Annika Jacobsen  Erik van Dijk  Halima Mouhib  Bas Stringer  Olga Ivanova
Jose Gavaldá-García Laura Hoekstra*  K. Anton Feenstra*  Sanne Abeln*  *
editorial responsability

##  Chapter 1 Introduction to Protein Structure

###### Contents

  1. 1 Introduction to Protein Structure
    1. 1.1 Protein structure basics
      1. 1.1.1 Primary structure
        1. The 20 natural amino acid residues
    2. 1.2 Secondary structure
      1. 1.2.1 Backbone hydrogen bonding
      2. 1.2.2 $\alpha$-helices
      3. 1.2.3 $\beta$-strands
      4. 1.2.4 Loops
      5. 1.2.5 Phi and psi angles
      6. 1.2.6 Secondary structure assignment
    3. 1.3 Tertiary structure
      1. 1.3.1 Hydrophobic core
      2. 1.3.2 Protein domains
    4. 1.4 Quarternairy structure
    5. 1.5 Key points
    6. 1.6 Further Reading
    7. Author contributions

Within the living cell, protein molecules perform specific functions,
typically by interacting with other proteins, DNA, RNA or small molecules.
They take on a specific three dimensional structure, or in some cases, an
ensemble of three dimensional structures. It is this three dimensional
structure that allows the protein to function within the cell. This structure
is with high specificity encoded by its amino acid sequence; the precise amino
acid sequence of a protein is in turn encoded by the genes of an organism.
Hence, the understanding of a protein’s function is tightly coupled to its
three dimensional structure.

The current state of scientific understanding allows us to comprehend how the
gene sequence encoded by the DNA is transcribed into RNA, and in its turn
translated into amino acid sequence. However, experiments to determine protein
structures and protein structural ensembles are difficult and laborious; we
will come back to that in detail in Chapter “LABEL:ch:ChDetVal”. Recently,
deep learning models like AlphaFold2, trained on existing protein structure
data, have achieved success in predicting protein structures from sequences.
However, simulating the transition from a protein sequence to its folded
structure computationally is still challenging for moderately sized proteins.
As a result, structural bioinformatics faces unresolved problems or,
alternatively, presents exciting scientific challenges.

Before going into protein structure analysis and prediction, and protein
folding and dynamics, we will first give a brief introduction into the basics
of protein structures. This is deliberately kept short and shallow. The
excellent book “Introduction to Protein Structure” by Branden and Tooze (1998)
provides a much more in-depth introduction into this exciting field.

Figure 1.1: Levels of protein structure. Top-left: Primary structure, given as
polypeptide sequence in the one-letter code of amino acids. Top-right:
Secondary structure, example of an alpha helix. Bottom-left: Tertiary
structure, structure of one of the monomers of hemoglobin. Bottom-right: Full
structure of Human hemoglobin, 4 chains make the whole structure (PDB:1BIJ).
Ribbon representation obtained with UCSF-chimera Pettersen et al. (2004).

###  1.1 Protein structure basics

A protein structure may be described at four levels as depicted in Figure 1.1:

  1. The primary structure

is simply the sequence of amino acids that make up the protein polypeptide
chain.

  2. Secondary structure

describes the organisation of this chain into regular $\alpha$-helices and
$\beta$-strands and anything else, called ‘coil’ or loop.

  3. Tertiary structure

is the three dimensional arrangement – or topology – of the protein chain; it
defines its overall shape.

  4. Quaternary structure

is the (three dimensional) organisation of the protein chain in context of the
proteins and molecules it interacts with; i.e. the configurational ensemble
multiple molecules adopt when binding to each other, forming macro-molecular
complexes.

####  1.1.1 Primary structure

There are 20 naturally occurring amino acids that constitute the building
blocks of proteins. Amino acids are linked together by a peptide-bond between
the carbonyl Carbon (C=O) of the preceding residue and the amide Nitrogen (NH)
of the next residue in its primary sequence. This is why proteins are also
referred to as “polypeptides”. Note that for each amino acid type, this part
of the chemical structure is identical; it is also referred to as the
_backbone_. The _sidechains_ branch out from the central Carbon atom
(C$\alpha$) in the backbone. Unlike the backbone, sidechains are chemically
different between the different amino acid types; see Panel “Amino acids,
residues, and the peptide bond” for more detail. We can view the primary
protein structure as a chain with 20 different colours of beads that all have
different properties.

The amino acid type in the polypeptide chain is encoded by codons (sequences
of three nucleotides) in the DNA sequence of a gene. After transcription, the
translation from RNA codons into amino acids occurs at the ribosome. The exact
sequence of the codon determines the amino acid, or may indicate the start or
end of a peptide chain. This codon table is universal across all species,
although several microorganisms are known that use a (slightly) different
table. The translation mechanism, including the codon table, the tRNA and the
aminoacyl-transferases, is beyond the scope of this book.

Roughly speaking, there are three important classes of amino acids:  i)
hydrophobic,  ii) charged, and  iii) polar . These classes are based on their
interaction properties with respect to water. Hydrophobic residues do not
interact with water, whereas polar and charged residues do make contact with
water favourably. Later in this chapter, we will see the importance of the
difference between hydrophobic and polar amino acids for protein folding. The
Panel “Amino acids, residues, and the peptide bond” gives more background
detail on the chemical characteristics of those amino acids.

#### Amino acids, residues, and the peptide bond

There are 20 naturally occurring amino acids that constitute the building
blocks of proteins, shown in Panel “The 20 natural amino acid residues” below.
(Chemically speaking many, many more types of amino acids are possible). To
build up a protein, amino acids react under the loss of water to form an
extremely stable peptide bond. The figure shows the formation of the peptide
bond between two alanine amino acids: Within proteins, amino acids differ in
the sidechain part, the backbone of the protein, i.e., (NH–C$\alpha$–C=O) is
repetitive. Note that each amino acid can be referred to using a three or one
letter code: here Ala or A for alanine. In Panel “The 20 natural amino acid
residues”, amino acid residues are categorized into charged
(positive/negative), polar (not charged), and hydrophobic (or aliphatic) amino
acids. Hydrophobic/aliphatic/apolar amino acids consist of only Carbon (and
for Cysteine, Sulphur) atoms in the sidechain. Aromatic residues all have a
regular six- or five-sided ring (tryptophan has both) consisting of mostly
carbon atoms. Tyrosine is aromatic but due to a hydroxyl group also polar.
Tryptophan does contain a nitrogen atom but is considered hydrophobic. Polar
and charged residues all have nitrogen and/or oxygen atoms in the sidechain.
Charged residues are also considered polar, and both are hydrophilic. Small,
medium, large: A further subdivision of the hydrophobic amino acids can be
made into small (glycine, alanine), medium (valine, leucine, isoleucine),
large (methionine) and aromatic/ring (proline, which is also medium size, and
phenylalanine and tryptophan which are also large). Of the charged amino
acids, lysine and arginine are considered large, and among the polar ones,
serine and threonine are small. Finally, the backbone contains N and O and is
therefore always polar. In the polar and charged residues, oxygen is always
negative and nitrogen always positive. Before moving on, it should be noted
that biologists and bioinformaticians often use the terms ‘amino acid’ and
‘residue’ equivalently. However, ‘residue’ is more general and can also refer
to e.g. a nucleotide in DNA or RNA. To be a bit more precise, for chemists,
the amino acid is the free molecule, and it is called ‘amino acid residue’
only when part of a protein.

##### The 20 natural amino acid residues

In addition to these broad categories of amino acids, there are a few special
ones (labelled in blue in the figure): Cysteine contains a sulphur atom. When
two cysteines are close in the structure, the two sulphur atoms will form a
covalent bond of similar strength to the other bonds within the amino acids.
These are much stronger than hydrogen bonds (see next 1.1.2 for hydrogen
bonds). Proline contains a ring that loops from the C$\alpha$ back to the
backbone nitrogen. This makes the backbone of the proline much less flexible
than for other residues; proline often terminates helices or otherwise induces
a kink, and proline is used to make a loop containing sharp turns. More about
this below in the Panel “The omega torsion angle”. Glycine has the smallest
possible sidechain: only a single hydrogen atom (which is much smaller than a
carbon). Due to this, there is less steric hindrance around the C$\alpha$ and
more flexibility in its Phi/Psi angles (more detail about phi/psi angles in
Section 1.2.5 below).

Figure 1.2: Hydrophobic collapse as the first step in a protein folding from
its unfolded state (on the left) to a folded state (right). Hydrophobic
residues, shown as black spheres, will tend to minimize contact with water and
therefore end up in the interior of the protein. Hydrophilic (polar and
charged) residues are not drawn explicitly here, they form the rest of the
backbone, between the black spheres.

Figure 1.3: Hydrogen bonding in the backbone of the protein (A) and in water
(B); hydrogen-bond forming groups are indicated with blue dashed lines.
Hydrogen bonds are caused by atoms with slight negative charges ($\delta-$)
being attracted to atoms with slightly positive charges ($\delta+$). In a
protein, hydrogens on a nitrogen or oxygen are positive, oxygens and nitrogens
themselves are negative (C).

###  1.2 Secondary structure

All amino acids have a common part, the backbone, as discussed in the previous
section. The backbone can make regular structures due to their chemical
properties, see also Figure 1.3. These regular backbone structures are called
secondary structure. Examples of $\alpha$-helices and $\beta$-strands are
shown in Figure 1.4. Below we will introduce how backbone hydrogen bonding
leads to secondary structure.

Figure 1.4: (Examples of $\alpha$-helical (left two) and $\beta$-strand (right
two) structures made out of alanines (note the single atom in the sidechain)
and a few cysteines (in the $\beta$-sheet). Both are shown in a ‘sticks’
(left) and a typical ‘cartoon’ (right) representation.

####  1.2.1 Backbone hydrogen bonding

Hydrogen bonds are a key part of the secondary and tertiary structure of a
protein. Hydrogen bonding takes places between hydrogen atoms, with a slight
positive charge and nitrogen or oxygen atoms with a slight negative charge.

The attraction of opposite charges leads to strong H$\cdots$O interactions
called hydrogen-bonds. The N–H and C=O parts of the backbone, can also make
these polar hydrogen-bond interactions (see Figure 1.3), and so can the polar
and charged sidechains (O–H, N–H, S–H and C=O groups as shown in Panel “The 20
natural amino acid residues”). Energetically, hydrogen-bonds are very
favourable, and most hydrogen bond donors and acceptors in the sequence of the
protein will therefore also make a hydrogen bond, in any stable structure.

There are two main ways in which the amino acid chain in proteins are
structured so that all backbone hydrogen bonds in the hydrophobic interior can
become satisfied: _helix_ or _strand_. In the helical structure, repeated
local hydrogen bonding occur, as shown in Figure 1.4. This is called the
$\alpha$-helix secondary structure type. An $\alpha$-helix only leaves
unsatisfied hydrogen bonding capacity at the ends of a helix, these ends are
thus usually found at the surface of a protein. In the strand structure, two
stretches of sequence are adjacent in the structure, and hydrogen bonds occur
‘laterally’ between adjacent strands. This is the ‘$\beta$-sheet’ secondary
structure. It leaves unsatisfied hydrogen bond capacity at the first and last
strands of a sheet, called the ‘edge’ strands, which like helix ends are
mostly found at the protein surface.

####  1.2.2 $\alpha$-helices

Helical secondary structures are characterized by repeated, local hydrogen
bonding between the backbone amide group of one residue, and the carbonyl
group of a subsequent residue, as shown in Figure 1.4. The most common of
these structures is the $\alpha$-helix, where the bond is formed between
residues $i$ and $i+4$. Helices can be anywhere from 4 to 40 residues long,
with an average length of $\sim$10 residues, or about 3 turns.

This periodicity of $\alpha$-helices can typically also be observed in the
sequence. Within a protein structure a helix typically has a solvent exposed
and a buried side; this will lead to hydrophilic residues tending to point
outside towards the solvent, and hydrophobic ones tending towards the inside
of the protein. The side sticking into the core are typically tightly packed
together, also referred to as helix packing. Helical structures are generally
considered easier to predict from sequence due to this periodicity in the
sequence, we will come back to this in Chapter “LABEL:ch:ChSSPred”. Please
refer to the Panel “Helices” below for further details on helices.

#### Helices

The $\alpha$-helix is the most common helix secondary structure type, where
the bond is formed between residues $i$ and $i+4$. So-called $3/10$\- and
$\pi$-helices, where the bond connects residues $i\rightarrow i+3$ and
$i\rightarrow i+5$ respectively, are less common. In the helical structure,
the carbonyl group (C=O) is oriented along the direction of the sequence,
while the amide group (NH) points in the opposite direction (Figure 1.4a).
This arrangement results in a tightly packed helix with minimal internal
space.

C D

Figure 1.5: Two types of $\beta$-sheet, schematically: a) parallel, and b)
anti-parallel; and in three-dimensions: c) parallel and d) anti-parallel
(ideal geometries, generated using Chimera).

A B C

Figure 1.6: Details of $\alpha$-helix (A), $\beta$-strand (B) and coil (C).
Note how regular patterns of hydrogen bonds (thin lines) stabilize
$\alpha$-helix (A) and $\beta$-strand (B), but not coil (C). Also note how the
hydrogen bonds in the $\alpha$-helix (A) point along the helix axis; the
hydrogen bonds go from the hydrogen atom (which is not shown) on the nitrogen
(blue) to the oxygen (red), pointing ’backwards’ along the direction of the
protein chain, which runs from bottom left to top right (A).

#### Strands and sheets

Due to the chirality of amino acids, $\beta$-sheets are often twisted or
pleated in a right-hand turn. Simple configurations of $\beta$-sheets include
the commonly found hairpin and so-called psi-loop motif, whereas larger sheets
can assume complex formations like $\beta$-barrels or $\beta$-propellers. When
the connecting sequence between two strands is a small loop (a
$\beta$-loop-$\beta$ motif, often referred to as $\beta$-hairpin) Figure 1.6b,
the sequence distance can be as low as 3. However, the sequence distance
between two strands in a beta-sheet can be much larger. An extreme case occurs
when a whole protein domain is in between the two strands, which might be
hundreds of residues (more on protein domains later in Chapter
“LABEL:ch:ChDBClass”). Therefore, no clear relation (such as ‘i–i+4’ for
$\alpha$-helix) occurs between hydrogen-bonded residues in a $\beta$-sheet.
Thus $\alpha$-helices can be considered “local” compared to $\beta$-sheets, as
the hydrogen-bonding in $\alpha$-helices is formed between nearby residues in
the sequence, while in $\beta$-sheets the hydrogen-bonded residues may be far
away in the sequence.

####  1.2.3 $\beta$-strands

A $\beta$-strand is a stretch of amino acids with the backbone in an extended
configuration, typically 3 to 10 amino acids long. Two or more $\beta$-strands
together make up a $\beta$-sheet. Hydrogen bonding patterns in the
$\beta$-sheet are distinctly different from those in the $\alpha$-helix. In
the $\beta$-sheet, hydrogen bonds occur ‘laterally’ between adjacent strands.

When two $\beta$-strands have the same direction, they are referred to as
parallel $\beta$-sheets. Conversely, if the two $\beta$-strands have opposite
directions, they are known as antiparallel $\beta$-sheets. These two types of
$\beta$-sheets can be distinguished by the geometry of the hydrogen bonds. In
parallel $\beta$-sheets, the hydrogen bonds are formed diagonally between the
carbonyl group of one amino acid residue and the amide group of the
neighboring residue on the adjacent strand, resulting in a slanted hydrogen
bonding pattern. On the other hand, in antiparallel $\beta$-sheets, the
hydrogen bonds are formed directly between the carbonyl group of one amino
acid residue and the amide group of the neighboring residue on the opposite
strand, creating a linear hydrogen bonding pattern Figure 1.5. Please refer to
the Panel “Strands and sheets” below for further details on beta-sheets.

####  1.2.4 Loops

In loop regions, see also Figure 1.6c, there is no regular pattern of hydrogen
bonding. Nevertheless, the hydrogen bond donors and acceptors, as present in
the backbone, do need to form hydrogen bonds. In loop structures, the backbone
atoms may make hydrogen bonds with the solvent, with the sidechains of polar
amino acids, or even with backbone atoms – but not in a regular pattern.

The configuration of loops are much less regular, or ordered compared the
helices and $\beta$-sheets. Generally, loops lie on the surface of a protein,
and are much more solvent exposed. Often loop regions can be flexible, and can
change conformation in the functional state of the protein, even when the
protein is fully folded. Loop regions are therefore also much more likely to
loose (deletion) or gain (insertion) small parts during evolution. In a
(multiple) sequence alignment, loop regions typically contain many gaps
compared to helical or sheet regions. Very long loops ($>20$ residues) are
also called _disordered regions_. Such regions will not take up a rigid three-
dimensional structure in their folded state, see also Panel “Unusual secondary
structures”.

A B

C D

E

F G

Figure 1.7: Three main classes of a-typical protein structures: amyloid-
fibrils or $\beta$-fibrils (A), as an example of bound ordered structure
flanked by disordered loops or termini (B). Disordered proteins or regions;
shown are schematically a disordered loop within a protein domain (C) and a
disordered linker between two protein domains (D). (E+F) $\alpha$-helical
coiled coils (PDB:2ZTA) which are characterized by the repetition of a Leucine
every 7th residue, hence also referred to as ‘leucine zippers’. Shown length-
wise (E), from the top (F) and schematically (G).

#### Unusual secondary structures

In addition to ‘typical’ proteins secondary structures, there are three main
classes of ‘a-typical’ cases: amyloid fibrils, coiled-coils, and disordered
proteins. Examples are shown in Figure 1.7. Amyloid fibrils ($\beta$-fibrils)
are a particular case of $\beta$-sheets. Here the $\beta$-strands are also
formed between the chains of different protein molecules, and such structures
can become infinitely long. The resulting fibrils may form larger aggregate
fibers, that may disrupt the cell functioning or even kill cells. Initially,
the ability to form these fibrils was thought to be a particular property of
specific proteins and associated with particular pathologies, like the prion
protein in scrapie (sheep), mad cow disease (cattle) or Creutzfeldt-Jacob’s
disease (human). It has now become clear that the ability of proteins to form
amyloidic structures tends to be generic Dobson (2003). Several other diseases
have now been associated with the formation of ‘amyloid plaques’, which are
large-scale deposits of $\beta$-fibrils that can be highly disruptive to
tissue. A well-known example is some forms of Parkinson’s disease. However, it
is not yet clear in most cases if these plaques are involved in causing the
disease or merely a result of the disease process. The coiled-coil is a
twisted rod formed by a pair of $\alpha$-helices, this is shown in Figure
1.7b. It resembles a pair of tweezers, with one end slightly open, and both
helix ends binding on either side of the DNA double helix in certain DNA
binding proteins. The coiled-coil has a repetitive element of 7 residues where
both helices are in direct contact. Typically, every 7th residue is a leucine,
and valines or isoleucines are found in between. This creates a pattern like
Lxx[VI][VI]xxL ([VI] means either V or I at that position). These structures
are also referred to as “leucine zippers”and “leucine-rich repeats”because of
the repeating leucine every 7th residue. Disordered protein regions: some
proteins never fold in a fixed three-dimensional structure, and are referred
to as “disordered proteins”. These lack a folded structure, but display a
highly flexible, random-coil-like conformation under physiological conditions.
They will be further discussed in Chapter “LABEL:ch:ChSSPred” will briefly go
into prediction of disordered proteins and regions based on sequence patterns.
Many proteins contain large disordered segments (33% of eukaryotic, 2% for
archaea, and 4.2% in bacteria) Ward et al. (2004).

####  1.2.5 Phi and psi angles

The backbone of a peptide consists of two flexible chemical bonds:
NH–C$\alpha$ and C$\alpha$–CO. These bonds can rotate around their axes, and
they are referred to as torsion angles or dihedral angles. In this context, we
will use the term torsion angles. The NH–C$\alpha$ torsion angle is denoted as
$\Phi$ or phi and is located at the beginning of each residue. The
C$\alpha$-CO torsion angle is denoted as $\Psi$ or psi and is found at the end
of each residue. Figure 1.8 illustrates this arrangement. The omega torsion
angle is covered in the Panel “The omega torsion angle”.

Specific combinations of phi and psi angles allow the formation of favourable
amide (NH) to carbonyl (C=O) hydrogen bonding patterns in the backbone. These
combinations facilitate the formation of either $\alpha$-helix or
$\beta$-sheet structures. However, certain phi and psi angle combinations can
result in clashes within the backbone or between adjacent sidechains in the
protein chain, particularly if the sidechains are large. In some cases,
clashes can even occur between the larger sidechains and the backbone of
neighboring residues. Steric hindrance caused by both the backbone atoms and
sidechains restrict the occurrence of certain combinations of phi and psi
angles. Consequently, the number of potential conformations that may be
adopted by the polypeptide is reduced. Sequence and propensity patterns that
arise from this are exploited in secondary structure prediction, to which we
will turn in Chapter “LABEL:ch:ChSSPred”.

Figure 1.8: (a) Phi or $\Phi$ and psi or $\Psi$ angles defined in the backbone
of an Alanine. (b) Phi and psi angles analyzed in a ramachandran plot. The
contoured areas indicated allowed (light) and preferred (dark) combinations of
phi and psi angles, which coincides with the two major secondary structure
elements: $\beta$-sheets and $\alpha$-helices; in addition the smaller area of
left-handed $\alpha$-helices can be seen in the positive quadrant Chen et al.
(2010). (c+d) Backbone re-arrangements in a tri-Alanine peptide, when
adjusting the $\Phi$ backbone dihedral angle of the central residue (c) or the
$\Psi$ angle (d). The backbone nitrogen (N) is in blue, the carboxyl (C=O)
oxygen in red, and the carbon atoms in tan. The C$\alpha$ atom is the one
without a (red) oxygen bound, and with the C$\beta$ (tan) branching off of the
backbone. These structural illustrations were created using Chimera.

Based on known protein structures, we can derive empirical distributions of
phi and psi angle combinations. This distribution is visualised in a so-called
Ramachandran plot of phi (horizontal) vs. psi (vertical), as shown in Figure
1.8. Firstly, we can observe that only some combinations of phi and psi angles
are allowed, e.g. light and dark outlined areas, whilst others are very
uncommon (outside areas). The allowed region are the secondary structure
elements, such as the $\alpha$-helix (with negative phi and psi angles) and
$\beta$-sheet (with negative phi and positive psi angles). Additionally, there
is a smaller area that corresponds to the left-handed helix, which is observed
but less frequently encountered. The areas without data points, the disallowed
regions, indicate combinations of phi and psi angles that result in steric
hindrance among the backbone atoms and are therefor not observed.

#### The omega torsion angle

The peptide bond (between C=O and N–H) chemically connects two amino acid
residues together. The consecutive peptide bonds form the backbone of the
protein. Strictly speaking the peptide bond is a torsion angle like the phi
and psi angles, however this bond is different. Due to the physiochemical
properties of this bond it cannot rotate freely, this is related to the fact
that it is in between a C=O and N–H group. This bond angle is called $\omega$
or omega. In proline residues, it can switch between two possible angles in a
process called ‘proline isomerisation’.

####  1.2.6 Secondary structure assignment

Secondary structure _assignment_ involves determining the secondary structure
class for each residue in a protein based on its structure. It is a structure-
based definition for secondary structure. Protein structures are typically
stored as a set of coordinates for each atom in the structure, see also
Chapter “LABEL:ch:ChDBClass”. Various features such as phi and psi angles or
hydrogen bonding patterns, can be used to assign secondary structure.

The most commonly used method to assign secondary structure is the Dictionary
of Secondary Structure of Proteins, or DSSP Kabsch and Sander (1983), but
several others exist such as Stride Heinig and Frishman (2004). DSSP first
assigns hydrogen bonds to pairs of atoms, and uses these pairs to infer the
secondary structure. For example, if several consecutive residues have
hydrogen bonds that are four places ahead in the sequence, these residues are
designated to be part of an $\alpha$-helix by DSSP. Minimum lenghts of
secondary structure elements are also considered by these methods, to avoid
assigning a single residue as an $\alpha$-helix.

###  1.3 Tertiary structure

The the tertiary structure of the protein, which represents its complete
structure, consists of secondary structure elements, or motifs (see also Panel
“Secondary structure motifs”). The arrangement of secondary structure elements
along the protein chain, and their folding to establish contacts in the three-
dimensional structure, is called the _protein fold_. This is also referred to
as ‘protein topology’. Four main fold categories are distinguished:
all-$\alpha$, all-$\beta$, $\alpha$/$\beta$ and $\alpha+\beta$ as shown in
Figure 1.9.

A B

C D

Figure 1.9: The four main protein fold classes, here showing a more or less
famous example for each of them. (A) all-$\alpha$: myoglobin, solved in 1960
by Sir John Kendrew, for which he received the Nobel prize (PDB:1mbn, Kendrew
et al., 1960), consisting of only alpha-helices. (B) all-$\beta$:
Immunoglobulin domain, consisting of only beta-strands (PDB:1igt, Harris et
al., 1997). (C) $\alpha$/$\beta$ lysozyme by DC Phillips, where one domain is
helical, and another strands (here on the bottom right) (PDB:1lyz, Diamond,
1974). (D) $\alpha$+$\beta$ triose phosphate isomerase, where helical and
strand regions intermingle (PDB:1tim, Banner et al., 1976).

#### Secondary structure motifs

Secondary structure elements often occur in the protein structure in
particular combinations, called ‘secondary structure motifs’. Some of these
can be very informative, e.g. for assessing protein function, which is why
they form the basis of structural classification schemes. As an example,
Figure 1.9 shows the four main fold classes from one of the protein databases,
SCOP Andreeva et al. (2008). For a comprehensive treatise on secondary
structure motifs, we refer to Branden and Tooze (1998). Also, you can find
more on this in Chapter “LABEL:ch:ChDBClass”.

####  1.3.1 Hydrophobic core

Proteins in a cell are typically surrounded by water (except for transmembrane
proteins which are located inside of cell membranes). Water is a polar
molecule: with the oxygen atom slightly negative and the hydrogen slightly
positive, see also Figure 1.3. Hydrophobic sidechains cannot make hydrogen
bonds with the water molecules, therefore the solvent avoids to make contact
with hydrophobic residues. Oil is also a hydrophobic substance, and as you may
well know: oil and water do not mix well.

In a protein, the hydrophobic residues want to be shielded from the water, in
any stable configuration. The result is that the protein will adopt a
conformation in which the exposure of the hydrophobic sidechains to the water
is minimized; hydrophobic residues will tend to become buried in the interior
of the protein. This effect is known as the ‘hydrophobic effect’ and is the
main driving force for protein folding. In the folding process, this leads to
what is called the ‘hydrophobic collapse’. Figure 1.2 sketches the role of
hydrophobic residues in the folded and unfolded states of a protein. We will
come back to the folding process and the thermodynamics and driving forces
behind in much more depth in Chapter “LABEL:ch:ChIntroDyn”.

For now, it is important to realize that the interior of the protein will
consist mostly of residues with hydrophobic sidechains, but the backbone is
polar. It is not possible to keep all the polar backbone parts of the buried
hydrophobic residues at the surface of the protein. At the surface, the polar
sidechains as well as the backbone, form hydrogen bonds with the water, but
the backbone of the buried hydrophobic residues cannot do this. This creates a
problem, as it is very unfavourable if these backbone hydrogen bonding
capacity remains unsatisfied. The solution to this problem is the formation of
secondary structure, as covered in the previous section. Regular secondary
structures will therefore usually make up the core of the protein.

####  1.3.2 Protein domains

Protein domains are conserved regions that will be mentioned often in this
book. More generally, we could define them as self-folding, evolutionary
conserved subunits of structure. Domains typically have a specific molecular
function, and may recurrently appear in different proteins. Most eukaryotic
proteins have multiple domains, which may be linked together by a small
linker, or large disordered regions. There are serveral distinct ways in which
domains may be described, each of which will be explained in further detail
elsewhere in this book. In Chapter “LABEL:ch:ChDBClass” we will see how
structural domains can be defined; in Chapter “LABEL:ch:ChIntroPred” it
becomes clear that structure prediction is most effective at the domain level.

###  1.4 Quarternairy structure

Protein-protein interactions (PPIs) involve the binding of two or more
proteins, leading to the formation of a protein complex known as the
quaternary protein structure. This structure represents a natural extension of
the primary, secondary, and tertiary structures. It is worth noting that
protein function often emerges at the level of the quaternary structure, as it
determines the specific function performed by the protein complex. We will
come back to protein function, and the role of interactions, in Chapter
“LABEL:ch:ChFuncPred”.

###  1.5 Key points

  * •

Proteins fold from an unstructured polypeptide coming from the ribosome into
their functional native conformations.

  * •

Structure Basics:

    * –

primary, secondary, tertiary, tertiary

    * –

phi/psi angles

    * –

hydrogen-bonds

  * •

Loops tend to be more flexible

  * •

Hydrogen bonds may be satisfied by backbone, sidechain or water

  * •

PDB & Structural genomics: bias in data

  * •

Protein structure may be predicted from sequence

  * •

Function may be derived from structure

###  1.6 Further Reading

  * •

“Sequence Analysis” Durbin et al. (1998)

  * •

“Introduction to Protein Structure” Branden and Tooze (1998)

### Author contributions

Wrote the text: | AJ, EvD, BS, HM, KAF, SA
---|---
Created figures: | HM, JG, KAF, SA
Review of current literature: | HM, KAF, SA
Critical proofreading: | BS, KAF, SA
Editorial responsibility: | SA, KAF

The authors thank Reza Haydarlou and Nicola Bonzanni @ for non-expert
feedback.

## References

  * Andreeva et al. (2008) Andreeva, A., Howorth, D., Chandonia, J. M., Brenner, S. E., Hubbard, T. J. P., Chothia, C., and Murzin, A. G. (2008).  Data growth and its impact on the SCOP database: New developments.  Nucleic Acids Research, 36(SUPPL. 1), 419–425.
  * Banner et al. (1976) Banner, D., Bloomer, A., Petsko, G., Phillips, D., and Wilson, I. (1976).  Atomic coordinates for triose phosphate isomerase from chicken muscle.  Biochemical and Biophysical Research Communications, 72(1), 146–155.
  * Branden and Tooze (1998) Branden, C. and Tooze, J. (1998).  Introduction to protein structure.  garland publishing, New York.
  * Chen et al. (2010) Chen, V. B., Arendall, W. B., Headd, J. J., Keedy, D. A., Immormino, R. M., Kapral, G. J., Murray, L. W., Richardson, J. S., Richardson, D. C., and IUCr (2010).  MolProbity: All-atom structure validation for macromolecular crystallography.  Acta Crystallographica Section D: Biological Crystallography, 66(1), 12–21.
  * Diamond (1974) Diamond, R. (1974).  Real-space refinement of the structure of hen egg-white lysozyme.  Journal of Molecular Biology, 82(3), 371–391.
  * Dobson (2003) Dobson, C. M. (2003).  Protein folding and misfolding.  Nature, 426(6968), 884–890.
  * Durbin et al. (1998) Durbin, R., Eddy, S. R., Krogh, A., and Mitchison, G. (1998).  Biological Sequence Analysis.  Cambridge University Press.
  * Harris et al. (1997) Harris, L. J., Larson, S. B., Hasel, K. W., and McPherson, A. (1997).  Refined Structure of an Intact IgG2a Monoclonal Antibody.
  * Heinig and Frishman (2004) Heinig, M. and Frishman, D. (2004).  STRIDE: a web server for secondary structure assignment from known atomic coordinates of proteins.  Nucleic Acids Research, 32(Web Server), W500–W502.
  * Kabsch and Sander (1983) Kabsch, W. and Sander, C. (1983).  Dictionary of Protein Secondary Structure: Pattern Recognition of Hydrogen-Bonded and Geometrical Features.  Biopolymers, 22, 2577–2637.
  * Kendrew et al. (1960) Kendrew, J. C., Dickerson, R. E., Strandberg, B. E., Hart, R. G., Davies, D. R., Phillips, D. C., and Shore, V. C. (1960).  Structure of myoglobin: A three-dimensional Fourier synthesis at 2 A resolution.  Nature, 185(4711), 422–427.
  * Pettersen et al. (2004) Pettersen, E. F., Goddard, T. D., Huang, C. C., Couch, G. S., Greenblatt, D. M., Meng, E. C., and Ferrin, T. E. (2004).  UCSF Chimera – A visualization system for exploratory research and analysis.  Journal of Computational Chemistry, 25(13), 1605–1612.
  * Ward et al. (2004) Ward, J. J., Sodhi, J. S., McGuffin, L. J., Buxton, B. F., and Jones, D. T. (2004).  Prediction and functional analysis of native disorder in proteins from the three kingdoms of life.  Journal of molecular biology, 337, 635645.


# Variable Stars in the giant satellite galaxy Antlia 2

A. Katherina Vivas Cerro Tololo Inter-American Observatory/NSF’s NOIRLab,
Casilla 603, La Serena, Chile  Clara E. Martínez-Vázquez Cerro Tololo Inter-
American Observatory/NSF’s NOIRLab, Casilla 603, La Serena, Chile  Gemini
Observatory/NSFʼs NOIRLab, 670 N. A’ohoku Place, Hilo, HI 96720, USA  Alistair
R. Walker Cerro Tololo Inter-American Observatory/NSF’s NOIRLab, Casilla 603,
La Serena, Chile  Vasily Belokurov Institute of Astronomy, University of
Cambridge, Madingley Road, Cambridge CB3 0HA, UK  Ting S. Li Department of
Astronomy and Astrophysics, University of Toronto, 50 St. George Street,
Toronto ON, M5S 3H4, Canada  Denis Erkal Department of Physics, University of
Surrey, Guildford GU2 7XH, UK

###### Abstract

We report 350 pulsating variable stars found in four DECam fields ($\sim 12$
sq. deg.) covering the Antlia 2 satellite galaxy. The sample of variables
includes 318 RR Lyrae stars and eight anomalous Cepheids in the galaxy.
Reclassification of several objects designated previously to be RR Lyrae as
Anomalous Cepheids gets rid of the satellite’s stars intervening along the
line of sight. This in turn removes the need for prolific tidal disruption of
the dwarf, in agreement with the recently updated proper motion and peri-
centre measurements based on Gaia EDR3. There are also several bright
foreground RR Lyrae stars in the field, and two distant background variables
located $\sim 45$ kpc behind Antlia 2. We found RR Lyrae stars over the full
search area, suggesting that the galaxy is very large and likely extends
beyond our observed area. The mean period of the RRab in Antlia 2 is 0.599
days, while the RRc have a mean period of 0.368 days, indicating the galaxy is
an Oosterhoff-intermediate system. The distance to Antlia 2 based on the RR
Lyrae stars is $124.1$ kpc ($\mu_{0}=20.47$) with a dispersion of $5.4$ kpc.
We measured a clear distance gradient along the semi-major axis of the galaxy,
with the South-East side of Antlia 2 being $\sim 13$ kpc farther away from the
North-West side. This elongation along the line of sight is likely due to the
ongoing tidal disruption of Ant 2.

††facilities: Blanco (DECam)††software: TOPCAT Taylor (2005); PHOTRED Nidever
et al. (2017)

##  1 Introduction

The environment of our Milky Way Galaxy (MW) contains more than 50 known
smaller galaxies, that range in size from large dwarf galaxies such as the
Magellanic Clouds with active star formation and absolute magnitude
$M_{V}\sim-18$, to the many quiescent ultra faint dwarf (UFD) galaxies with
luminosities similar to globular clusters (Simon, 2019), the faintest of which
have $M_{V}\sim 0$. Discovered mostly by deep wide-field imaging surveys in
the past two decades (see reviews by Willman, 2010; McConnachie, 2012;
Belokurov, 2013; Simon, 2019) many of these low stellar mass galaxies show
signs of their interaction with the MW by elongated shape or by associated
tidal debris. The plethora of stellar streams that are now known (see e.g.
Shipp et al., 2018) indicates that disruption events may be common. Analyses
of the structure of our galaxy, together with chemo-dynamic analyses of the
stellar content of the thick disk and halo, show that encounters and mergers
have had a substantial effect on the properties of the MW over its lifetime,
and are continuing to do so.

Figure 1: Absolute magnitude versus half-light radius for satellite galaxies
of the MW and M31 (McConnachie, 2012; Martin et al., 2016; Drlica-Wagner et
al., 2020; Ji et al., 2021). This plot zooms into the region of the brightest
and largest satellite galaxies, with most UFDs lying outside the plotted
region. The red dotted line indicates surface brightness $\mu=32$ mag/arcsec2.

A convenient way to view the totality of the MW companion galaxies is by the
size-luminosity plot (see for example Figure 11 in Torrealba et al., 2019)
which is well-populated over 18 magnitudes in luminosity and half light radii
($r_{h}$) from 20 to $\sim$4000 pc. However, the completeness as a function of
position in this diagram is not well-known except for the brighter systems.
Apart from galaxies hidden behind the Galactic plane, there is possible
confusion between low luminosity globular clusters and the fainter UFDs, with
the compilation of the fainter galaxies also likely to be severely incomplete.
Future surveys such as the Vera C. Rubin Legacy Survey of Space and Time
(LSST) are expected to help redress this situation. Figure 1 shows a zoom of
the size-luminosity plot in the region of the brightest and largest of the
satellite galaxies. The low luminosity/large size region in Figure 1 appears
uninhabited, but this could be an observational effect as such low surface
brightness galaxies will be dominated by Galactic foreground stars. Indeed,
the discovery of Crater 2 by Torrealba et al. (2016) and, in particular, the
subsequent discovery of Antlia 2 (Ant 2) by Torrealba et al. (2019) from Gaia
proper motions in a field with much higher foreground contamination than
Crater 2, shows how nearly invisible such objects can be111these galaxies can
also be found under the names Antlia II and Crater II in the literature.

Figure 2: Spatial coverage of our DECam observations of Ant 2 in equatorial
coordinates. The grey background, which shows the footprint of our survey, is
a density map made with all stars in our catalog. The two black ellipses
indicate the $1\,r_{h}$ and $2\,r_{h}$, as measured by Torrealba et al.
(2019). Colored symbols indicate the location of pulsating variable stars
found in the field: red circles and green diamonds are RRL stars and AC in Ant
2, while open blue squares indicate the location of bright RRL stars which are
presumably field halo stars. The two yellow triangles show two faint RRL stars
located beyond Ant 2. For reference the diagonal lines indicate lines of
constant galactic latitude.

The RR Lyrae (RRL) variable stars are a powerful tool for studying the
morphology, metallicity and age of, in particular, low surface brightness
galaxies (Catelan & Smith, 2015). Ubiquitous in any population more than $\sim
10$ Gyr old (Savino et al., 2020), they are easy to identify even in very
crowded fields, and being standard candles they can be definitively assigned
(or not) to a minority population galaxy immersed in the MW. Apart from the
rare case of Leo T (Clementini et al., 2012), all other UFD galaxies so far
known terminated their star formation early ($\sim 10$ Gyr or older Simon,
2019) and so the RRL stars are representative of the dominant (or only)
population present in these galaxies. These properties of RRL stars are
particularly useful when studying galaxies like Ant 2 which, being both a low
surface brightness object and located at a galactic latitude of
$b\sim+11\arcdeg$, suffers from a very high foreground contamination.

The discovery of Ant 2 by Torrealba et al. (2019) was triggered by the
identification of a group of three RRL stars in the Gaia DR2 catalog
(Clementini et al., 2019) which were close together in the sky, shared similar
proper motions, and were located at roughly the same distance. Further
investigation by the discovery team however concluded that the RRL stars were
not actually part of Ant 2 since they were located in front of it. Torrealba
et al. (2019) suggested that those three RRL stars were the near side of a
cloud of debris material originated from Ant 2 during its disruption by the
tidal forces of the Milky Way. A complete survey of RRL stars in this galaxy
is needed to confirm/deny such a scenario.

In this paper we describe the search and discovery of RRL stars and other
variables, either in Ant 2 or its line of sight, from observations made with
the Dark Energy Camera (DECam, Flaugher et al., 2015), and discuss the
properties of Ant 2 from an analysis of their pulsational properties and
distribution. In § 2 we describe the observations, data reduction and time
series analysis. The population of RRL stars in Ant 2 is discussed in detail
in § 3, and we compared their spatial distribution with a model of Ant 2’s
tidal disruption in § 4. Anomalous Cepheids in Ant 2 are described in § 5.
Finally, conclusions are presented in § 6, with time series data tabulated in
Appendix § A.

##  2 Observations

The Ant 2 observations presented here were collected using DECam on the Víctor
M. Blanco 4-meter telescope at Cerro Tololo Inter-American Observatory (CTIO),
Chile, on two part nights in November and December 2018, and two full nights
in January 2019, as detailed in Table 1. All these nights were close to Full
Moon, therefore we decided to observe in the $r$ and $i$ filters, with
exposures 180s and 240s respectively. With its 3 sq. deg. field of view (FoV),
DECam is an ideal instrument to study this large galaxy ($r_{h}=1\fdg 27$,
Torrealba et al., 2019). We used four pointings (Table 2), almost non-
overlapping, to cover the galaxy (see Figure 2). During photometric conditions
standard star fields were also observed.

Table 1: Log of the DECam Ant 2 observations. Run date | $r,i$ | Image Quality | Comments
---|---|---|---
| exposures | (arcsec) |
2018 Nov 23 | 32 | 0.8 | clear
2018 Dec 19 | 56 | 1.0 | clear
2019 Jan 20 | 71 | 1.0 | thin cirrus
2019 Jan 21 | 117 | 1.0 | thin cirrus

The observational strategy consisted of imaging consecutively the four fields
in $r$ and $i$, and then repeating the sequence but with an offset of
$75\arcsec$ and $60\arcsec$ in $\alpha$ and $\delta$, respectively, to fill in
the gaps between CCDs. During a night the typical time between observations of
the same field/filter was $\sim 30$ min.

Table 2: Central coordinates of observed fields Field |  $\alpha$ (J2000.0) |  $\delta$ (J2000.0)
---|---|---
| (deg) | (deg)
A | 143.08400 | -35.32892
B | 144.81242 | -36.43172
C | 142.87454 | -37.10664
D | 144.81225 | -38.25325

###  2.1 Data Reduction and Photometry

The images were processed by the DECam Community Pipeline (Valdes et al.,
2014), which removes the instrument signature and provides several data
products222Raw and reduced images are publicly available through the NOIRLab
Astro Data Archive (https://astroarchive.noirlab.edu), under propID
2018B-0941. This was followed by application of the photred package as
described in detail by Nidever et al. (2017). photred efficiently runs the
daophot photometry programs (Stetson, 1987, 1994) automatically on a night-by-
night basis, after choosing options via a setup file. For the individual
images, photometry was performed using the allstar program. Astrometry is
referenced to the system of the Gaia catalog. We also ran a separate
processing where all four nights were grouped together and the forced
photometry program allframe used to produce a single photometry list for each
pointing.

Figure 3: (Left) Observational CMD of the full observed area in Ant 2,
containing $\sim$ 1 million stars. The grey dashed line indicates the Gaia
limit ($G=20$) we used to explore the blue plume population seen at
$(r-i)\sim-0.2$. (Middle) Observational CMD showing only stars within
$1\arcdeg$ from the center of Ant 2, 297064 stars. (Right) Reddening-corrected
CMD of stars within $1\arcdeg$ from the center of Ant 2.

Photometric calibration was obtained from the standard star fields observed
during clear conditions. The resulting photometry is on the SDSS system. The
left color-magnitude diagram (CMD) shown in Figure 3 contains 1,036,351
objects after isolating point sources by requiring CHI$\leq 3.0$,
$-1.0\leq\rm{SHARP}\leq 1.0$, and PROB$\geq 0.8$. There are no clear features
of the Ant 2 system in this CMD except by a Horizontal Branch (HB) at $r\sim
21$. The CMD is dominated by foreground populations, which at these low
galactic latitudes ($b\sim 11\arcdeg$) is large. The HB looks extended in
brightness which is a likely consequence of both differential extinction and
distance gradient within the galaxy, as we discuss later in this paper (see §
3.3). There is a hint of a blue plume population at $(r-i)<0$ and $18<r<23.5$.
Just from the CMD it is not obvious if this blue plume is evidence of a
younger population present in Ant 2, or if it is formed by Galactic foreground
stars. To explore this we analyzed parallaxes by Gaia EDR3 (Gaia Collaboration
et al., 2021) for stars brighter than $G=20$, shown in Figure 3 (left panel)
as stars above the grey dashed line. The blue population only shows up for a
high parallax selection, and the resulting absolute magnitudes suggest these
blue stars are mostly white dwarfs and probably some more exotic objects like
extreme horizontal branch stars or extremely low mass white dwarfs, which are
significantly brighter than normal white dwarfs. Although this quick analysis
is limited only to the bright part of the CMD, the coherence of the observed
feature suggest all of them are MW white dwarfs, which is not surprising since
the line of sight to Ant 2 goes trough the Galactic disk. This conclusion does
not preclude Ant 2 of having some young main sequence or Blue Straggler stars,
but if these indeed exist they are likely few and hard to pick from the CMD.

The HB looks more defined and narrow when looking only at stars within a
radius $r<1\arcdeg$ (Figure 3, middle panel), where the extinction is more
uniform and the distance gradient is less noticeable. Only when the CMD is
corrected by extinction, a clear RGB and HB is visible (Figure 3, right
panel). We obtained E(B-V) from the Schlegel et al. (1998) interstellar dust
maps using the Python task `dustmaps` (Green, 2018). The photometry is not
deep enough to reach to the main sequence turnoff of Ant 2.

####  2.1.1 Variable Stars

Figure 4: Reddening-corrected CMD with the variable stars identified in this
work. For reference we also show the high probability spectroscopic members in
the RGB of Ant 2, as identified by Ji et al. (2021). Figure 5: Histogram of
the mean $r$ magnitudes of all periodic variable stars found in the field of
Ant 2. Figure 6: Sample of light curves. For each star the $r$, $i$ data are
displayed in the top/bottom panels. Stars V249 and V301 are bright
(foreground) RRL stars; V34 and V62 are AC; V29 and V139 are RRab in Ant 2;
V63 and V85 are RRc in Ant 2; V54 and V186 are RRd in Ant 2, phased with their
first overtone periods; V134 and V304 are the two faint RRL stars in the
background of Ant 2. For all the types $ab$ and $c$ the underlying blue line
is the best fitted template to the light curve.

We selected variable stars from our catalog following the same recipe as in
previous works by our group, namely Vivas et al. (2016, 2019, 2020). In
particular for this work, we pre-selected stars which were flagged as
variables in both the $r$ and $i$ band, have at least 12 observations in each
band, have magnitudes in the range $17<r<22.5$, colors in the range
$-0.3<(r-i)<0.4$, and an amplitude in the $r$ band of at least 0.1 mag. Then,
the pre-selected stars were searched for periodicity in the range $0.1-2.5$
days, with the final selection and classification was made by visual
inspection of the phased light curves. These constraints were designed to find
RRL and anomalous Cepheids (AC) in the region of the instability strip, with a
very loose color constraint to give room to variables with high reddening. The
light curves we examined have on average 33 epochs in each filter; in the
region of overlap between fields there are light curves with as many as 68
epochs/filter.

We discovered numerous eclipsing binaries, a consequence of the large disk
foreground population in our data, which are not studied further in this
paper. Stars identified as first-overtone RRL pulsators, or RRc stars, which
are prone to be contaminated by eclipsing binaries of the W Ursa Major type
(e.g. Kinman & Brown, 2010) because of their near to sinusoidal light curves,
were carefully examined by looking at their colors and their location in a
period-amplitude diagram. Several candidates were discarded as RRc because
either they were too red for being this type of pulsator or because their
amplitudes and periods did not lie in the correct locus of a Bailey (period
versus amplitude) diagram.

In total we found 350 periodic variable stars in the Ant 2 field which were
preliminarily classified as RRab (211 stars), RRc (115 stars), RRd (21 stars),
and AC (3 stars). In the latter group the periods were too long ($>1$ day) for
being classified as RRL. By placing the variable stars in the CMD (Figure 4),
it seems clear that all the variables in the range of $19.5<r<20.8$ should be
AC stars in Ant 2. In this group there are eight stars, including the three
variables with longer periods mentioned before as well as five stars
classified initially as RRab and RRc. So after reclassifying these as AC
stars, the final numbers are 341 RRL stars (207 RRab, 114 RRc, 21 RRc), and
eight AC. Table 3 contains the properties of all the stars: ID, right
ascension, declination, pulsational period, number of observations, amplitude
and mean magnitude in each band ($r$ and $i$), extinction in $i$, and type of
variable. The ID numbering from V1 to V350 was assigned according to the
elliptical distance (see 3.4), with the lower numbers being those closer to
the center of Ant 2. Amplitudes and mean magnitudes for RRab and RRc were
obtained from the best fitted template (from the library by Sesar et al.,
2010) to the light curves. The mean magnitudes were obtained by integrating
the templates in intensity units and transforming the result back to
magnitudes.

As shown in Figure 4 and in a histogram of magnitudes of the variable stars
(Figure 5), there is a group of 22 bright RRL stars with $r<19.0$ which are
classified as a foreground population from the halo, and possibly
alternatively from the thick disk, of the MW. These bright RRL stars are
located at distances between 16 kpc and 40 kpc from the Sun. The majority of
the RRL stars in our sample (318 stars, 91%), however, are concentrated in the
HB of Ant 2 at $r\sim 21.3$ in the CMD. We discuss these stars in detail in
the next section. In addition, there are two RRL stars (V134 and V304) which
lie well below the HB ($r>21.9$), and thus appear to be located behind Ant 2
(see § 3.3.1 for further discussion).

A sample of light curves is shown in Figure 6, including two bright
(foreground) RRL stars, two AC, six RRL stars in Ant 2 (two of each type), and
finally the two faint RRL stars likely located behind Ant 2. The full
photometry dataset and light curves for all the variables can be found in the
appendix (§ A). For the RRL stars in Ant 2 the typical photometric errors of
the individual epochs are $0.04$ and $0.03$ mag in $r$ and $i$ respectively

Most of the periodic variable stars found in this work are new discoveries
since they are fainter than the limiting magnitude for most wide surveys of
variables such as the CRTS (Drake et al., 2014) or Gaia (Clementini et al.,
2019). We matched our catalog with the Gaia DR2 RRL star listing (Clementini
et al., 2019) and found 17 stars in common, all of them brighter than
$r<20.3$. The RRL stars in Ant 2 are just too faint for Gaia. On the other
hand, there are 39 Gaia RRL stars within our footprint, and we did not recover
21 of them, mostly because they were too bright ($r<17$) for our survey. There
are, however, two Gaia RRL stars in the range $18.5<r<20.2$ that are in our
magnitude range; they were indeed flagged as variable but we were unable to
find a period for them333Gaia IDs are 5437028340146753664 and
5436057883696115328. In one case the star was located close to the border of
one field and had only $\sim 15$ epochs/band, which was not enough to obtain a
period, although our data is consistent with the Gaia period. In the second
case, the Gaia star has $G=20.2$, which is close to the faint limit for the
RRL stars in that catalog. Our data does not agree either with the period nor
with the amplitude given by Gaia, hinting for a possible misclassification.

Table 3: Periodic Variable stars in the field of Ant 2

ID | $\alpha$ | $\delta$ | Period | N (r) | Amp (r) | Mean r | N (i) | Amp (i) | Mean i | Ai | Dist |  $\sigma$Dist | TypeaaTypes: ab $=$ type ab RRL stars; c $=$ type c RRL stars; AC $=$ anomalous Cepheids; Fab $=$ type ab field RRL stars; Fc $=$ type c field RRL stars;
---|---|---|---|---|---|---|---|---|---|---|---|---|---
| (deg) | (deg) | (d) |  | (mag) | (mag) |  | (mag) | (mag) | (mag) | (kpc) | (kpc) |
V1 | 143.87486 | -36.91461 | 0.66093 | 41 | 0.61 | 21.29 | 41 | 0.38 | 21.16 | 0.27 | 129.4 | 2.6 | ab
V2 | 143.73833 | -36.86352 | 0.35250 | 65 | 0.66 | 21.10 | 67 | 0.41 | 20.98 | 0.26 | — | — | d
V3 | 143.90192 | -36.93597 | 0.39555 | 46 | 0.52 | 21.33 | 46 | 0.25 | 21.18 | 0.27 | 124.2 | 2.5 | c
V4 | 143.73605 | -36.91526 | 0.56934 | 26 | 0.88 | 21.31 | 25 | 0.66 | 21.19 | 0.26 | 127.2 | 2.5 | ab
V5 | 143.93247 | -36.79384 | 0.39872 | 67 | 0.49 | 21.37 | 66 | 0.30 | 21.25 | 0.26 | 129.2 | 2.6 | c
V6 | 143.94381 | -36.98518 | 0.60702 | 33 | 0.28 | 21.36 | 34 | 0.21 | 21.19 | 0.28 | 128.4 | 2.6 | ab
V7 | 143.83054 | -36.99803 | 0.58207 | 34 | 0.63 | 21.34 | 33 | 0.52 | 21.19 | 0.28 | 127.1 | 2.5 | ab
V8 | 143.83305 | -37.02513 | 0.37702 | 34 | 0.49 | 21.40 | 29 | 0.30 | 21.24 | 0.28 | 126.2 | 2.5 | c

Note. — Table 3 is published in its entirety in the machine-readable format. A
portion is shown here for guidance regarding its form and content.

##  3 RR Lyrae stars in Ant 2

There are 318 RRL stars in Ant 2 of which 193 are RRab, 104 are RRc, and 21
are double mode pulsators, or RRd. We discuss their properties in the
following subsections:

###  3.1 Oosterhoff Type

Figure 7: Bailey diagram of RRL stars in Ant 2. The black solid, grey solid
and black dashed lines represent the locus of Oo I, Oo II and Oo-int systems,
scaled to the r-band from Fabrizio et al. (2019).

The Oosterhoff type (Oo, Oosterhoff, 1939) was originally applied to RRL in
galactic globular clusters; it revealed a dichotomy in the mean periods and in
the ratio of the numbers of fundamental (RRab) and first-overtone (RRc)
variables. This dichotomy is not observed in most of the satellite galaxies of
the MW (Catelan, 2009) and M31 (Martínez-Vázquez et al., 2017), which are
usually classified as Oosterhoff-intermediate (Oo-int) since their properties
lie in between those for the two original Oo I and Oo II groups.

The mean period of the RRab in Ant 2 is 0.599 days, while the RRc have a mean
period of 0.368 days. The ratio $N_{c}/(N_{ab}+N_{c})$ is 0.35. From Smith
(1995), mean periods of RRab are 0.55d and 0.64d, and mean periods of RRc are
0.32d and 0.37d for Oo I and Oo II systems, respectively. From the same
source, the ratio of type $c$ stars over the sum of $ab$ and $c$ are 0.17 and
0.44 for Oo I and Oo II, respectively. Comparing these values with our data,
Ant 2 is clearly in the middle between the two Oo groups, suggesting a Oo-int
classification the same as found for many other dSph galaxies in the MW
neighborhood.

A Bailey diagram, a plot of amplitude of the light curve versus period, is now
considered (Smith, 1995) the best way to infer the Oo classification of a
stellar system. In Figure 7 we show the Bailey diagram for Ant 2, and the
fiducial lines for Oo I and Oo II as defined by Fabrizio et al. (2019) but
scaled by a factor of 0.94 to take into account that we have amplitudes in the
$r$ band and not in $V$. The scale factor was calculated by comparing the
amplitudes of RRL stars in common between SDSS Stripe 82 (Sesar et al., 2010)
and CRTS (Drake et al., 2014). The RRab stars in Ant 2 are mostly found
between the fiducial lines for the Oo I and Oo II group, confirming that Oo-
int is indeed the best classification for this system.

We estimate the percentage of Oo I and Oo II like stars in Ant 2 by counting
how many RRab stars are located on each side of the Oo-int relation by
Fabrizio et al. (2019). We obtained that 75% of the stars are Oo I while 25%
are Oo II like. These results are consistent with what was found in Martínez-
Vázquez et al. (2017) for RRL stars in Local Group dwarf galaxies where the
majority of stars ($\sim$ 80%) are distributed close to the locus of Oo I
type.

###  3.2 Spatial Distribution

Table 4: Shape parameters of Ant 2 |  $\alpha$(J2000.0) |  $\delta$ (J2000.0) | $\epsilon$ | PA |  $1\sigma$ semi-major axis | $r_{h}$
---|---|---|---|---|---|---
| (deg) | (deg) |  | (deg) | (deg) | (deg)
This work | $143.83\pm 0.02$ | $-36.86\pm 0.02$ | $0.28\pm 0.03$ | $141\pm 3$ | $0.88\pm 0.03$ |
Torrealba et al. (2019) | $143.87\pm 0.05$ | $-36.77\pm 0.10$ | $0.38\pm 0.08$ | $156\pm 6$ |  | $1.27\pm 0.12$
Ji et al. (2021) | $143.81\pm 0.05$ | $-36.70\pm 0.08$ | $0.60\pm 0.04$ | $154\pm 2$ |  | $1.11\pm 0.08$
Figure 8: Shape of the Ant 2 galaxy from fitting a bi-variate Gaussian to the
RRL star sample. In red we show the center and the $1\sigma$ and $3\sigma$
semi-major axis of the resulting ellipse. For comparison we also show the
center (blue and green crosses) and shape parameters (blue and green ellipses)
determined by Torrealba et al. (2019, T19) and Ji et al. (2021, J21). For
those two cases the semi-major axis of the ellipse represents the half-light
radius ($r_{h}$) of the galaxy.

The on-sky spatial distribution of the RRL stars in Ant 2 can be seen in
Figure 2. RRL stars were found in the full footprint of our observations,
which reaches $\sim 2r_{h}$. Although the density of stars clearly decreases
with distance from the center of the galaxy, it is very likely that there are
additional stars extending beyond $2r_{h}$.

Because of the very low surface brightness of Ant 2, combined with its low
galactic latitude, contamination by fore/background stars is a challenge when
analyzing the properties of the galaxy. By contrast, the RRL stars are a very
pure sample of members of the galaxy. There is virtually no contamination by
halo stars at this large distance from the Galactic center. Thus, we used the
RRL stars to infer the shape of Ant 2 by fitting a bi-variate Gaussian
distribution444using AstroML fit-bivariate_normal routine (Ivezić et al.,
2014) to the RRL stars to find the center, ellipticity ($\epsilon$), position
angle (PA) and size of Ant 2. The results can be seen in Figure 8, and in
Table 4. Within the $1\sigma$ errors, we found the same center and ellipticity
as Torrealba et al. (2019). The position angle is slightly different with
respect to the one obtained Torrealba et al. (2019) but within $2\sigma$
errors of each other. There is more disagreement with the structural
parameters found by Ji et al. (2021), particularly in the ellipticity, since
they find a significantly more elongated structure than us. We obtain a
$1\sigma$ semi-major axis of $52\farcm 6$. Since we fitted Gaussian
distributions this value is not directly comparable with $r_{h}$ from either
Torrealba et al. nor Ji et al.. We note that this elongation is aligned with
the reflex corrected proper motions, once the LMC is accounted for (see Ji et
al., 2021, for more details).

###  3.3 Distance to Ant 2 and Distance Gradient

Figure 9: (Top) Map in equatorial coordinates of the interstellar extinction in the $r$ band for all the RRL stars found in Ant 2 from Schlafly & Finkbeiner (2011). (Bottom) Map of the individual distances to RRL stars (type ab and c only). In both plots, the black cross marks the center of the distribution of the RRL stars.  Table 5: Distance to Ant 2 Type | Distance (kpc) | Std Dev (kpc) | N
---|---|---|---
ab | 124.7 | 5.5 | 193
c | 123.0 | 4.9 | 104
ALL | 124.1 | 5.4 | 297

Figure 10: (Left) Distance to the RRL stars along the semi-major axis of Ant
2. The red line is the best fit to the data. The bottom plot shows the same as
above but for the RRL stars in the low extinction sample. (Right, top)
Interstellar extinction, $A_{r}$, of RRL stars along the semi-major axis of
Ant 2. The dashed grey line at $A_{r}=0.46$ is an arbitrary limit to define a
low-extinction sample. (Right, bottom) Same as the left panels but with a
wider view in both axis. The cyan crosses in the background represent the
disruption model of Ant 2. The red line is the same as in the top left panel.

One of the most important characteristics of RRL stars is that they are very
good standard candles. Here we use the large number of variables in Ant 2 to
determine the distance to the galaxy. Extinction is high and variable in this
part of the sky due to the low galactic latitude location of Ant 2 (Figure 9).
We obtained extinctions from the Schlafly & Finkbeiner (2011)’s recalibration
of the dust maps by Schlegel et al. (1998). The mean extinction of the RRL
stars in Ant 2 in the $r$ band is $A_{r}=0.41$ mag, but is as high as 0.76 mag
for some stars. Figure 9 shows that there is a region of relatively low
extinction corresponding approximately with the central region of the galaxy.
The extinction increases towards the extremities of Ant 2, particularly
towards the South.

After correcting magnitudes for interstellar extinction, we calculated the
distance to each individual RRL star using the Period-Luminosity (PL) relation
by Cáceres & Catelan (2008) in the $i$ band, which has a formal uncertainty of
0.045 mag. This relationship has a metallicity dependence for which we used
the recent value of [Fe/H]$=-1.90$ (with a dispersion $\sigma=0.34$) derived
by Ji et al. (2021). The PL relation was applied to all RRab and RRc stars
(Table 5). For the later, we first fundamentalized the periods. We did not use
RRd stars because for these stars we did not fit a template to the light
curves and hence do not have a mean magnitude measured in the same way as the
other stars. The results from RRab and RRc are consistent with each other
(Table 5).

The mean distance given by the 297 RRL stars is 124.1 kpc, with a standard
deviation of 5.4 kpc. The corresponding distance modulus is $\mu_{0}=20.47$
with a dispersion of 0.09 mag. The mean of the individual errors in Ant 2 is
2.5 kpc, and thus significantly lower than the standard deviation of the
distribution. In order to ascertain what might be causing the large standard
deviation in the distance distribution we first explored any spatial
dependence of distance (Figure 9, bottom). It is clear from this map that
there is a gradient of distance in Ant 2 with the South-East part of the
galaxy being farther away than the North-West side. However, extinction is
much higher to the South-East of Ant 2 (Figure 9, top) and may be influencing
the distance determinations.

To better explore any possible correlation between the observed distance
gradient and the extinction we transformed the equatorial coordinates
($\alpha$, $\delta$) to planar coordinates ($\xi$, $\eta$) with Ant 2 centered
at ($0,0$), and we rotated the system so the semi-major axis of the galaxy
obtained here (Table 4) lies along the $x$-axis ($\xi^{\prime}$). Figure 10
(top) shows the extinction as a function of the semi-major axis. In this
coordinate system, the South-East part of Ant 2 is on the right side of the
plot (positive $\xi^{\prime}$). The middle panel shows the distance to the RRL
stars as a function of the semi-major axis and the distance gradient suggested
by the map in Figure 9 (bottom) is now clearer. The red line shows the best
linear fit to the data, which has a slope of 2.66 kpc/deg along the semi-major
axis, and a distance at $\xi^{\prime}=0\arcdeg$ of 124.2 kpc. Thus, in 5
degrees from one side of the galaxy to the other, there is a difference in
distance of $\sim 13$ kpc, which is much larger than the individual errors in
distance.

As seen in the upper panels of Figure 10, the behaviour of both extinction and
distance along the semi-major axis is completely different and thus the
observed distance gradient is likely real rather than an effect of improper
reddening correction. As a final check, we defined a “low-extinction” sample
defined (arbitrarily) as all stars with $A_{r}<0.46$ mag. The distance
gradient is still visible in this reduced sample of 238 stars (Figure 10,
bottom left panel). The best fitted line in this case has a slope of 2.72
kpc/deg along the semi-major axis, and intersection with the y-axis at 124.1
kpc. These values are almost identical to the full sample and confirm that
extinction is not causing the observed distance gradient. The gradient
measured as a function of declination is $-2.44$ kpc/deg (full sample). We
provide this alternative value since declination is a fixed parameter and the
semi-major axis depends instead on the assumed structural parameters of the
galaxy.

The bottom right panel in Figure 10 shows that the distance gradient observed
in the RRL star population agrees quite well with the expectations from the
disruption model of Ant 2 developed by Ji et al. (2021) and modified here to
account for the mean distance given by the RRL stars which is slightly
different to the value assumed in Ji et al. (2021, 132 kpc). More discussion
on the disruption model can be found below in § 4.

####  3.3.1 RR Lyrae stars beyond Ant 2?

We return to the case of stars V134 and V304, the two RRab stars that lie
below the HB of Ant 2, at mean $r$ magnitudes of 21.94 and 22.07 respectively.
We showed their light curves in Figure 6. They are well sampled on both
filters and they have small photometric errors, casting no doubts on their
classification. Following the same procedure to calculate distances discussed
in the previous section we estimate that V134 is located at $167\pm 4$ kpc and
V304 is at $173\pm 4$ kpc. Within $1\sigma$ errors, both stars are located at
the same distance, but they are $\sim 45$ kpc behind Ant 2, which is a
distance much larger than the distance errors or the distance dispersion of
Ant 2.

The stars are well within $2r_{h}$ of Ant 2, at $0\fdg 6$ and $1\fdg 4$ from
the center of the galaxy, both of them to the South-West side of the field
(Figure 2). They are separated by $47\arcmin$ from each other.

By integrating the number density radial profile of RRL from Medina et al.
(2018) between 150 and 200 kpc, we estimate only $0.2$ RRL stars are expected
in that range of distances in an area of 12 sq. deg. (our surveyed area).
Thus, the possibility of having two random halo field stars this close in the
sky, and at this distance is very low. These stars are either an indication of
a separate stellar system behind Ant 2, or they may be part of material that
have been torn apart from Ant 2 in the past. Since the stars are separated by
$47\arcmin$ from each other, it is unlikely they belong to a compact stellar
system such as a UFD galaxy. However, in principle they could be members of a
stream. Models of the disruption of Ant 2 (see § 4) do not support the
presence of debris material behind the main body of the galaxy. At present
then, we do not have a good explanation for the origin of these two very
distant RRL stars.

###  3.4 Radial Profiles

Figure 11: Running average of the number of RRL stars as a function of the
elliptical distance (r’). The shaded region shows the Poisson uncertainties.

The top panel of Figure 11 shows the profile of the number of RRL stars (only
RRab and RRc) as a function of the elliptical distance ($r^{\prime}$). This
distance was obtained taking into account the center, ellipticity and position
angle of the galaxy as derived in this work (Table 4), and considering it as
half the geometrical constant of the ellipse at the location of each
individual RRL star. The radial profile was obtained using a running average,
sorting the sample in distance, and counting the number of RRL stars within a
fixed-size box of $15\arcmin$ and moving in steps of $5\arcmin$. The radial
profile appears quite smooth, with just a slight overdensity near
$100\arcmin$.

##  4 Comparison with a Model of Ant 2’s tidal disruption

Figure 12: Top-down view of Ant 2 from above its orbital plane. The blue
points show the stream model while the orange points show the model limited to
the sky positions of the RRL stars (black circles). The model matches the
observed sample of RRL. The red vector shows the present-day velocity of Ant
2, and the dotted red line shows the past orbit of Ant 2.

Next we compare our RRL star sample with models of Ant 2’s disruption. We use
the same approach as in Ji et al. (2021) which simulated the tidal tails of
Ant 2 in the presence of the MW and the Large Magellanic Cloud (LMC). These
models use the modified Lagrange Cloud Stripping algorithm of Gibbons et al.
(2014) which was generalized in Erkal et al. (2019) to include the effect of
the LMC. This algorithm works by integrating the progenitor backwards from the
present day location of Ant 2 for 5 Gyr in the presence of the MW and LMC. The
system is then evolved forwards in time with particles ejected from the
Lagrange points to generate the tidal debris around Ant 2. As in Ji et al.
(2021), we model Ant 2 as a Plummer sphere with an initial mass of
$10^{7.92}M_{\odot}$ and a scale radius of 1 kpc. The MW is modelled using the
results of McMillan (2017). As in Ji et al. (2021), we use a MW model drawn
from the posterior chains of McMillan (2017) which several works have shown is
able to fit multiple streams in the MW (e.g. Li et al., 2021; Shipp et al.,
2021)555See Table A3 in Shipp et al. (2021) for the potential parameters. This
MW has a mass of $8.27\times 10^{11}M_{\odot}$ and gives a realistic past
orbit of the LMC, consistent with it being on first approach to the MW (e.g.
Besla et al., 2007). We evaluate the accelerations in this potential using
`galpot` (Dehnen & Binney, 1998). We model the LMC as a Hernquist profile with
a mass of $1.5\times 10^{11}M_{\odot}$ and a scale radius of 17.14 kpc
motivated by the results of Erkal et al. (2019). We place the Sun at a
Galactocentric distance of $8.122$ kpc with a velocity of $(11.1,245.04,7.25)$
km s-1. For the LMC, we use a present day proper motion, distance, and radial
velocity from Kallivayalil et al. (2013), Pietrzyński et al. (2013), and van
der Marel et al. (2002) respectively.

For Ant 2, we assume a distance of 124.1 kpc from Table 5, and use proper
motions and radial velocities from Ji et al. (2021),
$(\mu_{\alpha}^{*},\mu_{\delta})=(-0.094,0.103)$ mas yr-1, $v_{r}=288.8$ km
s-1 respectively. The resulting tidal debris is shown in Figure 12, alongside
the RRL stars identified in this work. We note that the coordinates shown here
are a top-down view of the present-day orbital plane of Ant 2. The red vector
shows the present day velocity vector of Ant 2 and the dashed-red curve shows
Ant 2’s past orbit. The black points show the RRL stars, the blue points show
the predicted tidal debris of Ant 2, and the orange points show the predicted
debris within the on-sky footprint of the RRL star sample. This shows that
within the orbital plane of Ant 2, the RRL stars are extended almost
perpendicular to the present day orbit of Ant 2, in agreement with the model.
In the model, the cloud of tidal debris close to the progenitor was stripped
during the previous pericentric passage, $\sim 800$ Myr ago, while the thinner
stream was stripped during the penultimate passage, $\sim 3$ Gyr ago. Thus,
the observed RRL stars were likely stripped during the most recent pericenter.
A future, wider area survey around Ant 2 would be useful to search for the
rest of the debris stripped during this pericentric passage and further
confirm that Ant 2 is tidally disrupting.

The model predicts quite well the observed depth along the line of sight. In
Figure 13 we show the histogram of the distribution of distances of the RRL
stars in Ant 2, and the one from the model particles in the same footprint of
our survey (the orange dots in Figure 12). The width of both distributions is
strikingly similar.

Figure 13: Distance distribution of the RRL stars in Ant 2 and the model
particles within the same footprint of our survey.

##  5 Anomalous Cepheids in Ant 2

We have found eight pulsating variable stars in the footprint with magnitudes
$r$ between 19.5 and 20.8, corresponding to 0.3-1.6 mags above the HB, which
is the expected place for AC stars in a CMD (Catelan & Smith, 2015).

There are enough observational similarities between AC and RRL stars that it
is worth to discuss with some detail the origin of these stars. Indeed, the
first hint that led to the discovery of Ant 2 by Torrealba et al. (2019) was a
group of three RRL stars in the Gaia catalog (Clementini et al., 2019) with
magnitudes $G\sim 20.2$. A group of three RRL stars, very close together in
the sky, with similar magnitudes, and similar proper motions, prompted the
search for an underlying stellar population, which was indeed quickly
identified. However, it was clear that the group of RRL stars were much closer
than the main body of Ant 2, at distances ranging between 50-95 kpc. The
authors speculated that the group of RRL stars may be part of material
stripped out from Ant 2. In this paper, these same three RRL stars are among
the group we are re-classifying as AC members of Ant 2.

Figure 14: Period distribution of AC in the Large Magellanic Cloud Soszyński
et al. (2017) and Ant 2 (this work.

The main clue that this group of stars are AC and not RRL stars is the period
distribution (Figure 14). Although both types of variables have overlapping
period distributions, ACs can have periods as long as $\sim 2.5$ d (Catelan &
Smith, 2015). RRL stars on the other hand have periods $<1.0$ d. In Figure 14
we show the period distribution of our sample of AC in Ant 2 compared to that
for the LMC from the OGLE survey (Soszyński et al., 2017). The presence of
three long-period variables ($>1$ d) in Ant 2 fits well with the expected
distribution of periods for AC found in the LMC.

AC are rare stars but they have been found in dSph galaxies around the MW,
including the Magellanic Clouds (Soszyński et al., 2017), Sculptor (Martínez-
Vázquez et al., 2016), Carina (Vivas & Mateo, 2013; Coppola et al., 2015),
Crater 2 (Vivas et al., 2020), Sextans (Mateo et al., 1995; Vivas et al.,
2019), Draco (Kinemuchi et al., 2008), and also in satellites of M31
(Martínez-Vázquez et al., 2017). It is thus not surprising that a galaxy as
massive as Ant 2 will also contain a population of these variables. AC have
two main formation channels. They may originate as evolved metal-poor stars of
an intermediate-age population (Fiorentino & Monelli, 2012, and references
therein), or alternatively originate from binary evolution of old stars (eg.
Gautschy & Saio, 2017). There are no obvious hints of an intermediate-age
population from the CMD of Ant 2, although the large field contamination may
hide such features, particularly if its overall contribution to the galaxy
population is small. With the current data we cannot with certainty discard
the intermediate-age formation channel for the AC.

Figure 15: Gaia EDR3 proper motions of AC stars in Ant 2 (red circles). For
reference the plot also shows the proper motions of spectroscopic members
selected by Ji et al. (grey open circles, 2021), and other bright RRLs in the
field of Ant 2 (cyan diamonds).

A final confirmation that the group of AC are members of Ant 2 come from their
proper motions. All the stars in this group are sufficiently bright to have
proper motion measurements in Gaia EDR3 (Gaia Collaboration et al., 2021). In
Figure 15 we show that the proper motions of all eight AC are consistent with
those for stars confirmed as radial velocity members of the galaxy (Ji et al.,
2021), although the errors for the faintest of our AC are quite high. In
contrast, the proper motions of other bright RRL stars in the field are more
widely distributed. Thus, the proper motions support this group of stars, or
most of them, being members of Ant 2 rather than field halo stars. In any
case, the latter is an unlikely scenario since halo RRL stars are rare at such
large distances. We again estimated the expected number of RRL stars by
integrating the number density radial profile of RRL from Medina et al. (2018)
between 50 and 100 kpc, which resulted in $1.4$ RRL stars over the full area
of our survey. At most a contamination of two Galactic halo RRL stars is
expected among the group of eight AC.

##  6 Conclusions

We present a variability survey of 12 sq. deg. around the Ant 2 satellite
galaxy, which reveled a large population of RRL stars (318) as well as eight
AC. Ant 2 is a very large galaxy, larger than even the SMC, but with a much
lower surface brightness. Additional challenges to study this galaxy are its
large distance (HB at $r\sim 21.3$) and a position in the sky at low galactic
latitude ($b\sim 14\arcdeg$), which results in a high contamination by field
stars. The large FoV of DECam was crucial to be able to survey the full galaxy
over just a few days, obtaining time series with excellent S/N at the level of
the HB of Ant 2. The RRL stars found in Ant 2 are considered a very pure
sample of members since virtually no contamination by MW RRL stars is expected
at a similar distance. Based on the RRL stars we derived a distance of $124.1$
kpc, with a dispersion of 5.4 kpc.

The variable star population of Ant 2 reveals some interesting facts about
this galaxy:

(i) Ant 2 is large. We find RRL stars over the full surveyed area. The
$3\sigma$ elipse that encloses the RRL stars has a major axis over $5\arcdeg$
on the sky. Although there is a decline on the number of RRL stars with
radius, it is very likely that there will be more such stars awaiting
discovery outside the observed area.

(ii) Ant 2 has a population of AC. First interpreted by Torrealba et al.
(2019) as foreground RRL stars, we demonstrated here that it is more likely
they are AC members of Ant 2. The existence of this population however does
not necessarily mean that there is an intermediate-age population in the
galaxy, a common interpretation when AC are present, as they also originate
from evolution of binary stars in an old population. The current data does not
allow us to differentiate with certainty between the formation channels.

The previous interpretation of these stars being RRL stars was consistent with
Ant 2 having lost most of its mass ($\sim 90\%$ Torrealba et al., 2019). In
such scenario there would be Ant 2 tidal material in front of the main body of
the galaxy. New metallicity measurements, and updated proper motions indicate
that although the galaxy may be disrupting, such a large mass loss is unlikely
Ji et al. (2021), making the existence of debris in front of the galaxy hard
to explain. The new interpretation of these stars being AC in Ant 2 solves
that controversy since it does not imply there is material in front of the
galaxy.

(iii) Ant 2 is disrupting. The spatial distribution of the RRL stars reveals
an elongation ($\epsilon=0.28$), which is approximately aligned with the
reflex corrected proper motions of Ant 2 (see Ji et al., 2021, for more
details). In addition, the precise distances of the RRL allow us to detect the
elongation along the line of sight which is almost perpendicular to the orbit
of Ant 2. Along similar lines, there is a significant gradient in distance
along the major axis of the galaxy. Based on an extensive spectroscopic survey
covering a similar area to the present work, Ji et al. (2021) also detected a
gradient along the major axis but for the radial velocity of RGB stars. Both
gradients, distance and radial velocity, can be reproduced by a model of the
disruption of Ant 2. In this model, the RRL stars we are observing here were
torn apart from the main body of Ant 2 during the last pericenter passage,
about 800 Myr ago.

The disruption model of Ant 2 predicts long tidal tails coming from the center
of the galaxy and extending over more than $100\deg$ in the sky. To search for
RRL stars in the tails will be difficult with current instrumentation because
of the large search volume. However, the tidal tails of Ant 2, if they indeed
exist, should be easily revealed by data from the Vera C. Rubin Observatory
after 1-2 years of survey operations.

This project used data obtained with the Dark Energy Camera (DECam), which was
constructed by the Dark Energy Survey (DES) collaboration. Funding for the DES
Projects has been provided by the U.S. Department of Energy, the U.S. National
Science Foundation, the Ministry of Science and Education of Spain, the
Science and Technology Facilities Council of the United Kingdom, the Higher
Education Funding Council for England, the National Center for Supercomputing
Applications at the University of Illinois at Urbana-Champaign, the Kavli
Institute of Cosmological Physics at the University of Chicago, the Center for
Cosmology and Astro-Particle Physics at the Ohio State University, the
Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M
University, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho
de Amparo à Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de
Desenvolvimento Científico e Tecnológico and the Ministério da Ciência,
Tecnologia e Inovacão, the Deutsche Forschungsgemeinschaft, and the
Collaborating Institutions in the Dark Energy Survey. The Collaborating
Institutions are Argonne National Laboratory, the University of California at
Santa Cruz, the University of Cambridge, Centro de Investigaciones
Enérgeticas, Medioambientales y Tecnológicas-Madrid, the University of
Chicago, University College London, the DES-Brazil Consortium, the University
of Edinburgh, the Eidgenössische Technische Hochschule (ETH) Zürich, Fermi
National Accelerator Laboratory, the University of Illinois at Urbana-
Champaign, the Institut de Ciències de l’Espai (IEEC/CSIC), the Institut de
Física d’Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-
Maximilians Universität München and the associated Excellence Cluster
Universe, the University of Michigan, NSF’s NOIRLab, the University of
Nottingham, the Ohio State University, the OzDES Membership Consortium the
University of Pennsylvania, the University of Portsmouth, SLAC National
Accelerator Laboratory, Stanford University, the University of Sussex, and
Texas A&M University. Based on observations at Cerro Tololo Inter-American
Observatory, NSF’s NOIRLab (NOIRLab Prop. ID 2018B-0941; PI: A. Walker), which
is managed by the Association of Universities for Research in Astronomy (AURA)
under a cooperative agreement with the National Science Foundation.

##  Appendix A Time series data

Table 6 presents the individual epoch photometry in $r$ and $i$ for all the
periodic variable stars measured in this work. Light curves for all the stars
are provided as Figure Set 16.

Table 6: Time series photometry of variable stars in the field of view of Ant
2.

ID | Filter | HJD | Mag | Error
---|---|---|---|---
|  | (d) | (mag) | (mag)
V1 | r | 2458472.709444 | 21.454 | 0.033
V1 | r | 2458472.753670 | 21.087 | 0.016
V1 | r | 2458472.797899 | 20.996 | 0.016
V1 | r | 2458472.842118 | 21.133 | 0.013
V1 | r | 2458504.731142 | 21.265 | 0.016
V1 | r | 2458504.776744 | 21.289 | 0.020
V1 | r | 2458504.821390 | 21.448 | 0.055
V1 | r | 2458504.865625 | 21.499 | 0.047

Note. — Table 6 is published in its entirety in the machine-readable format. A
portion is shown here for guidance regarding its form and content.

Figure 16: For each star the $r$, $i$ data are displayed in the top/bottom
panels. For all the types $ab$ and $c$ the underlying blue line is the best
fitted template to the light curve. The complete figure set (18 images) is
available in the online journal.

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