This work investigates the vertical profile of the stars in the disk of the Milky Way. The models investigated are of the form $sech^{2/n}(nz/(2H))$ where, setting $α= 2/n$, the three functions of the sequence $α= 0,1,2$ correspond to exponential, $sech$, $sech^2$ functions. We consider symmetric models and asymmetric models, above and below the plane. The study uses the large sample of K and M stars of Ferguson et al. (2017) and applies the methods of Bayesian model comparison to discriminate between the 6 models. Two inconsistencies in Ferguson et al. (2017), concerning the vertical height cut and the model continuity across the plane, are noted and addressed. We find that (1) in the Milky Way the symmetric disc models are decisively ruled out, with northern thin disc scale heights $\sim25\%$ larger than southern, (2) there is moderate evidence for the exponential and $sech$ models over the $sech^2$ model, though a sample extending further into the Galactic mid-plane is needed to strengthen this result, (3) the photometric distances used by Ferguson et al. underestimate the GAIA distances by a factor of roughly 1.16, and (4) the increase of scale height with Galactic latitude observed by Ferguson et al. is due to incorrect cuts to the data.
An oscillating vertical displacement of the Milky Way, with a wavelength of about 8 kpc and and amplitude of about 100 pc (increasing with distance from the Galactic center) is observed towards the Galactic anticenter. These oscillations are thought to be the result of disk perturbations from dwarf satellites of the Milky Way. They explain the Monoceros Ring and could be related to Milky Way spiral structure.
Recently, Widrow and collaborators announced the discovery of vertical density waves in the Milky Way disk. Here we investigate a scenario where these waves were induced by the Sagittarius dwarf galaxy as it plunged through the Galaxy. Using numerical simulations, we find that the Sagittarius impact produces North-South asymmetries and vertical wave-like behavior that qualitatively agrees with what is observed. The extent to which vertical modes can radially penetrate into the disc, as well as their amplitudes, depend on the mass of the perturbing satellite. We show that the mean height of the…
In this paper we model the vertical structure of mass distribution of the Milky Way galaxy in the framework of a finite-width global disk model. Assuming the Galactic rotation curve only, we test inside the solar orbit the predictions of the model for two measurable and unrelated to each other processes: the gravitational microlensing that allows to fix the disk width-scale by the best fit to measurements, and the vertical gradient of rotation modelled in the quasi-circular orbits approximation. The former is sensitive to the gravitating mass in compact objects and the latter is sensitive to a…
The self-consistent vertical density distribution in a thin, isothermal disc is typically given by a sech^2 law, as shown in the classic work by Spitzer (1942). This is obtained assuming that the radial and vertical motions are decoupled and only the vertical term is used in the Poisson equation. We argue that in the region of low density as in the outer disc this treatment is no longer valid. We develop a general, complete model that includes both radial and vertical terms in the Poisson equation and write these in terms of the full radial and vertical Jeans equations which take account of th…
We investigate the vertical metallicity gradients of five mono-age stellar populations between 0 and 11 Gyr for a sample of 18 435 dwarf stars selected from the cross-matched Tycho-Gaia Astrometric Solution (TGAS) and RAdial Velocity Experiment (RAVE) Data Release 5. We find a correlation between the vertical metallicity gradients and age, with no vertical metallicity gradient in the youngest population and an increasingly steeper negative vertical metallicity gradient for the older stellar populations. The metallicity at disc plane remains almost constant between 2 and 8 Gyr, and it becomes s…
We present a study of the vertical magnetic field of the Milky Way towards the Galactic poles, determined from observations of Faraday rotation toward more than 1000 polarized extragalactic radio sources at Galactic latitudes |b| > 77 degs, using the Westerbork Radio Synthesis Telescope and the Australia Telescope Compact Array. We find median rotation measures (RMs) of 0.0 +/- 0.5 rad/m^2 and +6.3 +/- 0.7 rad/m^2 toward the north and south Galactic poles, respectively, demonstrating that there is no coherent vertical magnetic field in the Milky Way at the Sun's position. If this is a global p…
We present a high resolution study of the impact of realistic satellite galaxies, extracted from cosmological simulations of Milky Way haloes including 6 Aquarius suites and Via Lactea \rom{2}, on the dynamics of the galactic disc. The initial conditions for the multi-component Milky Way galaxy were generated using the GalIC code, to ensure a system in dynamical equilibrium state prior to addition of satellites. Candidate subhaloes that came closer than 25\,kpc to the centre of the host DM haloes with initial mass enclosed within the tidal radius, $M_\textrm{tid}$ $\ge$ 10$^{8} M_{\odot}$\,=\,…
Based on published data, we have produced a sample of planetary nebulae (PNe) that is complete within 2 kpc of the Sun. We have estimated the total number of PNe in the Galaxy from this sample to be 17000+/-3000 and determined the vertical scale height of the thin disk based on an exponential density distribution to be 197+/-10 pc. The next sample includes PNe from the Stanghellini-Haywood catalog with minor additions. For this purpose, we have used about 200 PNe with Peimbert's types I, II, and III. In this case, we have obtained a considerably higher value of the vertical scale height that i…
We study the vertical stellar distribution of the Milky Way thin disk in detail with particular focus on the outer disk. We treat the galactic disk as a gravitationally coupled, three-component system consisting of stars, atomic hydrogen gas, and molecular hydrogen gas in the gravitational field of the dark matter halo. The self-consistent vertical distribution for stars and gas in such a realistic system is obtained for radii between 4-22 kpc. The inclusion of an additional gravitating component constrains the vertical stellar distribution toward the mid-plane, so that the mid-plane density i…
Vertically extended, high velocity dispersion stellar distributions appear to be a ubiquitous feature of disc galaxies, and both internal and external mechanisms have been proposed to be the major driver of their formation. However, it is unclear to what extent each mechanism can generate such a distribution, which is likely to depend on the assembly history of the galaxy. To this end, we perform 16 high resolution cosmological-zoom simulations of Milky Way-sized galaxies using the state-of-the-art cosmological magneto-hydrodynamical code \textlcsc{AREPO}, and analyse the evolution of the vert…
We use the number density distributions of K and M dwarf stars with vertical height from the Galactic disk, determined using observations from the Sloan Digital Sky Survey, to probe the structure of the Milky Way disk across the survey's footprint. Using photometric parallax as a distance estimator we analyze a sample of several million disk stars in matching footprints above and below the Galactic plane, and we determine the location and extent of vertical asymmetries in the number counts in a variety of thin- and thick-disk subsamples in regions of some 200 square degrees within 2 kpc in ver…
We present the Galactic disk vertical velocity analysis using OB type stars (OB), Red Clump stars (RC), and Main-Sequence-Turn-Off stars (MSTO) with different average age populations crossed matched with LAMOST DR5 and Gaia DR3. We reveal the vertical velocities of the three populations varies clearly with the Galactocentric distance ($R$) and the younger stellar population has stronger increasing trend in general. The bending and breathing modes indicated by the vertical motions are dependent on the populations and they are varying with spatial locations. These vertical motions may be due to …
We have mapped the number density and mean vertical velocity of the Milky Way's stellar disk out to roughly two kiloparsecs from the Sun using Gaia Data Release 3 (DR3) and complementary photo-astrometric distance information from StarHorse. For the number counts, we carefully masked spatial regions that are compromised by open clusters, great distances, or dust extinction and used Gaussian processes to arrive at a smooth, non-parametric estimate for the underlying number density field. We find that the number density and velocity fields depart significantly from an axisymmetric and mirror-sym…
Two alternative theories to dark matter are investigated by testing their ability to describe consistently the dynamics of the Milky Way. The first one refers to a modified gravity theory having a running gravitational constant and the second assumes that dark matter halos are constituted by a Bose-Einstein condensation. The parameters of each model as well as those characterizing the stellar subsystems of the Galaxy were estimated by fitting the rotation curve of the Milky Way. Then, using these parameters, the vertical acceleration profile at the solar position was computed and compared with…
The recent discovery of a spiral pattern in the vertical kinematic structure in the solar neighborhood provides a prime opportunity to study non-equilibrium dynamics in the Milky Way from local stellar kinematics. Furthermore, results from simulations indicate that even in a limited volume, differences in stellar orbital histories allow us to trace variations in the initial perturbation across large regions of the disk. We present $\texttt{ESCARGOT}$, a novel algorithm for studying these variations in both simulated and observed data sets. $\texttt{ESCARGOT}$ automatically extracts key quantit…
Aims: we studied the global distribution and kinematics of the extra-planar neutral gas in the Milky Way. Methods: we built 3D models for a series of Galactic HI layers, projected them for an inside view, and compared them with the Leiden-Argentina-Bonn 21-cm observations. Results: we show that the Milky Way disk is surrounded by an extended halo of neutral gas with a vertical scale-height of 1.6[+0.6/-0.4] kpc and an HI mass of 3.2[+1.0/-0.9]x10^8 solar masses, which is 5-10% of the total Galactic HI. This HI halo rotates more slowly than the disk with a vertical velocity gradient of -15[+/-4…
We develop a novel Bayesian methodology aimed at reliably and precisely inferring the distribution of dark matter within the Milky Way using rotation curve data. We identify a subset of the available rotation curve tracers that are mutually consistent with each other, thus eliminating data sets that might suffer from systematic bias. We investigate three different models for the mass distribution of the luminous (baryonic) component that bracket the range of likely morphologies. We demonstrate the statistical performance of our method on simulated data in terms of coverage, fractional distance…
Accurately reproducing the thin cold gas discs observed in nearby spiral galaxies has been a long standing issue in cosmological simulations. Here, we present measurements of the radially resolved HI scale height in 22 non-interacting Milky Way-mass galaxies from the FIREbox cosmological volume. We measure the HI scale heights using five different approaches commonly used in the literature: fitting the vertical volume density distribution with a Gaussian, the distance between maximum and half-maximum of the vertical volume density distribution, a semi-empirical description using the velocity d…
A vertical X-shaped structure was recently reported in the Galactic bulge. Here we present evidence of a similar X-shaped structure in the Shen et al. (2010) bar/boxy bulge model that simultaneously matches the stellar kinematics successfully. The X-shaped structure is found in the central region of our bar/boxy bulge model, and is qualitatively consistent with the observed one in many aspects. End-to-end separations of the X-shaped structure in the radial and vertical directions are roughly 3 kpc and 1.8 kpc, respectively. The X-shaped structure contains about 7% of light in the boxy bulge re…
We present a novel interpretation of the previously puzzling different behaviours of stellar populations of the Milky Way's bulge. We first show, by means of pure N-body simulations, that initially co-spatial stellar populations with different in-plane random motions separate when a bar forms. The radially cooler populations form a strong bar, and are vertically thin and peanut-shaped, while the hotter populations form a weaker bar and become a vertically thicker box. We demonstrate that it is the radial, not the vertical, velocity dispersion that dominates this evolution. Assuming that early …
Gaia DR2 has revealed new small-scale and large-scale patterns in the phase-space distribution of stars in the Milky Way. In cylindrical Galactic coordinates $(R,ϕ,z)$, ridge-like structures can be seen in the \vphiR{} plane and asymmetric arch-like structures in the \vphivR{} plane. We show that the ridges are also clearly present when the third dimension of the \vphiR{} plane is represented by $\langle z \rangle$, $\langle V_z \rangle$, $\langle V_R \rangle$, $\langle$[Fe/H]$\rangle$ and $\langle[α/{\rm Fe}]\rangle$. The maps suggest that stars along the ridges lie preferentially close to th…
We derive the mean velocity components at various Galactocentric radii from 8 to 14 kpc using about 40,000 red clump stars observed in the LAMOST survey. We find that the vertical bulk motion for younger red clump stars are significantly larger than that for the older red clump stars. This is likely the kinematical feature of the Galactic warp around its line-of-node, which is located close to the Galactic anti-center region. It is evident that the warp are mainly contributed by the younger stars rather than the older stars. The age variation in the vertical kinematics favors a formation scena…
We find that Galactic disk stars near the anticenter exhibit velocity asymmetries in both the Galactocentric radial and vertical components across the mid-plane as well as azimuthally. These findings are based on LAMOST spectroscopic velocities for a sample of ~400,000 F-type stars, combined with proper motions from the PPMXL catalog for which we have derived corrections to the zero points based in part on spectroscopically discovered galaxies and QSOs from LAMOST. In the region within 2 kpc outside the Sun's radius and +/-2 kpc from the Galactic midplane, we show that stars above the plane ex…
We introduce a method to infer the vertical distribution of stars in the Milky Way using a Poisson likelihood function, with a view to applying our method to the Gaia catalogue. We show how to account for the sample selection function and for parallax measurement uncertainties. Our method is validated against a simulated sample drawn from a model with two exponential discs and a power-law halo profile. A mock Gaia sample is generated using the Gaia astrometry selection function, whilst realistic parallax uncertainties are drawn from the Gaia Astrometric Spread Function. The model is fit to the…
Milky Way Dynamics Favor Dark Matter over Modified Gravity Models
Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台）；University of Science and Technology of China（中国科学技术大学）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；University of Chinese Academy of Sciences（中国科学院大学）；University of Saint Andrews（圣安德鲁斯大学）
We present a hierarchical Bayesian method for estimating the total mass and mass profile of the Milky Way Galaxy. The new hierarchical Bayesian approach further improves the framework presented by Eadie, Harris, & Widrow (2015) and Eadie & Harris (2016) and builds upon the preliminary reports by Eadie et al (2015a,c). The method uses a distribution function $f(\mathcal{E},L)$ to model the galaxy and kinematic data from satellite objects such as globular clusters (GCs) to trace the Galaxy's gravitational potential. A major advantage of the method is that it not only includes complete and incomp…
In this paper, we aim to estimate the vertical gradients in the rotational velocity of the Galaxy. This is carried out in the framework of a global thin disc model approximation. The predicted gradient values coincide with the observed vertical fall-off in the rotation curve of the Galaxy. The gradient is estimated based on a statistical analysis of trajectories of test bodies in the gravitational field of the disc and in an analytical way using a quasi-circular orbit approximation. The agreement of the results with the gradient measurements is remarkable in view of other more complicated, non…
Intermediate- and high-velocity clouds (IVCs, HVCs) are a potential source of fuel for star formation in the Milky Way (MW), but their origins and fates depend sensitively on their distances. We search for IVC and HVC in HST high-resolution ultraviolet spectra of 55 halo stars at vertical heights $|z| \gtrsim 1$ kpc. We show that IVCs ($40 \leq |v_{\rm LSR}| <90$ km/s) have a high detection rate - the covering factor, $f_c$ - that is about constant ($f_c =0.90\pm 0.04$) from $z=1.5$ to $14$ kpc, implying IVCs are essentially confined to $|z|\lesssim 1.5$ kpc. For the HVCs ($90 \leq |v_{\rm LSR…
We employ high-resolution N-body simulations of isolated spiral galaxy models, from low-amplitude, multi-armed galaxies to Milky Way-like disks, to estimate the vertical action of ensembles of stars in an axisymmetric potential. In the multi-armed galaxy the low-amplitude arms represent tiny perturbations of the potential, hence the vertical action for a set of stars is conserved, although after several orbital periods of revolution the conservation degrades significantly. For a Milky Way-like galaxy with vigorous spiral activity and the formation of a bar, our results show that the potential …
Recent studies have revealed an oscillating asymmetry in the vertical structure of the Milky Way's disc. Here we analyze 16 high-resolution, fully cosmological simulations of the evolution of individual Milky Way-sized galaxies, carried out with the MHD code AREPO. At redshift zero, about $70\%$ of our galactic discs show strong vertical patterns, with amplitudes that can exceed 2 kpc. Half of these are typical `integral sign' warps. The rest are oscillations similar to those observed in the Milky Way. Such structures are thus expected to be common. The associated mean vertical motions can be …
This paper is an initial stage of consideration of the general problem of joint modeling of the vertical structure of a Galactic flat subsystem and the average surface of the disk of the Galaxy, taking into account the natural and measurement dispersions. We approximate the average surface of the Galactic disk with a polynomial model and determine its parameters by minimizing the squared deviations of objects along the normal to the model surface. The developed method allows us to simultaneously identify significant details of the Galactic warping and estimate the offset $z_\odot$ of the Sun r…
We use 297 042 main sequence turn-off stars selected from the LSS-GAC to determine the radial and vertical gradients of stellar metallicity of the Galactic disk in the anti-center direction. We determine ages of those turn-off stars by isochrone fitting and measure the temporal variations of metallicity gradients. Our results show that the gradients, both in the radial and vertical directions, exhibit significant spatial and temporal variations. The radial gradients yielded by stars of oldest ages (>11 Gyr) are essentially zero at all heights from the disk midplane, while those given by younge…
Using N-body simulations of the Milky Way interacting with a satellite similar to the Sagittarius dwarf galaxy, we quantitatively analyse the vertical response of the Galactic disc to the satellite's repeated impacts. We approximate the vertical distortion of the Galactic disc as the sum of the first three Fourier azimuthal terms m = 0, 1 and 2, and observe their evolution in different dynamical regimes of interaction. After the first interaction, the m=0 term manifests itself as outgoing ring-like vertical distortions. The m=1 term (S-shape warp) is prograde when the impacts of the satellite …
The Schmidt law (SF law) in the Milky Way was investigated using 3D distribution maps of HII regions, HI and molecular (\Htwo) gases with spatial resolutions of $\sim 1$ kpc in the Galactic plane and a few tens of pc in the vertical direction. HII regions were shown to be distributed in a star-forming (SF) disk with nearly constant vertical full thickness 92 pc in spatial coincidence with the molecular gas disk. The vertically averaged volume star formation rate (SFR) $ρ_{\rm SFR}$ in the SF disk is related to the surface SFR $Σ_{\rm SFR}$ by $ρ_{\rm SFR} /[{\rm M_\odot y^{-1} kpc^{-3}}] =9.26…
We present the vertical kinematics of stars in the Milky Way's stellar disk inferred from SDSS/SEGUE G-dwarf data, deriving the vertical velocity dispersion, σ_z, as a function of vertical height |z| and Galactocentric radius R for a set of 'mono-abundance' sub-populations of stars with very similar elemental abundances [α/Fe] and [Fe/H]. We find that all components exhibit nearly isothermal kinematics in |z|, and a slow outward decrease of the vertical velocity dispersion: σ_z (z,R|[α/Fe],[Fe/H]) ~ σ_z ([α/Fe],[Fe/H]) x \exp (-(R-R_0)/7 kpc}). The characteristic velocity dispersions of these …
We use Gaia photometry and astrometry to estimate the vertical spatial structure of the Milky Way at the Solar radius, formally accounting for sample incompleteness (the selection function) and parallax measurement uncertainty. Our results show impressive precision demonstrating the power of the Gaia data. However, systematic errors dominate the parameter value uncertainties. We thoroughly test and quantify the impacts of all systematic uncertainties. The vertical tracer density is modelled as a sum of two exponential profiles for the thin and thick discs, together with a spherically symmetric…
We use $N$-body simulations to investigate the excitation of bending waves in a Milky Way-like disc-bulge-halo system. The dark matter halo consists of a smooth component and a population of subhaloes while the disc is composed of thin and thick components. Also considered is a control simulation where all of the halo mass is smoothly distributed. We find that bending waves are more vigorously excited in the thin disc than the thick one and that they are strongest in the outer regions of the disc, especially at late times. By way of a Fourier decomposition, we find that the complicated pattern…
The ongoing merger of the Sagittarius (Sgr) dwarf galaxy with the Milky Way is believed to strongly affect the dynamics of the Milky Way's disc. We present a suite of 13 $N$-body simulations, with 500 million to 1 billion particles, modelling the interaction between the Sagittarius dwarf galaxy (Sgr) and the Galactic disc. To quantify the perturbation to the disc's structure and dynamics in the simulation, we compute the number count asymmetry and the mean vertical velocity in a solar-neighbourhood-like volume. We find that overall the trends in the simulations match those seen in a simple one…
We investigate here the effect of the selection function on the metallicity distribution function (MDF) and on the vertical metallicity gradient by studying similar lines of sight using four different spectroscopic surveys (APOGEE, LAMOST, RAVE, and Gaia-ESO), which have different targeting strategies and therefore different selection functions. We use common fields between the spectroscopic surveys of APOGEE, LAMOST, RAVE (ALR) and APOGEE, RAVE, Gaia-ESO (AGR) and use two stellar population synthesis models, GALAXIA and TRILEGAL, to create mock fields for each survey. We apply the selection f…
A Vertically Orientated Dark Matter Halo Marks a Flip of the Galactic Disk
Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台）；Institute for Astronomy the School of Physics, Zhejiang University（浙江大学物理学院天体物理研究所）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；School of Physics and Optoelectronic Engineering, Hainan University（海南大学物理与电子工程学院）；Department of Astronomy, Westlake University（西湖大学天文系）；Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University（北京师范大学天文与前沿科学研究中心）
Observations show a clear vertical metallicity gradient in the Galactic bulge, which is often taken as a signature of dissipative processes in the formation of a classical bulge. Various evidence shows, however, that the Milky Way is a barred galaxy with a boxy bulge representing the inner three-dimensional part of the bar. Here we show with a secular evolution N-body model that a boxy bulge formed through bar and buckling instabilities can show vertical metallicity gradients similar to the observed gradient, if the initial axisymmetric disk had a comparable radial metallicity gradient. In thi…
We present mass and mass profile estimates for the Milky Way Galaxy using the Bayesian analysis developed by Eadie et al (2015b) and using globular clusters (GCs) as tracers of the Galactic potential. The dark matter and GCs are assumed to follow different spatial distributions; we assume power-law model profiles and use the model distribution functions described in Evans et al. (1997); Deason et al (2011, 2012a). We explore the relationships between assumptions about model parameters and how these assumptions affect mass profile estimates. We also explore how using subsamples of the GC popula…
Stars with a different vertical motion relative to the galactic disk have a different average acceleration. According to Modified Newtonian Dynamics (MOND) theories they should therefore have a different average orbital velocity while revolving around the Milky Way. We show that this property can be used to constrain MOND theories by studying stars in the local neighborhood. With the {\sc Hipparcos} dataset we can only place marginal constraints. However, the forthcoming {\sc GAIA} catalogue with its significantly fainter cutoff should allow placing a stringent constraint.
The stellar velocity distribution in the Solar Neighbourhood displays kinematic substructures, which are possibly signatures of the bar and spiral arms of the Milky Way and of previous accretion events. These kinematic substructures -- moving groups -- can be thought of as continuous manifolds in the 6D phase space, and the ridges in the $V_ϕ-R$ and arches in the $V_ϕ-V_R$ plane, discovered with the Gaia mission, as projections of these manifolds. We develop and apply a methodology to perform a blind search for substructure in the Gaia EDR3 6D data, and obtain a sampling of the manifolds. The …
Accurate determination of the local dark matter density is important for understanding the nature and distribution of dark matter in the universe. This requires that the local velocity distribution is characterised correctly. Here, we present a kinematic study of 16,276 SEGUE G-type dwarf stars in the solar neighbourhood, with which we determine the shape of the velocity ellipsoid in the meridional plane. We separate our G-dwarf stars based on their [Fe/H] and [alpha/Fe] abundances and infer the local velocity distribution independently for each sub-sample using a maximum-likelihood method tha…
We present N-body simulations of a Sagittarius-like dwarf spheroidal galaxy (Sgr) that follow its orbit about the Milky Way (MW) since its first crossing of the Galaxy's virial radius to the present day. As Sgr orbits around the MW, it excites vertical oscillations, corrugating and flaring the Galactic stellar disc. These responses can be understood by a two-phase picture in which the interaction is first dominated by torques from the wake excited by Sgr in the MW dark halo before transitioning to tides from Sgr's direct impact on the disc at late times. We show for the first time that a massi…
We study the structure, age and metallicity gradients, and dynamical evolution using a cosmological zoom-in simulation of a Milky Way-mass galaxy from the Feedback in Realistic Environments project. In the simulation, stars older than 6 Gyr were formed in a chaotic, bursty mode and have the largest vertical scale heights (1.5-2.5 kpc) by z=0, while stars younger than 6 Gyr were formed in a relatively calm, stable disk. The vertical scale height increases with stellar age at all radii, because (1) stars that formed earlier were thicker "at birth", and (2) stars were kinematically heated to an e…
The nuclear stellar disc (NSD) is a flattened stellar structure that dominates the gravitational potential of the Milky Way at Galactocentric radii $30 \lesssim R \lesssim 300{\, \rm pc}$. In this paper, we construct axisymmetric Jeans dynamical models of the NSD based on previous photometric studies and we fit them to line-of-sight kinematic data of APOGEE and SiO maser stars. We find that (i) the NSD mass is lower but consistent with the mass independently determined from photometry by Launhardt et al. (2002). Our fiducial model has a mass contained within spherical radius $r=100{\, \rm pc}$…
