The non-Gaussianity of the cosmic shear likelihood - or: How odd is the Chandra Deep Field South?

(abridged) We study the validity of the approximation of a Gaussian cosmic shear likelihood. We estimate the true likelihood for a fiducial cosmological model from a large set of ray-tracing simulations and investigate the impact of non-Gaussianity on cosmological parameter estimation. We investigate how odd the recently reported very low value of $\sigma_8$ really is as derived from the \textit{Chandra} Deep Field South (CDFS) using cosmic shear by taking the non-Gaussianity of the likelihood into account as well as the possibility of biases coming from the way the CDFS was selected. We find that the cosmic shear likelihood is significantly non-Gaussian. This leads to both a shift of the maximum of the posterior distribution and a significantly smaller credible region compared to the Gaussian case. We re-analyse the CDFS cosmic shear data using the non-Gaussian likelihood. Assuming that the CDFS is a random pointing, we find $\sigma_8=0.68_{-0.16}^{+0.09}$ for fixed $\Omega_{\rm m}=0.25$. In a WMAP5-like cosmology, a value equal to or lower than this would be expected in $\approx 5$ of the times. Taking biases into account arising from the way the CDFS was selected, which we model as being dependent on the number of haloes in the CDFS, we obtain $\sigma_8 = 0.71^{+0.10}_{-0.15}$. Combining the CDFS data with the parameter constraints from WMAP5 yields $\Omega_{\rm m} = 0.26^{+0.03}_{-0.02}$ and $\sigma_8 = 0.79^{+0.04}_{-0.03}$ for a flat universe.Comment: 18 pages, 16 figures, accepted for publication in A&A; New Bayesian treatment of field selection bia

Calibration of colour gradient bias in shear measurement using HST/CANDELS data

Accurate shape measurements are essential to infer cosmological parameters from large area weak gravitational lensing studies. The compact diffraction-limited point-spread function (PSF) in space-based observations is greatly beneficial, but its chromaticity for a broad band observation can lead to new subtle effects that could hitherto be ignored: the PSF of a galaxy is no longer uniquely defined and spatial variations in the colours of galaxies result in biases in the inferred lensing signal. Taking Euclid as a reference, we show that this colourgradient bias (CG bias) can be quantified with high accuracy using available multi-colour Hubble Space Telescope (HST) data. In particular we study how noise in the HST observations might impact such measurements and find this to be negligible. We determine the CG bias using HST observations in the F606W and F814W filters and observe a correlation with the colour, in line with expectations, whereas the dependence with redshift is weak. The biases for individual galaxies are generally well below 1%, which may be reduced further using morphological information from the Euclid data. Our results demonstrate that CG bias should not be ignored, but it is possible to determine its amplitude with sufficient precision, so that it will not significantly bias the weak lensing measurements using Euclid data

Cosmic shear analysis of archival HST/ACS data: I. Comparison of early ACS pure parallel data to the HST/GEMS Survey

This is the first paper of a series describing our measurement of weak lensing by large-scale structure using archival observations from the Advanced Camera for Surveys (ACS) on board the Hubble Space Telescope (HST). In this work we present results from a pilot study testing the capabilities of the ACS for cosmic shear measurements with early parallel observations and presenting a re-analysis of HST/ACS data from the GEMS survey and the GOODS observations of the Chandra Deep Field South (CDFS). We describe our new correction scheme for the time-dependent ACS PSF based on observations of stellar fields. This is currently the only technique which takes the full time variation of the PSF between individual ACS exposures into account. We estimate that our PSF correction scheme reduces the systematic contribution to the shear correlation functions due to PSF distortions to < 2*10^{-6} for galaxy fields containing at least 10 stars. We perform a number of diagnostic tests indicating that the remaining level of systematics is consistent with zero for the GEMS and GOODS data confirming the success of our PSF correction scheme. For the parallel data we detect a low level of remaining systematics which we interpret to be caused by a lack of sufficient dithering of the data. Combining the shear estimate of the GEMS and GOODS observations using 96 galaxies arcmin^{-2} with the photometric redshift catalogue of the GOODS-MUSIC sample, we determine a local single field estimate for the mass power spectrum normalisation sigma_{8,CDFS}=0.52^{+0.11}_{-0.15} (stat) +/- 0.07 (sys) (68% confidence assuming Gaussian cosmic variance) at fixed Omega_m=0.3 for a LambdaCDM cosmology. We interpret this exceptionally low estimate to be due to a local under-density of the foreground structures in the CDFS.Comment: Version accepted for publication in Astronomy & Astrophysics with 28 pages, 25 figures. A version with full resolution figures can be downloaded from http://www.astro.uni-bonn.de/~schrabba/papers/cosmic_shear_acs1_v2.pd

GaBoDS: The Garching-Bonn Deep Survey - III. Lyman-Break Galaxies in the Chandra Deep Field South

We present first results of our search for high-redshift galaxies in deep CCD mosaic images. As a pilot study for a larger survey, very deep images of the Chandra Deep Field South (CDFS), taken withWFI@MPG/ESO2.2m, are used to select large samples of 1070 U-band and 565 B-band dropouts with the Lyman-break method. The data of these Lyman-break galaxies are made public as an electronic table. These objects are good candidates for galaxies at z~3 and z~4 which is supported by their photometric redshifts. The distributions of apparent magnitudes and the clustering properties of the two populations are analysed, and they show good agreement to earlier studies. We see no evolution in the comoving clustering scale length from z~3 to z~4. The techniques presented here will be applied to a much larger sample of U-dropouts from the whole survey in near future.Comment: 11 pages, 11 figures, replaced with version accepted by A&A. Minor changes and tabular appendix with LBG catalogues. Version with full resolution figures available at http://www.astro.uni-bonn.de/~hendrik/2544.pd

The Hidden Fortress: Structure and substructure of the complex strong lensing cluster SDSS J1029+2623

We present Hubble Space Telescope (HST) ACS and WFC3 observations of SDSS J1029+2623, a three-image quasar lens system produced by a foreground cluster at z=0.584. Our strong lensing analysis reveals 6 additional multiply imaged galaxies. We confirm the complex nature of the mass distribution of the lensing cluster, with a bimodal distribution which deviates from the Chandra X-ray SB distribution. The Einstein radius is estimated to be \theta_E=15.2" \pm 0.5" for the quasar redshift of z=2.197. We derive a radial mass distribution from the combination of strong lensing, HST/ACS weak lensing, and Subaru/Suprime-cam weak lensing analysis results, finding a best-fit virial mass of M_vir=(1.5+0.40-0.35) \times 10^14 h^-1 M_sun and a concentration parameter of c_vir=25.7+14.1-7.5. The lensing mass estimate at the outer radius is smaller than the X-ray mass estimate by a factor of ~2. We ascribe this large mass discrepancy to shock heating of the intracluster gas during a merger, which is also suggested by the complex mass and gas distributions and the high value of the concentration parameter. In the HST image, we also identify a probable galaxy, GX, in the vicinity of the faintest quasar image C. The inclusion of GX explains the anomalous flux ratios between the quasar images. The morphology of the highly elongated quasar host galaxy is also well reproduced. The best-fit model suggests large total magnifications of 30 for the quasar and 35 for the quasar host galaxy, and has an AB time delay consistent with the measured value. (Abridged)Comment: 13 pages, 12 figures, accepted for publication in MNRA

The impact of galaxy colour gradients on cosmic shear measurement

Cosmic shear has been identified as the method with the most potential to constrain dark energy. To capitalize on this potential, it is necessary to measure galaxy shapes with great accuracy, which in turn requires a detailed model for the image blurring by the telescope and atmosphere, the point spread function (PSF). In general, the PSF varies with wavelength and therefore the PSF integrated over an observing filter depends on the spectrum of the object. For a typical galaxy the spectrum varies across the galaxy image, thus the PSF depends on the position within the image. We estimate the bias on the shear due to such colour gradients by modelling galaxies using two co-centred, co-elliptical Sérsic profiles, each with a different spectrum. We estimate the effect of ignoring colour gradients and find the shear bias from a single galaxy can be very large depending on the properties of the galaxy. We find that halving the filter width reduces the shear bias by a factor of about 5. We show that, to the first order, tomographic cosmic shear two point statistics depend on the mean shear bias over the galaxy population at a given redshift. For a single broad filter, and averaging over a small galaxy catalogue from Simard et al., we find a mean shear bias which is subdominant to the predicted statistical errors for future cosmic shear surveys. However, the true mean shear bias may exceed the statistical errors, depending on how accurately the catalogue represents the observed distribution of galaxies in the cosmic shear survey. We then investigate the bias on the shear for two-filter imaging and find that the bias is reduced by at least an order of magnitude. Lastly, we find that it is possible to calibrate galaxies for which colour gradients were ignored using two-filter imaging of a fair sample of noisy galaxies, if the galaxy model is known. For a signal-to-noise ratio of 25 the number of galaxies required in each tomographic redshift bin is of the order of 10

Measuring the Stellar Masses of z~7 Galaxies with Spitzer Ultrafaint Survey Program (SURFS UP)

We present Spitzer/IRAC observations of nine $z'$-band dropouts highly magnified (2<mu<12) by the Bullet Cluster. We combine archival imaging with our Exploratory program (SURFS UP), which results in a total integration time of ~30 hr per IRAC band. We detect (>3sigma) in both IRAC bands the brightest of these high-redshift galaxies, with [3.6]=23.80+-0.28 mag, [4.5]=23.78+-0.25 mag, and (H-[3.6])=1.17+-0.32 mag. The remaining eight galaxies are undetected to [3.6]~26.4 mag and [4.5]~26.0 mag with stellar masses of ~5x10^7 M_sol. The detected galaxy has an estimated magnification of mu=12+-4, which implies this galaxy has an ultraviolet luminosity of L_1500~0.3 L*_{z=7} --- the lowest luminosity individual source detected in IRAC at z>7. By modeling the broadband photometry, we estimate the galaxy has an intrinsic star-formation rate of SFR~1.3 M_sol/yr and stellar mass of M~2x10^9 M_sol, which gives a specific star-formation rate of sSFR~0.7 Gyr^-1. If this galaxy had sustained this star-formation rate since z~20, it could have formed the observed stellar mass (to within a factor of ~2), we also discuss alternate star-formation histories and argue the exponentially-increasing model is unlikely. Finally, based on the intrinsic star-formation rate, we estimate this galaxy has a likely [C II] flux of = 10^{-17} erg/s/cm2.Comment: Accepted to ApJL. 6 pages, 3 figures, 2 table

Dependence of cosmic shear covariances on cosmology - Impact on parameter estimation

In cosmic shear likelihood analyses the covariance is most commonly assumed to be constant in parameter space. Therefore, when calculating the covariance matrix (analytically or from simulations), its underlying cosmology should not influence the likelihood contours. We examine whether the aforementioned assumption holds and quantify how strong cosmic shear covariances vary within a reasonable parameter range. Furthermore, we examine the impact on likelihood contours when assuming different cosmologies in the covariance. We find that covariances vary significantly within the considered parameter range (Omega_m=[0.2;0.4], sigma_8=[0.6;1.0]) and that this has a non-negligible impact on the size of likelihood contours. This impact increases with increasing survey size, increasing number density of source galaxies, decreasing ellipticity noise, and when using non-Gaussian covariances. To improve on the assumption of a constant covariance we present two methods. The adaptive covariance is the most accurate method, but it is computationally expensive. To reduce the computational costs we give a scaling relation for covariances. As a second method we outline the concept of an iterative likelihood analysis. Here, we additionally account for non-Gaussianity using a ray-tracing covariance derived from the Millennium simulation.Comment: 11 pages, 8 figure

3D Cosmic Shear: Cosmology from CFHTLenS

This paper presents the first application of 3D cosmic shear to a wide-field weak lensing survey. 3D cosmic shear is a technique that analyses weak lensing in three dimensions using a spherical harmonic approach, and does not bin data in the redshift direction. This is applied to CFHTLenS, a 154 square degree imaging survey with a median redshift of 0.7 and an effective number density of 11 galaxies per square arcminute usable for weak lensing. To account for survey masks we apply a 3D pseudo-Cl approach on weak lensing data, and to avoid uncertainties in the highly non-linear regime, we separately analyse radial wave numbers k<=1.5h/Mpc and k<=5.0h/Mpc, and angular wavenumbers l~400-5000. We show how one can recover 2D and tomographic power spectra from the full 3D cosmic shear power spectra and present a measurement of the 2D cosmic shear power spectrum, and measurements of a set of 2-bin and 6-bin cosmic shear tomographic power spectra; in doing so we find that using the 3D power in the calculation of such 2D and tomographic power spectra from data naturally accounts for a minimum scale in the matter power spectrum. We use 3D cosmic shear to constrain cosmologies with parameters OmegaM, OmegaB, sigma8, h, ns, w0, wa. For a non-evolving dark energy equation of state, and assuming a flat cosmology, lensing combined with WMAP7 results in h=0.78+/-0.12, OmegaM=0.252+/-0.079, sigma8=0.88+/-0.23 and w=-1.16+/-0.38 using only scales k<=1.5h/Mpc. We also present results of lensing combined with first year Planck results, where we find no tension with the results from this analysis, but we also find no significant improvement over the Planck results alone. We find evidence of a suppression of power compared to LCDM on small scales 1.5 < k < 5.0 h/Mpc in the lensing data, which is consistent with predictions of the effect of baryonic feedback on the matter power spectrum.Comment: Full journal article here http://mnras.oxfordjournals.org/content/442/2/1326.full.pdf+htm

Spatial matter density mapping of the STAGES Abell A901/2 supercluster field with 3D lensing

We present weak lensing data from the Hubble Space Telescope(HST)/Space Telescope A901/902 Galaxy Evolution Survey (STAGES) survey to study the three-dimensional spatial distribution of matter and galaxies in the Abell 901/902 supercluster complex. Our method improves over the existing 3D lensing mapping techniques by calibrating and removing redshift bias and accounting for the effects of the radial elongation of 3D structures. We also include the first detailed noise analysis of a 3D lensing map, showing that even with deep HST-quality data, only the most massive structures, for example M200≳ 1015M⊙h-1 at z∼ 0.8, can be resolved in 3D with any reasonable redshift accuracy (Δz≈ 0.15). We compare the lensing map to the stellar mass distribution and find luminous counterparts for all mass peaks detected with a peak significance &gt;3σ. We see structures in and behind the z= 0.165 foreground supercluster, finding structure directly behind the A901b cluster at z∼ 0.6 and also behind the south-west (SW) group at z∼ 0.7. This 3D structure viewed in projection has no significant impact on recent mass estimates of A901b or the SW group components SWa and SWb. © 2011 The Authors Monthly Notices of the Royal Astronomical Society © 2011 RAS