No Time for Dead Time: Use the Fourier Amplitude Differences to Normalize Dead-time-affected Periodograms

Dead time affects many of the instruments used in X-ray astronomy, by producing a strong distortion in power density spectra. This can make it difficult to model the aperiodic variability of the source or look for quasi-periodic oscillations. Whereas in some instruments a simple a priori correction for dead-time-affected power spectra is possible, this is not the case for others such as NuSTAR, where the dead time is non-constant and long (~2.5 ms). Bachetti et al. 2015 suggested the cospectrum obtained from light curves of independent detectors within the same instrument as a possible way out, but this solution has always only been a partial one: the measured rms was still affected by dead time, because the width of the power distribution of the cospectrum was modulated by dead time in a frequency-dependent way. In this Letter we suggest a new, powerful method to normalize cospectra and, with some caveats, even power density spectra. Our approach uses the difference of the Fourier amplitudes from two independent detectors to characterize and filter out the effect of dead time. This method is crucially important for the accurate modelling of periodograms derived from instruments affected by dead time on board current missions like NuSTAR and ASTROSAT, but also future missions such as IXPEComment: 8 pages, 5 figures, Published on ApJL on 2018 January 3

Intermittency and Lifetime of the 625 Hz QPO in the 2004 Hyperflare from the Magnetar SGR 1806-20 as evidence for magnetic coupling between the crust and the core

Quasi-periodic oscillations (QPOs) detected in the 2004 giant flare from SGR 1806-20 are often interpreted as global magneto-elastic oscillations of the neutron star. There is, however, a large discrepancy between theoretical models, which predict that the highest frequency oscillations should die out rapidly, and the observations, which suggested that the highest-frequency signals persisted for ~100s in X-ray data from two different spacecraft. This discrepancy is particularly important for the high-frequency QPO at ~625 Hz. However, previous analyses did not systematically test whether the signal could also be there in much shorter data segments, more consistent with the theoretical predictions. Here, we test for the presence of the high-frequency QPO at 625 Hz in data from both the Rossi X-ray Timing Explorer (RXTE) and the Ramaty High Energy Solar Spectroscopic Imager (RHESSI) systematically both in individual rotational cycles of the neutron star, as well as averaged over multiple successive rotational cycles at the same phase. We find that the QPO in the RXTE data is consistent with being only present in a single cycle, for a short duration of ~0.5s, whereas the RHESSI data are as consistent with a short-lived signal that appears and disappears as with a long-lived QPO. Taken together, this data provides evidence for strong magnetic interaction between the crust and the core.Comment: Accepted for publication in ApJ. The data and simulations are available at http://figshare.com/articles/SGR_1806_20_Giant_Flare_Data_and_Simulations/1126082 , the code can be downloaded from https://github.com/dhuppenkothen/giantflare-paper , some documentation is under http://nbviewer.ipython.org/github/dhuppenkothen/giantflare-paper/blob/master/documents/giantflare-analysis.ipyn

Quasi-Periodic Oscillations in Short Recurring Bursts of the magnetars SGR 1806-20 and SGR 1900+14 Observed With RXTE

Quasi-periodic oscillations (QPOs) observed in the giant flares of magnetars are of particular interest due to their potential to open up a window into the neutron star interior via neutron star asteroseismology. However, only three giant flares have been observed. We therefore make use of the much larger data set of shorter, less energetic recurrent bursts. Here, we report on a search for QPOs in a large data set of bursts from the two most burst-active magnetars, SGR 1806-20 and SGR 1900+14, observed with the Rossi X-ray Timing Explorer (RXTE). We find a single detection in an averaged periodogram comprising 30 bursts from SGR 1806-20, with a frequency of 57 Hz and a width of 5 Hz, remarkably similar to a giant flare QPO observed from SGR 1900+14. This QPO fits naturally within the framework of global magneto-elastic torsional oscillations employed to explain the giant flare QPOs. Additionally, we uncover a limit on the applicability of Fourier analysis for light curves with low background count rates and strong variability on short timescales. In this regime, standard Fourier methodology and more sophisticated Fourier analyses fail in equal parts by yielding an unacceptably large number of false positive detections. This problem is not straightforward to solve in the Fourier domain. Instead, we show how simulations of light curves can offer a viable solution for QPO searches in these light curves.Comment: accepted for publication in ApJ; 12 pages, 7 figures; code + instructions at https://github.com/dhuppenkothen/MagnetarQPOSearchPaper ; associated data products at http://figshare.com/articles/SGR_1900_14_RXTE_Data/1184101 (SGR 1900+14) and http://figshare.com/articles/SGR_1806_20_Bursts_RXTE_data_set/1184427 (SGR 1806-20

On the Statistical Properties of Cospectra

In recent years, the cross-spectrum has received considerable attention as a means of characterizing the variability of astronomical sources as a function of wavelength. The cospectrum has only recently been understood as a means of mitigating instrumental effects dependent on temporal frequency in astronomical detectors, as well as a method of characterizing the coherent variability in two wavelength ranges on different timescales. In this paper, we lay out the statistical foundations of the cospectrum, starting with the simplest case of detecting a periodic signal in the presence of white noise, under the assumption that the same source is observed simultaneously in independent detectors in the same energy range. This case is especially relevant for detecting faint X-ray pulsars in detectors heavily affected by instrumental effects, including NuSTAR, Astrosat, and IXPE, which allow for even sampling and where the cospectrum can act as an effective way to mitigate dead time. We show that the statistical distributions of both single and averaged cospectra differ considerably from those for standard periodograms. While a single cospectrum follows a Laplace distribution exactly, averaged cospectra are approximated by a Gaussian distribution only for more than ~30 averaged segments, dependent on the number of trials. We provide an instructive example of a quasi-periodic oscillation in NuSTAR and show that applying standard periodogram statistics leads to underestimated tail probabilities for period detection. We also demonstrate the application of these distributions to a NuSTAR observation of the X-ray pulsar Hercules X-1

Hack Weeks as a model for Data Science Education and Collaboration

Across almost all scientific disciplines, the instruments that record our experimental data and the methods required for storage and data analysis are rapidly increasing in complexity. This gives rise to the need for scientific communities to adapt on shorter time scales than traditional university curricula allow for, and therefore requires new modes of knowledge transfer. The universal applicability of data science tools to a broad range of problems has generated new opportunities to foster exchange of ideas and computational workflows across disciplines. In recent years, hack weeks have emerged as an effective tool for fostering these exchanges by providing training in modern data analysis workflows. While there are variations in hack week implementation, all events consist of a common core of three components: tutorials in state-of-the-art methodology, peer-learning and project work in a collaborative environment. In this paper, we present the concept of a hack week in the larger context of scientific meetings and point out similarities and differences to traditional conferences. We motivate the need for such an event and present in detail its strengths and challenges. We find that hack weeks are successful at cultivating collaboration and the exchange of knowledge. Participants self-report that these events help them both in their day-to-day research as well as their careers. Based on our results, we conclude that hack weeks present an effective, easy-to-implement, fairly low-cost tool to positively impact data analysis literacy in academic disciplines, foster collaboration and cultivate best practices.Comment: 15 pages, 2 figures, submitted to PNAS, all relevant code available at https://github.com/uwescience/HackWeek-Writeu

Fourier Domain

The changes in brightness of an astronomical source as a function of time are key probes into that source's physics. Periodic and quasi-periodic signals are indicators of fundamental time (and length) scales in the system, while stochastic processes help uncover the nature of turbulent accretion processes. A key method of studying time variability is through Fourier methods, the decomposition of the signal into sine waves, which yields a representation of the data in frequency space. With the extension into \textit{spectral timing} the methods built on the Fourier transform can not only help us characterize (quasi-)periodicities and stochastic processes, but also uncover the complex relationships between time, photon energy and flux in order to help build better models of accretion processes and other high-energy dynamical physics. In this Chapter, we provide a broad, but practical overview of the most important relevant methods.Comment: 50 pages, 13 figures. This Chapter will appear in the Section "Timing Analysis" of the "Handbook of X-ray and Gamma-ray Astrophysics" (Editors in chief: C. Bambi and A. Santangelo

Magnetar giant flare high-energy emission

High energy ($> 250$ keV) emission has been detected persisting for several tens of seconds after the initial spike of magnetar giant flares. It has been conjectured that this emission might arise via inverse Compton scattering in a highly extended corona generated by super-Eddington outflows high up in the magnetosphere. In this paper we undertake a detailed examination of this model. We investigate the properties of the required scatterers, and whether the mechanism is consistent with the degree of pulsed emission observed in the tail of the giant flare. We conclude that the mechanism is consistent with current data, although the origin of the scattering population remains an open question. We propose an alternative picture in which the emission is closer to that star and is dominated by synchrotron radiation. The $RHESSI$ observations of the December 2004 flare modestly favor this latter picture. We assess the prospects for the Fermi Gamma-Ray Space Telescope to detect and characterize a similar high energy component in a future giant flare. Such a detection should help to resolve some of the outstanding issues.Comment: 20 pages, 14 figure

Constraining the limiting brightness temperature and Doppler factors for the largest sample of radio bright blazars

Relativistic effects dominate the emission of blazar jets complicating our understanding of their intrinsic properties. Although many methods have been proposed to account for them, the variability Doppler factor method has been shown to describe the blazar populations best. We use a Bayesian hierarchical code called {\it Magnetron} to model the light curves of 1029 sources observed by the Owens Valley Radio Observatory's 40-m telescope as a series of flares with an exponential rise and decay, and estimate their variability brightness temperature. Our analysis allows us to place the most stringent constraints on the equipartition brightness temperature i.e., the maximum achieved intrinsic brightness temperature in beamed sources which we found to be $\rm \langle T_{eq}\rangle=2.78\times10^{11}K\pm26\%$. Using our findings we estimated the variability Doppler factor for the largest sample of blazars increasing the number of available estimates in the literature by almost an order of magnitude. Our results clearly show that $\gamma$-ray loud sources have faster and higher amplitude flares than $\gamma$-ray quiet sources. As a consequence they show higher variability brightness temperatures and thus are more relativistically beamed, with all of the above suggesting a strong connection between the radio flaring properties of the jet and $\gamma$-ray emission.Comment: 14 pages, 8 figures, accepted for publication in AP