MOA-II Galactic Microlensing Constraints: The Inner Milky Way has a Low Dark Matter Fraction and a Near Maximal Disk

Microlensing provides a unique tool to break the stellar to dark matter degeneracy in the inner Milky Way. We combine N-body dynamical models fitted to the Milky Way's Boxy/Peanut bulge with exponential disk models outside this, and compute the microlensing properties. Considering the range of models consistent with the revised MOA-II data, we find low dark matter fractions in the inner Galaxy: at the peak of their stellar rotation curve a fraction $f_v=(0.88\pm0.07)$ of the circular velocity is baryonic (at $1\sigma$, $f_v > 0.72$ at $2\sigma$). These results are in agreement with constraints from the EROS-II microlensing survey of brighter resolved stars, where we find $f_v=(0.9\pm0.1)$ at $1\sigma$. Our fiducial model of a disk with scale length 2.6kpc, and a bulge with a low dark matter fraction of 12%, agrees with both the revised MOA-II and EROS-II microlensing data. The required baryonic fractions, and the resultant low contribution from dark matter, are consistent with the NFW profiles produced by dissipationless cosmological simulations in Milky Way mass galaxies. They are also consistent with recent prescriptions for the mild adiabatic contraction of Milky Way mass haloes without the need for strong feedback, but there is some tension with recent measurements of the local dark matter density. Microlensing optical depths from the larger OGLE-III sample could improve these constraints further when available.Comment: 14 pages, 13 figures, submitted to MNRA

The Structure of the Milky Way's Bar Outside the Bulge

While it is incontrovertible that the inner Galaxy contains a bar, its structure near the Galactic plane has remained uncertain, where extinction from intervening dust is greatest. We investigate here the Galactic bar outside the bulge, the long bar, using red clump giant (RCG) stars from UKIDSS, 2MASS, VVV, and GLIMPSE. We match and combine these surveys to investigate a wide area in latitude and longitude, |b|<9deg and |l|<40deg. We find: (1) The bar extends to l~25deg at |b|~5deg from the Galactic plane, and to l~30deg at lower latitudes. (2) The long bar has an angle to the line-of-sight in the range (28-33)deg, consistent with studies of the bulge at |l|<10deg. (3) The scale-height of RCG stars smoothly transitions from the bulge to the thinner long bar. (4) There is evidence for two scale heights in the long bar. We find a ~180pc thin bar component reminiscent of the old thin disk near the sun, and a ~45pc super-thin bar component which exists predominantly towards the bar end. (5) Constructing parametric models for the RC magnitude distributions, we find a bar half length of 5.0+-0.2kpc for the 2-component bar, and 4.6+-0.3kpc for the thin bar component alone. We conclude that the Milky Way contains a central box/peanut bulge which is the vertical extension of a longer, flatter bar, similar as seen in both external galaxies and N-body models.Comment: Accepted for publication by MNRA

The Initial Mass Function of the Inner Galaxy Measured From OGLE-III Microlensing Timescales

We use the timescale distribution of ~3000 microlensing events measured by the OGLE-III survey, together with accurate new made-to-measure dynamical models of the Galactic bulge/bar region, to measure the IMF in the inner Milky Way. The timescale of each event depends on the mass of the lensing object, together with the relative distances and velocities of the lens and source. The dynamical model provides statistically these distances and velocities allowing us to constrain the lens mass function, and from this to infer the IMF. Parameterising the IMF as a broken power-law, we find slopes in the main sequence $\alpha_{\rm ms}=1.31\pm0.10|_{\rm stat}\pm0.10|_{\rm sys}$ and brown dwarf region $\alpha_{\rm bd}=-0.7\pm0.9|_{\rm stat}\pm0.8|_{\rm sys}$ where we use a fiducial 50% binary fraction, and the systematic uncertainty covers the range of binary fractions 0-100%. Similarly for a log-normal IMF we conclude $M_c=(0.17\pm0.02|_{\rm stat}\pm0.01|_{\rm sys})M_\odot$ and $\sigma_m=0.49\pm0.07|_{\rm stat}\pm0.06|_{\rm sys}$. These values are very similar to a Kroupa or Chabrier IMF respectively, showing that the IMF in the bulge is indistinguishable from that measured locally, despite the lenses lying in the inner Milky Way where the stars are mostly ~10Gyr old and formed on a fast $\alpha$-element enhanced timescale. This therefore constrains models of IMF variation that depend on the properties of the collapsing gas cloud.Comment: 6 pages, 3 figures. Accepted by ApJ

The Stellar Halo in the Inner Milky Way: Predicted Shape and Kinematics

We have used N-body simulations for the Milky Way to investigate the kinematic and structural properties of the old metal-poor stellar halo in the barred inner region of the Galaxy. We find that the extrapolation of the density distribution for bulge RR Lyrae stars, $\rho\sim r^{-3}$, approximately matches the number density of RR Lyrae in the nearby stellar halo. We follow the evolution of such a tracer population through the formation and evolution of the bar and box/peanut bulge in the N-body model. We find that its density distribution changes from oblate to triaxial, and that it acquires slow rotation in agreement with recent measurements. The maximum radial velocity is $\sim15-25$ km/s at $| l|\!=10^\circ-30^\circ$, and the velocity dispersion is $\sim120$ km/s. Even though the simulated metal-poor halo in the bulge has a barred shape, just $12\%$ of the orbits follow the bar, and it does not trace the peanut/X structure. With these properties, the RR Lyrae population in the Galactic bulge is consistent with being the inward extension of the Galactic metal-poor stellar halo.Comment: 5 pages, 5 figures. Accepted for publication in MNRAS Letter

Revisiting the Tale of Hercules: how stars orbiting the Lagrange points visit the Sun

We propose a novel explanation for the Hercules stream consistent with recent measurements of the extent and pattern speed of the Galactic bar. We have adapted a made-to-measure dynamical model tailored for the Milky Way to investigate the kinematics of the solar neighborhood (SNd). The model matches the 3D density of the red clump giant stars (RCGs) in the bulge and bar as well as stellar kinematics in the inner Galaxy, with a pattern speed of 39 km s$^{-1}$ kpc$^{-1}$. Cross-matching this model with the $Gaia$ DR1 TGAS data combined with RAVE and LAMOST radial velocities, we find that the model naturally predicts a bimodality in the $U\!-\!V$-velocity distribution for nearby stars which is in good agreement with the Hercules stream. In the model, the Hercules stream is made of stars orbiting the Lagrange points of the bar which move outward from the bar's corotation radius to visit the SNd. While the model is not yet a quantitative fit of the velocity distribution, the new picture naturally predicts that the Hercules stream is more prominent inward from the Sun and nearly absent only a few $100$ pc outward of the Sun, and plausibly explains that Hercules is prominent in old and metal-rich stars.Comment: 7 pages, 5 figures. ApJ Letters, in pres

Structure and dynamics of the galactic bulge and bar

Understanding galaxy evolution is one of the most active research fields in astronomy today. The Milky Way, our home galaxy can be observed on a star-by-star basis, something impossible in other galaxies and is therefore a natural benchmark for testing in detail galaxy formation theories. Therefore, many recent and ongoing large scale surveys have been carried out, providing an unprecedented collection of data to analyze. It is however challenging from the Sun's perspective to infer the current state of the Galaxy. In the work presented here dynamical equilibrium models of the Galaxy in its current state are built, a key element for later inferring its formation history. The dynamics of stars and dark matter are modeled in a self-consistent way, reproducing as many datasets as possible using the flexible Made-to-Measure method. An inside-out approach is adopted, starting by focusing on the galactic bulge before moving out to the larger scales, the galactic bar and the nearby disk. First a set of dynamical models of the galactic bulge with different dark matter fractions is made Chapter 2. Those models are fitted to reproduce both the 3D density of bulge stars, with their boxy/peanut shape, and the radial stellar kinematics in bulge fields measured by the BRAVA spectroscopic survey. Results from the modelling of different stellar and dark matter masses in the bulge lead to the most accurate measurement of the total dynamical mass of the galactic bulge up to date, of (1.84 \pm 0.07) \times 10^{10}\, \Msun in a volume of (\pm 2.2 \times \pm 1.4 \times \pm 1.2 )\kpc oriented along the bulge's principal axis. The orbital structure of the boxy/peanut shape in these dynamical models is then analyzed (Chapter 3). The boxy/peanut shape is found to be supported by novel brezel-like orbits, from which a strong peanut shape with a relatively short extension can be built, thus showing that boxy/peanut bulges are not necessarily supported by the so-called banana orbits as had been previously claimed in the literature. Outside the central 2\kpc, the galactic bulge smoothly segues into the long bar. Taking advantage of recent new data, the modelling was extended to the entire long bar region (Chapter 4). Additional data were added to the previous bulge models, mainly the distribution of Red Clump Giants in the bar region from a combination of the VVV, UKIDSS and 2MASS photometric surveys together with stellar kinematics as a function of distance along the line of sight from the \argos survey. By modelling the dynamics of the bar region, the pattern speed of the galactic bulge and bar is found to be (39.0 \pm 3.5)\kmskpc. This places the bar corotation radius at (6.1 \pm 0.5 )\kpc, making the Milky Way bar a typical fast rotator. The stellar mass of the long bar and bulge structure is evaluated to $M_{\rm{bar/bulge}} = 1.88 \pm 0.12 \times 10^{10} \, \rm{M}_{\odot}$, larger than the mass of disk in the bar region, $M_{\rm{inner\ disk}} = 1.29\pm0.12 \times 10^{10} \, \rm{M}_{\odot}$. Thanks to more extended kinematic datasets and recent measurement of the bulge IMF, the dark matter is found to account for $17\%\pm2\%$ of the mass in the bulge, with a density profile that flattens from the solar neighborhood to a shallow cusp or core in the bulge region. Finally, dynamical evidence for an extra central mass of $\sim2\times10^{9} \,\rm{M}_{\odot}$ is found, probably in a nuclear disk or disky pseudobulge. This dynamical model of the bar region provides both the gravitational potential and a consistent library of N-body orbits that can be used as a basis for more advanced modelling of the Galaxy. Recent and future spectroscopic surveys such as \apogee or GALAH will provide hundreds of thousands of stellar abundances of elements that can allow tracing back the formation history of the Galaxy. Chemodynamical models, a natural extension of the dynamical models to also include chemical information, will be vital to understand these new data. To this end, the Made-to-Measure method was extended to include the metallicity distribution of stars, hence constructing the first Made-to-Measure chemodynamical model (Chapter 5). This method was applied to the \argos and \apogee data to successfully fit with the dynamical model of the galactic bar the spatial and kinematic variations of the metallicity in the inner Galaxy. The resulting phase-space distribution of the different metallicity components in the inner Galaxy is then analyzed. The variations as a function of metallicity observed in the data are described and explained in term of differences in spatial, kinematic and orbital structure. This demonstrates that chemodynamical models of the barred inner Milky Way can be constructed using the Made-to-Measure method. Such models describe the present chemodynamical state of the Galaxy and will in the future be a valuable resource in confronting galactic evolution simulations

Sculpting Andromeda -- made-to-measure models for M31's bar and composite bulge: dynamics, stellar and dark matter mass

The Andromeda galaxy (M31) contains a box/peanut bulge (BPB) entangled with a classical bulge (CB) requiring a triaxial modelling to determine the dynamics, stellar and dark matter mass. We construct made-to-measure models fitting new VIRUS-W IFU bulge stellar kinematic observations, the IRAC-3.6$\mu$m photometry, and the disc's HI rotation curve. We explore the parameter space for the 3.6$\mu$m mass-to-light ratio $(\Upsilon_{3.6})$, the bar pattern speed ($\Omega_p$), and the dark matter mass in the composite bulge ($M^B_{DM}$) within 3.2kpc. Considering Einasto dark matter profiles, we find the best models for $\Upsilon_{3.6}=0.72\pm0.02\,M_\odot/L_\odot$, $M^B_{DM}=1.2^{+0.2}_{-0.4}\times10^{10}M_\odot$ and $\Omega_p=40\pm5\,km/s/kpc$. These models have a dynamical bulge mass of $M_{dyn}^B=4.25^{+0.10}_{-0.29}\times10^{10}M_{\odot}$ including a stellar mass of $M^B=3.09^{+0.10}_{-0.12}\times10^{10}M_\odot$(73%), of which the CB has $M^{CB}=1.18^{+0.06}_{-0.07}\times10^{10}M_\odot$(28%) and the BPB $M^{BPB}=1.91\pm0.06\times10^{10}M_\odot$(45%). We also explore models with NFW haloes finding that, while the Einasto models better fit the stellar kinematics, the obtained parameters agree within the errors. The $M^B_{DM}$ values agree with adiabatically contracted cosmological NFW haloes with M31's virial mass and radius. The best model has two bulge components with completely different kinematics that only together successfully reproduce the observations ($\mu_{3.6},\upsilon_{los},\sigma_{los},h3,h4$). The modelling includes dust absorption which reproduces the observed kinematic asymmetries. Our results provide new constraints for the early formation of M31 given the lower mass found for the classical bulge and the shallow dark matter profile, as well as the secular evolution of M31 implied by the bar and its resonant interactions with the classical bulge, stellar halo and disc.Comment: 32 pages, 32 Figures; Published in MNRA

Dynamical modelling of the inner Galactic barred disk

Understanding the present state of the Milky Way disk is a necessary first step towards learning about the formation history of our Galaxy. While it is clear from infrared photometry that the inner disk hosts a 5 kpc long bar with a central Box/Peanut bulge, the interplay between the bar and the inner disk remains poorly known. To this end we build N-body dynamical models of the inner Galaxy with the Made-to-Measure method, combining deep photometry from the VVV, UKIDSS and 2MASS surveys with kinematics from the BRAVA, OGLE and ARGOS surveys. We explore their stellar to dark matter fraction together with their bar pattern speed and constrain from the modelling the effective Galactic potential (gravitational potential + bar pattern speed) inside the solar radius. Our best model is able to reproduce simultaneously (i) the Box/Peanut shape of the bulge, (ii) the transition between bulge and long bar, (iii) the bulge line-of-sight kinematics and proper motion dispersions, (iv) the ARGOS velocity field in the bar region and (v) the rotation curve of the Galaxy inside 10 kpc. Our effective potential will be an important input to more detailed chemodynamical studies of the stellar populations in the inner Galaxy, as revealed by the ARGOS or APOGEE surveys