GEODYNAMICS

Purpose. To investigate the features of the algorithm implementation for finding the derivatives of the spatial distribution function of the planet's masses with the use of high-order Stokes constants and, on the basis of this, to find its analytical expression. According to the given methodology, to carry out calculations with the help of which to carry on the study of dynamic phenomena occurring inside an ellipsoidal planet. The proposed method involves the determination of the derivatives of the mass distribution function by the sum, the coefficients of which are obtained from the system of equations, which is incorrect. In order to solve it, an error-resistant method for calculating unknowns was used. The implementation of the construction is carried out in an iterative way, while for the initial approximation we take the three-dimensional function of the density of the Earth's masses, built according to Stokes constants up to the second order inclusive, by dynamic compression by the one-dimensional density distribution, and we determine the expansion coefficients of the derivatives of the function in the variables to the third order inclusive. They are followed by the corresponding density function, which is then taken as the initial one. The process is repeated until the specified order of approximation is reached. To obtain a stable result, we use the Cesaro summation method (method of means).. The calculations performed with the help of programs that implement the given algorithm, while the achieved high (ninth) order of obtaining the terms of the sum of calculations. The studies of the convergence of the sum of the series have been carried out, and on this basis, a conclusion has been made about the advisability of using the generalized finding of the sums based on the Cesaro method. The optimal number of contents of the sum terms has been chosen, provides convergence both for the mass distribution function and for its derivatives. Calculations of the deviations of mass distribution from the mean value ("inhomogeneities") for extreme points of the earth's geoid, which basically show the total compensation along the radius of the Earth, have been performed. For such three-dimensional distributions, calculations were performed and schematic maps were constructed according to the taken into account values of deviations of three-dimensional distributions of the mean ("inhomogeneities") at different depths reflecting the general structure of the Earth's internal structure. The presented vector diagrams of the horizontal components of the density gradient at characteristic depths (2891 km - core-mantle, 700 km - middle of the mantle, also the upper mantle - 200, 100 km) allow us to draw preliminary conclusions about the global movement of masses. At the same time, a closed loop is observed on the “core-mantle” edge, which is an analogy of a closed electric circuit. For shallower depths, differentiation of vector motions is already taking place, which gives hope for attracting these vector-grams to the study of dynamic motions inside the Earth. In fact, the vertical component (derivative with respect to the z variable) is directed towards the center of mass and confirms the main property of mass distributions - growth when approaching the center of mass. The method of stable solution of incorrect linear systems is applied, by means of which the vector-gram of the gradient of the mass distribution function is constructed. The nature of such schemes provides a tool for possible causes of mass redistribution in the middle of the planet and to identify possible factors of tectonic processes in the middle of the Earth, i.e indirectly confirms the gravitational convection of masses. The proposed technique can be used to create detailed models of density functions and its characteristics (derivatives) of the planet's interior, and the results of numerical experiments - to solve tectonics problems.

The AGN–galaxy–halo connection: The distribution of AGN host halo masses to z = 2.5

It is widely reported, based on clustering measurements of observed active galactic nuclei (AGN) samples, that AGN reside in similar mass host dark matter halos across the bulk of cosmic time, with log $\mathcal {M}/\mathcal {M}_{\odot }\sim 12.5-13.0$ to z ∼ 2.5. We show that this is due in part to the AGN fraction in galaxies rising with increasing stellar mass, combined with AGN observational selection effects that exacerbate this trend. Here, we use AGN specific accretion rate distribution functions determined as a function of stellar mass and redshift for star-forming and quiescent galaxies separately, combined with the latest galaxy-halo connection models, to determine the parent and sub-halo mass distribution function of AGN to various observational limits. We find that while the median (sub-)halo mass of AGN, $\approx 10^{12}\mathcal {M}_{\odot }$, is fairly constant with luminosity, specific accretion rate, and redshift, the full halo mass distribution function is broad, spanning several orders of magnitude. We show that widely used methods to infer a typical dark matter halo mass based on an observed AGN clustering amplitude can result in biased, systematically high host halo masses. While the AGN satellite fraction rises with increasing parent halo mass, we find that the central galaxy is often not an AGN. Our results elucidate the physical causes for the apparent uniformity of AGN host halos across cosmic time and underscore the importance of accounting for AGN selection biases when interpreting observational AGN clustering results. We further show that AGN clustering is most easily interpreted in terms of the relative bias to galaxy samples, not from absolute bias measurements alone.

Reconstructing the Mass Distribution Function of a Two-Span Beam With an Overhang via the Fundamental Mode

In this paper, we discuss the following inverse problem: how to reconstruct the mass distribution function of a two-span beam with an overhang via its polynomial fundamental mode and polynomial stiffness function. This leads to a basic equations group constituted by the coefficients of the mass distribution and the stiffness distribution function. To make the basic equations group match, one way is to divide it into two sub- equations, and solve them. We specify the method for solving this inverse problem, and research the existence and rationality of the positive solutions.

The NIBLES bivariate luminosity–H I mass distribution function revised using Arecibo follow-up observations

We present a modified optical luminosity–H I mass bivariate luminosity function based on H I line observations from the Nançay Interstellar Baryons Legacy Extragalactic Survey (NIBLES), including data from our new, four times more sensitive follow-up H I line observations obtained with the Arecibo radio telescope. The follow-up observations were designed to probe the underlying H I mass distribution of the NIBLES galaxies that were undetected or marginally detected in H I at the Nançay Radio Telescope. Our total follow-up sample consists of 234 galaxies, and it spans the entire luminosity and color range of the parent NIBLES sample of 2600 nearby (900 < cz < 12 000 km s−1) SDSS galaxies. We incorporated the follow-up data into the bivariate analysis by scaling the NIBLES undetected fraction by an Arecibo-only distribution. We find the resulting increase in low H I mass-to-light ratio densities to be about 10% for the bins −1.0 ≤ log(MHI/M⊙/Lr/L⊙) ≤ −0.5, which produces an increased H I mass function (HIMF) low mass slope of α = −1.14 ± 0.07, being slightly shallower than the values of −1.35 ± 0.05 obtained by recent blind H I surveys. Applying the same correction to the optically corrected bivariate luminosity function from our previous paper produces a larger density increase of about 0.5 to 1 dex in the lowest H I mass-to-light ratio bins for a given luminosity while having a minimal effect on the resulting HIMF low mass slope, which still agrees with blind survey HIMFs. This indicates that while low H I-mass-to-light ratio galaxies do not contribute much to the one-dimensional HIMF, their inclusion has a significant impact on the densities in the two-dimensional distribution.

Neural physical engines for inferring the halo mass distribution function

ABSTRACT An ambitious goal in cosmology is to forward model the observed distribution of galaxies in the nearby Universe today from the initial conditions of large-scale structures. For practical reasons, the spatial resolution at which this can be done is necessarily limited. Consequently, one needs a mapping between the density of dark matter averaged over ∼Mpc scales and the distribution of dark matter haloes (used as a proxy for galaxies) in the same region. Here, we demonstrate a method for determining the halo mass distribution function by learning the tracer bias between density fields and halo catalogues using a neural bias model. The method is based on the Bayesian analysis of simple, physically motivated, neural network-like architectures, which we denote as neural physical engines, and neural density estimation. As a result, we are able to sample the initial phases of the dark matter density field while inferring the parameters describing the halo mass distribution function, providing a fully Bayesian interpretation of both the initial dark matter density distribution and the neural bias model. We successfully run an upgraded borg (Bayesian Origin Reconstruction from Galaxies) inference using our new likelihood and neural bias model with halo catalogues derived from full N-body simulations. In preliminary results, we notice there could potentially be orders of magnitude improvement in modelling compared to classical biasing techniques.

Supermassive Black Holes and Dark Halo from the Bose-Condensed Dark Matter

Most of the galaxies harbor supermassive Black Holes (SMBH) in their center. Some of them are observed in very high redshifts. We explore the possibility that SMBH form from the coherent waves of Bose-Einstein condensate (BEC) which are supposed to form the dark matter. We first study the isotropic and anisotropic collapses of BEC. We find the BEC wave can easily collapse to form SMBH but the realistic amount of angular momentum completely prevents the collapse. We further explore the Axion case with attractive interaction and find the moderate mass ratio between the SMBH and the dark halo around it. We also obtain the mass distribution function of BH within a single galaxy.

Bivariate luminosity-HI mass distribution function of galaxies based on the NIBLES survey

We present a new optical luminosity-HI mass bivariate luminosity function (BLF) based on HI line observations from the Nançay Interstellar Baryons Legacy Extragalactic Survey (NIBLES). NIBLES sources lie within the local universe (900 ≤ c z ≤ 12 000 km s−1) and were chosen from SDSS DR5 such that the optical luminosity function was sampled as uniformly as possible. The HI mass function (HIMF) derived from our raw-data BLF, which is based on HI detections only, is consistent with the HIMFs derived from other optically selected surveys in that the low-mass slope is flatter than those derived from blind HI surveys. However, spanning the entire luminosity range of NIBLES, we identify a highly consistent distribution of the HI gas mass to luminosity ratio (gas-to-light ratio) with a predictable progression in the mean MHI/L r ratio as a function of L r. This consistency allows us to construct plausible gas-to-light ratio distributions for very low-luminosity bins which lie outside the NIBLES sample. We also identify a ∼10% decrease in detection fraction for galaxies fainter than log(L r) = 9.25, consistent with the expected decrease due to distance and sensitivity effects. Accounting for these trends, we reconstruct plausible gas-to-light distributions spanning luminosity bins down to log(L r) = 5.25, thus producing a corrected BLF. This corrected BLF is in good qualitative agreement with optical luminosity-HI mass distributions from the ALFALFA survey and is able to accurately reproduce blind survey HIMFs, lending credibility that this two dimensional optical luminosity-HI mass distribution is an accurate representation of the volume density distribution of galaxies in the local universe. We also note that our agreement with HIMFs from other surveys is dependent on accounting for all systematic differences such as selection method, Hubble constant and HI flux scale.

Zeldovich and the Missing Baryons, Results from Gravitational Lensing

Central to Zeldovich's attempts to understand the origin of cosmological structure was his exploration of the fluid dynamical effects in the primordial gas, and how the baryonic dark matter formed. Unfortunately microlensing searches for condensed objects in the foreground of the Magellanic Clouds were flawed by the assumption that the objects would be uniformly (Gaussian) distributed, and because the cadence of daily observations strongly disfavored detection of planet mass microlenses. But quasar microlensing showed them to exist at planetary mass at the same time that a hydro-gravitational theory predicted the planet-mass population as fossils of turbulence at the time of recombination (z = 1100; Gibson 1996, 2001). Where the population has now been detected from MACHO searches to the LMC (Sumi et al. 2011) we compare the quasar microlensing results to the recent determination of the mass distribution function measured for the planetary mass function, and show that the population can account for the baryonic dark matter.