A. L. Zezas

BAYESIAN ESTIMATION OF HARDNESS RATIOS: MODELING AND COMPUTATIONS

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-population-based 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.

On Computing Upper Limits to Source Intensities

A common problem in astrophysics is determining how bright a source could be and still not be detected in an observation. Despite the simplicity with which the problem can be stated, the solution involves complicated statistical issues that require careful analysis. In contrast to the more familiar 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 (background fluctuations that are claimed as detections, or Type I error), and we invoke the complementary concept of false negatives (real sources that go undetected, or Type II 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 Type II 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. It 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, with examples, 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.

AN ACCRETION MODEL FOR THE ANOMALOUS X-RAY PULSAR 4U 0142+61

We propose that the quiescent emission of anomalous X-ray pulsars/soft gamma-ray repeaters (AXPs/SGRs) is powered by accretion from a fallback disk, requiring magnetic dipole fields in the range 1012-1013 G, and that the luminous hard tails of their X-ray spectra are produced by bulk-motion Comptonization in the radiative shock near the bottom of the accretion column. This radiation escapes as a fan beam, which is partly absorbed by the polar cap photosphere, heating it up to relatively high temperatures. The scattered component and the thermal emission from the polar cap form a polar beam. We test our model on the well-studied AXP 4U 0142+61, whose energy-dependent pulse profiles show double peaks, which we ascribe to the fan and polar beams. The temperature of the photosphere (kT ~ 0.4 keV) is explained by the heating effect. The scattered part forms a hard component in the polar beam. We suggest that the observed high temperatures of the polar caps of AXPs/SGRs, compared with other young neutron stars, are due to the heating by the fan beam. Using beaming functions for the fan beam and the polar beam and taking gravitational bending into account, we fit the energy-dependent pulse profiles and obtain the inclination angle and the angle between the spin axis and the magnetic dipole axis, as well as the height of the radiative shock above the stellar surface. We do not explain the high-luminosity bursts, which may be produced by the classical magnetar mechanism operating in super-strong multipole fields.

Deep Chandra Monitoring Observations of NGC 4649. II. Wide-field Hubble Space Telescope Imaging of the Globular Clusters

We present g and z photometry and size estimates for globular clusters (GCs) in the massive Virgo elliptical NGC 4649 (M60) using a five-pointing Hubble Space Telescope/Advanced Camera for Surveys mosaic. The metal-poor GCs show a monotonic negative metallicity gradient of −0.43 ±0.10 dex per dex in radius over the full radial range of the data, out to ∼24 kpc. There is evidence for substantial color substructure among the metal-rich GCs. The metal-poor GCs have typical sizes ∼0.4 pc larger than the metal-rich GCs out to large galactocentric distances (20 kpc), favoring an intrinsic explanation for the size difference rather than projection effects. There is no clear relation between half-light radius and galactocentric distance beyond ∼15 kpc, suggesting that the sizes of GCs are not generically set by tidal limitation. Finally, we identify ∼20 candidate ultracompact dwarfs that extend down to surprisingly faint absolute magnitudes (Mz ∼− 8.5), and may bridge the gap between this class and “extended clusters” in the Local Group. Three of the brighter candidates have published radial velocities and can be confirmed as bona fide ultracompact dwarfs; follow-up spectroscopy will determine the nature of the remainder of the candidates.

ACCOUNTING FOR CALIBRATION UNCERTAINTIES IN X-RAY ANALYSIS: EFFECTIVE AREAS IN SPECTRAL FITTING

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.

NuSTAR and Chandra Insight into the Nature of the 3-40 keV Nuclear Emission in NGC 253

We present results from three nearly simultaneous Nuclear Spectroscopic Telescope Array (NuSTAR) and Chandra monitoring observations between 2012 September 2 and 2012 November 16 of the local star-forming galaxy NGC 253. The 3-40 keV intensity of the inner ~20 arcsec (~400 pc) nuclear region, as measured by NuSTAR, varied by a factor of ~2 across the three monitoring observations. The Chandra data reveal that the nuclear region contains three bright X-ray sources, including a luminous (L_(2-10) keV ~ few × 10^39 erg s^–1) point source located ~1 arcsec from the dynamical center of the galaxy (within the 3σ positional uncertainty of the dynamical center); this source drives the overall variability of the nuclear region at energies ≳3 keV. We make use of the variability to measure the spectra of this single hard X-ray source when it was in bright states. The spectra are well described by an absorbed (N_H ≈ 1.6 × 10^23 cm^–2) broken power-law model with spectral slopes and break energies that are typical of ultraluminous X-ray sources (ULXs), but not active galactic nuclei (AGNs). A previous Chandra observation in 2003 showed a hard X-ray point source of similar luminosity to the 2012 source that was also near the dynamical center (θ ≈ 0.4 arcsec); however, this source was offset from the 2012 source position by ≈1 arcsec. We show that the probability of the 2003 and 2012 hard X-ray sources being unrelated is ≫99.99% based on the Chandra spatial localizations. Interestingly, the Chandra spectrum of the 2003 source (3-8 keV) is shallower in slope than that of the 2012 hard X-ray source. Its proximity to the dynamical center and harder Chandra spectrum indicate that the 2003 source is a better AGN candidate than any of the sources detected in our 2012 campaign; however, we were unable to rule out a ULX nature for this source. Future NuSTAR and Chandra monitoring would be well equipped to break the degeneracy between the AGN and ULX nature of the 2003 source, if again caught in a high state.

The Radial Distribution of X-Ray Binaries and Globular Clusters in NGC?4649 and their Relation with the Local Stellar Mass Density

We investigate the radial distribution of the low-mass X-ray binary (LMXB) population in the elliptical galaxy NGC 4649, using Chandra and Hubble data to separate the field and globular cluster (GC) populations. GCs with LMXBs have the same radial distribution as the parent red and blue GCs. The radial profile of field LMXBs follows the V-band profile within the D25 of NGC 4649. Using the spatial information provided by our data, we find that the global galaxy-wide relations among cumulative number and luminosity of LMXBs and the integrated stellar mass hold on local scales within D25. An excess of field LMXBs with respect to the V-band light is observed in the galaxys outskirts, which may be partially due to unidentified GC sources or to a rejuvenated field LMXB population caused by past merging interactions.

The quiescent state of the accreting X-ray pulsar SAX J2103.5+4545

We present an X-ray timing and spectral analysis of the Be/X-ray binary SAX J2103.5+4545 at a time when the Be stars circumstellar disk had disappeared and thus the main reservoir of material available for accretion had extinguished. In this very low optical state, pulsed X-ray emission was detected at a level of L_X~10^{33} erg/s. This is the lowest luminosity at which pulsations have ever been detected in an accreting pulsar. The derived spin period is 351.13 s, consistent with previous observations. The source continues its overall long-term spin-up, which reduced the spin period by 7.5 s since its discovery in 1997. The X-ray emission is consistent with a purely thermal spectrum, represented by a blackbody with kT=1 keV. We discuss possible scenarios to explain the observed quiescent luminosity and conclude that the most likely mechanism is direct emission resulting from the cooling of the polar caps, heated either during the most recent outburst or via intermittent accretion in quiescence.

A new candidate Wolf–Rayet X-ray binary in NGC 253

ABSTRACT We have discovered a persistent, but highly variable X-ray source in the nearby star-burst galaxy NGC 253. The source varies at the level of a factor of about 5 in countrate on timescales of a few hours. Two long observations of the source with Chandraand XMM-Newton show suggestive evidence for the source having a period of about14-15 hours, but the time sampling in existing data is insufficient to allow a firmdetermination that the source is periodic. Given the amplitude of variation and thelocation in a nuclear starburst, the source is likely to be a Wolf-Rayet X-ray binary,with the tentative period being the orbital period of the system. In light of the factthat we have demonstrated that careful examination of the variability of moderatelybright X-ray sources in nearby galaxies can turn up candidate Wolf-Rayet X-ray bi-naries, we discuss the implications of Wolf-Rayet X-ray binaries for predictions of thegravitational wave source event rate, and, potentially, interpretations of the events.Key words: X-rays:binaries – galaxies:individual:NGC 253 – galaxies:starburst –stars:Wolf-Rayet

INVESTIGATING THE NUCLEAR ACTIVITY OF BARRED SPIRAL GALAXIES: THE CASE OF NGC 1672

We have performed an X-ray study of the nearby barred spiral galaxy NGC 1672, primarily to ascertain the effect of the bar on its nuclear activity. We use both Chandra and XMM-Newton observations to investigate its X-ray properties, together with supporting high-resolution optical imaging data from the Hubble Space Telescope (HST), infrared imaging from the Spitzer Space Telescope, and Australia Telescope Compact Array ground-based radio data. We detect 28 X-ray sources within theD25 area of the galaxy; many are spatially correlated with star formation in the bar and spiral arms, and two are identified as background galaxies in the HST images. Nine of the X-ray sources are ultraluminous X-ray sources, with the three brightest (LX > 5 × 10 39 erg s −1 ) located at the ends of the bar. With the spatial resolution of Chandra, we are able to show for the first time that NGC 1672 possesses a hard (Γ ∼ 1.5) nuclear X-ray source with a 2‐10 keV luminosity of 4 × 10 38 erg s −1 . This is surrounded by an X-ray-bright circumnuclear star-forming ring, comprised of point sources and hot gas, which dominates the 2‐10 keV emission in the central region of the galaxy. The spatially resolved multiwavelength photometry indicates that the nuclear source is a low-luminosity active galactic nucleus (LLAGN), but with star formation activity close to the central black hole. A high-resolution multiwavelength survey is required to fully assess the impact of both large-scale bars and smaller-scale phenomena such as nuclear bars, rings, and nuclear spirals on the fueling of LLAGN.