arXiv subjects

Raul Angulo

Publications and source records attributed to Raul Angulo.

At least 19 recordsLinked to original sources

arXiv2025

Low-redshift constraints on structure growth from CMB lensing tomography

We present constraints on the amplitude of matter fluctuations from the clustering of galaxies and their cross-correlation with the gravitational lensing convergence of the cosmic microwave background (CMB), focusing on low redshifts ($z\lesssim0.3$), where potential deviations from a perfect cosmological constant dominating the growth of structure could be more prominent. Specifically, we make use of data from the 2MASS photometric survey (\tmpz) and the \wisc galaxy survey, in combination with CMB lensing data from \planck. Using a hybrid effective field theory (HEFT) approach to model galaxy bias we obtain constraints on the combination $S_8=\sigma_8\sqrt{\Omega_m/0.3}$, where $\sigma_8$ is the amplitude of matter fluctuations, and $\Omega_m$ is the non-relativistic matter fraction. Using a prior on $\Omega_m$ based on the baryon acoustic oscillation measurements of DESI, we find $S_8=0.79\pm0.06$, in reasonable agreement with CMB constraints. We also find that, in the absence of this prior, the data favours a value of $\Omega_m=0.245\pm0.024$, that is 2.8$\sigma$ lower than \planck. This result is driven by the broadband shape of the galaxy auto-correlation, and may be affected by theoretical uncertainties in the HEFT power spectrum templates. We further reconstruct the low-redshift growth history, finding it to be compatible with the \planck predictions, as well as existing constraints from lensing tomography. Finally, we study our constraints on the HEFT bias parameters of the galaxy samples studied, finding them to be in reasonable agreement with coevolution predictions.

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arXiv2024

SHAMe-SF: Predicting the clustering of star-forming galaxies with an enhanced abundance matching model

With the advent of several galaxy surveys targeting star-forming galaxies, it is important to have models capable of interpreting their spatial distribution in terms of astrophysical and cosmological parameters. To address this need, we introduce SHAMe-SF, an extension of the subhalo abundance matching (SHAM) technique designed specifically for analyzing the redshift-space clustering of star-forming galaxies. Our model directly links a galaxy's star formation rate to the properties of its host dark-matter halo, with further modulations based on effective models of feedback and gas stripping. To quantify the accuracy of our model, we show that it simultaneously reproduces key clustering statistics such as the projected correlation function, monopole, and quadrupole of star-forming galaxy samples at various redshifts and number densities. Notably, these tests were conducted over a wide range of scales $[0.6, 30]\hMpc$, using samples from both the TNG300 magneto-hydrodynamic simulation and from a semi-analytical model. SHAMe-SF can also reproduce the clustering of simulated galaxies that fall within the colour selection criteria employed by DESI for emission line galaxies. Our model exhibits several potential applications, including the generation of covariance matrices, exploration of galaxy formation processes, and even placing constraints on the cosmological parameters of the Universe.

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arXiv2020

A flexible subhalo abundance matching model for galaxy clustering in redshift space

We develop an extension of subhalo abundance matching (SHAM) capable of accurately reproducing the real and redshift-space clustering of galaxies in a state-of-the-art hydrodynamical simulation. Our method uses a low-resolution gravity-only simulation and it includes orphan and tidal disruption prescriptions for satellite galaxies, and a flexible amount of galaxy assembly bias. Furthermore, it includes recipes for star formation rate (SFR) based on the dark matter accretion rate. We test the accuracy of our model against catalogues of stellar-mass- and SFR-selected galaxies in the TNG300 hydrodynamic simulation. By fitting a small number of free parameters, our extended SHAM reproduces the projected correlation function and redshift-space multipoles for number densities $10^{-3} - 10^{-2}\, h^{3}{\rm Mpc}^{-3}$, at $z=1$ and $z=0$, and for scales $r \in [0.3 - 20] h^{-1}{\rm Mpc}$. Simultaneously, the SHAM results also retrieve the correct halo occupation distribution, the level of galaxy assembly bias, and higher-order statistics present in the TNG300 galaxy catalogues. As an application, we show that our model simultaneously fits the projected correlation function of the SDSS in 3 disjoint stellar mass bins, with an accuracy similar to that of TNG300 galaxies. This SHAM extension can be used to get accurate clustering prediction even when using low and moderate-resolution simulations.

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arXiv2020

Detection of a universal core-halo transition in dwarf galaxies as predicted by Bose-Einstein dark matter

The presence of large dark matter cores in dwarf galaxies has long been puzzling and many are now known to be surrounded by an extensive halo of stars. Distinctive core-halo structure is characteristic of dark matter as a Bose Einstein condensate, $\psi$DM, with a dense, soliton core predicted in every galaxy, representing the ground state, surrounded by a large, tenuous halo of excited density waves. A marked density transition is predicted between the core and the halo set by the de Broglie wavelength, as the soliton core is a prominent standing wave that is denser by over an order of magnitude than the surrounding halo. Here we identify this predicted behavior in the stellar profiles of the well known "isolated" dwarfs that lie outside the Milky Way, each with a clear density transition at $\simeq 1.0~{\rm kpc}$, implying a very light boson, $m_{\psi} \simeq 10^{-22}$eV. The classical dwarf galaxies orbiting within the Milky Way also show this predicted core-halo structure but with larger density transitions of over two orders of magnitude, that we show implies tidal stripping of dwarf galaxies by the Milky way, as the tenuous halo is more easily stripped than the stable soliton core. We conclude that dark matter as a light boson explains the observed family of classical dwarf profiles with tidal stripping included, in contrast to the standard heavy particle interpretation where low mass galaxies should be concentrated and core-less, quite unlike the core-halo structure observed.

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arXiv2020

A flexible modelling of galaxy assembly bias

We use the {\sc Illustris TNG300} magneto-hydrodynamic simulation, the {\sc SAGE} semi-analytical model, and the subhalo abundance matching technique (SHAM) to examine the diversity in predictions for galaxy assembly bias (i.e. the difference in the large scale clustering of galaxies at a fixed halo mass due to correlations with the assembly history and other properties of host haloes). We consider samples of galaxies selected according to their stellar mass or star formation rate at various redshifts. We find that all models predict an assembly bias signal of different magnitude, redshift evolution, and dependence with selection criteria and number density. To model these non-trivial dependences, we propose an extension to the standard SHAM technique so it can include arbitrary amounts of assembly bias. We do this by preferentially selecting subhaloes with the same internal property but different {\it individual} large-scale bias. We find that with this model, we can successfully reproduce the galaxy assembly bias signal in either {\sc SAGE} or the {\sc TNG}, for all redshifts and galaxy number densities. We anticipate that this model can be used to constrain the level of assembly bias in observations and aid in the creation of more realistic mock galaxy catalogues.

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arXiv2017

Evidence of Neutrino Enhanced Clustering in a Complete Sample of Sloan Survey Clusters, Implying $\sum m_{\nu}= 0.119 \pm 0.034$ eV

The clustering amplitude of 7143 clusters from the Sloan Digital Sky Survey (SDSS) is found to increase with cluster mass, closely agreeing with the Gaussian random field hypothesis for structure formation. The amplitude of the observed cluster correlation exceeds the predictions from pure cold dark matter (CDM) simulation by $\simeq 6\%$ for the standard Planck-based values of the cosmological parameters. We show that this excess can be naturally accounted for by free streaming of light neutrinos, which opposes gravitational growth, so clusters formed at fixed mass are fewer and hence more biased than for a pure CDM density field. An enhancement of the cluster bias by 7\% matches the observations, corresponding to a total neutrino mass, $m_{\nu} = 0.119 \pm 0.034$ eV at 67\% confidence level, for the standard relic neutrino density. If ongoing laboratory experiments favor a normal neutrino mass hierarchy then we may infer a somewhat larger total mass than the minimum oscillation based value, $\sum m_{\nu} \simeq 0.056eV$, with 90\% confidence. Much higher precision can be achieved by applying our method to a larger sample of more distant clusters with weak lensing derived masses.

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arXiv2017

The imprint of neutrinos on clustering in redshift-space

(abridged) We investigate the signatures left by the cosmic neutrino background on the clustering of matter, CDM+baryons and halos in redshift-space using a set of more than 1000 N-body and hydrodynamical simulations with massless and massive neutrinos. We find that the effect neutrinos induce on the clustering of CDM+baryons in redshift-space on small scales is almost entirely due to the change in $\sigma_8$. Neutrinos imprint a characteristic signature in the quadrupole of the matter (CDM+baryons+neutrinos) field on small scales, that can be used to disentangle the effect of $\sigma_8$ and $M_\nu$. We show that the effect of neutrinos on the clustering of halos is very different, on all scales, to the one induced by $\sigma_8$. We find that the effects of neutrinos of the growth rate of CDM+baryons ranges from $\sim0.3\%$ to $2\%$ on scales $k\in[0.01, 0.5]~h{\rm Mpc}^{-1}$ for neutrinos with masses $M_\nu \leqslant 0.15$ eV. We compute the bias between the momentum of halos and the momentum of CDM+baryon and find it to be 1 on large scales for all models with massless and massive neutrinos considered. This point towards a velocity bias between halos and total matter on large scales that it is important to account for in order to extract unbiased neutrino information from velocity/momentum surveys such as kSZ observations. We show that baryonic effects can affect the clustering of matter and CDM+baryons in redshift-space by up to a few percent down to $k=0.5~h{\rm Mpc}^{-1}$. We find that hydrodynamics and astrophysical processes, as implemented in our simulations, only distort the relative effect that neutrinos induce on the anisotropic clustering of matter, CDM+baryons and halos in redshift-space by less than $1\%$. Thus, the effect of neutrinos in the fully non-linear regime can be written as a transfer function with very weak dependence on astrophysics.

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arXiv2017

A Lightcone Catalogue from the Millennium-XXL Simulation

Future galaxy surveys require realistic mock catalogues to understand and quantify systematics in order to make precise cosmological measurements. We present a halo lightcone catalogue and halo occupation distribution (HOD) galaxy catalogue built using the Millennium-XXL (MXXL) simulation. The halo catalogue covers the full sky, extending to z = 2 with a mass resolution of ~1e11 Msun/h . We use this to build a galaxy catalogue, which has an r-band magnitude limit of r < 20.0, with a median redshift of z~0.2. A Monte Carlo HOD method is used to assign galaxies to the halo lightcone catalogue, and we evolve the HODs to reproduce a target luminosity function; by construction, the luminosity function of galaxies in the mock is in agreement with the Sloan Digital Sky Survey (SDSS) at low redshifts and the Galaxy and Mass Assembly (GAMA) survey at high redshifts. A Monte Carlo method is used to assign a 0.1(g-r) colour to each galaxy, and the colour distribution of galaxies at different redshifts agrees with measurements from GAMA. The clustering of galaxies in the mock for galaxies in different magnitude and redshift bins is in good agreement with measurements from SDSS and GAMA, and the colour-dependent clustering is in reasonable agreement. We show that the baryon acoustic oscillation (BAO) can be measured in the mock catalogue, and the redshift space distortions (RSDs) are in agreement with measurements from SDSS, illustrating that this catalogue will be useful for upcoming surveys.

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arXiv2016

Very Massive Tracers and Higher Derivative Biases

Most of the upcoming cosmological information will come from analyzing the clustering of the Large Scale Structures (LSS) of the universe through LSS or CMB observations. It is therefore essential to be able to understand their behavior with exquisite precision. The Effective Field Theory of Large Scale Structures (EFTofLSS) provides a consistent framework to make predictions for LSS observables in the mildly non-linear regime. In this paper we focus on biased tracers. We argue that in calculations at a given order in the dark matter perturbations, highly biased tracers will underperform because of their larger higher derivative biases. A natural prediction of the EFTofLSS is therefore that by simply adding higher derivative biases, all tracers should perform comparably well. We implement this prediction for the halo-halo and the halo-matter power spectra at one loop, and the halo-halo-halo, halo-halo-matter, and halo-matter-matter bispectra at tree-level, and compare with simulations. We find good agreement with the prediction: for all tracers, we are able to match the bispectra up to $k\simeq0.17\,h/$Mpc at $z=0$ and the power spectra to a higher wavenumber.

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arXiv2016

Precise Clustering and Density Evolution of redMaPPer Galaxy Clusters versus MXXL Simulation

We construct a large, redshift complete sample of distant galaxy clusters by correlating Sloan Digital Sky Survey (SDSS) Data Release 12 (DR12) redshifts with clusters identified with the red-sequence Matched-filter Probabilistic Percolation (redMaPPer) algorithm. Our spectroscopic completeness is 97% for ~ 7,000 clusters within the redMaPPer selection limit, $z \leqslant$ 0.325, so that our cluster correlation functions are much more precise than earlier work and not suppressed by photometric redshifts. We derive an accurate power-law mass-richness relation from the observed abundance with respect to the mass function from Millennium XXL (MXXL) simulation, adjusted to the Planck weighted cosmology. The number density of clusters is found to decline by 20% over the range 0.1 $< z <$ 0.3, in good agreement with the evolution predicted by MXXL. Our projected three-dimensional correlation function scales with richness, $\lambda$, rising from $r_0=$ 14 h$^{-1}$ Mpc at $\lambda\simeq$ 25, to $r_0=$ 22 h$^{-1}$ Mpc at $\lambda\simeq$ 60, with a gradient that matches MXXL when applying our mass-richness relation, whereas the observed amplitude of the correlation function at $\left =$ 0.24 exceeds the MXXL prediction by 20% at the $\simeq$ 2.5$\sigma$ level. This tension cannot be blamed on spurious, randomly located clusters as this would reduce the correlation amplitude. Full consistency between the correlation function and the abundances is achievable for the pre-Planck values of $\sigma_8=$ 0.9, $\Omega_m=$ 0.25, and h = 0.73, matching the improved distance ladder estimate of the Hubble constant.

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arXiv2015

On the Statistics of Biased Tracers in the Effective Field Theory of Large Scale Structures

With the completion of the Planck mission, in order to continue to gather cosmological information it has become crucial to understand the Large Scale Structures (LSS) of the universe to percent accuracy. The Effective Field Theory of LSS (EFTofLSS) is a novel theoretical framework that aims to develop an analytic understanding of LSS at long distances, where inhomogeneities are small. We further develop the description of biased tracers in the EFTofLSS to account for the effect of baryonic physics and primordial non-Gaussianities, finding that new bias coefficients are required. Then, restricting to dark matter with Gaussian initial conditions, we describe the prediction of the EFTofLSS for the one-loop halo-halo and halo-matter two-point functions, and for the tree-level halo-halo-halo, matter-halo-halo and matter-matter-halo three-point functions. Several new bias coefficients are needed in the EFTofLSS, even though their contribution at a given order can be degenerate and the same parameters contribute to multiple observables. We develop a method to reduce the number of biases to an irreducible basis, and find that, at the order at which we work, seven bias parameters are enough to describe this extremely rich set of statistics. We then compare with the output of $N$-body simulations. For the lowest mass bin, we find percent level agreement up to $k\simeq 0.3\,h\,{\rm Mpc}^{-1}$ for the one-loop two-point functions, and up to $k\simeq 0.15\,h\,{\rm Mpc}^{-1}$ for the tree-level three-point functions, with the $k$-reach decreasing with higher mass bins. This is consistent with the theoretical estimates, and suggests that the cosmological information in LSS amenable to analytical control is much more than previously believed.

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arXiv2014

Galaxy formation in the Planck Cosmology - I. Matching the observed evolution of star formation rates, colours and stellar masses

We have updated the Munich galaxy formation model to the Planck first-year cosmology, while modifying the treatment of baryonic processes to reproduce recent data on the abundance and passive fractions of galaxies from z= 3 down to z=0. Matching these more extensive and more precise observational results requires us to delay the reincorporation of wind ejecta, to lower the surface density threshold for turning cold gas into stars, to eliminate ram-pressure stripping in haloes less massive than ~10^14 Msun, and to modify our model for radio mode feedback. These changes cure the most obvious failings of our previous models, namely the overly early formation of low-mass galaxies and the overly large fraction of them that are passive at late times. The new model is calibrated to reproduce the observed evolution both of the stellar mass function and of the distribution of star formation rate at each stellar mass. Massive galaxies (M>10^11 [Msun]) assemble most of their mass before z=1 and are predominantly old and passive at z=0, while lower mass galaxies assemble later and, for M<10^9.5 (Msun), are still predominantly blue and star forming at z=0. This phenomenological but physically based model allows the observations to be interpreted in terms of the efficiency of the various processes that control the formation and evolution of galaxies as a function of their stellar mass, gas content, environment and time.

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arXiv2014

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.

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arXiv2013

Exploring the non-linear density field in the Millennium simulations with tessellations - I. The probability distribution function

We use the Delaunay Tessellation Field Estimator (DTFE) to study the one-point density distribution functions of the Millennium (MS) and Millennium-II (MS-II) simulations. The DTFE technique is based directly on the particle positions, without requiring any type of smoothing or analysis grid, thereby providing high sensitivity to all non-linear structures resolved by the simulations. In order to identify the detailed origin of the shape of the one-point density probability distribution function (PDF), we decompose the simulation particles according to the mass of their host FoF halos, and examine the contributions of different halo mass ranges to the global density PDF. We model the one-point distribution of the FoF halos in each halo mass bin with a set of Monte Carlo realizations of idealized NFW dark matter halos, finding that this reproduces the measurements from the N-body simulations reasonably well, except for a small excess present in simulation results. This excess increases with increasing halo mass. We show that its origin lies in substructure, which becomes progressively more abundant and better resolved in more massive dark matter halos. We demonstrate that the high density tail of the one-point distribution function in less massive halos is severely affected by the gravitational softening length and the mass resolution. In particular, we find these two parameters to be more important for an accurate measurement of the density PDF than the simulated volume. Combining our results from individual halo mass bins we find that the part of the one-point density PDF originating from collapsed halos can nevertheless be quite well described by a simple superposition of a set of NFW halos with the expected cosmological abundance over the resolved mass range. The transition region to the low-density unbound material is however not well captured by such an analytic halo model.

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arXiv2012

Simulations of the galaxy population constrained by observations from z=3 to the present day: implications for galactic winds and the fate of their ejecta

We apply Monte Carlo Markov Chain (MCMC) methods to large-scale simulations of galaxy formation in a LambdaCDM cosmology in order to explore how star formation and feedback are constrained by the observed luminosity and stellar mass functions of galaxies. We build models jointly on the Millennium and Millennium-II simulations, applying fast sampling techniques which allow observed galaxy abundances over the ranges 7<log(M*/Msun)<12 and z=0 to z=3 to be used simultaneously as constraints in the MCMC analysis. When z=0 constraints alone are imposed, we reproduce the results of previous modelling by Guo et al. (2012), but no single set of parameters can reproduce observed galaxy abundances at all redshifts simultaneously, reflecting the fact that low-mass galaxies form too early and thus are overabundant at high redshift in this model. The data require the efficiency with which galactic wind ejecta are reaccreted to vary with redshift and halo mass quite differently than previously assumed, but in a similar way as in some recent hydrodynamic simulations of galaxy formation. We propose a specific model in which reincorporation timescales vary inversely with halo mass and are independent of redshift. This produces an evolving galaxy population which fits observed abundances as a function of stellar mass, B- and K-band luminosity at all redshifts simultaneously. It also produces a significant improvement in two other areas where previous models were deficient. It leads to present day dwarf galaxy populations which are younger, bluer, more strongly star-forming and more weakly clustered on small scales than before, although the passive fraction of faint dwarfs remains too high.

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arXiv2012

Numerical Simulations of the Dark Universe: State of the Art and the Next Decade

We present a review of the current state of the art of cosmological dark matter simulations, with particular emphasis on the implications for dark matter detection efforts and studies of dark energy. This review is intended both for particle physicists, who may find the cosmological simulation literature opaque or confusing, and for astro-physicists, who may not be familiar with the role of simulations for observational and experimental probes of dark matter and dark energy. Our work is complementary to the contribution by M. Baldi in this issue, which focuses on the treatment of dark energy and cosmic acceleration in dedicated N-body simulations. Truly massive dark matter-only simulations are being conducted on national supercomputing centers, employing from several billion to over half a trillion particles to simulate the formation and evolution of cosmologically representative volumes (cosmic scale) or to zoom in on individual halos (cluster and galactic scale). These simulations cost millions of core-hours, require tens to hundreds of terabytes of memory, and use up to petabytes of disk storage. The field is quite internationally diverse, with top simulations having been run in China, France, Germany, Korea, Spain, and the USA. Predictions from such simulations touch on almost every aspect of dark matter and dark energy studies, and we give a comprehensive overview of this connection. We also discuss the limitations of the cold and collisionless DM-only approach, and describe in some detail efforts to include different particle physics as well as baryonic physics in cosmological galaxy formation simulations, including a discussion of recent results highlighting how the distribution of dark matter in halos may be altered. We end with an outlook for the next decade, presenting our view of how the field can be expected to progress. (abridged)

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arXiv2012

The clustering of galaxies at z~0.5 in the SDSS-III Data Release 9 BOSS-CMASS sample: a test for the LCDM cosmology

We present results on the clustering of 282,068 galaxies in the Baryon Oscillation Spectroscopic Survey (BOSS) sample of massive galaxies with redshifts 0.4 ~10%) in the correlation functions for scales less than ~1 Mpc/h and ~10-40 Mpc/h. A more realistic abundance matching model and better statistics from upcoming observations are needed to clarify the situation. We also estimate that about 12% of the "galaxies" in the abundance-matched sample are satellites inhabiting central haloes with mass M>~1e14 M_sun/h. Using the MultiDark simulation we also study the real space halo bias b(r) of the matched catalogue finding that b=2.00+/-0.07 at large scales, consistent with the one obtained using the measured BOSS projected correlation function. Furthermore, the linear large-scale bias depends on the number density n of the abundance-matched sample as b=-0.048-(0.594+/-0.02)*log(n/(h/Mpc)^3). Extrapolating these results to BAO scales we measure a scale-dependent damping of the acoustic signal produced by non-linear evolution that leads to ~2-4% dips at ~3 sigma level for wavenumbers k>~0.1 h/Mpc in the linear large-scale bias.

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arXiv2011

On the Effects of Line-of-Sight Structures on Lensing Flux-ratio Anomalies in a LCDM Universe

The flux-ratio anomalies observed in multiply-lensed quasar images are most plausibly explained as the result of perturbing structures superposed on the underlying smooth matter distribution of the primary lens. The cold dark matter cosmological model predicts that a large number of substructures should survive inside larger halos but, surprisingly, this population alone has been shown to be insufficient to explain the observed distribution of the flux ratios of quasar's multiple images. Other halos (and their own subhalos) projected along the line of sight to the primary lens have been considered as additional source of perturbation. In this work, we use ray tracing through the Millennium II simulation to investigate the importance of projection effects due to halos and subhalos of mass m>1E8 Msun/h and extend our analysis to lower masses, m>1E6 Msun/h, using Monte-Carlo halo distributions. We find that the magnitude of the violation depends strongly on the density profile and concentration of the intervening halos, but clustering plays only a minor role. For a typical lensing geometry (lens at redshift 0.6 and source at redshift 2), background haloes (behind the main lens) are more likely to cause a violation than foreground halos. We conclude that line-of-sight structures can be as important as intrinsic substructures in causing flux-ratio anomalies. The combined effect of perturbing structures within the lens and along the line of sight in the LCDM universe results in a cusp-violation probability of 20-30%. This alleviates the discrepancy between models and current data, but a larger observational sample is required for a stronger test of the theory.

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