Ast 8110 (LSS & GL)
Problem Set #1
Given a distribution of galaxies on the 2D sky calculate their auto-correlation function using
three different estimators. The bin size for your correltion function should be at most 5 length
units. The boundaries of the region populated by galaxies is defined by the coordinates of the
lower left and upper right points: (−90, −80) and (80, 90).
Generate between 10-30 random galaxy positions for every real galaxy (remembering to normalize by that number when calculating correlation functions). Calculate the correlation function
for every one of the 3 estimators below. To calculate the uncertainty in your estimator, repeat the
above experiment 10-30 times, and calculate the rms dispersion in w(θ) in every θ bin, for each of
the 3 estimators.
(a) w(θ) = hDD(θ)i
hRR(θ)i − 1
(b) w(θ) = hDD(θ)i
hDR(θ)i − 1
(c) w(θ) = hDD(θ)i−h2DR(θ)i+hRR(θ)i
hRR(θ)i
For each of the 3 parts above, plot the correlation function and associated uncertainties.
!b
