arXiv subjects

Mark Vogelsberger

Publications and source records attributed to Mark Vogelsberger.

At least 451 records · Page 25Linked to original sources

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.

astro-ph.CO↗

arXiv2013

Direct detection of self-interacting dark matter

Self-interacting dark matter offers an interesting alternative to collisionless dark matter because of its ability to preserve the large-scale success of the cold dark matter model, while seemingly solving its challenges on small scales. We present here the first study of the expected dark matter detection signal taking into account different self-scattering models. We demonstrate that models with constant and velocity dependent cross sections, which are consistent with observational constraints, lead to distinct signatures in the velocity distribution, because non-thermalised features found in the cold dark matter distribution are thermalised through particle scattering. Depending on the model, self-interaction can lead to a 10% reduction of the recoil rates at high energies, corresponding to a minimum speed that can cause recoil larger than 300 km/s, compared to the cold dark matter case. At lower energies these differences are smaller than 5% for all models. The amplitude of the annual modulation signal can increase by up to 25%, and the day of maximum amplitude can shift by about two weeks with respect to the cold dark matter expectation. Furthermore, the exact day of phase reversal of the modulation signal can also differ by about a week between the different models. In general, models with velocity dependent cross sections peaking at the typical velocities of dwarf galaxies lead only to minor changes in the detection signals, whereas allowed constant cross section models lead to significant changes. We conclude that different self-interacting dark matter scenarios might be distinguished from each other through the details of direct detection signals. Furthermore, detailed constraints on the intrinsic properties of dark matter based on null detections, should take into account the possibility of self-scattering and the resulting effects on the detector signal.

astro-ph.CO↗

arXiv2012

Moving mesh cosmology: properties of neutral hydrogen in absorption

We examine the distribution of neutral hydrogen in cosmological simulations carried out with the new moving-mesh code AREPO and compare it with the corresponding GADGET simulations based on the smoothed particle hydrodynamics (SPH) technique. The two codes use identical gravity solvers and baryonic physics implementations, but very different methods for solving the Euler equations, allowing us to assess how numerical effects associated with the hydro-solver impact the results of simulations. Here we focus on an analysis of the neutral gas, as detected in quasar absorption lines. We find that the high column density regime probed by Damped Lyman-alpha (DLA) and Lyman Limit Systems (LLS) exhibits significant differences between the codes. GADGET produces spurious artefacts in large halos in the form of gaseous clumps, boosting the LLS cross-section. Furthermore, it forms halos with denser central baryonic cores than AREPO, which leads to a substantially greater DLA cross-section from smaller halos. AREPO thus produces a significantly lower cumulative abundance of DLAs, which is intriguingly in much closer agreement with observations. The column density function, however, is not altered enough to significantly reduce the discrepancy with the observed value. For the low column density gas probed by the Lyman-alpha forest, the codes differ only at the level of a few percent, suggesting that this regime is quite well described by both methods, a fact that is reassuring for the many Lyman-alpha studies carried out with SPH thus far. While the residual differences are smaller than the errors on current Lyman-alpha forest data, we note that this will likely change for future precision experiments.

astro-ph.CO↗

arXiv2012

Numerical Simulations of the Dark Universe: State of the Art and the Next Decade

We present a review of the current state of the art of cosmological dark matter simulations, with particular emphasis on the implications for dark matter detection efforts and studies of dark energy. This review is intended both for particle physicists, who may find the cosmological simulation literature opaque or confusing, and for astro-physicists, who may not be familiar with the role of simulations for observational and experimental probes of dark matter and dark energy. Our work is complementary to the contribution by M. Baldi in this issue, which focuses on the treatment of dark energy and cosmic acceleration in dedicated N-body simulations. Truly massive dark matter-only simulations are being conducted on national supercomputing centers, employing from several billion to over half a trillion particles to simulate the formation and evolution of cosmologically representative volumes (cosmic scale) or to zoom in on individual halos (cluster and galactic scale). These simulations cost millions of core-hours, require tens to hundreds of terabytes of memory, and use up to petabytes of disk storage. The field is quite internationally diverse, with top simulations having been run in China, France, Germany, Korea, Spain, and the USA. Predictions from such simulations touch on almost every aspect of dark matter and dark energy studies, and we give a comprehensive overview of this connection. We also discuss the limitations of the cold and collisionless DM-only approach, and describe in some detail efforts to include different particle physics as well as baryonic physics in cosmological galaxy formation simulations, including a discussion of recent results highlighting how the distribution of dark matter in halos may be altered. We end with an outlook for the next decade, presenting our view of how the field can be expected to progress. (abridged)

astro-ph.CO↗

arXiv2012

Moving Mesh Cosmology: Properties of Gas Disks

We compare the structural properties of galaxies formed in cosmological simulations using the smoothed particle hydrodynamics (SPH) code GADGET with those using the moving-mesh code AREPO. Both codes employ identical gravity solvers and the same sub-resolution physics but use very different methods to track the hydrodynamic evolution of gas. This permits us to isolate the effects of the hydro solver on the formation and evolution of galactic gas disks in GADGET and AREPO haloes with comparable numerical resolution. In a matching sample of GADGET and AREPO haloes we fit simulated gas disks with exponential profiles. We find that the cold gas disks formed using the moving mesh approach have systematically larger disk scale lengths and higher specific angular momenta than their GADGET counterparts across a wide range in halo masses. For low mass galaxies differences between the properties of the simulated galaxy disks are caused by an insufficient number of resolution elements which lead to the artificial angular momentum transfer in our SPH calculation. We however find that galactic disks formed in massive halos, resolved with 10^6 particles/cells, are still systematically smaller in the GADGET run by a factor of ~2. The reasons for this are: 1) The excessive heating of haloes close to the cooling radius due to spurious dissipation of the subsonic turbulence in GADGET; and 2) The efficient delivery of low angular momentum gaseous blobs to the bottom of the potential well. While this large population of gaseous blobs in GADGET originates from the filaments which are pressure confined and fragment due to the SPH surface tension while infalling into hot halo atmospheres, it is essentially absent in the moving mesh calculation, clearly indicating numerical rather than physical origin of the blob material.

astro-ph.CO↗

arXiv2012

Moving mesh cosmology: characteristics of galaxies and haloes

We discuss cosmological hydrodynamic simulations of galaxy formation performed with the new moving-mesh code AREPO, which promises higher accuracy compared with the traditional SPH technique that has been widely employed for this problem. We use an identical set of physics in corresponding simulations carried out with the well-tested SPH code GADGET, adopting also the same high-resolution gravity solver. We are thus able to compare both simulation sets on an object-by-object basis, allowing us to cleanly isolate the impact of different hydrodynamical methods on galaxy and halo properties. In accompanying papers, we focus on an analysis of the global baryonic statistics predicted by the simulation codes, (Vogelsberger et al. 2011) and complementary idealized simulations that highlight the differences between the hydrodynamical schemes (Sijacki et al. 2011). Here we investigate their influence on the baryonic properties of simulated galaxies and their surrounding haloes. We find that AREPO leads to significantly higher star formation rates for galaxies in massive haloes and to more extended gaseous disks in galaxies, which also feature a thinner and smoother morphology than their GADGET counterparts. Consequently, galaxies formed in AREPO have larger sizes and higher specific angular momentum than their SPH correspondents. The more efficient cooling flows in AREPO yield higher densities and lower entropies in halo centers (and the opposite trend in halo outskirts) leading to higher star formation rates of massive galaxies. While both codes agree to acceptable accuracy on a number of baryonic properties of cosmic structures, our results clearly demonstrate that galaxy formation simulations greatly benefit from the use of more accurate hydrodynamical techniques such as AREPO.

astro-ph.CO↗

arXiv2012

Characterization of Dark-Matter-induced anisotropies in the diffuse gamma-ray background

The Fermi-LAT collaboration has recently reported the detection of angular power above the photon noise level in the diffuse gamma-ray background between 1 and 50 GeV. Such signal can be used to constrain a possible contribution from Dark-Matter-induced photons. We estimate the intensity and features of the angular power spectrum (APS) of this potential Dark Matter (DM) signal, for both decaying and annihilating DM candidates, by constructing template all-sky gamma-ray maps for the emission produced in the galactic halo and its substructures, as well as in extragalactic (sub)halos. The DM distribution is given by state-of-the-art N-body simulations of cosmic structure formation, namely Millennium-II for extragalactic (sub)halos, and Aquarius for the galactic halo and its subhalos. We use a hybrid method of extrapolation to account for (sub)structures that are below the resolution limit of the simulations, allowing us to estimate the total emission all the way down to the minimal self-bound halo mass. We describe in detail the features appearing in the APS of our template maps and we estimate the effect of various uncertainties such as the value of the minimal halo mass, the fraction of substructures hosted in a halo and the shape of the DM density profile. Our results indicate that the fluctuation APS of the DM-induced emission is of the same order as the Fermi-LAT APS, suggesting that one can constrain this hypothetical emission from the comparison with the measured anisotropy. We also quantify the uncertainties affecting our results, finding "theoretical error bands" spanning more than two orders of magnitude and dominated (for a given particle physics model) by our lack of knowledge of the abundance of low-mass (sub)halos.

astro-ph.HE↗

arXiv2012

Subhaloes in Self-Interacting Galactic Dark Matter Haloes

We present N-body simulations of a new class of self-interacting dark matter models, which do not violate any astrophysical constraints due to a non-power-law velocity dependence of the transfer cross section which is motivated by a Yukawa-like new gauge boson interaction. Specifically, we focus on the formation of a Milky Way-like dark matter halo taken from the Aquarius project and re-simulate it for a couple of representative cases in the allowed parameter space of this new model. We find that for these cases, the main halo only develops a small core (~1 kpc) followed by a density profile identical to that of the standard cold dark matter scenario outside of that radius. Neither the subhalo mass function nor the radial number density of subhaloes are altered in these models but there is a significant change in the inner density structure of subhaloes resulting in the formation of a large density core. As a consequence, the inner circular velocity profiles of the most massive subhaloes differ significantly from the cold dark matter predictions and we demonstrate that they are compatible with the observational data of the brightest Milky Way dSphs in such a velocity-dependent self-interacting dark matter scenario. Specifically, and contrary to the cold dark matter case, there are no subhaloes that are more concentrated than what is inferred from the kinematics of the Milky Way dSphs. We conclude that these models offer an interesting alternative to the cold dark matter model that can reduce the recently reported tension between the brightest Milky Way satellites and the dense subhaloes found in cold dark matter simulations.

astro-ph.CO↗

arXiv2012

Moving mesh cosmology: numerical techniques and global statistics

We present the first hydrodynamical simulations of structure formation using the new moving mesh code AREPO and compare the results with GADGET simulations based on a traditional smoothed particle hydrodynamics (SPH) technique. The two codes share the same Tree-PM gravity solver and include identical sub-resolution physics, but employ different methods to solve the equations of hydrodynamics. This allows us to assess the impact of hydro-solver uncertainties on the results of cosmological studies of galaxy formation. We focus on predictions for global baryon statistics, such as the cosmic star formation rate density, after we introduce our simulation suite and numerical methods. Properties of individual galaxies and haloes are examined by Keres et al. (2011), while a third paper by Sijacki et al. (2011) uses idealised simulations to analyse the differences between the hydrodynamical schemes. We find that the global baryon statistics differ significantly between the two simulation approaches. AREPO shows higher star formation rates at late times, lower mean temperatures, and different gas mass fractions in characteristic phases of the intergalactic medium, in particular a reduced amount of hot gas. Although both codes use the same implementation of cooling, more gas cools out of haloes in AREPO compared with GADGET towards low redshifts. We show that this is caused by a higher heating rate with SPH in the outer parts of haloes, owing to viscous dissipation of SPH's inherent sonic velocity noise and SPH's efficient damping of subsonic turbulence injected in the halo infall region, and because of a higher efficiency of gas stripping in AREPO. As a result of such differences, AREPO leads also to more disk-like morphologies compared to GADGET. Our results indicate that inaccuracies in hydrodynamic solvers can lead to comparatively large systematic differences.

astro-ph.CO↗

arXiv2012

Moving mesh cosmology: the hydrodynamics of galaxy formation

We present a detailed comparison between the well-known SPH code GADGET and the new moving-mesh code AREPO on a number of hydrodynamical test problems. Through a variety of numerical experiments we establish a clear link between test problems and systematic numerical effects seen in cosmological simulations of galaxy formation. Our tests demonstrate deficiencies of the SPH method in several sectors. These accuracy problems not only manifest themselves in idealized hydrodynamical tests, but also propagate to more realistic simulation setups of galaxy formation, ultimately affecting gas properties in the full cosmological framework, as highlighted in papers by Vogelsberger et al. (2011) and Keres et al. (2011). We find that an inadequate treatment of fluid instabilities in GADGET suppresses entropy generation by mixing, underestimates vorticity generation in curved shocks and prevents efficient gas stripping from infalling substructures. In idealized tests of inside-out disk formation, the convergence rate of gas disk sizes is much slower in GADGET due to spurious angular momentum transport. In simulations where we follow the interaction between a forming central disk and orbiting substructures in a halo, the final disk morphology is strikingly different. In AREPO, gas from infalling substructures is readily depleted and incorporated into the host halo atmosphere, facilitating the formation of an extended central disk. Conversely, gaseous sub-clumps are more coherent in GADGET simulations, morphologically transforming the disk as they impact it. The numerical artefacts of the SPH solver are particularly severe for poorly resolved flows, and thus inevitably affect cosmological simulations due to their hierarchical nature. Our numerical experiments clearly demonstrate that AREPO delivers a physically more reliable solution.

astro-ph.CO↗

arXiv2012

Multi-Dimensional, Compressible Viscous Flow on a Moving Voronoi Mesh

Numerous formulations of finite volume schemes for the Euler and Navier-Stokes equations exist, but in the majority of cases they have been developed for structured and stationary meshes. In many applications, more flexible mesh geometries that can dynamically adjust to the problem at hand and move with the flow in a (quasi) Lagrangian fashion would, however, be highly desirable, as this can allow a significant reduction of advection errors and an accurate realization of curved and moving boundary conditions. Here we describe a novel formulation of viscous continuum hydrodynamics that solves the equations of motion on a Voronoi mesh created by a set of mesh-generating points. The points can move in an arbitrary manner, but the most natural motion is that given by the fluid velocity itself, such that the mesh dynamically adjusts to the flow. Owing to the mathematical properties of the Voronoi tessellation, pathological mesh-twisting effects are avoided. Our implementation considers the full Navier-Stokes equations and has been realized in the AREPO code both in 2D and 3D. We propose a new approach to compute accurate viscous fluxes for a dynamic Voronoi mesh, and use this to formulate a finite volume solver of the Navier-Stokes equations. Through a number of test problems, including circular Couette flow and flow past a cylindrical obstacle, we show that our new scheme combines good accuracy with geometric flexibility, and hence promises to be competitive with other highly refined Eulerian methods. This will in particular allow astrophysical applications of the AREPO code where physical viscosity is important, such as in the hot plasma in galaxy clusters, or for viscous accretion disk models.

astro-ph.IM↗

arXiv2012

The Effects of Patchy Reionization on Satellite Galaxies of the Milky Way

We combine the high-resolution Aquarius simulations with three-dimensional models of reionization based on the initial density field of the Aquarius parent simulation, Millennium-II, to study the impact of patchy reionization on the faint satellite population of Milky Way halos. Because the Aquarius suite consists of zoom-in simulations of halos in the Millennium-II volume, we follow the formation of substructure and the growth of reionization bubbles due to the larger environment simultaneously, and thereby determine the reionization redshifts of satellite candidates. We do this for four different reionization models, and also compare results to instantaneous reionization. Using a simple procedure for selecting satellites and assigning luminosities in the simulations, we compare the resulting satellite populations. We find that the overall number of satellites depends sensitively on the reionization model, with a factor of 3-4 variation between the four models for a given host halo, although the difference is entirely in the population of faint satellites (M_V > -10). In addition, we find that for a given reionization model the total number of satellites differs by 10%-20% between the patchy and homogeneous scenarios, provided that the redshift is chosen appropriately for the instantaneous case. However, the halo-halo scatter from the six Aquarius halos is large, up to a factor of 2-3, and so is comparable to the difference between reionization scenarios. In order to use the population of faint dwarf galaxies around the Milky Way as a probe of the local reionization history, then, it is necessary to first better understand the general distribution of substructure around Milky Way-mass halos.

astro-ph.CO↗

arXiv2011

Dark Matter implications of the Fermi-LAT measurement of anisotropies in the diffuse gamma-ray background: status report

For the first time, the Fermi-LAT measured the angular power spectrum (APS) of anisotropies in the diffuse gamma-ray background. The data is found to be broadly compatible with a model with contributions from the point sources in the 1-year catalog, the galactic diffuse background, and the extragalactic isotropic emission; however deviations are present at both large and small angular scales. In this study, we complement the model with a contribution from Dark Matter (DM) whose distribution is modeled exploiting the results of the most recent N-body simulations, considering the contribution of extragalactic halos and subhalos (from Millennium-II) and of galactic substructures (from Aquarius). With the use of the Fermi Science Tools, these simulations serve as templates to produce mock gamma-ray count maps for DM gamma-ray emission, both in the case of an annihilating and a decaying DM candidate. The APS will then be computed and compared with the Fermi-LAT results to derive constraints on the DM particle physics properties. The possible systematic due to an imperfect model of the galactic foreground is also studied and taken into account properly. The present paper reports on the status of the project.

astro-ph.CO↗

arXiv2011

The Shape of Dark Matter Haloes in the Aquarius Simulations: Evolution and Memory

We use the high resolution cosmological N-body simulations from the Aquarius project to investigate in detail the mechanisms that determine the shape of Milky Way-type dark matter haloes. We find that, when measured at the instantaneous virial radius, the shape of individual haloes changes with time, evolving from a typically prolate configuration at early stages to a more triaxial/oblate geometry at the present day. This evolution in halo shape correlates well with the distribution of the infalling material: prolate configurations arise when haloes are fed through narrow filaments, which characterizes the early epochs of halo assembly, whereas triaxial/oblate configurations result as the accretion turns more isotropic at later times. Interestingly, at redshift z=0, clear imprints of the past history of each halo are recorded in their shapes at different radii, which also exhibit a variation from prolate in the inner regions to triaxial/oblate in the outskirts. Provided that the Aquarius haloes are fair representatives of Milky Way-like 10^12 Msun objects, we conclude that the shape of such dark matter haloes is a complex, time-dependent property, with each radial shell retaining memory of the conditions at the time of collapse.

astro-ph.CO↗

arXiv2011

The cosmic X-ray and gamma-ray background from dark matter annihilation

(Abridged) The extragalactic background light (EBL) observed at multiple wavelengths is a promising tool to probe the nature of dark matter since it might contain a significant contribution from gamma-rays produced promptly by dark matter annihilation. Additionally, the electrons and positrons produced in the annihilation give energy to the CMB photons to populate the EBL with X-rays and gamma-rays. We here create full-sky maps of the radiation from both of these contributions using the high-resolution Millennium-II simulation. We use upper limits on the contributions of unknown sources to the EBL to constrain the intrinsic properties of dark matter using a model-independent approach that can be employed as a template to test different particle physics models (including those with a Sommerfeld enhancement). These upper limits are based on observations spanning eight orders of magnitude in energy (from soft X-rays measured by CHANDRA to gamma-rays measured by Fermi), and on expectations for the contributions from blazars and star forming galaxies. To exemplify this approach, we analyze a set of benchmark Sommerfeld-enhanced models that give the correct dark matter abundance, satisfy CMB constraints, and fit the cosmic ray spectra measured by PAMELA and Fermi without any contribution from local subhalos. We find that these models are in conflict with the EBL constraints unless the contribution of unresolved subhalos is small and the annihilation signal dominates the EBL. We conclude that provided the collisionless cold dark matter paradigm is accurate, even for conservative estimates of the contribution from unresolved subhalos and astrophysical backgrounds, the EBL is at least as sensitive a probe of these types of scenarios as the CMB. Our results disfavor an explanation of the positron excess measured by PAMELA based only on dark matter annihilation in the smooth Galactic halo.

astro-ph.CO↗

arXiv2011

Consistent Scenarios for Cosmic-Ray Excesses from Sommerfeld-Enhanced Dark Matter Annihilation

Anomalies in direct and indirect detection have motivated models of dark matter consisting of a multiplet of nearly-degenerate states, coupled by a new GeV-scale interaction. We perform a careful analysis of the thermal freezeout of dark matter annihilation in such a scenario. We compute the range of "boost factors" arising from Sommerfeld enhancement in the local halo for models which produce the correct relic density, and show the effect of including constraints on the saturated enhancement from the cosmic microwave background (CMB). We find that boost factors from Sommerfeld enhancement of up to ~800 are possible in the local halo. When the CMB bounds on the saturated enhancement are applied, the maximal boost factor is reduced to ~400 for 1-2 TeV dark matter and sub-GeV force carriers, but remains large enough to explain the observed Fermi and PAMELA electronic signals. We describe regions in the DM mass-boost factor plane where the cosmic ray data is well fit for a range of final states, and show that Sommerfeld enhancement alone is enough to provide the large annihilation cross sections required to fit the data, although for light mediator masses (less than ~200 MeV) there is tension with the CMB constraints in the absence of astrophysical boost factors from substructure. Additionally, we consider the circumstances under which WIMPonium formation is relevant and find for heavy WIMPs (greater than ~2 TeV) and soft-spectrum annihilation channels it can be an important consideration; we find regions with dark matter mass greater than 2.8 TeV that are consistent with the CMB bounds and have ~600-700 present-day boost factors.

hep-ph↗

arXiv2011

Streams and caustics: the fine-grained structure of LCDM haloes

We present the first and so far the only simulations to follow the fine-grained phase-space structure of galaxy haloes formed from generic LCDM initial conditions. We integrate the geodesic deviation equation in tandem with the N-body equations of motion, demonstrating that this can produce numerically converged results for the properties of fine-grained phase-space streams and their associated caustics, even in the inner regions of haloes. Our effective resolution for such structures is many orders of magnitude better than achieved by conventional techniques on even the largest simulations. We apply these methods to the six Milky Way-mass haloes of the Aquarius Project. At 8 kpc from halo centre a typical point intersects about 10^14 streams with a very broad range of individual densities; the ~10^6 most massive streams contribute about half of the local dark matter density. As a result, the velocity distribution of dark matter particles should be very smooth with the most massive fine-grained stream contributing about 0.1% of the total signal. Dark matter particles at this radius have typically passed 200 caustics since the Big Bang. The peak densities on present-day caustics in the inner halo almost all lie well below the mean local dark matter density. As a result caustics provide a negligible boost (<0.1%) to the predicted local dark matter annihilation rate. The effective boost is larger in the outer halo but never exceeds about 10%. Thus fine-grained streams and their associated caustics have no effect on the detectability of dark matter, either directly in Earth-bound laboratories, or indirectly through annihilation radiation, with the exception that resonant cavity experiments searching for axions may see the most massive local fine-grained streams because of their extreme localisation in energy/momentum space. (abridged)

astro-ph.CO↗

arXiv2010

Bound and unbound substructures in Galaxy-scale Dark Matter haloes

We analyse the coarse-grained phase-space structure of the six Galaxy-scale dark matter haloes of the Aquarius Project using a state-of-the-art 6D substructure finder. Within r_50, we find that about 35% of the mass is in identifiable substructures, predominantly tidal streams, but including about 14% in self-bound subhaloes. The slope of the differential substructure mass function is close to -2, which should be compared to around -1.9 for the population of self-bound subhaloes. Near r_50 about 60% of the mass is in substructures, with about 30% in self-bound subhaloes. The inner 35 kpc of the highest resolution simulation has only 0.5% of its mass in self-bound subhaloes, but 3.3% in detected substructure, again primarily tidal streams. The densest tidal streams near the solar position have a 3-D mass density about 1% of the local mean, and populate the high velocity tail of the velocity distribution.

astro-ph.CO↗