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Desika Narayanan

Publications and source records attributed to Desika Narayanan.

At least 109 records · Page 6Linked to original sources

The CAMELS Multifield Dataset: Learning the Universe's Fundamental Parameters with Artificial Intelligence

We present the Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS) Multifield Dataset, CMD, a collection of hundreds of thousands of 2D maps and 3D grids containing many different properties of cosmic gas, dark matter, and stars from 2,000 distinct simulated universes at several cosmic times. The 2D maps and 3D grids represent cosmic regions that span $\sim$100 million light years and have been generated from thousands of state-of-the-art hydrodynamic and gravity-only N-body simulations from the CAMELS project. Designed to train machine learning models, CMD is the largest dataset of its kind containing more than 70 Terabytes of data. In this paper we describe CMD in detail and outline a few of its applications. We focus our attention on one such task, parameter inference, formulating the problems we face as a challenge to the community. We release all data and provide further technical details at https://camels-multifield-dataset.readthedocs.io.

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Robust marginalization of baryonic effects for cosmological inference at the field level

We train neural networks to perform likelihood-free inference from $(25\,h^{-1}{\rm Mpc})^2$ 2D maps containing the total mass surface density from thousands of hydrodynamic simulations of the CAMELS project. We show that the networks can extract information beyond one-point functions and power spectra from all resolved scales ($\gtrsim 100\,h^{-1}{\rm kpc}$) while performing a robust marginalization over baryonic physics at the field level: the model can infer the value of $Ω_{\rm m} (\pm 4\%)$ and $σ_8 (\pm 2.5\%)$ from simulations completely different to the ones used to train it.

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Quenching of star formation from a lack of inflowing gas to galaxies

Star formation in half of massive galaxies was quenched by the time the Universe was three billion years old. Very low amounts of molecular gas appear responsible for this, at least in some cases, though morphological gas stabilization, shock heating, or activity associated with accretion onto a central supermassive black hole is invoked in other cases. Recent studies of quenching by gas depletion have been based upon upper limits that are insufficiently sensitive to determine this robustly, or stacked emission with its problems of averaging. Here we report 1.3mm observations of dust emission from six strongly lensed galaxies where star formation has been quenched, with magnifications of up to a factor of 30. Four of the six galaxies are undetected in dust emission, with an estimated upper limit on the dust mass of 0.0001 times the stellar mass, and by proxy (assuming a Milky Way molecular gas-to-dust ratio) 0.01 times the stellar mass in molecular gas. This is two orders of magnitude less molecular gas per unit stellar mass than seen in star forming galaxies at similar redshifts. It remains difficult to extrapolate from these small samples, but these observations establish that gas depletion is responsible for a cessation of star formation in some fraction of high-redshift galaxies.

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Multifield Cosmology with Artificial Intelligence

Astrophysical processes such as feedback from supernovae and active galactic nuclei modify the properties and spatial distribution of dark matter, gas, and galaxies in a poorly understood way. This uncertainty is one of the main theoretical obstacles to extract information from cosmological surveys. We use 2,000 state-of-the-art hydrodynamic simulations from the CAMELS project spanning a wide variety of cosmological and astrophysical models and generate hundreds of thousands of 2-dimensional maps for 13 different fields: from dark matter to gas and stellar properties. We use these maps to train convolutional neural networks to extract the maximum amount of cosmological information while marginalizing over astrophysical effects at the field level. Although our maps only cover a small area of $(25~h^{-1}{\rm Mpc})^2$, and the different fields are contaminated by astrophysical effects in very different ways, our networks can infer the values of $Ω_{\rm m}$ and $σ_8$ with a few percent level precision for most of the fields. We find that the marginalization performed by the network retains a wealth of cosmological information compared to a model trained on maps from gravity-only N-body simulations that are not contaminated by astrophysical effects. Finally, we train our networks on multifields -- 2D maps that contain several fields as different colors or channels -- and find that not only they can infer the value of all parameters with higher accuracy than networks trained on individual fields, but they can constrain the value of $Ω_{\rm m}$ with higher accuracy than the maps from the N-body simulations.

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Finding universal relations in subhalo properties with artificial intelligence

We use a generic formalism designed to search for relations in high-dimensional spaces to determine if the total mass of a subhalo can be predicted from other internal properties such as velocity dispersion, radius, or star-formation rate. We train neural networks using data from the Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS) project and show that the model can predict the total mass of a subhalo with high accuracy: more than 99% of the subhalos have a predicted mass within 0.2 dex of their true value. The networks exhibit surprising extrapolation properties, being able to accurately predict the total mass of any type of subhalo containing any kind of galaxy at any redshift from simulations with different cosmologies, astrophysics models, subgrid physics, volumes, and resolutions, indicating that the network may have found a universal relation. We then use different methods to find equations that approximate the relation found by the networks and derive new analytic expressions that predict the total mass of a subhalo from its radius, velocity dispersion, and maximum circular velocity. We show that in some regimes, the analytic expressions are more accurate than the neural networks. We interpret the relation found by the neural network and approximated by the analytic equation as being connected to the virial theorem.

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Measuring the HI content of individual galaxies out to the epoch of reionization with [CII]

The HI gas content is a key ingredient in galaxy evolution, the study of which has been limited to moderate cosmological distances for individual galaxies due to the weakness of the hyperfine HI 21-cm transition. Here we present a new approach that allows us to infer the HI gas mass $M_{\rm HI}$ of individual galaxies up to $z\approx 6$, based on a direct measurement of the [CII]-to-HI conversion factor in star-forming galaxies at $z\gtrsim 2$ using $γ$-ray burst afterglows. By compiling recent [CII]-158 $μ$m emission line measurements we quantify the evolution of the HI content in galaxies through cosmic time. We find that the HI mass starts to exceed the stellar mass $M_\star$ at $z\gtrsim 1$, and increases as a function of redshift. The HI fraction of the total baryonic mass increases from around $20\%$ at $z = 0$ to about $60\%$ at $z\sim 6$. We further uncover a universal relation between the HI gas fraction $M_{\rm HI}/M_\star$ and the gas-phase metallicity, which seems to hold from $z\approx 6$ to $z=0$. The majority of galaxies at $z>2$ are observed to have HI depletion times, $t_{\rm dep,HI} = M_{\rm HI}/{\rm SFR}$, less than $\approx 2$ Gyr, substantially shorter than for $z\sim 0$ galaxies. Finally, we use the [CII]-to-HI conversion factor to determine the cosmic mass density of HI in galaxies, $ρ_{\rm HI}$, at three distinct epochs: $z\approx 0$, $z\approx 2$, and $z\sim 4-6$. These measurements are consistent with previous estimates based on 21-cm HI observations in the local Universe and with damped Lyman-$α$ absorbers (DLAs) at $z\gtrsim 2$, suggesting an overall decrease by a factor of $\approx 5$ in $ρ_{\rm HI}(z)$ from the end of the reionization epoch to the present.

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Molecular Line Observations in Two Dusty Star-Forming Galaxies at z = 6.9

SPT0311-58 is the most massive infrared luminous system discovered so far during the Epoch of Reionization (EoR). In this paper, we present a detailed analysis of the molecular interstellar medium at z = 6.9, through high-resolution observations of the CO(6-5), CO(7-6), CO(10-9), [CI](2-1), and p-H2O(211-202) lines and dust continuum emission with the Atacama Large Millimeter/submillimeter Array (ALMA). The system consists of a pair of intensely star-forming gravitationally lensed galaxies (labelled West and East). The intrinsic far-infrared luminosity is (16 $\pm$ 4)$\times\rm 10^{12} \ \rm L_{\odot}$ in West and (27 $\pm$ 4)$\times\rm 10^{11} \ \rm L_{\odot}$ in East. We model the dust, CO, and [CI] using non-local thermodynamic equilibrium radiative transfer models and estimate the intrinsic gas mass to be (5.4 $\pm$ 3.4)$\times\rm 10^{11} \ \rm M_{\odot}$ in West and (3.1 $\pm$ 2.7)$\times\rm 10^{10} \ \rm M_{\odot}$ in East. We find that the CO spectral line energy distribution in West and East are typical of high-redshift sub-millimeter galaxies (SMGs). The CO-to-H2 conversion factor ($α_{CO}$) and the gas depletion time scales estimated from the model are consistent with the high-redshift SMGs in the literature within the uncertainties. We find no evidence of evolution of depletion time with redshift in SMGs at z > 3. This is the most detailed study of molecular gas content of a galaxy in the EoR to-date, with the most distant detection of H2O in a galaxy without any evidence for active galactic nuclei in the literature.

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The CAMELS project: Cosmology and Astrophysics with MachinE Learning Simulations

We present the Cosmology and Astrophysics with MachinE Learning Simulations --CAMELS-- project. CAMELS is a suite of 4,233 cosmological simulations of $(25~h^{-1}{\rm Mpc})^3$ volume each: 2,184 state-of-the-art (magneto-)hydrodynamic simulations run with the AREPO and GIZMO codes, employing the same baryonic subgrid physics as the IllustrisTNG and SIMBA simulations, and 2,049 N-body simulations. The goal of the CAMELS project is to provide theory predictions for different observables as a function of cosmology and astrophysics, and it is the largest suite of cosmological (magneto-)hydrodynamic simulations designed to train machine learning algorithms. CAMELS contains thousands of different cosmological and astrophysical models by way of varying $Ω_m$, $σ_8$, and four parameters controlling stellar and AGN feedback, following the evolution of more than 100 billion particles and fluid elements over a combined volume of $(400~h^{-1}{\rm Mpc})^3$. We describe the simulations in detail and characterize the large range of conditions represented in terms of the matter power spectrum, cosmic star formation rate density, galaxy stellar mass function, halo baryon fractions, and several galaxy scaling relations. We show that the IllustrisTNG and SIMBA suites produce roughly similar distributions of galaxy properties over the full parameter space but significantly different halo baryon fractions and baryonic effects on the matter power spectrum. This emphasizes the need for marginalizing over baryonic effects to extract the maximum amount of information from cosmological surveys. We illustrate the unique potential of CAMELS using several machine learning applications, including non-linear interpolation, parameter estimation, symbolic regression, data generation with Generative Adversarial Networks (GANs), dimensionality reduction, and anomaly detection.

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A Long Stream of Metal-Poor Cool Gas around a Massive Starburst Galaxy at z = 2.67

We present the first detailed dissection of the circumgalactic medium (CGM) of massive starburst galaxies at z > 2. Our target is a submillimeter galaxy (SMG) at z = 2.674 that has a star formation rate of 1200 $M_\odot$/yr and a molecular gas reservoir of $1.3\times10^{11} M_\odot$. We characterize its CGM with two background QSOs at impact parameters of 93 kpc and 176 kpc. We detect strong HI and metal-line absorption near the redshift of the SMG towards both QSOs, each consisting of three main subsystems spanning over 1500 km/s. The absorbers show remarkable kinematic and metallicity coherence across a separation of 86 kpc. In particular, the cool gas in the CGM of the SMG exhibits high HI column densities ($\log N_{\rm HI}/{\rm cm}^{-2} = 20.2, 18.6$), low metallicities ([M/H] $\approx$ -2.0), and similar radial velocities ($\approx$ -300 km/s). While the HI column densities match previous results on the CGM around QSOs at z > 2, the metallicities are lower by more than an order of magnitude, making it an outlier in the line width$-$metallicity relation of damped Ly$α$ absorbers. The large physical extent, the velocity coherence, the high surface density, and the low metallicity are all consistent with the cool, inflowing, and near-pristine gas streams predicted to penetrate hot massive halos at z > 1.5. We estimate a total gas accretion rate of ~100 $M_\odot$/yr from three such streams, which falls short of the star formation rate but is consistent with simulations. At this rate, it takes about a gigayear to acquire the molecular gas reservoir of the central starburst.

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{\sc mirkwood:} Fast and Accurate SED Modeling Using Machine Learning

Traditional spectral energy distribution (SED) fitting codes used to derive galaxy physical properties are often uncertain at the factor of a few level owing to uncertainties in galaxy star formation histories and dust attenuation curves. Beyond this, Bayesian fitting (which is typically used in SED fitting software) is an intrinsically compute-intensive task, often requiring access to expensive hardware for long periods of time. To overcome these shortcomings, we have developed {\sc mirkwood}: a user-friendly tool comprising of an ensemble of supervised machine learning-based models capable of non-linearly mapping galaxy fluxes to their properties. By stacking multiple models, we marginalize against any individual model's poor performance in a given region of the parameter space. We demonstrate \textsc{mirkwood}'s significantly improved performance over traditional techniques by training it on a combined data set of mock photometry of z=0 galaxies from the \textsc{Simba}, \textsc{EAGLE} and \textsc{IllustrisTNG} cosmological simulations, and comparing the derived results with those obtained from traditional SED fitting techniques. \textsc{mirkwood} is also able to account for uncertainties arising both from intrinsic noise in observations, and from finite training data and incorrect modeling assumptions. To increase the added value to the observational community, we use Shapley value explanations (SHAP) to fairly evaluate the relative importance of different bands to understand why particular predictions were reached. We envisage \textsc{mirkwood} to be an evolving, open-source framework that will provide highly accurate physical properties from observations of galaxies as compared to traditional SED fitting.

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Reproducing sub-millimetre galaxy number counts with cosmological hydrodynamic simulations

Matching the number counts of high-$z$ sub-millimetre-selected galaxies (SMGs) has been a long standing problem for galaxy formation models. In this paper, we use 3D dust radiative transfer to model the sub-mm emission from galaxies in the SIMBA cosmological hydrodynamic simulations, and compare predictions to the latest single-dish observational constraints on the abundance of 850$\mathrm{μm}$-selected sources. We find good agreement with the shape of the integrated 850$\mathrm{μm}$ luminosity function, and the normalisation is within 0.25 dex at $> 3 \; \mathrm{mJy}$, unprecedented for a fully cosmological hydrodynamic simulation, along with good agreement in the redshift distribution of bright SMGs. The agreement is driven primarily by SIMBA's good match to infrared measures of the star formation rate (SFR) function between $z = 2-4$ at high SFRs. Also important is the self-consistent on-the-fly dust model in SIMBA, which predicts, on average, higher dust masses (by up to a factor of 2.5) compared to using a fixed dust-to-metals ratio of 0.3. We construct a lightcone to investigate the effect of far-field blending, and find that 52% of sources are blends of multiple components, which makes a small contribution to the normalisation of the bright-end of the number counts. We provide new fits to the 850$\mathrm{μm}$ luminosity as a function of SFR and dust mass. Our results demonstrate that exotic solutions to the discrepancy between sub-mm counts in simulations and observations, such as a top-heavy IMF, are unnecessary, and that sub-millimetre-bright phases are a natural consequence of massive galaxy evolution.

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The Origin of the Dust Extinction Curve in Milky Way-like Galaxies

We develop a cosmological model for the evolution of dust grains in galaxies with a distribution of sizes in order to understand the origin of the Milky Way dust extinction curve. Our model considers the formation of active dust in evolved stars, growth by accretion and coagulation, and destruction processes via shattering, sputtering, and astration in the ISM of galaxies over cosmic time. Our main results follow. Galaxies in our cosmological model with masses comparable to the Milky Way's at z~0 exhibit a diverse range of extinction laws, though with slopes and bump strengths comparable to the range observed in the Galaxy. The progenitors of the Milky Way have steeper slopes, and only flatten to slopes comparable to the Galaxy at $z \approx 1$. This owes to increased grain growth rates at late times/in high-metallicity environments driving up the ratio of large to small grains, with a secondary dependence on the graphite to silicate ratio evolution. The UV bump strengths depend primarily on the graphite to silicate ratio, and remain broadly constant in MW-like galaxies between z=3 and z=0, though show slight variability. Our models span comparable regions of bump-slope space as sightlines in the Galaxy do, though there is a lack of clear relationship between the model slopes and bump strengths owing to small scale fluctuations in the bump strength. Our models naturally produce slopes for some non-Milky Way analogs as steep as those of the LMC and SMC in metal poor galaxies, though notably the bump strengths are, on average, too large when comparing to the Magellanic clouds. This owes to the fact that we evolve the grain size distributions of graphites and silicates simultaneously, which is an oversimplification. Our model provides a novel framework to study the origins and variations of dust extinction curves in galaxies over cosmic time.

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ALMA measures rapidly depleted molecular gas reservoirs in massive quiescent galaxies at z~1.5

We present ALMA CO(2-1) spectroscopy of 6 massive (log$_{10}$M$_{\rm{*}}/\rm{M}_\odot>$11.3) quiescent galaxies at $z\sim1.5$. These data represent the largest sample using CO emission to trace molecular gas in quiescent galaxies above $z>1$, achieving an average 3$σ$ sensitivity of M$_{\rm{H_{2}}}\sim10^{10}\rm{M}_\odot$. We detect one galaxy at 4$σ$ significance and place upper limits on the molecular gas reservoirs of the other 5, finding molecular gas mass fractions M$_{\rm{H_{2}}}$/M$_{\rm{*}}$=f$_{\rm{H_{2}}}<2-6$% (3$σ$ upper limits). This is 1-2 orders of magnitude lower than coeval star-forming galaxies at similar stellar mass, and comparable to galaxies at $z=0$ with similarly low sSFR. This indicates that their molecular gas reservoirs were rapidly and efficiently used up or destroyed, and that gas fractions are uniformly low ($<$6%) despite the structural diversity of our sample. The implied rapid depletion time of molecular gas (t$_{\rm{dep}}<0.6$ Gyr) disagrees with extrapolations of empirical scaling relations to low sSFR. We find that our low gas fractions are instead in agreement with predictions from both the recent SIMBA cosmological simulation, and from analytical "bathtub" models for gas accretion onto galaxies in massive dark matter halos (log$_{10}M_{\rm{halo}}/\rm{M}_\odot\sim14$ at $z=0$). Such high mass halos reach a critical mass of log$_{10}M_{\rm{halo}}/\rm{M}_\odot>12$ by $z\sim4$ that halt the accretion of baryons early in the Universe. Our data is consistent with a simple picture where galaxies truncate accretion and then consume the existing gas at or faster than typical main sequence rates. Alternatively, we cannot rule out that these galaxies reside in lower mass halos, and low gas fractions may instead reflect either stronger feedback, or more efficient gas consumption.

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How Well Can We Measure the Stellar Mass of a Galaxy: The Impact of the Assumed Star Formation History Model in SED Fitting

The primary method for inferring the stellar mass ($M_*$) of a galaxy is through spectral energy distribution (SED) modeling. However, the technique rests on assumptions such as the galaxy star formation history and dust attenuation law that can severely impact the accuracy of derived physical properties from SED modeling. Here, we examine the effect that the assumed star formation history (SFH) has on the stellar properties inferred from SED fitting by ground truthing them against mock observations of high-resolution cosmological hydrodynamic galaxy formation simulations. Classically, SFHs are modeled with simplified parameterized functional forms, but these forms are unlikely to capture the true diversity of galaxy SFHs and may impose systematic biases with under-reported uncertainties on results. We demonstrate that flexible nonparametric star formation histories outperform traditional parametric forms in capturing variations in galaxy star formation histories, and as a result, lead to significantly improved stellar masses in SED fitting. We find a decrease in the average bias of 0.4 dex with a delayed-$τ$ model to a bias of just under 0.05 dex for the nonparametric model. Similarly, using nonparametric star formation histories in SED fitting result in increased accuracy in recovered galaxy star formation rates (SFRs) and stellar ages.

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Ubiquitous Molecular Outflows in z > 4 Massive, Dusty Galaxies I. Sample Overview and Clumpy Structure in Molecular Outflows on 500pc Scales

Massive galaxy-scale outflows of gas are one of the most commonly-invoked mechanisms to regulate the growth and evolution of galaxies throughout the universe. While the gas in outflows spans a large range of temperatures and densities, the cold molecular phase is of particular interest because molecular outflows may be capable of suppressing star formation in galaxies by removing the star-forming gas. We have conducted the first survey of molecular outflows at z > 4, targeting 11 strongly-lensed dusty, star-forming galaxies (DSFGs) with high-resolution Atacama Large Millimeter Array (ALMA) observations of OH 119um absorption as an outflow tracer. In this first paper, we give an overview of the survey, focusing on the detection rate and structure of molecular outflows. We find unambiguous evidence for outflows in 8/11 (73%) galaxies, more than tripling the number known at z > 4. This implies that molecular winds in z > 4 DSFGs must have both a near-unity occurrence rate and large opening angles to be detectable in absorption. Lensing reconstructions reveal that 500pc-scale clumpy structures in the outflows are common. The individual clumps are not directly resolved, but from optical depth arguments we expect that future observations will require 50-200pc spatial resolution to do so. We do not detect high-velocity [CII] wings in any of the sources with clear OH outflows, indicating that [CII] is not a reliable tracer of molecular outflows. Our results represent a first step toward characterizing molecular outflows at z > 4 at the population level, demonstrating that large-scale outflows are ubiquitous among early massive, dusty galaxies.

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Ubiquitous Molecular Outflows in z > 4 Massive, Dusty Galaxies II. Momentum-Driven Winds Powered by Star Formation in the Early Universe

Galactic outflows of molecular gas are a common occurrence in galaxies and may represent a mechanism by which galaxies self-regulate their growth, redistributing gas that could otherwise have formed stars. We previously presented the first survey of molecular outflows at z > 4 towards a sample of massive, dusty galaxies. Here we characterize the physical properties of the molecular outflows discovered in our survey. Using low-redshift outflows as a training set, we find agreement at the factor-of-two level between several outflow rate estimates. We find molecular outflow rates 150-800Msun/yr and infer mass loading factors just below unity. Among the high-redshift sources, the molecular mass loading factor shows no strong correlations with any other measured quantity. The outflow energetics are consistent with expectations for momentum-driven winds with star formation as the driving source, with no need for energy-conserving phases. There is no evidence for AGN activity in our sample, and while we cannot rule out deeply-buried AGN, their presence is not required to explain the outflow energetics, in contrast to nearby obscured galaxies with fast outflows. The fraction of the outflowing gas that will escape into the circumgalactic medium (CGM), though highly uncertain, may be as high as 50%. This nevertheless constitutes only a small fraction of the total cool CGM mass based on a comparison to z~2-3 quasar absorption line studies, but could represent >~10% of the CGM metal mass. Our survey offers the first statistical characterization of molecular outflow properties in the very early universe.

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Predictions of the L$_{\rm[CII]}$-SFR and [C$_{\rm II}$] Luminosity Function at the Epoch of Reionization

We present the first predictions for the $L_{\rm [CII]}$ - SFR relation and [CII] luminosity function (LF) in the Epoch of Reionization (EoR) based on cosmological hydrodynamics simulations using the SIMBA suite plus radiative transfer calculations via SÍGAME. The sample consists of 11,137 galaxies covering halo mass $\log M_{\rm halo}\in$[9, 12.4] $M_\odot$, star formation rate SFR$\in$[0.01, 330] $M_\odot$ yr$^{-1}$, and metallicity $ _{\rm SFR}\in$[0.1, 0.9] $Z_\odot$. The simulated $L_{\rm [CII]}$-SFR relation is consistent with the range observed, but with a spread of $\simeq$0.3 dex at the high end of SFR ($>$100 $M_\odot$ yr$^{-1}$) and $\simeq$0.6 dex at the lower end, and there is tension between our predictions and the values of $L_{\rm [CII]}$ above 10$^{8.5}$ $L_\odot$ observed in some galaxies reported in the literature. The scatter in the $L_{\rm [CII]}$-SFR relation is mostly driven by galaxy properties, such that at a given SFR, galaxies with higher molecular gas mass and metallicity have higher $L_{\rm [CII]}$. The [CII] LF predicted by SIMBA is consistent with the upper limits placed by the only existing untargeted flux-limited [CII] survey at the EoR (ASPECS) and those predicted by semi-analytic models. We compare our results with existing models and discuss differences responsible for the discrepant slopes in the $L_{\rm [CII]}$-SFR relatiion.

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SQuIGG$\vec{L}$E Survey: Massive z$\sim$0.6 Post-Starburst Galaxies Exhibit Flat Age Gradients

We present Gemini GMOS IFU observations of six massive ($M_\star\geq10^{11} \ M_\odot$) A-star dominated post-starburst galaxies at $z\sim0.6$. These galaxies are a subsample of the SQuIGG$\vec{L}$E Survey, which selects intermediate-redshift post-starbursts from the Sloan Digital Sky Survey spectroscopic sample (DR14) with spectral shapes that indicate they have recently shut off their primary epoch of star formation. Using $Hδ_A$ absorption as a proxy for stellar age, we constrain five of the galaxies to have young ($\sim 600$ Myr) light-weighted ages at all radii and find that the sample on average has flat age gradients. We examine the spatial distribution of mass-weighted properties by fitting our profiles with a toy model including a young, centrally concentrated burst superimposed on an older, extended population. We find that galaxies with flat $Hδ_A$ profiles are inconsistent with formation via a central secondary starburst. This implies that the mechanism responsible for shutting off this dominant episode of star formation must have done so uniformly throughout the galaxy.

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