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Ian G. McCarthy

Publications and source records attributed to Ian G. McCarthy.

At least 73 records · Page 4Linked to original sources

The BAHAMAS project: Effects of a running scalar spectral index on large-scale structure

Recent analyses of the cosmic microwave background (CMB) and the Lyman-alpha forest indicate a mild preference for a deviation from a power law primordial matter power spectrum (a so-called negative `running'). We use an extension to the BAHAMAS suite of cosmological hydrodynamic simulations to explore the effects that a running scalar spectral index has on large-scale structure (LSS), using Planck CMB constraints to initialize the simulations. We focus on 5 key statistics: i) the non-linear matter power spectrum ii) the halo mass function; iii) the halo two-point auto correlation function; iv) total mass halo density profiles; and v) the halo concentration-mass relation. In terms of the matter power spectrum, we find that a running scalar spectral index affects all k-scales examined in this study, with a negative (positive) running leading to an amplification (suppression) of power. These effects should be easily detectable with upcoming surveys such as LSST and Euclid. In the mass range sampled, a positive running leads to an increase in the mass of galaxy groups and clusters, with the favoured negative running leading to a decrease in mass of lower-mass (M <~ 10^13 M_solar) halos, but an increase for the most massive (M >~ 10^13 M_solar) halos. Changes in the mass are generally confined to 5-10% which, while not insignificant, cannot by itself reconcile the claimed tension between the primary CMB and cluster number counts. We find that running does not significantly affect the shapes of density profiles of matched halos, changing only their amplitude. Finally, we demonstrate that the observed effects on LSS due to a running scalar spectral index are separable from those of baryonic effects to typically a few percent precision.

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Exploring extensions to the standard cosmological model and the impact of baryons on small scales

It has been claimed that the standard model of cosmology (LCDM) cannot easily account for a number of observations on relatively small scales, motivating extensions to the standard model. Here we introduce a new suite of cosmological simulations that systematically explores three plausible extensions: warm dark matter, self-interacting dark matter, and a running of the scalar spectral index of density fluctuations. Current observational constraints are used to specify the additional parameters that come with these extensions. We examine a large range of observable metrics on small scales, including the halo mass function, density and circular velocity profiles, the abundance of satellite subhaloes, and halo concentrations. For any given metric, significant degeneracies can be present between the extensions. In detail, however, the different extensions have quantitatively distinct mass and radial dependencies, suggesting that a multi-probe approach over a range of scales can be used to break the degeneracies. We also demonstrate that the relative effects on the radial density profiles in the different extensions (compared to the standard model) are converged down to significantly smaller radii than are the absolute profiles. We compare the derived cosmological trends with the impact of baryonic physics using the EAGLE and ARTEMIS simulations. Significant degeneracies are also present between baryonic physics and cosmological variations (with both having similar magnitude effects on some observables). Given the inherent uncertainties both in the modelling of galaxy formation physics and extensions to LCDM, a systematic and simultaneous exploration of both is strongly warranted.

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Connecting the structure of dark matter haloes to the primordial power spectrum

A large body of work based on collisionless cosmological N-body simulations going back over two decades has advanced the idea that collapsed dark matter haloes have simple and approximately universal forms for their mass density and pseudo-phase space density (PPSD) distributions. However, a general consensus on the physical origin of these results has not yet been reached. In the present study, we explore to what extent the apparent universality of these forms holds when we vary the initial conditions (i.e., the primordial power spectrum of density fluctuations) away from the standard CMB-normalised case, but still within the context of LCDM with a fixed expansion history. Using simulations that vary the initial amplitude and shape, we show that the structure of dark matter haloes retains a clear memory of the initial conditions. Specifically, increasing (lowering) the amplitude of fluctuations increases (decreases) the concentration of haloes and, if pushed far enough, the density profiles deviate strongly from the NFW form that is a good approximation for the CMB-normalised case. Although, an Einasto form works well. Rather than being universal, the slope of the PPSD (or pseudo-entropy) profile steepens (flattens) with increasing (decreasing) power spectrum amplitude and can exhibit a strong halo mass dependence. Our results therefore indicate that the previously identified universality of the structure of dark matter haloes is mostly a consequence of adopting a narrow range of (CMB-normalised) initial conditions for the simulations. Our new suite provides a useful test-bench against which physical models for the origin of halo structure can be validated.

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Environment from cross-correlations: connecting hot gas and the quenching of galaxies

The observable properties of galaxies depend on both internal processes and the external environment. In terms of the environmental role, we still do not have a clear picture of the processes driving the transformation of galaxies. The use of proxies for environment (e.g., host halo mass, distance to the N^th nearest neighbour, etc.), as opposed to the real physical conditions (e.g., hot gas density) may bear some responsibility for this. Here we propose a new method that directly links galaxies to their local environments, by using spatial cross-correlations of galaxy catalogues with maps from large-scale structure surveys (e.g., thermal Sunyaev-Zel'dovich [tSZ] effect, diffuse X-ray emission, weak lensing of galaxies or the CMB). We focus here on the quenching of galaxies and its link to local hot gas properties. Maps of galaxy overdensity and quenched fraction excess are constructed from volume-limited SDSS catalogs, which are cross-correlated with tSZ effect and X-ray maps from Planck and ROSAT, respectively. Strong signals out to Mpc scales are detected for most cross-correlations and are compared to predictions from the EAGLE and BAHAMAS cosmological hydrodynamical simulations. The simulations successfully reproduce many, but not all, of the observed power spectra, with an indication that environmental quenching may be too efficient in the simulations. We demonstrate that the cross-correlations are sensitive to both the internal (e.g., AGN and stellar feedback) and external processes (e.g., ram pressure stripping, harassment, strangulation, etc.) responsible for quenching. The methods outlined in this paper can be adapted to other observables and, with upcoming surveys, will provide a stringent test of physical models for environmental transformation.

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Observable tests of self-interacting dark matter in galaxy clusters: cosmological simulations with SIDM and baryons

We present BAHAMAS-SIDM, the first large-volume, (400/h Mpc)^3, cosmological simulations including both self-interacting dark matter (SIDM) and baryonic physics. These simulations are important for two primary reasons: 1) they include the effects of baryons on the dark matter distribution 2) the baryon particles can be used to make mock observables that can be compared directly with observations. As is well known, SIDM haloes are systematically less dense in their centres, and rounder, than CDM haloes. Here we find that that these changes are not reflected in the distribution of gas or stars within galaxy clusters, or in their X-ray luminosities. However, gravitational lensing observables can discriminate between DM models, and we present a menu of tests that future surveys could use to measure the SIDM interaction strength. We ray-trace our simulated galaxy clusters to produce strong lensing maps. Including baryons boosts the lensing strength of clusters that produce no critical curves in SIDM-only simulations. Comparing the Einstein radii of our simulated clusters with those observed in the CLASH survey, we find that at velocities around 1000 km/s an SIDM cross-section of sigma/m > 1 cm^2/g is likely incompatible with observed cluster lensing.

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Weak lensing Analysis of X-Ray-selected XXL Galaxy Groups and Clusters with Subaru HSC Data

We present a weak-lensing analysis of X-ray galaxy groups and clusters selected from the XMM-XXL survey using the first-year data from the Hyper Suprime-Cam (HSC) Subaru Strategic Program. Our joint weak-lensing and X-ray analysis focuses on 136 spectroscopically confirmed X-ray-selected systems at 0.031 < z < 1.033 detected in the 25sqdeg XXL-N region. We characterize the mass distributions of individual clusters and establish the concentration-mass (c-M) relation for the XXL sample, by accounting for selection bias and statistical effects, and marginalizing over the remaining mass calibration uncertainty. We find the mass-trend parameter of the c-M relation to be β= -0.07 \pm 0.28 and the normalization to be c200 = 4.8 \pm 1.0 (stat) \pm 0.8 (syst) at M200=10^{14}Msun/h and z = 0.3. We find no statistical evidence for redshift evolution. Our weak-lensing results are in excellent agreement with dark-matter-only c-M relations calibrated for recent LCDM cosmologies. The level of intrinsic scatter in c200 is constrained as σ(\ln[c200]) < 24% (99.7% CL), which is smaller than predicted for the full population of LCDM halos. This is likely caused in part by the X-ray selection bias in terms of the relaxation state. We determine the temperature-mass (Tx-M500) relation for a subset of 105 XXL clusters that have both measured HSC lensing masses and X-ray temperatures. The resulting Tx-M500 relation is consistent with the self-similar prediction. Our Tx-M500 relation agrees with the XXL DR1 results at group scales, but has a slightly steeper mass trend, implying a smaller mass scale in the cluster regime. The overall offset in the Tx-M500 relation is at the $1.5σ$ level, corresponding to a mean mass offset of (34\pm 20)%. We also provide bias-corrected, weak-lensing-calibrated M200 and M500 mass estimates of individual XXL clusters based on their measured X-ray temperatures.

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Stellar Property Statistics of Massive Halos from Cosmological Hydrodynamics Simulations: Common Kernel Shapes

We study stellar property statistics, including satellite galaxy occupation, of massive halo populations realized by three cosmological hydrodynamics simulations: BAHAMAS + MACSIS, TNG300 of the IllustrisTNG suite, and Magneticum Pathfinder. The simulations incorporate independent sub-grid methods for astrophysical processes with spatial resolutions ranging from $1.5$ to $6$ kpc, and each generates samples of $1000$ or more halos with $M_{\rm halo}> 10^{13.5} M_{\odot}$ at redshift $z=0$. Applying localized, linear regression (LLR), we extract halo mass-conditioned statistics (normalizations, slopes, and intrinsic covariance) for a three-element stellar property vector consisting of: i) $N_{sat}$, the number of satellite galaxies with stellar mass, $M_{\star, \rm sat} > 10^{10} M_{\odot}$ within radius $R_{200c}$ of the halo; ii) $M_{\star,\rm tot}$, the total stellar mass within that radius, and; iii) $M_{\star,\rm BCG}$, the gravitationally-bound stellar mass of the central galaxy within a $100 \, \rm kpc$ radius. Scaling parameters for the three properties with halo mass show mild differences among the simulations, in part due to numerical resolution, but there is qualitative agreement on property correlations, with halos having smaller than average central galaxies tending to also have smaller total stellar mass and a larger number of satellite galaxies. Marginalizing over total halo mass, we find the satellite galaxy kernel, $p(\ln N_{sat}\,|\,M_{\rm halo},z)$ to be consistently skewed left, with skewness parameter $γ= -0.91 \pm 0.02$, while that of $\ln M_{\star,\rm tot}$ is closer to log-normal, in all three simulations. The highest resolution simulations find $γ\simeq -0.8$ for the $z=0$ shape of $p(\ln M_{\star,\rm BCG}\,|\,M_{\rm halo},z)$ and also that the fractional scatter in total stellar mass is below $10\%$ in halos more massive than $10^{14.3} M_{\odot}$.

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Painting with baryons: augmenting N-body simulations with gas using deep generative models

Running hydrodynamical simulations to produce mock data of large-scale structure and baryonic probes, such as the thermal Sunyaev-Zeldovich (tSZ) effect, at cosmological scales is computationally challenging. We propose to leverage the expressive power of deep generative models to find an effective description of the large-scale gas distribution and temperature. We train two deep generative models, a variational auto-encoder and a generative adversarial network, on pairs of matter density and pressure slices from the BAHAMAS hydrodynamical simulation. The trained models are able to successfully map matter density to the corresponding gas pressure. We then apply the trained models on 100 lines-of-sight from SLICS, a suite of N-body simulations optimised for weak lensing covariance estimation, to generate maps of the tSZ effect. The generated tSZ maps are found to be statistically consistent with those from BAHAMAS. We conclude by considering a specific observable, the angular cross-power spectrum between the weak lensing convergence and the tSZ effect and its variance, where we find excellent agreement between the predictions from BAHAMAS and SLICS, thus enabling the use of SLICS for tSZ covariance estimation.

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Probing hot gas around luminous red galaxies through the Sunyaev-Zel'dovich effect

We construct the mean thermal Sunyaev-Zel'dovich (tSZ) Comptonization y profile around Luminous Red Galaxies (LRGs) in the redshift range 0.16 < z < 0.47 from the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) using the Planck y map. The mean central tSZ signal for the full sample is y ~ 1.8 * 10^(-7) and we detect tSZ emission out to ~30 arcmin, which is well beyond the 10 arcmin angular resolution of the y map and well beyond the virial radii of the LRGs. We compare the measured profile with predictions from the cosmo-OWLS suite of cosmological hydrodynamical simulations. This comparison agrees well for models that include feedback from active galactic nuclei (AGN), but not with hydrodynamic models without this energetic feedback mechanism. This suggests that an additional heating mechanism is required over SNe feedback and star formation to explain the y data profile. We also compare our results with predictions based on the halo model with a universal pressure profile (UPP) giving the y signal. The predicted profile is consistent with the data, but only if we account for the clustering of haloes via a two-halo term and if halo masses are estimated using the mean stellar-to-halo mass (SHM) relation of Coupon et al. (2015) or Wang et al.(2016) estimated from gravitational lensing measurements. We also discuss the importance of scatter in the SHM relation on the model predictions.

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A Search for Warm/Hot Gas Filaments Between Pairs of SDSS Luminous Red Galaxies

We search the Planck data for a thermal Sunyaev-Zel'dovich (tSZ) signal due to gas filaments between pairs of Luminous Red Galaxies (LRG's) taken from the Sloan Digital Sky Survey Data Release 12 (SDSS/DR12). We identify $\sim$260,000 LRG pairs in the DR12 catalog that lie within 6-10 $h^{-1} \mathrm{Mpc}$ of each other in tangential direction and within 6 $h^{-1} \mathrm{Mpc}$ in radial direction. We stack pairs by rotating and scaling the angular positions of each LRG so they lie on a common reference frame, then we subtract a circularly symmetric halo from each member of the pair to search for a residual signal between the pair members. We find a statistically significant (5.3$σ$) signal between LRG pairs in the stacked data with a magnitude $Δy = (1.31 \pm 0.25) \times 10^{-8}$. The uncertainty is estimated from two Monte Carlo null tests which also establish the reliability of our analysis. Assuming a simple, isothermal, cylindrical filament model of electron over-density with a radial density profile proportional to $r_c/r$ (as determined from simulations), where $r$ is the perpendicular distance from the cylinder axis and $r_c$ is the core radius of the density profile, we constrain the product of over-density and filament temperature to be $δ_c \times (T_{\rm e}/10^7 \, {\rm K}) \times (r_c/0.5h^{-1} \, {\rm Mpc}) = 2.7 \pm 0.5$. To our knowledge, this is the first detection of filamentary gas at over-densities typical of cosmological large-scale structure. We compare our result to the BAHAMAS suite of cosmological hydrodynamic simulations (McCarthy et al. 2017) and find a slightly lower, but marginally consistent Comptonization excess, $Δy = (0.84 \pm 0.24) \times 10^{-8}$.

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Weak Lensing Minima and Peaks: Cosmological Constraints and the Impact of Baryons

We present a novel statistic to extract cosmological information in weak lensing data: the lensing minima. We also investigate the effect of baryons on the cosmological constraints from peak and minimum counts. Using the \texttt{MassiveNuS} simulations, we find that lensing minima are sensitive to non-Gaussian cosmological information and are complementary to the lensing power spectrum and peak counts. For an LSST-like survey, we obtain $95\%$ credible intervals from a combination of lensing minima and peaks that are significantly stronger than from the power spectrum alone, by $44\%$, $11\%$, and $63\%$ for the neutrino mass sum $\sum m_ν$, matter density $Ω_m$, and amplitude of fluctuation $A_s$, respectively. We explore the effect of baryonic processes on lensing minima and peaks using the hydrodynamical simulations \texttt{BAHAMAS} and \texttt{Osato15}. We find that ignoring baryonic effects would lead to strong ($\approx 4 σ$) biases in inferences from peak counts, but negligible ($\approx 0.5 σ$) for minimum counts, suggesting lensing minima are a potentially more robust tool against baryonic effects. Finally, we demonstrate that the biases can in principle be mitigated without significantly degrading cosmological constraints when we model and marginalize the baryonic effects.

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Exploring the effects of galaxy formation on matter clustering through a library of simulation power spectra

Upcoming weak lensing surveys require a detailed theoretical understanding of the matter power spectrum in order to derive accurate and precise cosmological parameter values. While galaxy formation is known to play an important role, its precise effects are currently unknown. We present a set of 92 matter power spectra from the OWLS, cosmo-OWLS and BAHAMAS simulation suites, including different $Λ$CDM cosmologies, neutrino masses, subgrid prescriptions and AGN feedback strengths. We conduct a detailed investigation of the dependence of the relative difference between the total matter power spectra in hydrodynamical and collisionless simulations on the effectiveness of stellar and AGN feedback, cosmology and redshift. The strength of AGN feedback can greatly affect the power on a range of scales, while a lack of stellar feedback can greatly increase the effectiveness of AGN feedback on large scales. We also examine differences in the initial conditions of hydrodynamic and N-body simulations that can lead to a ~1% discrepancy in the large-scale power, and furthermore show our results to be insensitive to cosmic variance. We present an empirical model capable of predicting the effect of galaxy formation on the matter power spectrum at z=0 to within 1% for k<1 h/Mpc, given only the mean baryon fraction in galaxy groups. Differences in group baryon fractions can also explain the quantitative disagreement between predictions from the literature. All total and dark matter only power spectra in this library will be made publicly available at powerlib.strw.leidenuniv.nl.

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The impact of baryonic physics and massive neutrinos on weak lensing peak statistics

We study the impact of baryonic processes and massive neutrinos on weak lensing peak statistics that can be used to constrain cosmological parameters. We use the BAHAMAS suite of cosmological simulations, which self-consistently include baryonic processes and the effect of massive neutrino free-streaming on the evolution of structure formation. We construct synthetic weak lensing catalogues by ray-tracing through light-cones, and use the aperture mass statistic for the analysis. The peaks detected on the maps reflect the cumulative signal from massive bound objects and general large-scale structure. We present the first study of weak lensing peaks in simulations that include both baryonic physics and massive neutrinos (summed neutrino mass $M_ν =$ 0.06, 0.12, 0.24, and 0.48 eV assuming normal hierarchy), so that the uncertainty due to physics beyond the gravity of dark matter can be factored into constraints on cosmological models. Assuming a fiducial model of baryonic physics, we also investigate the correlation between peaks and massive haloes, over a range of summed neutrino mass values. As higher neutrino mass tends to suppress the formation of massive structures in the Universe, the halo mass function and lensing peak counts are therefore modified as a function of $M_ν$. Over most of the S/N range, the impact of fiducial baryonic physics is greater (less) than neutrinos for 0.06 and 0.12 (0.24 and 0.48) eV models. Both baryonic physics and massive neutrinos should be accounted for when deriving cosmological parameters from weak lensing observations.

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Observable tests of self-interacting dark matter in galaxy clusters: BCG wobbles in a constant density core

Models of Cold Dark Matter predict that the distribution of dark matter in galaxy clusters should be cuspy, centrally concentrated. Constant density cores would be strong evidence for beyond-CDM physics, such as Self-Interacting Dark Matter (SIDM). An observable consequence would be oscillations of the Brightest Cluster Galaxy (BCG) in otherwise relaxed galaxy clusters. Offset BCGs have indeed been observed - but only interpreted via a simplified, analytic model of oscillations. We compare these observations to the BAHAMAS-SIDM suite of cosmological simulations, which include SIDM and a fully hydrodynamical treatment of star formation and feedback. We predict that the median offset of BCGs increases with the SIDM cross-section, cluster mass and the amount of stellar mass within 10kpc, while CDM exhibits no trend in mass. Interpolating between the simulated cross-sections, we find that the observations (of 10 clusters) is consistent with CDM at the ~1.5$σ$ level, and prefer cross-section $σ$/m < 0.12(0.39)cm$^2$/g at 68% (95%) confidence level. This is on the verge of ruling out velocity-independent dark matter self-interactions as the solution to discrepancies between the predicted and observed behaviour of dwarf galaxies, and will be improved by larger surveys by Euclid or SuperBIT.

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Modelling baryonic feedback for survey cosmology

Observational cosmology in the next decade will rely on probes of the distribution of matter in the redshift range between $0<z<3$ to elucidate the nature of dark matter and dark energy. In this redshift range, galaxy formation is known to have a significant impact on observables such as two-point correlations of galaxy shapes and positions, altering their amplitude and scale dependence beyond the expected statistical uncertainty of upcoming experiments at separations under 10 Mpc. Successful extraction of information in such a regime thus requires, at the very least, unbiased models for the impact of galaxy formation on the matter distribution, and can benefit from complementary observational priors. This work reviews the current state of the art in the modelling of baryons for cosmology, from numerical methods to approximate analytical prescriptions, and makes recommendations for studies in the next decade, including a discussion of potential probe combinations that can help constrain the role of baryons in cosmological studies. We focus, in particular, on the modelling of the matter power spectrum, $P(k,z)$, as a function of scale and redshift, and of the observables derived from this quantity. This work is the result of a workshop held at the University of Oxford in November of 2018.

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The gas fractions of dark matter haloes hosting simulated $\sim L^\star$ galaxies are governed by the feedback history of their black holes

We examine the origin of scatter in the relationship between the gas fraction and mass of dark matter haloes hosting present-day $\sim L^\star$ central galaxies in the EAGLE simulations. The scatter is uncorrelated with the accretion rate of the central galaxy's black hole (BH), but correlates strongly and negatively with the BH's mass, implicating differences in the expulsion of gas by active galactic nucleus feedback, throughout the assembly of the halo, as the main cause of scatter. Haloes whose central galaxies host undermassive BHs also tend to retain a higher gas fraction, and exhibit elevated star formation rates (SFRs). Diversity in the mass of central BHs stems primarily from diversity in the dark matter halo binding energy, as these quantities are strongly and positively correlated at fixed halo mass, such that $\sim L^\star$ galaxies hosted by haloes that are more (less) tightly-bound develop central BHs that are more (less) massive than is typical for their halo mass. Variations in the halo gas fraction at fixed halo mass are reflected in both the soft X-ray luminosity and thermal Sunyaev-Zel'dovich flux, suggesting that the prediction of a strong coupling between the properties of galaxies and their halo gas fractions can be tested with measurements of these diagnostics for galaxies with diverse SFRs but similar halo masses.

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The relationship between the morphology and kinematics of galaxies and its dependence on dark matter halo structure in EAGLE

We investigate the connection between the morphology and internal kinematics of the stellar component of central galaxies with mass $M_\star > {10}^{9.5} {\rm M}_\odot$ in the EAGLE simulations. We compare several kinematic diagnostics commonly used to describe simulated galaxies, and find good consistency between them. We model the structure of galaxies as ellipsoids and quantify their morphology via the ratios of their principal axes. We show that the differentiation of blue star-forming and red quiescent galaxies using morphological diagnostics can be achieved with similar efficacy to the use of kinematical diagnostics, but only if one is able to measure both the flattening and the triaxiality of the galaxy. Flattened oblate galaxies exhibit greater rotational support than their spheroidal counterparts, but there is significant scatter in the relationship between morphological and kinematical diagnostics, such that kinematically-similar galaxies can exhibit a broad range of morphologies. The scatter in the relationship between the flattening and the ratio of the rotation and dispersion velocities ($v/σ$) correlates strongly with the anisotropy of the stellar velocity dispersion: at fixed $v/σ$, flatter galaxies exhibit greater dispersion in the plane defined by the intermediate and major axes than along the minor axis, indicating that the morphology of simulated galaxies is influenced significantly by the structure of their velocity dispersion. The simulations reveal that this anisotropy correlates with the intrinsic morphology of the galaxy's inner dark matter halo, i.e. the halo's morphology that emerges in the absence of dissipative baryonic physics. This implies the existence of a causal relationship between the morphologies of galaxies and that of their host dark matter haloes.

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The BAHAMAS project: the CMB--large-scale structure tension and the roles of massive neutrinos and galaxy formation

Recent studies have presented evidence for tension between the constraints on Omega_m and sigma_8 from the cosmic microwave background (CMB) and measurements of large-scale structure (LSS). This tension can potentially be resolved by appealing to extensions of the standard model of cosmology and/or untreated systematic errors in the modelling of LSS, of which baryonic physics has been frequently suggested. We revisit this tension using, for the first time, carefully-calibrated cosmological hydrodynamical simulations, which thus capture the back reaction of the baryons on the total matter distribution. We have extended the BAHAMAS simulations to include a treatment of massive neutrinos, which currently represents the best motivated extension to the standard model. We make synthetic thermal Sunyaev-Zel'dovich effect, weak galaxy lensing, and CMB lensing maps and compare to observed auto- and cross-power spectra from a wide range of recent observational surveys. We conclude that: i) in general there is tension between the primary CMB and LSS when adopting the standard model with minimal neutrino mass; ii) after calibrating feedback processes to match the gas fractions of clusters, the remaining uncertainties in the baryonic physics modelling are insufficient to reconcile this tension; and iii) if one accounts for internal tensions in the Planck CMB dataset (by allowing the lensing amplitude, A_Lens, to vary), invoking a non-minimal neutrino mass, typically of 0.2-0.4 eV, can resolve the tension. This solution is fully consistent with separate constraints from the primary CMB and baryon acoustic oscillations.

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