Subpixel Spatial Resolution of the X-Ray Charge-Coupled Device Based on the Charge Cloud Shape

When an X-ray photon lands into a pixel (event pixel), the primary charge is mainly collected into the event pixel. If the X-ray landing position is sufficiently close to the pixel boundary, the primary charge spills over to the adjacent pixel forming split events. We can easily understand that there are three parameters coupled together; the X-ray landing position inside the pixel, the X-ray event pattern and the primary charge cloud shape. We can determine any one of them from the other two parameters. Since we know the charge cloud shape using the multi-pitch mesh experiment, we can calculate the X-ray landing position with subpixel resolution using the event pattern. We applied our method to Ti-K X-rays for the charge-coupled device with $12 \mu$m square pixel. Once the primary charge splits into the adjacent pixel, we can determine the X-ray landing position with subpixel resolution. Using three- or four-pixel split events, we can determine the X-ray landing position with an accuracy of less than $1 \mu$m. For a two-pixel split event, we obtained a similar position accuracy in the split direction with no improvement in the direction perpendicular to it. We will discuss the type of CCD which can achieve the subpixel resolution for the entire area of the CCD.Comment: 16pages, 5 figures. To appear in Jpn. J. Appl. Phys. March, 200

On the Nature of AX J2049.6+2939 and AX J2050.0+2914

AX J2049.6+2939 is a compact X-ray source in the vicinity of the southern blow-up region of the Cygnus Loop supernova remnant (Miyata et al. 1998a). This source was the brightest X-ray source inside the Cygnus Loop observed during the ASCA survey project. The X-ray spectrum was well fitted by a power-law function with a photon index of $-2.1 \pm 0.1$. Short-term timing analysis was performed and no coherent pulsation was found. Follow-up observations with ASCA have revealed a large variation in X-ray intensity by a factor of $\simeq$ 50, whereas the spectral shape did not change within the statistical uncertainties. In the second ASCA observation, we found another X-ray source, AX J2050.0+2941, at the north east of AX J2049.6+2939. During the three ASCA observations, the X-ray intensity of AX J2050.0+2941 varied by a factor of $\simeq$4. No coherent pulsations could be found for AX J2050.0+2941. We have performed optical photometric and spectroscopic observations in the vicinity of AX J2049.6+2939 at the Kitt Peak National Observatory (KPNO). As a result, all objects brighter than $B$-band magnitude of 22 in the error box can be identified with normal stars. Combined with the X-ray results and the fact that there are no radio counterparts, AX J2049.6+2939 is not likely to be either an ordinary rotation-powered pulsar or an AGN. The nature of AX J2049.6+2939 is still unclear and further observations over a wide energy band are strongly required. As to AX J2050.0+2941, the long-term X-ray variability and the radio counterpart suggests that it is an AGN.Comment: 23 pages, 4 figures, Accepted for publication by Astrophysical Journa

Chandra Observations of the Northeastern Rim of the Cygnus Loop

We present results from spatially resolved spectral analyses of the northeastern (NE) rim of the Cygnus Loop supernova remnant (SNR) based on two Chandra observations. One pointing includes northern outermost abundance-enhanced regions discovered by recent Suzaku observations, while the other pointing is located on regions with "normal" abundances in the NE rim of the Cygnus Loop. The superior spatial resolving power of Chandra allows us to reveal that the abundance-enhanced region is concentrated in an about 200"-thickness region behind the shock front. We confirm absolute metal abundances (i.e., relative to H) as well as abundance ratios between metals are consistent with those of the solar values within a factor of about 2. Also, we find that the emission measure in the region gradually decreases toward the shock front. These features are in contrast with those of the ejecta fragments around the Vela SNR, which leads us to believe that the abundance enhancements are not likely due to metal-rich ejecta. We suggest that the origin of the plasma in this region is the interstellar medium (ISM). In the "normal" abundance regions, we confirm that abundances are depleted to the solar values by a factor of about 5 that is not expected in the ISM around the Cygnus Loop. Introduction of non-thermal emission in our model fitting can not naturally resolve the abundance-depletion problem. The origin of the depletion still remains as an open question.Comment: 18 pages, 6 figure

Nonthermal X-Ray Emission from G266.2-1.2 (RX J0852.0-4622)

The newly discovered supernova remnant G266.2-1.2 (RX J0852.0-4622), along the line of sight to the Vela SNR, was observed with ASCA for 120 ks. We find that the X-ray spectrum is featureless, and well described by a power law, extending to three the class of shell-type SNRs dominated by nonthermal X-ray emission. Although the presence of the Vela SNR compromises our ability to accurately determine the column density, the GIS data appear to indicate absorption considerably in excess of that for Vela itself, indicating that G266.2-1.2 may be several times more distant. An unresolved central source may be an associated neutron star, though difficulties with this interpretation persist.Comment: 4 pages, 5 figures, uses aipproc.sty & epsfig.sty. To appear in "Young Supernova Remnants" (11th Annual Astrophysics Conference in Maryland), S. S. Holt & U. Hwang (eds), AIP, New York (2001

Chandra X-ray Observation of a Mature Cloud-Shock Interaction in the Bright Eastern Knot Region of Puppis A

We present Chandra X-ray images and spectra of the most prominent cloud-shock interaction region in the Puppis A supernova remnant. The Bright Eastern Knot (BEK) has two main morphological components: (1) a bright compact knot that lies directly behind the apex of an indentation in the eastern X-ray boundary and (2) lying 1' westward behind the shock, a curved vertical structure (bar) that is separated from a smaller bright cloud (cap) by faint diffuse emission. Based on hardness images and spectra, we identify the bar and cap as a single shocked interstellar cloud. Its morphology strongly resembles the ``voided sphere'' structures seen at late times in Klein et al.'s experimental simulations of cloud-shock interactions, when the crushing of the cloud by shear instabilities is well underway. We infer an interaction time of roughly 3 cloud-crushing timescales, which translates to 2000-4000 years, based on the X-ray temperature, physical size, and estimated expansion of the shocked cloud. This is the first X-ray identified example of a cloud-shock interaction in this advanced phase. Closer to the shock front, the X-ray emission of the compact knot in the eastern part of the BEK region implies a recent interaction with relatively denser gas, some of which lies in front of the remnant. The complex spatial relationship of the X-ray emission of the compact knot to optical [O III] emission suggests that there are multiple cloud interactions occurring along the line of sight.Comment: 22 pages LaTeX with multiple figures, to appear in Ap

The Radial Structure of the Cygnus Loop Supernova Remnant --- Possible evidence of a cavity explosion ---

We observed the North-East (NE) Limb toward the center region of the Cygnus Loop with the ASCA Observatory. We found a radial variation of electron temperature (kTe) and ionization timescale (log(\tau)) whereas no variation could be found for the abundances of heavy elements. In this paper, we re-analyzed the same data set and new observations with the latest calibration files. Then we constructed the precise spatial variations of kTe, log(\tau), and abundances of O, Ne, Mg, Si, and Fe over the field of view (FOV). We found a spatial variation not only in kTe and in log(\tau) but also in most of heavy elements. As described in Miyata et al. (1994), values of kTe increase and those of log(\tau) decrease toward the inner region. We found that the abundance of heavy elements increases toward the inner region. The radial profiles of O, Ne, and Fe show clear jump structures at a radius of 0.9 Rs, where Rs is the shock radius. Outside of 0.9 Rs, abundances of all elements are constant. On the contrary, inside of 0.9 Rs, abundances of these elements are 20--30 % larger than those obtained outside of 0.9 Rs. The radial profile of kTe also shows the jump structure at 0.9 Rs. This means that the hot and metal rich plasma fills the volume inside of 0.9 Rs. We concluded that this jump structure was the possible evidence for the pre-existing cavity produced by the precursor. If the ejecta fills inside of 0.9 Rs, the total mass of the ejecta was roughly 4\Msun. We then estimated the main-sequence mass to be roughly 15\Msun, which supports the massive star in origin of the Cygnus Loop supernova remnant and the existence of a pre-existing cavity.Comment: 37 pages, 14 figures. Accepted for publication of Ap

Influence of Model Accuracy on Load and Resistance Factor

Risk and Reliability in Geotechnical Engineerin

Reflection Shocked Gas in the Cygnus Loop Supernova Remnant

We performed spectroscopic X-ray observations of the eastern and northern regions of the Cygnus Loop with the ASCA observatory. The X-ray surface brightness of these regions shows a complex structure in the ROSAT all-sky survey image. We carried out a spatially-resolved analysis for both regions and found that $kT_{\rm e}$ did not increase toward the center region, but showed inhomogeneous structures. Such variation cannot be explained by a blast wave model propagating into a homogeneous interstellar medium. We thus investigated the interaction between a blast wave and an interstellar cloud. Two major emission mechanisms are plausible: a cloud evaporation model and a reflection shock model. In both regions, only a reflection shock model qualitatively explains our results. Our results suggest the existence of a large-scale interstellar cloud. We suppose that such a large-scale structure would be produced by a precursor.Comment: 27 pages, 15 figures. Accepted for publication of ApJ. High resolution and color figures are available at http://wwwxray.ess.sci.osaka-u.ac.jp/~miyata/paper/cygloop_reflection.pd

Equivariant log concavity and representation stability

We expand upon the notion of equivariant log concavity, and make equivariant log concavity conjectures for Orlik--Solomon algebras of matroids, Cordovil algebras of oriented matroids, and Orlik--Terao algebras of hyperplane arrangements. In the case of the Coxeter arrangement for the Lie algebra $\mathfrak{sl}_n$, we exploit the theory of representation stability to give computer assisted proofs of these conjectures in low degree