Effects of center offset and noise on weak-lensing derived concentration-mass relation of dark matter halos

With the halo catalog from the {\it Millennium Simulation}, we analyze the weak-lensing measured density profiles for clusters of galaxies, paying attention to the determination of the concentration-mass ($c$-$M$) relation which can be biased by the center offset, selection effect, and shape noise from intrinsic ellipticities of background galaxies. Several different methods of locating the center of a cluster from weak-lensing effects alone are explored. We find that, for intermediate redshift clusters, the highest peak from our newly proposed two-scale smoothing method applied to the reconstructed convergence field, first with a smoothing scale of $2^\prime$ and then $0\overset{\prime}{.}5$, corresponds best to the true center. Assuming the parameterized Navarro-Frenk-White profile, we fit the reduced tangential shear signals around different centers identified by different methods. It is shown that, for the ensemble median values, a center offset larger than one scale radius $r_s$ can bias the derived mass and concentration significantly lower than the true values, especially for low-mass halos. However, the existence of noise can compensate for the offset effect and reduce the systematic bias, although the scatter of mass and concentration becomes considerably larger. Statistically, the bias effect of center offset on the $c$-$M$ relation is insignificant if an appropriate center finding method is adopted. On the other hand, noise from intrinsic ellipticities can bias the $c$-$M$ relation derived from a sample of weak-lensing analyzed clusters if a simple $\chi^2$ fitting method is used. To properly account for the scatter and covariance between $c$ and $M$, we apply a Bayesian method to improve the statistical analysis of the $c$-$M$ relation. It is shown that this new method allows us to derive the $c$-$M$ relation with significantly reduced biases.Comment: Accepted for Publication in ApJ. 25 pages, 14 figures. Updated to match the published versio

The Effects of Relativistic Corrections on Cosmological Parameter Estimations from SZE Cluster Surveys

Sunyaev-Zel'dovich Effect (SZE) cluster surveys are anticipated to yield tight constraints on cosmological parameters such as the equation of state of dark energy. In this paper, we study the impact of relativistic corrections of the thermal SZE on the cluster number counts expected from a cosmological model and thus, assuming that other cosmological parameters are known to high accuracies, on the determination of the $w$ parameter and $\sigma_8$ from a SZE cluster survey, where $w=p/\rho$ with $p$ the pressure and $\rho$ the density of dark energy, and $\sigma_8$ is the rms of the extrapolated linear density fluctuation smoothed over $8\hbox{Mpc}h^{-1}$. For the purpose of illustrating the effects of relativistic corrections, our analyses mainly focus on $\nu=353 \hbox{GHz}$ and $S_{lim}=30\hbox{mJy}$, where $\nu$ and $S_{lim}$ are the observing frequency and the flux limit of a survey, respectively. These observing parameters are relevant to the {\it Planck} survey. It is found that from two measurable quantities, the total number of SZE clusters and the number of clusters with redshift $z\ge 0.5$, $\sigma_8$ and $w$ can be determined to a level of $\pm 1$ and $\pm 8$, respectively, with $1\sigma$ uncertainties from a survey of $10000\hbox{deg}^2$. Relativistic effects are important in determining the central values of $\sigma_8$ and $w$. If we choose the two quantities calculated relativistically from the flat cosmological model with $\sigma_8=0.8284$ and $w=-0.75$ as input, the derived $\sigma_8$ and $w$ would be 0.819 and -0.81, respectively, if relativistic effects are wrongly neglected. The location of the resulting $\sigma_8$ and $w$ in the $\sigma_8-w$ plane is outside the $3\sigma$ region around the real central $\sigma_8$ and $w$.Comment: ApJ in pres

Dynamical evolutin of quintessence dark energy in collapsing dark matter halos

In this paper, we analyze the dynamical evolution of quintessence dark energy induced by the collapse of dark matter halos. Different from other previous studies, we develop a numerical strategy which allows us to calculate the dark energy evolution for the entire history of the spherical collapse of dark matter halos, without the need of separate treatments for linear, quasi-linear and nonlinear stages of the halo formation. It is found that the dark energy perturbations evolve with redshifts, and their specific behaviors depend on the quintessence potential as well as the collapsing process. The overall energy density perturbation is at the level of $10^{-6}$ for cluster-sized halos. The perturbation amplitude decreases with the decrease of the halo mass. At a given redshift, the dark energy perturbation changes with the radius to the halo center, and can be either positive or negative depending on the contrast of $\partial_t \phi$, $\partial_r \phi$ and $\phi$ with respect to the background, where $\phi$ is the quintessence field. For shells where the contrast of $\partial_r \phi$ is dominant, the dark energy perturbation is positive and can be as high as about $10^{-5}$.Comment: 11 pages, 13 figure

Energy, angular momentum and wave action associated with density waves in a rotating magnetized gas disc

Both fast and slow magnetohydrodynamic (MHD) density waves propagating in a thin rotating magnetized gas disc are investigated. In the tight-winding or WKBJ regime, the radial variation of MHD density-wave amplitude during wave propagation is governed by the conservation of wave action surface density N which travels at a relevant radial group speed Cg. The wave energy surface density ℰ and the wave angular momentum surface density J are related to N by ℰ=ωN and J=mN respectively, where ω is the angular frequency in an inertial frame of reference and the integer m, proportional to the azimuthal wavenumber, corresponds to the number of spiral arms. Consequently, both wave energy and angular momentum are conserved for spiral MHD density waves. For both fast and slow MHD density waves, net wave energy and angular momentum are carried outward or inward for trailing or leading spirals, respectively. The wave angular momentum flux contains separate contributions from gravity torque, advective transport and magnetic torque. While the gravity torque plays an important role, the latter two can be of comparable magnitudes to the former. Similar to the role of gravity torque, the part of MHD wave angular momentum flux by magnetic torque (in the case of either fast or slow MHD density waves) propagates outward or inward for trailing or leading spirals, respectively. From the perspective of global energetics in a magnetized gas sheet in rotation, trailing spiral structures of MHD density waves are preferred over leading ones. With proper qualifications, the generation and maintenance as well as transport properties of MHD density waves in magnetized spiral galaxies are discusse

Constraints on Dark Energy Models Including Gamma Ray Bursts

In this paper we analyze the constraints on the property of dark energy from cosmological observations. Together with SNe Ia Gold sample, WMAP, SDSS and 2dFGRS data, we include 69 long Gamma-Ray Bursts (GRBs) data in our study and perform global fitting using Markov Chain Monte Carlo (MCMC) technique. Dark energy perturbations are explicitly considered. We pay particular attention to the time evolution of the equation of state of dark energy parameterized as $w_{DE}=w_0+w_a(1-a)$ with $a$ the scale factor of the universe, emphasizing the complementarity of high redshift GRBs to other cosmological probes. It is found that the constraints on dark energy become stringent by taking into account high redshift GRBs, especially for $w_a$, which delineates the evolution of dark energy.Comment: 7 pages and 3 figures. Replaced with version accepted for publication in Phys. Lett.

An analytical model of the large neutral regions during the late stage of reionization

In this paper we investigate the nature and distribution of large neutral regions during the late epoch of reionization. In the "bubble model" of reionization, the mass distribution of large ionized regions ("bubbles") during the early stage of reionization is obtained by using the excursion set model, where the ionization of a region corresponds to the first up-crossing of a barrier by random trajectories. We generalize this idea, and develop a method to predict the distribution of large scale neutral regions during the late stage of reionization, taking into account the ionizing background after the percolation of HII regions. The large scale neutral regions which we call "neutral islands" are not individual galaxies or minihalos, but larger regions where fewer galaxies formed and hence ionized later, and they are identified in the excursion set model with the first down-crossings of the island barrier. Assuming that the consumption rate of ionizing background photons is proportional to the surface area of the neutral islands, we obtained the size distribution of the neutral islands. We also take the "bubbles-in-island" effect into account by considering the conditional probability of up-crossing a bubble barrier after down-crossing the island barrier. We find that this effect is very important. An additional barrier is set to avoid islands being percolated through. We find that there is a characteristic scale for the neutral islands, while the small islands are rapidly swallowed up by the ionizing background, this characteristic scale does not change much as the reionization proceeds.Comment: 33 pages, 11 figures, accepted by The Astrophysical Journa