A commonly used measure to summarize the nature of a photon spectrum is the so-called hardness ratio, which compares the numbers of counts observed in different passbands. The hardness ratio is especially useful to distinguish between and categorize weak sources as a proxy for detailed spectral fitting. However, in this regime classical methods of error propagation fail, and the estimates of spectral hardness become unreliable. Here we develop a rigorous statistical treatment of hardness ratios that properly deals with detected photons as independent Poisson random variables and correctly deals with the non-Gaussian nature of the error propagation. The method is Bayesian in nature and thus can be generalized to carry out a multitude of source-populationYbased analyses. We verify our method with simulation studies and compare it with the classical method. We apply this method to real-world examples, such as the identification of candidate quiescent low-mass X-ray binaries in globular clusters and tracking the time evolution of a flare on a low-mass star.

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We present images from five observations of the quasar 3C 273 with the Chandra X-Ray Observatory. The jet has at least four distinct features that are not resolved in previous observations. The first knot in the jet (A1) is very bright in X-rays. Its X-ray spectrum is well fitted with a power law with (where a p 0.60 ‫ע‬ 0.05 ). Combining this measurement with lower frequency data shows that a pure synchrotron model can fit Ϫa S ∝ n n the spectrum of this knot from 1.647 GHz to 5 keV (over nine decades in energy) with , similar a p 0.76 ‫ע‬ 0.02 to the X-ray spectral slope. Thus, we place a lower limit on the total power radiated by this knot of 1.5 # ergs s Ϫ1 ; substantially more power may be emitted in the hard X-ray and g-ray bands. Knot A2 is also 43 10 detected and is somewhat blended with knot B1. Synchrotron emission may also explain the X-ray emission, but a spectral bend is required near the optical band. For knots A1 and B1, the X-ray flux dominates the emitted energy. For the remaining optical knots (C through H), localized X-ray enhancements that might correspond to the optical features are not clearly resolved. The position angle of the jet ridge line follows the optical shape with distinct, aperiodic excursions of ‫1ע‬Њ from a median value of Ϫ138Њ .0. Finally, we find X-ray emission from the "inner jet" between 5Љ and 10Љ from the core.

We present an exploratory Chandra ACIS-S3 study of the diffuse component of the cosmic X-ray background (CXB) in the 0.3-7 keV band for four directions at high Galactic latitudes, with emphasis on details of the ACIS instrumental background modeling. Observations of the dark Moon are used to model the detector background. A comparison of the Moon data and the data obtained with ACIS stowed outside the focal area showed that the dark Moon does not emit significantly in our band. Point sources down to 3 Â 10 À16 ergs s À1 cm À2 in the 0.5-2 keV band are excluded in our two deepest observations. We estimate the contribution of fainter, undetected sources to be less than 20% of the remaining CXB flux in this band in all four pointings. In the 0.3-1 keV band, the diffuse signal varies strongly from field to field and contributes between 55% and 90% of the total CXB signal. It is dominated by emission lines that can be modeled by a kT ¼ 0:1 0:4 keV plasma. In particular, the two fields located away from bright Galactic features show a prominent line blend at E % 580 eV (O vii+O viii) and a possible line feature at E $ 300 eV. The two pointings toward the North Polar Spur exhibit a brighter O blend and additional bright lines at 730-830 eV (Fe xvii). We measure the total 1-2 keV flux of 1:0 1:2 AE 0:2 ð Þ Â 10 À15 ergs s À1 cm À2 arcmin À2 (mostly resolved) and the 2-7 keV flux of 4:0 4:5 AE 1:5 ð Þ Â 10 À15 ergs s À1 cm À2 arcmin À2 . At E > 2 keV, the diffuse emission is consistent with zero, to an accuracy limited by the short Moon exposure and systematic uncertainties of the S3 background. Assuming Galactic or local origin of the line emission, we put an upper limit of $3 Â 10 À15 ergs s À1 cm À2 arcmin À2 on the 0.3-1 keV extragalactic diffuse flux.

We have analyzed data from two sets of calibration observations of the Moon made by the Chandra X-Ray Observatory. In addition to obtaining a spectrum of the bright side that shows several distinct fluorescence lines, we also clearly detect time-variable soft X-ray emission, primarily O VII Kα and O VIII Lyα, when viewing the optically dark side. The apparent dark-side brightness varied by at least an order of magnitude, up to ∼ 2 × 10 −6 phot s −1 arcmin −2 cm −2 between 500 and 900 eV, which is comparable to the typical 3/4-keV-band background emission measured in the ROSAT All-Sky Survey. The spectrum is also very similar to background spectra recorded by Chandra in low or moderate-brightness regions of the sky. Over a decade ago, ROSAT also detected soft X-rays from the dark side of the Moon, which were tentatively ascribed to continuum emission from energetic solar wind electrons impacting the lunar surface. The Chandra observations, however, with their better spectral resolution, combined with contemporaneous measurements of solar-wind parameters, strongly favor charge transfer between highly charged solar-wind ions and neutral hydrogen in the Earth's geocorona as the mechanism for this emission. We present a theoretical model of geocoronal emission and show that predicted spectra and intensities match the Chandra observations very well. We also model the closely related process of heliospheric charge transfer and estimate that the total charge transfer flux observed from Earth amounts to a significant fraction of the soft X-ray background, particularly in the ROSAT 3/4-keV band. Subject headings: atomic processes -Moon -solar wind -X-rays: diffuse background -X-rays: general Exposure Chandra ObsID Date CCDs (s) Time