arXiv subjects

Carlos Frenk

Publications and source records attributed to Carlos Frenk.

At least 37 records · Page 2Linked to original sources

arXiv2023

The MillenniumTNG Project: High-precision predictions for matter clustering and halo statistics

Cosmological inference with large galaxy surveys requires theoretical models that combine precise predictions for large-scale structure with robust and flexible galaxy formation modelling throughout a sufficiently large cosmic volume. Here, we introduce the MillenniumTNG (MTNG) project which combines the hydrodynamical galaxy formation model of IllustrisTNG with the large volume of the Millennium simulation. Our largest hydrodynamic simulation, covering (500 Mpc/h)^3 = (740 Mpc)^3, is complemented by a suite of dark-matter-only simulations with up to 4320^3 dark matter particles (a mass resolution of 1.32 x 10^8 Msun/h) using the fixed-and-paired technique to reduce large-scale cosmic variance. The hydro simulation adds 4320^3 gas cells, achieving a baryonic mass resolution of 2 x 10^7 Msun/h. High time-resolution merger trees and direct lightcone outputs facilitate the construction of a new generation of semi-analytic galaxy formation models that can be calibrated against both the hydro simulation and observation, and then applied to even larger volumes - MTNG includes a flagship simulation with 1.1 trillion dark matter particles and massive neutrinos in a volume of (3000 Mpc)^3. In this introductory analysis we carry out convergence tests on basic measures of non-linear clustering such as the matter power spectrum, the halo mass function and halo clustering, and we compare simulation predictions to those from current cosmological emulators. We also use our simulations to study matter and halo statistics, such as halo bias and clustering at the baryonic acoustic oscillation scale. Finally we measure the impact of baryonic physics on the matter and halo distributions.

astro-ph.CO↗

arXiv2023

The MillenniumTNG Project: The galaxy population at $z\geq 8$

The early release science results from $\textit{JWST}$ have yielded an unexpected abundance of high-redshift luminous galaxies that seems to be in tension with current theories of galaxy formation. However, it is currently difficult to draw definitive conclusions form these results as the sources have not yet been spectroscopically confirmed. It is in any case important to establish baseline predictions from current state-of-the-art galaxy formation models that can be compared and contrasted with these new measurements. In this work, we use the new large-volume ($L_\mathrm{box}\sim 740 \, \mathrm{cMpc}$) hydrodynamic simulation of the MillenniumTNG project, suitably scaled to match results from higher resolution - smaller volume simulations, to make predictions for the high-redshift ($z\gtrsim8$) galaxy population and compare them to recent $\textit{JWST}$ observations. We show that the simulated galaxy population is broadly consistent with observations until $z\sim10$. From $z\approx10-12$, the observations indicate a preference for a galaxy population that is largely dust-free, but is still consistent with the simulations. Beyond $z\gtrsim12$, however, our simulation results underpredict the abundance of luminous galaxies and their star-formation rates by almost an order of magnitude. This indicates either an incomplete understanding of the new $\textit{JWST}$ data or a need for more sophisticated galaxy formation models that account for additional physical processes such as Population~III stars, variable stellar initial mass functions, or even deviations from the standard $Λ$CDM model. We emphasise that any new process invoked to explain this tension should only significantly influence the galaxy population beyond $z\gtrsim10$, while leaving the successful galaxy formation predictions of the fiducial model intact below this redshift.

astro-ph.GA↗

arXiv2023

On the Edge: the relation between stellar and dark matter haloes of Milky Way-mass galaxies

We investigate the build-up of the accreted stellar and dark matter haloes of Milky Way-like galaxies in APOSTLE suite of cosmological hydrodynamics simulations. We show that the stellar halo is made up primarily of stars stripped from a small number of massive dwarfs, most of which are disrupted by the present day. The dark matter halo, on the other hand, is made up primarily of small unresolved subhaloes ($\lesssim 10^6$ M$_{\odot}$) and a ``smooth'' component consisting of particles which were never bound to a subhalo. Despite these differences, the massive dwarfs that make up the majority of the stellar halo also contribute a significant fraction of the dark matter. The stars and dark matter stripped from these dwarfs are related through their kinematics and this leaves imprints in the phase-space structure of the haloes. We examine the relation between the location of features, such as caustics, in the phase space of the stars and dark halo properties. We show that the ``edge'' of the stellar halo is a probe of dark matter halo mass and assembly history. The edges of Milky Way-mass galaxies should be visible at a surface brightness of 31-36 mag arcsec$^{-2}$.

astro-ph.GA↗

arXiv2022

The MillenniumTNG Project: Inferring cosmology from galaxy clustering with accelerated N-body scaling and subhalo abundance matching

We introduce a novel technique for constraining cosmological parameters and galaxy assembly bias using non-linear redshift-space clustering of galaxies. We scale cosmological N-body simulations and insert galaxies with the SubHalo Abundance Matching extended (SHAMe) empirical model to generate over 175,000 clustering measurements spanning all relevant cosmological and SHAMe parameter values. We then build an emulator capable of reproducing the projected galaxy correlation function at the monopole, quadrupole and hexadecapole level for separations between $0.1\,h^{-1}{\rm Mpc}$ and $25\,h^{-1}{\rm Mpc}$. We test this approach by using the emulator and Monte Carlo Markov Chain (MCMC) inference to jointly estimate cosmology and assembly bias parameters both for the MTNG740 hydrodynamic simulation and for a semi-analytical galaxy formation model (SAM) built on the MTNG740-DM dark matter-only simulation, obtaining unbiased results for all cosmological parameters. For instance, for MTNG740 and a galaxy number density of $n\sim 0.01 h^{3}{\rm Mpc}^{-3}$, we obtain $σ_{8}=0.799^{+0.039}_{-0.044}$ ($σ_{8,{\rm MTNG}} =$ 0.8159), and $Ω_\mathrm{M}h^2= 0.138^{+ 0.025}_{- 0.018}$ ($Ω_{\mathrm{M}} h^2_{\rm MTNG} =$ 0.142). For fixed Hubble parameter ($h$), the constraint becomes $Ω_\mathrm{M}h^2= 0.137^{+ 0.011}_{- 0.012}$. Our method performs similarly well for the SAM and for other tested sample densities. We almost always recover the true amount of galaxy assembly bias within one sigma. The best constraints are obtained when scales smaller than $2\,h^{-1}{\rm Mpc}$ are included, as well as when at least the projected correlation function and the monopole are incorporated. These methods offer a powerful way to constrain cosmological parameters using galaxy surveys.

astro-ph.GA↗

arXiv2022

The MillenniumTNG Project: The hydrodynamical full physics simulation and a first look at its galaxy clusters

Cosmological simulations are an important theoretical pillar for understanding nonlinear structure formation in our Universe and for relating it to observations on large scales. In several papers, we introduce our MillenniumTNG (MTNG) project that provides a comprehensive set of high-resolution, large volume simulations of cosmic structure formation aiming to better understand physical processes on large scales and to help interpreting upcoming large-scale galaxy surveys. We here focus on the full physics box MTNG740 that computes a volume of $(740\,\mathrm{Mpc})^3$ with a baryonic mass resolution of $3.1\times~10^7\,\mathrm{M_\odot}$ using \textsc{arepo} with $80.6$~billion cells and the IllustrisTNG galaxy formation model. We verify that the galaxy properties produced by MTNG740 are consistent with the TNG simulations, including more recent observations. We focus on galaxy clusters and analyse cluster scaling relations and radial profiles. We show that both are broadly consistent with various observational constraints. We demonstrate that the SZ-signal on a deep lightcone is consistent with Planck limits. Finally, we compare MTNG740 clusters with galaxy clusters found in Planck and the SDSS-8 RedMaPPer richness catalogue in observational space, finding very good agreement as well. However, {\it simultaneously} matching cluster masses, richness, and Compton-$y$ requires us to assume that the SZ mass estimates for Planck clusters are underestimated by $0.2$~dex on average. Thanks to its unprecedented volume for a high-resolution hydrodynamical calculation, the MTNG740 simulation offers rich possibilities to study baryons in galaxies, galaxy clusters, and in large scale structure, and in particular their impact on upcoming large cosmological surveys.

astro-ph.CO↗

arXiv2022

Is the core-cusp problem a matter of perspective: Jeans Anisotropic Modeling against numerical simulations

Mock member stars for 28 dwarf galaxies are constructed from the cosmological Auriga simulation, which reflect the dynamical status of realistic stellar tracers. The axis-symmetric Jeans Anisotropic Multi-Gaussian Expansion (JAM) modeling is applied to 6,000 star particles for each system, to recover the underlying matter distribution. The stellar or dark matter component individually is poorly recovered, but the total profile is constrained more reasonably. The mass within the half-mass radius of tracers is recovered the tightest, and the mass between 200 and 300 pc, $M(200-300\mathrm{pc})$, is constrained ensemble unbiasedly, with a scatter of 0.167 dex. If using 2,000 particles and only line-of-sight velocities with typical errors, the scatter in $M(200-300\mathrm{pc})$ is increased by $\sim$50%. Quiescent Sagittarius dSph-like systems and star-forming systems with strong outflows show distinct features, with $M(200-300\mathrm{pc})$ mostly under-estimated for the former, and likely over-estimated for the latter. The biases correlate with the dynamical status, which is a result of contraction motions due to tidal effects in quiescent systems or galactic winds in star-forming systems, driving them out of equilibrium. After including Gaia DR3 proper motion errors, we find proper motions can be as useful as line-of-sight velocities for nearby systems at $<\sim$60 kpc. By extrapolating the actual density profiles and the dynamical constraints down to scales below the resolution, we find the mass within 150 pc can be constrained ensemble unbiasedly, with a scatter of $\sim$0.255 dex. In the end, we show that the contraction of member stars in nearby systems is detectable based on Gaia DR3 proper motion errors.

astro-ph.GA↗

arXiv2022

Galactic satellite systems in CDM, WDM and SIDM

We investigate the population of bright satellites ($M_{*} \geq 10^{5} \mathrm{M}_{\odot}$) of haloes of mass comparable to that of the Milky Way in cosmological simulations in which the dark matter (DM) is either cold, warm or self-interacting (CDM, WDM and SIDM respectively). The nature of the DM gives rise to differences in the abundance and structural properties of field halos. In WDM, the main feature is a reduction in the total number of galaxies that form, reflecting a suppression of low-mass DM haloes and lower galaxy formation efficiency compared to CDM. For SIDM, the changes are structural, restricted to the central regions of haloes and dependent on the assumed self-interaction cross-section. We also consider different baryonic subgrid physics models for galaxy formation, in which supernova gas blowouts can or cannot induce the formation of a core in dwarf galaxies. Overall, the inclusion of baryons lessen the differences in the halo properties in the different DM models compared to DM-only simulations. This affects the satellite properties at infall and therefore their subsequent tidal stripping and survival rates. Nonetheless, we find slightly less concentrated satellite radial distributions as the SIDM cross-section increases. Unfortunately, we also find that the satellite populations in simulations with baryon-induced cores in CDM and WDM can mimic the results found in SIDM, making the satellite stellar mass and maximum circular velocity functions heavily degenerate on the assumed nature of the DM and the adopted subgrid modelling. These degeneracies preclude using the brightest satellites of the Milky Way to constrain the nature of DM.

astro-ph.GA↗

arXiv2022

The MillenniumTNG Project: Refining the one-halo model of red and blue galaxies at different redshifts

Luminous red galaxies (LRGs) and blue star-forming emission-line galaxies (ELGs) are key tracers of large-scale structure used by cosmological surveys. Theoretical predictions for such data are often done via simplistic models for the galaxy-halo connection. In this work, we use the large, high-fidelity hydrodynamical simulation of the MillenniumTNG project (MTNG) to inform a new phenomenological approach for obtaining an accurate and flexible galaxy-halo model on small scales. Our aim is to study LRGs and ELGs at two distinct epochs, $z = 1$ and $z = 0$, and recover their clustering down to very small scales, $r \sim 0.1 \ {\rm Mpc}/h$, i.e. the one-halo regime, while a companion paper extends this to a two-halo model for larger distances. The occupation statistics of ELGs in MTNG inform us that: (1) the satellite occupations exhibit a slightly super-Poisson distribution, contrary to commonly made assumptions, and (2) that haloes containing at least one ELG satellite are twice as likely to host a central ELG. We propose simple recipes for modeling these effects, each of which calls for the addition of a single free parameter to simpler halo occupation models. To construct a reliable satellite population model, we explore the LRG and ELG satellite radial and velocity distributions and compare them with those of subhalos and particles in the simulation. We find that ELGs are anisotropically distributed within halos, which together with our occupation results provides strong evidence for cooperative galaxy formation (manifesting itself as one-halo galaxy conformity); i.e.~galaxies with similar properties form in close proximity to each other. Our refined galaxy-halo model represents a useful improvement of commonly used analysis tools and thus can be of help to increase the constraining power of large-scale structure surveys.

astro-ph.CO↗

arXiv2022

The MillenniumTNG Project: An improved two-halo model for the galaxy-halo connection of red and blue galaxies

Approximate methods to populate dark matter halos with galaxies are of great utility to large galaxy surveys. However, the limitations of simple halo occupation models (HODs) preclude a full use of small-scale galaxy clustering data and call for more sophisticated models. We study two galaxy populations, luminous red galaxies (LRGs) and star-forming emission-line galaxies (ELGs), at two epochs, $z=1$ and $z=0$, in the large volume, high-resolution hydrodynamical simulation of the MillenniumTNG project. In a partner study we concentrated on the small-scale, one-halo regime down to $r\sim 0.1{\rm Mpc}/h$, while here we focus on modeling galaxy assembly bias in the two-halo regime, $r\gtrsim 1{\rm Mpc}/h$. Interestingly, the ELG signal exhibits scale dependence out to relatively large scales ($r\sim 20{\rm Mpc}/h$), implying that the linear bias approximation for this tracer is invalid on these scales, contrary to common assumptions. The 10-15\% discrepancy present in the standard halo model prescription is only reconciled when we augment our halo occupation model with a dependence on extrinsic halo properties ("shear" being the best-performing one) rather than intrinsic ones (e.g., concentration, peak mass). We argue that this fact constitutes evidence for two-halo galaxy conformity. Including tertiary assembly bias (i.e. a property beyond mass and "shear") is not an essential requirement for reconciling the galaxy assembly bias signal of LRGs, but the combination of external and internal properties is beneficial for recovering ELG the clustering. We find that centrals in low-mass haloes dominate the assembly bias signal of both populations. Finally, we explore the predictions of our model for higher-order statistics such as nearest-neighbor counts. The latter supplies additional information about galaxy assembly bias and can be used to break degeneracies between halo model parameters.

astro-ph.CO↗

arXiv2022

Baryon-driven decontraction in Milky Way mass haloes

We select a sample of Milky Way (MW) mass haloes from a high-resolution version of the EAGLE simulation to study their inner dark matter (DM) content and how baryons alter it. As in previous studies, we find that all haloes are more massive at the centre compared to their DM-only (DMO) counterparts at the present day as a result of the dissipational collapse of baryons during the assembly of the galaxy. However, we identify two processes that can reduce the central halo mass during the evolution of the galaxy. Firstly, gas blowouts induced by AGN feedback can lead to a substantial decrease of the central DM mass. Secondly, the formation of a stellar bar and its interaction with the DM can induce a secular expansion of the halo; the rate at which DM is evacuated from the central region by this process is related to the average bar strength and the timescale on which it acts determines how much the halo has decontracted. Although the inner regions of the haloes we have investigated are still more massive than their DMO counterparts at $z = 0$, they are significantly less massive than in the past and less massive than expected from the classic adiabatic contraction model. Since the MW has both a central supermassive black hole and a bar, the extent to which its halo has contracted is uncertain. This may affect estimates of the mass of the MW halo and of the expected signals in direct and indirect DM detection experiments.

astro-ph.GA↗

arXiv2021

The effects of self-interacting dark matter on the stripping of galaxies that fall into clusters

We use the Cluster-EAGLE (C-EAGLE) hydrodynamical simulations to investigate the effects of self-interacting dark matter (SIDM) on galaxies as they fall into clusters. We find that SIDM galaxies follow similar orbits to their Cold Dark Matter (CDM) counterparts, but end up with ${\sim}$25 per cent less mass by the present day. One in three SIDM galaxies are entirely disrupted, compared to one in five CDM galaxies. However, the excess stripping will be harder to observe than suggested by previous DM-only simulations because the most stripped galaxies form cores and also lose stars: the most discriminating objects become unobservable. The best test will be to measure the stellar-to-halo mass relation (SHMR) for galaxies with stellar mass $10^{10-11}\,\mathrm{M}_{\odot}$. This is 8 times higher in a cluster than in the field for a CDM universe, but 13 times higher for an SIDM universe. Given intrinsic scatter in the SHMR, these models could be distinguished with noise-free galaxy-galaxy strong lensing of ${\sim}32$ cluster galaxies.

astro-ph.CO↗

arXiv2021

Smoothed Particle Radiation Hydrodynamics: Two-Moment method with Local Eddington Tensor Closure

We present a new radiative transfer method (SPH-M1RT) that is coupled dynamically with smoothed particle hydrodynamics (SPH). We implement it in the (task-based parallel) SWIFT galaxy simulation code but it can be straightforwardly implemented in other SPH codes. Our moment-based method simultaneously solves the radiation energy and flux equations in SPH, making it adaptive in space and time. We modify the M1 closure relation to stabilize radiation fronts in the optically thin limit. We also introduce anisotropic artificial viscosity and high-order artificial diffusion schemes, which allow the code to handle radiation transport accurately in both the optically thin and optically thick regimes. Non-equilibrium thermo-chemistry is solved using a semi-implicit sub-cycling technique. The computational cost of our method is independent of the number of sources and can be lowered further by using the reduced speed of light approximation. We demonstrate the robustness of our method by applying it to a set of standard tests from the cosmological radiative transfer comparison project of Iliev et al. The SPH-M1RT scheme is well-suited for modelling situations in which numerous sources emit ionising radiation, such as cosmological simulations of galaxy formation or simulations of the interstellar medium.

astro-ph.IM↗

arXiv2021

Joint constraints on thermal relic dark matter from strong gravitational lensing, the Lyman-$α$ forest, and Milky Way satellites

We derive joint constraints on the warm dark matter (WDM) half-mode scale by combining the analyses of a selection of astrophysical probes: strong gravitational lensing with extended sources, the Lyman-$α$ forest, and the number of luminous satellites in the Milky Way. We derive an upper limit of $λ_{\rm hm}=0.089{\rm~Mpc~h^{-1} }$ at the 95 per cent confidence level, which we show to be stable for a broad range of prior choices. Assuming a Planck cosmology and that WDM particles are thermal relics, this corresponds to an upper limit on the half-mode mass of $M_{\rm hm }< 3 \times 10^{7} {\rm~M_{\odot}~h^{-1}}$, and a lower limit on the particle mass of $m_{\rm th }> 6.048 {\rm~keV}$, both at the 95 per cent confidence level. We find that models with $λ_{\rm hm}> 0.223 {\rm~Mpc~h^{-1} }$ (corresponding to $m_{\rm th }> 2.552 {\rm~keV}$ and $M_{\rm hm }< 4.8 \times 10^{8} {\rm~M_{\odot}~h^{-1}}$) are ruled out with respect to the maximum likelihood model by a factor $\leq 1/20$. For lepton asymmetries $L_6>10$, we rule out the $7.1 {\rm~keV}$ sterile neutrino dark matter model, which presents a possible explanation to the unidentified $3.55 {\rm~keV}$ line in the Milky Way and clusters of galaxies. The inferred 95 percentiles suggest that we further rule out the ETHOS-4 model of self-interacting DM. Our results highlight the importance of extending the current constraints to lower half-mode scales. We address important sources of systematic errors and provide prospects for how the constraints of these probes can be improved upon in the future.

astro-ph.CO↗

arXiv2021

Observing the stellar halo of Andromeda in cosmological simulations: the Auriga2PAndAS pipeline

We present a direct comparison of the Pan-Andromeda Archaeological Survey (PAndAS) observations of the stellar halo of M31 with the stellar halos of 6 galaxies from the Auriga simulations. We process the simulated halos through the Auriga2PAndAS pipeline and create PAndAS-like mocks that fold in all observational limitations of the survey data (foreground contamination from the Milky Way stars, incompleteness of the stellar catalogues, photometric uncertainties, etc). This allows us to study the survey data and the mocks in the same way and generate directly comparable density maps and radial density profiles. We show that the simulations are overall compatible with the observations. Nevertheless, some systematic differences exist, such as a preponderance for metal-rich stars in the mocks. While these differences could suggest that M31 had a different accretion history or has a different mass compared to the simulated systems, it is more likely a consequence of an under-quenching of the star formation history of galaxies, related to the resolution of the Auriga simulations. The direct comparison enabled by our approach offers avenues to improve our understanding of galaxy formation as they can help pinpoint the observable differences between observations and simulations. Ideally, this approach will be further developed through an application to other stellar halo simulations. To facilitate this step, we release the pipeline to generate the mocks, along with the six mocks presented and used in this contribution.

astro-ph.GA↗

arXiv2021

A high-resolution cosmological simulation of a strong gravitational lens

We present a cosmological hydrodynamical simulation of a 10^13 Msun galaxy group and its environment (out to 10 times the virial radius) carried out using the EAGLE model of galaxy formation. Exploiting a novel technique to increase the resolution of the dark matter calculation independently of that of the gas, the simulation resolves dark matter haloes and subhaloes of mass 5x10^6 Msun . It is therefore useful for studying the abundance and properties of the haloes and subhaloes targeted in strong lensing tests of the cold dark matter model. We estimate the halo and subhalo mass functions and discuss how they are affected both by the inclusion of baryons in the simulation and by the environment. We find that the halo and subhalo mass functions have lower amplitude in the hydrodynamical simulation than in its dark matter only counterpart. This reflects the reduced growth of haloes in the hydrodynamical simulation due to the early loss of gas by reionisation and galactic winds and, additionally, in the case of subhaloes, disruption by enhanced tidal effects within the host halo due to the presence of a massive central galaxy. The distribution of haloes is highly anisotropic reflecting the filamentary character of mass accretion onto the cluster. As a result, there is significant variation in the number of structures with viewing direction. The median number of structures near the centre of the halo, when viewed in projection, is reduced by a factor of two when baryons are included.

astro-ph.CO↗

arXiv2020

The detailed structure and the onset of galaxy formation in low-mass gaseous dark matter haloes

We present a model for the formation of the first galaxies before and after the reionization of hydrogen in the early universe. In this model, galaxy formation can only take place in dark matter haloes whose mass exceeds a redshift-dependent critical value, which, before reionization, is equal (in the simplest case) to the mass at which atomic hydrogen cooling becomes effective and, after reionization, is equal to the mass above which gas cannot remain in hydrostatic equilibrium. We define the Halo Occupation Fraction (HOF) as the fraction of haloes that host a luminous galaxy as a function of halo mass. The HOF is established by the interplay between the evolution of the critical mass and the assembly history of haloes and depends on three factors: the minimum halo mass for galaxy formation before reionization, the redshift of reionization, and the intensity of the (evolving) external photoheating rate. Our fiducial model predicts a cutoff in the galaxy mass function at a present-day halo mass, $M_{200} \sim 3\times 10^{8} M_{\odot}$; 100\% occupation at $M_{200} > 5\times 10^9 M_{\odot}$; and a population of starless gaseous haloes of present-day mass in the range $10^{6} \lesssim M_{200} / M_{\odot}\lesssim 5\times 10^{9}$, in which the gas is in thermal equilibrium with the ultraviolet background radiation and in hydrostatic equilibrium in the gravitational potential of the halo. The transition between HOF = 0 and HOF=1 reflects the stochastic nature of halo mass growth. We explore how these characteristic masses vary with model assumptions and parameter values. The results of our model are in excellent agreement with cosmological hydrodynamic simulations of galaxy formation.

astro-ph.GA↗

arXiv2020

Coming of Age of the Standard Model

Cosmology now has a standard model - a remarkably simple description of the universe, its contents and its history. A symposium held last September in Cambridge, UK, gave this model a 'health check' and discussed fascinating questions that lie beyond it.

astro-ph.CO↗

arXiv2019

Cusp or core? Revisiting the globular cluster timing problem in Fornax

We use N-body simulations to revisit the globular cluster (GC) ``timing problem'' in the Fornax dwarf spheroidal (dSph). In agreement with earlier work, we find that, due to dynamical friction, GCs sink to the center of dark matter halos with a cuspy inner density profile but ``stall'' at roughly 1/3 of the core radius ($r_{\rm core}$) in halos with constant-density cores. The timescales to sink or stall depend strongly on the mass of the GC and on the initial orbital radius, but are essentially the same for either cuspy (NFW) or cored halos normalized to have the same total mass within $r_{\rm core}$. Arguing against a cusp on the basis that GCs have not sunk to the center is thus no different from arguing against a core, unless all clusters are today at $\sim (1/3)\, r_{\rm core}$. This would imply a core radius exceeding $\sim 3$ kpc, much larger than seems plausible in any core-formation scenario. (The average projected distance of Fornax GCs is $\langle R_{\rm GC,Fnx}\rangle\sim 1$ kpc and its effective radius is $\sim 700$ pc.) A simpler explanation is that Fornax GCs have only been modestly affected by dynamical friction, as expected if clusters started orbiting at initial radii of order $\sim 1$-$2$ kpc, just outside Fornax's present-day half-light radius but well within the tidal radius imprinted by Galactic tides. This is not entirely unexpected. Fornax GCs are significantly older and more metal-poor than most Fornax stars, and such populations in dSphs tend to be more spatially extended than their younger and more metal-rich counterparts. Contrary to some earlier claims, our simulations further suggest that GCs do not truly ``stall'' at $\sim 0.3\, r_{\rm core}$, but rather continue decaying toward the center, albeit at reduced rates. We conclude that dismissing the presence of a cusp in Fornax based on the spatial distribution of its GC population is unwarranted.

astro-ph.GA↗