Learning to do multiframe wavefront sensing unsupervisedly: applications to blind deconvolution

Observations from ground based telescopes are affected by the presence of the Earth atmosphere, which severely perturbs them. The use of adaptive optics techniques has allowed us to partly beat this limitation. However, image selection or post-facto image reconstruction methods applied to bursts of short-exposure images are routinely needed to reach the diffraction limit. Deep learning has been recently proposed as an efficient way to accelerate these image reconstructions. Currently, these deep neural networks are trained with supervision, so that either standard deconvolution algorithms need to be applied a-priori or complex simulations of the solar magneto-convection need to be carried out to generate the training sets. Our aim here is to propose a general unsupervised training scheme that allows multiframe blind deconvolution deep learning systems to be trained simply with observations. The approach can be applied for the correction of point-like as well as extended objects. Leveraging the linear image formation theory and a probabilistic approach to the blind deconvolution problem produces a physically-motivated loss function. The optimization of this loss function allows an end-to-end training of a machine learning model composed of three neural networks. As examples, we apply this procedure to the deconvolution of stellar data from the FastCam instrument and to solar extended data from the Swedish Solar Telescope. The analysis demonstrates that the proposed neural model can be successfully trained without supervision using observations only. It provides estimations of the instantaneous wavefronts, from which a corrected image can be found using standard deconvolution technniques. The network model is roughly three orders of magnitude faster than applying standard deconvolution based on optimization and shows potential to be used on real-time at the telescope.Comment: 11 pages, 4 figures, accepted for publication in A&

Towards the automatic estimation of gravitational lenses' time delays

Estimation of time delays from a noisy and gapped data is one of the simplest data analysis problems in astronomy by its formulation. But as history of real experiments show, the work with observed data sets can be quite complex and evolved. By analysing in detail previous attempts to build delay estimation algorithms we try to develop an automatic and robust procedure to perform the task. To evaluate and compare different variants of the algorithms we use real observed data sets which have been objects of past controversies. In this way we hope to select the methods and procedures which have highest probability to succeed in complex situations. As a result of our investigations we propose an estimation procedure which can be used as a method of choice in large photometric experiments. We can not claim that proposed methodology works with any reasonably well sampled input data set. But we hope that the steps taken are in correct direction and developed software is truly useful for practising astronomers.Comment: Accepted by Baltic Astronomy, 21 pages, 4 figure

Multiperiodicity, modulations and flip-flops in variable star light curves I. Carrier fit method

The light curves of variable stars are commonly described using simple trigonometric models, that make use of the assumption that the model parameters are constant in time. This assumption, however, is often violated, and consequently, time series models with components that vary slowly in time are of great interest. In this paper we introduce a class of data analysis and visualization methods which can be applied in many different contexts of variable star research, for example spotted stars, variables showing the Blazhko effect, and the spin-down of rapid rotators. The methods proposed are of explorative type, and can be of significant aid when performing a more thorough data analysis and interpretation with a more conventional method.Our methods are based on a straightforward decomposition of the input time series into a fast "clocking" periodicity and smooth modulating curves. The fast frequency, referred to as the carrier frequency, can be obtained from earlier observations (for instance in the case of photometric data the period can be obtained from independently measured radial velocities), postulated using some simple physical principles (Keplerian rotation laws in accretion disks), or estimated from the data as a certain mean frequency. The smooth modulating curves are described by trigonometric polynomials or splines. The data approximation procedures are based on standard computational packages implementing simple or constrained least-squares fit-type algorithms.Comment: 14 pages, 23 figures, submitted to Astronomy and Astrophysic

STATISTICAL STUDY OF STRONG AND EXTREME GEOMAGNETIC DISTURBANCES AND SOLAR CYCLE CHARACTERISTICS

We study the relation between strong and extreme geomagnetic storms and solar cycle characteristics. The analysis uses an extensive geomagnetic index AA data set spanning over 150 yr. complemented by the Kakioka magnetometer recordings. We apply Pearson correlation statistics and estimate the significance of the correlation with a bootstrapping technique. We show that the correlation between the storm occurrence and the strength of the solar cycle decreases from a clear positive correlation with increasing storm magnitude toward a negligible relationship. Hence, the quieter Sun can also launch superstorms that may lead to significant societal and economic impact. Our results show that while weaker storms occur most frequently in the declining phase, the stronger storms have the tendency to occur near solar maximum. Our analysis suggests that the most extreme solar eruptions do not have a direct connection between the solar large-scale dynamo-generated magnetic field, but are rather associated with smaller-scale dynamo and resulting turbulent magnetic fields. The phase distributions of sunspots and storms becoming increasingly in phase with increasing storm strength, on the other hand, may indicate that the extreme storms are related to the toroidal component of the solar large-scale field.Peer reviewe

Multiperiodicity, modulations, and flip-flops in variable star light curves III. Carrier fit analysis of LQ Hydrae photometry for 1982-2014

Conclusions. The evolution of the spot distribution of the object is found to be very chaotic, with no clear signs of an azimuthal dynamo wave that would persist over longer timescales, although the short-lived coherent structures occasionally observed do not rotate with the same speed as the mean spot distribution. The most likely explanation of the bimodal period distribution is attributed to the high-and low-latitude spot formation regions confirmed from Doppler imaging and Zeeman Doppler imaging.</p

Transition from axi- to nonaxisymmetric dynamo modes in spherical convection models of solar-like stars

Context. Both dynamo theory and observations of stellar large-scale magnetic fields suggest a change from nearly axisymmetric configurations at solar rotation rates to nonaxisymmetric configurations for rapid rotation. Aims. We seek to understand this transition using numerical simulations. Methods. We use three-dimensional simulations of turbulent magnetohydrodynamic convection in spherical shell wedges and considered rotation rates between 1 and 31 times the solar value. Results. We find a transition from axi- to nonaxisymmetric solutions at around 1.8 times the solar rotation rate. This transition coincides with a change in the rotation profile from antisolar- to solar-like differential rotation with a faster equator and slow poles. In the solar-like rotation regime, the field configuration consists of an axisymmetric oscillatory field accompanied by an m = 1 azimuthal mode (two active longitudes), which also shows temporal variability. At slow (rapid) rotation, the axisymmetric (nonaxisymmetric) mode dominates. The axisymmetric mode produces latitudinal dynamo waves with polarity reversals, while the nonaxisymmetric mode often exhibits a slow drift in the rotating reference frame and the strength of the active longitudes changes cyclically over time between the different hemispheres. In the majority of cases we find retrograde waves, while prograde waves are more often found from observations. Most of the obtained dynamo solutions exhibit cyclic variability either caused by latitudinal or azimuthal dynamo waves. In an activity-period diagram, the cycle lengths normalized by the rotation period form two different populations as a function of rotation rate or magnetic activity level. The slowly rotating axisymmetric population lies close to what in observations is called the inactive branch, where the stars are believed to have solar-like differential rotation, while the rapidly rotating models are close to the superactive branch with a declining cycle to rotation frequency ratio and an increasing rotation rate. Conclusions. We can successfully reproduce the transition from axi- to nonaxisymmetric dynamo solutions for high rotation rates, but high-resolution simulations are required to limit the effect of rotational quenching of convection at rotation rates above 20 times the solar value.Peer reviewe

Towards the Automatic Estimation of Time Delays of Gravitational Lenses

Estimation of time delays from a noisy and gapped data is one of the simplest data analysis problems in astronomy by its formulation. But as history of real experiments show, the work with observed datasets can be quite complex and evolved. By analyzing in detail previous attempts to build delay estimation algorithms we try to develop an automatic and robust procedure to perform the task. To evaluate and compare different variants of the algorithms we use real observed datasets which have been objects of past controversies. In this way we hope to select the methods and procedures which have highest probability to succeed in complex situations. As a result of our investigations, we propose an estimation procedure which can be used as a method of choice in large photometric experiments. We cannot claim that the proposed methodology works with any reasonably well sampled input dataset. However we hope that the steps taken are in correct direction and the developed software will be useful for observational astronomers

Method for estimating cycle lengths from multidimensional time series: Test cases and application to a massive "in silico" dataset

Many real world systems exhibit cyclic behavior that is, for example, due to the nearly harmonic oscillations being perturbed by the strong fluctuations present in the regime of significant non-linearities. For the investigation of such systems special techniques relaxing the assumption to periodicity are required. In this paper, we present the generalization of one of such techniques, namely the D2 phase dispersion statistic, to multidimensional datasets, especially suited for the analysis of the outputs from three-dimensional numerical simulations of the full magnetohydrodynamic equations. We present the motivation and need for the usage of such a method with simple test cases, and present an application to a solar-like semi-global numerical dynamo simulation covering nearly 150 magnetic cycles