Very accurate Distances and Radii of Open Cluster Cepheids from a Near-Infrared Surface Brightness Technique

We have obtained the radii and distances of 16 galactic Cepheids supposed to be members in open clusters or associations using the new optical and near-infrared calibrations of the surface brightness (Barnes-Evans) method given by Fouque & Gieren (1997). We discuss in detail possible systematic errors in our infrared solutions and conclude that the typical total uncertainty of the infrared distance and radius of a Cepheid is about 3 percent in both infrared solutions, provided that the data are of excellent quality and that the amplitude of the color curve used in the solution is larger than ~0.3 mag. We compare the adopted infrared distances of the Cepheid variables to the ZAMS-fitting distances of their supposed host clusters and associations and find an unweighted mean value of the distance ratio of 1.02 +- 0.04. A detailed discussion of the individual Cepheids shows that the uncertainty of the ZAMS-fitting distances varies considerably from cluster to cluster. We find clear evidence that four Cepheids are not cluster members (SZ Tau, T Mon, U Car and SV Vul) while we confirm cluster membership for V Cen and BB Sgr for which the former evidence for cluster membership was only weak. After rejection of non-members, we find a weighted mean distance ratio of 0.969 +- 0.014, with a standard deviation of 0.05, which demonstrates that both distance indicators are accurate to better than 5%, including systematic errors, and that there is excellent agreement between both distance scales.Comment: LaTeX, 11 Figures, 5 Tables, to be published in The Astrophysical Journal, Oct. 10, 1997 issu

Primordial B-mode Diagnostics and Self Calibrating the CMB Polarization

Distortions in the primordial cosmic microwave background (CMB) along the line-of-sight can be modeled and described using 11 fields. These distortion fields correspond to various cosmological signals such as weak gravitational lensing of the CMB by large-scale structure, screening from patchy reionization, rotation of the plane of polarization due to magnetic fields or parity violating physics. Various instrumental systematics such as gain fluctuations, pixel rotation, differential gain, pointing, differential ellipticity are also described by the same distortion model. All these distortions produce B-mode that contaminate the primordial tensor B-modes signal. In this paper we show that apart from generating B-modes, each distortion uniquely couples different modes (\bfl_1\ne \bfl_2) of the CMB anisotropies, generating $$ correlations which for the primordial CMB are zero. We describe and implement unbiased minimum variance quadratic estimators which using the off diagonal correlations in the CMB can extract the map of distortions. We perform Monte-Carlo simulations to characterize the estimators and illustrate the level of distortions that can be detected with current and future experiments. The estimators can be used to look for cosmological signals, or to check for any residual systematics in the data. As a specific example of primordial tensor B-mode diagnostics we compare the level of minimum detectable distortions using our method with maximum allowed distortion level for the B-modes detection. We show that for any experiment, the distortions will be detected at high significance using correlations before they would show up as spurious B-modes in the power spectrum.Comment: 14 pages, 4 figure

On the BKS pairing for Kahler quantizations of the cotangent bundle of a Lie group

A natural one-parameter family of K\"ahler quantizations of the cotangent bundle $T^*K$ of a compact Lie group $K$, taking into account the half-form correction, was studied in \cite{FMMN}. In the present paper, it is shown that the associated Blattner-Kostant-Sternberg (BKS) pairing map is unitary and coincides with the parallel transport of the quantum connection introduced in our previous work, from the point of view of \cite{AdPW}. The BKS pairing map is a composition of (unitary) coherent state transforms of $K$, introduced in \cite{Ha1}. Continuity of the Hermitian structure on the quantum bundle, in the limit when one of the K\"ahler polarizations degenerates to the vertical real polarization, leads to the unitarity of the corresponding BKS pairing map. This is in agreement with the unitarity up to scaling (with respect to a rescaled inner product) of this pairing map, established by Hall.Comment: final version, to appear in Journ. Funct. Ana

Geometric quantization, complex structures and the coherent state transform

It is shown that the heat operator in the Hall coherent state transform for a compact Lie group $K$ is related with a Hermitian connection associated to a natural one-parameter family of complex structures on $T^*K$. The unitary parallel transport of this connection establishes the equivalence of (geometric) quantizations of $T^*K$ for different choices of complex structures within the given family. In particular, these results establish a link between coherent state transforms for Lie groups and results of Hitchin and Axelrod, Della Pietra and Witten.Comment: to appear in Journal of Functional Analysi