Bias
One of the most important ingredients of the Galaxy Clustering Weight function is the Galaxy Bias, that is, the statistical relation between the distribution of galaxies and matter
\[\delta_{g}(\boldsymbol{x})=b \delta(\boldsymbol{x})\]
In this page are listed the Bias Model we have implemented.
Piecewise Bias
The Piecewise Bias model is taken from the official Euclid forecast
\[b(z)= \sqrt{1+\bar{z}}\]
where $\bar{z}$ is the redshift value in the center of the tomographic bin where the redshift $z$ lies. The PiecewiseBias is plotted here.
GCWeightFunction = CosmoCentral.GCWeightFunction(WeightFunctionArray=
zeros(length(ConvolvedDensity.DensityGridArray[1,:]), length(CosmologicalGrid.ZArray)),
BiasKind = CosmoCentral.PiecewiseBias())
CosmoCentral.ComputeBiasGrid!(CosmologicalGrid, GCWeightFunction, ConvolvedDensity)
x = CosmologicalGrid.ZArray; y = GCWeightFunction.BiasArray[1, :];
plot(x, y, ylabel = L"\mathrm{Bias}\,(z)", xlabel=L"z")
Euclid Flagsip Bias
This model, obtained from the Flagship Euclid simulation is taken from Tutusaus et al 2021
\[b(z)=A+\frac{B}{1+\exp [-(z-D) C]}\]
GCWeightFunction = CosmoCentral.GCWeightFunction(WeightFunctionArray=
zeros(length(ConvolvedDensity.DensityGridArray[1,:]),
length(CosmologicalGrid.ZArray)), BiasKind = CosmoCentral.EuclidBias())
CosmoCentral.ComputeBiasGrid!(CosmologicalGrid, GCWeightFunction, ConvolvedDensity)
x = CosmologicalGrid.ZArray; y = GCWeightFunction.BiasArray[1, :];
plot(x, y, ylabel = L"\mathrm{Bias}\,(z)", xlabel= L"z")
CosmoCentral.ComputeBias
— FunctionComputeBias(z::Float64, ::PiecewiseBias,
ConvolvedDensity::AbstractConvolvedDensity)
This function evaluate the piecewise bias, given by $\sqrt{1+z}$, for a given redshift.
CosmoCentral.ComputeBiasGrid!
— FunctionComputeBiasGrid!(cosmogrid::CosmologicalGrid,
gcWeightFunction::GCWeightFunction, Bias::AbstractBias,
ConvolvedDensity::AbstractConvolvedDensity)
This function evaluate the bias, over the cosmological redshift grid.