Publ. Astron. Soc. Japan (2014) 00(0), 1–5
doi: 10.1093/pasj/xxx000

Photometric Redshifts for the Hyper Suprime-Cam
Subaru Strategic Program Data Release 3
HSC Collaboration, Atsushi J. Nishizawa1,2 , Bau-Ching Hsieh3 and Masayuki
Tanaka4
1Gifu Shotoku Gakuen University, 1-1 TakakuwaNishi, Yanaizucho, Gifu, 501-6194, Japan
Nagoya University, Furocho, Chikusa-ku, Nagoya, 464-8602, Japan
3Academia Sinica Institute of Astronomy and Astrophysics, 11F of AS/NTU
Astronomy-Mathematics Building, No.1, Sec. 4, Roosevelt Rd, Taipei 10617, Taiwan
4
National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan2∗ E-mail: atsushi.nishizawa@iar.nagoya-u.ac.jp

Received ; Accepted

Abstract
In this article, we present the 3rd public data release of the photometric redshift catalog of theHyper Suprime-Cam SSP survey. The full catalog can be available online from out data releasesite, https://hsc-release.mtk.nao.ac.jp/.

1 HSC PDR3 photometric data

The PDR3 photometric reshift catalog is computed basedon the photometric sample of the HSC PDR3 (S20A)(Aihara et al. 2022). Numerous updates on the dataset
and pipeline have been made from PDR2. The PDR3
data includes all the data taken before January 2020,
over 278 nights in total. The major updates since PDR2
can be summarized as follows.
1. Deep/Ultra-Deep layers reaches ∼ 80% completenessin the depth.
2. Wide layer has covered 670 deg2 in terms ofFDFC(Full Depth Full Color).
3. exposure times in izy bands are reduced and seeing
condition to take i band has been relaxed.
4. Apply the magnitude zero-point offset according to thestellar locus, as a result of new photometric calibration
FGCM.
5. Implemented a correction for different filter transmission between i/i2 bands and r/r2 bands.
6. Improved the PSF modeling and background subtraction.
© 2014. Astronomical Society of Japan.

2 Calibration Sample
To calibrate the photo-z, we collect publicly available
spectroscopic redshift samples as well as the private
spectroscopic sample.
We also use grism redshifts
and high accuracy photometric redshift samples inCOSMOS. We denote them as reference redshift samples. They are zCOSMOS DR3 (Lilly et al. 2009), 10k
DEIMOS (Hasinger et al. 2018), LEGA-C (van derWel et al. 2016), UDSz (Bradshaw et al. 2013; McLureet al. 2013), 3D-HST (Skelton et al. 2014; Momchevaet al. 2016), FMOS-COSMOS (Silverman et al. 2015),
VVDS Final DR(Le Fèvre et al. 2013), VIPERS PDR2(Scodeggio et al. 2018), eBOSS DR16 (Ahumada et al.
2020), GAMA DR3 (Baldry et al. 2018), C3R2 DR2(Masters et al. 2019), WiggleZ DR1 (Drinkwater et al.
2010), DEEP2/3 DR4 (Davis et al. 2003; Cooper et al.
2011; Cooper et al. 2012; Newman et al. 2013), PRIMUS
DR1 (Coil et al. 2011; Cool et al. 2013), VANDELS
DR2 (Pentericci et al. 2018), 2dFGRS (Colless et al.
2001) and 6dFGRS DR3 (Jones et al. 2009). Those
catalogs provide a quality control parameter to evaluate
the quality of spec-z. As in the PDR1, we construct
the homogenized bit flag and it is summarized below
for the catalogs which are newly available in this data
release. The following criteria should be satisfied before

12Publications of the Astronomical Society of Japan, (2014), Vol. 00, No. 0we match the catalog to the HSC photometric catalog.
– Public spec-z data: common selection
1. 0.01 < z < 9 (no stars, quasars, or failures)
2. σz < 0.005(1 + z) (error cut).
In addition, for individual catalog, we define the flag tohomogenize the quality of the reference sample.
1. zCOSMOS bright: 3 ≤ CC ≤ 4 or CC = 2.4, 2.5 or 9.3 ≤CC ≤ 9.5
2. eBOSS : zWarning = 0 (no apparent issues)
3. GAMA : 4 ≤ NQ
4. UDSz : Flag = 3, 4, A, B or B∗.
5. DEEP2/3 : qFlag = 4 (> 99.5% confidence)
6. VANDELS : zflg > 2 (> 95% confident)
7. C3R2 : 3 ≤ Qual.
8. VVDS : ZFLAGS = 3 or 4
9. DEIMOS : Qf = 2
10. FMOS : zflag ≥ 1
11. LEGA-C : f_use = 1
12. PRIMUS : zquality ≥ 3
13. VIPERS : n + 2.6 < zflg < n + 4.6 where n = 0, 10, 20or 210.
14. WiggleZ : Qop ≥ 4
15. DEEP2/3 : redshift_flag ≥ 3
16. 2dFGRS : quality ≥ 3
17. 6dFGRS : sum of comparison flags is 0.
– Private spec-z data:In addition to the public spec-z catalogs, we combine private catalogs of COSMOS spec-z ’s (Mara Salvato, private communication) exclusively used for our photo-z calibration (the private catalog is not included in the HSC
PDR3).
– Multiband photo-z data:
In order to cover the deep photometric data of HSC, we
also combine COSMOS2015 multiband photo-z (Laigleet al. 2016).
Those spec-z catalogs are matched to the HSC
UltraDeep/Deep photometric catalog and subsequently
to the HSC Wide catalog which meet the following criteria,
1. isprimary is True (no duplicates)
2. [grizy]_cmodel_flux > 0
3. [grizy]_cmodel_fluxsigma > 0
The matching radius is taken to 1 arcsec.
The following quantities are then selected and/or computed:
1. Identifiers: ID, (ra,dec), and (tract,patch) coordinates, but these are confidential during the calibration.

2. Fluxes: PSF fluxes, cmodel fluxes, cmodel_exp fluxes,
cmodel_dev fluxes, and PSF-matched aperture fluxes
with target 1.3 arcsec PSF and 1.5 arcsec apertures, and undeblended PSF matched aperture flux.
We also provide the Galactic attenuation estimates(a_[grizy]).
3. Shapes: sdss_shape parameters.
4. Redshift: redshift, 1σ error when available, parent survey (SDSS, etc.).
5. Depth: flag for UltraDeep/Deep, and Wide photometry.
6. Emulated errors: emulated wide-depth photometricerrors for the objects which do not match to the Widelayer data. For each UltraDeep/Deep objects, we assign the mean of the photometric errors over wide layer
objects located in the nearest neighbors in the magnitude and color hyperspace.
7. Weights: We compute the specific weights such thatthe magnitude and magnitude error distribution of thetraining sample after applying the weights matches tothe one for the entire wide layer photometric target
sample (Lima et al. 2008). The weights are thus used
to optimize the photo-z to maximize the performanceof the target photometric sample, and then used topredict the expected performance of the photo-z forthe target sample.
8. cross-validation ID: We divide the training sample into
5 subset to conduct a cross validation.

3 Photo-z codes
In the HSC PDR3, photo-z catalogs based on one template fitting code Mizuki and empirical-method-based
code DEmP and deep neural network based code DNNz areavailable. Here, we summarize the method of each photoz code.

3.1 DEmPThe Direct Empirical Photometric code (DEmP) is anempirical quadratic polynomial photometric redshift fitting code. Details are described in Hsieh & Yee (2014)
and Tanaka et al. (2018). As in the previous releases, thephoto-z , stellar mass, and SFR are provided, and they
are computed from undeblended convolved fluxes independently. The photo-z, as well as stellar mass and SFR,
for each object is calculated using the 40 nearest neighbors in a ten-dimensional parameter space (5 magnitudeaxes, 4 color axes, and the size derived from shape SDSS).
There is no number of filters cut, i.e., the output products are provided for objects with even one-band-onlyPublications of the Astronomical Society of Japan, (2014), Vol. 00, No. 03photometry. The PDF of photo-z for each galaxy is generated using Monte Carlo technique and the bootstraping
method. We use Monte Carlo technique to generate 500
data sets based on the photometry and uncertainties of
the input galaxies to account for the effects due to photometric uncertainties. We then bootstrap the training
set for each input galaxy 500 times for each of the Monte
Carlo generated data set, to estimate the sampling effectin the training set.

shift bin spaning from z = 0 to 7. It can approximate thePDF distribution of the galaxy’s redshift. We provide thefull PDF and point statistics as usual and outlier probability predicted from the DNNz architecture. The outlier
probability can be used to eﬀiciently remove the outlier.
Since zRisk or zConf is calculated based on the integration of PDF but DNNz utilizes full shape of the PDF todescriminate the outliers (Nishizawa et al. in prep.).

3.2 Mizuki

4 Performance Evaluation

We use a template fitting-code mizuki. Details are described in Tanaka (2015) and Tanaka et al. (2018), buta brief outline is given here. The code uses a set of templates generated with the Bruzual & Charlot (2003) stellar population synthesis code assuming a Chabrier (2003)
IMF and Calzetti et al. (2000) dust attenuation curve.
Emission lines are added to the templates assuming solar metallicity (Inoue 2011). Template error functions
are incorporated in order to account for systematic offsets and uncertainties in the templates. We apply a set ofBayesian priors on the physical properties and let the priors depend on redshift to keep the template parameters
within realistic ranges to reduce the degeneracy in themulti-color space and also to let templates evolve withredshift in an observationally motivated way.
As in the PDR2, the PDF recalibration is applied following Bordoloi et al. (2010), which delivers a small improvement in the overall performance. We use the undeblended convolved fluxes scaled to the cmodel fluxes sothat they are reasonably close to the total fluxes.

All the statistics shown in this note is based on thephotoz_best, which outperforms traditional point estimates such as mean, median or mode (Tanaka et al.
2018). Exceptionally, only for DEmP, photoz_mode is usually more accurate than photoz_best and therefore theDEmP photo-z users may consider using photoz_mode, instead of photoz_best.

3.3 DNNz

P all-wide (g, r, i, z, y) =In PDR3, deep learning code, DNNz. DNNz architecture isconsist of multi-layer perceptorons with 5 hidden layers.
The input layers can handle every types of observable andwe use cmodel fluxes, undeblended convolved flux,
PSF fluxes and size derived from shape SDSS. In total,
we have (3 fluxes + 1 size) × 5 bands = 20 attributes.
All fluxes are converted to asinh magnitude so that itcoinside with AB magnitude at the bright end. magnitude correction due to i/i2 and r/r2 filter transmission
difference has been applied and magnitude offset derived
from the stellar locus have been also applied. We observethat adding size information slightly improve the overall
photo-z accuracy. For training, 3/5 of the training set
is used and 1/5 is used for validation. Rest of the 1/5
is used for the accuracy test presented in this note. We
have 100 nodes in the output layer where each of them
represents the probability of the galaxy lying at the red-4.1 Scatter plots
Here we show the performance tests with the same metric done in the PDR2 (Nishizawa et al. 2020) Figure 1
shows the object to object comparison between photo-z
and reference-z. Upper panels show the raw distribution
for the wide sample. Dashed lines are 15% limit. The second row shows the distribution with reweighted to theentire wide photometric sample. The weight has been
computed so that the matnitude distributions match to
the target sample,∑wi P calib (g,r,i,z,y).

(1)i

In practice, the weight can be calculated by the local object density in the multi-dimensional space of the magnitude for the target sample divided by the local densityof the calibration sample about the given object, withina given fixed radius (Lima et al. 2008). The third row
shows the close up of the distribution for bright sample (i-mag< 22.5). We see that some fraction of objects
in Mizuki is lying at zp = 0 and zs > 1.0, which may becaused by the confusion of stars and galaxies. For thelatter analysis, we remove the objects zp = 0 as they arereadily removed by users. We do not see such population both in DEmP and DNNz . The bottom row in Figure
1 shows the distribution of dud sample. We can see clear
reduction of the scatter and outliers, outside the dashedlines.

4Publications of the Astronomical Society of Japan, (2014), Vol. 00, No. 0

Fig. 1. One-to-one basis comparison between photo-z and reference-z. From left to right, Mizuki, DEmP and DNNz. Upper panels are raw
distribution for wide photo-z, second row is reweighted to the entire wide photometric sample, third row is raw distribution but limited tosample brighter than imag 22.5 and the bottom row is raw dud distribution.

Publications of the Astronomical Society of Japan, (2014), Vol. 00, No. 0

4.2 statistics on the point estimates
Figures 2 shows the mean bias, scatter and outlier rate
as a function of i-band cut, i.e. the sample brighter
than the values in the horizontal axis is selected. As
described in the previous section, we remove the objects
zp = 0 for Mizuki . Upper panels are for wide sample
and lower sample for dud sample. ML based methods,DEmP and DNNz show consistent accuracy for all statistics
except that the sign of the bias is positive for DNNz but
negative for DEmP . Mizuki shows slightly larger bias andscatter but the outlier rate is almost consistent with others.

4.3 N(z) distribution
In various scientific cases, instead of the individual
galaxy’s photo-z, the redshift distribution for selectedsubsample is of great importance. Here in figure 4, weshow the redshift distribution for the tomographic binned
subsamples, where the bins are defined by the HSC-Y1
cosmic shear analysis (Hikage et al. 2019). The redshiftbinning is z = [0.0, 0.3, 0.6, 0.9, 1.2]. The sample is definedusing photoz_best for each code. Mizuki and DEmP spansredshift from 0 to 7 into 700 bins so that they capture
the detailed shape of the PDF, while the DNNz only have
100 bins but overall shape is consistent with others. We
confirm that for DNNz , 100 bins are suﬀicient for predicting point estimate and finner binning does not improve
the accuracy statistics. Figure 4 shows the stacked PDF
distribution of the tomographic subsamples. The distributions are normalized so that the maximum becomes
unity. Shaded and dashed lines are raw distribution fortest sample and reweighted distribution, respectively.

4.4 Tests on PDF
The quality of the PDF can be quantified using probability integral transform (PIT). The PIT analysis evaluates that the error of the photo-z is correctly reflectedin the PDF. When the PDF is properly calibrated, thehistogram will become flat distribution. However, if thePDF is narrow and the photo-z error is underestimated,
the PIT distribution will have peaks near 0 and 1 while
the PDF overestimates the error, PIT will have peak near
0.5. Figure 5 shows the PIT distributions for wide (upperpanel) and dud (lower). For the wide sample, DEmP andDNNz shows fairly similar shape while the Mizuki seem tohave slope toward higher value. The interpretation ofthis behavior is not trivial but at least we can observethat there are two peaks at PIT=0 and 1, which indicates the underestimation of the photo-z error. DEmP and5DNNz also shows similar features but the effect is marginal.
For the DUD sample, the PIT distribution is fairly flat
which suggests that the PDF is well calibrated except forthe spikes at 0 and 1.
All of the catalog products such as photo-z point estimates are available in the database. The full PDFs are
stored in the fits format and are available from the photoz page of the PDR3 site; https://hsc-release.mtk.
nao.ac.jp/. Tables 1 and 2 shows the available photo-z
quantities and number of objects in the database.

References
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Baldry I. K. et al., 2018, MNRAS, 474, 3875
Bordoloi R., Lilly S. J., Amara A., 2010, MNRAS, 406, 881
Bradshaw E. J. et al., 2013, MNRAS, 433, 194
Bruzual G., Charlot S., 2003, MNRAS, 344, 1000
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Chabrier G., 2003, PASP, 115, 763
Coil A. L., Weiner B. J., Holz D. E., Cooper M. C., Yan R.,
Aird J., 2011, ApJ, 743, 46
Colless M. et al., 2001, MNRAS, 328, 1039
Cool R. J. et al., 2013, ApJ, 767, 118
Cooper M. C. et al., 2011, ApJS, 193, 14
Cooper M. C. et al., 2012, MNRAS, 419, 3018
Davis M. et al., 2003, Society of Photo-Optical Instrumentation
Engineers (SPIE) Conference Series, Vol. 4834, Science
Objectives and Early Results of the DEEP2 Redshift
Survey, Guhathakurta P., ed., pp. 161–172
Drinkwater M. J. et al., 2010, MNRAS, 401, 1429
Hasinger G. et al., 2018, ApJ, 858, 77
Hikage C. et al., 2019, PASJ, 71, 43
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6Publications of the Astronomical Society of Japan, (2014), Vol. 00, No. 0Fig. 2. photo-z statistics as a function of i-band magnitude cut, i.e. the horizontal axis denotes the faintest magnitude of the subsample.
From left to right, mean bias, scatter and outlier rate. DEmP and DNNz shows well consistent accuracy while they are oppositely biased.

Fig. 3. Same as Fig. 2 but as a function of the photo-z.

Publications of the Astronomical Society of Japan, (2014), Vol. 00, No. 0

Fig. 4. dNdz distributions for binned samples. Shaded and dashed lines are for raw test sample and reweighted sample, respectively.

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8Publications of the Astronomical Society of Japan, (2014), Vol. 00, No. 0

key

description

object_id
photoz_X
photoz_mc
photoz_conf_X
photoz_risk_X
photoz_std_X
photoz_err68_min
photoz_err68_max
photoz_err95_min
photoz_err95_max

unique object id to be used to join with the photometry tables
Photo-z point estimate where X is either mean, mode, median, or best
Monte Carlo draw from the full PDF
Photo-z confidence value for photoz_X, defined by equation (15) of PDR1 paper
Risk parameter for photoz_X, defined by equation (13) of PDR1 paper
Second order moment around a point estimate (photoz_X) derived from full PDF.
16 % percentile in the PDF
84 % percentile in the PDF
2.5 % percentile in the PDF
97.5 % percentile in the PDF

Table 1. Common photo-z quantities available for all the codes.

CODE

target selection

number of objects

MizukiDEmP

detect_is_primary is True
objects with CModel fluxes in at least three bands
detect_is_primary is True

DNNz

detect_is_primary is True

214,484,923 (Wide)
18,383,344 (Deep/UltraDeep)
507,215,723 (Wide)
19,051,243 (Deep/UltraDeep)
507,215,729 (Wide)
19,051,243 (Deep/UltraDeep)

Table 2. Target selection and number of entries in the database.

Fig. 5. The PIT distribution for wide (Top) and dud (Bottom).
Horizontal dotted lines are just for guiding eyes.