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Ortwin Gerhard

Publications and source records attributed to Ortwin Gerhard.

At least 73 records · Page 4Linked to original sources

Chemodynamical Modelling of the Galactic Bulge and Bar

We present the first self-consistent chemodynamical model fitted to reproduce data for the galactic bulge, bar and inner disk. We extend the Made-to-Measure method to an augmented phase-space including the metallicity of stars, and show its first application to the bar region of the Milky Way. Using data from the ARGOS and APOGEE (DR12) surveys, we adapt the recent dynamical model from Portail et al. to reproduce the observed spatial and kinematic variations as a function of metallicity, thus allowing the detailed study of the 3D density distributions, kinematics and orbital structure of stars in different metallicity bins. We find that metal-rich stars with [Fe/H] > -0.5 are strongly barred and have dynamical properties that are consistent with a common disk origin. Metal-poor stars with [Fe/H] < -0.5 show strong kinematic variations with metallicity, indicating varying contributions from the underlying stellar populations. Outside the central kpc, metal-poor stars are found to have the density and kinematics of a thick disk while in the inner kpc, evidence for an extra concentration of metal-poor stars is found. Finally, the combined orbit distributions of all metallicities in the model naturally reproduce the observed vertex deviations in the bulge. This paper demonstrates the power of Made-to-Measure chemodynamical models, that when extended to other chemical dimensions will be very powerful tools to maximize the information obtained from large spectroscopic surveys such as APOGEE, GALAH and MOONS.

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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 $α_{\rm ms}=1.31\pm0.10|_{\rm stat}\pm0.10|_{\rm sys}$ and brown dwarf region $α_{\rm bd}=-0.7\pm0.9|_{\rm stat}\pm0.8|_{\rm sys}$ 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 $σ_m=0.49\pm0.07|_{\rm stat}\pm0.06|_{\rm sys}$. 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 $α$-element enhanced timescale. This therefore constrains models of IMF variation that depend on the properties of the collapsing gas cloud.

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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.

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The Galaxy in Context: Structural, Kinematic and Integrated Properties

Our Galaxy, the Milky Way, is a benchmark for understanding disk galaxies. It is the only galaxy whose formation history can be studied using the full distribution of stars from white dwarfs to supergiants. The oldest components provide us with unique insight into how galaxies form and evolve over billions of years. The Galaxy is a luminous (L-star) barred spiral with a central box/peanut bulge, a dominant disk, and a diffuse stellar halo. Based on global properties, it falls in the sparsely populated "green valley" region of the galaxy colour-magnitude diagram. Here we review the key integrated, structural and kinematic parameters of the Galaxy, and point to uncertainties as well as directions for future progress. Galactic studies will continue to play a fundamental role far into the future because there are measurements that can only be made in the near field and much of contemporary astrophysics depends on such observations.

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Andromeda chained to the Box -- Dynamical Models for M31: Bulge & Bar

Andromeda is our nearest neighbouring disk galaxy and a prime target for detailed modelling of the evolutionary processes that shape galaxies. We analyse the nature of M31's triaxial bulge with an extensive set of N-body models, which include Box/Peanut (B/P) bulges as well as initial classical bulges (ICBs). Comparing with IRAC 3.6$μm$ data, only one model matches simultaneously all the morphological properties of M31's bulge, and requires an ICB and a B/P bulge with 1/3 and 2/3 of the total bulge mass respectively. We find that our pure B/P bulge models do not show concentrations high enough to match the Sérsic index ($n$) and the effective radius of M31's bulge. Instead, the best model requires an ICB component with mass $M^{\rm ICB}=1.1\times10^{10}{\rm M_{\odot}}$ and three-dimensional half-mass radius $r_{\rm half}^{\rm ICB}$=0.53 kpc (140 arcsec). The B/P bulge component has a mass of $M^{\rm B/P}=2.2\times10^{10}{\rm M_{\odot}}$ and a half-mass radius of $r_{\rm half}^{\rm B/P}$=1.3 kpc (340 arcsec). The model's B/P bulge extends to $r^{\rm B/P}$=3.2 kpc (840 arcsec) in the plane of the disk, as does M31's bulge. In this composite bulge model, the ICB component explains the velocity dispersion drop observed in the centre within $R<$190 pc (50 arcsec), while the B/P bulge component reproduces the observed rapid rotation and the kinematic twist of the observed zero velocity line. This model's pattern speed is $Ω_p$=38 km/s/kpc, placing corotation at $r_{\rm cor}$=5.8 kpc (1500 arcsec). The outer Lindblad resonance (OLR) is then at $r_{\rm OLR}$=10.4kpc, near the 10kpc-ring of M31, suggesting that this structure may be related to the bar's OLR. By comparison with an earlier snapshot, we estimate that M31's thin bar extends to $r_{\rm bar}^{\rm thin}\sim$4.0 kpc (1000 arcsec) in the disk plane, and in projection extends to $R_{\rm bar}^{\rm thin}\sim$2.3 kpc (600 arcsec).

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Dynamical modelling of the Galactic bulge and bar: the Milky Way's bar pattern speed, stellar, and dark matter mass distribution

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 $39.0 \pm 3.5 \,\rm{km\,s^{-1}\,kpc^{-1}}$, placing the bar corotation radius at $6.1 \pm 0.5 \rm{kpc}$ and making the Milky Way bar a typical fast rotator. We evaluate the stellar mass of the long bar and bulge structure to be $M_{\rm{bar/bulge}} = 1.88 \pm 0.12 \times 10^{10} \, \rm{M}_{\odot}$, larger than the mass of disk in the bar region, $M_{\rm{inner\ disk}} = 1.29\pm0.12 \times 10^{10} \, \rm{M}_{\odot}$. The total dynamical mass in the bulge volume is $1.85\pm0.05\times 10^{10} \, \rm{M}_{\odot}$. Thanks to more extended kinematic data sets and recent measurement of the bulge IMF our models have a low dark matter fraction in the bulge of $17\%\pm2\%$. 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 $\sim0.2\times10^{10} \,\rm{M}_{\odot}$, probably in a nuclear disk or disky pseudobulge.

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The Radial Velocity Experiment (RAVE): Fifth Data Release

Data Release 5 (DR5) of the Radial Velocity Experiment (RAVE) is the fifth data release from a magnitude-limited (9< I < 12) survey of stars randomly selected in the southern hemisphere. The RAVE medium-resolution spectra ($R\sim7500$) covering the Ca-triplet region (8410-8795Å) span the complete time frame from the start of RAVE observations in 2003 to their completion in 2013. Radial velocities from 520,781 spectra of 457,588 unique stars are presented, of which 255,922 stellar observations have parallaxes and proper motions from the Tycho-Gaia astrometric solution (TGAS) in Gaia DR1. For our main DR5 catalog, stellar parameters (effective temperature, surface gravity, and overall metallicity) are computed using the RAVE DR4 stellar pipeline, but calibrated using recent K2 Campaign 1 seismic gravities and Gaia benchmark stars, as well as results obtained from high-resolution studies. Also included are temperatures from the Infrared Flux Method, and we provide a catalogue of red giant stars in the dereddened color $(J-Ks)_0$ interval (0.50,0.85) for which the gravities were calibrated based only on seismology. Further data products for sub-samples of the RAVE stars include individual abundances for Mg, Al, Si, Ca, Ti, Fe, and Ni, and distances found using isochrones. Each RAVE spectrum is complemented by an error spectrum, which has been used to determine uncertainties on the parameters. The data can be accessed via the RAVE Web site or the Vizier database.

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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, $ρ\sim r^{-3}$, 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.

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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 $1σ$, $f_v > 0.72$ at $2σ$). 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 $1σ$. 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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Gas dynamics in the Milky Way: a low pattern speed model

We present gas flow models for the Milky Way based on high-resolution grid-based hydrodynamical simulations. The basic galactic potential we use is from a N-body model constrained by the density of red clump giants in the Galactic bulge. We augment this potential with a nuclear bulge, two pairs of spiral arms and additional mass at the bar end to represent the long bar component. With this combined model we can reproduce many features in the observed ($l,v$) diagram with a bar pattern speed of $33\; {\rm km}\;{\rm s}^{-1}\;{\rm kpc}^{-1}$ and a spiral pattern speed of $23\; {\rm km}\;{\rm s}^{-1}\;{\rm kpc}^{-1}$. The shape and kinematics of the nuclear ring, Bania's Clump 2, the Connecting arm, the Near and Far 3-kpc arms, the Molecular Ring, and the spiral arm tangent points in our simulations are comparable to those in the observations. Our results imply that a low pattern speed model for the bar in our Milky Way reproduces the observations for a suitable Galactic potential. Our best model gives a better match to the ($l,v$) diagram than previous high pattern speed hydrodynamical simulations.

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The Nuclear Cluster of the Milky Way: Total Mass and Luminosity (long version)

Like many other late-type galaxies, the Milky Way contains a nuclear star cluster. In this work we obtain the basic properties of its dominant old stellar population. Firstly, we derive its structural properties by constructing a stellar surface density map of the central 1000" using extinction corrected star counts from VISTA, WFC3/IR and VLT/NACO data. We can describe the profile with a two-component model. The inner, slightly flattened (q=0.80+/-0.04) component is the nuclear cluster, while the outer component corresponds to the stellar component of the circumnuclear zone. We measure for the nuclear cluster a half-light radius of 178+/-51"~7+/-2 pc and a luminosity of M_Ks=-16.0+/-0.5. Secondly, we enlarge the range over which detailed dynamics are available from 1 pc to 4 pc. We obtain more than 10000 individual proper motions from NACO data, and more than 2500 radial velocities from VLT/SINFONI data. We determine the cluster mass by means of isotropic spherical Jeans modeling. We fix the distance to the Galactic Center and the mass of the supermassive black hole. We model the cluster either with a constant mass to light ratio or with a power law mass model. For the latter we obtain a slope of delta_M=1.18+/-0.06. Assuming spherical symmetry, we get a nuclear cluster mass within 100" of M_100"=6.09+/- 0.53_(fix_R_0) +/- 0.97_(R_0) * 10^6 M_sun for both modeling approaches. A model which includes the observed flattening gives a 47% larger mass, see Chatzopoulos et al. 2015. Our results slightly favor a core over a cusp in the mass profile. By minimizing the number of unbound stars within 8" in our sample we obtain a distance estimate of R$_0=8.53^{+0.21}_{-0.15}$ kpc, where an a priori relation between R_0 and SMBH mass from stellar orbits is used. Combining our mass and flux we obtain M/L=0.51+/-0.12 M_sun/L_(sun Ks). This is roughly consistent with a Chabrier IMF.

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Testing General Relativity with the Shadow Size of Sgr A*

In general relativity, the angular radius of the shadow of a black hole is primarily determined by its mass-to-distance ratio and depends only weakly on its spin and inclination. If general relativity is violated, however, the shadow size may also depend strongly on parametric deviations from the Kerr metric. Based on a reconstructed image of Sagittarius A* (Sgr A*) from a simulated one-day observing run of a seven-station Event Horizon Telescope (EHT) array, we employ a Markov chain Monte Carlo algorithm to demonstrate that such an observation can measure the angular radius of the shadow of Sgr A* with an uncertainty of ~1.5 uas (6%). We show that existing mass and distance measurements can be improved significantly when combined with upcoming EHT measurements of the shadow size and that tight constraints on potential deviations from the Kerr metric can be obtained.

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Spin-up of massive classical bulges during secular evolution

Classical bulges in spiral galaxies are known to rotate but the origin of this observed rotational motion is not well understood. It has been shown recently that a low-mass classical bulge (ClB) in a barred galaxy can acquire rotation from absorbing a significant fraction of the angular momentum emitted by the bar. Our aim here is to investigate whether bars can spin up also more massive ClBs during the secular evolution of the bar, and to study the kinematics and dynamics of these ClBs. We use a set of self-consistent N-body simulations to study the interaction of ClBs with a bar that forms self-consistently in the disk. We use orbital spectral analysis to investigate the angular momentum gain by the classical bulge stars. We show that the ClBs gain, on average, about 2 - 6% of the disk's initial angular momentum within the bar region. Most of this angular momentum gain occurs via low-order resonances, particularly 5:2 resonant orbits. A density wake forms in the ClB which corotates and aligns with the bar at the end of the evolution. The spin-up process creates a characteristic linear rotation profile and mild tangential anisotropy in the ClB. The induced rotation is small in the centre but significant beyond $\sim2$ bulge half mass radii, where it leads to mass-weighted $V/σ\sim 0.2$, and reaches a local $V_{max}/σ_{in} \sim 0.5$ at around the scale of the bar. The resulting $V/σ$ is tightly correlated with the ratio of the bulge size to the bar size. In all models, a box/peanut bulge forms suggesting that composite bulges may be common. Bar-bulge resonant interaction in barred galaxies can provide some spin up of massive ClBs, but the process appears to be less efficient than for low-mass ClBs. Further angular momentum transfer due to nuclear bars or gas inflow would be required to explain the observed rotation if it is not primordial.

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Planetary Nebulae and their parent stellar populations. Tracing the mass assembly of M87 and Intracluster light in the Virgo cluster core

The diffuse extended outer regions of galaxies are hard to study because they are faint, with typical surface brightness of 1% of the dark night sky. We can tackle this problem by using resolved star tracers which remain visible at large distances from the galaxy centres. This article describes the use of Planetary Nebulae as tracers and the calibration of their properties as indicators of the star formation history, mean age and metallicity of the parent stars in the Milky Way and Local Group galaxies . We then report on the results from a deep, extended, planetary nebulae survey in a 0.5 sqdeg region centred on the brightest cluster galaxy NGC 4486 (M87) in the Virgo cluster core, carried out with SuprimeCam@Subaru and FLAMES-GIRAFFE@VLT. Two PN populations are identified out to 150 kpc distance from the centre of M87. One population is associated with the M87 halo and the second one with the intracluster light in the Virgo cluster core. They have different line-of-sight velocity and spatial distributions, as well as different planetary nebulae specific frequencies and luminosity functions. The intracluster planetary nebulae in the surveyed region correspond to a luminosity of four times the luminosity of the Large Magellanic Cloud. The M87 halo planetary nebulae trace an older, more metal-rich, parent stellar population. A substructure detected in the projected phase-space of the line-of-sight velocity vs. major axis distance for the M87 halo planetary nebulae provides evidence for the recent accretion event of a satellite galaxy with luminosity twice that of M33. The satellite stars were tidally stripped about 1 Gyr ago, and reached apocenter at a major axis distance of 60-90 kpc from the centre of M87. The M87 halo is still growing significantly at the distances where the substructure is detected.

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Dust within the old nuclear star cluster in the Milky Way

The mean absolute extinction towards the central parsec of the Milky Way is A_K~3 mag, including both foreground and Galactic center dust. Here we present a measurement of dust extinction within the Galactic old nuclear star cluster (NSC), based on combining differential extinctions of NSC stars with their u_l proper motions along Galactic longitude. Extinction within the NSC preferentially affects stars at its far side, and because the NSC rotates, this causes higher extinctions for NSC stars with negative u_l, as well as an asymmetry in the u_l-histograms. We model these effects using an axisymmetric dynamical model of the NSC in combination with simple models for the dust distribution. Comparing the predicted asymmetry to data for ~7100 stars in several NSC fields, we find that dust associated with the Galactic center mini-spiral with extinction A_K~=0.15-0.8 mag explains most of the data. The largest extinction A_K~=0.8 mag is found in the region of the Western arm of the mini-spiral. Comparing with total A_K determined from stellar colors, we determine the extinction in front of the NSC. Finally, we estimate that for a typical extinction of A_K~=0.4 the statistical parallax of the NSC changes by ~0.4%.

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The outer regions of the giant Virgo galaxy M87. Kinematic separation of stellar halo and intracluster light

We present a spectroscopic study of 287 Planetary Nebulas (PNs) in a total area of ~0.4 deg^2 around the BCG M87 in Virgo A. With these data we can distinguish the stellar halo from the co-spatial intracluster light (ICL). PNs were identified from their narrow and symmetric redshifted lambda 5007\4959 Angstrom [OIII] emission lines, and the absence of significant continuum. We implement a robust technique to measure the halo velocity dispersion from the projected phase-space to identify PNs associated with the M87 halo and ICL. The velocity distribution of the spectroscopically confirmed PNs is bimodal, containing a narrow component centred on the systemic velocity of the BCG and an off-centred broader component, that we identify as halo and ICL, respectively. Halo and ICPN have different spatial distributions: the halo PNs follow the galaxy's light, whereas the ICPNs are characterised by a shallower power-law profile. The composite PN number density profile shows the superposition of different PN populations associated with the M87 halo and the ICL, characterised by different PN alpha-parameters, the ICL contributing ~3 times more PNs per unit light. Down to m_5007=28.8, the M87 halo PN luminosity function (PNLF) has a steeper slope towards faint magnitudes than the IC PNLF, and both are steeper than the standard PNLF for the M31 bulge. Moreover, the IC PNLF has a dip at ~1-1.5 mag fainter than the bright cutoff, reminiscent of the PNLFs of systems with extended star formation history. The M87 halo and the Virgo ICL are dynamically distinct components with different density profiles and velocity distribution. The different alpha values and PNLF shapes of the halo and ICL indicate distinct parent stellar populations, consistent with the existence of a gradient towards bluer colours at large radii. These results reflect the hierarchical build-up of the Virgo cluster.

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26Al kinematics: superbubbles following the spiral arms? Constraints from the statistics of star clusters and HI supershells

High energy resolution spectroscopy of the 1.8 MeV radioactive decay line of 26Al with the SPI instrument on board the INTEGRAL satellite has recently revealed that diffuse 26Al has large velocities in comparison to other components of the interstellar medium in the Milky Way. 26Al shows Galactic rotation in the same sense as the stars and other gas tracers, but reaches excess velocities up to 300 km/s. We investigate if this result can be understood in the context of superbubbles, taking into account the statistics of young star clusters and H I supershells, as well as the association of young star clusters with spiral arms. We derive energy output and 26Al mass of star clusters as a function of the cluster mass via population synthesis from stellar evolutionary tracks of massive stars. [...] We link this to the size distribution of HI supershells and assess the properties of likely 26Al-carrying superbubbles. 26Al is produced by star clusters of all masses above about 200 solar masses, roughly equally contributed over a logarithmic star cluster mass scale, and strongly linked to the injection of feedback energy. The observed superbubble size distribution cannot be related to the star cluster mass function in a straight forward manner. In order to avoid that the added volume of all superbubbles exceeds the volume of the Milky Way, individual superbubbles have to merge frequently. If any two superbubbles merge, or if 26Al is injected off-centre in a bigger HI supershell we expect the hot 26Al-carrying gas to obtain velocities of the order of the typical sound speed in superbubbles, about 300 km/s before decay. [...]

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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.

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