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Register a new userRotation Curve of the Milky Way and the Dark Matter Density
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Authors
Yoshiaki Sofue
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We review the~current status of the~study of rotation curve (RC) of the~Milky Way, and~present a~unified RC from the~Galactic Center to the galacto-centric distance of about 100 kpc. The~RC is used to directly calculate the~distribution of the~surface mass density (SMD). We then propose a~method to derive the~distribution of dark matter (DM) density in the~in the~Milky Way using the~SMD distribution. The~best-fit dark halo profile yielded a local DM density of $rho_odot = 0.36pm 0.02$ GeV/cc. We also review the~estimations of the~local DM density in the~last decade, and~show that the~value is converging to a~value at $rho_odot=0.39pm 0.09$ GeV/cc.
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With the increasing numbers of large stellar survey projects, the quality and quantity of excellent tracers to study the Milky Way is rapidly growing, one of which is the classical Cepheids. Classical Cepheids are high precision standard candles with very low typical uncertainties ($<$ 3%) available via the mid-infrared period-luminosity relation. About 3500 classical Cepheids identified from OGLE, ASAS-SN, Gaia, WISE and ZTF survey data have been analyzed in this work, and their spatial distributions show a clear signature of Galactic warp. Two kinematical methods are adopted to measure the Galactic rotation curve in the Galactocentric distance range of $4lesssim R_{rm GC} lesssim 19$ kpc. Gently declining rotation curves are derived by both the proper motion (PM) method and 3-dimensional velocity vector (3DV) method. The largest sample of classical Cepheids with most accurate 6D phase-space coordinates available to date are modeled in the 3DV method, and the resulting rotation curve is found to decline at the relatively smaller gradient of ($-1.33pm0.1$) ${rm km,s^{-1},kpc^{-1}}$. Comparing to results from the PM method, a higher rotation velocity (($232.5pm0.83$) ${rm km,s^{-1}}$) is derived at the position of Sun in the 3DV method. The virial mass and local dark matter density are estimated from the 3DV method which is the more reliable method, $M_{rm vir} = (0.822pm0.052)times 10^{12},M_odot$ and $rho_{rm DM,odot} = 0.33pm0.03$ GeV ${rm cm^{-3}}$, respectively.
In the fundamental quest of the rotation curve of the Milky Way, the tangent-point (TP) method has long been the simplest way to infer velocities for the inner, low latitude regions of the Galactic disk from observations of the gas component. We test the validity of the method on realistic gas distribution and kinematics of the Milky Way, using a numerical simulation of the Galaxy. We show that the resulting velocity profile strongly deviates from the true rotation curve of the simulation, as it overstimates it in the central regions, and underestimates it around the bar corotation. Also, its shape strongly depends on the orientation of the stellar bar. The discrepancies are caused by highly non-uniform azimuthal velocities, and the systematic selection by the TP method of high-velocity gas along the bar and spiral arms, or low-velocity gas in less dense regions. The velocity profile is in good agreement with the rotation curve only beyond corotation, far from massive asymmetric structures. Therefore the observed velocity profile of the Milky Way inferred by the TP method is expected to be very close to the true Galactic rotation curve for 4.5<R<8 kpc. Another consequence is that the Galactic velocity profile for R<4-4.5 kpc is very likely flawed by the non-uniform azimuthal velocities, and does not represent the true Galactic rotation curve, but instead local motions. The real shape of the innermost rotation curve is probably shallower than previously thought. Using a wrong rotation curve has a dramatic impact on the modelling of the mass distribution, in particular for the bulge component of which derived enclosed mass within the central kpc and scale radius are, respectively, twice and half of the actual values. We thus strongly argue against using terminal velocities or the velocity curve from the TP method for modelling the mass distribution of the Milky Way. (abridged)
Flat rotation curves of spiral galaxies are considered as an evidence for dark matter, but the rotation curve of the Milky Way is difficult to measure. Various objects were used to track the rotation curve in the outer parts of the Galaxy, but most studies rely on incomplete kinematical information and inaccurate distances. Here, we use a sample of 773 Classical Cepheids with precise distances based on mid-infrared period-luminosity relations coupled with proper motions and radial velocities from Gaia to construct the accurate rotation curve of the Milky Way up to the distance of ~20 kpc from the Galactic center. We use a simple model of Galactic rotation to measure the rotation speed of the Sun Theta_0 = 233.6 +/- 2.8 km/s, assuming a prior on the distance to the Galactic center R_0 = 8.122 +/- 0.031 kpc from the Gravity Collaboration. The rotation curve at Galactocentric distances 4 < R < 20 kpc is nearly flat with a small gradient of -1.34 +/- 0.21 km/s/kpc. This is the most accurate Galactic rotation curve at distances R > 12 kpc constructed so far.
We construct the rotation curve of the Milky Way in the extended solar neighbourhood using a sample of SEGUE (Sloan Extension for Galactic Understanding and Exploration) G-dwarfs. We investigate the rotation curve shape for the presence of any peculiarities just outside the solar radius as has been reported by some authors. We approach the problem in a framework of classical Jeans analysis. Using the most recent data from RAVE (RAdial Velocity Experiment), we determine the solar peculiar velocity and the radial scalelengths for the three populations of different metallicities representing the Galactic thin disc. Then with the same binning in metallicity for the SEGUE G-dwarfs, we construct the rotation curve in the range of Galactocentric distances 7-10 kpc. We derive the circular velocity by correcting the mean tangential velocity for the asymmetric drift in each distance bin. With SEGUE data we also calculate the radial scalelength of the thick disc taking as known the derived peculiar motion of the Sun and the slope of the rotation curve. The rotation curve constructed through SEGUE G-dwarfs appears to be smooth in the selected radial range. The local kinematics of the thin disc rotation as determined in the framework of our new careful analysis does not favour the presence of a massive overdensity ring just outside the solar radius.
We present $texttt{galkin}$, a novel compilation of kinematic measurements tracing the rotation curve of our Galaxy, together with a tool to treat the data. The compilation is optimised to Galactocentric radii between 3 and 20 kpc and includes the kinematics of gas, stars and masers in a total of 2780 measurements carefully collected from almost four decades of literature. A simple, user-friendly tool is provided to select, treat and retrieve the data of all source references considered. This tool is especially designed to facilitate the use of kinematic data in dynamical studies of the Milky Way with various applications ranging from dark matter constraints to tests of modified gravity.
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