11institutetext: European Southern Observatory, Alonso de Cordova 3107,
Vitacura, Casilla 19001, Santiago de Chile, Chile
11email<EMAIL_ADDRESS>22institutetext: European Southern Observatory, Karl-
Schwarzschild-Str. 2, 85748 Garching, Germany 33institutetext: Max-Planck-
Institut für Extraterrestrische Physik, Giessenbachstraße, 85748 Garching,
Germany 44institutetext: School of Physics and Astronomy, University of
Nottingham, NG7 2RD, United Kingdom 55institutetext: Leiden Observatory,
Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands
66institutetext: DARK, Niels Bohr Institute, University of Copenhagen,
Lyngbyvej 2, DK-2100 Copenhagen, Denmark 77institutetext: Inter University
Centre for Astronomy and Astrophysics, Ganeshkhind, Post Bag 4, Pune 411007,
India 88institutetext: Department of Physics, University of Oxford, Denys
Wilkinson Building, Keble Road, Oxford OX1 3RH, United Kingdom
99institutetext: INAF – Osservatorio Astronomico di Capodimonte, Via
Moiariello 16, 80131, Naples, Italy 1010institutetext: Departamento de
Astronomia, Instituto de Astronomia, Geofisica e Ciencias Atmosfericas da USP,
Cidade Universitaria, CEP:05508900 Sao Paulo, Brazil 1111institutetext:
Research School of Astronomy & Astrophysics Mount Stromlo Observatory, Cotter
Road, 2611 Canberra, Australia 1212institutetext: School of Physics and
Astronomy, Sun Yat-sen University, DaXue Road 2, 519082 Zhuhai, China
1313institutetext: CSST Science Center for the Guangdong-Hongkong-Macau
Greater Bay Area, DaXue Road 2, 519082 Zhuhai, China 1414institutetext:
Department of Physics & Astronomy, San José State University, One Washington
Square, San Jose, CA 95192, USA 1515institutetext: University of California
Observatories, 1156 High St., Santa Cruz, CA 95064, USA 1616institutetext:
Department of Astronomy and Astrophysics, University of California, Santa
Cruz, CA 95064, USA

# The halo of M105 and its group environment as traced by planetary nebulae
populations††thanks: This research is based on data collected at Subaru
Telescope, which is operated by the National Astronomical Observatory of
Japan. We are honoured and grateful for the opportunity of observing the
Universe from Maunakea, which has the cultural, historical and natural
significance in Hawaii. It is also based on observations made with the William
Herschel Telescope operated on the island of La Palma by the Isaac Newton
Group of Telescopes in the Spanish Observatorio del Roque de los Muchachos of
the Instituto de Astrofísica de Canarias.

II. Using kinematics of single stars to unveil the presence of intragroup
light around the Leo I galaxies NGC 3384 and M105

J. Hartke 1122 M. Arnaboldi 22 O. Gerhard 33 L. Coccato 22 M. Merrifield 44 K.
Kuijken 55 C. Pulsoni 33 A. Agnello 66 S. Bhattacharya 77 C. Spiniello 8899 A.
Cortesi 1010 K. C. Freeman 1111 N. R. Napolitano 12121313 A. J. Romanowsky
141415151616

###### Abstract

Context. M105 is an early-type galaxy in the nearby Leo I group, the closest
galaxy group to contain all galaxy types and therefore an excellent
environment to explore the low-mass end of intra-group light (IGL) assembly.

Aims. We present a new and extended kinematic survey of planetary nebulae
(PNe) in M105 and the surrounding $30\arcmin\times 30\arcmin$ in the Leo I
group with the Planetary Nebula Spectrograph (PN.S) to investigate
kinematically distinct populations of PNe in the halo and surrounding IGL.

Methods. We use PNe as kinematic tracers of the diffuse stellar light in the
halo and IGL and employ photo-kinematic Gaussian mixture models to (i)
separate contributions from the companion galaxy NGC 3384, and (ii) associate
PNe with structurally defined halo and IGL components around M105.

Results. We present a catalogue of $314$ PNe in the surveyed area. We firmly
associate $93$ with the companion galaxy NGC 3384 and $169$ with M105. The PNe
in M105 are further associated with its halo ($138$) and the surrounding
exponential envelope ($31$). We construct smooth velocity and velocity
dispersion fields and calculate projected rotation, velocity dispersion, and
$\lambda_{R}$ profiles for the different components. PNe associated with the
halo exhibit declining velocity dispersion and rotation profiles as a function
of radius, while the velocity dispersion and rotation of the exponential
envelope increase notably at large radii. The rotation axes of these different
components are strongly misaligned.

Conclusions. Based on the kinematic profiles, we identify three regimes with
distinct kinematics that are also linked to distinct stellar population
properties: (i) the _rotating core_ at the centre of the galaxy (within
$1\leavevmode\nobreak\ R_{\mathrm{eff}}$) formed _in situ_ and dominated by
metal-rich ([M/H]$\approx 0$) stars and likely formed in situ, (ii) the _halo_
from $1$ to $7.5\leavevmode\nobreak\ R_{\mathrm{eff}}$ consisting of a mixture
of intermediate-metallicity and metal-rich stars ([M/H]$>-1$), either formed
_in situ_ or brought in through major mergers, and (iii) the _exponential
envelope_ reaching beyond our farthest our farthest data point at 16
$R_{\mathrm{eff}}$, predominately composed of metal-poor ([M/H]$<-1$) stars.
The high velocity dispersion and moderate rotation of the latter are
consistent with that measured for the dwarf satellite galaxies in the Leo I
group, indicating that this exponential envelope traces the transition to the
IGL.

###### Key Words.:

galaxies: individual: M105 –- galaxies: elliptical and lenticular, cD -–
galaxies: groups: individual: Leo I – galaxies: halos – planetary nebulae:
general

##  1 Introduction

The galaxy M105 (NGC 3379) in the Leo I group figured predominantly in a
lively debate on the dark matter content and its spatial distribution in
massive early-type galaxies (ETGs) (Romanowsky et al. 2003; Dekel et al. 2005;
de Lorenzi et al. 2009; Napolitano et al. 2009; Morganti et al. 2013). Using
data obtained with the Planetary Nebula Spectrograph (PN.S), Romanowsky et al.
(2003) and Douglas et al. (2007) found that several intermediate luminosity
elliptical galaxies – M105 among them – appeared to have low-mass and low-
concentration DM halos, if any, based on their rapidly falling velocity
dispersion profiles. This is in contrast with inferences made on the massive
dark halos of giant elliptical galaxies from multiple tracers, such as spectra
of the integrated light (e.g. Kronawitter et al. 2000; Gerhard et al. 2001;
Cappellari et al. 2006), X-ray profiles of the hot gas atmospheres (e.g. Awaki
et al. 1994; Loewenstein 1999; Humphrey et al. 2012), as well as from weak and
strong gravitational lensing (e.g. Hoekstra et al. 2004; Mandelbaum et al.
2006; Wilson et al. 2001; Koopmans et al. 2006; Tortora et al. 2010, 2014).
Follow-up studies discussed whether the apparent lack of dark matter in the
halo of M105 was linked to the gravitational potential-orbital anisotropy
degeneracy and viewing-angle effects (Dekel et al. 2005; Douglas et al. 2007;
de Lorenzi et al. 2009; Weijmans et al. 2009; Morganti et al. 2013).
Furthermore, the strong decrease of the line-of-sight (LOS) velocity
dispersion may not continue in the outer halo; Pulsoni et al. (2018)
identified several ETGs where the decline of the LOS velocity dispersion was
followed by an increase in the outer halo (e.g. NGC 1023, NGC 2974, NGC 4374,
NGC 4472). Since Romanowsky et al. (2003) measurements were confined within
eight effective radii (i.e. within the field-of-view of a single PN.S
pointing), they may have missed a kinematic transition at larger radii.

Using new, extended imaging and kinematic samples of PNe, we aim to
investigate whether the LOS velocity dispersion profile decline in M105
continues in the outer halo or whether a change in kinematics is observed. Our
work builds on the first paper in this series, in which Hartke et al. (2020,
hereafter H+2020), presented a wide-field photometric survey of PN candidates
in M105 and the surrounding $0.5\times 0.5\deg^{2}$. H+2020 found a variation
of the luminosity-specific PN number $\alpha$ with radius in the halo of M105,
with the $\alpha$-parameter being seven times higher in the extended halo
compared to the inner halo. They inferred that the PN population with a high
$\alpha$-parameter is linked to a diffuse population of metal-poor stars
($\mathrm{[M/H]}\leq-1.0$, Lee & Jang 2016), whose light distribution is
governed by an exponential surface brightness (SB) profile. The light
distribution in the inner halo is dominated by intermediate and metal-rich
stars ($\mathrm{[M/H]}>-1.0$, Lee & Jang 2016) following a Sérsic SB profile
and a low-$\alpha$-parameter population of PNe. In this paper, which is the
second of the series, we wish to investigate whether the two PN populations
that H+2020 identified also possess distinct kinematic signatures and which
constraints these would place on the assembly history of M105 and its group
environment – the Leo I group.

The Leo I group is the closest group that contains all (i.e. early and late)
galaxy types (de Vaucouleurs 1975). The eleven brightest and most massive
member galaxies can be further divided into two subgroups. Four are associated
with the so-called Leo Triplet. The remaining seven, among them M105 and NGC
3384 that are the main subjects of this paper, are associated with the M96
(NGC 3368) group. In addition to these bright member galaxies, dwarf galaxies
make up the largest number of group members: Müller et al. (2018) compiled the
most recent catalogue of dwarf galaxies in the group, adding 36 new candidates
to the previously known 52 dwarf galaxies.

With its low mass and proximity, the Leo I group is an excellent environment
to explore the low-mass end of intra-group light (IGL) assembly. Based on deep
and wide-field photometry, Watkins et al. (2014) attributed at most a few per
cent of the light in their survey footprint to the IGL. Assuming that all PNe
associated with the exponential SB profile trace the IGL, H+2020 determine the
fraction of PNe associated with the IGL to be 22%, while the fraction in terms
of stellar SB is 3.8%. This low IGL fraction seemingly contradicts results
from numerical simulations, which predict IGL fractions between 12% and 45%
(Sommer-Larsen 2006; Rudick et al. 2006). However, it is unclear whether this
mismatch is a resolution effect or whether a dimmer IGL is expected in lower-
mass groups compared to more massive environments such as galaxy
clusters(Purcell et al. 2007; Watkins et al. 2014). Evaluating the dynamical
status of the PNe populations at large radii is imperative for constraining
the IGL properties in the Leo I group.

This paper is organised as follows: in Sect. 2, we describe the data from
photometric and slit-less spectroscopic surveys in the Leo I group and the
compilation of the final cross-matched data catalogues. Section 3 describes
the decomposition of the sample into PNe associated with NGC 3384 and M105,
based on photo-kinematic models. We describe the kinematics of PNe in the halo
and envelope of M105 in Sect. 4. We discuss our results in Sect. 5 and put
them into the context of the Leo I group at large. We summarise and conclude
our work in Sect. 6.

In this paper, we adopt a physical distance of 10.23 Mpc to M105. The
corresponding physical scale is $49.6\;\mathrm{pc}/\arcsec$. This tip of the
red giant branch (TRGB) distance was independently determined by Harris et al.
(2007a, b) and Lee & Jang (2016) and agrees well with that determined from the
bright cut-off of the planetary nebula luminosity function (PNLF) determined
by H+2020 as well as with that derived from from SB fluctuation measurements
(SBF; Tonry et al. 2001). The effective radius of M105, derived from broad-
band photometry, is $R_{\mathrm{eff,M105}}=54\aas@@fstack{\prime\prime}8\pm
3\aas@@fstack{\prime\prime}5$ (Capaccioli et al. 1990), corresponding to a
physical scale of 2.7 kpc.

##  2 The data

Figure 1: DSS-image of the Leo I group with a scale-bar in the lower-right
corner indicating a physical scale of 10 kpc. North is up, East to the left.
Left: Rectangles show the field outlines of the Surprime-Cam photometry survey
(grey dashed outline), individual fields of the e2PN.S survey (solid
outlines), and the Hubble Space Telescope (HST) fields analysed by Lee & Jang
(2016, hashed rectangles). Right: Overplotted are the PN candidates detected
with Surprime-Cam (Hartke et al. 2020, grey plus signs). The data from the
ePN.S survey (Pulsoni et al. 2018) for NGC 3384 (first published by Cortesi et
al. 2013a) and M105 (first published by Douglas et al. 2007) are indicated by
cyan and green points and diamonds respectively. Squares denoted the PNe from
the e2PN.S survey already presented in (H+2020) and bold crosses newly
detected PNe from this work. The colours of the symbols correspond to that of
the field outlines in the left panel.

###  2.1 Photometric survey

H+2020 presented the Subaru Surprime-Cam survey for PNe candidates in the Leo
I group. Here, we only briefly summarise the survey objectives, data
reduction, and PN candidate identification and validation. They identified PN
candidates from the combined use of narrow- [O iii]
($\lambda_{\mathrm{c,on}}=5500\;\textup{\AA}$) and broad-band $V$-band
($\lambda_{\mathrm{c,off}}=5029\;\textup{\AA}$) images. Using CMD-based
automated detection techniques (Arnaboldi et al. 2002, 2003), H+2020
identified $226$ PNe candidates within a limiting magnitude of
$m_{5007,\mathrm{lim}}=28.1$. These candidates are denoted with grey crosses
in the left panel of Fig. 1. The photometric survey thus covers $2.6$
magnitudes from the bright cut-off of the PNLF at $m^{\star}_{5007}=25.5$. The
unmasked survey area (excluding image artefacts and regions with a high
background value) covered $0.2365\;\mathrm{deg}^{2}$ on the sky, which
corresponds to $67.7$ kpc along M105’s major axis. The survey also covers the
halos of NGC 3384 and NGC 3389. The survey footprint is outlined by the grey
dashed rectangle in the right panel of Fig. 1. The IDs, coordinates, and
magnitudes of the PNe candidates brighter than the limiting magnitude are
presented in Table 4.

###  2.2 The extremely extended PN.S ETG (e2PN.S) survey in M105 and NGC 3384

Table 1: Summary of the PN.S observations used in this paper. The top part of
the table refers to new observations, while the bottom part summarises data
from published catalogues.

Field name | RA | dec | Exposure time | Year |  $N_{\mathrm{PN}}$(a)(a)footnotemark: $(a)$ | References
---|---|---|---|---|---|---
| [hh:mm:ss] | [dd:mm:ss] | [hours] |  |  |
M105-S | 10:47:49.59 | +12:25:53.8 | 3.5 | 2017 | 18 |
M105-W | 10:47:13.59 | +12:38:13.8 | 6.0 | 2017, 2019 | 13 |
M105-SW | 10:47:14.40 | +12:28:30.0 | 4.0 | 2019 | 11 |
M105-N | 10:47:42.39 | +12:43:53.8 | 4.0 | 2019 | 2 |
M105-C | 10:47:49.60 | +12:36:54.0 | 18.8(b)(b)footnotemark: $(b)$ | 2002, 2003 | 217 | (1)
N3384 | 10:48:14.40 | +12:37:12.0 | 5.95 | 2003-2011 | 94 | (2)

(1) Douglas et al. (2007); (2) Cortesi et al. (2013a) 111 $a$$a$footnotetext:
The number of PNe $N_{\mathrm{PN}}$ refers to the 3$\sigma$-clipped catalogue.
The sum of $N_{\mathrm{PN}}$ presented in this table is larger than the total
number of PNe in the main text as some PNe are observed in two fields.
$b$$b$footnotetext: This exposure time is considerably longer compared to the
other fields, but were obtained under a variety of seeing conditions. Had they
been taken in nominal 1″seeing conditions, the equivalent would be 7 hours
(see Douglas et al. 2007, for details).

The extremely extended PN.S ETG (e2PN.S) survey includes data from the ePN.S
survey (Arnaboldi et al. 2017; Pulsoni et al. 2018), namely two fields centred
on M105 and NGC 3384 respectively. The first PN.S observations of M105 were
part of the PN.S ETG survey (Douglas et al. 2007). The resulting $214$ PNe are
indicated with cyan circles in the right panel of Fig. 1 and in the left
panel, where the field is outlined in the same colour and denoted with M105-C.

In 2017, we observed two additional fields (M105-W and M105-S). They are
indicated by the brown and red rectangles in the left panel of Fig. 1. These
data were used to independently validate the photometric sample in H+2020. In
2019, M105-W was observed again, along with the fields M105-SW (blue
rectangle) and M105-N (purple rectangle). The total exposure times per field
are given in Table 1. NGC 3384 was first observed as part of the PN.S survey
of S0 galaxy kinematics (Cortesi et al. 2013a). In total, 101 PNe were
observed; they are denoted with green diamonds in the right panel of Fig. 1.
The availability of these data will enable an improved photo-kinematic
decomposition of the PN sample (see Sect. 3).

####  2.2.1 Field-to-field variation and catalogue matching within the e2PN.S
survey

Figure 2: Comparison of the velocity measurements obtained for PNe that lie in
the areas of intersection of two fields. The grey shaded regions indicate the
nominal $1\sigma$ and $2\sigma$ PN.S velocity uncertainties of $\pm 20$ and
$\pm 40\;\mathrm{km}\,\mathrm{s}^{-1}$, respectively. For the M105-W field,
prev. indicates the previous measurements by H+2020.

The PN.S pipeline processes the survey data field-by-field. We, therefore, had
to cross-match the individual catalogues to create a homogeneous master
catalogue encompassing data from the six fields. We used an iterative
coordinate-matching algorithm with a matching radius of $5\arcsec$. We chose
this seemingly large radius due to the positional uncertainties on the PN.S
data. As already stated in H+2020, we identify the $30$ PNe with measurements
in the fields M105-C and N3384. In addition to that, we identify $2$ PNe in
M105-S and M105-SW, $1$ PN in M105-N and M105-W, and $6$ in M105-C and M105-W.

Figure 2 shows a field-to-field comparison of the velocities. The velocity
measurements generally scatter about the one-to-one line, and the scatter is
within the 2$\sigma$ PN.S velocity error (light grey shaded region). H+2020
already discussed the nature of the 11 measurements that lie outside of the
grey shaded region: these 11 PNe were observed close to one of the field edges
in either of the two fields. For these objects, only the measurements taken
closer to the respective field centre were included in the final catalogue.
For the other PNe with repeat measurements, we included the mean velocities
and magnitudes instead. The IDs of PNe with repeated measurements were
concatenated in the final catalogue.

We also identified $5$ PNe in the western field based on 2017 data alone
(H+2020) and in the deeper stack, including the data from 2019. These are
denoted with orange squares in Fig. 2. They all scatter about the one-to-one
line, and the scatter is within the velocity error of the PN.S. We conclude
that there is no velocity offset between the observations taken in 2017 and
2019.

####  2.2.2 Photometric calibration and catalogue matching with Surprime-Cam
photometry

Figure 3: Comparison of the $AB$ magnitudes of PN candidates from H+2020 with
those from the e2PN.S survey. The colour-coding is the same as in the left
panel of Fig. 1. The grey shaded region indicates where $99\%$ of Subaru
sources would fall if one plotted two independent measurements of their
magnitudes $m_{\mathrm{AB,Subaru}}$ against each other (H+2020). The error bar
in the lower-right corner denotes the typical magnitude uncertainty of the
PN.S.

We matched the kinematic catalogue compiled in the previous section with the
photometric one from H+2020. Like H+2020, we used a matching radius of
$5\arcsec$ due to the relatively large positional uncertainty on the PN.S
data. We used this matched sample to determine the zero-point magnitude of
each of the newly-observed PN.S fields. Fig. 3 shows a comparison of the $AB$
magnitudes obtained with the PN.S after applying the zero-point offset with
those from Surprime-Cam. The colour-coding is the same as in Fig. 1.

The large scatter about the one-to-one line is not surprising, as the PN.S had
not been optimised to obtain accurate photometry. While the photometric
accuracy is acceptable in nearby galaxies (e.g. Merrett et al. 2006), Hartke
et al. (2018) found a similarly large scatter of PN.S magnitudes compared to
accurate Surprime-Cam ones in the Virgo galaxy M49. In order to convert the
$AB$ magnitudes to $m_{5007}$, we used the relation determined by Arnaboldi et
al. (2003): $m_{5007}=m_{AB}+2.49$.

Figure 4: PNLF of all PNe from the e2PN.S survey (black histogram) and its
individual fields. The colour-coding of the histograms corresponds to that in
Fig. 1. The dashed gray histogram denotes the PNLF from the Surprime-Cam
photometry. No completeness corrections have been applied to any of the LFs.
The black and gray dotted vertical lines denote the PNLF bright cut offs
corresponding to the distance of M105 and NGC 3384 respectively.

To gauge the depth of the e2PN.S survey, we construct the PNLF of each of the
fields. Figure 4 shows the PNLF for each field with the same colour-coding as
in Fig. 1. The black histogram denotes the PNLF of all e2PN.S PNe. For
comparison, we also show the PNLF based on the Surprime-Cam photometry in
grey. We only included data brighter than the limiting magnitude
$m_{5007,\mathrm{lim}}=28.1$. The vertical dotted lines denote the PNLF bright
cut-offs corresponding to the distances to M105 (black,
$m^{\star}_{5007,\mathrm{M105}}=25.54$) and NGC 3384 (grey,
$m^{\star}_{5007,\mathrm{N3384}}=25.76$) respectively. Except for one over-
luminous object, all PNe are fainter than the bright cut-off
$m^{\star}_{5007,\mathrm{M105}}$.

The deepest fields are centred on M105 and NGC 3384, with the faintest object
nearly reaching 30th magnitude. However, the e2PN.S survey is likely only
complete to a limiting magnitude of $m_{\mathrm{5007,lim}}=27.5$. This is the
magnitude at which the number of PNe starts to decrease as a function of
magnitude, contrary to the exponential increase that is theoretically expected
(see also H+2020).

####  2.2.3 Excluding velocity outliers

Figure 5: Left: Phase-space of PN candidates in the e2PN.S survey footprint,
including PNe associated with M105 and NGC 3384. The major axis of M105 is
denoted with $x_{\mathrm{M105}}$. Right: Line-of-sight velocity histogram of
the objects shown in the left panel. The dashed line denotes the systemic
velocity of M105, and the solid blue line the mean velocity of the sample. The
blue shaded regions denote the 1, 2, and $3\sigma$ intervals from the mean.
Objects beyond $3\sigma$ of the mean velocity are likely redshifted background
emission-line galaxies.

To remove velocity outliers that may be sources of contamination, we first
calculated the mean velocity and velocity dispersion $\sigma$ of the whole
sample – including PNe associated with M105 and NGC 3384 – using a robust
fitting technique (McNeil et al. 2010). The left panel of Fig. 5 shows the
phase-space of PN candidates in the e2PN.S footprint with the $x$-coordinate
along the major axis of M105. The right panel of Fig. 5 shows the
corresponding LOS velocity distribution (LOSVD) with the 1, 2, and $3\sigma$
intervals shaded in blue. The velocity range covered by the different filter
configurations is $-400<v\leq 2400\;\mathrm{km}\,\mathrm{s}^{-1}$. We clipped
four PNe with velocities outside the velocity range of $\pm 3\sigma$ about the
robust mean. Table 1 contains the final e2PN.S catalogue after combining
observations from multiple fields, correcting the magnitude zero-point, and
$3\sigma$-clipping. In summary, the final catalogue, provided in Table 5,
contains coordinates, velocities, and magnitudes for $319$ PNe.

####  2.2.4 Completeness and sources of contamination

The completeness of the photometric catalogue has been extensively discussed
in H+2020. Due to the nature of the PN.S instrument, we can immediately
discard objects with a continuum, as the continuum appears as a stripe in
slitless spectroscopy. This requirement excludes the majority of Ly-$\alpha$
emitters with a continuum redder than the [O iii]5007Å emission line.
Background [O ii] emitters at $z\simeq 0.34$ can be discarded as the spectral
resolution of the PN.S is sufficient to resolve both emissions from the
redshifted [O ii] 3727 Å doublet. However, we cannot use the second bluer line
of the [O iii] doublet commonly used to distinguish PNe from contaminants as
the PN.S bandpass does not cover it. We therefore resorted to statistical
methods to estimate the contamination from Ly-$\alpha$ galaxies without a
measurable continuum, assuming that the number of background galaxies should
be uniformly distributed in a velocity histogram (Spiniello et al. 2018).

Based on the presence of three objects in the velocity range $1400<v\leq
2400\;\mathrm{km}\,\mathrm{s}^{-1}$ and one in the velocity range $-400<v\leq
400\;\mathrm{km}\,\mathrm{s}^{-1}$ (see Fig. 5), which are likely not PNe, we
expect 7 objects such as background galaxies in the full velocity range,
corresponding to a fraction of $2.2\%$. The result is very similar to that
estimated by H+2020 (2.6%) based on a subset of the data and the estimate of
Spiniello et al. (2018, $\approx 2\%$) for slitless spectroscopy of PNe the
Fornax cluster.

##  3 Galaxy membership assignment based on photo-kinematic models

In order to decompose the kinematic PN sample into subcomponents associated
with M105 and NGC 3384, we model the observed PN in position-velocity space
using a luminosity-weighted multi-Gaussian model. The luminosity weights are
pre-determined from broad-band photometry, while the kinematic parameters are
free parameters of the Gaussian-mixture model. Gaussian-mixture models are
widespread in the astronomical literature to disentangle multi-component
LOSVDs (see e.g. Walker & Peñarrubia 2011; Amorisco & Evans 2012; Watkins et
al. 2013; Agnello et al. 2014; Hartke et al. 2018; Longobardi et al. 2018a).
In the following simple modelling we assume that there is no strong ongoing
interaction between the two galaxies. This assumption is supported by the
absence of strong tidal features or bridges of stars connecting the two
galaxies (Watkins et al. 2014).

###  3.1 Disk-bulge decomposition of NGC 3384

To model the kinematics of NGC 3384, we use the disk-bulge decomposition
method developed by Cortesi et al. (2011) and subsequently applied to the PN.S
survey of S0 galaxy kinematics (Cortesi et al. 2013b), including the
decomposition of NGC 3384 into its disk and bulge components.

The LOS velocity of the disk as function of azimuthal angle
$\phi_{\mathrm{3384}}$ and radius $r_{\mathrm{3384}}$ measured with respect to
the centre of NGC 3384 can be expressed as

$v_{\mathrm{LOS}}(r_{\mathrm{3384}},\phi_{\mathrm{3384}};v_{\mathrm{rot}})=v_{\mathrm{sys,3384}}+v_{\mathrm{rot}}\sin(i)\cos(\phi_{\mathrm{3384}}),$
(1)

where $v_{\mathrm{rot}}$ is the galaxy’s mean rotation velocity and $i$ the
inclination at which the disk is observed. The corresponding velocity
dispersion is

$\begin{split}\sigma_{\mathrm{LOS}}^{2}(r_{\mathrm{3384}},\phi_{\mathrm{3384}};v_{\mathrm{rot}},\sigma_{r},\sigma_{\phi})=\sigma_{r}^{2}\sin^{2}(i)\sin^{2}(\phi_{\mathrm{3384}})+\\\
+\sigma_{\phi_{\mathrm{3384}}}^{2}\sin^{2}(i)\cos^{2}(\phi_{\mathrm{3384}})+\sigma^{2}_{z}\cos^{2}(i),\end{split}$
(2)

where $\sigma_{r},\sigma_{\phi}$, and $\sigma_{z}$ are its components in
cylindrical coordinates. In edge-on galaxies the contribution along the
$z$-axis is small. Hence, in the following the term
$\sigma^{2}_{z}\cos^{2}(i)$ can be dropped. Assuming a Gaussian LOSVD, the
disk kinematics can be described as

$\begin{split}\mathcal{V}_{\mathrm{N3384,disk}}(v_{k},r_{\mathrm{3384},k},\phi_{\mathrm{3384},k};v_{\mathrm{rot}},\sigma_{r},\sigma_{\phi})=\\\
\frac{1}{\sqrt{2\pi}\sigma_{\mathrm{LOS}}}\exp\left(-\frac{(v_{k}-v_{\mathrm{LOS}})^{2}}{2\sigma_{\mathrm{LOS}}^{2}}\right)\end{split}$
(3)

The contribution from the bulge is described as a Gaussian centred on the
systemic velocity of NGC 3384 with velocity dispersion
$\sigma_{\mathrm{N3384,bulge}}$, assuming it does not rotate significantly:

$\begin{split}\mathcal{V}_{\mathrm{bulge}}(v_{k},r_{\mathrm{3384},k},\phi_{\mathrm{3384},k};\sigma_{\mathrm{N3384,bulge}})=\\\
\frac{1}{\sqrt{2\pi}\sigma_{\mathrm{N3384,bulge}}}\exp\left(\frac{(v_{k}-v_{\mathrm{sys,3384}})^{2}}{2\sigma_{\mathrm{N3384,bulge}}^{2}}\right).\end{split}$
(4)

The two kinematic components of the LOSVD are weighted by the SB profiles as
described in Sect. 3.3. In order to account for the variation of the LOSVD as
a function of radius, we evaluate it in five concentric elliptical bins with
the same geometry as the galaxy’s isophotes centred on NGC 3384. Therefore the
parameters $v_{\mathrm{rot}},\sigma_{r},\sigma_{\phi}$, and
$\sigma_{\mathrm{N3384,bulge}}$ are evaluated independently in each of the
five bins. Following Cortesi et al. (2011, 2013b), we can reduce the parameter
space by using the epicycle approximation that holds for disk galaxies with
approximately flat rotation curves (see, e.g. Binney & Tremaine 1987) and
links the radial velocity dispersion with the tangential one:
$\sigma_{\phi}=\sigma_{r}/\sqrt{2}$.

###  3.2 Kinematic model of M105

Figure 6: Modelled SB maps of NGC 3384 (left) and M105 (centre), with the
centres of the galaxies marked with red and blue crosses, respectively. The
right panel shows the composite SB map from both galaxies and green contours
where M105 contributes $90\%$, $50\%$ and $10\%$ to the total light
distribution.

Following the discovery of a PN population associated with an exponential SB
profile in addition to the Sérsic halo (H+2020), we model M105’s kinematics
LOSVD with two Gaussians; both centred on the galaxy’s systemic velocity
$v_{\mathrm{sys,M105}}$. They differ in their velocity dispersions, which we
denote with $\sigma_{\mathrm{M105,Ser}}$ and $\sigma_{\mathrm{M105,Exp}}$,
respectively:

$\begin{split}\mathcal{V}_{\mathrm{M105,Ser}}(v_{k},r_{\mathrm{M105},k};\sigma_{\mathrm{M105,Ser}})=\\\
\frac{1}{\sqrt{2\pi}\sigma_{\mathrm{M105,Ser}}}\exp\left(-\frac{(v_{k}-v_{\mathrm{sys,M105}})^{2}}{2\sigma_{\mathrm{M105,Ser}}^{2}}\right),\end{split}$
(5)
$\begin{split}\mathcal{V}_{\mathrm{M105,Exp}}(v_{k},r_{\mathrm{M105},k};\sigma_{\mathrm{M105,Exp}})=\\\
\frac{1}{\sqrt{2\pi}\sigma_{\mathrm{M105,Exp}}}\exp\left(-\frac{(v_{k}-v_{\mathrm{sys,M105}})^{2}}{2\sigma_{\mathrm{M105,Exp}}^{2}}\right).\end{split}$
(6)

Again, in order to account for any variation of the LOSVD with radius, the
parameters $\sigma_{\mathrm{M105,Ser}}$ and $\sigma_{\mathrm{M105,Exp}}$ are
evaluated in five concentric elliptical annuli with the same geometry as the
galaxy’s isophotes, but this time centred on M105. We assume that the LOS
velocity dispersion of the exponentially distributed PN population is larger
than that of the one following a Sérsic profile in each bin.

###  3.3 Constraints on galaxy membership from broad-band photometry and RGB
star number counts

Figure 7: Stellar SB profiles of NGC 3384 and M105 in comparison with PN
number density profiles scaled by the respective $\alpha$-parameters. In both
panels, the solid grey line denotes the total stellar SB, and the dark green
error bars the PN number density based on data from the PN.S.Left: the stellar
SB profile of NGC 3384 was decomposed into bulge (dotted red line) and disk
(dashed blue line) by Cortesi et al. (2013b) and the best-fit PN number
density profile is denoted by the dash-dotted green line. Right: the stellar
SB profile of M105 was decomposed into Sérsic (dotted orange line) and
exponential (dashed purple line) components by H+2020 with priors on the
number-densities of metal-poor (MP) and metal-rich (MR) RGB stars from Lee &
Jang (2016) and fit to the PN number density from Surprime-Cam data alone
(light green error bars). The grey dotted vertical line denotes the radius at
which the PN number density starts to deviate from the stellar SB profile and
the dashed vertical line where the exponential SB starts to dominate the total
light distribution.

As the number density distribution of PNe is closely linked to the stellar
light distribution, i.e. the galaxies’ SB profiles (see e.g. Coccato et al.
2009, and Fig. 7), we can obtain further constraints on which PN belongs to
which galaxy component from broad-band photometry. The SB profiles of M105 and
NGC 3384 are described by a combination of Sérsic profiles (Sérsic 1963). The
intensity $I$ as a function of radius $R$ is:

$I_{\mathrm{Ser}}(R)=I_{\mathrm{eff}}\exp\left(-b_{n}\left[\left(\frac{R}{R_{\mathrm{eff}}}\right)^{1/n}-1\right]\right),$
(7)

with

$b_{n}=2n-\frac{1}{3}+\frac{0.009876}{n}.$ (8)

The effective intensity $I_{\mathrm{eff}}$ is measured at the effective radius
$R_{\mathrm{eff}}$ at which half the luminosity is enclosed, and the steepness
of the profile is controlled by the Sérsic index $n$. The corresponding SB
profile is

$\mu_{\mathrm{Ser}}(R)=\mu_{\mathrm{eff}}+\frac{2.5b_{n}}{\ln
10}\left[\left(\frac{R}{R_{\mathrm{eff}}}\right)^{1/n}-1\right],$ (9)

with the effective SB $\mu_{\mathrm{eff}}=-2.5\log I_{\mathrm{eff}}$.

An exponential SB profile with scale length $h$ is a special case of the
Sérsic profile with index $n=1$:

$\mu_{\mathrm{Exp}}(R)=\mu_{0}+1.086\left(\frac{R}{h}\right)$ (10)

The scale length $h$ and central SB $\mu_{0}$ are related to the Sérsic
quantities as follows:

$\displaystyle R_{\mathrm{eff}}$ $\displaystyle=1.678\cdot h$
$\displaystyle\mu_{\mathrm{eff}}$ $\displaystyle=\mu_{0}+1.820$ (11)

In the following, we describe the structural parameters of NGC 3384 and M105
that were derived in previous works. Table 2 provides a summary in terms of
Sérsic structural parameters, and Fig. 6 shows the resulting SB maps for the
two galaxies separately, as well as a composite SB map.

Table 2: Structural parameters of M105 and NGC 3384 derived from broad-band surface photometry (Watkins et al. 2014; Cortesi et al. 2013b; Skrutskie et al. 2006) and PN number counts (H+2020) used as input for the photo-kinematic decomposition. Component | $\mu_{\mathrm{eff}}$ | $R_{\mathrm{eff}}$ | Sersic $n$ | Inclination $i$ | Ellipticity $\epsilon$ | $P.A.$ |  $\alpha_{2.5}$
---|---|---|---|---|---|---|---
| [mag arcsec-2] | [″] |  | [°] |  | [°] | [$\times 10^{8}\,\mathrm{PN}\,L_{\mathrm{bol}}^{-1}$]
M105 halo | 21.73 | 57 | 2.75 | - | $0.111\pm 0.005$ | $70.0\pm 1.0$ |  $1.00\pm 0.11$
M105 exponential envelope | 29.52 | 600 | 1 | - | $0.111\pm 0.005$ | $70.0\pm 1.0$ | $7.10\pm 1.87$
NGC 3384 bulge | 15.9 | 15.2 | 4 | - | 0.17 | 60.51 |  $1.41\pm 0.15$
NGC 3384 disk | 20.07 | 107 | 1 | 70 | 0.66 | 52.50 | $1.41\pm 0.15$

####  3.3.1 NGC 3384

Cortesi et al. (2013b) analysed 2MASS $K$-band images (Skrutskie et al. 2006)
with Galfit (Peng et al. 2010) for the disk-bulge decomposition of NGC 3384.
They found that the bulge’s light distribution in the $K$-band is best
described by a Sérsic profile with effective SB
$\mu_{\mathrm{eff,bulge}}=15.9$, Sérsic index $n=4$, effective radius
$R_{\mathrm{eff,bulge}}=15\aas@@fstack{\prime\prime}2$, ellipticity
$\epsilon_{\mathrm{bulge}}=0.17$, and position angle
$PA_{\mathrm{bulge}}=60\aas@@fstack{\circ}51$.

The light distribution of the disk is described with an exponential profile
with central SBs $\mu_{\mathrm{0,disk}}=18.25$, scale length
$h_{\mathrm{N3384,disk}}=63\aas@@fstack{\prime\prime}73$, ellipticity
$\epsilon_{\mathrm{N3384,disk}}=0.66$, inclination $i=70\degr$, and
$PA=52\aas@@fstack{\circ}5$. H+2020 determined a colour correction of
$B-K=-3.75$ for the profiles derived from the 2MASS data by Cortesi et al.
(2013b). The left panel of Fig. 7 shows the total $B$-band SB profile of NGC
3384 (grey line) and the contributions from the galaxy’s disk (blue dashed
line) and bulge (red dotted line).

####  3.3.2 M105

The light distribution of M105 was first analytically described by de
Vaucouleurs (1948), and is still regarded as one of the cornerstones of the de
Vaucouleurs law today. Combining number density profiles of resolved red giant
branch (RGB) stellar populations (Lee & Jang 2016) with deep wide-field
imaging (Watkins et al. 2014), and their wide-field photometric survey for
PNe, H+2020 established a two-component model for the SB profile of M105. The
light distribution in the inner halo is dominated by metal-rich stars
following a Sérsic profile with $n_{\mathrm{Ser}}=2.75$,
$R_{\mathrm{eff,Ser}}=57\arcsec$ and $\mu_{\mathrm{eff,Ser}}=21.73$, denoted
by the dotted orange line in the right panel of Fig. 7. In the outer halo, the
fractional contribution from metal-poor stars, denoted by the dashed purple
line, increases. Their light distribution is modelled with an exponential
profile with $h_{\mathrm{Exp}}=358\arcsec$ and $\mu_{\mathrm{0,Exp}}=27.7$.
Watkins et al. (2014) derived constant a ellipticity
$\epsilon_{\mathrm{M105}}=0.111\pm 0.005$ and a position angle of
$PA=70\aas@@fstack{\circ}0\pm 1\aas@@fstack{\circ}0$ in the outer halo of
M105.

###  3.4 PN-specific frequency dependency on stellar population parameters

Since the number of PNe has been shown to systematically vary with the colour
of the parent stellar population (Buzzoni et al. 2006; Longobardi et al. 2015;
Hartke et al. 2017), such dependency must be taken into account when using SB
profiles derived from integrated starlight as weights for the kinematic model.
The connection between a PN population and the underlying stellar population
is given by the PN-specific frequency, $\alpha$-parameter for short, that
relates the total number of PNe $N_{\mathrm{PN}}$ to the total bolometric
luminosity $L_{\mathrm{bol}}$ of the parent stellar population:

$N_{\mathrm{PN}}=\alpha L_{\mathrm{bol}}.$ (12)

For the bolometric correction, we use that derived from theoretical template
galaxy models as function of the galaxies’ colours (Buzzoni 2005; Buzzoni et
al. 2006). In the following, we will refer to $\alpha_{2.5}$ values, which are
calculated in the magnitude interval $m^{*}<m_{5007}\leq m^{*}+2.5$. The
observed PN number densities for NGC 3384 and M105 are indicated with green
error bars in the left and right panels of Fig. 7, respectively.

For NGC 3384, we assume that the $\alpha$-parameters for disk and bulge are
equal (since, due to incompleteness in the centre of the galaxy we cannot
calculate $\alpha_{\mathrm{bulge}}$ separately) and determined
$\alpha_{\mathrm{N3384}}=(1.41\pm 0.15)\times
10^{8}\,\mathrm{PN}\,L_{\mathrm{bol}}^{-1}$. We only considered PNe that lie
within the green $50\%$ contour shown in the right panel of Fig. 6. The
resulting best-fit PN number density profile is indicated by the green dash-
dotted line in the left panel of Fig. 7.

For M105, H+2020 determined $\alpha$-parameters for PNe associated with the
Sérsic and exponential SB profiles and found
$\alpha_{\mathrm{M105,Ser}}=(1.00\pm 0.11)\times
10^{8}\,\mathrm{PN}\,L_{\mathrm{bol}}^{-1}$ and
$\alpha_{\mathrm{M105,Exp}}=(7.10\pm 1.87)\times
10^{8}\,\mathrm{PN}\,L_{\mathrm{bol}}^{-1}$. The resulting best-fit PN number
density profile is indicated by the green dash-dotted line in the right panel
of Fig. 7. Since the bulk of the light in M105 is contributed by metal-rich
stars following the Sérsic profile, we use $\alpha_{\mathrm{M105,Ser}}$ as the
denominator of the normalisation. We therefore include the parameters
$\tilde{\alpha}_{N3384}=\alpha_{\mathrm{N3384}}/\alpha_{\mathrm{M105,Ser}}$
and
$\tilde{\alpha}_{\mathrm{M105,Exp}}=\alpha_{\mathrm{M105,Exp}}/\alpha_{\mathrm{M105,Ser}}$
that characterise the variation of $\alpha$ in the bulge and disk components
of NGC 3384, as well as in the outer halo of M105 with respect to the
$\alpha$-parameter of the main halo of M105.

###  3.5 Bayesian likelihood

The likelihood of a PN $k$ with observed position $RA,dec$ and velocity
$v_{k}\pm\delta v_{k}$ can be expressed in terms of the velocity and surface-
brightness distributions that we defined in the previous three sections. The
model component weights are defined as follows:

$\displaystyle w_{\mathrm{N3384,bulge}}$
$\displaystyle=\frac{\tilde{\alpha}_{\mathrm{N3384}}\Sigma_{\mathrm{N3384,bulge}}}{n_{\mathrm{tot}}},$
(13a) $\displaystyle w_{\mathrm{N3384,disk}}$
$\displaystyle=\frac{\tilde{\alpha}_{\mathrm{N3384}}\Sigma_{\mathrm{N3384,disk}}}{n_{\mathrm{tot}}},$
(13b) $\displaystyle w_{\mathrm{M105,Ser}}$
$\displaystyle=\frac{\Sigma_{\mathrm{M105,Ser}}}{n_{\mathrm{tot}}},$ (13c)
$\displaystyle w_{\mathrm{M105,Exp}}$
$\displaystyle=\frac{\tilde{\alpha}_{\mathrm{M105,Exp}}\Sigma_{\mathrm{M105,Exp}}}{n_{\mathrm{tot}}},$
(13d)

where both the $\alpha$-parameters and the surface-brightness profiles
$\Sigma$ are completely determined by the broad- and narrow-band photometry as
described in Sects. 3.3 and 3.4. The weights are normalised by

$\begin{split}n_{\mathrm{tot}}=\tilde{\alpha}_{\mathrm{N3384}}(\Sigma_{\mathrm{N3384,bulge}}+\Sigma_{\mathrm{N3384,disk}})+\\\
+\Sigma_{\mathrm{M105,Ser}}+\tilde{\alpha}_{\mathrm{M105,Exp}}\Sigma_{\mathrm{M105,Exp}}\end{split}$
(14)

The corresponding likelihood for a PN $k$ at its position in phase-space is

$\begin{split}\mathcal{L}_{k}=w_{\mathrm{N3384,bulge}}\mathcal{V}_{\mathrm{N3384,bulge}}+w_{\mathrm{N3384,disk}}\mathcal{V}_{\mathrm{N3384,disk}}+\\\
+w_{\mathrm{M105,Ser}}\mathcal{V}_{\mathrm{M105,Ser}}+w_{\mathrm{M105,Exp}}\mathcal{V}_{\mathrm{M105,Exp}}.\end{split}$
(15)

The total likelihood is the product of the individual likelihoods that is
calculated for each _individual_ PN with coordinates ($RA,dec$) and LOS
velocity $v\pm\delta v$:

$\mathcal{L}=\prod_{k=0}^{N}\mathcal{L}_{k}.$ (16)

This method allows us to exploit the information of every PN without the
explicit need for binning in velocity space. As discussed in Sects. 3.1 and
3.2, we evaluate the five LOSVD parameters
$v_{\mathrm{rot}},\sigma_{r},\sigma_{\mathrm{N3384,bulge}},\sigma_{\mathrm{M105,Ser}},\sigma_{\mathrm{M105,Exp}}$
independently in five elliptical annuli, centred on the respective galaxy
(solid and dashed ellipses in Fig. 9). This results in a 25-dimensional
parameter space that is explored using the ensemble-based MCMC sampler emcee
(Foreman-Mackey et al. 2013).

###  3.6 Priors and posteriors

Figure 8: Posterior probability distribution of the parameters
$\sigma_{\mathrm{sph}}$ (the velocity dispersion of the bulge of NGC 3384),
$\sigma_{r}$ and $v_{\mathrm{rot}}$ (the radial velocity dispersion and
circular velocity of the disk of NGC 3384), and $\sigma_{\mathrm{M105,Ser}}$
and $\sigma_{\mathrm{M105,Exp}}$ (the velocity dispersions of the Sérsic and
exponential populations in M105) in the innermost of the five elliptical bins.
To illustrate the Gaussian priors on the LOSVD parameters of NGC 3384, which
cover a larger range in parameter space, we inserted three additional subplots
showing the priors with red solid lines and the posteriors with black
histograms, utilising the same binning as the corner plots. The red shaded
regions below the Gaussians denote $1\sigma$ from the mean. On all plots, the
velocities or velocity dispersions are in units of
$[\mathrm{km}\,\mathrm{s}^{-1}]$.

As Cortesi et al. (2013b) already carried out a bulge-disk decomposition of
NGC 3384 based on the single PN.S field available to them at the time, we use
their best-fit parameters and corresponding errors as Gaussian priors on
$v_{\mathrm{rot}},\sigma_{r},\sigma_{\phi},\sigma_{\mathrm{N3384,bulge}}$. As
we evaluate the LOSVD in five elliptical bins instead of three, we
interpolated their best-fit profiles as a function of radius and used the
interpolated values at the bin centres. An example of the Gaussian priors for
the innermost of the five elliptical bins is indicated with red solid lines in
Fig. 8. We place uniform priors on $\sigma_{\mathrm{M105,Ser}}$ and
$\sigma_{\mathrm{M105,Exp}}$, but require
$\sigma_{\mathrm{M105,Ser}}\leq\sigma_{\mathrm{M105,Exp}}$ in each of the
bins.

The posterior probability distributions are calculated with emcee (Foreman-
Mackey et al. 2013), using 52 walkers ($2N_{\mathrm{dim}}+2$) and $2\,000$
steps. Figure 8 shows the resulting distributions visualised as a corner plot
for the innermost of the five elliptical bins. This is a convenient
representation of a subset of the parameter space. However, we stress that the
whole $25$-dimensional space is explored simultaneously for data in the whole
radial range. The best-fit parameters and their errors are the 50% and
(16%,84%) quantiles. While the best-fit parameters give a good first estimate
on the LOS velocity dispersion of the Sérsic and Elliptical PN populations in
the halo of M105, we will calculate more accurate radial velocity dispersion
profiles with robust methods and based on the final membership assignment
presented in the following.

###  3.7 Final membership assignment

Figure 9: Panel (a) Ternary plot of the probabilistic fractions $f_{i}$ with
$f_{\mathrm{M105,Ser}}>0.5$ coloured in orange, $f_{\mathrm{M105,Exp}}>0.5$
coloured in purple, and $f_{\mathrm{NGC3384}}>0.5$ represented by crosses on a
red-to-blue colour scale with red colours for $f_{\mathrm{NGC3384,bulge}}>0.5$
and blue colours for $f_{\mathrm{NGC3384,disk}}>0.5$. Points coloured in grey
do not satisfy any of the four criteria, and their firm association with any
of the components cannot be conclusively ascertained. Panel (b) Spatial
distribution of PNe with the same colour-coding as in panel (a). Panel (c)
Velocity phase-space along the major axis of M105 with the same colour-coding
as in panel (a). Panel (d) Velocity phase-space along the minor axis of M105
with the same colour-coding as in panel (a).

For each PN, we determine the probabilistic fraction $f_{i}$ to belong to one
of the four populations (NGC 3384’s disk and bulge, M105’s Sérsic and
exponential halos) based on its position and LOS velocity. Figure 9(a)
illustrates the probability space populated by our observations, with
$f_{\mathrm{M105,Ser}}>0.5$ coloured in orange (138 PNe),
$f_{\mathrm{M105,Exp}}>0.5$ coloured in purple (31 PNe), and
$f_{\mathrm{NGC3384}}>0.5$ being represented by crosses on a red-to-blue
colour scale with red colours for $f_{\mathrm{NGC3384,bulge}}>0.5$ (37 PNe)
and blue colours for $f_{\mathrm{NGC3384,disk}}>0.5$ (56 PNe). Points which
cannot be uniquely associated with any of the four components outlined
previously, are colour-coded in grey (7 PNe). Figure 9 (b) shows the
distribution of PNe colour-coded by $f_{i}$ in position-space, and Fig. 9(c)
and (d) in phase-space along the major and minor axes of M105, respectively.

Both in position- and phase-space, PNe can be robustly separated into those
associated with M105 and those with NGC 3384. This is important for the study
of the LOSVD of M105 that will be presented in the following sections. We have
maximised the number of PNe that will be considered for follow-up analysis
compared to conventional cuts in position space (as for example done by
Douglas et al. 2007), while ensuring that the derived LOSVDs are of sufficient
quality. The final column of Tab. 5 provides the probabilistic fraction to be
assigned to M105
$f_{\mathrm{M105}}=f_{\mathrm{M105,Ser}}+f_{\mathrm{M105,Exp}}$ for each PN in
the final sample. This can be easily translated to the probabilistic fraction
to be assigned to NGC 3384 $f_{\mathrm{NGC3384}}=1-f_{\mathrm{M105}}$.

##  4 Kinematics in the outer halo of M105

In the following section, we only consider PNe that we assigned to the M105
halo and envelope in the previous section. For the calculation of the smoothed
2D velocity and velocity dispersion fields and the extraction of the rotation
profiles, we assume that M105 is point-symmetric in the position-velocity
phase-space, as commonly done when constructing velocity fields based on PN
kinematics (e.g. Arnaboldi et al. 1998; Coccato et al. 2009; Pulsoni et al.
2018). This implies that each point $(x,y,v)$ in said phase-space has a
”mirror point” $(-x,-y,-v)$ and that the number of data points on which the
kinematic quantities are calculated is doubled. The resulting catalogue, i.e.
the concatenation of the _original_ and _mirrored_ catalogues, is called the
_folded_ catalogue.

###  4.1 Smoothed 2D velocity and velocity dispersion fields

Figure 10: Kernel-smoothed velocity (top row) and velocity dispersion fields
(bottom row) for PNe associated with M105 at large (left column), the Sérsic
component (middle column), and the exponential component (left column). Each
point denotes the position of an observed PN, colour-coded by the value of the
smoothed field. The solid (dotted) grey lines denote the photometric major
(minor) axis and the dashed red line the kinematic major axis. North is up,
and East is to the left.

We calculate kernel-smoothed velocity and velocity dispersion fields for all
PNe associated with M105 and for the Sérsic and exponential components
separately from the folded catalogues. We use a distance-dependent Gaussian
kernel as defined in Coccato et al. (2009)

$w_{i}=\exp\left(\frac{-D_{i}^{2}}{2k(x_{i},y_{i})^{2}}\right),$ (17)

where the kernel width $k(x,y)$ is proportional to the distance $R_{i,M}$ to
the $M$th closest tracers located at $(x_{M},y_{M})$:

$k(x_{i},y_{i})=AR_{i,M}(x_{M},y_{M})+B.$ (18)

We use the optimised kernel parameters $A=0.34$ and $B=16.2$ for the $M=20$
closest tracers, which were determined by Pulsoni et al. (2018) based on Monte
Carlo simulations of discrete velocity fields, allowing for the best
compromise between noise smoothing and spatial resolution.

Figure 10 shows the resulting smoothed velocity $v_{\mathrm{s}}$ (top row) and
velocity dispersion $\sigma_{\mathrm{s}}$ fields (bottom row) for all PNe
associated with M105 in the left column, and the Sérsic and exponential
components shown in the middle and right columns, respectively. The smoothed
velocity and velocity dispersion fields of the Sérsic and exponential
components show distinct features. As expected from the method with which PNe
were associated to either component, the LOS velocity dispersion of PNe in the
exponential component is much larger than that of those in the Sérsic one,
even at comparable radial ranges. The rotation signatures in the velocities
are also different, hinting towards different mechanisms that contributed to
the formation of the Sérsic and exponential components in the halo of M105.

###  4.2 Line-of-sight velocity dispersion profiles

Figure 11: Left: LOS velocity dispersion profiles of M105 calculated with
robust techniques for the total sample of PNe associated with M105 (solid
lines with grey dots), its Sérsic component (solid lines with orange squares),
and the exponential envelope (solid lines with purple diamonds). The
transparent bands denote the errors on the derived LOS velocity dispersions
estimated with robust methods. For comparison, we also show the LOS velocity
dispersion used by de Lorenzi et al. (2009, black error bars) and the one
derived from long-slit spectroscopy (small red error bars Statler & Smecker-
Hane 1999), as well as the globular cluster (GC) velocity dispersion from
Bergond et al. (2006, green triangles with errorbars). Right: As the left
panel, but with a logarithmic scale for the major-axis radius. The blue error
bars denote the velocity dispersion calculated from the LOS velocities of
satellites in the Leo I group (compiled by Müller et al. 2018). In both
panels, shaded regions indicate the robust errors, and the vertical lines are
the same as in Fig. 13.

To determine the LOS velocity dispersion profiles, we again only consider PNe
with $f_{\mathrm{M105}}=f_{\mathrm{M105,Ser}}+f_{\mathrm{M105,Exp}}>0.5$, i.e.
PNe firmly associated with M105 and the exponential envelope both in position
and velocity space. We already obtained velocity dispersions in the five
elliptical bins from the likelihood analysis presented in Sect. 3.7 for the
Sérsic and exponential components separately. However, to explore a finer
resolution along the radial direction and be more robust to potential
outliers, we re-bin the data and use robust estimation methods (McNeil et al.
2010) with a clipping range of $2\sigma$.

Figure 11 shows the resulting LOS velocity dispersion for all PNe associated
with M105 with grey dots and the corresponding uncertainty with a grey error
band. The overall velocity dispersion agrees well with that presented in de
Lorenzi et al. (2009, black error bars) where the data overlaps, as well as
with long-slit data in the innermost region of the galaxy from Statler &
Smecker-Hane (1999).

The velocity dispersion increases strongly beyond $400\arcsec$ (corresponding
to $\approx 7.5R_{\mathrm{eff}}$), which also corresponds to the radius at
which the PN number density starts to flatten due to a higher
$\alpha$-parameter value at large radii, as indicated by the dotted vertical
line. The rise in the LOS velocity at large radii is thus driven by PNe
associated with the exponential envelope (indicated by purple triangles on
Fig. 11). These PNe have a larger LOS velocity dispersion compared to those
associated with the Sérsic halo (orange squares). The strong decline of the
LOS velocity dispersion in the inner halo is instead driven by PNe associated
with the latter component.

###  4.3 Rotation

Figure 12: Radially integrated rotation profiles of PNe associated with the
Sérsic (top panel) and exponential (middle panel) populations from the kernel-
smoothed velocity maps (dots with error bars). The bottom panel shows
unsmoothed LOS velocities of satellite galaxies in the Leo I group colour-
coded by their on-sky distance to the centre of M105 (compiled by Müller et
al. 2018). In each panel, the best-fit rotation profiles are denoted with
solid grey curves, and the corresponding best-fit kinematic position angles
(with respect to the photometric one) and systemic velocities are denoted with
dashed and dotted grey lines. Open symbols denote PNe excluded from the fit as
they lie outside of the $2\sigma$ limits determined in Sect. 4.2.

We first assess the different rotation signatures, by separately fitting
rotation curves to the smoothed velocities $v_{s}$ for the Sérsic and
exponential populations separately as a function of position angle $\Theta$ as
shown on Fig. 12, excluding the 2$\sigma$ outliers identified in the previous
Sect. 4.2 from further analysis. Following Pulsoni et al. (2018), we fit the
mean velocity fields with the following function:

$\displaystyle\begin{split}v_{p}(R,\Theta)&=v_{\mathrm{sys}}(R)+v_{\mathrm{rot}}(R)\cos(\Theta-\Theta_{0}(R))\\\
&+s_{3}(R)\sin(3\Theta-3\Theta_{0})+a_{3}(R)\cos(3\Theta-3\Theta_{0}),\end{split}$
(19)

where $v_{\mathrm{sys}}$ is the systemic velocity, $v_{\mathrm{rot}}$ the
amplitude of the rotation, and $\Theta_{0}$ the kinematic position angle with
respect to the photometric position angle. These parameters describe the
rotation around the kinematic major axis, while $s_{3}$ and $a_{3}$ are the
amplitudes of the third-order terms.222As we assume that the phase-space is
point-symmetric, this prohibits even contributions to the higher-order terms.

Figure 12 shows the smoothed velocity as function of the position angle
$\Theta$ for the observed PNe in each of the two components. We fit rotation
profiles to these data, only considering the azimuthal dependence of eq. (19).
We evaluate whether the goodness of the fit is improved by including the
higher-order terms with amplitudes $a_{3}$ and $s_{3}$ by virtue of the
Bayesian information criterion (BIC). Table 3 summarises the best-fit
parameters fit to the velocity fields, and the resulting best-fit rotation
curves are denoted with solid grey lines. Models including higher moments are
preferred for both components. In the case of the Sérsic component, the fit
with higher moments has both lower BIC and reduced $\chi^{2}$ values. For the
exponential envelope, the BIC values are indistinguishable, but the fit with
higher moments has a lower reduced $\chi^{2}$ value.

Table 3: Best-fit parameters for the rotation models fit to the Sérsic and
exponential velocity fields.

Component | Higher modes |  $\Theta_{0}$(a)(a)footnotemark: $(a)$ |  $v_{\mathrm{sys}}$(b)(b)footnotemark: $(b)$ | $v_{\mathrm{rot}}$ | $s_{3}$ | $a_{3}$ | BIC |  $\chi^{2}_{\mathrm{red}}$
---|---|---|---|---|---|---|---|---
|  | $[\times\pi]$ | $[\mathrm{km\,s^{-1}}]$ | $[\mathrm{km\,s^{-1}}]$ | $[\mathrm{km\,s^{-1}}]$ | $[\mathrm{km\,s^{-1}}]$ |  |
Sérsic | Y | $0.00\pm 0.13$ | $935.1\pm 1.4$ | $15.9\pm 1.9$ | $-6.46\pm 5.66$ | $13.3\pm 3.1$ | -10.6 | 153.6
Sérsic | N | $0.00\pm 0.02$ | $933.7\pm 1.5$ | $15.5\pm 2.0$ |  |  | 28.4 | 200.2
Exponential | Y | $0.48\pm 0.09$ | $934.2\pm 9.9$ | $49.3\pm 8.1$ | $8.79\pm 14.30$ | $16.3\pm 8.4$ | 30.0 | 44.1
Exponential | N | $0.56\pm 0.09$ | $925.9\pm 9.0$ | $49.8\pm 8.0$ |  |  | 29.8 | 56.1

333 $a$$a$footnotetext: The kinematic position angle was determined with
respect to the photometric position angle. $b$$b$footnotetext: The systemic
velocity determined by Pulsoni et al. (2018) based on the M105-C field is
$v_{\mathrm{sys,M105}}=934\pm 14\;\mathrm{km\,s^{-1}}$.

The Sérsic component has a rotation amplitude of $v_{\mathrm{rot,Ser}}=16.0\pm
1.8\;\mathrm{km}\,\mathrm{s}^{-1}$ and a kinematic major axis that is
consistent with the photometric major axis within the errors, as well as a
systemic velocity of $v_{\mathrm{sys,Ser}}=935.1\pm
1.4\;\mathrm{km}\,\mathrm{s}^{-1}$ that agrees with that determined by Pulsoni
et al. (2018) based on the central field of M105. In contrast to this, the
rotation amplitude of the PNe in the exponential envelope is more than three
times higher, being $v_{\mathrm{rot,Exp}}=49.2\pm
6.7\;\mathrm{km}\,\mathrm{s}^{-1}$, and the kinematic major axis is aligned
with the photometric minor axis of M105, while their systemic velocity of
$v_{\mathrm{sys,Exp}}=934.2\pm 9.9\;\mathrm{km}\,\mathrm{s}^{-1}$ agrees with
that of the Sérsic component within the errors. To visualise the on-sky
orientation of the photometric and kinematic major axes, they are overplotted
on top of the smoothed velocity fields in Fig. 10 with solid grey and dashed
red lines, respectively.

Figure 13: Top: Rotation amplitude along the major axis of M105 for all PNe
associated with the galaxy (grey circles), and the Sérsic (orange squares) and
exponential (purple diamonds) components. The red points with associated error
bars denote the rotation profile derived from long-slit spectroscopy (Statler
& Smecker-Hane 1999). Middle: Systemic velocity as function of majr-axis
radius with the same colour-coding as in the top panel. Bottom: Best-fit
kinematic position angle with respect to the photometric one as function of
major-axis radius with the same colour coding as in the top panel. In both
panels, shaded regions indicate the standard errors from the maximum-
likelihood fit, the dotted grey lines denote the radius at which the
$\alpha$-parameter changes, and the grey dashed vertical lines where the
exponential SB starts to dominate the total light distribution. The dotted red
vertical line denotes the kinematic transition radius determined by Pulsoni et
al. (2018).

To evaluate the radial dependence of the rotation profile, we again fitted eq.
19 to the data, but in elliptical bins, for all PNe associated with M105 as
well as to the Sérsic and exponential populations separately. Due to the
smaller number of tracers per bin, we did not fit the third-order modes, as
this led to noisier fits. The resulting best-fit profiles of the rotation
amplitude $v_{\mathrm{rot}}$, systemic velocity $v_{\mathrm{sys}}$ and
kinematic position angle $\theta_{0}$ are shown in Fig. 13 from top to bottom.
As already observed by Pulsoni et al. (2018), the rotation amplitude decreases
in the inner halo with hints for growing rotation in the outskirts. This
decrease was also inferred from long-slit spectroscopy (Statler & Smecker-Hane
1999). Our new extended data reveal that there is a transition region where
the rotation amplitude remains small, followed by a strong increase of the
rotation amplitude in the exponential envelope which is driven by the PNe
associated with this component (purple diamonds).

This transition goes hand in hand with a twisting of the kinematic position
angle that is illustrated in the bottom panel of Fig. 13. In the inner halo,
where the Sérsic population dominates, the kinematic position angle is aligned
with the photometric one. In contrast, in the outer halo, the position angle
twists by more than 90°and is more or less aligned with the photometric minor
axis of the inner high SB regions.

###  4.4 Angular-momentum content

Figure 14: Left: Local $\lambda_{R}$ profiles calculated for the total sample
of PNe associated with M105 (grey), its Sérsic component (orange), and the
exponential envelope (purple). Horizontal error bars denote the bins in which
$\lambda_{R}$ was evaluated. Right: Cumulative $\lambda_{R}$ profiles, with
the same colour-coding as in the left panel. In both panels, the dotted grey
line at $\lambda_{R}$ = 0.1 separates fast from slow rotator regions assuming
constant ellipticity. (Emsellem et al. 2007). The vertical dotted lines are
the same as in Fig. 13.

Emsellem et al. (2007) introduced a kinematic classification scheme for
galaxies based on the so-called $\lambda_{R}$ parameter, which quantifies
rotational support and can be used as a proxy to quantify the observed
projected stellar angular momentum. To infer the angular momentum content
locally, i.e. in elliptical bins with mean radius $R_{\mathrm{mean}}$ and bin
edges $R_{\mathrm{min}}$ and $R_{\mathrm{max}}$, $\lambda_{R}$ can be
calculated from the smoothed velocity and velocity dispersion fields $V$ and
$\sigma$:

$\lambda_{R}(R_{\mathrm{mean}})=\frac{\sum_{R_{i}=R_{\mathrm{min}}}^{R_{\mathrm{max}}}R_{i}\left|V_{i}\right|}{\sum_{R_{i}=R_{\mathrm{min}}}^{R_{\mathrm{max}}}R_{i}\sqrt{V_{i}^{2}+\sigma_{i}^{2}}}.$
(20)

The cumulative $\lambda_{R}$ profiles instead are calculated from the centre
of the galaxy to the outer bin edge $R_{\mathrm{max}}$ and corrected for
geometric incompleteness $c_{\mathrm{geo}}$:

$\lambda_{R}(<R_{\mathrm{max}})=\frac{\sum_{R_{i}=0}^{R_{\mathrm{max}}}R_{i}\left|V_{i}\right|/c_{\mathrm{geo}}}{\sum_{R_{i}=0}^{R_{\mathrm{max}}}R_{i}/c_{\mathrm{geo}}\sqrt{V_{i}^{2}+\sigma_{i}^{2}}}.$
(21)

The cumulative $\lambda_{R}$ is weighted by the flux associated with each
radial bin. For PNe, this is implicitly incorporated as the PN number density
traces the light distribution (Coccato et al. 2009). When ordered motion, i.e.
rotation, dominates, $\lambda_{R}$ approaches unity. Within one effective
radius, $\lambda_{R}$ can be used as a proxy to divide galaxies into the
categories of fast ($\lambda_{R}>0.1$) and slow rotators ($\lambda_{R}<0.1$).
M105 has been classified as a fast rotator (Emsellem et al. 2007; Coccato et
al. 2009; Pulsoni et al. 2018).

The left panel of Fig. 14 shows the local $\lambda_{R}$ profiles for all PNe
associated with M105 (grey), the Sérsic halo (orange) and the exponential
envelope (purple), evaluated in the same elliptical annuli as used in Figs. 13
and 11. In the inner halo, the kinematic transition radius identified by
Pulsoni et al. (2018, dotted vertical red line on Fig. 14) is marked by a
decrease in the local $\lambda_{R}$ profile, which pertains until $\sim
2R_{\mathrm{eff}}$. At $\sim 4R_{\mathrm{eff}}$ the $\lambda_{R}$ profile
peaks again. At large radii, i.e. in the exponential envelope, $\lambda_{R}$
increases, reaching values of $\lambda_{R}=0.4$ in the outermost bin. The
right panel of Fig. 14 shows the cumulative $\lambda_{R}$ profiles with the
same colour coding. Based on the two panels, we identify three distinct
kinematic components, which will be discussed further in the following
section:

  1. 1.

the _rotating core_ within $1\leavevmode\nobreak\ R_{\mathrm{eff}}$,

  2. 2.

the _halo_ , from $1\leavevmode\nobreak\ R_{\mathrm{eff}}$ to
$7.5\leavevmode\nobreak\ R_{\mathrm{eff}}$, and

  3. 3.

the _exponential envelope_ , from $7.5\leavevmode\nobreak\ R_{\mathrm{eff}}$
to the last data point at $16\leavevmode\nobreak\ R_{\mathrm{eff}}$.

##  5 Discussion

In this work, we have efficiently associated PNe in the Leo I group to
different subpopulations in the velocity phase-space centred on M105. Vital
for measuring the LOS kinematics at large radii from the centre of M105 was
the division of the sample into PNe associated with M105, the exponential
envelope, and with the companion galaxy NGC 3384. We refer the reader to
Cortesi et al. (2013a, b) for a discussion of the kinematics of the S0 galaxy
NGC 3384 and discuss the kinematics of M105 and the surrounding IGL in what
follows.

###  5.1 Metal-rich and intermediate-metallicity populations in the inner halo
of M105

Pulsoni et al. (2018) identified a kinematic transition in the inner halo at
$1\leavevmode\nobreak\ R_{\mathrm{eff}}$, which is marked by a decrease of the
rotation amplitude (Fig. 13), the LOS velocity dispersion (Fig. 11), and the
local $\lambda_{R}$ parameter (Fig. 14) with radius. The first kinematic
component of M105 that we identified is thus the _rotating core_ in the centre
of the galaxy. Our measurements of $V$ and $\sigma$ agree with those of
Weijmans et al. (2009) based on SAURON integral-field spectroscopy in the
regions of overlap and the long-slit data from Statler & Smecker-Hane (1999).
Weijmans et al. (2009) inferred an age of $\approx 12$ Gyr and approximately
solar metallicity for the rotating core.

Beyond the transition at $1\leavevmode\nobreak\ R_{\mathrm{eff}}$, the
metallicity decreases, reaching 20% of the solar value, i.e. $\approx-0.7$ at
$3-4\leavevmode\nobreak\ R_{\mathrm{eff}}$ (Weijmans et al. 2009), which is
similar to the peak of the metallicity distribution function in the inner HST
field located $4\lesssim R_{\mathrm{eff}}\lesssim 6$ to the northeast of the
centre of M105 (Lee & Jang 2016, see also the hatched regions in the right
panel of Fig. 1). The PN population in the inner halo is characterised by a
low $\alpha$-parameter $\alpha_{\mathrm{2.5,MR+IM}}=(1.00\pm 0.11)\times
10^{-8}\;\mathrm{PN}\,L_{\mathrm{bol}}^{-1}$ and a shallow, but still steeper
than the “standard” Ciardullo et al. (1989) PNLF slope (H+2020).

In the $\lambda_{R}$ profile shown in Fig. 14, a second peak is visible at
around $4\leavevmode\nobreak\ R_{\mathrm{eff}}$. This peak is due to an
increase in rotation at these radii, while the LOS velocity dispersion profile
monotonously declines in the inner halo. This peak is co-spatial with a change
in position angle of the isophotes of M105 and an increased ellipticity (VEGAS
collaboration, priv. communication) and may be related to a secondary rotating
component, reviving the original suggestion of Capaccioli et al. (1991) that
M105 may be a S0 galaxy observed face-on.

Based on results from the IllustrisTNG cosmological hydrodynamical simulations
Pulsoni et al. (2021) argued that the observed kinematic transition radii do
not trace the transition between in-situ and ex-situ dominated regions. The
innermost transition radius at $1\leavevmode\nobreak\ R_{\mathrm{eff}}$
therefore does not necessarily represent a transition to a component dominated
by accreted stars. Instead, the characteristic peaked and outwardly decreasing
rotation profile of stars in the inner halo (see top panel of Fig. 13) is
similar to that of the in-situ stars in low-mass ETGs in cosmological
hydrodynamical simulations (Pulsoni et al. 2021).

###  5.2 The extended, metal-poor envelope in the outer halo of M105 and the
IGL of the Leo I group

The more extended PN.S data in the halo of M105 has allowed us to reveal a
second kinematic transition at $\approx 7.5R_{\mathrm{eff}}$, where both the
LOS velocity dispersion as well as the rotation amplitude increase
significantly. This increase is driven by the exponential envelope; a
population of PNe associated with a metal-poor population ([M/H] $\leq-1$) of
RGB stars following an exponential SB profile (H+2020). Since M105 is a member
of the Leo I group, we now place these findings into the context of the
kinematics of the group at large.

The increase of the velocity dispersion at large radii may indicate that PNe
in the exponential envelope of M105 are bound to the gravitational potential
of the Leo I group and thus part of its IGL. We therefore compare the
kinematics in the outer halo of M105 with that of satellite galaxies in the
Leo I group. We use the compilation of Müller et al. (2018, Tab. A.4 therein),
and selected dwarf galaxies in the M96 subgroup with LOS velocity measurements
(from Ferguson et al. 1998; Staveley-Smith et al. 1992; Huchtmeier et al.
2003; Karachentsev et al. 2004; Karachentsev & Karachentseva 2004; Haynes et
al. 2011; Karachentsev et al. 2013). Unfortunately, the majority of dwarf
galaxies in this sample did not have accurate (if any) distance measurements.

With this caveat in mind, we fit the overall rotation profile and determined
the LOS velocity dispersion of these 27 galaxies. The bottom panel of Fig. 12
shows their unsmoothed LOS velocities, colour-coded by the on-sky distance to
the centre of M105. We fit eq. (19) to the data and determine a best-fit
systemic velocity of $v_{\mathrm{sys,Leo\leavevmode\nobreak\ I}}=850\pm
35\;\mathrm{km}\,\mathrm{s}^{-1}$ (dotted horizontal line on Fig. 12), which
is lower than that of the PNe in the Sérsic halo of M105
$v_{\mathrm{sys,Ser}}=935.1\pm 1.4\;\mathrm{km}\,\mathrm{s}^{-1}$ and in the
exponential envelope $v_{\mathrm{sys,Exp}}=934.2\pm
9.9\;\mathrm{km}\,\mathrm{s}^{-1}$. The rotation amplitude of the dwarf
galaxies $v_{\mathrm{rot,Leo\leavevmode\nobreak\ I}}=148\pm
53\;\mathrm{km}\,\mathrm{s}^{-1}$ is significantly larger than that in the
outer halo of M105 ($83\pm 5\;\mathrm{km}\,\mathrm{s}^{-1}$ at the last data
point). The kinematic position angle of the dwarf galaxies is $PA=125\pm
17\degr$ (dashed vertical line), which is nearly aligned with the photometric
minor axis of the inner high SB region of M105 and thus also with the
kinematic position angle of the exponential envelope, within the errors. The
best fit is indicated by the solid grey line on the bottom panel of Fig. 12.

The blue error bars on the right panel of Fig. 11 denote the LOS velocity
dispersion of the dwarf galaxies that was determined in three elliptical bins
with the same position angle and ellipticity as used when binning the PN data.
The LOS velocity dispersion of PNe tracing the exponential envelope (purple
diamonds) reaches that of the Leo I group as traced by the dwarf galaxies.
This indicates that both the PNe in the exponential envelope and the
surrounding dwarf galaxies trace the group potential. This is corroborated by
the similar rotation properties (cf. Fig. 12).

The increase of LOS velocity dispersion profile at large radii inferred from
PNe is corroborated by velocity measurements of globular clusters (GCs).
Bergond et al. (2006) obtained radial velocities of 42 GCs in the Leo I group,
of which they associated 30 with M105, and combined those with previous
velocity measurements of eight GCs centred on M105 (Puzia et al. 2004). The
LOS velocity dispersion measurement of Bergond et al. (2006) is indicated by
green triangles with errorbars in the left panel of Fig. 11. At large radii,
the measurements from GCs and PNe are in excellent agreement, while the
velocity dispersion measured from GCs in the inner halo is larger than that
from PNe. This is expected, since the the GCs have a shallower number density
profile than the PNe at these radii (Puzia et al. 2004; Bergond et al. 2006).
Dividing the sample by colour into blue (and metal-poor) and red (and metal-
rich) GCs, Puzia et al. (2004) find the blue GCs to have a shallower number
density profile than the red ones, and in agreement with the measurements from
resolved stellar populations (Lee & Jang 2016) the fraction of blue and metal-
poor GCs increases with radius (Bergond et al. 2006). Because of the small
number of GC radial velocities around M105, it is not possible to robustly
establish whether the projected rotation of the GCs cospatial with the
exponential outer envelope is consistent with that measured using PNe.

Similar trends of increasing LOS velocity dispersion profiles have been
observed for discrete tracers such as PNe and GCs of the IGL or intra-cluster
light (ICL) in the Virgo (Hartke et al. 2018; Longobardi et al. 2018a, b) and
Fornax Clusters (Spiniello et al. 2018; Pota et al. 2018), as well as based on
integrated light in more distant clusters (Dressler 1979; Kelson et al. 2002;
Bender et al. 2015). While the ICL fraction in these environments is much
higher and measured at SB levels larger than that in the Leo I group, the
kinematic signature of halo-to-ICL transition is the same in the low-mass Leo
I group.

H+2020 argued that the high $\alpha$-parameter value and steeper PNLF slope of
the exponential envelope traced by the metal-poor stellar population is
indicative for a distinct origin compared to the metal-richer main halo.
Furthermore, the metallicity distribution function of RGB stars in the western
HST field in the outer halo (Harris et al. 2007b; Lee & Jang 2016) resembles
that of the resolved intra-cluster RGB stars in the Virgo Cluster core
(Williams et al. 2007). Combined with the stellar kinematics discussed
previously, we thus conclude that the population of PNe associated with the
metal-poor exponential envelope trace the IGL of the Leo I group.

###  5.3 Halo and IGL formation scenarios

Lee & Jang (2016) proposed a two-mode formation scenario for the metal-rich
and metal-poor stellar populations in M105, in which the metal-rich _inner
halo_ was formed in situ or through major mergers or relatively massive, and
thus metal-rich progenitors. Later, the blue and metal-poor halo that we
identify as the _exponential envelope_ in this work was assembled through
dissipationless mergers and accretion.

In addition to the inferences based on their metal-rich nature, the kinematics
of stars in the inner halo point towards an in-situ origin or they may have
been brought in through few massive and ancient mergers. The outwardly
decreasing rotation and LOS velocity dispersion profiles are similar to those
of in-situ stars in massive ETGs in cosmological hydrodynamical simulations
such as IllustrisTNG (Pulsoni et al. 2021). The formation of the metal-rich
inner stellar halo through massive and ancient mergers is also observed in
IllustrisTNG (Zhu et al. 2021). The PN population properties, such as the
lower $\alpha$-parameter value and shallower PNLF slope, are consistent with
relatively massive and old parent stellar populations (Buzzoni et al. 2006).

The blue and metal-poor exponential envelope instead is traced by a PN-rich
population, whose high $\alpha$-parameter value is similar to that of Local
Group dwarf irregular galaxies (such as Leo I, and Sextans A and B; Buzzoni et
al. 2006). The high velocity dispersion and moderate rotation of these PNe
corroborate the late accretion scenario of Lee & Jang (2016). Lastly, H+2020
already noted that their luminosity estimate for the exponential envelope
($2.04\times 10^{9}\;L_{\odot}$) is similar to the luminosity of single ultra-
faint galaxies (UFGs) in group and cluster environments (Mihos et al. 2015).
Lee & Jang (2016) postulate that UDGs are strong candidates to be responsible
for the metal-poor stellar population in the exponential envelope of M105, as
they have comparable metallicity distribution functions (e.g. Jang & Lee
2014). Due to their low mass and density, UFGs can be easily stripped, and
their debris can be deposited at large radii from the massive ETG (Amorisco
2017), making them viable progenitors of the IGL stars.

###  5.4 The case of the ICL surrounding M49 in the Virgo Cluster

Hartke et al. (2017) showed that PN populations in the inner halo (within 60
kpc, corresponding to $\approx 2.8R_{\mathrm{eff}}$) and the outskirts of the
ETG M49 in the massive ($10^{15}\;M_{\odot}$) Virgo Cluster have distinct
spatial distributions and arise from stellar populations with different
$\alpha$-parameters and with distinct PNLF slopes. Based on data from the
PN.S, Hartke et al. (2018) also showed that bright and faint PN populations
have distinct kinematics, with the faint population tracing the transition to
the ICL of the Virgo Subcluster B signalled by an increase of the LOS velocity
dispersion as function of radius, reaching that of satellite galaxies orbiting
the subcluster at large radii.

In the case of M49, Hartke et al. (2018) had to rely on the combination of
galaxy colours and PN dynamics to infer a link between the high
$\alpha$-parameter measured in the transition region between the halo and ICL
and an old, metal-poor underlying stellar population to explain the blue
colours observed in the outer halo of M49 (Mihos et al. 2013). However, with
studying the nearby galaxy M105, in the much less massive ($6.4\times
10^{11}\;M_{\odot}$; Schneider 1985) Leo I group of galaxies, it is now
possible to unambiguously link the presence of a PN population with a high
$\alpha$-parameter (H+2020) to a co-spatial metal-poor stellar population
forming part of the IGL of the Leo I group.

##  6 Summary and Conclusions

In this paper, we have presented a new wide-field kinematic survey of PNe in
the Leo I group. We have discussed the sample selection and catalogue
construction, as well as the overlap with previous photometric and kinematic
surveys. The photometric and kinematic catalogues are included in Appendix A
and _will be made available in full through the CDS_. We have separated PNe
into populations associated with the bulge and disk of the group galaxy NGC
3384, and with the Sérsic halo and exponential envelope of our main target,
M105.

We have identified three kinematically distinct populations of PNe in the halo
of M105, whose properties we summarise in turn.

  1. 1.

The _rotating core_ within $1\leavevmode\nobreak\ R_{\mathrm{eff}}$ (2.7 kpc),
characterised by a solar-metallicity stellar population that was likely formed
in situ.

  2. 2.

The _inner halo_ , from $1\leavevmode\nobreak\ R_{\mathrm{eff}}$ to
$7.5\leavevmode\nobreak\ R_{\mathrm{eff}}$ (2.7 kpc to 20.25 kpc), made up by
old intermediate-metallicity and metal-rich stars and characterised by low
rotation and LOS velocity dispersion PNe with a low $\alpha$-parameter. The
inner halo was either entirely formed in situ, or through notable
contributions from massive and metal-rich merging events.

  3. 3.

The _exponential envelope_ , from $7.5\leavevmode\nobreak\ R_{\mathrm{eff}}$
(20.25 kpc) to the last data point at $16\leavevmode\nobreak\
R_{\mathrm{eff}}$ (43.2 kpc), containing a metal-poor and PN-rich stellar
population with increasing rotation and constantly high LOS velocity
dispersion. The exponential envelope was formed through dissipationless
mergers and accretion of dwarf galaxies and very likely forms part of the
extended IGL of the Leo I group.

Future work will focus on dynamical modelling of the PN subpopulations to
determine the mass profile of M105 and its group environment. We will also
carry out an in-depth comparison of the kinematic transitions identified in
this work with new deep photometry. Lastly, this data set will also allow us
to investigate changes of the PNLF bright cut-off for the kinematically
distinct populations of PNe in the inner halo and exponential envelope.

## Acknowledgements

We are grateful to Nigel G. Douglas for his fundamental contribution to the
Planetary Nebula Spectrograph. We greatly acknowledge the support and advice
of the staff of the Isaac Newton Group on La Palma. We thank E. Iodice, R.
Ragusa, and M. Spavone for the insightful discussions about the deep
photometry of M105 from the VEGAS survey. AA was supported by Villum
Investogator grant (proj.n. 16599) and a Villum Experiment grant (proj.n.
36225). JH acknowledges the hospitality of the Sub-department of Astrophysics
of the University of Oxford. AJR was supported as a Research Corporation for
Science Advancement Cottrell Scholar. CS is supported by a ‘Hintze Fellowship’
at the Oxford Centre for Astrophysical Surveys, which is funded through
generous support from the Hintze Family Charitable Foundation.

This research made use of astropy (Astropy Collaboration et al. 2013),
astroplan (Morris et al. 2018), astroquery (Ginsburg et al. 2019), astromatic-
wrapper, corner (Foreman-Mackey 2016), emcee (Foreman-Mackey et al. 2013),
lmfit (Newville et al. 2014), matplotlib (Hunter 2007), and numpy (Van Der
Walt et al. 2011). This research has made use of the SIMBAD database, operated
at CDS, Strasbourg, France (Wenger et al. 2000). This research has made use of
the VizieR catalogue access tool, CDS, Strasbourg, France. The original
description of the VizieR service was published in Ochsenbein et al. (2000).
This publication has made use of data products from the Two Micron All Sky
Survey, which is a joint project of the University of Massachusetts and the
Infrared Processing and Analysis Center/California Institute of Technology,
funded by the National Aeronautics and Space Administration and the National
Science Foundation. The Digitized Sky Surveys were produced at the Space
Telescope Science Institute under U.S. Government grant NAG W-2166. The images
of these surveys are based on photographic data obtained using the Oschin
Schmidt Telescope on Palomar Mountain and the UK Schmidt Telescope. The plates
were processed into the present compressed digital form with the permission of
these institutions. This research has made use of NASA’s Astrophysics Data
System.

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##  Appendix A Tabular data

In this appendix we present the catalogues of PNe observed in the Leo I group
with Surprime-Cam at Subaru Telescope and the PN.S at the William Herschel
Telescope. Table 4 provides the IDs, coordinates (J2000 with the 2MASS
catalogue as astrometric reference), and $AB$ [O iii] and $V$-band magnitudes
of all PN candidates brighter than the limiting magnitude
$m_{\mathrm{5007,lim}}=28.1$, which were discovered based on Surprime-Cam
observations. The survey objectives, data reduction, and PN candidate
identification and validation are described in detail in the companion paper
H+2020 and briefly summarised in Sect. 2.1 of this work.

Table 5 provides the IDs, coordinates (J2000 with the 2MASS catalogue as
astrometric reference), $AB$ [O iii] magnitudes, LOS velocities and
corresponding errors, as well as the membership probability to be associated
with M105 (see Sect. 3). Two concatenated IDs denote PNe that were observed in
two fields, and objects with IDs starting with M105-C and N3384 were observed
first by Douglas et al. (2007) and Cortesi et al. (2013a) respectively. The
catalogue only contains PNe with velocities within $3\sigma$ about the robust
mean (see Sect. 2.2.1). Both catalogues will be made available in full through
the CDS.

Table 4: IDs, coordinates, magnitudes, and velocities of PNe candidates from Surprime-Cam photometry (H+2020). Only objects brighter than the limiting magnitude are included. The full table will be made available through the CDS. ID | RA | dec | $m_{[{o\textsc{iii}}],AB}$ |  $V_{AB}$
---|---|---|---|---
| [hh:mm:ss] (J2000) | [$\degr$:′:″] (J2000) | [$\mathrm{mag}$] | [$\mathrm{mag}$]
M105-SCAM-001 | 10:47:21.6842 | 12:23:27.1824 | 25.3 | 27.3
M105-SCAM-002 | 10:47:40.7357 | 12:23:33.2999 | 25.0 | 26.4
M105-SCAM-003 | 10:47:29.4416 | 12:23:45.1158 | 25.1 | 27.3
$\vdots$ | $\vdots$ | $\vdots$ | $\vdots$ | $\vdots$
M105-SCAM-226 | 10:47:17.8139 | 12:48:02.209 | 25.5 | 28.7
Table 5: IDs, coordinates, magnitudes, velocities and membership probabilities of PNe in the Leo I galaxies M105 and NGC 3384. Objects with IDs starting with M105-C and N3384 were observed first by Douglas et al. (2007) and Cortesi et al. (2013a) respectively. Two concatenated IDs denote PNe that were observed in two fields. The catalogue only contains PNe with velocities within $3\sigma$ about the robust mean (see Sect. 2.2.1). The full table will be made available through the CDS. ID | RA | dec | $m_{[{o\textsc{iii}}],AB}$ | $v_{\mathrm{los}}$ | $\Delta v_{\mathrm{los}}$ |  $f_{\mathrm{M105}}$
---|---|---|---|---|---|---
| [hh:mm:ss] (J2000) | [$\degr$:′:″] (J2000) | $[\mathrm{mag}]$ | $[\mathrm{km\,s^{-1}}]$ | $[\mathrm{km\,s^{-1}}]$ |
M105-C001_M105-W001 | 10:47:31.1951 | 12:39:20.1428 | 24.9 | 1002.0 | 19.1 | 0.99631
M105-C002 | 10:47:32.2051 | 12:32:09.7428 | 24.3 | 909.0 | 20.0 | 0.99354
M105-C003 | 10:47:33.5851 | 12:34:08.5428 | 25.4 | 892.0 | 20.0 | 0.99072
$\vdots$ | $\vdots$ | $\vdots$ | $\vdots$ | $\vdots$ | $\vdots$ | $\vdots$
N3384-C093 | 10:48:33.2169 | 12:36:27.0622 | 23.8 | 629.0 | 20.0 | 0.01520