The combination of seven-year data from WMAP and improved astrophysical data rigorously tests the standard cosmological model and places new constraints on its basic parameters and extensions. By combining the WMAP data with the latest distance measurements from the baryon acoustic oscillations (BAO) in the distribution of galaxies and the Hubble constant (H0) measurement, we determine the parameters of the simplest six-parameter ΛCDM model. The power-law index of the primordial power spectrum is ns = 0.968 ± 0.012 (68% CL) for this data combination, a measurement that excludes the Harrison–Zel’dovich–Peebles spectrum by 99.5% CL. The other parameters, including those beyond the minimal set, are also consistent with, and improved from, the five-year results. We find no convincing deviations from the minimal model. The seven-year temperature power spectrum gives a better determination of the third acoustic peak, which results in a better determination of the redshift of the matter-radiation equality epoch. Notable examples of improved parameters are the total mass of neutrinos, � mν < 0.58 eV (95% CL), and the effective number of neutrino species, Neff = 4.34 +0.86 −0.88 (68% CL), which benefit from better determinations of the third peak and H0. The limit on a constant dark energy equation of state parameter from WMAP+BAO+H0, without high-redshift Type Ia supernovae, is w =− 1.10 ± 0.14 (68% CL). We detect the effect of primordial helium on the temperature power spectrum and provide a new test of big bang nucleosynthesis by measuring Yp = 0.326 ± 0.075 (68% CL). We detect, and show on the map for the first time, the tangential and radial polarization patterns around hot and cold spots of temperature fluctuations, an important test of physical processes at z = 1090 and the dominance of adiabatic scalar fluctuations. The seven-year polarization data have significantly improved: we now detect the temperature–E-mode polarization cross power spectrum at 21σ , compared with 13σ from the five-year data. With the seven-year temperature–B-mode cross power spectrum, the limit on a rotation of the polarization plane due to potential parity-violating effects has improved by 38% to Δα =− 1. 1 ± 1. 4(statistical) ± 1. 5(systematic) (68% CL). We report significant detections of the Sunyaev–Zel’dovich (SZ) effect at the locations of known clusters of galaxies. The measured SZ signal agrees well with the expected signal from the X-ray data on a cluster-by-cluster basis. However, it is a factor of 0.5–0.7 times the predictions from “universal profile” of Arnaud et al., analytical models, and hydrodynamical simulations. We find, for the first time in the SZ effect, a significant difference between the cooling-flow and non-cooling-flow clusters (or relaxed and non-relaxed clusters), which can explain some of the discrepancy. This lower amplitude is consistent with the lower-than-theoretically expected SZ power spectrum recently measured by the South Pole Telescope Collaboration.

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Seven-year wilkinson microwave anisotropy probe (wmap *) observations: cosmological interpretation

WMAP precision data enable accurate testing of cosmological models. We find that the emerging standard model of cosmology, a flat � -dominated universe seeded by a nearly scale-invariant adiabatic Gaussian fluctuations, fits the WMAP data. For the WMAP data only, the best-fit parameters are h ¼ 0:72 � 0:05, � bh 2 ¼ 0:024 � 0:001, � mh 2 ¼ 0:14 � 0:02, � ¼ 0:166 þ0:076 � 0:071 , ns ¼ 0:99 � 0:04, and � 8 ¼ 0:9 � 0:1. With parameters fixed only by WMAP data, we can fit finer scale cosmic microwave background (CMB) measure- ments and measurements of large-scale structure (galaxy surveys and the Lyforest). This simple model is also consistent with a host of other astronomical measurements: its inferred age of the universe is consistent with stellar ages, the baryon/photon ratio is consistent with measurements of the (D/H) ratio, and the inferred Hubble constant is consistent with local observations of the expansion rate. We then fit the model parameters to a combination of WMAP data with other finer scale CMB experiments (ACBAR and CBI), 2dFGRS measurements, and Lyforest data to find the model's best-fit cosmological parameters: h ¼ 0:71 þ0:04 � 0:03 , � bh 2 ¼ 0:0224 � 0:0009, � mh 2 ¼ 0:135 þ0:008 � 0:009 , � ¼ 0:17 � 0:06, ns(0.05 Mpc � 1 )=0 :93 � 0:03, and � 8 ¼ 0:84 � 0:04. WMAP's best determination of � ¼ 0:17 � 0:04 arises directly from the temperature- polarization (TE) data and not from this model fit, but they are consistent. These parameters imply that the age of the universe is 13:7 � 0:2 Gyr. With the Lyforest data, the model favors but does not require a slowly varying spectral index. The significance of this running index is sensitive to the uncertainties in the Ly� forest. By combining WMAP data with other astronomical data, we constrain the geometry of the universe, � tot ¼ 1:02 � 0:02, and the equation of state of the dark energy, w < � 0:78 (95% confidence limit assuming w �� 1). The combination of WMAP and 2dFGRS data constrains the energy density in stable neutrinos: � � h 2 < 0:0072 (95% confidence limit). For three degenerate neutrino species, this limit implies that their mass is less than 0.23 eV (95% confidence limit). The WMAP detection of early reionization rules out warm dark matter. Subject headings: cosmic microwave background — cosmological parameters — cosmology: observations — early universe On-line material: color figure

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First year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Determination of cosmological parameters

Statistics for Spatial Data.

We discuss the cosmological simulation code GADGET-2, a new massively parallel TreeSPH code, capable of following a collisionless fluid with the N-body method, and an ideal gas by means of smoothed particle hydrodynamics (SPH). Our implementation of SPH manifestly conserves energy and entropy in regions free of dissipation, while allowing for fully adaptive smoothing lengths. Gravitational forces are computed with a hierarchical multipole expansion, which can optionally be applied in the form of a TreePM algorithm, where only short-range forces are computed with the ‘tree’ method while long-range forces are determined with Fourier techniques. Time integration is based on a quasi-symplectic scheme where long-range and short-range forces can be integrated with different time-steps. Individual and adaptive short-range time-steps may also be employed. The domain decomposition used in the parallelization algorithm is based on a space-filling curve, resulting in high flexibility and tree force errors that do not depend on the way the domains are cut. The code is efficient in terms of memory consumption and required communication bandwidth. It has been used to compute the first cosmological N-body simulation with more than 10 10 dark matter particles, reaching a homogeneous spatial dynamic range of 10 5 per dimension in a three-dimensional box. It has also been used to carry out very large cosmological SPH simulations that account for radiative cooling and star formation, reaching total particle numbers of more than 250 million. We present the algorithms used by the code and discuss their accuracy and performance using a number of test problems. GADGET-2 is publicly released to the research community. Ke yw ords: methods: numerical ‐ galaxies: interactions ‐ dark matter.

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The Cosmological simulation code GADGET-2

We present cosmological parameter constraints based on the final nine-year WMAP data, in conjunction with a number of additional cosmological data sets. The WMAP data alone, and in combination, continue to be remarkably well fit by a six-parameter CDM model. When WMAP data are combined with measurements of the high-l cosmic microwave background (CMB) anisotropy, the baryon acoustic oscillation (BAO) scale, and the Hubble constant, the matter and energy densities, bh 2 , ch 2 , and , are each determined to a precision of 1.5%. The amplitude of the primordial spectrum is measured to within 3%, and there is now evidence for a tilt in the primordial spectrum at the 5 level, confirming the first detection of tilt based on the five-year WMAP data. At the end of the WMAP mission, the nine-year data decrease the allowable volume of the six-dimensional CDM parameter space by a factor of 68,000 relative to pre-WMAP measurements. We investigate a number of data combinations and show that their CDM parameter fits are consistent. New limits on deviations from the six-parameter model are presented, for example: the fractional contribution of tensor modes is limited to r < 0.13 (95% CL); the spatial curvature parameter is limited to k = 0.0027 +0.0039 0.0038 ; the summed mass of neutrinos is limited to P m < 0.44 eV (95% CL); and the number of relativistic species is found to lie within Ne = 3.84±0.40, when the full data are analyzed. The joint constraint on Ne and the primordial helium abundance, YHe, agrees with the prediction of standard Big Bang nucleosynthesis. We compare recent Planck measurements of the Sunyaev‐Zel’dovich eect with our seven-year measurements, and show their mutual agreement. Our analysis of the polarization pattern around temperature extrema is updated. This confirms a fundamental prediction of the standard cosmological model and provides a striking illustration of acoustic oscillations and adiabatic initial conditions in the early universe. Subject headings: cosmic microwave background, cosmology: observations, early universe, dark matter, space vehicles, space vehicles: instruments, instrumentation: detectors, telescopes

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Nine-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results

We analyze circumgalactic medium (CGM) in a suite of high-resolution cosmological re-simulations of a Milky-Way size galaxy and show that CGM properties are quite sensitive to details of star formation--feedback loop modelling. The simulation that produces a realistic late-type galaxy, fails to reproduce existing observations of the CGM. In contrast, simulation that does not produce a realistic galaxy has the predicted CGM in better agreement with observations. This illustrates that properties of galaxies and properties of their CGM provide strong ${\it complementary}$ constraints on the processes governing galaxy formation. Our simulations predict that column density profiles of ions are well described by an exponential function of projected distance $d$: $N \propto e^{-d/h_s}$. Simulations thus indicate that the sharp drop in absorber detections at larger distances in observations does not correspond to a "boundary" of an ion, but reflects the underlying steep exponential column density profile. Furthermore, we find that ionization energy of ions is tightly correlated with the scale height $h_s$: $h_s \propto E_{\rm ion}^{0.74}$. At $z \approx 0$, warm gas traced by low-ionization species (e.g., Mg II and C IV) has $ h_s \approx 0.03-0.07 R_{\rm vir}$, while higher ionization species (O VI and Ne VIII) have $h_s \approx 0.32-0.45R_{\rm vir}$. Finally, the scale heights of ions in our simulations evolve slower than the virial radius for $z\leq 2$, but similarly to the halo scale radius, $r_s$. Thus, we suggest that the column density profiles of galaxies at different redshifts should be scaled by $r_s$ rather than the halo virial radius.

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Column density profiles of multiphase gaseous haloes

We present analysis of the three-dimensional shape of intracluster gas in clusters formed in cosmological simulations of the Lambda CDM cosmology and compare it to the shape of dark matter distribution and the shape of the overall isopotential surfaces. We find that in simulations with radiative cooling, star formation, and stellar feedback (CSF), intracluster gas outside the cluster core (r >= 0.1r(500)) is more spherical compared to non-radiative (NR) simulations, while in the core the gas in the CSF runs is moretriaxial and has a distinctly oblate shape. The latter reflects the ongoing cooling of gas, which settles into a thick oblate ellipsoid as it loses thermal energy. The shape of the gas in the inner regions of clusters can therefore be a useful diagnostic of gas cooling. We find that gas traces the shape of the underlying potential rather well outside the core, as expected in hydrostatic equilibrium. At smaller radii, however, the gas and potential shapes differ significantly. In the CSF runs, the difference reflects the fact that gas is partly rotationally supported. Interestingly, we find that in NR simulations the difference between gas and potential shape at small radii is due to random gas motions, which make the gas distribution more spherical than the equipotential surfaces. Finally, we use mock Chandra X-ray maps to show that the differences in shapes observed in a three-dimensional distribution of gas are discernible in the ellipticity of X-ray isophotes. Contrasting the ellipticities measured in simulated clusters against observations can therefore constrain the amount of cooling in the intracluster medium and the presence of random gas motions in cluster cores.

https://iopscience.iop.org/article/10.1088/0004-637X/734/2/93/pdf

Shapes of Gas, Gravitational Potential, and Dark Matter in ΛCDM Clusters

The density field in the outskirts of dark matter halos is discontinuous as a result of a caustic formed by matter at its first apocenter after infall. In this paper, we present an algorithm to identify the "splashback shell" formed by these apocenters in individual simulated halos using only a single snapshot of the density field. We implement this algorithm in the code Shellfish (SHELL Finding In Spheroidal Halos) and demonstrate that the code identifies splashback shells correctly and measures their properties with an accuracy of for halos with more than 50,000 particles and mass accretion rates of . Using Shellfish, we present the first estimates for several basic properties of individual splashback shells, such as radius, , mass, and overdensity, and provide fits to the distribution of these quantities as functions of , , and We confirm previous findings that decreases with increasing , but we show that, independent of accretion rate, it also decreases with increasing . We also study the 3D structures of these shells and find that they generally have non-ellipsoidal oval shapes. We find that splashback radii estimated by Shellfish are 20%–30% larger than those estimated in previous studies from stacked density profiles at high accretion rates. We demonstrate that the latter are biased low owing to the contribution of high-mass subhalos to these profiles, and we show that using the median instead of mean density in each radial bin mitigates the effect of substructure on density profiles and removes the bias.

Splashback Shells of Cold Dark Matter Halos

We present a study of numerical effects in dissipationless cosmological simulations. The numerical effects are evaluated and studied by comparing the results of a series of 643-particle simulations of varying force resolution and number of time-steps, performed using three of the N-body techniques currently used for cosmological simulations: the Particle–Mesh (PM), the Adaptive Particle–Particle–Particle–Mesh (AP3M) and the newer Adaptive Refinement Tree (ART) codes. This study can therefore be interesting both as an analysis of numerical effects and as a systematic comparison of different codes.

We find that the AP3M and the ART codes produce similar results given that convergence is reached within the code type. We also find that numerical effects may affect the high-resolution simulations in ways that have not been discussed before. In particular, our study revealed the presence of two-body scattering, the effects of which can be greatly amplified by inaccuracies in time integration. This process appears to affect the correlation function of matter, the mass function, the inner density of dark matter haloes and other statistics at scales much larger than the force resolution, although different statistics may be affected in a different fashion. We discuss the conditions for which strong two-body scattering is possible and discuss the choice of the force resolution and integration time-step. Furthermore, we discuss recent claims that simulations with force softening smaller than the mean interparticle separation are not trustworthy and argue that this claim is incorrect in general, and applies only to the phase-sensitive statistics. Our conclusion is that, depending on the choice of mass and force resolution and the integration time-step, a force resolution as small as 0.01 of the mean interparticle separation can be justified.

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On the effects of resolution in dissipationless cosmological simulations

We find, using cosmological simulations of galaxy clusters, that the hot X-ray emitting intra-cluster medium (ICM) enclosed within the outer accretion shock extends out to $R_{\rm shock}\sim(2 - 3) R_{\rm vir}$, where $R_{\rm vir}$ is the standard virial radius of the halo. Using a simple analytic model for satellite galaxies in the cluster, we evaluate the effect of ram pressure stripping on the gas in the inner discs and in the haloes at different distances from the cluster centre. We find that significant removal of star-forming disc gas occurs only at $r \lesssim 0.5 R_{\rm vir}$, while gas removal from the satellite halo is more effective and can occur when the satellite is found between $ R_{\rm vir}$ and $R_{\rm shock}$. Removal of halo gas sets the stage for quenching of the star formation by starvation over $2\textrm{--}3\,\mathrm{Gyr}$, prior to the satellite entry to the inner cluster halo. This scenario explains the presence of quenched galaxies, preferentially discs, at the outskirts of galaxy clusters, and the delayed quenching of satellites compared to central galaxies.

Andrey V. Kravtsov

Papers

Column density profiles of multiphase gaseous haloes

Shapes of Gas, Gravitational Potential, and Dark Matter in ΛCDM Clusters

Splashback Shells of Cold Dark Matter Halos

On the effects of resolution in dissipationless cosmological simulations

Quenching of satellite galaxies at the outskirts of galaxy clusters