arXiv subjects

Robert C. Nichol

Publications and source records attributed to Robert C. Nichol.

At least 109 records · Page 6Linked to original sources

arXiv2011

Cosmological Measurements with Forthcoming Radio Continuum Surveys

We present forecasts for constraints on cosmological models which can be obtained by forthcoming radio continuum surveys: the wide surveys with the LOw Frequency ARray (LOFAR), Australian Square Kilometre Array Pathfinder (ASKAP) and the Westerbork Observations of the Deep APERTIF Northern sky (WODAN). We use simulated catalogues appropriate to the planned surveys to predict measurements obtained with the source auto-correlation, the cross-correlation between radio sources and CMB maps (the Integrated Sachs-Wolfe effect), the cross-correlation of radio sources with foreground objects due to cosmic magnification, and a joint analysis together with the CMB power spectrum and supernovae. We show that near future radio surveys will bring complementary measurements to other experiments, probing different cosmological volumes, and having different systematics. Our results show that the unprecedented sky coverage of these surveys combined should provide the most significant measurement yet of the Integrated Sachs-Wolfe effect. In addition, we show that using the ISW effect will significantly tighten constraints on modified gravity parameters, while the best measurements of dark energy models will come from galaxy auto-correlation function analyses. Using the combination of EMU and WODAN to provide a full sky survey, it will be possible to measure the dark energy parameters with an uncertainty of \{$σ(w_0) = 0.05$, $σ(w_a) = 0.12$\} and the modified gravity parameters \{$σ(η_0) = 0.10$, $σ(μ_0) = 0.05$\}, assuming Planck CMB+SN(current data) priors. Finally, we show that radio surveys would detect a primordial non-Gaussianity of $f_{\rm NL}$ = 8 at 1-$σ$ and we briefly discuss other promising probes.

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arXiv2011

The Lyman-alpha forest in three dimensions: measurements of large scale flux correlations from BOSS 1st-year data

Using a sample of approximately 14,000 z>2.1 quasars observed in the first year of the Baryon Oscillation Spectroscopic Survey (BOSS), we measure the three-dimensional correlation function of absorption in the Lyman-alpha forest. The angle-averaged correlation function of transmitted flux (F = exp(-tau)) is securely detected out to comoving separations of 60 Mpc/h, the first detection of flux correlations across widely separated sightlines. A quadrupole distortion of the redshift-space correlation function by peculiar velocities, the signature of the gravitational instability origin of structure in the Lyman-alpha forest, is also detected at high significance. We obtain a good fit to the data assuming linear theory redshift-space distortion and linear bias of the transmitted flux, relative to the matter fluctuations of a standard LCDM cosmological model (inflationary cold dark matter with a cosmological constant). At 95% confidence, we find a linear bias parameter 0.16<b<0.24 and redshift-distortion parameter 0.44<beta<1.20, at central redshift z=2.25, with a well constrained combination b(1+β)=0.336 +/- 0.012. The errors on beta are asymmetric, with beta=0 excluded at over 5 sigma confidence level. The value of beta is somewhat low compared to theoretical predictions, and our tests on synthetic data suggest that it is depressed (relative to expectations for the Lyman-alpha forest alone) by the presence of high column density systems and metal line absorption. These results set the stage for cosmological parameter determinations from three-dimensional structure in the Lyman-alpha forest, including anticipated constraints on dark energy from baryon acoustic oscillations.

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arXiv2011

Improved Constraints on Type Ia Supernova Host Galaxy Properties using Multi-Wavelength Photometry and their Correlations with Supernova Properties

We improve estimates of stellar mass and mass-weighted average age of Type Ia supernova (SN Ia) host galaxies by combining UV and near-IR photometry with optical photometry in our analysis. Using 206 SNe Ia drawn from the full three-year SDSS-II Supernova Survey (median redshift of z {\approx} 0.2) and multi-wavelength host-galaxy photometry from SDSS, GALEX, and UKIDSS, we present evidence of a correlation (1.9σ confidence level) between the residuals of SNe Ia about the best-fit Hubble relation and the mass-weighted average age of their host galaxies. The trend is such that older galaxies host SNe Ia that are brighter than average after standard light-curve corrections are made. We also confirm, at the 3.0σ level, the trend seen by previous studies that more massive galaxies often host brighter SNe Ia after light-curve correction.

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arXiv2011

A More General Model for the Intrinsic Scatter in Type Ia Supernova Distance Moduli

We describe a new formalism to fit the parameters $α$ and $β$ that are used in the SALT2 model to determine the standard magnitudes of Type Ia supernovae. The new formalism describes the intrinsic scatter in Type Ia supernovae by a covariance matrix in place of the single parameter normally used. We have applied this formalism to the Sloan Digital Sky Survey Supernova Survey (SDSS-II) data and conclude that the data are best described by $α=0.135_{-.017}^{+.033}$ and $β=3.19_{-0.24}^{+0.14}$, where the error is dominated by the uncertainty in the form of the intrinsic scatter matrix. Our result depends on the introduction of a more general form for the intrinsic scatter of the distance moduli of Type Ia supernovae than is conventional, resulting in a larger value of $β$ and a larger uncertainty than the conventional approach. Although this analysis results in a larger value of $β$ and a larger error, the SDSS data differ (at a 98% confidence level) with $β=4.1$, the value expected for extinction by the type of dust found in the Milky Way. We have modeled the distribution of supernovae Ia in terms of their color and conclude that there is strong evidence that variation in color is a significant contributor to the scatter of supernovae Ia around their standard candle magnitude.

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arXiv2011

Ameliorating Systematic Uncertainties in the Angular Clustering of Galaxies: A Study using SDSS-III

We investigate the effects of potential sources of systematic error on the angular and photometric redshift, z_phot, distributions of a sample of redshift 0.4 < z < 0.7 massive galaxies whose selection matches that of the Baryon Oscillation Spectroscopic Survey (BOSS) constant mass sample. Utilizing over 112,778 BOSS spectra as a training sample, we produce a photometric redshift catalog for the galaxies in the SDSS DR8 imaging area that, after masking, covers nearly one quarter of the sky (9,913 square degrees). We investigate fluctuations in the number density of objects in this sample as a function of Galactic extinction, seeing, stellar density, sky background, airmass, photometric offset, and North/South Galactic hemisphere. We find that the presence of stars of comparable magnitudes to our galaxies (which are not traditionally masked) effectively remove area. Failing to correct for such stars can produce systematic errors on the measured angular auto-correlation function, w, that are larger than its statistical uncertainty. We describe how one can effectively mask for the presence of the stars, without removing any galaxies from the sample, and minimize the systematic error. Additionally, we apply two separate methods that can be used to correct the systematic errors imparted by any parameter that can be turned into a map on the sky. We find that failing to properly account for varying sky background introduces a systematic error on w. We measure w, in four z_phot slices of width 0.05 between 0.45 < z_phot < 0.65 and find that the measurements, after correcting for the systematic effects of stars and sky background, are generally consistent with a generic LambdaCDM model, at scales up to 60 degrees. At scales greater than 3 degrees and z_phot > 0.5, the magnitude of the corrections we apply are greater than the statistical uncertainty in w.

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arXiv2011

The XMM Cluster Survey: Optical analysis methodology and the first data release

The XMM Cluster Survey (XCS) is a serendipitous search for galaxy clusters using all publicly available data in the XMM-Newton Science Archive. Its main aims are to measure cosmological parameters and trace the evolution of X-ray scaling relations. In this paper we present the first data release from the XMM Cluster Survey (XCS-DR1). This consists of 503 optically confirmed, serendipitously detected, X-ray clusters. Of these clusters, 255 are new to the literature and 356 are new X-ray discoveries. We present 464 clusters with a redshift estimate (0.06 < z < 1.46), including 261 clusters with spectroscopic redshifts. In addition, we have measured X-ray temperatures (Tx) for 402 clusters (0.4 < Tx < 14.7 keV). We highlight seven interesting subsamples of XCS-DR1 clusters: (i) 10 clusters at high redshift (z > 1.0, including a new spectroscopically-confirmed cluster at z = 1.01); (ii) 67 clusters with high Tx (> 5 keV); (iii) 131 clusters/groups with low Tx (< 2 keV); (iv) 27 clusters with measured Tx values in the SDSS `Stripe 82' co-add region; (v) 78 clusters with measured Tx values in the Dark Energy Survey region; (vi) 40 clusters detected with sufficient counts to permit mass measurements (under the assumption of hydrostatic equilibrium); (vii) 105 clusters that can be used for applications such as the derivation of cosmological parameters and the measurement of cluster scaling relations. The X-ray analysis methodology used to construct and analyse the XCS-DR1 cluster sample has been presented in a companion paper, Lloyd-Davies et al. (2010).

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arXiv2011

The XMM Cluster Survey: X-ray analysis methodology

The XMM Cluster Survey (XCS) is a serendipitous search for galaxy clusters using all publicly available data in the XMM-Newton Science Archive. Its main aims are to measure cosmological parameters and trace the evolution of X-ray scaling relations. In this paper we describe the data processing methodology applied to the 5,776 XMM observations used to construct the current XCS source catalogue. A total of 3,675 > 4-sigma cluster candidates with > 50 background-subtracted X-ray counts are extracted from a total non-overlapping area suitable for cluster searching of 410 deg^2. Of these, 993 candidates are detected with > 300 background-subtracted X-ray photon counts, and we demonstrate that robust temperature measurements can be obtained down to this count limit. We describe in detail the automated pipelines used to perform the spectral and surface brightness fitting for these candidates, as well as to estimate redshifts from the X-ray data alone. A total of 587 (122) X-ray temperatures to a typical accuracy of < 40 (< 10) per cent have been measured to date. We also present the methodology adopted for determining the selection function of the survey, and show that the extended source detection algorithm is robust to a range of cluster morphologies by inserting mock clusters derived from hydrodynamical simulations into real XMM images. These tests show that the simple isothermal beta-profiles is sufficient to capture the essential details of the cluster population detected in the archival XMM observations. The redshift follow-up of the XCS cluster sample is presented in a companion paper, together with a first data release of 503 optically-confirmed clusters.

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arXiv2011

Measuring Coherent Motions in the Universe

We present new measurements of the coherent motion of galaxies based on observations of the large-scale redshift-space distortions seen in the two-dimensional two-point correlation function of Luminous Red Galaxies in Data Release Seven of the Sloan Digital Sky Survey. We have developed a new methodology for estimating these coherent motions, which is less dependent on the details of galaxy bias and of the cosmological model to explain the late-time acceleration of the expansion of the Universe. We measure a one-dimensional velocity dispersion of galaxies on large-scales of σ_v=3.01^{+0.45}_{-0.46} Mpc/h and σ_v=3.69^{+0.47}_{-0.47} \mpcoh$ at a mean redshift of z=0.25 and 0.38 respectively. These values are fully consistent with predictions for a WMAP7-normalised LCDM Universe and inconsistent at confidence of 3.8σwith a Dvali-Gabadadze-Porrati (DGP) model for the Universe. We can convert the units of these $σ_v$ measurements to 270^{+40}_{-41} km/s and 320^{+41}_{-41} km/s respectively (assuming a $Λ$CDM universe), which are lower that expected based on recent low redshift (z<0.2) measurements of the peculiar velocity field (or "bulk flows"). It is difficult to directly compare these measurements as they cover different redshift ranges and different areas of the sky. However, one possible cosmological explanation for this discrepancy is that our Galaxy is located in unusually over, or under, dense region of the Universe.

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arXiv2011

Galaxy Zoo: Bar Lengths in Nearby Disk Galaxies

We present an analysis of bar length measurements of 3150 local galaxies in a volume limited sample of low redshift (z < 0.06) disk galaxies. Barred galaxies were initially selected from the Galaxy Zoo 2 project, and the lengths and widths of the bars were manually drawn by members of the Galaxy Zoo community using a Google Maps interface. Bars were measured independently by different observers, multiple times per galaxy (>=3), and we find that observers were able to reproduce their own bar lengths to 3% and each others' to better than 20%. We find a "color bimodality" in our disk galaxy population with bar length, i.e., longer bars inhabit redder disk galaxies and the bars themselves are redder, and that the bluest galaxies host the smallest galactic bars (< 5 kpc/h). We also find that bar and disk colors are clearly correlated, and for galaxies with small bars, the disk is, on average, redder than the bar colors, while for longer bars the bar then itself is redder, on average, than the disk. We further find that galaxies with a prominent bulge are more likely to host longer bars than those without bulges. We categorise our galaxy populations by how the bar and/or ring are connected to the spiral arms. We find that galaxies whose bars are directly connected to the spiral arms are preferentially bluer and that these galaxies host typically shorter bars. Within the scatter, we find that stronger bars are found in galaxies which host a ring (and only a ring). The bar length and width measurements used herein are made publicly available for others to use (http://data.galaxyzoo.org).

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arXiv2011

Galaxy Clustering in the Completed SDSS Redshift Survey: The Dependence on Color and Luminosity

We measure the luminosity and color dependence of galaxy clustering in the SDSS DR7 main galaxy sample, focusing on the projected correlation function w_p(r_p) of volume-limited samples. We interpret our measurements using halo occupation distribution (HOD) modeling assuming a Lambda-CDM cosmology. The amplitude of w_p(r_p) grows slowly with luminosity for L < L_* and increases sharply at higher luminosities, with bias factor b(>L)=1.06+0.23(L/L_*)^{1.12}. At fixed luminosity, redder galaxies have a stronger and steeper w_p(r_p), a trend that runs steadily from the bluest galaxies to the reddest galaxies. The individual luminosity trends for the red and blue galaxy populations are strikingly different. Blue galaxies show a slow but steady increase of w_p(r_p) with luminosity, at all scales. The large-scale clustering of red galaxies shows little luminosity dependence until a sharp increase at L > 4L_*, but the lowest luminosity red galaxies (0.04-0.25 L_*) show very strong clustering on scales r_p < 2 Mpc/h. Most of the observed trends can be naturally understood within the LCDM+HOD framework. The growth of w_p(r_p) with luminosity reflects an overall shift in the halo mass scale, in particular an increase in the minimum host halo mass Mmin. The mass at which a halo has, on average, one satellite galaxy brighter than L is M_1 ~ 17 Mmin(L) over most of the luminosity range. The growth and steepening of w_p(r_p) for redder galaxies reflects the increasing fraction of galaxies that are satellite systems in high mass halos instead of central systems in low mass halos, a trend that is especially marked at low luminosities. Our extensive measurements, provided in tabular form, will allow detailed tests of theoretical models of galaxy formation, a firm grounding of semi-empirical models of the galaxy population, and new cosmological tests.

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arXiv2010

Results from the Supernova Photometric Classification Challenge

We report results from the Supernova Photometric Classification Challenge (SNPCC), a publicly released mix of simulated supernovae (SNe), with types (Ia, Ibc, and II) selected in proportion to their expected rate. The simulation was realized in the griz filters of the Dark Energy Survey (DES) with realistic observing conditions (sky noise, point-spread function and atmospheric transparency) based on years of recorded conditions at the DES site. Simulations of non-Ia type SNe are based on spectroscopically confirmed light curves that include unpublished non-Ia samples donated from the Carnegie Supernova Project (CSP), the Supernova Legacy Survey (SNLS), and the Sloan Digital Sky Survey-II (SDSS-II). A spectroscopically confirmed subset was provided for training. We challenged scientists to run their classification algorithms and report a type and photo-z for each SN. Participants from 10 groups contributed 13 entries for the sample that included a host-galaxy photo-z for each SN, and 9 entries for the sample that had no redshift information. Several different classification strategies resulted in similar performance, and for all entries the performance was significantly better for the training subset than for the unconfirmed sample. For the spectroscopically unconfirmed subset, the entry with the highest average figure of merit for classifying SNe~Ia has an efficiency of 0.96 and an SN~Ia purity of 0.79. As a public resource for the future development of photometric SN classification and photo-z estimators, we have released updated simulations with improvements based on our experience from the SNPCC, added samples corresponding to the Large Synoptic Survey Telescope (LSST) and the SDSS, and provided the answer keys so that developers can evaluate their own analysis.

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arXiv2010

Single or Double Degenerate Progenitors? Searching for Shock Emission in the SDSS-II Type Ia Supernovae

From the set of nearly 500 spectroscopically confirmed type~Ia supernovae and around 10,000 unconfirmed candidates from SDSS-II, we select a subset of 108 confirmed SNe Ia with well-observed early-time light curves to search for signatures from shock interaction of the supernova with a companion star. No evidence for shock emission is seen; however, the cadence and photometric noise could hide a weak shock signal. We simulate shocked light curves using SN Ia templates and a simple, Gaussian shock model to emulate the noise properties of the SDSS-II sample and estimate the detectability of the shock interaction signal as a function of shock amplitude, shock width, and shock fraction. We find no direct evidence for shock interaction in the rest-frame $B$-band, but place an upper limit on the shock amplitude at 9% of supernova peak flux ($M_B > -16.6$ mag). If the single degenerate channel dominates type~Ia progenitors, this result constrains the companion stars to be less than about 6 $M_{\odot}$ on the main sequence, and strongly disfavors red giant companions.

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arXiv2010

Galaxy Zoo: Bars in Disk Galaxies

We present first results from Galaxy Zoo 2, the second phase of the highly successful Galaxy Zoo project (www.galaxyzoo.org). Using a volume-limited sample of 13665 disk galaxies (0.01< z < 0.06 and M_r<-19.38), we study the fraction of galaxies with bars as a function of global galaxy properties like colour, luminosity and bulge prominence. Overall, 29.4+/-0.5% of galaxies in our sample have a bar, in excellent agreement with previous visually classified samples of galaxies (although this overall fraction is lower than measured by automated bar-finding methods). We see a clear increase in the bar fraction with redder (g-r) colours, decreased luminosity and in galaxies with more prominent bulges, to the extent that over half of the red, bulge-dominated, disk galaxies in our sample possess a bar. We see evidence for a colour bi-modality for our sample of disk galaxies, with a "red sequence" that is both bulge and bar-dominated, and a "blue cloud" which has little, or no, evidence for a (classical) bulge or bar. These results are consistent with similar trends for barred galaxies seen recently both locally and at higher redshift, and with early studies using the RC3. We discuss these results in the context of internal (secular) galaxy evolution scenarios and the possible links to the formation of bars and bulges in disk galaxies.

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arXiv2010

Galaxy and Mass Assembly (GAMA): FUV, NUV, ugrizYJHK Petrosian, Kron and Sèrsic photometry

In order to generate credible 0.1-2 μm SEDs, the GAMA project requires many Gigabytes of imaging data from a number of instruments to be re-processed into a standard format. In this paper we discuss the software infrastructure we use, and create self-consistent ugrizYJHK photometry for all sources within the GAMA sample. Using UKIDSS and SDSS archive data, we outline the pre-processing necessary to standardise all images to a common zeropoint, the steps taken to correct for seeing bias across the dataset, and the creation of Gigapixel-scale mosaics of the three 4x12 deg GAMA regions in each filter. From these mosaics, we extract source catalogues for the GAMA regions using elliptical Kron and Petrosian matched apertures. We also calculate Sérsic magnitudes for all galaxies within the GAMA sample using SIGMA, a galaxy component modelling wrapper for GALFIT 3. We compare the resultant photometry directly, and also calculate the r band galaxy LF for all photometric datasets to highlight the uncertainty introduced by the photometric method. We find that (1) Changing the object detection threshold has a minor effect on the best-fitting Schechter parameters of the overall population (M* +/- 0.055mag, α +/- 0.014, Φ* +/- 0.0005 h^3 Mpc^{-3}). (2) An offset between datasets that use Kron or Petrosian photometry regardless of the filter. (3) The decision to use circular or elliptical apertures causes an offset in M* of 0.20mag. (4) The best-fitting Schechter parameters from total-magnitude photometric systems (such as SDSS modelmag or Sérsic magnitudes) have a steeper faint-end slope than photometry dependent on Kron or Petrosian magnitudes. (5) Our Universe's total luminosity density, when calculated using Kron or Petrosian r-band photometry, is underestimated by at least 15%.

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arXiv2010

The Effect of Host Galaxies on Type Ia Supernovae in the SDSS-II Supernova Survey

We present an analysis of the host galaxy dependencies of Type Ia Supernovae (SNe Ia) from the full three year sample of the SDSS-II Supernova Survey. We rediscover, to high significance, the strong correlation between host galaxy typeand the width of the observed SN light curve, i.e., fainter, quickly declining SNe Ia favor passive host galaxies, while brighter, slowly declining Ia's favor star-forming galaxies. We also find evidence (at between 2 to 3 sigma) that SNe Ia are ~0.1 magnitudes brighter in passive host galaxies, than in star-forming hosts, after the SN Ia light curves have been standardized using the light curve shape and color variations: This difference in brightness is present in both the SALT2 and MCLS2k2 light curve fitting methodologies. We see evidence for differences in the SN Ia color relationship between passive and star-forming host galaxies, e.g., for the MLCS2k2 technique, we see that SNe Ia in passive hosts favor a dust law of R_V ~1, while SNe Ia in star-forming hosts require R_V ~2. The significance of these trends depends on the range of SN colors considered. We demonstrate that these effects can be parameterized using the stellar mass of the host galaxy (with a confidence of >4 sigma) and including this extra parameter provides a better statistical fit to our data. Our results suggest that future cosmological analyses of SN Ia samples should include host galaxy information.

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arXiv2010

The age-redshift relation for Luminous Red Galaxies in the Sloan Digital Sky Survey

We present a detailed analysis of 17,852 quiescent, Luminous Red Galaxies (LRGs) selected from Sloan Digital Sky Survey (SDSS) Data Release Seven (DR7) spanning a redshift range of 0.0 < z < 0.4. These galaxies are co-added into four equal bins of velocity dispersion and luminosity to produce high signal-to-noise spectra (>100A^{-1}), thus facilitating accurate measurements of the standard Lick absorption-line indices. In particular, we have carefully corrected and calibrated these indices onto the commonly used Lick/IDS system, thus allowing us to compare these data with other measurements in the literature, and derive realistic ages, metallicities ([Z/H]) and alpha-element abundance ratios ([alpha/Fe]) for these galaxies using Simple Stellar Population (SSP) models. We use these data to study the relationship of these galaxy parameters with redshift, and find little evidence for evolution in metallicity or alpha-elements (especially for our intermediate mass samples). This demonstrates that our subsamples are consistent with pure passive evolving (i.e. no chemical evolution) and represent a homogeneous population over this redshift range. We also present the age-redshift relation for these LRGs and clearly see a decrease in their age with redshift (5 Gyrs over the redshift range studied here) which is fully consistent with the cosmological lookback times in a concordance Lambda CDM universe. We also see that our most massive sample of LRGs is the youngest compared to the lower mass galaxies. We provide these data now to help future cosmological and galaxy evolution studies of LRGs, and provide in the appendices of this paper the required methodology and information to calibrate SDSS spectra onto the Lick/IDS system.

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arXiv2010

Photometric Estimates of Redshifts and Distance Moduli for Type Ia Supernovae

Large planned photometric surveys will discover hundreds of thousands of supernovae (SNe), outstripping the resources available for spectroscopic follow-up and necessitating the development of purely photometric methods to exploit these events for cosmological study. We present a light-curve fitting technique for SN Ia photometric redshift (photo-z) estimation in which the redshift is determined simultaneously with the other fit parameters. We implement this "LCFIT+Z" technique within the frameworks of the MLCS2k2 and SALT-II light-curve fit methods and determine the precision on the redshift and distance modulus. This method is applied to a spectroscopically confirmed sample of 296 SNe Ia from the SDSS-II Supernova Survey and 37 publicly available SNe Ia from the Supernova Legacy Survey (SNLS). We have also applied the method to a large suite of realistic simulated light curves for existing and planned surveys, including SDSS, SNLS, and LSST. When intrinsic SN color fluctuations are included, the photo-z precision for the simulation is consistent with that in the data. Finally, we compare the LCFIT+Z photo-z precision with previous results using color-based SN photo-z estimates.

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arXiv2010

Probing modifications of General Relativity using current cosmological observations

We test General Relativity (GR) using current cosmological data: the cosmic microwave background (CMB) from WMAP5 (Komatsu et al. 2009), the integrated Sachs-Wolfe (ISW) effect from the cross-correlation of the CMB with six galaxy catalogs (Giannantonio et al. 2008), a compilation of supernovae Type Ia (SNe) including the latest SDSS SNe (Kessler et al. 2009), and part of the weak lensing (WL) data from CFHTLS (Fu et al. 2008, Kilbinger et al. 2009) that probe linear and mildly non-linear scales. We first test a model where the effective Newton's constant, mu, and the ratio of the two gravitational potentials, eta, transit from the GR value to another constant at late times; in this case, we find that standard GR is fully consistent with the combined data. The strongest constraint comes from the ISW effect which would arise from this gravitational transition; the observed ISW signal imposes a tight constraint on a combination of mu and eta that characterizes the lensing potential. Next, we consider four pixels in time and space for each function mu and eta, and perform a Principal Component Analysis (PCA) finding that seven of the resulting eight eigenmodes are consistent with GR within the errors. Only one eigenmode shows a 2-sigma deviation from the GR prediction, which is likely to be due to a systematic effect. However, the detection of such a deviation demonstrates the power of our time- and scale-dependent PCA methodology when combining observations of structure formation and expansion history to test GR.

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