Measuring angular diameter distances of strong gravitational lenses

The distance-redshift relation plays a fundamental role in constraining cosmological models. In this paper, we show that measurements of positions and time delays of strongly lensed images of a background galaxy, as well as those of the velocity dispersion and mass profile of a lens galaxy, can be combined to extract the angular diameter distance of the lens galaxy. Physically, as the velocity dispersion and the time delay give a gravitational potential ($GM/r$) and a mass ($GM$) of the lens, respectively, dividing them gives a physical size ($r$) of the lens. Comparing the physical size with the image positions of a lensed galaxy gives the angular diameter distance to the lens. A mismatch between the exact locations at which these measurements are made can be corrected by measuring a local slope of the mass profile. We expand on the original idea put forward by Paraficz and Hjorth, who analyzed singular isothermal lenses, by allowing for an arbitrary slope of a power-law spherical mass density profile, an external convergence, and an anisotropic velocity dispersion. We find that the effect of external convergence cancels out when dividing the time delays and velocity dispersion measurements. We derive a formula for the uncertainty in the angular diameter distance in terms of the uncertainties in the observables. As an application, we use two existing strong lens systems, B1608+656 ($z_{\rm L}=0.6304$) and RXJ1131$-$1231 ($z_{\rm L}=0.295$), to show that the uncertainty in the inferred angular diameter distances is dominated by that in the velocity dispersion, $\sigma^2$, and its anisotropy. We find that the current data on these systems should yield about 16% uncertainty in $D_A$ per object. This improves to 13% when we measure $\sigma^2$ at the so-called sweet-spot radius. Achieving 7% is possible if we can determine $\sigma^2$ with 5% precision.Comment: Accepted to JCA

A Study of the Dark Core in A520 with Hubble Space Telescope: The Mystery Deepens

We present a Hubble Space Telescope/Wide Field Planetary Camera 2 weak-lensing study of A520, where a previous analysis of ground-based data suggested the presence of a dark mass concentration. We map the complex mass structure in much greater detail leveraging more than a factor of three increase in the number density of source galaxies available for lensing analysis. The "dark core" that is coincident with the X-ray gas peak, but not with any stellar luminosity peak is now detected with more than 10 sigma significance. The ~1.5 Mpc filamentary structure elongated in the NE-SW direction is also clearly visible. Taken at face value, the comparison among the centroids of dark matter, intracluster medium, and galaxy luminosity is at odds with what has been observed in other merging clusters with a similar geometric configuration. To date, the most remarkable counter-example might be the Bullet Cluster, which shows a distinct bow-shock feature as in A520, but no significant weak-lensing mass concentration around the X-ray gas. With the most up-to-date data, we consider several possible explanations that might lead to the detection of this peculiar feature in A520. However, we conclude that none of these scenarios can be singled out yet as the definite explanation for this puzzle.Comment: Published in ApJ. Figures are slightly degraded to meet the size limi

Time-delay Cosmography: Increased Leverage with Angular Diameter Distances

Strong lensing time-delay systems constrain cosmological parameters via the so-called time-delay distance and the angular diameter distance to the lens. In previous studies, only the former information was used. In this paper, we show that the cosmological constraints improve significantly when the latter information is also included. Specifically, the angular diameter distance plays a crucial role in breaking the degeneracy between the curvature of the Universe and the time-varying equation of state of dark energy. Using a mock sample of 55 bright quadruple lens systems based on expectations for ongoing/future imaging surveys, we find that adding the angular diameter distance information to the time-delay distance information and the cosmic microwave background data of Planck improves the constraint on the constant equation of state by 30%, on the time variation in the equation of state by a factor of two, and on the Hubble constant in the flat $\Lambda$CDM model by a factor of two. Therefore, previous forecasts for the statistical power of time-delay systems were significantly underestimated, i.e., time-delay systems are more powerful than previously appreciated.Comment: [v2] 18 pages, 12 figures, submitted to JCAP. An error in the fisher matrix for SNIa fixed; conclusions unchange

Hubble Space Telescope Weak-lensing Study of the Galaxy Cluster XMMU J2235.3-2557 at z=1.4: A Surprisingly Massive Galaxy Cluster when the Universe is One-third of its Current Age

We present a weak-lensing analysis of the z=1.4 galaxy cluster XMMU J2235.3-2557, based on deep Advanced Camera for Surveys images. Despite the observational challenge set by the high redshift of the lens, we detect a substantial lensing signal at the >~ 8 sigma level. This clear detection is enabled in part by the high mass of the cluster, which is verified by our both parametric and non-parametric estimation of the cluster mass. Assuming that the cluster follows a Navarro-Frenk-White mass profile, we estimate that the projected mass of the cluster within r=1 Mpc is (8.5+-1.7) x 10^14 solar mass, where the error bar includes the statistical uncertainty of the shear profile, the effect of possible interloping background structures, the scatter in concentration parameter, and the error in our estimation of the mean redshift of the background galaxies. The high X-ray temperature 8.6_{-1.2}^{+1.3} keV of the cluster recently measured with Chandra is consistent with this high lensing mass. When we adopt the 1-sigma lower limit as a mass threshold and use the cosmological parameters favored by the Wilkinson Microwave Anisotropy Probe 5-year (WMAP5) result, the expected number of similarly massive clusters at z >~ 1.4 in the 11 square degree survey is N ~ 0.005. Therefore, the discovery of the cluster within the survey volume is a rare event with a probability < 1%, and may open new scenarios in our current understanding of cluster formation within the standard cosmological model.Comment: Accepted to ApJ for publication. 40 pages and 14 figure

Role of allostatic load and health behaviours in explaining socioeconomic disparities in mortality: a structural equation modelling approach

BACKGROUND: The relationship between socioeconomic status and mortality has been well established; however, the extent to which biological factors mediate this relationship is less clear, and empirical evidence from non-Western settings is limited. Allostasis, a cumulative measure of physiological dysregulation, has been proposed as the underlying mechanism linking socioeconomic status to adverse health outcomes. The current study aimed to ascertain the contribution of allostatic load (AL) and health behaviours to socioeconomic inequalities in mortality among Korean adults. METHODS: The sample comprised 70 713 middle-aged and older-aged adults, aged 40-79 years from the Korean Metabolic Syndrome Mortality Study. Using structural equation modelling (SEM), mediation analyses were performed to estimate the effects of socioeconomic position (SEP) on mortality over the follow-up and the extent to which AL, physical exercise and non-smoking status mediate the association between SEP and mortality. RESULTS: A total of 5618 deaths (7.9%) occurred during the mean follow-up of 15.2 years (SD 2.9). SEM confirmed a direct significant effect of SEP on mortality, as well as significant indirect paths through AL, physical exercise and non-smoking status. CONCLUSIONS: Our findings provide support for the mediating role of AL and health behaviours in the link between SEP and mortality. Policies designed to reduce social disparities in mortality in the long term should primarily focus on reducing stress and promoting healthy lifestyles among the socially disadvantaged groups. Future studies should further assess the role of other mediators such as psychosocial factors, which may contribute to socioeconomic inequalities in mortality

Principal Component Analysis of the Time- and Position-Dependent Point Spread Function of the Advanced Camera for Surveys

We describe the time- and position-dependent point spread function (PSF) variation of the Wide Field Channel (WFC) of the Advanced Camera for Surveys (ACS) with the principal component analysis (PCA) technique. The time-dependent change is caused by the temporal variation of the $HST$ focus whereas the position-dependent PSF variation in ACS/WFC at a given focus is mainly the result of changes in aberrations and charge diffusion across the detector, which appear as position-dependent changes in elongation of the astigmatic core and blurring of the PSF, respectively. Using >400 archival images of star cluster fields, we construct a ACS PSF library covering diverse environments of the $HST$ observations (e.g., focus values). We find that interpolation of a small number ($\sim20$) of principal components or ``eigen-PSFs'' per exposure can robustly reproduce the observed variation of the ellipticity and size of the PSF. Our primary interest in this investigation is the application of this PSF library to precision weak-lensing analyses, where accurate knowledge of the instrument's PSF is crucial. However, the high-fidelity of the model judged from the nice agreement with observed PSFs suggests that the model is potentially also useful in other applications such as crowded field stellar photometry, galaxy profile fitting, AGN studies, etc., which similarly demand a fair knowledge of the PSFs at objects' locations. Our PSF models, applicable to any WFC image rectified with the Lanczos3 kernel, are publicly available.Comment: Accepted to PASP. To appear in December issue. Figures are degraded to meet the size limit. High-resolution version can be downloaded at http://acs.pha.jhu.edu/~mkjee/acs_psf/acspsf.pd

Fear extinction across development: The involvement of the medial prefrontal cortex as assessed by temporary inactivation and immunohistochemistry

Extinction in adult animals, including humans, appears to involve the medial prefrontal cortex (mPFC). However, the role of mPFC in extinction across development has not yet been studied. Given several recent demonstrations of developmental differences in extinction of conditioned fear at a behavioral level, different neural circuitries may mediate fear extinction across development. In all experiments, noise conditioned stimulus (CS) and shock unconditioned stimulus (US) were used. In experiment 1A, temporary unilateral inactivation of the mPFC during extinction training impaired long-term extinction the following day in postnatal day 24 (P24) rats but not in P17 rats. In experiment 1B, bilateral inactivation of them PFC again failed to disrupt long-term extinction in P17 rats. In experiment 2, extinction training increased phosphorylated mitogen-activated protein kinase (pMAPK) in the mPFC for P24 rats but not for P17 rats, whereas rats of both ages displayed elevated pMAPK in the amygdala. Across both ages, "not trained," "reactivated, " and "no extinction" control groups expressed very low numbers of pMAPK immunoreactive (IR) neurons across both neural structures. This result indicates that the mere conditioning experience, the exposure to the CS, or the expression of CS-elicited fear in and of itself is not sufficient to explain the observed increase in pMAPK-IR neurons in them PFC and/or the amygdala after extinction. Together, these findings show that extinction in P17 rats does not involve the mPFC, which has important theoretical and clinical implications for the treatment of anxiety disorders in humans

Fear extinction across development: The involvement of the medial prefrontal cortex as assessed by temporary inactivation and immunohistochemistry

Extinction in adult animals, including humans, appears to involve the medial prefrontal cortex (mPFC). However, the role of mPFC in extinction across development has not yet been studied. Given several recent demonstrations of developmental differences in extinction of conditioned fear at a behavioral level, different neural circuitries may mediate fear extinction across development. In all experiments, noise conditioned stimulus (CS) and shock unconditioned stimulus (US) were used. In experiment 1A, temporary unilateral inactivation of the mPFC during extinction training impaired long-term extinction the following day in postnatal day 24 (P24) rats but not in P17 rats. In experiment 1B, bilateral inactivation of them PFC again failed to disrupt long-term extinction in P17 rats. In experiment 2, extinction training increased phosphorylated mitogen-activated protein kinase (pMAPK) in the mPFC for P24 rats but not for P17 rats, whereas rats of both ages displayed elevated pMAPK in the amygdala. Across both ages, "not trained," "reactivated, " and "no extinction" control groups expressed very low numbers of pMAPK immunoreactive (IR) neurons across both neural structures. This result indicates that the mere conditioning experience, the exposure to the CS, or the expression of CS-elicited fear in and of itself is not sufficient to explain the observed increase in pMAPK-IR neurons in them PFC and/or the amygdala after extinction. Together, these findings show that extinction in P17 rats does not involve the mPFC, which has important theoretical and clinical implications for the treatment of anxiety disorders in humans

Scaling Relations and Overabundance of Massive Clusters at z>~1 from Weak-Lensing Studies with HST

We present weak gravitational lensing analysis of 22 high-redshift (z >~1) clusters based on Hubble Space Telescope images. Most clusters in our sample provide significant lensing signals and are well detected in their reconstructed two-dimensional mass maps. Combining the current results and our previous weak-lensing studies of five other high-z clusters, we compare gravitational lensing masses of these clusters with other observables. We revisit the question whether the presence of the most massive clusters in our sample is in tension with the current LambdaCDM structure formation paradigm. We find that the lensing masses are tightly correlated with the gas temperatures and establish, for the first time, the lensing mass-temperature relation at z >~ 1. For the power law slope of the M-TX relation (M propto T^{\alpha}), we obtain \alpha=1.54 +/- 0.23. This is consistent with the theoretical self-similar prediction \alpha=3/2 and with the results previously reported in the literature for much lower redshift samples. However, our normalization is lower than the previous results by 20-30%, indicating that the normalization in the M-TX relation might evolve. After correcting for Eddington bias and updating the discovery area with a more conservative choice, we find that the existence of the most massive clusters in our sample still provides a tension with the current Lambda CDM model. The combined probability of finding the four most massive clusters in this sample after marginalization over current cosmological parameters is less than 1%.Comment: ApJ in press. See http://www.supernova.lbl.gov for additional information pertaining to the HST Cluster SN Surve