Adding velocity gradient measurement

[tonywong94]

Let me start by saying I've found this package extraordinarily useful and I see it being used in a lot of analysis of ALMA molecular line maps.

I've been wondering about a way to incorporate into the 'PPVStatistic' some measure of the bulk velocity gradient across a structure. Traditionally this is done by fitting a plane to the moment-1 velocity field, but I don't see why this can't be calculated from the 3D data.

It seems like the ingredients are already there with both 'paxes' and 'projected_paxes' functions defined in analysis.py. The latter is used to get the cloud's orientation in the sky plane (as it should be), but the former could potentially be used to get the cloud's orientation in PPV space. The interesting things to record would be the [1] sky-projected direction of the 3D major axis, [2] the spatial velocity gradient (km/s/arcsec) implied by the 3D major axis, and [3] the product of this gradient and a suitable sky angle (maybe the 2nd moment, velocity integrated, along direction [1]).

I'd be happy to help with generating models for testing this over the summer if someone more familiar with the code is able to take a crack at this.

[low-sky]

Thanks @tonywong94
This sounds like a good improvement and the basics are already there. Indeed the diagonalization approach to radius finding could be generalized effectively here. The issue which is worthy of some thought, but I've usually shied away from it since PPV ≠ 3D and it makes some sense to treat the cube as a 2+1 D structure. Mathematically, I'm not sure it makes a significant difference though.