The flux autocorrelation function is a two-point statistic used for description of fluctuations of the transmitted flux in Ly forest in spectra of distant quasars, which is used for statistical analysis of density fluctuations of neutral intergalactic gas and can be defined as a line-of-sight (or longitudinal) projection of more general case — the (2D) flux correlation function. That is why sometimes flux autocorrelation function is called longitudinal flux correlation function (see e. g. [1]).

The flux autocorrelation function was introduced by Zuo & Bond [2]. For velocity separation it was defined by them as where denotes the pixel flux at velocity and is the measured mean transmitted flux at the relevant redshift. Note, that the data (quasar spectrum) is given in the form of pixels with wavelength label and the flux value . Thus the line-of-sight distance between pixels and in units of the local velocity scale is usually defined as (see e. g. [6]) where the wavelength at the redshift is , and is the line-of-sight comoving distance between two pixels. In most of the literature the mean flux changes over the velocity separations are assumed to be negligible. Thus more common definition of (see e.g. [3],[4],[5]) is where is the variance (or fluctuations) of transmitted flux.

The flux autocorrelation function is related to (1D) flux power spectrum through the following formula:

The flux autocorrelation function was introduced by Zuo & Bond [2]. For velocity separation it was defined by them as where denotes the pixel flux at velocity and is the measured mean transmitted flux at the relevant redshift. Note, that the data (quasar spectrum) is given in the form of pixels with wavelength label and the flux value . Thus the line-of-sight distance between pixels and in units of the local velocity scale is usually defined as (see e. g. [6]) where the wavelength at the redshift is , and is the line-of-sight comoving distance between two pixels. In most of the literature the mean flux changes over the velocity separations are assumed to be negligible. Thus more common definition of (see e.g. [3],[4],[5]) is where is the variance (or fluctuations) of transmitted flux.

The flux autocorrelation function is related to (1D) flux power spectrum through the following formula:

References:

- [1]^ Coppolani F., Petitjean P., Stoeh F. et al., 2006, MNRAS, 370, 1804, 2006MNRAS.370.1804C
- [2]^ Zuo L. & Bond J. R., 1994, ApJ, 423, 73, 1994ApJ...423...73Z
- [3]^ McDonald P., Seljak U., Scott S. et al., 2006, ApJSS, 163, 80, 2006ApJS..163...80M
- [4]^ Croft R. A. C., Weinberg D. H., Bolte M. et al., 2002, ApJ, 581, 20, 2002ApJ...581...20C
- [5]^ D'Odorico V., Viel M., Saitta F. et al., 2006, MNRAS, 372, 1333, 2006MNRAS.372.1333D
- [6]^ Meiksin A. A., 2009, Rev. Mod. Phys., 81, 1405, 2009RvMP...81.1405M