2-halo Term Research Articles

Cosmological inference from an emulator based halo model. I. Validation tests with HSC and SDSS mock catalogs

We present validation tests of emulator-based halo model method for cosmological parameter inference, assuming hypothetical measurements of the projected correlation function of galaxies, $w_{\rm p}(R)$, and the galaxy-galaxy weak lensing, $\Delta\!\Sigma(R)$, from the spectroscopic SDSS galaxies and the Hyper Suprime-Cam Year1 (HSC-Y1) galaxies. To do this, we use \textsc{Dark Emulator} developed in Nishimichi et al. based on an ensemble of $N$-body simulations, which is an emulation package enabling a fast, accurate computation of halo clustering quantities for flat-geometry $w$CDM cosmologies. Adopting the halo occupation distribution, the emulator allows us to obtain model predictions of $\Delta\!\Sigma$ and $w_{\rm p}$ for the SDSS-like galaxies at a few CPU seconds for an input set of parameters. We present performance and validation of the method by carrying out Markov Chain Monte Carlo analyses of the mock signals measured from a variety of mock catalogs that mimic the SDSS and HSC-Y1 galaxies. We show that the halo model method can recover the underlying true cosmological parameters to within the 68\% credible interval, except for the mocks including the assembly bias effect (although we consider the unrealistically-large amplitude of assembly bias effect). Even for the assembly bias mock, we demonstrate that the cosmological parameters can be recovered {\it if} the analysis is restricted to scales $R\gtrsim 10~h^{-1}{\rm Mpc}$. We also show that, by using a single population of source galaxies to infer the relative strengths of $\Delta\!\Sigma$ for multiple lens samples at different redshifts, the joint probes method allows for self-calibration of photometric redshift errors and multiplicative shear bias. Thus we conclude that the emulator-based halo model method can be safely applied to the HSC-Y1 dataset, achieving a precision of $\sigma(S_8)\simeq 0.04$.

Galaxy and Mass Assembly (GAMA): probing galaxy-group correlations in redshift space with the halo streaming model

ABSTRACT We have studied the galaxy-group cross-correlations in redshift space for the Galaxy And Mass Assembly (GAMA) Survey. We use a set of mock GAMA galaxy and group catalogues to develop and test a novel ‘halo streaming’ model for redshift-space distortions. This treats 2-halo correlations via the streaming model, plus an empirical 1-halo term derived from the mocks, allowing accurate modelling into the non-linear regime. In order to probe the robustness of the growth rate inferred from redshift-space distortions, we divide galaxies by colour, and divide groups according to their total stellar mass, calibrated to total mass via gravitational lensing. We fit our model to correlation data, to obtain estimates of the perturbation growth rate, fσ8, validating parameter errors via the dispersion between different mock realizations. In both mocks and real data, we demonstrate that the results are closely consistent between different subsets of the group and galaxy populations, considering the use of correlation data down to some minimum projected radius, rmin. For the mock data, we can use the halo streaming model to below $r_{\rm min} = 5{\, h^{-1}\, \rm Mpc}$, finding that all subsets yield growth rates within about 3 per cent of each other, and consistent with the true value. For the actual GAMA data, the results are limited by cosmic variance: fσ8 = 0.29 ± 0.10 at an effective redshift of 0.20; but there is every reason to expect that this method will yield precise constraints from larger data sets of the same type, such as the Dark Energy Spectroscopic Instrument (DESI) bright galaxy survey.

First Identification of a CMB Lensing Signal Produced by 1.5Million Galaxies at z∼4: Constraints on Matter Density Fluctuations at High Redshift.

We report the first detection of the dark matter distribution around Lyman break galaxies (LBGs) at high redshift through the cosmic microwave background (CMB) lensing measurements with the public Planck PR3 κ map. The LBG sample consists of 1 473 106 objects with the median redshift of z∼4 that are identified in a total area of 305 deg^{2} observed by the Hyper Suprime-Cam Strategic Survey Program survey. After careful investigations of systematic uncertainties, such as contamination from foreground galaxies and cosmic infrared background, we obtain the significant detection of the CMB lensing signal at 5.1σ that is dominated by 2-halo term signals of the LBGs. Fitting a simple model consisting of the Navarro-Frenk-White profile and the linear-bias model, we obtain the typical halo mass of M_{h}=2.9_{-2.5}^{+9.5}×10^{11} h^{-1} M_{⊙}. Combining the CMB lensing and galaxy-galaxy clustering signals on the large scales, we demonstrate the first cosmological analysis at z∼4 that constrains (Ω_{m0},σ_{8}). We find that our constraint on σ_{8} is roughly consistent with the Planck cosmology, while this σ_{8} constraint is lower than the Planck cosmology over the 1σ level. This study opens up a new window for constraining cosmological parameters at high redshift by the combination of CMB and high-z galaxies, as well as studying the interplay between galaxy evolution and large-scale structure at such high redshift, by upcoming CMB and optical and near-infrared imaging surveys.

The BAHAMAS project: evaluating the accuracy of the halo model in predicting the non-linear matter power spectrum

ABSTRACT The halo model formalism is widely adopted in cosmological studies for predicting the growth of large-scale structure in the Universe. However, to date there have been relatively few direct comparisons of the halo model with more accurate (but much more computationally expensive) cosmological simulations. We test the accuracy of the halo model in reproducing the non-linear matter power spectrum, P(k), when the main inputs of the halo model (specifically the matter density profiles, halo mass function, and linear bias) are taken directly from the BAHAMAS simulations, and we assess how well the halo model reproduces P(k) from the same simulations. We show that the halo model generally reproduces P(k) in the deep non-linear regime (1-halo) to typically a few per cent accuracy, but struggles to reproduce (approx. 15 per cent error) P(k) at intermediate scales of $0.1 \la k \ [h/{\rm Mpc}] \la 3$ at $z$ = 0, marking the transition between the 1-halo and 2-halo terms. We show that the magnitude of this error is a strong function of the halo mass definition (through its effects on radial extent of haloes) and of redshift. Furthermore, we test the accuracy of the halo model in recovering the relative impact of baryons on P(k). We show that the systematic errors in recovering the absolute P(k) largely cancel when considering the relative impact of baryons. This suggests that the halo model can make precise predictions for the baryonic suppression, offering a fast and accurate way to adjust collisionless matter power spectra for the presence of baryons and associated processes.

The conformity of H i galaxies in ALFALFA-SDSS sample

The conformity effect, indicating the evolution of galaxies is related to its surrounding neighbor galaxies as far as a few Mpc, is an interesting phenomenon in the modeling of galaxy and evolution. Here we study the conformity effect of HI galaxies in a matched galaxy sample between SDSS DR7 and ALFALFA surveys. By checking the probability difference for the detected H i galaxies as a function of distance around a normal or an H i galaxy, we find that this effect is significant out to 5 Mpc. It also shows a dependence on the stellar mass of galaxies, with the strength the strongest in the stellar mass range of 1010 < M */M⊙ < 1010.5. However, when the sample is confined to central galaxies in groups with virial radii smaller than 1 Mpc, the 1-halo conformity signal is still evident, while the 2-halo conformity signal is reduced to a very weak amplitude. Our results confirm the previous study in the optical band that the 2-halo term is possibly caused by the bias effect in the sample selection. Furthermore, we confirm the existence of the 1-halo conformity discovered in the optical and radio band in previous investigations. Our results provide another viewpoint on the conformity effect and hope to shed light on the co-evolution of the galaxies and their neighbors in the current galaxy formation models.

Removing the giants and learning from the crowd: A new SZ power spectrum method and revised Compton y-map analysis

ABSTRACT The Sunyaev–Zeldovich (SZ) effect provides a powerful cosmological probe, which traditionally is approached independently as cluster number count (CNC) or power spectrum (PS) analysis. Here, we devise a new method for analysing the y-map by introducing the survey completeness function, conventionally only used in the CNC analysis, in the yy-PS modelling. This provides a systematic method, based mainly on SZ observables, for obtaining two complementary y-maps, one incorporating detected/resolved clusters and the other relying only on diffuse/unresolved SZ contributions. We use the catalogue of clusters obtained in the Planck CNC analysis to define the completeness function linking these two y-maps. The split depends on the chosen signal-to-noise detection threshold, which we vary in our discussion. We carefully propagate the effect of completeness cuts on the non-Gaussian error contributions in the yy-PS analysis, highlighting the benefits of masking massive clusters. Our analysis of the Planck yy-PS for the unresolved component yields a mass bias of b = 0.15 ± 0.04, consistent with the standard value (b ≈ 0.2), in comparison to b = 0.4 ± 0.05 for the total yy-PS. We find indications for this drift being driven by the CIB-tSZ cross-correlation, which dominantly originates from clusters in the resolved component of the y-map. Another possible explanation is the presence of a mass-dependent bias, which has been theoretically motivated and can be quantified with our novel method. We furthermore find first hints for the presence of the 2-halo terms in the yy-PS. Finally, the proposed method provides a new framework for combining the complementary information of the CNC and PS analyses in upcoming SZ surveys.

The Halo Void (Dust) Model of large scale structure

Within the Halo Model of large scale structure, all matter is contained in dark matter halos. This simple yet powerful framework has been broadly applied to multiple data sets and enriched our comprehension of how matter is distributed in the Universe. In this work we extend this assumption by allowing for matter to rest not only inside halos but also within cosmic voids and in between halos and voids (which we call `dust'). This assumption leads to additional contributions (1Void, 2Void, Halo-Void, etc.) to the predictions of correlation functions, spectra and profiles for both halos and voids. Whereas the Halo Model can only make predictions for halo quantities, the Halo Void Model extends those for void statistics and halo-void cross-correlations. We provide recipes for all new ingredients of the Halo Void (Dust) Model, such as the void abundance, linear bias and density profile and test their validity in a N-body simulation. Including voids and dust into the calculations improves the transition between the 1Halo and the 2Halo terms by up to ∼ 6%. It also eliminates the need to include low-mass structures on the normalization of large-scale terms, suggesting that halos and voids are complementary cosmic structures to effectively describe matter distribution on large scales of the Universe.

Amending the halo model to satisfy cosmological conservation laws

One of the most powerful tools in the arsenal of theoretical cosmologists is the halo model of large scale structure, which provides a phenomenological description of nonlinear structure in our universe. However, it is well known that there is no simple way to impose conservation laws in the halo model. This can severely impair the predictions on large scales for observables such as weak lensing or the kinematic Sunyaev-Zel'dovich effect, which should satisfy mass and momentum conservations, respectively. For example, the standard halo model overpredicts weak lensing power spectrum by $> 8\%$ on scales $>20$ degrees. To address this problem, we present an $Amended ~ Halo ~ Model$, explicitly separating the linear perturbations from $compensated$ halo profiles. This is guaranteed to respect conservation laws, as well as linear theory predictions on large scales. We then provide a simple fitting function for the compensated halo profiles, and discuss the modified predictions for 1-halo and 2-halo terms, as well as other cosmological observations such weak lensing power spectrum. Furthermore, we argue that the amended halo model provides a more accurate framework to capture physical effects that happen in the process of cosmological structure formation.

The impact of braiding covariance and in-survey covariance on next-generation galaxy surveys

As galaxy surveys improve their precision thanks to lower levels of noise and the push toward small, non-linear scales, the need for accurate covariances beyond the classical Gaussian formula becomes more acute. Here I investigate the analytical implementation and impact of non-Gaussian covariance terms that I had previously derived for the galaxy angular power spectrum. Braiding covariance is such an interesting class of such terms and it gets contributions both from in-survey and super-survey modes, the latter proving difficult to calibrate through simulations. I present an approximation for braiding covariance which speeds up the process of numerical computation. I show that including braiding covariance is a necessary condition for including other non-Gaussian terms, namely the in-survey 2-, 3-, and 4-halo covariance. Indeed these terms yield incorrect covariance matrices with negative eigenvalues if considered on their own. I then move to quantify the impact on parameter constraints, with forecasts for a survey with Euclid-like galaxy density and angular scales. Compared with the Gaussian case, braiding and in-survey covariances significantly increase the error bars on cosmological parameters, in particular by 50% for the dark energy equation of state w. The error bars on the halo occupation distribution (HOD) parameters are also affected between 12% and 39%. Accounting for super-sample covariance (SSC) also increases parameter errors, by 90% for w and between 7% and 64% for HOD. In total, non-Gaussianity increases the error bar on w by 120% (between 15% and 80% for other cosmological parameters) and the error bars on HOD parameters between 17% and 85%. Accounting for the 1-halo trispectrum term on top of SSC, as has been done in some current analyses, is not sufficient for capturing the full non-Gaussian impact: braiding and the rest of in-survey covariance have to be accounted for. Finally, I discuss why the inclusion of non-Gaussianity generally eases up parameter degeneracies, making cosmological constraints more robust for astrophysical uncertainties. I released publicly the data and a Python notebook reproducing the results and plots of the article.

Relation between the turnaround radius and virial mass in f(R) model

We investigate the relationship between the turnaround radius Rt and the virial mass Mv of cosmic structures in the context of ΛCDM model and in an f(R) model of modified gravity—namely, the Hu-Sawicki model. The turnaround radius is the distance from the center of the cosmic structure to the shell that is detaching from the Hubble flow at a given time, while the virial mass is defined, for this work, as the mass enclosed within the volume where the density is 200 times the background density. We employ a new approach by considering that, on average, gravitationally bound astrophysical systems (e.g., galaxies, groups and clusters of galaxies) follow, in their innermost region, a Navarro-Frenk-White density profile, while beyond the virial radius (Rv) the profile is well approximated by the 2-halo term of the matter correlation function. By combining these two properties together with the information drawn from solving the spherical collapse for the structures, we are able to connect two observables that can be readily measured in cosmic structures: the turnaround radius and the virial mass. In particular, we show that, in ΛCDM, the turnaround mass at z=0 is related to the virial mass of that same structure by Mt ≃ 3.07 Mv, while in terms of the radii we have that Rt ≃ 3.7 Rv (for virial masses of 1013 h−1 M⊙). In the f(R) model, on the other hand, we have Mt ≃ 3.43 Mv and Rt ≃ 4.1 Rv, for |fR0|=10−6 and the same mass scale. Therefore, the difference between ΛCDM and f(R) in terms of these observable relations is of order ∼ 10−20% even for a relatively mild strength of the modification of gravity (|fR0|=10−6). For the turnaround radius itself we find a difference of ∼ 9% between the weakly modification in gravity considered in this work (|fR0|=10−6) and ΛCDM for a mass of 1013 h−1 M⊙. Once observations allow precisions of this order or better in measurements of the turnaround Rt, as well as the virial mass Mv (and/or the virial radius Rv), these quantities will become powerful tests of modified gravity.

AMICO galaxy clusters in KiDS-DR3: weak lensing mass calibration

We present the mass calibration for galaxy clusters detected with the AMICO code in KiDS DR3 data. The cluster sample comprises $\sim$ 7000 objects and covers the redshift range 0.1 < $z$ < 0.6. We perform a weak lensing stacked analysis by binning the clusters according to redshift and two different mass proxies provided by AMICO, namely the amplitude $A$ (measure of galaxy abundance through an optimal filter) and the richness $\lambda^*$ (sum of membership probabilities in a consistent radial and magnitude range across redshift). For each bin, we model the data as a truncated NFW profile plus a 2-halo term, taking into account uncertainties related to concentration and miscentring. From the retrieved estimates of the mean halo masses, we construct the $A$-$M_{200}$ and the $\lambda^*$-$M_{200}$ relations. The relations extend over more than one order of magnitude in mass, down to $M_{200} \sim 2 (5) \times 10^{13} M_\odot/h$ at $z$ = 0.2 (0.5), with small evolution in redshift. The logarithmic slope is $\sim 2.0$ for the $A$-mass relation, and $\sim 1.7$ for the $\lambda^*$-mass relation, consistent with previous estimations on mock catalogues and coherent with the different nature of the two observables.

Halo occupation distribution (HOD) modelling of high redshift galaxies using the BlueTides simulation

We construct halo occupation distribution (HOD) models of high redshift ($z \gtrsim 7.5$) galaxies with $M_{*}>10^8~M_{\odot}/h$ using the BlueTides hydrodynamic simulation suite, with a particular emphasis on modelling the small scale / 1-halo clustering ($0.01\lesssim r \lesssim 1~ h^{-1}\rm{Mpc}$). Similar to low redshift studies, we find that the central and satellite mean HODs ($\left<N_{\mathrm{cen}}\right>$ and $\left<N_{\mathrm{sat}}\right>$) can be modeled by a smoothed step function and a power law respectively. The number density of satellite galaxies is however significantly suppressed compared to low redshift (satellite fractions drop from $\sim 50 \%$ at $z=0$ to $\lesssim 10 \%$ at $z=7.5$). The mean number of satellites, $\left<N_{\mathrm{sat}}\right> < 1$ for halo masses below $3 \times 10^{11} M_{\odot}/h$ (a rare halo at these redshifts). For the radial number density profiles, satellites with $10^8 \lesssim M^* \lesssim 10^{9} M_{\odot}/h$ in halos with $M_H \gtrsim 3 \times10^{11} M_{\odot}/h$ are consistent with NFW (with concentrations $c_{\mathrm{sat}} \sim 10-40$). Within halos of mass $M_H\lesssim 3 \times 10^{11} M_{\odot}/h$ satellites exhibit a power law profile with slope -3. Because these halos dominate the small scale clustering, the resulting 1-halo term is steeper than predicted using standard NFW profiles. Using this power-law profile for satellites, we can successfully reproduce the small-scale clustering exhibited by BlueTides galaxies using HOD modelling. We predict the highest probability of detecting satellites at $z>7.5$ is around centrals of $M^*\sim 3 \times 10^{10} M_{\odot}/h$ (with $M^{*}\gtrsim$ a few $10^{7} M_{\odot}/h$ ). This should be achievable with the James Webb Space Telescope (JWST).

The abundance, distribution, and physical nature of highly ionized oxygen O vi, O vii, and O viii in IllustrisTNG

We explore the abundance, spatial distribution, and physical properties of the OVI, OVII, and OVIII ions of oxygen in circumgalactic and intergalactic media (the CGM, IGM, and WHIM). We use the TNG100 and TNG300 large volume cosmological magneto-hydrodynamical simulations. Modeling the ionization states of simulated oxygen, we find good agreement with observations of the low-redshift OVI column density distribution function (CDDF), and present its evolution for all three ions from z=0 to z=4. Producing mock quasar absorption line spectral surveys, we show that the IllustrisTNG simulations are fully consistent with constraints on the OVI content of the CGM from COS-Halos and other low redshift observations, producing columns as high as observed. We measure the total amount of mass and average column densities of each ion using hundreds of thousands of simulated galaxies spanning 10^11 < Mhalo/Msun < 10^15 corresponding to 10^9 < M*/Msun < 10^12 in stellar mass. Stacked radial profiles of OVI are computed in 3D number density and 2D projected column, decomposing into the 1-halo and 2-halo terms. Relating halo OVI to properties of the central galaxy, we find a correlation between the (g-r) color of a galaxy and the total amount of OVI in its CGM. In comparison to the COS-Halos finding, this leads to a dichotomy of columns around star-forming versus passive galaxies at fixed stellar (or halo) mass. We demonstrate that this correlation is a direct result of blackhole feedback associated with quenching and represents a causal consequence of galactic-scale baryonic feedback impacting the physical state of the circumgalactic medium.

The VIMOS Public Extragalactic Redshift Survey (VIPERS)

We used the VIMOS Public Extragalactic Redshift Survey (VIPERS) final data release (PDR-2) to investigate the performance of colour-selected populations of galaxies as tracers of linear large-scale motions. We empirically selected volume-limited samples of blue and red galaxies as to minimise the systematic error on the estimate of the growth rate of structure fσ8 from the anisotropy of the two-point correlation function. To this end, rather than rigidly splitting the sample into two colour classes we defined the red or blue fractional contribution of each object through a weight based on the (U − V) colour distribution. Using mock surveys that are designed to reproduce the observed properties of VIPERS galaxies, we find the systematic error in recovering the fiducial value of fσ8 to be minimised when using a volume-limited sample of luminous blue galaxies. We modelled non-linear corrections via the Scoccimarro extension of the Kaiser model (with updated fitting formulae for the velocity power spectra), finding systematic errors on fσ8 of below 1–2%, using scales as small as 5 h−1 Mpc. We interpret this result as indicating that selection of luminous blue galaxies maximises the fraction that are central objects in their dark matter haloes; this in turn minimises the contribution to the measured ξ(rp,π) from the 1-halo term, which is dominated by non-linear motions. The gain is inferior if one uses the full magnitude-limited sample of blue objects, consistent with the presence of a significant fraction of blue, fainter satellites dominated by non-streaming, orbital velocities. We measured a value of f σ8 = 0.45 ± 0.11 over the single redshift range 0.6 ≤ z ≤ 1.0, corresponding to an effective redshift for the blue galaxies 〈z〉=0.85. Including in the likelihood the potential extra information contained in the blue-red galaxy cross-correlation function does not lead to an appreciable improvement in the error bars, while it increases the systematic error.

The clustering of z &gt; 7 galaxies: predictions from the BLUETIDES simulation

We study the clustering of the highest-z galaxies (from ~ $0.1$ to a few tens Mpc scales) using the BLUETIDES simulation and compare it to current observational constraints from Hubble legacy and Hyper Suprime Cam (HSC) fields (at $z=6-7.2$). With a box length of $400$ $Mpc/h$ on each side and $0.7$ trillion particles, BLUETIDES is the largest high resolution cosmological hydrodynamic simulation to date ideally suited for studies of high-z galaxies. We find that galaxies with magnitude $m_{UV}<27.7$ have a bias ($b_g$) of $8.1\pm 1.2$ at $z=8$, and typical halo masses $M_H \gtrsim 6\times10^{10} M_{\odot}$. Given the redshift evolution between $z=8$ to $z=10$ ($b_g\propto(1+z)^{1.6}$), our inferred values of the bias and halo masses are consistent with measured angular clustering at $z \sim 6.8$ from these brighter samples. The bias of fainter galaxies (in the Hubble legacy field at $H_{160} \lesssim29.5$) is $5.9\pm0.9$ at $z=8$ corresponding to halo masses $M_H \gtrsim 10^{10} M_{\odot}$. We investigate directly the 1-halo term inthe clustering and show that it dominates on scales $r \lesssim 0.1$ Mpc/$h$ ($\Theta \lesssim 3"$) with non-linear effect at transition scales between the 1-halo and 2-halo term affecting scales 0.1 $\lesssim r \lesssim $ 20 Mpc/$h$ ($3"\lesssim \Theta \lesssim 90"$). Current clustering measurements probe down to the scales in the transition between 1-halo to 2-halo regime where non-linear effects are important. The amplitude of the 1-halo term implies that occupation numbers for satellites in \texttt{BLUETIDES} are somewhat higher than standard HODs adopted in these analyses (which predict amplitudes in the 1-halo regime suppressed by a factor 2-3). That possibly implies a higher number of galaxies detected by JWST (at small scales and even fainter magnitudes) observing these fields.

Fourier analysis of multitracer cosmological surveys

We present optimal quadratic estimators for the Fourier analysis of cosmological surveys that detect several different types of tracers of large-scale structure. Our estimators can be used to simultaneously fit the matter power spectrum and the biases of the tracers - as well as redshift-space distortions (RSDs), non-Gaussianities (NGs), or any other effects that are manifested through differences between the clusterings of distinct species of tracers. Our estimators reduce to the one by Feldman, Kaiser & Peacock (ApJ 1994, FKP) in the case of a survey consisting of a single species of tracer. We show that the multi-tracer estimators are unbiased, and that their covariance is given by the inverse of the multi-tracer Fisher matrix (Abramo, MNRAS 2013; Abramo & Leonard, MNRAS 2013). When the biases, RSDs and NGs are fixed to their fiducial values, and one is only interested in measuring the underlying power spectrum, our estimators are projected into the estimator found by Percival, Verde & Peacock (MNRAS 2003). We have tested our estimators on simple (lognormal) simulated galaxy maps, and we show that it performs as expected, being either equivalent or superior to the FKP method in all cases we analyzed. Finally, we have shown how to extend the multi-tracer technique to include the 1-halo term of the power spectrum.

Galaxy power spectrum in redshift space: Combining perturbation theory with the halo model

Theoretical modeling of the redshift-space power spectrum of galaxies is crucially important to correctly extract cosmological information from redshift surveys. The task is complicated by the nonlinear biasing and redshift space distortion effects, which change with halo mass, and by the wide distribution of halo masses and their occupations by galaxies. One of the main modeling challenges is the existence of satellite galaxies that have both radial distribution and large virial velocities inside halos, a phenomenon known as the Finger-of-God effect. We present a model for the galaxy power spectrum of in which we decompose a given galaxy sample into central and satellite galaxies and relate different contributions to 1- and 2-halo terms in a halo model. Our primary goal is to ensure that any parameters that we introduce have physically meaningful values, and are not just fitting parameters. For the 2-halo terms we use the previously developed RSD modeling of halos in the context of distribution function and perturbation theory approach. This term needs to be multiplied by the effect of radial distances and velocities of satellites inside the halo. To this one needs to add the 1-halo terms, which are non-perturbative. We show that the real space 1-halo terms can be modeled as almost constant, with the finite extent of the satellites inside the halo inducing a small k^2R^2 term, where R is related to the size of the halo. We adopt a similar model for FoG in redshift space, ensuring that FoG velocity dispersion is related to the halo mass. For FoG k^2 type expansions do not work and FoG resummation must be used instead. We test several damping functions to model the velocity dispersion FoG effect. Applying the formalism to mock galaxies modeled after the "CMASS" sample of the BOSS survey, we find that our predictions for the redshift-space power spectra are accurate up to k~0.4Mpc/h.

Scaling of the 1-halo terms with bias

In the Halo Model, galaxies are hosted by dark matter halos, while the halos themselves are biased tracers of the underlying matter distribution. Measurements of galaxy correlation functions include contributions both from galaxies in different halos, and from galaxies in the same halo (the so-called 1-halo terms). We show that, for highly biased tracers, the 1-halo term of the power spectrum obeys a steep scaling relation in terms of bias. We also show that the 1-halo term of the trispectrum has a steep scaling with bias. The steepness of these scaling relations is such that the 1-halo terms can become key contributions to the $n$-point correlation functions, even at large scales. We interpret these results through analytical arguments and semi-analytical calculations in terms of the statistical properties of halos.

Probing the diffuse baryon distribution with the lensing-tSZ cross-correlation

Approximately half of the Universe's baryons are in a form that has been hard to detect directly. However, the missing component can be traced through the cross-correlation of the thermal Sunyaev-Zeldovich (tSZ) effect with weak gravitational lensing. We build a model for this correlation and use it to constrain the extended baryon component, employing data from the Canada France Hawaii Lensing Survey and the Planck satellite. The measured correlation function is consistent with an isothermal β-model for the halo gas pressure profile, and the 1- and 2-halo terms are both detected at the 4σ level. In addition, we measure the hydrostatic mass bias (1−b)=0.79+0.07−0.10, which is consistent with numerical simulation results and the constraints from X-ray observations. The effective temperature of the gas is found to be in the range (7×105–3 ×108) K, with approximately 50% of the baryons appearing to lie beyond the virial radius of the halos, consistent with current expectations for the warm-hot intergalactic medium.

The halo model in a massive neutrino cosmology

We provide a quantitative analysis of the halo model in the context of massive neutrino cosmologies. We discuss all the ingredients necessary to model the non-linear matter and cold dark matter power spectra and compare with the results of N-body simulations that incorporate massive neutrinos. Our neutrino halo model is able to capture the non-linear behavior of matter clustering with a ∼20% accuracy up to very non-linear scales ofk = 10 h/Mpc (which would be affected by baryon physics). The largest discrepancies arise in the range k = 0.5 – 1 h/Mpc where the 1-halo and 2-halo terms are comparable and are present also in a massless neutrino cosmology. However, at scales k < 0.2 h/Mpc our neutrino halo model agrees with the results of N-body simulations at the level of 8% for total neutrino masses of < 0.3 eV. We also model the neutrino non-linear density field as a sum of a linear and clustered component and predict the neutrino power spectrum and the cold dark matter-neutrino cross-power spectrum up to k = 1 h/Mpc with ∼30% accuracy. For masses below 0.15 eV the neutrino halo model captures the neutrino induced suppression, casted in terms of matter power ratios between massive and massless scenarios, with a 2% agreement with the results of N-body/neutrino simulations. Finally, we provide a simple application of the halo model: the computation of the clustering of galaxies, in massless and massive neutrinos cosmologies, using a simple Halo Occupation Distribution scheme and our halo model extension.