First Constraints on Growth Rate from Redshift-space Ellipticity Correlations of SDSS Galaxies at 0.16 < z < 0.70

Akitsu, K., Li, Y., & Okumura, T. 2021, JCAP, 2021, 041

Alam, S., Ata, M., Bailey, S., et al. 2017, MNRAS, 470, 2617

Bernstein, G. M., & Jarvis, M. 2002, AJ, 123, 583

Blazek, J. A., MacCrann, N., Troxel, M. A., & Fang, X. 2019, PhRvD, 100,

103506

Bridle, S., & King, L. 2007, NJPh, 9, 444

Catelan, P., Kamionkowski, M., & Blandford, R. D. 2001, MNRAS, 320, L7

Chisari, N. E., & Dvorkin, C. 2013, JCAP, 12, 029

Chuang, Y.-T., Okumura, T., & Shirasaki, M. 2022, MNRAS, 515, 4464

Croft, R. A. C., & Metzler, C. A. 2000, ApJ, 545, 561

DESI Collaboration, Aghamousa, A., Aguilar, J., et al. 2016, arXiv:1611.

00036

Eisenstein, D. J., Annis, J., Gunn, J. E., et al. 2001, AJ, 122, 2267

Eisenstein, D. J., Zehavi, I., Hogg, D. W., et al. 2005, ApJ, 633, 560

Hahn, O., Angulo, R. E., & Abel, T. 2015, MNRAS, 454, 3920

Heavens, A., Refregier, A., & Heymans, C. 2000, MNRAS, 319, 649

Hikage, C., Oguri, M., Hamana, T., et al. 2019, PASJ, 71, 43

Hirata, C., & Seljak, U. 2003, MNRAS, 343, 459

Hirata, C. M., & Seljak, U. 2004, PhRvD, 70, 063526

Joachimi, B., Mandelbaum, R., Abdalla, F. B., & Bridle, S. L. 2011, A&A,

527, A26

Kaiser, N. 1987, MNRAS, 227, 1

Kurita, T., & Takada, M. 2022, PhRvD, 105, 123501

Kurita, T., Takada, M., Nishimichi, T., et al. 2021, MNRAS, 501, 833

Landy, S. D., & Szalay, A. S. 1993, ApJ, 412, 64

Lee, J., Ryu, S., & Baldi, M. 2022, ApJ, 945, 15

Li, C., Jing, Y. P., Faltenbacher, A., & Wang, J. 2013, ApJL, 770, L12

Mandelbaum, R., Hirata, C. M., Ishak, M., Seljak, U., & Brinkmann, J. 2006,

MNRAS, 367, 611

Matsubara, T. 2022, arXiv:2210.10435

Okumura, T., & Jing, Y. P. 2009, ApJL, 694, L83

Okumura, T., & Jing, Y. P. 2011, ApJ, 726, 5

Okumura, T., Jing, Y. P., & Li, C. 2009, ApJ, 694, 214

Okumura, T., & Taruya, A. 2020, MNRAS, 493, L124

Okumura, T., & Taruya, A. 2022, PhRvD, 106, 043523

Okumura, T., Taruya, A., & Nishimichi, T. 2019, PhRvD, 100, 103507

Okumura, T., Taruya, A., & Nishimichi, T. 2020, MNRAS, 494, 694

Planck Collaboration, Aghanim, N., Akrami, Y., et al. 2020, A&A, 641, A6

Reid, B., Ho, S., Padmanabhan, N., et al. 2016, MNRAS, 455, 1553

Saga, S., Okumura, T., Taruya, A., & Inoue, T. 2023, MNRAS, 518, 4976

Samushia, L., Percival, W. J., & Raccanelli, A. 2012, MNRAS, 420, 2102

Schmidt, F., Chisari, N. E., & Dvorkin, C. 2015, JCAP, 10, 032

Scoccimarro, R. 2004, PhRvD, 70, 083007

Seljak, U., Hamaus, N., & Desjacques, V. 2009, PhRvL, 103, 091303

Singh, S., & Mandelbaum, R. 2016, MNRAS, 457, 2301

Singh, S., Mandelbaum, R., & More, S. 2015, MNRAS, 450, 2195

Takada, M., Ellis, R. S., Chiba, M., et al. 2014, PASJ, 66, 1

Takahashi, R., Sato, M., Nishimichi, T., Taruya, A., & Oguri, M. 2012, ApJ,

761, 152

Taruya, A., Nishimichi, T., & Saito, S. 2010, PhRvD, 82, 063522

Taruya, A., Nishimichi, T., Saito, S., & Hiramatsu, T. 2009, PhRvD, 80,

123503

Taruya, A., & Okumura, T. 2020, ApJL, 891, L42

Tonegawa, M., & Okumura, T. 2022, ApJL, 924, L3

Vlah, Z., Chisari, N. E., & Schmidt, F. 2020, JCAP, 1, 025

Zwetsloot, K., & Chisari, N. E. 2022, MNRAS, 516, 787

Appendix B

Effect of PSF on Parameter Constraints

As described in Section 2, the ellipticity of LRG is defined

by the isophote of the light profile while that of LOWZ and

CMASS galaxies is by the adaptive moment. Singh &

Mandelbaum (2016) constructed the shape catalog for the

LRG and LOWZ samples using a re-Gaussianization technique, which is based on the adaptive moment but involves

additional steps to correct for non-Gaussianity of both the PSF

and galaxy surface brightness profile (Hirata & Seljak 2003).

Utilizing it, Singh & Mandelbaum (2016) found that while the

isophotal shape is not corrected for the PSF, the measured IA

statistics are not so biased because the method uses the outer

shape of the galaxies. Eventually, the uncorrected PSF affects

only the amplitude of the measured IA statistics, not the shape,

which has already been confirmed by our earlier work

(Okumura et al. 2009). Furthermore, Okumura & Jing (2009)

showed that the amplitude of IA, namely the shape bias bK,

determined by the GI and II correlations is fully consistent with

each other. Therefore, while the constraint on bK can be

different from the true value, that on the growth rate f is not

expected to be biased after bK is marginalized over. While the

adaptive moment corrects for the PSF in the ellipticity, it results

in a small bias (Hirata & Seljak 2003). However, it is a constant

bias, and thus it affects the amplitude of bK , similarly to the

isophotal shape definition but the effect is smaller. To be

conservative, we exclude the II correlation at r > 25 h−1 Mpc,

which is affected if we adopt the less accurate, de Vaucouleurs

model fit (Singh & Mandelbaum 2016). Namely, the

constraints from LOWZ and CMASS samples on fσ8 with

rmin = 25 h-1 Mpc in Figure 5 do not use the data of the II

correlation., Nevertheless, the constraints are almost equivalent

to those with rmin = 15 h-1 Mpc. It implies that the bias that

arises from the uncorrected PSF is negligible for the shape

definition of LOWZ and CMASS galaxies.

For all the three galaxy samples, constrained values of the

model parameters do not change significantly by combining the

IA statistics with the clustering statistics but shrink the error

bars. It demonstrates that systematic effects associated with the

shape measurement do not contribute to biases in the parameter

...