Most stars become white dwarfs after they have exhausted their nuclear fuel (the Sun will be one such). Between one-quarter and one-half of white dwarfs have elements heavier than helium in their atmospheres, even though these elements ought to sink rapidly into the stellar interiors (unless they are occasionally replenished). The abundance ratios of heavy elements in the atmospheres of white dwarfs are similar to the ratios in rocky bodies in the Solar System. This fact, together with the existence of warm, dusty debris disks surrounding about four per cent of white dwarfs, suggests that rocky debris from the planetary systems of white-dwarf progenitors occasionally pollutes the atmospheres of the stars. The total accreted mass of this debris is sometimes comparable to the mass of large asteroids in the Solar System. However, rocky, disintegrating bodies around a white dwarf have not yet been observed. Here we report observations of a white dwarf--WD 1145+017--being transited by at least one, and probably several, disintegrating planetesimals, with periods ranging from 4.5 hours to 4.9 hours. The strongest transit signals occur every 4.5 hours and exhibit varying depths (blocking up to 40 per cent of the star's brightness) and asymmetric profiles, indicative of a small object with a cometary tail of dusty effluent material. The star has a dusty debris disk, and the star's spectrum shows prominent lines from heavy elements such as magnesium, aluminium, silicon, calcium, iron, and nickel. This system provides further evidence that the pollution of white dwarfs by heavy elements might originate from disrupted rocky bodies such as asteroids and minor planets.

The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large datasets. Gaussian Processes are a popular class of models used for this purpose but, since the computational cost scales, in general, as the cube of the number of data points, their application has been limited to small datasets. In this paper, we present a novel method for Gaussian Process modeling in one-dimension where the computational requirements scale linearly with the size of the dataset. We demonstrate the method by applying it to simulated and real astronomical time series datasets. These demonstrations are examples of probabilistic inference of stellar rotation periods, asteroseismic oscillation spectra, and transiting planet parameters. The method exploits structure in the problem when the covariance function is expressed as a mixture of complex exponentials, without requiring evenly spaced observations or uniform noise. This form of covariance arises naturally when the process is a mixture of stochastically-driven damped harmonic oscillators -providing a physical motivation for and interpretation of this choice -but we also demonstrate that it can be a useful effective model in some other cases. We present a mathematical description of the method and compare it to existing scalable Gaussian Process methods. The method is fast and interpretable, with a range of potential applications within astronomical data analysis and beyond. We provide well-tested and documented open-source implementations of this method in C++, Python, and Julia.

Among the available methods for dating stars, gyrochronology is a powerful one because it requires knowledge of only the star's mass and rotation period. Gyrochronology relations have previously been calibrated using young clusters, with the Sun providing the only age dependence, and are therefore poorly calibrated at late ages. We used rotation period measurements of 310 Kepler stars with asteroseismic ages, 50 stars from the Hyades and Coma Berenices clusters and 6 field stars (including the Sun) with precise age measurements to calibrate the gyrochronology relation, whilst fully accounting for measurement uncertainties in all observable quantities. We calibrated a relation of the form Pwhere P is rotation period in days, A is age in Myr, B and V are magnitudes and a, b and n are the free parameters of our model. We found a = 0.40 +0.3 −0.05 , b = 0.31 +0.05 −0.02 and n = 0.55 +0.02 −0.09 . Markov Chain Monte Carlo methods were used to explore the posterior probability distribution functions of the gyrochronology parameters and we carefully checked the effects of leaving out parts of our sample, leading us to find that no single relation beween rotation period, colour and age can adequately describe all the subsets of our data. The Kepler asteroseismic stars, cluster stars and local field stars cannot all be described by the same gyrochronology relation. The Kepler asteroseismic stars may be subject to observational biases, however the clusters show unexpected deviations from the predicted behaviour, providing concerns for the overall reliability of gyrochronology as a dating method.

Variability in the light curves of spotted, rotating stars is often non-sinusoidal and quasiperiodic -spots move on the stellar surface and have finite lifetimes, causing stellar flux variations to slowly shift in phase. A strictly periodic sinusoid therefore cannot accurately model a rotationally modulated stellar light curve. Physical models of stellar surfaces have many drawbacks preventing effective inference, such as highly degenerate or high-dimensional parameter spaces. In this work, we test an appropriate effective model: a Gaussian Process with a quasi-periodic covariance kernel function. This highly flexible model allows sampling of the posterior probability density function of the periodic parameter, marginalising over the other kernel hyperparameters using a Markov Chain Monte Carlo approach. To test the effectiveness of this method, we infer rotation periods from 333 simulated stellar light curves, demonstrating that the Gaussian process method produces periods that are more accurate than both a sinefitting periodogram and an autocorrelation function method. We also demonstrate that it works well on real data, by inferring rotation periods for 275 Kepler stars with previously measured periods. We provide a table of rotation periods for these 1102 Kepler objects of interest and their posterior probability density function samples. Because this method delivers posterior probability density functions, it will enable hierarchical studies involving stellar rotation, particularly those involving population modelling, such as inferring stellar ages, obliquities in exoplanet systems, or characterising star-planet interactions. The code used to implement this method is available online.