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

We have used a statistical technique “Shuffle” (Bhavsar & Ling 1988; Bharadwaj, Bhavsar & Sheth 2004) in seven nearly two dimensional strips from the Sloan Digital Sky Survey Data Release Six (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 it’s measured values in SDSS against the predictions of ΛCDM N-body simulations and find that ΛCDM model is consistent with observations. The average filamentarity is known to be very sensitive to the bias parameter. Using ΛCDM N-body simulations we simulate mock galaxy distributions for SDSS NGP 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 class 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 ΛCDM 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 statistically significant length scale of filaments is a robust measure of the galaxy distribution.