Confusion noise due to clustered extragalactic point sources. Application of logarithmic cumulants for parameter estimation. (arXiv:1906.01679v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Argueso_F/0/1/0/all/0/1">Francisco Argüeso</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Herranz_D/0/1/0/all/0/1">Diego Herranz</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Toffolatti_L/0/1/0/all/0/1">Luigi Toffolatti</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Gonzalez_Nuevo_J/0/1/0/all/0/1">Joaquín González-Nuevo</a>
The calculation of the characteristic function of the signal fluctuations due
to clustered astrophysical sources is performed in this paper. For the typical
case of power-law differential number counts and two-point angular correlation
function, we present an extension of Zolotarev’s theorem that allows us to
compute the cumulants of the logarithm of the absolute value of the intensity.
As a test, simulations based on recent observations of radio galaxies are then
carried out, showing that these cumulants can be very useful for determining
the fundamental parameters defining the number counts and the correlation. If
the angular correlation scale of the observed source population is known, the
method presented here is able to obtain estimators of the amplitude and slope
of the power-law number counts with mean absolute errors that are one order of
magnitude better than previous techniques, that did not take into account the
correlation. Even if the scale of correlation is not well known, the method is
able to estimate it and still performs much better than if the effect of
correlations is not considered.
The calculation of the characteristic function of the signal fluctuations due
to clustered astrophysical sources is performed in this paper. For the typical
case of power-law differential number counts and two-point angular correlation
function, we present an extension of Zolotarev’s theorem that allows us to
compute the cumulants of the logarithm of the absolute value of the intensity.
As a test, simulations based on recent observations of radio galaxies are then
carried out, showing that these cumulants can be very useful for determining
the fundamental parameters defining the number counts and the correlation. If
the angular correlation scale of the observed source population is known, the
method presented here is able to obtain estimators of the amplitude and slope
of the power-law number counts with mean absolute errors that are one order of
magnitude better than previous techniques, that did not take into account the
correlation. Even if the scale of correlation is not well known, the method is
able to estimate it and still performs much better than if the effect of
correlations is not considered.
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