The Origin of the Small-Scale Stellar Orbit(-Phase) Substructure in the Milky Way's Disk

Practical Context

These are some notes on a sequence of possible projects that should on-board Verena Fürnkranz to her thesis project, provide a first sketch of her foreseen thesis project & mesh this with the wrap-up projects of Johanna Coronado. Broadly speaking, the goal of the research line is to

• characterize the "orbit substructure of the Galactic disk"
• develop and apply tools that tell us what caused that substructure (birth memory or resonances)
• ask (and answer) what this tells us about the transition to "field stars" and the role of resonances in creating the orbit distribution on the Galactic Solar neighbourhood.

Observed orbit(&phase) sub-structure in the Galactic Disk

It is easily said, and partially true, that the orbits of stars - when combined with their ages and abundances - encode much about the formation history of the Milky Way. It is true that the distribution p(age, abundance, orbit) of stars is the dominant observational foundation of learning about the particular formation history of our Galaxy.

And it is also true that with the advent of Gaia and spectroscopic surveys we can construct  and approximate version of p(age, abundance, orbit) over a sizeable portion of the Galactic disk (<2 kpc around the Sun).

At face value, the kinematics of a star are described by (x,v). Given a gravitational potential, Φ (x,t), this determines an orbit. If the gravitational potential is nearly symmetric, say axisymmetric, and nearly time-independent, then an orbit can be described by a set of orbit numbers (integrals-of-motions or actions), which are time-independent, and orbital phases.

In particular, then transformation to action-angle variables,

(x,v) + Φ (x) --> (J,θ) proves useful, as the actions J are constant and "adiabatic invariants"; and the angles, θ, just increase linearly with time. Transforming the 6D (x,v) to 3 actions (constants along the orbits) and 3 angles (effectively orbital phases) is maybe the most elegant coordinates to use. J_phi is the angular momentum, J_R quantifies the orbit's radial oscillation, and J_z its up-and-down motion.

If one then looks at the distribution of orbits in this space, one finds it to be "clumpy", both in orbit-space (J only) and orbit&phase-space, (J,θ); this is especially true for stars of the same abundance [Fe/H], i.e. the same birth-material composition. Some of these clumps reflect clusters, others not. This is a main results of Johanna Coronado's thesis. Others have found related results: in particular, Pisc-Eri !!

Now, there is no simple model for a 'clumpy distribution', which raises the question what we can learn. One way to look at a clumpy distribution is to consider high density regions to be distinct sub-structures, sitting on top of a smooth background. This is an excellent starting point, but has the drawbacks of some arbitrary decisions:

-- where to cut off membership in a given structure?

-- deciding when a density lump is significant enough to warrant its consideration as distinct structure. 

Possible origins of the sub-structure

There are at least two distinct origins of clumps on orbit&phase space:

• the stress were born on nearly the same orbits, and are still clumped; this leads to a set of questions:
• How close are they in phase, θ?
• Is there evidence that they are dispersing?  In that case we would expect Δθ~ΔJ
• What can we learn about the cluster/association --> field transition?
• stars, possibly born on quite different orbits, are being "herded" onto particular orbits (or orbit&phase) by quasi-periodic perturbations of the potential's symmetry (== resonances).
• What does that teach about resonances, and the features (spirals, bar) that may create them?

Goal of the project(s)

The overall goal would be to develop a comprehensive understanding of the small-scale orbit sub-substructure of stars in the Galactic Solar neighbourhood, in order to

• see which substructures reflect birth-memory
• see which substructures reflect resonances
• see what can be learned about clusters star formation and the role of resonances in either case.

Project Steps and Issues

Finding and Characterizing Orbit Clumps

This entails several steps:

• How to best find them; Johanna's approach can be a very good baseline for now?
• calculate action-angle variables
• use friends-of-friends algorithm (FoF) to cluster them.
• How to decide what to include in a clump (Johanna's linking length)?
• How to quantify the clump-aground contrast? [Johanna has not yet done that]

Basic Data Sets

We need 6D phase space coordinates, which means in practice (alpha, delta,D,mu_alpha,mu_delta,v_los); in the longer run getting abundances would be good, too.

But to start, we will take Gaia DR2 and eDR3, specifically the subset of objects that has RV, to get 6D.

Note that at the moment, only stars with 4300K < T < 7500K are included in the Gaia RV catalog. For populations <400Myrs, the "turn-off" stars (that can tell us the age of the population) are too hot to be included in the RC sample.

Diagnostic tools for the origin of clumps

• are clumps birth remnants of clusters and associations? Then they should be nearly co-eval; and they should be young (< t_dyn ~ 250 Myrs). This can be done by drawing up a CMD, and seeing whether it looks like a mono-age "cluster".
• are they a consequence of resonances? In that case we would expect a wide spread of ages. And we would expect that stars have a streak-like morphology in, e.g., the J_phi - J_R diagram (see Trick et al 2018). And we should expect gradual changes with position in the (R,phi) Galactic plane.
• are they dispersing? If so, there should be a correlation Δθ~ΔJ , where the slope is given by dΩ/dJ * t_age

Next Steps

Let's look at Pisc-Eri in action-angle space as well as we can. If Johanna can Walk Verena through all the steps:

• calculate actions and angles with galley
• run FoF on them, and identify Pisc-Eri in (J,θ) space (with Johanna's software)
• vary the linking length to see what works best.
• project (J,θ) into (x,mu_alpha,mu_delta)-space, and find members without RV. This is the first step of really new terrain.