How to interpret skewness and kurtosis plots of galaxy snapshots?

Question

What I did:- I am analysing some simulation snapshots of the Milky Way and it is modelled as a dark matter halo – bulge – disc system. I produced some skewness (using scipy.stats.skew() in python) and kurtosis (using scipy.stats.kurtosis) plots of line of sight velocity (LOSV)that I am attaching here. To produce these plots I simply extracted the $v_x,v_y,v_z$ components of the velocities of the stars and I picked the $z$-axis as the line of sight. I overlaid a grid on the galaxy snapshot, and at different inclinations ($\theta=0,45,60,90$ degrees) of the galaxy I plotted the skewness and kurtosis in the grid cells ($v_z$ is the $z$-component of the velocities). [![enter image description here][1]][1]

My question: I want to now understand and interpret my plots. What can I deduce from the plots for the different angles of inclinations? My model galaxy has a halo, bulge at centre and disk. What can we tell about the losv distributions or the components of the galaxy? I'm new to astrophysics so these kind of plots and concepts are new to me. Any help is much appreciated, thanks so much!

Answer 1

To begin with, I would suggest also plotting the line-of-sight velocity and velocity dispersion maps for each inclination. In particular, you should see a clear anti-correlation between the velocity and the skewness, especially in the edge-on case. This is a signature of rotation-dominated kinematics and a flat or slowly changing rotation curve, due to the line-of-sight vetor intersecting (nearly) circular orbits at different angles outside the tangent radius:

Edited to add: The idea is that your line of sight (dashed green line) is tangent to the point A, and so the projected lines-of-sight velocity = the rotation velocity at that radius. The line of sight intersects stellar orbits at larger radii at increasingly large angles, so the projected velocity along the line of sight gets smaller and smaller (if the stellar velocity curve is flat or decreasing or even mildly increasing). Assuming a locally Gaussian distribution of stellar velocities at each radius, the contributions from radii $> A$ show up at smaller velocities (curves in the right-hand figure). Assuming that stellar density decreases at larger radii, the contributions from larger radii are smaller (lower heights in the right-hand figure). The net effect will be a shape with negative skew. For the other side of the galaxy, where velocities are negative (blueshifted), you will get the mirror situation, with a positively skewed LOSVD.

(One small suggestion would be to plot positive quantities with read and negativity quantities with blue -- the opposite of what you're currently doing -- since then positive velocities correspond directly to redshifts and negative velocities to blueshifts.)

The strong pixel-to-pixel variations in the outer part of the disk in your plots is almost certainly just due to low S/N (since the number density of particles is low at large radii).

Note that the standard approach in analyzing galaxy stellar kinematics is to model the line-of-sight velocity distribution using Gauss-Hermite polynomials, where the first- and second-order terms correspond to the mean velocity ($V$) and the velocity dispersion ($\sigma$), and the third- and fourth-order terms ($h_{3}$ and $h_{4}$) to the skewness and kurtosis, respectively. (See, e.g., van der Marel & Franx (1993) and Gerhard (1993).) I point this out mainly in case you want to compare your results with published analyses of other models and real galaxies.