Auto-Frame: centering & orientation

"Find the centre, then rotate to face-on / edge-on" is a ritual every disk-galaxy analysis repeats by hand. center_of and face_on / edge_on do it from the data: the centre from the mass distribution, the orientation from the gas angular momentum. The result drops straight into projection.

Face-on and edge-on views of the spiral_clumps disk, both obtained automatically from the gas angular momentum with face_on(gas) and edge_on(gas).

fr = face_on(gas)        # line of sight = the disk's spin axis
projection(gas, :sd; los=fr.los, up=fr.up, center=fr.center, range_unit=fr.center_unit)

Finding the centre

center_of returns [x, y, z]:

center_of(gas)                    # mass-weighted centre of mass (default)
center_of(gas, method=:densest)   # position of the densest hydro cell
center_of(gas, unit=:kpc)         # in physical units

For :standard the result is a box fraction (0–1) — the convention that projection, subregion and getvar(…; center=…) expect — so it feeds straight back into them.

Orienting: face-on and edge-on

face_on and edge_on compute the net angular momentum L about the centre and return a GalaxyFrame:

face_on → line of sight along the spin axis (look down on the disk).
edge_on → line of sight in the disk plane, with the spin axis pointing up.

fr = face_on(gas)
fr.los       # unit vector the camera looks along
fr.up        # camera up vector
fr.center    # centre, in fr.center_unit
fr.angmom    # the net angular-momentum vector it was built from

Why it works without subtracting the bulk velocity: angular momentum measured about the centre of mass cancels any net translation, because $\sum_i m_i \mathbf{r}_i = 0$ there. (The same cancellation removes the Hubble flow in cosmological runs, since $\mathbf{r} \times H\mathbf{r} = 0$.)

Several galaxies, mergers, cosmological boxes

The bare call assumes one object

face_on(gas) / center_of(gas) use the global CoM and the summed angular momentum. In a box with many galaxies that is meaningless — the CoM lands between them and unrelated spins cancel. Point the tool at the object with a seed center plus an aperture; it then re-centres on the local CoM inside that sphere and measures only that object's spin:

# the densest galaxy in the box (good first guess in a cosmological run)
fr = face_on(gas; center=:densest, aperture=30, range_unit=:kpc)

# a galaxy at a known/catalogued position (e.g. from a halo or clump finder)
fr = face_on(gas; center=[x, y, z], aperture=30, range_unit=:kpc)

Equivalently, cut the object out first and frame that:

gal = subregion(gas, :sphere; center=[x,y,z], radius=30, range_unit=:kpc)
fr  = face_on(gal)

Because the spin is then taken about the local CoM, this is also the correct recipe for a merger progenitor and for any galaxy moving through a cosmological box. Choosing the aperture to enclose the disk (but not the neighbours) is the one judgement call.

Options

function	keyword	default	meaning
`center_of`	`method`	`:com`	`:com` (centre of mass) or `:densest` (densest hydro cell)
`center_of`	`unit`	`:standard`	output unit; `:standard` → box fraction, else physical
`center_of`	`mask`	`[false]`	restrict to masked cells/particles
`face_on`/`edge_on`	`center`	`:com`	`:com`, `:densest`, or an explicit `[x,y,z]`
`face_on`/`edge_on`	`aperture`	`nothing`	sphere radius (in `range_unit`) to isolate one object
`face_on`/`edge_on`	`range_unit`	`:standard`	unit of `center`/`aperture`/output centre

Works on hydro and particle data (both carry mass and velocity → angular momentum).

Method and references

Aperture. The aperture keyword is a sphere radius (in range_unit) around the seed centre — the region within which the local centre and the spin axis are measured. The name is borrowed from aperture photometry: only data inside the sphere contributes, which is what isolates one object from its neighbours. aperture=nothing (the default) uses all the data, which is correct only for an already-isolated object.

Orientation. face_on / edge_on take the net, mass-weighted angular momentum

\[\mathbf{L} = \sum_i m_i\, \mathbf{r}_i \times \mathbf{v}_i\]

of the selected region about the centre, and use $\hat{\mathbf{L}}$ as the spin axis (the face-on line of sight); edge-on looks along a direction in the disc plane. This is the same recipe the established simulation-analysis tools use — e.g. pynbody's angmom.faceon/sideon and yt's angular-momentum / off-axis projection.

Centring. :com is the mass-weighted centre of mass; :densest is the density peak. With a seed centre plus an aperture, the frame re-centres on the local CoM inside the sphere — one iteration of the shrinking-sphere centre commonly used for haloes.

Why no bulk-velocity subtraction. Angular momentum about the centre of mass separates into centre-of-mass and internal parts (König's theorem), so a net translation contributes nothing about the CoM. The Hubble flow $\mathbf{v} = H\mathbf{r}$ is parallel to $\mathbf{r}$, so $\mathbf{r} \times \mathbf{v} = 0$ — hence the recipe is also correct in cosmological runs.

These are standard techniques in galaxy-simulation analysis rather than any single source; the authoritative references for the ingredients:

A. Pontzen, R. Roškar, G. Stinson, et al., pynbody: Astrophysics Simulation Analysis for Python (2013), Astrophysics Source Code Library, ascl:1305.002 — faceon/sideon orientation by angular momentum.
M. J. Turk, B. D. Smith, J. S. Oishi, et al., "yt: A Multi-code Analysis Toolkit for Astrophysical Simulation Data", ApJS 192, 9 (2011).
C. Power, J. F. Navarro, A. Jenkins, et al., "The inner structure of ΛCDM haloes — I. A numerical convergence study", MNRAS 338, 14 (2003) — iterative shrinking-sphere centre.
V. Springel, N. Yoshida, S. D. M. White, "GADGET … and the SUBFIND algorithm", MNRAS 328, 726 (2001) — density-peak substructure centres.
J. Binney & S. Tremaine, Galactic Dynamics, 2nd ed. (Princeton University Press, 2008) — angular momentum and disc dynamics.
H. Goldstein, C. Poole, J. Safko, Classical Mechanics, 3rd ed. (Addison-Wesley, 2002) — König's theorem (decomposition of angular momentum about the CoM).