Dynamics of Milky Way globular clusters and satellite galaxies in the Gaia era globular clusters satellite galaxies 1 10 100 distance Eugene Vasiliev Institute of Astronomy, Cambridge IAG-USP seminar, 1 September 2021 Gaia mission: the Milky Way in motion Gaia mission timeline Dec 2013 launch Sep 2016 DR1: G-band photometry for > 109 sources, astrometry for 2×106 bright stars previously observed by Hipparcos (1990s) 9 Apr 2018 DR2: G, GBP , GRP photometry for 1:4 × 10 sources, astrometry (parallaxes & proper motions) for 1:3 × 109 stars, line-of-sight velocity for 7 × 106 bright stars Jun 2019 end of nominal 5-year mission; extended for a few years Dec 2020 Early DR3: improved photometry and astrometry for 1:5 × 109 sources 1h 2022 DR3: astrometry/photometry remains the same, line-of-sight velocity for ∼ 3 × 107 stars, mean BP, RP and RVS spectra, astrometric solutions for non-single stars, lightcurves for variable sources ∼2024 end of extended mission (limited by onboard fuel supply) 2024 ? DR4: full analysis of the nominal 5-year mission data; improved astrometry, photometry, spectroscopy; individual epoch data ? DR5: full analysis of the extended mission, final catalogue. Gaia astrometric precision PM uncertainty [mas/yr] µ & 0:01 mas/yr in EDR3 0.01 0.02 0.05 0.1 0.2 0.5 1 −3=2 µ / T : 6 expect 2:5× improvement in DR4 8 1 mas/yr = 4:7 km/s × (D=1 kpc) σ ∼ 2 − 10 km/s in clusters 10 NGC 5272 (M 3), D=10 kpc 12 12 14 14 G magnitude 16 16 G 18 18 20 20 systematic error 0.5 0.0 0.5 1.0 1.5 0.5 1 2 5 10 20 50 100 g-r velocity uncertainty at 10 kpc [km/s] Determination of cluster membership 10 10 NGC 6544 12 5 5 14 ] r 10 y / s 0 a 16 m [ G [mag] δ Y [arcmin] µ 15 18 5 20 20 10 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 10 5 0 5 10 10 5 0 5 BP-RP [mag] X [arcmin] µα [mas/yr] 10 10 NGC 6352 0 12 5 2 14 ] r 4 y / s 0 a 16 m [ G [mag] δ 6 Y [arcmin] µ 18 5 8 20 10 10 0.0 0.5 1.0 1.5 2.0 2.5 3.0 10 5 0 5 10 8 6 4 2 0 2 BP-RP [mag] X [arcmin] µα [mas/yr] Determination of cluster membership 10 10 NGC 6544 12 5 5 14 ] r 10 y / s 0 a 16 m [ G [mag] δ Y [arcmin] µ 15 18 5 20 20 10 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 10 5 0 5 10 10 5 0 5 BP-RP [mag] X [arcmin] µα [mas/yr] 10 10 NGC 6352 0 12 5 2 14 ] r 4 y / s 0 a 16 m [ G [mag] δ 6 Y [arcmin] µ 18 5 8 20 10 10 0.0 0.5 1.0 1.5 2.0 2.5 3.0 10 5 0 5 10 8 6 4 2 0 2 BP-RP [mag] X [arcmin] µα [mas/yr] Determination of cluster membership and parameters A hard cutoff in PM space is not always possible and is conceptually unsatisfactory. 5 ] r 10 y A more mathematically well-grounded alternative: / s a m [ mixture modelling [Gaussian or more general]. δ µ 15 Write down the distribution functions for both cluster and field populations, and vary their parameters θ 20 to maximize the likelihood of the observed data data: 10 5 0 5 µα [mas/yr] true DF convolved with errors measurements: $; µ; R measurement uncertainties XNstars ln L ≡ ln η fmemb(xi ;δ xi j θmemb) + (1 − η) ffield(xi ;δ xi j θfield) i=1 fraction of members parameters of distributions Results: cluster properties $; µ; σµ(R); µrot(R); η; : : : η fmemb(xi ) and membership probability of each star: pi = . η fmemb(xi ) + (1 − η) ffield(xi ) Internal kinematics of star clusters: rotation, dispersion [Vasiliev & Baumgardt 2021;Good see agreement also with Bianchini+ 2018, HST Baumgardt+ 2019, Vasiliev 2019, Sollima+ 2019] µ σ rot µ σ µ [Watkins+ 2015, Cohen+ 2021] 0.6 NGC 104 (47 Tuc) NGC 288 NGC 6838 (M 71) 3.5 N=39931 (33144), D=4.5 kpc 0.08 N=4690 (226), D=9.0 kpc N=3021 (833), D=4.0 kpc 3 0.15 10 3.0 ] 0.4 ] ] r r 0.06 r y y 2.5 y ] ] ] / / / s s s s s s 0.10 2 a a a 5 / 2.0 / / m m m m m m [ 0.2 [ [ k k k [ 0.04 [ [ µ µ µ s 1.5 s s σ σ σ o o o l l l , , , σ σ σ t t t 0.05 1 o o o r r 1.0 r µ 0.0 0 µ 0.02 µ 0.5 0.00 0 0.2 0.00 0.0 5 0 5 10 15 20 25 30 35 40 0 2 4 6 8 10 12 14 0 2 4 6 8 10 and R [arcmin] R [arcmin] R [arcmin] 25 σ NGC 5139 (ω Cen) 0.20 NGC 4590 (M 68) 5 NGC 6681 (M 70) LOS 0.10 N=53122 (37288), D=5.4 kpc N=3284 (148), D=10.4 kpc N=857 (48), D=9.4 kpc 8 0.8 20 0.08 4 0.15 ] ] ] r r r 6 y y y from literature ] ] ] / / / s s s s 0.6 15 s 0.06 3 s a a a / / 0.10 / m m m m m m [ [ [ k k 4 k [ 2 [ [ µ µ µ 0.04 s s s σ σ σ o o o l l l 0.4 , 10 , , σ σ σ t t t o o o 0.05 r r 0.02 1 r 2 µ µ µ 0.2 5 0.00 0 0.00 0 0.02 1 0.0 0 0 5 10 15 20 25 30 35 40 0 2 4 6 8 10 12 14 0 1 2 3 4 5 6 R [arcmin] R [arcmin] R [arcmin] PM anisotropy profiles 0.3 NGC 104 0.3 NGC 3201 0.3 NGC 6218 1 0.2 1 0.2 1 0.2 − 0.1 − 0.1 − 0.1 R R R , , , tangential µ 0.0 µ 0.0 µ 0.0 σ σ σ / / / $ t 0.1 t 0.1 t 0.1 , , , µ 0.2 µ 0.2 µ 0.2 σ σ σ 0.3 0.3 0.3 radial 0 5 10 15 20 25 30 0 5 10 15 20 0 2 4 6 8 Radius [arcmin] Radius [arcmin] Radius [arcmin] 0.3 NGC 5139 0.3 NGC 6121 0.1 NGC 7078 1 0.2 1 0.2 1 0.0 − 0.1 − 0.1 − 0.1 R R R , , , µ 0.0 µ 0.0 µ 0.2 σ σ σ / / / t 0.1 t 0.1 t 0.3 , , , µ 0.2 µ 0.2 µ 0.4 σ σ σ 0.3 0.3 0.5 0 5 10 15 20 25 30 35 0 5 10 15 20 0 2 4 6 8 Radius [arcmin] Radius [arcmin] Radius [arcmin] variety of profiles, mostly weakly radial or isotropic [Vasiliev & Baumgardt 2021; see also Jindal+ 2019, Bianchini+ 2019] Distances to globular clusters compilation of ∼ 1300 literature measure- ments (CMD, RR Lyrae, eclipsing binaries) + HST/Gaia dynamical fits & parallaxes [Baumgardt & Vasiliev 2021] https://people.smp.uq.edu.au/HolgerBaumgardt/globular/ Orbits of globular clusters each cluster is shown by a cloud representing its measurement uncertainties (primarily in distance) NGC 6712 M 79 M 72 1.0 NGC 362 NGC 4147 Pal 14 1.0 NGC 1851 NGCNGC 6287 5946 NGC 6229 Pal 6 M 92 Pal 2 NGC 7006 NGC 6642 Pal 15 M 2 UKS 1 IC 1257 NGC 5694 Pal 4 NGC 5286 NGC 2298 NGC 1261 NGC 6401 M 75 NGC 6638VVV CL002 NGCM 6544 70 NGC 6355 NGC 6934 NGC 4833 M 56 NGC 5986 NGC 6284 ESO 280 NGC 2808 ESO 452 M 4 NGC 7492 NGC 6584 Eridanus NGC 6528 Ryu 879 M 5 NGC 6293 Liller 1 NGC 5634 M 9 NGC 2419 NGC 6652 M 19 Djorg 1 Terzan 10 Pal 13 AM 1 0.8 NGC 6453 M 13 NGC 6558 M 14 NGC 6440 Terzan 9 Laevens 3 NGC 6380 NGC 6517 M 30 NGC 288 Rup 106 NGC 5466 Ryu 059 Terzan 5 0.5 BH 229 M 28 M 55 M 80 BH 140 Pyxis ω NGC 6426 VVV CL001 NGC 6316 C Kim 3 e ) n NGC 5897 FSR 1758 IC 4499 L Terzan 1 NGC 6535 NGC 6624 0.6 / z M 22 Terzan 6 M 107 NGC 6139 L Gran 1 Pal 8 NGC 6749 NGC 6101 Terzan 7 ( NGCNGCFSR 63886541 1735 Pal 12 Terzan 8 M 62 NGC 6366 M 3 NGC 3201 M 68 M 54 n Terzan 4 0.0 o NGC 6144 Whiting 1 i NGC 6723 NGC 6441 Mercer 5 NGC 6397 Arp 2 M 15 t BHM 184 10 NGC 6760 NGC 6325 NGC 4372 M 53 NGC 6342 a NGC 6522 NGCNGC 6235 6356 Pal 9 n M 12 NGC 5824 i BH 261 l eccentricity Terzan 2 0.4 c NGC 6496 NGC 6362 n FSR 1716 i Terzan 12 Ton 2 Pfleiderer 2 Pal 3 Djorg 2 NGC 6540 Pal 7 Bliss 1 Pal 5 M 69 NGC 6304 NGC 5053 Ko 2 Pal 11 NGC 6752 Pal 10 Ko 1 NGC 6539 Munoz 1 0.5 Terzan 3 NGC 6256 0.2 NGC 6569 M 71 BH 176 Crater NGC 6553 47 Tuc E 3 NGC 5927 Pal 1 NGC 6352 ESO 93-8 Segue 3 AM 4 0.0 1.0 0.7 1 2 3 5 7 10 20 30 50 70 100 semimajor axis [kpc] [Vasiliev & Baumgardt 2021] Clusters in the space of integrals of motion (energy, angular momentum, actions.