TY - JOUR
T1 - Stochastic Order Redshift Technique (SORT)
T2 - A simple, efficient and robust method to improve cosmological redshift measurements
AU - Tejos, Nicolas
AU - Rodríguez-Puebla, Aldo
AU - Primack, Joel R.
N1 - Publisher Copyright:
© 2018 The Author(s).
PY - 2018/1/1
Y1 - 2018/1/1
N2 - We present a simple, efficient and robust approach to improve cosmological redshift measurements. The method is based on the presence of a reference sample for which a precise redshift number distribution (dN/dz) can be obtained for different pencil-beam-like sub-volumes within the original survey. For each sub-volume we then impose that: (i) the redshift number distribution of the uncertain redshift measurements matches the reference dN/dz corrected by their selection functions and (ii) the rank order in redshift of the original ensemble of uncertain measurements is preserved. The latter step is motivated by the fact that random variables drawn from Gaussian probability density functions (PDFs) of different means and arbitrarily large standard deviations satisfy stochastic ordering. We then repeat this simple algorithm for multiple arbitrary pencil-beam-like overlapping sub-volumes; in this manner, each uncertain measurement has multiple (non-independent) 'recovered' redshifts which can be used to estimate a new redshift PDF. We refer to this method as the Stochastic Order Redshift Technique (SORT). We have used a state-of-the-art N-body simulation to test the performance of SORT under simple assumptions and found that it can improve the quality of cosmological redshifts in a robust and efficient manner. Particularly, SORT redshifts (zsort) are able to recover the distinctive features of the so-called 'cosmic web' and can provide unbiased measurement of the two-point correlation function on scales ≳4 h-1Mpc. Given its simplicity, we envision that a method like SORT can be incorporated into more sophisticated algorithms aimed to exploit the full potential of large extragalactic photometric surveys.
AB - We present a simple, efficient and robust approach to improve cosmological redshift measurements. The method is based on the presence of a reference sample for which a precise redshift number distribution (dN/dz) can be obtained for different pencil-beam-like sub-volumes within the original survey. For each sub-volume we then impose that: (i) the redshift number distribution of the uncertain redshift measurements matches the reference dN/dz corrected by their selection functions and (ii) the rank order in redshift of the original ensemble of uncertain measurements is preserved. The latter step is motivated by the fact that random variables drawn from Gaussian probability density functions (PDFs) of different means and arbitrarily large standard deviations satisfy stochastic ordering. We then repeat this simple algorithm for multiple arbitrary pencil-beam-like overlapping sub-volumes; in this manner, each uncertain measurement has multiple (non-independent) 'recovered' redshifts which can be used to estimate a new redshift PDF. We refer to this method as the Stochastic Order Redshift Technique (SORT). We have used a state-of-the-art N-body simulation to test the performance of SORT under simple assumptions and found that it can improve the quality of cosmological redshifts in a robust and efficient manner. Particularly, SORT redshifts (zsort) are able to recover the distinctive features of the so-called 'cosmic web' and can provide unbiased measurement of the two-point correlation function on scales ≳4 h-1Mpc. Given its simplicity, we envision that a method like SORT can be incorporated into more sophisticated algorithms aimed to exploit the full potential of large extragalactic photometric surveys.
KW - Large-scale structure of Universe
KW - Methods: data analysis
KW - Methods: statistical
KW - Techniques: photometric
KW - Techniques: spectroscopic
UR - http://www.scopus.com/inward/record.url?scp=85046148956&partnerID=8YFLogxK
U2 - 10.1093/MNRAS/STX2317
DO - 10.1093/MNRAS/STX2317
M3 - Article
AN - SCOPUS:85046148956
SN - 0035-8711
VL - 473
SP - 366
EP - 379
JO - Monthly Notices of the Royal Astronomical Society
JF - Monthly Notices of the Royal Astronomical Society
IS - 1
ER -