Isospectral deformations of closed Riemannian manifolds with different scalar curvature

We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds, more precisely, on $S^n\times T^m$, where $T^m$ is a torus of dimension $m\ge 2$ and $S^n$ is a sphere of dimension $n\ge 4$. These metrics are not locally homogeneous; in particular, the scalar curvature of each metric is nonconstant. For some of the deformations, the maximum scalar curvature changes during the deformation.Comment: amstex, 10 pages, no figure

An X-ray measurement of Titan's atmospheric extent from its transit of the Crab Nebula

Saturn's largest satellite, Titan, transited the Crab Nebula on 5 January 2003. We observed this astronomical event with the {\it Chandra} X-ray Observatory. An ``occultation shadow'' has clearly been detected and is found to be larger than the diameter of Titan's solid surface. The difference gives a thickness for Titan's atmosphere of 880 $\pm$ 60 km. This is the first measurement of Titan's atmospheric extent at X-ray wavelengths. The value measured is consistent with or slightly larger than those estimated from earlier Voyager observations at other wavelengths. We discuss the possibility of temporal variations in the thickness of Titan's atmosphere.Comment: 14 pages, 5 figures, AASTeX preprint. Accepted for publication in the Astrophysical Journa

Melanophore migration and survival during zebrafish adult pigment stripe development require the immunoglobulin superfamily adhesion molecule Igsf11.

The zebrafish adult pigment pattern has emerged as a useful model for understanding the development and evolution of adult form as well as pattern-forming mechanisms more generally. In this species, a series of horizontal melanophore stripes arises during the larval-to-adult transformation, but the genetic and cellular bases for stripe formation remain largely unknown. Here, we show that the seurat mutant phenotype, consisting of an irregular spotted pattern, arises from lesions in the gene encoding Immunoglobulin superfamily member 11 (Igsf11). We find that Igsf11 is expressed by melanophores and their precursors, and we demonstrate by cell transplantation and genetic rescue that igsf11 functions autonomously to this lineage in promoting adult stripe development. Further analyses of cell behaviors in vitro, in vivo, and in explant cultures ex vivo demonstrate that Igsf11 mediates adhesive interactions and that mutants for igsf11 exhibit defects in both the migration and survival of melanophores and their precursors. These findings identify the first in vivo requirements for igsf11 as well as the first instance of an immunoglobulin superfamily member functioning in pigment cell development and patterning. Our results provide new insights into adult pigment pattern morphogenesis and how cellular interactions mediate pattern formation

Chandra X-Ray Study of Galactic Supernova Remnant G299.2-2.9

We report on observations of the Galactic supernova remnant (SNR) G299.2$-$2.9 with the {\it Chandra X-Ray Observatory}. The high resolution images with {\it Chandra} resolve the X-ray-bright knots, shell, and diffuse emission extending beyond the bright shell. Interior to the X-ray shell is faint diffuse emission occupying the central regions of the SNR. Spatially-resolved spectroscopy indicates a large foreground absorption ($N_{\rm H}$ $\sim$ 3.5 $\times$ 10$^{21}$ cm$^{-2}$), which supports a relatively distant location ($d$ $\sim$ 5 kpc) for the SNR. The blast wave is encountering a highly inhomogeneous ambient medium with the densities ranging over more than an order of magnitude ($n_0$ $\sim$ 0.1 $-$ 4 cm$^{-3}$). Assuming the distance of $d$ $\sim$ 5 kpc, we derive a Sedov age of $\tau$ $\sim$ 4500 yr and an explosion energy of $E_0$ $\sim$ 1.6 $\times$ 10$^{50}$ ergs. The ambient density structure and the overall morphology suggest that G299.2$-$2.9 may be a limb-brightened partial shell extending to $\sim$7 pc radius surrounded by fainter emission extending beyond that to a radius of $\sim$9 pc. This suggests the SNR exploded in a region of space where there is a density gradient whose direction lies roughly along the line of sight. The faint central region shows strong line emission from heavy elements of Si and Fe, which is caused by the presence of the overabundant stellar ejecta there. We find no evidence for stellar ejecta enriched in light elements of O and Ne. The observed abundance structure of the metal-rich ejecta supports a Type Ia origin for G299.2$-$2.9.Comment: 16 pages (AASTex emulator style), 3 Tables, 10 Figures (including 1 color: Figure 1), Accepted by Ap

The Radial Structure of SNR N103B

We report on the results from a Chandra ACIS observation of the young, compact, supernova remnant N103B. The unprecedented spatial resolution of Chandra reveals sub-arcsecond structure, both in the brightness and in spectral variations. Underlying these small-scale variations is a surprisingly simple radial structure in the equivalent widths of the strong Si and S emission lines. We investigate these radial variations through spatially resolved spectroscopy using a plane-parallel, non-equilibrium ionization model with multiple components. The majority of the emission arises from components with a temperature of 1 keV: a fully ionized hydrogen component; a high ionization timescale (n_e*t > 10^12 s cm^-3) component containing Si, S, Ar, Ca, and Fe; and a low ionization timescale (n_e*t ~ 10^{11} s cm^-3) O, Ne, and Mg component. To reproduce the strong Fe Kalpha line, it is necessary to include additional Fe in a hot (> 2 keV), low ionization (n_e*t ~ 10^10.8 s cm^-3) component. This hot Fe may be in the form of hot Fe bubbles, formed in the radioactive decay of clumps of 56Ni. We find no radial variation in the ionization timescales or temperatures of the various components. Rather, the Si and S equivalent widths increase at large radii because these lines, as well as those of Ar and Ca, are formed in a shell occupying the outer half of the remnant. A shell of hot Fe is located interior to this, but there is a large region of overlap between these two shells. In the inner 30% of the remnant, there is a core of cooler, 1 keV Fe. We find that the distribution of the ejecta and the yields of the intermediate mass species are consistent with model prediction for Type Ia events.Comment: 34 pages, including 7 tables and 7 figures, Accepted by Ap