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David N. Spergel

Publications and source records attributed to David N. Spergel.

At least 163 records · Page 9Linked to original sources

Toward an Understanding of Foreground Emission in the BICEP2 Region

BICEP2 has reported the detection of a degree-scale B-mode polarization pattern in the Cosmic Microwave Background (CMB) and has interpreted the measurement as evidence for primordial gravitational waves. Motivated by the profound importance of the discovery of gravitational waves from the early Universe, we examine to what extent a combination of Galactic foregrounds and lensed E-modes could be responsible for the signal. We reanalyze the BICEP2 results and show that the 100x150 GHz and 150x150 GHz data are consistent with a cosmology with r=0.2 and negligible foregrounds, but also with a cosmology with r=0 and a significant dust polarization signal. We give independent estimates of the dust polarization signal in the BICEP2 region using four different approaches. While these approaches are consistent with each other, the expected amplitude of the dust polarization power spectrum remains uncertain by about a factor of three. The lower end of the prediction leaves room for a primordial contribution, but at the higher end the dust in combination with the standard CMB lensing signal could account for the BICEP2 observations, without requiring the existence of primordial gravitational waves. By measuring the cross-correlations between the pre-Planck templates used in the BICEP2 analysis and between different versions of a data-based template, we emphasize that cross-correlations between models are very sensitive to noise in the polarization angles and that measured cross-correlations are likely underestimates of the contribution of foregrounds to the map. These results suggest that BICEP1 and BICEP2 data alone cannot distinguish between foregrounds and a primordial gravitational wave signal, and that future Keck Array observations at 100 GHz and Planck observations at higher frequencies will be crucial to determine whether the signal is of primordial origin. (abridged)

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Joint likelihood function of cluster counts and $n$-point correlation functions: Improving their power through including halo sample variance

Naive estimates of the statistics of large scale structure and weak lensing power spectrum measurements that include only Gaussian errors exaggerate their scientific impact. Non-linear evolution and finite volume effects are both significant sources of non-Gaussian covariance that reduce the ability of power spectrum measurements to constrain cosmological parameters. Using a halo model formalism, we derive an intuitive understanding of the various contributions to the covariance and show that our analytical treatment agrees with simulations. This approach enables an approximate derivation of a joint likelihood for the cluster number counts, the weak lensing power spectrum and the bispectrum. We show that this likelihood is a good description of the ray-tracing simulation. Since all of these observables are sensitive to the same finite volume effects and contain information about the non-linear evolution, a combined analysis recovers much of the "lost" information and obviates the non-Gaussian covariance. For upcoming weak lensing surveys, we estimate that a joint analysis of power spectrum, number counts and bispectrum will produce an improvement of about $30-40\%$ in determinations of the matter density and the scalar amplitude. This improvement is equivalent to doubling the survey area.

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The Gaia inertial reference frame and the tilting of the Milky Way disk

While the precise relationship between the Milky Way disk and the symmetry planes of the dark matter halo remains somewhat uncertain, a time-varying disk orientation with respect to an inertial reference frame seems probable. Hierarchical structure formation models predict that the dark matter halo is triaxial and tumbles with a characteristic rate of ~2 rad/Hubble time (~30 muas/yr). These models also predict a time-dependent accretion of gas, such that the angular momentum vector of the disk should be misaligned with that of the halo. These effects, as well as tidal effects of the LMC, will result in the rotation of the angular momentum vector of the disk population with respect to the quasar reference frame. We assess the accuracy with which the positions and proper motions from Gaia can be referred to a kinematically non-rotating system, and show that the spin vector of the transformation from any rigid self-consistent catalog frame to the quasi-inertial system defined by quasars should be defined to better than 1 muas/yr. Determination of this inertial frame by Gaia will reveal any signature of the disk orientation varying with time, improve models of the potential and dynamics of the Milky Way, test theories of gravity, and provide new insights into the orbital evolution of the Sagittarius dwarf galaxy and the Magellanic Clouds.

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Joint analysis of cluster number counts and weak lensing power spectrum to correct for the super-sample covariance

A coherent over- or under-density contrast across a finite survey volume causes an upward- or downward-fluctuation in the observed number of halos. This fluctuation in halo number adds a significant co-variant scatter in the observed amplitudes of weak lensing power spectrum at nonlinear, small scales -- the so-called super-sample variance or the halo sample variance. In this paper, we show that by measuring both the number counts of clusters and the power spectrum in the same survey region, we can mitigate this loss of information and significantly enhance the scientific return from the upcoming surveys. First, using the halo model approach, we derive the cross-correlation between the halo number counts and the weak lensing power spectrum, taking into account the super-sample covariance effect, which well matches the distributions measured from 1000 realizations for a Lambda-dominated cold dark matter model. Then we show that adding the observed number counts of massive halos with M> 10^14 Ms/h can significantly improve the information content of weak lensing power spectrum, almost recovering the Gaussian information up to lmax~1000, if the average mass profiles of the massive halos are known, which can be estimated from stacked lensing. When combined with the halo number counts for M > 3 or 1 x 10^14 Ms/h, the improvement is up to a factor of 1.4 or 2 at lmax~1000 --2000, equivalent to a factor 2 or 4 times larger survey volume, compared to the power spectrum measurement alone.

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The Atacama Cosmology Telescope: Cross Correlation with Planck maps

We present the temperature power spectrum of the Cosmic Microwave Background obtained by cross-correlating maps from the Atacama Cosmology Telescope (ACT) at 148 and 218 GHz with maps from the Planck satellite at 143 and 217 GHz, in two overlapping regions covering 592 square degrees. We find excellent agreement between the two datasets at both frequencies, quantified using the variance of the residuals between the ACT power spectra and the ACTxPlanck cross-spectra. We use these cross-correlations to calibrate the ACT data at 148 and 218 GHz, to 0.7% and 2% precision respectively. We find no evidence for anisotropy in the calibration parameter. We compare the Planck 353 GHz power spectrum with the measured amplitudes of dust and cosmic infrared background (CIB) of ACT data at 148 and 218 GHz. We also compare planet and point source measurements from the two experiments.

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Detection of Thermal SZ -- CMB Lensing Cross-Correlation in Planck Nominal Mission Data

The nominal mission maps from the Planck satellite contain a wealth of information about secondary anisotropies in the cosmic microwave background (CMB), including those induced by the thermal Sunyaev-Zel'dovich (tSZ) effect and gravitational lensing. As both the tSZ and CMB lensing signals trace the large-scale matter density field, the anisotropies sourced by these processes are expected to be correlated. We report the first detection of this cross-correlation signal, which we measure at 6.2 sigma significance using the Planck data. We take advantage of Planck's multifrequency coverage to construct a tSZ map using internal linear combination techniques, which we subsequently cross-correlate with the publicly-released Planck CMB lensing potential map. [Abridged] We interpret the signal using halo model calculations, which indicate that the tSZ -- CMB lensing cross-correlation is a unique probe of the physics of intracluster gas in high-redshift, low-mass groups and clusters. Our results are consistent with extrapolations of existing gas physics models to this previously unexplored regime and show clear evidence for contributions from both the one- and two-halo terms, but no statistically significant evidence for contributions from diffuse, unbound gas outside of collapsed halos. We also show that the amplitude of the signal depends rather sensitively on the amplitude of fluctuations ($σ_8$) and the matter density ($Ω_m$). We constrain the degenerate combination $σ_8 (Ω_m/0.282)^{0.26} = 0.824 \pm 0.029$, a result that is in less tension with primordial CMB constraints than some recent tSZ analyses. Our detection is a direct confirmation that hot, ionized gas traces the dark matter distribution over a wide range of scales in the universe ($\sim 0.1$--$50 \, {\rm Mpc}/h$).

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How does non-linear dynamics affect the baryon acoustic oscillation?

We study the non-linear behavior of the baryon acoustic oscillation in the power spectrum and the correlation function by decomposing the dark matter perturbations into the short- and long-wavelength modes. The evolution of the dark matter fluctuations can be described as a global coordinate transformation caused by the long-wavelength displacement vector acting on short-wavelength matter perturbation undergoing non-linear growth. Using this feature, we investigate the well known cancellation of the high-$k$ solutions in the standard perturbation theory. While the standard perturbation theory naturally satisfies the cancellation of the high-$k$ solutions, some of the recently proposed improved perturbation theories do not guarantee the cancellation. We show that this cancellation clarifies the success of the standard perturbation theory at the 2-loop order in describing the amplitude of the non-linear power spectrum even at high-$k$ regions.We propose an extension of the standard 2-loop level perturbation theory model of the non-linear power spectrum that more accurately models the non-linear evolution of the baryon acoustic oscillation than the standard perturbation theory. The model consists of simple and intuitive parts: the non-linear evolution of the smoothed power spectrum without the baryon acoustic oscillations and the non-linear evolution of the baryon acoustic oscillations due to the large-scale velocity of dark matter and due to the gravitational attraction between dark matter particles. Our extended model predicts the smoothing parameter of the baryon acoustic oscillation peak at $z=0.35$ as $\sim 7.7\ {\rm Mpc}/h$ and describes the small non-linear shift in the peak position due to the galaxy random motions.

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A WISE measurement of the ISW effect

The Integrated Sachs-Wolfe effect (ISW) measures the decay of the gravitational potential due to cosmic acceleration and is thus a direct probe of Dark Energy. In some of the earlier studies, the amplitude of the ISW effect was found to be in tension with the predictions of the standard $Λ$CDM model. We measure the cross-power of galaxies and AGN from the WISE mission with CMB temperature data from WMAP9 in order to provide an independent measurement of the ISW amplitude. Cross-correlations with the recently released Planck lensing potential maps are used to calibrate the bias and contamination fraction of the sources, thus avoiding systematic effects that could be present when using auto-spectra to measure bias. We find an amplitude of the cross-power of $\mathcal{A} = 1.24\pm 0.47$ from the galaxies and $\mathcal{A} = 0.88 \pm 0.74$ from the AGN, fully consistent with the $Λ$CDM prediction of $\mathcal{A} =1$. The ISW measurement signal-to-noise ratio is 2.7 and 1.2 respectively, giving a combined significance close to $3 σ$. Comparing the amplitudes of the galaxy and AGN cross-correlations, which arise from different redshifts, we find no evidence for redshift evolution in Dark Energy properties, consistent with a Cosmological Constant.

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Probing patchy reionization through tau-21cm correlation statistics

We consider the cross-correlation between free electrons and neutral hydrogen during the epoch of reionization. The free electrons are traced by the optical depth to reionization tau, while the neutral hydrogen can be observed through 21 cm photon emission. As expected, this correlation is sensitive to the detailed physics of reionization. Foremost, if reionization occurs through the merger of relatively large halos hosting an ionizing source, the free electrons and neutral hydrogen are anti-correlated for most of the reionization history. A positive contribution to the correlation can occur when the halos that can form an ionizing source are small. A measurement of this sign change in the cross-correlation would directly measure the bubble bias and as, such, the halo mass. We estimate the signal-to-noise of the cross-correlation using the estimator for inhomogeneous reionization tau_{lm} proposed by Dvorkin and Smith (2009). We find that with upcoming radio interferometers and CMB experiments, the cross-correlation is measurable going up to multipoles l ~ 1000. We also derive parameter constraints and conclude that, despite the foregrounds, the cross-correlation proofs a complementary measurement of the EoR parameters to the 21 cm and CMB polarization auto-correlations expected to be observed in the coming decade.

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Searching for Oscillations in the Primordial Power Spectrum: Perturbative Approach (Paper I)

In this first of two papers, we present a new method for searching for oscillatory features in the primordial power spectrum. A wide variety of models predict these features in one of two different flavors: logarithmically spaced oscillations and linearly spaced oscillations. The proposed method treats the oscillations as perturbations on top of the scale-invariant power spectrum, allowing us to vary all cosmological parameters. This perturbative approach reduces the computational requirements for the search as the transfer functions and their derivatives can be precomputed. We show that the most significant degeneracy in the analysis is between the distance to last scattering and the overall amplitude at low frequencies. For models with logarithmic oscillations, this degeneracy leads to an uncertainty in the phase. For linear spaced oscillations, it affects the frequency of the oscillations. In this first of two papers, we test our code on simulated Planck-like data, and show we are able to recover fiducial input oscillations with an amplitude of a few times order 10^{-2}. We apply the code to WMAP9-year data and confirm the existence of two intriguing resonant frequencies for log spaced oscillations. For linear spaced oscillations we find a single resonance peak. We use numerical simulations to assess the significance of these features and conclude that the data do not provide compelling evidence for the existence of oscillatory features in the primordial spectrum.

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The Atacama Cosmology Telescope: Cosmological parameters from three seasons of data

We present constraints on cosmological and astrophysical parameters from high-resolution microwave background maps at 148 GHz and 218 GHz made by the Atacama Cosmology Telescope (ACT) in three seasons of observations from 2008 to 2010. A model of primary cosmological and secondary foreground parameters is fit to the map power spectra and lensing deflection power spectrum, including contributions from both the thermal Sunyaev-Zeldovich (tSZ) effect and the kinematic Sunyaev-Zeldovich (kSZ) effect, Poisson and correlated anisotropy from unresolved infrared sources, radio sources, and the correlation between the tSZ effect and infrared sources. The power ell^2 C_ell/2pi of the thermal SZ power spectrum at 148 GHz is measured to be 3.4 +\- 1.4 muK^2 at ell=3000, while the corresponding amplitude of the kinematic SZ power spectrum has a 95% confidence level upper limit of 8.6 muK^2. Combining ACT power spectra with the WMAP 7-year temperature and polarization power spectra, we find excellent consistency with the LCDM model. We constrain the number of effective relativistic degrees of freedom in the early universe to be Neff=2.79 +\- 0.56, in agreement with the canonical value of Neff=3.046 for three massless neutrinos. We constrain the sum of the neutrino masses to be Sigma m_nu < 0.39 eV at 95% confidence when combining ACT and WMAP 7-year data with BAO and Hubble constant measurements. We constrain the amount of primordial helium to be Yp = 0.225 +\- 0.034, and measure no variation in the fine structure constant alpha since recombination, with alpha/alpha0 = 1.004 +/- 0.005. We also find no evidence for any running of the scalar spectral index, dns/dlnk = -0.004 +\- 0.012.

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Measuring the Thermal Sunyaev-Zel'dovich Effect Through the Cross Correlation of Planck and WMAP Maps with ROSAT Galaxy Cluster Catalogs

We measure a significant correlation between the thermal Sunyaev-Zel'dovich effect in the Planck and WMAP maps and an X-ray cluster map based on ROSAT. We use the 100, 143 and 343 GHz Planck maps and the WMAP 94 GHz map to obtain this cluster cross spectrum. We check our measurements for contamination from dusty galaxies using the cross correlations with the 220, 545 and 843 GHz maps from Planck. Our measurement yields a direct characterization of the cluster power spectrum over a wide range of angular scales that is consistent with large cosmological simulations. The amplitude of this signal depends on cosmological parameters that determine the growth of structure (σ_8 and Ω_M) and scales as σ_8^7.4 and Ω_M^1.9 around the multipole (ell) ~ 1000. We constrain σ_8 and Ω_M from the cross-power spectrum to be σ_8 (Ω_M/0.30)^0.26 = 0.8 +/- 0.02. Since this cross spectrum produces a tight constraint in the σ_8 and Ω_M plane the errors on a σ_8 constraint will be mostly limited by the uncertainties from external constraints. Future cluster catalogs, like those from eRosita and LSST, and pointed multi-wavelength observations of clusters will improve the constraining power of this cross spectrum measurement. In principle this analysis can be extended beyond σ_8 and Ω_M to constrain dark energy or the sum of the neutrino masses.

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The Atacama Cosmology Telescope: the stellar content of galaxy clusters selected using the Sunyaev-Zel'dovich effect

We present a first measurement of the stellar mass component of galaxy clusters selected via the Sunyaev-Zel'dovich (SZ) effect, using 3.6 um and 4.5 um photometry from the Spitzer Space Telescope. Our sample consists of 14 clusters detected by the Atacama Cosmology Telescope (ACT), which span the redshift range 0.27 < z < 1.07 (median z = 0.50), and have dynamical mass measurements, accurate to about 30 per cent, with median M500 = 6.9 x 10^{14} MSun. We measure the 3.6 um and 4.5 um galaxy luminosity functions, finding the characteristic magnitude (m*) and faint-end slope (alpha) to be similar to those for IR-selected cluster samples. We perform the first measurements of the scaling of SZ-observables (Y500 and y0) with both brightest cluster galaxy (BCG) stellar mass and total cluster stellar mass (M500star). We find a significant correlation between BCG stellar mass and Y500 (E(z)^{-2/3} DA^2 Y500 ~ M*^{1.2 +/- 0.6}), although we are not able to obtain a strong constraint on the slope of the relation due to the small sample size. Additionally, we obtain E(z)^{-2/3} DA^2 Y500 ~ M500star^{1.0 +/- 0.6} for the scaling with total stellar mass. The mass fraction in stars spans the range 0.006-0.034, with the second ranked cluster in terms of dynamical mass (ACT-CL J0237-4939) having an unusually low total stellar mass and the lowest stellar mass fraction. For the five clusters with gas mass measurements available in the literature, we see no evidence for a shortfall of baryons relative to the cosmic mean value.

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Where are the Luminous Red Galaxies (LRGs)? Using correlation measurements and lensing to relate LRGs to dark matter halos

Nonlinear redshift-space distortions, the Finger-of-God (FoG) effect, can complicate the interpretation of the galaxy power spectrum. Here, we demonstrate the method proposed by Hikage et al. (2012) to use complimentary observations to directly constrain this effect on the data. We use catalogs of Luminous Red Galaxies (LRGs) and photometric galaxies from the SDSS DR7 to measure the redshift-space power spectrum of LRGs, the cross-correlation of LRGs with the shapes of background photometric galaxies (galaxy-galaxy weak lensing), and the projected cross-correlation of LRGs with photometric galaxies having similar photometric redshifts to the LRG spectroscopic redshift. All of these measurements use a reconstructed halo field. While we use the position of each LRG for single LRG systems, we compare the measurements using different halo-center proxies for multiple-LRG systems (4.5 per cent of all the halos): the brightest LRG position (BLRG), the faintest LRG position (FLRG) and their arithmetical mean position (Mean), respectively, in each system. We find significant differences in the measured correlations of different centers, showing consistent off-centering effects in the three observables. By comparing the measurements with a halo model that treats the satellite photometric galaxies as being distributed according to a generalized NFW profile, we find that about 40 (70) per cent of BLRGs (FLRGs) are off-centered satellite galaxies in the multiple-LRG systems. The satellite LRGs have typical off-centering radius of about 400 kpc/h, and velocity dispersion of about 500 km/s in host halos with a mean mass of 1.6x10^14 Ms/h. We show that, if LRGs in the single LRG systems have similar offsets, the residual FoG contamination in the LRG power spectrum can be significant at k>0.1 h/Mpc, which may cause a bias in cosmological parameters such as the neutrino mass.

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Extragalactic Science, Cosmology and Galactic Archaeology with the Subaru Prime Focus Spectrograph (PFS)

The Subaru Prime Focus Spectrograph (PFS) is a massively-multiplexed fiber-fed optical and near-infrared 3-arm spectrograph (N_fiber=2400, 380<lambda<1260nm, 1.3 degree diameter FoV), offering unique opportunities in survey astronomy. Here we summarize the science case feasible for a survey of Subaru 300 nights. We describe plans to constrain the nature of dark energy via a survey of emission line galaxies spanning a comoving volume of 9.3 (Gpc/h)^3 in the redshift range 0.8<z<2.4. In each of 6 redshift bins, the cosmological distances will be measured to 3% precision via BAO, and redshift-space distortions will be used to constrain structure growth to 6% precision. In the GA program, radial velocities and chemical abundances of stars in the Milky Way and M31 will be used to infer the past assembly histories of spiral galaxies and the structure of their dark matter halos. Data will be secured for 10^6 stars in the Galactic thick-disk, halo and tidal streams as faint as V~22, including stars with V < 20 to complement the goals of the Gaia mission. A medium-resolution mode with R = 5000 to be implemented in the red arm will allow the measurement of multiple alpha-element abundances and more precise velocities for Galactic stars, elucidating the detailed chemo-dynamical structure and evolution of each of the main stellar components of the Milky Way Galaxy and of its dwarf spheroidal galaxies. For the extragalactic program, our simulations suggest the wide avelength range will be powerful in probing the galaxy population and its clustering over a wide redshift range. We propose to conduct a color-selected survey of 1<z<2 galaxies and AGN over 16 deg^2 to J~23.4, yielding a fair sample of galaxies with stellar masses above ~10^{10}Ms at z~2. A two-tiered survey of higher redshift LBGs and LAEs will quantify the properties of early systems close to the reionization epoch.

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The Atacama Cosmology Telescope: Sunyaev-Zel'dovich Selected Galaxy Clusters at 148 GHz from Three Seasons of Data

[Abridged] We present a catalog of 68 galaxy clusters, of which 19 are new discoveries, detected via the Sunyaev-Zel'dovich effect (SZ) at 148 GHz in the Atacama Cosmology Telescope (ACT) survey of 504 square degrees on the celestial equator. A subsample of 48 clusters within the 270 square degree region overlapping SDSS Stripe 82 is estimated to be 90% complete for M_500c > 4.5e14 Msun and 0.15 < z < 0.8. While matched filters are used to detect the clusters, the sample is studied further through a "Profile Based Amplitude Analysis" using a single filter at a fixed θ_500 = 5.9' angular scale. This new approach takes advantage of the "Universal Pressure Profile" (UPP) to fix the relationship between the cluster characteristic size (R_500) and the integrated Compton parameter (Y_500). The UPP scalings are found to be nearly identical to an adiabatic model, while a model incorporating non-thermal pressure better matches dynamical mass measurements and masses from the South Pole Telescope. A high signal to noise ratio subsample of 15 ACT clusters is used to obtain cosmological constraints. We first confirm that constraints from SZ data are limited by uncertainty in the scaling relation parameters rather than sample size or measurement uncertainty. We next add in seven clusters from the ACT Southern survey, including their dynamical mass measurements based on galaxy velocity dispersions. In combination with WMAP7 these data simultaneously constrain the scaling relation and cosmological parameters, yielding σ_8 = 0.829 \pm 0.024 and Ω_m = 0.292 \pm 0.025. The results include marginalization over a 15% bias in dynamical mass relative to the true halo mass. In an extension to LCDM that incorporates non-zero neutrino mass density, we combine our data with WMAP7+BAO+Hubble constant measurements to constrain Σm_ν< 0.29 eV (95% C. L.).

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The Atacama Cosmology Telescope: Dynamical Masses and Scaling Relations for a Sample of Massive Sunyaev-Zel'dovich Effect Selected Galaxy Clusters

We present the first dynamical mass estimates and scaling relations for a sample of Sunyaev-Zel'dovich effect (SZE) selected galaxy clusters. The sample consists of 16 massive clusters detected with the Atacama Cosmology Telescope (ACT) over a 455 sq. deg. area of the southern sky. Deep multi-object spectroscopic observations were taken to secure intermediate-resolution (R~700-800) spectra and redshifts for ~60 member galaxies on average per cluster. The dynamical masses M_200c of the clusters have been calculated using simulation-based scaling relations between velocity dispersion and mass. The sample has a median redshift z=0.50 and a median mass M_200c~12e14 Msun/h70 with a lower limit M_200c~6e14 Msun/h70, consistent with the expectations for the ACT southern sky survey. These masses are compared to the ACT SZE properties of the sample, specifically, the match-filtered central SZE amplitude y, the central Compton parameter y0, and the integrated Compton signal Y_200c, which we use to derive SZE-Mass scaling relations. All SZE estimators correlate with dynamical mass with low intrinsic scatter (<~20%), in agreement with numerical simulations. We explore the effects of various systematic effects on these scaling relations, including the correlation between observables and the influence of dynamically disturbed clusters. Using the 3-dimensional information available, we divide the sample into relaxed and disturbed clusters and find that ~50% of the clusters are disturbed. There are hints that disturbed systems might bias the scaling relations but given the current sample sizes these differences are not significant; further studies including more clusters are required to assess the impact of these clusters on the scaling relations.

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Understanding the nature of luminous red galaxies (LRGs): Connecting LRGs to central and satellite subhalos

We develop a novel abundance matching method to construct a mock catalog of luminous red galaxies (LRGs) in SDSS, using catalogs of halos and subhalos in N-body simulations for a LCDM model. Motivated by observations suggesting that LRGs are passively-evolving, massive early-type galaxies with a typical age >5Gyr, we assume that simulated halos at z=2 (z2-halo) are progenitors for LRG-host subhalos observed today, and we label the most tightly bound particles in each progenitor z2-halo as LRG ``stars''. We then identify the subhalos containing these stars to z=0.3 (SDSS redshift) in descending order of the masses of z2-halos until the comoving number density of the matched subhalos becomes comparable to the measured number density of SDSS LRGs, n=10^{-4} (h/Mpc)^3. Once the above prescription is determined, our only free parameter is the number density of halos identified at z=2 and this parameter is fixed to match the observed number density at z = 0.3. By tracing subsequent merging and assembly histories of each progenitor z2-halo, we can directly compute, from the mock catalog, the distributions of central and satellite LRGs and their internal motions in each host halo at z=0.3. While the SDSS LRGs are galaxies selected by the magnitude and color cuts from the SDSS images and are not necessarily a stellar-mass-selected sample, our mock catalog reproduces a host of SDSS measurements: the halo occupation distribution for central and satellite LRGs, the projected auto-correlation function of LRGs, the cross-correlation of LRGs with shapes of background galaxies (LRG-galaxy weak lensing), and the nonlinear redshift-space distortion effect, the Finger-of-God effect, in the angle-averaged redshift-space power spectrum.

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