arXiv subjects

Khee-Gan Lee

Publications and source records attributed to Khee-Gan Lee.

At least 37 records · Page 2Linked to original sources

arXiv2024

The Dependence of Galaxy Properties on the Underlying 3D Matter Density Field at 2.0 < z < 2.5

We study the environmental effect of galaxy evolution as a function of the underlying 3D dark matter density for the first time at $z=2-2.5$, in which the underlying matter density is reconstructed from observed galaxies through dynamical forward modeling techniques. Utilizing this map, we investigate the dependence of the star formation activities and galaxy types (mergers, submillimeter galaxies, active galactic nuclei, and quiescent galaxies) on the matter overdensity $Δ_\text{local}$ and stellar mass. For the first time, we are able to probe underdense regions ($Δ_\text{local}<1$) in addition to overdensities. We find that star formation activity generally depends on the stellar mass, not the matter density. We also find evidence that: (1) an absence of mergers and submillimeter galaxies in higher-density regions but otherwise no trend across lower-density bins, (2) the increase of active galactic nuclei and quiescent galaxy prevalence as a function of matter density, and (3) the increase of all aforementioned categories with the stellar mass. These results indicate that stellar mass is the main driver of galaxy evolution at the cosmic noon. Our novel approach directly using reconstructed dark matter density maps demonstrates the new capability of the environmental effect studies in galaxy evolution at higher redshift.

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arXiv2024

The Cosmic Baryon Partition between the IGM and CGM in the SIMBA Simulations

We use the Simba suite of cosmological hydrodynamical simulations to investigate the importance of various stellar and AGN feedback mechanisms in partitioning the cosmic baryons between the intergalactic (IGM) and circumgalactic (CGM) media in the $z\leq 1$ Universe. We identify the AGN jets as the most prominent mechanism for the redistribution of baryons between the IGM and CGM. In contrast to the full feedback models, deactivating AGN jets results in $\approx20$ per cent drop in fraction of baryons residing in the IGM and a consequent increase of CGM baryon fraction by $\approx 50$ per cent. We find that stellar feedback modifies the partition of baryons on a $10$ per cent level. We further examine the physical properties of simulated haloes in different mass bins, and their response to various feedback models. On average, a sixfold decrease in the CGM mass fraction due to the inclusion of feedback from AGN jets is detected in $10^{12}M_{\odot} \leq M_{\rm 200} \leq 10^{14}M_{\odot}$ haloes. Examination of the average radial gas density profiles of $M_{200} > 10^{12}M_{\odot}$ haloes reveals up to an order of magnitude decrease in gas densities due to the AGN jet feedback. We compare gas density profiles from Simba simulations to the predictions of the modified NFW model, and show that the latter provides a reasonable approximation within the virial radii of the full range of halo masses, but only when rescaled by the appropriate mass-dependent CGM fraction of the halo. The relative partitioning of cosmic baryons and, subsequently, the feedback models can be constrained observationally with fast radio bursts (FRBs) in upcoming surveys.

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arXiv2023

${\rm H{\scriptsize ALO}F{\scriptsize LOW}}$ I: Neural Inference of Halo Mass from Galaxy Photometry and Morphology

We present ${\rm H{\scriptsize ALO}F{\scriptsize LOW}}$, a new machine learning approach for inferring the mass of host dark matter halos, $M_h$, from the photometry and morphology of galaxies. ${\rm H{\scriptsize ALO}F{\scriptsize LOW}}$ uses simulation-based inference with normalizing flows to conduct rigorous Bayesian inference. It is trained on state-of-the-art synthetic galaxy images from Bottrell et al. (2023; arXiv:2308.14793) that are constructed from the IllustrisTNG hydrodynamic simulation and include realistic effects of the Hyper Suprime-Cam Subaru Strategy Program (HSC-SSP) observations. We design ${\rm H{\scriptsize ALO}F{\scriptsize LOW}}$ to infer $M_h$ and stellar mass, $M_*$, using $grizy$ band magnitudes, morphological properties quantifying characteristic size, concentration, and asymmetry, total measured satellite luminosity, and number of satellites. We demonstrate that ${\rm H{\scriptsize ALO}F{\scriptsize LOW}}$ infers accurate and unbiased posteriors of $M_h$. Furthermore, we quantify the full information content in the photometric observations of galaxies in constraining $M_h$. With magnitudes alone, we infer $M_h$ with $σ_{\log M_h} \sim 0.115$ and 0.182 dex for field and group galaxies. Including morphological properties significantly improves the precision of $M_h$ constraints, as does total satellite luminosity: $σ_{\log M_h} \sim 0.095$ and 0.132 dex. Compared to the standard approach using the stellar-to-halo mass relation, we improve $M_h$ constraints by $\sim$40\%. In subsequent papers, we will validate and calibrate ${\rm H{\scriptsize ALO}F{\scriptsize LOW}}$ with galaxy-galaxy lensing measurements on real observational data.

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arXiv2023

The FRB20190520B Sightline Intersects Foreground Galaxy Clusters

The repeating fast radio burst FRB20190520B is an anomaly of the FRB population thanks to its high dispersion measure (DM$=1205\,$pc/cc) despite its low redshift of $z_\mathrm{frb}=0.241$. This excess has been attributed to a large host contribution of $DM_{host}\approx 900\,$pc/cc, far larger than any other known FRB. In this paper, we describe spectroscopic observations of the FRB20190520B field obtained as part of the FLIMFLAM survey, which yielded 701 galaxy redshifts in the field. We find multiple foreground galaxy groups and clusters, for which we then estimated halo masses by comparing their richness with numerical simulations. We discover two separate $M_{halo} >10^{14}\,M_\odot$ galaxy clusters, at $z=0.1867$ and $z=0.2170$, respectively, that are directly intersected by the FRB sightline within their characteristic halo radius \rvir{}. Subtracting off their estimated DM contributions as well that of the diffuse intergalactic medium, we estimate a host contribution of $DM_{host}=430^{+140}_{-220}\,$pc/cc or $DM_{host}=280^{+140}_{-170}\,$pc/cc (observed frame) depending on whether we assume the halo gas extends to $r_{200}$ or $2\times r_{200}$. This significantly smaller $DM_{host}$ -- no longer the largest known value -- is now consistent with H$α$ emission measures of the host galaxy without invoking unusually high gas temperatures. Combined with the observed FRB scattering timescale, we estimate the turbulent fluctuation and geometric amplification factor of the scattering layer to be $\tilde{F} G\approx4.5 - 11\,(\mathrm{pc^2\;km})^{-1/3}$, suggesting most of the gas is close to the FRB host. This result illustrates the importance of incorporating foreground data for FRB analyses, both for understanding the nature of FRBs and to realize their potential as a cosmological probe.

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arXiv2023

Alignments Between Galaxies and the Cosmic Web at $z \sim 1-2$ in the IllustrisTNG Simulations

Galaxy formation theories predict that galaxy shapes and angular momenta have non-random alignments with the cosmic web. This leads to so-called intrinsic alignment between pairs of galaxies, which is important to quantify as a nuisance parameter for weak lensing. We study galaxy-cosmic web alignment in the IllustrisTNG suite of hydrodynamical simulations at redshifts 1 and 2, finding that alignment trends are consistent with previous studies. However, we find that the magnitude of the spin alignment signal is $\sim 2.4 \times$ weaker than seen in previous studies of the Horizon-AGN simulation, suggesting that this signal may have significant dependence on subgrid physics. Based on IllustrisTNG, we then construct mock observational spectroscopic surveys that can probe shape-cosmic web alignment at $z \sim 1-2$, modeled on the low-$z$ galaxy redshift and IGM tomography surveys on the upcoming Subaru Prime Focus Spectrograph Galaxy Evolution (PFS GE) survey. However, even over box sizes of $L=205\,h^{-1}\,\mathrm{Mpc}$, we find that global anisotropies induce a sample variance in the 2D projected alignment signal that depend on the projected direction -- this induces significant errors in the observed alignment. We predict a $5.3σ$ detection of IllustrisTNG's shape alignment signal at $z \sim 1$ from Subaru PFS GE, although a detection would be challenging at $z \sim 2$. However, a rough rescaling of the relative alignment signal strengths between the TNG and HorizonAGN simulations suggests that PFS GE should be able to more easily constrain the latter's stronger signal.

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arXiv2023

Observational Evidence for Large-Scale Gas Heating in a Galaxy Protocluster at z=2.30

We report a $z=2.30$ galaxy protocluster (COSTCO-I) in the COSMOS field, where the Lyman-$α$ forest as seen in the CLAMATO IGM tomography survey does not show significant absorption. This departs from the transmission-density relationship (often dubbed the fluctuating Gunn-Peterson approximation; FGPA) usually expected to hold at this epoch, which would lead one to predict strong Ly$α$ absorption at the overdensity. For comparison, we generate mock Lyman-$α$ forest maps by applying FGPA to constrained simulations of the COSMOS density field, and create mocks that incorporate the effects of finite sightline sampling, pixel noise, and Wiener filtering. Averaged over $r=15\,h^{-1}\,\mathrm{Mpc}$ around the protocluster, the observed Lyman-$α$ forest is consistently more transparent in the real data than in the mocks, indicating a rejection of the null hypothesis that the gas in COSTCO-I follows FGPA ($p=0.0026$, or $2.79 σ$ significance). It suggests that the large-scale gas associated with COSTCO-I is being heated above the expectations of FGPA, which might be due to either large-scale AGN jet feedback or early gravitational shock heating. COSTCO-I is the first known large-scale region of the IGM that is observed to be transitioning from the optically-thin photoionized regime at Cosmic Noon, to eventually coalesce into an intra-cluster medium (ICM) by $z=0$. Future observations of similar structures will shed light on the growth of the ICM and allow constraints on AGN feedback mechanisms.

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arXiv2023

Searching for the sources of excess extragalactic dispersion of FRBs

The FLIMFLAM survey is collecting spectroscopic data of field galaxies near fast radio burst (FRB) sightlines to constrain key parameters describing the distribution of matter in the Universe. In this work, we leverage the survey data to determine the source of the excess extragalactic dispersion measure (DM), compared to the Macquart relation estimate of four FRBs: FRB20190714A, FRB20200430A, FRB20200906A, and FRB20210117A. By modeling the gas distribution around the foreground galaxy halos and galaxy groups of the sightlines, we estimate $\rm DM_{halos}$, their contribution to the FRB dispersion measures. The FRB20190714A sightline shows a clear excess of foreground halos which contribute roughly 2/3$^{rd}$ of the observed excess DM, thus implying a baryon-dense sightline. FRB20200906A shows a smaller but non-negligible foreground halo contribution, and further analysis of the IGM is necessary to ascertain the true cosmic contribution to its DM. RB20200430A and FRB20210117A show negligible foreground contributions, implying a large host galaxy excess and/or progenitor environment excess.

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arXiv2023

The SSA22 HI Tomography Survey (SSA22-HIT). I. Data Set and Compiled Redshift Catalog

We conducted a deep spectroscopic survey, named SSA22-HIT, in the SSA22 field with the DEep Imaging MultiObject Spectrograph (DEIMOS) on the Keck telescope, designed to tomographically map high-z HI gas through analysis of Lya absorption in background galaxies' spectra. In total, 198 galaxies were spectroscopically confirmed at 2.5 < z < 6 with a few low-z exceptions in the 26 x 15 arcmin^2 area, of which 148 were newly determined in this study. Our redshift measurements were merged with previously confirmed redshifts available in the 34 x 27 arcmin^2 area of the SSA22 field. This compiled catalog containing 730 galaxies of various types at z > 2 is useful for various applications, and it is made publicly available. Our SSA22-HIT survey has increased by approximately twice the number of spectroscopic redshifts of sources at z > 3.2 in the observed field. From a comparison with publicly available redshift catalogs, we show that our compiled redshift catalog in the SSA22 field is comparable to those among major extragalactic survey fields in terms of a combination of wide area and high surface number density of objects at z > 2. About 40 % of the spectroscopically confirmed objects in SSA22-HIT show reasonable quality of spectra in the wavelengths shorter than Lya when a sufficient amount of smoothing is adopted. Our data set enables us to make the HI tomographic map at z > 3, which we present in a parallel study.

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arXiv2023

Second Data Release of the COSMOS Lyman-alpha Mapping and Tomographic Observation: The First 3D Maps of the Detailed Cosmic Web at 2.05<z<2.55

We present the second data release of the COSMOS Lyman-Alpha Mapping And Tomography Observations (CLAMATO) Survey conducted with the LRIS spectrograph on the Keck-I telescope. This project used Lyman-alpha forest absorption in the spectra of faint star forming galaxies and quasars at z ~ 2-3 to trace neutral hydrogen in the intergalactic medium. In particular, we use 320 objects over a footprint of ~0.2 deg^2 to reconstruct the absorption field at 2.05 < z < 2.55 at ~2 h^{-1}Mpc resolution. We apply a Wiener filtering technique to the observed data to reconstruct three dimensional maps of the field over a volume of 4.1 x 10^5 comoving cubic Mpc. In addition to the filtered flux maps, for the first time we infer the underlying dark matter field through a forward modeling framework from a joint likelihood of galaxy and Lyman-alpha forest data, finding clear examples of the detailed cosmic web consisting of cosmic voids, sheets, filaments, and nodes. In addition to traditional figures, we present a number of interactive three dimensional models to allow exploration of the data and qualitative comparisons to known galaxy surveys. We find that our inferred over-densities are consistent with those found from galaxy fields. Our reduced spectra, extracted Lyman-alpha forest pixel data, and reconstructed tomographic maps are available publicly at https://doi.org/10.5281/zenodo.7524313

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arXiv2022

Constraining the Fluctuating Gunn-Peterson Approximation Using Lyman-$α$ Forest Tomography at $z=2$

The fluctuating Gunn-Peterson approximation (FGPA) is a commonly-used method to generate mock Lyman-$α$ (Ly$α$) forest absorption skewers at Cosmic Noon ($z\gtrsim 2$) from the matter-density field of $N$-body simulations without running expensive hydrodynamical simulations. Motivated by recent developments in 3D IGM tomography observations as well as matter density field reconstruction techniques applied to galaxy redshift samples at $z\sim 2$, we examine the possibility of observationally testing FGPA by directly examining the relationship between the Ly$α$ transmission and the underlying matter density field. Specifically, we analyze the EAGLE, Illustris, IllustrisTNG and Nyx cosmological hydrodynamic simulations, that were run with different codes and sub-grid models. While the FGPA is an excellent description of the IGM in lower-density regions, the slope of the transmission-density distribution at higher densities is significantly affected by feedback processes causing the FGPA to break down in that regime. Even without added feedback, we find significant deviations caused by hydrodynamical effects arising from non-linear structure growth. We then proceed to make comparisons using realistic mock data assuming the sightline sampling and spectral properties of the recent CLAMATO survey, and find that it would be challenging to discern between the FGPA and hydrodynamical models with current data sets. However, the improved sightline sampling from future extremely large telescopes or large volumes from multiplexed spectroscopic surveys such as Subaru PFS should allow for stringent tests of the FGPA, and make it possible to detect the effect of galaxy feedback on the IGM.

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arXiv2022

Predicted future fate of COSMOS galaxy protoclusters over 11 Gyr with constrained simulations

Cosmological simulations are crucial tools in studying the Universe, but they typically do not directly match real observed structures. Constrained cosmological simulations, on the other hand, are designed to match the observed distribution of galaxies. Here we present constrained simulations based on spectroscopic surveys at a redshift of z~2.3, corresponding to an epoch of nearly 11 Gyrs ago. This allows us to 'fast-forward' the simulation to our present-day and study the evolution of observed cosmic structures self-consistently. We confirm that several previously-reported protoclusters will evolve into massive galaxy clusters by our present epoch, including the 'Hyperion' structure that we predict will collapse into a giant filamentary supercluster spanning 100 Megaparsecs. We also discover previously unknown protoclusters, with lower final masses than typically detectable by other methods, that nearly double the number of known protoclusters within this volume. Constrained simulations, applied to future high-redshift datasets, represents a unique opportunity for studying early structure formation and matching galaxy properties between high and low redshifts.

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arXiv2022

The extragalactic $γ$-ray background: imprints from the physical properties and evolution of star-forming galaxy populations

Star-forming galaxies (SFGs) harbour an abundant reservoir of cosmic rays (CRs). At GeV energies, these CRs undergo interactions with their environment to produce $γ$-rays, and the unresolved $γ$-ray emission from populations of SFGs forms a component of the isotropic extragalactic $γ$-ray background (EGB). In this work, we investigate the contribution to the 0.01 - 50 GeV EGB from SFG populations located up to redshift $z=3$. We find this is dominated by starbursts, while the contribution from main sequence SFGs is marginal at all energies. We also demonstrate that most of the $γ$-ray contribution from SFGs emanates from low mass galaxies, with over 80 per cent of the emission originating from galaxies with stellar masses below $10^8 \;\!{\rm M}_{\odot}$. Many of these galaxies are located at relatively high redshift, with their peak EGB contribution arising $\sim$ 700 Myr before the noon of cosmic star-formation. We find that the precise redshift distributions of EGB sources at different energies imprint intensity signatures at different angular scales, which may allow their contribution to be distinguished using analyses of small-scale EGB intensity anisotropies, particularly if the diffuse EGB is dominated by hadronic CR-driven $γ$-ray emission from SFGs. We show that the EGB is sensitive to the evolution of low mass populations of galaxies, particularly around $z\sim2.5$, and that it provides a new means to probe the engagement of CRs in these galaxies before the high noon of cosmic star-formation.

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arXiv2022

Constraining the Cosmic Baryon Distribution with Fast Radio Burst Foreground Mapping

The dispersion measures (DM) of fast radio bursts (FRBs) encode the integrated electron density along the line-of-sight, which is typically dominated by the intergalactic medium (IGM) contribution in the case of extragalactic FRBs. In this paper, we show that incorporating wide-field spectroscopic galaxy survey data in the foreground of localized FRBs can significantly improve constraints on the partition of diffuse cosmic baryons. Using mock DMs and realistic lightcone galaxy catalogs derived from the Millennium simulation, we define spectroscopic surveys that can be carried out with 4m and 8m-class wide field spectroscopic facilities. On these simulated surveys, we carry out Bayesian density reconstructions in order to estimate the foreground matter density field. In comparison with the `true' matter density field, we show that these can help reduce the uncertainties in the foreground structures by $\sim 2-3\times$ compared to cosmic variance. We calculate the Fisher matrix to forecast that $N=30\: (96)$ localized FRBs should be able to constrain the diffuse cosmic baryon fraction to $\sim 10\%\: (\sim 5\%) $, and parameters governing the size and baryon fraction of galaxy circumgalactic halos to within $\sim 20-25\%\: (\sim 8-12\%)$. From the Fisher analysis, we show that the foreground data increases the sensitivity of localized FRBs toward our parameters of interest by $\sim 25\times$. We briefly introduce FLIMFLAM, an ongoing galaxy redshift survey that aims to obtain foreground data on $\sim 30$ localized FRB fields.

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arXiv2022

Detecting preheating in proto-clusters with Lyman-$α$ Forest Tomography

Studies of low redshift galaxy clusters suggest the intra-cluster medium (ICM) has experienced non-gravitational heating during the formation phase of the clusters. Using simple phenomenological heating prescriptions, we simulate the effect of this preheating of the nascent ICM in galaxy proto-clusters and examine its effect on Lyman-$α$ (Ly$α$) forest tomographic maps. We analyse a series of cosmological zoom-in simulations of proto-clusters within the framework of the Ly$α$ transmission-dark matter (DM) density distribution. We find that the more energy is injected into the proto-ICM at $z$ = 3, the more the distribution at high DM density tilts towards higher Ly$α$ transmission. This effect has been confirmed in both low-resolution simulations adopting a preheating scheme based on entropy floors, as well as in higher-resolution simulations with another scheme based on energy floors. The evolution of the slope of this distribution is shown to vary with redshift. The methodology developed here can be applied to current and upcoming Ly$α$ forest tomographic survey data to help constrain feedback models in galaxy proto-clusters.

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arXiv2021

Estimating the contribution of foreground halos to the FRB 180924 dispersion measure

Fast Radio Burst (FRB) dispersion measures (DMs) record the presence of ionized baryons that are otherwise invisible to other techniques enabling resolution of the matter distribution in the cosmic web. In this work, we aim to estimate the contribution to FRB 180924 DM from foreground galactic halos. Localized by ASKAP to a massive galaxy, this sightline is notable for an estimated cosmic web contribution to the DM ($\rm DM_{cosmic} = 220~pc~cm^{-3}$), which is less than the average value at the host redshift ($\rm z = 0.3216$) estimated from the Macquart relation ($280~\rm pc~cm^{-3}$). In the favored models of the cosmic web, this suggests few intersections with foreground halos at small impact parameters ($\lesssim 100$ kpc). To test this hypothesis, we carried out spectroscopic observations of the field galaxies within $\sim$1' of the sightline with VLT/MUSE and Keck/LRIS. Furthermore, we developed a probabilistic methodology that leverages photometric redshifts derived from wide-field DES and WISE imaging. We conclude that there is no galactic halo that closely intersects the sightline and also that the net DM contribution from halos, $\rm DM_{halos}< 45~pc~cm^{-3}$ (95 % c.l.). This value is lower than the $\rm DM_{halos}$ estimated from an "average" sightline ($121~\rm pc~cm^{-3}$) using the Planck $ΛCDM$ model and the Aemulus halo mass function and reasonably explains its low $\rm DM_{cosmic}$ value. We conclude that FRB 180924 represents the predicted majority of sightlines in the universe with no proximate foreground galactic halos. Our framework lays the foundation for a comprehensive analysis of FRB fields in the near future.

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arXiv2021

Assessing the signatures imprinted by star-forming galaxies in the cosmic $γ$-ray background

In recent years, $γ$-ray emission has been detected from star-forming galaxies (SFGs) in the local universe, including M82, NGC 253, Arp 220 and M33. The bulk of this emission is thought to be of hadronic origin, arising from the interactions of cosmic rays (CRs) with the interstellar medium of their host galaxy. Distant SFGs are presumably also bright in $γ$-rays. Although they would not be resolvable as point sources, distant unresolved SFG populations contribute $γ$-rays to the extra-galactic $γ$-ray background (EGB). Despite the wealth of high-quality all-sky EGB data collected over more than a decade of operation with the \textit{Fermi}-LAT $γ$-ray space telescope, the exact contribution of SFGs to the EGB remains unsettled. In this study, we model the $γ$-ray emission from SFG populations and demonstrate that such emission can be characterized by just a small number of physically-motivated parameters. We further show that source populations would leave anisotropic signatures in the EGB, which could be used to yield information about the underlying properties, dynamics and evolution of CR-rich SFGs.

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arXiv2021

Probing Feedback via IGM tomography and Ly$α$ forest with Subaru PFS, TMT/ELT, and JWST

In preparation for the IGM tomography study by Subaru Prime Focus Spectrograph (PFS) survey and other large future telescopes such as TMT/ELT/GMT, we present the results of our pilot study on Ly$α$ forest and IGM tomography statistics using the GADGET3-OSAKA cosmological smoothed particle hydrodynamical simulation. Our simulation includes models for star formation and supernova feedback, which enables more realistic cross-correlation studies between galaxies, neutral hydrogen (HI) and metals in circumgalactic and intergalactic medium. We create a light-cone data set at $z=2-3$ from our simulations and generate mock Ly$α$ forest data. As a first step, in this paper, we focus on the distribution of HI and galaxies, and present statistical results on 1D flux PDF, 1D power spectrum, flux contrast vs. impact parameter, HI$-$galaxy cross-correlations. Our results show overall agreement with current observational data, with some interesting discrepancies on small scales that are due to either feedback effects or varying observational conditions. Our simulation shows stronger HI absorption with decreasing transverse distance from galaxies. We find that the massive galaxies with $M_\star \ge 10^{10}\,M_\odot$ contribute strongly to the flux contrast signal, and that the lower-mass galaxies with $M_\star \sim 10^8-10^{10}\,M_\odot$ tend to dilute the flux contrast signal from massive galaxies. On large scales, the average flux contrast smoothly connects to the IGM level, supporting the concordance $Λ$ cold dark matter model. We also find an increase in the HI absorption toward the center of a protocluster.

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arXiv2021

Characterising the signatures of star-forming galaxies in the extra-galactic $γ$-ray background

Galaxies experiencing intense star-formation episodes are expected to be rich in energetic cosmic rays (CRs). These CRs undergo hadronic interactions with the interstellar gases of their host to drive $γ$-ray emission, which has already been detected from several nearby starbursts. Unresolved $γ$-ray emission from more distant star-forming galaxies (SFGs) is expected to contribute to the extra-galactic $γ$-ray background (EGB). However, despite the wealth of high-quality all-sky data from the Fermi-LAT $γ$-ray space telescope collected over more than a decade of operation, the exact contribution of such SFGs to the EGB remains unsettled. We investigate the high-energy $γ$-ray emission from SFGs up to redshift $z=3$ above a GeV, and assess the contribution they can make to the EGB. We show the $γ$-ray emission spectrum from a SFG population can be determined from just a small number of key parameters, from which we model a range of possible EGB realisations. We demonstrate that populations of SFGs leave anisotropic signatures in the EGB, and that these can be accessed using the spatial power spectrum. Moreover, we show that such signatures will be accessible with ongoing operation of current $γ$-ray instruments, and detection prospects will be greatly improved by the next generation of $γ$-ray observatories, in particular the Cherenkov Telescope Array.

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