damonge / tidal Goto Github PK

@xzackli after a quick look at your notebooks I'm wondering if we've corrected for the following:

• The theta vs. dec sign. This should (I think) come down to changing t21 -> -t21.
• The fact that t11 corresponds to t_theta_theta and not t_phi_phi (i.e. the 1st coordinate is what one would naively consider to be y)

Just some thoughts on quality cuts that could clean up our sample and possibly enhance the signal. The resulting "clean" samples could then be used for any of the methods in #2 or #3

• Cuts in sphericity (elongated galaxies should have a better measured position angles)
• Cuts in size (larger galaxies should have better shapes)
• Cuts in magnitude (do things for a brighter sample that may have better measured shapes)
• Colour cuts (try to select a red sample, which should show a stronger alignment signal). Tom Jarrett suggested "using SDSS, using galaxy color as a proxy for morphological type (spheroids vs disks, etc)", but we could think about whether just using the 3 2MASS bands could do.
• Redshift cuts. 2MASS doesn't have redshifts, but 2MPZ does. We could repeat the analysis for a few thinner redshift slices to enhance the signal.
• We could think whether it'd be possible to get better measured shapes by cross-matching 2MASS/2MPZ with SDSS and using those shapes.

A generalization of the methods in #2 would be to use T and I as spin-2 fields, and to compute their power spectrum:

1. Construct the (I,Q,U) equivalents of the tidal field maps (essentially I=T11+T22, Q=T11-T22, U=T12).
2. Construct a map of the equivalent thing for the inertia tensor of the galaxies (i.e. compute a map of it from the galaxy shapes).
3. Compute the (EE) cross-power spectrum of both maps.
4. Estimate the error bars of this cross-power spectrum by using the random simulations described in #2 . If needed, it's possible (and not too hard) to generate lognormal simulations of the tidal field maps.

Method 1 - Eigenvector cosines

Make a few histograms of , where is the i-th eigenvector of the tidal field and

Method 2 - Overall amplitude

Let be the tidal tensor in the pixel of galaxy g, and let be its inertia tensor (constructed from its sphericity, its size and its position angle.

We can then fit for an overall amplitude linking both as:

Doing this for a large number of mock realizations where we rotate galaxy shapes by a random angle, we can estimate the variance of this estimator, which then allows us to quantify whether we have detected anything.