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James S. Bullock

Publications and source records attributed to James S. Bullock.

At least 37 records · Page 2Linked to original sources

An analytic surface density profile for $Λ$CDM halos and gravitational lensing studies

We introduce an analytic surface density profile for dark matter halos that accurately reproduces the structure of simulated halos of mass $M_{\rm vir} = 10^{7-11}\ M_\odot$, making it useful for modeling line-of-sight perturbers in strong gravitational lensing models. The two-parameter function has an analytic deflection potential and is more accurate than the projected Navarro, Frenk & White (NFW) profile commonly adopted at this mass scale for perturbers, especially at the small radii of most relevant for lensing perturbations. Using a characteristic radius, $R_{-1}$, where the log slope of surface density is equal to $-1$, and an associated surface density, $Σ_{-1}$, we can represent the expected lensing signal from line-of-sight halos statistically, for an ensemble of halo orientations, using a distribution of {\em projected concentration} parameters, $\mathcal{C}_{\rm vir} := r_{\rm vir}/ R_{-1}$. Though an individual halo can have a projected concentration that varies with orientation with respect to the observer, the range of projected concentrations correlates with the usual three-dimensional halo concentration in a way that enables ease of use.

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Starburst-induced gas-stars kinematic misalignment

A kinematic misalignment of the stellar and gas components is a phenomenon observed in a significant fraction of galaxies. However, the underlying physical mechanisms are not well understood. A commonly proposed scenario for the formation of a misaligned component requires any pre-existing gas disc to be removed, via fly-bys or ejective feedback from an active galactic nucleus. In this Letter, we study the evolution of a Milky Way mass galaxy in the FIREbox cosmological volume that displays a thin, counter-rotating gas disc with respect to its stellar component at low redshift. In contrast to scenarios involving gas ejection, we find that pre-existing gas is mainly removed via the conversion into stars in a central starburst, triggered by a merging satellite galaxy. The newly-accreted, counter-rotating gas eventually settles into a kinematically misaligned disc. About 4.4 (8 out of 182) of FIREbox galaxies with stellar masses larger than 5e9 Msun at z=0 exhibit gas-star kinematic misalignment. In all cases, we identify central starburst-driven depletion as the main reason for the removal of the pre-existing co-rotating gas component, with no need for feedback from, e.g., a central active black hole. However, during the starburst, the gas is funneled towards the central regions, likely enhancing black hole activity. By comparing the fraction of misaligned discs between FIREbox and other simulations and observations, we conclude that this channel might have a non-negligible role in inducing kinematic misalignment in galaxies.

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Born this way: thin disc, thick disc, and isotropic spheroid formation in FIRE-2 Milky-Way-mass galaxy simulations

We investigate the formation of Milky-Way-mass galaxies using FIRE-2 LCDM cosmological zoom-in simulations by studying the orbital evolution of stars formed in the main progenitor of the galaxy, from birth to the present day. We classify in situ stars as isotropic spheroid, thick-disc, and thin-disc according to their orbital circularities and show that these components are assembled in a time-ordered sequence from early to late times, respectively. All simulated galaxies experience an early phase of bursty star formation that transitions to a late-time steady phase. This transition coincides with the time that the inner CGM virializes. During the early bursty phase, galaxies have irregular morphologies and new stars are born on radial orbits; these stars evolve into an isotropic spheroidal population today. The bulk of thick-disc stars form at intermediate times, during a clumpy-disc ``spin-up'' phase, slightly later than the peak of spheroid formation. At late times, once the CGM virializes and star formation ``cools down," stars are born on circular orbits within a narrow plane. Those stars mostly inhabit thin discs today. Broadly speaking, stars with disc-like or spheroid-like orbits today were born that way. Mergers onto discs and secular processes do affect kinematics in our simulations, but play only secondary roles in populating thick-disc and in situ spheroid populations at z=0. The age distributions of spheroid, thick disc, and thin disc populations scale self-similarly with the steady-phase transition time, which suggests that morphological age dating can be linked to the CGM virialization time in galaxies.

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FIREbox: Simulating galaxies at high dynamic range in a cosmological volume

We introduce a suite of cosmological volume simulations to study the evolution of galaxies as part of the Feedback in Realistic Environments project. FIREbox, the principal simulation of the present suite, provides a representative sample of galaxies (~1000 galaxies with Mstar > 10^8 Msun at z=0) at a resolution (~20 pc, m_b ~ 6x10^4 Msun) comparable to state-of-the-art galaxy zoom-in simulations. FIREbox captures the multiphase nature of the interstellar medium in a fully cosmological setting (L=22.1 Mpc) thanks to its exceptionally high dynamic range (~10^6) and the inclusion of multi-channel stellar feedback. Here, we focus on validating the simulation predictions by comparing to observational data. We find that simulated galaxies with Mstar < 10^{10.5-11} Msun have star formation rates, gas masses, and metallicities in broad agreement with observations. These galaxy scaling relations extend to low masses (Mstar ~ 10^7 Msun) and follow a (broken) power-law relationship. Also reproduced are the evolution of the cosmic HI density and the HI column density distribution at z~0-5. At low z, FIREbox predicts a peak in the stellar-mass--halo-mass relation, but also a higher abundance of massive galaxies and a higher cosmic star formation rate density than observed, showing that stellar feedback alone is insufficient to reproduce the properties of massive galaxies at late times. Given its high resolution and sample size, FIREbox offers a baseline prediction of galaxy formation theory in a $Λ$CDM Universe while also highlighting modeling challenges to be addressed in next-generation galaxy simulations.

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Public data release of the FIRE-2 cosmological zoom-in simulations of galaxy formation

We describe a public data release of the FIRE-2 cosmological zoom-in simulations of galaxy formation, available at http://flathub.flatironinstitute.org/fire, from the Feedback In Realistic Environments (FIRE) project. FIRE-2 simulations achieve parsec-scale resolution to explicitly model the multi-phase interstellar medium while implementing direct models for stellar evolution and feedback, including stellar winds, core-collapse and Ia supernovae, radiation pressure, photoionization, and photoelectric heating. We release complete snapshots from 3 suites of simulations. The first comprises 20 simulations that zoom in on 14 Milky Way-mass galaxies, 5 SMC/LMC-mass galaxies, and 4 lower-mass galaxies including 1 ultra-faint; we release 39 snapshots across z = 0 - 10. The second comprises 4 massive galaxies, with 19 snapshots across z = 1 - 10. Finally, a high-redshift suite comprises 22 simulations, with 11 snapshots across z = 5 - 10. Each simulation also includes dozens of resolved lower-mass (satellite) galaxies in its zoom-in region. Snapshots include all stored properties for all dark matter, gas, and star particles, including 11 elemental abundances for stars and gas, and formation times (ages) of star particles. We also release accompanying (sub)halo catalogs, which include galaxy properties and member star particles. For the simulations to z = 0, including all Milky Way-mass galaxies, we release the formation coordinates and an "ex-situ" flag for all star particles, pointers to track particles across snapshots, catalogs of stellar streams, and multipole basis expansions for the halo mass distributions. We describe publicly available python packages for reading and analyzing these simulations.

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The JWST Resolved Stellar Populations Early Release Science Program II. Survey Overview

We present the JWST Resolved Stellar Populations Early Release Science (ERS) science program. We obtained 27.5 hours of NIRCam and NIRISS imaging of three targets in the Local Group (Milky Way globular cluster M92, ultra-faint dwarf galaxy Draco II, star-forming dwarf galaxy WLM), which span factors of $\sim10^5$ in luminosity, $\sim10^4$ in distance, and $\sim10^5$ in surface brightness. We describe the survey strategy, scientific and technical goals, implementation details, present select NIRCam color-magnitude diagrams (CMDs), and validate the NIRCam exposure time calculator (ETC). Our CMDs are among the deepest in existence for each class of target. They touch the theoretical hydrogen burning limit in M92 ($<0.08$ $M_{\odot}$; SNR $\sim5$ at $m_{F090W}\sim28.2$; $M_{F090W}\sim+13.6$), include the lowest-mass stars observed outside the Milky Way in Draco II (0.09 $M_{\odot}$; SNR $=10$ at $m_{F090W}\sim29$; $M_{F090W}\sim+12.1$), and reach $\sim1.5$ magnitudes below the oldest main sequence turnoff in WLM (SNR $=10$ at $m_{F090W}\sim29.5$; $M_{F090W}\sim+4.6$). The PARSEC stellar models provide a good qualitative match to the NIRCam CMDs, though are $\sim0.05$ mag too blue compared to M92 F090W$-$F150W data. The NIRCam ETC (v2.0) matches the SNRs based on photon noise from DOLPHOT stellar photometry in uncrowded fields, but the ETC may not be accurate in more crowded fields, similar to what is known for HST. We release beta versions of DOLPHOT NIRCam and NIRISS modules to the community. Results from this ERS program will establish JWST as the premier instrument for resolved stellar populations studies for decades to come.

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Motivations for a Large Self-Interacting Dark Matter Cross Section from Milky Way Satellites

We explore the properties of Milky Way subhalos in self-interacting dark matter models for moderate cross sections of 1 to 5 cm$^2$g$^{-1}$ using high-resolution zoom-in N-body simulations. We include the gravitational potential of a baryonic disk and bulge matched to the Milky Way, which is critical for getting accurate predictions. The predicted number and distribution of subhalos within the host halo are similar for 1 and 5 cm$^2$g$^{-1}$ models, and they agree with observations of Milky Way satellite galaxies only if subhalos with peak circular velocity over all time > 4.5 km/s are able to form galaxies. We do not find distinctive signatures in the pericenter distribution of the subhalos that could help distinguish the models. Using an analytic model to extend the simulation results, we are able to show that subhalos in models with cross sections between 1 and 5 cm$^2$g$^{-1}$ are not dense enough to match the densest ultra-faint and classical dwarf spheroidal galaxies in the Milky Way. This motivates velocity-dependent cross sections with values larger than 5 cm$^2$g$^{-1}$ at the velocities relevant for the satellites such that core collapse would occur in some of the ultra-faint and classical dwarf spheroidals.

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Dwarf galaxy formation with and without dark matter-baryon streaming velocities

We study how supersonic streaming velocities of baryons relative to dark matter -- a large-scale effect imprinted at recombination and coherent over $\sim 3$ Mpc scales -- affects the formation of dwarf galaxies at $z \gtrsim 5$. We perform cosmological hydrodynamic simulations, including and excluding streaming velocities, in regions centered on halos with $M_{\rm vir}(z=0) \approx 10^{10}$ M$_{\odot}$; the simulations are part of the Feedback In Realistic Environments (FIRE) project and run with FIRE-3 physics. Our simulations comprise many thousands of systems with halo masses between $M_{\rm vir} = 2\times10^{5}$ M$_{\odot}$ and $2\times10^9$ M$_{\odot}$ in the redshift range $z=20-5$. A few hundred of these galaxies form stars and have stellar masses ranging from 100 to $10^7$ M$_{\odot}$. While star formation is globally delayed by approximately 50 Myr in the streaming relative to non-streaming simulations and the number of luminous galaxies is correspondingly suppressed at high redshift in the streaming runs, these effects decay with time. By $z=5$, the properties of the simulated galaxies are nearly identical in the streaming versus non-streaming runs, indicating that any effects of streaming velocities on the properties of galaxies at the mass scale of classical dwarfs and larger do not persist to $z=0$.

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The Hubble Space Telescope Survey of M31 Satellite Galaxies I. RR Lyrae-based Distances and Refined 3D Geometric Structure

We measure homogeneous distances to M31 and 38 associated stellar systems ($-$16.8$\le M_V \le$ $-$6.0), using time-series observations of RR Lyrae stars taken as part of the Hubble Space Telescope Treasury Survey of M31 Satellites. From $>700$ orbits of new/archival ACS imaging, we identify $>4700$ RR Lyrae stars and determine their periods and mean magnitudes to a typical precision of 0.01 days and 0.04 mag. Based on Period-Wesenheit-Metallicity relationships consistent with the Gaia eDR3 distance scale, we uniformly measure heliocentric and M31-centric distances to a typical precision of $\sim20$ kpc (3%) and $\sim10$ kpc (8%), respectively. We revise the 3D structure of the M31 galactic ecosystem and: (i) confirm a highly anisotropic spatial distribution such that $\sim80$% of M31's satellites reside on the near side of M31; this feature is not easily explained by observational effects; (ii) affirm the thin (rms $7-23$ kpc) planar "arc" of satellites that comprises roughly half (15) of the galaxies within 300 kpc from M31; (iii) reassess physical proximity of notable associations such as the NGC 147/185 pair and M33/AND XXII; and (iv) illustrate challenges in tip-of-the-red-giant branch distances for galaxies with $M_V > -9.5$, which can be biased by up to 35%. We emphasize the importance of RR Lyrae for accurate distances to faint galaxies that should be discovered by upcoming facilities (e.g., Rubin Observatory). We provide updated luminosities and sizes for our sample. Our distances will serve as the basis for future investigation of the star formation and orbital histories of the entire known M31 satellite system.

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Amplified J-factors in the Galactic Center for velocity-dependent darkmatter annihilation in FIRE simulations

We use FIRE-2 zoom cosmological simulations of Milky Way size galaxy halos to calculate astrophysical J-factors for dark matter annihilation and indirect detection studies. In addition to velocity-independent (s-wave) annihilation cross sections $σ_v$, we also calculate effective J-factors for velocity-dependent models, where the annihilation cross section is either either p-wave ($\propto v^2/c^2$) or d-wave ($\propto v^4/c^4$). We use 12 pairs of simulations, each run with dark-matter-only (DMO) physics and FIRE-2 physics. We observe FIRE runs produce central dark matter velocity dispersions that are systematically larger than in DMO runs by factors of $\sim 2.5-4$. They also have a larger range of central ($\sim 400$ pc) dark matter densities than the DMO runs ($ρ_{\rm FIRE}/ρ_{\rm DMO} \simeq 0.5 - 3$) owing to the competing effects of baryonic contraction and feedback. At 3 degrees from the Galactic Center, FIRE J-factors are $5-50$ (p-wave) and $15-500$ (d-wave) times higher than in the DMO runs. The change in s-wave signal at 3 degrees is more modest and can be higher or lower ($\sim 0.3-6$), though the shape of the emission profile is flatter (less peaked towards the Galactic Center) and more circular on the sky in FIRE runs. Our results for s-wave are broadly consistent with the range of assumptions in most indirect detection studies. We observe p-wave J-factors that are significantly enhanced compared to most past estimates. We find that thermal models with p-wave annihilation may be within range of detection in the near future.

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Comparing Implementations of Self-Interacting Dark Matter in the Gizmo and Arepo Codes

Self-interacting dark matter (SIDM) models have received great attention over the past decade as solutions to the small-scale puzzles of astrophysics. Though there are different implementations of dark matter (DM) self-interactions in N-body codes of structure formation, there has not been a systematic study to compare the predictions of these different implementations. We investigate the implementation of dark matter self-interactions in two simulation codes: Gizmo and Arepo. We begin with identical initial conditions for an isolated $10^{10}$ M$_\odot$ dark matter halo and investigate the evolution of the density and velocity dispersion profiles in Gizmo and Arepo for SIDM cross-section over mass of 1, 5, and 50 $\rm cm^2 g^{-1}$. Our tests are restricted to the core expansion phase where the core density decreases and core radius increases with time. We find better than 30% agreement between the codes for the density profile in this phase of evolution, with the agreement improving at higher resolution. We find that varying code-specific SIDM parameters changes the central halo density by less than 10% outside of the convergence radius. We argue that SIDM core formation is robust across the two different schemes and conclude that these codes can reliably differentiate between cross-sections of 1, 5, and 50 $\rm cm^2 g^{-1}$ but finer distinctions would require further investigation.

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Formation of proto-globular cluster candidates in cosmological simulations of dwarf galaxies at $z>4$

We perform cosmological hydrodynamical simulations to study the formation of proto-globular cluster candidates in progenitors of present-day dwarf galaxies $(M_{\rm vir} \approx 10^{10}\, {\rm M}_\odot$ at $z=0$) as part of the "Feedback in Realistic Environment" (FIRE) project. Compact ($r_{1/2}<30$ pc), relatively massive ($0.5 \times 10^5 \lesssim M_{\star}/{\rm M}_\odot \lesssim 5\times10^5$), self-bound stellar clusters form at $11\gtrsim z \gtrsim 5$ in progenitors with $M_{\rm vir} \approx 10^9\,{\rm M}_\odot$. Cluster formation is triggered when at least $10^7\,{\rm M}_\odot$ of dense, turbulent gas reaches $Σ_{\rm gas} \approx 10^4\, {\rm M}_\odot\, {\rm pc}^{-2}$ as a result of the compressive effects of supernova feedback or from cloud-cloud collisions. The clusters can survive for $2-3\,{\rm Gyr}$; absent numerical effects, they would likely survive substantially longer, perhaps to $z=0$. The longest-lived clusters are those that form at significant distance -- several hundreds of pc -- from their host galaxy. We therefore predict that globular clusters forming in progenitors of present-day dwarf galaxies will be offset from any pre-existing stars within their host dark matter halos as opposed to deeply embedded within a well-defined galaxy. Properties of the nascent clusters are consistent with observations of some of the faintest and most compact high-redshift sources in \textit{Hubble Space Telescope} lensing fields and are at the edge of what will be detectable as point sources in deep imaging of non-lensed fields with the \textit{James Webb Space Telescope}. By contrast, the star clusters' host galaxies will remain undetectable.

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FIRE-3: Updated Stellar Evolution Models, Yields, & Microphysics and Fitting Functions for Applications in Galaxy Simulations

Increasingly, uncertainties in predictions from galaxy formation simulations (at sub-Milky Way masses) are dominated by uncertainties in stellar evolution inputs. In this paper, we present the full set of updates from the FIRE-2 version of the Feedback In Realistic Environments (FIRE) project code, to the next version, FIRE-3. While the transition from FIRE-1 to FIRE-2 focused on improving numerical methods, here we update the stellar evolution tracks used to determine stellar feedback inputs, e.g. stellar mass-loss (O/B and AGB), spectra (luminosities and ionization rates), and supernova rates (core-collapse and Ia), as well as detailed mass-dependent yields. We also update the low-temperature cooling and chemistry, to enable improved accuracy at $T \lesssim 10^{4}\,$K and densities $n\gg 1\,{\rm cm^{-3}}$, and the meta-galactic ionizing background. All of these synthesize newer empirical constraints on these quantities and updated stellar evolution and yield models from a number of groups, addressing different aspects of stellar evolution. To make the updated models as accessible as possible, we provide fitting functions for all of the relevant updated tracks, yields, etc, in a form specifically designed so they can be directly 'plugged in' to existing galaxy formation simulations. We also summarize the default FIRE-3 implementations of 'optional' physics, including spectrally-resolved cosmic rays and supermassive black hole growth and feedback.

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Galaxies lacking dark matter produced by close encounters in a cosmological simulation

The standard cold dark matter plus cosmological constant model predicts that galaxies form within dark-matter haloes, and that low-mass galaxies are more dark-matter dominated than massive ones. The unexpected discovery of two low-mass galaxies lacking dark matter immediately provoked concerns about the standard cosmology and ignited explorations of alternatives, including self-interacting dark matter and modified gravity. Apprehension grew after several cosmological simulations using the conventional model failed to form adequate numerical analogues with comparable internal characteristics (stellar masses, sizes, velocity dispersions and morphologies). Here we show that the standard paradigm naturally produces galaxies lacking dark matter with internal characteristics in agreement with observations. Using a state-of-the-art cosmological simulation and a meticulous galaxy-identification technique, we find that extreme close encounters with massive neighbours can be responsible for this. We predict that approximately 30 percent of massive central galaxies (with at least 1e11 solar masses in stars) harbour at least one dark-matter-deficient satellite (with 1e8 - 1e9 solar masses in stars). This distinctive class of galaxies provides an additional layer in our understanding of the role of interactions in shaping galactic properties. Future observations surveying galaxies in the aforementioned regime will provide a crucial test of this scenario.

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The effects of LMC-mass environments on their dwarf satellite galaxies in the FIRE simulations

Characterizing the predicted environments of dwarf galaxies like the Large Magellanic Cloud (LMC) is becoming increasingly important as next generation surveys push sensitivity limits into this low-mass regime at cosmological distances. We study the environmental effects of LMC-mass halos ($M_{200m} \sim 10^{11}$ M$_\odot$) on their populations of satellites ($M_\star \geq 10^4$ M$_\odot$) using a suite of zoom-in simulations from the Feedback In Realistic Environments (FIRE) project. Our simulations predict significant hot coronas with $T\sim10^5$ K and $M_\text{gas}\sim10^{9.5}$ M$_\odot$. We identify signatures of environmental quenching in dwarf satellite galaxies, particularly for satellites with intermediate mass ($M_\star = 10^{6-7}$ M$_\odot$). The gas content of such objects indicates ram-pressure as the likely quenching mechanism, sometimes aided by star formation feedback. Satellites of LMC-mass hosts replicate the stellar mass dependence of the quiescent fraction found in satellites of MW mass hosts (i.e. that the quiescent fraction increases as stellar mass decreases). Satellites of LMC-mass hosts have a wider variety of quenching times when compared to the strongly bi-modal distribution of quenching times of nearby centrals. Finally, we identify significant tidal stellar structures around four of our six LMC-analogs, suggesting that stellar streams may be common. These tidal features originated from satellites on close orbits, extend to $\sim$80 kpc from the central galaxy, and contain $\sim10^{6-7}$ M$_\odot$~of stars.

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The bursty origin of the Milky Way thick disc

We investigate thin and thick stellar disc formation in Milky-Way-mass galaxies using twelve FIRE-2 cosmological zoom-in simulations. All simulated galaxies experience an early period of bursty star formation that transitions to a late-time steady phase of near-constant star formation. Stars formed during the late-time steady phase have more circular orbits and thin-disc-like morphology at $z=0$, whilst stars born during the bursty phase have more radial orbits and thick-disc structure. The median age of thick-disc stars at $z=0$ correlates strongly with this transition time. We also find that galaxies with an earlier transition from bursty to steady star formation have a higher thin-disc fractions at $z=0$. Three of our systems have minor mergers with LMC-size satellites during the thin-disc phase. These mergers trigger short starbursts but do not destroy the thin disc nor alter broad trends between the star formation transition time and thin/thick disc properties. If our simulations are representative of the Universe, then stellar archaeological studies of the Milky Way (or M31) provide a window into past star-formation modes in the Galaxy. Current age estimates of the Galactic thick disc would suggest that the Milky Way transitioned from bursty to steady phase $\sim$6.5 Gyr ago; prior to that time the Milky Way likely lacked a recognisable thin disc.

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Out of sight, out of mind? The impact of correlated clustering in substructure lensing

A promising route for revealing the existence of dark matter structures on mass scales smaller than the faintest galaxies is through their effect on strong gravitational lenses. We examine the role of local, lens-proximate clustering in boosting the lensing probability relative to contributions from substructure and unclustered line-of-sight (LOS) halos. Using two cosmological simulations that can resolve halo masses of $M_{\rm halo} \simeq 10^{9}\ M_{\odot}$ (in a simulation box of length $L_{\rm box}{\sim}100\,{\rm Mpc}$) and $10^{7}\ M_{\odot}$ ($L_{\rm box}\sim20\,{\rm Mpc}$), we demonstrate that clustering in the vicinity of the lens host produces a clear enhancement relative to an assumption of unclustered halos that persists to $> 20\,R_{\rm vir}$. This enhancement exceeds estimates that use a two-halo term to account for clustering, particularly within $2-5\,R_{\rm vir}$. We provide an analytic expression for this excess, clustered contribution. We find that local clustering boosts the expected count of $10^9 \ M_\odot$ perturbing halos by ${\sim}35\%$ compared to substructure alone, a result that will significantly enhance expected signals for low-redshift ($z_l \simeq 0.2$) lenses, where substructure contributes substantially compared to LOS halos. We also find that the orientation of the lens with respect to the line of sight (e.g., whether the line of sight passes through the major axis of the lens) can also have a significant effect on the lensing signal, boosting counts by an additional $\sim 50\%$ compared to a random orientations. This could be important if discovered lenses are biased to be oriented along their principal axis.

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The time-scales probed by star formation rate indicators for realistic, bursty star formation histories from the FIRE simulations

Understanding the rate at which stars form is central to studies of galaxy formation. Observationally, the star formation rates (SFRs) of galaxies are measured using the luminosity in different frequency bands, often under the assumption of a time-steady SFR in the recent past. We use star formation histories (SFHs) extracted from cosmological simulations of star-forming galaxies from the FIRE project to analyze the time-scales to which the H$α$ and far-ultraviolet (FUV) continuum SFR indicators are sensitive. In these simulations, the SFRs are highly time variable for all galaxies at high redshift, and continue to be bursty to z=0 in dwarf galaxies. When FIRE SFHs are partitioned into their bursty and time-steady phases, the best-fitting FUV time-scale fluctuates from its ~10 Myr value when the SFR is time-steady to >~100 Myr immediately following particularly extreme bursts of star formation during the bursty phase. On the other hand, the best-fitting averaging time-scale for H$α$ is generally insensitive to the SFR variability in the FIRE simulations and remains ~5 Myr at all times. These time-scales are shorter than the 100 Myr and 10 Myr time-scales sometimes assumed in the literature for FUV and H$α$, respectively, because while the FUV emission persists for stellar populations older than 100 Myr, the time-dependent luminosities are strongly dominated by younger stars. Our results confirm that the ratio of SFRs inferred using H$α$ vs. FUV can be used to probe the burstiness of star formation in galaxies.

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