1. Dynamics, Chemistry, and Inside-Out galaxy formation
Paul McMillan
(Collaborator: Ralph Schönrich)

2. Galactic Dynamics = orbits

3. We need good ways of describing & following orbits
How do I know if the star up here moving slowly…
…is on the same orbit as the one down there moving fast?

4. We need sensible constants of motion
One example:
Angular momentum
But what else?

5. Orbit not at z=0
What I’’ show are vr & r at z=0

6. Orbit not at z=0

7. Orbit not at z=0
2π×JR

8. Is it a useful quantity?
What it happens to be doing at z=0 is one thing…

9. z= 2 1 R= 8 10 12 JR Jz JR Jz JR Jz

10. Using action-angle variables in Galactic potentials
Not 100% simple, but the work has been done
For details see McMillan & Binney 2008, Sanders & Binney 2015, Binney & McMillan 2016

11. Link to chemistry
Chemical evolution = gas flowing and stars exploding

12. Stars don’t stay where they’re born
They move on their orbits
They change orbits
Change in orbit = change in actions

13. Metallicity gradients
Metal rich gas
Metal rich young stars
Metal poor gas
Metal poor young stars

14. Can also be seen in local Vϕ velocities
From R>R0
From R<R0

15. But in some high redshift galaxies – positive radial gradient in stars & Thick (α-rich) disc of the Milky Way - positive Vϕ-[Fe/H] correlation

16. Metallicity gradient reversed in early life of galaxies?

17. Not necessarily
Inside out formation
t = 3 Gyr
[ Fe/H ]
t = 0 R

18. This relies on gas mixing, otherwise…
t = 3 Gyr
[ Fe/H ]
t = 0 R

19. But even more…
Recall that azimuthal velocity also depends on velocity dispersion Vφ σ2

20. Means that stars with low [Fe/H] tend to be at smaller R
So low Vϕ for low [Fe/H]
Means that stars with low [Fe/H] tend to be at smaller R
and/or
Means that stars with low [Fe/H] tend to have higher velocity dispersions

21. Put this in to a full chemodynamical model…

22. And in Vϕ

23. Note that our dynamical model also predicts behaviour away from the galactic plane

24. Thank you

25. The big advantage of action coordinates*
You get (for free!) conjugate variables called the angles (θ), which have the beautiful property that they increase linearly with time
They’re periodic: Increase by 2π and you get back where you started
The rate they increase is therefore an (angular) frequency Ω
dH/dJ = theta
*Also useful – they are adiabatically invariant – don’t change under slow changes in Φ