# Deterministic components in the light curve amplitude of Y Oph

## Abstract

About two decades after the discovery of the amplitude decline of the light curve of the classical Cepheid Y Oph, its study is resumed using an increased amount of homogenized data and an extended time base.

In our approach, the investigation of different time series concerning the light curve amplitude of Y Oph is not only the reason for the present study, but also a stimulus for developing a coherent methodology for studying long- and short-term variability phenomena in variable stars, taking into account the details of concrete observing conditions: amount of data, data sampling, time base, and individual errors of observational data. The statistical significance of this decreasing trend was estimated by assuming its linearity. We approached the decision-making process by formulating adequate null and alternative hypotheses, and testing the value of the regression line slope for different data sets via Monte Carlo simulations. A variability analysis, through various methods, of the original data and of the residuals obtained after removing the linear trend was performed.

We also proposed a new statistical test, based on amplitude spectrum analysis and Monte Carlo simulations, intended to evaluate how detectible is a given (linear) trend in well-defined observing conditions: the trend detection probability. The main conclusion of our study on Y Oph is that, even if the false alarm probability is low enough to consider the decreasing trend to be statistically significant, the available data do not allow us to obtain a reasonably powerful test.

We are able to confirm the light curve amplitude decline, and the order of magnitude of its slope with a better statistical substantiation. According to the obtained values of the trend detection probability, it seems that the trend we are dealing with is marked by a low detectibility.

Our attempt to find signs of possible variability phenomena at shorter timescales ended by emphasizing the relative constancy of our data, within their precision limits.

## Authors

A. Pop
– Astronomical Institute, Cluj-Napoca, Romania

C. Vamoș
-Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

V. Turcu
– Astronomical Institute, Cluj-Napoca, Romania

## Cite this paper as:

A. Pop, C. Vamoş, and V. Turcu, Deterministic components in the light curve amplitude of Y Oph, The Astronomical Journal, vol. 139 (2010) 425, doi: 10.1088/0004-6256/139/2/425

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