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

59Co-NMR Knight Shift of Superconducting Three-Layer NaxCoO2.yH2O

The superconducting state of NaxCoO2.yH2O with three CoO2 layers in a unit cell has been studied by 59Co-NMR. The Knight shift measured for a peak of the NMR spectra corresponding to the external magnetic field H along one of the principal directions within the CoO2 plane, exhibits a rapid decrease with decreasing temperature T below the superconducting transition temperature Tc, indicating that the spin susceptibility is suppressed in the superconducting phase, at least, for this field direction. Because differences of the superconducting properties are rather small between this three-layer NaxCoO2.yH2O and previously reported NaxCoO2.yH2O with two CoO2 layers within a unit cell, the present result of the Knight shift studies indicates that the Cooper pairs of the former system are in the singlet state as in the latter, for which the spin susceptibility is suppressed for both directions of H parallel and perpendicular to the CoO2 plane.Comment: 5 page

The Skewness of the Aperture Mass Statistic

We present simple formulae for calculating the skewness and kurtosis of the aperture mass statistic for weak lensing surveys which is insensitive to masking effects of survey geometry or variable survey depth. The calculation is the higher order analog of the formula given by Schneider et al (2002) which has been used to compute the variance of the aperture mass from several lensing surveys. As our formula requires the three-point shear correlation function, we also present an efficient tree-based algorithm for measuring it. We show how our algorithm would scale in computing time and memory usage for future lensing surveys. Finally, we apply the procedure to our CTIO survey data, originally described in Jarvis et al (2003). We find that the skewness is positive (inconsistent with zero) at the 2 sigma level. However, the signal is too noisy from this data to usefully constrain cosmology.Comment: 16 pages, accepted by MNRAS. Minor revisions; this replacement matches the accepted versio

The Surprisingly Steep Mass Profile of Abell 1689, from a Lensing Analysis of Subaru Images

Subaru observations of A1689 (z=0.183) are used to derive an accurate, model-independent mass profile for the entire cluster, r<2 Mpc/h, by combining magnification bias and distortion measurements. The projected mass profile steepens quickly with increasing radius, falling away to zero at r~1.0 Mpc/h, well short of the anticipated virial radius. Our profile accurately matches onto the inner profile, r<200 kpc/h, derived from deep HST/ACS images. The combined ACS and Subaru information is well fitted by an NFW profile with virial mass, (1.93 \pm 0.20)10^15 M_sun, and surprisingly high concentration, c_vir=13.7^{+1.4}_{-1.1}, significantly larger than theoretically expected (c_vir~4), corresponding to a relatively steep overall profile. A slightly better fit is achieved with a steep power-law model that has its 2D logarithmic slope -3 and core radius theta_c~1.7' (r_c~210 kpc/h), whereas an isothermal profile is strongly rejected. These results are based on a reliable sample of background galaxies selected to be redder than the cluster E/S0 sequence. By including the faint blue galaxy population a much smaller distortion signal is found, demonstrating that blue cluster members significantly dilute the true signal for r~400 kpc/h. This contamination is likely to affect most weak lensing results to date.Comment: 5 pages, 3 figures, to appear in ApJ

Possibility of f-wave spin-triplet superconductivity in the CoO superconductor: a case study on a 2D triangular lattice in the repulsive Hubbard model

Stimulated by the recent finding of Na$_{0.35}$CoO$_2$.1.3H$_2$O superconductor, we investigate superconducting instabilities on a 2D triangular lattice in the repulsive Hubbard model. Using the third-order perturbation expansion with respect to the on-site repulsion $U$, we evaluate the linearized Dyson-Gor'kov equation. We find that an $f$-wave spin-triplet pairing is the most stable in a wide range of the next nearest neighbor hopping integral $t'$ and an electron number density $n$. The introduction of $t'$ is crucial to adjust the van Hove singularities to the neighborhood of the Fermi surface crossing around K point. In this case, the bare spin susceptibility shows the broad peak around $\Gamma$ point. These conditions stabilize the $f$-wave pairing. Although the $f$-wave pairing is also given by the fluctuation-exchange approximation, the transition temperature is too low to be observed. This is because the depairing effect by the spin fluctuation is over-estimated. Thus, the third-order vertex corrections are important for the spin-triplet superconductivity, like the case in Sr$_2$RuO$_4$.Comment: 4 pages, 7 figure

Effects of two dimensional plasmons on the tunneling density of states

We show that gapless plasmons lead to a universal $(\delta\nu(\epsilon)/\nu\propto |\epsilon|/E_F)$ correction to the tunneling density of states of a clean two dimensional Coulomb interacting electron gas. We also discuss a counterpart of this effect in the "composite fermion metal" which forms in the presence of a quantizing perpendicular magnetic field corresponding to the half-filled Landau level. We argue that the latter phenomenon might be relevant for deviations from a simple scaling observed by A.Chang et al in the tunneling $I-V$ characteristics of Quantum Hall liquids.Comment: 12 pages, Latex, NORDITA repor

Behavior of a frustrated quantum spin chain with bond dimerization

We clarified behavior of the excitation gap in a frustrated S=1/2 quantum spin chain with bond dimerization by using the numerical diagonalization of finite systems and a variational approach. The model interpolates between the independent dimer model and the S=1 spin chain by changing a strength of the dimerization. The energy gap is minimum at the fully-frustrated point, where a localized kink and a freely mobile anti-kink govern the low-lying excitations. Away from the point, a kink and an antikink form a bound state by an effective triangular potential between them. The consequential gap enhancement and the localization length of the bound state is obtained exactly in the continuous limit. The gap enhancement obeys a power law with exponent 2/3. The method and the obtained results are common to other frustrated double spin-chain systems, such as the one-dimensional J_1 - J_2 model, or the frustrated ladder model.Comment: 11 pages, REVTeX, 8 figures in eps-fil

Galactic chemical evolution : Carbon through zinc

Copyright © 2006. The American Astronomical Society. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the final published version of the work, which was originally published at https://doi.org/10.1086/508914We calculate the evolution of heavy-element abundances from C to Zn in the solar neighborhood, adopting our new nucleosynthesis yields. Our yields are calculated for wide ranges of metallicity (Z = 0-Z circle dot) and the explosion energy (normal supernovae and hypernovae), based on the light-curve and spectra fitting of individual supernovae. The elemental abundance ratios are in good agreement with observations. Among the alpha-elements, O, Mg, Si, S, and Ca show a plateau at [Fe/H] <= -1, while Ti is underabundant overall. The observed abundance of Zn ([Zn/Fe] similar to 0) can be explained only by the high-energy explosion models, as it requires a large contribution of hypernovae. The observed decrease in the odd-Z elements (Na, Al, and Cu) toward low [Fe/H] is reproduced by the metallicity effect on nucleosynthesis. The iron-peak elements (Cr, Mn, Co, and Ni) are consistent with the observed mean values at -2.5 less than or similar to [Fe/H] less than or similar to -1, and the observed trend at the lower metallicity can be explained by the energy effect. We also show the abundance ratios and the metallicity distribution functions of the Galactic bulge, halo, and thick disk. Our results suggest that the formation timescale of the thick disk is similar to 1-3 Gyr.Peer reviewe

NaxCoO2: Enhanced low-energy excitations of electrons on a 2D triangular lattice

To elucidate the low-energy excitation spectrum of correlated electrons on a 2D triangular lattice, we have studied the electrical resistance and specific heat down to 0.5 K and in magnetic fields up to 14 T, in NaxCoO2 samples with a Na content ranging from x \approx 0.5 to 0.82. Two distinct regimes are observed: for x from about 0.6 to x \approx 0.75 the specific heat is strongly enhanced, with a pronounced upturn of C/T below about 10 K, reaching 47 mJ/(mol K^2). This enhancement is suppressed in a magnetic field indicative of strong low-energy spin fluctuations. At higher Na content the fluctuations are reduced and mu-SR data confirm the SDW ground state below 22 K and the much reduced heat capacity is field independent.Comment: Accepted in Physica