Streams, shells, galactic archeology
Eugene Vasiliev
Institute of Astronomy, Cambridge
45th Heidelberg Physics Graduate Days, October 2020 Outline
I Stellar systems in a tidal field I Formation of streams and shells I Observational evidence for streams I Detection methods I Streams as dynamical probes I Galactic archeology Motion in the rotating frame A satellite galaxy or a star cluster on a circular orbit in the host galaxy: consider a rotating coordinate system so that the x axis points towards the cluster, y is the direction of its motion, and z is the normal to the orbital plane. Φh(x) and Φc(x) are the potentials of the host galaxy and the cluster; the centre-of-mass position of the cluster is {R0, 0, 0}, q its velocity in the inertial frame is {0, V0, 0}, where V0 = R0 ∂Φ/∂x ; x=R0 Ω ≡ {0, 0, V0/R0} is the angular velocity of the cluster.
1 2 HJ = Φ(x) + 2 p − Ω · L (where L ≡ x × p, Φ ≡ Φh + Φc) V0 Hamilton’s equations of motion: y x˙ = p − Ω × x p˙ = −∇Φ − Ω × p | {z } x R0 Note that canonical momentum p is the velocity in the inertial frame! Tidal radius (Jacobi radius, Hill sphere, Roche lobe, . . . ) Note that the energy or angular momentum in the inertial frame 1 2 E ≡ Φ + 2 p , L ≡ x × p are not conserved individually, but the Jacobi integral EJ = E − Ω · L is conserved. 1 2 It can be written as EJ = Φeff + 2 x˙ , where the effective potential includes the centrifugal term: 1 2 Φeff (x) ≡ Φ(x) − 2 Ω × x .
Saddle points of Φeff (Lagrange points L2, L3) are defined by ∂Φeff /∂x = 0 . Φ For a pointlike satellite R0 R Φ = −√ GMs , s 2 2 2 (x−R0) +y +z host satellite two solutions are at x ≈ R0 ± Rt: " #1/3 centrifugal GMs total (effective) 2 Rt ≈ 1 ∂Φh ∂ Φh L L − 2 3 2 R0 ∂x ∂x x=R0 Tidal radius (Jacobi radius, Hill sphere, Roche lobe, . . . )
1/3 " GMs # L4 2 Rt ≈ 1 ∂Φh ∂ Φh − 2 R0 ∂x ∂x x=R0 Example: host system is also a point mass Mh, 1/3 then Rt ≈ R0 Ms/[3 Mh] . More generally: the denominator in Rt is 2 3 ∝ Ω ∝ Mh( epicyclic overdensities circular orbit, weak tidal stripping Stellar system in a tidal field 15 60 10 40 5 20 0 0 20 5 40 10 60 15 60 40 20 0 20 40 60 15 10 5 0 5 10 15 circular orbit, strong tidal stripping Stellar system in a tidal field 15 60 10 40 5 20 0 0 20 5 40 10 60 15 60 40 20 0 20 40 60 15 10 5 0 5 10 15 circular orbit, strong tidal stripping leading to a complete disruption Stellar system in a tidal field eccentric orbit, bursty stripping in tidal shocks Evolution of tidal debris in the E − L space apocentre Evolution of tidal debris in the E − L space pericentre: tidal shock unbinds some stars Evolution of tidal debris in the E − L space next apocentre: formation of the two tails Evolution of tidal debris in the E − L space next pericentre: another iteration of stripping Evolution of tidal debris in the E − L space each stripping episode produces a “feather” and a “wedge” in each tail Evolution of tidal debris in the action – angle space Dynamical friction A moving massive object creates a trailing density wake, which slows it down. Standard expression in an infinite homogeneous medium [Chandrasekhar 1943]: √ 2 h v 2 i dvM 4π G M ρ ln Λ √vM √2 vM M = − 2 erf − exp − 2 dt vM 2 σ π σ 2 σ M, vM – mass and velocity of the object; ρ, σ – density and velocity dispersion of the field stars; ln Λ 'O(1) – Coulomb logarithm. [illustration: M.Whittle] Tidal stripping is accelerated by dynamical friction massive satellite, ignoring dynamical friction Tidal stripping is accelerated by dynamical friction massive satellite with dynamical friction Formation of shells in head-on collisions 150 20 15 100 10 50 5 0 0 radial velocity 5 50 10 100 15 150 20 150 100 50 0 50 100 150 0 50 100 150 200 distance Formation of shells in head-on collisions 150 20 15 100 10 50 5 0 0 radial velocity 5 50 10 100 15 150 20 150 100 50 0 50 100 150 0 50 100 150 200 distance Formation of shells in head-on collisions 150 20 15 100 10 50 5 0 0 radial velocity 5 50 10 100 15 150 20 150 100 50 0 50 100 150 0 50 100 150 200 distance Formation of shells in head-on collisions 150 20 15 100 10 50 5 0 0 radial velocity 5 50 10 100 15 150 20 150 100 50 0 50 100 150 0 50 100 150 200 distance Shells and streams in external galaxies: NGC 5907 [credit: J.Gabany] Shells and streams in external galaxies: NGC 474 [view in Aladin] [credit: P.-A.Duc, J.-C.Cuillandre] Shells and streams in external galaxies: M 31 (Andromeda) [credit: A.Ferguson, PAndAS survey] Streams in the Milky Way Globular cluster Pal 5 [Odenkirchen+ 2001] – SDSS commissioning data Streams in the Milky Way Globular cluster Pal 5 [Grillmair&Dionatos 2006] – SDSS DR4 10 zoom around cluster 1.0 0.8 5 Jacobi radius 11.20 0.6 0 0.4 Dec. [deg] 5 0.2 membership probability 10 0.0 250 245 240 235 230 225 220 215 RA [deg] [Odenkirchen+ 2001] – SDSS commissioning data [Price-Whelan+ 2019] – DECaLS+GaiaDR2 Streams in the Milky Way A cold stream with no known progenitor: GD-1 [Grillmair&Dionatos 2006] – SDSS Proper motion selection 10 ] 10 1 − r ] 5 g y e s d a [ 0 0 2 m [ φ 2 5 φ 10 µ 10 10 5 0 5 1 µφ1 [mas yr− ] Proper motion + photometry selection 14 10 12 Gyr Previously [Fe/H]= 1.35 Spur Progenitor? − ] undetected 16 g e 0 d [ 0 g 18 2 φ 20 10 Gaps Blob 22 100 80 60 40 20 0 20 0.0 0.5 1.0 1.5 φ [deg] (g i) 1 − 0 [Price-Whelan&Bonaca 2018] – PanSTARRS+GaiaDR2 Streams in the Milky Way [Belokurov+ 2006] – SDSS field of streams [Shipp+ 2018] – Dark Energy Survey [Ibata+ 2018] – GaiaDR2 GalStreams database [C.Mateu+] Sagittarius: the King of Streams colour selection corresponding to M giants in 2MASS [Majewski+ 2003] leading arm trailing arm Ks mag. 11 12 13 14 Sagittarius: the King of Streams colour selection in SDSS: stream bifurcation [Belokurov+ 2006; Koposov+ 2012] Sagittarius: the King of Streams All-sky panorama of the stream provided by Gaia DR2 [Vasiliev+ 2020] [Ibata+ 2020] [Antoja+ 2020; Ramos+ 2020] How to find stuff, part 0: look at your data How to find stuff, part 0: look at your data Sgr field control field How to find stuff, part I: simple filters [Gaia Collaboration: Helmi+ 2018] How to find stuff, part I: simple filters If the distance is not known: try different magnitude offsets for the CMD filter, or use a colour–colour filter optimized for selecting giant stars control field Sgr field [Majewski+ 2003] [source: Wikipedia] How to find stuff, part II: matched filters Improve the signal-to-noise ratio by boosting the parts of the CMD filter (or any other data dimension) where the contrast between the object and the foreground is stronger (e.g., Rockosi+ 2002 for Pal 5). [Bonaca+ 2012] How to find stuff, part II: matched filters Improve the signal-to-noise ratio by boosting the parts of the CMD filter (or any other data dimension)NGC where the 288 contrast between the object and the foreground is stronger (e.g., Rockosi+ 2002 for Pal 5). Note: high-quality and deep photometry is crucial here! (and elsewhere) Gaia DES globular cluster NGC 288 How to find stuff, part III: statistical decontamination Clean up the CMD by ”subtracting” the back- ground population at the level of individual objects, without binning them first. For each star in the field of interest, find a close analogue (in terms of CMD location) in the control field, and if found, remove this star with some probability. binned (Hess difference): [Jethwa+ 2017] unbinned: [Bica&Bonato 2011] How to find stuff, part IV: unsharp masking Example: finding shells by looking for apocentre turnaround points disrupted satellite in r vs vr space 150 20 15 100 10 50 5 0 0 radial velocity 5 50 10 100 15 150 20 150 100 50 0 50 100 150 0 50 100 150 200 distance How to find stuff, part IV: unsharp masking Example: finding shells by looking for apocentre turnaround points all stars including the foreground 150 20 15 100 10 50 5 0 0 radial velocity 5 50 10 100 15 150 20 150 100 50 0 50 100 150 0 50 100 150 200 distance How to find stuff, part IV: unsharp masking 60 Poisson noise 40 Example: finding shells by looking 20 0 20 excess 40 for apocentre turnaround points 60 all stars including the foreground 1000 150 20 800 600 15 100 counts 400 high-res historgram (bin size=1) 200 10 smoothed with σ =5 0 50 0 50 100 150 200 5 distance 0 0 radial velocity 5 50 10 100 15 150 20 150 100 50 0 50 100 150 0 50 100 150 200 distance How to find stuff, part V: search for orbital segments Great circle cell count (GC3) method [Johnston+ 1996] and its extensions to kinematic datasets (nGC3, mGC3) [Mateu+ 2011, 2017] [Ramos+ 2020] How to find stuff, part V: search for orbital segments Streamfinder: consider all possible orbits emanating from a given star and count the number of other stars aligned with the orbit segment [Malhan&Ibata 2018] (a) 2 j j p p 11 pi pi (b) 2 wi j wj p 1 pi [Malhan+ 2018] Finding streams with Gaia Finding streams with Gaia Finding streams with Gaia GD-1 stream [Grillmair & Dionatos 2006] How to find stuff, part VI: structures in the velocity space “Moving groups” in the Solar neighbourhood: believed to be associated with non-axisymmetric features in the Galactic disc (bar, spiral arms), not with accreted structures [Dehnen 2000] [Trick+ 2019] How to find stuff, part VI: structures in the velocity space velocity space action space distant stars nearby stars [Trick+ 2019] How to find stuff, part VII: structures in the integral space E :Lz , L⊥ :Lz , Jr :Jφ,... [Helmi+ 1999] [Koppelman+ 2019] [Myeong+ 2018] How to find stuff, part VII: structures in the integral space E :Lz , L⊥ :Lz , Jr :Jφ,... Sagittarius Arjuna+ GSE Helmi Sequoia+ St. Wukong I’itoi Aleph MWTD High-α Thamnos Disk In-Situ Halo =−Jφ [Helmi+ 1999] [Naidu+ 2020] [Koppelman+ 2019] [Myeong+ 2018] How to find stuff, part VII: structures in the integral space Jz polar (Jφ =0) E :Lz , L⊥polar:Lz , Jr :Jφ,... 5 10 20 50 100 Rcirc [Kpc] Sagittarius prograde 0 [e.g., Law & Majewski 2010] → y J t NGC 5053 φ i c i r t Terzan 7 180 ◦ inclination 0 ◦ Terzan 8 n Pal 5 c 0) ir e c ← →= u retrograde c r la (J Arp 2 M 53 r c r M 54 ( a J e l u r = c 0 ir ) c Whiting 1 ← 1 NGC 5824 radial Pal 12 NGC 5897 J NGC 6235 M 3 r M 30 Pyxis IC 4499 47 Tuc [Helmi+ 1999] NGC 6401 NGC 6752E 3 NGC 6397 prograde NGC 6356 Pal 11 NGC 288 M 13 Pal 1 NGC 7492 M 68 FSR 1716 NGC 5927 M 71 M 15 BH 176 NGC 5466 NGC 6287 Pal 7 Pal 10 NGC 6101 NGC 6496 retrograde NGC 4372 NGC 6284 NGC 3201 M 22 FSR 1758 NGC 5634 ω M 5 M 9 C e n Pal 13 ESO280 M 92 NGC 6426 NGC 2298 Rup 106 i NGC 362 n NGC 6584 ) -p 0 la = n z e M 75 (J ( e J NGCM 126156 n z IC 1257 NGC 5286 M 2 Djorg 1 a = NGC 4147 l 0 -p ) in NGC 7006 NGC 4833 NGC 5694 M 72NGC 6229 NGC 6934 NGC 1851 NGC 2808 M 79 Sequoia Pal 2 radially anisotropic population [Myeong et al. 2019] [Myeong et al. 2018; Helmi et al. 2018] radial (Jφ =0) [Koppelman+ 2019] [Vasiliev 2019] How to find stuff: summary I choose the right projection: streams are thin in two out of three dimensions I subtract the smooth background: decontamination, unsharp masking I if possible, use a curvilinear projection: methods based on orbit fitting or integrals of motion – the results do depend on the potential! I use as many dimensions of data as possible: contrast increases with the number of dimensions – colours, chemistry, . . . I don’t be afraid to throw away much of your data, if this increases contrast