Introduction¶
The CM-2PCF-WL is expected to provide the covariance matrices for 3x2pt correlations: tomographic cosmic shear, angular or galaxy-galaxy lensing 2-point correlation functions (2PCF), as well as the covariance matrices for spectra. Covariance matrices for COSEBIs are also estimated from tomographic cosmic shear.
Two anticipated processing are considered:
the first one is based on spatial block-jackknife, and the realisations used to estimate the covariance matrices are obtained with the resampling parameter “spatialResample” set to “Boostrap” or “Jackknife”. This implies to set the spatial splitting parameters according to the number of realisations expected.
In the other scenario, the covariance matrices estimation encompasses multiple 2-PCFs with a specified number of realisations, whether via Bootstrap or (partial) Jackknife. The same inputs are needed as for the 2PCF (i.e. shear catalog and potentially position catalog), with additional parameters. This could be used for instance if the effect of shear or PHZ estimate uncertainty needs be propagated by picking realisations under the posterior of the shear measurement.
In the following, we first present tomographic cosmic shear covariance products, tomographic galaxy-galaxy lensing covariance products, tomographic angular covariance products and finally Resample Process.
Tomographic cosmic shear covariance¶
To derive the tomographic cosmic shear covariance matrices, resampling parameters DpdCovarTwoPCFWLParams are needed, on top of the same input catalogues and parameters used for computing the 2-point statistics (DpdTwoPCFWLParamsShearShear2D, DpdTwoPCFWLParamsPEBShearShear2D and DpdTwoPCFWLParamsCOSEBIShearShear2D).
The catalogue-resampled 2PCFs are stored in DpdCovarTwoPCFWLResampleShearShear2D while the resampled spectra in DpdCovarTwoPCFWLResamplePEBShearShear2D and the COSEBI realisations in DpdCovarTwoPCFWLResampleCOSEBIShearShear2D).
The block-jackknife or catalogue-resampled covariance matrices for cosmic shear are stored in DpdCovarTwoPCFWLShearShear2D, the covariance matrix for E/B spectra in DpdCovarTwoPCFWLPEBShearShear2D, and the covariance matrix for COSEBIs in DpdCovarTwoPCFWLCOSEBIShearShear2D.
Tomographic galaxy-galaxy lensing covariance¶
To derive the tomographic galaxy-galaxy lensing covariance matrices, resampling parameters DpdCovarTwoPCFWLParams are needed, on top of the same input catalogues and parameters used for computing the 2-point statistics (DpdTwoPCFWLParamsPosShear2D, DpdTwoPCFWLParamsPEBPosShear2D).
The catalogue-resampled 2PCFs are stored in DpdCovarTwoPCFWLResamplePosShear2D while the resampled spectra in DpdCovarTwoPCFWLResamplePEBPosShear2D.
The block-jackknife or catalogue-resampled covariance matrices for cosmic shear are stored in DpdCovarTwoPCFWLPosShear2D, the covariance matrix for E/B spectra in DpdCovarTwoPCFWLPEBPosShear2D.
Tomographic angular covariance¶
To derive the tomographic angular covariance matrices, resampling parameters DpdCovarTwoPCFWLParams are needed, on top of the same input catalogues and parameters used for computing the 2-point statistics (DpdTwoPCFWLParamsPosPos2D, DpdTwoPCFWLParamsClPosPos2D).
The catalogue-resampled 2PCFs are stored in DpdCovarTwoPCFWLResamplePosPos2D while the resampled spectra in DpdCovarTwoPCFWLResampleClPosPos2D.
The block-jackknife or catalogue-resampled covariance matrices for cosmic shear are stored in DpdCovarTwoPCFWLPosPos2D, the covariance matrix for spectra in DpdCovarTwoPCFWLClPosPos2D.
The flowchart for products related to covariance of tomographic angular 2PCF is the following:
For galaxy-galaxy lensing, the flowchart contains the following covariance products:
Finally, covariance of cosmic shear products with additional covariance of COSEBI decomposition are described in the following:
Resample Process¶
In order to compute the covariance matrix the CM-2PCF-WL works with a set of sky samples. The duration of the Euclid mission being short, only one static sky catalogue will be available. However, for getting cosmic shear variance and errors provided by Euclid, it is necessary to resample the sky.
Two processes have been defined: Either input resample catalogues (produced by SHE with MCMC method) or a single catalogue with no resamples are/is ingested in the CM-2PCF-WL.
The resamples creation in the second case will be done by the CM-2PCF-WL. The first resample process being too heavy on computational resources, the CM-2PCF-WL implements the second resample process based on either a block jackknife or block bootstrap method. Nevertheless, the data-model keeps the definition of the SHE external resample in case of a big increasing power of the data centers.
For doing the resample products, the CM-2PCF-WL resamples the correlations created from the sky patches defined by the 2PCF-WL.
For getting the underlying parameters of the sky, the block jackknife method creates each resample by removing one sky patch.
All the correlations related to the removed patch do not participate to the building of the resample. With the block bootstrap, a non exhaustive drawing is done, so the correlations related to one patch can have different weight.
The resample products will be stored in the DPS for a possible re-use by any post processing function. Stored in the database as final product, the data-model of the resamples is detailed in this DPDD.
Inputs products
Outputs products
Output Product: Covariance of Tomographic Angular Power Spectra
Output Product: Covariance of Tomographic Cosmic Shear COSEBI
Output Product: Covariance of Tomographic Galaxy-Galaxy Lensing EB Power Spectra
Output Product: Covariance of Tomographic Cosmic Shear EB Power Spectra
Output Product: Covariance of Tomographic Angular Correlation
Output Product: Covariance of Tomographic Galaxy-Galaxy Lensing Correlation
Output Product: Covariance of Tomographic Cosmic Shear Correlation
Output Product: Resampled Galaxy-Galaxy Lensing E/B Power Spectra
Output Product: Resampled Tomographic Galaxy-Galaxy Lensing Correlation
Output Product: Resampled Tomographic Cosmic Shear Correlation