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Strong gravitational lensing can detect the presence of low-mass haloes and subhaloes through their effect on the surface brightness of lensed arcs. We carry out an extended analysis of the density profiles and mass distributions of two detected subhaloes, intending to determine if their properties are consistent with the predictions of the cold dark matter (CDM) model. We analyse two gravitational lensing systems in which the presence of two low-mass subhaloes has been previously reported: SDSSJ0946+1006 and JVASB1938+66. We model these detections assuming four different models for their density profiles and compare our results with predictions from the IllustrisTNG50-1 simulation. We find that the detected subhaloes are well-modelled by steep inner density slopes, close to or steeper than isothermal. The NFW profile thus needs extremely high concentrations to reproduce the observed properties, which are outliers of the CDM predictions. We also find a characteristic radius within which the best-fitting density profiles predict the same enclosed mass. We conclude that the lens modelling can constrain this quantity more robustly than the inner slope. We find that the diversity of subhalo profiles in TNG50, consistent with tidally stripping and baryonic effects, is able to match the observed steep inner slopes, somewhat alleviating the tension reported by previous works even if the detections are not well fit by the typical subhalo. However, while we find simulated analogues of the detection in B1938+666, the stellar content required by simulations to explain the central density of the detection in J0946+1006 is in tension with the upper limit in luminosity estimated from the observations. New detections will increase our statistical sample and help us reveal more about the density profiles of these objects and the dark matter content of the Universe., Comment: 23 pages, 19 figures, submitted to A&A. Comments welcome

As it collapses to form a halo, the shape of a protohalo patch is deformed by the initial shear field. This deformation is often modeled using the "deformation" tensor, constructed from second derivatives of the gravitational potential, whose trace gives the initial overdensity. However, especially for lower mass protohalos, this matrix is not always positive definite: one of its eigenvalues has a different sign from the others. We show that the evolution of a patch is better described by the "energy shear" tensor, which is positive definite and plays a direct role in the evolution. This positive-definiteness simplifies models of halo abundances, assembly and of the cosmic web., Comment: 9 pages, 10 figures

This work aims at assessing the impact of DM self-interactions on the properties of galaxy clusters. In particular, the goal is to study the angular dependence of the cross section by testing rare (large angle scattering) and frequent (small angle scattering) SIDM models with velocity-dependent cross sections. We re-simulate six galaxy cluster zoom-in initial conditions with a dark matter only run and with a full-physics setup simulations that includes a self-consistent treatment of baryon physics. We test the dark matter only setup and the full physics setup with either collisionless cold dark matter, rare self-interacting dark matter, and frequent self-interacting dark matter models. We then study their matter density profiles as well as their subhalo population. Our dark matter only SIDM simlations agree with theoretical models, and when baryons are included in simulations, our SIDM models substantially increase the central density of galaxy cluster cores compared to full-physics simulations using collisionless dark matter. SIDM subhalo suppression in full-physics simulations is milder compared to the one found in dark matter only simulations, because of the cuspier baryionic potential that prevent subhalo disruption. Moreover SIDM with small-angle scattering significantly suppress a larger number of subhaloes compared to large angle scattering SIDM models. Additionally, SIDM models generate a broader range of subhalo concentration values, including a tail of more diffuse subhaloes in the outskirts of galaxy clusters and a population of more compact subhaloes in the cluster cores., Comment: 14 pages, 15 figures, abstract abridged to fit arXiv character limit, submitted to Astronomy and Astrophysics

We present a machine-learning-based model for the total density profiles of subhaloes with masses $M \gtrsim 7\times 10^8\,h^{-1}{\rm M}_\odot$ in the IllustrisTNG100 simulation. The model is based on an interpretable variational encoder (IVE) which returns the independent factors of variation in the density profiles within a low-dimensional representation, as well as the predictions for the density profiles themselves. The IVE returns accurate and unbiased predictions on all radial ranges, including the outer region profile where the subhaloes experience tidal stripping; here its fit accuracy exceeds that of the commonly used Einasto profile. The IVE discovers three independent degrees of freedom in the profiles, which can be interpreted in terms of the formation history of the subhaloes. In addition to the two parameters controlling the normalization and inner shape of the profile, the IVE discovers a third parameter that accounts for the impact of tidal stripping onto the subhalo outer profile; this parameter is sensitive to the mass loss experienced by the subhalo after its infall onto its parent halo. Baryonic physics in the IllustrisTNG galaxy formation model does not impact the number of degrees of freedom identified in the profile compared to the pure dark matter expectations, nor their physical interpretation. Our newly proposed profile fit can be used in strong lensing analyses or other observational studies which aim to constrain cosmology from small-scale structures., Comment: 13 pages, 7 figures. Minor changes to match version accepted for publication in MNRAS

Context. Weak gravitational lensing offers a powerful method to investigate the projected matter density distribution within galaxy clusters, granting crucial insights into the broader landscape of dark matter on cluster scales. Aims. In this study, we make use of the large photometric galaxy cluster data set derived from the publicly available Third Data Release of the Kilo-Degree Survey, along with the associated shear signal. Our primary objective is to model the peculiar sharp transition in the cluster profile slope, that is what is commonly referred to as the splashback radius. The data set under scrutiny includes 6962 galaxy clusters, selected by AMICO - an optimised detection algorithm of galaxy clusters - on the KiDS-DR3 data, in the redshift range of 0.1 < z < 0.6, all observed at a signal-to-noise ratio greater than 3.5. Methods. Employing a comprehensive Bayesian analysis, we model the stacked excess surface mass density distribution of the clusters. We adopt a model from recent results on numerical simulations that capture the dynamics of both orbiting and infalling materials, separated by the region where the density profile slope undergoes a pronounced deepening. Results. We find that the adopted profile successfully characterizes the cluster masses, consistent with previous works, and models the deepening of the slope of the density profiles measured with weak-lensing data up to the outskirts. Moreover, we measure the splashback radius of galaxy clusters and show that its value is close to the radius within which the enclosed overdensity is 200 times the mean matter density of the Universe, while theoretical models predict a larger value consistent with a low accretion rate. This points to a potential bias of optically selected clusters preferentially characterized by a high density at small scales compared to a pure mass-selected cluster sample., Comment: Accepted for publication in A&A. Added a discussion about prior parameters, as suggested by the reviewer. arXiv admin note: text overlap with arXiv:2103.05653

The gravitational lensing signal produced by a galaxy or a galaxy cluster is determined by its total matter distribution, providing us with a way to directly constrain their dark matter content. State-of-the-art numerical simulations successfully reproduce many observed properties of galaxies and can be used as a source of mock observations and predictions. Many gravitational lensing studies aim at constraining the nature of dark matter, discriminating between cold dark matter and alternative models. However, many past results are based on the comparison to simulations that did not include baryonic physics. Here we show that the presence of baryons can significantly alter the predictions: we look at the structural properties (profiles and shapes) of elliptical galaxies and at the inner density slope of subhaloes. Our results demonstrate that future simulations must model the interplay between baryons and alternative dark matter, to generate realistic predictions that could significantly modify the current constraints., Comment: Invited contribution for the Proceedings of IAU Symposium 381: "Strong gravitational lensing in the era of Big Data", H. Stacey, C. Grillo, and A. Sonnenfeld eds. 5 pages, 2 figures

In this work, we analyse the density profiles of subhaloes with masses $M_\mathrm{sh} \geq 1.4 \times 10^8$ M$_\odot$ in the TNG50 simulation, with the aim of including baryonic effects. We evaluate the performance of frequently used models, such as the standard 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, $V_\mathrm{max}$, 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 $10^8$ M$_\odot$ $\leq M_\mathrm{sh} \leq$ $10^{13}$ M$_\odot$ that can be influenced by the presence of baryons., Comment: 15+5 pages, 17+13 figures, submitted to MNRAS, comments welcome

In this study, we investigate a recent finding based on strong lensing observations, which suggests that the sub-halos observed in clusters exhibit greater compactness compared to those predicted by $\Lambda$CDM simulations. To address this discrepancy, we performed a comparative analysis by comparing the cumulative mass function of sub-halos and the $M_{\text{sub}}$-$V_{\text{circ}}$ relation between observed clusters and 324 simulated clusters from The Three Hundred project, focusing on re-simulations using GADGET-X and GIZMO-SIMBA baryonic models. The sub-halos' cumulative mass function of the GIZMO-SIMBA simulated clusters agrees with observations, while the GADGET-X simulations exhibit discrepancies in the lower sub-halo mass range possibly due to its strong SuperNova feedback. Both GADGET-X and GIZMO-SIMBA simulations demonstrate a redshift evolution of the sub-halo mass function and the $V_{max}$ function, with slightly fewer sub-halos observed at lower redshifts. Neither the GADGET-X nor GIZMO-SIMBA(albeit a little closer) simulated clusters' predictions for the $M_{\text{sub}}$-$V_{\text{circ}}$ relation align with the observational result. Further investigations on the correlation between sub-halo/halo properties and the discrepancy in the $M_{\text{sub}}$-$V_{\text{circ}}$ relation reveals that the sub-halo's half mass radius and galaxy stellar age, the baryon fraction and sub-halo distance from the cluster's centre, as well as the halo relaxation state play important roles on this relation. Nevertheless, we think it is still challenging in accurately reproducing the observed $M_{\text{sub}}$-$V_{\text{circ}}$ relation in our current hydrodynamic cluster simulation under the standard $\Lambda$CDM cosmology., Comment: see the companion paper, Meneghetti et al. (2023), on today's arxiv list

Previous studies have revealed that the estimated probability of galaxy-galaxy strong lensing in observed galaxy clusters exceeds the expectations from the $\Lambda$ Cold Dark Matter cosmological model by one order of magnitude. We aim to understand the origin of this excess by analyzing a larger set of simulated galaxy clusters and investigating how the theoretical expectations vary under different adopted prescriptions and numerical implementations of star formation and feedback in simulations. We perform a ray-tracing analysis of 324 galaxy clusters from the Three Hundred project, comparing the Gadget-X and Gizmo-Simba runs. These simulations, which start from the same initial conditions, are performed with different implementations of hydrodynamics and galaxy formation models tailored to match different observational properties of the Intra-Cluster-Medium and cluster galaxies. We find that galaxies in the Gizmo-Simba simulations develop denser stellar cores than their Gadget-X counterparts. Consequently, their probability for galaxy-galaxy strong lensing is higher by a factor of $\sim 3$. This increment is still insufficient to fill the gap with observations, as a discrepancy by a factor $\sim 4$ still persists. In addition, we find that several simulated galaxies have Einstein radii that are too large compared to observations. We conclude that a persistent excess of galaxy-galaxy strong lensing exists in observed galaxy clusters. The origin of this discrepancy with theoretical predictions is still unexplained in the framework of the cosmological hydrodynamical simulations. This might signal a hitherto unknown issue with either the simulation methods or our assumptions regarding the standard cosmological model., Comment: 6 pages, 2 figures, accepted for publication on A&A Letters. See companion paper Srivastava et al. (2023)

Context. Strong lenses are a biased subset of the general population of galaxies. Aims. The goal of this work is to quantify how lens galaxies and lensed sources differ from their parent distribution, namely the strong lensing bias. Methods. We first studied how the strong lensing cross-section varies as a function of lens and source properties. Then, we simulated strong lensing surveys with data similar to that expected for Euclid and measured the strong lensing bias in different scenarios. We focused particularly on two quantities: the stellar population synthesis mismatch parameter, $\alpha_{sps}$, defined as the ratio between the true stellar mass of a galaxy and the stellar mass obtained from photometry, and the central dark matter mass at fixed stellar mass and size. Results. Strong lens galaxies are biased towards larger stellar masses, smaller half-mass radii and larger dark matter masses. The amplitude of the bias depends on the intrinsic scatter in the mass-related parameters of the galaxy population and on the completeness in Einstein radius of the lens sample. For values of the scatter that are consistent with observed scaling relations and a minimum detectable Einstein radius of $0.5''$, the strong lensing bias in $\alpha_{sps}$ is $10\%$, while that in the central dark matter mass is $5\%$. The bias has little dependence on the properties of the source population: samples of galaxy-galaxy lenses and galaxy-quasar lenses that probe the same Einstein radius distribution are biased in a very similar way. Conclusions. Given current uncertainties, strong lensing observations can be used directly to improve our current knowledge of the inner structure of galaxies, without the need to correct for selection effects. Time-delay measurements of $H_0$ from lensed quasars can take advantage of prior information obtained from galaxy-galaxy lenses with similar Einstein radii., Comment: Published on Astronomy & Astrophysics. A two-minute summary video of this paper is available at https://youtu.be/UmS9jRHTmZU

We investigate the ability of human 'expert' classifiers to identify strong gravitational lens candidates in Dark Energy Survey like imaging. We recruited a total of 55 people that completed more than 25$\%$ of the project. During the classification task, we present to the participants 1489 images. The sample contains a variety of data including lens simulations, real lenses, non-lens examples, and unlabeled data. We find that experts are extremely good at finding bright, well-resolved Einstein rings, whilst arcs with $g$-band signal-to-noise less than $\sim$25 or Einstein radii less than $\sim$1.2 times the seeing are rarely recovered. Very few non-lenses are scored highly. There is substantial variation in the performance of individual classifiers, but they do not appear to depend on the classifier's experience, confidence or academic position. These variations can be mitigated with a team of 6 or more independent classifiers. Our results give confidence that humans are a reliable pruning step for lens candidates, providing pure and quantifiably complete samples for follow-up studies., Comment: 16 pages, 20 Figures

We use hydrodynamical cosmological simulations to test the differences between cold and self-interacting dark matter models (CDM and SIDM) in the mass range of massive galaxies ($10^{12}M_{\odot}h^{-1}10^{13}M_{\odot}h^{-1}$) show cored profiles, while the least massive ones ($M<10^{12.5}M_{\odot}h^{-1}$) have cuspier profiles. Finally, we compare the predictions of our simulations to observational results, by looking at the dark matter fractions and the distribution of strong lensing Einstein radii. We find that in SIDM the DM-fractions decrease more rapidly with increasing stellar mass than in CDM, leading to lower fractions at $M_{*}>10^{11}M_{\odot}$, a distinctive signature of SIDM. At the same time, the distribution of Einstein radii, derived from both CDM and SIDM hydro runs, is comparable to observed samples of strong lenses with $M>10^{13}M_{\odot}h^{-1}$. We conclude that the interplay between self-interaction and baryons can greatly reduce the expected differences between CDM and SIDM models at this mass scale, and that techniques able to separate the dark and luminous mass in the inner regions of galaxies are needed to constrain self-interactions., Comment: 13 pages, 12 figures

We introduce a machine learning method for estimating the sensitivity of strong lens observations to dark matter subhaloes in the lens. Our training data include elliptical power-law lenses, Hubble Deep Field sources, external shear, and noise and PSF for the Euclid VIS instrument. We set the concentration of the subhaloes using a $v_\mathrm{max}$-$r_\mathrm{max}$ relation. We then estimate the dark matter subhalo sensitivity in $16{,}000$ simulated strong lens observations with depth and resolution resembling Euclid VIS images. We find that, with a $3\sigma$ detection threshold, $2.35$ per cent of pixels inside twice the Einstein radius are sensitive to subhaloes with a mass $M_\mathrm{max}\leq 10^{10}M_\odot$, $0.03$ per cent are sensitive to $M_\mathrm{max}\leq 10^{9}M_\odot$, and, the limit of sensitivity is found to be $M_\mathrm{max}=10^{8.8\pm0.2}M_\odot$. Using our sensitivity maps and assuming CDM, we estimate that Euclid-like lenses will yield $1.43^{+0.14}_{-0.11}[f_\mathrm{sub}^{-1}]$ detectable subhaloes per lens in the entire sample, but this increases to $35.6^{+0.9}_{-0.9}[f_\mathrm{sub}^{-1}]$ per lens in the most sensitive lenses. Estimates are given in units of the inverse of the substructure mass fraction $f_\mathrm{sub}^{-1}$. Assuming $f_\mathrm{sub}=0.01$, one in every $70$ lenses in general should yield a detection, or one in every $\sim$ three lenses in the most sensitive sample. From $170,000$ new strong lenses detected by Euclid, we expect $\sim 2500$ new subhalo detections. We find that the expected number of detectable subhaloes in warm dark matter models only changes relative to cold dark matter for models which have already been ruled out, i.e., those with half-mode masses $M_\mathrm{hm}>10^8M_\odot$., Comment: 15 pages, 14 figures, accepted by MNRAS

We study the effect of self-interacting dark matter (SIDM) and baryons on the shape of early-type galaxies (ETGs) and their dark matter haloes, comparing them to the predictions of the cold dark matter (CDM) scenario. We use five hydrodynamical zoom-in simulations of haloes hosting ETGs ($M_{\rm vir}\sim 10^{13}M_{\odot}$ and $M_{*}\sim10^{11}M_{\odot}$), simulated in CDM and a SIDM model with constant cross-section of $\sigma_T/m_\chi = 1\ \mathrm{cm}^2 \mathrm{g}^{-1}$. We measure the three-dimensional and projected shapes of the dark matter haloes and their baryonic content using the inertia tensor and compare our measurements to the results of three $HST$ samples of gravitational lenses and $Chandra$ and $XMM-Newton$ X-ray observations. We find that the inclusion of baryons greatly reduces the differences between CDM and a SIDM, together with the ability to draw constraints based on shapes. Lensing measurements reject the predictions of CDM dark-matter-only simulations and prefer one of the hydro scenarios. When we consider the total sample of lenses, observational data prefer the CDM hydro scenario. The shapes of the X-ray emitting gas are compatible with observational results in both hydro runs, with CDM predicting higher elongations only in the very centre. Contrary to previous claims at the scale of elliptical galaxies, we conclude that both CDM and our SIDM model can still explain observed shapes once we include baryons in the simulations. Our results demonstrate that this is essential to derive realistic constraints and that new simulations are needed to confirm and extend our findings., Comment: 17 pages, 13 figures, revised version accepted for publication in MNRAS

In this paper, we assess the impact of numerical resolution and of the implementation of energy input from AGN feedback models on the inner structure of cluster sub-haloes in hydrodynamic simulations. We compare several zoom-in re-simulations of a sub-sample of the cluster-sized haloes studied in Meneghetti et al. (2020), obtained by varying mass resolution, softening length and AGN energy feedback scheme. We study the impact of these different setups on the subhalo abundances, their radial distribution, their density and mass profiles and the relation between the maximum circular velocity, which is a proxy for subhalo compactness. Regardless of the adopted numerical resolution and feedback model, subhaloes with masses Msub < 1e11Msun/h, the most relevant mass-range for galaxy-galaxy strong lensing, have maximum circular velocities ~30% smaller than those measured from strong lensing observations of Bergamini et al. (2019). We also find that simulations with less effective AGN energy feedback produce massive subhaloes (Msub> 1e11 Msun/h ) with higher maximum circular velocity and that their Vmax - Msub relation approaches the observed one. However the stellar-mass number count of these objects exceeds the one found in observations and we find that the compactness of these simulated subhaloes is the result of an extremely over-efficient star formation in their cores, also leading to larger-than-observed subhalo stellar mass. We conclude that simulations are unable to simultaneously reproduce the observed stellar masses and compactness (or maximum circular velocities) of cluster galaxies. Thus, the discrepancy between theory and observations that emerged from the analysis of Meneghetti et al. (2020) persists. It remains an open question as to whether such a discrepancy reflects limitations of the current implementation of galaxy formation models or the LCDM paradigm., Comment: 11 pages, 10 figures, abstract is redacted to fit arXiv character count limit

Meneghetti et al. (2020) recently reported an excess of galaxy-galaxy strong lensing (GGSL) in galaxy clusters compared to expectations from the LCDM cosmological model. Theoretical estimates of the GGSL probability are based on the analysis of numerical hydrodynamical simulations in the LCDM cosmology. We quantify the impact of the numerical resolution and AGN feedback scheme adopted in cosmological simulations on the predicted GGSL probability and determine if varying these simulation properties can alleviate the gap with observations. We repeat the analysis of Meneghetti et al. (2020) on cluster-size halos simulated with different mass and force resolutions and implementing several independent AGN feedback schemes. We find that improving the mass resolution by a factor of ten and twenty-five, while using the same galaxy formation model that includes AGN feedback, does not affect the GGSL probability. We find similar results regarding the choice of gravitational softening. On the contrary, adopting an AGN feedback scheme that is less efficient at suppressing gas cooling and star formation leads to an increase in the GGSL probability by a factor between three and six. However, we notice that such simulations form overly massive subhalos whose contribution to the lensing cross-section would be significant while their Einstein radii are too large to be consistent with the observations. The primary contributors to the observed GGSL cross-sections are subhalos with smaller masses, that are compact enough to become critical for lensing. The population with these required characteristics appears to be absent in simulations., Comment: 13 pages, 11 figures. Submitted for publication on Astronomy and Astrophysics

This paper aims to quantify how the lowest halo mass that can be detected with galaxy-galaxy strong gravitational lensing depends on the quality of the observations and the characteristics of the observed lens systems. Using simulated data, we measure the lowest detectable NFW mass at each location of the lens plane, in the form of detailed \emph{sensitivity maps}. In summary, we find that: (i) the lowest detectable mass $M_{\rm low}$ decreases linearly as the signal-to-noise ratio (SNR) increases and the sensitive area is larger when we decrease the noise; (ii) a moderate increase in angular resolution (0.07" vs 0.09") and pixel scale (0.01" vs 0.04") improves the sensitivity by on average 0.25 dex in halo mass, with more significant improvement around the most sensitive regions; (iii) the sensitivity to low-mass objects is largest for bright and complex lensed galaxies located inside the caustic curves and lensed into larger Einstein rings (i.e $r_{E}\geq1.0"$). We find that for the sensitive mock images considered in this work, the minimum mass that we can detect at the redshift of the lens lies between $1.5\times10^{8}$ and $3\times10^{9}M_{\odot}$. We derive analytic relations between $M_{\rm low}$, the SNR and resolution and discuss the impact of the lensing configuration and source structure. Our results start to fill the gap between approximate predictions and real data and demonstrate the challenging nature of calculating precise forecasts for gravitational imaging. In light of our findings, we discuss possible strategies for designing strong lensing surveys and the prospects for HST, Keck, ALMA, Euclid and other future observations., Comment: 17 pages, 11 figures, accepted for publication in MNRAS. Comments welcome

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-$\alpha$ forest, and the number of luminous satellites in the Milky Way. We derive an upper limit of $\lambda_{\rm hm}=0.089{\rm~Mpc~h^{-1} }$ 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 $\lambda_{\rm hm}> 0.223 {\rm~Mpc~h^{-1} }$ (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., Comment: 16 pages, 3 Figures, minor updates of the results

We use high-resolution hydrodynamical simulations run with the EAGLE model of galaxy formation to study the differences between the properties of - and subsequently the lensing signal from - subhaloes of massive elliptical galaxies at redshift 0.2, in Cold and Sterile Neutrino (SN) Dark matter models. We focus on the two 7 keV SN models that bracket the range of matter power spectra compatible with resonantly-produced SN as the source of the observed 3.5 keV line. We derive an accurate parametrisation for the subhalo mass function in these two SN models relative to CDM, as well as the subhalo spatial distribution, density profile, and projected number density and the dark matter fraction in subhaloes. We create mock lensing maps from the simulated haloes to study the differences in the lensing signal in the framework of subhalo detection. We find that subhalo convergence is well described by a log-normal distribution and that signal of subhaloes in the power spectrum is lower in SN models with respect to CDM, at a level of 10 to 80 per cent, depending on the scale. However, the scatter between different projections is large and might make the use of power-spectrum studies on the typical scales of current lensing images very difficult. Moreover, in the framework of individual detections through gravitational imaging a sample of ~30 lenses with an average sensitivity of M_sub=5x10^7M_sun would be required to discriminate between CDM and the considered sterile neutrino models., Comment: 16 pages, 11 figures, accepted for publication in MNRAS

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 MNRAS

We use high-resolution hydrodynamical simulation to test the difference of halo properties in cold dark matter (CDM) and a self-interacting dark matter (SIDM) scenario with a constant cross-section of $\sigma^\text{T}/m_{\chi}=1\;\text{cm}^{2}\text{g}^{-1}$. We find that the interplay between dark matter self-interaction and baryonic physics induces a complex evolution of the halo properties, which depends on the halo mass and morphological type, as well as on the halo mass accretion history. While high mass haloes, selected as analogues of early-type galaxies, show cored profiles in the SIDM run, systems of intermediate mass and with a significant disk component can develop a profile that is similar or cuspier than in CDM. The final properties of SIDM haloes - measured at z=0.2 - correlate with the halo concentration and formation time, suggesting that the differences between different systems are due to the fact that we are observing the impact self-interaction. We also search for signatures of self-interacting dark matter in the lensing signal of the main haloes and hints of potential differences in the distribution of Einstein radii, which suggests that future wide-field survey might be able to distinguish between CDM and SIDM models on this basis. Finally, we find that the subhalo abundances are not altered in the adopted SIDM model with respect to CDM., Comment: 11 pages, 11 figures, accepted for publication in MNRAS

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 welcome

We study the statistical properties of mergers between central and satellite galaxies in galaxy clusters in the redshift range $0

Strong gravitational lenses with measured time delay are a powerful tool to measure cosmological parameters, especially the Hubble constant ($H_0$). Recent studies show that by combining just three multiply-imaged AGN systems, one can determine $H_0$ to 2.4% precision. Furthermore, the number of time-delay lens systems is growing rapidly, enabling the determination of $H_0$ to 1% precision in the near future. However, as the precision increases it is important to ensure that systematic errors and biases remain subdominant. For this purpose, challenges with simulated datasets are a key component in this process. Following the experience of the past challenge on time delay, where it was shown that time delays can indeed be measured precisely and accurately at the sub-percent level, we now present the "Time Delay Lens Modeling Challenge" (TDLMC). The goal of this challenge is to assess the present capabilities of lens modeling codes and assumptions and test the level of accuracy of inferred cosmological parameters given realistic mock datasets. We invite scientists to model a set of simulated HST observations of 50 mock lens systems. The systems are organized in rungs, with the complexity and realism increasing going up the ladder. The goal of the challenge is to infer $H_0$ for each rung, given the HST images, the time delay, and stellar velocity dispersion of the deflector for a fixed background cosmology. The TDLMC challenge starts with the mock data release on 2018 January 8th. The deadline for blind submission is different for each rung. The deadline for Rung 0-1 is 2018 September 8; the deadline for Rung 2 is 2019 April 8 and the one for Rung 3 is 2019 September 8. This first paper gives an overview of the challenge including the data design, and a set of metrics to quantify the modeling performance and challenge details., Comment: 6 pages, 2 figures, submitted to MNRAS

We investigate how Einstein rings and magnified arcs are affected by small-mass dark-matter haloes placed along the line-of-sight to gravitational lens systems. By comparing the gravitational signature of line-of-sight haloes with that of substructures within the lensing galaxy, we derive a mass-redshift relation that allows us to rescale the detection threshold (i.e. lowest detectable mass) for substructures to a detection threshold for line-of-sight haloes at any redshift. We then quantify the line-of-sight contribution to the total number density of low-mass objects that can be detected through strong gravitational lensing. Finally, we assess the degeneracy between substructures and line-of-sight haloes of different mass and redshift to provide a statistical interpretation of current and future detections, with the aim of distinguishing between CDM and WDM. We find that line-of-sight haloes statistically dominate with respect to substructures, by an amount that strongly depends on the source and lens redshifts, and on the chosen dark matter model. Substructures represent about 30 percent of the total number of perturbers for low lens and source redshifts (as for the SLACS lenses), but less than 10 per cent for high redshift systems. We also find that for data with high enough signal-to-noise ratio and angular resolution, the non-linear effects arising from a double-lens-plane configuration are such that one is able to observationally recover the line-of-sight halo redshift with an absolute error precision of 0.15 at the 68 per cent confidence level., Comment: 19 pages, 17 figures, accepted for publication in MNRAS

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 MNRAS

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 MNRAS

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.)

In this paper we investigate the strong lensing statistics in galaxy clusters. We extract dark matter haloes from the Millennium-XXL simulation, compute their Einstein radius distribution, and find a very good agreement with Monte Carlo predictions produced with the MOKA code. The distribution of the Einstein radii is well described by a log-normal distribution, with a considerable fraction of the largest systems boosted by different projection effects. We discuss the importance of substructures and triaxiality in shaping the size of the critical lines for cluster size haloes. We then model and interpret the different deviations, accounting for the presence of a Bright Central Galaxy (BCG) and two different stellar mass density profiles. We present scaling relations between weak lensing quantities and the size of the Einstein radii. Finally we discuss how sensible is the distribution of the Einstein radii on the cosmological parameters {\Omega}_M-{\sigma}_8 finding that cosmologies with higher {\Omega}_M and {\sigma}_8 possess a large sample of strong lensing clusters. The Einstein radius distribution may help distinguish Planck13 and WMAP7 cosmology at 3{\sigma}., Comment: replaced to match the accepted version for publication on MNRAS

The abundance of galaxy clusters can constrain both the geometry and growth of structure in our Universe. However, this probe could be significantly complicated by recent claims of nonuniversality -- non-trivial dependences with respect to the cosmological model and redshift. In this work we analyse the dependance of the mass function on the way haloes are identified and establish if this can cause departures from universality. In order to explore this dependance, we use a set of different N-body cosmological simulations (Le SBARBINE simulations), with the latest cosmological parameters from the Planck collaboration; this first suite of simulations is followed by a lower resolution set, carried out with different cosmological parameters. We identify dark matter haloes using a Spherical Overdensity algorithm with varying overdensity thresholds (virial, 2000rho_c, 1000rho_c, 500rho_c, 200rho_c and 200rho_b) at all redshifts. We notice that, when expressed in term of the rescaled variable nu, the mass functionfor virial haloes is a nearly universal as a function of redshift and cosmology, while this is clearly not the case for the other overdensities we considered. We provide fitting functions for the halo mass function parameters as a function of overdensity, that allow to predict, to within a few percent accuracy, the halo mass function for a wide range of halo definitions, redshifts and cosmological models. We then show how the departures from universality associated with other halo definitions can be derived by combining the universality of the virial definition with the expected shape of the density profile of halos., Comment: 22 pages, 21 figures, accepted for publication in MNRAS - some changes with respect to the previous version and a new appendix

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 figures

We present a detailed analysis of dark matter halo shapes, studying how the distributions of ellipticity, prolateness and axial ratios evolve as a function of time and mass. With this purpose in mind, we analysed the results of three cosmological simulations, running an ellipsoidal halo finder to measure triaxial halo shapes. The simulations have different scales, mass limits and cosmological parameters, which allows us to ensure a good resolution and statistics in a wide mass range, and to investigate the dependence of halo properties on the cosmological model. We confirm the tendency of haloes to be prolate at all times, even if they become more triaxial going to higher redshifts. Regarding the dependence on mass, more massive haloes are also less spherical at all redshifts, since they are the most recent forming systems and so still retain memory of their original shape at the moment of collapse. We then propose a rescaling of the shape-mass relations, using the variable $\nu = \delta_{c}/\sigma$ to represent the mass, which absorbs the dependence on both cosmology and time, allowing to find universal relations between halo masses and shape parameters (ellipticity, prolateness and the axial ratios) which hold at any redshift. This may be very useful to determine prior distributions of halo shapes for observational studies., Comment: 11 pages, 9 figures, accepted for publication on MNRAS - Fig.1 updated, minor changes

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 MNRAS