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galaxies: Galaxy: halo — Galaxy: substructure

# The Milky Way Tomography with Subaru Hyper Suprime-Cam. I. Halo
substructures

Yoshihisa Suzuki11affiliation: Astronomical Institute, Tohoku University,
Aoba-ku, Sendai 980-8578, Japan
E-mail<EMAIL_ADDRESS>Masashi Chiba11affiliationmark:
Yutaka Komiyama22affiliation: Department of Advanced Sciences, Faculty of
Science and Engineering, Hosei University, 184-8584 Tokyo, Japan Kohei
Hayashi33affiliation: National Institute of Technology, Sendai College, 48
Nodayama, Medeshima-Shiote, Natori-shi, Miyagi 981-1239, Japan
11affiliationmark:  Masayuki Tanaka44affiliation: National Astronomical
Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
55affiliation: The Graduate University for Advanced Studies, Osawa 2-21-1,
Mitaka, Tokyo 181-8588, Japan Tetsuya Fukushima44affiliationmark:  Scott G.
Carlsten66affiliation: Department of Astrophysical Sciences, Princeton
University, Peyton Hall, Princeton NJ 08544 USA Akira Tokiwa77affiliation:
Kavli Institute for the Physics and Mathematics of the Universe, Kashiwa,
Chiba, 277-8583, Japan Tian Qiu77affiliationmark:  and Masahiro
Takada77affiliationmark:

###### Abstract

We analyze the photometric data in the Wide layer of the Hyper Suprime-Cam
Subaru Strategic Program (HSC-SSP) over $\sim 1,200$ deg2 to uncover new halo
substructures beyond the distance, $D_{\odot}\sim$ 30 kpc, from the Sun. For
this purpose, we develop an isochrone filter for an old, metal-poor stellar
system to extract the faint main-sequence stars at a range of distances. With
this method, we detect, not only the previously discovered substructures such
as the Orphan Stream, but also the new overdensity toward Boötes at about
$D_{\odot}\sim$ 60 kpc and the new stream-like feature toward Pisces at around
$D_{\odot}\sim$ 60 kpc. It has been suggested that a small-scale overdensity
exists in this direction of Pisces (the so-called Pisces Overdensity), but our
results show that the overdensity is widely spread with a tidally elongated
feature. Combining our results with the ongoing Hyper Suprime-Cam narrow-band
survey and the near-future spectroscopic survey with Prime Focus Spectrograph
(PFS) will allow us to place strong constraints on the origin of these halo
substructures.

##  1 Introduction

Stars in the Milky Way (MW) halo hold much fundamental information on how a
galaxy like our own formed. These stars, identified first with high radial
velocities (Oort, 1922, 1926) and later with weak metal lines (Roman, 1950)
near the Sun, show a different chemo-dynamical structure from those in the
luminous disk component, where most of the stars reside. The quest for the
origin of these halo stars has opened up Galactic Archaeology studies for
constructing a possible scenario of Galaxy formation based on their
kinematical and chemical properties since the seminal paper by Eggen et al.
(1962). While these authors proposed a picture of a monolithic, free-fall
dissipative collapse of a proto-Galactic cloud, the advent of newly analyzed
datasets in the halo population has revealed a more complex picture of
developing the MW halo through accretion and merging of smaller stellar
systems (Searle & Zinn, 1978), which actually accords with the modern picture
of galaxy formation.

A currently standard scenario for galaxy formation is based on Cold Dark
Matter models in the $\Lambda$-dominated Universe ($\Lambda$CDM). In this
context, galaxies are thought to have been formed by the repeated merging and
accretion of the smaller objects through gravitational interaction (e.g.,
White & Rees (1978)). The numerical simulations based on the $\Lambda$CDM
model have shown that the relics of the past formation history should still be
inscribed in the halo (Bekki & Chiba, 2001; Bullock & Johnston, 2005; Cooper
et al., 2010). Several lines of evidence for these past accretion events are
actually observed in the halo of nearby galaxies in the form of halo streams
and substructures (e.g., Martínez-Delgado et al. (2010); Ferguson & Mackey
(2016)). These studies have provided significant insight into our
understanding of the galaxy formation process.

For the MW, thanks to the advent of wide-field systematic photometric and
spectroscopic surveys such as the Sloan Digital Sky Survey (SDSS) and the
precise astrometry survey with Gaia, our understanding of the MW structure,
especially in the inner part of the MW halo at the heliocentric distance of
$D_{\odot}\hskip
3.00003pt\raisebox{1.72218pt}{$<$}\raisebox{-3.01385pt}{$\sim$}\hskip
3.00003pt30$ kpc, has been advanced significantly (e.g., York et al. (2000);
Gaia Collaboration (2016)). These modern data allow us to carry out the
reconstruction of the past merging history of halo building blocks based on
high-precision 6D phase-space information and chemical abundance patterns of
halo stars (e.g., Helmi et al. (2018); Belokurov et al. (2018)).

On the other hand, our understanding of the MW outer halo beyond
$D_{\odot}\sim$ 30 kpc is still far from complete. This is mainly because the
halo substructures to be found there are characterized as low surface
brightness, thereby being difficult to detect (Shipp et al., 2023; Horta et
al., 2023). Although many works have been performed using intrinsically bright
stars such as the horizontal branch stars and RR Lyrae variables as a halo
tracer, it is not straightforward to find halo substructures because of the
small number of available sample stars. In fact, in order to search for halo
structures with sufficient statistical significance, the wide and deep
photometric survey of abundant faint stars along the main-sequence is desired.

Here, we make use of the photometric data obtained from the Subaru Strategic
Program using the Hyper Suprime-Cam (HSC), hereafter called HSC-SSP. By virtue
of its wide footprint ($\sim$ 1,200 $\mathrm{deg^{2}}$) and deep photometry
($\lesssim$ 26.5 mag in the $i$-band with 5$\sigma$ depth), it is possible to
search for new substructures at the outer part of the MW halo. In this paper,
we report on the first detection of a candidate stellar stream at around
$D_{\odot}\sim$ 60 kpc toward Pisces and also the global overdensity toward
Boötes at that distance. In Section 2, we show the photometric data for our
analysis and then describe the methodology for the detection of distant halo
substructures. In Section 3, we show our results and discuss the origin of the
candidate halo substructure in Section 4. Finally, our conclusion is drawn in
Section 5. In this paper, magnitudes are given in the AB system (Oke & Gunn,
1983).

##  2 Data and Method

We first briefly introduce the survey design of the HSC-SSP, which is the
basis for the current work. We next show how to extract candidate stellar
objects as many as possible by using the color index information, then explain
how to select halo stars to use the following analysis. Finally, we introduce
an isochrone filter to extract many of main-sequence stars located at a
certain range of distances.

###  2.1 HSC-SSP

The HSC-SSP is a large imaging survey that began in March 2014 and was
completed in January 2022, a period of about 7.5 years. The observation has
been conducted using the HSC (Miyazaki et al., 2018) installed on the prime
focus of the 8.2 m Subaru Telescope. Over the course of $\sim$ 330 nights,
this program has acquired photometric data with various optical filters and
depths. Here, we utilize the photometric data observed in the Wide layer,
composed of three fields: Spring, Fall, and North (see Table 1). In total, it
covers $\sim 1200$ deg2 in five photometric bands ($g$, $r$, $i$, $z$, and
$y$) with $5\sigma$ limiting magnitude ($26.5^{+0.2}_{-0.2}$,
$26.5^{+0.2}_{-0.2}$, $26.2^{+0.2}_{-0.3}$, $25.2^{+0.2}_{-0.3}$ and
$24.4^{+0.2}_{-0.3}$) (Aihara et al., 2022). The HSC-SSP catalog (S21A) was
generated by the hscPipe 8.4, updated with an FGCM code (hscPipe 8.5.3), based
on the pipeline developed for Vera C. Rubin Observatory (Ivezic et al., 2008;
Jurić et al., 2017; Bosch et al., 2019) and calibrated against Pan-STARRS1
photometry and astrometry (Schlafly et al., 2012; Tonry et al., 2012; Magnier
et al., 2013; Chambers et al., 2016).

Table 1: The HSC-SSP survey footprint in the Wide Layer. The observed areas in the equatorial and Galactic coordinates for the Spring, North, and Fall fields are summarized. Over the course of 7.5 years, $\sim$ 1200 $\rm{deg}^{2}$ has been swept into the sky in this program. Field | RA | DEC | l | b | area
---|---|---|---|---|---
| (deg) | (deg) | (deg) | (deg) | (deg2)
Spring | [127.5, 225.0] | [-2.0, 5.0] | [225.0, 360.0] | [20.0, 65.0] |  $\sim$ 680
North | [200.0, 250.0] | [42.0, 44.5] | [70.0, 90.0] | [40.0, 75.0] |  $\sim$ 125
Fall | [330.0, 360,0] & [0.0, 30.0] | [-1.0, 7.0] | [60.0, 150.0] | [-65.0,-35.0] |  $\sim$ 395
Wide layer |  |  |  |  |  $\sim$ 1200
Figure 1:  The HSC-SSP footprint in the Wide layer in the equatorial
coordinate. The pink, orange, and cyan-colored areas correspond to the Spring,
Fall, and North fields, respectively. The symbols show previously discovered
dwarf galaxies (plus) and globular clusters (star). The continuous lines are
the stellar streams already found. The color represents the distance from the
Sun, being close (yellow) to far (purple), sequentially. From this figure,
while we can see that many stellar streams have been identified within 30 kpc
of the Sun, the deeper HSC data is expected to allow us to examine farther out
than that.

In Fig.1, we show the three fields in the Wide layer in the equatorial
coordinate system (J=2000.0). Areas painted in pink, orange, and cyan are
Spring, Fall, and North fields, respectively. In addition, we overplot the
distribution of previously discovered dwarf galaxies (McConnachie, 2012),
globular clusters (Harris, 1996), and stellar streams (Mateu, 2023) in the MW,
represented as symbols of plus, stars, and continuous lines, respectively. The
colors range from yellow to purple, meaning increasing distance from the Sun.
Most of the known stellar streams are seen within $D_{\odot}\sim$ 30 kpc from
the Sun, whereas beyond $D_{\odot}\sim$ 30 kpc, only the dwarf galaxies are
detected. However, numerical experiments have demonstrated that more coherent
stellar streams originated from low- and intermediate-mass stellar progenitors
can be found beyond $D_{\odot}\sim$ 30 kpc (Horta et al., 2023). Since the
photometric data obtained with HSC-SSP can capture faint main-sequence stars
within about 100 kpc, it is highly expected that stellar streams at such large
distances will be detected with this dataset.

###  2.2 Selection of halo stars

First, we extract objects that are considered to be point sources; in the HSC-
SSP catalog, each source is binary classified as a point source or extended
source by the ${\it i\\_extendedness\\_value}$: point source (as value 0) and
extended source (as value 1). This criterion is determined by whether the
$i$-band photometric magnitude difference is larger (point-source) or smaller
(extended-source) than -0.018 for the cases between using the point spread
function (PSF) model and using the model that combines the PSF model and
typical galaxy surface brightness such as an exponential profile in
photometry. Note that the HSC-SSP uses the best-seeing ($\sim$ 0.6 arcsec)
$i$-band images as the first priority for source detection, which is
especially sensitive for the weak-lensing survey.

Figure 2:  The distribution of objects considered as point sources on the
color-color diagram ($g$-$r$, $r$-$i$) for those brighter than 22 mag in the
$i$-band. We plot them as black dots. The gray-scale contours show the number
distribution on a common logarithmic scale from $10^{3}$ to $10^{5}$,
corresponding to the stellar locus. In the following analysis, the point
sources within the region indicated by red dots are considered halo stars.

We then extract as many stars as possible from the obtained data. To do so, we
sample objects brighter than 24.5 mag in the $i$-band photometry based on the
PSF model. This is because the probability that the selected point sources are
correctly distinguished as stars or galaxies is less than 50% for objects
fainter than $i$=24.5. This is based on the result of cross-matching the
objects considered as point sources by the HSC-SSP catalog with those after
distinguishing stars and galaxies by Hubble observations obtained in the
COSMOS region of the HSC-SSP footprint (Aihara et al., 2018a).

After the major contaminants are removed, we make a further selection using
the color-color diagram. In Fig.2, we show the distribution of objects
identified as ‘pure’ point sources on the color-color diagram ($g$-$r$,
$r$-$i$). For clarification, we plot the objects brighter than 22 mag in
$i$-band. Besides we overplot the gray-scale contours from $10^{3}$ to
$10^{5}$ in number on the common logarithmic scale. In this space, we can
first identify a sequence where the objects are most concentrated, called the
stellar locus. On this sequence, there is a bend around ($g$-$r$, $r$-$i$)
$\sim$ (1.3, 0.5), which is known to be mainly due to the presence of many M-
and K-type stars in the thin disk. There is also a component near ($g$-$r$,
$r$-$i$) $\sim$ (0.0, 0.2), which deviates from the stellar locus. This
component is composed of quasars and star-forming galaxies, as revealed by
SDSS spectroscopic follow-up observations (Ahumada et al., 2020; Lyke et al.,
2020).

Based on these properties of point sources in this diagram, we extract the
most likely halo stars based on the following three aspects. First, we remove
objects with $g-r>$ 1.0 to remove M- and K-type stars in the thin disk. Next,
we remove quasars and galaxies with active star formation outside the main
stellar locus. Finally, we extract only the sources that are inside the
stellar locus. As a result, the sources brighter than $i$=24.5 within the
region indicated by the red dots in Fig.2 are regarded as halo stars in the
following analysis.

###  2.3 Isochrone-filter method

In order to effectively find substructures in the halo of the MW, we make an
isochrone filter based on a theoretical stellar evolution model (Bressan et
al., 2012). The results of this publicly available calculation, however, do
not exactly cover the case for the HSC photometry. Therefore we use an
empirical linear equation for converting SDSS-based filters to HSC-based
filters for the spectroscopic follow-up stars using one-color index
information as deduced in Akiyama et al. (2018) as follows, under the
assumption that this relation is applicable to all the sky:

$\left(\begin{array}[]{c}g_{\mathrm{HSC}}\\\ r_{\mathrm{HSC}}\\\
i_{\mathrm{HSC}}\\\ z_{\mathrm{HSC}}\\\
y_{\mathrm{HSC}}\end{array}\right)=A\left(\begin{array}[]{c}g_{\mathrm{SDSS}}\\\
r_{\mathrm{SDSS}}\\\ i_{\mathrm{SDSS}}\\\ z_{\mathrm{SDSS}}\\\
y_{\mathrm{SDSS}}\end{array}\right)+\left(\begin{array}[]{c}-0.011\\\
-0.001\\\ 0.003\\\ -0.006\\\ 0.003\end{array}\right)$ (1)

$A=\left(\begin{array}[]{ccccc}0.926&0.074&0&0&0\\\ 0&0.996&0.004&0&0\\\
0&-0.016&1.106&0&0\\\ 0&0&0.006&0.094&0\\\
0&0&-0.419&1.419&0\end{array}\right)$ (2)

We then determine the width of the filter to cover the stellar population.
Under the plausible assumption that most of the stellar systems in the outer
halo are metal-poor and old, we adopt the theoretical isochrone with an age of
13.5 Gyr and metallicity [M/H] of -1.8. Also, to reduce the influence of
foreground bright stars, our isochrone filter is focused and limited to the
extraction of faint main-sequence stars. Then, the width of the filter is
given at each 0.2 mag interval between $i$=18 and 24 mag, taken from the
median photometric error in the corresponding $i$-band magnitude. The
metallicity distribution is expressed with a shift of about 0.1 magnitude in
the color index ($g$-$i$) at $i$=24.5 mag. Thus, our isochrone filter and its
width take into account the dispersion of the intrinsic metallicity
(-2.1$<$[M/H]$<$-1.3) for old main-sequence stars with $\gtrsim$ 10 Gyr.

In order to apply the filter to the HSC-SSP photometry, we first consider the
dust extinction using the maps calculated in Schlegel et al. (1998). Then we
make isochrone filters with distance moduli from 17.1 mag ($D_{\odot}\sim
26.3$ kpc) to 19.3 ($D_{\odot}\sim 72.4$ kpc) mag as evenly shifted from top
to bottom on the color-magnitude diagram. As for the distance error associated
with the finite width of the filter, it ranges from 10% ($D_{\odot}\sim$ 25
$\mathrm{kpc}$) to 28% ($D_{\odot}\sim$ 60 $\mathrm{kpc}$).

Figure 3:  The application of the isochrone-filter method to the Spring field.
(left) The halo stars (black dots) in the color-magnitude diagram
$((g-i)_{0},i_{0})$. The typical photometric error in each $i$-band bin is
shown as black circles with error bars. (right) The top panel shows the
spatial distribution of all the halo stars (black dots) in this field. We also
add the previously discovered dwarf galaxies, globular clusters, and stellar
streams as the same symbols in Fig.1. The middle and bottom panels show the
number of stars within each pixel ($\Delta$RA=0.6875 deg, $\Delta$DEC=0.16
deg) after isochrone-filtering in the left panel shown with orange and blue
dotted regions, respectively. The corresponding distance modulus and distance
are ((m-M)=16.9 mag, $D_{\odot}\sim$ 24.0 kpc) and (m-M)=17.5 mag,
$D_{\odot}\sim$ 31.6 kpc), respectively. For the star count, we remove the
Sextans dSph surrounded in the dashed region in the top panel. From the middle
panel, we can clearly see the Orphan stream over (RA, DEC) = ($162^{\circ}$,
-$2^{\circ}$) to ($160^{\circ}$, $4^{\circ}$), indicating that this technique
is valid for stellar stream detection.

##  3 Results

In each subsection for the Spring, North, and Fall fields below, we summarize
the general characteristics of the field and explain the distribution of stars
in the color-magnitude diagram. We especially focus on only the notable
feature in the spatial distribution of stars inside an isochrone filter at a
selected range of distances from the Sun, whereas in Appendix 1, we show all
the spatial distributions of stars in each field while varying distance moduli
with a small interval.

Figure 4:  The application of the isochrone-filter method to the North field
in the same manner as shown in Fig.3. The orange and blue dotted isochrones in
the left panel pick out the stars at ((m-M)=16.0 mag, $D_{\odot}\sim$ 15.9
kpc) and ((m-M)=17.0 mag, $D_{\odot}\sim$ 25.0 kpc), respectively, and the
right middle and bottom panels show the corresponding distribution of stars
within each pixel ($\Delta$RA=0.6875 deg, $\Delta$DEC=0.16 deg). As shown in
the text, the color-magnitude diagram exhibits the presence of a previously
undiscovered structure at $i$ = 23$\sim$24 mag, though is hardly spatially
dense. This suggests the presence of a faint overdense structure in this
direction, for which we dub ”Boötes Overdensity”.

###  3.1 Spring field

The Spring field is the most crowded area with substructures, because of the
presence of the Sagittarius stream at $D_{\odot}\sim$ 40 kpc: this stream
reveals many main sequence stars in the color-magnitude diagram at
corresponding distance modulus, thereby making it difficult to investigate
other substructures. Therefore, we perform a substructure search for the
region excluding such regions.

In Fig.3, we summarize the characteristic features of stars in the Spring
field. In the left panel, all the halo stars in the color-magnitude diagram
($(g-i)_{0}$, $i_{0}$) are shown as black points. Note that the subscript ’0’
with filters means that dust extinction correction has been performed. Also,
the median photometric error for each object is indicated by a black circle
with an error bar at each step of 0.5 mag between $i$=18.5 and 24 mag.

Focusing on the main-sequence stars in this panel, we remark that the
foreground and the outer halo stars can be distinguished owing to the small
photometric error. Therefore, it is sufficient to apply an isochrone filter
only to the abundant main-sequence stars in the color-magnitude diagram
compared to the use of bright stars such as RR Lyrae, blue horizontal-branch
(BHB), and red giant branch (RGB) stars.

In the right panels of Fig.3, we show the spatial distribution of halo stars
in the Spring field. The top panel shows the spatial distribution of all the
halo stars in this field. The middle and bottom panels show the number density
in each pixel ($\Delta$RA=0.6875 deg, $\Delta$DEC=0.16 deg) after isochrone-
filtering with a distance modulus of (m-M)=16.9 mag ($D_{\odot}\sim$ 24.0 kpc)
and 17.5 mag ($D_{\odot}\sim$ 31.6 kpc), respectively, corresponding to stars
in the orange and blue dashed regions in the left panel. We note that we do
not normalize the star counts, so the range of the color bar is different in
each panel. For the number counts, we mask the known dwarf galaxy, Sextans
dSph at (RA, DEC) = ($162^{\circ}$, $-2^{\circ}$). As is clear, the previously
discovered stellar stream, the Orphan stream, is confirmed over (RA, DEC) =
($162^{\circ}$, $-2^{\circ}$) to ($160^{\circ}$, $4^{\circ}$) at a distance of
about $D_{\odot}=24$ kpc (right middle panel). This demonstrates that the
method using our isochrone filter is effective for exploring substructures in
the outer halo. However, except this known stream, there are no notable
substructures, where the density variation of stars is confined only within 1
sigma over the field111Some local overdensities are present around Sextans
dSph, including a globular cluster and dwarf candidate as reported elsewhere..

Figure 5:  The application of the isochrone-filter method to the Fall field in
the same manner as shown in Fig.3. The orange and blue dotted isochrones in
the left panel pick out the stars at ((m-M)=16.9 mag, $D_{\odot}\sim$ 24.0
kpc) and ((m-M)=19.1 mag, $D_{\odot}\sim$ 66.1 kpc), respectively, and the
right middle and bottom panels show the corresponding distribution of stars
within each pixel ($\Delta$RA=0.6875 deg, $\Delta$DEC=0.16 deg). From both the
color-magnitude diagram and the spatial distribution of the stars, we can see
the stream-like feature toward Pisces over 330 $<$ RA $<$ 360 at around 60 kpc
from the Sun (right bottom panel).

###  3.2 North field

The North field has only a few known stellar streams that are located
approximately within a few 10 kpc from the Sun based on the combination of the
stellar population and kinematics by Gaia satellite (Ibata et al., 2019).
Since these nearby streams do not affect our search for streams in the outer
halo beyond $D_{\odot}\sim$ 30 kpc, we apply the isochrone filter without any
masking.

We show the result of this application to the North field in Fig.4. In the
left panel, we plot the color-magnitude diagram for all the halo stars and the
typical photometric errors in the same way as in Fig.3. In the right panels,
we show the distribution of the halo stars in the North field. The top panel
shows the spatial distribution of all the halo stars. The middle and bottom
panels show the number density within each pixel of ($\Delta$RA=0.6875 deg,
$\Delta$DEC=0.16 deg) after applying the isochrone filters with the distance
modulus of (m-M)= 16.0 mag ($D_{\odot}\sim$ 15.9 kpc) and 17.0 mag
($D_{\odot}\sim$ 25 kpc), respectively, corresponding to stars in the orange
and blue dashed regions in the left panel.

Compared to the Spring field, there exist no apparent stream-like
substructures, except for the following two features. We recognize from the
color-magnitude diagram that the signature of a rather large-scale
substructure appears at distances larger than 30 kpc from the Sun. This
structure, however, is not clearly seen as a high-density stellar stream but
in the form of widely spread overdensity over 240 $<$ RA $<$ 250 deg in the
spatial distribution (right middle and bottom panels of Fig.4). From this
characteristic, we call it as “the Boötes overdensity”, which appears to be
present over $D_{\odot}\sim$ 60 kpc (see Appendix 1 for the sequential
distribution of stars at different distant moduli). In this series of our
papers, we attempt to investigate the possible origin of this overdensity from
the viewpoints of the kinematics and chemical abundance of the K-type, RR
Lyrae, or BHB stars at the same distance (Suzuki et al., in preparation).

As seen in the right middle and bottom panels of Fig.4, there appears yet
another overdensity at around RA $\sim$ 210 deg. Although this overdensity is
rather weak in these panels, this feature is seen in all the isochrone filters
with different distance moduli as shown in Appendix 1 (See Figure 9), whereas
it disappears when the selection of stars is limited to bright ones of i$<$24
mag (see Figure 11). Therefore, we doubt that this overdensity is due to
contamination such as galaxies. To confirm whether this overdensity is true or
not, in the near future, it will be possible to utilize the data obtained by
the Euclid Satellite, which will be able to carry out star-galaxy separation
more precisely taking advantage of observations from space (e.g., Laureijs et
al. (2011)). Since this North region overlaps with the planned observation
area of Euclid, the identification of this overdensity will be eagerly
performed.

###  3.3 Fall field

The Fall field, like the Spring field, is a region where the many main-
sequence stars from the Sagittarius stream are dominant at around
$D_{\odot}\sim$ 30 kpc. Also, a dwarf galaxy such as IC 1613 is present.
Therefore, we apply the isochrone filter by excluding these regions.

We show the result of this application to the Fall field in Fig.5. In the left
panel, we plot the color-magnitude diagram for all the halo stars and the
typical photometric errors in the same manner as in Fig.3. In the right
panels, we show the distribution of halo stars in the Fall field. The top
panel shows the spatial distribution of all the halo stars. The middle and
bottom panels show the number density within each pixel ($\Delta$RA=0.6875
deg, $\Delta$DEC=0.16 deg) after applying the isochrone filters with the
distance modulus of (m-M)=16.9 mag ($D_{\odot}\sim$ 24.0 kpc) and 19.1 mag
($D_{\odot}\sim$ 66.1 kpc), respectively, corresponding to stars in the orange
and blue dashed regions in the left panel. For the star count in this field,
we set to mask the region bounded by RA=($358^{\circ}$, $359^{\circ}$) and
DEC=($-1.0^{\circ}$, $0.0^{\circ}$). This is because the analysis using only
stars near the main-sequence turn-off has suggested the local number density
excess, indicating a new dwarf galaxy candidate. We summarize its structural
parameters and physical quantities in this series of papers (Suzuki et al., in
preparation).

As seen in the right middle and bottom panels, we can identify the highly
overdense structure over 330 $<$ RA $<$ 360 deg, or more specifically extended
from (RA, DEC)=($345^{\circ}\sim 360^{\circ}$, $0^{\circ}$) to (RA,
DEC)=($330^{\circ}\sim 345.6^{\circ}$, $5^{\circ}$). This may be a part of the
so-called Herclues-Aquila Cloud (HAC) (Belokurov et al., 2007) at the distance
below 30 kpc (right middle panel). A recent orbital analysis of RR Lyrae stars
obtained with the Gaia DR2 dataset has shown that the apogalactic distances of
the HAC member stars are in the range of 15-25 kpc, i.e., do not exceed
$D_{\odot}$ $\sim$ 50 kpc (Simion et al., 2018). However, our analysis
indicates that this structure is extended up to the distance of 60 kpc from
the Sun, where the influence of the HAC is negligible (right bottom panel),
thereby suggesting that these stream-like features are discovered for the
first time thanks to the deep HSC photometry. The density contrast at this
distance scale is apparently high: while the number density of stars per pixel
($\Delta$RA=0.6875 deg, $\Delta$DEC=0.16 deg) is almost 0 at around RA$\sim
360^{\circ}$, this overdensity shows the significantly larger number density
of stars of around 30. The existence of this substructure is also apparent in
the color-magnitude diagram in the left panel, and also in Appendix 1 (Figure
10) beyond $D_{\odot}\sim$ 30 kpc. We can identify the concentration of the
main-sequence stars, and also confirm the signature of the RGB stars, which
appears to continuously connect with the main-sequence stars distributed along
a single isochrone.

Figure 6:  The schematic view of the substructures in the Fall field. The
depth structure of the Pisces Overdensity, which is clarified by the faint
main-sequence stars in this study, is shown by the blue-filled area; the
distribution of RR Lyrae stars, where the existence of the Pisces Overdensity
has first been noted, is shown by red dots (RRab) and blue triangles (RRc),
respectively. The presence of Helcules-Aquila Cloud around 30 kpc from the Sun
and that of the Pisces Overdensity above 50 kpc from the Sun are indicated by
the clustering of RR Lyrae stars. Also, the estimated spatial distribution of
the Pisces Overdensity using blue-horizontal branch stars is shown by the
gray-filled area. This figure shows that the distance from the Sun of the
Pisces overdensity derived in this study is almost consistent with the
previous studies, while its projected spatial distribution is more extended
than before.  Figure 7:  The stellar stream candidate at the distance modulus
of 18.9 mag ($D_{\odot}\sim$ 66 kpc) and the distribution of the independently
selected Blue Stragglers (BSs) in the Fall region using the HSC catalog. The
circles in the figure indicate BSs with sequential colors corresponding to the
distance from the Sun. This figure shows that there is a correspondence
between the stream-like feature and the BS distribution.

##  4 Discussion

We first discuss the property of the morphologically stream-like candidate
identified in the Fall field and its possible origin. The prospect for probing
large-scale overdensity appeared in the North field, named ”Boötes
Overdensity” here, is also discussed.

The feature reported here in the Fall field can be related to the previously
discovered substructure: Pisces Overdensity. It is pointed out by Watkins et
al. (2009) that the distribution of RR Lyrae stars is somewhat concentrated
between $D_{\odot}\sim$ 60 and 100 kpc (see Figure 6), and the metallicity
[Fe/H] estimated as about -1.5. Based on the direction of the overdensity,
they named it Pisces Ovedensity. However, it was not clear what is the origin
of the concentration of these few tens of RR Lyrae stars. Since then, several
observational analyses have been conducted, resulting in the following, three
scenarios to explain the origin of the Pisces Ovedensity.

The first scenario is proposed by Nie et al. (2015). They conducted the SCUSS
survey, where using the $u$-band filters, they selected the blue horizontal-
branch (BHB) stars as the standard candle. From the number distribution of BHB
stars (Figure 6), they argued that the progenitor of the Pisces Ovedensity is
a small dwarf galaxy like Carina dwarf. However, there is no direct evidence
to support this progenitor galaxy.

The second scenario is suggested by Deason et al. (2018). They use the public
data obtained by Subaru/HSC. By using the $z$-band filters, they effectively
extracted the BHB stars as the distance indicator. From the distribution of
the BHB stars, they first discovered ‘the Pisces Plume’, which was named after
the stretched feature from the Sun. Besides they conclude that the Pisces
Overdensity originated from the Large Magellanic Cloud (LMC) from the orbital
analysis.

The third scenario is advocated by Chandra et al. (2023a) based on the H3
survey (Conroy et al., 2019). By using multiple photometry, they selected the
RGB stars as the distance indicator. From the spectroscopic follow-up by using
the Magellan Inamori Kyocera Echelle (MIKE), they first mentioned that the
progenitor is the same as that producing the Gaia Enceladus Sausage (hereafter
GE/S, (Helmi et al., 2018; Belokurov et al., 2018)) from the orbital analysis
in the H3 footprint. A recent work by Chandra et al. (2023b) shows the
relationship among these three scenarios: The origin of the Pisces Overdensity
is tidal debris of the GE/S, whereas the Pisces Plume originates from tidal
debris of the LMC. They argued that there is no correlation between them.

Our result is complementary to these previous studies. That is, instead of
using only a few tens of the BHB, RR Lyrae, and RGB stars, our work is based
on the abundant main-sequence stars at a certain range of distances like what
SDSS photometry has done (e.g., Belokurov et al. (2006)). From our result, it
is suggested that the Pisces Overdensity is much wider than expected (Figure
6). Therefore, there is a possibility that the Pisces Plume and Pisces
Ovedensity are related to each other. To constrain the nature of the
progenitor more tightly, we need wider photometric and spectroscopic surveys
because of the spatial spread of the Pisces Overdenisty.

We corroborate the existence of this extended overdensity that we have
identified in this region by comparing with the distribution of Blue Straggler
stars (BSs), which have been selected based on HSC ${\it griz}$ photometry to
select BHBs with the same A-type spectra, as reported elsewhere (Fukushima et
al. prep., see also Fukushima et al. (2019) for the selection method of BSs
and BHBs from the HSC photometric data). The result is shown in Fig.7, for
which the distribution of halo stars is derived from the isochrone filter with
the distance modulus 18.9 mag ($D_{\odot}\sim$ 66 kpc). The color code for the
number density of stars is the same as used in Fig.3. The circles show the
most likely BS candidates, for which the probability is higher than 0.8 based
on the extended Bayesian analysis. Also, we limit the BS sample to the
distance between $D_{\odot}$=50 kpc and 70 kpc to match the distribution of
the discovered stream-like feature located around 60 kpc. As is clear from
Fig.7, the distribution of these independently selected BSs and that of the
main-sequence stars are well overlapped with each other. This indicates that
the progenitor of this overdensity is a metal-poor, old stellar system.

To get further insight into this overdensity in the context of the formation
of the MW, we have the following prospects using the Subaru Telescope. First,
the photometric mapping of this overdensity is planned by using the narrow
band filter $NB395$ for HSC, which is designed to cover Ca II H&K absorption
lines as a measure of stellar metallicities222This observation is a part of
our program for hunting extremely metal-poor stars with the use of NB395,
called ZERO (Zero Enrichment Rare Objects) survey.. By combining $NB395$ with
the $g$ and $i$ band photometry from the HSC-SSP, we can estimate the [Fe/H]
for each star.

Second, a direct spectroscopic follow-up of the stars in the overdensity will
be important to obtain not only their metallicities but also their chemical
abundance patterns. This will be possible with Subaru Prime Focus Spectrograph
(PFS), which will allow us a wide-field and massively multiplexed
spectroscopic capability. Therefore, we will obtain a more detailed picture of
the origin of the Pisces Overdenisty.

In summary, the substructure discovered in the Fall field is almost overlapped
with Pisces Overdensity, but its stream-like feature is first discovered in
this study. Moreover, this candidate substructure is extended than that found
by Nie et al. (2015). It is likely that Pisces Overdensity is a part of a
large stellar stream having a more extended structure. Also, as shown in
Fig.7, this structure associates the enhancement of the BSs: BSs are thought
to be abundant in old stellar systems (Piotto et al., 2004). Therefore, we
conclude that this candidate halo substructure is considered to be a
relatively old stellar system.

Regarding the North field, there have been no previous reports on the
overdensity toward Böotes at around the distance of 60 kpc from the Sun. To
further constrain the origin of this substructure, we plan to conduct a
spectroscopic follow-up observation for the K-giant stars extrapolated from
the isochrone on the color-magnitude diagram. Then the combination with the
proper motions from the Gaia DR3 will enable us to perform a chemo-dynamical
analysis for the halo overdensity. In particular, it will be possible to
investigate whether this halo substructure is associated with the tidally
disruption of the GE/S event or not.

##  5 Conclusion

In order to detect new halo substructures in the outer halo regions of the MW,
we have analyzed the photometric data of the HSC-SSP Wide layer covering over
$\sim$ 1,200 $\mathrm{deg}^{2}$ in the sky. For this purpose, we have focused
on the abundant, faint main-sequence stars available from HSC, which allow us
to identify and analyze distant halo structures with sufficient statistical
significance, in contrast to the studies using sparse RR Lyr or BHB stars.
Also, motivated by the fact that many of the known stellar streams originate
from globular clusters or dwarf spheroidal galaxies, we have developed the
isochrone filter for such an old, metal-deficient stellar system to extract
the halo structure consisting of many main-sequence stars at a range of large
distances from the Sun.

With this method, we have found a part of the previously discovered
substructure, Pisces Overdensity at around $D_{\odot}\sim$ 60 $\mathrm{kpc}$
from the Sun. Wide and deep HSC data in this region show, for the first time,
that this substructure reveals a clear stream-like feature, suggesting that it
is associated with the tidal disruption of a stellar system. Furthermore, this
halo substructure is overlapped with the spatial distribution of the BSs,
i.e., the sample of old, metal-poor stars, which therefore suggests such a
stellar population for the progenitor stellar system. In addition to this
substructure toward Pisces, we have also identified the global overdensity
toward Boötes, which should exist at around 60 $\mathrm{kpc}$. Further
constraints on these halo substructures, based on the acquisition of
photometric or spectroscopic metallicity as well as kinematics, will enable us
to get insight into the origin of its progenitor galaxy.

The HSC-SSP Wider layer that we have focused on halo substructures in this
paper also includes more information on the MW halo, such as the global
density profile in the various directions and yet unidentified star clusters
and satellites, which will be addressed in our next papers.

This work is supported in part by JSPS Grant-in-Aid for Scientific Research
(B) (No. 25287062) and MEXT Grant-in-Aid for Scientific Research (No.
16H01086, 17H01101 and 18H04334 for MC, No. 18H04359 and No. 18J00277 for KH).
TM is supported by Grant-in-Aid for JSPS Fellows (No. 18J11326). The HSC
collaboration includes the astronomical communities of Japan and Taiwan and
Princeton University. The HSC instrumentation and software were developed by
the National Astronomical Observatory of Japan (NAOJ), the Kavli Institute for
the Physics and Mathematics of the Universe (Kavli IPMU), the University of
Tokyo, the High Energy Accelerator Research Organization (KEK), the Academia
Sinica Institute for Astronomy and Astrophysics in Taiwan (ASIAA), and
Princeton University. Funding was contributed by the FIRST program from the
Japanese Cabinet Office, the MEXT, JSPS, JST, the Toray Science Foundation,
NAOJ, Kavli IPMU, KEK, ASIAA, and Princeton University. This paper makes use
of software developed for the Large Synoptic Survey Telescope. We thank the
LSST Project for making their code freely available. The Pan-STARRS1 (PS1)
Surveys have been made possible through contributions of the Institute for
Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-
Planck Society and its participating institutes, the Max Planck Institute for
Astronomy and the Max Planck Institute for Extraterrestrial Physics, The Johns
Hopkins University, Durham University, the University of Edinburgh, Queen’s
University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las
Cumbres Observatory Global Telescope Network Incorporated, the National
Central University of Taiwan, the Space Telescope Science Institute, the
National Aeronautics and Space Administration under Grant No. NNX08AR22G
issued through the Planetary Science Division of the NASA Science Mission
Directorate, the National Science Foundation under Grant No.AST-1238877, the
University of Maryland, and Eotvos Lorand University (ELTE).

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##  Appendix A A tomographic view of the HSC-SSP footprint

Here we show how the structure of the Milky Way halo changes with the
isochrone-filter method used in this study, i.e., ”the tomography of the Milky
Way halo”. We make isochrone filters with distance modulus from 17.1 mag
($D_{\odot}\sim 26.3$ kpc) to 19.3 ($D_{\odot}\sim 72.4$ kpc) mag at the
interval of 0.2 mag. The tomography in the Spring, North, and Fall fields are
shown in Fig.8, 9, and 10, respectively.

Figure 8:  Stellar number density distribution in the Spring field after our
isochrone-filter selection. The filter is the same as in Fig.3. The distance
modulus is varied from 17.1 (26.3 kpc) to 19.3 (72.4 kpc) in 0.2 mag
increments to be equally spaced on the color-magnitude diagram. The color bar
indicates the number density, meaning that the number contained in each pixel
increases from purple to yellow. Note that the color bar here shows absolute
numbers that are not normalized throughout. This figure shows that in the
Spring field, the Orphan stream is dominant within 30 kpc of the sun, while
beyond that point, the distribution is smooth except around Sextans.  Figure
9:  Stellar number density distribution in the North field after our
Isochrone-filter selection. The panels are shown in the same way as Fig.8.
This figure shows that in the North field, there are no stream-like features.
Note that there is an overdensity at around RA $\sim$ 210 deg, but this might
be due to contamination such as galaxies as clearly shown in Appendix 2.
Figure 10:  Stellar number density distribution in the Fall field after our
isochrone-filter selection. This figure shows that there is an excess around
RA=330 deg at 30 kpc from the sun. This is the known Helcules-Aquila Cluod. At
greater distances, the location of the overdensity region shifts, and a
stream-like structure is seen. This corresponds to the Pisces overdensity, and
the present study suggests that it may have a stream-like structure and be
more spatially extensive than previously thought.

##  Appendix B Effect of the criteria for the star-galaxy separation in the
North field

We show how the same isochrone-filter results change when only objects
brighter than 24 mag in the $i$-band are extracted to investigate the effect
of star/galaxy separation. In particular, we show the case for the North field
in Fig.11, where the effect of this selection is particularly pronounced.

Figure 11:  Stellar number density distribution in the North field for the
stars with $i$ $\leqq$ 24.0 mag. The panels are shown in the same way as
Fig.8. From this figure, it can be confirmed that the overdensity region
around RA=210 deg seen in Fig.9 disappears by changing the criteria for star-
galaxy separation. This suggests that this structure is caused by
contamination from distant galaxies. Note, however, that this result does not
rule out the existence of Böotes overdensity, which is clearly indicated on
the color-magnitude diagram.