The M68 stellar stream in angle-action coordinates

The M68 s ella s eam in angle-ac ion coo dina es
Ca les Ga cia Palau1
Jiaxin Han - Wen ing Wang
Shanghai Jiao Tong Uni e si y (SJTU)
Talk
Oc obe 12, 2025
1: [email p o ec ed]
In oduc ion
In oduc ion: S ella s eams
•S ella s eams a e o med by s a s s ipped om a p ogeni o clus e by he idal o ces
caused by i s hos galaxy.
•A s ella s eam can be used o in e he p ope ies o i s p ogeni o and hos galaxy:
-F om he su ace densi y:
·Acc e ion ime o he p ogeni o clus e
(s eam age)
·Mass loss o he clus e
-The s eam s a s a e s ipped om he
clus e and app oxima ely ollow i s obi :
·The po en ial o he hos galaxy
•We de elop wo me hods in angle-ac ion
coo dina es o de e mine hese p ope ies,
and apply hem o he globula clus e
M68 (NGC 4590) (a Xi : 2412.15091,
2508.21408).
Paloma 5 s ella s eam (Bonaca e al. 2019).
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Obse ed M68 s ella s eam
M68 s ella s eam
•We ocus on he M68 s ella s eam:
-Known p ogeni o : M68 globula clus e
-P ojec ed on o o he halo
-Loca ed close o he Sun a ∼5 kpc
-291 s a s iden i ied om he Gaia-DR3 ca alogue
-Long, hin, and dynamically cold
•The obse ed s a s a e loca ed in he leading
a m o he s eam.
•
The obse ed sec ion is disconnec ed om he
clus e .
•Mos o he s eam is obscu ed by o eg ound
s a con amina ion. M68 s ella s eam s a s (black do s). The blue
shaded a eas a e co e ed by o eg ound s a s.
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Simula ed M68 s ella s eam
N-body simula ion
•We simula e he M68 s eam o ob ain a p elimina y unde s anding:
-Phase-space model: T unca ed iso he mal
-Syn he ic popula ion: Isoc hone PARSEC/COLIBRI
-Axisymme ic s a ic MW po en ial: Buldge, Miyamo o-Nagai disc, and NFW halo
-In eg a ion: Collisional N-body code PeTa
-Du a ion: T= 1.5 Gy
•The clus e unde goes h ee pe icen e passages.
M68 simula ed s eam s a s ( ed do s). Clus e 1.5 Gy pas o bi (solid line) and 250 My u u e o bi (dashed line)
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Simula ed M68 s ella s eam
Angle-Ac ion coo dina es
•Dynamics is simpli ied in angle-ac ion coo dina es (Binney & T emaine 2008).
•I is de ined as a sys em o coo dina es in phase-space (q,p)≡(θ, J) such ha :
-I is canonical: ˙
J=−∂H
∂θ
˙
θ=−∂H
∂J, whe e H(J)
-The angles a e aken as pe iodic θ∈[0,2π) wi h equency ˙
θ≡Ω
-Pa icles mo e in s aigh line wi h cons an J:θ( )=Ω +θ(0)
•We apply he ollowing ans o ma ions:
-T ansla ion o pu he clus e a he o igin: (θ, J)→(∆θ, ∆J)
-Ro a ion o align wi h he p incipal axis o he H: (∆θ, ∆J)→(∆¯
θ, ∆¯
J)
•Axis along he s eam: {∆¯
θ1,∆¯
J1,∆¯
Ω1}
•In angle space, he s eam appea s as an elonga ed symme ical s uc u e:
Leading (black) and ailing (blue) a ms o he s eam, and M68 clus e ( ed).
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Simula ed M68 s ella s eam
•The ac ions a e clus e ed a ound he globula clus e cen e:
•The equency ∆ ¯
Ω1≫∆¯
Ω2and ∆¯
Ω3:
•S ipping ime o he s eam s a s: s≈ − ∥∆θ∥
∥∆Ω∥
-S a simula ion: =−T
-Cu en ime: = 0
•S eams ha e been modelled in
angle-ac ion space assuming
cons an mass loss
(Sande s 2014; Bo y 2014).
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Simula ed M68 s ella s eam
Mass loss along an eccen ic o bi
•Tidal o ces a e maximal a pe icen es, whe e he clus e expe iences a idal shock.
•The s a s a e s ipped in bu s s and mo e along he s eam a a cons an equency.
•Each pe icen e passage appea s as a peak in angle- equency space.
Le : Mass Mgc and mass loss Mloss o he M68 globula clus e along he o bi .
Righ : Angle and equency along he s eam.
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Model M68 s ella s eam
Angle- equency model o he s ella s eam
•We ha e de eloped a me hod o modelling
s eams in angle- equency space:
-Fas e han a N-body simula ion
-Accu a ely ep oduces he su ace densi y o he
s eam
•Me hodology o gene a ing s ella s eam
models:
1De e mina ion o he dis ibu ion o s ipped
s a s along he clus e o bi
2De e mina ion o he o al numbe o s ipped
s a s
3Gene a ion o a andom sample o s ipping
imes s
4De e mina ion o he equency ∆ ¯
Ωand he
ini ial s ipping angle ∆¯α o each s a
5In eg a ion o each s a o wa d in ime
Top: Su ace densi y.
Bo om: In e nal componen s.
•
We compa e his model wi h obse a ions in o de o es ima e he acc e ion ime and mass
loss o he clus e .
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Model M68 s ella s eam
Numbe o s ipped s a s along he o bi
•Numbe o s ipped s a s Nses ima ed om
he s ipping ime s.
•Radial angle o he globula clus e θGC
:
Fo an in ege n:
-Pe icen es: 2πn ad
-Apocen es: (2n+ 1)π ad
•Delay D≃6 My be ween he peaks and he
pe icen es. Co ec ed angle:
-θM
≡θGC
+θD
•We es ic o he wo comple e pe iods:
-θM
∈[−4π, 0] ad
•Asymme ic peaks modelled using a double
exponen ial model:
- (θM
)
=
Aexp−θM
τ1+ expθM
−2π
τ2
+
CTop: Numbe o s ipped s a s Ns.
Bo om: Double exponen ial model ( ed line).
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Acc e ion ime and mass loss
Acc e ion ime and mass loss o he clus e
•Acc e ion ime Tde e mined using a maximum pos e io echnique (Bayes’ heo em):
-Da a: 199 obse ed GDR3 s a s in he main componen o he s eam
-P io : Uni o m dis ibu ion T∈[0 , 12] Gy
•Bes - i ing con igu a ion: ˆ
T= 3039.7 My
•Unce ain iy es ima e: T= 3.04+5.63
−0.29 Gy
•Mass loss: 0.496 ±0.030 M⊙My −1a m−1
Bes - i ing su ace densi y ( ed) and obse a ional da a (g ey). Pos e io dis ibu ion.
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Cons aining he Galac ic po en ial
Cons aining he Galac ic po en ial
•Cons ain he Milky Way po en ial using he in e nal s uc u e o he s eam:
1De e mine he o ma ion imes o he in e nal componen s o he s eam (peaks).
2De e mine he po en ial whe e he clus e is a he pe icen es a he es ima ed imes.
•Cons ain s along an o bi wi h as many adial pe iods as obse ed peaks.
-Fo M68: T ∼457 My
-Obse ed M68 s eam sec ion ∼33 My
•Mass loss peaks coincide wi h he idal shocks a he pe icen es:
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Cons aining he Galac ic po en ial
•Applica ion o he M68 s ella s eam:
1De e mine he peaks using he s ipping
ime so he s eam s a s:
-P oblem: Dis ance and GDR3/5 p ope mo ions
o he M68 s eam s a s a e no su icien ly
p ecise.
2De e mine main peak using i s
mean angle and equency:
-P oblem: The main peak o he M68
s ella s eam is obscu ed by
o eg ound con amina ion.
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Cons aining he Galac ic po en ial
•Al e na i e me hod o cons ain he po en ial:
-The s eam s a s e u n o he clus e o he co ec po en ial (Johns on e al. 1999).
-The s ipping angle ∆¯αcan be de e mined in eg a ing backwa ds a ime δ ≡ ∥∆θ∥/∥∆Ω∥
-The s ipping angle is mo e obus han s o obse a ional e o s.
-Space educed o a plane: ∆ ¯
Ω1≫∆¯
Ω2and ∆¯
Ω3→∆¯α1∼0
•In e se ime in eg a ion me hod (in i):
1Fo a gi en po en ial, in eg a e backwa ds
in ime o de e mine he ∆
¯α
o he s eam
s a s.
2Op imise he po en ial maximising he
clus e ing o ∆¯αa ound he clus e cen e.
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The in i me hod
•We es he in i me hod wi h mock obse a ional samples:
-GDR3 selec ion unc ion and obse a ional unce ain ies.
-Heliocen ic dis ance hand adial eloci y es ima ed om he clus e o bi .
•Obse a ional e o s inc ease he en opy o he s ipping poin s ∆¯α(p ima ily p ope mo ions).
•The s a s do no e u n o he clus e when he es ima ed equency along he s eam ∆ ¯
Ω1<0
(In he obse able sec ion ∆ ¯
Ω1>0).
O ange a ea: Dis ibu ion o ∆¯α o he co ec po en ial.
•Reduce he obse a ional e o s:
-Op imise wi h only he b igh es s a s →Fewe s a s →Inc ease s a is ical e o .
•We use a obus es ima e (median) o de e mine he clus e ing in ∆¯α.
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The in i me hod
•Pa ame e op imisa ion:
-Disc: mass Mdand scale leng h ad
-Da k halo: la ening qhand scale leng h ah
•S a is ical e o :
-De e mined op imising 350 mock obse ed s a
samples.
-I inc eases when we es ic he mock obse ed
samples o he b igh es s a s.
•Obse a ional e o :
-De e mined op imising samples gene a ed om he
e o dis ibu ions o a mock obse ed s a sample.
-I dec eases when we es ic he mock obse ed
sample o he b igh es s a s.
•Fu u e imp o emen s:
-Radial eloci ies om spec oscopy (e.g. DESI) →Simple me hodology.
-Upcoming GDR4 →Mo e p ecise p ope mo ions.
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Conclusion
Conclusion
Model s ella s eam
•Model o he M68 s ella s eam in angle-ac ion coo dina es:
-Accu a ely models he e ec s o a iable idal o ces:
·Mass loss globula clus e
·Dis ibu ion o equencies o he s eam s a s
·Dis ibu ion o s ipping angles
-Based on a simple double exponen ial model.
-Rep oduces he esul s o he N-body simula ion.
-Gene a es a bi a y long s eams and andom samples o s a s.
•Fu u e wo k:
-Exp ess he ee pa ame e s in e ms o he p ope ies and o bi o he globula clus e .
-Explain semi-analy ically he double exponen ial model.
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Conclusion
Obse ed s ella s eam
•We iden i y 291 s a s o he M68 s eam om he GDR3 ca alogue.
-The s eam is wide han he expec ed om he size o he clus e and he MW po en ial.
-Acc e ion ime: T= 3.04+5.63
−0.29 Gy
-Mass loss: 0.496 ±0.030 M⊙My −1a m−1
•Fu u e wo k:
-Imp o e he s a selec ion using spec oscopic obse a ions (DESI).
-Es ima e age and mass loss o o he globula clus e (e.g. NGC 3201).
Cons ain s on he MW po en ial
•Me hod o cons aining he po en ial o he MW in angle-ac ion coo dina es:
-In eg a e backwa ds in ime o e u n he s a s o he clus e .
-We op imize ou ee pa ame e s o he po en ial.
-We eco e he co ec po en ial wi h ∼8 pe cen accu acy using mock obse a ions.
•Fu u e wo k:
-Apply he me hod o eal obse ed s eam s a s.
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