distinction between galaxy position angle and beta

[jchiang87]

I wanted to note a possible inconsistency regarding the galaxy ellipticity components and galaxy position angles described in the current schema.

@rmjarvis describes in slack a distinction between beta and galaxy position angle:

beta is the angle of the galaxy major axis CCW from the +x axis.  In sky coordinates this means it is the angle
North of West.  (West being +x direction and North from there being CCW.)
I believe PA is traditionally defined as the angle East of North.  So with these definitions, beta = PA + 90.

I think this means that the ellipticity_1 computed here should instead be

return ellipticity*np.cos(2.0*pos_angle + np.pi)

and similarly for ellipticity_2, etc..

[rmjarvis]

Except the schema you linked to defines position_angle as "Position angle (arctan(E2/E1)), for galaxy, lensed", which is not the same as the traditional astronomy definition of position angle. So this might not be a bug.

[jchiang87]

Right, which is why I wondered if we needed the 90 degree shift to begin with. So if it's not a bug here, then we don't need that 90 degree shift in skyCatalogs and imSim? Regardless, it was applied in the DC2 sims.

[jchiang87]

A related issue is that arctan(E2/E1) doesn't necessarily get the right quadrant for the angle, so it's not clear to me that it's a useful definition since it has the same value for E1-> -E1, E2-> -E2, which has the same effect as adding that 90 degrees.

[rmjarvis]

My point was just that I don't know if the pos_angle that is being applied here is the same one we have in imsim. If it is the same PA, then I think both (1) the schema here has the wrong definition of position_angle and (2) the code to calculate e1,e2 from it is wrong.