Euclid preparation. LXXIV. Euclidised observations of Hubble Frontier Fields and CLASH galaxy clusters

TL;DR

This paper introduces a Python tool to create realistic Euclid-like images from HST data, enabling simulations for galaxy cluster studies, lensing analysis, and survey planning, thus aiding preparation for Euclid mission data analysis.

Contribution

The authors developed HST2EUCLID, a novel Python code that generates realistic Euclid mock images from HST observations, facilitating various scientific applications and survey preparations.

Findings

Simulated Euclid images incorporate real observational complexity.

Estimated galaxy counts and size distributions for Euclid fields.

Previewed strong lensing systems in Euclid survey regions.

Abstract

We present HST2EUCLID, a novel Python code to generate Euclid realistic mock images in the $H_{\rm E}$, $J_{\rm E}$, $Y_{\rm E}$, and $I_{\rm E}$ photometric bands based on panchromatic Hubble Space Telescope observations. The software was used to create a simulated database of Euclid images for the 27 galaxy clusters observed during the Cluster Lensing And Supernova survey with Hubble (CLASH) and the Hubble Frontier Fields (HFF) program. Since the mock images were generated from real observations, they incorporate, by construction, all the complexity of the observed galaxy clusters. The simulated Euclid data of the galaxy cluster MACS J0416.1$-$2403 were then used to explore the possibility of developing strong lensing models based on the Euclid data. In this context, complementary photometric or spectroscopic follow-up campaigns are required to measure the redshifts of multiple images and cluster member galaxies. By Euclidising six parallel blank fields obtained during the HFF program, we provide an estimate of the number of galaxies detectable in Euclid images per ${\rm deg}^2$ per magnitude bin (number counts) and the distribution of the galaxy sizes. Finally, we present a preview of the Chandra Deep Field South that will be observed during the Euclid Deep Survey and two examples of galaxy-scale strong lensing systems residing in regions of the sky covered by the Euclid Wide Survey. The methodology developed in this work lends itself to several additional applications, as simulated Euclid fields based on HST (or JWST) imaging with extensive spectroscopic information can be used to validate the feasibility of legacy science cases or to train deep learning techniques in advance, thus preparing for a timely exploitation of the Euclid Survey data.

Tables

Table 1. Table 1: Relevant quantities of the EWS.

Euclid wide survey (EWS)
Euclid band	${𝒕}_{\mathrm{𝐞𝐱𝐩}}$	${𝒎}_{\mathrm{𝐥𝐢𝐦}}$	${\mathrm{𝐒𝐍}}_{\mathrm{𝐥𝐢𝐦}}$	Aperture size	${𝑵}_{\mathrm{𝐚𝐩}}^{\mathrm{𝐩𝐱}}$
${𝑰}_{𝐄}$	2280 s	24.5	15.9	$r=0.″65$	132.7
${𝒀}_{𝐄}$	448 s	24	6.5	$0.″9\times 0.″9$	9
${𝑱}_{𝐄}$	448 s	24	7.8	$0.″9\times 0.″9$	9
${𝑯}_{𝐄}$	448 s	24	7.2	$0.″9\times 0.″9$	9

Equations

$$f[\mathrm{erg}{\mathrm{s}}^{-1}{\mathrm{cm}}^{-2}{\mathrm{Hz}}^{-1}]=F[\mathrm{e}{\mathrm{s}}^{-1}]\times 10^{-0.4\left({\mathrm{ZP}}_{\mathrm{HST}}+48.6\right)},$$

$$\begin{gathered} {\mathrm{ZP}}_{\mathrm{HST}}=-2.5\mathrm{lo}{\mathrm{g}}_{10}\left(\text{PHOTFLAM}\right) \\ -5\mathrm{lo}{\mathrm{g}}_{10}\left(\text{PHOTPLAM}\right)-2.4079. \end{gathered}$$

$$F_{\mathrm{Q}}=\sum _{j=1}^N{w}_j{F}_{{\mathrm{R}}_j}={\mathbf{w}}^{\mathrm{T}}{\mathbf{F}}_{\mathbf{R}},$$

$$f(\lambda )=\sum _{i=1}^N{k}_i{f}_i(\lambda )=\frac{c}{{\lambda }^2}\sum _{i=1}^N{k}_i{f}_i(\nu ).$$

$$f_i(\lambda )=(c/{\lambda }^2)f_i(\nu ),$$

$$F_{{\mathrm{R}}_j}=\sum _i{\mathcal{R}}_{ij}{k}_i,\mathrm{or}{\mathbf{F}}_{\mathbf{R}}=\mathcal{R}\mathbf{k},$$

$$F_{\mathrm{Q}}=\sum _i{q}_i{k}_i={\mathbf{q}}^{\mathrm{T}}\mathbf{k},$$

$${\mathcal{R}}_{ij}$$

$$q_i$$

$$F_{\mathrm{Q}}={\mathbf{q}}^{\mathrm{T}}\mathbf{k}={\mathbf{q}}^{\mathrm{T}}{\mathcal{R}}^{-1}{\mathbf{F}}_{\mathbf{R}}.$$

$$\mathbf{w}=({\mathbf{q}}^{\mathrm{T}}{\mathcal{R}}^{-1}{)}^{\mathrm{T}}={\mathcal{R}}^{-\mathrm{T}}\mathbf{q}.$$

$$w_{F606W\to I_{\mathrm{E}}}$$

$$w_{F814W\to I_{\mathrm{E}}}$$

$$w_{F125W\to J_{\mathrm{E}}}$$

$$w_{F160W\to J_{\mathrm{E}}}$$

$$\begin{gathered} {\mathrm{BK}}_{\mathrm{sky}}[\mathrm{e}{\mathrm{s}}^{-1}]=\left\{{\left(F_{\lim }[\mathrm{e}{\mathrm{s}}^{-1}]\right)}^2\times t_{\exp }\times {\left({\mathrm{SN}}_{\lim }\right)}^{-2}-F_{\lim }[\mathrm{e}{\mathrm{s}}^{-1}]\right\} \\ \times {\left(N_{\mathrm{ap}}^{\mathrm{px}}\right)}^{-1}, \end{gathered}$$

$$F_{\lim }[\mathrm{e}{\mathrm{s}}^{-1}]=10^{0.4\left({\mathrm{ZP}}_{\mathrm{Euclid}}-m_{\lim }\right)}.$$

$${\varphi }_{\mathrm{tot}}=\sum _{i=1}^{N_{\mathrm{h}}}{\varphi }_i^{\mathrm{halo}}+\sum _{j=1}^{N_{\mathrm{G}}}{\varphi }_j^{\mathrm{gas}}+\sum _{k=1}^{N_{\mathrm{g}}}{\varphi }_k^{\mathrm{gal}}+{\varphi }^{\mathrm{fg}}.$$

$${\chi }^2(\mathbf{\xi }):=\sum _{j=1}^{N_{\mathrm{sou}}}\sum _{i=1}^{N_{\mathrm{im}}^j}{\left(\frac{\Vert {\mathbf{x}}_{i,j}^{\mathrm{obs}}-{\mathbf{x}}_{i,j}^{\mathrm{pred}}(\mathbf{\xi })\Vert }{\Delta x_{i,j}}\right)}^2,$$

$${\Delta }_{\mathrm{RMS}}=\sqrt{\frac{1}{N_{\mathrm{im}}^{\mathrm{tot}}}\sum _{i=1}^{N_{\mathrm{im}}^{\mathrm{tot}}}{\Vert {\mathbf{x}}_i^{\mathrm{pred}}-{\mathbf{x}}_i^{\mathrm{obs}}\Vert }^2},$$

Full text

1 Introduction

Galaxy clusters, the most powerful gravitational lenses in the Universe, can distort dozens of background sources simultaneously, producing gravitational arcs and multiple images (e.g. Bergamini et al., 2021). Researchers routinely use these features to constrain the total mass distribution in cluster cores.

Various algorithms, including parametric and free form methods, have been developed for this task (e.g. Kneib et al., 1993; Bradač et al., 2005; Diego et al., 2005; Liesenborgs et al., 2006; Coe et al., 2008; Jullo et al., 2007; Zitrin & Broadhurst, 2009; Oguri, 2010; Zitrin et al., 2013; Lam et al., 2014). Parametric models represent the cluster’s total mass distribution as a collection of mass components, each characterised by parameters varied to fit the strong lensing constraints. These components account for cluster-scale dark matter haloes and the galaxy-scale substructure traced by cluster member galaxies. In contrast, the free-form approach often employs meshes or radial-basis functions to depict the cluster’s total mass distributions. Several of these techniques are discussed and compared in Meneghetti et al. (2017). Bergamini et al. (2019) suggested combining strong lensing with stellar velocity dispersion measurements of cluster galaxies, obtained from the Multi Unit Spectroscopic Explorer (MUSE, at the Very Large Telescope, Bacon et al., 2012) spectra, to enhance the precision of mass models on smaller scales (see also Bergamini et al., 2021; Meneghetti et al., 2020; Granata et al., 2022; Meneghetti et al., 2022, 2023). These additional data help reduce degeneracies between large- and small-scale cluster mass components. Accurate reconstruction of the inner cluster mass distribution is essential for enabling a variety of astrophysical and cosmological applications of strong lensing by galaxy clusters, including studying the nature of dark matter, examining the interplay between baryons and dark matter, exploring cosmic structure formation and evolution, constraining cosmological parameters, and utilising galaxy clusters as cosmic telescopes (see Kneib & Natarajan, 2011; Meneghetti et al., 2013; Bartelmann et al., 2013; Moresco et al., 2022, for extensive reviews).

Until recently, only a few tens of galaxy clusters could be accurately modelled for their total mass distributions. Strong lensing modelling requires high spatial resolution and deep observations, previously achievable mainly by the Hubble Space Telescope (HST) and, more recently, the James Webb Space Telescope (JWST). Most known strong lensing clusters were identified in ground-based observations (e.g. Bayliss et al., 2011), or by following up on galaxy clusters pre-selected based on their X-ray emission or the Sunyaev–Zeldovich effect amplitude (Ebeling et al., 2001, 2007, 2010; Planck Collaboration: Ade et al., 2016). Confirming strong lensing features and measuring their redshifts required additional data from the HST (or JWST) and spectrographs on large telescopes.

This situation is set to change dramatically. Since last year, Euclid has been observing most of the extragalactic sky with spatial resolution in the $I_{\scriptscriptstyle\rm E}$ band comparable to that of HST (Laureijs et al., 2011; Euclid Collaboration: Scaramella et al., 2022). The Euclid Wide Survey (EWS) aims to cover about $15\,000\,\deg^{2}$ of the extragalactic sky to a minimum depth of $m_{\rm AB}=24.5$ mag in the $I_{\scriptscriptstyle\rm E}$ band (Cropper et al., 2016), with a signal-to-noise ratio (S/N) of 10 for extended sources. Euclid will also survey the same area in the near-infrared $Y_{\scriptscriptstyle\rm E}$, $J_{\scriptscriptstyle\rm E}$, and $H_{\scriptscriptstyle\rm E}$ bands (Maciaszek et al., 2022) to a depth of $m_{\rm AB}=24.0$ mag with a minimum S/N of 5 for point sources. Additionally, its slitless spectroscopy will detect line emission with a sensitivity of $f_{{\rm H}\alpha}\gtrsim 2\times 10^{-16}\,{\rm erg}\,{\rm s}^{-1}{\rm cm}^{-2}$ and a S/N of 3.5 for a typical source of size [math].

The primary goal of Euclid is to reveal the nature of dark energy and dark matter, the two dominant components of the Universe, using weak lensing and galaxy clustering as the main probes. However, Euclid will also significantly contribute to the discovery of galaxy clusters. During its lifetime, Euclid is expected to observe over 60 000 galaxy clusters (Sartoris et al., 2016), with a S/N greater than 3, in the redshift range $0.2\leq z\leq 2$. About 5000 of these clusters are anticipated to be strong gravitational lenses containing multiple families of lensed images of background sources and strongly distorted radial and tangential arcs (Boldrin et al., 2012, 2016). Developing accurate strong lensing models for even a subset of this large number of cluster lenses will provide critical insights into the nature of dark matter and the growth of cosmic structures, provided that a large number of multiple images and cluster member galaxies can be identified from Euclid observations.

This work introduces a tool to convert HST observations into Euclid-like imaging data. We focus on HST observations of massive galaxy clusters collected in the Cluster Lensing and Supernova Survey with Hubble (CLASH,111https://archive.stsci.edu/prepds/clash/ Postman et al. 2012) and the Hubble Frontier Fields (HFF,222https://archive.stsci.edu/prepds/frontier/ Lotz et al. 2014, 2017) programmes. We produced a simulated dataset from these images, consisting of mock observations of the same clusters in the EWS. We used simulated observations for the galaxy cluster MACS J0416.1$-$2403 (hereafter, MACS J0416) to quantify the number of strong lensing features detectable in future Euclid observations of lens galaxy clusters. These are then used to preliminarily test the strengths and weaknesses of Euclid-based cluster strong lensing models. Finally, the HFF parallel fields are employed to estimate the magnitude and size distributions of the luminous sources detectable in the Euclid images.

The paper is organised as follows. In Sect. 2, we present the HST observational dataset used as input for the simulations. The simulation pipeline is detailed in Sect. 3. In Sect. 4, we describe various tests conducted on the mock Euclid images to validate the simulations. In Sect. 5, we present Euclid-based strong lensing models for the galaxy cluster MACS J0416, and the results of the strong lensing analysis are reported in Sect. 6. In Sect. 7, we discuss other applications of the Euclid simulated images, and the main conclusions of this work are outlined in Sect. 8. Throughout this work, magnitudes are given in the AB system (Oke & Gunn, 1983).

2 Input data

The simulated Euclid database of galaxy cluster observations presented in this work is based on the photometric data collected by the HST during the CLASH and HFF programmes. The former is a multi-cycle treasury programme that provided panchromatic images of 25 massive galaxy clusters in the redshift range [0.187, 0.890], for a total of 524 orbits from November 2010 to July 2013. The observations were carried out in 16 photometric bands ranging from UV to NIR wavelengths, using the Advanced Camera for Surveys (ACS, with filters: F435W, F475W, F606W, F625W, F775W, F814W, and F850W) and the Wide-Field Camera-3 (WFC3, with filters: F105W, F110W, F125W, F140W, F160W, F225W, F275W, F336W, and F390W). The HFF programme provided deeper HST observations (840 HST orbits) of six massive clusters (four in common with CLASH), selected among the strongest known gravitational lenses, in seven ACS (F435W, F606W, and F814W) and WFC3 (F105W, F125W, F140W, and F160W) bands. The depth of the HFF images corresponds to a limiting magnitude of $m_{\rm AB}\sim 29$ with a S/N of 5 for point sources within an aperture of [math] radius. This depth is about 1.5 magnitudes deeper than the CLASH observations.

We note that the HFF and CLASH imaging is much deeper than the Euclid observations we wish to produce, as discussed in the following sections. The images used in this work are drizzled to pixel scales of $65\,{\rm mas}\,{\rm px}^{-1}$ and $60\,{\rm mas}\,{\rm px}^{-1}$ for the CLASH and HFF data, respectively.

3 Simulation pipeline

This section describes the Python333https://www.python.org/ code HST2EUCLID developed to simulate realistic Euclid images from HST multi-band observations. Although our primary use in this work is the production of mock Euclid observations of galaxy clusters, HST2EUCLID is generally applicable to convert every sufficiently deep HST image into a Euclid-like observation, with the only requirement being that the available HST bands overlap with the Euclid photometric filters to be simulated (see Fig. 1). In particular, the HST F606W and F814W filters were used to simulate the Euclid $I_{\scriptscriptstyle\rm E}$ band, while from the HST F105W, F125W, and F160W filters we simulate the $Y_{\scriptscriptstyle\rm E}$, $J_{\scriptscriptstyle\rm E}$, and $H_{\scriptscriptstyle\rm E}$ bands (see Sect. 3.3). In Sect. 6, we present selected examples of Euclid observations different from galaxy cluster fields.

Figure 2 visually summarises the different steps of the simulation pipeline (labelled a to e) implemented in the HST2EUCLID code. These are described in detail in the following subsections, adopting the same letters as in Fig. 2, for clarity.

3.1 STEP a: Conversion of HST images to flux densities and image alignment

In this first step of the Euclidisation pipeline, we converted the pixel values of the HST images from units of electrons per second (${\rm e}\,{\rm s}^{-1}$) to physical flux densities (${\rm erg}\,{\rm s}^{-1}\,{\rm cm}^{-2}\,{\rm Hz}^{-1}$). The conversion was performed using the following equation:

[TABLE]

where ${\rm ZP}_{\rm HST}$ is the instrumental HST zero point, defined as the AB magnitude of an object producing a signal of one electron per second in the HST image. The ${\rm ZP}_{\rm HST}$ value was computed from the pivot wavelength (PHOTPLAM) and the inverse sensitivity (PHOTFLAM), whose values are provided in the header of the HST Flexible Image Transport System (FITS, Pence et al. 2010) files. Specifically, we used:444www.stsci.edu/hst/instrumentation/acs/data-analysis/zeropoints

[TABLE]

Subsequently, we co-aligned the HST images in the different bands so that they shared the same pixel grid and astrometric calibration. For this purpose, we used the Python function reproject_exact of the module reproject.555https://reproject.readthedocs.io/en/stable/

3.2 STEP b: Matching the HST and Euclid point spread functions

The HST point spread functions (PSFs) have different shapes and full width at half maximum (FWHM) compared with the corresponding Euclid PSFs.666The FWHM values of the HST PSFs in the F606W, F814W, F105W, F125W, and F160W filters range from approximately 70 mas to 130 mas. These values are smaller than those of the Euclid bands at comparable wavelengths (for example, Euclid Collaboration: Mellier et al. 2025 report a measured PSF FWHM of 130 mas in the $I_{\scriptscriptstyle\rm E}$ band). Therefore, we can reliably match the HST resolution to that of Euclid by convolving the HST images with the appropriate matching kernels. These differences must be taken into account to simulate realistic Euclid observations. For each HST band, we derived a kernel function (hereafter, matching kernel) which, when convolved with the corresponding HST images, reproduced the correct PSF in the Euclid simulated data.

The matching kernels between corresponding pairs of HST and Euclid PSFs (see Sect.  3.3) were computed using the Python function create_matching_kernel of the Photutils package (Bradley et al., 2023).777https://photutils.readthedocs.io/en/stable/psf_matching.html The HST PSF models were obtained with the TinyTim software.888https://www.stsci.edu/hst/instrumentation/focus-and-pointing/focus/tiny-tim-hst-psf-modeling Although we verified that these PSFs yielded accurate results, HST2EUCLID allows users full flexibility to implement alternative or customised PSF models. In panel (b) of Fig. 2, we show the effect of convolving the HST/F606W image of the galaxy cluster MACS J0416 with the corresponding matching kernel (shown in the inset of the same panel) to the $I_{\scriptscriptstyle\rm E}$ band.

3.3 STEP c: Combination of HST filters to generate the Euclid bands

In this step, we expressed the flux in a Euclid band Q as a linear combination of $N$ fluxes in nearby HST filters $\{\mathrm{R}_{j}\}$:

[TABLE]

where the final term is expressed in linear algebra notation, with $\boldsymbol{w}$ and $\boldsymbol{F}_{\mathbf{R}}$ denoting column vectors. Below, we derive an expression for the weight vector $\boldsymbol{w}$.

We assumed that the spectral density of flux $f(\lambda)$,–defined as the energy per unit time, per unit spherical angle, per unit detector area, per unit wavelength emitted by a source, (or $f(\nu)$ if it is expressed in terms of unit frequency)–could be described as a linear combination of $N$ base functions \bigl{\{}f_{i}(\lambda)\bigr{\}} (or \bigl{\{}f_{i}(\nu)\bigr{\}}):

[TABLE]

Here, $k_{i}$ are constants associated with the decomposition of the spectral flux density. In computing the last term, we note that $f_{i}(\lambda)$ can be expressed as a function of frequency as

[TABLE]

with $c$ being the light velocity in vacuum. We can then express both $F_{\mathrm{Q}}$ and $F_{\mathrm{R}_{j}}$ as

[TABLE]

where the matrix $\mathcal{R}$ is associated with the transmissivity of the HST filters, as detailed below. Assuming the AB magnitude system, all quantities above can be computed as (see Eq. 4 of Hogg et al. 2002)

[TABLE]

where $g^{\mathrm{AB}}_{\nu}$ is the zero point for the AB magnitude system ($g^{\mathrm{AB}}_{\nu}=3631\,\mathrm{Jy}$, where $1\,\mathrm{Jy}=10^{-26}\,\mathrm{W}\,\mathrm{m}^{-2}\,\mathrm{Hz}^{-1}$), and $R_{j}(\lambda)$ and $Q(\lambda)$ are the transmissivities of the HST and Euclid photometric bandpasses, respectively (see Fig. 1).

By combining the two expressions in Eq. (LABEL:eq.:_FR_FQ), we obtained999A necessary condition for the matrix $\mathcal{R}$ to be invertible is that the number of input filters has to be equal to the number of $f_{i}(\lambda)$ functions in Eq. (4) (i.e. $\mathcal{R}$ has to be a square matrix).

[TABLE]

Finally, by inserting this equation into Eq. (3), we derived the following general expression for the weights:

[TABLE]

In Fig. 1, we present the transmission functions of the Euclid photometric bands ($I_{\scriptscriptstyle\rm E}$, $Y_{\scriptscriptstyle\rm E}$, $J_{\scriptscriptstyle\rm E}$, and $H_{\scriptscriptstyle\rm E}$, Euclid Collaboration: Schirmer et al. 2022) along with the HST filters used for simulations that cover a similar wavelength range to Euclid (F606W, F814W, F105W, F125W, and F160W). The figure highlights that the wavelength range of the $Y_{\scriptscriptstyle\rm E}$ band is well aligned with the HST F105W filter, while the $H_{\scriptscriptstyle\rm E}$ band overlaps solely with the F160W filter. For both cases, we assumed that the spectral density of flux per unit frequency, $f(\nu)$, of the sources in the images remains constant over the entire wavelength range covered by the input ($\mathrm{R}_{1}$) and output ($\mathrm{Q}_{1}$) filters, i.e. $f(\lambda)\propto c/\lambda^{2}$. For the $H_{\scriptscriptstyle\rm E}$ band, this assumption, necessitated by the absence of HST data covering the reddest part of the $H_{\scriptscriptstyle\rm E}$ band (see Fig. 1), is crucial to correctly recovering the measured magnitudes of the luminous sources in the simulated field. However, this represents a rough approximation of the true flux in the real $H_{\scriptscriptstyle\rm E}$ band, as it lacks photometric information from the source spectra at $\lambda>17\,000\,\AA$. Notably, Balmer break galaxies at redshift $z>3$ would appear brighter in $H_{\scriptscriptstyle\rm E}$ than in the F160W band. Under the previous assumption, $\mathcal{R}$ and $\boldsymbol{q}$ are one-dimensional matrices with $\mathcal{R}=\boldsymbol{q}=\mathrm{const.}$ and $\boldsymbol{w}=1$. Thus, the magnitudes of the sources in the $Y_{\scriptscriptstyle\rm E}$ and $H_{\scriptscriptstyle\rm E}$ Euclid bands are identical to those in the F105W and F160W HST filters, respectively.

In contrast, the $I_{\scriptscriptstyle\rm E}$ and $J_{\scriptscriptstyle\rm E}$ transmission functions span two HST bands. Specifically, the $I_{\scriptscriptstyle\rm E}$ band overlaps with both the F606W and F814W filters, while the $J_{\scriptscriptstyle\rm E}$ band overlaps with the F125W and F160W filters. In these cases, the weights, $\boldsymbol{w}$, were computed by assuming that the spectral density of flux, $f(\lambda)$, could be modelled as a sum of two top-hat functions $f_{\{1,2\}}(\nu)$ (see Eq. 4). The $f_{1}(\nu)$ base function is assumed to be constant within one of the two input HST bands and zero outside, while the opposite holds for $f_{2}(\nu)$. In this scenario, $\mathcal{R}$ is a two-dimensional matrix with $\mathcal{R}\propto\mathbb{I}$, where $\mathbb{I}$ represents the identity matrix, and the weights, $w_{j}$, assume the following values:

[TABLE]

We note that, according to the previous hypotheses, the weights corresponding to the same Euclid band sum to one. In panel (c) of Fig. 2, we show the result of combining the two HST F606W and F814W filters into a single image, obtained using Eq. (3).

3.4 STEP d: Projection onto the Euclid pixel grid

In this step, we re-binned the images from the HST pixel grid to the correct Euclid pixel scale. To this aim, we employed the Python function reproject_exact introduced above. The resulting images have pixel scales of $100\,{\rm mas}\,{\rm px}^{-1}$ in the $I_{\scriptscriptstyle\rm E}$ band and $300\,{\rm mas}\,{\rm px}^{-1}$ in $Y_{\scriptscriptstyle\rm E}$, $J_{\scriptscriptstyle\rm E}$, and $H_{\scriptscriptstyle\rm E}$ filters.

The re-binned images, expressed in units of physical flux, were then converted into units of electrons per second by inverting Eq. (1). For this conversion, we assumed a zero point of ${\rm ZP}_{\mathrm{Euclid}}=23.9\,{\rm mag}$ for all bands. The resulting surface brightness per pixel in the Euclid band $X$ is hereafter denoted as $F_{X,{\rm rebin}}$. Panel (d) of Fig. 2 illustrates the result of the re-binning procedure for the $I_{\scriptscriptstyle\rm E}$ band.

3.5 STEP e: Noise addition

The final step of the Euclidisation pipeline involved incorporating the appropriate noise into the Euclid simulated images. To accomplish this, we assumed that the noise in the input HST background subtracted images was negligible compared to the final noise. This approximation is supported by the significantly greater depth of the HST observations compared to that of the Euclid images.

The noise level was determined by adjusting the sky surface brightness of the Euclid images to achieve the expected nominal S/N for a source with a specific limiting magnitude. Specifically, to measure a S/N of ${\rm SN}_{\rm lim}$ for a source with flux of $F_{\rm lim}\,[{\rm e}\,{\rm s}^{-1}]$ measured within an aperture containing $N_{\rm ap}^{\rm px}$ pixels, the sky surface brightness per pixel in units of [${\rm e}\,{\rm s}^{-1}$] was calculated as

[TABLE]

where $t_{\mathrm{exp}}$ is the exposure time of the Euclid observations. In the EWS, this corresponds to 2280 s for the $I_{\scriptscriptstyle\rm E}$ band and 448 s for the $Y_{\scriptscriptstyle\rm E}$, $J_{\scriptscriptstyle\rm E}$, and $H_{\scriptscriptstyle\rm E}$ bands (Euclid Collaboration: Scaramella et al., 2022). The limiting flux, $F_{\mathrm{lim}}$, was computed from the limiting magnitude, $m_{\rm lim}$, using the zero point introduced in Sect. 3.4:

[TABLE]

The expected limiting magnitudes and S/N in the EWS are reported in Table 1 (Euclid Collaboration: Scaramella et al., 2022). The noise was generated using a Poisson process, where the noise variance is equal to the sum of $F_{X,{\rm rebin}}$ and ${\rm BK}_{\mathrm{sky}}$. Panel (e) of Fig. 2 shows the resulting simulated Euclid image in the $I_{\scriptscriptstyle\rm E}$ band, including the noise.

Fig. 3 presents the results of applying the simulation pipeline, from step (a) to (e), to create mock Euclid observations in all the photometric bands for a region with an approximate size of $\times$ encompassing the core of the galaxy cluster MACS J0416. The left-hand panels show the input HST photometric data (excluding the HST F814W filter) while the right-hand panels show the output simulated Euclid images in the $I_{\scriptscriptstyle\rm E}$, $Y_{\scriptscriptstyle\rm E}$, $J_{\scriptscriptstyle\rm E}$, and $H_{\scriptscriptstyle\rm E}$ bands. Despite the shallower depth of the EWS observations compared to the CLASH and HFF observations, many strong lensing features, including some prominent gravitational arcs, are clearly visible in the Euclid images. Notably, the higher spatial resolution of the $I_{\scriptscriptstyle\rm E}$ band allowed us to distinguish small details, such as stellar clumps and spiral structures, which appear in some of the multiple images of background lensed galaxies. These features are fundamental in constraining the total mass distribution of galaxy clusters through strong gravitational lensing (e.g. Bergamini et al., 2021; Pignataro et al., 2021), as discussed in subsequent sections. Simulated Euclid images similar to those presented in this section were created for all 27 galaxy clusters observed during the CLASH and HFF programmes.

4 Simulation validation

This section discusses three tests performed on the mock Euclid images to validate the simulation pipeline. In the first test, we verified that the expected depth of the EWS observations was correctly reproduced in the simulations. In the second, we derived the distribution of the sizes of the galaxies in blank fields. Finally, in the third test, we estimated the number counts of galaxies detected in the Euclid images. For tests two and three, we made use of simulated $I_{\scriptscriptstyle\rm E}$ images of six cluster-parallel blank fields obtained during the HFF observations.

The coloured dots in the left panel of Fig. 4 show the measured S/N for the luminous sources identified in the different Euclid bands of the galaxy cluster MACS J0416, plotted as a function of their magnitude. These sources include cluster members and galaxies in the cluster foreground or background. Both the S/N and the magnitudes were measured within circular apertures containing 132.7 pixels for the $I_{\scriptscriptstyle\rm E}$ band and 9 pixels for the $Y_{\scriptscriptstyle\rm E}$, $J_{\scriptscriptstyle\rm E}$, and $H_{\scriptscriptstyle\rm E}$ filters (see Table 1). The figure shows that for source magnitude values equal to the limiting magnitude, the measured S/N precisely matches the expected EWS value (dashed coloured lines; see also Table 1). This test demonstrates that the noise in the simulated Euclid images reproduces the expected depth of the EWS data.

The right panel of Fig. 4 shows the distribution of the circularised FWHM for 1748 galaxies, with $I_{\scriptscriptstyle\rm E}$ magnitudes $\leq 24.5$ (i.e. down to the limiting magnitude), identified in the $I_{\scriptscriptstyle\rm E}$ images of the six Euclidised parallel fields described above. The cumulative probability distribution is also plotted in red. This analysis reveals that $93.8\%$ of the selected galaxies have {\rm FWHM}\leq$$$, with a median value of [math]. Assuming a Gaussian profile for the galaxy surface brightness distribution and a median FWHM equal to [math], we find that 96.4%$of the brightness of the galaxies is enclosed within an aperture of [math] radius. This value corresponds to the size of the aperture used to measure the limiting magnitude and S/N in the$I_{\scriptscriptstyle\rm E}$ band (see Table 1).

Finally, Fig. 5 shows the measured distribution of number counts, i.e. the number of detected galaxies per ${\rm deg}^{2}$ per magnitude bin, in the six HFF parallel fields. In the figure, the Euclid number counts (grey histogram) are compared with those estimated from HST observations (black curve, Capak et al., 2007). From the cumulative distribution of galaxies (red dashed line), we estimate that the density of resolved galaxies brighter than the limiting magnitude ($I_{\scriptscriptstyle\rm E}$ magnitude $\leq 24.5$) is equal to $28\pm 1$ galaxies per ${\rm arcmin}^{2}$, in full agreement with expectations for the EWS observations (Laureijs et al., 2011).

5 Parametric strong lensing models of galaxy clusters based on Euclid observations

As a possible application of the simulated Euclid photometric images, we present a preliminary analysis to quantify the precision and accuracy achievable by parametric strong lensing models of galaxy clusters based on Euclid data. Our analysis focuses on the HFF galaxy cluster MACS J0416, for which Bergamini et al. (2023) developed a high-precision strong lensing model (hereafter the B23 model), based on the spectrophotometric data obtained with HST and MUSE. Both the B23 model and the other lens models presented in this work are constructed using the publicly available parametric software LensTool (Jullo et al., 2007; Limousin et al., 2005; Jullo & Kneib, 2009).

In the B23 model, the total projected gravitational potential of MACS J0416 is expressed as the sum of several contributions, each corresponding to a different mass component:

[TABLE]

The $\phi_{i}^{\mathrm{halo}}$ terms represent the contribution from $N_{\rm h}=4$ cluster-scale haloes to the total cluster gravitational potential. Three of these haloes are parametrised as elliptical dual pseudo-isothermal mass distributions (dPIEs, Limousin et al., 2005; El´ıasdóttir et al., 2007; Bergamini et al., 2019) with an infinite truncation radius: two are centred close to the positions of the two brightest cluster galaxies (BCGs), and one is located in the southern part of the cluster, providing second-order corrections to the total mass distribution in that region. The fourth halo is a circular, non-truncated, dPIE profile that accounts for an overdensity of galaxies in the north-eastern region of the cluster. In addition to these cluster-scale haloes, $N_{\rm G}=4$ dPIEs ($\phi_{j}^{\mathrm{gas}}$ in Eq. 14) are used to describe the hot gas content of the cluster. The values of the parameters of these profiles are fixed in the B23 lens model, as they were determined from the analysis of Chandra X-ray data of the cluster performed by Bonamigo et al. (2018). The sub-halo mass component of MACS J0416 (corresponding to the terms $\phi_{k}^{\mathrm{gal}}$ in Eq. 14) comprises a total of $N_{\rm g}=213$ cluster member galaxies, including the two BCGs. Of these galaxies, 212 are parametrised as circular, core-less dPIEs, whose central velocity dispersions ($\sigma_{0}$) and truncation radii ($r_{\mathrm{cut}}$) are scaled with their luminosities, following the two scaling relations reported in Eq. (4) of Bergamini et al. (2023). The remaining galaxy, identified as Gal-8971, is separately parametrised as an elliptical, core-less dPIE since its total mass is responsible for the formation of a galaxy-galaxy strong lensing system that creates four multiple images of a background source at $z=3.221$. Finally, the last term in Eq. (14), $\phi^{\mathrm{fg}}$, accounts for the contribution to the lensing observables from a single foreground galaxy in the southwestern region of the cluster. This galaxy is described as a circular core-less dPIE.

The optimal values of the free parameters of the profiles defined in Eq. (14) were determined by minimising the following $\chi^{2}$ function, which quantifies how well the lens model predicts the observed positions of the multiple images:

[TABLE]

where $\Delta x_{i,j}$ are the uncertainties on the observed positions of the images, $N_{\mathrm{im}}^{j}$ is the number of multiple images of the same $j\mathrm{-th}$ background source, and $N_{\mathrm{sou}}$ is the total number of sources. The B23 lens model is constrained by the observed positions of 237 spectroscopically confirmed multiple images from 88 background sources within the redshift range $0.94\leq z\leq 6.63$. We refer to Bergamini et al. (2023) for a detailed description of the lens model.

By exploiting the Euclid simulated images of the galaxy cluster MACS J0416 in the $I_{\scriptscriptstyle\rm E}$, $Y_{\scriptscriptstyle\rm E}$, $J_{\scriptscriptstyle\rm E}$, and $H_{\scriptscriptstyle\rm E}$ bands, we developed two Euclid-based lens models, hereafter identified as $\mathrm{EM_{spec}}$ and $\mathrm{EM_{phot}}$. Both $\mathrm{EM_{spec}}$ and $\mathrm{EM_{phot}}$ assume a parametrisation for the total mass of MACS J0416 similar to that adopted in the B23 model, but with the following three important differences. First, the cluster-scale component of MACS J0416 is parametrised by using just two non-truncated dPIE profiles centred on the positions of the BCGs. Second, the hot-gas mass component is not considered (i.e. the $\phi_{j}^{\mathrm{gas}}$ terms are not present in the models). Third, the sub-halo mass component of the cluster contains only those 125 cluster galaxies that are identifiable in the Euclid $I_{\scriptscriptstyle\rm E}$ band and with an $I_{\scriptscriptstyle\rm E}$ magnitude $\leq 22.5$ (see Fig. 6). All these galaxies are parametrised as circular, core-less dPIEs, adopting the $\sigma_{0}$–$L$ and $r_{\rm cut}$–$L$ scaling relations mentioned above, where the luminosity $L$ corresponds to the Kron magnitude of the galaxies measured in the $I_{\scriptscriptstyle\rm E}$ band (instead of the HST F160W Kron magnitude adopted in the B23 model). Since Gal-8971 now follows the scaling relations, the number of free parameters in the lens model is reduced by four. Thus, the Euclid-based lens models count a total of 16 free parameters (12 associated with the parametric profiles used to describe the cluster-scale total mass distribution, two are the normalisations of the $\sigma_{0}$–$L$ and $r_{\rm cut}$–$L$ cluster member scaling relations, and two are used to parameterise the foreground galaxy residing in the south-western region of the cluster). We also note that, contrary to the B23 lens model, we did not assume any Gaussian prior on the normalisation of the $\sigma_{0}$–$L$ scaling relation. In the B23 model, this Gaussian prior is inferred from the measure stellar kinematics of the cluster member galaxies, through the procedure described by Bergamini et al. (2019).

The $\mathrm{EM_{spec}}$ and $\mathrm{EM_{phot}}$ were constrained by the observed positions of 31 multiple images from 12 background sources within the spectroscopic redshift interval $1.01\leq z\leq 2.30$. This corresponds to the subsample of multiple images of the original B23 catalogue that were identifiable through visual inspecting the Euclid $I_{\scriptscriptstyle\rm E}$ simulated observation. The larger pixel scale and lower resolution and depth of the Euclid images compared to the original HST data allowed the secure detection of 13% of the multiple images used in the B23 model. Figure 6 shows examples of detected and non-detected cluster galaxies and multiple images in the $I_{\scriptscriptstyle\rm E}$ image.

The $\mathrm{EM_{spec}}$ and $\mathrm{EM_{phot}}$ models differ in that, while in the former we used the spectroscopic redshifts of the observed multiple images, in the latter we assumed photometric redshift measurements. To simulate the photometric redshift measurements, we randomly extracted, for each source, a redshift value from a Gaussian distribution centred on the source spectroscopic redshift, $z_{\rm spec}$, and with a standard deviation equal to $(1+z_{\rm spec})\,0.05$. This corresponds to the expected uncertainty on photometric redshift measurements in the EWS (Laureijs et al., 2011; Euclid Collaboration: Desprez et al., 2020; Euclid Collaboration: Paltani et al., 2024).

We note that $\mathrm{EM_{spec}}$ and $\mathrm{EM_{phot}}$ are optimistic examples of lens models based on Euclid data. To construct these models, we used the multiple images and cluster member catalogues from Bergamini et al. 2023, based on HST photometric data and VIMOS and MUSE spectroscopic data, to identify the sources detectable in the Euclid simulated observations. In more realistic cases, these components for the strong lensing models will be derived solely from the Euclid data. For example, we will identify the cluster galaxies from the observations in the four Euclid bands. Angora et al. (2020) show that this task can be accomplished using convolutional neural networks (CNNs). The proposed technique will be tested with simulated Euclid images obtained with HST2EUCLID in an upcoming paper (Angora et al. in preparation). Spectroscopic follow-up observations will also be critical for identifying pure and complete samples of cluster members and candidate multiple images, as well as for measuring their redshifts. Despite these considerations, our results are informative regarding the precision and accuracy potentially achievable in strong lensing models based on Euclid data. Previous studies, such as those by Johnson & Sharon (2016) and Meneghetti et al. (2017), discuss how the accuracy and precision of strong lensing models depend on the availability of multiple images and spectroscopic redshifts.

6 Results of the strong lensing analysis on the simulated Euclid clusters

To accurately constrain the total mass distribution of galaxy clusters using strong gravitational lensing, it is crucial to determine the positions of a large sample of multiple images from numerous background sources at different redshifts. Likewise, identifying a pure and complete sample of cluster member galaxies is essential for characterising the sub-halo component of the clusters. Additionally, due to degeneracies between lens model parameters, an inaccurate characterisation of the sub-halo mass distribution can introduce biases in determining the other components in Eq. (14).

Figure 7 shows the displacements in the sky plane between the observed and model-predicted positions for the multiple images of the $\mathrm{EM_{spec}}$ (red) and $\mathrm{EM_{phot}}$ (blue) models compared to those obtained from the reference lens model by Bergamini et al. 2023 (light grey). We quantified the precision of each model in terms of the root-mean-square separation ($\Delta_{\rm RMS}$) between the observed ($\mathbf{x}^{obs}$) and model-predicted ($\mathbf{x}^{pre}$) positions of the multiple images:

[TABLE]

where $N_{\mathrm{im}}^{\mathrm{tot}}$ is the total number of images in the model.

The $\mathrm{EM_{phot}}$ model is characterised by a \Delta_{\rm RMS}^{\mathrm{EM_{phot}}}=$$$ in predicting the positions of the multiple images, which is approximately 33% higher than the other two models. This increased \Delta_{\rm RMS}$is attributed to weaker lensing constraints from the less accurate photometric redshift measurements, as opposed to spectroscopic redshifts, for the lensed background sources. In contrast, the$\mathrm{EM_{spec}}$predicts the positions of the observed multiple images with a$\Delta_{\rm RMS}$of [math], which is about 9$\mathrm{EM_{spec}}$must reproduce the positions of 31 multiple images from 12 background sources (i.e. about 13$\Delta_{\rm RMS}$ (see Fig. 7).

In Figs. 8 and 9, we compare the convergence and magnification maps obtained from the three lens models. The results are shown on a grid of panels $(i,j)$, where the indices $i,j\in[1,3]$ identify the lens models. Thus, the maps from the $i$-th lens model are displayed along the diagonal ($i=j$) of the figures. The model names are reported at the bottom of each column and on the left side of each row of panels. The panels in the $i-$th row and $j-$th column show the relative differences between the maps of models $j$ and $i$.

We note that while the convergence maps of the $\mathrm{EM_{spec}}$ and $\mathrm{EM_{phot}}$ models are quite similar, with a median absolute relative difference of $\sim 4$% (second panel in the bottom row), larger discrepancies exist between these models and the B23 model (first column of panels). This is expected, given the different total mass parametrisations adopted in the Euclid and HST-based lens models. As described in Sect. 5, the large-scale total mass distribution of MACS J0416 in the $\mathrm{EM_{spec}}$ and $\mathrm{EM_{phot}}$ is parametrised using only two elliptical dPIEs, in contrast to the four included in the B23 model. The two additional haloes in the latter model (a circular one north-east of the northern BCG and a highly elliptical one close to the southern BCG) are clearly identifiable in the panels in the first column of Fig. 8. They correspond to regions of large relative differences between the maps. The models also differ at galaxy scales due to the lower number of cluster galaxies included in the Euclid-based lens models (125 out of 213 in the B23 model), and due to the absence of the Gaussian prior on the value of the normalisation of the $\sigma_{0}$–$L$ scaling relation used to model the cluster galaxies (see Sect. 5). In particular, the mass in galaxy-scale haloes in the Euclid-based lens models is larger than in the B23 model (see Fig. 10). Some of the differences between the models are also due to the lack of large-scale haloes describing the hot gas mass distribution in the $\mathrm{EM_{spec}}$ and $\mathrm{EM_{phot}}$ models.

The Euclid-based models also exhibit similar magnification patterns, as shown in Fig. 9. However, the magnification is derived from the second spatial derivatives of the lensing potential (Meneghetti, 2021). Thus, even small differences between the model mass distributions can lead to large variations in magnification on small scales. These variations are most significant along the critical lines, i.e. the lines where the magnification diverges. The differences are larger when the Euclid-based maps are compared to the B23 model. For example, the region along the northern section of the cluster critical lines exhibits large variations between the Euclid-based and B23 models. The $\mathrm{EM_{spec}}$ and $\mathrm{EM_{phot}}$ models lack constraints in this region. Most of the multiple images detected in the HST data are too faint to be detected by Euclid, as they originate from distant sources at $z\gtrsim 6$.

Despite these differences, both the $\mathrm{EM_{spec}}$ and $\mathrm{EM_{phot}}$ models can be used to accurately measure the total projected mass profile in the cluster core. In the upper panel of Fig. 10, we present the cumulative mass profiles derived from the different lens models. We show profiles for both the total mass distributions and the cluster member (CM) components. We report the ratios between the mass profiles derived from the Euclid-based and B23 models in the bottom panel. The radius $R$ is measured with respect to the position of the northern BCG (BCG-N). The total cumulative mass profiles agree at the level of $\lesssim 5\%$ in the radial range covered by the strong lensing constraints, as indicated by the vertical segments at the top of the figure. Significant deviations between the Euclid-based models and the B23 model arise only at distances smaller than $\sim$ 10 kpc from BCG-N. This result is not surprising, as strong lensing is a robust estimator of the total mass within the Einstein radius (i.e. within the lens critical lines; Meneghetti et al., 2017). However, as highlighted earlier, the Euclid-based models measure a larger mass in cluster members compared to the B23 model. Disentangling the large- and small-scale mass components of the cluster requires additional constraints derived from stellar kinematics measurements (e.g. Bergamini et al., 2019, 2021).

Although not shown in Fig. 10, strong lensing alone is unable to constrain the mass profile far outside the region containing the multiple images. However, due to its large field of view and survey strategy, Euclid will measure the shear out to the virial radius and beyond, at least for massive galaxy clusters (Euclid Collaboration: Giocoli et al., 2024; Euclid Collaboration: Lesci et al., 2024). Several studies have demonstrated that combining weak and strong lensing enhances the precision and accuracy of mass profile measurements out to large radii (e.g. Meneghetti et al., 2010). Moreover, mapping the two-dimensional mass distributions within large regions around the cluster centre allows us to characterise complex mass distributions such as merging clusters and filaments (Bradač et al., 2006; Merten et al., 2011, 2015; Diego et al., 2023).

7 HST2EUCLID applications

Although this work mainly focuses on the analysis of EWS-like data of galaxy clusters, the HST2EUCLID code is designed to simulate customised Euclid imaging observations. In particular, one can use any kind of HST image as an input and specify a number of parameters (exposure times, PSF models, limiting magnitude, and S/N) to generate mock images. As an example, Fig. 11 shows simulated Euclid images of two galaxy-galaxy strong lensing systems, as observed in the EWS. The system shown in the left panels of the figure is identified as SDSS J0946$+$1006, also known as the Jackpot lens, and consists of a double Einstein ring lensed by a galaxy at $z=0.222$ (at the centre of the left images). The inner ring, with a radius of approximately [math], has a redshift of $z=0.609$, while the outer ring, with a radius of $\sim$ [math], has $z=2.035$ (Gavazzi et al., 2008). A third source at $z=5.975$ is also lensed in two additional multiple images (Collett & Smith, 2020). The system shown in the right panels is instead a quadruple imaged quasi-stellar object (QSO) at $z=1.693$, lensed by a galaxy at $z=0.455$, known as HE0435$-$1223 (Wisotzki et al., 2002; Bonvin et al., 2017). Fig. 12 shows a simulated preview of a portion of the Chandra Deep Field South (Giacconi et al., 2002) that will be observed in the Euclid Deep Survey (EDS). This simulation assumes an exposure time of $90\,744\,{\rm s}$ and a limiting S/N of 15.9 for a source with an $I_{\scriptscriptstyle\rm E}$ magnitude of 26.5, measured within a circular aperture of [math] radius. These values correspond to the EDS expected requirements.

Since HST2EUCLID is fully modular, it can be easily generalised to simulate a wide range of imaging data. Although this work focuses on converting HST to Euclid data, the software can be extended to include multiple input and output instruments, provided that the input images have higher spatial resolution and depth than the simulated output observations. In this context, the new JWST and the future Extremely Large Telescope (ELT) data can be used to generate the simulations. The JWST data can also be used to fully cover the $H_{\scriptscriptstyle\rm E}$ filter as discussed in Sect. 3.3.

Another possible application of the HST2EUCLID code, beyond testing the accuracy of Euclid-based strong lensing models, is the search for transient sources (e.g. supernovae and active galactic nuclei) in previously observed HST (or JWST) fields. In particular, a direct comparison between the upcoming real Euclid data and simulated images allows the identification of transient sources by subtracting the simulated images (before the addition of noise; step d of the simulation pipeline presented in Sect.  3 and Fig.  2) from the real observations of the same region. This application is particularly useful for identifying multiple imaged variable sources lensed by galaxy clusters, such as lensed supernovae. The time delays measured between multiple images of these sources can then be used to constrain cosmological parameter values through the time-delay cosmography technique (e.g. Grillo et al., 2020; Treu et al., 2022; Acebron et al., 2023).

In addition, HST2EUCLID can be used to provide the training set for CNN-based techniques aimed at identifying cluster members, galaxy-scale lensing systems, and strong lensing features in clusters (e.g. Angora et al. 2020, 2023; Bazzanini et al. in prep.). More generally, mock HST fields with extensive spectroscopic information are crucial for validating the performance of Euclid across a range of legacy science cases (e.g. the search for high-$z$ dropout galaxies and morphological characterisation of galaxies at various redshifts).

8 Conclusions

In this article, we present the HST2EUCLID code developed to create simulated Euclid images in the $I_{\scriptscriptstyle\rm E}$, $Y_{\scriptscriptstyle\rm E}$, $J_{\scriptscriptstyle\rm E}$, and $H_{\scriptscriptstyle\rm E}$ bands using real HST observations in the ACS F606W, ACS F814W, WFC3 F105W, WFC3 F125W, and WFC3 F160W filters. The code is written entirely in Python and can be easily customised for a wide range of studies that make use of Euclid images. A high-level interface based on textual input files allows users to access the full functionalities of the code. As a preliminary application, we used HST2EUCLID to simulate EWS data for 27 clusters observed by the HST during the CLASH and HFF surveys (21 CLASH and 6 HFF clusters). The cluster redshifts range from 0.19 to 0.89.

By using the simulated Euclid images of the galaxy cluster MACS J0416, we tested the possibility of developing high-precision strong lensing models of galaxy clusters based on Euclid data. Our results demonstrate that the Euclid-based lens models are sufficiently accurate to yield precise estimates of the total mass within the cluster critical lines.

The precision and accuracy achievable with Euclid-based lens models rely on the identification of multiple images and cluster members. Both types of sources serve as inputs for constructing the lens models. In this context, redshift measurements from spectroscopic follow-up campaigns will be essential. However, machine and deep learning techniques can automate the search for these sources. Given the paucity of known lenses, especially on the scale of galaxy clusters, training deep learning models requires realistic and sophisticated image simulations, which HST2EUCLID can deliver. For instance, strongly lensed galaxies can be injected into Euclidised HST images to construct a training set (Angora et al. in prep.; Bazzanini et al. in prep.).

Despite our work mainly focusing on analysing EWS-like data of galaxy clusters, the HST2EUCLID code is designed to simulate any kind of Euclid imaging data.

Acknowledgements.

We acknowledge financial support through grants PRIN-MIUR 2017WSCC32 and 2020SKSTHZ. PB acknowledges financial support from ASI through the agreement ASI-INAF n. 2018-29-HH.0. MM acknowledges support from the Italian Space Agency (ASI) through contract “Euclid - Phase E” and “Euclid - Phase D”. LB is indebted to the communities behind the multiple free, libre, and open-source software packages on which we all depend on. The Euclid Consortium acknowledges the European Space Agency and a number of agencies and institutes that have supported the development of Euclid, in particular the Agenzia Spaziale Italiana, the Austrian Forschungsförderungsgesellschaft funded through BMK, the Belgian Science Policy, the Canadian Euclid Consortium, the Deutsches Zentrum für Luft- und Raumfahrt, the DTU Space and the Niels Bohr Institute in Denmark, the French Centre National d’Etudes Spatiales, the Fundação para a Ciência e a Tecnologia, the Hungarian Academy of Sciences, the Ministerio de Ciencia, Innovación y Universidades, the National Aeronautics and Space Administration, the National Astronomical Observatory of Japan, the Netherlandse Onderzoekschool Voor Astronomie, the Norwegian Space Agency, the Research Council of Finland, the Romanian Space Agency, the State Secretariat for Education, Research, and Innovation (SERI) at the Swiss Space Office (SSO), and the United Kingdom Space Agency. A complete and detailed list is available on the Euclid web site (www.euclid-ec.org). This work uses the following software packages: Astropy (Astropy Collaboration: Robitaille et al., 2013; Price-Whelan et al., 2018), matplotlib (Hunter, 2007), NumPy (van der Walt et al., 2011; Harris et al., 2020), Python (Van Rossum & Drake, 2009), Scipy (Virtanen et al., 2020), acstools (Lim et al., 2020), reproject, argparse, re, pickle, os, photutils (Bradley et al., 2023).