# Monte Carlo Simulation of Lutz-Kelker Corrections

## Location

CSU

## Student's Major

Physics and Astronomy

## Student's College

Science, Engineering and Technology

## Mentor's Name

Steve Kipp

## Mentor's Department

Physics and Astronomy

## Mentor's College

Science, Engineering and Technology

## Description

The Lutz-Kelker (LK) correction adjusts the absolute magnitudes for a parallax-limited sample of stars. The parallax of a star is the measured parameter which is proportional to a star's distance. The absolute magnitude of a star is a measure of its luminosity and is calculated from Its parallax. For stars that are uniformly distributed in space, more stars lie outside than inside a given radius than inside. But random error in parallax measurement scatters more stars inside a radius than outside. This will cause the sample of stars to have observed parallaxes that are on average larger than the true parallaxes. Lutz and Kelker used an analytical technique to develop a table of corrections. The corrections are limited by the technique itself. Their calculations involve division by numbers close to zero and become unstable. We plan to calculate the correction factors by using Monte Carlo simulation to introduce random error into a population of stars with known parameters and compare the population with error to the known population. This method is general and can possibly be applied to other radially distributed phenomena, such as point source pollution.

Monte Carlo Simulation of Lutz-Kelker Corrections

CSU

The Lutz-Kelker (LK) correction adjusts the absolute magnitudes for a parallax-limited sample of stars. The parallax of a star is the measured parameter which is proportional to a star's distance. The absolute magnitude of a star is a measure of its luminosity and is calculated from Its parallax. For stars that are uniformly distributed in space, more stars lie outside than inside a given radius than inside. But random error in parallax measurement scatters more stars inside a radius than outside. This will cause the sample of stars to have observed parallaxes that are on average larger than the true parallaxes. Lutz and Kelker used an analytical technique to develop a table of corrections. The corrections are limited by the technique itself. Their calculations involve division by numbers close to zero and become unstable. We plan to calculate the correction factors by using Monte Carlo simulation to introduce random error into a population of stars with known parameters and compare the population with error to the known population. This method is general and can possibly be applied to other radially distributed phenomena, such as point source pollution.