Characterizing the Lyα forest flux probability distribution function using Legendre polynomials
Abstract
The Lymanα forest is a highly nonlinear field with considerable information available in the data beyond the power spectrum. The flux probability distribution function (PDF) has been used as a successful probe of smallscale physics. In this paper we argue that measuring coefficients of the Legendre polynomial expansion of the PDF offers several advantages over measuring the binned values as is commonly done. In particular, the nth Legendre coefficient can be expressed as a linear combination of the first n moments, allowing these coefficients to be measured in the presence of noise and allowing a clear route for marginalisation over mean flux. Moreover, in the presence of noise, our numerical work shows that a finite number of coefficients are well measured with a very sharp transition into noise dominance. This compresses the available information into a small number of wellmeasured quantities. In conclusion, we find that the amount of recoverable information is a very nonlinear function of spectral noise that strongly favors fewer quasars measured at better signal to noise.
 Authors:

 Brookhaven National Lab. (BNL), Upton, NY (United States)
 Publication Date:
 Research Org.:
 Brookhaven National Lab. (BNL), Upton, NY (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25)
 OSTI Identifier:
 1413953
 Report Number(s):
 BNL1147932017JA
Journal ID: ISSN 14757516; TRN: US1800602
 Grant/Contract Number:
 SC0012704
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Cosmology and Astroparticle Physics
 Additional Journal Information:
 Journal Volume: 2017; Journal Issue: 10; Journal ID: ISSN 14757516
 Publisher:
 Institute of Physics (IOP)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTRONOMY AND ASTROPHYSICS; Lyman alpha forest; intergalactic media; cosmological simulations
Citation Formats
Cieplak, Agnieszka M., and Slosar, Anze. Characterizing the Lyα forest flux probability distribution function using Legendre polynomials. United States: N. p., 2017.
Web. doi:10.1088/14757516/2017/10/013.
Cieplak, Agnieszka M., & Slosar, Anze. Characterizing the Lyα forest flux probability distribution function using Legendre polynomials. United States. doi:10.1088/14757516/2017/10/013.
Cieplak, Agnieszka M., and Slosar, Anze. Thu .
"Characterizing the Lyα forest flux probability distribution function using Legendre polynomials". United States. doi:10.1088/14757516/2017/10/013. https://www.osti.gov/servlets/purl/1413953.
@article{osti_1413953,
title = {Characterizing the Lyα forest flux probability distribution function using Legendre polynomials},
author = {Cieplak, Agnieszka M. and Slosar, Anze},
abstractNote = {The Lymanα forest is a highly nonlinear field with considerable information available in the data beyond the power spectrum. The flux probability distribution function (PDF) has been used as a successful probe of smallscale physics. In this paper we argue that measuring coefficients of the Legendre polynomial expansion of the PDF offers several advantages over measuring the binned values as is commonly done. In particular, the nth Legendre coefficient can be expressed as a linear combination of the first n moments, allowing these coefficients to be measured in the presence of noise and allowing a clear route for marginalisation over mean flux. Moreover, in the presence of noise, our numerical work shows that a finite number of coefficients are well measured with a very sharp transition into noise dominance. This compresses the available information into a small number of wellmeasured quantities. In conclusion, we find that the amount of recoverable information is a very nonlinear function of spectral noise that strongly favors fewer quasars measured at better signal to noise.},
doi = {10.1088/14757516/2017/10/013},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 10,
volume = 2017,
place = {United States},
year = {2017},
month = {10}
}