\section{Introduction}\label{sec:Intro}
Globular clusters (GCs) are among the oldest observable objects in the universe
\citep{Pen11}. They are characterized by high densities with typical half-light
radii of $\le$10 pc \citep{Vanderburg2010}, and typical masses ranging from
$10^{4}$--$10^{5}$ M$_{\odot}$ \citep{Bro06} --- though some GCs are
significantly larger than these typical values \citep[e.g. $\omega$ Cen,
][]{Richer1991}. GCs provide a unique way to probe stellar evolution
\textbf{\citep{Kalirai2010}}, galaxy formation models \citep{Boy18,Kra05}, and dark matter
halo structure \citep{Hud18}.

The traditional view of globular clusters is that they consist of a single
stellar population (SSP, in some publications this is referred to as a Simple
Stellar Population). This view was supported by spectroscopically uniform heavy
element abundances \citep{Carretta2010, Bastian2018} across most clusters (M54
and $\omega$Cen are notable exceptions, see \citet{Marino2015} for further
details), and the lack of evidence for multiple stellar populations (MPs) in
past color-magnitude diagrams of GCs \citep[i.e.][]{Sandage1953, Alcaino1975}.
However, over the last 40 years non-trivial star-to-star light-element
abundance variations have been observed \citep[i.e.][]{Smith1987} and, in the
last two decades, it has been definitively shown that most, if not all, Milky Way
GCs have MPs \citep{Gratton2004, Gratton2012, Piotto2015}. The lack of
photometric evidence for MPs prior to the 2000, can be attributed to the more
narrow color bands available, until very recently, to ground-based photometric
surveys \citep{Milone2017}.

The prevalence of multiple populations in GCs is so distinct that the proposed
definitions for what constitutes a globular cluster now often center on the
existence of MPs \citep[e.g.][]{Carretta2010}. Whereas people have have often
tried to categorize objects as GCs through relations between half-light
radius, density, and surface brightness profile, in fact many objects which are
generally thought of as GCs don't cleanly fit into these cuts
\citep{Peebles1968, Brown1991, Brown1995, Bekki2002}. Consequently,
\citet{Carretta2010} proposed a definition of GCs based on observed chemical
inhomogeneities in their stellar populations. The modern understanding of GCs
then is not simply that of a dense cluster of stars that may have chemical
inhomogeneities and multiple populations; rather, it is one where those
chemical inhomogeneities and multiple populations themselves are the defining
elements of a GC.

All Milky Way globular clusters studied in detail show populations enriched in
He, N, and Na while also being depleted in O and C
\citep{Piotto2015,Bastian2018}. {\bf Further, studies of Magellenic Cloud
massive clusters have shown that these light element abundance variations exist
in clusters as young as $\sim 2$ Gyr but not in younger clusters
\citep{Martocchia2019} while there is also evidence of nitrogen variability in
the $\sim 1.5$ Gyr old cluster NGC 1783 \citep{Cadelano2022}}.  These light
element abundance patterns also are not strongly correlated with variations in
heavy element abundance, resulting in spectroscopically uniform Fe abundances
between populations \citep[{\bf though recent work indicates that there may be
[Fe/H] variations within the first population, e.g.}][]{Legnardi2022,
Lardo2022} . Further, high-resolution spectral studies reveal anti-correlations
between N-C abundances, Na-O abundances, and potentially Al-Mg
\citep{Sneden1992, Gratton2012}. Typical stellar fusion reactions can deplete
core oxygen; however, the observed abundances of Na, Al, and Mg cannot be
explained by the CNO cycle \citep{Prantzos2007}. Consequently, globular cluster
populations must be formed by some novel means.

Formation channels for these multiple populations remain a point of debate
among astronomers. Most proposed formation channels consist of some older,
more massive population of stars polluting the pristine cluster media before a
second population forms, now enriched in heavier elements which they themselves could
not have generated \citep[for a detailed review see ][]{Gratton2012}. The four
primary candidates for these polluters are asymptotic giant branch stars
\citep[AGBs,][]{Ventura2001,DErcole2010}, fast rotating massive stars
\citep[FRMSs,][]{Decressin2007}, super massive stars
\citep[SMSs,][]{Denissenkov2014}, and massive interacting binaries
\citep[MIBs,][]{deMink2009, Bastian2018}. 

Hot hydrogen burning (i.e. proton capture), material transport to the surface, and
material ejection into the intra-cluster media are features of each of these
models and consequently they can all be made to {\it qualitatively} agree with
the observed elemental abundances. However, none of the standard models can
currently account for all specific abundances \citep{Gratton2012}. AGB and FRMS
models are the most promising; however, both models have difficulty reproducing
severe O depletion \citep{Ventura2009,Decressin2007}. Moreover, AGB and FRMS
models require significant mass loss ($\sim 90\%$) between cluster formation
and the current epoch --- implying that a significant fraction of halo stars
formed in GCs \citep{Renzini2008,DErcole2008,Bastian2015}.

In addition to the light-element anti-correlations observed, it is also known
that second populations are significantly enhanced in helium
\citep{Piotto2007, Piotto2015, Latour2019}. Depending on the cluster, helium
mass fractions as high as $Y=0.4$ have been inferred \citep[e.g][]{Milone2015}.
However, due to both the relatively high and tight temperature range of partial
ionization for He and the efficiency of gravitational settling in core helium
burning stars, the initial He abundance of globular cluster stars cannot be
observed; consequently, the evidence for enhanced He in GCs originates from
comparison of theoretical stellar isochrones to the observed
color-magnitude-diagrams of globular clusters. Therefore, a careful handling of
chemistry is essential when modeling with the aim of discriminating between
MPs; yet only a very limited number of GCs have been studied with
chemically self-consistent (structure and atmosphere) isochrones
\citep[e.g.][NGC 6752]{Dotter2015}. 

NGC 2808 is the prototype globular cluster to host multiple populations.
Various studies since 2007 have identified that it may host anywhere from two to five 
stellar populations. These populations have been identified both
spectroscopically \citep[i.e.][]{Carretta2004, Carretta2006, Carretta2010,
Gratton2011, Carretta2015, Hong2021} and photometrically
\citep[i.e.][]{Piotto2007, Piotto2015, Milone2015, Milone2017, Pasquato2019}.
Note that recent work \citep{Valle2022} calls into question the statistical
significance of the detections of more than two populations in the spectroscopic
data. Here we present \textbf{the first stellar structure and evolutionary
models built in a chemically self-consistent manner of NGC 2808}.

We model the photometry of the \textbf{primordial population (hereafter P1) and
the helium enriched population (hereafter P2). \citet{Milone2015} identifies five
populations within NGC 2808, given that the aim of this work is not to identify
sub-populations; rather, to measure the effect that chemical self consistant
stellar structure and evolutionary have on the inferred helium abundance for
the two most extreme cases, we do not consider more than those two
populations.} We use archival photometry from the Hubble UV Globular Cluster
Survey (HUGS) \citep{Piotto2015, Milone2017} in the F275W and F814W passbands
to characterize multiple populations in NGC 2808 \citep{Milone2015,
Milone2015b} \citep[This data is available on MAST, ][]{HUGS}. Additionally, we
present a likelihood analysis of the photometric data of NGC 2808 to determine
the number of populations present in the cluster.


