-4.13}$ \\
N/H ($10^{-4}$) & 0.81$^{+0.54}_{-0.50}$ & 0.89$^{+105.96}_{-0.89}$ & \nodata & \nodata & \nodata \\
O/H ($10^{-4}$) & 2.54$^{+1.54}_{-1.19}$ & 5.31$^{+12.47}_{-4.71}$ & 4.72$^{+1.30}_{-0.92}$ & 4.25$^{+1.78}_{-1.01}$ & 5.02$^{+2.23}_{-1.21}$ \\
Ne/H ($10^{-5}$) & 4.27$^{+2.81}_{-2.64}$ & 10.94$^{+20.68}_{-10.94}$ & 8.05$^{+4.83}_{-4.34}$ & 2.02$^{+1.69}_{-1.57}$ & 9.14$^{+8.24}_{-6.90}$ \\
S/H ($10^{-6}$) & 5.05$^{+3.27}_{-3.10}$ & 2.30$^{+3.73}_{-2.30}$ & \nodata & \nodata & \nodata \\
Ar/H ($10^{-7}$) & 20.84$^{+6.07}_{-12.72}$ & 12.25$^{+20.11}_{-12.25}$ & 17.22$^{+9.39}_{-9.46}$ & 16.33$^{+13.18}_{-12.70}$ & 15.89$^{+12.95}_{-12.50}$ \\
\tableline
[O III] $T_{e}$ (K) & 12800 & 9500 & 10000 & 10800 & 9600 \\
C III] $N_{e}$ ($cm^{-3}$) & 4600 & 11100 & 5600 & 6500 & 4200 \\
icf (O)  & 1.31 & 1.02 & 1.07 & 1.08 & 1.07 \\
icf (Ar)  & 1.28 & 1.05 & 1.28 & 1.25 & 1.28 \\
icf (Ne)  & 1.10 & 0.91 & 0.94 & 0.94 & 0.93 \\
icf (S)  & 4.41 & 1.52 & \nodata & \nodata & \nodata \\
Model RMS ($10^{-2}$)  & 5.09 & 7.93 & 1.70 & 4.42 & 2.04 \\
Observed RMS ($10^{-2}$)  & 11.40 & 32.67 & 13.39 & 17.49 & 19.79 \\
\tableline
\tablebreak
%\\
Parameter & IC3568 3 & NGC2440 Full & NGC2440 1 & NGC2440 2 & NGC2440 3 \\
\tableline
$T_{star}$ (kK) & 69.6 & 169.8$^{+20.2}_{-17.7}$ & 169.8 & 169.8 & 169.8 \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & 3.52 & 2.74$^{+0.04}_{-0.04}$ & 2.74 & 2.74 & 2.74 \\
Distance (kpc) & 2.29 & 1.63$^{+0.14}_{-0.13}$ & 1.63 & 1.63 & 1.63 \\
$H_{den}$ (log[$H_{density}$]) & 3.77$^{+0.11}_{-0.25}$ & 3.69$^{+0.02}_{-0.02}$ & 3.40$^{+0.03}_{-0.03}$ & 3.95$^{+0.08}_{-0.15}$ & 3.80$^{+0.03}_{-0.03}$ \\
Inner Radius ($10^{-2}$pc) & 3.83$^{+0.14}_{-3.83}$ & 2.30$^{+0.70}_{-1.20}$ & 3.86$^{+0.94}_{-1.06}$ & 2.46$^{+0.36}_{-0.86}$ & 2.28$^{+0.58}_{-0.78}$ \\
Outer Radius ($10^{-2}$pc) & 4.01$^{+0.10}_{-0.12}$ & 5.14$^{+0.12}_{-0.14}$ & 7.54$^{+0.50}_{-0.45}$ & 2.93$^{+0.12}_{-0.15}$ & 4.13$^{+0.16}_{-0.18}$ \\
Filling Factor ($10^{-1}$) & 10.00$^{+0.00}_{-7.00}$ & 1.76$^{+0.14}_{-0.16}$ & 3.01$^{+0.48}_{-0.44}$ & 2.42$^{+1.25}_{-1.40}$ & 2.09$^{+0.26}_{-0.30}$ \\
He/H ($10^{-2}$) & 9.73$^{+12.15}_{-9.73}$ & 12.27$^{+1.85}_{-2.04}$ & 14.93$^{+3.44}_{-3.34}$ & 12.25$^{+19.38}_{-5.94}$ & 11.40$^{+2.72}_{-2.69}$ \\
C/H ($10^{-4}$) & 24.89$^{+56.39}_{-24.89}$ & 2.54$^{+1.26}_{-1.06}$ & 3.56$^{+3.36}_{-2.33}$ & 1.08$^{+2.90}_{-1.08}$ & 2.45$^{+2.33}_{-1.62}$ \\
N/H ($10^{-4}$) & \nodata & 6.71$^{+2.00}_{-1.93}$ & 8.71$^{+4.78}_{-3.81}$ & 3.41$^{+4.91}_{-3.41}$ & 6.34$^{+3.43}_{-2.95}$ \\
O/H ($10^{-4}$) & 7.96$^{+31.85}_{-4.65}$ & 2.90$^{+0.77}_{-0.72}$ & 4.06$^{+2.10}_{-1.49}$ & 1.07$^{+1.22}_{-1.07}$ & 2.53$^{+1.10}_{-0.98}$ \\
Ne/H ($10^{-5}$) & 11.53$^{+25.62}_{-11.53}$ & 4.02$^{+1.61}_{-1.62}$ & 7.50$^{+5.38}_{-4.87}$ & 0.92$^{+1.71}_{-0.92}$ & 3.16$^{+2.09}_{-1.98}$ \\
S/H ($10^{-6}$) & \nodata & 1.64$^{+0.65}_{-0.64}$ & 2.09$^{+1.38}_{-1.33}$ & 0.59$^{+1.07}_{-0.59}$ & 1.37$^{+0.86}_{-0.85}$ \\
Ar/H ($10^{-7}$) & 24.38$^{+41.69}_{-24.38}$ & 14.96$^{+6.17}_{-5.84}$ & 23.44$^{+15.46}_{-14.93}$ & 7.59$^{+13.79}_{-7.59}$ & 12.79$^{+8.10}_{-8.01}$ \\
\[O III] $T_{e}$ (K) & 8800 & 14400 & 13300 & 16900 & 14600 \\
\[[S II] N$_{e}$($cm^{-3}$) & \nodata & 6400 & 3400 & \nodata & 8200 \\
C III] $N_{e}$ ($cm^{-3}$) & 6700 & 5800 & 2800 & 11300 & 7600 \\
icf (O)  & 1.08 & 1.60 & 1.46 & 2.05 & 1.54 \\
icf (Ar)  & 1.26 & 1.21 & 1.24 & 1.39 & 1.20 \\
icf (Ne)  & 0.95 & 1.46 & 1.45 & 0.17 & 1.39 \\
icf (S)  & \nodata & 1.83 & 1.66 & 2.53 & 1.80 \\
Model RMS ($10^{-2}$)  & 1.00 & 1.49 & 8.45 & 9.20 & 6.97 \\
Observed RMS ($10^{-2}$)  & 49.97 & 7.44 & 8.35 & 35.57 & 8.75 \\
\tableline
\tablebreak
%\\
 & NGC3242 Full & NGC3242 1 & NGC3242 2 & NGC3242 3 & NGC3242 4 \\
\tableline
$T_{star}$ (kK) & $89.7^{+7.3}_{-4.7}$ & $89.7$ & $89.7$ & $89.7$ & $89.7$  \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & $3.36^{+0.28}_{-0.22}$ & $3.36$ & $3.36$ & $3.36$ & $3.36$  \\
Distance (kpc) & 0.84$^{+0.15}_{-0.32}$ & 0.84 & 0.84 & 0.84 & 0.84 \\
$H_{den}$ (log[$H_{density}$]) & 3.62$^{+0.04}_{-0.06}$ & 3.25$^{+0.06}_{-0.06}$ & 3.77$^{+0.04}_{-0.03}$ & 3.50$^{+0.06}_{-0.07}$ & 3.50$^{+0.06}_{-0.07}$ \\
Inner Radius ($10^{-2}$pc) & 1.86$^{+0.74}_{-1.86}$ & 2.04$^{+1.36}_{-2.04}$ & 3.33$^{+0.12}_{-0.16}$ & 2.52$^{+0.48}_{-0.82}$ & 1.96$^{+0.74}_{-1.96}$ \\
Outer Radius ($10^{-2}$pc) & 3.80$^{+0.30}_{-0.30}$ & 10.50$^{+2.90}_{-2.40}$ & 3.90$^{+0.13}_{-0.09}$ & 4.59$^{+0.81}_{-0.59}$ & 10.20$^{+2.60}_{-2.10}$ \\
Filling Factor ($10^{-1}$) & 4.36$^{+1.14}_{-1.06}$ & 4.39$^{+1.31}_{-1.19}$ & 4.80$^{+1.00}_{-0.90}$ & 5.93$^{+1.77}_{-1.63}$ & 1.56$^{+0.54}_{-0.46}$ \\
He/H ($10^{-2}$) & 10.45$^{+4.34}_{-3.03}$ & 11.53$^{+4.34}_{-3.38}$ & 11.02$^{+3.11}_{-2.31}$ & 10.30$^{+4.15}_{-3.39}$ & 9.57$^{+4.23}_{-3.95}$ \\
C/H ($10^{-4}$) & 5.97$^{+7.52}_{-3.73}$ & 4.85$^{+4.92}_{-3.50}$ & 3.67$^{+2.35}_{-1.89}$ & 5.01$^{+5.46}_{-3.19}$ & 4.10$^{+4.03}_{-2.32}$ \\
O/H ($10^{-4}$) & 4.70$^{+2.71}_{-1.81}$ & 4.26$^{+2.35}_{-1.30}$ & 3.76$^{+1.25}_{-0.94}$ & 3.76$^{+2.41}_{-1.57}$ & 4.21$^{+2.55}_{-1.58}$ \\
Ne/H ($10^{-5}$) & 7.40$^{+6.73}_{-6.24}$ & 7.78$^{+7.36}_{-6.37}$ & 6.40$^{+3.60}_{-3.24}$ & 6.19$^{+5.03}_{-4.72}$ & 6.90$^{+5.40}_{-5.04}$ \\
\tableline
[O III] $T_{e}$ (K) & 11800 & 11100 & 11600 & 11800 & 11800 \\
C III] $N_{e}$ ($cm^{-3}$) & 4600 & 1500 & 6800 & 3500 & 3600 \\
icf (O)  & 1.57 & 1.13 & 1.22 & 1.56 & 1.51 \\
icf (Ne)  & 1.24 & 1.00 & 1.03 & 1.18 & 1.18 \\
Model RMS ($10^{-2}$)  & 6.26 & 2.40 & 3.75 & 4.46 & 1.63 \\
Observed RMS ($10^{-2}$)  & 15.02 & 20.91 & 10.68 & 17.06 & 18.57 \\
\tableline
\tablebreak
Parameter & NGC3242 5 & NGC3242 6 & NGC3242 7 & NGC3242 8 & NGC3242 9 \\
\tableline
$T_{star}$ (kK) & $89.7$ & $89.7$ & $89.7$ & $89.7$ & $89.7$  \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & $3.36$ & $3.36$ & $3.36$ & $3.36$ & $3.36$  \\
Distance (kpc) & 0.84 & 0.84 & 0.84 & 0.84 & 0.84 \\
$H_{den}$ (log[$H_{density}$]) & 3.60$^{+0.05}_{-0.06}$ & 3.60$^{+0.05}_{-0.06}$ & 3.90$^{+0.04}_{-0.04}$ & 3.55$^{+0.05}_{-0.06}$ & 3.25$^{+0.06}_{-0.07}$ \\
Inner Radius ($10^{-2}$pc) & 2.52$^{+0.48}_{-0.32}$ & 1.88$^{+0.52}_{-1.88}$ & 2.02$^{+0.08}_{-0.12}$ & 2.98$^{+0.22}_{-0.28}$ & 3.56$^{+0.84}_{-3.56}$ \\
Outer Radius ($10^{-2}$pc) & 4.21$^{+0.69}_{-0.41}$ & 6.49$^{+1.31}_{-0.96}$ & 2.52$^{+0.08}_{-0.12}$ & 3.72$^{+0.28}_{-0.22}$ & 8.40$^{+1.90}_{-1.50}$ \\
Filling Factor ($10^{-1}$) & 3.77$^{+1.03}_{-0.97}$ & 1.52$^{+0.48}_{-0.42}$ & 4.53$^{+0.87}_{-0.83}$ & 1.00$^{+0.00}_{-0.27}$ & 4.34$^{+1.36}_{-1.34}$ \\
He/H ($10^{-2}$) & 10.12$^{+3.69}_{-2.87}$ & 9.20$^{+3.68}_{-3.32}$ & 9.29$^{+2.19}_{-1.88}$ & 7.69$^{+2.78}_{-2.56}$ & 10.50$^{+4.64}_{-4.04}$ \\
C/H ($10^{-4}$) & 6.30$^{+6.29}_{-2.39}$ & 5.60$^{+5.12}_{-3.09}$ & 4.47$^{+4.04}_{-2.65}$ & 3.51$^{+3.91}_{-2.36}$ & 4.81$^{+5.19}_{-3.15}$ \\
O/H ($10^{-4}$) & 5.30$^{+2.65}_{-1.75}$ & 5.08$^{+2.68}_{-1.84}$ & 3.77$^{+1.60}_{-1.14}$ & 3.30$^{+1.94}_{-1.35}$ & 4.54$^{+2.38}_{-1.59}$ \\
Ne/H ($10^{-5}$) & 7.93$^{+6.20}_{-5.74}$ & 8.07$^{+6.38}_{-5.67}$ & 5.85$^{+3.92}_{-3.71}$ & 5.48$^{+4.52}_{-4.10}$ & 7.38$^{+6.42}_{-5.72}$ \\
\tableline
[O III] $T_{e}$ (K)  & 11500 & 11700 & 11700 & 11900 & 11500 \\
C III] $N_{e}$ ($cm^{-3}$) & 4500 & 4400 & 9200 & 3900 & 1600 \\
icf (O)  & 1.54 & 1.74 & 1.35 & 1.46 & 1.46 \\
icf (Ne)  & 1.19 & 1.30 & 1.09 & 1.07 & 1.16 \\
Model RMS ($10^{-2}$)  & 4.03 & 1.67 & 2.63 & 9.90 & 3.22 \\
Observed RMS ($10^{-2}$)  & 16.46 & 17.63 & 15.16 & 13.12 & 18.50 \\
\tableline
\tablebreak
Parameter & NGC5315 Full & NGC5315 1 & NGC5315 2 & NGC5315 3 & NGC5315 4 \\
\tableline
$T_{star}$ (kK) & 69.9$^{+6.5}_{-2.1}$ &  69.9 &  69.9 &  69.9 &  69.9 \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & 4.89$^{+0.16}_{-0.15}$ & 4.89 & 4.89 & 4.89 & 4.89 \\
Distance (kpc) & 2.02$^{+0.07}_{-0.08}$ & 2.02 & 2.02 & 2.02 & 2.02 \\
$H_{den}$ (log[$H_{density}$]) & 4.71$^{+0.02}_{-0.02}$ & 4.76$^{+0.04}_{-0.05}$ & 4.72$^{+0.02}_{-0.02}$ & 4.71$^{+0.03}_{-0.03}$ & 4.53$^{+0.06}_{-0.09}$ \\
Inner Radius ($10^{-2}$pc) & 1.31$^{+0.01}_{-0.01}$ & 1.56$^{+0.03}_{-0.04}$ & 1.88$^{+0.01}_{-0.01}$ & 2.13$^{+0.01}_{-0.01}$ & 1.89$^{+0.25}_{-0.72}$ \\
Outer Radius ($10^{-2}$pc) & 1.46$^{+0.01}_{-0.01}$ & 1.63$^{+0.02}_{-0.02}$ & 1.98$^{+0.01}_{-0.01}$ & 2.15$^{+0.01}_{-0.01}$ & 2.33$^{+0.09}_{-0.11}$ \\
Filling Factor ($10^{-1}$) & 9.59$^{+0.41}_{-0.71}$ & 2.39$^{+0.58}_{-0.60}$ & 9.43$^{+0.57}_{-0.63}$ & 8.77$^{+1.23}_{-1.41}$ & 0.45$^{+0.18}_{-0.18}$ \\
He/H ($10^{-2}$) & 11.40$^{+1.78}_{-2.07}$ & 11.99$^{+5.38}_{-5.98}$ & 13.21$^{+2.28}_{-2.25}$ & 16.29$^{+4.60}_{-4.81}$ & 16.48$^{+10.43}_{-11.80}$ \\
C/H ($10^{-4}$) & 16.44$^{+3.51}_{-2.64}$ & 19.82$^{+11.09}_{-10.04}$ & 9.77$^{+1.71}_{-1.64}$ & 14.49$^{+5.01}_{-4.72}$ & 100.69$^{+50.66}_{-63.54}$ \\
%N/H ($10^{-5}$) & 5.74$^{+}_{-}$ & 2.12$^{+}_{-}$ & 11.89$^{+}_{-}$ & 11.91$^{+}_{-}$ & 1.87$^{+}_{-}$ \\
O/H ($10^{-4}$) & 6.31$^{+1.10}_{-0.81}$ & 6.81$^{+3.91}_{-2.24}$ & 7.46$^{+1.05}_{-0.86}$ & 9.93$^{+2.95}_{-1.80}$ & 15.31$^{+14.89}_{-6.40}$ \\
Ne/H ($10^{-5}$) & 14.59$^{+3.61}_{-3.37}$ & 10.79$^{+7.83}_{-7.07}$ & 18.24$^{+4.67}_{-4.11}$ & 18.97$^{+9.22}_{-8.25}$ & 3.33$^{+4.44}_{-3.04}$ \\
S/H ($10^{-6}$) & 421.70$^{+35.39}_{-32.65}$ & 287.08$^{+101.97}_{-82.90}$ & 248.89$^{+26.54}_{-25.01}$ & 245.47$^{+56.52}_{-41.30}$ & 314.05$^{+132.63}_{-95.27}$ \\
Ar/H ($10^{-7}$) & 954.99$^{+219.90}_{-196.42}$ & 743.02$^{+487.25}_{-447.90}$ & 603.95$^{+137.36}_{-136.21}$ & 623.73$^{+267.52}_{-252.20}$ & 961.61$^{+1033.65}_{-936.49}$ \\
\tableline
[O III] $T_{e}$ (K) & 8800 & 9600 & 8900 & 8600 & 7500 \\
\[[S II] N$_{e}$($cm^{-3}$) & 20000\tablenotemark{a} & 20000\tablenotemark{a} & \nodata & 20000\tablenotemark{a} & 20000\tablenotemark{a} \\
C III] $N_{e}$ ($cm^{-3}$) & 64000 & 73400 & 66300 & 67200 & 45400 \\
icf (O)  & 1.36 & 1.70 & 1.31 & 1.50 & 1.55 \\
icf (Ar)  & 1.96 & 2.23 & 1.85 & 2.03 & 1.52 \\
icf (Ne)  & 1.21 & 1.46 & 1.18 & 1.34 & 1.35 \\
icf (S)  & 47.27 & 38.16 & 21.26 & 20.11 & 29.07 \\
Model RMS ($10^{-2}$)  & 2.23 & 0.93 & 3.16 & 5.19 & 3.80 \\
Observed RMS ($10^{-2}$)  & 3.90 & 16.53 & 3.53 & 7.06 & 23.73 \\
\tableline
\tablebreak
%\\
Parameter & NGC5882 Full & NGC5882 1 & NGC5882 2 & NGC5882 3 & \\
\tableline
$T_{star}$ (kK) & 78.7$^{+3.3}_{-7.0}$ & 78.7 & 78.7 & 78.7 & \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & 3.45$^{+0.20}_{-0.14}$ & 3.45 & 3.45 & 3.45 & \\
Distance (kpc) & 1.81$^{+0.60}_{-0.82}$ & 1.81 & 1.81 & 1.81 & \\
$H_{den}$ (log[$H_{density}$]) & 4.34$^{+0.05}_{-0.06}$ & 4.35$^{+0.05}_{-0.07}$ & 4.35$^{+0.04}_{-0.06}$ & 4.35$^{+0.06}_{-0.15}$ & \\
Inner Radius ($10^{-2}$pc) & 2.72$^{+0.03}_{-0.03}$ & 2.75$^{+0.03}_{-0.03}$ & 2.71$^{+0.03}_{-0.03}$ & 2.25$^{+0.63}_{-0.76}$ & \\
Outer Radius ($10^{-2}$pc) & 2.81$^{+0.03}_{-0.03}$ & 2.83$^{+0.03}_{-0.03}$ & 2.80$^{+0.03}_{-0.03}$ & 2.96$^{+0.08}_{-0.10}$ & \\
Filling Factor ($10^{-1}$) & 3.47$^{+0.94}_{-0.87}$ & 2.47$^{+0.76}_{-0.72}$ & 3.14$^{+0.78}_{-0.76}$ & 2.91$^{+0.95}_{-1.49}$ & \\
He/H ($10^{-2}$) & 12.59$^{+6.71}_{-5.39}$ & 12.19$^{+7.76}_{-6.02}$ & 12.97$^{+6.53}_{-5.39}$ & 11.35$^{+13.77}_{-11.35}$ & \\
C/H ($10^{-4}$) & 4.19$^{+3.72}_{-3.34}$ & 2.37$^{+1.90}_{-1.73}$ & 6.30$^{+3.70}_{-3.66}$ & 9.33$^{+16.37}_{-9.33}$ & \\
N/H ($10^{-4}$) & 2.89$^{+2.76}_{-2.78}$ & 4.28$^{+3.67}_{-3.65}$ & 1.43$^{+0.97}_{-1.01}$ & 1.48$^{+2.41}_{-1.48}$ & \\
O/H ($10^{-4}$) & 12.82$^{+6.13}_{-3.15}$ & 11.86$^{+6.34}_{-2.95}$ & 13.77$^{+5.28}_{-2.81}$ & 16.14$^{+31.72}_{-5.18}$ & \\
Ne/H ($10^{-5}$) & 23.23$^{+24.78}_{-19.43}$ & 19.05$^{+19.85}_{-15.16}$ & 29.04$^{+22.25}_{-18.08}$ & 3.08$^{+7.16}_{-3.08}$ & \\
S/H ($10^{-6}$) & 7.85$^{+6.94}_{-5.82}$ & 8.30$^{+7.55}_{-6.92}$ & 7.33$^{+4.97}_{-5.09}$ & 7.36$^{+12.14}_{-7.36}$ & \\
Ar/H ($10^{-7}$) & 38.90$^{+35.19}_{-35.04}$ & 36.81$^{+33.98}_{-31.32}$ & 40.46$^{+27.15}_{-28.71}$ & 40.64$^{+65.51}_{-40.64}$ & \\
\tableline
[O III] $T_{e}$ (K) & 8400 & 8600 & 8200 & 7700 & \\
\[[S II] N$_{e}$($cm^{-3}$) & 20000\tablenotemark{a} & 20000\tablenotemark{a} & 20000\tablenotemark{a} & 20000\tablenotemark{a} & \\
C III] $N_{e}$ ($cm^{-3}$) & 26700 & \nodata & \nodata & \nodata & \\
icf (O)  & 1.12 & 1.12 & 1.13 & 1.10 & \\
icf (Ar)  & 1.18 & 1.17 & 1.19 & 1.10 & \\
icf (Ne)  & 0.98 & 0.99 & 0.99 & 0.97 & \\
icf (S)  & 1.89 & 1.86 & 1.88 & 1.58 & \\
Model RMS ($10^{-2}$)  & 5.58 & 7.60 & 9.20 & 7.50 & \\
Observed RMS ($10^{-2}$)  & 14.20 & 16.48 & 11.56 & 41.36 & \\
\tableline
\tablebreak
%\\
Parameter & NGC7662 Full & NGC7662 1 & NGC7662 2 & NGC7662 3 & NGC7662 4 \\ 
\tableline
$T_{star}$ (kK) & 109.9$^{+9.1}_{-5.9}$ & 109.9 & 109.9 & 109.9 & 109.9 \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & 3.24$^{+0.18}_{-0.14}$ & 3.24 & 3.24 & 3.24 & 3.24 \\
Distance (kpc) & 1.02$^{+0.15}_{-0.22}$ & 1.02 & 1.02 & 1.02 & 1.02 \\
$H_{den}$ (log[$H_{density}$]) & 3.42$^{+0.04}_{-0.04}$ & 3.54$^{+0.04}_{-0.04}$ & 3.70$^{+0.05}_{-0.08}$ & 3.60$^{+0.04}_{-0.04}$ & 3.32$^{+0.06}_{-0.08}$ \\
Inner Radius ($10^{-2}$pc) & 3.42$^{+0.36}_{-0.63}$ & 4.69$^{+0.11}_{-0.09}$ & 4.24$^{+0.10}_{-0.08}$ & 3.81$^{+0.06}_{-0.09}$ & 3.34$^{+0.54}_{-3.34}$ \\
Outer Radius ($10^{-2}$pc) & 5.28$^{+0.36}_{-0.34}$ & 5.47$^{+0.19}_{-0.18}$ & 4.55$^{+0.13}_{-0.12}$ & 4.37$^{+0.16}_{-0.15}$ & 8.49$^{+1.61}_{-1.69}$ \\
Filling Factor ($10^{-1}$) & 10.00$^{+0.00}_{-1.80}$ & 9.40$^{+0.60}_{-1.80}$ & 10.00$^{+0.00}_{-3.38}$ & 10.00$^{+0.00}_{-1.87}$ & 10.00$^{+0.00}_{-3.1}$ \\
He/H ($10^{-2}$) & 9.53$^{+2.77}_{-2.61}$ & 9.10$^{+8.28}_{-4.83}$ & 10.35$^{+4.78}_{-4.98}$ & 8.32$^{+5.49}_{-3.75}$ & 5.02$^{+3.29}_{-3.54}$ \\
C/H ($10^{-4}$) & 5.94$^{+5.81}_{-2.99}$ & 4.86$^{+2.90}_{-2.05}$ & 3.66$^{+5.25}_{-2.79}$ & 4.89$^{+3.15}_{-3.55}$ & 3.19$^{+5.13}_{-2.12}$ \\
N/H ($10^{-4}$) & 0.77$^{+0.44}_{-0.41}$ & 0.75$^{+0.40}_{-0.39}$ & 0.77$^{+0.82}_{-0.77}$ & 0.85$^{+0.50}_{-0.46}$ & 0.38$^{+0.45}_{-0.38}$ \\
O/H ($10^{-4}$) & 4.11$^{+1.78}_{-1.48}$ & 4.10$^{+1.15}_{-0.94}$ & 3.62$^{+2.69}_{-1.80}$ & 4.63$^{+1.39}_{-1.17}$ & 2.70$^{+2.67}_{-1.83}$ \\
Ne/H ($10^{-5}$) & 6.85$^{+5.73}_{-5.16}$ & 7.52$^{+3.97}_{-3.80}$ & 5.42$^{+6.33}_{-5.42}$ & 6.17$^{+3.38}_{-3.28}$ & 4.60$^{+5.17}_{-4.60}$ \\
S/H ($10^{-6}$) & 3.54$^{+2.77}_{-2.69}$ & 2.29$^{+1.18}_{-1.17}$ & 3.56$^{+3.67}_{-3.56}$ & 3.46$^{+1.79}_{-1.87}$ & 1.81$^{+2.17}_{-1.81}$ \\
Ar/H ($10^{-7}$) & 25.18$^{+19.49}_{-19.15}$ & 16.94$^{+8.76}_{-8.63}$ & 18.58$^{+19.44}_{-18.58}$ & 28.64$^{+15.10}_{-15.46}$ & 10.47$^{+12.44}_{-10.47}$ \\
\tableline
[O III] $T_{e}$ (K) & 12200 & 12300 & 13100 & 12600 & 13400\\
C III] $N_{e}$ ($cm^{-3}$) & 2800 & 3800 & 5800 & 4400 & 1900\\
icf (O)  & 1.62 & 1.39 & 1.43 & 1.78 & 1.74\\
icf (Ar)  & 1.36 & 1.27 & 1.26 & 1.38 & 1.29 \\
icf (Ne)  & 1.27 & 1.11 & 1.12 & 1.31 & 1.35\\
icf (S)  & 4.83 & 3.03 & 3.01 & 4.28 & 3.48 \\
Model RMS ($10^{-2}$)  & 4.67 & 3.17 & 10.99 & 4.95 & 18.65 \\
Observed RMS ($10^{-2}$)  & 12.42 & 10.17 & 17.98 & 9.55 & 12.60 \\
\tableline
\tablebreak
%\\
Parameter & NGC7662 5 & NGC7662 6 & NGC7662 7 & NGC7662 8 & \\
\tableline
$T_{star}$ (kK) & 109.9 & 109.9 & 109.9 & 109.9 & \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & 3.24 & 3.24 & 3.24 & 3.24 & \\
Distance (kpc) & 1.02 & 1.02 & 1.02 & 1.02 & \\
$H_{den}$ (log[$H_{density}$]) & 3.34$^{+0.05}_{-0.07}$ & 3.54$^{+0.03}_{-0.03}$ & 3.37$^{+0.04}_{-0.04}$ & 3.42$^{+0.05}_{-0.07}$ & \\
Inner Radius ($10^{-2}$pc) & 3.05$^{+0.64}_{-3.05}$ & 3.33$^{+0.10}_{-0.08}$ & 1.84$^{+0.76}_{-1.84}$ & 3.70$^{+0.25}_{-0.17}$ & \\
Outer Radius ($10^{-2}$pc) & 7.53$^{+1.11}_{-1.34}$ & 4.86$^{+0.22}_{-0.21}$ & 5.45$^{+0.55}_{-0.61}$ & 5.22$^{+0.56}_{-0.45}$ & \\
Filling Factor ($10^{-1}$) & 10.00$^{+0.00}_{-2.94}$ & 10.00$^{+0.00}_{-1.25}$ & 10.00$^{+0.00}_{-1.80}$ & 10.00$^{+0.00}_{-2.59}$ & \\
He/H ($10^{-2}$) & 6.46$^{+4.01}_{-3.83}$ & 8.83$^{+1.88}_{-1.75}$ & 12.05$^{+3.44}_{-2.72}$ & 4.89$^{+4.23}_{-2.54}$ & \\
C/H ($10^{-4}$) & 3.77$^{+5.35}_{-2.25}$ & 4.56$^{+2.36}_{-1.61}$ & 5.48$^{+6.82}_{-3.19}$ & 4.28$^{+3.85}_{-2.04}$ & \\
N/H ($10^{-4}$) & 0.51$^{+0.38}_{-0.37}$ & 0.55$^{+0.25}_{-0.24}$ & 0.56$^{+0.54}_{-0.27}$ & 0.55$^{+0.37}_{-0.33}$ & \\
O/H ($10^{-4}$) & 2.82$^{+2.42}_{-1.62}$ & 3.56$^{+1.11}_{-0.93}$ & 3.44$^{+1.93}_{-1.53}$ & 3.18$^{+1.60}_{-1.18}$ & \\
Ne/H ($10^{-5}$) & 4.70$^{+5.53}_{-4.70}$ & 5.25$^{+2.51}_{-2.30}$ & 6.34$^{+3.48}_{-5.31}$ & 6.27$^{+4.45}_{-4.03}$ & \\
S/H ($10^{-6}$) & 2.32$^{+2.58}_{-2.32}$ & 2.54$^{+1.18}_{-1.12}$ & 3.12$^{+2.91}_{-2.72}$ & 2.05 & \\
Ar/H ($10^{-7}$) & 13.87$^{+14.97}_{-13.87}$ & 18.11$^{+8.19}_{-7.88}$ & 23.50$^{+22.21}_{-20.68}$ & 14.72 & \\
\tableline
[O III] $T_{e}$ (K) & 13100 & 12800 & 12400 & 13300 & \\
C III] $N_{e}$ ($cm^{-3}$) & 2100 & 3700 & 2500 & 2600 & \\
icf (O)  & 1.72 & 1.62 & 1.35 & 1.67 & \\
icf (Ar)  & 1.30 & 1.32 & 1.33 & 1.47 & \\
icf (Ne)  & 1.34 & 1.26 & 1.10 & 1.59 & \\
icf (S)  & 3.96 & 4.46 & 5.21 & 5.51 & \\
Model RMS ($10^{-2}$)  & 14.78 & 3.41 & 7.16 & 11.80 & \\
Observed RMS ($10^{-2}$)  & 13.29 & 7.61 & 13.83 & 9.35 & 
\enddata
\tablenotetext{a}{High Density Limit Default.}
\end{deluxetable}
\end{landscape}

As stated in the previous chapter, ionization correction factors account for the unseen ionization states when calculating elemental abundances. Therefore, it is important to have accurate ICFs whenever they are used. From the models, an exact ICF can be determined since the elemental abundance is an input parameter. This allows for a check on the accuracy of the observed ICFs based off the model. The oxygen and argon model ionization correction factors for IC 3568, NGC 5315, and NGC 5882 are larger than their observed counterparts, while the same ICFs are smaller for IC 2165, NGC 2440, NGC 3242, and NGC 7662. Also, IC 3568, NGC 5315, and NGC 5882 have lower stellar temperatures than IC 2165, NGC 2440, NGC 3242, and NGC 7662. Therefore, the ICF equations employed by ELSA could be under-correcting for PN with lower stellar temperatures and over-correcting for those with higher stellar temperatures. The ICF equations for argon and oxygen are $\frac{1}{1-(N^+/N)}*\frac{He^++He^{+2}}{He^+}$ and $\frac{He^++He^{+2}}{He^+}$, respectively. For lower stellar temperatures, the He$^{+}$ ionic state will be populated more than in the case of a higher stellar temperature, reducing the ratio and subsequent ICF value. The neon model ICFs are smaller in all PNe except for NGC 5315, and upon inspection of the ICF equation, $\frac{O^++O^{+2}}{O^{+2}}*\frac{He^++He^{+2}}{He^+}$, no clear reason can be found to explain the differences. Calculating the average observed Ne/O for this sample and comparing to the average modeled Ne/O shows a discrepancy of about 10\%, 0.20$\pm$0.02 and 0.18 for the observed and modeled ratio, respectively. Thus, on average, the systematic error introduced by using ICFs seems to be minor in this case. Interestingly for neon, many regions have ICFs less than 1, which may point to a problem in the neon abundance calculations. Specifically, the atomic constants such as the collision strengths or Einstein A values may be slightly off from their true values, resulting in an ionic abundance of neon that is too large. Alternatively, it could be minor numerical errors introduced in the calculations, i.e. rounding. Lastly, all PN except NGC 5882 have model ICFs of sulphur larger than their observed ICFs with the largest discrepancy seen in NGC 5315. There is a well-known sulfur anomaly where the calculated abundances of sulfur for PNe are systematically lower than those of H II regions of the same metallicity (\citet{hen04}). It has been shown by \citet{hen12} that this may be the result of the sulfur ICF calculated from observations failing to account for populated ionization stages above S$^{+2}$. This looks to be the case here as well since all of the model sulfur abundances are larger than the observed sulfur abundance by nearly the same factor that the model ICF is larger than the observed counterpart.

To further investigate the ICFs of oxygen, argon and neon, a suite of over 400 Cloudy models provided by Gary Ferland was used. This suite covers a large range of stellar temperatures (50-500 kK, $\bigtriangleup$ = 0.1 dex), metallicities (10$^{-0.6}$-10$^{0.4}$ times solar, $\bigtriangleup$ = 0.2 dex), and nebular densities (10$^{2}$-10$^{5}$ cm$^{-3}$, $\bigtriangleup$ = 0.5 dex). Each model uses the Rauch H-Ca atmospheric simulation and typical planetary nebula values for all other input parameters. For each model, the ICFs for O, Ar, and Ne from the equations used by ELSA and the value from the model are compared in Figure~\ref{icfcomp}. The stellar temperature is limited to include only up to 200 kK, as none of the stars in this sample are above this value. The models increase in stellar metallicity first (repeats every 6th model), then nebular density (repeats every 36th model), and finally stellar temperature for each successive model number. For the majority of models, the oxygen ICF from the ELSA equation is smaller than the model ICF and vice versa for neon. This is what is seen for the PN in this sample, albeit at different stellar temperatures and smaller percent differences. Also, all of the model argon ICFs are smaller than the ELSA equation counterparts, which is not observed in this PN sample. These discrepancies may be the result of the boundaries of the nebular gas and the stellar atmosphere model being different (Rauch H-Ca vs. Rauch H-Ni) and warrants further investigation. 
%\begin{landscape}
\begin{figure}
\caption{Relative percent error of the oxygen, argon, and neon ICFs calculated with the equations in ELSA with respect to the ICF from each model. The models increase in stellar metallicity first (repeats every 6th model), then nebular density (repeats every 36th model), and finally stellar temperature for each successive model number.\newline}
\includegraphics[scale=0.30]{icfcomp.png}
\label{icfcomp}
\end{figure}
%\end{landscape}

The parameters for the best fit models for the Gaussian and Gaussian with a power-law density profiles are in Table~\ref{gaudenmods1}. This table has the same format as Table~\ref{condenmods1} but only contains the full regions. The difference between these stellar parameters and the constant density models is small in most cases. Only IC 3568 had a somewhat large change in the luminosity of 0.16 dex. However, this is small compared to the errors estimated for the best fit constant density model. Therefore, the choice of density structure only has a minor effect on the final stellar temperature and luminosity and the adoption of the stellar parameters from the constant density models is reasonable. The Gaussian and Gaussian with a power-law density profiles also generate similar electron temperatures but higher electron densities when compared with the constant density profile. This makes sense, since these two profiles have peak density values significantly above the constant density profile (see Figures~\ref{densfig1}~\&~\ref{densfig2}). The ionization correction factors are either slightly larger or smaller than the constant density ICFs as well. This could be an indication that the choice of density structure affects the ICFs but is fairly negligible. Lastly, the rms values for the non-constant density profiles of IC 2165 and NGC 2440 are considerably larger than their constant density counterparts while the rms of the Gaussian profile for NGC 5882 is smaller than the constant density rms value. This indicates that IC 2165 and NGC 2440 are better represented using a constant density model while a Gaussian density profile appears more suitable in the case of NGC 5882.
\begin{landscape}
\begin{deluxetable}{ccccccc}
\tabletypesize{\footnotesize}
\tablewidth{0in}
%%%\rotate
\tablecaption{Non-constant Density Models\label{gaudenmods1}}
\tablehead{
\multicolumn{7}{c}{Non-constant Density Models}
}
\startdata
 & \multicolumn{2}{c}{IC2165 Full} & \multicolumn{2}{c}{IC3568 Full} & \multicolumn{2}{c}{NGC2440 Full}\\
\cline{2-7}
 & Gaussian & Gaussian With & Gaussian & Gaussian With & Gaussian & Gaussian With\\
Parameter & & power-law & & power-law & & power-law \\ 
\tableline
$T_{star}$ (kK) & 110.0 & 110.0 & 69.2 & 66.6 & 171.8 & 171.9 \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & 3.19 & 3.19 & 3.67 & 3.68 & 2.74 & 2.73\\
Filling Factor ($10^{-1}$) & 9.51 & 9.45 & 9.70 & 8.67 & 1.76 & 1.71\\
He/H ($10^{-2}$) & 10.19 & 10.14 & 9.27 & 9.04 & 12.27 & 12.27\\
C/H ($10^{-4}$) & 3.84 & 3.92 & 5.35 & 5.24 & 2.54 & 2.54\\
N/H ($10^{-4}$) & 1.18 & 1.15 & 0.15 & 0.17 & 0.74 & 0.74\\
O/H ($10^{-4}$) & 2.54 & 2.54 & 4.83 & 4.45 & 2.71 & 2.69\\
Ne/H ($10^{-5}$) & 3.04 & 3.00 & 7.69 & 7.57 & 3.42 & 3.58\\
S/H ($10^{-6}$) & 2.80 & 2.82 & 12.08 & 13.30 & 1.49 & 1.49\\
Ar/H ($10^{-7}$) & 14.26 & 14.35 & 15.35 & 16.11 & 13.03 & 13.00\\
\tableline
\[O III] $T_{e}$ (K) & 13700 & 13700 & 10000 & 10000 & 14200 & 14200\\
\[[S II] N$_{e}$($cm^{-3}$) & 12600 & 12500 & \nodata & \nodata & 8700 & 8500\\
C III] $N_{e}$ ($cm^{-3}$) & 11800 & 11700 & 9100 & 8500 & 8300 & 8100\\
icf (O) & 1.45 & 1.45 & 1.09 & 1.08 & 1.44 & 1.43\\
icf(Ar) & 1.26 & 1.26 & 1.27 & 1.32 & 1.16 & 1.16\\
icf (Ne) & 1.14 & 1.15 & 0.94 & 0.95 & 1.26 & 1.27\\
% & \multicolumn{2}{c}{IC2165 Full} & \multicolumn{2}{c}{IC3568 Full} & \multicolumn{2}{c}{NGC2440 Full}\\
%\cline{2-7}
% & Gaussian & Gaussian With & Gaussian & Gaussian With & Gaussian & Gaussian With\\
%Parameter & & power-law & & power-law & & power-law \\ 
%\tableline
icf(S) & 3.29 & 3.36 & \nodata & \nodata & 1.64 & 1.62\\
RMS ($10^{-2}$) & 3.40 & 3.60 & 3.13 & 2.31 & 10.25 & 9.97 \\
\tableline
\tablebreak
 & \multicolumn{2}{c}{NGC5315 Full} & \multicolumn{2}{c}{NGC5882 Full} & \multicolumn{2}{c}{NGC3242 Full}\\
\cline{2-7}
 & Gaussian & Gaussian With & Gaussian & Gaussian With & Gaussian & Gaussian With\\
Parameter & & power-law & & power-law & & power-law \\
\tableline
$T_{star}$ (kK) & 69.9 & 69.9 & 79.2 & 78.7 & 91.6 & 91.2 \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & 4.92 & 4.94 & 3.42 & 3.42 & 3.26 & 3.29\\
Filling Factor ($10^{-1}$) & 9.68 & 9.75 & 8.30 & 8.26 & 9.77 & 9.83\\
He/H ($10^{-2}$) & 11.94 & 11.80 & 12.62 & 12.59 & 9.84 & 9.93\\
C/H ($10^{-4}$) & 16.87 & 17.82 & 4.29 & 4.29 & 5.28 & 5.21\\
N/H ($10^{-4}$) & 0.57 & 0.57 & 2.41 & 0.24 & \nodata & \nodata\\
O/H ($10^{-4}$) & 6.59 & 6.52 & 12.88 & 12.88 & 4.54 & 4.46\\
Ne/H ($10^{-5}$) & 14.89 & 14.83 & 23.66 & 23.66 & 7.11 & 6.61\\
S/H ($10^{-6}$) & 431.52 & 454.99 & 7.66 & 7.69 & \nodata & \nodata\\
Ar/H ($10^{-7}$) & 959.40 & 1016.25 & 38.11 & 38.46 & \nodata & \nodata\\
\tableline
\[O III] $T_{e}$ (K) & 8900 & 8900 & 8400 & 8300 & 11900 & 12000\\
% & \multicolumn{2}{c}{NGC5315 Full} & \multicolumn{2}{c}{NGC5882 Full} & \multicolumn{2}{c}{NGC7662 Full}\\
%\cline{2-7}
% & Gaussian & Gaussian With & Gaussian & Gaussian With & Gaussian & Gaussian With\\
%Parameter & & power-law & & power-law & & power-law \\
%\tableline
\[[S II] N$_{e}$($cm^{-3}$) & 20000\tablenotemark{a} & 20000\tablenotemark{a} & 20000\tablenotemark{a} & 20000\tablenotemark{a} & \nodata & \nodata \\
C III] $N_{e}$ ($cm^{-3}$) & 72100 & 72200 & 27400 & 26700 & 4700 & 4700\\
icf (O) & 1.39 & 1.40 & 1.12 & 1.12 & 1.52 & 1.53\\
icf(Ar) & 1.98 & 1.99 & 1.17 & 1.22 & \nodata & \nodata\\
icf (Ne) & 1.23 & 1.24 & 0.99 & 0.99 & 1.22 & 1.23\\
icf(S) & 47.57 & 50.88 & 1.84 & 1.96 & \nodata & \nodata\\
RMS ($10^{-2}$) & 3.32 & 3.45 & 5.52 & 7.97 & 7.88 & 8.61\\ 
\tableline
\tablebreak
 & \multicolumn{2}{c}{NGC7662 Full} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{}\\
\cline{2-7}
 & Gaussian & Gaussian With \\
Parameter & & power-law  \\
\tableline
$T_{star}$ (kK) & 108.8 & 108.8 \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & 3.36 & 3.36\\
Filling Factor ($10^{-1}$) & 10.00 & 10.00\\
He/H ($10^{-2}$) & 9.84 & 9.59\\
C/H ($10^{-4}$) & 5.81 & 5.78\\
N/H ($10^{-4}$) & 0.75 & 0.74\\
O/H ($10^{-4}$) & 3.94 & 3.94\\
Ne/H ($10^{-5}$) & 6.44 & 6.35\\
S/H ($10^{-6}$) & 3.43 & 3.48\\
Ar/H ($10^{-7}$) & 24.89 & 25.23\\
\tableline
\[O III] $T_{e}$ (K) & 12400 & 12400\\
% & \multicolumn{2}{c}{NGC5315 Full} & \multicolumn{2}{c}{NGC5882 Full} & \multicolumn{2}{c}{NGC7662 Full}\\
%\cline{2-7}
% & Gaussian & Gaussian With & Gaussian & Gaussian With & Gaussian & Gaussian With\\
%Parameter & & power-law & & power-law & & power-law \\
%\tableline
C III] $N_{e}$ ($cm^{-3}$) & 4300 & 4200\\
icf (O) & 1.51 & 1.51\\
icf(Ar) & 1.36 & 1.36\\
icf (Ne) & 1.19 & 1.19\\
icf(S) & 2.22 & 4.75\\
RMS ($10^{-2}$) & 4.87 & 5.50 
\enddata
\tablenotetext{a}{High Density Limit Default.}
\end{deluxetable}
\end{landscape}

Stellar parameters determined by various authors over the last three decades are compared to the best-fit constant density values in Table~\ref{tlstar} and Figure~\ref{tefflumfig}. The first column in Table~\ref{tlstar} gives the name of each sample PN followed in subsequent columns by the luminosities [in log(L/L$_{\astrosun}$)] and temperatures (in kK) for each source. As can be seen in Figure~\ref{tefflumfig}, the stellar parameters for IC 2165 agree within the 1$\sigma$ uncertainties with those from Paper~II and the temperature agrees with that of \citet{zha93}. The stellar parameters for IC 3568 are consistent with the other authors, except for the temperature of Paper~II (300 K smaller than the lower limit). The luminosity for NGC 2440 is significantly lower than the other published values, although the temperature matches (given the uncertainties) with that of \citet{zha93}. NGC 3242's temperature and luminosity are consistent with all authors except for \citet{zha93} and \citet{cor03}, respectively. For NGC 5315, the luminosity is significantly higher compared to the values from the other authors, except for the upper bound determined by \citet{sha89}. The temperatures for NGC 5315 and NGC 5882 are consistent with Paper~II and \citet{zha93}, respectively. The luminosities for NGC 5882 and NGC 7662 match with the values of \citet{fre08} and Paper~II, within uncertainties. Lastly, \citet{sha85} and \citet{fre08} have temperatures consistent with the value for NGC 7662. 
\begin{deluxetable}{lcccccc}
\tabletypesize{\footnotesize}
%%%\rotate
\tablecaption{Comparison: Stellar Parameters \label{tlstar}}
\tablewidth{0pt}
\tablehead{
\colhead{Object} & \colhead{Model} & \colhead{SK85/89\tablenotemark{a}} & \colhead{ZK93\tablenotemark{b}} & \colhead{CSSP03\tablenotemark{c}} & \colhead{F08\tablenotemark{d}} & \colhead{Paper~II\tablenotemark{e}} \\
\cline{1-7} \colhead{} & \multicolumn{5}{c}{Luminosity (log[L/L$_{\astrosun}$])} 
}
\startdata
IC 2165 & 3.17 & 3.76 & 3.95 & 3.51 & \nodata & 3.16\\
IC 3568 & 3.52 & 4.12 & 3.78 & 3.73 & \nodata & 3.88\\
NGC 2440 & 2.74 & 3.88 & 3.51 & \nodata & 3.32 & 3.10\\
NGC 3242 & 3.36 & 3.59 & 3.40 & 3.88 & 3.54 & 3.64 \\
NGC 5315 & 4.89 & $<$5.25 & 3.95 & \nodata & \nodata & 3.50\\
NGC 5882 & 3.45 & 3.72 & 3.80 & \nodata & 3.52 & 3.45\\
NGC 7662 & 3.24 & 3.89 & 3.76 & 3.99 & 3.42 & 3.42\\
\tableline
 & \multicolumn{5}{c}{Effective Temperature (kK)}\\
\tableline
IC 2165 & 110.0 & 118.0 & 112.1 & 154.9 & \nodata & 110.0\\
IC 3568 & 69.6 & 52.0 & 51.3 & 55.0 & \nodata & 51.0\\
NGC 2440 & 169.8 & 112.0 & 178.8 & \nodata & 208.0 & 198.0\\
NGC 3242 & 89.7 & 90.0 & 75.0 & 89.0 & 89.0 & 89.0 \\
NGC 5315 & 69.9 & 61.0 & 59.9 & \nodata & \nodata & 70.0\\
NGC 5882 & 78.7 & 70.0 & 73.0 & \nodata & 68.0 & 70.0\\
NGC 7662 & 109.9 & 113.0 & 96.8 & 100.0 & 111.0 & 95.0\\
\enddata
\tablenotetext{a}{\citet{sha85} and \citet{sha89}, Observation.}
\tablenotetext{b}{\citet{zha93}, Observation.}
\tablenotetext{c}{\citet{cor03}, Observation.}
\tablenotetext{d}{\citet{fre08}, Observation.}
\tablenotetext{e}{\citet{hen15}, Model.}
\end{deluxetable}
\begin{landscape}
\begin{figure}
\caption{Comparison of the best fit constant density stellar temperature and luminosity for each planetary nebula to other values in the literature.\newline}
\includegraphics[scale=0.46]{Rtefflum.png}
\label{tefflumfig}
\end{figure}
\end{landscape}

Values of the final mass and radius as well as the main sequence lifespan, ZAMS mass, radius, luminosity, temperature, and spectral type can be estimated from the model-derived T and L values for each planetary nebula. Each of these derived properties is shown in Table~\ref{stellprop}. The final and ZAMS masses are estimated by interpolating between theoretical post-AGB evolutionary tracks on the H-R diagram shown in Figure~\ref{agbmods}. For NGC 5315, the mass estimates are from extrapolation since there are no post-AGB evolutionary tracks that have been successfully modeled with luminosities that high. Each track is from either \citet{vas94} (VW 1994, red solid lines), \citet{sch83} (S 1983, blue dash lines), or \citet{ber16} (MB 2016, green dash and purple dash-dot lines). Beneath each author on the plot is the ZAMS/final mass in solar masses following each evolutionary track from top to bottom. The ZAMS/final masses from different interpolations were averaged together when overlapping occurred, since a single set of models was insufficient for all calculations. The final masses for five of the PNe match with the white dwarf mass peak, 0.565$M_{\astrosun}$, from \citet{lie05}. The current radius was calculated using the Stefan-Boltzmann law. Mass-luminosity and mass-radius relations from \citet{dem91} (appropriate for a given mass) were used to calculate the ZAMS luminosity and radius, respectively. The Stefan-Boltzmann law was also employed to calculate the ZAMS temperature. The main sequence lifespan was based on the approximate lifespan of the Sun, $\tau_{\astrosun}\approx$ M$_{\astrosun}$/L$_{\astrosun}$ = 9.5 Gyr, and the age of the Milky Way Galaxy, 13.2 Gyr, was used as a hard upper limit. Lastly, the ZAMS spectral type was determined from the ZAMS luminosity with the spectral type range within the brackets being based on the uncertainties in the luminosity.
\begin{landscape}
\begin{deluxetable}{cccccccc}
\tabletypesize{\footnotesize}
\tablewidth{0in}
%%%\rotate
\tablecaption{Derived Stellar Parameters.\label{stellprop}}
\tablehead{
\colhead{Stellar Property} &
\colhead{IC 2165} &
\colhead{IC 3568} &
\colhead{NGC 2440} &
\colhead{NGC 3242} &
\colhead{NGC 5315} &
\colhead{NGC 5882} &
\colhead{NGC 7662}
}
\startdata
Final Mass (M$_{\astrosun}$)				& 0.56$^{+0.02}_{-0.01}$ & 0.55$^{+0.26}_{-0.01}$ & 0.66$^{+0.08}_{-0.06}$ & 0.56$^{+0.01}_{-0.01}$ & 1.17$^{+0.09}_{-0.09}$ & 0.56$^{+0.03}_{-0.01}$ & 0.56$^{+0.02}_{-0.01}$ \\
Current Radius (R$_{\astrosun}$) 				& 0.11$^{+0.08}_{-0.03}$ & 0.16$^{+0.36}_{-0.07}$ & 0.03$^{+0.01}_{-0.01}$ & 0.20$^{+0.10}_{-0.07}$ & 1.90$^{+0.53}_{-0.55}$ & 0.29$^{+0.15}_{-0.06}$ & 0.12$^{+0.04}_{-0.03}$ \\
Main Sequence Lifespan (Gyr) 				& 9.5$^{+3.7}_{-4.3}$ & 8.3$^{+4.9}_{-8.1}$ & 0.5$^{+0.8}_{-0.2}$ & 10.7$^{+2.5}_{-6.4}$ & 0.04$^{+0.01}_{-0.01}$ & 8.9$^{+3.5}_{-4.4}$ & 8.7$^{+3.4}_{-4.0}$ \\
ZAMS Mass (M$_{\astrosun}$)			& 0.99$^{+0.22}_{-0.15}$ & 1.04$^{+3.02}_{-0.23}$ & 2.81$^{+0.66}_{-0.81}$ & 0.95$^{+0.35}_{-0.09}$ & 6.55$^{+0.66}_{-0.65}$ & 1.02$^{+0.27}_{-0.11}$ & 1.02$^{+0.24}_{-0.11}$ \\
ZAMS Radius (R$_{\astrosun}$) 			& 1.05$^{+0.22}_{-0.15}$ & 1.10$^{+1.79}_{-0.23}$ & 2.36$^{+0.29}_{-0.40}$ & 1.01$^{+0.34}_{-0.09}$ & 3.78$^{+0.21}_{-0.21}$ & 1.08$^{+0.27}_{-0.11}$ & 1.08$^{+0.24}_{-0.11}$ \\
ZAMS $L_{star}$ ($L_{\astrosun}$) 		& 0.99$^{+1.21}_{-0.47}$ & 1.20$^{+247.43}_{-0.75}$ & 58.65$^{+75.32}_{-43.09}$ & 0.84$^{+1.98}_{-0.27}$ & 1618.68$^{+734.07}_{-546.60}$ & 1.09$^{+1.68}_{-0.39}$ & 1.12$^{+1.47}_{-0.40}$ \\
ZAMS Temperature (kK) 				& 5.6$^{+6.0}_{-4.0}$ & 5.8$^{+7.7}_{-0.7}$ & 10.4$^{+1.7}_{-2.2}$ & 5.5$^{+0.9}_{-0.3}$ & 18.9$^{+1.3}_{-1.3}$ & 5.7$^{+0.7}_{-0.3}$ & 5.7$^{+0.6}_{-0.3}$ \\
ZAMS Spectral Type 				& G2 [F6-G8] & G0 [B6-K3] & B8 [B7-A3] & G4 [G7-F5] & B2 [B2-B3] & G1 [F5-G5] & G1 [F5-G5] \\
\enddata
\end{deluxetable}
\end{landscape}
%\begin{landscape}
\begin{figure}
\caption{Log \textit{L/L$_{sun}$} vs. log \textit{T$_{eff}$} for the entire planetary nebula sample. Post-AGB model tracks from \citet{vas94} (VW 1994, solid red lines, Z=0.016), \citet{sch83} (S 1983, blue dashed lines, Z=0.016) and \citet{ber16} (MB 2016, purple dash-dot lines, Z=0.02 and green dash lines, Z=0.01) are overlaid. Beneath each author on the plot is the ZAMS/final mass in solar masses following each evolutionary track from top to bottom.}
\includegraphics[scale=0.85]{RagbModels7PNe.eps}
\label{agbmods}
\end{figure}
%\end{landscape}

\citet{amn95} suggested that an increase in progenitor mass would increase the probability of low mass companions, which would determine the axisymmetric morphology of the planetary nebula. As can be seen in Table~\ref{stellprop}, the central stars of IC 2165, IC 3568, NGC 3242, NGC 5882, and NGC 7662 are each solar-like while those of NGC 2440 and NGC 5315 are super-solar. NGC 5882, NGC 2440, and NGC 5315 are the only PN in this sample to exhibit very asymmetric structures (Figures~\ref{fig:slits1}~\&~\ref{fig:slits2}), in support of the claim made by \citet{amn95} that increasing the progenitor mass would increase the probability of a companion, assuming each does indeed have a companion. 