The M68 stellar stream in angle-action coordinates

The M68 stellar stream in angle-action coordinates Carles Garcia Palau1 Jiaxin Han - Wenting Wang Shanghai Jiao Tong University (SJTU) Talk October 12, 2025 1: [email protected] Introduction Introduction: Stellar streams •Stellar streams are formed by stars stripped from a progenitor cluster by the tidal forces caused by its host galaxy. •A stellar stream can be used to infer the properties of its progenitor and host galaxy: -From the surface density: ·Accretion time of the progenitor cluster (stream age) ·Mass loss of the cluster -The stream stars are stripped from the cluster and approximately follow its obit: ·The potential of the host galaxy •We develop two methods in angle-action coordinates to determine these properties, and apply them to the globular cluster M68 (NGC 4590) (arXiv: 2412.15091, 2508.21408). Palomar 5 stellar stream (Bonaca et al. 2019). Carles G. Palau : [email protected] arXiv: 2412.15091, 2508.21408 2 / 23 Observed M68 stellar stream M68 stellar stream •We focus on the M68 stellar stream: -Known progenitor: M68 globular cluster -Projected onto to the halo -Located close to the Sun at ∼5 kpc -291 stars identified from the Gaia-DR3 catalogue -Long, thin, and dynamically cold •The observed stars are located in the leading arm of the stream. • The observed section is disconnected from the cluster. •Most of the stream is obscured by foreground star contamination. M68 stellar stream stars (black dots). The blue shaded areas are covered by foreground stars. Carles G. Palau : [email protected] arXiv: 2412.15091, 2508.21408 3 / 23 Simulated M68 stellar stream N-body simulation •We simulate the M68 stream to obtain a preliminary understanding: -Phase-space model: Truncated isothermal -Synthetic population: Isocrhone PARSEC/COLIBRI -Axisymmetric static MW potential: Buldge, Miyamoto-Nagai disc, and NFW halo -Integration: Collisional N-body code PeTar -Duration: T= 1.5 Gyr •The cluster undergoes three pericentre passages. M68 simulated stream stars (red dots). Cluster 1.5 Gyr past orbit (solid line) and 250 Myr future orbit (dashed line) Carles G. Palau : [email protected] arXiv: 2412.15091, 2508.21408 4 / 23 Simulated M68 stellar stream Angle-Action coordinates •Dynamics is simplified in angle-action coordinates (Binney & Tremaine 2008). •It is defined as a system of coordinates in phase-space (q,p)≡(θ, J) such that: -It is canonical: ˙ J=−∂H ∂θ ˙ θ=−∂H ∂J, where H(J) -The angles are taken as periodic θ∈[0,2π) with frequency ˙ θ≡Ω -Particles move in straight line with constant J:θ(t)=Ωt+θ(0) •We apply the following transformations: -Translation to put the cluster at the origin: (θ, J)→(∆θ, ∆J) -Rotation to align with the principal axis of the H: (∆θ, ∆J)→(∆¯ θ, ∆¯ J) •Axis along the stream: {∆¯ θ1,∆¯ J1,∆¯ Ω1} •In angle space, the stream appears as an elongated symmetrical structure: Leading (black) and trailing (blue) arms of the stream, and M68 cluster (red). Carles G. Palau : [email protected] arXiv: 2412.15091, 2508.21408 5 / 23 Simulated M68 stellar stream •The actions are clustered around the globular cluster centre: •The frequency ∆ ¯ Ω1≫∆¯ Ω2and ∆¯ Ω3: •Stripping time of the stream stars: ts≈ − ∥∆θ∥ ∥∆Ω∥ -Start simulation: t=−T -Current time: t= 0 •Streams have been modelled in angle-action space assuming constant mass loss (Sanders 2014; Bovy 2014). Carles G. Palau : [email protected] arXiv: 2412.15091, 2508.21408 6 / 23 Simulated M68 stellar stream Mass loss along an eccentric orbit •Tidal forces are maximal at pericentres, where the cluster experiences a tidal shock. •The stars are stripped in bursts and move along the stream at a constant frequency. •Each pericentre passage appears as a peak in angle-frequency space. Left: Mass Mgc and mass loss Mloss of the M68 globular cluster along the orbit. Right: Angle and frequency along the stream. Carles G. Palau : [email protected] arXiv: 2412.15091, 2508.21408 7 / 23 Model M68 stellar stream Angle-frequency model of the stellar stream •We have developed a method of modelling streams in angle-frequency space: -Faster than a N-body simulation -Accurately reproduces the surface density of the stream •Methodology for generating stellar stream models: 1Determination of the distribution of stripped stars along the cluster orbit 2Determination of the total number of stripped stars 3Generation of a random sample of stripping times ts 4Determination of the frequency ∆ ¯ Ωand the initial stripping angle ∆¯αfor each star 5Integration of each star forward in time Top: Surface density. Bottom: Internal components. • We compare this model with observations in order to estimate the accretion time and mass loss of the cluster. Carles G. Palau : [email protected] arXiv: 2412.15091, 2508.21408 8 / 23 Model M68 stellar stream Number of stripped stars along the orbit •Number of stripped stars Nsestimated from the stripping time ts. •Radial angle of the globular cluster θGC r: For an integer n: -Pericentres: 2πnrad -Apocentres: (2n+ 1)πrad •Delay tD≃6 Myr between the peaks and the pericentres. Corrected angle: -θM r≡θGC r+θD r •We restrict to the two complete periods: -θM r∈[−4π, 0] rad •Asymmetric peaks modelled using a double exponential model: -f(θM r) = Aexp−θM r τ1+ expθM r−2π τ2 + CTop: Number of stripped stars Ns. Bottom: Double exponential model (red line). Carles G. Palau : [email protected] arXiv: 2412.15091, 2508.21408 9 / 23 Accretion time and mass loss Accretion time and mass loss of the cluster •Accretion time Tdetermined using a maximum posterior technique (Bayes’ theorem): -Data: 199 observed GDR3 stars in the main component of the stream -Prior: Uniform distribution T∈[0 , 12] Gyr •Best-fitting configuration: ˆ T= 3039.7 Myr •Uncertaintiy estimate: T= 3.04+5.63 −0.29 Gyr •Mass loss: 0.496 ±0.030 M⊙Myr−1arm−1 Best-fitting surface density (red) and observational data (grey). Posterior distribution. Carles G. Palau : [email protected] arXiv: 2412.15091, 2508.21408 16 / 23 Constraining the Galactic potential Constraining the Galactic potential •Constrain the Milky Way potential using the internal structure of the stream: 1Determine the formation times of the internal components of the stream (peaks). 2Determine the potential where the cluster is at the pericentres at the estimated times. •Constraints along an orbit with as many radial periods as observed peaks. -For M68: Tr∼457 Myr -Observed M68 stream section ∼33 Myr •Mass loss peaks coincide with the tidal shocks at the pericentres: Carles G. Palau : [email protected] arXiv: 2412.15091, 2508.21408 17 / 23 Constraining the Galactic potential •Application to the M68 stellar stream: 1Determine the peaks using the stripping time tsof the stream stars: -Problem: Distance and GDR3/5 proper motions of the M68 stream stars are not sufficiently precise. 2Determine main peak using its mean angle and frequency: -Problem: The main peak of the M68 stellar stream is obscured by foreground contamination. Carles G. Palau : [email protected] arXiv: 2412.15091, 2508.21408 18 / 23 Constraining the Galactic potential •Alternative method to constrain the potential: -The stream stars return to the cluster for the correct potential (Johnston et al. 1999). -The stripping angle ∆¯αcan be determined integrating backwards a time δt≡ ∥∆θ∥/∥∆Ω∥ -The stripping angle is more robust than tsto observational errors. -Space reduced to a plane: ∆ ¯ Ω1≫∆¯ Ω2and ∆¯ Ω3→∆¯α1∼0 •Inverse time integration method (invi): 1For a given potential, integrate backwards in time to determine the ∆ ¯α of the stream stars. 2Optimise the potential maximising the clustering of ∆¯αaround the cluster centre. Carles G. Palau : [email protected] arXiv: 2412.15091, 2508.21408 19 / 23 The invi method •We test the invi method with mock observational samples: -GDR3 selection function and observational uncertainties. -Heliocentric distance rhand radial velocity vrestimated from the cluster orbit. •Observational errors increase the entropy of the stripping points ∆¯α(primarily proper motions). •The stars do not return to the cluster when the estimated frequency along the stream ∆ ¯ Ω1<0 (In the observable section ∆ ¯ Ω1>0). Orange area: Distribution of ∆¯αfor the correct potential. •Reduce the observational errors: -Optimise with only the brightest stars →Fewer stars →Increase statistical error. •We use a robust estimate (median) to determine the clustering in ∆¯α. Carles G. Palau : [email protected] arXiv: 2412.15091, 2508.21408 20 / 23 The invi method •Parameter optimisation: -Disc: mass Mdand scale length ad -Dark halo: flattening qhand scale length ah •Statistical error: -Determined optimising 350 mock observed star samples. -It increases when we restrict the mock observed samples to the brightest stars. •Observational error: -Determined optimising samples generated from the error distributions of a mock observed star sample. -It decreases when we restrict the mock observed sample to the brightest stars. •Future improvements: -Radial velocities from spectroscopy (e.g. DESI) →Simpler methodology. -Upcoming GDR4 →More precise proper motions. Carles G. Palau : [email protected] arXiv: 2412.15091, 2508.21408 21 / 23 Conclusion Conclusion Model stellar stream •Model of the M68 stellar stream in angle-action coordinates: -Accurately models the effects of variable tidal forces: ·Mass loss globular cluster ·Distribution of frequencies of the stream stars ·Distribution of stripping angles -Based on a simple double exponential model. -Reproduces the results of the N-body simulation. -Generates arbitrary long streams and random samples of stars. •Future work: -Express the free parameters in terms of the properties and orbit of the globular cluster. -Explain semi-analytically the double exponential model. Carles G. Palau : [email protected] arXiv: 2412.15091, 2508.21408 22 / 23 Conclusion Observed stellar stream •We identify 291 stars of the M68 stream from the GDR3 catalogue. -The stream is wider than the expected from the size of the cluster and the MW potential. -Accretion time: T= 3.04+5.63 −0.29 Gyr -Mass loss: 0.496 ±0.030 M⊙Myr−1arm−1 •Future work: -Improve the star selection using spectroscopic observations (DESI). -Estimate age and mass loss of other globular cluster (e.g. NGC 3201). Constraints on the MW potential •Method for constraining the potential of the MW in angle-action coordinates: -Integrate backwards in time to return the stars to the cluster. -We optimize four free parameters of the potential. -We recover the correct potential with ∼8 per cent accuracy using mock observations. •Future work: -Apply the method to real observed stream stars. Carles G. Palau : [email protected] arXiv: 2412.15091, 2508.21408 23 / 23