A method for the determination of cosmic distances

Sharaf, M. A.; Issa, Islam; Saad, A. S.

doi:10.1016/s1384-1076(02)00198-7

Cited by 8 publications

(10 citation statements)

References 8 publications

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“…The approach introduced by Sharaf et al (2003) has been followed. Sharaf et al (2003) adopted the mean absolute magnitude (M 0 ) and dispersion given by Mihalas and Binney (1981).…”

Section: Abdel-rahman Et Almentioning

confidence: 99%

“…Sharaf et al (2003) adopted the mean absolute magnitude (M 0 ) and dispersion given by Mihalas and Binney (1981). Sharaf et al (2007) derived the dispersion corresponding to the minimum percentage error.…”

Section: Abdel-rahman Et Almentioning

confidence: 99%

“…(b) Case B (GB) Sharaf et al (2003) assumed that all the members in a given cosmic group are nearly at the same distance, r (in parsecs) and are normally distributed. Statistically, this can be written as M ≈ N (M ; M 0 , σ 2 M ).…”

Section: Abdel-rahman Et Almentioning

confidence: 99%

“…In the present case (GB), we changed the limits of the integrands from that used by Sharaf et al (2003) in such way that we considered all members between two apparent magnitudes m L and m g (m L > m g ) where m L is the faintest side and m g is the brightest side of the star cluster sample. Changing the limits of integration requires adding another variable to the problem, which facilitates the optimization process and may lead to better results.…”

Section: Abdel-rahman Et Almentioning

confidence: 99%

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Statistical Gaussian Distribution Function as a Distance Indicator to Stellar Groups

Abdel-Rahman¹,

Issa²,

Sharaf³

et al. 2009

Journal of The Korean Astronomical Society

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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.

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“…The approach introduced by Sharaf et al (2003) has been followed. Sharaf et al (2003) adopted the mean absolute magnitude (M 0 ) and dispersion given by Mihalas and Binney (1981).…”

Section: Abdel-rahman Et Almentioning

confidence: 99%

Section: Abdel-rahman Et Almentioning

confidence: 99%

Section: Abdel-rahman Et Almentioning

confidence: 99%

Section: Abdel-rahman Et Almentioning

confidence: 99%

See 2 more Smart Citations

Statistical Gaussian Distribution Function as a Distance Indicator to Stellar Groups

Abdel-Rahman¹,

Issa²,

Sharaf³

et al. 2009

Journal of The Korean Astronomical Society

Self Cite

View full text Add to dashboard Cite

show abstract

“…Moreover, empirical astrophysics researches have seen a paradigm shift in recent years in that it routinely involves data mining of large multi wavelength data sets, requiring complex automated processes that must invoke a very diverse set of statistical techniques (e.g. [2] [3]). …”

Section: Introductionmentioning

confidence: 99%

An Error Controlled Method to Determine the Stellar Density Function in a Region of the Sky

Sharaf¹,

Mominkhan²

2014

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In this paper, a reliable computational tool will be developed for the determination of the parameters of the stellar density function in a region of the sky with complete error controlled estimates. Of these error estimates are, the variance of the fit, the variance of the least squares solutions vector, the average square distance between the exact and the least-squares solutions, finally the variance of the density stellar function due to the variance of the least squares solutions vector. Moreover, all these estimates are given in closed analytical forms.

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Computational developments for distance determination of stellar groups

Sharaf

Sendi

2010

J Astrophys Astron

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In this paper, we consider a statistical method for distance determination of stellar groups. The method depends on the assumption that the members of the group scatter around a mean absolute magnitude in Gaussian distribution. The mean apparent magnitude of the members is then expressed by frequency function, so as to correct for observational incompleteness at the faint end. The problem reduces to the solution of a highly transcendental equation for a given magnitude parameter α. For the computational developments of the problem, continued fraction by the Top-Down algorithm was developed and applied for the evaluation of the error function erf(z). The distance equation (y) = 0 was solved by an iterative method of second order of convergence using homotopy continuation technique. This technique does not need any prior knowledge of the initial guess, a property which avoids the critical situations between divergent and very slow convergent solutions, that may exist in the applications of other iterative methods depending on initial guess.Finally, we apply the method for the nearby main sequence late type stars assuming that the stars of each group of the same spectral type scatter around a mean absolute magnitude in a Gaussian distribution. The accuracies of the numerical results are satisfactory, in that, the percentage errors between r and the mean values are respectively: (2.4%, 1.6%, 0.72%, 0.66%, 3.5%, 2.4%, 2%, 2.5%, 0.9%) for the stars of spectral types: (F5V, F6V, F7V, F8V, F9V, G0V, G2V, G5V, G8V).

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A method for the determination of cosmic distances

Cited by 8 publications

References 8 publications

Statistical Gaussian Distribution Function as a Distance Indicator to Stellar Groups

Statistical Gaussian Distribution Function as a Distance Indicator to Stellar Groups

An Error Controlled Method to Determine the Stellar Density Function in a Region of the Sky

Computational developments for distance determination of stellar groups

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