Variable selection for the absolute magnitude of Type Ia supernovae

M. Uemura, K. S. Kawabata, S. Ikeda, and K. Maeda, “Variable selection for modeling the absolute magnitude at maximum of Type Ia supernovae”, PASJ, vol. 67, 55, 2015


We discuss what is an appropriate set of explanatory variables in order to predict the absolute magnitude at the maximum of Type Ia supernovae. In order to have a good prediction, the error for future data, which is called the “generalization error,” should be small. We use cross-validation in order to control the generalization error and a LASSO-type estimator in order to choose the set of variables. This approach can be used even in the case that the number of samples is smaller than the number of candidate variables. We studied the Berkeley supernova database with our approach. Candidates for the explanatory variables include normalized spectral data, variables about lines, and previously proposed flux ratios, as well as the color and light-curve widths. As a result, we confirmed the past understanding about Type Ia supernovae: (i) The absolute magnitude at maximum depends on the color and light-curve width. (ii) The light-curve width depends on the strength of Si II. Recent studies have suggested adding more variables in order to explain the absolute magnitude. However, our analysis does not support adding any other variables in order to have a better generalization error.



Doppler tomography by total variation minimization

M. Uemura, T. Kato, D. Nogami, and R. Mennickent, “Doppler tomography by total variation minimization,” PASJ, vol. 67, p. 22, 2015

We have developed a new model of Doppler tomography using total variation minimization (DTTVM). This method can reconstruct localized and nonaxisymmetric profiles with sharp edges in the Doppler map. This characteristic is emphasized in the case where input data are small in number. We apply this model to natural data for the dwarf nova WZ Sge in superoutburst and TU Men in quiescence. We confirm that DTTVM can reproduce the observed spectra with high precision. Compared with the models based on the maximum entropy method, our new model can provide Doppler maps that little depend on the hyperparameter and on the presence of the absorption core. We also introduce a cross-validation method of estimating reasonable values of a hyperparameter in the model from the data themselves.



Height Mapping of Dwarf Nova Accretion Disks

M. Uemura, T. Kato, T. Ohshima, and H. Maehara, “Reconstruction of the Structure of Accretion Disks in Dwarf Novae from the Multi-Band Light Curves of Early Superhumps,” PASJ, vol. 64, p. 92, 2012.

We propose a new method to reconstruct the structure of accretion disks in dwarf novae using multi-band light curves of early superhumps. Our model assumes that early superhumps are caused by the rotation effect of non-axisymmetrically flaring disks. We have developed a Bayesian model for this reconstruction, in which a smoother disk-structure tends to have a higher prior probability. We analyzed simultaneous optical and near-infrared photometric data of early superhumps of the dwarf nova, V455 And using this technique. The reconstructed disk has two flaring parts in the outermost region of the disk. These parts are responsible for the primary and secondary maxima of the light curves. The height-to-radius ratio is h/r 0.20-0.25 in the outermost region. In addition to the outermost flaring structures, flaring arm-like patterns can be seen in an inner region of the reconstructed disk. The overall profile of the reconstructed disk is reminiscent of the disk structure that is deformed by the tidal effect. However, an inner arm-like pattern, which is responsible for the secondary minimum in the light curve, cannot be reproduced only by the tidal effect. It implies the presence of another mechanism that deforms the disk structure. Alternatively, the temperature distribution of the disk could be non-axisymmetric. We demonstrate that the disk structure with weaker arm-like patterns is optimal in the model including the irradiation effect. However, the strongly irradiated disk gives quite blue colors, which may conflict with the observation. Our results suggest that the amplitude of early superhumps depends mainly on the height of the outermost flaring regions of the disk. We predict that early superhumps can be detected with an amplitude of > 0.02 mag in about 90% of WZ Sge stars.

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