Spectral/timing evolution of black-hole binaries

I briefly outline the state-paradigm that has emerged from the study of black-hole binaries with RossiXTE. This is the starting point of a number of studies that address the connection between accretion and jet ejection and the physical nature of the hard spectral components in these systems.Comment: 4 pages, 2 figures.To appear in Proceedings of "X-ray Astronomy 2009: Present Status, Multi-Wavelength Approach and Future Perspectives", Bologna, Italy, September 7-11, 2009, AIP, eds. A. Comastri, M. Cappi, and L. Angelin

Does GRS 1915+105 exhibit "canonical" black-hole states?

We have analysed RXTE data of the superluminal source GRS 1915+105 in order to investigate if, despite its extreme variability, it also exhibits the canonical source states that characterise other black-hole candidates. The phenomenology of GRS 1915+105 has been described in terms of three states (named A, B and C) based on their hardness ratios and position in the colour-colour diagram. We have investigated the connection between these states and the canonical behaviour and found that the shape of the power spectral continuum and the values of the best-fit model parameters to the noise components in all three states indicate that the source shows properties similar to the canonical very high state.Comment: 5 pages, 3 figures, accepted for publication in A&

From Multiwavelength to Mass Scaling: Accretion and Ejection in Microquasars and AGN

A solid theoretical understanding of how inflowing, accreting plasma around black holes and other compact objects gives rise to outflowing winds and jets is still lacking, despite decades of observations. The fact that similar processes and morphologies are observed in both X-ray binaries as well as active galactic nuclei has led to suggestions that the underlying physics could scale with black hole mass, which could provide a new handle on the problem. In the last decade, simultaneous broadband campaigns of the fast-varying X-ray binaries particularly in their microquasar state have driven the development of, and in some cases altered, our ideas about the inflow/outflow connection in accreting black holes. Specifically the discovery of correlations between the radio, infrared and X-ray bands has revealed a remarkable connectivity between the various emission regions, and argued for a more holistic approach to tackling questions about accretion. This article reviews the recent major observational and theoretical advances that focus specifically on the relation between the two "sides" of the accretion process in black holes, with an emphasis on how new tools can be derived for comparisons across the mass scale.Comment: 31 pages, 6 figures, To appear in Belloni, T. (ed.): The Jet Paradigm - From Microquasars to Quasars, Lect. Notes Phys. 794 (2009

On the harmonics of the low-frequency quasi-periodic oscillation in GRS 1915+105

GRS 1915+105 is a widely studied black hole binary, well known because of its extremely fast and complex variability. Flaring periods of high variability alternate with "stable" phases (the plateaux) when the flux is low, the spectra are hard and the timing properties of the source are similar to those of a number of black hole candidates in hard spectral state. In the plateaux the power density spectra are dominated by a low frequency quasi periodic oscillation (LFQPO) superposed onto a band limited noise continuum and accompanied by at least one harmonic. In this paper we focus on three plateaux, presenting the analysis of the power density spectra and in particular of the LFQPO and its harmonics. While plotting the LFQPO and all the harmonics together on a frequency-width plane, we found the presence of a positive trend of broadening when the frequency increases. This trend can shed light in the nature of the harmonic content of the LFQPO and challenges the usual interpretation of these timing features.Comment: 10 pages, 8 figures. Accepted for publication in MNRA

On the Computational Complexity of MCMC-based Estimators in Large Samples

In this paper we examine the implications of the statistical large sample theory for the computational complexity of Bayesian and quasi-Bayesian estimation carried out using Metropolis random walks. Our analysis is motivated by the Laplace-Bernstein-Von Mises central limit theorem, which states that in large samples the posterior or quasi-posterior approaches a normal density. Using the conditions required for the central limit theorem to hold, we establish polynomial bounds on the computational complexity of general Metropolis random walks methods in large samples. Our analysis covers cases where the underlying log-likelihood or extremum criterion function is possibly non-concave, discontinuous, and with increasing parameter dimension. However, the central limit theorem restricts the deviations from continuity and log-concavity of the log-likelihood or extremum criterion function in a very specific manner. Under minimal assumptions required for the central limit theorem to hold under the increasing parameter dimension, we show that the Metropolis algorithm is theoretically efficient even for the canonical Gaussian walk which is studied in detail. Specifically, we show that the running time of the algorithm in large samples is bounded in probability by a polynomial in the parameter dimension $d$, and, in particular, is of stochastic order $d^2$ in the leading cases after the burn-in period. We then give applications to exponential families, curved exponential families, and Z-estimation of increasing dimension.Comment: 36 pages, 2 figure

Discovery of high-frequency quasi-periodic oscillations in the black-hole candidate IGR J17091-3624

We report the discovery of 8.5 sigma high-frequency quasi-periodic oscillations (HFQPOs) at 66 Hz in the RXTE data of the black hole candidate IGR J17091-3624, a system whose X-ray properties are very similar to those of microquasar GRS 1915+105. The centroid frequency of the strongest peak is ~66 Hz, its quality factor above 5 and its rms is between 4 and 10%. We found a possible additional peak at 164 Hz when selecting a subset of data; however, at 4.5 sigma level we consider this detection marginal. These QPOs have hard spectrum and are stronger in observations performed between September and October 2011, during which IGR J17091-3624 displayed for the first time light curves which resemble those of the gamma variability class in GRS 1915+105. We find that the 66 Hz QPO is also present in previous observations (4.5 sigma), but only when averaging ~235 ksec of relatively high count rate data. The fact that the HFQPOs frequency in IGR J17091-3624 matches surprisingly well that seen in GRS 1915+105 raises questions on the mass scaling of QPOs frequency in these two systems. We discuss some possible interpretations, however, they all strongly depend on the distance and mass of IGR J17091-3624, both completely unconstrained today.Comment: 6 pages, 4 figures, Accepted for publication in ApJ

Least squares after model selection in high-dimensional sparse models

In this article we study post-model selection estimators that apply ordinary least squares (OLS) to the model selected by first-step penalized estimators, typically Lasso. It is well known that Lasso can estimate the nonparametric regression function at nearly the oracle rate, and is thus hard to improve upon. We show that the OLS post-Lasso estimator performs at least as well as Lasso in terms of the rate of convergence, and has the advantage of a smaller bias. Remarkably, this performance occurs even if the Lasso-based model selection "fails" in the sense of missing some components of the "true" regression model. By the "true" model, we mean the best s-dimensional approximation to the nonparametric regression function chosen by the oracle. Furthermore, OLS post-Lasso estimator can perform strictly better than Lasso, in the sense of a strictly faster rate of convergence, if the Lasso-based model selection correctly includes all components of the "true" model as a subset and also achieves sufficient sparsity. In the extreme case, when Lasso perfectly selects the "true" model, the OLS post-Lasso estimator becomes the oracle estimator. An important ingredient in our analysis is a new sparsity bound on the dimension of the model selected by Lasso, which guarantees that this dimension is at most of the same order as the dimension of the "true" model. Our rate results are nonasymptotic and hold in both parametric and nonparametric models. Moreover, our analysis is not limited to the Lasso estimator acting as a selector in the first step, but also applies to any other estimator, for example, various forms of thresholded Lasso, with good rates and good sparsity properties. Our analysis covers both traditional thresholding and a new practical, data-driven thresholding scheme that induces additional sparsity subject to maintaining a certain goodness of fit. The latter scheme has theoretical guarantees similar to those of Lasso or OLS post-Lasso, but it dominates those procedures as well as traditional thresholding in a wide variety of experiments.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ410 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm