arXiv subjects

Andrew Benson

Publications and source records attributed to Andrew Benson.

At least 19 recordsLinked to original sources

arXiv2026

Hot off the Stacks: X-rays in Romulus25, Part I - Comparisons to Observations from eRosita

Recent observations from the from Spectrum Roentgen Gamma (SRG)/eROSITA all-sky survey data have helped to illuminate the hot circumgalactic medium (CGM) around galaxies at Milky Way-masses and above. In our study, we explore the hot X-ray emitting (T \textgreater 10$^6$ K) component of the CGM in over 750 galaxies from the Romulus25 cosmological simulation (Tremmel et al. 2017) between 10.0 < log(M$_*/M_{\odot}$) < 11.5. We forward-model soft X-ray [0.5 - 2.0] keV observations of our simulated galaxies using pyXSIM and SIXTE to measure the X-ray surface brightness (SB) profiles of the hot CGM. We then compare the average X-ray surface brightness profiles of six stellar-mass selected sub-samples to compare to the observational results from Chadayammuri et al. (2022a) and Zhang et al. 2024a. Broadly, we find that our stacked SB profiles are too bright compared to observations from Chadayammuri et al. (2022a) and Zhang et al.(2024a) particularly in the inner CGM. Additionally, we calculate the X-ray luminosity (L$_χ$) of the hot CGM for each galaxy and compare the average L$_χ$ across stellar mass to observations from Zhang et al. (2024b) as well as measurements from the EAGLE, TNG, SIMBA simulations. Across stellar mass, the average L$_χ$ of galaxies from Romulus25 are brighter than observations except at the lower, Milky Way-mass end where we are in relative agreement with both observations and most other simulations. We also consider a zero-metallicity emission model, because Romulus25 does not have metal-line cooling, finding the average L$_χ$ decreases by nearly an order-of-magnitude, which better matches observations particularly in the Milky Way-mass regime.

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arXiv2026

Extra! Extra! X-ray Emission!: X-rays in Romulus25, Part II - Physical Drivers of X-ray Emission in the CGM

Characterizing the hot (T ~ 10$^{6}$ K) circumgalactic medium (CGM) around Milky Way-mass (MW-mass) galaxies is critical to a full understanding of galaxy evolution. In this second paper of the "X-rays in Romulus25" series, we unpack the specific physical processes giving rise to the presence of hot X-ray emitting gas in the halos of galaxies from the Romulus25 (R25) simulation, focusing on L$_{*}$ galaxies. We determine that a strong correlation appears between the mass of hot CGM gas, M$_{gas, T > 10^{5.5} K}$, and the X-ray emissivity, $ε_χ$, measured in the first paper of this series, (Sanchez et al. 2026a, submitted). There is also a secondary correlation between M$_{gas, T > 10^{5.5} K}$ and $ε_χ$ with the average metallicity of the hot CGM gas, $\bar{Z}_{gas, T > 10^{5.5} K}$. We use the well-studied PIONEER simulations from Sanchez et al. (2019), a set of zoom-in MW-mass galaxies run with the genetic modification technique of Roth et al. (2016) and the same physics as R25, to interpret these correlations. We determine that the presence of hot X-ray emitting gas is determined by two key processes: 1) the quantity of hot gas mass in the CGM, M$_{gas, T > 10^{5.5} K}$, is set by the combined total energy injection of $both$ stellar and AGN feedback, and 2) together the average temperature and metallicity of the hot CGM changes the soft X-ray spectrum of the gas resulting in brighter metal-rich CGM and dimmer metal-poor CGM for the same quantity of M$_{gas, T > 10^{5.5} K}$. These results indicate, for the first time, that metal-rich gas halos may bias X-ray observations of MW-mass galaxies.

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arXiv2026

The SIRMOS mission concept: a space-based near-IR spectroscopic survey of 100 million galaxies in the Euclid Wide Survey footprint

SIRMOS is a mission concept for a future NASA Astrophysics Explorer opportunity that aims to revolutionize our understanding of the universe by mapping the large-scale structure of galaxies in unprecedented breadth and detail to explore cosmic origins and evolution. Specifically, the primary science goals of SIRMOS are to discover how cosmic inflation seeded large-scale structure, reveal the nature of the accelerating expansion of the universe, and measure the sum of neutrino masses to exceptionally high precision. Its secondary science goals include determining how environment shapes galaxy evolution at cosmic noon and beyond, and probing the Milky Way's dust-enshrouded regions, reaching the far side of our Galaxy. To accomplish its transformative science goals, SIRMOS executes a 3-year cosmology survey over the Euclid footprint of ~14,000 deg$^2$, obtaining slit spectra for ~100 million galaxies at 1<z<4. SIRMOS is the first space mission designed specifically to leverage Euclid's wide near-infrared (IR) imaging survey for target selection and employs a digital micro-mirror device (DMD) to acquire up to 4,000 simultaneous spectra over a wide 0.9 deg$^2$ field of view. The instrument's excellent spectral resolution of $R=1300$ and continuous wavelength coverage from 1.25--2.5 $μ$m capture the redshifts of distant galaxies with no gaps, reducing systematic biases to achieve ground-breaking science.

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arXiv2026

COZMIC. II. Cosmological Zoom-in Simulations with Fractional non-CDM Initial Conditions

We present $24$ cosmological dark matter (DM)-only zoom-in simulations of a Milky Way analog with initial conditions appropriate for scenarios where non-cold dark matter (NCDM) is a fraction of the total DM abundance (f-NCDM models) as the second installment of the COZMIC suite. We initialize our simulations using transfer functions, $T_{\mathrm{f-NCDM}}(k)\equiv\sqrt{P_{\mathrm{f-NCDM}}(k)/P_{\mathrm{CDM}}(k)}$ (where $P(k)$ is the linear matter power spectrum), with an initial suppression similar to thermal-relic warm dark matter (WDM) followed by a constant-amplitude plateau. We simulate suppression wavenumbers $[22.8,~ 32.1,~ 41.8,~ 52.0,~ 57.1,~ 95.3]~\mathrm{Mpc}^{-1}$, corresponding to thermal-relic WDM masses $m_{\mathrm{WDM}}\in [3,~ 4,~ 5,~ 6,~ 6.5,~ 10]~\mathrm{keV}$, and plateau amplitudes $δ\in [0.2,~ 0.4,~ 0.6,~ 0.8]$. We model the subhalo mass function in terms of the suppression wavenumber and $δ$. Integrating these models into a forward model of the MW satellite galaxy population yields new limits on f-NCDM scenarios, with suppression wavenumbers greater than $46$ and $ 40~\mathrm{Mpc}^{-1}$ for $δ=0.2$, $0.4$, respectively, at $95\%$ confidence. The current data do not constrain $δ>0.4$. We map these limits to scenarios where a fraction $f_{\mathrm{WDM}}$ of DM behaves as a thermal relic, which yields the following bounds on cosmologies with a mixture of WDM and CDM: $m_{\mathrm{WDM}}>3.6,~ 4.1,~ 4.6,~ 4.9,~ 5.4~\mathrm{keV}$ for $f_{\mathrm{WDM}}=0.5,~ 0.6,~ 0.7,~ 0.8,~ 0.9$, respectively, at $95\%$ confidence. The current data do not constrain WDM fractions $f_{\mathrm{WDM}}<0.5$. Our results affirm that low-mass halo abundances are sensitive to partial suppression in $P(k)$, indicating the possibility of using galactic substructure to reconstruct $P(k)$ on small scales.

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arXiv2026

COZMIC. I. Cosmological Zoom-in Simulations with Initial Conditions Beyond Cold Dark Matter

We present 72 cosmological dark matter-only $N$-body zoom-in simulations with initial conditions beyond cold, collisionless dark matter (CDM), as the first installment of the COZMIC suite. We simulate Milky Way (MW) analogs with linear matter power spectra $P(k)$ for i) thermal-relic warm dark matter (WDM) with masses $m_{\mathrm{WDM}}\in [3,4,5,6,6.5,10]~\mathrm{keV}$, ii) fuzzy dark matter (FDM) with masses $m_{\mathrm{FDM}}\in [25.9,69.4,113,151,185,490]\times 10^{-22}~\mathrm{eV}$, and iii) interacting dark matter (IDM) with a velocity-dependent elastic proton scattering cross section $σ=σ_0 v^n$ relative particle velocity scaling $n\in [2,4]$, and dark matter mass $m_{\mathrm{IDM}}\in[10^{-4},~ 10^{-2},~ 1]$ GeV. Subhalo mass function (SHMF) suppression is significantly steeper in FDM versus WDM, while dark acoustic oscillations in $P(k)$ can reduce SHMF suppression for IDM. We fit SHMF models to our simulation results and derive new bounds on WDM and FDM from the MW satellite population, obtaining $m_{\mathrm{WDM}}>5.9~\mathrm{keV}$ and $m_{\mathrm{FDM}}>1.4\times 10^{-20}~\mathrm{eV}$ at $95\%$ confidence; these limits are $\approx 10\%$ weaker and $5\times$ stronger than previous constraints owing to the updated transfer functions and SHMF models, respectively. We estimate IDM bounds for $n=2$ ($n=4$) and obtain $σ_0 < 1.0\times 10^{-27}$, $1.3\times 10^{-24}$, and $3.1\times 10^{-23}~\mathrm{cm}^2$ ($σ_0 < 9.9\times 10^{-27}$, $9.8\times 10^{-21}$, and $2.1\times 10^{-17}~\mathrm{cm}^2$) for $m_{\mathrm{IDM}}=10^{-4}$, $10^{-2}$, and $1$ GeV, respectively. Thus, future development of IDM SHMF models can improve IDM cross section bounds by up to a factor of $\sim 20$ with current data. COZMIC presents an important step toward accurate small-scale structure modeling in beyond-CDM cosmologies, critical to upcoming observational searches for dark matter physics.

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arXiv2026

The Effects of Linear Matter Power Spectrum Enhancement on Dark Matter Substructure

We present cosmological dark matter (DM)--only zoom-in simulations of a Milky Way analog originating from enhanced linear matter power spectra $P(k)$ relative to the standard cold, collisionless DM (CDM) cosmology. We consider a Gaussian power excess in $P(k)$ followed by a cutoff in select cases; this behavior could arise from early-Universe physics that alters the primordial matter power spectrum or DM physics in the radiation-dominated epoch. We find that enhanced initial conditions (ICs) lead to qualitative differences in substructure relative to CDM. In particular, the subhalo mass function (SHMF) resulting from ICs with both an enhancement and cutoff is amplified at high masses and suppressed at low masses, indicating that DM substructure is sensitive to features in $P(k)$. Critically, the amplitude and shape of the SHMF enhancement depend on the wavenumber of the $P(k)$ excess and the presence or absence of a cutoff on smaller scales. These alterations to the SHMF are mainly imprinted at infall rather than during tidal evolution. Additionally, subhalos are found systematically closer to the host center, and their concentrations are increased in scenarios with $P(k)$ enhancement. Our work thus reveals effects that must be captured to enable $P(k)$ reconstruction using DM substructure.

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arXiv2026

Which Milky Way Streams Make the Best Dark Matter Detectors?

The abundance and properties of low-mass dark matter subhalos can be inferred by measuring the density and velocity structure of stellar streams, testing physical models of dark matter. Which streams make the most promising dark matter detectors, and which subhalos would they encounter? We use the semi-analytic model galacticus to simulate the Milky Way's dark subhalos, including tidal stripping under the influence of the galactic disk. Deriving stream initial conditions that best match present-day observations, we forecast subhalo encounters for 24 globular cluster streams around the Milky Way. Over their lifetimes, the 10 most perturbed streams are predicted to each experience $\approx 2$-$12$ significant subhalo encounters with velocity kicks $v_\mathrm{kick} > 0.1$ km s$^{-1}$. Jet, AAU, GD-1, and Palomar 5 lead the list, with Jet encountering twice the subhalos of any other stream. The subhalos that encounter streams have been tidally stripped to $1$-$20\%$ of their peak mass and are twice as compact as previous works have assumed. A spectroscopic survey of streams with sub-km s$^{-1}$ precision could reveal the influence of dark subhalos below the threshold of galaxy formation. Predicting the abundance and scatter of low-mass subhalos that reach the inner galaxy remains a dominant uncertainty in connecting stellar streams to models of dark matter.

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arXiv2026

Feeding the Void: Co-evolution of the SIDM-seeded Black Hole and the dark halo after core-collapse

While the gravothermal collapse of self-interacting dark matter (SIDM) halos provides a compelling mechanism for seeding supermassive black holes (BHs), the post-collapse macroscopic co-evolution of the BH and its host halo remains largely unexplored. In this paper, we introduce a novel N-body framework to dynamically model the dark matter accretion onto the central BH. By bracketing the accretion rate with two complementary phenomenological schemes---a `multi-round core-collapse' scenario and a `continuous accretion' scenario---we establish bounds on the BH mass growth trajectory. We find that the BH mass reaches $5\%-12\%$ of the total halo mass within $\lesssim2$ Gyr post-collapse. Concurrently, this sustained mass depletion drives a `gravothermal supply chain' that forces outer dark matter inward, severely depleting the inner halo density ($\lesssim 2r_s$). This unique structural imprint qualitatively matches the recently detected anomaly in the strong lens JVAS B1938+666 (detection V), where the best-fit lens model consists of an unresolved central point mass and a shallow, uniform-surface-density extended disk, offering a distinct observational signature for SIDM-seeded BHs.

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arXiv2026

Correlation between baryonic process and galaxy assembly bias

Galaxy assembly bias (GAB) is the dependence of galaxy clustering on secondary properties beyond halo mass. In this work, we study the connections between GAB and baryonic processes using the Galacticus semianalytic model (SAM) for galaxy formation and evolution applied to the UNIT simulation. By generating hundreds of galaxy mocks with varying parameters governing gas cooling, star formation, stellar feedback, and active galactic nucleus (AGN) feedback, we quantify the GAB signal using a shuffling technique that compares the clustering of the original galaxy samples with that of shuffled samples, in which galaxies are randomly reassigned among halos of the same mass. We then compare the GAB signals associated with halo concentration and smoothed environmental density, and use the random forest (RF) algorithm to identify which baryonic processes are most correlated with GAB within the explored SAM parameter space. We find that for stellar-mass-selected galaxies, the dominant baryonic processes are gas cooling and stellar feedback, and the result does not change significantly with the number density; for star formation rate (SFR)-selected galaxies, the primary process shifts from star formation to gas cooling as the number density increases. These results reveal a correlational dependence of GAB on baryonic processes within the explored Galacticus SAM parameter space.

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arXiv2026

A graph-based Neural Network surrogate model for accelerating semi-analytical model of galaxy formation and evolution

Understanding how galaxy populations emerge and evolve from the growth of dark matter structure is a central challenge in galaxy formation theory. Semi-analytic models (SAMs) provide an efficient framework to address this problem, but exploring large ensembles of merger trees across broad parameter spaces remains computationally demanding. We develop a conditional graph neural network surrogate model that combines merger tree information with SAM parameters to predict galaxy properties across cosmic time. Using merger trees of dark matter halos from the Uchuu simulation and the Galacticus SAM, the model predicts stellar mass, luminosity, angular momentum, gas metal mass, and specific star formation rate across the wide redshift range of 0 <= z <= 5. For instance, the model can predict stellar mass at 0 <= z <= 3 with a scatter of 0.19-0.28 dex and coefficient of determination R^2 of 0.946-0.973 (R^2 close to 1 indicates prediction closely matching the truth). The results show that a single graph based model can reproduce these galaxy properties with good accuracy over multiple SAM realizations, merger trees and redshifts. This catalog-level model provides a practical route for accelerating SAM based studies of galaxy formation to enable a more detailed investigation of the model parameter space. The inference code, trained models, and example data products are publicly available at https://github.com/MutongCat/sam2galaxy-gnn.

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arXiv2026

Bypassed Core Formation in Milky Way-Mass SIDM Halos: Implications for the Local Group Past-Pericenter Scenario

We consider a scenario in which the Milky Way (MW) and M31 have had a previous pericentric passage, and investigate its compatibility with self-interacting dark matter (SIDM). Using initial conditions sampled from Local Group (LG) analogues in the IllustrisTNG simulation, we perform controlled re-simulations of the MW-M31 orbit, evolving the system under both standard cold dark matter (CDM) and various SIDM cross-sections. We find that the deep baryonic potential of the MW preconditions the halo's thermal structure, establishing an initial negative temperature gradient. This drives SIDM halos to bypass the standard core-formation phase and enter immediate core-collapse, resulting in monotonically increasing central densities. In full orbital simulations, the compact stellar component (disk/bulge) of the MW analog remains robust against tidal disruption for pericenter distances as close as $r_{\rm peri}\lesssim20$ kpc during an encounter at cosmic time $\sim8$ Gyr. The diffuse stellar halo is comparatively more susceptible, facing disruption for $r_{\rm peri}\lesssim100$ kpc. Our results demonstrate a dichotomy in structural evolution: the compact disk/bulge is sensitive to intrinsic SIDM thermodynamics but dynamically robust against the pericenter encounter, whereas the diffuse stellar halo is largely independent of the specific SIDM model but more vulnerable to orbital tidal disruptions.

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arXiv2026

Emulator-Assisted Calibration of a Semi-Analytic Galaxy Formation Model for the Roman Galaxy Redshift Survey

Mock catalogues for the Roman Galaxy Redshift Survey benefit from galaxy populations whose physical properties and emission-line observables are predicted within a single galaxy-formation framework. We present an emulator-assisted calibration of the semi-analytic model Galacticus for this purpose. Because direct posterior exploration with Galacticus is computationally prohibitive, we train Gaussian-process emulators to predict the observables entering the calibration likelihood. We calibrate the model simultaneously to stellar mass functions, the star-formation-rate function, size--mass relations, the black-hole mass--velocity-dispersion relation, the mass--metallicity relation, and H-alpha luminosity functions. Combining these observables breaks parameter degeneracies present in individual fits and can reveal tensions where different observables favour different regions of parameter space. The resulting model provides a broadly successful simultaneous description of the calibration data, including the abundance and redshift evolution of H-alpha emitters relevant to the Roman Galaxy Redshift Survey. A direct Galacticus calculation at the maximum a posteriori point gives similarly good agreement with the calibration data, providing a calibrated galaxy-formation model suitable for constructing physically consistent mock catalogues for Roman.

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arXiv2026

Advancing Stellar Streams as a Dark Matter Probe -- I: Evolution of the CDM subhalo population

Stellar streams, long, thin streams of stars, have been used as sensitive probes of dark matter substructure for over two decades. Gravitational interactions between dark matter substructures and streams lead to the formation of low-density ``gaps'' in streams, with any given stream typically containing no more than a few such gaps. Prior models for the statistics of such gaps have relied on several simplifying assumptions for the properties of the subhalo population in the cold dark matter scenario. With the expected forthcoming increase in the number of streams and gaps observed, this work develops a more detailed model for the statistics of subhalos interacting with streams and tests some of the assumptions made in prior works. Instead of using simple fits to N-body estimates of subhalo population statistics at $z=0$ as in previous work, we make use of realizations of time-dependent subhalo populations generated from an entirely physical model, incorporating structure formation and subhalo orbital evolution, including tidal heating and stripping physics, which has been carefully calibrated to match results of cosmological N-body simulations. We find that this model predicts 20% more gaps (up to 60% for deep gaps) on average in Pal-5-like streams than prior works.

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arXiv2026

Warm, not Fuzzy: Generalized Ultralight Dark Matter Limits from Milky Way Satellites

We generalize lower limits on the dark matter (DM) particle mass $m$ derived from Milky Way (MW) satellite galaxy abundances to scenarios in which DM is an ultralight scalar field produced with a field power spectrum peaked at a subhorizon wavenumber $k_*$. In these models, the DM field free-streams similarly to warm DM while also exhibiting significant small-scale wave interference effects. The resulting dimensionless density power spectrum shows two effects: (i) free-streaming suppression at $k_{\rm fs}\sim k_{\rm eq}/[(k_*/a_{\rm eq}m)\ln(a_{\rm eq}m/k_*)]$; (ii) Poisson-like enhancement related to wave interference at $k\gtrsim10^{-2}k_*$, which saturates near the Jeans scale $k_{\rm J}\sim k_{\rm eq}/(k_*/a_{\rm eq}m)$. Comparing these predictions with established constraints on a free-streaming cutoff in the linear matter power spectrum from the MW satellite population and assuming that warm ultralight DM does not change the form of the galaxy--halo connection relative to cold DM, we obtain $m>6\times10^{-18}\,{\rm eV}\,(k_*/10^4\,{\rm Mpc}^{-1})$ for $k_*>10^4\,{\rm Mpc}^{-1}$ at 95% confidence. For smaller $k_*$, Poisson-noise enhancement on MW satellite scales weakens the constraint, yielding $m>6\times10^{-18}\,{\rm eV}\,(k_*/10^4\,{\rm Mpc}^{-1})^2$ for $k_*<10^4\,{\rm Mpc}^{-1}$ at 95% confidence.

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arXiv2026

Testing warm dark matter with kinematics of the smallest galaxies

Every dark matter halo forms with a $ρ\propto r^{-1.5}$ density cusp at its center. For warm dark matter (WDM), these prompt cusps can be massive enough to influence the kinematics of dwarf galaxies. By implementing prompt cusps in the Galacticus galaxy formation model, we show that the measured velocity dispersions of Tucana V and Triangulum II are serious outliers for dwarf galaxies arising in WDM models. For thermal-relic dark matter, the three faintest Milky Way satellites together constrain the particle mass to be $m_χ>5.8$ keV at 95 percent confidence or $m_χ>9.4$ keV at 90 percent confidence. Improved velocity dispersion measurements for these systems could greatly refine this constraint, as could identification and kinematic characterization of more such galaxies.

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arXiv2026

Mixed Dark Matter: Limits from the Milky Way Satellite Galaxies

The Standard Model of particle physics contains a diverse set of particle species, motivating the possibility of a similarly complex dark sector. Here we study two-component dark matter (DM) mixtures, in which one component behaves as standard CDM while the other suppresses the formation of small-scale structure, either through an astrophysically relevant de~Broglie wavelength (fuzzy DM; FDM) or collisional damping from temperature-independent scattering (interacting DM; IDM). Using the observed population of Milky Way satellite galaxies, we derive new leading constraints on the parameter spaces of mixed FDM and of mixed IDM coupled to photons ($γ$-DM), neutrinos ($ν$-DM), or baryons ($p$-DM), for beyond-CDM fractions down to $50\%$. We require that the linear matter power spectra of allowed models remain less suppressed than a constrained reference model. The resulting $95\%$ confidence bounds on FDM mass and IDM cross section weaken systematically with decreasing fraction, following distinct power-law scalings. At $50\%$ fraction, IDM cross section bounds weaken by a factor of $\sim$2--6 and FDM mass bounds by $\sim$1.5, relative to the $100\%$ case. We forecast that idealized future satellite surveys, which adopt approximate LSST sensitivity thresholds, can improve these $100\%$ bounds by a factor of $\sim$1.6--14 for IDM and $\sim$3 for FDM. Self-consistent cosmological simulations of mixed DM scenarios will be essential to more robustly characterize the degeneracy between particle physics parameters and fractional contribution, to extend constraints to lower fractions, and to identify signatures beyond satellite abundance to further inform these models.

astro-ph.CO↗

arXiv2026

The Sensitivity of Substructure Lensing to SIDM Core-collapse Model Variation

Strong gravitational lensing has emerged as a powerful probe of dark matter substructure, and shows particularly strong promise as a test of self-interacting dark matter (SIDM). The compact halos produced by SIDM can leave distinct imprints on lensing observations, but the core-collapse timeline for subhalos is difficult to model accurately. This difficulty is an obstacle to accurate substructure lensing predictions, where small variations in core-collapsing subhalos can lead to significant differences in the lensing power. To quantify this problem and inform future lensing analyses, we test various methods of modeling core-collapsing halos and show the effect of each variation on the two-point correlation function of the effective deflection field's divergence and curl. Our tests include smoothly evolving density profiles versus instantaneously collapsing halos, probabilistic collapse versus individual halo evolution, and variation of the initial and final density profile parameters. We find that the two-point correlation function is sensitive to most of these variations at small length scales, but the detectability of these differences will depend on the observational probe.

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arXiv2026

The pre-infall bias of subhalos

Dark matter halos destined to fall into a more massive host differ from typical field halos of the same mass even before infall. In cosmological simulations, we find that the progenitor mass functions of these "future subhalos" are systematically shifted toward higher masses, with the shift growing as infall approaches. The bias takes a compact form within extended Press-Schechter theory: the collapse barrier is multiplied by a function $β(D/D_\mathrm{infall},a)$, where $D$ is the linear growth factor at scale factor $a$ and $D_\mathrm{infall}$ is the growth factor at infall. We find $β(x,a)=(1-x)^{1.20+0.14a}$ for the $M_{200\mathrm{c}}$ mass definition and $(1-x)^{1.20+0.05a}$ for $M_{200\mathrm{m}}$; the explicit scale-factor dependence captures the late-time influence of dark energy. One consequence is that halos shortly before infall are 10-15% more centrally concentrated than typical field halos of the same mass.

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