The
cross-correlation function is a subclass of the
two-point correlation function used in case of two different classes of objects (e.g. two types of galaxies from two different surveys in the same volume)
and
. It defines a (symmetric) probability to find a pair in which
is occupied by an object from a first catalogue and
by one from the second as
Another definition (see e.g.
[1, 2]) can be given in terms of density contrast
when considering the objects distributions as continuous functions of density
and
, the mean values of which are
and
. In this case:
or
where the angle brackets indicate an averaging over the sample volume
.
The
cross-correlation function gives information about the density profile around objects, e.g.
between galaxies and clusters measures the average galaxy density profile around clusters, at least out to radii where clusters overlap (see e.g.
[2]).
References:- [1]^ Peebles P. J. E. The Large-Scale Structure of the Universe, Princeton University Press, Princeton, New Jersey, 1980
- [2]^ab Peacock J. A. Cosmological Physics, Cambridge University Press, Cambridge, UK, 2007