HOLISMOKES

S. Schuldt; S. H. Suyu; T. Meinhardt; L. Leal-Taixé; R. Cañameras; S. Taubenberger; A. Halkola

doi:10.1051/0004-6361/202039574e

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A&A, 664 (2022) C2

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Erratum

This article is an erratum for:
[https://doi.org/10.1051/0004-6361/202039574]

Issue		A&A Volume 664, August 2022


Article Number		C2
Number of page(s)		1
Section		Cosmology (including clusters of galaxies)
DOI		https://doi.org/10.1051/0004-6361/202039574e
Published online		24 August 2022

A&A 664, C2 (2022)

IV. Efficient mass modeling of strong lenses through deep learning (Corrigendum)

S. Schuldt¹^,2, S. H. Suyu¹^,2^,3, T. Meinhardt⁴, L. Leal-Taixé⁴, R. Cañameras¹, S. Taubenberger¹ and A. Halkola⁵

¹ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild Str. 1, 85748 Garching, Germany
e-mail: schuldt@mpa-garching.mpg.de
² Physik Department, Technische Universität München, James-Franck Str. 1, 85748 Garching, Germany
³ Institute of Astronomy and Astrophysics, Academia Sinica, 11F of ASMAB, No.1, Section 4, Roosevelt Road, Taipei 10617, Taiwan
⁴ Informatik Department, Technische Universität München, Bolzmannstr. 3, 85741 Garching, Germany
⁵ Pyörrekuja 5 A, FI-04300 Tuusula, Finland

Key words: gravitational lensing: strong / methods: data analysis / errata, addenda

Erratum for: A&A, 646, A126 (2020), https://doi.org/10.1051/0004-6361/202039574

In this erratum, we would like to correct a typographical mistake in Eq. (5) from Schuldt et al. (2021) that converts the complex ellipticity of an ellipse into its axis ratio q and position angle θ. Eq. (4) from Schuldt et al. (2021) gives the definition of the complex ellipticity as

$\begin{matrix} e_{x} & = \frac{1 - q^{2}}{1 + q^{2}} cos (2 θ), \\ e_{y} & = \frac{1 - q^{2}}{1 + q^{2}} sin (2 θ), \end{matrix}$ $\begin{aligned} e_x&=\frac{1-q^2}{1+q^2} \, \cos (2\theta ), \nonumber \\ e_y&=\frac{1-q^2}{1+q^2} \, \sin (2\theta ), \end{aligned}$ (1)

which was used throughout the published article. For completeness, we gave a back transformation of the complex ellipticity into the axis ratio q and the position angle θ in Eq. (5). The expression for the axis ratio q ∈ (0, 1] is correct,

$\begin{matrix} q = \sqrt{\frac{1 - \sqrt{e_{x}^{2} + e_{y}^{2}}}{1 + \sqrt{e_{x}^{2} + e_{y}^{2}}}} . \end{matrix}$ $\begin{aligned} q = \sqrt{\frac{1-\sqrt{e_x^2+e_y^2}}{1+\sqrt{e_x^2+e_y^2}}}\, . \end{aligned}$ (2)

The error concerns the second part, the position angle θ ∈ [0, π), defined counter-clockwise with respect to the positive x-axis. According to Eq. (1) of this erratum, the cosine function corresponds to e _x and the sine function corresponds to e _y, which was unfortunately switched for the back transformation. A clearer and correct transformation is given by

$\begin{matrix} θ = {\begin{matrix} f & if e_{x} \geq 0 and e_{y} \geq 0 \\ f + π & if e_{x} \geq 0 and e_{y} < 0 \\ \frac{1}{2} π - f & if e_{x} < 0 \end{matrix} \end{matrix}$ $\begin{aligned} \theta = \left\{ \!\begin{array}{cc} f&\text{ if } e_{\mathrm{x}} \ge 0 \text{ and } e_\text{ y} \ge 0\\ f + \pi&\text{ if } e_{\mathrm{x}} \ge 0 \text{ and } e_\text{y} < 0\\ \frac{1}{2}\pi -f&\text{ if } e_\text{x} < 0 \end{array} \right. \end{aligned}$ (3)

with

$\begin{matrix} f = \frac{1}{2} arcsin (e_{y} \frac{1 + q^{2}}{1 - q^{2}}) \end{matrix}$ $\begin{aligned} f = \frac{1}{2} \arcsin \left( e_\text{y} \frac{1+q^2}{1-q^2} \right) \, \end{aligned}$ (4)

and

$\begin{matrix} f \in [- π / 4, + π / 4] . \end{matrix}$ $\begin{aligned} f \in [-\pi /4, +\pi /4]. \end{aligned}$ (5)

Since we only used Eq. (1) (i.e., Eq. (4) from Schuldt et al. 2021) to transform the axis ratio q and position angle θ of our mock lenses into the complex parameterization for training the networks, and as we worked from then on in complex notation, we never used the back transformation. Therefore, this mistake does not affect any results in Schuldt et al. (2021).

References

Schuldt, S., Suyu, S. H., Meinhardt, T., et al. 2021, A&A, 646, A126 [EDP Sciences] [Google Scholar]

Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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[1] Schuldt, S., Suyu, S. H., Meinhardt, T., et al. 2021, A&A, 646, A126 [EDP Sciences] [Google Scholar]