Publ. Astron. Soc. Japan (2022) 74(1), 1–4
doi: 10.1093/pasj/psab0??

Erratum: Cosmological constraints from cosmic
shear two-point correlation functions with HSC
survey first-year data
Takashi H AMANA1,2 , Masato S HIRASAKI1 , Satoshi M IYAZAKI1,2 , Chiaki
H IKAGE3 , Masamune O GURI4,5,3 , Surhud M ORE6,3 , Robert A RMSTRONG7 ,Alexie L EAUTHAUD8 , Rachel M ANDELBAUM9 , Hironao M IYATAKE10,11,3,12 ,Atsushi J. N ISHIZAWA10,11 , Melanie S IMET13,12 , Masahiro TAKADA3 , Hiroaki
A IHARA5 , James B OSCH14 , Yutaka KOMIYAMA1,2 , Robert L UPTON14 , Hitoshi
M URAYAMA3,15,16 , Michael A. S TRAUSS14 and Masayuki TANAKA1
1National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, JapanThe Graduate University for Advanced Studies, SOKENDAI, 2-21-1 Osawa, Mitaka, Tokyo
181-8588, Japan
3
Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU, WPI), The
University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa, Chiba 277-8583, Japan
4
Research Center for the Early Universe, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku,Tokyo 113-0033, Japan
5
Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033,
Japan
6
The Inter-University Center for Astronomy and Astrophysics, Post bag 4, Ganeshkhind,Pune, 411007, India
7
Lawrence Livermore National Laboratory, Livermore, CA 94551, USA
8
University of California Santa Cruz, 1156 High St., Santa Cruz, CA 95064, USA
9
McWilliams Center for Cosmology, Department of Physics, Carnegie Mellon University,
Pittsburgh, PA 15213, USA
10
Institute for Advanced Research, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi
464-8602, Japan
11
Division of Particle and Astrophysical Science, Graduate School of Science, Nagoya
University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8602, Aichi, Japan12
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive,Pasadena, CA 91109, USA
13
University of California, Riverside, 900 University Avenue, Riverside, CA 92521, USA
14
Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ08544, USA
15
Department of Physics and Center for Japanese Studies, University of California, Berkeley,CA 94720, USA
16
Theoretical Physics Group, Lawrence Berkeley National Laboratory, MS 50A-5104,Berkeley, CA 94720, USA2Received ; Accepted

Key words: Errata, addenda — cosmology: observations — cosmological parameters — dark matter —c 2022. Astronomical Society of Japan.

12Publications of the Astronomical Society of Japan, (2022), Vol. 74, No. 1

large-scale structure of universe

Fig. 1. Marginalized posterior contours (68% and 95% confidence levels)in the Ωm –σ8 plane (top panel) and in the Ωm –S8 plane (bottom panel),p
where S8 = σ8 Ωm /0.3 in the fiducial flat ΛCDM model.

Table 1. Summary of revised constraints (mean and 68% confidence interval) on the cosmological parameters derived from thefiducial flat ΛCDM model with the incorrect original version’s results.

S 8 = σ8Ωmσ8pΩm /0.3

Error
0.804+0.032−0.0290.346+0.052−0.1000.766+0.110−0.098Correction
0.823+0.032−0.0280.332+0.050−0.096
0.799+0.112−0.101In the original publication of “Cosmological constraints
from cosmic shear two-point correlation functions with
HSC survey first-year data” [PASJ, 72, 16 (2020); doi:
10.1093/pasj/psz138], we discovered a couple of bugs inthe software used for numerical computations. Here wepresent revised results obtained from corrected computations.

The first bug affects the fiducial model adopted in thisstudy. We found that an incorrect numerical coefficient
was used in the code to compute the fitting function of
the nonlinear matter power spectrum, given by Takahashi
et al. (2012) as an improvement to the halofit model ofSmith et al. (2003). Owing to this bug, the nonlinear matter power spectrum at quasi-nonlinear scales was overestimated by >8%, leading to an overestimation of the cosmic
shear two-point correlation function (TPCF) of approximately 6% on scales used in this study. This results inp
an underestimation of S8 = σ8 Ωm /0.3 by about 2%–3%which is the parameter of our primary interest. Figure 1shows the marginalized posterior contours in the Ωm –σ8and Ωm –S8 planes obtained from the corrected computation of the fiducial model. Figure 2 shows the marginalized
one-dimensional posterior distributions for model parameters (three top rows) in the fiducial flat ΛCDM model,and derived parameters (bottom row). Marginalized onedimensional constraints are (mean and 68% confidence in+0.050terval) found to be S8 = 0.823+0.032−0.028 , Ωm = 0.332−0.096 , and+0.112
σ8 = 0.799−0.101 (see table 1 for changes from the incorrect
original version’s results). We have explicitly confirmedthat the rest of our conclusions remain unchanged and,especially, the fact that astrophysical modeling uncertainties and systematic ones in measurements do not have asignificant impact on the cosmological constraints. This isbecause all the systematic tests were affected by the bugin a consistent manner.
In figure 3, our revised constraint on S8 from the fiducial ΛCDM model is compared with other results in theliterature. Since the revised result of S8 is larger thanthe original version’s one by about +0.02, we find that itbetter overlaps with the Planck 2018 CMB result (PlanckCollaboration 2020, TT + TE + EE + lowE without CMBlensing) as well as the Planck 2015 CMB result. On theother hand, our revised result is located on the higher
side among recent cosmic shear studies, and the KiDS +VIKING-450 (Hildebrandt et al. 2020) result is lower thanour result by ∼2 σ.
In addition to the main cosmological inference describedabove, there is another analysis that was affected by thefirst bug. It is the analysis of the cross correlation between cosmological constraints obtained from this study
and the cosmic shear power spectrum (PS) analysis byHikage et al. (2019) that used the same HSC 1st year data
but derived cosmological constraints overlap only mildlywith our constraints as is seen in figure 3. The analysis was based on cosmological inferences on 100 realisticPublications of the Astronomical Society of Japan, (2022), Vol. 74, No. 13Fig. 2. The upper three rows show the marginalized one-dimensional posterior distributions of model parameters in the fiducial flat ΛCDM model; the cosmological parameters are in the top-row, and the astrophysical and systematics parameters are in two middle rows. Three panels in the bottom-row are forderived parameters. For parameters with flat prior ranges, the plotted range of the horizontal-axis indicates its prior range. For parameters with Gaussianpriors, Gaussian priors are shown by the dashed curves. Dotted vertical lines represent the approximate 68% confidence intervals, which are not shown forpoorly constrained parameters.

Fig. 3. 68% confidence intervals of marginalized posterior distributions ofp
S8 = σ8 Ωm /0.3. Our result from the fiducial ΛCDM model is compared with other results in the literature, HSC first year cosmic shear
power spectra (Hikage et al. 2019, labeled as HSC-Y1 PS), DES-Y1 cosmic
shear TPCFs (Troxel et al. 2018), KiDS+VIKING-450 cosmic shear TPCFs(Hildebrandt et al. 2020), and Planck 2018 CMB (Planck Collaboration 2020,
TT+TE+EE+lowE), and Planck 2015 CMB (Planck Collaboration 2016, TT+ lowP without lensing). Since different studies adopt different definitionsof the central values (mean, median, or peak of the posterior distribution),
central values are not shown to avoid possible misunderstanding.

HSC mock catalogs using softwares of the two studies (seesubsection 6.7 of the original version for details), and wehave re-done the cosmological inferences using the corrected software. Figure 4 shows the revised scatter plot
comparing S8 values from these two cosmological analyses
on the same mock catalogs. Comparing the original version’s results, the points are moved to up by 0.005–0.022.
Revised statistics are as follows: for S8 , eight cases out ofone hundred have a difference ∆S8 = S8 (PS) − S8 (TPCF)
less than the observed value of −0.042, and for Ωm , seventeen cases out of one hundred have a difference ∆Ωmless than the observed difference of −0.16. If we take thetwo-side estimate, we find that for S8 (Ωm ), twelve (nineteen) cases out of one hundred have an absolute differenceof |∆S8 | > 0.042 (|∆Ωm | > 0.16). These mean that thesedifferences can be explained by a statistical fluctuation atthe ∼1.6 σ level, which is slightly larger than the originalvalue of ∼1.4σ. The revised correlation coefficients definedin equation (23) of the original version are r(S8 ) = 0.51 and4Publications of the Astronomical Society of Japan, (2022), Vol. 74, No. 1

Fig. 4. Scatter plot showing median values of marginalized one-dimensional
posterior distributions of S8 derived from cosmological analyses on 100
mock catalogs. Results from the power spectrum (PS) analysis by Hikage
et al. (2019) are compared with ones from the two-point correlation function(TPCF) analysis in this study. The red cross shows the value of S8 adopted
in generating the mock catalogs. (Color online)

Fig. 5. Marginalized one-dimensional posterior distributions of the baryon
feedback model parameter AB derived from non-fiducial models, the “ABvaried” setup.

r(Ωm ) = 0.17. Since the changes of the above correlation
coefficients are not significant, the original conclusion thatthe correlation between derived cosmological constraints
from the two analyses is weak remains unchanged.
The second bug affects one of the ancillary models
tested in this study to test the effect of baryons on thematter power spectrum based on the fitting function derived by Harnois-Déraps et al. (2015) with an additional
nuisance parameter (AB ) that controls the strength. In
addition to the first bug mentioned above, we also incor-

rectly set an upper limit to the modification of the matter
power spectrum by the baryon effect. As a consequence,for cases with negative AB values which are expected toenhance the power spectrum at nonlinear scales, were notleading to an appropriate modification to the power spectrum, resulting in a smaller effect and a higher likelihood.
The corrected result of the marginalized one-dimensional
posterior distributions of AB derived from the “AB varied” setup, is shown in figure 5, where a shape cut-off at
AB < 0 is seen. The revised confidence interval (mean andσ) is found to be AB = 1.2 ± 0.9 (cf. the original version’s
result AB = −1.8 ± 1.8). Note that this does not significantly change any other results in this study, because theeffect of baryons on the cosmological inference is weak. Infact, the revised confidence interval of S8 from “AB varied”
setup is S8 = 0.829+0.032−0.030 which agrees well with one fromthe fiducial case S8 = 0.823+0.032−0.028 . Therefore, the original
version’s conclusion that the impact of the baryon effecton cosmological constraints is not significant remains unchanged.
Finally, we comment on the impact of our recomputations on the original blinding cosmological analysis that aims to avoid confirmation bias. The bugs wereoriginally found by a non-coauthor who inspected a sourcecode of our software in his cross-checking work of an independent software. Then we fixed the bugs and re-did computations without changing any analysis setup. Therefore,
we consider that the results of re-computations are notaffected by any confirmation bias.
A modified version of the original publication, including the corrected results and figures, is available athttps://arxiv.org/abs/1906.06041, or, upon request, directly from the corresponding author (TH). The revised
chains are available on the HSC SSP website.1
We thank Y. Okochi for finding out the mistake in anumerical calculation program.

References
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Hikage, C., et al. 2019, PASJ, 71, 43
Hildebrandt, H., et al. 2020, A&A, 633, A69
Planck Collaboration 2016, A&A, 594, A13
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Smith, R. E., et al. 2003, MNRAS, 341, 1311
Takahashi, R., Sato, M., Nishimichi, T., Taruya, A., & Oguri,M. 2012, ApJ, 761, 152
Troxel, M. A., et al. 2018, Phys. Rev. D, 98, 043528

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hhttps://hsc.mtk.nao.ac.jp/ssp/i.