Photometric Redshift Requirements for Self-Calibration of Cluster Dark Energy Studies

The ability to constrain dark energy from the evolution of galaxy cluster counts is limited by the imperfect knowledge of cluster redshifts. Ongoing and upcoming surveys will mostly rely on redshifts estimated from broad-band photometry (photo-z's). For a Gaussian distribution for the cluster photo-z errors and a high cluster yield cosmology defined by the WMAP 1 year results, the photo-z bias and scatter needs to be known better than 0.003 and 0.03, respectively, in order not to degrade dark energy constrains by more than 10% for a survey with specifications similar to the South Pole Telescope. Smaller surveys and cosmologies with lower cluster yields produce weaker photo-z requirements, though relative to worse baseline constraints. Comparable photo-z requirements are necessary in order to employ self-calibration techniques when solving for dark energy and observable-mass parameters simultaneously. On the other hand, self-calibration in combination with external mass inferences helps reduce photo-z requirements and provides important consistency checks for future cluster surveys. In our fiducial model, training sets with spectroscopic redshifts for ~5%-15% of the detected clusters are required in order to keep degradations in the dark energy equation of state lower than 20%.Comment: 18 pages, 8 figures, submitted to PR

Photometric Redshift Biases from Galaxy Evolution

Proposed cosmological surveys will make use of photometric redshifts of galaxies that are significantly fainter than any complete spectroscopic redshift surveys that exist to train the photo-z methods. We investigate the photo-z biases that result from known differences between the faint and bright populations: a rise in AGN activity toward higher redshift, and a metallicity difference between intrinsically luminous and faint early-type galaxies. We find that even very small mismatches between the mean photometric target and the training set can induce photo-z biases large enough to corrupt derived cosmological parameters significantly. A metallicity shift of ~0.003dex in an old population, or contamination of any galaxy spectrum with ~0.2% AGN flux, is sufficient to induce a 10^-3 bias in photo-z. These results highlight the danger in extrapolating the behavior of bright galaxies to a fainter population, and the desirability of a spectroscopic training set that spans all of the characteristics of the photo-z targets, i.e. extending to the 25th mag or fainter galaxies that will be used in future surveys

Constraining Dark Energy by Combining Cluster Counts and Shear-Shear Correlations in a Weak Lensing Survey

We study the potential of a large future weak-lensing survey to constrain dark energy properties by using both the number counts of detected galaxy clusters (sensitive primarily to density fluctuations on small scales) and tomographic shear-shear correlations (restricted to large scales). We use the Fisher matrix formalism, assume a flat universe and parameterize the equation of state of dark energy by w(a)=w_0+w_a(1-a), to forecast the expected statistical errors from either observable, and from their combination. We show that the covariance between these two observables is small, and argue that therefore they can be regarded as independent constraints. We find that when the number counts and the shear-shear correlations (on angular scales l < 1000) are combined, an LSST (Large Synoptic Survey Telescope)-like survey can yield statistical errors on (Omega_DE, w_0, w_a) as tight as (0.003, 0.03, 0.1). These values are a factor of 2-25 better than using either observable alone. The results are also about a factor of two better than those from combining number counts of galaxy clusters and their power spectrum.Comment: 17 pages, 5 figures, 10 tables, submitted to PR

Baryon Oscillations and Consistency Tests for Photometrically-Determined Redshifts of Very Faint Galaxies

Weak lensing surveys that can potentially place strong constraints on dark energy parameters can only do so if the source redshift means and error distributions are very well known. We investigate prospects for controlling errors in these quantities by exploiting their influence on the power spectra of the galaxies. Although, from the galaxy power spectra alone, sufficiently precise and simultaneous determination of redshift biases and variances is not possible, a strong consistency test is. Given the redshift error rms, galaxy power spectra can be used to determine the mean redshift of a group of galaxies to subpercent accuracy. Although galaxy power spectra cannot be used to determine the redshift error rms, they can be used to determine this rms divided by the Hubble parameter, a quantity that may be even more valuable for interpretation of cosmic shear data than the rms itself. We also show that galaxy power spectra, due to the baryonic acoustic oscillations, can potentially lead to constraints on dark energy that are competitive with those due to the cosmic shear power spectra from the same survey.Comment: 8 pages, 6 figures, submitted to Ap

Photometric Redshifts and Photometry Errors

We examine the impact of non-Gaussian photometry errors on photometric redshift performance. We find that they greatly increase the scatter, but this can be mitigated to some extent by incorporating the correct noise model into the photometric redshift estimation process. However, the remaining scatter is still equivalent to that of a much shallower survey with Gaussian photometry errors. We also estimate the impact of non-Gaussian errors on the spectroscopic sample size required to verify the photometric redshift rms scatter to a given precision. Even with Gaussian {\it photometry} errors, photometric redshift errors are sufficiently non-Gaussian to require an order of magnitude larger sample than simple Gaussian statistics would indicate. The requirements increase from this baseline if non-Gaussian photometry errors are included. Again the impact can be mitigated by incorporating the correct noise model, but only to the equivalent of a survey with much larger Gaussian photometry errors. However, these requirements may well be overestimates because they are based on a need to know the rms, which is particularly sensitive to tails. Other parametrizations of the distribution may require smaller samples.Comment: submitted to ApJ

How Future Space-Based Weak Lensing Surveys Might Obtain Photometric Redshifts Independently

We study how the addition of on-board optical photometric bands to future space-based weak lensing instruments could affect the photometric redshift estimation of galaxies, and hence improve estimations of the dark energy parameters through weak lensing. Basing our study on the current proposed Euclid configuration and using a mock catalog of galaxy observations, various on-board options are tested and compared with the use of ground-based observations from the Large Synoptic Survey Telescope (LSST) and Pan-STARRS. Comparisons are made through the use of the dark energy Figure of Merit, which provides a quantifiable measure of the change in the quality of the scientific results that can be obtained in each scenario. Effects of systematic offsets between LSST and Euclid photometric calibration are also studied. We find that adding two (U and G) or even one (U) on-board optical band-passes to the space-based infrared instrument greatly improves its photometric redshift performance, bringing it close to the level that would be achieved by combining observations from both space-based and ground-based surveys while freeing the space mission from reliance on external datasets.Comment: Accepted for publication in PASP. A high-quality version of Fig 1 can be found on http://www.ap.smu.ca/~sawicki/DEphoto

Systematic Errors in Future Weak Lensing Surveys: Requirements and Prospects for Self-Calibration

We study the impact of systematic errors on planned weak lensing surveys and compute the requirements on their contributions so that they are not a dominant source of the cosmological parameter error budget. The generic types of error we consider are multiplicative and additive errors in measurements of shear, as well as photometric redshift errors. In general, more powerful surveys have stronger systematic requirements. For example, for a SNAP-type survey the multiplicative error in shear needs to be smaller than 1%(fsky/0.025)^{-1/2} of the mean shear in any given redshift bin, while the centroids of photometric redshift bins need to be known to better than 0.003(fsky/0.025)^{-1/2}. With about a factor of two degradation in cosmological parameter errors, future surveys can enter a self-calibration regime, where the mean systematic biases are self-consistently determined from the survey and only higher-order moments of the systematics contribute. Interestingly, once the power spectrum measurements are combined with the bispectrum, the self-calibration regime in the variation of the equation of state of dark energy w_a is attained with only a 20-30% error degradation.Comment: 20 pages, 9 figures, to be submitted to MNRAS. Comments are welcom

Accelerating Universes with Scaling Dark Matter

Friedmann-Robertson-Walker universes with a presently large fraction of the energy density stored in an $X$-component with $w_X<-1/3$, are considered. We find all the critical points of the system for constant equations of state in that range. We consider further several background quantities that can distinguish the models with different $w_X$ values. Using a simple toy model with a varying equation of state, we show that even a large variation of $w_X$ at small redshifts is very difficult to observe with $d_L(z)$ measurements up to $z\sim 1$. Therefore, it will require accurate measurements in the range $1<z<2$ and independent accurate knowledge of $\Omega_{m,0}$ (and/or $\Omega_{X,0}$) in order to resolve a variable $w_X$ from a constant $w_X$.Comment: submitted to IJMPD (uses Latex, 12 pages, 6 Figures) Minor corrections, Figures 4, 6 revised. Conclusions unchange