Gaia EDR3 view on Galactic globular clusters Eugene Vasiliev Institute of Astronomy, Cambridge 1 10 100 distance IAP seminar, 17 June 2021 based on: Vasiliev & Baumgardt (2102.09568), Baumgardt & Vasiliev (2105.09526) The Gaia [r]evolution all-sky photome- astrometry and improved preci- try: 109 stars colours: > 109, sion and reduced Vlos: 7M stars calibration errors with G . 13 Hipparcos + Gaia = TGAS (1989{1993) astrometry: 2M 22 months 34 months nearby stars DR1 =) DR2 =) EDR3 The Gaia [r]evolution all-sky photome- astrometry and improved preci- Vlos for fainter try: 109 stars colours: > 109, sion and reduced stars; binary pa- Vlos: 7M stars calibration errors rameters; epoch with G . 13 astrometry and Hipparcos + Gaia = TGAS photometry... (1989{1993) astrometry: 2M 22 months 34 months nearby stars pre-Gaia =) DR1 =) DR2 =) EDR3 =) DR3, 4, 5 Determination of cluster membership Determination of cluster membership Determination of cluster membership and parameters A hard cutoff in PM space is not always possible and is conceptually unsatisfactory. A more mathematically well-grounded alternative: mixture modelling [Gaussian or more general]. Write down the distribution functions for both cluster and field populations, and vary their parameters θ to maximize the likelihood of the observed data data: 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 ) 6d kinematics of star clusters typical PM uncertainty: δµ ' 0:025 mas/yr distance uncertainty: ∼ a few percent v µ D = 4:74 km=s mas=yr kpc distance uncertainty usually dominates 100 AM 1 AM 4 Crater orbits for the last 100 Myr 50 Munoz 1 Pal 3 Laevens 3 Ko 1 Ko 2 Pal 4 20 Eridanus Pal 14 NGC 2419 10 5 104 2 103 velocity uncertainty 2 1 10 1 0.5 10 number of stars 2 5 10 20 50 100 orbits for the last 10 Gyr distance [Kpc] Orbits of star clusters 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] Clusters in the space of integrals of motion polar 5 10 20 50 100 EDR3 semimajor axis [kpc] DR2 Ko 1 NGC 5053 Sagittarius 0 NGC 5053 → [Law&Majewski 2010, . ] circular Terzan 7 Terzan 8 y Pal 5 t i M 53 WhitingArp 2 M 53 1 Pal 5 Arp 2 Terzan 8 M 54 c circular Terzan 7 M 54 i r Whiting 1 t Kim 3 180 ◦ inclination 0 ◦ n ← → NGC 5824 NGC 5824 e c Pal 12 NGC 5897 NGC 5897 NGC 6235 c Pyxis M 3 M 3 Pal 12 NGC 6235 Pyxis e 47 Tuc 47 Tuc IC 4499 IC 4499 M 30 Segue 3 prograde M 30 E 3 NGC 6397 E 3 Pal 11 ← NGC 6397 NGC 6356 NGC 6287 NGC 6356 Pal 11 M 13 Pal 1 NGC 6284 NGC 288 NGC 7492 1 Terzan 10 Pal 1 NGC 288 Ko 2 M 68 M 13 M 68 Bliss 1 FSR 1716 M 15 M 71 Terzan 10 Pfleiderer 2 NGCM 592771 M 15 NGC 5466 ESO 93-8 BH 176 NGC 5466 BH 176 NGC 6101 NGC 6284 Pal 10 Pal 7 Pal 10 NGC 6101 NGC 6496 NGC 4372 Pal 7 NGC 3201 M 92 NGC 4372 NGC 3201 ω M 22 M 22 retrograde C FSR 1758e NGC 5634 n NGC 5634 NGC 7492 Pal 13 ω M 5 M 5 C Pal 13 e M 92 M 9 M 9 NGC 6426 n NGC 6426 ESO 280 NGC 362 NGC 1261 Rup 106 Rup 106 ESO 280 M 56 NGC 2298 BH 140 NGC 6584 M 75 NGC 6584 NGC 4147NGC 362 Ryu 059 M 75 NGC 1261 NGC 2298 in-plane NGC 5286 NGC 4147 IC 1257 NGC 5286 M 56 M 2 NGC 4833 M 2 NGC 4833 Djorg 1 Djorg 1 NGC 7006 NGC 5694 NGC 6229 NGC 6229 NGC 1851 Pal 15 in-plane NGC 7006 NGC 5694 NGC 1851 NGC 6934 NGC 6934 UKS 1 radially M 72 NGC 2808 NGC 2808 IC 1257 Sequoia M 72 anisotropic M 79 M 79 [Myeong+ 2019] Pal 14 Pal 2 population [Myeong+ 2018, Pal 2 radial Helmi+ 2018] Clusters in the space of integrals of motion Jackson Pollock, \Convergence" Kliment Redko, \Uprising" Distances to star clusters compilation of ∼ 1300 measurements from literature by Holger Baumgardt (CMD, RR Lyrae, eclipsing binaries) + HST/Gaia dynamical fits & parallaxes Internal kinematics: rotation, dispersion Good agreement with HST 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 R [arcmin] R [arcmin] R [arcmin] and 25 NGC 5139 (ω Cen) NGC 4590 (M 68) 0.20 NGC 6681 (M 70) 0.10 5 N=53122 (37288), D=5.4 kpc N=3284 (148), D=10.4 kpc N=857 (48), D=9.4 kpc 8 σ 0.8 20 0.08 4 0.15 LOS ] ] ] r r r 6 y y y ] ] ] / / / s s s s 0.6 15 s 0.06 3 s a a a / / 0.10 / m m m m m m from literature [ [ [ 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 radial 0.3 0.3 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 Perspective effects in the radial PM component Perspective contraction/expansion due to line-of-sight motion: ◦ µR (R) = ξ R; ξexpected = −vLOS=D × (π=180 =4:74) mas/yr/degree.