LSS Mocks - User contributions [en-ca]

Jan 27, 2022 - Considering shear

2022-01-28T15:05:20Z

Motloch:

During Jason's presentation at Penn it was commented that we should probably also include shear in the magnification coefficients, given that it is the same order as kappa^2 we find significant.

Based on information presented in the [https://arxiv.org/pdf/2105.13539.pdf DES paper] and [https://healpix.sourceforge.io/html/sub_alm2map_spin.htm Healpix convention] we have

<math>
\gamma_1 + i \gamma_2 = \gamma = \sum_{lm} \gamma_{lm} {}_2Y_{lm} = \sum_{lm} \left(- \sqrt{\frac{(l-1)(l+2)}{l(l+1)}}\right)\kappa_{lm}{}_2Y_{lm}
</math>
<math>
\gamma_1 - i \gamma_2 = \gamma^* = \sum_{lm} \gamma_{lm}^* {}_2Y_{lm}^* = \sum_{lm} \left(- \sqrt{\frac{(l-1)(l+2)}{l(l+1)}}\right)\kappa_{lm}^*{}_2Y_{lm}^* = \sum_{lm} \left(- \sqrt{\frac{(l-1)(l+2)}{l(l+1)}}\right)\kappa_{lm}{}_{-2}Y_{lm}
</math>

In the Healpix convention we have the values entering alm2map_spin (notice the minus sign at the end)

<math>
{}_2a_{lm}^+ = -\left(\kappa_{lm}(-\sqrt{\dots}) + \kappa_{lm}(-\sqrt{\dots})\right)/2 = \kappa_{lm}\sqrt{\dots} = - \gamma_{lm}
</math>

<math>
{}_2a_{lm}^- = -\left(\kappa_{lm}(-\sqrt{\dots}) - \kappa_{lm}(-\sqrt{\dots})\right)/2i = 0
</math>

The two maps that are returned are then

<math>
{}_2S^+ = (\gamma + \gamma^*)/2 = \gamma_1
</math>

<math>
{}_2S^- = (\gamma - \gamma^*)/2i = \gamma_2
</math>

Jan 27, 2022 - Considering shear

2022-01-27T15:40:48Z

Motloch: Created page with "During Jason's presentation at Penn it was commented that we should probably also include shear in the magnification coefficients, given that it is the same order as kappa^2 w..."

During Jason's presentation at Penn it was commented that we should probably also include shear in the magnification coefficients, given that it is the same order as kappa^2 we find significant.

Based on information presented in the [https://arxiv.org/pdf/2105.13539.pdf DES paper] and [https://healpix.sourceforge.io/html/sub_alm2map_spin.htm Healpix convention] we have

<math>
\gamma_1 + i \gamma_2 = \gamma = \sum_{lm} \gamma_{lm} {}_2Y_{lm} = \sum_{lm} \left(- \sqrt{\frac{(l-1)(l+2)}{l(l+1)}}\right)\kappa_{lm}{}_2Y_{lm}
</math>
<math>
\gamma_1 - i \gamma_2 = \gamma^* = \sum_{lm} \gamma_{lm}^* {}_2Y_{lm}^* = \sum_{lm} \left(- \sqrt{\frac{(l-1)(l+2)}{l(l+1)}}\right)\kappa_{lm}^*{}_2Y_{lm}^* = \sum_{lm} \left(- \sqrt{\frac{(l-1)(l+2)}{l(l+1)}}\right)\kappa_{lm}{}_{-2}Y_{lm}
</math>

In the Healpix convention we have the values entering alm2map_spin (notice the minus sign at the end)

<math>
{}_2a_{lm}^+ = -\left(\kappa_{lm}(-\sqrt{\dots}) + \kappa_{lm}(-\sqrt{\dots})\right) = \kappa_{lm}\sqrt{\dots} = - \gamma_{lm}
</math>

<math>
{}_2a_{lm}^- = -\left(\kappa_{lm}(-\sqrt{\dots}) - \kappa_{lm}(-\sqrt{\dots})\right) = 0
</math>

The two maps that are returned are then

<math>
{}_2S^+ = (\gamma + \gamma^*)/2 = \gamma_1
</math>

<math>
{}_2S^- = (\gamma - \gamma^*)/2i = \gamma_2
</math>

Pavel Logbook

2022-01-27T15:31:30Z

Motloch:

Pavel's notes about CIB lensing

[[Jan 27, 2022 - Considering shear]]

[[Sep 09, 2021 - Effects of lensing with smooth kappa]]

[[Sep 09, 2021 - Smoothed kappa maps]]

[[Sep 02, 2021 - Cut on galaxy level]]

[[Sep 01, 2021 - Thresholding kappa]]

[[Aug 30, 2021 - Effects of lensing on variance, skewness, curtosis]]

[[Aug 27, 2021 - Planck comparison]]

[[Aug 27, 2021 - Number of CIB hot pixels]]

[[Aug 26, 2021 - Check final kappa maps]]

[[May 18, 2021 - Lensing through deflections, first results]]

[[May 17, 2021 - Lensing through deflections, practical]]

[[May 13, 2021 - Lensing through deflections]]

[[Nov 4, 2019 - Looking at factor 3 in bispectra]]

[[May 28, 2019 - Resolving the discrepancy with theory skewness]]

[[May 21, 2019 - Using George's source catalog]]

[[May 20, 2019 - Bispectra of the Poisson field]]

[[May 18, 2019 - Statistics of Poisson fields - analytics]]

[[May 18, 2019 - Statistics of the new CIB maps]]

[[Mar 31, 2019 - Brightness temperature]]

[[Feb 5, 2019 - Dig into where Jason's skewness is coming from]]

[[Feb 4, 2019 - Extend the top hat filter with blunt edges to higher lmax]]

[[Jan 23, 2019 - Comparison of mine and Jason's filters]]

[[Jan 23, 2019 - Skewness and Kurtosis, top hat filter with blunt edges]]

[[Jan 22, 2019 - Using wrong map: Skewness and Kurtosis, top hat filter with blunt edges]]

[[Jan 21, 2019 - Using wrong map: Skewness and Kurtosis, top hat filter]]

[[Dec 13, 2018 - Resolving low redshift CIB]]

[[Nov 8, 2018 - Lensing effect on CIB power spectra]]

[[Nov 8, 2018 - Wrong: Lensing effect on CIB power spectra]]

[[Nov 1, 2018 - Check kappa power spectra]]

[[Oct 31, 2018 - Statistics of George's maps]]

[[Oct 29, 2018 - Deciphering what Remi did]]

[[Sep 19, 2018 - Installing software]]

Sep 09, 2021 - Effects of lensing with smooth kappa

2021-09-10T02:59:17Z

Motloch:

We used the full lensing code (deflections, magnifications) to see how variance/skewness/curtosis in ell bins changes due to lensing. We perform a map level cut.

We show results for three flux threshold values (colors) with smoothed kappa (1 pixel, solid) and without smoothed kappa (dashed)

[[File:sm_variance_217.png|250px]]
[[File:sm_skewness_217.png|250px]]
[[File:sm_curtosis_217.png|250px]]

[[File:sm_variance_353.png|250px]]
[[File:sm_skewness_353.png|250px]]
[[File:sm_curtosis_353.png|250px]]

[[File:sm_variance_545.png|250px]]
[[File:sm_skewness_545.png|250px]]
[[File:sm_curtosis_545.png|250px]]

As expected, smoothing kappa decreases the effect of non-Gaussianities.

We also check stability when the hot pixels are replaced with twice the mean of the map (as opposed to map mean above), changes are not huge and mostly invisible in many of the plots.

[[File:2mean_variance_217.png|250px]]
[[File:2mean_skewness_217.png|250px]]
[[File:2mean_curtosis_217.png|250px]]

[[File:2mean_variance_353.png|250px]]
[[File:2mean_skewness_353.png|250px]]
[[File:2mean_curtosis_353.png|250px]]

[[File:2mean_variance_545.png|250px]]
[[File:2mean_skewness_545.png|250px]]
[[File:2mean_curtosis_545.png|250px]]

File:2mean curtosis 545.png

2021-09-10T02:58:43Z

Motloch:

File:2mean skewness 545.png

2021-09-10T02:58:28Z

Motloch:

File:2mean variance 545.png

2021-09-10T02:58:13Z

Motloch:

File:2mean curtosis 353.png

2021-09-10T02:57:58Z

Motloch:

File:2mean skewness 353.png

2021-09-10T02:57:44Z

Motloch:

File:2mean variance 353.png

2021-09-10T02:57:28Z

Motloch:

File:2mean curtosis 217.png

2021-09-10T02:57:11Z

Motloch:

File:2mean skewness 217.png

2021-09-10T02:56:54Z

Motloch:

File:2mean variance 217.png

2021-09-10T02:56:28Z

Motloch:

File:Sm curtosis 545.png

2021-09-10T02:56:10Z

Motloch:

File:Sm skewness 545.png

2021-09-10T02:55:51Z

Motloch:

File:Sm variance 545.png

2021-09-10T02:55:35Z

Motloch:

File:Sm curtosis 353.png

2021-09-10T02:55:17Z

Motloch:

File:Sm skewness 353.png

2021-09-10T02:54:58Z

Motloch:

File:Sm variance 353.png

2021-09-10T02:54:42Z

Motloch:

File:Sm curtosis 217.png

2021-09-10T02:54:08Z

Motloch:

File:Sm skewness 217.png

2021-09-10T02:53:49Z

Motloch:

File:Sm variance 217.png

2021-09-10T02:53:32Z

Motloch:

Sep 09, 2021 - Effects of lensing with smooth kappa

2021-09-10T02:53:14Z

Motloch: Created page with "We used the full lensing code (deflections, magnifications) to see how variance/skewness/curtosis in ell bins changes due to lensing. We perform a map level cut. We show resu..."

We used the full lensing code (deflections, magnifications) to see how variance/skewness/curtosis in ell bins changes due to lensing. We perform a map level cut.

We show results for three flux threshold values (colors) with smoothed kappa (1 pixel, solid) and without smoothed kappa (dashed)

[[File:sm_variance_217.png|250px]]
[[File:sm_skewness_217.png|250px]]
[[File:sm_curtosis_217.png|250px]]

[[File:sm_variance_353.png|250px]]
[[File:sm_skewness_353.png|250px]]
[[File:sm_curtosis_353.png|250px]]

[[File:sm_variance_545.png|250px]]
[[File:sm_skewness_545.png|250px]]
[[File:sm_curtosis_545.png|250px]]

As expected, smoothing kappa decreases the effect of non-Gaussianities.

We also check stability when the hot pixels are replaced with twice the mean of the map (as opposed to map mean above), changes are not huge.

[[File:2mean_variance_217.png|250px]]
[[File:2mean_skewness_217.png|250px]]
[[File:2mean_curtosis_217.png|250px]]

[[File:2mean_variance_353.png|250px]]
[[File:2mean_skewness_353.png|250px]]
[[File:2mean_curtosis_353.png|250px]]

[[File:2mean_variance_545.png|250px]]
[[File:2mean_skewness_545.png|250px]]
[[File:2mean_curtosis_545.png|250px]]

Pavel Logbook

2021-09-10T02:50:41Z

Motloch:

Pavel's notes about CIB lensing

[[Sep 09, 2021 - Effects of lensing with smooth kappa]]

[[Sep 09, 2021 - Smoothed kappa maps]]

[[Sep 02, 2021 - Cut on galaxy level]]

[[Sep 01, 2021 - Thresholding kappa]]

[[Aug 30, 2021 - Effects of lensing on variance, skewness, curtosis]]

[[Aug 27, 2021 - Planck comparison]]

[[Aug 27, 2021 - Number of CIB hot pixels]]

[[Aug 26, 2021 - Check final kappa maps]]

[[May 18, 2021 - Lensing through deflections, first results]]

[[May 17, 2021 - Lensing through deflections, practical]]

[[May 13, 2021 - Lensing through deflections]]

[[Nov 4, 2019 - Looking at factor 3 in bispectra]]

[[May 28, 2019 - Resolving the discrepancy with theory skewness]]

[[May 21, 2019 - Using George's source catalog]]

[[May 20, 2019 - Bispectra of the Poisson field]]

[[May 18, 2019 - Statistics of Poisson fields - analytics]]

[[May 18, 2019 - Statistics of the new CIB maps]]

[[Mar 31, 2019 - Brightness temperature]]

[[Feb 5, 2019 - Dig into where Jason's skewness is coming from]]

[[Feb 4, 2019 - Extend the top hat filter with blunt edges to higher lmax]]

[[Jan 23, 2019 - Comparison of mine and Jason's filters]]

[[Jan 23, 2019 - Skewness and Kurtosis, top hat filter with blunt edges]]

[[Jan 22, 2019 - Using wrong map: Skewness and Kurtosis, top hat filter with blunt edges]]

[[Jan 21, 2019 - Using wrong map: Skewness and Kurtosis, top hat filter]]

[[Dec 13, 2018 - Resolving low redshift CIB]]

[[Nov 8, 2018 - Lensing effect on CIB power spectra]]

[[Nov 8, 2018 - Wrong: Lensing effect on CIB power spectra]]

[[Nov 1, 2018 - Check kappa power spectra]]

[[Oct 31, 2018 - Statistics of George's maps]]

[[Oct 29, 2018 - Deciphering what Remi did]]

[[Sep 19, 2018 - Installing software]]

Sep 09, 2021 - Smoothed kappa maps

2021-09-10T02:13:31Z

Motloch:

Dick suggested that our problems with sensitivity to places where kappa is close to one and magnification diverges can be solved by smoothing the kappa maps. A natural first guess for the smoothing scale is an effective radius of the pixel. It is given by

<math>
\pi \theta^2 = \frac{4\pi}{N_{pix}}
</math>

and evaluates to

<math>
\theta = (\sqrt{3}N_{side})^{-1} .
</math>

Using the healpy smoothing routine with <math>\sigma = \theta</math>, we pre-process the maps before lensing.

As visible from histograms, it helps to cure the tails:

[[File:smooth_kappa_1.png|300px]]
[[File:smooth_kappa_9.png|300px]]
[[File:smooth_kappa_17.png|300px]]

Just for illustration we show what the smoothing does to the kappa map (shell 17):

[[File:kappa_example_17.png|600px]]
[[File:smooth_kappa_example_17.png|600px]]

File:Smooth kappa example 17.png

2021-09-10T02:13:11Z

Motloch:

File:Kappa example 17.png

2021-09-10T02:12:55Z

Motloch:

Sep 09, 2021 - Smoothed kappa maps

2021-09-10T02:12:45Z

Motloch:

Sep 09, 2021 - Smoothed kappa maps

2021-09-10T02:11:11Z

Motloch:

Dick suggested that our problems with sensitivity to places where kappa is close to one and magnification diverges can be solved by smoothing the kappa maps. A natural first guess for the smoothing scale is an effective radius of the pixel. It is given by

<math>
\pi \theta^2 = \frac{4\pi}{N_{pix}}
</math>

and evaluates to

<math>
\theta = (\sqrt{3}N_{side})^{-1} .
</math>

Using the healpy smoothing routine with <math>\sigma = \theta</math>, we pre-process the maps before lensing.

As visible from histograms, it helps to cure the tails:

[[File:smooth_kappa_1.png|300px]]

[[File:smooth_kappa_9.png|300px]]

[[File:smooth_kappa_17.png|300px]]

File:Smooth kappa 17.png

2021-09-10T02:10:46Z

Motloch:

File:Smooth kappa 9.png

2021-09-10T02:10:26Z

Motloch:

File:Smooth kappa 1.png

2021-09-10T02:10:11Z

Motloch:

Sep 09, 2021 - Smoothed kappa maps

2021-09-10T02:09:48Z

Motloch: Created page with "Dick suggested that our problems with sensitivity to places where kappa is close to one and magnification diverges can be solved by smoothing the kappa maps. A natural first g..."

Dick suggested that our problems with sensitivity to places where kappa is close to one and magnification diverges can be solved by smoothing the kappa maps. A natural first guess for the smoothing scale is an effective radius of the pixel. It is given by

<math>
\pi \theta^2 = \frac{4\pi}{N_{pix}}
</math>

and evaluates to

<math>
\theta = (\sqrt{3}N_{side})^{-1} .
</math>

Using the healpy smoothing routine with <math>\sigma = \theta</math>, we pre-process the maps before lensing.

As visible from histograms, it helps cure the tails:

[[File:smooth_kappa_1.png|100px]]

[[File:smooth_kappa_9.png|100px]]

[[File:smooth_kappa_17.png|100px]]

Pavel Logbook

2021-09-10T02:02:23Z

Motloch:

Pavel's notes about CIB lensing

[[Sep 09, 2021 - Smoothed kappa maps]]

[[Sep 02, 2021 - Cut on galaxy level]]

[[Sep 01, 2021 - Thresholding kappa]]

[[Aug 30, 2021 - Effects of lensing on variance, skewness, curtosis]]

[[Aug 27, 2021 - Planck comparison]]

[[Aug 27, 2021 - Number of CIB hot pixels]]

[[Aug 26, 2021 - Check final kappa maps]]

[[May 18, 2021 - Lensing through deflections, first results]]

[[May 17, 2021 - Lensing through deflections, practical]]

[[May 13, 2021 - Lensing through deflections]]

[[Nov 4, 2019 - Looking at factor 3 in bispectra]]

[[May 28, 2019 - Resolving the discrepancy with theory skewness]]

[[May 21, 2019 - Using George's source catalog]]

[[May 20, 2019 - Bispectra of the Poisson field]]

[[May 18, 2019 - Statistics of Poisson fields - analytics]]

[[May 18, 2019 - Statistics of the new CIB maps]]

[[Mar 31, 2019 - Brightness temperature]]

[[Feb 5, 2019 - Dig into where Jason's skewness is coming from]]

[[Feb 4, 2019 - Extend the top hat filter with blunt edges to higher lmax]]

[[Jan 23, 2019 - Comparison of mine and Jason's filters]]

[[Jan 23, 2019 - Skewness and Kurtosis, top hat filter with blunt edges]]

[[Jan 22, 2019 - Using wrong map: Skewness and Kurtosis, top hat filter with blunt edges]]

[[Jan 21, 2019 - Using wrong map: Skewness and Kurtosis, top hat filter]]

[[Dec 13, 2018 - Resolving low redshift CIB]]

[[Nov 8, 2018 - Lensing effect on CIB power spectra]]

[[Nov 8, 2018 - Wrong: Lensing effect on CIB power spectra]]

[[Nov 1, 2018 - Check kappa power spectra]]

[[Oct 31, 2018 - Statistics of George's maps]]

[[Oct 29, 2018 - Deciphering what Remi did]]

[[Sep 19, 2018 - Installing software]]

Sep 02, 2021 - Cut on galaxy level

2021-09-02T18:52:47Z

Motloch:

At some point we were discussing possibility of doing the cuts at the level of individual galaxies - if its lensed flux is above the threshold, throw it away - rather than at the map level. We see that it helps and leads to better results than doing no cuts at all, but still not enough:

[[File:galcut_variance_217.png|250px]]
[[File:galcut_skewness_217.png|250px]]
[[File:galcut_curtosis_217.png|250px]]

[[File:galcut_variance_353.png|250px]]
[[File:galcut_skewness_353.png|250px]]
[[File:galcut_curtosis_353.png|250px]]

[[File:galcut_variance_545.png|250px]]
[[File:galcut_skewness_545.png|250px]]
[[File:galcut_curtosis_545.png|250px]]

To see where this is coming from, we compared pixel flux distributions for the three possibilities (no cut, map cut and galaxy cut) and found that while the galaxy cut helps, there are still plenty of pixels above the Planck cutoff. The vertical line is the cutoff; the accumulation on the left side is zero flux pixels padded by 100.

[[File:galcut_histogram.png]]

File:Galcut histogram.png

2021-09-02T18:51:34Z

Motloch:

File:Galcut curtosis 545.png

2021-09-02T18:51:21Z

Motloch:

File:Galcut skewness 545.png

2021-09-02T18:51:06Z

Motloch:

File:Galcut variance 545.png

2021-09-02T18:50:54Z

Motloch:

File:Galcut curtosis 353.png

2021-09-02T18:50:39Z

Motloch:

File:Galcut skewness 353.png

2021-09-02T18:50:22Z

Motloch:

File:Galcut variance 353.png

2021-09-02T18:50:08Z

Motloch:

File:Galcut curtosis 217.png

2021-09-02T18:49:55Z

Motloch:

File:Galcut skewness 217.png

2021-09-02T18:49:40Z

Motloch:

File:Galcut variance 217.png

2021-09-02T18:49:25Z

Motloch:

Sep 02, 2021 - Cut on galaxy level

2021-09-02T18:49:04Z

Motloch: Created page with "At some point we were discussing possibility of doing the cuts at the level of individual galaxies - if its lensed flux is above the threshold, throw it away - rather than at..."

File:Kappamax curtosis 545.png

2021-09-02T18:36:09Z

Motloch:

File:Kappamax skewness 545.png

2021-09-02T18:35:53Z

Motloch:

File:Kappamax variance 545.png

2021-09-02T18:35:37Z

Motloch:

File:Kappamax curtosis 353.png

2021-09-02T18:35:21Z

Motloch: