# NIHAO-LG: The uniqueness of Local Group dwarf galaxies

Nikhil Arora,1 Andrea V. Macciò,2,3,4 Stéphane Courteau,1 Tobias Buck,5 Noam
I. Libeskind,5,6 Jenny G. Sorce,5 Chris B. Brook,10,11 Yehuda Hoffman9 Gustavo
Yepes,7,8 and Edoardo Carlesi9
1Department of Physics, Engineering Physics and Astronomy, Queen’s University,
Kingston, ON K7L 3N6, Canada
2New York University Abu Dhabi, PO Box 129188, Abu Dhabi, United Arab Emirates
3Center for Astro, Particle and Planetary Physics (CAP3), New York University
Abu Dhabi
4Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg,
Germany
5 Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16,
D-14482 Potsdam, Germany
6 University Lyon, University Claude Bernard Lyon 1, CNRS, IP2I Lyon/IN2P3,
IMR 5822, F-69622, Villeurbanne, France
7Departamento de Física Teórica, Módulo 8, Facultad de Ciencias, Universidad
Autónoma de Madrid, 28049 Madrid, Spain
8Centro de Investigación Avanzada en Física Fundamental (CIAFF), Universidad
Autónoma de Madrid, 28049 Madrid, Spain
9Racah Institute of Physics, Hebrew University, Jerusalem 91904, Israel
10Universidad de La Laguna. Avda. Astrofísico Fco. Sánchez, E-38200, La
Laguna, Tenerife, Spain
11Instituto de Astrofísica de Canarias, Calle Via Láctea s/n, E-38206 La
Laguna, Tenerife, Spain E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Recent observational and theoretical studies of the Local Group (LG) dwarf
galaxies have highlighted their unique star formation history, stellar
metallicity, gas content, and kinematics. We investigate the commonality of
these tantalizing features by comparing constrained LG and field central dwarf
halo simulations in the NIHAO project. For the first time, constrained LG
simulations performed with NIHAO hydrodynamics which track the evolution of MW
and M31 along with $\sim$100 dwarfs in the Local Group are presented. The
total gas mass and stellar properties (velocity dispersion, evolution history,
etc.) of present-day LG dwarfs are found to be similar to field systems.
Overall, the simulated LG dwarfs show representative stellar properties to
other dwarfs in the Universe. However, relative to fields, LG dwarfs have more
cold gas in their central parts and more metal-rich gas in the halo stemming
from interactions with MW/M31 and/or feedback. The larger gas metal content in
LG dwarfs results in early star formation events that lead to strong feedback
and subsequent quenching. We also test for the impact of metal diffusion on
the chemical evolution of LG dwarfs, and find that metal diffusion does not
affect the stellar or gaseous content of LG relative to field dwarfs; the
largest differences are found with the gas metallicity ($\sim 0.1$ dex). Our
results show that properties from LG dwarfs may be used as general constraints
for studying the overall dwarf population in the Universe, providing a
powerful local laboratory for galaxy formation tests and comparisons.

###### keywords:

galaxies: formation – Local Group – galaxies: evolution – galaxies: dwarf –
methods: numerical

††pubyear: 2021††pagerange: NIHAO-LG: The uniqueness of Local Group dwarf
galaxies–NIHAO-LG: The uniqueness of Local Group dwarf galaxies

##  1 Introduction

In the $\Lambda$CDM paradigm, galaxy growth occurs through hierarchical
assembly and secular evolution (White & Rees, 1978; White & Frenk, 1991;
Kormendy & Sanders, 1992). As a result, galaxies are dynamic entities that
form and evolve within groups and clusters. This holds for our Milky Way (MW)
and the Andromeda galaxy (M31), which along with numerous dwarf galaxies, form
the Local Group (LG) of galaxies (Mateo, 1998; McConnachie, 2012; Kirby et
al., 2013).

LG dwarf galaxies offer a superb laboratory to study the physics of galaxy
formation. Indeed numerous observational studies of the very nearby dwarf
galaxies have been conducted. In parallel dwarf galaxies in general have been
the subject of many theoretical studies, mostly by means of cosmological
numerical simulations. A fundamental question than arises as to how
representative are the LG dwarfs of the general dwarf galaxies population.
Alternatively one can ask to what extent the study of the LG dwarfs teaches us
about galaxy formation at large. One might think that tidal interactions
between dwarf galaxies and MW/M31 can lead to formation of streams and
eventual phase mixing into the stellar halos of MW/M31. These interactions can
also attract pristine gas that may induce star formation and evolution of
metals in dwarf galaxies (Buck, 2020). Such interactions can also lead to the
stripping of gas leading to a “freeze out" of the stellar population in LG
dwarfs. Can such environmental interactions distinguish the LG dwarfs from the
general population of dwarfs in the Universe? What are the cosmological
ramifications of such difference? This Copernican question is the main
motivation that leads to the present paper.

The stellar assembly of dwarf galaxies in the LG is sensitive to internal
(feedback and winds) and environmental (ram pressure and tidal stripping)
processes, as well as the reionization of gas due to the UV background at
early times. As a result, the star formation histories (SFH) for many LG
dwarfs have been extensively studied to better understand the influence of
these internal and external processes. Some of these dwarfs form a large
fraction of their stars at early times and are quenched after reionization
(Sand et al., 2010; Brown et al., 2012; Okamoto et al., 2012) while others
show moderate and continuous star formation to present day (Weisz et al.,
2014; Gallart et al., 2015). Overall, SFHs of dwarfs are the product of
reionization and the environment in which they formed. Gallart et al. (2015)
have also shown that dwarfs with no current star formation could form in
dense, cluster/group-like environments. Dwarfs that form in low density
environment could retain their gas reservoir for continuous star formation and
a younger stellar populations.

The presence of MW/M31 is likely to influence the gas, and therefore the
stellar, content of LG dwarfs. Indeed, the fraction of neutral hydrogen in LG
dwarf galaxies increases with distance from the MW (Spekkens et al., 2014;
Putman et al., 2021). Dwarfs within the virial radius of the MW are especially
deficient in cold gas while those outside the virial radius abound in neutral
gas, almost by a factor 100 (Einasto et al., 1974; Grcevich & Putman, 2009;
McConnachie, 2012; Spekkens et al., 2014). Gas poor systems result largely
from interactions with the hot halo of the MW typically characterized by ram
pressure stripping, viscous stripping, and starvation (Gunn & Gott, 1972;
Hester, 2006; Kawata & Mulchaey, 2008; Fillingham et al., 2016).

While the evolution of dwarf galaxies seems broadly understood, the key
question remains: are the observed features of LG dwarfs unique or do field
dwarfs, with no massive companion, show similar evolutionary tracks? A robust
answer to this question must rest on two pillars. One is our ability to
simulate the formation of the LG and its nearby neighborhood in way that
reproduces the main features of the LG. Namely, simulations that are
constrained to emulate the formation and evolution of the LG dwarfs within the
‘context’ of the actual observed LG. The other pillar consists of a detailed
census of LG and field dwarfs in the Local Universe. Depending on the choice
of Stellar Mass - Halo Mass relation (SHMR), espcially for the low mass end,
about 0.3-0.4 deg-2 of field dwarfs with surface brightness of $\sim$30 mag
arcsec-2 are expected in the Local Volume, with distances between 3 and 10 Mpc
from us (Danieli et al., 2018). Until the advent of deep large sky surveys,
such as those provided by the Rubin Observatory with a limiting magnitude of
32 mag arcsec-2, comparisons with complete census of field dwarfs is beyond
reach. While, the presence (or the lack) of unique aspects of the LG cannot
currently be characterized with observed galaxies, high resolution simulations
may provide much valuable insight.

Identifying differences between LG and field dwarf galaxies can help in better
isolating the role of environment in shaping the galaxy properties in the
Local Universe. In the context of other groups and cluster, galaxy properties
like mean stellar age (Thomas et al., 2005; Clemens et al., 2006), morphology
(Blanton & Moustakas, 2009, and references therein), colour (Wilman et al.,
2010; Cluver et al., 2020) and star formation rates (Fossati et al., 2015)
have been shown to be strongly dependent on environment. Similar conclusions
have been drawn about the influence of MW/M31 on LG dwarfs (e.g., Gottloeber
et al. 2010; Benítez-Llambay et al. 2015, 2016; Buck et al. 2019; Genina et
al. 2019; Libeskind et al. 2020; Di Cintio et al. 2021). However, if there
exist no differences between LG and field dwarf, the nearby dwarf population
(which are more easily accessible) can be used to study systems further away.

This paper presents such a comparison between the dwarf populations found in
the LG and in the field through high-resolution simulations in order to
highlight any similarities and differences. To this end, we take advantage of
the NIHAO simulations which trace the evolution of individual dark matter
halos and its baryonic components for the complete history of the Universe
(Wang et al., 2015). The NIHAO simulations have already proven to be
successful in matching various observations aspects of galaxy formation and
evolution (Macciò et al., 2016, 2017; Obreja et al., 2019; Buck et al., 2020;
Blank et al., 2021, to name a few). More details for the simulations are
provided in Sec. 2.1.

Our field dwarfs sample uses NIHAO halos as presented in Wang et al. (2015).
The LG dwarf sample is comprised of two constrained LG simulations with
initial conditions provided from the CLUES collaboration (Gottloeber et al.,
2010), presented here for the first time, and performed with the exact same
code and hydrodynamics used for the NIHAO project. The constrained LG
simulation allowed for the evolution of LG environment containing the MW and
M31 like halos and their associated dwarfs. Our comparisons rely mostly on
well-known galaxy scaling relations such as the stellar mass–metallicity
relation (hereafter MZR; Gallazzi et al. 2005; McConnachie 2012; Kirby et al.
2013), stellar mass–gas mass relation (Peeples et al., 2014), star formation
main sequence (SFMS; Cluver et al. 2017), and the SHMR (Behroozi et al., 2013;
Moster et al., 2014).

Because the formation and evolution of dwarfs in high-resolution simulations
is sensitive to the implemented subgrid prescriptions such as feedback,
chemical enrichment and metal diffusion, we also compare the subgrid physics
formalism that may drive the pre-enrichment of LG dwarfs; namely metal
diffusion. The impact of metal diffusion of the stellar assembly, star
formation rates and chemical evolution of dwarfs galaxies still remains
unclear. For instance, while Su et al. (2017) used the FIRE (Feedback In
Realistic Environment; Hopkins et al. 2018) simulations to show that the sub-
grid metal diffusion does not impact star formation rates on the galactic
scales, Pilkington et al. (2012) and Williamson et al. (2016) found opposite
results for the abundance of low-metallicity stars in dwarf galaxies (see also
Kawata et al. 2014 and Escala et al. 2018). Given the current muddled picture
about the evolution and abundance of metals in LG and field dwarfs, we present
results from two constrained LG simulations; with and without metal diffusion.

This paper is organised as follows: Sec. 2 outlines the NIHAO galaxy
simulation which provides the field galaxy sample for this study. The two
constrained Local Group simulations are also presented in Sec. 2. Sec. 3
highlights the similarities and differences between the constrained LG dwarf
galaxies and the NIHAO dwarf galaxies at $\rm z\sim 0$. A multi-faceted
analysis of the dwarf galaxies using various galaxy scaling relations is also
presented. The evolution of galaxy properties in all three simulations to
better understand the difference seen at $\rm z=0$ between the LG and the
field is addressed in Sec. 4, and conclusions are presented in Sec. 5 as we
ponder the uniqueness (or lack thereof) of LG dwarfs and its implications.

##  2 Simulations

###  2.1 NIHAO Galaxy Simulations

Our field central galaxy sample relies on the “Numerical Investigation of a
Hundred Astrophysical Objects" (NIHAO) cosmological zoom-in simulations
presented in Wang et al. (2015). The simulations were run with a flat
$\rm\Lambda$CDM cosmology with parameters from the Planck satellite: $\rm
H_{0}=100h\,km\,s^{-1}\,Mpc^{-1}$ with $\rm
h=0.671,\,\Omega_{m}=0.3175,\,\Omega_{\Lambda}=0.6824,\,\Omega_{b}=0.049,\,\sigma_{8}=0.8344$
and $\rm n=0.9624$ (Planck Collaboration et al., 2014). The hydrodynamics were
performed with the updated N-body SPH solver GASOLINE2 (Wadsley et al., 2017)
which includes the treatment of $\rm P/\rho^{2}$ proposed by Ritchie & Thomas
(2001). Gas cooling was performed through hydrogen, helium and various metal-
lines in a uniform UV ionizing background. Photo-ionization and heating of the
gas also occur via UV background and Compton cooling with temperatures from 10
to $\rm 10^{9}\,K$ (Shen et al., 2010).

All NIHAO galaxies were allowed to form stars provided that the gas follows
the Kennicutt-Schmidt law (Kennicutt, 1998) with suitable density and
temperature thresholds, $\rm T<15000\,K$ and $\rm n_{th}>10.3\,cm^{-3}$.
Energy is re-injected back into the interstellar medium (ISM) from stars
through stellar and blast wave supernova feedback. Massive stars also ionize
the ISM prior to their supernova explosion; this is referred to as “early
stellar feedback" (Stinson et al., 2006; Wang et al., 2015) where 13% of the
total stellar flux of $2\times 10^{50}{\rm erg\,M_{\odot}^{-1}}$ is injected
into the ISM. This differs from the original prescription presented in Stinson
et al. (2013) in order to account for the increased mixing of gas and aligns
with the abundance matching results on MW scale presented in Behroozi et al.
(2013). For supernova feedback, massive stars with $8\,{\rm
M_{\odot}}<M_{*}<40\,{\rm M_{\odot}}$ inject energy of $10^{51}{\rm erg}$ and
metals into the the ISM. Because the energy is injected into high density gas,
it radiates away via efficient cooling on short timescales. Therefore, for gas
particles inside the blast radius, cooling is delayed by $30\,{\rm Myr}$
(Stinson et al., 2013) to prevent immediate radiation from high density gas
particles (Stinson et al., 2006). The spiral and dwarf galaxies generated by
NIHAO simulations have been shown to match numerous observed galaxy properties
and scaling relations (Macciò et al., 2016; Obreja et al., 2016; Buck et al.,
2017; Dutton et al., 2017). The NIHAO galaxy simulations result in numerically
converged galaxies as shown by the ultra high-definition NIHAO runs Buck et
al. (2020).

Figure 1: Stellar mass versus halo mass relation at redshift $\rm z=0$ for
NIHAO (red stars) and two constrained LG simulations with (purple circles) and
without (gold circles) metal diffusion. The dashed lines and shaded regions
depict popular abundance matching relations from Moster et al. (2014),
Behroozi et al. (2013) and Kravtsov et al. (2018). The zoomed inset panel show
MW and M31 analogues and comparisons with massive NIHAO spirals. The observed
stellar and halo masses for the MW (Bland-Hawthorn & Gerhard, 2016)[pink
square] and M31 (stellar mass; Yin et al. 2009 and halo mass; Sofue 2015)[blue
square] are also presented.

###  2.2 NIHAO Local Group Simulations

Simulation | Box Size $\rm[Mpc\,h^{-1}]$ | $\rm m_{dark}\,[M_{\odot}]$ | $\rm\epsilon_{dark}\,[pc]$ | $\rm\epsilon_{gas}\,[pc]$ | $\rm N_{halos}$ | $\rm N_{dwarfs}$ | Metal Diffusion? | Environment
---|---|---|---|---|---|---|---|---
NIHAO | 60.1 | $1.74\times 10^{6}$ | 931.5 | 398.0 | 91 | 37 | Yes | Field
NIHAO-LG | 100.0 | $1.62\times 10^{6}$ | 860.3 | 487.7 | 104 | 64 | Yes | Local Group
NIHAO-LG (nmd) | 100.0 | $1.62\times 10^{6}$ | 860.3 | 487.7 | 115 | 73 | No | Local Group
Table 1: Various properties of our three NIHAO simulations. Columns give the
box size, mass resolution of the DM particles, softening length of the dark
and gas particles, number of halos at $\rm z=0$ , usage of metal diffusion,
and the simulated environment.

Our sample of dwarf galaxies in a LG environment was created with initial
conditions from the Constrained Local UniversE Simulations (CLUES)
project111http://www.clues-project.org. (Gottloeber et al., 2010; Carlesi et
al., 2016; Sorce et al., 2016; Libeskind et al., 2020). Constrained
simulations allowed us to track the position and environment of the MW, M31
like-galaxies and their associated dwarfs. The halos were identified and
tracked in a cosmological box of $\rm 100\,Mpc\,h^{-1}$ on a side, and
constrained by observational data of the nearby Universe. The initial
conditions for the simulation box relied on the Weiner filter (WF; Hoffman &
Ribak, 1991; Hoffman, 2009), a Bayesian linear algorithm, and constrained
realizations of the Gaussian matter density field from observations of the
Local Universe and an assumed prior model (Zaroubi et al., 1995). The WF
filter allowed for the construction of the cosmic displacement field needed to
robustly model particle positions as a function of time for the constrained
objects. The cosmic displacement field was created via a peculiar velocity
field of the Local Universe using the CosmicFlows-2 (CF2) catalogue of galaxy
redshift and direct distances (Tully et al., 2013). Malmquist biases and
lognormal errors in the CF2 dataset are corrected using the bias minimization
technique described in Sorce (2015). To correct for such displacements due to
cosmic evolution, to calculate the positions of the galaxies progenitors, the
reverse Zel’dovich approximation was applied (Doumler et al., 2013; Sorce et
al., 2014). Finally, re-normalization of the velocity field is performed to
get particles with initial velocity values of the particles in the simulation
box. A more detailed description of the CLUES initial conditions is found in
Carlesi et al. (2016); Sorce & Guo (2016); Sorce (2018); Libeskind et al.
(2020).

The initial conditions from CLUES simulations with the cosmology of NIHAO and
hydrodynamics from ESF-GASOLINE2 lead to the constrained NIHAO-LG simulations.
Along with the effect of environment (field vs. LG), we also monitored the
variations in galaxy properties due to changes in subgrid physics
implementations; esp. the chemical evolution in dwarfs. To that end, we
created two sets of constrained LG simulations; (i) NIHAO-LG: full NIHAO
cosmology and hydrodynamics included along with metal diffusion from Wadsley
et al. (2008), and (ii) NIHAO-LG(nmd): full NIHAO cosmology and hydrodynamics
with no metal diffusion. We use the Chabrier Initial Mass Function (IMF;
Chabrier, 2003) for stellar sampling in the simulation. As we seek differences
between field central dwarfs and LG dwarfs, the variation of chemical
evolution is an obvious implementation to modulate. In Tab. 1, we summarize
basic properties of the three NIHAO simulations used in this study. Within our
constrained LG simulations, two massive halos are found with total mass
$M_{\rm 200}\sim 10^{12}{\rm M_{\odot}}$, a ratio of stellar masses for the
massive halos of $M_{*}^{\rm MW}/M_{*}^{\rm M31}\sim 1.05$, and circular
velocities of $\sim$230 $\rm km\,s^{-1}$. The two massive halos have a virial
radii of $\sim$ 200 kpc and are separated by $\sim$ 700 kpc. In both
constrained LG simulations, the massive halos harbour disky stellar systems
with the Virgo cluster nearby.

Unless stated otherwise, all quantities (stellar mass, cold gas mass, etc.)
are measured within 0.2R200 and dwarfs are defined as central systems at $\rm
z=0$ with $7.0\leq\log(M_{*}/M_{\odot})\leq 9.5$. From the constrained LG
simulations, we selected all halos with 100 per cent high resolution DM
particles (i.e., no pollution), having at least 1000 particles (baryon and DM)
and at least 100 stellar particles. To make comparisons more robust, our study
focuses on central galaxies from the LG simulations. We expect numerical
resolution and convergence to only play a small role in the results presented
here. The hydrodynamics, performed with Gasoline2, as is the case for NIHAO
and the constrained LG simulations, were stable with respect to convergence.
Galaxy properties in the NIHAO simulations have also been shown to converge
despite the varying spatial and mass resolution over a large range of halo
masses. The highest resolution NIHAO dwarf galaxies presented in (Macciò et
al., 2017, 2019) yielded galaxy properties in broad agreement with the general
NIHAO simulated galaxy population (Wang et al., 2015).

Fig. 1 shows the stellar mass - halo mass relation (SHMR) at $\rm z=0$ for the
NIHAO and constrained NIHAO-LG simulations. For comparisons, the halo
abundance matching relations from Moster et al. (2014), Behroozi et al. (2013)
and Kravtsov et al. (2018) are also shown. The inset panel in Fig. 1 features
the NIHAO field and constrained LG analogues for the MW and M31 along with
observed measurements. The simulated stellar and halo masses for the MW/M31
agree with current estimates for the observed stellar and halo masses for MW
(Bland-Hawthorn & Gerhard, 2016) and M31 (Yin et al., 2009; Sofue, 2015). As
stated in Wang et al. (2015), the NIHAO galaxies, which serve as our field
galaxy sample, also agree well with halo abundance matching results (Kravtsov
et al., 2018). The dwarf galaxies ($\rm\log(M_{200}/M_{\odot})\leq 10.5$) in
the constrained LG simulations also match the abundance matching relation from
Behroozi et al. (2013). Likewise, the galaxies from the constrained LG
simulations with $\rm\log(M_{200}/M_{\odot})\geq 10.5$ match the parameters of
NIHAO field centrals and the SHMR of Kravtsov et al. (2018). However, dwarfs
in LG simulations have stellar masses that exceed their NIHAO field
counterparts by 0.2-0.3 dex, possibly indicative of additional pre-enriched
gas material from the MW and M31.

The shallow potential of LG dwarf galaxies is insufficient for retaining high
metallicity gas due to strong supernovae feedback and stellar winds (Dekel &
Silk, 1986). Therefore, excess stellar mass in the LG dwarfs, in comparison
with field systems, is likely built up from high metallicity, easily cooled
gas from the larger halos (MW/M31). The dwarfs in the LG may also have lower
dark matter fraction for the same stellar mass in comparison with field
systems as a result of interaction episodes with the massive halos (Munshi et
al., 2017; Buck et al., 2019).

Figure 2: Specific star formation rate, sSFR($={\rm SFR}/M_{\rm*}$), versus
stellar mass, $M_{\rm*}$, for the NIHAO (red stars) and the LG dwarf samples
(purple and gold circles). The underlying grey number density distribution of
SFR and $M_{\rm*}$ measurements for MPA-JHU SDSS galaxies (Kauffmann et al.,
2003; Brinchmann et al., 2004) is shown for comparison.

To further validate the NIHAO and LG simulations, we compare with observations
the ${\rm sSFR}$–$M_{\rm*}$ relation in Fig. 2. The specific star formation
rate, ${\rm sSFR}={\rm SFR}/M_{\rm*}$ , is the ratio of the average star
formation rate (SFR) within the last 100 Myr and the enclosed stellar mass
within $0.2R_{\rm 200}$, $M_{\rm*}$. In general, both NIHAO and the
constrained LG simulations match the distribution of SDSS galaxies, albeit
simulated dwarfs falling in the outskirts of the observed distribution. Given
the uneven selection function of the simulated NIHAO systems and the
variations in measuring the observed quantities in Fig. 2, comparison of NIHAO
galaxies with large-scale surveys is a non-trivial task. However, even with
this complication, the overall agreement between NIHAO and the SDSS is
comforting.

##  3 Local Group Galaxies

Our analysis begins with a variety of galaxy scaling relations at $\rm z=0$ ,
highlighted by differences between the field and LG dwarf populations. Along
with the role of environment, the impact of metal diffusion in setting some of
the properties of LG dwarfs is also examined.

###  3.1 Gas Properties

Figure 3: Total gas mass (left panel) and cold gas mass ($\rm T<20000\,K$;
right panel) versus stellar mass at $\rm z=0$ for the three samples of
simulated dwarf galaxies. The coloured circles represent the constrained LG
simulations with (purple) and without (gold) metal diffusion. The solid red
line and shaded region represent a best fit for the field NIHAO dwarf galaxies
and 1-$\sigma$ scatter about that fit, respectively. Total gas mass are
measured within $\rm R_{200}$ while cold gas and stellar masses are measured
within $\rm 0.2R_{200}$. Also shown are the cold gas - stellar mass relations
from Peeples et al. (2014) and Bradford et al. (2015) in the right panel. The
residuals with respect to the field dwarfs are shown in both bottom panels.
Figure 4: Average gas metallicity versus stellar mass for the three simulated
dwarf samples. The left-hand panel shows the metallicity for all the gas
within $\rm R_{200}$ and the right-hand panel shows the metallicity for the
cold gas within $\rm 0.2R_{200}$. All other details as in Fig. 3

We start by comparing the gas content of dwarf galaxies in the LG and in the
field. The left-hand panel of Fig. 3 shows total gas mass within R200 versus
stellar mass (measured within $0.2R_{200}$) for the field and LG dwarfs. The
red line and shaded region are linear best fit and scatter for the
$M_{g}$–$M_{*}$ relation of the NIHAO simulation, and the data points are
dwarfs from the constrained LG simulations. It is found that the overall gas
content for all LG dwarfs lies within the $1-\sigma$ scatter ($=$0.30$\pm$0.06
dex) of the NIHAO field galaxies. A few LG dwarfs ($\log M_{*}\leq 7.8$)
deviate from the observed trends for field dwarf systems which might be
associated to random scatter about the field galaxy relation. Most of these LG
dwarfs with low gas content exhibit older, metal-poor stellar content as 50
percent of the stellar mass is formed within the first $\sim$5 Gyr. Stripping
due to interaction with larger halos could explain the dearth of gas content
in the LG dwarfs.

The right-hand panel of Fig. 3 shows the cold gas ($\rm T<20000\,K$) content
in the field and LG dwarf systems at redshift $\rm z=0$ within $0.2\,R_{200}$.
This choice of radius isolates the central parts of halos as $\sim$90% of the
atomic and molecular gas resides within $0.2\,R_{200}$ of both the field
galaxies and LG dwarfs. The $1-\sigma$ scatter for the field dwarf relation is
$\rm 0.46\pm 0.10\,dex$ or three times as large as the average residual for
NIHAO-LG(nmd) of $\rm 0.14\,dex$. While the average residual, across the
complete dwarf range, is less than the scatter for the field relation, LG
dwarfs with $\log M_{*}\leq 8.0$ show a larger ($\sim$0.5 dex) central cold
gas content compared to field galaxies. While the total gas distribution for
field and LG are very similar, a larger fraction of the total gas within the
LG dwarfs appears to be cold gas. The residuals for the LG dwarfs with respect
to the field systems, shown in the bottom right-hand panel in Fig. 3, shows a
systematic trend for LG galaxies where an excess cold gas compared to fields
on the low mass end and a dearth of cold gas on the high mass end.

Various observed cold gas mass - stellar mass relations from Peeples et al.
(2014) and Bradford et al. (2015) are also presented in Fig. 3. The green
squares represent the median cold gas mass - stellar mass relation in Peeples
et al. (2014) using the observed data from McGaugh (2005, 2012), Leroy et al.
(2008) and Saintonge et al. (2011). The error bars represent the $16\%-84\%$
interquartile range of the observed data. The cyan line and shaded region,
taken from Bradford et al. (2015), delineate the distribution of atomic gas
mass for low mass galaxies ($\log M_{*}\leq 8.6$) in the Sloan Digital Sky
(SDSS; Aihara et al. 2011) and ALFALFA surveys (Haynes et al., 2011). While
the ALFALFA survey only detects H i gas contents, the total (atomic +
molecular) gas content is calculated as $M_{\rm g}=1.4M_{\text{H\,{i}}}$.

The cold gas content in dwarfs from both LG simulations is higher than the
observed relation from Bradford et al. (2015). On the other hand, the median
observed and simulated field relations show great agreement for the slopes and
scatters. However, even after accounting for the atomic gas to get total gas
mass, the mean observed trend shows a slightly smaller zero-point than the
simulated field sample. The smaller observed gas content can attributed to
differences in how the measurements of total gas content between simulations
and observations. For NIHAO, all gas particles are counted within $0.2\,R_{\rm
200}$; however, observed measurements are limited by signal-to-noise (S/N) and
the cold gas content may not be fully accounted for. A similar difference
exists in the comparison of simulated LG dwarfs and the observed data by
Peeples et al. (2014). At all stellar masses, LG dwarfs have higher cold gas
content than observations. However, given the large error bars at the low mass
end for Peeples et al. (2014), a fraction of the simulated LG dwarfs agree
with the observations.

In summary, we find that the total gas contents within the field and LG dwarfs
show similar distributions. The LG dwarfs, even accompanied by MW/M31, do not
gain additional gas that might be generated because of the outflows from the
massive halo. However, most gas within the LG dwarfs is found to be cold
resulting in a larger cold gas content (especially the low mass dwarfs)
compared to field dwarfs. The larger cold gas fraction in LG dwarfs maybe due
to the metallicity of the inflowing gas.

Fig. 4 shows a comparison of the gas metallicity between field NIHAO galaxies
and the LG dwarf systems. The left-hand and right-hand panels present the
average gas metallicity for all the gas within the halo and the average gas
metallicity for the cold gas within $0.2\,R_{\rm 200}$ respectively. The field
NIHAO systems have $Z_{\rm g}\propto M_{\rm*}^{0.56\pm 0.05}$ with a scatter
of $0.12\pm 0.03$ dex. The LG dwarfs, on the other hand, exhibit a bimodal
distribution in the $Z_{\rm g}$–$M_{\rm*}$. Low-mass LG dwarfs
($\log(M_{*}/M_{\odot})\leq 8.0$) have a higher, though constant, gas
metallicity than field centrals with $\log(Z_{*}/Z_{\odot})\sim-1.6$. High-
mass LG dwarfs follow the same trend and scatter than field NIHAO galaxies.
The higher metallicity in the halo of low-mass LG dwarfs likely results from
the outflows induced in the Local Group by the MW and M31.

The right-hand panel of Fig. 4 shows the cold gas metallicity versus stellar
mass for the three simulated dwarf samples. The field sample follows a similar
relation to all the gas in the halo, with $Z_{\rm g}\propto M_{\rm*}^{0.50\pm
0.06}$ but with a larger scatter of $0.19\pm 0.04$ dex. The LG dwarf galaxies
fall within the field relation, presenting no difference in the central cold
gas metallicity as a result of environment. Comparing the left- and right-hand
panels of Fig. 4, we conclude that metal rich gas in the LG systems is found
at radii greater than $0.2\,R_{\rm 200}$. This is indicative of recent
inflowing gas for LG dwarf systems which has yet to cool down and be available
for star formation. We defer a comparison of field and LG dwarfs in the
$M_{\rm g}$–$M_{*}$ and $Z_{\rm g}$–$M_{*}$ relations as a function of time to
Sec. 4.

###  3.2 Stellar Properties

Figure 5: Left-hand panel: Stellar metallicity versus stellar mass (MZR) for
the complete stellar mass range of NIHAO and LG simulated galaxies at $\rm
z=0$ . The color scheme is as in Fig. 3. The cyan line and shaded region
represent the observed relation from Gallazzi et al. (2005). Right-hand panel:
MZR relation zoom-in for the simulated NIHAO and LG dwarf galaxies.

The mean stellar metallicity versus stellar mass for the three samples of
dwarf galaxies at $\rm z=0$ can inform us about chemical evolution of the
galaxies. Most of the heavy metals were formed within the stars and are
distributed into the galaxy via stellar feedback. The left panel of Fig. 5
presents the MZR for all NIHAO and LG simulations and a comparison with the
observed relation of Gallazzi et al. (2005). While the observed data are only
available for relatively massive systems ($\log(M_{*}/M_{\rm\odot})\gtrsim
9.0$), both NIHAO and LG simulated system match observations well. The MW and
M31 galaxies from both constrained simulations also fall within the observed
relation from Gallazzi et al. (2005).

The right panel of Fig. 5 is a zoom-in of the dwarf stellar mass regime. Field
dwarfs follow $Z_{\rm*}\propto M_{\rm*}^{0.47\pm 0.04}$ with a scatter of $\rm
0.09\pm 0.02\,dex$; both LG dwarf simulations have similar median residuals of
$\rm\sim-0.10\,dex$. In general, within the broad dispersions of each
distribution, the field and LG dwarfs follow two statistically matching
distributions. The NIHAO field MZR slope, $\rm\alpha\simeq 0.47\pm 0.04$, the
NIHAO-LG(nmd) dwarf relation with a slope of $\rm\alpha\simeq 0.48\pm 0.03$,
and the slope for NIHAO-LG, $\rm\alpha\simeq 0.54\pm 0.07$, all fall within
statistical errors. The errors calculated for the simulation slopes are
standard deviations of 1000 bootstrap runs. Small differences between
simulations and observations slope measurements are expected from the sample
sizes of our respective studies (Sorce & Guo, 2016). While our LG samples
contain $\sim$100 dwarfs, the observed sample only contains 30 dwarf systems.

Figure 6: Iron abundance, $\langle[{\rm Fe/H}]\rangle_{*}$, versus stellar
mass for the three samples of simulated dwarf galaxies. The color scheme is as
in Fig. 3. $\langle[{\rm Fe/H}]\rangle_{*}$ was averaged over all stellar
particles within $R_{\rm 1/2}$. The left-hand panel shows the mass-weighted
averages carried out in linear space (see Eq. (2) for definition) while the
right-hand panel shows mass-weighted averages calculated in log space (see Eq.
(1) for definition). In cyan, the right-hand panel shows the observed relation
for Local Group dwarf galaxies from Kirby et al. (2013).

Observers typically measure stellar chemical abundance of galaxies using
bright metal absorption lines such as those of iron or magnesium. Here we
present a comparison of the stellar iron abundances between the three
simulated dwarf samples and observations from Kirby et al. (2013). With most
of the iron concentrated in the central parts of the galaxies, the average
iron abundance weighted by stellar mass encompasses all star particles within
the half-light radius. An essential aspect of this chemical comparison is the
averaging process for the star particles in the simulation. At first, similar
to the observing process, the averaging is carried out with the metallicity in
logarithmic space (Evan Kirby, private communication.). The average iron
abundance then becomes,

$\langle{\rm[Fe/H]}\rangle_{\rm*,log}=\frac{\displaystyle\sum_{i}({\rm[Fe/H]}_{*,i}m_{*,i})}{\displaystyle\sum_{i}(m_{*,i})},$
(1)

where $\rm[Fe/H]$ is the iron abundance and $m_{\rm*}$ is the stellar mass of
the star particle $i$. However, the averaging process in logarithmic units is
inappropriate. A proper expression for the mean iron abundance is given by

$\langle{\rm[Fe/H]}\rangle_{\rm*,lin}=\log\left(\frac{\displaystyle\sum_{i}(10^{{\rm[Fe/H]}_{*,i}}m_{*,i})}{\displaystyle\sum_{i}(m_{*,i})}\right).$
(2)

In Eq. (2), the iron abundance per star particle, $i$, is calculated in linear
space and the logarithm of the complete expression is taken once the average
is computed. Our comparison of the simulated dwarf systems uses linear
averages (Eq. (2)). For complementarity and comparison with observations, the
stellar iron abundances averaged in logarithmic space are also reported.

The left-hand panel of Fig. 6 presents the linearly averaged iron abundance
versus stellar mass for the three simulated dwarfs samples. Field dwarf
galaxies from NIHAO follow $\langle{\rm[Fe/H]}\rangle\propto M_{\rm*}^{0.36\pm
0.04}$ with a scatter of $0.09\pm 0.02$ dex. The NIHAO-LG(nmd) dwarfs and
field galaxies have an identical distribution, and NIHAO-LG low mass dwarfs
are somewhat poorer in metals than the field. A linear average for the stellar
iron abundance is preferentially biased towards metal rich stars. With the “no
metal diffusion” feature removed from NIHAO-LG(nmd), metal-rich stars form
more easily resulting in higher stellar iron abundances than NIHAO-LG.

The presence of massive spirals like the MW and M31 around these dwarfs can
lead to strong outflows, likely leading to metal-enriched stellar populations
in LG dwarfs. However, contrary to this expectation, NIHAO-LG shows metal-poor
stellar populations relative to field systems. Given the deep potential of the
MW and M31, a significant fraction of the outflowing gas and metals may turn
up with a galactic fountain and be retained by the massive halo. Such an
effect can yield a metal-poor stellar population for the LG dwarfs relative to
field centrals. The impact of pre-enrichment due to MW/M31 may erode leading
to similar stellar populations within the field and LG. Our result in the
left-hand panel of Fig. 6 is quantitatively similar to that of FIRE (Escala et
al., 2018) or the high-resolution NIHAO simulations (Buck et al., 2019).

The right-hand panel of Fig. 6 shows the logarithmic averaged stellar iron
abundance for the three simulated dwarf samples and observed relation from
Kirby et al. (2013). With a different averaging technique comes a revised
relation; the field galaxies relation,
$\langle{\rm[Fe/H]}\rangle_{*}$–$M_{\rm*}$, is now slightly steeper and
tighter with a slope of $0.39\pm 0.04$ and scatter $0.09\pm 0.02$. The
differences between linear and logarithmic averaging of the
$\langle{\rm[Fe/H]}\rangle_{*}$–$M_{\rm*}$ relations are still well within the
errors. The observed relation shows similar linear slope ($0.30\pm 0.02$) but
with a larger scatter (0.17 dex) and lower zero-point. The simulated field
galaxies from NIHAO are more iron-poor, as is expected for these low mass
galaxies who cannot retain metal-rich gas due to stellar feedback and winds.
The simulated LG dwarfs show an even poorer metal content in stars, with their
[Fe/H] distribution lower than observations by a factor 15. The three
simulations and observations differ only in their zero-point offset (the
trends have the same slope) which is directly linked to the implementation of
supernovae feedback in the simulations (Escala et al., 2018). The study of
Buck et al. (2021) provides an improved chemical enrichment scheme for NIHAO
simulations that should yield a better match with observations. We shall
return to such data-model comparison in a future study. Fig. 3 shows the
excess cold gas mass in LG dwarfs compared to field dwarfs. That excess gas
dilutes metal production through stellar evolution and yields a metal-poorer
stellar populations in LG dwarfs. Figs. 5 and the left-hand panel of Fig. 6
tell a similar story.

| NIHAO | NIHAO-LG | NIHAO-LG(nmd)
---|---|---|---
Scaling Relation | Slope | Zero–point | Scatter | Average Difference [dex] | Average Difference [dex]
(1) | (2) | (3) | (4) | (5) | (6)
$M_{\rm gas}-M_{*}$ | 0.73$\pm$0.09 |  -3.47$\pm$0.73 | 0.30$\pm$0.06 | 0.00$\pm$0.05 | 0.03$\pm$0.06
$M_{\rm coldgas}-M_{*}$ | 1.09$\pm$0.15 |  -0.12$\pm$1.27 | 0.46$\pm$0.10 | 0.41$\pm$0.11 | 0.49$\pm$0.09
$Z_{\rm gas}-M_{*}$ | 0.56$\pm$0.05 | -5.92$\pm$0.37 | 0.12$\pm$0.03 | 0.18$\pm$0.06 | 0.26$\pm$0.06
$Z_{\rm coldgas}-M_{*}$ | 0.50$\pm$0.06 | -5.24$\pm$0.49 | 0.19$\pm$0.04 | 0.00$\pm$0.04 | 0.08$\pm$0.03
$Z_{*}-M_{*}$ | 0.47$\pm$0.04 | -5.25$\pm$0.31 | 0.09$\pm$0.02 | 0.02$\pm$0.03 | 0.07$\pm$0.02
${\rm\langle[Fe/H]\rangle_{*}}-M_{*}$ | 0.36$\pm$0.04 | -4.29$\pm$0.31 | 0.09$\pm$0.02 | 0.09$\pm$0.03 | 0.03$\pm$0.03

Table 2: Summary of the scaling relations used for comparison of the three
different simulated dwarf populations. Column (1) lists the scaling relation;
columns (2-4) present the slope, zero-point and scatter, respectively for the
NIHAO dwarfs (acting as the field population); and columns (5-6) show the
average difference between the NIHAO field and LG dwarf populations from the
constrained simulations. If the values in columns 5 and/or 6 are greater than
the scatter of the NIHAO field scaling relations (column 4), the LG dwarf
population is considered statistically different. The errors are bootstrapped
over 2000 runs.

Finally, Tab. 2 presents a quantitative summary of our comparisons of field
and LG dwarf populations. For the scaling relations used here, the slope,
zero-point, and scatter for the field NIHAO populations are shown. The average
difference between the LG and field dwarf populations is also presented in
Tab. 2. That difference is calculated by randomly sampling the same number of
LG dwarfs as the field dwarfs (see Tab. 1) and calculating the median residual
with respect to the field galaxy scaling relation. This process is
bootstrapped 2000 times to estimate the error of the average difference. Tab.
2 reiterates the larger differences in the gas properties of the LG dwarfs
relative to field systems. The stellar properties of the LG dwarfs show little
to no difference with field galaxies.

###  3.3 Star Formation Rates

Figure 7: The SFMS at redshift $\rm z=0$ for the three samples of simulated
galaxies. The color scheme follows Fig. 3. The NIHAO central galaxies are
presented as the best-fit with the shaded region representing $1\sigma$
scatter in the relation. The gray, green and cyan lines show mid-infrared SFMS
inferred by Hall et al. (2018) for Calzetti et al. (2007), Davies et al.
(2016), and Cluver et al. (2017). The points with error bars in the lower
right corner represent the scatter of these observed relations. Also shown are
the recent SFRs and stellar masses for the MW (Bland-Hawthorn & Gerhard, 2016)
and M31 (Yin et al., 2009; Ford et al., 2013) as pink and blue squares,
respectively.

Fig. 7 shows the present-day Star Formation Main Sequence (SFMS) for the three
samples of simulated galaxies in this study. Our robust measurements of star
formation rates (SFR) used the average SFR over the last 100 Myr. The central
field galaxies from the NIHAO sample are shown as a best-fit line and shaded
region representing the $\rm 1-\sigma$ region; the constrained LG simulations
are shown as colored circles; SFR–M∗ measurements for the MW and M31 from Yin
et al. (2009) and Bland-Hawthorn & Gerhard (2016), as well as observed SFMS
studies from Calzetti et al. (2007), Davies et al. (2016) and Cluver et al.
(2017) are also shown as coloured lines for comparison.

The $1-\sigma$ scatter for these observed relations are in the lower right
corner of the plot as point with error bars. For this discussion of the SFMS,
the full stellar mass range is used for the simulated sample. The simulated
NIHAO sample follows ${\rm SFR}\propto M_{\rm*}^{0.76\pm 0.08}$ with a scatter
of 0.50 dex. This agrees well with the observed relations along with their
scatter; however, the scatter of the simulated relation exceeds the observed
scatter by 0.2 dex.

The massive galaxies $\rm(\log(M_{*}/M_{\odot})>9.5)$ for both constrained LG
samples fall within the $\rm 1-\sigma$ region of the NIHAO field galaxies
relation. The dwarf galaxies $\rm(\log(M_{*}/M_{\odot})<9.5)$ in the
constrained LG simulations show slightly lower SFRs compared to their field
dwarf companions. Most LG dwarfs, from both simulations, are not star-forming
galaxies at present day. Most of the LG dwarfs contain mainly older stellar
populations; nearly 50 per cent of the LG dwarfs (in NIHAO-LG and NIHAO-
LG(nmd)) have formed half of their present stellar mass in the first $\sim$5
Gyr. In general, LG and field NIHAO galaxies follow the same distribution, in
agreement with recent empirical renditions of the SFMS. We also note the large
differences between observed relations presented in Davies et al. (2016) and
Cluver et al. (2017). Those are mainly due to the variations in sample sizes;
Davies et al. (2016) used 3749 galaxies from the GAMA sample (Driver et al.,
2016) while Cluver et al. (2017) used only 79 galaxies from the SINGS/KINGFISH
survey (Kennicutt et al., 2003, 2011).

Halo/Simulation | SFR$\rm[M_{\odot}\,yr^{-1}]$ | $M_{\rm*}[{10^{10}\rm M_{\odot}]}$
---|---|---
(1) | (2) | (3)
M31 (NIHAO-LG) | 0.27 | 5.57
M31 (NIHAO-LG(nmd)) | 0.23 | 4.66
M31 (Observed) | $0.25^{0.06}_{0.04}$ | $5.9-8.7$
MW (NIHAO-LG) | 0.73 | 6.02
MW (NIHAO-LG(nmd)) | 0.51 | 4.69
MW (NIHAO; g8.26e11) | 2.05 | 4.68
MW (Observed) | $1.65\pm 0.19$ | $5.0\pm 1.0$
Table 3: Present SFR and $M_{\rm*}$ measurements for the MW and M31 from our
constrained LG simulations and observation. Column (1) gives the halo and
simulations, while columns (2) and (3) give the SFR and $M_{\rm*}$ in units of
$\rm M_{\odot}\,yr^{-1}$ and $\rm 10^{10}M_{\odot}$, respectively. Observed
measurements for MW (Bland-Hawthorn & Gerhard, 2016) and M31 (Yin et al.,
2009; Ford et al., 2013) are also presented.

Fig. 7 includes observed measurements of SFR and $M_{\rm*}$ for the MW (Bland-
Hawthorn & Gerhard, 2016) and M31 (Yin et al., 2009; Ford et al., 2013).
These, along with the simulated properties, are also presented in Tab. 3. Once
again, the stellar masses for the MW and M31 from the LG simulations are in
broad agreement with the observed estimates and g8.26e11 (a Milky-Way analog
from the NIHAO simulations).

The SFR, on the other hand, shows more variability. The simulated LG M31 halos
agree with observed SFR from Ford et al. (2013) who used far ultraviolet and
24$\mu$m emission measurements for their estimates of the global
SFR$=0.25^{0.06}_{0.04}\,{\rm M_{\odot}\,yr^{-1}}$ for M31. However, the LG MW
halos under-predict the SFRs relative to observed measurements. For instance,
Bland-Hawthorn & Gerhard (2016) reported SFR$=1.65\pm 0.19\,{\rm
M_{\odot}\,yr^{-1}}$ from calculations by Licquia & Newman (2015) and assuming
a Kroupa Initial Mass Function (IMF). The assumption of the underlying IMF is
always a significant source of error in the calculation of SFR (Hennebelle &
Chabrier, 2013).

NIHAO halo g8.26e11 (presented in Tab. 3) over-predict the SFR relative to the
observed MW SFR, whereas the observed and simulated values agree within
2$\sigma$. However, while the high SFR value for g8.26e11 disagree with the
constrained LG simulations and observations, they still fall within the
$1-\sigma$ scatter of the field SFMS. The field relation, and therefore
g8.26e11, also agrees with the observed SFMS relations of Calzetti et al.
(2007), Davies et al. (2016) and Cluver et al. (2017).

Figure 8: Total outflowing gas mass (left-hand panel) and gas metals (center
panel) within a spherical shell of $1.5R_{\rm vir}\leq r\leq 2R_{\rm vir}$ as
function of time for the most massive halo in the two constrained LG
simulations (purple and gold lines). The right-hand panel shows the SFH of the
two LG halos. Redshifts are shown on the top x-axis.

##  4 Evolution of the Local Group

We have found so far that the properties of simulated field and LG dwarf
galaxies at low redshift ( $\rm z=0$ ) showed small, though non-negligeable,
differences at low redshift. LG dwarfs have larger (0.2 dex) stellar masses
and a larger (0.35 dex) cold gas content within $0.2R_{200}$ than field dwarfs
at $\rm z=0$ . The hot gas content for LG dwarfs is also more metal rich than
field systems. In this section, we study the evolution of various galaxy
properties in an attempt to isolate, if present, evolutionary differences
between LG and field dwarf systems.

Motivated by our objective to study pre-enrichment in LG dwarfs due to co-
evolution with MW and M31, we shall first examine the outflowing gas
properties from the most massive halos in the two constrained LG simulations
and NIHAO. We will then trace the evolution of some key dwarf galaxy scaling
relations with time. In doing so, we wish to isolate specific times in the
evolutionary history of LG and correlated with the evolution of the MW and
M31. Ultimately, we wish to constrain the influence of massive galaxies on the
evolution of LG dwarfs. Given our two constrained LG simulations, we can also
address the influence of metal diffusion in simulations.

###  4.1 MW/M31

The mass of outflowing gas in the two constrained LG simulations and as a
function of time or redshift can inform us about star formation driven
outflows which can be correlated with inflows in LG dwarfs. This is shown in
the left-hand panel in Fig. 8. The gas mass is calculated within a spherical
shell between $\rm 1.5R_{vir}\leq r\leq 2R_{vir}$ and with radial velocity
$v_{\rm r}>0\,{\rm km\,s^{-1}}$. The evolution of both constrained LG
simulations with time is nearly identical until $\rm\sim$5 Gyr, with a gentle
decrease in outflowing gas mass by $\rm\sim 0.2\,dex$. Differences become
noticeable after $\rm\sim$5 Gyr where the trends diverge; outflowing gas
decreases by 0.2 dex for NIHAO-LG(nmd) but increases by 0.1 dex for NIHAO-LG.
These different trends between NIHAO-LG and NIHAO-LG(nmd) stem from slightly
different SFH between the halos from the LG constrained simulations. At $z\leq
1$, the most massive halo in NIHAO-LG(nmd) shows a $\sim 0.1$ dex lower SFR
compared to NIHAO-LG (see right-hand panel for Fig. 8). The outflowing gas
content for the two halos in Fig. 8 agree from $z\sim 0.1$ to the present
time.

Similar conclusions are drawn from the center panel of Fig. 8 which shows the
outflowing gas metals from the most massive halo in the constrained LG
simulations. Both constrained LG halos expel a similar metal content in their
outflowing gas. The differences in outflowing metals is directly correlated to
the higher SFR for the LG halos presented in the right-hand panel for Fig. 8.
The higher SFR leads to enhanced feedback and enriched outflows. Between
$z\sim 2-0.5$, as a result of metal diffusion, the most massive halo from
NIHAO-LG expels relatively metal-poor gas. The metallicity of gas particles in
NIHAO-LG simulation will decrease as it interacts with the environment due to
the inclusion of metal diffusion, resulting in lower overall metallicity.

In all three panels of Fig. 8, the massive halos from both constrained LG
simulations depict very similar evolution history. Varying subgrid physics
implementations, including/excluding metal diffusion in our cases, does not
lead to significant changes to the MW/M31 galaxy properties and therefore
surrounding dwarfs. In general, the most massive halos from both constrained
LG simulations present very similar outflowing gas properties. For massive
halos, the presence or absence of metal diffusion does not affect the galaxy
population properties.

###  4.2 Dwarf Galaxies

We turn our attention to the time evolution of the LG and field dwarf systems
using galaxy scaling relations presented in Sec. 3. The co-evolution of LG
dwarfs with the MW/M31 should be apparent in the gas properties of the LG
dwarfs relative to the field systems. The full set of LG and field dwarfs at
all redshifts are compared using the average residual from the field galaxy
scaling relations. The average residual for the constrained LG simulations is:

$\langle\Delta(y_{\rm LG}|M_{\rm*})\rangle_{\rm LG}(t)=\langle y_{\rm
LG}(t)-(\alpha_{\rm N}(t)M_{\rm*,LG}(t)+c_{\rm N}(t))\rangle,$ (3)

where $y_{\rm LG}$ is a galaxy property presented in Sec. 3, $\alpha_{\rm
N}(t)$ and $c_{\rm N}(t)$ are the slope and intercept of the fitted scaling
relation from the field NIHAO sample, $M_{\rm*,LG}(t)$ is the stellar mass of
the LG system, and all properties are calculated at time $t$. The variables on
the right-hand side of Eq. (3) all yield the average residual at time t,
$\langle\Delta(y_{\rm LG}|M_{\rm*})\rangle_{\rm LG}(t)$. The error on the
average residuals are calculated as $\epsilon_{\rm LG}=\sigma(y_{\rm
LG}|M_{\rm*})/\sqrt{N}$; where $\sigma(y_{\rm LG}|M_{\rm*})$ is the standard
deviation of the residual from the field scaling relation and $N$ is the
number of data points. In this formalism, we define the LG and field dwarfs as
different galaxy populations when $\epsilon_{\rm N}<\langle\Delta(y_{\rm
LG}|M_{\rm*})\rangle_{\rm LG}(t)$ where $\epsilon_{\rm N}$ is the error of the
linear fit to the NIHAO galaxies. In this comparison of the LG and field
dwarfs, the scatter of the field galaxy scaling relations is also presented.
Due to evolution in time, the slopes of nearly all scaling relations vary;
therefore, the forward scatter ($\sigma_{\rm N,f}$) alone is not a robust
comparison metric. Instead, we use the orthogonal scatter, defined as
$\sigma_{\rm N}=\sigma_{\rm N,f}/\sqrt{1+\alpha_{\rm N}^{2}}$, for our
comparisons.

####  4.2.1 Gas Content

Figure 9: Evolution in the residual for the gas mass - stellar mass relation
as a function of redshift for dwarf galaxies with
$\rm(7.0\leq\log(M_{*}/M_{\odot})\leq 9.5)$ for the two constrained LG
simulations shown as coloured bands (purple and gold). The gas mass - stellar
mass relation of NIHAO central dwarfs is the horizontal line at
$\rm\langle\Delta(M_{Gas}|M_{*})\rangle=0.0$, the dark red region present the
error on the average relation, and the lighter shaded region showing the $\rm
1-\sigma$ scatter of the scaling relation at each redshift. The top and bottom
panels show the total and cold gas mass, respectively. The redshift is
represented on the top x-axis.

We study the evolution of gas properties, in particular mass and metallicity,
for both field and LG dwarfs. A comparison of the mass and/or metallicity of
the total and/or gas in the LG halos with the field systems, can provide
evidence of the pre-enrichment of LG dwarfs from the more massive halos in the
constrained LG simulations. Fig. 9 shows the comparison of the field and LG
systems as a function of time for the $M_{g}$–$M_{*}$ relation. The top and
bottom panels show all total gas content within $R_{\rm 200}$ and the cold gas
content within $0.2R_{\rm 200}$, respectively. The orthogonal scatter in the
total $M_{g}$–$M_{*}$ relation increases from $\sim$0.11 dex, at $z\sim 3.2$,
to 0.26 dex, at present day. The slope of the relation, however, shows little
change over time.

Both LG and field dwarfs have the same distribution for the total gas content
for the complete evolutionary history as the purple and gold error band follow
the dark red shaded region (see Fig. 9). The field systems occupy the central
regions of their respective dark matter halo and are fed gaseous material from
the cosmic filaments, major/minor gas rich mergers. The LG dwarfs accumulate
their gas content predominantly by the outflows from the larger halos
(MW/M31). The outflows from the larger halos, in the constrained simulations,
are substantial enough to build up the gas content similar to the central
field dwarfs.

While the evolution of the total gas content of the LG and field systems is
very similar, the slope and the scatter of the cold $M_{g}$–$M_{*}$ relation
in the field evolve significantly as a function of time (bottom panel of Fig.
9). The slope changes range from 0.80 at $z\sim 3.2$ to 1.10 at present day,
while the scatter grows from 0.09 dex at $z\sim 3.2$ to 0.31 dex at $\rm z=0$
. Furthermore, most of the gas within the LG dwarf is cold gas within
$0.2R_{\rm 200}$. The difference in the cold gas mass between field and LG
dwarfs continues to increase from $z\lesssim 2$ to present day. At $z=0$, the
LG dwarfs contain 0.4 dex more cold gas within $0.2R_{\rm 200}$ than the field
systems. The increasing cold gas mass in the LG dwarfs, compared to the field,
is evidence of the co-evolution with MW/M31. The star formation episodes and
interactions with MW/M31 allow for the build-up of cold gas content, and
therefore provide excess fuel for star formation, in the LG dwarfs
populations.

####  4.2.2 Chemical Content

Figure 10: Same as Fig. 9 but for gas metallicity.

The chemical content of gas in LG dwarf halos can inform us about the origin
of the gas content. A similar chemical content as the field dwarfs for the LG
system could indicate that the evolution history of dwarfs is independent of
the environment. Fig. 10 shows the metallicity of the gas content in the field
and LG samples. The format of Fig. 10 is the same as Fig. 9. In the top panel,
where gas metallicity of total gas content is computed within $R_{\rm 200}$,
field dwarfs display little variation in the scatter of the $Z_{\rm
g}$–$M_{*}$ relation. The two constrained LG simulations behave slightly
differently with time, though both simulations show dwarfs with more metal
rich gas than the field systems.

From $z\sim 1$ to present day, the NIHAO-LG dwarfs possess a higher metal rich
gas content (by 0.15 dex; which is $3-\sigma$ different from the field). While
the total gas mass of the field and LG dwarfs evolve in similar ways (see top
panel of Fig. 9), the gas content of the LG dwarfs is significantly more
enriched. The metal enriched gas in these LG dwarfs is a direct consequence of
outflows generated by the MW/M31 halo. The metal build-up in NIHAO-LG dwarfs
is related to the peak of metal rich gas outflowing from the most massive halo
(see left-hand and center panels of Fig. 8). The metal rich content of the
inflowing gas from MW/M31 allows for it to cool down on shorter timescales
(than fresh, metal poor gas in field dwarfs) and be available for further star
formations events. Such star formation events would allow for the LG dwarfs to
build up their stellar mass. Field dwarf systems, on the other hand, have
access to metal enriched gas mostly through the mergers.

The excess metal rich gas is more pronounced in NIHAO-LG(nmd) compared to
NIHAO-LG and field NIHAO systems. The gas content in LG dwarfs from NIHAO-
LG(nmd) are nearly 0.3 dex (or $5-\sigma$ different) more enriched than field
systems. The absence of metal diffusion in NIHAO-LG(nmd) leads to gas
particles building up their metal content and thus yields systematically
higher metallicities. Similar signatures are seen at $\rm z=0$ in Fig. 4 with
more metal rich gas in NIHAO-LG compared to NIHAO-LG(nmd).

The bottom panel in Fig. 10 depicts the cold gas metals within the three
sample of dwarfs. Unlike the $Z_{\rm g}$–$M_{*}$ relation for total gas, the
cold gas $Z_{\rm g}$–$M_{*}$ relation for the field shows increasing scatter
as a function of time. Once again, the two constrained LG simulations behave
differently; NIHAO-LG(nmd) dwarfs at all times have the same distribution as
the field systems, whereas NIHAO-LG dwarfs for their complete history lie
$1-\sigma$ scatter above from the field systems. The excess metal in the gas
within the halo translates into metal-rich cold gas within $0.2R_{\rm 200}$.
The metal rich hot gas flowing in from MW/M31 due to intense periods of star
formation quickly contributes to building up the cold gas content in the LG
dwarfs. However, both NIHAO-LG and NIHAO-LG(nmd) show marginal evolutionary
differences from the field dwarfs. The lack of evolution of the cold gas
metallicity could be linked to the lack of star formation in LG dwarfs. Nearly
70 percent of the LG dwarfs (both NIHAO-LG and NIHAO-LG(nmd)) are quenched by
the first 4.5 Gyr of their formation. A quenched star formation hinders the
recycling of metals in gas and yields a static metal content in the LG cold
gas.

##  5 Summary and Conclusions

The Local Group offers us with a superb laboratory for the study of the
formation and evolution of the dwarf galaxies; the most abundant cosmological
structures in the Universe. The main questioned that we have addressed here is
to what extent this laboratory can be used to teach us about galaxy formation
at large and its cosmological implications. In this comparative study, we have
highlighted the similarities and differences between simulated LG and field
dwarf galaxies as a function of time/redshift and a comparison with
observations. This comparison relied on dwarf halos from the NIHAO high
resolution zoom-in simulations as our field control sample. For the LG dwarfs,
we present and analysed the constrained LG simulations run with NIHAO
hydrodynamics. To further analyse the role of chemical evolution in LG dwarfs,
two different LG constrained simulations were used; with and without metal
diffusion.

Present-day field and LG dwarfs were found to have similar stellar populations
but significantly different gas contents. While the total gas content of
dwarfs is not influenced by environment (Sawala et al., 2012), a larger
fraction of the gas within LG dwarfs is cold and resides within $0.2R_{\rm
200}$. The latter is correlated to the higher metal content (than field
dwarfs) of the gas in the halo. The higher gas metal content of the LG dwarfs
is accumulated via interactions with the host halos (MW/M31) which allows the
LG dwarfs to collect the heavy metal generated during peak star formation
episodes of the host halos. High metallicity allows for shorter cooling times
and is available for star formation episodes and further metal processing in
the LG dwarfs. However, such episodes in LG dwarfs lead to strong feedback
events and force metals out of the galaxy (where stars reside) while still
being locked in the halo. The time evolution of the cold gas mass within LG
dwarfs shows departures from the field sample around $z\sim 1-2$. This also
coincides with the peak in the SFH of the most massive host halos in our
constrained LG simulations. Close passage of the LG dwarfs around the host
halos would allow for the accumulation of the higher metal-rich gas content
(eg. Di Cintio et al., 2021).

However, relative to field systems, LG dwarfs show little evolution in cold
gas metallicity with time. While the higher metallicity in the halo should
allow for gas to cool down efficiently and lead to SF events, stellar feedback
and outflows in the dwarfs will suppress any episodes and further stellar
evolution leading to a quenched system. Therefore, the stellar and cold gas
evolution of LG dwarfs is strongly dictated by in-situ processes such as
stellar feedback, winds and photoevaporation due to re-ionization, more so
than environmental processes (Sawala et al., 2012). A significant fraction of
the dwarfs in our constrained LG simulations build up their stellar content
early in their evolution history and remain quenched thereafter (eg. Sand et
al., 2010; Simon et al., 2021). The LG and field have, therefore, similar
galaxy populations; esp. in stellar properties.

We also found that changing the metal diffusion sub-grid prescription does not
affect the gas mass within the LG dwarfs through their complete evolution
histories. However, the LG simulation with metal diffusion results in a metal
poor gas content, by $\sim 0.1$ dex relative to no metal diffusion simulation.
This is expected as metal diffusion drives the metallicity of gas particles
closer to the average metallicity. The average metallicity of stellar
particles at $\rm z=0$ does not change after including metal diffusion. Both
constrained LG simulations produce stellar metallicities in agreement with
simulated field dwarfs and observations. The average iron abundance in LG
simulations show only marginal differences due to metal diffusion, albeit less
pronounced. At $\rm z=0$ , the stellar iron abundances in the two constrained
LG simulations differ by $\sim 0.05$ dex (left-hand panel of Fig. 6). However,
the difference is only found in the offsets while the slope of the stellar
mass – iron abundance relations are similar for field and LG dwarfs. The
simulated stellar mass – iron abundance relation also showed no dependence
with environment and appears to be regulated by in-situ processes such as
feedback and photoevaporation (Skillman et al., 1989; Escala et al., 2018).
The different normalizations are likely related to the manner by which
supernovae feedback are modelled in the simulations.

Finally, we also compared the SHMR between field and LG dwarfs (see Fig. 1).
We found that, for the same halo mass, both constrained LG simulations have
larger stellar contents than field systems. The larger stellar content
relative to the total mass is likely due to enrichment from larger halos
allowing for gas to cool down efficiently. and interactions with the host
halos inducing star burst events (Munshi et al., 2017; Buck et al., 2020).

Local Group dwarf galaxies possess very similar stellar properties to those
found in the field. Field and LG dwarfs had early bursts of star formation but
remain quenched for the rest of their history. The evolution of their stellar
properties is strongly dictated by in-situ processes and less so by
environmental processes. On the other hand, the gas properties of LG dwarfs
show signs of pre-enrichment from the host halos, with the larger cold gas
mass and metal content being directly associated with the outflows generated
by the MW and/or M31. Given the similar stellar properties of simulated
dwarfs, high-resolution dwarf simulations such as NIHAO (Wang et al., 2015)
and FIRE (Garrison-Kimmel et al., 2019) may then be used to analyse the
general dwarf population. Our results have demonstrated the value of LG
observations, specifically their stellar properties, to be used as constrains
for the overall dwarf populations in our Universe. The Local Group provides us
with a powerful and most valuable laboratory for understanding galaxy
formation and evolution processes nearby. The unique aspects seen in the gas
properties of the LG can be examined using high-resolution constrained LG
simulations (Gottloeber et al., 2010; Sorce et al., 2016; Carlesi et al.,
2016; Libeskind et al., 2020). Furthermore, with the advent of next generation
telescopes such as JWST, Euclid, Rubin/LSST, and SKA, observational signatures
of pre-enrichment can ultimately be teased out of high redshift LG analogs and
their accompanying dwarfs.

## Data Availability

The data underlying this article will be shared upon request to the
corresponding author(s).

## Acknowledgements

NA and SC are grateful to the Natural Sciences and Engineering Research
Council of Canada and Queen’s University for generous support through various
scholarships and grants. TB also acknowledges support from the European
Research Council under ERC-CoG grant CRAGSMAN-646955. NIL acknowledges
financial support from the Project IDEXLYON at the University of Lyon under
the Investments for the Future Program (ANR-16-IDEX-0005) GY thanks the
Spanish Ministry of Science, Innovation and Universities (MICIU/FEDER) for
financial support under research grant PGC2018-094975-C2. YH has been
partially supported by the Israel Science Foundation grant ISF 1358/18.
Barbara Catinella, Luca Cortese and Ananthan Karunakaran provided valuable
references for our observational comparisons to simulated data. Aaron Dutton
is also thanked for earlier contributions and comments relevant to this work.
The research was performed using the PYNBODY package (Pontzen et al., 2013),
SCIPY (Virtanen et al., 2020), NUMPY (Harris et al., 2020) and used MATPLOTLIB
(Hunter, 2007) for all graphical representation. The authors gratefully
acknowledge the Gauss Centre for Supercomputing e.V. (www.gauss-centre.eu) for
funding this project by providing computing time on the GCS Supercomputer
SuperMUC at Leibniz Supercomputing Centre (www.lrz.de). This research was
carried out on the High Performance Computing resources at New York University
Abu Dhabi. We greatly appreciate the contributions of all these computing
allocations.

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