Weak Gravitational Lensing by a Sample of X-Ray Luminous Clusters of Galaxies -- II. Comparison with Virial Masses

Dynamic velocity dispersion and mass estimates are given for a sample of five X-ray luminous rich clusters of galaxies at intermediate redshifts (z~0.3) drawn from a sample of 39 clusters for which we have obtained gravitational lens mass estimates. The velocity dispersions are determined from between 9 and 20 redshifts measured with the LDSS spectrograph of the William Herschel Telescope, and virial radii are determined from imaging using the UH8K mosaic CCD camera on the University of Hawaii 2.24m telescope. Including clusters with velocity dispersions taken from the literature, we have velocity dispersion estimates for 12 clusters in our gravitational lensing sample. For this sample we compare the dynamical velocity dispersion estimates with our estimates of the velocity dispersions made from gravitational lensing by fitting a singular isothermal sphere profile to the observed tangential weak lensing distortion as a function of radius. In all but two clusters, we find a good agreement between the velocity dispersion estimates based on spectroscopy and on weak lensing.Comment: 9 pages, 4 figures, accepted for publication in ApJ. Version in emulateapj format with only minor change

Radial Redshift Space Distortions

The radial component of the peculiar velocities of galaxies cause displacements in their positions in redshift space. We study the effect of the peculiar velocities on the linear redshift space two point correlation function. Our analysis takes into account the radial nature of the redshift space distortions and it highlights the limitations of the plane parallel approximation. We consider the problem of determining the value of \beta and the real space two point correlation function from the linear redshift space two point correlation function. The inversion method proposed here takes into account the radial nature of the redshift space distortions and can be applied to magnitude limited redshift surveys that have only partial sky coverage.Comment: 26 pages including 11 figures, to appear in Ap

The Correlation Function in Redshift Space: General Formula with Wide-angle Effects and Cosmological Distortions

A general formula for the correlation function in redshift space is derived in linear theory. The formula simultaneously includes wide-angle effects and cosmological distortions. The formula is applicable to any pair with arbitrary angle $\theta$ between lines of sight, and arbitrary redshifts, $z_1$, $z_2$, which are not necessarily small. The effects of the spatial curvature both on geometry and on fluctuation spectrum are properly taken into account, and thus our formula holds in a Friedman-Lema\^{\i}tre universe with arbitrary cosmological parameters $\Omega_0$ and $\lambda_0$. We illustrate the pattern of the resulting correlation function with several models, and also show that validity region of the conventional distant observer approximation is $\theta \le 10^\circ$.Comment: 45 pages including 9 figures, To Appear in Astrophys. J. 535 (2000

CMB component separation by parameter estimation

We propose a solution to the CMB component separation problem based on standard parameter estimation techniques. We assume a parametric spectral model for each signal component, and fit the corresponding parameters pixel by pixel in a two-stage process. First we fit for the full parameter set (e.g., component amplitudes and spectral indices) in low-resolution and high signal-to-noise ratio maps using MCMC, obtaining both best-fit values for each parameter, and the associated uncertainty. The goodness-of-fit is evaluated by a chi^2 statistic. Then we fix all non-linear parameters at their low-resolution best-fit values, and solve analytically for high-resolution component amplitude maps. This likelihood approach has many advantages: The fitted model may be chosen freely, and the method is therefore completely general; all assumptions are transparent; no restrictions on spatial variations of foreground properties are imposed; the results may be rigorously monitored by goodness-of-fit tests; and, most importantly, we obtain reliable error estimates on all estimated quantities. We apply the method to simulated Planck and six-year WMAP data based on realistic models, and show that separation at the muK level is indeed possible in these cases. We also outline how the foreground uncertainties may be rigorously propagated through to the CMB power spectrum and cosmological parameters using a Gibbs sampling technique.Comment: 20 pages, 10 figures, submitted to ApJ. For a high-resolution version, see http://www.astro.uio.no/~hke/docs/eriksen_et_al_fgfit.p

The Radio-Optical Correlation in Steep-Spectrum Quasars

Using complete samples of steep-spectrum quasars, we present evidence for a correlation between radio and optical luminosity which is not caused by selection effects, nor caused by an orientation dependence (such as relativistic beaming), nor a byproduct of cosmic evolution. We argue that this rules out models of jet formation in which there are no parameters in common with the production of the optical continuum. This is arguably the most direct evidence to date for a close link between accretion onto a black hole and the fuelling of relativistic jets. The correlation also provides a natural explanation for the presence of aligned optical/radio structures in only the most radio luminous high-redshift galaxies.Comment: MNRAS in press. Uses BoxedEPS (included

Engaging students in scenario-based assessment for final exams

We present our approaches to enhancing the authenticity of final exams across large first-year first semester biology units of cohort sizes between 300-1200 students. Historically exams were primarily used as an instrument that mainly assessed knowledge retention with limited provision of feedback to students. The necessity to shift to online learning during the height of the COVID-19 pandemic provided us with a challenging, yet opportune moment to transform our final examinations into an authentic learning experience for undergraduate biology students. We placed a large focus on integrating scenario-based questions in the final exam thereby assessing students’ ability to apply knowledge to real-world contexts. To enhance engagement with the assessment, we also provided personalised feedback for each student. With additional challenges around access to artificial intelligence and academic integrity, we share our experiences returning to in-person final examinations and evaluate the relevancy and benefits of scenario-based questions for student assessment and learning. We also share our approaches to feedforwarding initiatives to prepare students for examinations that is different to what most students would have experienced in their secondary schooling

Correlations of Richness and Global Properties in Galaxy Clusters

We measure the optical richness of galaxy clusters from the CNOC1 cluster redshift survey using the galaxy-cluster center correlation amplitude B_gc. We show that the B_gc values measured using photometric catalogs are consistent with those derived from redshift catalogs, indicating that richness can be measured reliably from photometric data alone, even at moderate redshifts of \~0.6. We establish the correlations between optical richness and other important attributes of a galaxy cluster, such as velocity dispersion, mass, radius, and X-ray temperature and luminosity. We find that the scaling relations of these quantities with richness are entirely consistent with those derived by assuming a simple mass density profile at 0.5 Mpc of rho~r^{-1.8}. The excellent correlations between B_gc and velocity dispersion and X-ray temperature allow one to use richness, an easily measurable quantity using relatively shallow optical imaging data alone, as a predictor of these quantities at moderate redshifts. The B_gc parameter can be used to estimate the velocity dispersion of a cluster to a precision of approximately 15% (~+/-100 km/s), and X-ray temperature to about 20%. Similar correlations, but with larger scatter, are also obtained between richness and the characteristic radius and mass of the clusters. We compare the relative merits of B_gc, T_x, and L_x as predictors of the dynamical mass, and find that they are comparable, providing estimates at an accuracy of ~30%. We also perform similar analyses of correlations between richness and velocity dispersion, T_x and L_x with a sample of low-redshift Abell clusters and find consistent results, but with larger scatter, which may be the result of a less homogeneous database, or sample-dependent effects.Comment: 18 pages. Accepted; to appear in ApJ, March 200