Distances and Cosmology From Galaxy Cluster CMB Data

The measurement of angular diameter distance to galaxy clusters, through combined Sunyaev-Zel'dovich (SZ) effect data with X-ray emission observations, is now a well-known probe of cosmology. Using a combination of SZ data and a map of the lensed CMB anisotropies by the galaxy cluster potential, we propose an alternative geometric technique to measure distance information primarily through cluster related multi-frequency CMB measurements. We discuss necessary requirements to implement this measurement, potential errors including systematic biases, and the extent to which cosmological parameters can be extracted. While individual cluster distances are not likely to be precise, with upcoming subarcminute resolution wide-area CMB observations, useful information on certain cosmological parameters, such as the equation of state of dark energy, can be obtained from a large sample of galaxy clusters.Comment: 4 pages, 2 figure

Galaxy Cluster Shapes and Systematic Errors in H0 Measured by the Sunyaev-Zel'dovich Effect

Imaging of the Sunyaev-Zel'dovich (SZ) effect in galaxy clusters combined with cluster plasma x-ray diagnostics can measure the cosmic distance scale to high redshift. Projecting the inverse-Compton scattering and x-ray emission along the cluster line-of-sight introduces systematic errors in the Hubble constant, H0, because the true shape of the cluster is not known. I present a study of the systematic errors in the value of H0, as determined by the x-ray and SZ properties of theoretical samples of triaxial isothermal ``beta'' model clusters, caused by projection effects and observer orientation. I calculate estimates for H0 for each cluster based on their large and small apparent angular core radii and their arithmetic mean. I demonstrate that the estimates for H0 for a sample of 25 clusters have 99.7% confidence intervals for the mean estimated H0 analyzing the clusters using either their large or mean angular core radius are within 14% of the ``true'' (assumed) value of H0 (and enclose it), for a triaxial beta model cluster sample possessing a distribution of apparent x-ray cluster ellipticities consistent with that of observed x-ray clusters. This limit on the systematic error in H0 caused by cluster shape assumes that each sample beta model cluster has fixed shape; deviations from constant shape within the clusters may introduce additional uncertainty or bias into this result.Comment: Accepted for publication in the Astrophysical Journal, 24 March 1998; 4 pages, 2 figure

Can Strong Gravitational Lensing Constrain Dark Energy?

We discuss the ratio of the angular diameter distances from the source to the lens, $D_{ds}$, and to the observer at present, $D_{s}$, for various dark energy models. It is well known that the difference of $D_s$s between the models is apparent and this quantity is used for the analysis of Type Ia supernovae. However we investigate the difference between the ratio of the angular diameter distances for a cosmological constant, $(D_{ds}/D_{s})^{\Lambda}$ and that for other dark energy models, $(D_{ds}/D_{s})^{\rm{other}}$ in this paper. It has been known that there is lens model degeneracy in using strong gravitational lensing. Thus, we investigate the model independent observable quantity, Einstein radius ($\theta_E$), which is proportional to both $D_{ds}/D_s$ and velocity dispersion squared, $\sigma_v^2$. $D_{ds}/D_s$ values depend on the parameters of each dark energy model individually. However, $(D_{ds}/D_s)^{\Lambda} - (D_{ds}/D_{s})^{\rm{other}}$ for the various dark energy models, is well within the error of $\sigma_v$ for most of the parameter spaces of the dark energy models. Thus, a single strong gravitational lensing by use of the Einstein radius may not be a proper method to investigate the property of dark energy. However, better understanding to the mass profile of clusters in the future or other methods related to arc statistics rather than the distances may be used for constraints on dark energy.Comment: 15 pages, 13 figures, Accepted in PR

An Ultra Low Mass and Small Radius Compact Object in 4U 1746-37?

Photospheric radius expansion (PRE) bursts have already been used to constrain the masses and radii of neutron stars. RXTE observed three PRE bursts in 4U 1746-37, all with low touchdown fluxes. We discuss here the possibility of low mass neutron star in 4U 1746-37 because the Eddington luminosity depends on stellar mass. With typical values of hydrogen mass fraction and color correction factor, a Monte-Carlo simulation was applied to constrain the mass and radius of neutron star in 4U 1746-37. 4U 1746-37 has a high inclination angle. Two geometric effects, the reflection of the far side accretion disc and the obscuration of the near side accretion disc have also been included in the mass and radius constraints of 4U 1746-37. If the reflection of the far side accretion disc is accounted, a low mass compact object (mass of $0.41\pm0.14~M_{\odot}$ and radius of $8.73\pm1.54~\rm km$ at 68% confidence) exists in 4U 1746-37. If another effect operated, 4U 1746-37 may contain an ultra low mass and small radius object ($M=0.21\pm0.06~M_{\odot},~R=6.26\pm0.99~\rm km$ at 68% confidence). Combined all possibilities, the mass of 4U 1746-37 is $0.41^{+0.70}_{-0.30}~M_\odot$ at 99.7% confidence. For such low mass NS, it could be reproduced by a self-bound compact star, i.e., quark star or quark-cluster star.Comment: accepted by Ap

Critical percolation in the dynamics of the 2d ferromagnetic Ising model

We study the early time dynamics of the 2d ferromagnetic Ising model instantaneously quenched from the disordered to the ordered, low temperature, phase. We evolve the system with kinetic Monte Carlo rules that do not conserve the order parameter. We confirm the rapid approach to random critical percolation in a time-scale that diverges with the system size but is much shorter than the equilibration time. We study the scaling properties of the evolution towards critical percolation and we identify an associated growing length, different from the curvature driven one. By working with the model defined on square, triangular and honeycomb microscopic geometries we establish the dependence of this growing length on the lattice coordination. We discuss the interplay with the usual coarsening mechanism and the eventual fall into and escape from metastability.Comment: 67 pages, 33 figure

Spectral Unmixing with Multiple Dictionaries

Spectral unmixing aims at recovering the spectral signatures of materials, called endmembers, mixed in a hyperspectral or multispectral image, along with their abundances. A typical assumption is that the image contains one pure pixel per endmember, in which case spectral unmixing reduces to identifying these pixels. Many fully automated methods have been proposed in recent years, but little work has been done to allow users to select areas where pure pixels are present manually or using a segmentation algorithm. Additionally, in a non-blind approach, several spectral libraries may be available rather than a single one, with a fixed number (or an upper or lower bound) of endmembers to chose from each. In this paper, we propose a multiple-dictionary constrained low-rank matrix approximation model that address these two problems. We propose an algorithm to compute this model, dubbed M2PALS, and its performance is discussed on both synthetic and real hyperspectral images

Microarcsecond astrometry with Gaia: the solar system, the Galaxy and beyond

Gaia is an all sky, high precision astrometric and photometric satellite of the European Space Agency (ESA) due for launch in 2010-2011. Its primary mission is to study the composition, formation and evolution of our Galaxy. Gaia will measure parallaxes and proper motions of every object in the sky brighter than V=20, amounting to a billion stars, galaxies, quasars and solar system objects. It will achieve an astrometric accuracy of 10muas at V=15 - corresponding to a distance accuracy of 1% at 1kpc. With Gaia, tens of millions of stars will have their distances measured to a few percent or better. This is an improvement over Hipparcos by several orders of magnitude in the number of objects, accuracy and limiting magnitude. Gaia will also measure radial velocities for source brighter than V~17. To characterize the objects, each object is observed in 15 medium and broad photometric bands with an onboard CCD camera. With these capabilities, Gaia will make significant advances in a wide range of astrophysical topics. These include a detailed kinematical map of stellar populations, stellar structure and evolution, the discovery and characterization of thousands of exoplanetary systems and General Relativity on large scales. I give an overview of the mission, its operating principles and its expected scientific contributions. For the latter I provide a quick look in five areas on increasing scale size in the universe: the solar system, exosolar planets, stellar clusters and associations, Galactic structure and extragalactic astronomy.Comment: (Errors corrected) Invited paper at IAU Colloquium 196, "Transit of Venus: New Views of the Solar System and Galaxy". 14 pages, 6 figures. Version with higher resolution figures available from http://www.mpia-hd.mpg.de/homes/calj/gaia_venus2004.htm