Paper: The Halo Bias inside Cosmic Voids
Authors: Giovanni Verza, Carmelita Carbone, Alessandro Renzi
Figure caption: Differential number density ﹩{{ \mathcal N }}_{{\rm{h}}}﹩ of halos at z = 1.05, 0.49, 0 (from left to right). Symbols represent measurements in the entire comoving box (red squares) and in spherical shells ﹩{ \mathcal S }(r)﹩, (blue triangles), at r/R eff = 0.23, 37, 0.5 (up to down) for voids detected in the halo distribution with M ≥ 1013 h −1 M ⊙. Error bars show the Poissonian uncertainty. Lines show the theoretical models ﹩{{ \mathcal N }}_{{\rm{h}}}^{{\rm{T}}}﹩ as discussed in the text: ﹩{{ \mathcal N }}_{{\rm{h}}}^{{\rm{T}}}({p}_{{\rm{U}}},{q}_{{\rm{U}}},0)﹩ is case (i), i.e., ﹩{{ \mathcal N }}_{{\rm{h}}}^{{\rm{T}}}﹩ via Equation (2) (red dashed–dotted lines); ﹩{{ \mathcal N }}_{{\rm{h}}}^{{\rm{T}}}({p}_{{\rm{U}}},{q}_{{\rm{U}}},{\delta }_{{\rm{m}}}^{{\rm{v}}})﹩ is case (ii), i.e., ﹩{{ \mathcal N }}_{{\rm{h}}}^{{\rm{T}}}﹩ via Equation (4) (orange dotted lines); ﹩{{ \mathcal N }}_{{\rm{h}}}^{{\rm{T}}}({p}_{{\rm{v}}},{q}_{{\rm{v}}},{\delta }_{{\rm{m}}}^{{\rm{v}}})﹩ is case (iii), i.e., ﹩{{ \mathcal N }}_{{\rm{h}}}^{{\rm{T}}}﹩ via Equation (6) (blue solid lines); ﹩{{ \mathcal N }}_{{\rm{h}}}^{{\rm{T}}}({p}_{{\rm{v}}}^{{\rm{A}}},{q}_{{\rm{v}}}^{{\rm{A}}},{\delta }_{{\rm{m}}}^{{\rm{A}}})﹩ is case (iv), i.e., ﹩{{ \mathcal N }}_{{\rm{h}}}^{{\rm{T}}}﹩ via Equation (6) with ﹩{p}_{{\rm{v}}}^{{\rm{A}}}(r)﹩, ﹩{q}_{{\rm{v}}}^{{\rm{A}}}(r)﹩, and ﹩{\delta }_{{\rm{m}}}^{{\rm{A}}}(r)﹩ (magenta dashed lines). Shaded areas show the uncertainty on the p and q parameters. The subplots in each panel show the percent differences of ﹩{{ \mathcal N }}_{{\rm{h}}}^{\mathrm{SD}}﹩ measured in the comoving box with respect to ﹩{{ \mathcal N }}_{{\rm{h}}}^{{\rm{T}}}({p}_{{\rm{U}}},{q}_{{\rm{U}}},0)﹩, i.e., case (i) (red squares); ﹩{{ \mathcal N }}_{{\rm{h}}}^{\mathrm{SD}}﹩ measured in ﹩{ \mathcal S }(r)﹩ with respect to ﹩{{ \mathcal N }}_{{\rm{h}}}^{{\rm{T}}}({p}_{{\rm{v}}},{q}_{{\rm{v}}},{\delta }_{{\rm{m}}}^{{\rm{v}}})﹩, i.e., case (iii) (blue triangles); ﹩{{ \mathcal N }}_{{\rm{h}}}^{{\rm{T}}}({p}_{{\rm{U}}},{q}_{{\rm{U}}},{\delta }_{{\rm{m}}}^{{\rm{v}}})﹩, i.e., case (ii), with respect to ﹩{{ \mathcal N }}_{{\rm{h}}}^{{\rm{T}}}({p}_{{\rm{v}}},{q}_{{\rm{v}}},{\delta }_{{\rm{m}}}^{{\rm{v}}})﹩, i.e., case (iii) (orange dotted lines); ﹩{{ \mathcal N }}_{{\rm{h}}}^{{\rm{T}}}({p}_{{\rm{v}}}^{{\rm{A}}},{q}_{{\rm{v}}}^{{\rm{A}}},{\delta }_{{\rm{m}}}^{{\rm{A}}})﹩, i.e., case (iv), with respect to ﹩{{ \mathcal N }}_{{\rm{h}}}^{{\rm{T}}}({p}_{{\rm{v}}},{q}_{{\rm{v}}},{\delta }_{{\rm{m}}}^{{\rm{v}}})﹩, i.e., case (iii) (magenta dashed lines). Blue shaded areas show the relative uncertainties of ﹩{{ \mathcal N }}_{{\rm{h}}}^{{\rm{T}}}({p}_{{\rm{v}}},{q}_{{\rm{v}}},{\delta }_{{\rm{m}}}^{{\rm{v}}})﹩, i.e., case (iii) due to q v and p v errors; magenta hatched areas show the relative uncertainties of ﹩{{ \mathcal N }}_{{\rm{h}}}^{{\rm{T}}}({p}_{{\rm{v}}}^{{\rm{A}}},{q}_{{\rm{v}}}^{{\rm{A}}},{\delta }_{{\rm{m}}}^{{\rm{A}}})﹩, i.e., case (iv), with respect to ﹩{{ \mathcal N }}_{{\rm{h}}}^{{\rm{T}}}({p}_{{\rm{v}}},{q}_{{\rm{v}}},{\delta }_{{\rm{m}}}^{{\rm{v}}})﹩, i.e., case (iii) due to ﹩{q}_{{\rm{v}}}^{{\rm{A}}}﹩ and ﹩{p}_{{\rm{v}}}^{{\rm{A}}}﹩ errors.