Time-varying external potentials in NBODY6 Or: The evolution of - - PowerPoint PPT Presentation

Time-varying external potentials in NBODY6

Mark Gieles Florent Renaud, Maxime Delorme

Or: “The evolution of KZ(14)”

Evolution without tides

Baumgardt, Hut & Heggie 2002

KZ(14)=0

Odenkirchen+ 2002

Horizon simulation (Teyssier et al.) Agertz & Kravtsov

§8.5-8.6 x y

Galactic centre

r

RI

Pro: numerical accuracy Con: work out (linearised) terms for each !G Solve EoM in rotating reference frame

e.g. Oh, Lin & Aarseth 1992

Coriolis centrifugal Euler cluster

¨ r = rφc + ¨ RI ¨ RI0 2Ω ⇥ ˙ r Ω ⇥ (Ω ⇥ r) ˙ Ω ⇥ r

tidal

Existing methods: NBODY5

Existing methods: NBODY6

§8.5-8.6 KZ(14)=1: Galactic disc (Oort constants) KZ(14)=2: Point-mass galaxy Coriolis tidal+centrifugal Euler cluster

¨ r = rφc 2Ω ⇥ ˙ r + Ω2(3xex zez)

Solve EoM in rotating reference frame

e.g. Giersz & Heggie 1997

Pro: numerical accuracy, conserved Jacobi energy EJ Con: circular orbits, derive (linearised) terms & for each !G

j ≡... r

x y x y

Galactic centre

Pro: all orbits, (relatively) easy to sum components Con: work out tidal terms & j for each !G, time independent !G

Existing methods: NBODY6

§8.5-8.6

Solve EoM in non-rotating (accelerating) frame

e.g. Baumgardt & Makino 2003; Hurley+; Küpper+

KZ(14)=3: 4 component Galaxy model:

• 1. Miyamoto - Nagai disc
• 2. (singular) isothermal halo
• 3. Dehnen/Tremaine bulge
• 4. Central point-mass (i.e. black hole)

¨ r = rφc + ¨ RI ¨ RI0

tidal cluster

Note on energy conservation:

Existing methods: NBODY6

KZ(14)=3 §8.5-8.6

Renaud & Gieles 2015a; Heggie priv. comm.

Existing time-varying potential NBODY6

KZ(14)=4

Background time dependent Plummer (1911) potential “gas expulsion”

e.g. Kroupa++

¨ r = rφc + T tid · r

KZ(14)=9 “Mode A”: Renaud, Gieles & Boily 2011

T tid = − ∂2φG ∂xi∂xj

tidal cluster Tidal tensor:

Time-varying potentials: NBODY6tt

Pro: !G can be anything Con: linearised tides, not good for streams

https://github.com/florentrenaud/nbody6tt

KZ(14)=9 “Mode A”: Renaud, Gieles & Boily 2011

Time-varying potentials: NBODY6tt

• ttinit.f: reads tdal tensor file tt.dat (time + 9 TT components)
• ttcal.f: quadratic interpolation of TT in time, get TT derivative
• Some changes to xtrnlf.f:

https://github.com/florentrenaud/nbody6tt see also: http://personal.ph.surrey.ac.uk/~fr0005/nbody6tt.php

How it works:

KZ(14)=9 vs KZ(14)=3

Test Mode A NBODY6tt

A TALE OF TWO CLUSTERS

Renaud & Gieles (2013)

KZ(14)=9 “Mode B”: Renaud & Gieles 2015a

Time-varying potentials: NBODY6tt

Pro: !G can be anything, external forces not linearised: streams Con: analytical expression for !G(r,t) !G can have any dependence on space and time!

tidal cluster

¨ r = rφc + aG(r, t) aG0(r, t)

NBODY6tt: KZ(14)=9 “Mode B”

Stepsize hi

(Press+ 2007) machine precision (~10-16) 1/5 = curvature scale

✏ = ⇣ = xc = ✓ G @5G/@x5 ◆1/5

For fourth order:

Stepsize hi

Freg precision (GPU) Firr precision (CPU)

• Computation galactic force and its derivative: ttforce.f

(comparable to ttfnuc.f, fhalo.f, etc.)

• User defined !G(r,t): ttgalaxy.f

How it works:

NBODY6tt: KZ(14)=9 “Mode B”

KZ(14)=9 (Mode B) vs KZ(14)=3

Test Mode B NBODY6tt

Dissolution in point-mass galaxy Disc crossing

THREE TIDAL HISTORIES

Static potential z = 5

most realist one

Static potential z = 0

not really used

Growing potential
 5 > z > 0

most often used

Static (z=0) Time-dependent

NBODY6TT RUNS

RENAUD & GIELES 2015B

Static (z=0) Time-dependent

NBODY6TT RUNS

500 pc

RENAUD & GIELES 2015B

Static (z=0) Time-dependent

NBODY6TT RUNS

500 pc

RENAUD & GIELES 2015B

Horizon simulation (Teyssier et al.) Agertz & Kravtsov