\section{Chemical Consistency}\label{sec:const}
There are three primary areas in which the stellar models must be made
chemically consistent: the atmospheric boundary conditions, the opacities, and
interior abundances. The interior abundances are relatively easily handled by
adjusting parameters within our stellar evolutionary code. However, the other
two areas are more difficult to make consistent. Atmospheric boundary
conditions and opacities must both be calculated with a consistent set of
chemical abundances outside of the stellar evolution code.
{\bf Nearly all prior efforts at modeling multiple stellar populations in
globular clusters have adjusted the abundances used in the atmospheric interior
models, and in the high temperature opacities, but have not self-consistently
modified the corresponding low-temperature opacities and surface boundary
conditions, as these are found from stellar atmosphere codes, and not the
stellar interior codes which are used to create stellar models and isochrones.
In this work, as in Dotter (2016), the stellar interior models are chemically
self-consistent with the stellar atmosphere models.} For evolution, we use the Dartmouth Stellar
Evolution Program (DSEP) \citep{Dotter2008}, a well-tested 1D stellar evolution
code which has a particular focus on modeling low mass stars ($\le 2$
M$_{\odot}$)

\subsection{Atmospheric Boundary Conditions}\label{sec:atm}
Certain assumptions, primarily that the radiation field is at equilibrium and
radiative transport is diffusive \citep{Salaris2005}, made in stellar structure
codes, such as DSEP, are valid when the optical depth of a star is large.
However, in the atmospheres of stars, the number density of particles drops low
enough and the optical depth consequently becomes small enough that these
assumptions break down, and separate, more physically motivated, plasma-
modeling code is required. Generally, structure code will use tabulated
atmospheric boundary conditions generated by these specialized codes, such as ATLAS9
\citep{Kurucz1993}, PHOENIX \citep{Husser2013}, MARCS \citep{Gustafsson2008},
and MPS-ATLAS \citep{Kostogryz2023}. Often, because the boundary conditions are
expensive to compute, they are not updated as interior abundances vary. 

One key element when building chemically self-consistent models of NGC 2808 is the
incorporation of new atmospheric boundary conditions with the same elemental abundances as
the structure code. We use atmospheres generated from the \texttt{MARCS} grid
of model atmospheres \citep{Plez2008}. \texttt{MARCS} provides one-dimensional,
hydrostatic, plane-parallel and spherical LTE atmospheric models
\citep{Gustafsson2008}. Model atmospheres are made to match the
spectroscopically measured elemental abundances of \citet{Milone2015} populations A\&E.
Moreover, for each population, atmospheres with various helium mass fractions
are generated. These range from Y=0.24 to Y=0.36 in steps of 0.03. All
atmospheric models are computed to an optical depth of $\tau = 100$ where their
temperature and pressure serve as boundary conditions for the structure code.
In general, enhancing helium in the atmosphere has only a small impact on the atmospheric
temperature profile, while leading to a drop in the pressure by $\sim 10 - 20 \%$.

\subsection{Opacities}\label{sec:opac}
In addition to the atmospheric boundary conditions, both the high and low
temperature opacities used by DSEP must be made chemically consistent. Here we
use OPLIB high temperature opacity tables \citep{Colgan2016} retrieved using
the TOPS web-interface. Retrival of high termperature opacities is done using
\texttt{pyTOPSScrape}, first introduced in \citet{Boudreaux2023}. Low
temperature opacity tables are retrieved from the Aesopus 2.0 web-interface
\citep{Marigo2009, Marigo2022}. Ideally, these opacities would be the same used
in the atmospheric models. However, the opacities used in the MARCS models are
not publicly available. As such, we use the opacities provided by the TOPS and
Aesopus 2.0 web-interfaces.
