SAG: Stars and Galaxies Vol. 4, id. 6, 2021 December 28
c 2021. Center for Astronomy, University of Hyogo.
⃝

Distributions of dwarf galaxies around giant elliptical galaxies NGC 3923 andNGC 4636
Miyako Tozuka 1 , Koji S. Kawabata 2 , Yasushi Fukazawa 2 , Shingo Nishiura 3 , and Junko S. Hiraga 4
1

Nishi-Harima Astronomical Observatory, Center for Astronomy, University of Hyogo,407-2 Nishigaichi, Sayo-cho, Hyogo 679-5313, Japan
2
Hiroshima University, 1-3-1 Kagamiyama, Higashihiroshima-shi, Hiroshima 739-8526, Japan
3
Tokyo gakugei University, 4-1-1 Nukuikita-machi, Koganei-shi, Tokyo 184-8501, Japan
4
Kwansei gakuinn University, 2-1 Gakuen, Sanda-shi, Hyogo 669-1337, Japan
tozuka@nhao.jp(Received 2021 October 14; accepted 2021 December 27)

Abstract
To obtain more information on the environment around elliptical galaxies, we observed the properties of dwarf
galaxies around two giant elliptical galaxies, NGC 4636 and NGC 3923, using optical wide-ﬁeld deep imaging.
These galaxies have similar optical luminosities but have widely varying X-ray luminosities. We applied a convolution technique to detect low surface brightness objects, such as dwarf galaxies and used detection algorithms toidentify groups of connected pixels exceeding a predetermined threshold above the background level. The wellobserved radial proﬁles around NGC 4636 reveal that its dwarf galaxies are highly concentrated, especially its red
dwarf galaxies. Although both NGC 4636 and NGC 3923 are similarly massive elliptical galaxies (M > 1011 M⊙ ),based on gravitational mass proﬁles, NGC 4636 has a larger-scale potential structure than NGC 3923, with its dark
matter surroundings becoming dominant. At a large distance of 300 kpc, NGC 4636 seems to have a deeper dark
matter halo than NGC 3923, with a slightly higher number density of dwarf galaxies. In this work, our analyses obtained complete optical number density of dwarf galaxies around elliptical galaxies down to an absolute magnitudeof MV = −15.5 within 300 kpc, which is the region of dark matter dominance. Given that elliptical galaxies typically have an absolute magnitude of around MV = −22 mag, the faint end corresponded to a stellar mass ∼ 1/1000
that of a giant elliptical galaxy, with a typical mass of ∼ 108 M⊙ . The number density of galaxies at MV = −15.5
is 112.2 ± 65.21 Mpc−2 around the X-ray-bright NGC 4636 and 38.7 ± 36.15 Mpc−2 around the X-ray-faint NGC
3923. These values are lower than that of rich clusters of galaxies but higher than that of our local galaxy group that
includes M31.
Key words: elliptical galaxies; dwarf galaxies; number density

1. Introduction
Optical observations can provide information on the brightness, color, spatial distribution, velocity, and elemental abundances of elliptical galaxies. Additionally, because ellipticalgalaxies emit hot interstellar medium (ISM), X-ray observations can give insights into the temperature and density distributions of plasma in such galaxies.
Giant elliptical galaxies contain a signiﬁcant amount of
hot ISM, with a plasma temperature of 106 –107 K, meaning they are often X-ray-bright (Makishima et al. 2001;
Fukazawa et al.
2006). ISM consists of accumulated
lost stellar mass and supernova ejecta and is gravitationally bound by the galaxy potential (e.g., Forman et al.
1985; Matsushita 2001; Fukazawa et al. 2006). Therefore,
ISM provides information on the galaxy’s gravitational potential through the plasma’s temperature and density distribution.
Furthermore, ISM contains heavy elements (e.g., Matsushita
2001; Matsushita et al. 2003; Xu et al. 2002; Tozuka andFukazawa 2008; Konami et al. 2014) possibly provided bystars; the conﬁnement of heavy elements is related to galactic
gravitational potential. Thus, ISM is important as it relates toboth the chemical and dynamical evolution of elliptical galaxies and galaxy clusters.
One unresolved problem in X-ray observation is the large
scatter of X-ray luminosities of giant elliptical galaxies withsimilar optical luminosities (Matsushita 2001; Boroson et al.
2011; Kim & Fabbiano 2013, 2015; Su et al.
2015;
Goulding et al. 2016; Babyk et al. 2018). This scattercan be up to one order of magnitude even when optical luminosity is homogenous, indicating that ISM considerably differs in composition among galaxies with similar stellar masses
and thus is related to galaxies’ evolutionary histories. Extreme
cases include overluminous elliptical galaxies that can have Xray luminosities as high as that of a bright group of galaxies
but that have a surrounding galaxy population with very poor
X-ray luminosity (Matsushita 2001). This indicates the existence of galactic gravitational potentials that are as deep as2

M. Tozuka et al.

those of galaxy groups or poor clusters, and the presence ofa large amount of dark matter binding to hot X-ray-emittinggases. The large scatter of X-ray luminosities can be attributed
to the differences in ISM properties, and many studies havebeen attempted to resolve this issue. X-ray-bright ellipticalgalaxies are often at the low end of the gravitational potentialof galaxy clusters and are thus embedded in the X-ray-bright
intragroup medium (Eskridge et al. 1995; Makishima et al.
2001). In contrast, elliptical galaxies that are X-ray-faint areeither isolated or at the peripheries of clusters. Therefore,
an elliptical galaxy’s X-ray luminosity is not strictly related
to the number of surrounding galaxies. ASCA and ROSAT
satellites show that X-ray isophotes of bright elliptical galaxies are larger than those of X-ray-faint ones (Matsushita et al.
1998; Matsushita 2001). Chandra’s observations have also revealed that the radial proﬁle of plasma temperatures in X-raybright galaxies exhibits a positive gradient toward the outer region, whereas that of X-ray-faint galaxies has a negative or ﬂat
gradient (Fukazawa et al. 2006). Gravitational mass proﬁlesshow that X-ray-faint galaxies contain their own dark matterwith masses of 1.5–2 times greater than the stellar mass within
6 re . In contrast, X-ray-bright galaxies are in a larger-scalepotential structure. This affects the gravitational potential proﬁle of the galaxy itself, in turn leading to the differences in thetemperature proﬁle and X-ray ISM luminosity of X-ray-brightand X-ray-faint galaxies (Nagino & Matsushita 2009). The
origins of these phenomena remain unresolved, especially regarding what creates the gravitational potential differences andhow these galaxies differ in their evolution.
The universe’s hierarchical structure is currently understoodin terms of the cold dark matter (CDM) model, which predicts that several small objects evolve into a larger one throughmerging (Moore et al. 1999). In this paradigm, small subhalos are expected to exist around a massive galaxy even after evolution. Consequently, studies of dwarf galaxies aroundmassive galaxies are crucial for obtaining a better understanding of CDM properties. In fact, many deep observations are being conducted near the Milky Way (Weisz et al. 2014) as wellas in nearby rich clusters such as the Hydra I (Yamanoi et al.
2007), Coma (Yamanoi et al. 2012), and Centaurus clusters (Chiboucas & Mateo 2006). Current CDM theories areconstrained by the faint-end slope of the luminosity functions(LFs) obtained when counting galaxies. Trentham and Tully(2002) found that LF depends on the environment and reﬂects
galaxy formation and evolution history. The different faint-end
slopes of LFs of elliptical galaxies in different X-ray environments provide insight into the differences in ISM properties relative to galaxy formation and evolution. Comparisons of LFs
in different environments have been conducted, including comparisons between the inner and outer regions of clusters; between elliptical-rich cores and spiral-rich ﬁelds (Phillipps et al.
1998a, 1998b); between central and peripheral or ﬁeld regionsof galaxy clusters (Blanton et al. 2005; Popesso et al.
2006; Yamanoi et al. 2007); and among the center, intermediate region, and outskirts of a cluster (Yamanoi et al. 2012).
However, no comparisons of LFs in different environments
originating within galaxies exist. In this work, we compared
the properties of dwarf galaxies distributed 300 kpc around two
elliptical galaxies with different X-ray luminosities.

Vol. 4,We also observed the color of these dwarf galaxies, whichappears to correlate with the stars it contains. Some semianalytical techniques of studying galaxy formation indicatethat dwarf galaxy distribution and colors depend on the depthof the dark matter halo around the neighboring giant ellipticalgalaxy (Wang & Simon 2012; Wang et al. 2014; Sales et al.
2015).
2. Observations
We conducted deep optical observations of dwarf galaxies
around two isolated giant elliptical galaxies, NGC 4636 andNGC 3923. As shown in Table 1, NGC 4636 and NGC 3923
show nearly identical optical B-band luminosity; however, theNGC 4636 has X-ray luminosity that is one order of magnitude brighter than NGC 3923. NGC 3923 is X-ray-faint, witha compact X-ray isophote and a small X-ray to optical luminosity ratio (Lx / LB ). In contrast, NGC 4636 is X-ray-bright,
with hot gas extending beyond 100 kpc.
Both elliptical galaxies are isolated. NGC 4636 is a member of the Virgo cluster but is 10◦ south of the cluster’s center,and no interactions have been observed. NGC 3923 is in asmall group, and no interaction with that group has been observed. This indicates that both NGC 4636 and NGC 3923 are
not affected by the gravitational potential of larger gravitating
systems such as clusters of galaxies or neighboring galaxies.
Thus, this provides an opportunity to compare the dwarf galaxy
distributions around two elliptical galaxies with different X-ray
luminosities.
We observed several positions around the two ellipticalgalaxies to map radial distributions up to >∼ 300 kpc from eachgalaxy’s center. Public data on isolated X-ray-faint galaxies
are scarce. Although the Sloan Digital Sky Survey (SDSS)-IV
data (Blanton et al. 2017) covers the X-ray-bright NGC 4636
area, the X-ray-faint NGC 3923 area has not been recorded.
For comparison, obtaining data from NGC 4636 and NGC
3923 under the same conditions is necessary. The data usedin this paper were obtained with a 2k-charge coupled device(CCD) camera attached to the 1.05 m Schmidt telescope at
Kiso Observatory at the Institute of Astronomy, University ofTokyo, from January 2008 to July 2009. The camera has aback-illuminated SITe TK2048E CCD (2048 × 2048 pixels,
24 × 24 µm). The ﬁeld of view (FoV) is ∼ 50′ × 50′ with ascale of 1.′′ 5 pixel−1 . At a working temperature of 170 K, theCCD’s dark count, ∼ 1 e−1 h−1 pixel−1 , and readout noise (23e−1 pixel−1 ) are commonly negligible compared to the photon
statistical noise of the object ﬂux and sky background. On adark night, the sky background ﬂux was typically 21 and 18
mag arcsec−2 for the V and I bands, respectively.
A typical observation sequence for a single position consisted of 10–14 successive integrations with small telescope
position offsets (four positions with ∆α = ±1′ and ∆δ = ±1′ )through either a Johnson-Cousins V - or I- band ﬁlter. Each integration had an exposure time of 5 min. In the subsequent
data reduction, we combined the acquired images for the same
position and the same band using the shift-and-add method tominimize the harmful effects of bad pixels on the CCD. We
deleted the effects of cosmic rays by combining images withvarious small offsets. Therefore, the total exposure time for a

id. 6

Distributions of dwarf galaxies around giant elliptical galaxies

3

Table 1. Basic properties of the two elliptical galaxies and ﬁeld data.

Galaxy/Field

PositionDa

log LbX

log LcBRA J2000DEC J2000(Mpc)(erg s−1 )(LB⊙ )

12h 42m 49.s 827+02◦ 41′ 15.′′ 99

15.92

41.59

10.51

11h 51m 01.s 694-28◦ 48′ 21.′′ 66

17.86

40.66

10.52

–

–

–

X-ray-bright Galaxy
NGC 4636
X-ray-faint Galaxy
NGC 3923
Field data
a

d

h

m

s

12 29 20◦′

+20 08 00′′

Distance (O’Sullivan et al. 2001).

b

X-ray luminosity LX (O’Sullivan et al. 2001).

c

Optical B-band luminosity LB (O’Sullivan et al. 2001).

d

Field position neighboring the Virgo cluster observed for counting the number of ﬁeld galaxies.

radial distribution. We adopted magnitude results from the image with the deepest limiting magnitude. Table 2 summarized
the observational data.
Table 2 also shows the visible size and limiting magnitude ofeach position image. We could not obtain any signiﬁcant dataat position 3 because of our limited telescope time and poor
weather conditions during the observations.
We also collected ﬁeld data in addition to target data. We
selected the genuine ﬁeld region using the 2MASS Extended
Sources Catalog (2MASX IPAC/UMass, 2003–2006). The region was separated from the center of the Virgo cluster by 447
kpc or ∆α = +0.72◦ and ∆δ = +7.41◦ from the center of theVirgo cluster, and the number density of galaxies approached
an asymptotic value at the cluster outer limit (Figure 2).
Fig. 1. Position offsets against the galaxy.
∆α ≃ −20′ and∆δ ≃ +20′ for position 1, where ∆α and ∆δ ≃ ±20′ are offsets
along the right ascension the declination of the center of the ﬁeld ofview against the galaxy. ∆α ≃ +20′ and ∆δ ≃ +20′ for position 2,∆α ≃ +20′ and ∆δ ≃ −20′ for position 3, and ∆α ≃ −20′ and∆δ ≃ −20′ for position 4, and ∆α ≃ −40′ for position 5 as an outerregion.

single position was typically 50–70 min.
To cover the ∼ 90′ × 90′ ﬁeld around the galaxy centers, we
captured images at four positions (positions 1–4) with offsetsof ∆α = ±20′ and ∆δ = ±20′ to the galaxy, which produces
an overlapped ﬁeld of 10′ × 10′ . Thus, we set the position toensure that the center of the galaxy appeared in all frames, i.e.,in the overlapped region (Figure 1). This four-region observation covers <∼ 200 kpc from the center of the galaxy. Thus,
to enlarge the sample ﬁeld, we captured images at one outerregion (∆α = −40′ ) as position 5 for both galaxies (Figure1). Because of the large area of the image, a slight dithering
movement generated translation and some rotation, meaning
there are gaps of a few arcseconds in the overlapped region.
We identiﬁed the identical objects in the two images when the
difference in position between these two images was 5 arcsec
and the magnitude difference was 0.1. We also rechecked theseobjects by eye. The resulting gaps are too small to affect the

3. Data Reduction and Analyses
Fixing the boundaries of stars and galaxies using the stargalaxy classiﬁer of SExtractor1 software was difﬁcult because of bad seeing and a 1.5 arcsec pixel scale. Additionally,
with a poor signal-to-noise ratio, the standard detection algorithm for the connected pixels sometimes fails to ﬁnd extended
objects with low surface brightness, such as dwarf galaxies.
Consequently, we adopted a frequency domain technique described by Sabatini et al. (2003) to extract as many galaxies as
possible from the objects SExtractor detected. This method isbased on a convolution of images with matched ﬁlters, making
it possible to use a galaxy’s total ﬂux instead of its very low
local surface brightness.
3.1. First common process
We processed the data through a standard CCD data
reduction method, mainly using IRAF2 , but also used1
2

SExtractor, “Source Extractor,” free software for making a catalog ofsources from astronomical images.(Bertin & Arnouts 1996)
IRAF, “Image Reduction and Analysis Facility” which is distributed by
the National Optical Astronomy Observatory (NOAO) and operated by
the Association of Universities for Research in Astronomy (AURA) undera cooperative agreement with the National Science Foundation (NSF).

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M. Tozuka et al.

Vol. 4,

Table 2. Observation data

Galaxy/Field

Positiona

tbV

tbI

Observation dateSeeingc

Limiting magnituded

(min)

(min)

(YYMMDD)(arcsec)

V (mag)I (mag)Around X-ray-bright Galaxy NGC 4636
1

70

70

090719

5.3

16.9

16.9

2

95

95

090720

2.9

17.8

17.8

4

70

70

090719

3.8

18.8

18.7

5

65

65

090719

3.9

18.7

19.2

Around X-ray-faint Galaxy NGC 3923
1

80

80

080114

4.8

18.3

17.9

2

70

70

080429

4.3

18.0

17.5

3

70

70

080430

3.3

17.4

17.7

4

50

50

080507

3.7

17.1

16.6

5

50

50

080507

3.5

18.9

19.1

–

80

80

080113

7.4

16.4

16.3

Field dataaPosition offsets against the galaxy (See Figure 1).

b

Total exposure times of the V and I bands, respectively.

c

Radial proﬁle ﬁtting by a Gaussian model. Pixel scale is 1.5 arcsecd

The photometric error exceeds 0.1 mag in each ﬁeld (see section 3.3.2)

SExtractor, STSDAS3 , and HEASOFT4 software tools.
First, we de-biased and ﬂat-ﬁelded the obtained images. Bad
pixels were masked at this stage (Figure 3). We then ﬁtted
and subtracted the background sky component of each image,
making the sky level as ﬂat as possible across the different offset images of crucial importance for detecting galaxies withlow surface brightness such as dwarf galaxies. We ﬁtted a loworder (second or third) two-dimensional function to the images.
To obtain the background sky map, harmful ﬂuctuations (e.g.,bright stars and galaxies), which are pixels with two standard
deviations (2 σ) brighter than the sky background level, were
replaced with linear interpolations along lines using the IRAF
command ﬁxpix . We then performed a normal shift-and-add
method to combine frames taken at the same position.
For calibration, we obtained dome ﬂat-ﬁeld images andbias frames. We performed the magnitude calibration using multiple (typically 20 in each position frame) stars listed
in the AAVSO Photometric All Sky Survey (APASS) DR9(Henden et al.
2016). We obtained the V - and I-band
magnitudes of these stars from the APASS g ′ -, r′ -, and i′ band magnitudes using the transformation equation of J.Allyn
Smith et al. (2002).
3

4

STSDAS, “Space Telescope Science Data Analyses System,” preparedby the Space Telescope Science Institute (STScl) under the United States
Government contract NAS5-26555.
HEASOFT is supported by the High Energy Astrophysics Science
Archive Research Center (HEASARC), which is the primary archive forNASA missions.

3.2. Bright galaxies
Stars and bright galaxies can be easily detected with
SExtractor. We assumed that every object (stellar andgalactic) had more than 15 connected pixels and exceeded theambient background ﬂuctuation level by a factor of two. We
distinguished between stellar objects and galaxies following
criteria based on objects dimensions and peak ﬂux describedin Sabatini et al. (2003). This method has merit in that achange in image size within a frame due to aberration does
not have much effect. Figure 4 shows the isophotal area as afunction of surface isophotal ﬂux weighted by the peak ﬂux
of objects detected in NGC 3923 position 3. The stellar locus(red points) and the region occupied by diffuse objects suchas galaxies (green points) are visible; however, the stellar locus is not prominent. Thus, additional criteria are required todiscriminate between stellar and diffuse objects.
As shown in the right panel of Figure 4, most of the detected
objects were stellar objects, and their image sizes are comparable with the seeing size. We divided all data points into subsets consisting of 100 neighboring points along the vertical axis
(i.e., 100 data points with similar surface isophotal ﬂux values
weighted by peak ﬂux) and the derived mean and standard deviation (σ) values of each subset’s isophotal area. However,data points were still insufﬁcient to derive meaningful criteria. Therefore, we added an additional 100 neighboring points
along the vertical axis (50 upper and 50 lower values) in eachsubset to calculate mean and σ. We then considered objects
that had isophotal areas 2 σ larger than the subset mean to beid. 6

Distributions of dwarf galaxies around giant elliptical galaxies

5

diffuse objects, i.e., a galaxy.
To identify bright galaxies, we adopted the photometric parameters derived by SExtractor and calibrated those parameters relative to the standard star observations.
3.3. Faint galaxies
3.3.1. Masking stars and bright galaxies
Before detecting low surface brightness objects, such as faintgalaxies, we must mask high-count objects in advance. This
greatly reduces mis-sampling of faint galaxies in the later process. First, we prepared the object image and corresponding
sky background image derived through low-order function ﬁtting (see section 3.2). Second, we identiﬁed galaxies brighter
than V = 16 mag and all stellar objects and then derived theirradii at which the ﬂux fell within 1 σ of sky noise from the
SExtractor calculations. Third, we masked each object byreplacing it with a corresponding circular region of the sky
background image with the object radius. With this, we obtained masked images.
However, this masking procedure decreases the number ofgalaxies in the dataset due to the loss of usable area for galaxy
detection, which would lead to fewer faint galaxies counted.
We will simulate and evaluate this effect later.

Fig. 2. Upper: Map of dwarf galaxies around the Virgo cluster fromthe 2MASS Extended Sources Catalog. The center of the Virgo cluster
is at the center of this map. The blue square shows the region selected
as our genuine ﬁeld. This ﬁeld located 447 kpc or ∆α = +0.72◦
and ∆δ = +7.41◦ from the center of the Virgo cluster. Lower: The
number density distribution of dwarf galaxies versus distance from thecenter of the Virgo cluster, as deduced from the left panel. The density
distribution of the whole region is shown in black. The number densityof each quadrant is shown in a different color. The vertical blue line
indicates the position of the genuine ﬁeld.

3.3.2. Convolution by multiscale ﬁlter
We adopted a sophisticated convolution method developedby Sabatini et al. (2003) to detect faint and diffuse galaxies.
Our procedure was essentially the same as that described in
sections 4.3–4.4 of Sabatini et al. (2003), except for the negative region of the ﬁlter function, which is not described in theirpaper. The ﬁlter we deﬁned consists of an object with an exponential brightness distribution (F∗ ∝ exp[−r/(3α)], at r ≤ 3α)
and a doughnut-like region with negative values (∝ −exp(−r)
at 3 α < r ≤ 6 α). Thus, this function is zero at r = 3 α andr ≥ 6 α. The full-width at half-maximum (FWHM) of the ﬁlter can be approximated with 1 α, and the typical size of theobject is represented by the scale size (H = 3 α). We adopted
many ﬁlter sizes, ranging from α = 1.5′′ (corresponding to thetypical seeing size) to α = 12′′ (corresponding to 1 kpc at theVirgo cluster) with a 0.1′′ step, to match various objects. Eachﬁlter was scaled and adjusted to give zero for blank sky areas.
After performing convolution for the cleaned images withthe ﬁlter combinations, we built a signiﬁcance image which
had a pixel value equal to the maximum value among theseries of convolution images. On a different array with thesame dimensions as the signiﬁcance image, we saved the ﬁlter scale α on which the maximum value was found (i.e., α ofthe best-matched ﬁlter), which serves as an estimate of the object’s radius. We then detected galaxy candidates by taking all
peaks above the 3 σ threshold in the signiﬁcance image. Whenthe scale size of ﬁlter H matched the scale size of galaxy h(h ≃ H = 3 α in the signiﬁcance image), the value of the convolution can be represented as follows:∫F∗
I = f0 e−r/h (F∗ er/H ) 2 πrdr =(1)
πf0 h2 ,2
where f0 e−r/h is the assumed exponential proﬁle of the galaxy
and F∗ e−r/H is the positive part of the ﬁlter.

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Vol. 4,

Fig. 3. Combined V -band image of X-ray-bright elliptical galaxies NGC 3923 (left) and NGC 4636 (right). For good contrast, images include thebackground sky component.

We can then estimate surface brightness at the center of theobject in the original image as follows:
f0 =

I

.
2 πh2best F∗(2)

To conﬁrm the reliability of these calculations, we show f0 derived by this method against the peak brightness derived bynormal aperture photometry in Figure 5. As shown in the ﬁgure, the two are consistent.
We performed magnitude calibration as follows. First, weselected several galaxies with modest brightness (i.e., galaxies that were not masked in the cleaned image) detected by
SExtractor. We then calibrated the magnitudes of thesegalaxies with the same method used for bright galaxies. Next,
we compared those magnitudes against their peak V value inthe signiﬁcance image, which is shown in Figure 6. Using thisrelationship, we derived the magnitude of all candidate galaxies. We estimated the limiting magnitude of the detection to
be the magnitude where the photometric error determined by
SExtractor results exceeded 0.1 mag in each ﬁeld.
3.4. Contamination by false and background galaxies
The convolution method described above ﬁnds many dwarf
galaxies, with a typical number of galaxies detected in each
image (45′ × 45′ , neglecting the edge of the FoV due to an
incomplete convolution process) reaching ∼ 102 . However, itremains unclear how well the procedure works for less luminous, diffuse galaxies. Furthermore, a non-negligible fractionof these detected galaxies may be background galaxies.
To test the detection reliability and measure the completeness of contamination by false or background galaxies, we
performed a simulation using an artiﬁcial image that mimicked Virgo cluster observation. To the image, we added cluster members following the Schechter luminosity distribution,
background galaxies following the power-law luminosity distribution, stars within our own galaxy, and typical backgroundsky counts with Poisson noise. We then reduced the artiﬁcial
image using the same methods as the observation data.
We found that background galaxy contamination was negligible (< 2%), as our masking procedure would reject mostbackground galaxies as stars and because the scale length was
small. This is consistent with the numerical estimation of
Sabatini et al. (2003). As another estimation of backgroundgalaxy contamination, we observed the ﬁeld position of theVirgo cluster (see section 2) and counted the dwarf galaxies
using the same method. We detected only a few galaxies ineach FoV, which is consistent with the test results. Figure 7
shows the detection completeness estimated by our simulation.
In the artiﬁcial image, the limiting magnitude (σ = 0.1 mag)is V = 19.4 mag. There was a signiﬁcant loss of detection forgalaxies equal to or fainter than the limiting magnitude of theobservation. Thus, discussing such faint galaxies in our data
is undoubtedly difﬁcult. In contrast, the detection was almost
complete at V < 16.5 mag. In the following section, we discuss galaxies brighter than V < 16.5 mag, which corresponds
to absolute magnitude values MV = −14.99 for NGC 4636
and MV = −15.07 for NGC 3923.
4. Results and Discussion
We obtained the number density of dwarf galaxies aroundgiant elliptical galaxies down to an absolute magnitude of
MV = −15.5. As the typical absolute magnitude of a giant
elliptical galaxy is approximately MV = −22 mag, our faintend of galaxy brightness corresponds to ∼ 1/1000 of a giant elliptical galaxy with a mass of ∼ 108 M⊙ . Such a deep surveyof areas around elliptical galaxies in low galactic latitudes remains insufﬁcient. Although the SDSS-IV data (Blanton et al.
2017) covers the area around NGC 4636, areas around X-rayfaint regions, such as NGC 3923, have yet to be recorded.
We individually analyzed V - and I-band data and then compiled them with cross-correlation of both band samples. In

id. 6

Distributions of dwarf galaxies around giant elliptical galaxies

7Fig. 5. Comparison of the peak value of the signiﬁcance image withthat of the raw image.

Peak count (ADU)

1000

-60

-40

-20

0

20

40

60

80

500
200
100
50

100

16

17

18
v (mag)19✂

Fig. 7. Detection completeness of galaxies estimated using an artiﬁcial
image. The gray dashed line shows the limiting magnitude (19.4 mag).
There was a loss in detection completeness for galaxies brighter thanthe limiting magnitude because the artiﬁcial image contains no galaxies
at this magnitude.

✁

other words, we included only galaxies that had been detectedin both bands and also checked the detected galaxies by eye.
Figure 8 shows the galaxies adopted as a sample around NGC
3923 (left) and NGC 4636 (right).
Figure 9 shows that the radial number density distributionof dwarf galaxies is almost constant in the outer region and increases toward the center within 100 kpc. Our sample of dwarf
galaxies contains three components: a component consistingof the giant elliptical galaxy (galaxy component), a uniform
ﬁeld component of the sky (ﬁeld component), and a component associated with the ambient group of galaxies around thegiant elliptical galaxy, which has a larger structure than the giant elliptical galaxy (group component). Therefore, we should
consider the ﬁeld and the group components.
For the ﬁeld component, we observed one region 7◦ northeast from the center of the Virgo cluster, as described in section
2. In Figure 9, the black data represent the total component after data reduction and the gray data represent the ﬁeld compo-✄

Fig. 6. Relationship between the peak V value of the signiﬁcance image and the magnitudes obtained by SExtractor for the detectedgalaxies.

✗✖✕✔✓✒✑✏✎✍✌☞ ☛✡✠✟✞✝✆☎✥

Fig. 4. Upper: Surface isophotal ﬂux weighted by the peak ﬂux is plotted versus the isophotal area of NGC 3923 position1 data in the V-band.
There is a clear locus of the stellar samples. Using a curve ﬁtted to thisstellar locus, we can distinguish stars and galaxies. Lower: Regionof NGC 3923 and the detection of normal objects. Red circles denotestellar objects, and green circles denote galaxy samples.

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-12

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5

21

38

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71

87

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-19

-5.4

8.5

22

36

50

64

78

92

Fig. 8. Final samples of dwarf galaxies were detected in one region (which shows about 50 × 50 arcmin cutouts). The upper side of the images shows thenorth direction and the left side shows the east direction around NGC 3923 (left) and NGC 4636 (right). Red circles denote the detected dwarf galaxies
in each region. The limiting magnitude of the NGC 3923 region is V = 18.3 mag, and that of the NGC 4636 region is V = 18.8 mag.

NGC 3923

600
400
200
0

800
Number density (N/Mpc2)

Number density (N/Mpc2)

800

0

100
200
300
400
Distance from NGC 3923 (kpc)

NGC 4636

600
400
200
0

0

100
200
300
400
Distance from NGC 4636 (kpc)

Fig. 9. Number density of dwarf galaxies as a function of their distances from the elliptical galaxy. The black data represent the total component, andthe gray dots data are the results after subtracting the ﬁeld component.

nent. The ﬁeld component is 41.5 ± 23.97 Mpc−2 ; therefore,
the number densities of dwarf galaxies in these plots are higher
than the ﬁeld components.
Regarding the group component, Ferguson and Sandage(1990) surveyed galaxies more than 1 Mpc from the center ofﬁve nearby groups of galaxies and reported that the radial distribution of galaxies well ﬁt the King model, which has coreradii of 200–700 kpc.
Therefore, the constant component of dwarf galaxy density
more than 300 kpc from the galaxy cluster center can be explained by the group component if the giant galaxy has a coreradius > 300 kpc. Figure 10 shows the number density of dwarf
galaxies as a function of MV within 300 kpc.
Next, we divided NGC 4636 and NGC 3923 into red andblue distributions at V − I = 0.2. Figure11 shows colormagnitude diagrams of dwarf galaxies in the observed regionsof NGC 3923 and NGC 4636. Using V − I ≥ 0.2, we sep-arated the galaxies around NGC 4636 into approximately two
equal parts. In this analysis, V − I ≥ 0.2 corresponds to the
distribution of red dwarf galaxies and V − I < 0.2 corresponds
to that of blue dwarf galaxies.
Figure 12 shows the number density of dwarf galaxies asa function of distance from parent elliptical galaxies. Each
number density is what remains after subtracting the average
number density at 350–450 kpc as the group component includes the ﬁeld component. The black line indicates the remainder after subtracting the group component from the total component. These results reveal previously undetected andmuch redder dwarf galaxies concentrated around NGC 4636.
Contrastingly, NGC 3923 showed a much weaker concentration. Some previous research (Wang et al. 2014; Sales et al.
2015) indicated that the satellite populations around NGC 3923
and NGC 4636 within 0.2 virial radii, which corresponds tohundreds of kpc, were similar because they have similar stellar

id. 6

Distributions of dwarf galaxies around giant elliptical galaxies

NGC 4636−20−18
Mv/mag

−16

1000
100
10

Number density (Mpc−2 )

1000
100
10

Number density (Mpc−2 )NGC 3923

−22

9

−22

−20
−18
Mv/mag−16

Fig. 10. Number density of dwarf galaxies as a function of absolute magnitude (MV ). The black data represent the total component, and the gray dot
data are the ﬁeld component results.

2

NGC 3923

2

1

V−I

V−I

1

0

0

−1

−1

−2

NGC 4636

−2

−22

−20
Mv/mag

−18

−20

−18
Mv/mag−16

Fig. 11. Color-magnitude diagrams of NGC 3923 (left) and NGC 4636 (right). Red data represent the distribution of red dwarf galaxies (V − I ≥ 0.2).
Blue data represent the distribution of blue dwarf galaxies (V − I < 0.2)

masses. Both NGC 4636 and NGC 3923 are massive ellipticalgalaxies (M > 1011 M⊙ ), and for the most massive ellipticalgalaxies, red satellites galaxies dominate and tend to be more
steeply distributed than bluer ones.
These proﬁles of dwarf galaxies, including red dwarf galaxies around NGC 4636, agree with the semi-analytical techniques of Wang and Simon (2012), Wang et al. (2014), andSales et al. (2015). Although NGC 3923 and NGC 4636
have comparable optical luminosities, NGC 4636 has a higher
gravitational mass than NGC 3923 based on X-ray observation(Nagino & Matsushita 2009). Only two examples with large
systematic error exist to date; therefore, systematic observationof these tendencies for other elliptical galaxies is required forfurther discussion.
Figure 13 also shows number densities of dwarf galaxies asa function of magnitude. These number densities are the remainder after subtracting the average number density at 350 to

450 kpc, where the group component includes the ﬁeld component. Data on the color of these dwarf galaxies do not appear
because of large systematic error.
Our results indicate that the typical number density of galaxies is 112.2 ± 65.21 Mpc−2 around NGC 4636 and 38.7 ±36.15 Mpc−2 around NGC 3923 at MV = −15.5. These values are lower than that of nearby rich clusters of galaxies, including the Hydra I cluster (Yamanoi et al. 2007), which has
approximately 300 Mpc−2 in the B-band and 600 Mpc−2 inthe R-band; the Coma cluster (Yamanoi et al. 2012), withapproximately 200 Mpc−2 in the R-band; and the Centaurus
cluster (Chiboucas & Mateo 2006), which has approximately
160 Mpc−2 in the V -band after correction for background contamination. On the other hand, this value is higher than that of
our local galaxy group including M31, which has 2 Mpc−2 at
MV = −15.5 (Weisz et al. 2014).
We also found a slight difference in the number density be-

10

M. Tozuka et al.
NGC 3923

800

600

Number density (N/Mpc2)

Number density (N/Mpc2)

800

Blue gal
Red gal0.2>=(V−I)

400
200
0

0

100
200
Distance from NGC 3923 (kpc)

Vol. 4,
NGC 4636

600

Blue gal
Red gal0.2>=(V−I)

400
200
0

300

0

100
200
Distance from NGC 4636 (kpc)

300

Fig. 12. Number density of dwarf galaxies as a function of distance from the parent elliptical galaxy. Each number density is what is left after subtracting
the average number density at 350–450 kpc as the group component including the ﬁeld component. The black line shows the remainder after subtracting
the group component from the total component. The red line is the distribution of red dwarf galaxies (V − I ≥ 0.2). The blue line is the distribution ofblue dwarf galaxies(V − I < 0.2)

NGC 4636−20−18
Mv/mag−16

1000

Blue gal
Red gal100(V−I)>=0.2

10

100

(V−I)>=0.2−22

Number density (Mpc )

−2

1000

Blue gal
Red gal10

Number density (Mpc−2 )NGC 3923

−22

−20
−18
Mv/mag−16

Fig. 13. Number density of dwarf galaxies as a function of a magnitude of V . Number density is the remainder after subtracting the average number
density at 350–450 kpc as the group component including the ﬁeld component. Data on the color of dwarf galaxies do not appear to large systematic
error.

tween NGC 4636 and NGC 3923. Nagino and Matsushita(2009) indicated that NGC 4636 has a higher gravitational
mass than NGC 3923 at over 6 re , which corresponds to 45.0
kpc for NGC 4636 and 27.6 kpc for NGC 3923. Previous research (Wang et al. 2014; Sales et al. 2015) also indicated thatsatellite galaxies roughly follow the distribution of dark matterin a distance range of 0.2–1 virial radii, which corresponds toseveral hundreds of kpc and includes in the outer regions where
dark matter dominates (Schuberth et al. 2006; Schuberth et al.
2012; Norris et al. 2012). Although we found no obvious evidence of a relationship between the number density of satellite
galaxies and the dark matter halo of elliptical galaxies, NGC
4636 appears to have a deeper dark matter halo than NGC 3923
and has a slightly higher number density of dwarf galaxies thanNGC 3923. However, a more detailed discussion will require
better velocity dispersion.

5. Conclusion
We observed the properties of dwarf galaxies around two
examples of elliptical galaxies, NGC 4636 and NGC 3923, toobtain more information on the environment around ellipticalgalaxies. NGC 4636 and NGC 3923 have similar optical luminosities, which are used to calculate component stellar mass,
but have different X-ray luminosities, which can be used to calculate total mass. Thus, both NGC 4636 and NGC 3923 have
similar stellar masses but NGC 4636, which is X-ray-bright,
has a higher gravitational mass. When we observe the environment around elliptical galaxies to greater distances, we candetermine not only stellar mass but also the total gravitational
mass.
Both NGC 4636 and NGC 3923 are similarly massive elliptical galaxies (M > 1011 M⊙ ). On the other hand, based on
their gravitational mass proﬁles NGC 4636 contains a largerscale potential structure than NGC 3923 both within and over
6 re (Nagino & Matsushita 2009). In the outer regions, dark
matter dominates (Schuberth et al. 2006, 2012; Norris et al.

id. 6

Distributions of dwarf galaxies around giant elliptical galaxies2012). Previous research (Wang et al. 2014; Sales et al. 2015)
also indicated that satellite galaxies roughly follow the distribution of dark matter in a distance ranging from 0.2 to 1 virial
radii. Comparing NGC 4636 to NGC 3923 at large 300 kpc distances, NGC 4636, which seems to have a deeper dark matter
halo than NGC 3923, shows a slightly higher number densityof dwarf galaxies than NGC 3923. Dwarf galaxies are also
observed to be more highly concentrated around NGC 4636.
More information on the dispersion velocity of dwarf galaxies
is required to better understand the dynamic equilibrium processes of elliptical galaxies. Therefore, systematic observationof these tendencies for other elliptical galaxies is required forfurther discussion.
Although the SDSS-IV data (Blanton et al. 2017) coveran area of 200–700 kpc around the NGC 4636, areas around
X-ray-faint galaxies, such as NGC 3923, have yet to be analyzed. We obtained the number density of dwarf galaxies
around both elliptical galaxies down to an absolute magnitudeof MV = −15.5. Given that the typical absolute magnitude ofelliptical galaxies is around MV = −22 mag, the faint end corresponded to a stellar mass ∼ 1/1000 that of a giant ellipticalgalaxy or a galaxy mass of ∼ 108 M⊙ . The observed radial proﬁle around the NGC 4636 revealed its satellite dwarf galaxies
were relatively concentrated, especially its red dwarf galaxies.
We also found a slight difference in the galaxy number density
between NGC 4636 and NGC 3923 within a radius of approximately 300 kpc. The typical number density of galaxies at
MV = −15.5 around NGC 4636 is 112.2 ± 65.21 Mpc−2 ,whereas it is 38.7 ± 36.15 Mpc−2 around NGC 3923. These
values are lower than that of the nearby rich cluster of galaxies
but higher than that of our local groups including M31.
6. Acknowledgement
Finally, we are grateful to the referees for their helpful comments. The authors also thank members of the Kiso observatory for the opportunity of our observation.
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