arXiv subjects

Matthew G. Walker

Publications and source records attributed to Matthew G. Walker.

At least 73 records · Page 4Linked to original sources

arXiv2015

The SLUGGS Survey: Multi-population dynamical modelling of the elliptical galaxy NGC 1407 from stars and globular clusters

We perform in-depth dynamical modelling of the luminous and dark matter (DM) content of the elliptical galaxy NGC 1407. Our strategy consists of solving the spherical Jeans equations for three independent dynamical tracers: stars, blue GCs and red GCs in a self-consistent manner. We adopt a maximum-likelihood Markov-Chain Monte Carlo fitting technique in the attempt to constrain the inner slope of the DM density profile (the cusp/core problem), and the stellar initial mass function (IMF) of the galaxy. We find the inner logarithmic slope of the DM density profiles to be $γ= 0.6\pm0.4$, which is consistent with either a DM cusp ($γ= 1$) or with a DM core $(γ= 0)$. Our findings are consistent with a Salpeter IMF, and marginally consistent with a Kroupa IMF. We infer tangential orbits for the blue GCs, and radial anisotropy for red GCs and stars. The modelling results are consistent with the virial mass--concentration relation predicted by $Λ$CDM simulations. The virial mass of NGC 1407 is $\log$ $M_{\rm vir} = 13.3 \pm 0.2 M_{\odot}$, whereas the stellar mass is $\log M_* = 11.8 \pm 0.1 M_{\odot}$. The overall uncertainties on the mass of NGC 1407 are only 5 per cent at the projected stellar effective radius. We attribute the disagreement between our results and previous X-ray results to the gas not being in hydrostatic equilibrium in the central regions of the galaxy. The halo of NGC 1407 is found be DM dominated, with a dynamical mass-to-light ratio of $M/L=260_{-100} ^{+174} M_{\odot}/L_{\odot, B}$. However, this value can be larger up to a factor of 3 depending on the assumed prior on the DM scale radius.

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arXiv2015

Bayesian analysis of resolved stellar spectra: application to MMT/Hectochelle Observations of the Draco dwarf spheroidal

We introduce a Bayesian method for fitting faint, resolved stellar spectra in order to obtain simultaneous estimates of redshift and stellar-atmospheric parameters. We apply the method to thousands of spectra---covering 5160-5280 Angs. at resolution R~20,000---that we have acquired with the MMT/Hectochelle fibre spectrograph for red-giant and horizontal branch candidates along the line of sight to the Milky Way's dwarf spheroidal satellite in Draco. The observed stars subtend an area of ~4 deg^2, extending ~3 times beyond Draco's nominal `tidal' radius. For each spectrum we tabulate the first four moments---central value, variance, skewness and kurtosis---of posterior probability distribution functions representing estimates of the following physical parameters: line-of-sight velocity v_los, effective temperature (T_eff), surface gravity (logg) and metallicity ([Fe/H]). After rejecting low-quality measurements, we retain a new sample consisting of 2813 independent observations of 1565 unique stars, including 1879 observations for 631 stars with (as many as 13) repeat observations. Parameter estimates have median random errors of sigma_{v_los}=0.88 km/s, sigma_{T_eff}=162 K, sigma_logg=0.37 dex and sigma_[Fe/H]=0.20 dex. Our estimates of physical parameters distinguish ~470 likely Draco members from interlopers in the Galactic foreground.

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arXiv2015

A Comprehensive Search for Dark Matter Annihilation in Dwarf Galaxies

We present a new formalism designed to discover dark matter annihilation occurring in the Milky Way's dwarf galaxies. The statistical framework extracts all available information in the data by simultaneously combining observations of all the dwarf galaxies and incorporating the impact of particle physics properties, the distribution of dark matter in the dwarfs, and the detector response. The method performs maximally powerful frequentist searches and produces confidence limits on particle physics parameters. Probability distributions of test statistics under various hypotheses are constructed exactly, without relying on large sample approximations. The derived limits have proper coverage by construction and claims of detection are not biased by imperfect background modeling. We implement this formalism using data from the Fermi Gamma-ray Space Telescope to search for an annihilation signal in the complete sample of Milky Way dwarfs whose dark matter distributions can be reliably determined. We find that the observed data is consistent with background for each of the dwarf galaxies individually as well as in a joint analysis. The strongest constraints are at small dark matter particle masses. Taking the median of the systematic uncertainty in dwarf density profiles, the cross section upper limits are below the pure s-wave weak scale relic abundance value (2.2 x 10^-26 cm^3/s) for dark matter masses below 26 GeV (for annihilation into b quarks), 29 GeV (tau leptons), 35 GeV (up, down, strange, and charm quarks and gluons), 6 GeV (electrons/positrons), and 114 GeV (two-photon final state). For dark matter particle masses less than 1 TeV, these represent the strongest limits obtained to date using dwarf galaxies.

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arXiv2014

A dynamical model of the local cosmic expansion

We combine the equations of motion that govern the dynamics of galaxies in the local volume with Bayesian techniques in order to fit orbits to published distances and velocities of galaxies within $\sim 3$ Mpc. We find a Local Group (LG) mass $2.3\pm 0.7\times 10^{12}{\rm M}_\odot$ that is consistent with the combined dynamical masses of M31 and the Milky Way, and a mass ratio $0.54^{+0.23}_{-0.17}$ that rules out models where our Galaxy is more massive than M31 with $\sim 95\%$ confidence. The Milky Way's circular velocity at the solar radius is relatively high, $245\pm 23$ km/s, which helps to reconcile the mass derived from the local Hubble flow with the larger value suggested by the `timing argument'. Adopting {\it Planck}'s bounds on $Ω_Λ$ yields a (local) Hubble constant $H_0=67\pm 5$km/s/Mpc which is consistent with the value found on cosmological scales. Restricted N-body experiments show that substructures tend to fall onto the LG along the Milky Way-M31 axis, where the quadrupole attraction is maximum. Tests against mock data indicate that neglecting this effect slightly overestimates the LG mass without biasing the rest of model parameters. We also show that both the time-dependence of the LG potential and the cosmological constant have little impact on the observed local Hubble flow.

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arXiv2014

Is the Universe Simpler than LCDM?

In the standard cosmological model, the Universe consists mainly of two invisible substances: vacuum energy with constant mass-density rho_v=Λ/(8pi G) (where Lambda is a `cosmological constant' originally proposed by Einstein and G is Newton's gravitational constant) and cold dark matter (CDM) with mass density that is currently rho_{DM,0}\sim 0.3 rho_v. This `LCDM' model has the virtue of simplicity, enabling straightforward calculation of the formation and evolution of cosmic structure against the backdrop of cosmic expansion. Here we review apparent discrepancies with observations on small galactic scales, which LCDM must attribute to complexity in the baryon physics of galaxy formation. Yet galaxies exhibit structural scaling relations that evoke simplicity, presenting a clear challenge for formation models. In particular, tracers of gravitational potentials dominated by dark matter show a correlation between orbital size, R, and velocity, V, that can be expressed most simply as a characteristic acceleration, a_{DM}\sim 1 km^2 s^{-2} pc^{-1} \approx 3 x 10^{-9} cm s^{-2} \approx 0.2c\sqrt{G rho_v}, perhaps motivating efforts to find a link between localized and global manifestations of the Universe's dark components.

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arXiv2013

Measuring the slopes of mass profiles for dwarf spheroidals in triaxial CDM potentials

We generate stellar distribution functions (DFs) in triaxial haloes in order to examine the reliability of slopes $Γ\equiv Δ{\rm log} M / Δ{\rm log} r$ inferred by applying mass estimators of the form $M\propto R_eσ^2$ (i.e. assuming spherical symmetry, where $R_e$ and $σ$ are luminous effective radius and global velocity dispersion, respectively) to two stellar sub-populations independently tracing the same gravitational potential. The DFs take the form $f(E)$, are dynamically stable, and are generated within triaxial potentials corresponding directly to subhaloes formed in cosmological dark-matter-only simulations of Milky Way and galaxy cluster haloes. Additionally, we consider the effect of different tracer number density profiles (cuspy and cored) on the inferred slopes of mass profiles. For the isotropic DFs considered here, we find that halo triaxiality tends to introduce an anti-correlation between $R_e$ and $σ$ when estimated for a variety of viewing angles. The net effect is a negligible contribution to the systematic error associated with the slope of the mass profile, which continues to be dominated by a bias toward greater overestimation of masses for more-concentrated tracer populations. We demonstrate that simple mass estimates for two distinct tracer populations can give reliable (and cosmologically meaningful) lower limits for $Γ$, irrespective of the degree of triaxiality or shape of the tracer number density profile.

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arXiv2013

Constraining Self-Interacting Dark Matter with the Milky Way's dwarf spheroidals

Self-Interacting Dark Matter is an attractive alternative to the Cold Dark Matter paradigm only if it is able to substantially reduce the central densities of dwarf-size haloes while keeping the densities and shapes of cluster-size haloes within current constraints. Given the seemingly stringent nature of the latter, it was thought for nearly a decade that SIDM would be viable only if the cross section for self-scattering was strongly velocity-dependent. However, it has recently been suggested that a constant cross section per unit mass of sigma_T/m~0.1cm^2/g is sufficient to accomplish the desired effect. We explicitly investigate this claim using high resolution cosmological simulations of a Milky-Way size halo and find that, similarly to the Cold Dark Matter case, such cross section produces a population of massive subhaloes that is inconsistent with the kinematics of the classical dwarf spheroidals, in particular with the inferred slopes of the mass profiles of Fornax and Sculptor. This problem is resolved if sigma_T/m~1cm^2/g at the dwarf spheroidal scales. Since this value is likely inconsistent with the halo shapes of several clusters, our results leave only a small window open for a velocity-independent Self-Interacting Dark Matter model to work as a distinct alternative to Cold Dark Matter.

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arXiv2012

The coupling between the core/cusp and missing satellite problems

We calculate the energy that baryons must inject in cold dark matter (CDM) haloes in order to remove centrally-divergent DM cusps on scales relevant to observations of dwarf spheroidal galaxies (dSphs). We estimate that the CDM haloes often associated with the Milky Way's dSphs (M_vir/M_\odot \sim 10^{9-10}) require ΔE/erg \sim 10^{53-55} in order to form cores on scales comparable to the luminous size of these galaxies. While supernova type II (SNeII) explosions can in principle generate this energy, the actual contribution is limited by the low star formation efficiency implied by the abundance of luminous satellites. Considering that CDM's well-known `core/cusp' and `missing satellite' problems place opposing demands on star formation efficiencies, existing observational evidences for large cores in the most luminous dSphs require that CDM models invoke some combination of the following: (i) efficient (of order unity) coupling of SNeII energy into dark matter particles, (ii) star formation histories peaking at unexpectedly high redshifts (z>6), (iii) a top-heavy stellar IMF, and/or (iv) substantial satellite disruption or other stochastic effects to ease the substructure abundance constraints. Our models show that the tension between CDM problems on small scales would increase if cored DM profiles were to be found in fainter dwarves.

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arXiv2012

A statistical method for measuring the Galactic potential and testing gravity with cold tidal streams

We introduce the Minimum Entropy Method, a simple statistical technique for constraining the Milky Way gravitational potential and simultaneously testing different gravity theories directly from 6D phase-space surveys and without adopting dynamical models. We demonstrate that orbital energy distributions that are separable (i.e. independent of position) have an associated entropy that increases under wrong assumptions about the gravitational potential and/or gravity theory. Of known objects, `cold' tidal streams from low-mass progenitors follow orbital distributions that most nearly satisfy the condition of separability. Although the orbits of tidally stripped stars are perturbed by the progenitor's self-gravity, systematic variations of the energy distribution can be quantified in terms of the cross-entropy of individual tails, giving further sensitivity to theoretical biases in the host potential. The feasibility of using the Minimum Entropy Method to test a wide range of gravity theories is illustrated by evolving restricted N-body models in a Newtonian potential and examining the changes in entropy introduced by Dirac, MONDian and f(R) gravity modifications.

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arXiv2012

Dark Matter in the Milky Way's Dwarf Spheroidal Satellites

The Milky Way's dwarf spheroidal satellites include the nearest, smallest and least luminous galaxies known. They also exhibit the largest discrepancies between dynamical and luminous masses. This article reviews the development of empirical constraints on the structure and kinematics of dSph stellar populations and discusses how this phenomenology translates into constraints on the amount and distribution of dark matter within dSphs. Some implications for cosmology and the particle nature of dark matter are discussed, and some topics/questions for future study are identified.

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arXiv2011

Dwarf spheroidal galaxy kinematics and spiral galaxy scaling laws

Kinematic surveys of the dwarf spheroidal (dSph) satellites of the Milky Way are revealing tantalising hints about the structure of dark matter (DM) haloes at the low-mass end of the galaxy luminosity function. At the bright end, modelling of spiral galaxies has shown that their rotation curves are consistent with the hypothesis of a Universal Rotation Curve whose shape is supported by a cored dark matter halo. In this paper, we investigate whether the internal kinematics of the Milky Way dSphs are consistent with the particular cored DM distributions which reproduce the properties of spiral galaxies. Although the DM densities in dSphs are typically almost two orders of magnitude higher than those found in (larger) disk systems, we find consistency between dSph kinematics and Burkert DM haloes whose core radii r0 and central densities ρ0 lie on the extrapolation of the scaling law seen in spiral galaxies: log ρ0 \simeq α log r0 + const with 0.9 < α < 1.1. We similarly find that the dSph data are consistent with the relation between ρ0 and baryon scale length seen in spiral galaxies. While the origin of these scaling relations is unclear, the finding that a single DM halo profile is consistent with kinematic data in galaxies of widely varying size, luminosity and Hubble Type is important for our understanding of observed galaxies and must be accounted for in models of galaxy formation.

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arXiv2011

A Method for Measuring (Slopes of) the Mass Profiles of Dwarf Spheroidal Galaxies

We introduce a method for measuring the slopes of mass profiles within dwarf spheroidal (dSph) galaxies directly from stellar spectroscopic data and without adopting a dark matter halo model. Our method combines two recent results: 1) spherically symmetric, equilibrium Jeans models imply that the product of halflight radius and (squared) stellar velocity dispersion provides an estimate of the mass enclosed within the halflight radius of a dSph stellar component, and 2) some dSphs have chemo-dynamically distinct stellar \textit{sub}components that independently trace the same gravitational potential. We devise a statistical method that uses measurements of stellar positions, velocities and spectral indices to distinguish two dSph stellar subcomponents and to estimate their individual halflight radii and velocity dispersions. For a dSph with two detected stellar subcomponents, we obtain estimates of masses enclosed at two discrete points in the same mass profile, immediately defining a slope. Applied to published spectroscopic data, our method distinguishes stellar subcomponents in the Fornax and Sculptor dSphs, for which we measure slopes $Γ\equiv Δ\log M / Δ\log r=2.61_{-0.37}^{+0.43}$ and $Γ=2.95_{-0.39}^{+0.51}$, respectively. These values are consistent with 'cores' of constant density within the central few-hundred parsecs of each galaxy and rule out `cuspy' Navarro-Frenk-White (NFW) profiles ($d\log M/d\log r \leq 2$ at all radii) with significance $\ga 96%$ and $\ga 99%$, respectively. Tests with synthetic data indicate that our method tends systematically to overestimate the mass of the inner stellar subcomponent to a greater degree than that of the outer stellar subcomponent, and therefore to underestimate the slope $Γ$ (implying that the stated NFW exclusion levels are conservative).

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arXiv2010

Binary stars as probes of dark substructures in dwarf galaxies

We use analytical and N-body methods to examine the survival of wide stellar binaries against repeated encounters with dark substructures orbiting in the dark matter haloes of dwarf spheroidal galaxies (dSphs). Our models adopt cosmologically-motivated conditions wherein dSphs are dark-matter dominated systems that form hierarchically and orbit about a host galaxy. Our analytical estimates show that wide binaries are disrupted at a rate that is proportional to the local density of dark substructures averaged over the life-time of the binary population. The fact that external tides can efficiently strip dark substructures from the outskirts of dSphs implies that the present number and distribution of binaries is strongly coupled with the mass evolution of individual galaxies. Yet we show that for the range of dynamical masses and Galactocentric distances spanned by Milky Way dSphs, a truncation in the separation function at a_max <~ 0.1 pc is expected in all these galaxies. An exception may be the Sagittarius dSph, which has lost most of is dark matter envelope to tides and is close to full disruption. Our simulations indicate that at separations larger than a_max the perturbed binary distribution scales as dN/da \propto a^{-2.1} independently of the mass and density of substructures. These results may be used to determine whether the binary separation function found in dwarf galaxies is compatible with the scale-free hierarchical picture that envisions the existence of dark substructures in all galactic haloes. We show that the ACS camera on board of the Hubble telescope may be able to test this prediction in dSphs at heliocentric distances <100 kpc, even if the binary fraction amounts only 10% of the stellar population.

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arXiv2010

The impact of dark matter cusps and cores on the satellite galaxy population around spiral galaxies

(Abridged) We use N-body simulations to study the effects that a divergent (i.e. "cuspy") dark matter (DM) profile introduces on the tidal evolution of dwarf spheroidal galaxies (dSphs). Our models assume cosmologically-motivated initial conditions where dSphs are DM-dominated systems on eccentric orbits about a host galaxy composed of a dark halo and a baryonic disc. We find that the resilience of dSphs to tidal stripping is extremely sensitive to the halo cuspiness; whereas dwarfs with a cored profile can be easily destroyed by the host disc, those with cusps always retain a bound remnant. For a given halo profile the evolution of the structural parameters as driven by tides is controlled solely by the total amount of mass lost. This information is used to construct a semi-analytic code that simulates the hierarchical build-up of spiral galaxies assuming different halo profiles and disc masses. We find that tidal encounters with discs tend to decrease the average mass of satellites at all galactocentric radii. Interestingly, satellites accreted before re-ionization (z>6), which may be singled out by anomalous metallicity patterns, survive only if haloes are cuspy. We show that the size-mass relation established from Milky Way (MW) dwarfs strongly supports the presence of cusps in the majority of these systems, as cored models systematically underestimate the masses of the known Ultra-Faint dSphs. Our models also indicate that a massive M31 disc may explain why many of its dSphs fall below the size-mass relationship derived from MW dSphs. We use our models to constrain the mass threshold below which star formation is suppressed in DM haloes, finding that luminous satellites must be accreted with masses above 10^8--10^9 M_sol in order to explain the size-mass relation observed in MW dwarfs.

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arXiv2010

Comparing the Dark Matter Halos of Spiral, Low Surface Brightness and Dwarf Spheroidal Galaxies

We consider dark masses measured from kinematic tracers at discrete radii in galaxies for which baryonic contributions to overall potentials are either subtracted or negligible. Recent work indicates that rotation curves due to dark matter (DM) halos at intermediate radii in spiral galaxies are remarkably similar, with a mean rotation curve given by $\log_{10}[V_{c,\mathrm{DM}}/(\mathrm{km s^{-1}})]=1.47_{-0.19}^{+0.15}+0.5\log_{10}[r/\mathrm{kpc}]$. Independent studies show that while estimates of the dark mass of a given dwarf spheroidal (dSph) galaxy are robust only near the half-light radius, data from the Milky Way's (MW's) dSph satellites are consistent with a narrow range of mass profiles. Here we combine published constraints on the dark halo masses of spirals and dSphs and include available measurements of low surface brightness galaxies for additional comparison. We find that most measured MW dSphs lie on the extrapolation of the mean rotation curve due to DM in spirals. The union of MW-dSph and spiral data appears to follow a mass-radius relation of the form $M_{\mathrm{DM}}(r)/M_{\odot}=200_{-120}^{+200}(r/\mathrm{pc})^2$, or equivalently a constant acceleration $g_{\mathrm{DM}}=3_{-2}^{+3}\times 10^{-9}\mathrm{cm s^{-2}}$, spanning $0.02\la r \la 75$ kpc. Evaluation at specific radii immediately generates two results from the recent literature: a common mass for MW dSphs at fixed radius and a constant DM central surface density for galaxies ranging from MW dSphs to spirals. However, recent kinematic measurements indicate that M31's dSph satellites are systematically less massive than MW dSphs of similar size. Such deviations from what is otherwise a surprisingly uniform halo relation presumably hold clues to individual formation and evolutionary histories.

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arXiv2010

Searching for dark matter in X-rays: how to check the dark matter origin of a spectral feature

A signal from decaying dark matter (DM) can be unambiguously distinguished from spectral features of astrophysical or instrumental origin by studying its spatial distribution. We demonstrate this approach by examining the recent claim of 0912.0552 regarding the possible DM origin of the 2.5 keV line in Chandra observations of the Milky Way satellite known as Willman 1. Our conservative strategy is to adopt a relatively large dark mass for Willman 1 and relatively small dark masses for the comparison objects. We analyze archival observations by XMM-Newton of M31 and Fornax dwarf spheroidal galaxy (dSph) and Chandra observations of Sculptor dSph. By performing a conservative analysis of X-ray spectra, we show the absence of a DM decay line with parameters consistent with those of 0912.0552. For M31, the observations of the regions between 10 and 20 kpc from the center, where the uncertainties in the DM distribution are minimal, make a strong exclusion at the level above 10sigma. The minimal estimate for the amount of DM in the central 40 kpc of M31 is provided by the model of 0912.4133, assuming the stellar disk's mass to light ratio ~8 and almost constant DM density within a core of 28 kpc. Even in this case one gets an exclusion at 5.7sigma from central region of M31 whereas modeling all processed data from M31 and Fornax produces more than 14sigma exclusion. Therefore, despite possible systematic uncertainties, we exclude the possibility that the spectral feature at ~2.5 keV found in 0912.0552 is a DM decay line. We conclude, however, that the search for DM decay line, although demanding prolonged observations of well-studied dSphs, M31 outskirts and other similar objects, is rather promising, as the nature of a possible signal can be checked. An (expected) non-observation of a DM decay signal in the planned observations of Willman 1 should not discourage further dedicated observations.

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arXiv2010

Are stellar over-densities in dwarf galaxies the "smoking gun" of triaxial dark matter haloes?

We use N-body simulations to study the tidal evolution of globular clusters (GCs) in dwarf spheroidal (dSph) galaxies. Our models adopt a cosmologically motivated scenario in which the dSph is approximated by a static NFW halo with a triaxial shape. For a large set of orbits and projection angles we examine the spatial and velocity distribution of stellar debris deposited during the complete disruption of stellar clusters. Our simulations show that such debris appears as shells, isolated clumps and elongated over-densities at low surface brightness (>26 mag/arcsec^2), reminiscent of substructure observed in several MW dSphs. Such features arise from the triaxiality of the galaxy potential and do not dissolve in time. Stellar over-densities reported in several MW dSphs may thus be the telltale evidence of dark matter haloes being triaxial in shape. We explore a number of kinematic signatures that would help to validate (or falsify) this scenario. The mean angular momentum of the cluster debris associated with box and resonant orbits, which are absent in spherical potentials, is null. As a result, we show that the line-of-sight velocity distribution may exhibit a characteristic "double-peak" depending on the oriention of the viewing angle with respect to the progenitor's orbital plane. Kinematic surveys of dSphs may help to detect and identify substructures associated with the disruption of stellar clusters, as well as to address the shape of the dark matter haloes in which dSphs are embedded.

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arXiv2009

A Universal Mass Profile for Dwarf Spheroidal Galaxies?

(abridged) We apply the Jeans equation to estimate masses for eight of the brightest dSph galaxies. For Fornax we obtain a model-independent constraint on the maximum-circular velocity, Vmax=18_{-3}^{+5} km/s. Although we obtain only lower-limits of Vmax > 10 km/s for the remaining dSphs, we find that in all cases the enclosed mass at the projected half-light radius is well constrained and robust to a wide range of halo models and velocity anisotropies. We derive a simple analytic formula that estimates M(rhalf) accurately with respect to results from the full Jeans analysis. Applying this formula to the entire population of Local Group dSphs, we demonstrate a correlation such that M(rhalf)\propto rhalf^{1.4\pm 0.4}, or in terms of the mean density interior to the half-light radius, \propto rhalf^{-1.6\pm 0.4}. This relation is driven by the fact that the dSph data exhibit a correlation between global velocity dispersion and half-light radius. We argue that tidal forces are unlikely to have introduced this relation, but tides may have increased the scatter and/or altered the slope. While the data are well described by mass profiles ranging over a factor of < 2 in normalization (Vmax ~ 10-20 km/s), we consider the hypothesis that all dSphs are embedded within a "universal" dark matter halo. We show that in addition to the power law M\propto r^{1.4}, viable candidates include a cuspy "NFW" halo with Vmax ~ 15 km/s and scale radius r_0 ~ 800 pc, as well as a cored halo with Vmax ~ 13 km/s and r_0 ~ 150 pc. Finally, assuming that their measured velocity dispersions accurately reflect their masses, the smallest dSphs now allow us to resolve dSph densities at radii as small as a few tens of pc. At these small scales we find mean densities as large as <ρ> ~ 5 Msun/pc^3 (200 GeV/cm^3).

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