Ultra-diffuse galaxies without dark matter

TL;DR

This paper proposes a high velocity galaxy collision model to explain ultra-diffuse galaxies with little dark matter, predicting globular cluster formation, high relative velocities, and detectable dark halos with relic stars.

Contribution

It introduces a novel collision-based model to account for dark matter-deficient ultra-diffuse galaxies, linking their properties to early universe dynamics.

Findings

Overpressured dense clouds form globular clusters.

High relative velocities in protogroup environments.

Dark halos with relic low metallicity stars may be detectable.

Abstract

I develop a high velocity galaxy collision model to explain a rare but puzzling phenomenon, namely the apparent existence of ultra-diffuse galaxies with little dark matter. Predictions include simultaneous triggering of overpressured dense clouds to form luminous old globular clusters, a protogroup environment to generate high relative velocities of the initially gas-rich galaxies in the early universe, and spatially separated dark halos, possibly detectable via gravitational lensing and containing relic low metallicity stars with enhanced [alpha/Fe] at ultralow surface brightness.

Equations

$$logf(>v_{sub})=-{\left(\frac{v_{sub}/v_{200}}{1.6}\right)}^{3.3},$$

Full text

1 Introduction

Ultra-diffuse galaxies (UDGs) may have been discovered that have essentially no dark matter, at least in excess of their stellar content: one has been extensively studied [van Dokkum et al. 2018], and a second has recently been reported. Both are in the outskirts of the NGC 1052 group [van Dokkum et al. 2019)].

The existence of such dark-matter deficient UDGs is disputed on the grounds of uncertain kinematic tracers [Laporte et al. 2019] and distance estimators [Trujillo et al. 2018, Nusser 2019], although these arguments seem not to be definitive either for kinematics [Danieli et al. 2019] or for distance [van Dokkum et al. 2019]. The distance issue provides the outstanding uncertainty in assigning dark matter mass, but should be resolvable with new HST data.

Suppose such DM-deficient UDGs exist. I argue that this is a challenge for galaxy formation theory. Our most likely candidates, dwarfs formed via gas condensation in tidal tails, TDGs, are known to be deficient in dark matter. However even aged counterparts of typical tidal dwarfs would be more gas-rich and significantly brighter than the UDGs [Lelli et al. 2015].

Generation of the extremely low surface brightnesses observed requires either the formation of stars in tidal dwarfs, observed to be efficient [Fensch et al. 2019], followed by strong tidal heating, which seems a contrived sequence of events, or a very low efficiency star formation rate in the first place. Moreover, the associated bright globular clusters are an important clue that is suggestive of a somewhat more exotic formation pathway [van Dokkum et al. 2018], as proposed in the mechanism that I describe below.

There is also a kinematic argument against a tidal interpretation of DM-deficient UDGs. Tidal heating of compact dwarfs indeed offers a means of removing dark matter outside a scale length [Peñarrubia et al. 2010]. If the dwarf is cored, this can even result in formation of a UDG [Ogiya 2018]. In this case, the SFE would be normal but the observed low surface brightness is due to tidal heating.

One consequence would be predominantly radial stellar orbits. However, any gradient, and in particular the ensuing relaxation to the observed cold and apparently relaxed kinematics, is claimed to not be supported by the dynamical data and modeling of orbital parameter space in the UDGs [Wasserman et al. 2018]. Moreover, low surface brightness features are ubiquitous in the NGC 1052 group and do not support the case for tidal interactions of the two UDGs with their possible hosts [Müller et al. 2019]. In fact the dynamical data is far too sparse in terms of numbers of data points to reach any definitive conclusion about the role of tidal interactions.

The allegedly dark matter-deficient UDGs are relatively luminous for low surface brightness dwarfs, and one might also consider initial conditions as a formation pathway, due to high initial spin [Amorisco & Loeb 2016]. Their ultra-diffuse nature may also be due to tidal heating [Carleton et al. 2019] or to early supernova-driven gas outflows [Di Cintio et al. 2019]. However these mechanisms do not obviously account for the dark matter deficiency, nor most significantly for the bright globular clusters.

The existence of dark matter-deficient UDGs is a rare phenomenon, and I argue here that it is due to a mini-Bullet cluster-like event, involving the high velocity collisions of gas-rich dwarfs occurring at early epochs in a protogroup or protocluster environment. Gas dissipation and low efficiency star formation, along with DM separation from the baryonic gas component and consequent expansion of the residual stellar systems, are a natural consequence of high velocity infall and collisions between gas-rich dwarfs.

Ram pressure stripping, generally more significant than tidal stripping in the group environment [Jiang et al. 2018], provides a means of depleting the low density gas reservoir whose accretion ordinarily enhances star formation in isolated galaxies. At the same time, dense self-gravitating clouds within the colliding systems are highly overpressured and collapse to form protoglobular-like star clusters at relatively high star formation efficiency. I give simple arguments below to support these conjectures.

2 High velocity collisions of gas-rich dwarf galaxies

Collisions and mergers are common between dwarf galaxies even at high redshift. The Fornax dwarf is a classic example of past mergers as evidenced in shells [del Pino et al. 2017] and complex substructures [Wang et al. 2018]. The ultra-diffuse dwarfs require special initial conditions. I suggest here that they, and especially the supposedly dark matter-free UDGs, are the consequence of high velocity gas-rich collisions in the past, typically in proto-group environments. In such conditions, the induced star formation is highly inefficient. Hence if the colliding dwarfs had not previously undergone significant star formation, only UDG-like systems would be produced. Moreover at the highest collision velocities envisaged ($v_{coll}\sim 300$ km/s), the non-dissipative dark matter would be well separated from the dissipative gas components that eventually merge and form stars, and the resulting decrease in self-gravity further contributes to expansion of the newly formed stellar system. Nor is the present mechanism limited only to dwarfs: high velocity collisions of more massive gas-rich systems are equally capable of forming UDGs.

2.1 Star formation

Star formation is generally inefficient, at the 1% level in GMCs and in nearby star-forming galaxies. This is directly measured for galaxies via the Schmidt-Kennicutt relation. However the observed diversity in the star formation efficiency (SFE) of individual GMCs ranges from of order 50% in dense star-forming cloud cores to 0.01% in the most quiescent giant molecular clouds [Grisdale et al. 2019]. Understanding this variance is where all the physics resides.

A promising approach to understanding the diversity of SFEs models supersonic turbulence in the presence of magnetic fields. This exponentially reduces the SFE [Padoan et al. 2012]. The SFE per cloud free-fall time is likely to be very low because the high velocity collision/merger generates turbulence and shear in the gas. Typical cloud collisions are oblique and induce shear. This is very effective at suppressing fragmentation in the diffuse gas [Anathpindika et al. 2018]. The local dynamical time will be much less than the local free-fall time in colliding clouds.

The SFE has been shown to be exponentially suppressed in such situations, provided that interstellar magnetic fields are initially present to cushion the impact. The fields are amplified by stretching and compression according to MHD simulations [Padoan et al. 2012]. The SFE is found to be reduced by a factor $\rm exp(-t_{ff}/t_{dyn}),$ where $t_{ff}=\sqrt{3\pi/32G\rho_{cl}},$ $t_{dyn}=L/2\sigma_{turb},$ $\rho_{cl}$ is the mean density, $L$ is the cloud size, and $\sigma_{turb}$ is the 3-d turbulent velocity dispersion in the cloud.

2.2 Application to UDGs

There are four key issues to be explained in UDGs. I focus on the two examples which allegedly lack dark matter.

A. Why do some UDGs have no DM?

B. Why is the SFE so low?

C. Why do they have large core radii and low surface brightnesses?

D. And why are there many bright globular star clusters?

The mini-Bullet cluster hypothesis potentially explains all four issues.

Gas dissipates during a gas-rich merger in analogy with cold cloud precipitation from the circumgalactic medium into the galaxy. Ensuing cooling and star formation can occur once the gas cooling time-scale is less than 10 times the local free-fall time [Voit et al. 2015]. Hence the gas agglomerates and eventually is Jeans unstable. The Jeans mass increases by a factor $\mathcal{M}^{2}.$ The high Mach number $\mathcal{M}$ and low gas density, more specifically the large ratio $t_{ff}/t_{dyn},$ guarantees low SFE.

Kelvin-Helmholtz instabilities are important during the gas-rich collision of merging galaxies. The ensuing turbulence leads to a large core radius for the distribution of triggered star formation. Disruption of clouds by Kelvin-Helmholtz instabilities is suppressed at high Mach number [Scannapieco and Brüggen 2015], hence star formation is not completely quenched.

High column density clouds are not significantly accelerated and are compressed into dense, potentially star-forming filaments [Brüggen and Scannapieco 2016]. Kelvin-Helmholtz mixing between the hot wind and cold cloud helps preserve cold gas clumps [Gronke and Oh 2018]. The role of self-gravity however has not been incorporated into these simulations.

For SFE suppression, one needs a combination of long $t_{ff}$ and short $t_{dyn}$. Consider the Central Molecular Zone of our galaxy. Here the inferred turbulence Mach number $\mathcal{M}\sim 10$ [Dale et al. 2019] and the SFE is low [Lu et al. 2019].

Comparison of $t_{cool}$ with $t_{dyn}$ in high velocity gas cloud collisions, eg with Mach numbers in the range 10-100, suggests that only the densest clouds cool within a dynamical time. High velocity, of order 100 km/s collisions, are needed for inefficient star formation in gas-rich dwarfs. This points to dwarf formation in protogroups or especially in protoclusters as providing high velocities due to gas-rich galaxy infall into a gas-rich environment.

If the infall velocity is too high, cooling becomes too inefficient, e.g. at collision velocity $v_{coll}\sim 1000$ km/s for gas aggregation and star formation. Group environments are the sweet spot, possibly also in protoclusters. The infalling galaxies need to be gas-rich, hence the protogroup/protocluster environment is optimal.

The combination of low SFE and expansion should account for the low surface brightnesses. Firstly, a factor of 10 or more comes from the reduced SFE. One can infer this from the galaxy main sequence or the Schmidt-Kennicutt relation. The SFE is expected to be proportional to the ratio of $t_{dyn}$ to $t_{ff}$, which is of order \sigma_{turb}/v_{coll}\lower 2.15277pt\hbox{;\buildrel<\over{\sim};}0.1. So this gives a total reduction of up to 3 magnitudes in surface brightness.

Secondly, the orbital momentum adiabatic invariant implies that the outflow has a dramatic effect on the final distribution of newly formed stars. I assume that $r\sigma_{\ast}$ is constant, where $r$ is the stellar orbit perihelion and $\sigma_{\ast}$ is the stellar velocity dispersion. Hence for a cloud expansion velocity $\sim 10\sigma_{*}$, one can reduce the final surface brightness by up to $\sim 1000.$

2.3 Globular cluster formation

It is a challenge to generate extremely low surface brightness dwarfs which nevertheless have significant populations of (possibly anomalously bright) globular clusters. High pressure environments are essential to globular cluster formation [Elmegreen and Efremov 1997]. The extreme high pressure environment $p_{coll}$ achieved in a fast collision should lead to enhanced masses of newly formed globular clusters at a given cloud density.

For example, the mass of a self-gravitating cloud is $M_{cloud}=(9/16)(\pi)^{-1/2}(p_{coll}/G)^{3/2}\rho_{cl}^{-2}.$ Cloud collision velocities in excess of 50-100 km/s are argued to account for the dynamical and optical characteristics of globular clusters [Kumai et al.1993] and confirmed in more recent simulations [Bekki et al. 2004].

Moreover, the shear induced by encounters imparts angular momentum, and another consequence is that enhanced shear drives fission of dense molecular clouds. For example, binary globular clusters constitute about 20% of the mostly young globulars in the LMC [Priyatikanto et al. 2019] and likely formed in high velocity cloud collisions [Fujimoto and Kumai 1997]. They are destined to merge via torquing in the local tidal field [Priyatikanto et al. 2016] to further enhance the population of massive globular clusters and potentially account for the puzzling age gap in LMC globulars [Bekki et al. 2004]. Collision-enhanced pathways boost the numbers of anomalously bright globular clusters as possibly observed in the two DM-free UDGs. Numerical simulations of colliding gas streams are found to provide a plausible formation mechanism for dark matter-free globular star clusters, in a study that appeared after this paper was initially submitted [Madau et al. 2019]. Observations are equally suggestive. As many as 60 extraplanar star-forming HII regions with masses $10^{3}-10^{5}\rm M_{\odot}$ have been mapped outside the optical disk in the gas tidally stripped from a single disk galaxy, likely progenitors of globular clusters or ultra-compact dwarf galaxies [Boselli et al. 2018].

Ram pressure stripping indeed leads to induced star formation as in the jelly fish phenomenon [Vulcani et al.2018]. The effects of a high velocity collision should enhance such effects, reducing the SFE in diffuse gas but enhancing self-gravity and hence fragmentation in dense clouds

Dense clouds are not significantly accelerated by ram pressure. There is a trade-off in their eventual fate as Kelvin-Helmholtz instabilities on cloud boundaries lead to mixing and heating [Begelman and Fabian 1990] with consequent stabilization against gravitational fragmentation. However inclusion of self-gravity into the simulations would argue strongly for compression and triggering of star formation, as inferred from simulations of jets [Gaibler et al. 2012] and winds [Dugan et al.2017]. Thermal conduction most likely is not important in suppressing the instabilities once magnetic fields are included [McCourt et al. 2018].

2.4 Frequency

The dwarf galaxy merger rates are low at the present epoch, of order 0.03/Gyr according to recent simulations [Rodriguez-Gomez et al. 2015]. Some occur as evidenced by morphological distortions such as shells but these are relatively rare, although close dwarf pair frequency increases with reduced stellar mass [Besla et al. 2018]. However redshift scaling suggests that they will be much more common at higher redshift, when galaxies are gas-rich. For example, over a wide range of masses, the major merger fraction increases as $\sim(1+z)^{6}$ to $z\sim 2$, peaking near the maximum in star formation rate density, and then flattens towards higher $z$ [Ventou et al. 2017]. For dwarfs, some 10% experience major mergers within the host group virial radius since $z\sim 1$ [Deason et al. 2014]. Faint shells are seen at several effective radii around dwarfs in a deep survey of the Virgo cluster, indicative of high velocity interactions and recent equal mass gas-free mergers [Paudel et al. 2017]. This suggests that such interactions should have been frequent at early epochs when assembly is dominant in a gas-rich environment at first infall beyond the group or protocluster virial radius.

To try to crudely quantify the expected collision velocity, I assume that the probability distribution of finding the most massive subhalos with a velocity larger than $v_{sub}$ is fit at $z\sim 0.5$ by

[TABLE]

where $v_{200}$ is the cluster velocity dispersion [Hayashi and White 2006]. This calculation, originally performed for the Bullet cluster and assuming gaussianity, underestimates the high velocity tail, which is effectively nongaussian [Bouillot et al. 2015]. Rare collisions at 2-3 times the mean protogroup/cluster velocity should suffice to maintain a low SFE while at the same time maintaining a high enough dissipation rate to separate the gas from the weakly interacting DM concentration. One requires protoclusters and protogroups containg such infalling clouds to be sufficiently rare in terms of gaussian theory in order to have gas clouds infalling without previously making excessive numbers of stars.

2.5 The IMBH connection

Quenching and gas outflows are likely to be driven by central intermediate mass black hole (IMBH) AGN in dwarfs, although the details are still poorly known. Angular momentum transfer leads to extreme gas densities. IMBH formation is increased as fragmentation is reduced. Shear is further increased in high velocity mergers, and this in turn drives Kelvin-Helmholtz instabilities. These effects can also lead to suppression of fragmentation [Vietri et al. 1997].

In fractal clouds, effects of compression allow retention of high density nuclei that survive and allow mass loading into the hot outflows [Banda-Barragán et al. 2019]. However radiative cooling eventually results in fragmentation until the clouds are fully dissolved in the hot wind [Sparre et al. 2019]. Hence IMBH formation occurs without excessive fragmentation into stars.

IMBH may be ubiquitous in dwarfs, as suggested by theoretical considerations [Silk 2017] and by recent surveys especially using IR diagnostics [Marleau et al. 2017, Satyapal et al. 2018]. It is possible that IMBH form before significant fragmentation into stars. If IMBH indeed form early, they would help suppress Pop III star formation via generation of UV Werner band flux. Various alternative schemes have been suggested for suppressing fragmentation and early star formation in dwarfs, including disk gravitational stability [Inayoshi and Haiman 2014] and magnetic disk levitation [Begelman and Silk 2017].

3 Discussion

I have argued that high velocity shocks and associated turbulence both lower the mean SFE and simultaneously overpressurize dense gas clumps to form compact star clusters. The collision model requires the stars and the globular clusters to have similar old ages, around 10 Gyr corresponding to the gas-rich phase of the newly formed dwarfs. Violent star formation is expected to induce $\alpha/Fe$-rich chemistry, because only SNII will play a role in enrichment. There will not be time for SNIa superovae to contribute to stellar metallicities, hence one expects both the UDGs and the associated globular clusters, formed contemporaneously in the present model, to have $[\alpha/Fe]\sim 0.3$ and [Fe]\lower 2.15277pt\hbox{;\buildrel<\over{\sim};}-1 in the UDGs that lack DM.

Some $\sim 10\%$ of the stars are expected to be ejected in the GC mergers, according to the simulations, and UDG halos should contain some old $\alpha-$rich metal-poor stars. One cannot resolve individual stars but the globular clusters in the UDGs can be assessed for age, metallicity and any $\alpha$-element excess by population synthesis analysis of stacked spectra [van Dokkum et al. 2018].

The frequency of tidal tail galaxies as well as of UDGs should be enhanced in groups where galaxy mergers and collisions are likely to be prevalent. The gas-rich environment at early epochs suggests that protogroups may be especially promising for forming UDGs because one has a gas-rich environment, an enhanced frequency of dwarfs, and a high velocity tail in the galaxy velocity distribution. UDGs without DM should therefore be old and in dense environments if of collisional origin.

In summary, if indeed UDGs exist with little dark matter, there are at least two possible mechanisms for explaining their origin. These are origin via tidal tail instability in the vicinity of a massive host galaxy or via high velocity collisions of dwarfs. A unique aspect of the latter model is that it provides a plausible way of forming UDGs with associated globular clusters of enhanced brightness.

The predicted presence of displaced dark halos that should contain residual metal-poor stars is potentially detectable by weak lensing. Another is the morphology of the globular cluster distribution surrounding the two candidate dark matter-deficient UDGs in the NGC 1052 group. Yet another relic would be the displaced gas that has mostly not formed stars. Presumably, this is sufficiently diffuse to remain hot and only be accessible by x-ray observations or absorption towards distant quasars.

A third possibility would involve a supermassive black hole (SMBH), hosted by the central galaxy and fueled by gas accretion and generating a powerful jet or outflow. Star formation is plausibly triggered in overpressured dense halo clouds. This is observationally plausible, cf. local systems such as Minkowski’s object [Fragile et al. 2017] and Cen A [Salomé et al. 2017], along with more remote examples [Cresci and Maiolino 2018]. However, an improved understanding of massive cloud survival is needed to decide whether jet entrainment of ambient gas clouds is indeed followed by compressionally-triggered star formation and formation of UDGs, or rather by cloud erosion.

The presence of a SMBH in the host galaxy NGC 1052 [Fernández-Ontiveros et al. 2019] of the two likely DM-free UDGs may support the possible role of early jet-triggering. Morphology and kinematics of the UDGs, and especially of their associated globular clusters, could help decide this issue.

IMBH outflows have recently been detected in dwarfs that contain AGN [Manzano-King et al. 2019]. The outflows are potential creators of UDGs. AGN outflows in the group environment can be effective at several virial radii in gas removal from dwarfs [Dashyan et al. 2018] but could also trigger star formation in dense gas clumps. Self-gravity has not hitherto been included in the simulations to properly address this point.

High velocity clouds are another environment where star formation may have occurred inefficiently as in UDGs. Recent detections of associated ultra-faint galaxies with comparable amounts of gas and old stars, but no evidence of recent star formation [Janesh et al. 2019], suggest that these systems that are infalling to the MWG or Local Group might be relics of a high velocity encounter that induced star formation.. Only the residual gas core remains along with associated stars that are diffusely distributed. A similar phenomenon has been found for an ultrafaint galaxy detected in deep imaging of the Virgo cluster [Bellazzini et al. 2018]. These are generally old stellar systems, and so it is likely that the observed gas is a relic of a far more extensive gas component, favoring low star formation efficiency.

Primordial black holes (PBHs) of stellar mass are a currently popular form predicted for a component of dark matter via explanations of the LIGO event rates [Ali-Haïmoud et al. 2017]. Destruction of UDGs has been suggested [Brandt 2016] as an argument against stellar mass PBHs being a dominant component of the dark matter. However it is possible that PBHs, if sufficiently numerous, could equally create UDGs via their dynamical effects on dwarf galaxies.

With improved treatment of self-gravity in numerical simulations, survival of UDGs is an option that should be considered. Simulations of the Fornax dwarf galaxy find that the observed globular clusters are not necessarily incompatible with a NFW dark matter profile [Boldrini et al. 2019], in contrast to earlier discussions of the core/cusp problem for dark matter [Bullock and Boylan-Kolchin 2017]. The action of dynamical friction leading to infall and merging of globular clusters is sensitive to initial orbital parameters, which in turn come from cosmological simulations.

More generally, the effects of tidal heating can be significant. They are argued to play an important role in reducing the number of dwarfs predicted in the Local Group in the standard CDM model [Garrison-Kimmel et al. 2017]. It remains to be seen whether such effects could also lead to survival of objects morphologically resembling UDGs.

Acknowledgements

I thank Annette Ferguson, Sadegh Khochfar and Maxime Trebitsch for discussions.