Oct 17, 2018 - Lensing the CIB

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CIB Lensing of Individual Shells and Analysis

Here is what I was able to do.

1. Lens the 23 CIB maps with the 23 kappa maps, creating a "cib_i^lensed" and a "cib_i^unlensed" set of 23 maps.

  I only used the field maps for both the kappa and the CIB maps. There were only 16 maps for the field (from z = 0 to z = 3.2). 
  Used the bash script Remi left. The following is the part of my script that did the lensing.
  It turned out this was where I made a mistake before and got such high values for the fractional difference between the lensed 
  and unlensed maps. I had been lensing a CIB map with the kappa map of the same range of z which does not make sense since a CIB shell 
  will only be lensed by the kappa before it. For example, CIB_z_1.0_1.2 has to be lensed by Kappa_z_0.8_1.0_zsource_0.9 but I was 
  lensing it with Kappa_z_1.0_1.2_zsource_1.1. 
     for i in seq 0.2 0.2 3.2;
  do
      echo "-----------$i----------"
      zmid=`awk "BEGIN {print $i-0.1}"`
      zfield=`awk "BEGIN {print $i+0.2}"`
      echo "$zmid"
      echo "$zfield"
      python lens.py ../jason_cib_lensing/maps/kappa/field/kappa_field_nside2048_zmin0.0_zmax${i}_zsource${zmid}_kap.fits 
      ../jason_cib_lensing/maps/cib/field/2048/unlensed_maps/cib_field_nside2048_zmin${i}_zmax${zfield}_cib.fits  
      ../jason_cib_lensing/maps/lensed/phi/run2/kap_zmax${i}_phi_field.fits 
      ../jason_cib_lensing/maps/lensed/field/run2/cib_field_nside2048_zmin${i}_zmax${zfield}_cib_lensed.fits -np 40

2. Plot cartview "zoom ins" of a few cib maps, lensed and unlensed, to make sure the lensing makes sense.

  I tried this out for z = 1.0 to 1.2 and z = 2.0 to 2.2, the whole map and some cartviews. The scales at the bottom were synchronized between
  lensed and unlensed maps.
  
   z = 1.0 to 1.2 
unlensed total
lensed total
  There isn't a clear difference between the two maps so I subtracted the lensed map from the unlensed (linearly) and made a map out of it.
  I will refer to these as 'difference maps.' (It may be different from the difference maps mentioned in the last meeting.)
difference total
  Now there is a difference for sure.
unlensed -30º~-60º
lensed -30º~-60º
  Again, the two maps look virtually the same and these cannot be differentiated even with blinking.
difference -30º~-60º
  This looks better.
unlensed 0º~20º
lensed 0º~20º
  The same goes for these maps even though the range is smaller.
difference 0º~20º
unlensed 35º~40º
lensed 35º~40º
  When the maps are zoomed into 5º patches, the two maps certainly display a difference even though details are blurred due to the resolution.
    z = 2.0 to 2.2 
unlensed total
lensed total
difference total
unlensed 0º~20º
lensed 0º~20º
difference 0º~20º
unlensed 35º~40º
lensed 35º~40º
  These two maps seem much different from each other compared to the 35º~40º for z = 1.0 to 1.2.
difference 35º~40º
  What luck!

3. Add these 23 maps together to get a [math]\displaystyle{ cib_{total}^{lensed} = \sum_i cib_i^{lensed} }[/math] , and a [math]\displaystyle{ cib_{total}^{unlensed} = \sum_i cib_i^{unlensed} }[/math].

  Used a python script to add the maps up (with help from George). I also added CIB_z_0.0_0.2 which is the same before and after lensing. The script goes:
  
  import healpy as hp
  import glob
  import sys
  nside_f = 2048
  filelist = sorted(glob.glob('./*fit*'))
  map_f = 0
  for i in range(len(filelist)):
      print "adding map = ", filelist[i]
      map_i = hp.read_map(filelist[i])
      print(map_i)
      map_f = map_f + map_i
      print(map_f)
  hp.write_map("added_map.fits", map_f)   


4. Plot these, and also take their power spectrums and plot those just like you did for the CMB lensing (getting a [math]\displaystyle{ DeltaC_l/C_l }[/math] too).

Total Maps

unlensed total
lensed total
  The scales have become bigger but there isn't an obvious difference.
difference total
  Now the scales are about 2~3 times the range of the difference maps given above with individual shells. (z = 1.0 to 1.2 and z = 2.0 to 2.2 must contribute a lot.)

Power Spectrum

C l unlensed vs.lensed total with difference.png
C l unlensed vs.lensed total axes2.png
C l fd range.png
C l fd range log.png
Fractional Difference C l absolute.png

5. power spectra of each of the 23 slices lensed and unlensed seperately to see whats going on.

  Lensed vs. unlensed.png    Lensed vs. unlensed log.png 
  Delta T.png    (log) 
                                                                   (log)
   Kappa map
     view of a patch from 5º~10ºN, 5º~10ºE 
      view of a patch from 5º~10ºN,
      5º~10ºE using 'cartview'