Dark-matter-deficient dwarf galaxies form via tidal stripping of dark matter in interactions with massive companions

In the standard Lambda-CDM paradigm, dwarf galaxies are expected to be dark-matter-rich, as baryonic feedback is thought to quickly drive gas out of their shallow potential wells and quench star formation at early epochs. Recent observations of local dwarfs with extremely low dark matter contents appear to contradict this picture, potentially bringing the validity of the standard model into question. We use NewHorizon, a high-resolution cosmological simulation, to demonstrate that sustained stripping of dark matter, in tidal interactions between a massive galaxy and a dwarf satellite, naturally produces dwarfs that are dark-matter deficient, even though their initial dark-matter fractions are normal. The process of dark matter stripping is responsible for the large scatter in the stellar-to-halo mass relation in the dwarf regime. The degree of stripping is driven by the closeness of the orbit of the dwarf around its massive companion and, in extreme cases, produces dwarfs which exhibit stellar-to-halo mass ratios as low as unity, consistent with the findings of recent observational studies. Given their close orbits, a significant fraction of DM deficient dwarfs merge with their massive companions (e.g. ~70 per cent merge over timescales of ~3.5 Gyrs), with the DM deficient population being constantly replenished by new interactions between dwarfs and massive companions. The creation of these galaxies is, therefore, a natural by-product of galaxy evolution and the existence of these systems is not in tension with the standard paradigm.


INTRODUCTION
In the standard ΛCDM paradigm, dwarf galaxies (M ★ < 10 9.5 M ) are expected to be dark matter (DM) rich, because their shallow potential wells make it easier for processes like stellar and supernova feedback to drive gas out from their central regions at early epochs (Dubois & Teyssier 2008;Di Cintio et al. 2017;Chan et al. 2018;Jackson et al. 2020). This reduces their star formation rates, while leaving the rate of DM accretion unaffected. Dwarf galaxies are expected to form a natural extension to the stellar-to-halo mass relation ★ E-mail: r.jackson9@herts.ac.uk in massive galaxies (Moster et al. 2010;Read et al. 2017), with the M halo /M ★ values expected to increase towards progressively lower stellar masses.
However, some recent observational studies appear to challenge this picture. A growing number of studies suggest that some dwarf galaxies may deviate strongly from the expected stellar-tohalo mass relation (e.g. van Dokkum et al. 2018avan Dokkum et al. , 2019Guo et al. 2019;Hammer et al. 2020), with unexpectedly low DM fractions. For example, Guo et al. (2019) have found 19 nearby dwarf galaxies that are DM deficient. The majority of these galaxies (14/19) appear relatively isolated, with no indication of nearby bright galaxies or high-density environments implying that they might have been born DM deficient. van Dokkum et al. (2018avan Dokkum et al. ( , 2019 have studied two dwarf galaxies in group environments which could exhibit M halo /M ★ values close to unity, suggesting that they may have DM fractions that are around 400 times lower than that expected for galaxies of their stellar mass. There is still some controversy surrounding the validity of these findings (e.g. Oman et al. 2016;Martin et al. 2018b;Blakeslee & Cantiello 2018;Emsellem et al. 2019;Fensch et al. 2019a;Trujillo et al. 2019), mostly focusing on the reliability of obtaining accurate distance measurements to these systems. For example, in the case of the van Dokkum et al. (2018a) galaxy, a measured distance of 13 Mpc (as suggested in Trujillo et al. (2019)), rather than the quoted ∼ 20 Mpc in van Dokkum et al. (2018a), would make M halo /M ★ > 20, making it a relatively normal dwarf galaxy (but see van Dokkum et al. (2018b) for an alternate view). The existence of galaxies that are deficient in DM could pose a serious challenge to the ΛCDM model, as it is difficult for galaxies that are rich in baryons to form in halos that are deficient in DM. It is, therefore, important to investigate whether there are natural channels for the formation of such galaxies in the standard model. Some formation methods for DM deficient galaxies have been suggested in the recent literature. A well-known channel for forming such systems are tidal dwarfs (Wetzstein et al. 2007;Bournaud et al. 2008a,b;Kaviraj et al. 2012;Kroupa 2012;Ploeckinger et al. 2015;Haslbauer et al. 2019). These dwarf galaxies are formed in the tidal tails that emerge as a result of gas-rich major mergers of massive galaxies, either through Jeans instabilities within the gas which lead to gravitational collapse and the formation of self-bound objects (Elmegreen et al. 1993), or a large fraction of the stellar material in the progenitor disk being ejected and providing a local potential well into which gas condenses and fuels star formation (e.g. Barnes & Hernquist 1992;Duc et al. 2004;Hancock et al. 2009). However, the contribution of tidal dwarfs to the galaxy population, particularly at the stellar masses of the DM deficient galaxies found by recent observational studies (∼10 9 M ), is extremely small (e.g. Kaviraj et al. 2012).
Another potential formation method is via high velocity, gasrich mergers of dwarf galaxies themselves (Silk 2019;Shin et al. 2020). In this scenario, DM deficient galaxies form as these mergers separate DM from the warm disc gas, which is then compressed by tidal interactions and shocks to form stars. A further formation channel is DM stripping of satellite galaxies, particularly in extreme environments such as clusters (Ogiya 2018;Jing et al. 2019;Niemiec et al. 2019). Indeed, both N-body simulations in a range of environments, from Milky-Way mass halos (Hayashi et al. 2003;Kravtsov et al. 2004;Diemand et al. 2007;Rhee et al. 2017;Buck et al. 2019) to clusters (Ghigna et al. 1998;Gao et al. 2004;Tormen et al. 2004;Nagai & Kravtsov 2005;van den Bosch et al. 2005;Giocoli et al. 2008;Xie & Gao 2015), and analytical models (e.g. Mamon 2000;Gan et al. 2010;Han et al. 2016;Hiroshima et al. 2018) have shown that DM stripping is capable of removing parts of a galaxy's halo in group and cluster environments. It has been suggested that this process could drive a large scatter in the stellar-to-halo mass relation for satellite galaxies in groups and clusters, moving them from their initial positions towards lower halo masses (Vale & Ostriker 2004;Smith et al. 2016;Bahé et al. 2017;Rhee et al. 2017;Niemiec et al. 2017Niemiec et al. , 2019, and therefore lower M halo /M ★ values. A comprehensive analysis of whether DM deficient systems (dwarfs in particular) can form naturally as a by-product of the process of galaxy evolution demands a hydrodynamical simulation in a cosmological volume which has both high mass and spatial resolution. The hydrodynamics is required for spatially-resolved predictions for the DM and baryons. The cosmological volume enables us to probe galaxy populations in a statistical manner, taking into account environmental effects (which idealised studies, for instance, cannot do), and is particularly important for making meaningful comparisons to large observational surveys (e.g. forthcoming datasets like LSST, Robertson et al. 2019).
In recent years, large hydrodynamical cosmological simulations (e.g. Horizon-AGN (Dubois et al. 2014b), Illustris (Vogelsberger et al. 2014), EAGLE (Schaye et al. 2015) and Simba (Davé et al. 2019)) have been successful in reproducing many properties of (massive) galaxies over cosmic time (e.g. Kaviraj et al. 2017). For example, Saulder et al. (2020) have investigated the properties of massive (M ★ > 10 9.5 M ) DM deficient galaxies which are isolated in these large cosmological simulations, akin to those found in Guo et al. (2019). They find that these galaxies are probably regular objects that undergo un-physical processes at the boundary of the simulation box and are therefore artefacts. Jing et al. (2019) on the other hand have studied the formation of massive (10 9 M < M ★ < 10 10 M ) DM deficient galaxies in the EAGLE and Illustris simulations, in denser environments. They find that a non-negligible fraction (2.6% in EAGLE, and 1.5% in Illustris) of satellite galaxies, in large groups and clusters (M 200 > 10 13 M ), are DM deficient in their central regions. These galaxies, which are not initially DM deficient, become so through the stripping of DM by tidal interactions with their host galaxy an effect that has also been noted in Horizon-AGN (Volonteri et al. 2016)).
However, given that these environments are relatively rare, and that the majority of dwarfs have lower stellar masses than the galaxies in these studies, it remains unclear from these studies (1) whether DM deficient galaxies can form in low-density environments which host the majority of objects, and (2) whether they can form in the dwarf regime where galaxies are expected to be significantly more DM dominated at early epochs, and where most observational studies that have found DM deficient galaxies are focussed. It is worth noting that it is challenging to probe dwarf galaxy evolution using the large-scale cosmological simulations mentioned above due to their relatively low mass and spatial resolutions. For example, the DM mass resolution is ∼10 8 M in Horizon-AGN, EAGLE and Illustris and the spatial resolution of these simulations is around a kpc. Recall that the scale height of the Milky Way, for example, is ∼300 pc (e.g. Kent et al. 1991;López-Corredoira et al. 2002;McMillan 2011), so much better spatial resolution is needed to properly resolve dwarfs.
An accurate exploration of the evolution of dwarf galaxies therefore requires a cosmological simulation with significantly better mass and spatial resolution, in order to properly resolve the processes on the small spatial scales involved. In this study, we use the NewHorizon hydrodynamical cosmological simulation, which offers a maximum spatial resolution of 34 pc and mass resolutions of 10 4 M and 10 6 M in the stars and DM respectively, to understand the formation of DM deficient galaxies in the stellar mass range M ★ > 10 8 M . NewHorizon currently has the best spatial resolution of any simulation with a comparable volume, making it an ideal tool to study the processes involved in the evolution of dwarf galaxies (e.g. Jackson et al. 2020). At the lower limit of our stellar mass range, a typical low-redshift dwarf galaxy contains ∼10,000 stellar and ∼10,000 DM particles respectively. Our aims are to (1) study whether DM deficient dwarf galaxies form naturally in NewHorizon, (2) estimate the frequency with which they are created and (3) quantify the processes that produce these galaxies. This paper is structured as follows. In Section 2, we briefly describe the NewHorizon simulation and the selection of DM defi-cient galaxies. In Section 3, we study the processes that create these objects. We summarise our findings in Section 4.

SIMULATION
The NewHorizon cosmological, hydrodynamical simulation (Park et al. 2019;Jackson et al. 2020;Dubois et al. 2020), is a highresolution simulation, produced using a zoom-in of a region of the Horizon-AGN simulation (Dubois et al. 2014b;Kaviraj et al. 2017, H-AGN hereafter). H-AGN employs the adaptive mesh refinement code RAMSES (Teyssier 2002) and utilises a grid that simulates a 142 comoving Mpc 3 volume (achieving a spatial resolution of 1 kpc), using 1024 3 uniformly-distributed cubic cells that have a constant mass resolution, using MPGrafic (Prunet et al. 2008).
For NewHorizon, we resample this grid at higher resolution (using 4096 3 uniformly-distributed cubic cells), with the same cosmology as that used in H-AGN (Ω = 0.272, Ω = 0.0455, Ω Λ = 0.728, H 0 = 70.4 km s −1 Mpc −1 and = 0.967; Komatsu et al. (2011)). The high-resolution volume occupied by NewHorizon is a sphere which has a radius of 10 comoving Mpc, centred on a region of average density within H-AGN. NewHorizon has a DM mass resolution of 10 6 M (compared to 8×10 7 M in H-AGN), stellar mass resolution of 10 4 M (compared to 2×10 6 M in H-AGN) and a maximum spatial resolution of 34 pc (compared to 1 kpc in H-AGN). The simulation has been performed down to = 0.25. NewHorizon currently has the highest spatial and stellarmass resolutions for simulations of similar volume and is an ideal tool for studying dwarf galaxy evolution over cosmic time.

Star formation and stellar feedback
NewHorizon employs gas cooling via primordial Hydrogen and Helium, which is gradually enriched by metals produced by stellar evolution (Sutherland & Dopita 1993;Rosen & Bregman 1995). An ambient UV background is switched on after the Universe is re-ionized at = 10 (Haardt & Madau 1996). Star formation is assumed to take place in gas that has a hydrogen number density greater than >10 H cm −3 and a temperature lower than 2×10 4 K, following a Schmidt relation (Schmidt 1959;Kennicutt 1998). The star-formation efficiency is dependent on the local turbulent Mach number and the virial parameter = 2 /| |, where E is the kinetic energy of the gas and E is the gas gravitational binding energy (Kimm et al. 2017). A probability of forming a star particle of mass M * , =10 4 M is drawn at each time step using a Poissonian sampling method, as described in Rasera & Teyssier (2006).
Each star particle represents a set of coeval stellar populations, with 31 percent of the stellar mass of this star particle (corresponding to stars more massive than 6 M ) assumed to explode as Type II supernovae, 5 Myr after its birth. This fraction is calculated using a Chabrier initial mass function, with upper and lower mass limits of 150 M and 0.1 M (Chabrier 2005). Supernova feedback takes the form of both energy and momentum, with the final radial momentum capturing the snowplough phase of the expansion (Kimm & Cen 2014). The initial energy of each supernova is 10 51 erg and the supernova has a progenitor mass of 10 M . Pre-heating of the ambient gas by ultraviolet radiation from young O and B stars is included by augmenting the final radial momentum from supernovae following Geen et al. (2015).

Supermassive black holes and black-hole feedback
Supermassive black holes (SMBHs) are modelled as sink particles. These accrete gas and impart feedback to their ambient medium via a fraction of the rest-mass energy of the accreted material. SMBHs are allowed to form in regions that have gas densities larger than the threshold of star formation, with a seed mass of 10 4 M . New SMBHs do not form at distances less than 50 kpc from other existing black holes. A dynamical gas drag force is applied to the SMBHs (Ostriker 1999) and two SMBHs are allowed to merge if the distance between them is smaller than 4 times the cell size, and if the kinetic energy of the binary is less than its binding energy.
The Bondi-Hoyle-Lyttleton accretion rate determines the accretion rate on to SMBHs, with a value capped at Eddington (Hoyle & Lyttleton 1939;Bondi & Hoyle 1944). The SMBHs release energy back into the ambient gas via a thermal quasar mode and a jet 'radio' mode, when accretion rates are above and below 1 percent of the Eddington rate respectively (Dubois et al. 2012). The spins of these SMBHs are evolved self-consistently through gas accretion in the quasar mode and coalescence of black hole binaries (Dubois et al. 2014a), which modifies the radiative efficiencies of the accretion flow (following the models of thin Shakura & Sunyaev accretion discs) and the corresponding Eddington accretion rate, mass-energy conversion, and bolometric luminosity of the quasar mode (Shakura & Sunyaev 1973). The quasar mode imparts 15 percent of the bolometric luminosity as thermal energy into the surrounding gas. The radio mode employs a spin-dependent variable efficiency and spin up and spin down rates that follow the simulations of magneticallychoked accretion discs (see e.g. McKinney et al. 2012).

Identification of galaxies and merger trees
We use the AdaptaHOP algorithm to identify haloes (Aubert et al. 2004;Tweed et al. 2009). AdaptaHOP efficiently removes subhaloes from principal structures and keeps track of the fractional number of low-resolution DM particles within the virial radius of the halo in question. We identify galaxies in a similar fashion, using the HOP structure finder applied directly on star particles (Eisenstein & Hut 1998). The difference between HOP and AdaptaHOP lies in the fact that HOP does not remove substructures from the main structure, since this would result in star-forming clumps being removed from galaxies. We then produce merger trees for each galaxy in the final snapshot at = 0.25, with an average timestep of ∼ 15 Myr, enabling us to track the main progenitor of every galaxy with high temporal resolution.
Given that NewHorizon is a high resolution zoom of Horizon-AGN, it is worth considering the DM purity of galaxies, since higher-mass DM particles may enter the high resolution region of NewHorizon from the surrounding lower-resolution regions. Given the large mass difference, these DM particles may interact with galaxies they are passing through in unusual ways. The vast majority of galaxies affected by low DM purity exist at the outer edge of the NewHorizon sphere. The DM deficient galaxies studied in this paper all have DM halos with a purity of 100 per cent. Figure 1 shows the stellar mass (M ★ ) vs the ratio of the DM halo (M halo ) and stellar mass, for galaxies in NewHorizon at z=0.25. Here, M halo corresponds to the mass enclosed within the virial radius of the halo. We study galaxies which have stellar masses above 10 8 M , which remain well-resolved in the simulation to early and stellar mass for galaxies in NewHorizon at = 0.25. In this study, we focus on galaxies with M ★ >10 8 M , which are well-resolved in the simulation to early epochs. We split this population into objects that are centrals (open black circles) and satellites (coloured circles). The satellites are further divided into 'DM deficient' galaxies, defined as objects that exhibit M halo /M ★ <10 (blue circles), satellites that coincide with the relatively tight locus defined by the centrals (orange circles) and 'DM poor' galaxies (green circles) which fall in between these two populations. The satellites that coincide with the centrals (orange circles) are essentially unstripped in their DM. We use these unstripped satellites as a control sample, since these galaxies show normal levels of DM. epochs. We note that, while there are some galaxies in our sample above the mass threshold that we use to define dwarfs (M ★ < 10 9.5 M ), the overwhelming majority of galaxies in our study are dwarfs. We split this galaxy population into objects that are centrals (open black circles) and satellites (coloured circles). The satellites are further divided into 'DM deficient' galaxies (blue circles), defined as objects that exhibit M halo /M ★ <10, satellites that coincide with the relatively tight locus defined by the centrals (orange circles) and 'DM poor' galaxies (green circles) which fall in between these populations. The satellites that occupy the same region in the M ★ -M halo /M ★ plane as the centrals (orange circles) are essentially unstripped in their DM. For the analysis below, where we study the reasons for the DM stripping in the DM deficient and DM poor populations, we use these unstripped satellites as a control sample, since these galaxies show 'normal' levels of DM (i.e. a similar DM content to that of centrals).

Selection of galaxies that are deficient in DM
Note that in this study we define M halo to be the total mass of the DM halo associated with the galaxy. This is in contrast to previous studies (e.g. Jing et al. 2019) that have mostly looked at the central regions of the DM halo (two times the half-stellar-mass radii). Thus, galaxies identified as 'DM deficient' in NewHorizon will be even more deficient if the criteria of other studies were used. The fractions of DM deficient, DM poor, control and central galaxies in NewHorizon are 12, 19, 18 and 51 per cent respectively. Recall that the centrals and the controls (i.e. the unstripped satellites) show normal levels of DM, so that the fraction of galaxies that show some sort of a deficiency in their DM content is around 30 per cent. In Figure 2 we show the evolution of the median properties of each population. The top, middle and bottom panels show the evolution in the stellar mass, DM halo mass and the M halo /M ★ ratios respectively. While the stellar mass evolution is similar across all populations, the DM halo mass evolves differently, with the DM deficient and DM poor galaxies exhibiting declines in DM content at late epochs. The scatter in the M ★ vs M halo /M ★ relation seen in Figure 1 is therefore driven by the removal of DM in these galaxies, which produces systems that are poorer in DM for their stellar mass.
While the gradual change from the locus of centrals and controls seen in Figure 1 indicates that the DM deficient and DM poor populations are not simply artefacts and are likely created by a persistent process that operates on these galaxies, we perform several checks to ensure that this is indeed the case. The galaxies in these populations are found in all parts of the simulation sphere (as discussed further in Section 3 and Figure 3) and not just at the edges of this volume where boundary effects can produce spurious effects. They also exhibit 100 per cent purity in DM, so that their evolution is not driven by interactions with massive low-resolution DM particles passing through them. Finally, as shown in the analysis below ( Figure 5) the reduction of DM is very gradual, rather than abrupt,  . The local 3D number density is calculated using an adaptive kernel density estimation method (see text in Section 3 for details). Recall that NewHorizon does not contain rich clusters and therefore the highest density regions in the simulation (i.e. the highest density percentile values) correspond to large groups, with halo masses of ∼10 12.9 M . The local densities of the DM deficient, DM poor and control galaxies are similar, consistent with the fact that these populations are all satellites. which indicates that this phenomenon is not a result of misallocation of particles between DM halos.

FORMATION OF DM DEFICIENT GALAXIES THROUGH STRIPPING OF DM IN TIDAL INTERACTIONS
We begin our analysis by exploring the local environment of our different satellite populations (DM poor, DM deficient and controls). Figure 3 shows the positions of these populations in the cosmic web. To explore local galaxy density more quantitatively, we follow Martin et al. (2018a) and define a 3-D local number density of objects around each galaxy. The local density is calculated using an adaptive kernel density estimation method 1 , where the width of the kernel used for multivariate density estimation is responsive to the local density of the region, such that the error between the density estimate and the true density is minimised (Breiman et al. 1977;Ferdosi et al. 2011;Martin et al. 2018a). The density estimate takes into account all galaxies with stellar masses above 10 8 M . In Figure 4 we show the density percentiles occupied by our different populations (higher percentiles indicate higher density regions).
Recall that NewHorizon does not contain rich clusters and therefore the highest density regions in the simulation correspond to large groups with halo masses of ∼10 13 M . Figures 3 and 4 indicate that the DM deficient and DM poor populations form in all parts of the Universe (note again that NewHorizon does not contain clusters or large voids so these environments are not probed here). While the DM deficient galaxies generally show a preference for the nodes of the cosmic web, the local densities of the DM deficient, DM poor and control galaxies are reasonably similar, consistent with the fact that these populations are all satellites. Not unexpectedly, the dwarf centrals reside in lower density environments, where the chances of interacting with and becoming the satellite of a larger galaxy are lower.
The evolution of galaxies is influenced by a combination of internal processes, like supernova (e.g. Kimm & Cen 2014) and AGN (e.g. Croton et al. 2006) feedback, and external processes such as tidal perturbations (e.g. Martin et al. 2019), mergers (e.g. Kaviraj 2014a,b;Kaviraj et al. 2019) and ram pressure (e.g. Hester 2006). Baryonic feedback and ram pressure are not capable of removing significant amounts of DM in galaxies, except in the very central regions through rapid expansion of gas (Governato et al. 2012;Teyssier et al. 2013). Furthermore, the steady stripping of DM, which drives the creation of the DM poor and DM deficient populations, requires a dynamical process, suggesting that tidal perturbations (possibly including mergers) are likely to be important in giving rise to these systems. In particular, interactions between a massive galaxy and a lower mass companion typically results in the stripping of material from the small companion. This is because, Figure 5. The rows show (from top to bottom) the evolution of the stellar mass, DM halo mass, the halo level (central [level 1] or satellite [level > 1]), perturbation index (PI) and the M halo /M ★ ratio of the galaxy in question. The PI is split into contributions from 'similar-mass' galaxies (those that have stellar masses within a factor of 3 of the galaxy in question), 'smaller galaxies' (those that have stellar masses less than a factor of 3 of the galaxy in question) and 'larger galaxies' (those that have stellar masses greater than a factor of 3 of the galaxy in question). The 'median dwarf PI' indicates the median PI experienced by galaxies of a similar mass (within 0.5 dex). In the bottom panel the dashed black line is the median halo to stellar mass relation and the shaded region is the 1 dispersion. The left-hand column shows a DM deficient galaxy, while the right-hand column shows a control galaxy. The dotted red lines indicate times when galaxy mergers, with mass ratios greater than 10:1, take place. while the same tidal force acts on both objects, the smaller companion is not as strongly bound and stripping typically takes place from the outskirts of the system where the depth of the gravitational potential well is shallowest (Smith et al. 2016). To quantify the effect of tidal perturbations, we follow Martin et al. (2019) and Jackson et al. (2020) to define a dimensionless 'perturbation index' (PI) that quantifies the strength of the ambient tidal field around a galaxy: where M halo is the halo mass of the galaxy in question, R vir is the virial radius of its DM halo, M i is the DM halo mass of the th perturbing galaxy and D i is the distance to the th perturbing galaxy.
We consider all perturbing galaxies within 3 Mpc of the object in question.
We use the PI to explore the trends in the tidal perturbations in our different populations and study how these perturbations may be driving the DM stripping in the DM poor and DM deficient populations. In Figure 5, we visually illustrate the evolution of two typical objects (selected randomly) in the DM deficient and control populations. The left-hand column shows the DM deficient galaxy, while the right-hand column shows the control galaxy. Recall that the control galaxies are satellites in which DM is not stripped and that the DM deficient galaxies are systems which have the lowest values of M halo /M ★ (Figure 1). These two populations therefore bracket the dwarf population as a whole. The rows show (from top to bottom) the evolution of the stellar mass, DM halo mass, halo level (central [level 1] or satellite [level > 1]), PI and the M halo /M ★ Figure 6. Evolution of the DM density profile in the DM deficient galaxy described in the left-hand column of Figure 5. The evolution is shown from the point at which the galaxy becomes a satellite, which is also the point at which the DM stripping starts ('max mass'), through to the end of the simulation. The DM stripping takes place in the outskirts of the dwarf where the gravitational potential well is shallowest and DM particles are more loosely bound. ratio of the galaxy in question. Satellite galaxies are defined in the usual way, as systems whose DM haloes have been accreted by a larger halo. The PI is split into contributions from 'similar-mass' galaxies (those that have stellar masses within a factor of 3 of the galaxy in question), 'smaller galaxies' (those that have stellar masses less than a factor of 3 of the galaxy in question) and 'larger galaxies' (those that have stellar masses greater than a factor of 3 of the galaxy in question).
While the DM deficient galaxy shows a steady increase in stellar mass (row 1), it exhibits sustained DM stripping after a lookback time of around 6 Gyrs (row 2). The stripping coincides with the galaxy transitioning from being a central to a satellite (row 3) and an increase in the PI from massive galaxies, even as that from smaller galaxies decreases (row 4). The DM stripping drives the M halo /M ★ ratio down, until it is below the region traced by the median ratio for galaxies which have stellar masses within ±0.5 dex (row 5). The principal difference between the DM deficient galaxy and its control counterpart is that, even after the control object becomes a satellite, the PI due to massive galaxies does not increase and the control galaxy does not exhibit significant DM stripping.
In Figure 6, we show the evolution of the DM density profile (calculated using all DM particles associated with the galaxy) of the DM deficient galaxy described in the left-hand column of Figure 5. The evolution is shown from the point at which the galaxy becomes a satellite (which is also the point at which the DM stripping starts), through to the end of the simulation. Not unexpectedly, the DM stripping typically takes place in the outskirts of the dwarf, where the gravitational potential well is shallower and DM particles are less well bound. The trends are identical in all DM deficient and DM poor galaxies.
In Table 1, we present the four largest PI contributions from individual companions, for the DM deficient and control galaxy in Figure 5, at the point where each galaxy becomes a satellite. The left hand table, which corresponds to the DM deficient galaxy, shows that ∼80 per cent of the total PI comes from one larger companion (which is the central that hosts this dwarf), with the next largest PI contribution being an order of magnitude smaller. For the control galaxy, on the other hand, the largest PI contribution, while also derived from a larger companion (again the host central), is a factor of 5 smaller than that in the DM deficient galaxy and contributes only 25 per cent of the total PI. Indeed, many smaller companions contribute PI values which are within a factor of 2 of that from the larger companion. Note that, in all cases, the larger companion which dominates the PI in the DM deficient and DM poor galaxies is the central that hosts the dwarf satellite in question. While Figure 5 illustrates the trends seen in typical galaxies in the DM deficient and control populations, Figure 7 summarises the differences in the PI from massive galaxies seen in our different satellite populations, after the galaxies become satellites. We do not show the PI from equal mass and smaller companions because these do not show any differences across our three populations (DM deficient, DM poor and control). The PI is measured halfway through the object's lifetime as a satellite (the trends are the same if the PI is measured at a different point in the lifetime of the galaxy after it turns into a satellite). DM deficient galaxies show, on average, both larger values for the total PI and the PI from larger companions, compared to their control counterparts, with the DM poor galaxies falling in between the two populations, as might be expected. This indicates that the DM stripping in the DM deficient and DM poor galaxies is indeed driven by stronger interactions with a massive (central) companion.
We proceed by exploring why the DM deficient dwarfs exhibit higher values of PI due to their massive companions. Figure 8 indicates that both the halo and stellar masses of the central that host the dwarfs are similar. Therefore, the mass of the central is unlikely to be driving the higher values of PI in these populations. However, given the strong dependence of the PI on the distance between galaxies (Equation 1), it is likely that the higher PI in DM deficient and DM poor galaxies is driven by orbits that bring them closer to their corresponding centrals.
In Figure 9, we first illustrate this graphically by plotting the orbits of four galaxies (selected to span the mass range in our study) in each of the DM deficient, DM poor and control populations around their centrals. The orbital distances are normalised by the virial radius of the central and orbits are shown from the point at which the dwarf in question becomes a satellite to the end of the simulation. It is clear that DM deficient galaxies have orbits that bring them significantly closer to their massive central than in their control counterparts. Figure 10 presents this more quantitatively, by comparing both the orbital distances (normalised by the virial radius of the central) in the period after individual galaxies become satellites, and the minimum distances between the satellites and centrals during these orbits. DM deficient dwarfs spend most of their orbits at significantly smaller distances from their centrals compared to their control counterparts, with the DM poor galaxies lying in between these two populations. The same patterns are apparent in the minimum orbital distances. Recalling that the DM deficient, DM poor and control populations reside in similar environments ( Figure 4) and orbit around centrals of similar mass (Figure 8), the larger PI values from larger galaxies in these populations are therefore simply driven by orbits which bring these galaxies closer to their massive central companions. The degree of DM stripping is correlated with Figure 7. Perturbation index (PI) from massive companions (left) and total PI (right) for our satellite different populations. The PI is measured halfway through the lifetimes of the objects as satellites. DM deficient galaxies show both larger values of PI from massive companions and total PI compared to their control counterparts (with the DM poor galaxies falling in between these two populations).   these orbital distances, with DM deficient population (which exhibits the largest amount of stripping) spending their orbital time at much smaller distances than their other counterparts.
Given that the DM deficient galaxies are in tight orbits around nearby massive companions, it is worth considering how long these dwarfs may survive. We explore this by considering the evolution of the DM deficient population (selected in an identical way) at = 0.7 i.e. around 3.5 Gyrs before the epoch ( = 0.25) at which the analysis above is performed. The stellar mass distribution of DM deficient galaxies at both epochs is similar. We find that only 30 per cent of DM deficient galaxies that exist at ∼ 0.7 still survive at ∼ 0.25. This indicates that the creation of DM deficient galaxies is a constant process over cosmic time. In other words, satellites that are in close orbits are not only stripped of their DM, but many also do not survive after the stripping starts as they are accreted by their larger companions. Thus, the DM deficient population at a given redshift are largely systems that have formed recently enough that they still exist in the simulation at that epoch.
We also consider whether dwarfs that may be candidates for being DM deficient systems could potentially be identified using Figure 11. -band mock images of two example systems that bracket the types of interactions that lead to DM stripping. In all images, the DM deficient galaxy in question is at the centre of the image and indicated by the red arrow. The blue circle shows the virial radius of the DM deficient galaxy. The sequence (where time moves forward from left to right) shows ∼3 Gyrs of evolution. The top row shows a two body interaction, while the bottom row shows a more complex interaction where the dwarf interacts with a larger companion which dominates a small group. In both cases, the dwarf undergoes significant DM stripping and ends up as a DM deficient galaxy.  Figure 5, at the point where the galaxy becomes a satellite. Columns in each table show (from left to right) the PI contributed by the individual companion, the fraction this represents of the total PI, the cumulative fraction of PI contributed by this, and previous rows and the mass ratio of the companion and the dwarf galaxy in question. The left hand table, which corresponds to the DM deficient galaxy, shows that ∼80 per cent of the total PI comes from one larger companion with the next largest PI contribution being an order of magnitude smaller. For the control galaxy the largest PI contribution, while also derived from a larger companion is a factor of 5 smaller than that in the DM deficient galaxy and contributes only 25 per cent of the total PI, with many smaller companions contributing PI values which are within a factor of 2 of that from the larger companion.
quantities that are readily available in imaging survey data. As described above, the process that drives the creation of these objects are tidal interactions with more massive companions on very close orbits. In the appendix we show a version of the right-hand panel of Figure 10 without normalising the orbital distances of the dwarfs by the virial radius of the massive companion ( Figure A1), because virial radii are not measurable quantities in imaging data. Combining Figures 8,10,11 and A1 indicates that dwarfs that are found close to massive companions with M ★ > 10 10 M (Figure 8) at distances of less ∼150 kpc ( Figure A1) and show stellar tidal features ( Figure 11) are likely to be good candidates for being DM deficient systems. As is typical of interactions between massive galaxies and dwarf companions (e.g. Kaviraj 2010Kaviraj , 2014b, the tidal features (e.g. the ones visible in Figure 11) are faint with surface brightnesses typically fainter than 29 mag arcsec −2 . This suggests that finding large samples of DM deficient candidates would ideally re-quire deep wide-area surveys, such as LSST (Robertson et al. 2019), which have limiting surface-brightnesses that are fainter than such values. We complete our study by considering our results in the context of recent observational studies. DM deficient galaxies form in NewHorizon via tidal interactions in close orbits with a more massive (central) companion. This appears consistent with the recent studies by van Dokkum et al. (2018a) and van Dokkum et al. (2019), who find multiple DM deficient dwarf galaxies in group environments. These galaxies are likely to have been subjected to strong tidal forces that would have stripped their DM halo (see e.g. the lower panel of Figure 11 which shows a possible analog of this in NewHorizon). The formation of DM deficient dwarfs via tidal interactions also appears consistent with the excess number of globular clusters (GCs) reported in these systems (e.g. Fensch et al. 2019a;Müller et al. 2020). Since tidal interactions between dwarfs and larger companions can trigger enhanced GC formation (e.g. Fensch et al. 2019b;Carleton et al. 2020;Somalwar et al. 2020), systems like DM deficient dwarfs, that undergo strong tidal interactions, could be expected to show an excess number of GCs. Note, however, that the resolution of NewHorizon is not sufficient for us to directly study the formation of GCs.
The formation channel outlined in this paper appears less wellaligned with the findings of Guo et al. (2019), who suggest that most of their DM deficient galaxies lie at distances greater than three times the virial radius of the nearest group or cluster. However, it is worth noting that the nearest groups and clusters in Guo et al. are significantly more massive than those in our study. It is possible that the tidal forces required to strip dwarfs of their DM can be produced at larger distances around much more massive groups. Furthermore, without deep images it is difficult to identify tidal features which are the tell-tale signatures of the tidal stripping process that creates DM deficient galaxies.

SUMMARY
In the standard ΛCDM paradigm, dwarf galaxies are expected to be dark-matter-rich because their shallow gravitational potential wells make it easier for processes like stellar and supernova feedback to deplete their gas reservoirs. This results in a reduction of star formation at early epochs, leaving these objects with relatively high DM fractions. However, recent observational work suggests that some local dwarfs exhibit DM fractions as low as unity, around 400 times lower than what is expected for systems of their stellar mass. The existence of such DM deficient galaxies appears to contradict our classical expectations of the DM properties of dwarf galaxies, potentially bringing the validity of the standard paradigm into serious question. Understanding the origins of these galaxies, using a high-resolution cosmological simulation which can make realistic statistical predictions of dwarf galaxies, is, therefore, a key exercise.
Here, we have used the NewHorizon simulation to explain the formation of DM deficient galaxies. We are able to perform this exercise, for the first time, in a statistical fashion, as the cosmological volume of NewHorizon allows us to study large numbers of dwarf galaxies, while its high spatial resolution enables us to resolve these systems with the requisite detail. We have shown that interactions between massive central galaxies and dwarf satellites can drive sustained and significant stripping of DM from the dwarfs, which reduces their DM content. The level of stripping is determined by the details of the orbit, with dwarfs that are heavily stripped typically spending significant fractions of their time in relatively close proximity to their corresponding massive central, after they turn into satellites. DM stripping is responsible for a large dispersion in the stellar-to-halo mass relation in the dwarf regime, with ∼30 per cent of dwarfs (i.e. the populations we have labelled as 'DM deficient' and 'DM poor') scattering off the tight locus traced by the dwarf centrals and those dwarf satellites that remain unstripped.
In extreme cases, this DM stripping produces dwarfs which exhibit M halo /M ★ ratios as low as unity, consistent with the findings of recent observational studies. Given their close orbits, a significant fraction of DM deficient dwarfs will merge with their massive companions and disappear from the galaxy population (e.g. ∼70 per cent of such dwarfs will merge over timescales of ∼3.5 Gyrs). But the DM deficient population is replenished by new interactions between dwarfs and massive companions. It is worth noting that our results are robust with respect to the details of the sub-grid recipes implemented in NewHorizon, as this formation mechanism is principally driven by gravitational forces.
The formation of DM deficient galaxies through tidal stripping of DM, as hypothesised here, appears consistent with recent observational studies (e.g. van Dokkum et al. 2018a), which are located in similar environments to the DM deficient galaxies in NewHorizon.
Observations of an excess of GCs in these galaxies, although not directly testable in NewHorizon, also appear to support this formation mechanism. The results of our study offer a route to identifying dwarf galaxies that may have low DM content, purely from data that is typically available in imaging surveys. Dwarfs that are found close to massive companions with M ★ > 10 10 M , at distances less than ∼150 kpc, and show stellar tidal features, are likely to be good candidates for being DM deficient systems. The faintness of the tidal features produced by such interactions (typically fainter than 29 mag arcsec −2 ) suggests that future deep wide surveys like LSST could be used to identify large samples of such DM deficient dwarf candidates.
Our study demonstrates that stripping of DM via a tidal interaction, a process that takes place in all environments, can routinely create dwarfs that have DM fractions that deviate significantly from their initial values in the early Universe and, in extreme cases, produces systems that are DM deficient. The existence of such galaxies is therefore an integral feature of galaxy evolution in the standard ΛCDM paradigm and their existence is not in tension with the predictions of this model. Wetzstein M., Naab T., Burkert A., 2007, MNRAS, 375, 805 Xie L., Gao L., 2015, MNRAS, 454, 1697van Dokkum P., et al., 2018a van Dokkum P., Danieli S., Cohen Y., Romanowsky A. J., Conroy C., 2018b, ApJ, 864, L18 van Dokkum P., Danieli S., Abraham R., Conroy C., Romanowsky A. J., 2019, ApJ, 874, L5 van den Bosch F. C., Tormen G., Giocoli C., 2005, MNRAS, 359, 1029 Figure A1 shows the orbital distances of dwarfs around their massive centrals in our different satellite populations. This figure is a version of the right-hand panel of Figure 10 without the distance being normalised by the virial radius of the halo of the massive central. This paper has been typeset from a T E X/L A T E X file prepared by the author.