Destroying Aliases from the Ground and Space: Super-Nyquist ZZ Cetis in K2 Long Cadence Data

With typical periods of order 10 minutes, the pulsation signatures of ZZ Ceti variables (pulsating hydrogen-atmosphere white dwarf stars) are severely undersampled by long-cadence (29.42 minutes per exposure) K2 observations. Nyquist aliasing renders the intrinsic frequencies ambiguous, stifling precision asteroseismology. We report the discovery of two new ZZ Cetis in long-cadence K2 data: EPIC 210377280 and EPIC 220274129. Guided by 3-4 nights of follow-up, high-speed (<=30 s) photometry from McDonald Observatory, we recover accurate pulsation frequencies for K2 signals that reflected 4-5 times off the Nyquist with the full precision of over 70 days of monitoring (~0.01 muHz). In turn, the K2 observations enable us to select the correct peaks from the alias structure of the ground-based signals caused by gaps in the observations. We identify at least seven independent pulsation modes in the light curves of each of these stars. For EPIC 220274129, we detect three complete sets of rotationally split ell=1 (dipole mode) triplets, which we use to asteroseismically infer the stellar rotation period of 12.7+/-1.3 hr. We also detect two sub-Nyquist K2 signals that are likely combination (difference) frequencies. We attribute our inability to match some of the K2 signals to the ground-based data to changes in pulsation amplitudes between epochs of observation. Model fits to SOAR spectroscopy place both EPIC 210377280 and EPIC 220274129 near the middle of the ZZ Ceti instability strip, with Teff = 11590+/-200 K and 11810+/-210 K, and masses 0.57+/-0.03 Msun and 0.62+/-0.03 Msun, respectively.Comment: 13 pages, 9 figures, 7 tables; accepted for publication in Ap

Beyond the frame rate: Measuring high-frequency fluctuations with light intensity modulation

Power spectral density measurements of any sampled signal are typically restricted by both acquisition rate and frequency response limitations of instruments, which can be particularly prohibitive for video-based measurements. We have developed a new method called Intensity Modulation Spectral Analysis (IMSA) that circumvents these limitations, dramatically extending the effective detection bandwidth. We demonstrate this by video-tracking an optically-trapped microsphere while oscillating an LED illumination source. This approach allows us to quantify fluctuations of the microsphere at frequencies over 10 times higher than the Nyquist frequency, mimicking a significantly higher frame rate.Comment: 4 pages, 2 figure

White Dwarf Rotation as a Function of Mass and a Dichotomy of Mode Linewidths: Kepler Observations of 27 Pulsating DA White Dwarfs Through K2 Campaign 8

We present photometry and spectroscopy for 27 pulsating hydrogen-atmosphere white dwarfs (DAVs, a.k.a. ZZ Ceti stars) observed by the Kepler space telescope up to K2 Campaign 8, an extensive compilation of observations with unprecedented duration (>75 days) and duty cycle (>90%). The space-based photometry reveals pulsation properties previously inaccessible to ground-based observations. We observe a sharp dichotomy in oscillation mode linewidths at roughly 800 s, such that white dwarf pulsations with periods exceeding 800 s have substantially broader mode linewidths, more reminiscent of a damped harmonic oscillator than a heat-driven pulsator. Extended Kepler coverage also permits extensive mode identification: We identify the spherical degree of 61 out of 154 unique radial orders, providing direct constraints of the rotation period for 20 of these 27 DAVs, more than doubling the number of white dwarfs with rotation periods determined via asteroseismology. We also obtain spectroscopy from 4m-class telescopes for all DAVs with Kepler photometry. Using these homogeneously analyzed spectra we estimate the overall mass of all 27 DAVs, which allows us to measure white dwarf rotation as a function of mass, constraining the endpoints of angular momentum in low- and intermediate-mass stars. We find that 0.51-to-0.73-solar-mass white dwarfs, which evolved from 1.7-to-3.0-solar-mass ZAMS progenitors, have a mean rotation period of 35 hr with a standard deviation of 28 hr, with notable exceptions for higher-mass white dwarfs. Finally, we announce an online repository for our Kepler data and follow-up spectroscopy, which we collect at http://www.k2wd.org.Comment: 33 pages, 31 figures, 5 tables; accepted for publication in ApJS. All raw and reduced data are collected at http://www.k2wd.or

Measuring the broadband power spectra of active galactic nuclei with RXTE

We have developed a Monte Carlo technique to test models for the true power spectra of intermittently sampled lightcurves against the noisy, observed power spectra, and produce a reliable estimate of the goodness of fit of the given model. We apply this technique to constrain the broadband power spectra of a sample of four Seyfert galaxies monitored by the Rossi X-ray Timing Explorer (RXTE) over three years. We show that the power spectra of three of the AGN in our sample (MCG-6-30-15, NGC5506 and NGC3516) flatten significantly towards low frequencies, while the power spectrum of NGC5548 shows no evidence of flattening. We fit two models for the flattening, a `knee' model, analogous to the low-frequency break seen in the power spectra of BHXRBs in the low state (where the power-spectral slope flattens to \alpha=0) and a `high-frequency break' model (where the power-spectral slope flattens to \alpha=1), analogous to the high-frequency break seen in the high and low-state power spectra of the classic BHXRB Cyg X-1. Both models provide good fits to the power spectra of all four AGN. For both models, the characteristic frequency for flattening is significantly higher in MCG-6-30-15 than in NGC 3516 (by factor ~10) although both sources have similar X-ray luminosities, suggesting that MCG-6-30-15 has a lower black hole mass and is accreting at a higher rate than NGC 3516. Assuming linear scaling of characteristic frequencies with black hole mass, the high accretion rate implied for MCG-6-30-15 favours the high-frequency break model for this source and further suggests that MCG-6-30-15 and possibly NGC 5506, may be analogues of Cyg X-1 in the high state [ABRIDGED].Comment: 23 pages, accepted for publication in MNRA

An alternative approach to aeroservoelastic design and clearance

The interaction between an aircraft's structural dynamics, unsteady aerodynamics and flight control system is known as aeroservoelasticity. The problem can occur because the control system sensors are of sufficient bandwidth to sense the structural vibrations as well as the rigid-body motion of the aircraft. This sensed structural vibration can result in further excitation of the structure through both aerodynamic and inertial excitation, leading to a potential closed-loop instability. At present, such an unstable interaction is prevented by the inclusion of notch filters within the feedback path which have a detrimental effect on the aircraft's rigid-body performance. The current clearance procedure is restricted by a poor understanding of the array of complex issues involved. The aim of the project was to develop a clearer understanding of the interactions between system components leading to a reduction in the clearance requirements. Work has concentrated on the effects of system nonlinearities and on the digital nature of modem control systems. A major source of nonlinearities within the control system are the servo-hydraulic actuators. Through detailed actuator modelling confirmed by rig testing of actual hardware, these nonlinearities are analysed and a method for predicting the response of the actuators in the presence of two input signals proposed. As a result, it is demonstrated that an unstable structural oscillation would cause a limit-cycle oscillation as opposed to an unbounded response. Through nonlinear system theory the criteria for the existence of such limit-cycles are obtained, enabling them to be predicted and therefore prevented. Consideration of the true nonlinear nature of the aeroservoelastic system has enabled an alternative design and clearance procedure to be proposed which reduces the attenuation requirements of the structural-mode filters whilst ensuring satisfactory aircraft performance even in the presence of modelling errors. This design procedure is demonstrated on both a model of the aircraft system and a simple test system enabling verification of the nonlinear analysis and comparison between the current and proposed alternative procedures. As a result, it is demonstrated that consideration of the true nonlinear nature of the aeroservoelastic interaction has the potential for allowing a significant reduction in structural filter attenuation requirements. Consequently, a reduction in the phase lag due to the filters is possible resulting in an improvement in closed-loop system performance whilst ensuring the safe operation of the aircraft

Investigating the A-type stars using Kepler data

Rotation is a key physical process operating in the A stars. We present a method by which rotation periods might be measured with Fourier transforms of Kepler data, potentially removing the requirement of spectroscopic observations to acquire similar information. Angular rotational velocities reach their maximum at about A5, but slowly rotating A stars are also seen and these tend to be chemically peculiar. For Ap stars, rotational braking is understood, but too few progenitors are observed. A review of a rare class of stars, the ‘sn’ stars, leads us to suggest these may contribute to the ‘missing’ Ap progenitors. For Am stars, we find the tidal braking mechanisms proposed in the literature induce mixing that is incompatible with observed abundance anomalies. At the other end of the scale are the λ Boo stars, whose rotation velocities are above average. The two main theories for the origin of their metal underabundances are discussed and it is suggested that both of them imply the λ Boo stars contain a high fraction of pulsators – a suggestion that is backed up by observations in the literature. Many λ Boo stars also have circumstellar material, suggesting they are potential planet hosts. This, and the use of asteroseismology to study their interiors, are two excellent reasons to adopt them as prime targets for detailed investigation with Kepler. Pulsation is a common phenomenon in A stars. The δ Sct stars receive wide attention but the fraction of stars that pulsate at the 50 μmag level is shown to be only 56 per cent. The non-δ Sct stars in the δ Sct instability strip receive far less attention. Some of these stars, without appreciable granulation or stellar winds, are probably the least variable objects on the HR diagram. It is shown that they have the potential to be among the most peculiar Am stars. Their investigation has led to two important conclusions: (1) the presence of γ Dor pulsation in non-δ Sct stars in the δ Sct instability strip may inhibit the development of the expected Am peculiarities; and (2) chemically normal, non-δ Sct stars in the δ Sct instability strip do exist at the μmag level. Fourier transforms are invaluable tools in the field of stellar pulsation. The Kepler Space Telescope is providing data of exquisite precision, and thus more detail is seen in the Fourier transform than ever before. Truly understanding the properties of the data is fundamental to their successful utilisation. Through statistical analysis of noise levels in over 20 000 stars, granulation is concluded to be visible in Fourier transforms of stars cooler than 7500 K. Another property investigated is the Nyquist frequency. We found that periodically modulated sampling on board Kepler allows distinction between real pulsation frequencies and Nyquist aliases, even when those real frequencies exceed the Nyquist frequency of the data. This discovery opens up study of many hundreds of stars previously thought to have insurmountable Nyquist ambiguities in their data

Periodogram Analysis under the Popper-Bayes Approach

In this chapter, we discuss the use of the Lomb-Scargle periodogram, its advantages, and pitfalls on a geometrical rather than statistical point of view. It means emphasizing more on the transformation properties of the finite sampling – the available data – rather than on the ensemble properties of the assumed model statistical distributions. We also present a brief overview and criticism of recent literature on the subject and its new developments. The whole discussion is under the geophysical inverse theory point of view, the Tarantola’s combination of information or the so-called Popper-Bayes approach. This approach has been very successful in dealing with large ill-conditioned, or under-determined complex problems. In the case of periodogram analysis, this approach allows us to manage more naturally the experimental data distributions and its anomalies (uncorrelated noise, sampling artifacts, windowing, aliasing, spectral leakage, among others). Finally, we discuss the Lomb-Scargle-Tarantola (LST) periodogram: an estimator of spectral content existing in irregularly sampled time series that implements these principles