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Dynamical Modelling of Stellar Systems in the Gaia Era

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Dynamical Modelling of Stellar Systems in the Gaia Era Dynamical modelling of stellar systems in the Gaia era Eugene Vasiliev Institute of Astronomy, Cambridge Synopsis Overview of dynamical modelling Overview of the Gaia mission Examples: Large Magellanic Cloud Globular clusters Measurement of the Milky Way gravitational potential Fred Hoyle vs. the Universe What does \dynamical modelling" mean? It does not refer to a simulation (e.g. N-body) of the evolution of a stellar system. Most often, it means \modelling a stellar system in a dynamical equilibrium" (used interchangeably with \steady state"). vs. the Universe What does \dynamical modelling" mean? It does not refer to a simulation (e.g. N-body) of the evolution of a stellar system. Most often, it means \modelling a stellar system in a dynamical equilibrium" (used interchangeably with \steady state"). Fred Hoyle What does \dynamical modelling" mean? It does not refer to a simulation (e.g. N-body) of the evolution of a stellar system. Most often, it means \modelling a stellar system in a dynamical equilibrium" (used interchangeably with \steady state"). Fred Hoyle vs. the Universe 3D Steady-state assumption =) Jeans theorem: f (x; v)= f I(x; v;Φ) observations: 3D { 6D integrals of motion (≤ 3D?), e.g., I = fE; L;::: g Why steady state? Distribution function of stars f (x; v; t) satisfies [sometimes] the collisionless Boltzmann equation: @f (x; v; t) @f (x; v; t) @Φ(x; t) @f (x; v; t) + v − = 0: @t @x @x @v Potential , mass distribution @f (x; v; t) ; t ; t ; t + @t 3D observations: 3D { 6D integrals of motion (≤ 3D?), e.g., I = fE; L;::: g Why steady state? Distribution function of stars f (x; v; t) satisfies [sometimes] the collisionless Boltzmann equation: @f (x; v ) @Φ(x ) @f (x; v ) v − = 0: @x @x @v Steady-state assumption =) Jeans theorem: f (x; v)= f I(x; v;Φ) @f (x; v; t) ; t ; t ; t + @t Why steady state? Distribution function of stars f (x; v; t) satisfies [sometimes] the collisionless Boltzmann equation: @f (x; v ) @Φ(x ) @f (x; v ) v − = 0: @x @x @v 3D Steady-state assumption =) Jeans theorem: f (x; v)= f I(x; v;Φ) observations: 3D { 6D integrals of motion (≤ 3D?), e.g., I = fE; L;::: g Flavours of dynamical modelling Tracers individual stars integrated light Photometry star counts surface brightness profile Kinematics line-of-sight velocities (vLOS), LOS velocity distribution f (vLOS), proper motions (PM) v; σ, Gauss{Hermite moments Methods Jeans eqns; distribution functions f (I); orbit superposition ZZZ Dynamical r2Φ(x) = 4π G ρ(x) = 4π G f (x; v) d 3v self-consistency? Outcome total potential Φ; dark matter distribution; internal kinematics { All-purpose galaxy modeling architecture I Extensive collection of gravitational potential models (analytic profiles, azimuthal- and spherical-harmonic expansions) constructed from smooth density profiles or N-body snapshots; I Conversion to/from action/angle variables; I Self-consistent multicomponent models with action-based DFs; I Schwarzschild orbit-superposition models; I Generation of initial conditions for N-body simulations; I Various math tools: 1d,2d,3d spline interpolation, penalized spline fitting and density estimation, multidimensional sampling; I Efficient and carefully designed C++ implementation, examples, Python and Fortran interfaces, plugins for Galpy, NEMO, AMUSE. arXiv:1802.08239, 1802.08255, 1912.04288; http://agama.software Astrometry 101 Position on the sky α; δ Parallax $ = 1=distance Proper motion µα; µδ Line-of-sight velocity vlos Binary orbit parameters How Gaia astrometry works Overview of Gaia Data Release 2 Scanning the entire sky every couple of weeks I G I DR2 based on 22 months of observations I Astrometry for sources down to 21 mag (1:3 × 109) BP RP RVS I Broad-band blue/red photometry (1:4 × 109) I Radial velocity down to ∼ 13 mag (∼ 7 × 106 stars) ! No special treatment of binary stars ] 10 ! Poor completeness in crowded fields 1 ¡ r proper motion uncertainty [mas/yr] y 5 s a 8 m 10 [ ) Teff ICRF3 prototype x a 2 m 7 vrad SSO ; 10 m Variable Gaia DR1 p ¾ 1 Gaia-CRF2 Gaia DR2 ( : n 6 i 10 m : b 0 5 : p g n a 105 i e m s p 1 0:2 i . l l 0 4 e 10 r r e o 0:1 r p r e r 3 10 f e o b 0:05 s i m 2 x u 10 a systematic error N r o j 0:02 1 a 10 m ¡ i 0:01 1 mas/yr = 4:7 km/s × (D=1 Kpc) 0 m 10 e S 0:005 5 10 15 20 25 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Mean G [mag] G magnitude [Brown+ 2018] [Lindegren+ 2018] Example 1: Large Magellanic Cloud Example 1: Large Magellanic Cloud [credit: ESA/Gaia/DPAC, 25/04/2018] Gaia DR2 stars in the Large Magellanic Cloud 12 12 12 All stars Filtered by parallax and 13 13 13 radial astrometric excess noise velocities 14 14 14 15 15 15 16 16 16 Foreground LMC G [mag] 17 17 17 18 18 18 19 19 19 20 20 20 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 BP-RP [mag] BP-RP [mag] BP-RP [mag] 25 15 8 20 6 15 10 ] r 10 y 4 / s a 5 5 m [ 2 Y 0 µ 5 0 0 10 15 5 2 20 15 10 5 0 5 10 15 20 10 5 0 5 10 4 2 0 2 4 6 µX [mas/yr] µX [mas/yr] µX [mas/yr] Gaia DR2 stars in the Large Magellanic Cloud 12 107 12 12 All stars Filtered by parallax and 13 6 13 13 radial 10 astrometric excess noise velocities 14 14 all 14 105 astrometry 15 15 15 104 red giants 16 16 16 3 Foreground LMC G [mag] 17 10 17 17 2 combined 18 number of stars 10 18 18 19 101 19 19 10 5 0 5 10 20 20 20 0.5 0.0 0.5 1.0 1.5 2.0 µ2.5Y, m3.0as/y0.5r 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 BP-RP [mag] BP-RP [mag] BP-RP [mag] 25 15 8 104 20 data with errors 3 6 15 10 deconvolved 10 ] r 10 bootstrapped y 2 4 / s 10 a 5 5 m [ 1 2 Y 0 10 µ 5 0 typical 0errors: number of stars 10 best 5% 0 median 10 worst 5% 10-1 15 0.5 0.0 0.5 1.0 1.55 2.0 2.5 3.0 2 20 15 10 5 0 5 10 15 20 10 5 0 5 10 4 2 0 2 4 6 µ , mas/yr µX [mas/yr] X µX [mas/yr] µX [mas/yr] Internal kinematics of the Large Magellanic Cloud 8 520 8 160 8 40 8 40 6 µX 500 6 µY 140 6 σX 6 σY 4 480 4 120 4 30 4 30 2 460 2 100 2 2 0 440 0 80 0 20 0 20 Y [deg] 2 420 2 60 2 2 4 400 4 40 4 10 4 10 observations 6 380 6 20 6 6 8 360 8 0 8 0 8 0 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 X [deg] 8 8 105 8 0.8 340 6 vLOS 6 Σ 6 r 0.6 320 4 4 4 0.4 300 4 2 2 10 2 0.2 280 0 0 0 0.0 260 Y [deg] 2 2 3 2 0.2 240 10 4 4 4 0.4 220 6 6 6 0.6 200 8 8 102 8 0.8 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 X [deg] X [deg] X [deg] Internal kinematics of the Large Magellanic Cloud 8 520 8 160 8 40 8 40 6 µX 500 6 µY 140 6 σX 6 σY 4 480 4 120 4 30 4 30 2 460 2 100 2 2 0 440 0 80 0 20 0 20 Y [deg] 2 420 2 60 2 2 4 400 4 40 4 10 4 10 observations 6 380 6 20 6 6 8 360 8 0 8 0 8 0 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 X [deg] 8 520 8 116005 8 400.8 8 40 340 6 vµLXOS 500 6 ΣµY 140 6 σrX 0.6 6 σY 320 4 480 4 120 4 300.4 4 30 300 4 2 460 2 10010 2 0.2 2 280 0 440 0 80 0 200.0 0 20 260 Y [deg] Y [deg] 2 420 2 603 2 0.2 2 240 10 4 400 4 40 4 100.4 4 10 220 6 380 6 20 6 0.6 6 200 8 360 8 1002 8 00.8 8 0 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 X [deg] X [deg] X [deg] 8 20 8 20 8 20 8 20 ∆µ ∆µ ∆σ ∆σ 6 X 15 6 Y 15 6 X 15 6 Y 15 4 10 4 10 4 10 4 10 2 5 2 5 2 5 2 5 0 0 0 0 0 0 0 0 Y [deg] 2 5 2 5 2 5 2 5 residuals4 model 10 4 10 4 10 4 10 6 15 6 15 6 15 6 15 8 20 8 20 8 20 8 20 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 X [deg] X [deg] X [deg] X [deg] Internal dynamics of the Large Magellanic Cloud [1805.08157] z Method: axisymmetric Jeans Anisotropic model (a generalization of Cappellari 2002).
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