Dottori, Horacio
Brasil -Universidade Federal do Rio Grande do Sul
The Sésic law, Elliptical Galaxies and the Lerch Phi Functions
In this research paper, we explore the disparities in the parameters of the Sérsic model, which is employed to achieve the best-fit for the light profile along the major axis of elliptical galaxies. We discover that these parameters can significantly deviate from the ones obtained for the minor axis profile. Our investigation reveals that such discrepancies arise naturally due to the variation in isophote eccentricity concerning the isophote’s radius.
To address this phenomenon, we introduce a novel mathematical transformation that enables the calculation of the Sérsic model for the minor axis based on the major axis model. For this transformation to be applicable, certain conditions must be met: the elliptical isophotes need to be aligned and concentric, and their eccentricity can be described by a well-behaved, albeit fairly general, function of the radius.
In cases where the eccentricity remains constant, the only change observed in the Sérsic model is the effective radius. However, when eccentricity varies radially, the transformation becomes more intricate, relying on the Lerch Φ transcendental function.
To validate the proposed transformation, we conducted extensive testing using photometric data gathered from 28 early-type galaxies. The results affirm the effectiveness and accuracy of our approach in bridging the gap between major and minor axis Sérsic models, shedding light on the nature of these galaxies’ intricate light profiles. This study contributes to a deeper understanding of elliptical galaxies and offers valuable insights into their structural properties.
Dottori, Horacio and Ferrari, Fabricio, Brasil