Image simulations of highly magnified clumpy galaxies

TL;DR

The paper presents ClumPyLen, a Python-based pipeline to generate realistic mock observations of strongly lensed, high-redshift, clumpy galaxies. It models host galaxies with Sérsic disks and bulges, populates them with clumps drawn from a Schechter-like mass function in the range $10^4\,M_{\odot}$ to $10^7\,M_{\odot}$, and adds spiral structure and SEDs via Yggdrasil models at $Z=0.004$ with Kroupa IMF and prescribed SFHs. Lensing is implemented through deflection-angle maps (e.g., Lenstool for MACS J0416.1-2403), combined with realistic observational effects—PSF, sky background, and Poisson noise—for HST and JWST instruments. The tool is demonstrated on two cases (Cosmic Archipelago and Abell 2744 System 3), illustrating clump detectability and blending across resolutions and magnifications, and enabling forward modeling, ML training data generation, and statistical studies of clump properties in the early universe.

Abstract

We present ClumPyLen, a Python-based simulator designed to produce realistic mock observations of strongly lensed, high-redshift, clumpy star-forming galaxies. The tool models galaxy components such as disks, bulges, and spiral arms using Sérsic profiles, and it populates them with stellar clumps whose properties are sampled from physically motivated distributions. ClumPyLen includes the effects of gravitational lensing through user-provided deflection angle maps and simulates realistic observational conditions by accounting for instrumental effects, Point-Spread-Function convolution, sky background, and photon noise. The simulator can support a wide range of filters and instruments; here we focus on HST/ACS, HST/WFC3-IR, and JWST/NIRCam. We demonstrate the capabilities of the code through two examples, including a detailed simulation of the z = 6.145 source Cosmic Archipelago lensed by MACS J0416.1-2403. The simulated images closely match the morphology and limiting magnitudes of real observations. ClumPyLen is designed to explore the detectability of stellar clumps in terms of mass and size, especially in the low-mass regime, and it allows the study of clump blending effects. Thanks to its modular design, the code is highly adaptable to a wide range of scientific goals, including lensing studies, galaxy evolution, and the generation of synthetic datasets for machine learning or forward modeling applications.

Figures (9)

• Figure 1: (a) Example of a host galaxy consisting of an exponential disk with two spiral arms and a spherical bulge. Details on the adopted parameters are reported in the text. (b) Model of a host galaxy, made of an exponential disk, a spherical bulge, and two spiral arms, populated with Sérsic stellar clumps. Details on the adopted parameters are reported in the text. The galaxy center coincides with the center of the field of view. (c) RGB color image of the same source. Here, we assume the bulge is 1 Gyr old, while the disk is 500 Myr old. For the stellar clumps, their ages span in the range 1-500 Myr. In this case, the red, green, and blue channels correspond to effective wavelengths $\lambda_e = 5$, $3$, and $2~\mu m$, respectively (0.70, 0.42 and 0.28 $\rm \mu m$, rest-frame, taking into account an assumed redshift $\rm z=6.145$). These images have an angular resolution of $0.25$ mas/pix, which at a $z \sim 6$ corresponds to a physical scale of approximately 1 pc per pixel. As a result, our clumps, all of which have sizes between 1 and 10 pc, are resolved in the high-resolution images.
• Figure 2: Upper panel: Magenta histogram showhing the stellar mass function of the star clumps populating our simulated galaxy. Lower panel: Clump sizes (in units of parsec) as a function of the clump stellar mass. Clumps are represented by magenta points. The underlying average size-mass relation given by Eq. \ref{['r_eff']}brown2021 is shown in a blue solid line. At a given stellar mass, we assume the size distribution follows a lognormal distribution with a standard deviation of $\sigma = 0.3$.
• Figure 3: Upper panel: Histogram of the clump's ages. Lower panel: Clump stellar masses as a function of their ages in years.
• Figure 4: Mass map of galaxy cluster MACS J0416.1-2403 Bergamini_2023 at $z = 0.396$ (RA: 64.038142 deg, Dec: -24.067472 deg). This model is generated with the software Lenstool. The yellow lines represent the caustics of a source at $z = 6.145$, while the white lines are the corresponding critical lines on the lens plane. The magenta marker indicates the position of our source ($\beta_1 = -13.72$ arcsec and $\beta_2 = 3.62$ arcsec), and the three cyan markers show the corresponding multiple images on the lens plane: a stretched arc at the position $\theta_1 = -35.57$ and $\theta_2 = 18.85$, and two counter-images in $\theta_1 = -42.66$ and $\theta_2 = 8.46$ and $\theta_1 = -20.16$ and $\theta_2 = 31.53$), respectively. In this work, we focus on the gravitational arc.
• Figure 5: Simulated observations using HST WFC3 (the top three panels, for F105W, F125W, and F160W) and JWST NIRCam (the remaining panels for F115W, F150W, F200W, F277W, F356W, and F444W). In each subfigure, we show the same source at $z = 6.145$ lensed by MACS J0416.1-2403. Each panel uses its own flux range to optimize visibility of the source structure. The typical background level and exposure time for each filter are listed in Table \ref{['noise_HST_WFC3']} and \ref{['noise_JWST']}. Further details are reported in the text. The black squares in the bottom right corner of every subfigure show how the source galaxy appears when the gravitational lensing effect is not included. The unlensed and lensed sources are represented using the same pixel scale. A blue circle highlights the same clump in both the lensed and unlensed images, showing its corresponding position in the lens and source planes.