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 | θmemb) + (1 − η) ffield(xi ,δ xi | 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
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 σµ 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 µrot 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]
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 0.8 20 0.08 4 0.15 ] ] ]
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 [ [ [
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] Good agreement with HST σµ [Watkins+ 2015, Cohen+ 2021] and σLOS from literature 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.
0.2 20 M 22 M 13 0.1
M 3 15 0.0 47 Tuc NGC 6752 NGC 6397 d e r M 5 u 0.1 s a n M 4 10 e e C
count ω m
ξ 0.2
0.3 5
0.4 NGC 3201 0 0.4 0.3 0.2 0.1 0.0 0.1 0.2 2 1 0 1 2 ξexpected (ξ ξ )/² meas − exp ξ (error bars take into account spatially correlated systematics) Caveat 1: statistical uncertainties are slightly underestimated NGC 5139 (ω Cen) bright ⇐⇒ faint
10-1
10-2
η=1.203 η=1.165 η=1.142 η=1.188 -3 10 N=2083 N=5822 N=7253 N=8980 0 10-1 10-2 ⇐⇒ η=1.087 η=1.080 η=1.077 η=1.127 -3 10 N=1043 N=5055 N=11879 N=7231 14 10-1 outskirts 10-2 η=1.108 η=1.073 η=1.041 η=1.066 -3 10 N=664 N=3679 N=9952 N=4046 20 1.30 5p, 13.0 t 1.20 5139 c a 5272 f n 1.15 5904 o i t 6121 a l 1.10 f 6205 n i 6254 r 1.05 o 6362 r r e 6397 1.00 6752 0.95 6809 3 10 30 100 300 3 10 30 100 300 3 10 30 100 300 3 10 30 100 300 density [sources/arcmin²] Actual vs. formal uncertainty: 2 2 2 2 actual = η formal + add, See also uncertainty calibration studies: error inflation factor Fabricius+ 2012.06242, ζ η = (1 + Σ/Σ0) , Ma´ızApell´aniz+ 2101.10206, 2 El-Badry+ 2101.05282: Σ0 = 10 stars/arcmin , ζ = 0.04, η ∼ 1.1 − 1.3 for well-behaved sources add = 0.01 mas. Caveat 2: variation of parallax zero point across CMD stars coloured by the offset of $ from the mean value for each cluster 10 NGC 104 (47 Tuc) NGC 3201 NGC 5139 (ω Cen) NGC 5272 (M 3) NGC 5904 (M 5) 12 14 G 16 18 20 10 NGC 6121 (M 4) NGC 6205 (M 13) NGC 6397 NGC 6752 NGC 6809 (M 55) 12 0.02 14 0.01 G 16 0.00 ∆ 18 0.01 20 0.02 10 Collinder 261 NGC 2437 NGC 2477 NGC 7789 Trumpler 5 12 14 G 16 18 20 0.5 0.0 0.5 1.0 1.5 2.0 2.5 0.5 0.0 0.5 1.0 1.5 2.0 2.5 0.5 0.0 0.5 1.0 1.5 2.0 2.5 0.5 0.0 0.5 1.0 1.5 2.0 2.5 0.5 0.0 0.5 1.0 1.5 2.0 2.5 BP-RP BP-RP BP-RP BP-RP BP-RP Analysis of parallaxes in the Large Magellanic Cloud ∼ 9M stars in the LMC selected using a mixture model in CMD + astrometry space Analysis of parallaxes in the Large Magellanic Cloud spatial correlations in the mean parallax of stars described by a covariance function V$(θ) = ($i − $)($j − $) , where θ is the angular distance between stars i and j. 0.035 8 8 BP-RP<0.5 BP-RP>0.9 6 6 0.030 true value 4 4 ] 0.025 2 2 0.04 s a m [ 0 0 0.020 2 2 0.03 0.015 4 4 6 6 0.010 13 14 15 16 17 18 19 20 = 0. 0228 0. 0052stat 0. 0116sys = 0. 0228 0. 0045stat 0. 0082sys 13 400 400 6 6 BP-RP<0.5 13 s 200 s 200 a a 0 0 µ µ [ [ ) ) θ θ ( 100 ( 100 2 2 0.00 V V 4 4 0 0 6 6 = 0. 0234 0. 0079 0. 0129 = 0. 0216 0. 0084 0. 0132 ± stat ± sys stat sys 18.5 6 6 BP-RP<0.5 BP-RP>0.9 0.025 true value 4 4 0.04 2 2 ] 0.020 s a m [ 0 0 0.015 0.03 2 2 0.010 4 4 0.02 0.005 = 0. 0144 0. 0087 0. 0157 = 0. 0216 0. 0104 0. 0101 13 14 15 16 17 18 19 20 ± stat ± sys stat sys 13 s 200 s 200 a a 0 0 0.00 µ µ [ [ ) ) θ θ ( 100 ( 100 2 2 V V 0 0 4 4 = 0. 0239 0. 0113stat 0. 0141sys = 0. 0182 0. 0118stat 0. 0125sys 18.5 3 0.055 2 0.050 1 ] 0.06 s 0.045 a true value m [ 0.040 0 0.035 1 0.05 0.030 2 0.025 13 14 15 16 17 18 19 20 3 = 0. 0528 0. 0093stat 0. 0094sys 13 s 200 a 0 µ [ ) θ ( 100 1 0.02 V 2 0 3 = 0. 0404 0. 0102 0. 0127 ± stat ± sys 100 17 2 40 6752 s Y [arcmin] a 10 µ [ 50 100 20 20 ) θ ( 0 0 0 30 30 20 10 0 10 20 30 V X [arcmin] 20 NGC 5139 parallax 50 100 0.17 0.18 0.19 0.20 0.21 40 30 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 20 θ [deg] θ [deg] θ [deg] 10 Spatial covariance function: V$(θ) = ($i − $)($j − $) , 0 Y [arcmin] where θ is the angular distance between stars i and j. 10 20 see also Lindegren+ 2012.03380, Ma´ızApell´aniz+ 2101.10206 30 ◦ 30 20 10 0 10 20 30 for V$(θ) determined on scales θ & 1 from LMC stars and quasars. X [arcmin] p For bright stars (13 < G < 18): $,sys ≡ V$(θ = 0) ' 0.01 mas; DR2: for fainter stars it may be ∼ 1.5 − 2× higher. $,sys ∼ 0.043 µ,sys ∼ 0.066 Same for PM: µ,sys ' 0.025 mas/yr. Caveat 4: parallaxes appear to be slightly overestimated 0.05 mean parallaxes of cluster members vs. literature distances 0.04 after applying the parallax zero-point correction from Lindegren+ 2012.01742 Pal 11 0.03 NGC 7492 NGC 6284 ESO 452 M 19 M 62 NGC 5824 NGC 288 NGC 5897 M 55 M 72 0.02 M 75 NGC 6397 NGC 2298 E 3 NGC 6293 Rup 106 M 68 M 53 NGC 6342 M 9 NGC 5634 M 70 M 54 M 30 NGC 5986 M 12 NGC 6496 M 3 NGC 6101 NGC 6752 M 107 NGC 6652 Terzan 8 M 28 NGC 6934 M 4 NGC 6541 M 5 NGC 6388 NGC 2808 NGC 6638 0.01 NGC 6723 n M 79 e C NGC 6712 ω NGC 6352 NGC 6144 NGC 6229 NGC 4833 NGC 3201 NGC 6441 NGC 1851 47 Tuc NGC 6535 M 22 NGC 6624 M 80 NGC 1261 M 69 NGC 6235 NGC 5927 NGC 6584 M 15 NGC 6426 0.00 NGC 6362 Pal 5 M 71 IC 4499 parallax - 1 / distance NGC 362 Pal 12 M 92 NGC 5466 M 13 M 10 NGC 5286 M 56 M 2 0.01 104 NGC 5053 103 Pal 9 0.02 102 101 number of stars NGC 4147 0.03 2 3 5 7 10 20 30 distance [Kpc] Caveat 4: parallaxes appear to be slightly overestimated distance modulus 2 2 +0.0290 error 0.0271 0.0192 $i − 1/Di ∼ N (∆$, $,i + $,sys), − ∆$ ' 0.01 mas, 12 largest µ 70 other ² $,sys ' 0.01 mas. offset combined +0.0353 0.0034 0.0369 − − See also zero-point calibration studies by 0.2 0.1 µ 0.0 ∆ parallax Riess+ 2012.08534 (cepheids), 0.1 error +0.0010 0.2 0.0088 0.0009 Bhardwaj+ 2012.13495 (RR Lyrae), − 0.020 Stassun & Torres 2101.03425, 0.015 ² 0.010 offset Ren+ 2103.16096( eclipsing binaries), 0.005 +0.0023 0.0098 0.0022 0.000 − Zinn 2101.07252 (asteroseismology), 0.024 0.016 Huang+ 2101.09691 (red clump stars), ∆ 0.008 0.000 Groenewegen 2106.08128 (quasars) 0.008 0.2 0.1 0.0 0.1 0.2 0.00 0.04 0.08 0.12 0.16 0.0000.0050.0100.0150.0200.0080.0000.0080.0160.024 ²µ ∆µ ² ∆ Summary: Gaia EDR3 ⇐⇒ globular clusters I Mean parallaxes, PM and orbits determined for 170 globular clusters; I PM dispersions and dynamical distances – for ∼ 100 clusters; I Rotation detected in ∼ 20 clusters; I PM anisotropy measured in ∼ 15 clusters. I Statistical uncertainties are underestimated by 10 − 20% in dense regions (even for the clean subset); I Spatially correlated systematic errors on sub-degree scales: $ ' 0.01 − 0.02 mas, µ ' 0.025 mas/yr; I Parallax zero-point correction overshoots by ∼ 0.01 mas. Despite these caveats, Gaia is great and EDR3 significantly improves its quality! Amanda Smith, IoA