Elsevier

New Astronomy Reviews

Volume 57, Issues 3–4, September–October 2013, Pages 52-79
New Astronomy Reviews

Internal kinematics and dynamical models of dwarf spheroidal galaxies around the Milky Way

https://doi.org/10.1016/j.newar.2013.05.003Get rights and content

Abstract

We review our current understanding of the internal dynamical properties of the dwarf spheroidal galaxies surrounding the Milky Way. These are the most dark matter dominated galaxies, and as such may be considered ideal laboratories to test the current concordance cosmological model, and in particular provide constraints on the nature of the dominant form of dark matter. We discuss the latest observations of the kinematics of stars in these systems, and how these may be used to derive their mass distribution. We tour through the various dynamical techniques used, with emphasis on the complementarity and limitations, and discuss what the results imply also in the context of cosmological models. Finally we provide an outlook on exciting developments in this field.

Introduction

With absolute magnitudes ranging from MV-9 to -13.5 and central surface brightness between μ0,V22.527 mag arcsec−2, the “dwarf spheroidals” (dSphs) are the faintest and lowest surface brightness galaxies known to date, beaten only by the relatively recently discovered ultra-faint dwarf galaxies (UFDs).

Although of dull appearance, dSphs reveal an unexpectedly complex stellar populations mix (for a recent review see Tolstoy et al., 2009) that makes them very useful laboratories for understanding star formation and chemical enrichment processes at the faint end of the galaxy luminosity function. In terms of their internal dynamics, they might well be key in constraining the nature of dark matter. Even though the very first measurement of the line-of-sight velocity dispersion of a dSph was based on just 3 carbon stars in Draco (Aaronson, 1983), it already hinted at a dynamical mass-to-light ratio about one order of magnitude larger than for globular clusters. Subsequent works have confirmed this result using larger samples that included red giant stars (e.g. Armandroff and Da Costa, 1986, Aaronson and Olszewski, 1987, Hargreaves et al., 1994a, Hargreaves et al., 1994b, see also Sections 2 Observed kinematics, 3 Dynamical modeling). If in dynamical equilibrium, dSphs have the highest mass-to-light ratios known to date,1 with M/L100 s M/L.

In the remainder of the Introduction we describe the latest observational surveys of the kinematics of dSphs, place these systems in a cosmological context and briefly discuss why most of these systems may be considered to be in dynamical equilibrium. In Section 2 we describe the determination of the kinematic properties of dSphs from spectroscopic samples of individual stars. In Section 3 we review the methods used to model the internal dynamics of spheroidal systems and discuss their application to dSphs around the Milky Way. We discuss possible future developments in Section 4, and in Section 5 we briefly summarize the current status of the field.

Determining the mass content of a system requires observations of the kinematics of suitable tracers. Since dSphs are devoid of a neutral interstellar medium, the only tracers available are stars. Because of their distance, to-date all measurements of their internal kinematics are based on line-of-sight velocities. The stars accessible for spectroscopic observations with current facilities are resolved for systems within the Local Group, since there is no crowding because of the low surface brightness of these galaxies. In this review, we concentrate on the dwarf galaxies that are satellites of the Milky Way (hereafter, MW). We refer the reader to Walker (2013), for a nice and comprehensive historical excursus on the growing kinematic samples for MW dSphs.

The first attempt to go beyond the determination of a global l.o.s. velocity dispersion of a dSph was made by Mateo et al. (1991b) using a 2.5 m telescope. These authors measured the kinematics of 30 stars in the Fornax dSph, in the center and in a field located at about two core radii. This first l.o.s. velocity dispersion “profile” turned out to be approximately flat, and this led the authors to suggest that it could be due to a dark halo spatially more extended than the visible matter. These results opened a whole line of investigation to measure l.o.s. velocity dispersion profiles of dSphs around the Milky Way, and to use these to determine their dark matter (hereafter, DM) distribution, orbital structure and dynamical state.

The samples of l.o.s. velocities collected in the 90s contained a few dozens of individual members per dSph (e.g. Mateo et al., 1991b, Mateo et al., 1998, Hargreaves et al., 1994a, Hargreaves et al., 1994b, Olszewski et al., 1996, Queloz et al., 1995). An increase in sample size became possible with multi-object spectrographs such as the KPNO/4 m Hydra multi-fiber positioner (100 members in Draco and Ursa Minor, Armandroff et al., 1995), and the AF2/Wide Field Fibre Optical Spectrograph on the WHT (150 members in Draco, Kleyna et al., 2001).

In the second half of the 2000s several large spectroscopic surveys of the classical MW dSphs were carried out. In broad terms we can distinguish them in 3 main “streams”:

  • 1.

    Surveys that obtained l.o.s. velocities for typically 100–150 members per dSph, with a large success ratio of dSph members/target stars thanks to an optimized target selection using Washington photometry (M, T2, and DDO51 filters, e.g. Majewski et al., 2005, Muñoz et al., 2005, Muñoz et al., 2006, Westfall et al., 2006, Sohn et al., 2007). These have made use of Keck/HIRES, Magellan/MIKE, CTIO/Hydra and Keck/DEIMOS.

  • 2.

    Surveys to obtain several 100s of stars per dSph to determine both the internal kinematics and the metallicity distribution from Ca II triplet lines using intermediate resolution spectroscopy. This includes the Dwarf Abundances and Radial velocities Team (DART, PI: Tolstoy) (∼570, 800, 170 members for the Sculptor, Fornax, Sextans dSphs, respectively, at R  6500 over the wavelength range 8200–9400 Å, Tolstoy et al., 2004, Tolstoy et al., 2006, Battaglia et al., 2006, Battaglia et al., 2008b, Battaglia et al., 2011, Helmi et al., 2006, Starkenburg et al., 2010; and program 171.B-0520 (PI: Gilmore) “Towards the Temperature of Cold Dark Matter” (500, 170 members for the Carina and Leo II dSphs with the same set-up as for the DART data-set, Koch et al., 2006, Koch et al., 2007a). These have taken advantage of the VLT’s large collecting area coupled to the wide-field, multi-object capability and stability of the FLAMES-GIRAFFE spectrograph (Pasquini et al., 2002) and, also of Keck/DEIMOS and GeminiN/GMOS (Koch et al., 2007c).

  • 3.

    Surveys to obtain several 100s to 1000s of l.o.s. velocities and spectral indices (providing estimates of the relative metallicity of red giants) on a restricted wavelength range (5140–5180 Å) at resolution R  20,000 (PI: M.Mateo, e.g. ∼800, 2500, 1400, 400 members for Carina, Fornax, Sculptor and Sextans, respectively Walker et al., 2007a, Walker et al., 2009a). These have been mainly carried out with the Michigan/MIKE Fiber System (MMFS) at the Magellan/Clay (6.5 m) telescope and with MMT/Hectochelle (see Mateo et al., 2008, for Leo I). With a comparable field-of-view to FLAMES (20 arcmin), MMFS has the advantage of almost double the number of fibres (equally shared between the blue and red channel of the MIKE spectrograph).

Therefore, to-date the combined data-sets for the best studied dSphs have impressive sizes (∼2900 and 1700 probable members for Fornax and Sculptor, respectively), permitting studies of their internal properties to a level of detail that was unthinkable a little more than a decade ago.

The low luminosities of UFDs imply that very few red giant branch (RGB) stars (the most luminous targets available for galaxies with old stellar populations) are available for spectroscopy. The size and spatial coverage of existing kinematic samples resemble those in the early days of the“classical” MW dSphs, even when targeting fainter stars (on the horizontal branch, and/or close to the main-sequence turn-off). Given our interest in exploiting the full l.o.s. velocity distribution, in what follows we concentrate on the “classical” dSphs and discuss only briefly results on the internal kinematics of UFDs.

In our current understanding of the Universe, a mere 5% of the total mass/energy density budget consists of baryons, atoms essentially, with the remaining 95% comprising about 24% non-baryonic “dark matter” and 71% “dark energy” (see Hinshaw et al., 2012, for the 9-years WMAP results). This has become known as the Λ cold-dark matter (ΛCDM) model. As the evocative naming suggests, we are ignorant of the nature of the great majority of constituents of the Universe.

There are several DM candidates such as weakly interacting massive particles, axions, sterile neutrinos, light gravitinos etc., whose existence is also motivated to solve problems in the Standard Model of particle physics (for a review see Feng, 2010). Some of these behave as cold and some as warm dark matter, where e.g. “cold” is defined as being non-relativistic at the time of structure formation. A wealth of experiments and strategies for direct and indirect detections of DM particles are underway (e.g. for reviews see Bertone et al., 2005, Hooper and Baltz, 2008, Feng, 2010), but at present the evidence for the existence of DM (based on the validity of Newton’s law of gravity on all gravitational acceleration regimes) is provided by astrophysical observations on a variety of scales, from the smallest galaxies such as the dSphs up to the largest structures in the Universe.2

Potentially, astrophysical observations can provide important constraints on the dominant form of DM, as the characteristics of the DM particle are expected to influence the growth of structures, the substructure content and internal properties of DM halos. Rather than reviewing the extensive literature on the topic, we proceed to discuss results that are most directly related to this review, highlighting the crucial role of dwarf galaxies.

Cosmological pure DM N-body simulations, carried out in the ΛCDM framework, show that the halos formed follow very specific functional forms, such as the Navarro, Frenk & White profile (NFW, Navarro et al., 1996b, Navarro et al., 1997)ρ(r)=ρ0r/rs(1+r/rs)2where ρ0 and rs are a characteristic density and radius. More recently the Einasto form has been found to provide better fits (e.g. Navarro et al., 2004, Merritt et al., 2006, Graham et al., 2006, Prada et al., 2006, Springel et al., 2008, Navarro et al., 2010)ρ(r)=ρ-2exp-2αErr-2αE-1,where ρ-2 and r-2 are the density and radius where the logarithmic slope dlogρ/dlogr=-γDM=-2, and αE is a shape parameter.3 These density profiles are rather steep near the centre, with the NFW being cuspy with γDM=1, while the Einasto profile has γDM=0 at the centre.

Although not necessarily theoretically motivated, other density profiles are also often employed in the literature. Typically they have the formρ(r)=ρ0(r/rs)γ(1+(r/rs)κ)(α-γ)/κ,where α,γ,κ0. Note that γ and α correspond to the inner and outer slopes respectively. The sharpness of the transition between these two regimes is thus given by κ. A cuspy profile has γ>0, while for a cored one γ=0 and κ>1. This is because in the cored case, the profile must have a flat shape at the centre, i.e. dρ/dr=0. A profile that has γ=0 and κ1 has at the centre dlogρ/dlogr=0 and a finite density, but in this case dρ/dr is non-zero, and hence this profile should not be confused with a core.

In the ΛCDM high-resolution cosmological N-body simulations described above the sub-halo mass function of MW-sized main halos is dN/dMM-α, with α=1.9 down to the simulations’ resolution limit (Springel et al., 2008), which is smaller than the mass estimates for the faintest dSphs (see Section 3). These simulations predict that MW halos contain 20% of the mass in subhalos, which results in a very large number of (mostly extremely low mass) satellites.

A comparison between the results of these pure DM N-body simulations with observations on galactic scales is not straightforward. Part of the issue lies in making the link between a luminous satellite to what should be its corresponding sub-halo in a DM simulation (e.g. of what mass? how dense?, see Strigari et al., 2010). This is particularly difficult because such simulations do not include baryons. This has motivated numerous theoretical efforts to provide a realistic treatment of baryonic effects using semi-analytical models and hydrodynamical simulations of dwarf galaxies (e.g. Revaz et al., 2009, Li et al., 2010, Font et al., 2011, Sawala et al., 2012, Starkenburg et al., 2013). Observationally, it is clearly important to obtain reliable estimates of the mass content and its distribution in dwarf galaxies.

For example, there is a debate about the inner shape of the density profiles of the DM halos hosting galaxies. For dSphs, this issue is still very open (see Section 3). On the other hand, for isolated late-type dwarfs and low surface brightness galaxies, the rotation curves seem to favor cored rather than cusped DM distributions (e.g. de Blok, 2010), and references therein. It has been suggested that feedback from supernovae explosions for these more massive systems could transform a cuspy halo into a cored one (e.g. Navarro et al., 1996a, Read and Gilmore, 2005, Governato et al., 2010, Pontzen and Governato, 2012, Teyssier et al., 2013). Note that in the case of an UFD, a single SN event releases an amount of energy comparable to the binding energy of the whole system. On the other hand, it is still to be assessed whether this mechanism is important or relevant on the scales of the MW dSphs, also given their low star formation rates (see Peñarrubia et al., 2012).

The “missing satellites” problem refers to the large mismatch between the observed number of dwarf galaxies satellites of the MW and M31 and the predicted number of DM subhalos (Klypin et al., 1999, Moore et al., 1999). The discovery of dozens low-luminosity dwarf galaxies in the Local Group, mainly by SDSS around the MW (e.g. Willman et al., 2005, Zucker et al., 2006, Belokurov et al., 2006, Belokurov et al., 2007, to mention a few) and the PandAS survey for M31 (e.g. McConnachie et al., 2009, Martin et al., 2009), has mitigated somewhat the “missing satellite” problem, after taking into account the surveys’ coverage and selection function (Koposov et al., 2009). The most appealing solution to reconcile predictions and observations is to suppress star formation, or gas accretion, in low-mass halos because of the joint effects of feedback and of a photo-ionizing background due to re-ionization (e.g. Bullock et al., 2000, Benson et al., 2002, Somerville, 2002).

Another interesting issue was the recently reported “too big too fail problem” pointed out by Boylan-Kolchin et al. (2011), who used the Aquarius suite of DM simulations to argue that there exists a population of subhalos that are too massive and too dense to be consistent with the internal kinematics of the MW dSphs, and yet they do not have an observed stellar counterpart. However, as argued by Wang et al., 2012, Vera-Ciro et al., 2013, the number of massive satellites is a stochastic quantity that also depends on the mass of the host. For example, if the mass of the MW is around 8×1011 M, i.e. the least massive MW-like halos of the Aquarius suite (which reproduces well the observed MW satellite luminosity function, see Koposov et al., 2008, Starkenburg et al., 2013), the mismatch disappears. Furthermore, Vera-Ciro et al. (2013) show that M31, if assumed to be more massive than the Milky Way, does not miss such a population.

A plausible alternative to CDM is warm dark matter (WDM). The warm component has the effect of reducing the small-scale power in the primordial fluctuations spectrum, yielding fewer subhalos and of lower central densities (Colín et al., 2000, Colín et al., 2008, Lovell et al., 2012). Specifically, in the numerical simulations of Macciò et al., 2012, Macciò et al., 2013, which explore a range of masses for the WDM particles, cored density profiles arise naturally. However, either the core sizes are too small to be consistent with those suggested in some studies of the internal kinematics of MW dSphs (see Section 3) or if large enough, they would be due to particles whose masses are inconsistent with the limits imposed by observations of the Lyman-α forest (e.g. Viel et al., 2005, Viel et al., 2008, Seljak et al., 2006). Note however that e.g. Busha et al. (2007) find in their WDM simulations that the halos are well described by an NFW form (i.e. cuspy) while Wang and White (2009) find this even holds for halos in hot dark matter simulations. Given that the state-of-the-art of WDM simulations is not as extensive and developed as for CDM, we await future developments.

From the above it is clear that there are numerous reasons to try and pin down the DM content and its distribution in the dSphs. Given that the overall evolution of small systems like dwarf galaxies will most likely be sensitive to their relatively small potential well (e.g. Revaz and Jablonka, 2012, Sawala et al., 2012), obtaining such measurements will also allow us to make sense of the variety of star formation and chemical enrichment histories of these galaxies, in particular in conjunction with the information on the dSphs orbital history that the Gaia satellite mission (Prusti, 2011) will provide.

An assumption in dynamical modeling of dSphs is that these objects are in dynamical equilibrium, while if they were significantly affected by tidal interactions with the MW this would need to be taken into account.

The possibility that dSphs are fully tidally disrupted dark-matter free galaxies has been excluded on the basis of their observed internal kinematic and structural properties (see for example Klessen et al., 2003, Muñoz et al., 2008), the large distances of some of these galaxies (up to 250 kpc from the MW) and a well-established luminosity-metallicity relation. It would also be difficult to explain the dSphs’ extended SFHs and broad metallicity distributions (see e.g.Tolstoy et al., 2004, Battaglia et al., 2006, Battaglia et al., 2011, Koch et al., 2006, Starkenburg et al., 2010) if the potential well would be due solely to the dSph stars (amounting to typically 105–106 M, e.g. McConnachie, 2012).

Partly because of the lack of knowledge of the orbits of dSphs around the MW, the importance of tides on the stellar components of dSphs is largely unknown. This also depends on the degree of embedding of this component in its dark matter halo, as well as on the average density of the system. Mayer et al. (2001) propose that dSph galaxies are what results when a disky dwarf is tidally stirred by the MW. For this process to be effective, the stellar component of the dSph today has to be tidally limited, in which case tidal tails are expected. However, Peñarrubia et al. (2008b) find that the stars are very resilient to tides in their simulations where the stellar component follows a King-profile and is deeply embedded in an NFW halo. In any case, there is general consensus that the central velocity dispersion (or the dispersion at the half-light radius) continues being a good indicator of the present maximum circular velocity and bound mass, as long as the objects retain a bound core (e.g. Muñoz et al., 2008, Peñarrubia et al., 2008b, Klimentowski et al., 2009, Kazantzidis et al., 2011a).

Besides the obvious case of Sagittarius, the only classical dSph presenting unambiguous signs of tidal disturbance such as tails and isophote twists is Carina (Battaglia et al., 2012). This object has been a candidate for tidal disturbance for a long time, with convincing arguments given by the presence of spectroscopically confirmed RGB stars, probable members, out to very large distances from its center (4.5 times the central King limiting radius), observed together with a break in the surface brightness profile, a velocity shear with turn-around, and a rising line-of-sight velocity dispersion profile (e.g. Muñoz et al., 2006). Among the classical dSphs, other candidates for tidal disruption are Leo I (e.g. Sohn et al., 2007, Mateo et al., 2008) and Ursa Minor (e.g. Martínez-Delgado et al., 2001, Palma et al., 2003, Muñoz et al., 2005), although the observational evidence is not as strong as for Carina. Note that even for Carina, the N-body simulations by Muñoz et al., 2008 show that large amounts of DM (M/L40 M/L) within the remaining bound core are still needed to explain its characteristics.

N-body simulations of tidally perturbed dSphs agree in predicting rising l.o.s. velocity dispersion profiles in the majority of cases, while only Carina and perhaps Draco (Walker, 2013) are observed to show such feature. Together with the fact that most classical dSphs show no tidal streams, this may be taken as indicative that the outer parts of the stellar components of dSphs have not been significantly affected by tides. All these arguments provide some justification for the assumptions made in this review, namely that we may consider the dSphs to be in dynamical equilibrium.

However, it would be well-worth the effort to carry out observational campaigns designed to maximize the chances of detecting the smoking-gun signature of tidal disruption, i.e. tidal tails. Detection of these low-surface brightness features needs deep and spatially extended photometric data-sets. Instruments like CTIO/DECam and the forthcoming Subaru/HyperCam, but also the proper motion information from the Gaia mission, are excellent matches to this type of problem.

Section snippets

Observed kinematics

The heliocentric distances to MW dSphs, ranging from 75 to 250 kpc, have made it unfeasible to obtain accurate proper motions of individual stars in these galaxies with current facilities. This implies that we only have access to one component of their velocity vector, namely that along line-of-sight (l.o.s.) vl.o.s. Therefore, all current studies of the internal kinematics of dwarf galaxies are based on their line-of-sight velocity distributions (LOSVD) and their moments.

In this Section we

Dynamical modeling

The techniques to model the internal dynamics of spheroidal systems have long been in place. However, their application to nearby dwarf spheroidals has only really taken off in the last decade, with the need for more sophisticated approaches thanks to the manifold increase in data samples. In this section we review the methods used, briefly discuss their limitations and the results obtained thus far for these systems. Table 1 gives an overview of the various modeling techniques applied to the

Future directions

In the previous sections we have discussed the status of the field, and have begun to identify directions where more research would be desirable to understand the properties and dynamics of dSphs. In the case of the dynamical modeling, as this review reflects, much of this work has been done assuming that the dSphs are embedded in spherical dark matter halos (and often, even assuming their light distribution is approximately spherical). First attempts to veer from this assumption have been made

Conclusions

In the last decade, we have experienced the vast increase in the number and extent of datasets with kinematic measurements of stars in the dSphs of the MW.

The leap forward in sample size and spatial coverage, coupled to exquisite velocity accuracy, due to advent of wide-field multi-object spectrographs on the largest telescopes world-wide allowed us to uncover velocity gradients of a few km s−1 deg−1 (e.g. Muñoz et al., 2006, Battaglia et al., 2008a, Walker et al., 2008, Ho et al., 2012) and to

Acknowledgments

G. Battaglia gratefully acknowledges support through a Marie-Curie action Intra European Fellowship, funded from the European Union Seventh Framework Program (FP7/2007-2013) under Grant agreement number PIEF-GA-2010-274151. A. Helmi and M.A. Breddels acknowledge financial support from NOVA (the Netherlands Research School for Astronomy), and the European Research Council under ERC-StG Grant GALACTICA-24027. We are also grateful to numerous enjoyable interactions throughout the past few years

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