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 number 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.Comment: 43 pages, 10 figures, 3 tables; submitted to Ap

Radiative accretion shocks along nonuniform stellar magnetic fields in classical T Tauri stars

(abridged) AIMS. We investigate the dynamics and stability of post-shock plasma streaming along nonuniform stellar magnetic fields at the impact region of accretion columns. We study how the magnetic field configuration and strength determine the structure, geometry, and location of the shock-heated plasma. METHODS. We model the impact of an accretion stream onto the chromosphere of a CTTS by 2D axisymmetric magnetohydrodynamic simulations. Our model takes into account the gravity, the radiative cooling, and the magnetic-field-oriented thermal conduction. RESULTS. The structure, stability, and location of the shocked plasma strongly depend on the configuration and strength of the magnetic field. For weak magnetic fields, a large component of B may develop perpendicular to the stream at the base of the accretion column, limiting the sinking of the shocked plasma into the chromosphere. An envelope of dense and cold chromospheric material may also develop around the shocked column. For strong magnetic fields, the field configuration determines the position of the shock and its stand-off height. If the field is strongly tapered close to the chromosphere, an oblique shock may form well above the stellar surface. In general, a nonuniform magnetic field makes the distribution of emission measure vs. temperature of the shocked plasma lower than in the case of uniform magnetic field. CONCLUSIONS. The initial strength and configuration of the magnetic field in the impact region of the stream are expected to influence the chromospheric absorption and, therefore, the observability of the shock-heated plasma in the X-ray band. The field strength and configuration influence also the energy balance of the shocked plasma, its emission measure at T > 1 MK being lower than expected for a uniform field. The above effects contribute in underestimating the mass accretion rates derived in the X-ray band.Comment: 11 pages, 11 Figures; accepted for publication on A&A. Version with full resolution images can be found at http://www.astropa.unipa.it/~orlando/PREPRINTS/sorlando_accretion_shocks.pd

Compressive Earth Observatory: An Insight from AIRS/AMSU Retrievals

We demonstrate that the global fields of temperature, humidity and geopotential heights admit a nearly sparse representation in the wavelet domain, offering a viable path forward to explore new paradigms of sparsity-promoting data assimilation and compressive recovery of land surface-atmospheric states from space. We illustrate this idea using retrieval products of the Atmospheric Infrared Sounder (AIRS) and Advanced Microwave Sounding Unit (AMSU) on board the Aqua satellite. The results reveal that the sparsity of the fields of temperature is relatively pressure-independent while atmospheric humidity and geopotential heights are typically sparser at lower and higher pressure levels, respectively. We provide evidence that these land-atmospheric states can be accurately estimated using a small set of measurements by taking advantage of their sparsity prior.Comment: 12 pages, 8 figures, 1 tabl

Bright X-ray flares in Orion young stars from COUP: evidence for star-disk magnetic fields?

We have analyzed a number of intense X-ray flares observed in the Chandra Orion Ultradeep Project (COUP), a 13 days observation of the Orion Nebula Cluster (ONC). Analysis of the flare decay allows to determine the size, peak density and magnetic field of the flaring structure. A total of 32 events (the most powerful 1% of COUP flares), have sufficient statistics for the analysis. A broad range of decay times (from 10 to 400 ks) are present in the sample. Peak flare temperatures are often very high, with half of the flares in the sample showing temperatures in excess of 100 MK. Significant sustained heating is present in the majority of the flares. The magnetic structures which are found, are in a number of cases very long, with semi-lengths up to 10^12 cm, implying the presence of magnetic fields of hundreds of G extending to comparable distance from the stellar photosphere. These very large sizes for the flaring structures ($ >> R_*) are not found in more evolved stars, where, almost invariably, the same type of analysis results in structures with L <= R_*. As the majority of young stars in the ONC are surrounded by disks, we speculate that the large magnetic structures which confine the flaring plasma are actually the same type of structures which channel the plasma in the magnetospheric accretion paradigm, connecting the star's photosphere with the accretion disk.Comment: Accepted to ApJS, COUP special issu

Hot Plasma Detected in Active Regions by HINODE/XRT and SDO/AIA

Multiple ratios of Hinode/XRT filters showed evidence of a minor very hot emission measure component in active regions. Recently also SDO/AIA detected hot plasma in the core of an active region. Here we provide estimates showing that the amount of emission measure of the hot component detected with SDO is consistent with that detected with Hinode/XRT

Extreme Value GARCH modelling with Bayesian Inference

RePEC Working Paper Series No: 05/2009Extreme value theory is widely used financial applications such as risk analysis, forecasting and pricing models. One of the major difficulties in the applications to finance and economics is that the assumption of independence of time series observations is generally not satisfied, so that the dependent extremes may not necessarily be in the domain of attraction of the classical generalised extreme value distribution. This study examines a conditional extreme value distribution with the added specification that the extreme values (maxima or minima) follows a conditional autoregressive heteroscedasticity process. The dependence has been modelled by allowing the location and scale parameters of the extreme distribution to vary with time. The resulting combined model, GEV-GARCH, is developed by implementing the GARCH volatility mechanism in these extreme value model parameters. Bayesian inference is used for the estimation of parameters and posterior inference is available through the Markov Chain Monte Carlo (MCMC) method. The model is firstly applied to relevant simulated data to verify model stability and reliability of the parameter estimation method. Then real stock returns are used to consider evidence for the appropriate application of the model. A comparison is made between the GEV-GARCH and traditional GARCH models. Both the GEV-GARCH and GARCH show similarity in the resulting conditional volatility estimates, however the GEV-GARCH model differs from GARCH in that it can capture and explain extreme quantiles better than the GARCH model because of more reliable extrapolation of the tail behaviour

High-Lundquist Number Scaling in Three-Dimensional Simulations of Parker's Model of Coronal Heating

Parker's model is one of the most discussed mechanisms for coronal heating and has generated much debate. We have recently obtained new scaling results in a two-dimensional (2D) version of this problem suggesting that the heating rate becomes independent of resistivity in a statistical steady state [Ng and Bhattacharjee, Astrophys. J., 675, 899 (2008)]. Our numerical work has now been extended to 3D by means of large-scale numerical simulations. Random photospheric footpoint motion is applied for a time much longer than the correlation time of the motion to obtain converged average coronal heating rates. Simulations are done for different values of the Lundquist number to determine scaling. In the high-Lundquist number limit, the coronal heating rate obtained so far is consistent with a trend that is independent of the Lundquist number, as predicted by previous analysis as well as 2D simulations. In the same limit the average magnetic energy built up by the random footpoint motion tends to have a much weaker dependence on the Lundquist number than that in the 2D simulations, due to the formation of strong current layers and subsequent disruption when the equilibrium becomes unstable. We will present scaling analysis showing that when the dissipation time is comparable or larger than the correlation time of the random footpoint motion, the heating rate tends to become independent of Lundquist number, and that the magnetic energy production is also reduced significantly.Comment: Accepted for publication in Astrophysical Journa

X-ray flares in Orion young stars. I. Flare characteristics

Pre-main sequence (PMS) stars are known to produce powerful X-ray flares which resemble magnetic reconnection solar flares scaled by factors up to 10^4. However, numerous puzzles are present including the structure of X-ray emitting coronae and magnetospheres, effects of protoplanetary disks, and effects of stellar rotation. To investigate these issues in detail, we examine 216 of the brightest flares from 161 PMS stars observed in the Chandra Orion Ultradeep Project (COUP). These constitute the largest homogeneous dataset of PMS, or indeed stellar flares at any stellar age, ever acquired. Our effort is based on a new flare spectral analysis technique that avoids nonlinear parametric modeling. It can be applied to much weaker flares and is more sensitive than standard methods. We provide a catalog with >30 derived flare properties and an electronic atlas for this unique collection of stellar X-ray flares. The current study (Paper I) examines the flare morphologies, and provides general comparison of COUP flare characteristics with those of other active X-ray stars and the Sun. Paper II will concentrate on relationships between flare behavior, protoplanetary disks, and other stellar properties. Several results are obtained. First, the COUP flares studied here are among the most powerful, longest, and hottest stellar X-ray flares ever studied. Second, no significant statistical differences in peak flare luminosity or temperature distributions are found among different morphological flare classes, suggesting a common underlying mechanism for all flares. Third, comparison with the general solar-scaling laws indicates that COUP flares may not fit adequately proposed power-temperature and duration-temperature solar-stellar fits. Fourth, COUP super-hot flares are found to be brighter but shorter than ... ABRIDGEDComment: Accepted for publication in ApJ (07/11/08); 63 pages, 16 figures, 4 table