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Simon D. M. White

Publications and source records attributed to Simon D. M. White.

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Prompt cusps and the dark matter annihilation signal

As the first dark matter objects gravitationally condense, a density cusp forms immediately at every initial density maximum. Numerical simulations and theoretical arguments suggest that these prompt cusps can survive until the present day. We show that if dark matter is a thermally produced weakly interacting massive particle, many thousands of prompt cusps with individual masses similar to that of the Earth may be present in every solar mass of dark matter. This radically alters predictions for the amount and spatial distribution of dark matter annihilation radiation. The annihilation rate is boosted by at least an order of magnitude compared to previous predictions, both in the cosmological average and within galaxy-scale halos. Moreover, the signal is predominantly boosted outside of the centers of galactic halos, so alternative targets become significantly more attractive for indirect-detection searches. For example, prompt cusps present new opportunities to test the dark matter interpretation of the Galactic Center gamma-ray excess by searching for similar spectral signatures in the isotropic gamma-ray background and large-scale cosmic structure.

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Phase-space simulations of prompt cusps: simulating the formation of the first haloes without artificial fragmentation

The first generation of haloes forms from the collapse of the smallest peaks in the initial density field. $N$-body simulations of this process suggest a prompt formation of a steep power-law cusp, but these calculations are plagued by numerical artifacts which casts some doubt on this result. Here, we develop new simulation methods based on the dark matter phase-space sheet approach and present results which are entirely free of artificial clumps. We find that a cusp with density $ρ\propto r^{-1.5}$ is indeed formed promptly, subsequently accreting a more extended halo and participating in the hierarchical growth of later halo generations. However, our simulations also suggest that the presence of artificial clumps just before peak collapse can significantly shallow the inner profiles of the cusps. We use $N$-body simulations with controlled amounts of small-scale power to place a conservative upper limit on the scales affected by artificial clumps. Finally, we used these results to simulate the collapse of the first generation of peaks of various types and in different cosmologies, finding prompt cusps to form in all cases. We conclude that prompt cusps are a generic feature of the collapse of peaks on the free-streaming scale of the initial density field, and their structure can safely be studied using $N$-body simulations provided care is taken to excise the region potentially affected by artificial clumps.

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The MillenniumTNG Project: Intrinsic alignments of galaxies and halos

The intrinsic alignment (IA) of observed galaxy shapes with the underlying cosmic web is a source of contamination in weak lensing surveys. Sensitive methods to identify the IA signal will therefore need to be included in the upcoming weak lensing analysis pipelines. Hydrodynamical cosmological simulations allow us to directly measure the intrinsic ellipticities of galaxies and thus provide a powerful approach to predict and understand the IA signal. Here we employ the novel, large-volume hydrodynamical simulation MTNG740, a product of the MillenniumTNG (MTNG) project, to study the IA of galaxies. We measure the projected correlation functions between the intrinsic shape/shear of galaxies and various tracers of large-scale structure, $w_{+g},\ w_{+m},\ w_{++}$ over the radial range $r_{\rm p} \in [0.02 , 200]\,h^{-1}{\rm Mpc}$ and at redshifts $z=0.0$, $0.5$ and $1.0$. We detect significant signal-to-noise IA signals with the density field for both elliptical and spiral galaxies. We also find significant intrinsic shear-shear correlations for ellipticals. We further examine correlations of the intrinsic shape of galaxies with the local tidal field. Here we find a significant IA signal for elliptical galaxies assuming a linear model. We also detect a weak IA signal for spiral galaxies under a quadratic tidal torquing model. Lastly, we measure the alignment between central galaxies and their host dark-matter halos, finding small to moderate misalignments between their principal axes that decline with halo mass.

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A lensed radio jet at milli-arcsecond resolution II: Constraints on fuzzy dark matter from an extended gravitational arc

Using a single gravitational lens system observed at $\lesssim5$ milli-arcsecond resolution with very long baseline interferometry (VLBI), we place a lower bound on the mass of the fuzzy dark matter (FDM) particle, ruling out $m_χ\leq 4.4\times10^{-21}~\mathrm{eV}$ with a 20:1 posterior odds ratio relative to a smooth lens model. We generalize our result to non-scalar and multiple-field models, such as vector FDM, with $m_{χ,\mathrm{vec}} > 1.4 \times 10^{-21}~\mathrm{eV}$. Due to the extended source structure and high angular resolution of the observation, our analysis is directly sensitive to the presence of granule structures in the main dark matter halo of the lens, which is the most generic prediction of FDM theories. A model based on well-understood physics of ultra-light dark matter fields in a gravitational potential well makes our result robust to a wide range of assumed dark matter fractions and velocity dispersions in the lens galaxy. Our result is competitive with other lower bounds on $m_χ$ from past analyses, which rely on intermediate modelling of structure formation and/or baryonic effects. Higher resolution observations taken at 10 to 100 GHz could improve our constraints by up to 2 orders of magnitude in the future.

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Interpreting Sunyaev-Zel'dovich observations with MillenniumTNG: Mass and environment scaling relations

In the coming years, Sunyaev-Zel'dovich (SZ) measurements can dramatically improve our understanding of the Intergalactic Medium (IGM) and the role of feedback processes on galaxy formation, allowing us to calibrate important astrophysical systematics in cosmological constraints from weak lensing galaxy clustering surveys. However, the signal is only measured in a two-dimensional projection, and its correct interpretation relies on understanding the connection between observable quantities and the underlying intrinsic properties of the gas, in addition to the relation between the gas and the underlying matter distribution. One way to address these challenges is through the use of hydrodynamical simulations such as the high-resolution, large-volume MillenniumTNG suite. We find that measurements of the optical depth, $τ$, and the Compton-y parameter, $Y$, receive large line-of-sight contributions which can be removed effectively by applying a Compensated Aperture Photometry (CAP) filter. In contrast with other $τ$ probes (e.g., X-rays and Fast Radio Bursts), the kSZ-inferred $τ$ receives most of its signal from a confined cylindrical region around the halo due to the velocity decorrelation along the line-of-sight. Additionally, we perform fits to the $Y-M$ and $τ-M$ scaling relations and report best-fit parameters adopting the smoothly broken power law (SBPL) formalism. We note that subgrid physics modeling can broaden the error bar on these by 30\% for intermediate-mass halos ($\sim$$10^{13} \, {\rm M}_{\odot}$). The scatter of the scaling relations can be captured by an intrinsic dependence on concentration, and an extrinsic dependence on tidal shear. Finally, we comment on the effect of using galaxies rather than halos in real observations, which can bias the inferred SZ profiles by $\sim$20\% for $L_\ast$-galaxies.

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The MillenniumTNG Project: The large-scale clustering of galaxies

Modern redshift surveys are tasked with mapping out the galaxy distribution over enormous distance scales. Existing hydrodynamical simulations, however, do not reach the volumes needed to match upcoming surveys. We present results for the clustering of galaxies using a new, large volume hydrodynamical simulation as part of the MillenniumTNG (MTNG) project. With a computational volume that is $\approx15$ times larger than the next largest such simulation currently available, we show that MTNG is able to accurately reproduce the observed clustering of galaxies as a function of stellar mass. When separated by colour, there are some discrepancies with respect to the observed population, which can be attributed to the quenching of satellite galaxies in our model. We combine MTNG galaxies with those generated using a semi-analytic model to emulate the sample selection of luminous red galaxies (LRGs) and emission line galaxies (ELGs), and show that although the bias of these populations is approximately (but not exactly) constant on scales larger than $\approx10$ Mpc, there is significant scale-dependent bias on smaller scales. The amplitude of this effect varies between the two galaxy types, and also between the semi-analytic model and MTNG. We show that this is related to the distribution of haloes hosting LRGs and ELGs. Using mock SDSS-like catalogues generated on MTNG lightcones, we demonstrate the existence of prominent baryonic acoustic features in the large-scale galaxy clustering. We also demonstrate the presence of realistic redshift space distortions in our mocks, finding excellent agreement with the multipoles of the redshift-space clustering measured in SDSS data.

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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.

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The effect of stellar encounters on the dark matter annihilation signal from prompt cusps

Prompt cusps are the densest quasi-equilibrium dark matter objects; one forms at the instant of collapse within every isolated peak of the initial cosmological density field. They have power-law density profiles, $ρ\propto r^{-1.5}$ with central phase-space density set by the primordial velocity dispersion of the dark matter. At late times they account for $\sim 1\%$ of the dark matter mass but for $>90\%$ of its annihilation luminosity in all but the densest regions, where they are tidally disrupted. Here we demonstrate that individual stellar encounters, rather than the mean galactic tide, are the dominant disruptors of prompt cusps within galaxies. Their cumulative effect is fully (though stochastically) characterised by an impulsive shock strength $B_* = 2πG\intρ_*({\bf x}(t))\, \mathrm{d}t$ where $ρ_*$, the total mass density in stars, is integrated over a cusp's entire post-formation trajectory. Stellar encounters and mean tides have only a small effect on the halo annihilation luminosity seen by distant observers, but this is not true for the Galactic halo because of the Sun's position. For a 100 GeV WIMP, Earth-mass prompt cusps are predicted, and stellar encounters suppress their mean annihilation luminosity by a factor of two already at 20 kpc, so that their annihilation emission is predicted to appear almost uniform over the sky. The Galactic Center $γ$-ray Excess is thus unaffected by cusps. If it is indeed dark matter annihilation radiation, then prompt cusps in the outer Galactic halo and beyond must account for 20-80% of the observed isotropic $γ$-ray background in the 1 to 10 GeV range.

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Consistent and simultaneous modelling of galaxy clustering and galaxy-galaxy lensing with Subhalo Abundance Matching

The spatial distribution of galaxies and their gravitational lensing signal offer complementary tests of galaxy formation physics and cosmology. However, their synergy can only be fully exploited if both probes are modelled accurately and consistently. In this paper, we demonstrate that this can be achieved using an extension of Subhalo Abundance Matching, dubbed SHAMe. Specifically, we use mock catalogues built from the TNG300 hydrodynamical simulation to show that SHAMe can simultaneously model the multipoles of the redshift-space galaxy correlation function and galaxy-galaxy lensing, without noticeable bias within the statistical sampling uncertainties of a SDSS volume and on scales r = [0.6-30] Mpc/h. Modelling the baryonic processes in galaxy-galaxy lensing with a baryonification scheme allows SHAMe's range of validity to be extended to r = [0.1-30] Mpc/h. Remarkably, our model achieves this level of precision with just five free parameters beyond those describing the baryonification model. At fixed cosmology, we find that galaxy-galaxy lensing provides a general consistency test but little additional information on galaxy modelling parameters beyond that encoded in the redshift-space multipoles. It does, however, improve constraints if only the projected correlation function is available, as in surveys with only photometric redshifts. We expect SHAMe to have a higher fidelity across a wider range of scales than more traditional methods such as Halo Occupation Distribution modelling. Thus it should provide a significantly more powerful and more robust tool for analysing next-generation large-scale surveys.

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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.

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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.

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Inner cusps of the first dark matter haloes: Formation and survival in a cosmological context

We use very high resolution cosmological zoom simulations to follow the early evolution of twelve first-generation haloes formed from gaussian initial conditions with scale-free power spectra truncated on small scales by a gaussian in wavenumber. Initial collapse occurs with a diverse range of sheet- or filament-like caustic morphologies, but in almost all cases it gives rise to a numerically converged density cusp with $ρ= Ar^{-3/2}$ and total mass comparable to that of the corresponding peak in the initial linear density field. The constant $A$ can be estimated to within about 10 per cent from the properties of this peak. This outcome agrees with earlier work on the first haloes in cold and warm dark matter universes. Within central cusps, the velocity dispersion is close to isotropic, and the equidensity surfaces tend to align with those of the main body of the halo at larger radii. As haloes grow, their cusps are often (but not always) overlaid with additional material at intermediate radii to produce profiles more similar to the Einasto or NFW forms typical of more massive haloes. Nevertheless, to the extent that we can resolve them, cusps survive at the smallest radii. Major mergers can disturb them, but the effect is quite weak in the cases that we study. The cusps extend down to the resolution limits of our simulations, which are typically a factor of several larger than the cores that would be produced by phase-space conservation if the initial power spectrum cutoff arises from free streaming.

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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.

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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.

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Prompt cusp formation from the gravitational collapse of peaks in the initial cosmological density field

I present an analytic model for the early post-collapse evolution of a spherical density peak on the coherence scale of the initial fluctuations in a universe filled with collisionless and pressure-free "dust". On a time-scale which is short compared to the peak's collapse time $t_0$, its inner regions settle into an equilibrium cusp with a power-law density profile, $ρ\propto r^{-12/7}$. Within this cusp, the circular orbit period $P$ at each radius is related to the enclosed mass $M$ by $P = t_0 (M/M_c)^{2/3}$ where $M_c$ is a suitably defined characteristic mass for the initial peak. The relaxation mechanism which produces this cusp gives insight into those which are active in high-resolution simulations of first halo formation in Cold or Warm Dark Matter universes, and, indeed, a simple argument suggests that the same power-law index $γ=-12/7$ should describe the prompt cusps formed during the collapse of generic peaks, independent of any symmetry assumption. Further work is needed to investigate whether additional factors are required to explain the slightly flatter exponent, $γ\approx -1.5$, found in high-resolution numerical simulations of peak collapse.

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The Physical Origin of Galactic Conformity: From Theory to Observation

We employ several galaxy formation models, in particular, L-GALAXIES, IllustrisTNG, and EAGLE, as well as observational samples from SDSS and DESI, to investigate galactic conformity, the observed large-scale correlation between the star-formation properties of central (primary) galaxies and those of their neighbours. To analyse the models and observations uniformly, we introduce CENSAT, a new algorithm to define whether a galaxy is a central or a satellite system based on an isolation criterion. We find that the conformity signal is present, up to at least 5 Mpc from the centres of low- and intermediate-mass centrals in the latest version of L-GALAXIES (Ayromlou et al. 2021), IllustrisTNG, and EAGLE, as well as in SDSS and DESI observational samples. In comparison, the conformity signal is substantially weaker in an older version of L-GALAXIES (Henriques et al. 2020). One of the main differences between this older model and the other models is its neglect of ram-pressure stripping of the gas reservoirs of galaxies except within the boundaries of massive cluster haloes. Our observational comparisons demonstrate that this difference significantly affects the observed large-scale conformity signal. Furthermore, by examining the contribution of backsplash, fly-by, central, and satellite galaxies to the conformity signal, we show that much, but not all, of it arises from primary galaxies near massive systems. Remaining tensions between the models and observations may be solved by modifying the physical prescriptions for how feedback processes affect the distribution and kinematics of gas and the environment around galaxies out to scales of several Megaparsecs.

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Disc instability and bar formation: view from the IllustrisTNG simulations

We make use of z = 0 samples of strongly barred and unbarred disc galaxies from the TNG100 and TNG50 cosmological hydrodynamical simulations to assess the performance of the simple disc instability criterion proposed by Efstathiou, Lake & Negroponte (1982) (ELN-criterion). We find that strongly barred galaxies generally assemble earlier, are more star-dominated in their central regions, and have more massive and more compact discs than unbarred galaxies. The ELN-criterion successfully identifies ~75% and ~80% of the strongly barred and the unbarred galaxies, respectively. Strongly barred galaxies that the criterion fails to identify tend to have more extended discs, higher spin values and bars that assembled later than is typical for the bulk of the barred population. The bars in many of these cases appear to be produced by an interaction with a close neighbour (i.e. to be externally triggered) rather than to result from secular growth in the disc. On the other hand, we find that unbarred galaxies misclassified as barred by the ELN-criterion typically have stellar discs similar to those of barred galaxies, although more extended in the vertical direction and less star-dominated in their central regions, possibly reflecting later formation times. In addition, the bulge component of these galaxies is significantly more prominent at early times than in the strongly barred sample. Thus, the ELN-criterion robustly identifies secular bar instabilities in most simulated disc galaxies, but additional environmental criteria are needed to account for interaction-induced bar formation.

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Dark matter annihilation and the Galactic Centre Excess

We compare the surface brightness profile and morphology of the Galactic Centre Excess (GCE) identified in wide-angle $γ$-ray maps from the Fermi-Large Area Telescope to dark matter annihilation predictions derived from high-resolution $Λ$CDM magnetohydrodynamic simulations of galaxy formation. These simulations produce isolated, disc-dominated galaxies with structure, stellar populations, gas content, and stellar and halo masses comparable to those of the Milky Way. For a specific choice of annihilation cross-section, they agree well with the Fermi-LAT data over the full observed angular range, $1^{\circ}$ to $15^{\circ}$, whereas their dark-matter only counterparts, lacking any compression of the inner halo by the gravitational effects of the baryons, fail to predict emission as centrally concentrated as observed. These results provide additional support to the hypothesis that the GCE is produced by annihilating dark matter. If, however, it is produced by a different mechanism, they imply a strong upper limit on annihilation rates which can be translated into upper limits on the expected $γ$-ray flux not only from the inner Galaxy but also from any substructure, with or without stars, in the Galactic halo.

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