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The production of complex astronomical data is accelerating, especially with newer telescopes producing ever more large-scale surveys. The increased quantity, complexity, and variety of astronomical data demand a parallel increase in skill and sophistication in developing, deciding, and deploying statistical methods. Understanding limitations and appreciating nuances in statistical and machine learning methods and the reasoning behind them is essential for improving data-analytic proficiency and acumen. Aiming to facilitate such improvement in astronomy, we delineate cautionary tales in statistics via six maxims, with examples drawn from the astronomical literature. Inspired by the significant quality improvement in business and manufacturing processes by the routine adoption of Six Sigma, we hope the routine reflection on these Six Maxims will improve the quality of both data analysis and scientific findings in astronomy.

We present a new method to distinguish between different states (e.g., high and low, quiescent and flaring) in astronomical sources with count data. The method models the underlying physical process as latent variables following a continuous-space Markov chain that determines the expected Poisson counts in observed light curves in multiple passbands. For the underlying state process, we consider several autoregressive processes, yielding continuous-space hidden Markov models of varying complexity. Under these models, we can infer the state that the object is in at any given time. The continuous state predictions from these models are then dichotomized with the help of a finite mixture model to produce state classifications. We apply these techniques to X-ray data from the active dMe flare star EV Lac, splitting the data into quiescent and flaring states. We find that a first-order vector autoregressive process efficiently separates flaring from quiescence: flaring occurs over 30-40% of the observation durations, a well-defined persistent quiescent state can be identified, and the flaring state is characterized by higher plasma temperatures and emission measures., Comment: 27 pages, 13 figures, 12 tables

We estimate the coronal density of Capella using the O VII and Fe XVII line systems in the soft X-ray regime that have been observed over the course of the Chandra mission. Our analysis combines measures of error due to uncertainty in the underlying atomic data with statistical errors in the Chandra data to derive meaningful overall uncertainties on the plasma density of the coronae of Capella. We consider two Bayesian frameworks. First, the so-called pragmatic-Bayesian approach considers the atomic data and their uncertainties as fully specified and uncorrectable. The fully-Bayesian approach, on the other hand, allows the observed spectral data to update the atomic data and their uncertainties, thereby reducing the overall errors on the inferred parameters. To incorporate atomic data uncertainties, we obtain a set of atomic data replicates, the distribution of which captures their uncertainty. A principal component analysis of these replicates allows us to represent the atomic uncertainty with a lower-dimensional multivariate Gaussian distribution. A $t$-distribution approximation of the uncertainties of a subset of plasma parameters including a priori temperature information, obtained from the temperature-sensitive-only Fe XVII spectral line analysis, is carried forward into the density- and temperature-sensitive O VII spectral line analysis. Markov Chain Monte Carlo based model fitting is implemented including Multi-step Monte Carlo Gibbs Sampler and Hamiltonian Monte Carlo. Our analysis recovers an isothermally approximated coronal plasma temperature of $\approx$5 MK and a coronal plasma density of $\approx$10$^{10}$ cm$^{-3}$, with uncertainties of 0.1 and 0.2 dex respectively.

We present a new method for joint likelihood deconvolution (Jolideco) of a set of astronomical observations of the same sky region in the presence of Poisson noise. The observations may be obtained from different instruments with different resolution, and different point spread functions. Jolideco reconstructs a single flux image by optimizing the posterior distribution based on the joint Poisson likelihood of all observations under a patch-based image prior. The patch prior is parameterised via a Gaussian Mixture model which we train on high-signal-to-noise astronomical images, including data from the James Webb Telescope and the GLEAM radio survey. This prior favors correlation structures among the reconstructed pixel intensities that are characteristic of those observed in the training images. It is, however, not informative for the mean or scale of the reconstruction. By applying the method to simulated data we show that the combination of multiple observations and the patch-based prior leads to much improved reconstruction quality in many different source scenarios and signal to noise regimes. We demonstrate that with the patch prior Jolideco yields superior reconstruction quality relative to alternative standard methods such as the Richardson-Lucy method. We illustrate the results of Jolideco applied to example data from the Chandra X-ray Observatory and the Fermi-LAT Gamma-ray Space Telescope. By comparing the measured width of a counts based and the corresponding Jolideco flux profile of an X-ray filament in SNR 1E 0102.2-721} we find the deconvolved width of 0.58+- 0.02 arcsec to be consistent with the theoretical expectation derived from the known width of the PSF., Comment: 25 pages, 11 figures

Spectral fitting of X-ray data usually involves minimizing statistics like the chi-square and the Cash statistic. Here we discuss their limitations and introduce two measures based on the cumulative sum (CuSum) of model residuals to evaluate whether model complexity could be increased: the percentage of bins exceeding a nominal threshold in a CuSum array (pct$_{CuSum}$), and the excess area under the CuSum compared to the nominal (p$_\textit{area}$). We demonstrate their use with an application to a $\textit{Chandra}$ ACIS spectral fit., Comment: 3 pages, 1 figure, published in the Research Notes of the American Astronomical Society (RNAAS)

We outline some of the highlights of the scientific case for the advancement of stellar high energy physics using the Line Emission Mapper X-ray Probe ({\it LEM}). The key to advancements with LEM lie in its large effective area -- up to 100 times that of the {\it Chandra} MEG -- and 1~eV spectral resolution. The large effective area opens up for the first time the ability to study time-dependent phenomena on their natural timescales at high resolution, such as flares and coronal mass ejections, and also opens the sky to much fainter targets than available to {\it Chandra} or {\it XMM-Newton}., Comment: A Line Emission Mapper X-ray Probe White Paper

GRS 1747-312 is a bright Low-Mass X-ray Binary in the globular cluster Terzan 6, located at a distance of 9.5 kpc from the Earth. It exhibits regular outbursts approximately every 4.5 months, during which periodic eclipses are known to occur. These eclipses have only been observed in the outburst phase, and are not clearly seen when the source is quiescent. Recent Chandra observations of the source were performed in June 2019 and April, June, and August of 2021. Two of these observations captured the source during its outburst, and showed clear flux decreases at the expected time of eclipse. The other two observations occurred when the source was quiescent. We present the discovery of a dip that occurred during the quiescent state. The dip is of longer duration and its time of occurrence does not fit the ephemeris of the shorter eclipses. We study the physical characteristics of the dip and determine that it has all the properties of an eclipse by an object with a well defined surface. We find that there are several possibilities for the nature of the object causing the 5.3 ks eclipse. First, GRS 1747-312 may be an X-ray triple, with an LMXB orbited by an outer third object, which could be an M-dwarf, brown dwarf, or planet. Second, there could be two LMXBs in close proximity to each other, likely bound together. Whatever the true nature of the eclipser, its presence suggests that the GRS 1747-312 system is unique., Comment: 38 pages, 30 figures, submitted to MNRAS

We have devised a predominantly Naive Bayes method to classify the optical/IR matches to X-ray sources detected by Chandra in the Cygnus OB2 association into foreground, member, and background objects. We employ a variety of X-ray, optical, and infrared characteristics to construct likelihoods using training sets defined by well-measured sources. Combinations of optical photometry from SDSS (riz) and IPHAS (riHa), IR magnitudes from UKIDSS and 2MASS (JHK), X-ray quantiles and hardness ratios, and estimates of extinction Av are used to compute the relative probabilities that a given source belongs to one of the classes. We use Principal Component Analysis of photometric magnitude combinations to isolate the best axes for classification. We incorporate measurement errors into the classification. We evaluate the accuracy of the classification by inspection and reclassify a number of sources based on IR magnitudes, presence of disks, and X-ray spectral hardness. We also consider systematic errors due to extinction. We find that about 6100 objects are association members, 1400 are background, and 500 are foreground objects. The overall classification accuracy is 95%., Comment: 27 pages, 23 figures, 6 tables; accepted for publication in ApJS. Full Table 3 is in Zenodo at https://zenodo.org/record/8025756

Astrophysical jets are present in a range of environments, including young stellar objects, X-ray binaries, and active galactic nuclei, but their formation is still not fully understood. As one of the nearest symbiotic binary stars, R Aquarii ($D \sim 220$ pc) offers a unique opportunity to study the inner region within $\sim$ 600 AU of the jet source, which is particularly crucial to our understanding of non-relativistic jet formation and origin. We present high-angular resolution ultraviolet and optical imaging from the \emph{Hubble} Space Telescope in six emission-line regions of the inner jet. Using these observations to obtain a range of representative line ratios for our system and kinematic data derived from a comparison with previous studies, we model the shocked gas in order to determine the relative roles of shock heating and photoionization in the R Aquarii system. We find that our shock models suggest a nonzero magnetic field is needed to describe the measured line ratios. We also find that the Mg~II$\lambda\lambda$2795,2802 intensities are overpredicted by our models for most of the jet regions, perhaps because of depletion onto grains or to opacity in these resonance lines., Comment: 22 pages, 10 figures, accepted for publication in ApJ

Studying Doppler shifts provides deeper insights into the flow of mass and energy in the solar atmosphere. We perform a comprehensive measurement of Doppler shifts in the transition region and its center-to-limb variation (CLV) in the strong field regions ($|\textbf{B}| \geq$ 50 G) of 50 active regions (ARs), using the \ion{Si}{4} 1394~{\AA} line recorded by the Interface Region Imaging Spectrometer(IRIS). To locate the ARs and identify strong field regions, we have used the magnetograms obtained by the Helioseismic and Magnetic Imager (HMI). We find that in strong field regions, on average, all the ARs show mean redshifts ranging between 4{--}11~ km/s, which varies with ARs. These flows show a mild CLV, with sizable magnitudes at the limb and substantial scatter at the mid-longitude range. Our observations do not support the idea that redshifts in the lower transition region (T $<\sim$ 0.1 MK) are produced by field-aligned downflows as a result of impulsive heating and warrant alternative interpretation, such as downflow of type-\rm{II} spicules in the presence of a chromospheric wall created by cooler type-\rm{I} spicules., Comment: Accepted for publication in the Astrophysical Journal on 16th January 2023

We carry out detailed spectral and timing analyses of the $Chandra$ X-ray data of HD 179949, a prototypical example of a star with a close-in giant planet with possible star-planet interaction (SPI) effects. We find a low coronal abundance $A({\rm Fe})/A({\rm H}){\approx}0.2$ relative to the solar photospheric baseline of Anders & Grevesse (1989), and significantly lower than the stellar photosphere as well. We further find low abundances of high First Ionization Potential (FIP) elements $A({\rm O})/A({\rm Fe}){\lesssim}1$, $A({\rm Ne})/A({\rm Fe}){\lesssim}0.1$, but with indications of higher abundances of $A({\rm N})/A({\rm Fe}){\gg}1, A({\rm Al})/A({\rm Fe}){\lesssim}10$. We estimate a FIP bias for this star in the range $\approx{-0.3}$ to ${-0.1}$, larger than the ${\lesssim}-$0.5 expected for stars of this type, but similar to stars hosting close-in hot Jupiters. We detect significant intensity variability over time scales ranging from 100 s - 10 ks, and also evidence for spectral variability over time scales of 1-10 ks. We combine the $Chandra$ flux measurements with $Swift$ and XMM-$Newton$ measurements to detect periodicities and determine that the dominant signal is tied to the stellar polar rotational period, consistent with expectations that the corona is rotational-pole dominated. We also find evidence for periodicity at both the planetary orbital frequency and at its beat frequency with the stellar polar rotational period, suggesting the presence of a magnetic connection between the planet and the stellar pole. If these periodicities represent an SPI signal, it is likely driven by a quasi-continuous form of heating (e.g., magnetic field stretching) rather than sporadic, hot, impulsive flare-like reconnections., Comment: 26 pages, 12 figures, 11 tables. Accepted for publication in the Astrophysical Journal

Data from high-energy observations are usually obtained as lists of photon events. A common analysis task for such data is to identify whether diffuse emission exists, and to estimate its surface brightness, even in the presence of point sources that may be superposed. We have developed a novel non-parametric event list segmentation algorithm to divide up the field of view into distinct emission components. We use photon location data directly, without binning them into an image. We first construct a graph from the Voronoi tessellation of the observed photon locations and then grow segments using a new adaptation of seeded region growing, that we call Seeded Region Growing on Graph, after which the overall method is named SRGonG. Starting with a set of seed locations, this results in an over-segmented dataset, which SRGonG then coalesces using a greedy algorithm where adjacent segments are merged to minimize a model comparison statistic; we use the Bayesian Information Criterion. Using SRGonG we are able to identify point-like and diffuse extended sources in the data with equal facility. We validate SRGonG using simulations, demonstrating that it is capable of discerning irregularly shaped low surface-brightness emission structures as well as point-like sources with strengths comparable to that seen in typical X-ray data. We demonstrate SRGonG's use on the Chandra data of the Antennae galaxies, and show that it segments the complex structures appropriately.

A variety of statistical methods for understanding variability in the time domain for low count rate X-ray and gamma-ray sources are explored. Variability can be detected using nonparametric (Anderson-Darling and overdispersion tests) and parametric (sequential likelihood-based tests) tools. Once detected, variability can be characterized by nonparametric (autocorrelation function, structure function,wavelet analysis) and parametric (multiple change point model such as Bayesian Blocks, integer autoregressive models, C-statistic and Poisson regression) methods. New multidimensional variability detection approaches are outlined. Software packages designed for high energy data analysis are deficient but tools are available in the R statistical software environment. Most of the methods presented here are not commonly used in high energy astronomy., Comment: 26 pages, 9 figures. To appear in Handbook for X-ray and Gamma-Ray Astrophysics, Volume 4: Analysis techniques, Section XVIII: Timing Analysis (Belloni & Bhattacharya, eds., Springer)

We describe a process for cross-calibrating the effective areas of X-ray telescopes that observe common targets. The targets are not assumed to be "standard candles" in the classic sense, in that we assume that the source fluxes have well-defined, but {\it a priori} unknown values. Using a technique developed by Chen et al. (2019, arXiv:1711.09429) that involves a statistical method called {\em shrinkage estimation}, we determine effective area correction factors for each instrument that brings estimated fluxes into the best agreement, consistent with prior knowledge of their effective areas. We expand the technique to allow unique priors on systematic uncertainties in effective areas for each X-ray astronomy instrument and to allow correlations between effective areas in different energy bands. We demonstrate the method with several data sets from various X-ray telescopes., Comment: 37 pages, 9 figures, and 10 tables plus an appendix with 7 data tables. Accepted for publication in the Astronomical Journal

Small scale transients occur in the Solar corona at much higher frequencies than flares and play a significant role in coronal dynamics. Here we study three well-identified transients discovered by Hi-C and also detected by the EUV channels of Atmospheric Imaging Assembly (AIA) on board Solar Dynamics Observatory (SDO). We use 0-D enthalpy-based hydrodynamical simulations and produce synthetic light curves to compare with AIA observations. We have modeled these transients as loops of ~ 1.0~Mm length depositing energies ~ 10^23 ergs in ~ 50 seconds. The simulated synthetic light curves show reasonable agreement with the observed light curves. During the initial phase, conduction flux from the corona dominates over the radiation, like impulsive flaring events. Our results further show that the time-integrated net enthalpy flux is positive, hence into the corona. The fact that we can model the observed light curves of these transients reasonably well by using the same physics as those for nanoflares, microflares, and large flares, suggests that these transients may have a common origin., Comment: Published in ApJ, 16 pages, 13 figures, and 3 tables

The analysis of individual X-ray sources that appear in a crowded field can easily be compromised by the misallocation of recorded events to their originating sources. Even with a small number of sources, that nonetheless have overlapping point spread functions, the allocation of events to sources is a complex task that is subject to uncertainty. We develop a Bayesian method designed to sift high-energy photon events from multiple sources with overlapping point spread functions, leveraging the differences in their spatial, spectral, and temporal signatures. The method probabilistically assigns each event to a given source. Such a disentanglement allows more detailed spectral or temporal analysis to focus on the individual component in isolation, free of contamination from other sources or the background. We are also able to compute source parameters of interest like their locations, relative brightness, and background contamination, while accounting for the uncertainty in event assignments. Simulation studies that include event arrival time information demonstrate that the temporal component improves event disambiguation beyond using only spatial and spectral information. The proposed methods correctly allocate up to 65% more events than the corresponding algorithms that ignore event arrival time information. We apply our methods to two stellar X-ray binaries, UV Cet and HBC515 A, observed with Chandra. We demonstrate that our methods are capable of removing the contamination due to a strong flare on UV Cet B in its companion approximately 40 times weaker during that event, and that evidence for spectral variability at timescales of a few ks can be determined in HBC515 Aa and HBC515 Ab.

Many astrophysical phenomena are time-varying, in the sense that their intensity, energy spectrum, and/or the spatial distribution of the emission suddenly change. This paper develops a method for modeling a time series of images. Under the assumption that the arrival times of the photons follow a Poisson process, the data are binned into 4D grids of voxels (time, energy band, and x-y coordinates), and viewed as a time series of non-homogeneous Poisson images. The method assumes that at each time point, the corresponding multi-band image stack is an unknown 3D piecewise constant function including Poisson noise. It also assumes that all image stacks between any two adjacent change points (in time domain) share the same unknown piecewise constant function. The proposed method is designed to estimate the number and the locations of all the change points (in time domain), as well as all the unknown piecewise constant functions between any pairs of the change points. The method applies the minimum description length (MDL) principle to perform this task. A practical algorithm is also developed to solve the corresponding complicated optimization problem. Simulation experiments and applications to real datasets show that the proposed method enjoys very promising empirical properties. Applications to two real datasets, the XMM observation of a flaring star and an emerging solar coronal loop, illustrate the usage of the proposed method and the scientific insight gained from it., Comment: 22 pages, 10 figures

Do external galaxies host planetary systems? Many lines of reasoning suggest that the answer must be 'yes'. In the foreseeable future, however, the question cannot be answered by the methods most successful in our own Galaxy. We report on a different approach which focuses on bright X-ray sources (XRSs). M51-ULS-1b is the first planet candidate to be found because it produces a full, short-lived eclipse of a bright XRS. M51-ULS-1b has a most probable radius slightly smaller than Saturn. It orbits one of the brightest XRSs in the external galaxy M51, the Whirlpool Galaxy, located 8.6 Megaparsecs from Earth. It is the first candidate for a planet in an external galaxy. The binary it orbits, M51-ULS-1, is young and massive. One of the binary components is a stellar remnant, either a neutron star (NS) or black hole (BH), and the other is a massive star. X-ray transits can now be used to discover more planets in external galaxies and also planets orbiting XRSs inside the Milky Way., Comment: 19 pages, 13 figures, 2 tables. Submitted

All cool stars show magnetic activity, and X-ray emission is the hallmark of this activity. Gaining an understanding of activity aids us in answering fundamental questions about stellar astrophysics and in determining the impact of activity on the exoplanets that orbit these stars. Stellar activity is driven by magnetic fields, which are ultimately powered by convection and stellar rotation. However, the resulting dynamo properties heavily depend on the stellar interior structure and are far from being understood. X-ray radiation can evaporate exoplanet atmospheres and damage organic materials on the planetary surface, reducing the probability that life can form or be sustained, but also provides an important source of energy for prebiotic chemical reactions. Over the next two years, the TESS mission will deliver a catalog of the closest exoplanets, along with rotation periods and activity diagnostics for millions of stars, whether or not they have a planet. We propose to include all cool stars that are TESS targets and bright enough for Chandra observations, as determined by their detection and flux in the ROSAT all-sky survey (RASS), to the list of Chandra Cool Attitude Targets (CATs). For each target, the signal will be sufficient to fit the coronal plasma with at least two temperature components, and compare abundances of groups of elements with low, medium, or high first ionization potential. Similar to the known relation between X-ray luminosity $L_X$ and rotation period, we can correlate stellar properties with coronal temperatures and abundances to constrain models for stellar activity, coronal heating, and stellar dynamos. Detailed X-ray characterization for even a subset of planet-hosting systems would dramatically advance our knowledge of what impact these emissions have on orbiting planets., Comment: White paper for Chandra cool attitude targets (4 pages)

The X-ray and EUV emission of stars plays a key role in the loss and evolution of the atmospheres of their planets. The coronae of dwarf stars later than M6 appear to behave differently to those of earlier spectral types and are more X-ray dim and radio bright. Too faint to have been observed by the Extreme Ultraviolet Explorer, their EUV behavior is currently highly uncertain. We have devised a method to use the Chandra X-ray Observatory High Resolution Camera to provide a measure of EUV emission in the 50-170 \AA\ range and have applied it to the M6.5 dwarf LHS 248 in a pilot 10 ks exposure. Analysis with model spectra using simple, idealised coronal emission measure distributions inspired by an analysis of Chandra HETG spectra of the M5.5 dwarf Proxima Cen and results from the literature, finds greatest consistency with a very shallow emission measure distribution slope, $DEM \propto T^{3/2}$ or shallower, in the range $\log T=5.5$-$6.5$. Within $2\sigma$ confidence, a much wider range of slopes can be accommodated. Model spectra constrained by this method can provide accurate (within a factor of 2-4) synthesis and extrapolation of EUV spectra for wavelengths $<400$-500 \AA. At longer wavelengths models are uncertain by an order of magnitude or more, and depend on the details of the emission measure distribution at temperatures $\log T < 5.5$. The method is sensitive to possible incompleteness of plasma radiative loss models in the 30 170 \AA\ range for which re-examination would be warranted., Comment: Submitted to ApJ

Information about the physical properties of astrophysical objects cannot be measured directly but is inferred by interpreting spectroscopic observations in the context of atomic physics calculations. Ratios of emission lines, for example, can be used to infer the electron density of the emitting plasma. Similarly, the relative intensities of emission lines formed over a wide range of temperatures yield information on the temperature structure. A critical component of this analysis is understanding how uncertainties in the underlying atomic physics propagates to the uncertainties in the inferred plasma parameters. At present, however, atomic physics databases do not include uncertainties on the atomic parameters and there is no established methodology for using them even if they did. In this paper we develop simple models for the uncertainties in the collision strengths and decay rates for Fe XIII and apply them to the interpretation of density sensitive lines observed with the EUV Imagining spectrometer (EIS) on Hinode. We incorporate these uncertainties in a Bayesian framework. We consider both a pragmatic Bayesian method where the atomic physics information is unaffected by the observed data, and a fully Bayesian method where the data can be used to probe the physics. The former generally increases the uncertainty in the inferred density by about a factor of 5 compared with models that incorporate only statistical uncertainties. The latter reduces the uncertainties on the inferred densities, but identifies areas of possible systematic problems with either the atomic physics or the observed intensities., Comment: in press at ApJ

We study the thermal structure and energetics of the point-like EUV brightenings within a system of fan loops observed in the active region \textsl{AR~11520}. These brightenings were simultaneously observed on 2012 July 11 by the HIgh-resolution Coronal (Hi-C) imager and the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). We identified 27 brightenings by automatically determining intensity enhancements in both Hi-C and AIA ~193~{\AA} light curves. The energetics of these brightenings were studied by using the Differential Emission Measure (DEM) diagnostics. The DEM weighted temperatures of these transients are in the range $\log{T} (K) = 6.2 - 6.6$ with radiative energies ${\approx}10^{24-25}$~ergs and densities ${\approx}$ a few times $10^{9}$~cm$^{-3}$. To the best of our knowledge, these are the smallest brightenings in EUV ever detected. We used these results to determine the mechanism of energy loss in these brightenings. Our analysis reveals that the dominant mechanism of energy loss for all the identified brightenings is conduction rather than radiation., Comment: 17 pages, 8 Figures, 3 tables, accepted for publication in Astronomy and Astrophysics

We propose a new soft clustering scheme for classifying galaxies in different activity classes using simultaneously 4 emission-line ratios; log([NII ]/Ha), log([SII]/Ha), log([OI]/Ha) and log([OIII]/Hb). We fit 20 multivariate Gaussian distributions to the 4-dimensional distribution of these lines obtained from the Sloan Digital Sky Survey (SDSS) in order to capture local structures and subsequently group the multivariate Gaussian distributions to represent the complex multi-dimensional structure of the joint distribution of galaxy spectra in the 4 dimensional line ratio space. The main advantages of this method are the use of all four optical-line ratios simultaneously and the adoption of a clustering scheme. This maximises the available information, avoids contradicting classifications, and treats each class as a distribution resulting in soft classification boundaries and providing the probability for an object to belong to each class. We also introduce linear multi-dimensional decision surfaces using support vector machines based on the classification of our soft clustering scheme. This linear multi-dimensional hard clustering technique shows high classification accuracy with respect to our soft-clustering scheme.

Calibration data are often obtained by observing several well-understood objects simultaneously with multiple instruments, such as satellites for measuring astronomical sources. Analyzing such data and obtaining proper concordance among the instruments is challenging when the physical source models are not well understood, when there are uncertainties in "known" physical quantities, or when data quality varies in ways that cannot be fully quantified. Furthermore, the number of model parameters increases with both the number of instruments and the number of sources. Thus, concordance of the instruments requires careful modeling of the mean signals, the intrinsic source differences, and measurement errors. In this paper, we propose a log-Normal hierarchical model and a more general log-t model that respect the multiplicative nature of the mean signals via a half-variance adjustment, yet permit imperfections in the mean modeling to be absorbed by residual variances. We present analytical solutions in the form of power shrinkage in special cases and develop reliable MCMC algorithms for general cases. We apply our method to several data sets obtained with a variety of X-ray telescopes such as Chandra. We demonstrate that our method provides helpful and practical guidance for astrophysicists when adjusting for disagreements among instruments.

We analyze Chandra X-ray images of a sample of 11 quasars that are known to contain kiloparsec scale radio jets. The sample consists of five high-redshift (z >= 3.6) flat-spectrum radio quasars, and six intermediate redshift (2.1 < z < 2.9) quasars. The dataset includes four sources with integrated steep radio spectra and seven with flat radio spectra. A total of 25 radio jet features are present in this sample. We apply a Bayesian multi-scale image reconstruction method to detect and measure the X-ray emission from the jets. We compute deviations from a baseline model that does not include the jet, and compare observed X-ray images with those computed with simulated images where no jet features exist. This allows us to compute p-value upper bounds on the significance that an X- ray jet is detected in a pre-determined region of interest. We detected 12 of the features unambiguously, and an additional 6 marginally. We also find residual emission in the cores of 3 quasars and in the background of 1 quasar that suggest the existence of unresolved X-ray jets. The dependence of the X-ray to radio luminosity ratio on redshift is a potential diagnostic of the emission mechanism, since the inverse Compton scattering of cosmic microwave background photons (IC/CMB) is thought to be redshift dependent, whereas in synchrotron models no clear redshift dependence is expected. We find that the high-redshift jets have X-ray to radio flux ratios that are marginally inconsistent with those from lower redshifts, suggesting that either the X-ray emissions is due to the IC/CMB rather than the synchrotron process, or that high redshift jets are qualitatively different., Comment: 42 pages, 14 figures, submitted to ApJ

The gravitational field of a galaxy can act as a lens and deflect the light emitted by a more distant object such as a quasar. Strong gravitational lensing causes multiple images of the same quasar to appear in the sky. Since the light in each gravitationally lensed image traverses a different path length from the quasar to the Earth, fluctuations in the source brightness are observed in the several images at different times. The time delay between these fluctuations can be used to constrain cosmological parameters and can be inferred from the time series of brightness data or light curves of each image. To estimate the time delay, we construct a model based on a state-space representation for irregularly observed time series generated by a latent continuous-time Ornstein-Uhlenbeck process. We account for microlensing, an additional source of independent long-term extrinsic variability, via a polynomial regression. Our Bayesian strategy adopts a Metropolis-Hastings within Gibbs sampler. We improve the sampler by using an ancillarity-sufficiency interweaving strategy and adaptive Markov chain Monte Carlo. We introduce a profile likelihood of the time delay as an approximation of its marginal posterior distribution. The Bayesian and profile likelihood approaches complement each other, producing almost identical results; the Bayesian method is more principled but the profile likelihood is simpler to implement. We demonstrate our estimation strategy using simulated data of doubly- and quadruply-lensed quasars, and observed data from quasars Q0957+561 and J1029+2623., Comment: Accepted for publication in the Annals of Applied Statistics

Telescopes such as the Atmospheric Imaging Assembly aboard the Solar Dynamics Observatory, a NASA satellite, collect massive streams of high resolution images of the Sun through multiple wavelength filters. Reconstructing pixel-by-pixel thermal properties based on these images can be framed as an ill-posed inverse problem with Poisson noise, but this reconstruction is computationally expensive and there is disagreement among researchers about what regularization or prior assumptions are most appropriate. This article presents an image segmentation framework for preprocessing such images in order to reduce the data volume while preserving as much thermal information as possible for later downstream analyses. The resulting segmented images reflect thermal properties but do not depend on solving the ill-posed inverse problem. This allows users to avoid the Poisson inverse problem altogether or to tackle it on each of $\sim$10 segments rather than on each of $\sim$10$^7$ pixels, reducing computing time by a factor of $\sim$10$^6$. We employ a parametric class of dissimilarities that can be expressed as cosine dissimilarity functions or Hellinger distances between nonlinearly transformed vectors of multi-passband observations in each pixel. We develop a decision theoretic framework for choosing the dissimilarity that minimizes the expected loss that arises when estimating identifiable thermal properties based on segmented images rather than on a pixel-by-pixel basis. We also examine the efficacy of different dissimilarities for recovering clusters in the underlying thermal properties. The expected losses are computed under scientifically motivated prior distributions. Two simulation studies guide our choices of dissimilarity function. We illustrate our method by segmenting images of a coronal hole observed on 26 February 2015.

The Chandra Cygnus OB2 Legacy Survey is a wide and deep X-ray survey of the nearby and massive Cygnus OB2 association. The survey has detected ~8,000 X-ray sources, the majority of which are pre-main sequence X-ray emitting young stars in the association itself. To facilitate quantitative scientific studies of these sources as well as the underlying OB association it is important to understand the sensitivity of the observations and the level of completeness the observations have obtained. Here we describe the use of a hierarchical Monte Carlo simulation to achieve this goal by combining the empirical properties of the observations, analytic estimates of the source verification process, and an extensive set of source detection simulations. We find that our survey reaches a 90% completeness level for a pre-main-sequence population at the distance of Cyg OB2 at an X-ray luminosity of 4 x 10^30 ergs/s and a stellar mass of 1.3 Msun for a randomly distributed population. For a spatially clustered population such as Cyg~OB2 the 90% completeness level is reached at 1.1 Msun instead, as the sources are more concentrated in areas of our survey with a high exposure. These simulations can easily be adapted for use with other X-ray observations and surveys, and we provide X-ray detection efficiency curves for a very wide array of source and background properties to allow these simulations to be easily exploited by other users., Comment: Accepted for publication in ApJS as part of the special issue on the Chandra Cygnus OB2 Legacy Survey. 10 pages, 7 figures, 1 table. A full version of Table 1 is available at http://www.astro.keele.ac.uk/~njw/wright2015b_table1.dat

Unexpected structure in images of astronomical sources often presents itself upon visual inspection of the image, but such apparent structure may either correspond to true features in the source or be due to noise in the data. This paper presents a method for testing whether inferred structure in an image with Poisson noise represents a significant departure from a baseline (null) model of the image. To infer image structure, we conduct a Bayesian analysis of a full model that uses a multiscale component to allow flexible departures from the posited null model. As a test statistic, we use a tail probability of the posterior distribution under the full model. This choice of test statistic allows us to estimate a computationally efficient upper bound on a p-value that enables us to draw strong conclusions even when there are limited computational resources that can be devoted to simulations under the null model. We demonstrate the statistical performance of our method on simulated images. Applying our method to an X-ray image of the quasar 0730+257, we find significant evidence against the null model of a single point source and uniform background, lending support to the claim of an X-ray jet.

Variable-intensity astronomical sources are the result of complex and often extreme physical processes. Abrupt changes in source intensity are typically accompanied by equally sudden spectral shifts, i.e., sudden changes in the wavelength distribution of the emission. This article develops a method for modeling photon counts collected from observation of such sources. We embed change points into a marked Poisson process, where photon wavelengths are regarded as marks and both the Poisson intensity parameter and the distribution of the marks are allowed to change. To the best of our knowledge this is the first effort to embed change points into a marked Poisson process. Between the change points, the spectrum is modeled non-parametrically using a mixture of a smooth radial basis expansion and a number of local deviations from the smooth term representing spectral emission lines. Because the model is over parameterized we employ an $\ell_1$ penalty. The tuning parameter in the penalty and the number of change points are determined via the minimum description length principle. Our method is validated via a series of simulation studies and its practical utility is illustrated in the analysis of the ultra-fast rotating yellow giant star known as FK Com., Comment: 30 pages, 6 figures

A fine analysis of spectral line widths and Doppler shifts employing Fourier transform and cross-correlation techniques has been applied to Chandra HETG spectra obtained in 1999 October of the rapidly rotating young star AB Doradus in order to investigate its coronal topology. The observation lasted 52.3ks, covering 1.2 rotation periods. The X-ray light curve obtained from integrating the dispersed signal revealed a moderate intensity flare midway through the exposure in which the count rate increased sharply by about 50% and subsequently decayed over the next 10ks. We find no significant Doppler shifts in the spectra or modulation of the light curve that could be attributed to rotation of dominant coronal structures at this epoch. Individual spectral line widths are statistically consistent with thermal broadening and formally require no rotational broadening, while the $1\sigma$ limit to rotational broadening corresponds to a compact corona restricted to latitudes $>57\deg$. Fourier analysis suggests a small amount of rotational broadening is present consistent with a corona restricted largely to the poles, and excludes models with surface rotational broadening or greater. These results present direct spectroscopic evidence that the dominant coronal activity on rapidly-rotating active stars is associated with the dark polar spots commonly seen in photospheric Doppler images, and support models in which these spots are of mixed magnetic polarity that forms closed loops., Comment: To appear in the Astrophysical Journal

We present a powerful new algorithm that combines both spatial information (event locations and the point spread function) and spectral information (photon energies) to separate photons from overlapping sources. We use Bayesian statistical methods to simultaneously infer the number of overlapping sources, to probabilistically separate the photons among the sources, and to fit the parameters describing the individual sources. Using the Bayesian joint posterior distribution, we are able to coherently quantify the uncertainties associated with all these parameters. The advantages of combining spatial and spectral information are demonstrated through a simulation study. The utility of the approach is then illustrated by analysis of observations of FK Aqr and FL Aqr with the XMM-Newton Observatory and the central region of the Orion Nebula Cluster with the Chandra X-ray Observatory., Comment: 34 pages, 15 figures, references added

The Cygnus OB2 association is the largest concentration of young and massive stars within 2 kpc of the Sun, including an estimated 65 O-type stars and hundreds of OB stars. The Chandra Cygnus OB2 Legacy Survey is a large imaging program undertaken with the Advanced CCD Imaging Spectrometer onboard the Chandra X-ray Observatory. The survey has imaged the central 0.5 deg^2 of the Cyg OB2 association with an effective exposure of 120ks and an outer 0.35 deg^2 area with an exposure of 60ks. Here we describe the survey design and observations, the data reduction and source detection, and present a catalog of 8,000 X-ray point sources. The survey design employs a grid of 36 heavily (~50%) overlapping pointings, a method that overcomes Chandra's low off-axis sensitivity and produces a highly uniform exposure over the inner 0.5 deg^2. The full X-ray catalog is described here and is made available online., Comment: Accepted for publication in ApJS as part of the special issue on the Chandra Cygnus OB2 Legacy Survey. 15 pages, 8 figures, full catalog available on request

In astrophysics a common goal is to infer the flux distribution of populations of scientifically interesting objects such as pulsars or supernovae. In practice, inference for the flux distribution is often conducted using the cumulative distribution of the number of sources detected at a given sensitivity. The resulting "$\log(N>S)$-$\log (S)$" relationship can be used to compare and evaluate theoretical models for source populations and their evolution. Under restrictive assumptions the relationship should be linear. In practice, however, when simple theoretical models fail, it is common for astrophysicists to use prespecified piecewise linear models. This paper proposes a methodology for estimating both the number and locations of "breakpoints" in astrophysical source populations that extends beyond existing work in this field. An important component of the proposed methodology is a new interwoven EM algorithm that computes parameter estimates. It is shown that in simple settings such estimates are asymptotically consistent despite the complex nature of the parameter space. Through simulation studies it is demonstrated that the proposed methodology is capable of accurately detecting structural breaks in a variety of parameter configurations. This paper concludes with an application of our methodology to the Chandra Deep Field North (CDFN) data set., Comment: Published in at http://dx.doi.org/10.1214/14-AOAS750 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Sunspot numbers form a comprehensive, long-duration proxy of solar activity and have been used numerous times to empirically investigate the properties of the solar cycle. A number of correlations have been discovered over the 24 cycles for which observational records are available. Here we carry out a sophisticated statistical analysis of the sunspot record that reaffirms these correlations, and sets up an empirical predictive framework for future cycles. An advantage of our approach is that it allows for rigorous assessment of both the statistical significance of various cycle features and the uncertainty associated with predictions. We summarize the data into three sequential relations that estimate the amplitude, duration, and time of rise to maximum for any cycle, given the values from the previous cycle. We find that there is no indication of a persistence in predictive power beyond one cycle, and conclude that the dynamo does not retain memory beyond one cycle. Based on sunspot records up to October 2011, we obtain, for Cycle 24, an estimated maximum smoothed monthly sunspot number of 97 +- 15, to occur in January--February 2014 +- 6 months., Comment: Accepted for publication in Solar Physics

The first release of the Chandra Source Catalog (CSC) contains ~95,000 X-ray sources in a total area of ~0.75% of the entire sky, using data from ~3,900 separate ACIS observations of a multitude of different types of X-ray sources. In order to maximize the scientific benefit of such a large, heterogeneous data-set, careful characterization of the statistical properties of the catalog, i.e., completeness, sensitivity, false source rate, and accuracy of source properties, is required. Characterization efforts of other, large Chandra catalogs, such as the ChaMP Point Source Catalog (Kim et al. 2007) or the 2 Mega-second Deep Field Surveys (Alexander et al. 2003), while informative, cannot serve this purpose, since the CSC analysis procedures are significantly different and the range of allowable data is much less restrictive. We describe here the characterization process for the CSC. This process includes both a comparison of real CSC results with those of other, deeper Chandra catalogs of the same targets and extensive simulations of blank-sky and point source populations., Comment: To be published in the Astrophysical Journal Supplement Series (Fig. 52 replaced with a version which astro-ph can convert to PDF without issues.)

While considerable advance has been made to account for statistical uncertainties in astronomical analyses, systematic instrumental uncertainties have been generally ignored. This can be crucial to a proper interpretation of analysis results because instrumental calibration uncertainty is a form of systematic uncertainty. Ignoring it can underestimate error bars and introduce bias into the fitted values of model parameters. Accounting for such uncertainties currently requires extensive case-specific simulations if using existing analysis packages. Here we present general statistical methods that incorporate calibration uncertainties into spectral analysis of high-energy data. We first present a method based on multiple imputation that can be applied with any fitting method, but is necessarily approximate. We then describe a more exact Bayesian approach that works in conjunction with a Markov chain Monte Carlo based fitting. We explore methods for improving computational efficiency, and in particular detail a method of summarizing calibration uncertainties with a principal component analysis of samples of plausible calibration files. This method is implemented using recently codified Chandra effective area uncertainties for low-resolution spectral analysis and is verified using both simulated and actual Chandra data. Our procedure for incorporating effective area uncertainty is easily generalized to other types of calibration uncertainties., Comment: 61 pages double spaced, 8 figures, accepted for publication in ApJ

A common problem in astrophysics is determining how bright a source could be and still not be detected. Despite the simplicity with which the problem can be stated, the solution involves complex statistical issues that require careful analysis. In contrast to the confidence bound, this concept has never been formally analyzed, leading to a great variety of often ad hoc solutions. Here we formulate and describe the problem in a self-consistent manner. Detection significance is usually defined by the acceptable proportion of false positives (the TypeI error), and we invoke the complementary concept of false negatives (the TypeII error), based on the statistical power of a test, to compute an upper limit to the detectable source intensity. To determine the minimum intensity that a source must have for it to be detected, we first define a detection threshold, and then compute the probabilities of detecting sources of various intensities at the given threshold. The intensity that corresponds to the specified TypeII error probability defines that minimum intensity, and is identified as the upper limit. Thus, an upper limit is a characteristic of the detection procedure rather than the strength of any particular source and should not be confused with confidence intervals or other estimates of source intensity. This is particularly important given the large number of catalogs that are being generated from increasingly sensitive surveys. We discuss the differences between these upper limits and confidence bounds. Both measures are useful quantities that should be reported in order to extract the most science from catalogs, though they answer different statistical questions: an upper bound describes an inference range on the source intensity, while an upper limit calibrates the detection process. We provide a recipe for computing upper limits that applies to all detection algorithms., Comment: 30 pages, 12 figures, accepted in ApJ

The Chandra Source Catalog (CSC) is a general purpose virtual X-ray astrophysics facility that provides access to a carefully selected set of generally useful quantities for individual X-ray sources, and is designed to satisfy the needs of a broad-based group of scientists, including those who may be less familiar with astronomical data analysis in the X-ray regime. The first release of the CSC includes information about 94,676 distinct X-ray sources detected in a subset of public ACIS imaging observations from roughly the first eight years of the Chandra mission. This release of the catalog includes point and compact sources with observed spatial extents <~ 30''. The catalog (1) provides access to the best estimates of the X-ray source properties for detected sources, with good scientific fidelity, and directly supports scientific analysis using the individual source data; (2) facilitates analysis of a wide range of statistical properties for classes of X-ray sources; and (3) provides efficient access to calibrated observational data and ancillary data products for individual X-ray sources, so that users can perform detailed further analysis using existing tools. The catalog includes real X-ray sources detected with flux estimates that are at least 3 times their estimated 1 sigma uncertainties in at least one energy band, while maintaining the number of spurious sources at a level of <~ 1 false source per field for a 100 ks observation. For each detected source, the CSC provides commonly tabulated quantities, including source position, extent, multi-band fluxes, hardness ratios, and variability statistics, derived from the observations in which the source is detected. In addition to these traditional catalog elements, for each X-ray source the CSC includes an extensive set of file-based data products that can be manipulated interactively., Comment: To appear in The Astrophysical Journal Supplement Series, 53 pages, 27 figures