Revisiting the tale of Hercules: How stars orbiting the Lagrange points visit the Sun

Pérez-Villegas A., Portail M., Wegg C., Gerhard O., 2017, ApJ, 840, L2

U-V velocity distribution in our model within 300pc fro the Sun (central plot) and typical orbits in the bar frame of stars in the Solar neighborhood (all around). The main component is mostly made of epicycle orbits while the excess of stars around U~-30 km s-1, V~-50 km s-1 is due to stars orbiting (sometime partially) the Lagrange points.

 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. 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 TGAS Gaia DR1 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 outwards from the bar's corotation radius to visit the Solar neighborhood. This new picture of the Hercules stream naturally predicts that the Hercules stream is more prominent inwards from the Sun and nearly absent only a few 100 pc outwards of the Sun, and plausibly explains that Hercules is prominent in old and metal-rich stars.

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Dynamical modelling of the galactic bulge and bar: Pattern speed, stellar, and dark matter mass distributions

Matthieu Portail, Ortwin Gerhard, Christopher Wegg and Melissa Ness, 2012, MNRAS, 465, 1621

Surface density of the best-fitting model of the inner Galaxy.

We construct a large set of dynamical models of the galactic bulge, bar and inner disk using the Made-to-Measure method. Our models are constrained to match the red clump giant density from a combination of the VVV, UKIDSS and 2MASS infrared surveys together with stellar kinematics in the bulge from the BRAVA and OGLE surveys, and in the entire bar region from the ARGOS survey. We are able to recover the bar pattern speed and the stellar and dark matter mass distributions in the bar region, thus recovering the entire galactic effective potential. We find a bar pattern speed of 39.0 ± 3.5 km s-1 kpc -1, placing the bar corotation radius at 6.1 ± 0.5 kpc and making the Milky Way a typical fast rotator. We evaluate the mass of the long bar and bulge structure to be Mbar/bulge = 1.88 ± 0.12 x 1010 M, larger than the mass of disk in the bar region of only Minner disk = 1.29 ± 0.12 x 1010 M. The total dynamical mass in the bulge volume is 1.85 ±0.05 x 1010 M. Thanks to more extended kinematics datasets and recent measurement of the bulge IMF we we obtain a low dark matter fraction in the bulge of 17% ± 2%. We find a dark matter density profile which flattens to a shallow cusp or core in the bulge region. Finally, we find dynamical evidence for an extra central mass of 2∼109 M, probably in a nuclear disk or disky pseudobulge.

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MOA-II Galactic microlensing constraints: The inner Milky Way has a low dark matter fraction and a near maximal disk

Christopher Wegg, Ortwin Gerhard and Matthieu Portail, 2016, MNRAS, 463, 557

Comparison of the predicted optical depth of our fiducial model compared to the revised MOA-II data. The data and the model are averaged in the same manner: an Gaussian average with σ =0.4 deg of fields within 1 deg. We show from left to right comparison of the optical depth, the event rate per star, and the mean timescale in days. The optical depth and event rate maps show good qualitative agreement. The mean timescale map has large observational error due to the large statistical variance of timescale caused by the rare very long timescale events.

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 fv=(0.88 ± 0.07) of the circular velocity is baryonic at 1 sigma, fv > 0.72$ at 2 sigmas. These results are in agreement with constraints from the EROS-II microlensing survey of brighter resolved stars, where we find fv =(0.9 ± 0.1) 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.

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Peanuts, brezels and bananas: food for thought on the orbital structure of the Galactic bulge

Matthieu Portail, Christopher Wegg, Ortwin Gerhard, 2015, MNRAS, 450, L66

Side-on projections of the 5 classes of orbits identified by frequency analysis. The banana orbits are on class F and reach significant heights only at 2.5 kpc from the Galactic center, too far away to contribute significantly to the Peanut shape of the Galactic bulge. Most of the Peanut shape is made out of orbits in classes B and C.

Recent observations have discovered the presence of a box/peanut or X-shape structure in the Galactic bulge. Such box/peanut structures are common in external disc galaxies, and are well known in N-body simulations where they form following the buckling instability of a bar. From studies of analytical potentials and N-body models, it has been claimed in the past that box/peanut bulges are supported by ‘bananas’, or x1v1 orbits. We present here a set of N-body models where instead the peanut bulge is mainly supported by brezel-like orbits, allowing strong peanuts to form with short extent relative to the bar length. This shows that stars in the X-shape do not necessarily stream along banana orbits which follow the arms of the X-shape. The brezel orbits are also found to be the main orbital component supporting the peanut shape in our recent made-to-measure dynamical models of the Galactic bulge. We also show that in these models the fraction of stellar orbits that contribute to the X-structure account for 40–45 per cent of the stellar mass.

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Face-on (top) and side-on (bottom) projection of the brezel orbit, major component of the Peanut shape in our Made-to-Measure dynamical models for the Galactic bulge.

Made-to-measure models of the Galactic box/peanut bulge: stellar and total mass in the bulge region

Matthieu Portail, Christopher Wegg, Ortwin Gerhard & Inma Martinez-Valpuesta, 2015, MNRAS, 448, 713

Stellar and dark matter mass of the 5 models with different dark matter fraction. The total mass (stellar + dark matter) is remarkably fixed along this sequence.

We construct dynamical models of the Milky Way’s box/peanut (B/P) bulge by enforcing N-body models of barred stellar disk to reproduce a set observables data using the Made-to-measure method and our NMAGIC code. The stellar particles are constraint to match the 3D density of RCGs measured from the VVV data together with stellar kinematics from the BRAVA survey. The stellar dynamics respond to the total gravitational potential, that includes the contribution of the dark matter in the bulge. We work on several N-body models with different dark matter fractions in the bulge and find from the modelling a very accurate measurement of the total mass (i.e. stellar + dark matter mass) of the Galactic bulge of 18.4 ± 0.7 billions of solar masses, with an unprecedented accuracy.

How much dark matter there is in the inner Milky-Way? Unfortunately, the kinematic signature of the ratio of stellar to dark matter mass in the bulge is not strong enough to appear in the data we used. However, using additional luminosity measurements from the COBE satellite we compute the stellar mass-to-light ratio of our models and find values in the K band in the range 0.8–1.1. These values can be compared to predictions of population synthesis models for an old stellar population originating from different Initial Mass Functions (IMF). We find that our mass-to-light ratios are inconsistent with predictions from the Salpeter IMF, ruling it our for the Galactic bulge. Prediction from the Zoccali IMF requires about 40% dark matter in the bulge.

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Unifying a boxy bulge and planar long bar in the Milky Way

Inma Martinez-Valpuesta & Ortwin Gerhard, 2011, ApJL, 734, 20

Top panel: Face-on view of the simulation with bar rotating clockwise and its ends bend towards the leading side. Lower panel: edge-on  view of the same snapshot, as viewed from the  Sun. The boxy structure is noticeable.

We have known for sometime that the Milky Way is a barred disk galaxy. But more recently, several studies inferred from star count observations that the Galaxy must contain a separate, new, flat long bar component, twisted relative to the barred bulge. With a simulation we showed that these observations can be reproduced with a single boxy bulge and bar structure. In this simulation, a stellar bar evolved from the disk, and the boxy bulge originated from it through secular evolution and the buckling instability.

We calculated the star count distributions for this model at different longitudes and latitudes, in a similar way as observers have done for resolved star counts. We found good
quantitative agreement with the observations for a suitable model snapshot. The long bar signature in this model is partially is due to a volume effect in the star counts, and partially because of choosing a snapshot in which the planar bar has developed leading ends by interacting with the nearby spiral arm heads. We also calculated radial velocity predictions from this model for comparison with upcoming surveys.

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