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Using Gaia for Studying Milky Way Star Clusters

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Using Gaia for Studying Milky Way Star Clusters Using Gaia for studying Milky Way star clusters Eugene Vasiliev Institute of Astronomy, Cambridge IAU 351 / MODEST-19, Bologna, 27 May 2019 Internal kinematics and galactic orbits 1811.05345 1807.09775 Overview of Gaia mission and 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 m [ ) x RV measurements only for stars a 2 m ; m p ¾ 1 with Teff 2 [3500 ÷ 6900] K ( : m : 0:5 p n i e s p 0:2 i l l e r o 0:1 r r e f o 0:05 s i x a systematic error r o j 0:02 a m ¡ i 0:01 1 mas/yr = 4:7 km/s × (D=1 Kpc) m e S 0:005 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 G magnitude [Katz+ 2018] [Lindegren+ 2018] Determination of cluster membership Determination of cluster membership Probabilistic membership determination A hard cutoff in PM space is not always possible and is conceptually unsatisfactory. A more mathematically well-grounded alternative: gaussian mixture modelling. f (µi ) = qcl N (µi j µcl; Σcl;i ) + (1 − qcl) N (µi j µfg; Σfg;i ) exp − 1 (µ − µ)T Σ−1 (µ − µ) N (µ j µ; Σ) ≡ 2 p ; 2π det Σ where the mean PMs µ and dispersions Σ of the cluster and foreground distributions, and the fraction of cluster members qcl, are all inferred by maximizing the likelihood of the observed stellar PMs. Probabilistic membership determination Take into account the measurement errors µα ; µδ ; ρµαµδ for each star i: 2 2 ! σcl(ri ) + µα ρµαµδ µα µδ Σcl;i = ρ σ2 (r ) + 2 µαµδ µα µδ cl i µδ 2 ! Sαα + µα Sαδ + ρµαµδ µα µδ Σfg;i = S + ρ S + 2 αδ µαµδ µα µδ δδ µδ And allow for a spatially-dependent density of cluster members: qcl(ri ). N Pstars Maximize ln L ≡ ln f (µi ) by adjusting free parameters: i=1 µcl, µfg, Sαα; Sδδ; Sαδ, radius and normalization of qcl(r), normalization of σcl(r). Posterior membership probability for each star: qcl(ri ) N (µi j µcl; Σcl;i ) pcl;i = qcl(ri ) N (µi j µcl; Σcl;i ) + [1 − qcl(ri )] N (µi j µfg; Σfg;i ) Caveat: spatially correlated systematic errors in astrometry ] 2 ) r y Covariance function 1 / 0.004 Covariance function V (θij ) = hµi µj i, averaged over s a Covariance function 2 m pairs of sources separated by angular distance θ: ( [ Data for quasar pairs ) 0.003 θ ( quasars at large scales, LMC stars at small scales. V Data for pairs of LMC stars n o i t 0.002 ◦ c n V (θ) = 0:0008 exp(−θ=20 ) u f e c 0.001 " ◦ n a 0:0036 exp(−θ=0:25 ) (cov.fnc.1) i r + a ◦ v o 0:004 sinc(θ=0:5 + 0:25) (cov.fnc.2) c 0.000 M P 0 1 2 3 4 5 6 angular distance θ [deg] 0.07 4 0.10 ] µ µ µ µ r cov.fnc.1, unweighted α α δ δ y / − − 0.08 s 0.06 cov.fnc.1, error-weighted 3 a ­ ® ­ ® 0.06 m cov.fnc.2, unweighted [ 2 µ 0.05 cov.fnc.2, error-weighted 0.04 f o 1 r 0.02 o 0.04 r r e 0 0.00 c i 0.03 t Y [deg] a 1 0.02 m e 0.04 t 0.02 s 2 y s 0.06 S 0.01 3 M 0.08 R 0.00 4 0.10 10-2 10-1 100 101 102 4 3 2 1 0 1 2 3 44 3 2 1 0 1 2 3 4 angular size of the cluster [deg] X [deg] X [deg] How to properly account for correlated systematic errors N Likelihood function for the entire dataset (µ ≡ fµi gi=1): L = N (µ j 1 µ, Σ) 0 2 1 V (0) + 1 V (θ12) V (θ13) ··· V (θ1N ) B V (θ ) V (0) + 2 V (θ ) ··· V (θ ) C Σ = B 21 2 23 2N C B . .. C @ . A 2 V (θN1) V (θN2) V (θN3) ··· V (0) + N (1..N are statistical errors of each datapoint). This is easily generalized to 2d case with 2 × 2 covariance matrices of statistical errors, and allowing for spatially-dependent internal dispersion and mean value of µ. The downside is that one needs to invert the N × N covariance matrix Σ for the entire dataset (for the optimal error-weighted estimate). q 1 PN PN Alternatively, an unweighted estimate of the uncertainty on µ is N i=1 j=1 Σij . Spatial correlation should not be ignored! Doing so underestimates the error bars on fit parameters, even when systematic errors are much smaller than statistical errors. ignoring correlations taking correlations into account 0. 155 0. 005 2. 707 0. 004 0. 168 0. 044 2. 681 0. 043 − ± − ± − ± − ± µα 0. 123 µδ 2. 628 µα 0. 123 µδ 2. 628 0.20 − − 0.20 − − 0.15 0.15 0.2 0.1 0.0 2.7 2.6 2.5 0.2 0.1 0.0 2.7 2.6 2.5 ] ] r r y y / 0.10 / 0.10 s s a a m m [ [ µ µ σ σ , 0.05 , 0.05 µ µ 0.00 0.00 0.05 0.05 0 5 10 15 20 25 0 5 10 15 20 25 R [arcmin] R [arcmin] Internal kinematics of globular clusters see also Bianchini+ 2018, Sollima+ 2019,Clear Jindal+ signature 2019, of all rotation based in on Gaia data ∼ 10 clusters: 0.25 0.6 NGC 6656 (M 22) NGC 5904 (M 5) 8 N=4171, D=3.2 kpc N=4476, D=7.6 kpc 8 0.20 0.5 ] ] r r 6 ] ] y y / / 0.15 s s / / s 0.4 s a 6 a m m k k m m 4 [ [ [ [ 0.10 σ σ µ µ 0.3 σ σ , , t t , , v v t 4 t , , µ µ 2 r r 0.05 v v , , r 0.2 r µ µ 2 0.00 0 0.1 0.05 0.0 0 2 0 5 10 15 0 5 10 15 R [arcmin] R [arcmin] Internal kinematics of globular clusters HST measurements in central partssee [Bellini+ also 2014, Baumgardt+ Watkins+ 2018, 2015] Jindal+ 2019Good (Gaia match PM) between and line-of-sight velocity dispersion and PM dispersion: 6 0.5 NGC 6397 0.25 NGC 7089 (M 2) N=10000, D=2.4 kpc 5 N=1296, D=10.5 kpc 0.4 0.20 10 ] ] r 4 r ] ] y y / / s s / 0.15 / s 0.3 s a a m m k k m 3 m [ [ [ [ 0.10 5 σ σ µ µ σ σ 0.2 , , t t , , v v t 2 t , , µ µ 0.05 r r v v , , r r µ 0.1 µ 1 0.00 0 0.0 0 0.05 0 5 10 15 20 0 2 4 6 8 10 12 R [arcmin] R [arcmin] Internal kinematics of globular clusters likely due to crowding issues andMismatch aggressive between sample cleanup σ los and PM dispersion in central parts: 0.6 NGC 104 (47 Tuc) NGC 6752 0.4 8 N=10000, D=4.4 kpc N=10000, D=4.2 kpc 10 ] ] r 0.4 r 0.3 6 ] ] y y / / s s / / s s a a m m k k m 5 m [ [ [ [ 0.2 4 0.2 σ σ µ µ σ σ , , t t , , v v t t , , µ µ r r v v , , 0.1 2 r 0.0 0 r µ µ 0.0 0 0.2 5 0 5 10 15 20 25 30 0 5 10 15 20 R [arcmin] R [arcmin] Internal kinematics of globular clusters a prime method for measuring theOverall distance scale from mismatch kinematic between analysis σ los and σ µ : 0.6 4 NGC 6121 (M 4) 0.20 NGC 6838 (M 71) N=7538, D=2.0 kpc 5 N=1983, D=4.0 kpc 0.5 3 0.15 ] 4 ] r r ] ] y 0.4 y / / s s / / s s a a 2 3 m 0.10 m k k m m [ [ [ 0.3 [ σ σ µ µ σ σ , , t t , , v v t 2 t 0.05 1 0.2 , , µ µ r r v v , , r r µ 0.1 1 µ 0.00 0 0.0 0 0.05 1 0 5 10 15 20 0 1 2 3 4 5 6 7 8 R [arcmin] R [arcmin] Kinematics of the entire Milky Way globular cluster system see also Gaia Collaboration (Helmi+) 2018, Baumgardt+ 2018, de Boer+ 2019 ∼ 150 globular clusters in the Milky Way Previous measurements of mean PM of globular clusters 10 10 10 10 HST Dinescu Chemel Kharchenko 5 5 5 5 ] r y / s 0 0 0 0 a m [ r e t i 5 5 5 5 l , α µ 10 10 10 10 15 15 15 15 15 10 5 0 5 10 15 10 5 0 5 10 15 10 5 0 5 10 15 10 5 0 5 10 µα, this [mas/yr] µα, this [mas/yr] µα, this [mas/yr] µα, this [mas/yr] 5 5 5 5 0 0 0 0 ] r y / s 5 5 5 5 a m [ r e t i 10 10 10 10 l , δ µ 15 15 15 15 20 20 20 20 20 15 10 5 0 5 20 15 10 5 0 5 20 15 10 5 0 5 20 15 10 5 0 5 µδ, this [mas/yr] µδ, this [mas/yr] µδ, this [mas/yr] µδ, this [mas/yr] 1.0 6 6 15 ] r 4 4 10 y / s 0.5 a NGC 6838 M 71 2 2 5 m [ s i h Terzan 5 Terzan 5 11 t , 0.0 0 0 0 δ Terzan 8 µ NGC 6101 − Pyxis 2 2 5 r NGC 5466 e t i 0.5 l , δ 4 4 10 µ 1.0 6 6 15 1.0 0.5 0.0 0.5 1.0 6 4 2 0 2 4 6 6 4 2 0 2 4 6 15 10 5 0 5 10 15 µ µ [mas/yr] µ µ [mas/yr] µ µ [mas/yr] µ µ [mas/yr] α, liter − α, this α, liter − α, this α, liter − α, this α, liter − α, this Distribution of globular clusters in position/velocity space [Fe/H] 2 1 0 200 Crater Crater Crater AM 1 AM 1 AM 1 Pal 4 Pal 4 Pal 4 100 Pal 3 Eridanus Eridanus Pal 3 Eridanus Pal 3 NGC 2419 NGC 2419 NGC 2419 Pal 14 Pal 14 Pal 14 50 Pyxis Pal 15 Pyxis Pyxis NGC 7006Pal 15 NGC 7006 NGC 7006Pal 15 Pal 2 Pal 2 Whiting 1 Pal 2 Whiting 1 Whiting 1 NGC 5694 NGC 6229 NGCNGC 6229 5694 NGC 5824 NGC 5694 Pal 13 Pal 13 Pal 13 NGC 6229 NGC 7492 NGC 7492 NGC 5824 NGC 5824 NGC 5634 NGC 7492 NGC 4147 NGCNGC 4147 5634 NGC 4147 Arp 2 Arp 2 Arp 2 M 79 NGC 1261M 79 NGC 5634 20 Rup 106 NGC 1261M 79 Terzan 8 NGCM 5053 53 Pal 5 M 53 Pal 5 M 53 M 54 NGC 1851 TerzanM 854 Pal 5 NGC 5053 NGC 1261 M 54 Rup 106 Terzan 8 IC 1257NGC 1851 NGC 5053 Pal 1 Pal 1 NGC 5466 IC 4499 Pal 1 NGC 1851 NGCIC 12572298 Rup 106 Pal 12 IC 1257 IC 4499 NGC 5466 NGC 2298 NGC 5466 Pal 12 NGC 2298 IC 4499 Pal 12 Terzan 7 NGC 6426 Terzan 7 BH 176 M 75 M 75 M 75 M 72 Terzan 7 NGC 6426 ESO280 NGC 6426 NGC 6101 ESO280 BH 176 ESO280 M 72 NGC 288 M 72 M 3 NGC 288 NGC 6934 NGCM 288 3 NGC 2808 NGC 6934 BH 176 M 3 NGC 6934 NGC 2808 M 15 NGC 6101 NGC 2808 M 2 M 2 M 15 NGC 6101 M 68 M 68 M 2 M 68 M 92 M 15 M 92 NGC 5286 10 NGC 362 NGCM 5286 92 M 56 E 3 NGC 362 M 56 NGC 5286 M 56 E 3 NGC 3201 NGC 362 E 3 NGC 3201 NGC 3201 M 13 NGC 6284 M 13 M 13 NGC 6356 47 TucPal 11 Pal 11NGC 5897 Pal 11 47 Tuc NGC 483347 Tuc M 30 M 30 M 30 NGC 4372 NGC 4372 M 71 NGC 4833 M 71 NGC 4372 NGC 4833 NGC 5897 r [kpc] NGC 5897 M 71 ω Cen ω Cen NGC 6356NGC 6284 Cen NGC 6284 NGC 6356 Pal 10 Pal 10 M 4 Pal 10 NGC 6584 ω NGC 6584 NGC 6397 NGC 6397 M 5 M 5 M 4 NGCM 6584 5 M 4 NGC 6752 NGC 6366NGC 6544 NGC 6397 NGC 5946 NGCPal 8 6362 M 22 NGC 5946 NGC 5946 M 22 Pal 8 NGC 6760 Pal 8 M 12 M 10 NGC 6362 NGC 6362 NGC 6749M 12 NGC 6752 NGC 6544 NGC 6760NGC 6752M 22 5 NGC 6544 NGC 6760 FSR 1735 NGC 6749 NGC 5927 NGC 6366 NGC 5927 NGC 6235 NGC 6366 M 10 M 1210 NGC 5986 FSR 1735 NGC 6749 NGC 5986 NGC 5986 NGC 5927 NGC 6517BH 184 BH 184 BH 184 M 55 FSR 1735 Pal 7 NGC 6535 Terzan 12 NGC 6352 M 80 M 14 NGC 6535 M 55 M 14 M 14 NGC 6535 M 55 Pal 7 NGC 6380 NGC 6496 NGC 6380 NGC 6712 NGC 6496 NGC
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