.. _plots: Plots ====== *Voiager* produces several figures to visualize the input data and the inferred results, these are all stored in the `results/ `_ folder. Catalog properties ------------------ .. figure:: ../results/Beyond2pt/C_mock_lightcone_0300/plots/void_sky.png :scale: 15 % :align: center The file named ``void_sky`` contains a Mollweide projection of the angular distribution of void centers on the sky, color-coded by redshift. .. figure:: ../results/Beyond2pt/C_mock_lightcone_0300/plots/void_box.png :scale: 25 % :align: center In the file ``void_box`` the same void centers are shown in a Cartesian (comoving) coordinate system. .. figure:: ../results/Beyond2pt/C_mock_lightcone_0300/plots/void_redshift.png :scale: 20 % :align: center ``void_redshift`` is a scatter plot of the effective radius vs. the redshift of each void in the catalog. Void abundance -------------- The most basic void features can be summarized via distributions. These are typically expressed as number densities per logarithmic interval of the void property. The file names start with ``n_``, followed by one of the following properties: ``compensation``, ``core-density``, ``density-contrast``, ``effective-radius``, ``ellipticity``, ``redshift``, ``richness``. Some examples are shown below: .. figure:: ../results/Beyond2pt/C_mock_lightcone_0300/plots/n_effective-radius.png :scale: 20 % :align: center Distribution of void ``effective-radius`` (void size function) and corresponding randoms (dotted). .. figure:: ../results/Beyond2pt/C_mock_lightcone_0300/plots/n_ellipticity.png :scale: 20 % :align: center Distribution of void ``ellipticity`` (void shape function). .. figure:: ../results/Beyond2pt/C_mock_lightcone_0300/plots/n_redshift.png :scale: 20 % :align: center Distribution of void (and galaxy) ``redshift`` (selection function) and corresponding randoms (dotted). Correlation functions --------------------- Spatial correlations between void centers and tracers (galaxies) are provided in three variants: projected correlations on the sky named ``xi_p``, multipoles of the 3D correlation function named ``xi_ell``, and plane-of-sky vs. line-of-sight 2D correlation functions named ``xi_2d``. In addition, the file ``xi_ell=`` provides only one specified multipole order, appended as an integer in the name. Finally, the file ``xi_p_test`` features a test for the projected and deprojected correlation function from a best-fit HSW profile as a template for the real data. All of these file names are appended by an additional integer that specifies the particular bin of the data (e.g., redshift or effective radius). .. figure:: ../results/Beyond2pt/C_mock_lightcone_0300/plots/xi_p_2.png :scale: 20 % :align: center ``xi_p``: projected void-galaxy correlation function (downward triangles with model as dashed line), its deprojection (upward triangles with model as dotted line), and monopole in redshift space (circles with model as solid line). .. figure:: ../results/Beyond2pt/C_mock_lightcone_0300/plots/xi_ell_2.png :scale: 20 % :align: center ``xi_ell``: monopole (circles with model as solid line), quadrupole (upward triangles with model as dashed line), and hexadecapole (downward triangles with model as dotted line) of void-galaxy correlation function. .. figure:: ../results/Beyond2pt/C_mock_lightcone_0300/plots/xi_2d_2.png :scale: 20 % :align: center ``xi_2d``: 2D void-galaxy cross-correlation function along and perpendicular to the line of sight (black contours with color scale) with best-fit model (white contour lines). .. figure:: ../results/Beyond2pt/C_mock_lightcone_0300/plots/xi_p_test_2.png :scale: 20 % :align: center ``xi_p_test``: best-fit HSW profile to deprojected void-galaxy correlation function (solid line), its projection on the sky (dashed line), and subsequent deprojection based on the inverse Abel transform (dotted line). Covariance ---------- Covariance matrices for the void-galaxy correlation function are available, both for its multipoles, as well as for its 2D version with directions along and perpendicular to the line of sight. .. figure:: ../results/Beyond2pt/C_mock_lightcone_0300/plots/cov_ell_2.png :scale: 30 % :align: center ``cov_ell``: covariance matrix for multipoles of the void-galaxy correlation function, normalized by its diagonal. .. figure:: ../results/Beyond2pt/C_mock_lightcone_0300/plots/cov_2d_2.png :scale: 30 % :align: center ``cov_2d``: covariance matrix for the 2D void-galaxy correlation function, normalized by its diagonal. Parameter inference ------------------- The likelihood analysis of the void-galaxy correlation function provides constraints on dynamic and geometric distortions, which can be paramerized via the ratio of growth rate and bias :math:`f/b`, and the *Alcock-Paczynski* parameter ratio :math:`q_\perp/q_\parallel`, respectively. The files named ``triangle`` contain a corner plot of the posterior probability distribution (including nuisance parameters :math:`\mathcal{M}` and :math:`\mathcal{Q}`) for each bin of the data vector. These parameters are proportional to the product of growth rate and rms fluctuation amplitude :math:`f\sigma_8`, as well as the product of comoving angular diameter distance and Hubble rate :math:`D_\mathrm{A}H`, which are shown in the file ``fs8_DAH``. In turn, measurements of :math:`D_\mathrm{A}H` probe the expansion history of the Universe and can be used to infer some fundamental cosmological parameters. The files named ``triangle``, appended by the particular assumed model (e.g., ``LCDM``, ``wCDM``, or ``w0waCDM``) contain the posterior distribution of the constrained cosmological parameters of the specified model. .. figure:: ../results/Beyond2pt/C_mock_lightcone_0300/plots/triangle_2.png :scale: 20 % :align: center ``triangle``: corner plot of posterior distribution for model and nuisance parameters with its maximum (white cross). Shown are 68% and 95% confidence regions and the fiducial model as dashed lines. .. figure:: ../results/Beyond2pt/C_mock_lightcone_0300/plots/fs8_DAH.png :scale: 25 % :align: center ``fs8_DAH``: measurements of :math:`f\sigma_8` and :math:`D_\mathrm{A}H` as a function of redshift (fiducial model as dotted line). .. figure:: ../results/Beyond2pt/C_mock_lightcone_0300/plots/triangle_wCDM.png :scale: 30 % :align: center ``triangle_wCDM``: posterior of model parameters in a \ *w*\ CDM cosmology (blinded by mean) with its maximum (white cross). An extended banana-shaped degeneracy emerges, which leads to projection effects in the marginalized posteriors.