arXiv subjects

Julio F. Navarro

Publications and source records attributed to Julio F. Navarro.

At least 73 records · Page 4Linked to original sources

arXiv2021

Velocity-dependent J-factors for annihilation radiation from cosmological simulations

We determine the dark matter pair-wise relative velocity distribution in a set of Milky Way-like halos in the Auriga and APOSTLE simulations. Focusing on the smooth halo component, the relative velocity distribution is well-described by a Maxwell-Boltzmann distribution over nearly all radii in the halo. We explore the implications for velocity-dependent dark matter annihilation, focusing on four models which scale as different powers of the relative velocity: Sommerfeld, s-wave, p-wave, and d-wave models. We show that the J-factors scale as the moments of the relative velocity distribution, and that the halo-to-halo scatter is largest for d-wave, and smallest for Sommerfeld models. The J-factor is strongly correlated with the dark matter density in the halo, and is very weakly correlated with the velocity dispersion. This implies that if the dark matter density in the Milky Way can be robustly determined, one can accurately predict the dark matter annihilation signal, without the need to identify the dark matter velocity distribution in the Galaxy.

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arXiv2021

Globular clusters as tracers of the dark matter content of dwarfs in galaxy clusters

Globular clusters (GCs) are often used to estimate the dark matter content of galaxies, especially dwarfs, where other kinematic tracers are lacking. These estimates typically assume spherical symmetry and dynamical equilibrium, assumptions that may not hold for the sparse GC population of dwarfs in galaxy clusters. We use a catalog of GCs tagged onto the Illustris simulation to study the accuracy of GC-based mass estimates. We focus on galaxies in the stellar mass range 10$^{8} - 10^{11.8}$ M$_{\odot}$ identified in $9$ simulated Virgo-like clusters. Our results indicate that mass estimates are, on average, quite accurate in systems with GC numbers $N_{\rm GC} \geq 10$ and where the uncertainty of individual GC line-of-sight velocities is smaller than the inferred velocity dispersion, $σ_{\rm GC}$. In cases where $N_{\rm GC} \leq 10$, however, biases may result depending on how $σ_{\rm GC}$ is computed. We provide calibrations that may help alleviate these biases in methods widely used in the literature. As an application, we find a number of dwarfs with $M_{*} \sim 10^{8.5}\, M_{\odot}$ (comparable to the ultradiffuse galaxy DF2, notable for the low $σ_{GC}$ of its $10$ GCs) with $σ_{\rm GC} \sim 7$ - $15\; \rm km \rm s^{-1}$. These DF2 analogs correspond to relatively massive systems at their infall time ($M_{200} \sim 1$ - $3 \times 10^{11}$ $M_{\odot}$) which have retained only $3$-$17$ GCs and have been stripped of more than 95$\%$ of their dark matter. Our results suggest that extreme tidal mass loss in otherwise normal dwarf galaxies may be a possible formation channel for ultradiffuse objects like DF2.

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arXiv2020

Observational constraints on the slope of the radial acceleration relation at low accelerations

The radial acceleration relation (RAR) locally relates the `observed' acceleration inferred from the dynamics of a system to the acceleration implied by its baryonic matter distribution. The relation as traced by galaxy rotation curves is one-to-one with remarkably little scatter, implying that the dynamics of a system can be predicted simply by measuring its density profile as traced by e.g. stellar light or gas emission lines. Extending the relation to accelerations below those usually probed by practically observable kinematic tracers is challenging, especially once accounting for faintly emitting baryons, such as the putative warm-hot intergalactic medium, becomes important. We show that in the low-acceleration regime, the (inverted) RAR predicts an unphysical, declining enclosed baryonic mass profile for systems with `observed' acceleration profiles steeper than $g_{\rm obs}\propto r^{-1}$ (corresponding to density profiles steeper than isothermal - $ρ(r)\propto r^{-2}$). If the RAR is tantamount to a natural law, such acceleration profiles cannot exist. We apply this argument to test the compatibility of an extrapolation of the rotation curve-derived RAR to low accelerations with data from galaxy-galaxy weak lensing, dwarf spheroidal galaxy stellar kinematic, and outer Milky~Way dynamical measurements, fully independent of the uncertainties inherent in direct measurements of the baryonic matter distribution. In all cases we find that the data weakly favour a break to a steeper low-acceleration slope. Improvements in measurements and modelling of the outer Milky~Way, and weak lensing, seem like the most promising path toward stronger constraints on the low-acceleration behaviour of the RAR.

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arXiv2020

The missing dwarf galaxies of the Local Group

We study the Local Group (LG) dwarf galaxy population predicted by the \apostle $Λ$CDM cosmological hydrodynamics simulations. These indicate that: (i)~the total mass within $3$ Mpc of the Milky Way-Andromeda midpoint ($M_{\rm 3Mpc}$) typically exceeds $\sim 3$ times the sum of the virial masses ($M_{\rm 200crit}$) of the two primaries and (ii)~the dwarf galaxy formation efficiency per unit mass is uniform throughout the volume. This suggests that the satellite population within the virial radii of the Milky Way and Andromeda should make up fewer than one third of all LG dwarfs within $3$ Mpc. This is consistent with the fraction of observed LG galaxies with stellar mass $M_*>10^7\,M_{\odot}$ that are satellites ($12$ out of $42$; i.e., $28$ per cent). For the \apostle galaxy mass-halo mass relation, the total number of such galaxies further suggests a LG mass of $M_{\rm 3 Mpc}\sim 10^{13} \, M_{\odot}$. At lower galaxy masses, however, the observed satellite fraction is substantially higher ($42$ per cent for $M_*>10^5\,M_{\odot}$). If this is due to incompleteness in the field sample, then $\sim 50$ dwarf galaxies at least as massive as the Draco dwarf spheroidal must be missing from the current LG {\it field} dwarf inventory. The incompleteness interpretation is supported by the pronounced flattening of the LG luminosity function below $M_*\sim 10^7\, M_{\odot}$, and by the scarcity of low-surface brightness LG field galaxies compared to satellites. The simulations indicate that most missing dwarfs should lie near the virial boundaries of the two LG primaries, and predict a trove of nearby dwarfs that await discovery by upcoming wide-field imaging surveys.

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arXiv2020

The APOSTLE project: Local Group kinematic mass constraints and simulation candidate selection

We use a large sample of isolated dark matter halo pairs drawn from cosmological N-body simulations to identify candidate systems whose kinematics match that of the Local Group of Galaxies (LG). We find, in agreement with the "timing argument" and earlier work, that the separation and approach velocity of the Milky Way (MW) and Andromeda (M31) galaxies favour a total mass for the pair of $\sim 5\times 10^{12} \,M_{\odot}$. A mass this large, however, is difficult to reconcile with the small relative tangential velocity of the pair, as well as with the small deceleration from the Hubble flow observed for the most distant LG members. Halo pairs that match these three criteria have average masses a factor of $\sim 2$ times smaller than suggested by the timing argument, but with large dispersion. Guided by these results, we have selected $12$ halo pairs with total mass in the range $1.6$-$3.6 \times 10^{12}\,M_{\odot}$ for the APOSTLE project (A Project Of Simulating The Local Environment), a suite of hydrodynamical resimulations at various numerical resolution levels (reaching up to $\sim10^{4}\,M_{\odot}$ per gas particle) that use the subgrid physics developed for the EAGLE project. These simulations reproduce, by construction, the main kinematics of the MW-M31 pair, and produce satellite populations whose overall number, luminosities, and kinematics are in good agreement with observations of the MW and M31 companions. The APOSTLE candidate systems thus provide an excellent testbed to confront directly many of the predictions of the $Λ$CDM cosmology with observations of our local Universe.

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arXiv2020

Exploring the origin of low-metallicity stars in Milky Way-like galaxies with the NIHAO-UHD simulations

The kinematics of the most metal-poor stars provide a window into the early formation and accretion history of the Milky Way. Here, we use 5~high-resolution cosmological zoom-in simulations ($\sim~5\times10^6$ star particles) of Milky Way-like galaxies taken from the NIHAO-UHD project, to investigate the origin of low-metallicity stars ([Fe/H]$\leq-2.5$). The simulations show a prominent population of low-metallicity stars confined to the disk plane, as recently discovered in the Milky Way. The ubiquity of this finding suggests that the Milky Way is not unique in this respect. Independently of the accretion history, we find that $\gtrsim~90$ per cent of the retrograde stars in this population are brought in during the initial build-up of the galaxies during the first few Gyrs after the Big Bang. Our results therefore highlight the great potential of the retrograde population as a tracer of the early build-up of the Milky Way. The prograde planar population, on the other hand, is accreted during the later assembly phase and samples the full galactic accretion history. In case of a quiet accretion history, this prograde population is mainly brought in during the first half of cosmic evolution ($t\lesssim7$~Gyr), while, in the case of an on-going active accretion history, later mergers on prograde orbits are also able to contribute to this population. Finally, we note that the Milky Way shows a rather large population of eccentric, very metal-poor planar stars. This is a feature not seen in most of our simulations, with the exception of one simulation with an exceptionally active early building phase.

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arXiv2020

The hidden past of M92: Detection and characterization of a newly formed 17° long stellar stream using the Canada-France Imaging Survey

We present an analysis of the structure, kinematics and orbit of a newly found stellar stream emanating from the globular cluster M92 (NGC 6341). This stream was discovered in an improved matched-filter map of the outer Galaxy, based on a "color-color-magnitude" diagram, created using photometry from the Canada-France Imaging Survey (CFIS) and the Pan-STARRS 1 3$π$ survey (PS1). We find the stream to have a length of 17° (2.5 kpc at the distance of M92), a width dispersion of $0.29$°(42 pc) and a stellar mass of $[3.17 \pm{0.89}] \times 10^{4} $ M$_\odot$ ($10 \%$ of the stellar mass of the current main body of M92). We examine the kinematics of main sequence, red giant and blue horizontal branch stars belonging to the stream and that have proper motion measurements from the second data release of Gaia. N-body simulations suggest that the stream was likely formed very recently (during the last $\sim 500$ Myr) forcing us to question the orbital origin of this ancient, metal-poor globular cluster.

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arXiv2020

To beta or not to beta: can higher-order Jeans analysis break the mass-anisotropy degeneracy in simulated dwarfs?

We test a non-parametric higher-order Jeans analysis method, GravSphere, on 32 simulated dwarf galaxies comparable to classical Local Group dwarfs like Fornax. The galaxies are selected from the APOSTLE suite of cosmological hydrodynamics simulations with Cold Dark Matter (CDM) and Self-Interacting Dark Matter (SIDM) models, allowing us to investigate cusps and cores in density distributions. We find that, for CDM dwarfs, the recovered enclosed mass profiles have a bias of no more than 10 per cent, with a 50 per cent scatter in the inner regions and a 20 per cent scatter near the half-light radius, consistent with standard mass estimators. The density profiles are also recovered with a bias of no more than 10 per cent and a scatter of 30 per cent in the inner regions. For SIDM dwarfs, the mass and density profiles are recovered within our 95 per cent confidence intervals, but are biased towards cuspy dark matter distributions. This is mainly due to a lack of sufficient constraints from the data. We explore the sources of scatter in the accuracy of the recovered profiles and suggest a $χ^2$ statistic to separate successful models from biased ones. Finally, we show that the uncertainties on the mass profiles obtained with GravSphere are smaller than those for comparable Jeans methods, and that they can be further improved if stronger priors, motivated by cosmological simulations, are placed on the velocity anisotropy. We conclude that GravSphere is a promising Jeans-based approach for modelling dark matter distributions in dwarf galaxies.

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arXiv2020

The $R$-Process Alliance: Fourth Data Release from the Search for $r$-Process-Enhanced Stars in the Galactic Halo

This compilation is the fourth data release from the $R$-Process Alliance (RPA) search for $r$-process-enhanced stars, and the second release based on "snapshot" high-resolution ($R \sim 30,000$) spectra collected with the du Pont 2.5m Telescope. In this data release, we propose a new delineation between the $r$-I and $r$-II stellar classes at $\mathrm{[Eu/Fe]} = +0.7$, instead of the empirically chosen $\mathrm{[Eu/Fe]} = +1.0$ level previously in use, based on statistical tests of the complete set of RPA data released to date. We also statistically justify the minimum level of [Eu/Fe] for definition of the $r$-I stars, [Eu/Fe] $> +0.3$. Redefining the separation between $r$-I and $r$-II stars will aid in analysis of the possible progenitors of these two classes of stars and whether these signatures arise from separate astrophysical sources at all. Applying this redefinition to previous RPA data, the number of identified $r$-II and $r$-I stars changes to 51 and 121, respectively, from the initial set of data releases published thus far. In this data release, we identify 21 new $r$-II, 111 new $r$-I (plus three re-identified), and 7 new (plus one re-identified) limited-$r$ stars out of a total of 232 target stars, resulting in a total sample of 72 new $r$-II stars, 232 new $r$-I stars, and 42 new limited-$r$ stars identified by the RPA to date.

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arXiv2020

The Formation of Ultra-Diffuse Galaxies in Clusters

We use the IllustrisTNG cosmological hydrodynamical simulation to study the formation of ultra-diffuse galaxies (UDGs) in galaxy clusters. We supplement the simulations with a realistic mass-size relation for galaxies at the time of infall into the cluster, as well as an analytical model to describe the tidally-induced evolution of their stellar mass, velocity dispersion and size. The model assumes "cuspy" NFW halos and, contrary to recent claims, has no difficulty reproducing the observed number of UDGs in clusters. Our results further suggest that the UDG population consists of a mixture of "normal" low surface brightness galaxies such as those found in the field ("born" UDGs, or B-UDGs), as well as a distinct population that owe their large size and low surface brightness to the effects of cluster tides ("tidal", or T-UDGs). The simulations indicate that T-UDGs entered the cluster earlier and should be more prevalent than B-UDGs near the cluster centres. T-UDGs should also have, at given stellar mass, lower velocity dispersion, higher metallicities, and lower dark matter content than B-UDGs. Our results suggest that systems like DF-44 are consistent with having been born as UDGs, while others such as DF2, DF4 and VLSB-D are possibly extreme T-UDG examples.

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arXiv2020

The Edge of the Galaxy

We use cosmological simulations of isolated Milky Way-mass galaxies, as well as Local Group analogues, to define the "edge" -- a caustic manifested in a drop in density or radial velocity -- of Galactic-sized haloes, both in dark matter and in stars. In the dark matter, we typically identify two caustics: the outermost caustic located at ~1.4r_200m corresponding to the "splashback" radius, and a second caustic located at ~0.6r_200m which likely corresponds to the edge of the virialized material which has completed at least two pericentric passages. The splashback radius is ill defined in Local Group type environments where the halos of the two galaxies overlap. However, the second caustic is less affected by the presence of a companion, and is a more useful definition for the boundary of the Milky Way halo. Curiously, the stellar distribution also has a clearly defined caustic, which, in most cases, coincides with the second caustic of the dark matter. This can be identified in both radial density and radial velocity profiles, and should be measurable in future observational programmes. Finally, we show that the second caustic can also be identified in the phase-space distribution of dwarf galaxies in the Local Group. Using the current dwarf galaxy population, we predict the edge of the Milky Way halo to be 292 +/- 61 kpc.

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arXiv2020

The Pristine Inner Galaxy Survey (PIGS) II: Uncovering the most metal-poor populations in the inner Milky Way

Metal-poor stars are important tools for tracing the early history of the Milky Way, and for learning about the first generations of stars. Simulations suggest that the oldest metal-poor stars are to be found in the inner Galaxy. Typical bulge surveys, however, lack low metallicity ([Fe/H] < -1.0) stars because the inner Galaxy is predominantly metal-rich. The aim of the Pristine Inner Galaxy Survey (PIGS) is to study the metal-poor and very metal-poor (VMP, [Fe/H] < -2.0) stars in this region. In PIGS, metal-poor targets for spectroscopic follow-up are selected from metallicity-sensitive CaHK photometry from the CFHT. This work presents the ~250 deg^2 photometric survey as well as intermediate-resolution spectroscopic follow-up observations for ~8000 stars using AAOmega on the AAT. The spectra are analysed using two independent tools: ULySS with an empirical spectral library, and FERRE with a library of synthetic spectra. The comparison between the two methods enables a robust determination of the stellar parameters and their uncertainties. We present a sample of 1300 VMP stars -- the largest sample of VMP stars in the inner Galaxy to date. Additionally, our spectroscopic dataset includes ~1700 horizontal branch stars, which are useful metal-poor standard candles. We furthermore show that PIGS photometry selects VMP stars with unprecedented efficiency: 86%/80% (lower/higher extinction) of the best candidates satisfy [Fe/H] < -2.0, as do 80%/63% of a larger, less strictly selected sample. We discuss future applications of this unique dataset that will further our understanding of the chemical and dynamical evolution of the innermost regions of our Galaxy.

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arXiv2020

The Sixth Data Release of the Radial Velocity Experiment (RAVE) -- II: Stellar Atmospheric Parameters, Chemical Abundances and Distances

We present part 2 of the 6th and final Data Release (DR6 or FDR) of the Radial Velocity Experiment (RAVE), a magnitude-limited (9<I<12) spectroscopic survey of Galactic stars randomly selected in the southern hemisphere. The RAVE medium-resolution spectra (R~7500) cover the Ca-triplet region (8410-8795A) and span the complete time frame from the start of RAVE observations on 12 April 2003 to their completion on 4 April 2013. In the second of two publications, we present the data products derived from 518387 observations of 451783 unique stars using a suite of advanced reduction pipelines focussing on stellar atmospheric parameters, in particular purely spectroscopically derived stellar atmospheric parameters (Teff, log(g), and the overall metallicity), enhanced stellar atmospheric parameters inferred via a Bayesian pipeline using Gaia DR2 astrometric priors, and asteroseismically calibrated stellar atmospheric parameters for giant stars based on asteroseismic observations for 699 K2 stars. In addition, we provide abundances of the elements Fe, Al, and Ni, as well as an overall [alpha/Fe] ratio obtained using a new pipeline based on the GAUGUIN optimization method that is able to deal with variable signal-to-noise ratios. The RAVE DR6 catalogs are cross matched with relevant astrometric and photometric catalogs, and are complemented by orbital parameters and effective temperatures based on the infrared flux method. The data can be accessed via the RAVE Web site (http://rave-survey.org) or the Vizier database.

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arXiv2020

The Sixth Data Release of the Radial Velocity Experiment (RAVE) -- I: Survey Description, Spectra and Radial Velocities

The Radial Velocity Experiment (RAVE) is a magnitude-limited (9<I<12) spectroscopic survey of Galactic stars randomly selected in the southern hemisphere. The RAVE medium-resolution spectra (R~7500) cover the Ca-triplet region (8410-8795A). The 6th and final data release (DR6 or FDR) is based on 518387 observations of 451783 unique stars. RAVE observations were taken between 12 April 2003 and 4 April 2013. Here we present the genesis, setup and data reduction of RAVE as well as wavelength-calibrated and flux-normalized spectra and error spectra for all observations in RAVE DR6. Furthermore, we present derived spectral classification and radial velocities for the RAVE targets, complemented by cross matches with Gaia DR2 and other relevant catalogs. A comparison between internal error estimates, variances derived from stars with more than one observing epoch and a comparison with radial velocities of Gaia DR2 reveals consistently that 68% of the objects have a velocity accuracy better than 1.4 km/s, while 95% of the objects have radial velocities better than 4.0 km/s. Stellar atmospheric parameters, abundances and distances are presented in subsequent publication. The data can be accessed via the RAVE Web (http://rave-survey.org) or the Vizier database.

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arXiv2020

The Pristine Dwarf-Galaxy survey -- III. Revealing the nature of the Milky Way globular cluster Sagittarius II

We present a new spectroscopic study of the faint Milky Way satellite Sagittarius II. Using multi-object spectroscopy from the Fibre Large Array Multi Element Spectrograph, we supplement the dataset of Longeard et al. (2020) with 47 newly observed stars, 19 of which are identified as members of the satellite. These additional member stars are used to put tighter constraints on the dynamics and the metallicity properties of the system. We find a low velocity dispersion of SgrII v = 1.7 +/- 0.5 km s-1, in agreement with the dispersion of Milky Way globular clusters of similar luminosity. We confirm the very metal-poor nature of the satellite ([Fe/H]_SgrII = -2.23 +/- 0.07) and find that the metallicity dispersion of Sgr II is not resolved, reaching only 0.20 at the 95% confidence limit. No star with a metallicity below -2.5 is confidently detected. Therefore, despite the unusually large size of the system (rh = 35.5 +1.4-1.2 pc), we conclude that Sgr II is an old and metal-poor globular cluster of the Milky Way.

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arXiv2020

Baryonic clues to the puzzling diversity of dwarf galaxy rotation curves

We use a compilation of disc galaxy rotation curves to assess the role of the luminous component ("baryons") in the rotation curve diversity problem. As in earlier work, we find that rotation curve shape correlates with baryonic surface density: high surface density galaxies have rapidly-rising rotation curves consistent with cuspy cold dark matter halos; slowly-rising rotation curves (characteristic of galaxies with inner mass deficits or "cores") occur only in low surface density galaxies. The correlation, however, seems too weak to be the main driver of the diversity. In addition, dwarf galaxies exhibit a clear trend, from "cuspy" systems where baryons are unimportant in the inner mass budget to "cored" galaxies where baryons actually dominate. This trend constrains the various scenarios proposed to explain the diversity, such as (i) baryonic inflows and outflows during galaxy formation; (ii) dark matter self-interactions; (iii) variations in the baryonic mass structure coupled to rotation velocities through the "mass discrepancy-acceleration relation" (MDAR); or (iv) non-circular motions in gaseous discs. Together with analytical modeling and cosmological hydrodynamical simulations, our analysis shows that each of these scenarios has promising features, but none seems to fully account for the observed diversity. The MDAR, in particular, is inconsistent with the observed trend between rotation curve shape and baryonic importance; either the trend is caused by systematic errors in the data or the MDAR does not apply. The origin of the dwarf galaxy rotation curve diversity and its relation to the structure of cold dark matter halos remains an open issue.

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arXiv2020

The Milky Way total mass profile as inferred from Gaia DR2

We determine the Milky Way (MW) mass profile inferred from fitting physically motivated models to the Gaia DR2 Galactic rotation curve and other data. Using various hydrodynamical simulations of MW-mass haloes, we show that the presence of baryons induces a contraction of the dark matter (DM) distribution in the inner regions, r<20 kpc. We provide an analytic expression that relates the baryonic distribution to the change in the DM halo profile. For our galaxy, the contraction increases the enclosed DM halo mass by factors of roughly 1.3, 2 and 4 at radial distances of 20, 8 and 1 kpc, respectively compared to an uncontracted halo. Ignoring this contraction results in systematic biases in the inferred halo mass and concentration. We provide a best-fitting contracted NFW halo model to the MW rotation curve that matches the data very well. The best-fit has a DM halo mass, $M_{200}^{\rm DM}=0.97_{-0.19}^{+0.24}\times10^{12} M_\odot$, and concentration before baryon contraction of $9.4_{-2.6}^{+1.9}$, which lie close to the median halo mass--concentration relation predicted in $Λ$CDM. The inferred total mass, $M_{200}^{\rm total}=1.08_{-0.14}^{+0.20} \times 10^{12} M_\odot$, is in good agreement with recent measurements. The model gives a MW stellar mass of $5.04_{-0.52}^{+0.43}\times10^{10} M_\odot$ and infers that the DM density at the Solar position is $ρ_{\odot}^{\rm DM}=8.8_{-0.5}^{+0.5}\times10^{-3} M_\odot \rm{pc}^{-3}\equiv0.33_{-0.02}^{+0.02}~\rm{GeV}~\rm{cm}^{-3}$. The rotation curve data can also be fitted with an uncontracted NFW halo model, but with very different DM and stellar parameters. The observations prefer the physically motivated contracted NFW halo, but the measurement uncertainties are too large to rule out the uncontracted NFW halo.

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arXiv2019

The Pristine survey X: a large population of low-metallicity stars permeates the Galactic disk

The orbits of the least chemically enriched stars open a window on the formation of our Galaxy when it was still in its infancy. The common picture is that these low-metallicity stars are distributed as an isotropic, pressure-supported component since these stars were either accreted from the early building blocks of the assembling Milky Way, or were later brought by the accretion of faint dwarf galaxies. Combining the metallicities and radial velocities from the Pristine and LAMOST surveys and Gaia DR2 parallaxes and proper motions for an unprecedented large and unbiased sample of very metal-poor stars at $[Fe/H]\leq-2.5$ we show that this picture is incomplete. This sample shows strong statistical evidence (at the $5.0σ$ level) of asymmetry in their kinematics, favouring prograde motion. Moreover, we find that $31\%$ of the stars that currently reside in the disk do not venture outside of the disk plane throughout their orbit. The discovery of this population implies that a significant fraction of stars with iron abundances $[Fe/H]\leq-2.5$ formed within or concurrently with the Milky Way disk and that the history of the disk was quiet enough to allow them to retain their disk-like orbital properties.

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