Statistical Gaussian Distribution Function as a Distance Indicator to Stellar Groups

Abstract

In this paper, statistical distribution functions are developed for distance determination of stellar groups. This method depends on the assumption that absolute magnitudes and apparent magnitudes follow a Gaussian distribution function. Due to the limits of the integrands of the frequency function of apparent and absolute magnitudes, we introduce Case A, B, and C Gaussian distributions. The developed approaches have been implemented to determine distances to some clusters and stellar associations. The comparison with the distances derived by different authors reveals good agreement.

Statistical Magnitude Analysis and Distance Determination of the Nearby F8V Stars

“…The importance of the distance of F8V stars derives from that if its moving stellar vertex and its distance of each member are known, then one can easily determine the velocity of the cluster, the position of its centre [3,4] and also the distribution of the cluster's members about this centre [5,6].…”

Statistical distance determination of the Camelopardalis area

“…We used the Gaussian approach (hereafter G B ) as suggested by Abdel-Rahman et al (2009) to model the distribution of the absolute magnitude, therefore, the distance d could be determined from the following relation…”

“…Calculating distance to the astronomical objects using statistical distributions is performed by many authors. Examples are, Sharaf et al (2003) used the Gaussian distribution function to estimate cosmological distance, Abdel-Rahman et al (2009) modified the method of Sharaf et al (2003) by change the limits of the integral and derive the distance equation and, Abdel-Rahman et al (2012) used the exponential distribution function to estimate the new distance equation.…”