Statistically significant length-scale of filaments as a robust measure of galaxy distribution

We have used a statistical technique 'Shuffle' in seven nearly two-dimensional strips from the Sloan Digital Sky Survey Data Release 6 (SDSS DR6) to test if the statistically significant length-scale of filaments depends on luminosity, colour and morphology of galaxies. We find that although the average filamentarity depends on these galaxy properties, the statistically significant length-scale of filaments does not depend on them. We compare its measured values in SDSS against the predictions of Lambda cold dark matter (Lambda CDM) N-body simulations and find that Lambda CDM model is consistent with observations. The average filamentarity is known to be very sensitive to the bias parameter. Using Lambda CDM N-body simulations, we simulate mock galaxy distributions for SDSS Northern Galactic Cap equatorial strip for different biases and test if the statistically significant length-scale of filaments depends on bias. We find that statistically significant length-scale of filaments is nearly independent of bias. This result is possibly related to the fact that statistically significant length-scale of filaments is nearly the same for different classes of galaxies which are differently biased with respect to underlying dark matter distribution. The average filamentarity is also known to be dependent on the galaxy number density and size of the samples. We use Lambda CDM dark matter N-body simulations to test if the statistically significant length-scale of filaments depends on number density of galaxies and size of the samples. Our analysis shows that the statistically significant length-scale of filaments very weakly depends on these factors. Finally, we test the reliability of our method by applying it to controlled samples of segment Cox process and find that our method successfully recovers the length of the inputted segments. Summarizing these results, we conclude that the length-scale up to which the filaments are statistically significant is a robust measure of galaxy distribution.