Sample size calculations for cluster randomised controlled trials with a fixed number of clusters

Background\ud Cluster randomised controlled trials (CRCTs) are frequently used in health service evaluation. Assuming an average cluster size, required sample sizes are readily computed for both binary and continuous outcomes, by estimating a design effect or inflation factor. However, where the number of clusters are fixed in advance, but where it is possible to increase the number of individuals within each cluster, as is frequently the case in health service evaluation, sample size formulae have been less well studied. \ud \ud Methods\ud We systematically outline sample size formulae (including required number of randomisation units, detectable difference and power) for CRCTs with a fixed number of clusters, to provide a concise summary for both binary and continuous outcomes. Extensions to the case of unequal cluster sizes are provided. \ud \ud Results\ud For trials with a fixed number of equal sized clusters (k), the trial will be feasible provided the number of clusters is greater than the product of the number of individuals required under individual randomisation ($n_i$) and the estimated intra-cluster correlation ($\rho$). So, a simple rule is that the number of clusters ($\kappa$) will be sufficient provided: \ud \ud $\kappa$ > $n_i$ x $\rho$\ud \ud Where this is not the case, investigators can determine the maximum available power to detect the pre-specified difference, or the minimum detectable difference under the pre-specified value for power. \ud \ud Conclusions\ud Designing a CRCT with a fixed number of clusters might mean that the study will not be feasible, leading to the notion of a minimum detectable difference (or a maximum achievable power), irrespective of how many individuals are included within each cluster. \ud \u

Hunting For Eclipses: High Speed Observations of Cataclysmic Variables

We present new time-resolved photometry of 74 cataclysmic variables (CVs), 47 of which are eclipsing. 13 of these eclipsing systems are newly discovered. For all 47 eclipsing systems we show high cadence (1-20 seconds) light curves obtained with the high-speed cameras ultracam and ultraspec. We provide new or refined ephemerides, and supply mid-eclipse times for all observed eclipses. We assess the potential for light curve modelling of all 47 eclipsing systems to determine their system parameters, finding 20 systems which appear to be suitable for future study

Once in a blue moon: detection of ‘bluing’ during debris transits in the white dwarf WD 1145+017

The first transiting planetesimal orbiting a white dwarf was recently detected in K2 data of WD 1145+017 and has been followed up intensively. The multiple, long and variable transits suggest the transiting objects are dust clouds, probably produced by a disintegrating asteroid. In addition, the system contains circumstellar gas, evident by broad absorption lines, mostly in the u΄ band, and a dust disc, indicated by an infrared excess. Here we present the first detection of a change in colour of WD 1145+017 during transits, using simultaneous multiband fast-photometry ULTRACAM measurements over the u΄g΄r΄i΄ bands. The observations reveal what appears to be ‘bluing' during transits; transits are deeper in the redder bands, with a u΄ − r΄ colour difference of up to ∼−0.05 mag. We explore various possible explanations for the bluing, including limb darkening or peculiar dust properties. ‘Spectral' photometry obtained by integrating over bandpasses in the spectroscopic data in and out of transit, compared to the photometric data, shows that the observed colour difference is most likely the result of reduced circumstellar absorption in the spectrum during transits. This indicates that the transiting objects and the gas share the same line of sight and that the gas covers the white dwarf only partially, as would be expected if the gas, the transiting debris and the dust emitting the infrared excess are part of the same general disc structure (although possibly at different radii). In addition, we present the results of a week-long monitoring campaign of the system using a global network of telescopes

Using Gaussian processes to model light curves in the presence of flickering: the eclipsing cataclysmic variable ASASSN-14ag

The majority of cataclysmic variable (CV) stars contain a stochastic noise component in their light curves, commonly referred to as flickering. This can significantly affect the morphology of CV eclipses and increases the difficulty in obtaining accurate system parameters with reliable errors through eclipse modelling. Here we introduce a new approach to eclipse modelling, which models CV flickering with the help of Gaussian processes (GPs). A parameterised eclipse model - with an additional GP component - is simultaneously fit to 8 eclipses of the dwarf nova ASASSN-14ag and system parameters determined. We obtain a mass ratio $q$ = 0.149 $\pm$ 0.016 and inclination $i$ = 83.4 $^{+0.9}_{-0.6}$ $^{\circ}$. The white dwarf and donor masses were found to be $M_{w}$ = 0.63 $\pm$ 0.04 $M_{\odot}$ and $M_{d}$ = 0.093 $^{+0.015}_{-0.012}$ $M_{\odot}$, respectively. A white dwarf temperature $T_{w}$ = 14000 $^{+2200}_{-2000}$ K and distance $d$ = 146 $^{+24}_{-20}$ pc were determined through multicolour photometry. We find GPs to be an effective way of modelling flickering in CV light curves and plan to use this new eclipse modelling approach going forward

A precision study of two eclipsing white dwarf plus M dwarf binaries

We use a combination of X-shooter spectroscopy, ULTRACAM high-speed photometry and SOFI near-infrared photometry to measure the masses and radii of both components of the eclipsing post common envelope binaries SDSS J1212-0123 and GK Vir. For both systems we measure the gravitational redshift of the white dwarf and combine it with light curve model fits to determine the inclinations, masses and radii. For SDSS J1212-0123 we find a white dwarf mass and radius of 0.439 +/- 0.002 Msun and 0.0168 +/- 0.0003 Rsun, and a secondary star mass and radius of 0.273 +/- 0.002 Msun and 0.306 +/- 0.007 Rsun. For GK Vir we find a white dwarf mass and radius of 0.564 +/- 0.014 Msun and 0.0170 +/- 0.0004 Rsun, and a secondary star mass and radius of 0.116 +/- 0.003 Msun and 0.155 +/- 0.003 Rsun. The mass and radius of the white dwarf in GK Vir are consistent with evolutionary models for a 50,000K carbon-oxygen core white dwarf. Although the mass and radius of the white dwarf in SDSS J1212-0123 are consistent with carbon-oxygen core models, evolutionary models imply that a white dwarf with such a low mass and in a short period binary must have a helium core. The mass and radius measurements are consistent with helium core models but only if the white dwarf has a very thin hydrogen envelope, which has not been predicted by evolutionary models. The mass and radius of the secondary star in GK Vir are consistent with evolutionary models after correcting for the effects of irradiation by the white dwarf. The secondary star in SDSS J1212-0123 has a radius ~9 per cent larger than predicted.Comment: 21 pages, 14 Figures and 11 Tables. Accepted for publication in MNRA

An Eclipsing 47 minute Double White Dwarf Binary at 400 pc

We present the discovery of the eclipsing double white dwarf (WD) binary WDJ 022558.21-692025.38 that has an orbital period of 47.19 min. Following identification with the Transiting Exoplanet Survey Satellite, we obtained time-series ground based spectroscopy and high-speed multi-band ULTRACAM photometry which indicate a primary DA WD of mass 0.40 +- 0.04 Msol and a 0.28 +- 0.02 Msol mass secondary WD, which is likely of type DA as well. The system becomes the third-closest eclipsing double WD binary discovered with a distance of approximately 400 pc and will be a detectable source for upcoming gravitational wave detectors in the mHz frequency range. Its orbital decay will be measurable photometrically within 10 yrs to a precision of better than 1%. The fate of the binary is to merge in approximately 41 Myr, likely forming a single, more massive WD.Comment: Accepted for publication in MNRAS, 8 pages + 2 appendix pages, 6 figure

Configuration of readout electronics and data acquisition for the HiPERCAM instrument

© 2018 SPIE. HiPERCAM is a five channel fast photometer to study high temporal variability of the universe, covering from 0.3 to 1.0 microns in five wavebands. HiPERCAM uses custom-made 2Kx1K split-frame transfer CCDs mounted in separate compact camera heads and cooled by thermoelectric coolers to 180K. The demands on the readout system are very unique to this instrument in that all five CCDs are operated in a pseudo drift window mode along with the normal windowing, binning and full-frame modes. The pseudo drift mode involves reading out small window regions from 2 quadrants of each CCD, with the possibility to exceed 1 kHz window rates per output channel. The CCDs are custom manufactured by Teledyne e2v to allow independent serial clock controls for each output. The devices are manufactured in standard and deep-depletion processes with appropriate anti-reflection coatings to achieve high quantum efficiencies in each of the five wavebands. An ESO NGC controller has been configured to control and readout all five CCDs. The data acquisition software has been modified to provide GPS timestamping of the data and access to the acquired data in real time for the data reduction software. The instrument has had its first light and first science observations on the 4.2m William Herschel Telescope, La Palma during a commissioning run in October 2017 and subsequently on the 10.4m Gran Telescopio Canarias in February 2018 and science observations in April 2018. This paper will present the details of the preamplifier electronics, configuration of the readout electronics and the data acquisition software to support the unique readout modes along with the overall performance of the instrument

Long-term eclipse timing of white dwarf binaries: an observational hint of a magnetic mechanism at work

We present a long-term programme for timing the eclipses of white dwarfs in close binaries to measure apparent and/or real variations in their orbital periods. Our programme includes 67 close binaries, both detached and semi-detached and with M-dwarfs, K-dwarfs, brown dwarfs or white dwarfs secondaries. In total, we have observed more than 650 white dwarf eclipses. We use this sample to search for orbital period variations and aim to identify the underlying cause of these variations. We find that the probability of observing orbital period variations increases significantly with the observational baseline. In particular, all binaries with baselines exceeding 10 yr, with secondaries of spectral type K2 – M5.5, show variations in the eclipse arrival times that in most cases amount to several minutes. In addition, among those with baselines shorter than 10 yr, binaries with late spectral type (>M6), brown dwarf or white dwarf secondaries appear to show no orbital period variations. This is in agreement with the so-called Applegate mechanism, which proposes that magnetic cycles in the secondary stars can drive variability in the binary orbits. We also present new eclipse times of NN Ser, which are still compatible with the previously published circumbinary planetary system model, although only with the addition of a quadratic term to the ephemeris. Finally, we conclude that we are limited by the relatively short observational baseline for many of the binaries in the eclipse timing programme, and therefore cannot yet draw robust conclusions about the cause of orbital period variations in evolved, white dwarf binaries

A rotating white dwarf shows different compositions on its opposite faces

White dwarfs, the extremely dense remnants left behind by most stars after their death, are characterised by a mass comparable to that of the Sun compressed into the size of an Earth-like planet. In the resulting strong gravity, heavy elements sink toward the centre and the upper layer of the atmosphere contains only the lightest element present, usually hydrogen or helium. Several mechanisms compete with gravitational settling to change a white dwarf's surface composition as it cools, and the fraction of white dwarfs with helium atmospheres is known to increase by a factor ~2.5 below a temperature of about 30,000 K; therefore, some white dwarfs that appear to have hydrogen-dominated atmospheres above 30,000 K are bound to transition to be helium-dominated as they cool below it. Here we report observations of ZTF J203349.8+322901.1, a transitioning white dwarf with two faces: one side of its atmosphere is dominated by hydrogen and the other one by helium. This peculiar nature is likely caused by the presence of a small magnetic field, which creates an inhomogeneity in temperature, pressure or mixing strength over the surface. ZTF J203349.8+322901.1 might be the most extreme member of a class of magnetic, transitioning white dwarfs -- together with GD 323, a white dwarf that shows similar but much more subtle variations. This new class could help shed light on the physical mechanisms behind white dwarf spectral evolution.Comment: 45 pages, 11 figure