This is the galaxy shape catalog measured using the re-Gaussianization technique and the associated weight factors and calibrations derived from image simulations (Li et al. 2022). This shape catalog can be used for weak lensing science cases. The shape catalog is based on the intermediate data release S19a (which is also being made public as part of an incremental data release of PDR3). The shape catalog and the associated calibrations consist of a subset of galaxies that satisfy the weak lensing flag as described in the shape catalog paper (Li et al. 2022). The shapes should be cross-matched to the positional catalogs using object_id in the S19a_wide database. The star mask, as described by Li et al (2022), is used in order to prepare this catalog.

Use this sql query to obtain the shape catalogs for the different fields:

select
b.*, c.i_ra, c.i_dec, a.i_hsmshaperegauss_e1, a.i_hsmshaperegauss_e2
from
s19a_wide.meas2 a
inner join s19a_wide.weaklensing_hsm_regauss b using (object_id)
inner join s19a_wide.meas c using (object_id)

This should give a list of columns for each field separately:

• i_ra, i_dec: RA and DEC of the object
• object_id: object_id to be cross matched to get photometric redshifts.
• i_hsmshaperegauss_e1/2:  Galaxy distortion (e1, e2) in sky coordinates
• i_hsmshaperegauss_derived_sigma_e: per-component shape measurement uncertainty
• i_hsmshaperegauss_derived_rms_e: per-component RMS ellipticity estimate
• i_hsmshaperegauss_derived_weight: Weight factor to be used for lensing calculations, corresponding to inverse variance weighting based on shape uncertainty
• i_hsmshaperegauss_derived_shear_bias_m : Multiplicative bias factor effectively averaged over components
• i_hsmshaperegauss_derived_shear_bias_c1/2: Additive bias factor with a value for each component
• i_hsmshaperegauss_resolution: The resolution compared to the PSF with which the galaxy was detected
• i_apertureflux_10_mag: The flux in aperture with radius 1 arcsec
• hsc_y3_zbin: the redshift bin for the HSC Y3 cosmic shear analysis
• b_mode_mask: mask to remove the region with large B-mode.
• i_sdssshape_psf_shape11/22/12: PSF moments that is used to correct additive selection bias

The column “hsc_y3_zbin” is the redshift bin for the HSC Y3 cosmic shear analysis. hsc_y3_zbin==1 refers to the first redshift bin, hsc_y3_zbin==2 is the second redshift bin. Using this column, the galaxies with the bimodal P(z) (Li et al., 2023) is automatically removed. Note that in the 3x2pt analyses (Sugiyama et al., 2023; Miyatake et al, 2023), we did not remove the galaxies with the bimodal P(z).

The column “b_mode_mask” is the cut to remove the region with large B-mode. In our cosmology analyses, we removed this region. Depending on your analysis, e.g., an analysis that does not have a high signal-to-noise ratio, it may not have to be removed.

If you need point estimates of photo-z, perform “inner join” with the photo-z table “photoz_v2_demp,” “photoz_v2_dnnz,” photoz_v2_mizuki”.

The full photo-z PDFs for each tract is available here. Note that you need to select galaxies using object_id in the shape catalog. The definition of redshift binning for the PDF is available here as well. The column “BINS” is the center of redshift bins for the corresponding photo-z PDF.

The shape catalog has been ingested into the database and the database query is the best way to get it. But, the flat files are also available here.

• GAMA09H = [“equator08h”, “equator09h”,  “equator10h”] and ra < 153.5
• WIDE12H =  [“equator10h”, “equator11h”, “equator12h”, “equator13h”]  and ra BETWEEN 153.5 AND 202
• GAMA15H = [“equator13h”, “equator14h”, “equator15h”] and ra > 202
• XMM ＝  [“equator01h”, “equator02h”]
• VVDS = [“equator21h”, “equator22h”, “equator23h”, “equator00h”]

Note that the S19A tables are available only in PDR3, not in PDR3 Citus. We are sorry for the inconvenience, but please make sure to select the right ‘release’ in CAS.

The shape distortions (with |e| = (1-q^2) / (1+q^2), q denotes the axis ratio) need to be used to construct an ensemble shear estimator. The full process for deriving the ensemble shear estimator is given in Section 3.1.3 and 3.1.4 of the shape catalog paper (Li et al., 2022). This section includes equations and the correspondence between the quantities in equations and the catalog columns.

Note that, in case you are using point photometric redshift estimates or full photometric redshift PDFs, you should apply corrections for the inaccuracies of the photometric redshifts, or for dilution factors (see Rau et al. 2023). When using the point estimates, you need to correct the dilution effect following the prescription described in Section 7.1 in Nakajima et al. (2012). When using the full PDFs, you can take into account the dilution effect by following Section 3.1 in Miyatake et al. (2019).

The selection of galaxies used to measure the weak lensing signal is expected to be affected by selection biases. The measured signal can be corrected for these selection biases (see Sec 3.1.4 in Li et al. 2023).

The systematics of the weak lensing tests have been checked and reported in the shape catalog paper (Li et al. 2023). In short, we have checked that PSF determinations are accurate enough for cosmological constraints either from cosmic shear or from a combined galaxy-galaxy clustering and lensing analysis. We have also checked that the shape catalog passed a number of null tests, such as the B-mode test, and random point test, after the multiplicative and additive bias corrections are applied.

Upon request from the community, we make our code to produce the HSC Y3 shape catalog calibrations available here.

Selection of the PSF and non-PSF star catalog is described in Section 4.1 in Zhang et al. 2023.

• The PSF star catalog: hscy3_star_moments_psf.fits
• The non-PSF star catalog: hscy3_star_moments_nonpsf.fits

Column Definition, and corresponding definition in Zhang et al. 2023

• i_sdssshape_shapexy == PSF second moments Ixy of the star image, defined in Eq. 8-12.
• i_sdssshape_psf_shapexy == PSF second moments Ixy of the PSF image, defined in Eq. 8-12.
• star_momentpq == PSF higher moments Mpq of the star image, defined in Eq. 14-15.
• model_momentpq == PSF higher moments Mpq of the PSF image, defined in Eq. 14-15.

Cosmic shear measurements were carried out using the pseudo-Cl approach in Dalal et al. (2023). The corresponding measurements and chains are made available here.

hsc_y3_fourier_space_data_vector.sacc includes the following:

• Data vector – these are the band powers of tomographic lensing spectra, i.e. $C_{\ell}$s. We provide the auto and cross-correlation power spectra measured for 4 tomographic redshift bins (10 total spectra), equally spaced between z=0.3 and z=1.5. Each power spectrum is measured in 17 bins, over the $\ell$ range $\ell$=100 to $\ell$=15,800, with the following bin edges: [100, 200, 300, 400, 600, 800, 1000, 1400, 1800, 2200, 3000, 3800, 4600, 6200, 7800, 9400, 12600, 15800]. Our fiducial analysis uses scales between 300<$\ell$<1800, where the large scale cut is due to evidence of systematics leading to the detection of significant B-modes, while the small scale cut is based on the range of scales in which we believe our modeling of intrinsic alignments and baryonic feedback to be reliable and robust.
• Data vector covariance – as described in Dalal et al. 2023, the covariance is measured using mock catalogs. The full covariance matrix has a size of 170×170, covering the 17 $\ell$ bins of the 10 power spectra. The covariance matrix should have the same scale cuts applied as the power spectra.
• Source redshift distribution, N(z) – the measurement of the source redshift distribution combines photometric information with clustering redshifts based on CAMIRA LRGs, as described in detail in Rau et al. 2023.

To access data from the sacc file, one can use:

s = sacc.Sacc.load_fits(‘hsc_y3_fourier_space_data_vector.sacc’)
l, cl, cov = s.get_ell_cl('cl_ee', 'wl_'+bin1_index, 'wl_'+bin2_index, return_cov=True)
full_covariance_matrix = s.covariance.covmat
z, nz = s.tracers['wl_'+bin_index].z, s.tracers['wl_'+bin_index].nz

Where “bin1_index” and “bin2_index” run from 0 to 3 to indicate the tomographic redshift bin. Note that we only include the EE power spectra which contain the cosmological signal, but can make the BB and EB power spectra available upon request.

For further examples of reading and writing information with sacc files, please refer to these example notebooks.

PSF systematics file:

• ppcorr_psf_all_ells_lmax_1800_catalog2.npz – contains measurements of the auto- and cross-correlations between the second moment leakage, second moment modeling error, fourth moment leakage and fourth moment modeling error of the point spread function. This is used for computing the additive bias to the Cls from the PSF (see Zhang et al. 2023 and Dalal et al. 2023 for details). The measurements are only non-zero in the range of our fiducial scale cuts (300<$\ell$<1800).

To access the measurements one can use:

data = np.load('ppcorr_psf_all_ells_lmax_1800_catalog2.npz')
ell_bins, correlations = data['arr_0'], data[‘arr_1]

where the correlations are given in the following order:

[pp, pq, pp4, pq4], [qp, qq, qp4, qq4], [pp4, qp4, p4p4, p4q4], [pq4, qq4, p4q4, q4q4]

where p represents the second moment leakage, q represents the second moment modeling error, p4 represents the fourth moment leakage, and q4 represents the fourth moment modeling error.

• psf_transform_matrix_lmax_1800_catalog2.npz – this is the matrix used to transform the four uncorrelated, normally distributed PSF parameters that we sample into our original definitions of the second and fourth moment PSF leakage and modeling error parameters (see Section V. D. of Dalal et al. 2023).

To access the transformation matrix and mean parameter values, one can use:

transformation_matrix, mean_values = data['arr_0'], data[‘arr_1]

Fiducial likelihood chain from polychord sampling.

The fiducial likelihood is available as an example in the CosmoSIS standard library. Note that the likelihood version made public in CosmoSIS uses the linear matter power spectrum from CAMB. The fiducial likelihood used in our analysis obtains the linear matter power spectrum from the BACCO emulator. While the latter is less computationally expensive, there is no difference in the results between the two approaches.

For questions or requests for other data products, please contact Roohi Dalal (rdalal@alumni.princeton.edu). When using the above data, please cite the paper by Dalal et al. 2023, PRD, Volume 108, Issue 12, article id.123519 (arXiv:2304.00701).

Cosmic shear measurements were carried out using the real space two point correlation function approach in Li et. al (2023). The corresponding measurements and chains are made available below.

• Data vectors
  • Two point correlation functions (xi_+, xi_-) provided for a 4 bin tomographic analysis (1×1, 1×2, 1×3, 1×4, 2×2, 2×3, 2×4, 3×3, 3×4, 4×4) are in the file.
  • The data format file follows here.
• Data vector covariance
  • This provides the covariance estimated from mock catalogs.
  • Examples plotting the data vector with error can be found here.
• Source redshift distribution n(z)
  • These provide the source redshift distributions based on the methodology described in Rau et al. (2023).
• The PSF systematics data vectors
  • These provide the PSF systematics based on the methodology described in Zhang et. al (2023) .
• Fiducial posterior samples from polychord with the fiducial setup can be found here. The COSMOSIS configuration can be found here.

For questions or requests for other data products, please contact Xiangchong Li (xli6@bnl.gov). When using the above data, please cite the paper by Li et al. 2023, PRD, Volume 108, Issue 12, article id.123518, (arXiv:2304.00702).

1. Likelihood code (Sugiyama+, Miyatake+ 2023)
   1. Sunao’s pipeline is a fiducial product, used in the 3x2pt analysis
   2. The CosmoSIS implementation will be provided as a supplemental product (in progress with Tianqing and Joe)
2. Measurements (More+, Sugiyama+, Miyatake+ 2023)

• Minimalbias: minimal bias model folder
• Halohod: halo model result

Each folder contains, fiducial, dempzxwx, mizuki, and dnnz subfolders, which are for fiducial analysis, analysis with dempz x WX photoz, analysis with mizuki photoz, and analysis with dnnz photoz respectively.

Each subfolder contains following contents

• dataset = all data needed to perform parameter inference.
  • bin_dSigma_logcen.dat = radial bin of g-g lensing = R [Mpc/h]
  • bin_wp_logcen.dat = radial bin of galaxy clustering = R [Mpc/h]
  • bin_xi_logcen.dat = radial bin of cosmic shear = theta [arcmin]
  • covariance.dat = covariance matrix
  • nzl_z[n]_100bin.dat = lens redshift bin for lens redshift bin [n=0,1,2]
  • photoz_bin.dat = bin of photometric redshift distribution
  • stacked_pofz_all.dat = stacked photometric redshift distribution after source sample selection.
  • psf_pp_pq_qq.dat = psf 2pcf for cosmic shear analysis, using all stars
  • psf_pp_pq_qq_reserved.dat = same as above but with reserved starts
  • psf_pp_pq_qq_used.dat = same as above but with used stars
  • signal_dSigma[n].dat = g-g lensing signal for lens redshift bin [n=0,1,2]
  • signal_wp[n]_100RSD.dat = galaxy clustering signal for lens redshift bin [n=0,1,2]
  • signal_xi[pm].dat = cosmic shear signal of plus/minus mode [pm=p, m]
  • sumwlssigcritinvPz_z[n].dat = lens-source pair weight for g-g lensing for each lens redshift bin [n=0,1,2], used for cosmology, photo-z correction (measurement correction).
• dataset.fits = alternate format of dataset in fits, used for the CosmoSIS likelihood (in progress with Tianqing and Joe)
• sumwlssigcritinvPz.fits = alternate format of lens-source pair weight in fits, used for cosmCosmoSISosis likelihood
• analysis_config.yaml = config file for this analysis, passed to the Likelihood code
• chain_equal_weights.dat = equally weighted chain by multinest
• param_names.dat = list of names of parameters in the above chain.

The full sky ray tracing simulations of Takahashi et al. (2017), were used to generate 1404 mock catalogs for the Subaru HSC survey three-year shear catalog (More et al. 2023). The details of the catalog production process is found in More et al. 2023 and is based on Shirasaki et al. (2019). The mock data has the following contents:

• col1: tract ID
• col2: an integer number for debug
• col3: object ID
• col4: RA [deg]
• col5: dec [deg]
• col6: e_1 (ellipticity)
• col7: e_2 (ellipticity)
• col8: shear_1 (lensing shear w/o any shape noises)
• col9: shear_2 (lensing shear w/o any shape noises)
• col10: kappa (lensing convergence)
• col11: lensing weight
• col12: source redshift

Note that the source redshift of each mock galaxy follows the photo-z posterior distribution by the dnnz algorithm (Nishizawa et al 2020). For galaxies without the DNNZ photo-z information, the source redshift (col12) was set equal to -1. The catalog is available here.

As the cosmic shear catalogs, the same full-sky simulations of Takahashi et al 2017 were used to generate the 1404 mock galaxy catalogs of lens LOWZ/CMASS1/CMASS2 samples defined in More et al. 2023. The mock data has the following contents

1. Col 1: The object ID in the parent halo catalog
2. Col 2: RA (degree)
3. Col 3: Dec (degree)
4. Col 4: Redshift
5. Col 5: The host halo mass (M_200b in units of h^{-1}M_\odot)
6. Col 6: The number of satellites in the host halo
7. Col 7: If this object is central, we set column 7 to -1, otherwise, it is a non-zero integer.

The catalog is available here.

The above mock galaxy catalogs are generated based on the halo catalog in Takahashi et al 2017. The original halo catalogs are available here. Please see the description there for the details of the mock catalogs.