Week of Friday July 5

http://arxiv.org/abs/0805.2552 (Reiko will lead the discussion)

Halo mass - concentration relation from weak lensing

Rachel Mandelbaum, Uros Seljak, Christopher M. Hirata

(Submitted on 16 May 2008) We perform a statistical weak lensing analysis of dark matter profiles around tracers of halo mass from galactic- to cluster-size halos. In this analysis we use 170,640 isolated ~L* galaxies split into ellipticals and spirals, 38,236 groups traced by isolated spectroscopic Luminous Red Galaxies (LRGs) and 13,823 MaxBCG clusters from the Sloan Digital Sky Survey (SDSS) covering a wide range of richness. Together these three samples allow a determination of the density profiles of dark matter halos over three orders of magnitude in mass, from 10^{12} M_{sun} to 10^{15} M_{sun}. The resulting lensing signal is consistent with an NFW or Einasto profile on scales outside the central region. We find that the NFW concentration parameter c_{200b} decreases with halo mass, from around 10 for galactic halos to 4 for cluster halos. Assuming its dependence on halo mass in the form of c_{200b} = c_0 [M/(10^{14}M_{sun}/h)]^{\beta}, we find c_0=4.6 +/- 0.7 (at z=0.22) and \beta=0.13 +/- 0.07, with very similar results for the Einasto profile. The slope (\beta) is in agreement with theoretical predictions, while the amplitude is about two standard deviations below the predictions for this mass and redshift, but we note that the published values in the literature differ at a level of 10-20% and that for a proper comparison our analysis should be repeated in simulations. We discuss the implications of our results for the baryonic effects on the shear power spectrum: since these are expected to increase the halo concentration, the fact that we see no evidence of high concentrations on scales above 20% of the virial radius suggests that baryonic effects are limited to small scales, and are not a significant source of uncertainty for the current weak lensing measurements of the dark matter power spectrum. [ABRIDGED]

Week of Friday May 16

http://arxiv.org/abs/0805.0117

Non-linear structure formation and the acoustic scale

Hee-Jong Seo, Ethan R. Siegel, Daniel J. Eisenstein, Martin White

We present high signal-to-noise measurements of the acoustic scale in the presence of nonlinear growth and redshift distortions using 320(Gpc/h)^3 of cosmological PM simulations. Using simple fitting methods, we obtain robust measurements of the acoustic scale with scatter close to that predicted by the Fisher matrix. We detect and quantify the shift in the acoustic scale by analyzing the power spectrum: we detect at greater than 5 sigma a decrease in the acoustic scale in the real-space matter power spectrum of 0.2% at z=1.5, growing to 0.45% at z=0.3. In redshift space, the shifts are about 25% larger: we detect a decrease of 0.25% of at z=1.5 and 0.54% at z=0.3. Despite the nonzero amounts, these shifts are highly predictable numerically, and hence removable within the standard ruler analysis of clustering data. Moreover, we show that a simple density-field reconstruction method substantially reduces the scatter and nonlinear shifts of the acoustic scale measurements: the shifts are reduced to less than 0.1% at z=0.3-1.5, even in the presence of non-negligible shot noise. Finally, we show that the ratio of the cosmological distance to the sound horizon that would be inferred from these fits is robust to variations in the parameterization of the fitting method and reasonable differences in the template cosmology.

http://arxiv.org/abs/0805.2155

Improved estimation of cluster mass profiles from the cosmic microwave background

Jaiyul Yoo, Matias Zaldarriaga

We develop a new method for reconstructing cluster mass profiles and large-scale structure from the cosmic microwave background (CMB). By analyzing the likelihood of CMB lensing, we analytically prove that standard quadratic estimators for CMB lensing are unbiased and achieve the optimal condition only in the limit of no lensing; they become progressively biased and sub-optimal, when the lensing effect is large, especially for clusters that can be found by ongoing Sunyaev-Zel’dovich surveys. Adopting an alternative approach to the CMB likelihood, we construct a new maximum likelihood estimator that utilizes delensed CMB temperature fields based on an assumed model. We analytically show that this estimator asymptotically approaches the optimal condition as our assumed model is refined, and we numerically show that our estimator quickly converges to the true model as we iteratively apply it to CMB maps. For realistic CMB experiments, we demonstrate the applicability of the maximum likelihood estimator with tests against numerical simulations in the presence of CMB secondary contaminants. With significant improvement on the signal-to-noise ratio, our new maximum likelihood estimator can be used to measure the cluster-mass cross-correlation functions at different redshifts, probing the evolution of dark energy.

Week of Friday April 25

http://arxiv.org/abs/0804.0799

Constraining Anisotropic Baryon Oscillations (to be discussed by Nikhil)

Nikhil Padmanabhan, Martin White

We present an analysis of anisotropic baryon acoustic oscillations and elucidate how a mis-estimation of the cosmology, which leads to incorrect values of the angular diameter distance, d_A, and Hubble parameter, H, manifest themselves in changes to the monopole and quadrupole power spectrum of biased tracers of the density field. Previous work has focused on the monopole power spectrum, and shown that the isotropic “dilation” combination d_A^2/H is robustly constrained by an overall shift in the scale of the baryon feature. We extend this by demonstrating that the quadrupole power spectrum is sensitive to an anisotropic “warping” mode d_A H, allowing one to break the degeneracy between d_A and H. We describe a method for measuring this warping, explicitly marginalizing over the form of redshift space distortions. We verify this method on N-body simulations and estimate that d_A H can be measured with a fractional accuracy of ~ 3/sqrt(V) % where the survey volume is estimated in (Gpc/h)^3.

http://arxiv.org/abs/0803.2706 (to be discussed by Oliver)

Toward a halo mass function for precision cosmology: the limits of universality

Jeremy L Tinker, Andrey V Kravtsov, Anatoly Klypin, Kevork Abazajian, Michael S Warren, Gustavo Yepes, Stefan Gottlober, Daniel E Holz

We measure the mass function of dark matter halos in a large set of collisionless cosmological simulations of flat LCDM cosmology and investigate its evolution at z<~2. Halos are identified as isolated density peaks, and their masses are measured within a series of radii enclosing specific overdensities. We argue that these spherical overdensity masses are more directly linked to cluster observables than masses measured using the friends-of-friends algorithm (FOF), and are therefore preferable for accurate forecasts of halo abundances. Our simulation set allows us to calibrate the mass function at z=0 for virial masses in the range 10^{11} Msol/h < M < 10^{15} Msol/h, to <~ 5%. We derive fitting functions for the halo mass function in this mass range for a wide range of overdensities, both at z=0 and earlier epochs. In addition to these formulae, which improve on previous approximations by 10-20%, our main finding is that the mass function cannot be represented by a universal fitting function at this level of accuracy. The amplitude of the “universal” function decreases monotonically by ~20-50%, depending on the mass definition, from z=0 to 2.5. We also find evidence for redshift evolution in the overall shape of the mass function.

Week of Friday April 18

Unfortunately we may not be able to have a discussion this day because of the Northern California meeting in Stanford.

Week of Friday April 11

cancelled due to widespread unavailability of participants

Week of Friday April 4 http://xxx.lanl.gov/abs/0804.0233 (NP)

What is the best way to measure baryonic acoustic oscillations?

Ariel G. Sanchez, Carlton M. Baugh, Raul Angulo

Oscillations in the baryon-photon fluid prior to recombination imprint different signatures on the power spectrum and correlation function of matter fluctuations. The measurement of these features using galaxy surveys has been proposed as means to determine the equation of state of the dark energy. The accuracy required to achieve competitive constraints demands an extremely good understanding of systematic effects which change the baryonic acoustic oscillation (BAO) imprint. We use 50 very large volume N-body simulations to investigate the BAO signature in the two-point correlation function. The location of the BAO bump does not correspond to the sound horizon scale at the level of accuracy required by future measurements, even before any dynamical or statistical effects are considered. Careful modelling of the correlation function is therefore required to extract the cosmological information encoded on large scales. We find that the correlation function is less affected by scale dependent effects than the power spectrum. This means that information from the large scale shape of the correlation function, in addition to the form of the BAO peak, can be used to provide robust constraints on cosmological parameters. The correlation function therefore provides a better constraint on the distance scale (~ 50% smaller errors) than the more conservative approach required when using the power spectrum.

http://arxiv.org/abs/0803.3453 (posted by oliver)

Halo Assembly Bias in Hierarchical Structure Formation

Neal Dalal (CITA), Martin White (Berkeley), J. Richard Bond (CITA), Alexander Shirokov (CITA)

We investigate the origin of halo assembly bias, the dependence of halo clustering on assembly history. We relate halo assembly to peak properties measured in the Lagrangian space of the initial linear Gaussian random density field, and show how these same Lagrangian properties determine large-scale bias. We focus on the two regimes where assembly bias has been observed to be significant: at masses very large and very small compared to the nonlinear mass scale. At high masses, we show that assembly bias is expected from the statistics of the peaks of Gaussian random fluctuations, and we show that the extent of assembly bias found in N-body simulations of rare halos is in excellent agreement with our theoretical prediction. At low masses, we argue that assembly bias largely arises from a sub-population of low mass halos whose mass accretion has ceased. Due to their arrested development, these halos naturally become unbiased, in contrast to their anti-biased peers. We show that a simple toy model incorporating these effects can roughly reproduce the bias trends found in N-body simulations.

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