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Register a new userApproximating Density Probability Distribution Functions Across Cosmologies
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Using a suite of self-similar cosmological simulations, we measure the probability distribution functions (PDFs) of real-space density, redshift-space density, and their geometric mean. We find that the real-space density PDF is well-described by a function of two parameters: $n_s$, the spectral slope, and $sigma_L$, the linear rms density fluctuation. For redshift-space density and the geometric mean of real- and redshift-space densities, we introduce a third parameter, $s_L={sqrt{langle(dv^L_{rm pec}/dr)^2rangle}}/{H}$. We find that density PDFs for the LCDM cosmology is also well-parameterized by these three parameters. As a result, we are able to use a suite of self-similar cosmological simulations to approximate density PDFs for a range of cosmologies. We make the density PDFs publicly available and provide an analytical fitting formula for them.
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We introduce the position-dependent probability distribution function (PDF) of the smoothed matter field as a cosmological observable. In comparison to the PDF itself, the spatial variation of the position-dependent PDF is simpler to model and has distinct dependence on cosmological parameters. We demonstrate that the position-dependent PDF is characterized by variations in the local mean density, and we compute the linear response of the PDF to the local density using separate universe N-body simulations. The linear response of the PDF to the local density field can be thought of as the linear bias of regions of the matter field selected based on density. We provide a model for the linear response, which accurately predicts our simulation measurements. We also validate our results and test the separate universe consistency relation for the local PDF using global universe simulations. We find excellent agreement between the two, and we demonstrate that the separate universe method gives a lower variance determination of the linear response.
In this work, we studied the impact of galaxy morphology on photometric redshift (photo-$z$) probability density functions (PDFs). By including galaxy morphological parameters like the radius, axis-ratio, surface brightness and the Sersic index in addition to the $ugriz$ broadbands as input parameters, we used the machine learning photo-$z$ algorithm ANNz2 to train and test on galaxies from the Canada-France-Hawaii Telescope Stripe-82 (CS82) Survey. Metrics like the continuous ranked probability score (CRPS), probability integral transform (PIT), Bayesian odds parameter, and even the width and height of the PDFs were evaluated, and the results were compared when different number of input parameters were used during the training process. We find improvements in the CRPS and width of the PDFs when galaxy morphology has been added to the training, and the improvement is larger especially when the number of broadband magnitudes are lacking.
We measure the Voronoi density probability distribution function (PDF) for both dark matter and halos in N-body simulations. For the dark matter, Voronoi densities represent the matter density field smoothed on a uniform mass scale, which approximates the Lagrangian density field. For halos, the Voronoi densities contain information about the local environment of each halo. We measure the halo virial masses, the total amount of dark matter within each halo Voronoi cell, and the halo Voronoi cell volumes, and we show how halo abundances depend on these three quantities. We then study the position-dependent Voronoi density PDF, measured within finite subregions of the Universe, using separate universe simulations. We demonstrate that the spatial variation of the position-dependent PDF is due to large-scale density fluctuations, indicating that the position-dependent PDF is a biased tracer of large-scale structure. We measure this bias for the dark matter, and interpret it as the bias of regions of the Lagrangian density field that are selected based on density. For the halos, this bias can be interpreted as a form of assembly bias. We present the mapping from late-time to early-time Voronoi density for each simulation dark matter particle, which is highly stochastic. We compare the median of this stochastic map with spherical collapse calculations and discuss challenges involved in modeling the evolution of the density field on these scales.
In a search for the signature of turbulence in the diffuse interstellar medium in gas density distributions, we determined the probability distribution functions (PDFs) of the average volume densities of the diffuse gas. The densities were derived from dispersion measures and HI column densities towards pulsars and stars at known distances. The PDFs of the average densities of the diffuse ionized gas (DIG) and the diffuse atomic gas are close to lognormal, especially when lines of sight at |b|<5 degrees and |b|>=5 degrees are considered separately. The PDF of <n_HI> at high |b| is twice as wide as that at low |b|. The width of the PDF of the DIG is about 30 per cent smaller than that of the warm HI at the same latitudes. The results reported here provide strong support for the existence of a lognormal density PDF in the diffuse ISM, consistent with a turbulent origin of density structure in the diffuse gas.
Despite the high accuracy of photometric redshifts (zphot) derived using Machine Learning (ML) methods, the quantification of errors through reliable and accurate Probability Density Functions (PDFs) is still an open problem. First, because it is difficult to accurately assess the contribution from different sources of errors, namely internal to the method itself and from the photometric features defining the available parameter space. Second, because the problem of defining a robust statistical method, always able to quantify and qualify the PDF estimation validity, is still an open issue. We present a comparison among PDFs obtained using three different methods on the same data set: two ML techniques, METAPHOR (Machine-learning Estimation Tool for Accurate PHOtometric Redshifts) and ANNz2, plus the spectral energy distribution template fitting method, BPZ. The photometric data were extracted from the KiDS (Kilo Degree Survey) ESO Data Release 3, while the spectroscopy was obtained from the GAMA (Galaxy and Mass Assembly) Data Release 2. The statistical evaluation of both individual and stacked PDFs was done through quantitative and qualitative estimators, including a dummy PDF, useful to verify whether different statistical estimators can correctly assess PDF quality. We conclude that, in order to quantify the reliability and accuracy of any zphot PDF method, a combined set of statistical estimators is required.
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