The impact of baryonic physics on the subhalo mass function and implications for gravitational lensing

We investigate the impact of baryonic physics on the subhalo population by analyzing the results of two recent hydrodynamical simulations (EAGLE and Illustris), which have very similar configuration, but a different model of baryonic physics. We concentrate on haloes with a mass between $10^{12.5}$ and $10^{14}M_{\odot}h^{-1}$ and redshift between 0.2 and 0.5, comparing with observational results and subhalo detections in early-type galaxy lenses. We compare the number and the spatial distribution of subhaloes in the fully hydro runs and in their dark matter only counterparts, focusing on the differences between the two simulations. We find that the presence of baryons reduces the number of subhaloes, especially at the low mass end ($\leq 10^{10}M_{\odot}h^{-1}$), by different amounts depending on the model. The variations in the subhalo mass function are strongly dependent on those in the halo mass function, which is shifted by the effect of stellar and AGN feedback. Finally, we search for analogues of the observed lenses (SLACS) in the simulations, selecting them in velocity dispersion and dynamical properties. We use the selected galaxies to quantify detection expectations based on the subhalo populations in the different simulations, calculating the detection probability and the predicted values for the projected dark matter fraction in subhaloes $f_{DM}$ and the slope of the mass function $\alpha$. We compare these values with those derived from subhalo detections in observations and conclude that the dark-matter-only and hydro EAGLE runs are both compatible with observational results, while results from the hydro Illustris run do not lie within the errors.Comment: 15 pages, 11 figures, accepted for publication in MNRA

Ellipsoidal halo finders and implications for models of triaxial halo formation

We describe an algorithm for identifying ellipsoidal haloes in numerical simulations, and quantify how the resulting estimates of halo mass and shape differ with respect to spherical halo finders. Haloes become more prolate when fit with ellipsoids, the difference being most pronounced for the more aspherical objects. Although the ellipsoidal mass is systematically larger, this is less than 10% for most of the haloes. However, even this small difference in mass corresponds to a significant difference in shape. We quantify these effects also on the initial mass and deformation tensors, on which most models of triaxial collapse are based. By studying the properties of protohaloes in the initial conditions, we find that models in which protohaloes are identified in Lagrangian space by three positive eigenvalues of the deformation tensor are tenable only at the masses well-above $M_*$. The overdensity $\delta$ within almost any protohalo is larger than the critical value associated with spherical collapse (increasing as mass decreases); this is in good qualitative agreement with models which identify haloes requiring that collapse have occured along all three principal axes, each axis having turned around from the universal expansion at a different time. The distributions of initial values are in agreement with the simplest predictions associated with ellipsoidal collapse, assuming initially spherical protohaloes, collapsed around random positions which were sufficiently overdense. However, most protohaloes are not spherical and departures from sphericity increase as protohalo mass decreases. [Abridged]Comment: 18 pages, 17 figures, accepted for publication in MNRA

A look to the inside of haloes: a characterisation of the halo shape as a function of overdensity in the Planck cosmology

In this paper we study the triaxial properties of dark matter haloes of a wide range of masses extracted from a set of cosmological N-body simulations. We measure the shape at different distances from the halo centre (characterised by different overdensity thresholds), both in three and in two dimensions. We discuss how halo triaxiality increases with mass, redshift and distance from the halo centre. We also examine how the orientation of the different ellipsoids are aligned with each other and what is the gradient in internal shapes for halos with different virial configurations. Our findings highlight that the internal part of the halo retains memory of the violent formation process keeping the major axis oriented toward the preferential direction of the in-falling material while the outer part becomes rounder due to continuous isotropic merging events. This effect is clearly evident in high mass haloes - which formed more recently - while it is more blurred in low mass haloes. We present simple distributions that may be used as priors for various mass reconstruction algorithms, operating in different wavelengths, in order to recover a more complex and realistic dark matter distribution of isolated and relaxed systems.Comment: accepted for publication by MNRAS (15 pag. and 14 fig.

Universality of dark matter haloes shape over six decades in mass: Insights from the Millennium XXL and SBARBINE simulations

For the last 30 years many observational and theoretical evidences have shown that galaxy clusters are not spherical objects, and that their shape is much better described by a triaxial geometry. With the advent of multi-wavelength data of increasing quality, triaxial investigations of galaxy clusters is gathering a growing interest from the community, especially in the time of "precision cosmology". In this work, we aim to provide the first statistically significant predictions in the unexplored mass range above 3x10^14 Mo/h, using haloes from two redshifts (z=0 and z=1) of the Millennium XXL simulation. The size of this cosmological dark matter only simulation (4.1 Gpc) allows the formation of a statistically significant number of massive cluster scale haloes (about 500 with M>2x10^15 Mo/h and 780000 with M>10^14 Mo/h). Besides, we aim to extend this investigation to lower masses in order to look for universal predictions across nearly six orders of magnitude in mass, from 10^10 to almost 10^16 Mo/h. For this purpose we use the SBARBINE simulations, allowing to model haloes of masses starting from 10^10 Mo/h. We use an elliptical overdensity method to select haloes and compute the shapes of the unimodal ones (approximately 50%), while we discard the unrelaxed. The minor to major and intermediate to major axis ratio are found to be well described by simple functional forms. For a given mass we can fully characterize the shape of a halo and give predictions about the distribution of axis ratios for a given cosmology and redshift. Moreover, these results are in some disagreement with the findings of Jing & Suto (2002) which are widely used in the community even though they have to be extrapolated far beyond their original mass range. This "recipe" is made available to the community in this paper and in a dedicated web page.Comment: 13 pages, 16 figure

Flux-ratio anomalies from discs and other baryonic structures in the Illustris simulation

The flux ratios in the multiple images of gravitationally lensed quasars can provide evidence for dark matter substructure in the halo of the lensing galaxy if the flux ratios differ from those predicted by a smooth model of the lensing galaxy mass distribution. However, it is also possible that baryonic structures in the lensing galaxy, such as edge-on discs, can produce flux-ratio anomalies. In this work, we present the first statistical analysis of flux-ratio anomalies due to baryons from a numerical simulation perspective. We select galaxies with various morphological types in the Illustris simulation and ray-trace through the simulated halos, which include baryons in the main lensing galaxies but exclude any substructures, in order to explore the pure baryonic effects. Our ray-tracing results show that the baryonic components can be a major contribution to the flux-ratio anomalies in lensed quasars and that edge-on disc lenses induce the strongest anomalies. We find that the baryonic components increase the probability of finding high flux-ratio anomalies in the early-type lenses by about 8% and by about 10 - 20% in the disc lenses. The baryonic effects also induce astrometric anomalies in 13% of the mock lenses. Our results indicate that the morphology of the lens galaxy becomes important in the analysis of flux-ratio anomalies when considering the effect of baryons, and that the presence of baryons may also partially explain the discrepancy between the observed (high) anomaly frequency and what is expected due to the presence of subhalos as predicted by the CDM simulations.Comment: 16 pages, 11 figures, accepted by MNRA

Accretion of satellites onto central galaxies in clusters: merger mass ratios and orbital parameters

We study the statistical properties of mergers between central and satellite galaxies in galaxy clusters in the redshift range $0<z<1$, using a sample of dark-matter only cosmological N-body simulations from Le SBARBINE dataset. Using a spherical overdensity algorithm to identify dark-matter haloes, we construct halo merger trees for different values of the over-density $\Delta_c$. While the virial overdensity definition allows us to probe the accretion of satellites at the cluster virial radius $r_{vir}$, higher overdensities probe satellite mergers in the central region of the cluster, down to $\approx 0.06 r_{vir}$, which can be considered a proxy for the accretion of satellite galaxies onto central galaxies. We find that the characteristic merger mass ratio increases for increasing values of $\Delta_c$: more than $60\%$ of the mass accreted by central galaxies since $z\approx 1$ comes from major mergers. The orbits of satellites accreting onto central galaxies tend to be more tangential and more bound than orbits of haloes accreting at the virial radius. The obtained distributions of merger mass ratios and orbital parameters are useful to model the evolution of the high-mass end of the galaxy scaling relations without resorting to hydrodynamic cosmological simulations.Comment: accepted by MNRAS (minor comments

Not all subhaloes are created equal: modelling the diversity of subhalo density profiles in TNG50

In this work, we analyse the density profiles of subhaloes with masses Msh ≥ 1.4 × 108 M in the TNG50 simulation, with the aim of including baryonic effects. We evaluate the performance of frequently used models, such as the standard Navarro–Frenk–White (NFW), the Einasto, and a smoothly truncated version of the NFW profile. We find that these models do not perform well for the majority of subhaloes, with the NFW profile giving the worst fit in most cases. This is primarily due to mismatches in the inner and outer logarithmic slopes, which are significantly steeper for a large number of subhaloes in the presence of baryons. To address this issue, we propose new three-parameter models and show that they significantly improve the goodness of fit independently of the subhalo’s specific properties. Our best-performing model is a modified version of the NFW profile with an inner log-slope of −2 and a variable truncation that is sharper and steeper than the slope transition in the standard NFW profile. Additionally, we investigate how both the parameter values of the best density profile model and the average density profiles vary with subhalo mass, Vmax, distance from the host halo centre, baryon content, and infall time, and we also present explicit scaling relations for the mean parameters of the individual profiles. The newly proposed fit and the scaling relations are useful to predict the properties of realistic subhaloes in the mass range 108 M ≤Msh ≤ 1013 M that can be influenced by the presence of baryons

Constraining the mass density of free-floating black holes using razor-thin lensing arcs

Strong lensing of active galactic nuclei in the radio can result in razor-thin arcs, with a thickness of less than a milli-arcsecond, if observed at the resolution achievable with very long baseline interferometry (VLBI). Such razor-thin arcs provide a unique window on the coarseness of the matter distribution between source and observer. In this paper, we investigate to what extent such razor-thin arcs can constrain the number density and mass function of `free-floating' black holes, defined as black holes that do not, or no longer, reside at the centre of a galaxy. These can be either primordial in origin or arise as by-products of the evolution of super-massive black holes in galactic nuclei. When sufficiently close to the line of sight, free-floating black holes cause kink-like distortions in the arcs, which are detectable by eye in the VLBI images as long as the black hole mass exceeds $\sim 1000$ Solar masses. Using a crude estimate for the detectability of such distortions, we analytically compute constraints on the matter density of free-floating black holes resulting from null-detections of distortions along a realistic, fiducial arc, and find them to be comparable to those from quasar milli-lensing. We also use predictions from a large hydrodynamical simulation for the demographics of free-floating black holes that are not primordial in origin, and show that their predicted mass density is roughly four orders of magnitude below the constraints achievable with a single razor-thin arc.Comment: 17 pages, 13 figures, 1 table, comments welcom

Ellipsoidal collapse of dark matter haloes in cosmological simulations

Nowadays different observational campaigns agree on the standard cosmological model to explain and describe the formation and evolution of large scale structures in our Universe. In this scenario, almost 95% of the energy content of the Universe is in unknown forms of energy and matter, generally called dark energy and dark matter. The structures observed today are assumed to have grown gravitationally from small and initially Gaussian density fluctuations. As the universe expands, sufficiently overdense regions expand until they reach a maximum size and then collapse under the action of their own gravity: since dark matter is believed to be the dominant matter component of the universe, it leads the gravitational collapse process, forming structures called dark matter haloes. It is within the potential wells of these haloes that gas can shock, cool and eventually form stars and galaxies. The main theoretical models on the gravitational collapse of dark matter haloes are the spherical collapse and the ellipsoidal collapse (EC) models. The former describes haloes as spherical overdense regions embedded in an uniform background, while the latter allows more possible shapes, defining haloes as homogeneous ellipsoids. Moreover, the ellipsoidal collapse model predicts that there is a direct connection between the evolution of an halo and the properties of the corresponding region in the initial conditions. Despite the fact that a triaxial modelling is obviously more realistic, the spherical approximation is still the most common choice. In this work we analysed the results of several cosmological simulations (the GIF2 , Le SBARBINE - designed and run in Padova by our group - and the Millennium XXL simulations), with the aim of study the triaxiality of dark matter haloes in detail. In particular, we developed a new halo finder, called ``Ellipsoidal Overdensity Halo Finder'' (EO), which identifies dark matter haloes as triaxial ellipsoids at all times, thus following the prescription of the EC model. Using its results, we studied the properties of protohaloes in the initial conditions and their evolution through the whole history of the Universe: this is crucial to understand the role of the initial density peaks, which are believed to be the seeds of all the observed structures. Our results help to understand the dynamics of halo collapse, confirming many predictions of the EC model, but also provide hints for a more realistic modelling. As the issue of halo triaxiality is still not completely solved in theory and simulations, it started to be considered very recently in observational studies. Galaxy clusters are the largest virialized systems in the Universe and, following hierarchical clustering, also the last to form; almost 80% of their mass is attributed to dark matter, while the rest to baryons. The estimate of mass of clusters is still an open problem and the uncertainties are also related to the triaxiality of the haloes that surrounds them. For example, the estimated mass is on average biased to be lower than the true one, due to the fact that the haloes are embedded are typically prolate and so the spherical modelling is not able to capture their real structure. We studied the shape distributions of dark matter haloes at all times and for different cosmologies, using Le SBARBINE and the MXXL simulations. In this way, we derived some universal relations between the shape parameters and the mass of haloes, independent from the cosmological model and redshift. These results will be useful to generate mock halo catalogues with given triaxial properties and can be used in triaxial mass reconstruction methods that require priors for the axial ratio distributions. Then, we concentrated on very massive haloes to provide more accurate predictions for cluster-size haloes. Finally, we studied the halo mass function and tested its universality. With this purpose, we identified dark matter haloes at six different density thresholds (the virial one and other multiples of the background and the critical densities, which are commonly used in literature). Our results confirm the universality of the halo mass function, when measured with virialized haloes, while it does not hold for other halo identifications. We provide the fitting formulae for all the overdensity, believing that they could be useful for observers, and a method to rescale from one to the others

SHARP -- VII. New constraints on the dark matter free-streaming properties and substructure abundance from gravitationally lensed quasars

We present an analysis of seven strongly gravitationally lensed quasars and the corresponding constraints on the properties of dark matter. Our results are derived by modelling the lensed image positions and flux-ratios using a combination of smooth macro models and a population of low-mass haloes within the mass range 10^6 to 10^9 Msun. Our lens models explicitly include higher-order complexity in the form of stellar discs and luminous satellites, as well as low-mass haloes located along the observed lines of sight for the first time. Assuming a Cold Dark Matter (CDM) cosmology, we infer an average total mass fraction in substructure of f_sub = 0.012^{+0.007}_{-0.004} (68 per cent confidence limits), which is in agreement with the predictions from CDM hydrodynamical simulations to within 1 sigma. This result is closer to the predictions than those from previous studies that did not include line-of-sight haloes. Under the assumption of a thermal relic dark matter model, we derive a lower limit on the particle relic mass of m th > 5.58 keV (95 per cent confidence limits), which is consistent with a value of m_th > 5.3 keV from the recent analysis of the Ly-alpha forest. We also identify two main sources of possible systematic errors and conclude that deeper investigations in the complex structure of lens galaxies as well as the size of the background sources should be a priority for this field.Comment: 14 pages, 7 figures, accepted for publication in MNRA