What can we learn from the new phase space complexity

of old globular clusters?

Anna Lisa Varri University of Edinburgh

Marie Curie Fellow | Institute for Astronomy

Maria Tiongco, Enrico Vesperini (Indiana)Paolo Bianchini (McMaster), Giuseppe Bertin (Milano)

Kate Daniel (Bryn Mawr), Phil Breen, Douglas Heggie (Edinburgh)

Gaia Challenge: Eduardo Balbinot, Ian Claydon, Mark Gieles (Surrey), Elena Pancino (Arcetri) , Vincent Hénault-Brunet (Nijmegen),

Antonio Sollima, Alice Zocchi (Bologna)

Globular clusters? not simply spherical, non-rotating, isotropic, stellar systems with a single, coeval stellar population

“Lowered” Maxwellian DFs offers a successful zeroth-order dynamical interpretation of the fundamental observables, but ...

King 1966 AJ

… time is ripe for a paradigm shift!

Why?

We have outgrown (too) many dimensions of the traditional interpretative picture. Globular clusters offer a unique perspective many topical open problems in modern astrophysics we must study them as they are, not as we would wish them to be!

Why now?

We are about to enter a new “golden age”, as determined by the alignment of

I. Conceptual revolution -- several recent structural, kinematic, chemical discoveries II. Observational revolution -- access to full phase space of several Galactic globulars

III. Computational revolution -- finally ready to crack the gravitational million body problem

I. Conceptual revolution

(a) New phase space laboratories: emerging kinematical complexity(b) Challenging chemodynamical puzzles multiple stellar populations(c) Black holes cradles? Stellar-mass and (possibly) intermediate-mass scale (d) Gala Rotation(e) ctic beacons progenitor of several newly discovered streams

M5 | Fabricius et al. 2014 ApJL Watkins et al. 2015 ApJ (HSTPROMO)

(a) Anisotropy

I. Conceptual revolution

(a) New phase space laboratories emerging kinematical complexity(b) Challenging chemodynamical puzzles: multiple stellar populations(c) Black holes cradles? Stellar-mass and (possibly) intermediate-mass scale (d) Galactic beacons progenitor of several newly discovered streams

Carretta et al. 2009 A&ANGC 2808 | Piotto et al. 2007 ApJ

see Matthias Frank’s talk

I. Conceptual revolution

(a) New phase space laboratories emerging kinematical complexity(b) Challenging chemodynamical puzzles multiple stellar populations(c) Black holes cradles? Stellar-mass and (possibly) intermediate-mass scale (d) Galactic beacons progenitor of several newly discovered streams

NGC 6388 | Luetzgendorf et al 2015 A&A, Lanzoni et al. 2013 ApJM22 | Strader et al. 2012 Nature

see Anna Sippel’s talk

I. Conceptual revolution

(a) New phase space laboratories emerging kinematical complexity(b) Challenging chemodynamical puzzles multiple stellar populations(c) Black holes cradles? Stellar-mass and (possibly) intermediate-mass scale (d) Galactic beacons: streams progenitors and contributors to Galactic halo assembly history

Palomar 5 | for modelling see Kuepper et al. 2015 MNRAS Phoenix stream | Balbinot et al 2016 ApJ (DES)

Synergy between Gaia and HST proper motions,

supplemented by high-quality spectroscopic measurements

(e.g., Gaia-ESO)

Phase-space properties of many Galactic globular clusters soon unlocked

for the first time

II. Observational revolution

II. Observational revolution

NGC 2808 | Bellini, Vesperini et al 2015, see also Watkins et al (HSTPROMO) 2015a,b ApJ

ω Cen | PM van Leeuwen et al 2000 A&A (HIPPARCOS), Anderson & van der Marel 2010 ApJ (HST)

Synergy between Gaia and HST proper motions,

supplemented by high-quality spectroscopic measurements

(e.g., Gaia-ESO)

Phase-space properties of many Galactic globular clusters soon unlocked

for the first time

see Laura Watkins’ talk

N-body model of M4 (N=484710) | Heggie 2014 MNRAS, see alsoPal 14 (N= 70000) | Hasani Zonoozi et al 2010 MNRASPal 4 (N= 100000) | Hasani Zonoozi et al 2014 MNRAS

DRAGON series of N-body simulations | Wang et al. 2016 ApJ

III. Computational revolution see Tarav Panamarev’s talk

A. Anisotropy in the velocity space

B. Angular momentum

C. External tidal field

D. Multiple stellar populations

E. IMBHs (?)

Renewed efforts in theoretical understanding are needed, towards a more realistic dynamical paradigm

A. Anisotropy in the velocity space

B. Angular momentum

C. External tidal field

D. Multiple stellar populations

E. IMBHs (?)

Renewed efforts in theoretical understanding are needed, towards a more realistic dynamical paradigm

1. Do they contain fingerprints of cluster formation process?

2. How do they shape their present-day properties?

3. Which impact on the subsequent dynamical evolution?

A. Anisotropy in the velocity space

B. Angular momentum

C. External tidal field

D. Multiple stellar populations

E. IMBHs (?)

Renewed efforts in theoretical understanding are needed, towards a more realistic dynamical paradigm

1. Do they contain fingerprints of cluster formation process?

2. How do they shape their present-day properties?

3. Which impact on the subsequent dynamical evolution?

Van Albada 1982 MNRASLynden-Bell 1967 MNRAS

Violent relaxation for cold isolated stellar systems

Radial

Isotropy

#1

Stiavelli & Bertin 1985 MNRAS

∞

Families of spherical anisotropic models#2

Entropy extrema with E, M,constant

∞

Trenti & Bertin 2005a A&A

Families of spherical anisotropic models#2

∞

De Vita, Bertin, Zocchi 2016 A&A

Families of spherical anisotropic models#2

Kingf (ḓ)

Partially relaxed globulars well represented

NGC 2419 | Zocchi, Bertin, Varri 2012 A&A -- Systematic study of a sample of GGCs in different relaxation conditions

#2

log(t_rh) =10.63!

NGC 2419 | Zocchi, Bertin, Varri 2012 A&A -- Systematic study of a sample of GGCs in different relaxation conditions

Kingf (ḓ)

Partially relaxed globulars well represented

log(t_rh) =10.63!

Effects of “primordial” anisotropy: May be imprinted by the formation process, and preserved throughout the evolution (especially in the outer regions). It has significant effects of the dynamical evolution of collisional systems (tangential anisotropy accelerates core collapse, radial anisotropy slows it down).

Breen, Varri, Heggie 2017a submitted

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#3

Effects of “primordial” anisotropy: May be imprinted by the formation process, and preserved throughout the evolution (especially in the outer regions). It has significant effects of the dynamical evolution of collisional systems (tangential anisotropy accelerates core collapse, radial anisotropy slows it down).

Breen, Varri, Heggie 2017a submitted

Build up of “evolutionary” anisotropy: a natural outcome of long-term dynamical evolution, especially post core collapse.

In the presence of an external tidal field, it strongly responds to its strength.

Zocchi, Gieles Hénault-Brunet, Varri 2016 MNRAS Tiongco, Vesperini, Varri 2016a MNRAS6e

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see Maria Tiongco’s talk

#3

A. Anisotropy in the velocity space

B. Angular momentum

C. External tidal field

D. Multiple stellar populations

E. IMBHs (?)

Renewed efforts in theoretical understanding are needed, towards a more realistic dynamical paradigm

1. Do they contain fingerprints of cluster formation process?

2. How do they shape their present-day properties?

3. Which impact on the subsequent dynamical evolution?

Violent relaxation with non-vanishing total angular momentum

Explored as formation scenario for EllipticalsGott 1973, Hohl & Zang 1979, Akiyama & Sugimoto 1989, Aguilar & Merritt 1990

… what about star clusters?

Aguilar & Merritt 1990

Gott 1973

Aguilar & Merritt 1990

#1

Homogeneous and fractal spheres (D=3.0, 2.8, 2.4) Initial solid body rotation

Qran = 2Kran/|W|= 0.1, 0.25, 0.5, 0.75

Qrot = 2Krot/|W| = [0.0], 0.16, 0.33, 0.50

N=60000, equal-mass particlesStarlab, survey of 32 models

Reference modelsx

z

x

y

Varri, Tiongco, Vesperini et al., in preparation

Violent relaxation with non-vanishing total angular momentum #1

Rotation curves and anisotropy profiles

log(r/rh)

<vφ>

log(r/rh)

β

Varri, Tiongco, Vesperini et al., in preparation

Radial

Tangential

#1

Rotation curves and anisotropy profiles

log(r/rh)

β

Varri, Tiongco, Vesperini et al., in preparation

Radial

Tangential

Trenti, Bertin, Van Albada 2005 A&A

Tangential

Radial

Violent relaxation from cold homogeneous sphere, no angular momentum (corr. H1a)

#1

A glimpse of the

phase space

(vr , r ) (vφ , r ) (vθ , r )

Homogeneous, cold, non-rotating

Homogeneous, cold, rotating

Varri, Tiongco, Vesperini et al., in preparation #1

Family of axisymmetric, anisotropic models with differential rotation

Varri & Bertin 2012Self-consistent solution of the Poisson equationvia a spectral iteration method

Varri & Bertin A&A 2012

#2

Application to 47 Tucanae

RV Gebhardt+ 1995, Lane+ 2011 A&A SB Trager+ 1995 AJ, Noyola & Gebhardt 2006 AJ

Bellini et al. 2017 ApJ submitted

Bianchini, Varri, Bertin, Zocchi 2013 ApJKacharov, Bianchini et al. 2014 A&A

#2

Application to 47 Tucanae

RV Gebhardt+ 1995, Lane+ 2011 A&A SB Trager+ 1995 AJ, Noyola & Gebhardt 2006 AJ #2

Bellini et al. 2017 ApJ submitted

Bianchini, Varri, Bertin, Zocchi 2013 ApJKacharov, Bianchini et al. 2014 A&A

EP White & Shawl 1987 ApJ

Application to 47 Tucanae

#2

Bellini et al. 2017 ApJ submitted

Bianchini, Varri, Bertin, Zocchi 2013 ApJKacharov, Bianchini et al. 2014 A&A

EP White & Shawl 1987 ApJ

Application to 47 Tucanae

#2

Bellini et al. 2017 ApJ submitted

Bianchini, Varri, Bertin, Zocchi 2013 ApJKacharov, Bianchini et al. 2014 A&A

EP White & Shawl 1987 ApJ

Application to 47 Tucanae

#2

Bellini et al. 2017 ApJ submitted

Bianchini, Varri, Bertin, Zocchi 2013 ApJKacharov, Bianchini et al. 2014 A&A

EP White & Shawl 1987 ApJ

Application to 47 Tucanae

Bellini et al. 2017 ApJ submitted

Bianchini, Varri, Bertin, Zocchi 2013 ApJKacharov, Bianchini et al. 2014 A&A

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Stability: Highly unexplored chapter of fundamental stellar dynamics. “Low-T/W” dynamical instability found for strongly

differentially rotating models. Striking analogy with rotating fluid polytropes!

Varri, Vesperini, McMillan, Bertin, submitted Breen, Varri, Heggie - III, in preparation

#3

Stability: Highly unexplored chapter of fundamental stellar dynamics. “Low-T/W” dynamical instability found for strongly

differentially rotating models. Striking analogy with rotating fluid polytropes!

Evolution: Deep understanding of the role of angular momentum in “gravothermodynamics” is still missing. Essential to decouple the structure. Rotation determines an acceleration of the dynamical evolution (Spurzem et al.), but signatures of rotation and anisotropy are long-lived. Working towards a complete theory.

Varri, Vesperini et al, in preparationBreen, Varri, Heggie - II, in preparation

Varri, Vesperini, McMillan, Bertin, submitted Breen, Varri, Heggie - III, in preparation

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#3

A. Anisotropy in the velocity space

B. Angular momentum

C. External tidal field

D. Multiple stellar populations

E. IMBHs (?)

Renewed efforts in theoretical understanding are needed, towards a more realistic dynamical paradigm

1. Do they contain fingerprints of cluster formation process?

2. How do they shape their present-day properties?

3. Which impact on the subsequent dynamical evolution?

Violent relaxation in a tidal field

Homogeneous spheres

Q = 2K/|W| = 0.02, 0.2

Rt /RJ = 0.5

External potential Isothermal halo, local Galactic disk

N=60000, equal-mass particlesStarlab

For a study of the tidal torque on triaxial end-products of violent relaxation, see Boily et al. 1999, 2001, Theis et al. 2002

Coriolis force bends the orbits in opposite directions during the infall and re-expansion phases.

Reference models

Vesperini, Varri, McMillan, Zepf 2014

#1

Differential rotation and distinct anisotropy profile

<vφ>/

σ

#1

Vesperini, Varri, McMillan, Zepf 2014

Tangential

Radial

isolated(classic van Albada 1982)

Heggie & Ramamani 1995 MNRASBertin & Varri 2008 ApJ Varri & Bertin 2009 ApJ

#2

Self-consistent triaxial tidal models

Kuepper, Kroupa, Baumgardt, Heggie 2010 MNRAS

Heggie & Ramamani 1995 MNRASBertin & Varri 2008 ApJ Varri & Bertin 2009 ApJ

“Potential escapers” = energetically unbound, yet spatially confined stars

#2

Heggie & Ramamani 1995 MNRASBertin & Varri 2008 ApJ Varri & Bertin 2009 ApJ

Kuepper, Kroupa, Baumgardt, Heggie 2010 MNRAS

“Potential escapers” = energetically unbound, yet spatially confined stars

#2

Analytic model with “potential escapers”

Inspired by Hénon’s family “ f ” (periodic orbits, among solutions of the circular Hill’s problem)High-inclination orbits behave as Lidov-Kozai theory (in quadrupole approximation).

Daniel, Heggie, Varri 2017 MNRAS in press

#2

i0

r0

Analytic model with “potential escapers”

Kepler energy averaged over Kepler motion

z-component of angular momentum, averaged over Kepler and orbital motions

“Generalized Lindblad diagram”

Three integral of the motions used to identify “potential escapers” in phase space (via discrimination criterion)

Daniel, Heggie, Varri 2017 MNRAS in press

#2

Γ = 3

Daniel, Heggie, Varri 2017 MNRAS in press

Analytic model with “potential escapers”#2

∩

Theory of escape so far, in the case of a GC on an elliptic orbit, the corresponding Hill’s problem has never been studied. Significant ramifications on the study of star cluster lifetime and on the density structure of tidal tails.

Cai, Gieles, Heggie, Varri, 2016 MNRASBar-Or, Heggie, Varri, in preparation

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#3

Theory of escape so far, in the case of a GC on an elliptic orbit, the corresponding Hill’s problem has never been studied. Significant ramifications on the study of star cluster lifetime and on the density structure of tidal tails.

Nexus between internal kinematics and external perturbations we usually rely on the assumption

of synchronization between internal and orbital motions, but how well-posed is it?

Cai, Gieles, Heggie, Varri, 2016 MNRASBar-Or, Heggie, Varri, in preparation

Tiongco, Vesperini, Varri 2016b MNRASTiongco, Vesperini, Varri 2017 MNRAS submitted

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see Maria Tiongco’s talk

#3

A. Anisotropy in the velocity space

B. Angular momentum

C. External tidal field

D. Multiple stellar populations

E. IMBHs (?)

Renewed efforts in theoretical understanding are needed, towards a more realistic dynamical paradigm

Phase space properties of multiple stellar populations

47 Tuc | Richer et al. 2013 ApJLNGC 2808 | Bellini, Vesperini et al. 2015 ApJL

M13 | Cordero, Hénault-Brunet et al. 2017 MNRAS

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I. Multicomponent self-consistent axisymmetric truncated models with differential rotation and anisotropy Physically-motivated, mathematically well-posed coupling condition is achievable (not the same physics driving the coupling in traditional multi-mass self-consistent models!)

2. Phase space tagging, as counterpart of chemical tagging

Leverage the power of the fingerprints left in phase space for

- Identification of the progenitors of faint orphan tidal streams

- Contribution of globulars to the Galactic halo build-up

Constraints of different formation scenarios? Initial kinematical properties may leave distinct imprints in the velocity space (especially rotation).

Hénault-Brunet et al. 2015 MNRASMastrobuono-Battisti & Perets 2013, 2016 MNRAS

6elected evolutionary aspects

New purely dynamical questions Transport of angular momentum between

the two components? Coupling of two angular momentum vectors? Resulting

anisotropy profiles? Ellipticity?

Constraints of different formation scenarios? Initial kinematical properties may leave distinct imprints in the velocity space (especially rotation).

Hénault-Brunet et al. 2015 MNRASMastrobuono-Battisti & Perets 2013, 2016 MNRAS

Tiongco, Vesperini, Varri, in preparation

6elected evolutionary aspects

see Maria Tiongco’s talk

A. Anisotropy in the velocity space

B. Angular momentum

C. External tidal field

D. Multiple stellar populations

E. IMBHs (?)

Renewed efforts in theoretical understanding are needed, towards a more realistic dynamical paradigm

Intermediate-mass black holes?

NGC 6388 | Luetzgendorf et al 2015 A&A , Lanzoni et al. 2013 ApJ ω Cen | van der Marel & Anderson 2010 ApJ

Dynamical signatures on surface brightness and velocity dispersion highly degenerate. Alternative diagnostics needed.

“Loaded” polytropes

Saslow 1975 ApJ

Miocchi 2007 MNRAS

“Stitched” King models

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Self-consistent DF (rotating) models with central black hole

II. Soon available full phase space information screams for a proper treatment of physical ingredients traditionally considered as “second-order complications”. DF-based equilibria are a very natural tool.

Synergy between ground-based spectroscopic surveys and HST + Gaia PMs will be key. We are getting ready for it.

IV. Interesting (new) science often lives at the intersections -- let’s open these Pandora’s boxes.rotation 䏖 anisotropy, anisotropy 䏖 tides, rotation 䏖 tides.

V. Investigation of the role of “classical” physical ingredients is a key step to understand any dynamical signature of more complex phenomena in star clusters (e.g., IMBHs and MSPs ).Phase space, phase space, phase space (sorry).

I. A new golden age for the study of the internal dynamics of globulars is about to start.

They offer a fresh perspective on many topical open problems in modern astrophysics.

Take-home messages: towards a new dynamical paradigm

III. Fingerprints of their formation �+! signatures of their evolution are hidden in such ingredients.Some degeneracies, but also some distinctive features!