Fractal Analysis and Non-linear Multivariate Model of Keplers stars

Abstract

The stellar surface rotation is the indicator of internal dynamo process. The dynamo generates many active phenomena like stellar spots and also affect stellar evolution. In this study we have analyzed the surface rotation and evolutionary parameters such as mass, density, radius, effective temperature, surface gravity and metallicity of stars all together. Surface rotation is used in different forms such as rotational shear, relative differential rotation and average surface rotation. Approximately 12000 Keplers star data of rotation and above mentioned evolutionary parameters were used. Fractal dimension and the Hurst exponent technique is used to analyze the persistency and persistency correlation of data in different spectral classes. Strong persistency correlation is found between data of rotational shear vs effective temperature (0.992), rotational shear vs radius (-0.82) and average differential rotation vs metallicity (0.995). Additionally, correlation between other evolutionary parameters and rotational parameters are also found. On the basis of these correlations and physical relationship the nonlinear models between luminosity, radius and rotation (relative differential rotation and rotational shear) are established for main sequence.