scholarly journals Statistical deprojection of intervelocities, interdistances, and masses in the Isolated Galaxy Pair Catalog

2020 ◽  
Vol 641 ◽  
pp. A115
Author(s):  
Laurent Nottale ◽  
Pierre Chamaraux
Keyword(s):  
Dark Matter ◽  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Orbital Velocity ◽  
Internal Dynamics ◽  
Luminous Matter ◽  
Velocity Peak ◽  
Velocity Probability ◽  
Third Law

Aims. In order to study the internal dynamics of actual galaxy pairs, we need to derive the probability distribution function (PDF) of true 3D, orbital intervelocities and interdistances between pair members from their observed projected values along with the pair masses from Kepler’s third law. For this research, we used 13 114 pairs from the Isolated Galaxy Pair Catalog (IGPC). Methods. The algorithms of statistical deprojection previously elaborated were applied to these observational data. We derived the orbital velocity PDFs for the whole catalog and for several selected subsamples. The interdistance PDF is deprojected and compared to the analytical profiles expected from semi-theoretical arguments. Results. The PDF of deprojected pair orbital velocities is characterized by the existence of a main probability peak around ≈150 km s−1 for all subsamples of the IGPC as well as for the Uppsala Galaxy Pair Catalog. The interdistance PDFs of both the projected and deprojected data are described at large distances by the same power law with exponent ≈ − 2. The whole distributions, including their cores, are fairly fitted by King profiles. The mass deprojection yields a mass/luminosity ratio for the pairs of M/L = (30 ± 5) in solar units. Conclusions. The orbital velocity probability peak is observed at the same value, ≈150 km s−1, as the main exoplanet velocity peak, which points toward a possible universality of Keplerian structures, whatever the scale. The pair M/L ratio is just seven times the standard ratio for luminous matter, which does not require the existence of nonbaryonic dark matter in these systems.

scholarly journals An Improved Double-Gaussian Closure for the Subgrid Vertical Velocity Probability Distribution Function

2019 ◽  
Vol 76 (1) ◽  
pp. 285-304 ◽  
Author(s):  
A. C. Fitch
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Vertical Velocity ◽  
Probability Distribution Function ◽  
Cumulus Cloud ◽  
Turbulence Statistics ◽  
Shallow Cumulus ◽  
Velocity Probability ◽  
Non Gaussian ◽  
Skewness And Kurtosis

Abstract The vertical velocity probability distribution function (PDF) is analyzed throughout the depth of the lower atmosphere, including the subcloud and cloud layers, in four large-eddy simulation (LES) cases of shallow cumulus and stratocumulus. Double-Gaussian PDF closures are examined to test their ability to represent a wide range of turbulence statistics, from stratocumulus cloud layers characterized by Gaussian turbulence to shallow cumulus cloud layers displaying strongly non-Gaussian turbulence statistics. While the majority of the model closures are found to perform well in the former case, the latter presents a considerable challenge. A new model closure is suggested that accounts for high skewness and kurtosis seen in shallow cumulus cloud layers. The well-established parabolic relationship between skewness and kurtosis is examined, with results in agreement with previous studies for the subcloud layer. In cumulus cloud layers, however, a modified relationship is necessary to improve performance. The new closure significantly improves the estimation of the vertical velocity PDF for shallow cumulus cloud layers, in addition to performing well for stratocumulus. In particular, the long updraft tail representing the bulk of cloudy points is much better represented and higher-order moments diagnosed from the PDF are also greatly improved. However, some deficiencies remain owing to fundamental limitations of representing highly non-Gaussian turbulence statistics with a double-Gaussian PDF.

scholarly journals One-point probability distribution function from spherical collapse: early dark energy versus ΛCDM

2020 ◽  
Vol 498 (1) ◽  
pp. 355-372
Author(s):  
Ankush Mandal ◽  
Sharvari Nadkarni-Ghosh
Keyword(s):  
Dark Matter ◽  
Distribution Function ◽  
Dark Energy ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Linear Density ◽  
Linear Growth ◽  
Linear Regime ◽  
Spherical Collapse ◽  
Non Linear

ABSTRACT We compute the one-point probability distribution function (PDF) of an initially Gaussian dark matter density field using spherical collapse (SC). We compare the results to other forms available in the literature and also compare the PDFs in the Λ-cold dark matter model with an early dark energy (EDE) model. We find that the skewed lognormal distribution provides the best fit to the non-linear PDF from SC for both cosmologies, from a = 0.1 to 1 and for scales characterized by the comoving width of the Gaussian: σG = 0.5, 1, and 2. To elucidate the effect of cosmology, we examine the linear and non-linear growth rates through test cases. For overdensities, when the two models have the same initial density contrast, the differences due to cosmology are amplified in the non-linear regime, whereas, if the two models have the same linear density contrast today, then the differences in cosmology are damped in the non-linear regime. This behaviour is in contrast with voids, where the non-linear growth becomes ‘self-regulatory’ and is less sensitive to cosmology and initial conditions. To compare the PDFs, we examine the difference of the PDFs and evolution of the width of the PDF. The trends with scale and redshift are as expected. A tertiary aim of this paper was to check if the fitting form for the non-linear density–velocity divergence relation, derived for constant equation of state (w) models by Nadkarni-Ghosh holds for the EDE model. We find that it does with an accuracy of 4 per cent, thus increasing its range of validity.

scholarly journals An Online Application for ΔR Calculation

Radiocarbon ◽  
2016 ◽  
Vol 59 (5) ◽  
pp. 1623-1627 ◽  
Author(s):  
Ron W Reimer ◽  
Paula J Reimer
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Calibration Curve ◽  
Probability Distribution Function ◽  
Museum Collections ◽  
Online Program ◽  
Online Application ◽  
Radiocarbon Calibration

AbstractA regional offset (ΔR) from the marine radiocarbon calibration curve is widely used in calibration software (e.g. CALIB, OxCal) but often is not calculated correctly. While relatively straightforward for known-age samples, such as mollusks from museum collections or annually banded corals, it is more difficult to calculate ΔR and the uncertainty in ΔR for 14C dates on paired marine and terrestrial samples. Previous researchers have often utilized classical intercept methods that do not account for the full calibrated probability distribution function (pdf). Recently, Soulet (2015) provided R code for calculating reservoir ages using the pdfs, but did not address ΔR and the uncertainty in ΔR. We have developed an online application for performing these calculations for known-age, paired marine and terrestrial 14C dates and U-Th dated corals. This article briefly discusses methods that have been used for calculating ΔR and the uncertainty and describes the online program deltar, which is available free of charge.

scholarly journals Optimal Taylor–Couette turbulence

2012 ◽  
Vol 706 ◽  
pp. 118-149 ◽  
Author(s):  
Dennis P. M. van Gils ◽  
Sander G. Huisman ◽  
Siegfried Grossmann ◽  
Chao Sun ◽  
Detlef Lohse
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Angular Velocity ◽  
Probability Distribution Function ◽  
Neutral Line ◽  
Velocity Ratio ◽  
Outer Cylinder ◽  
Taylor Number ◽  
Counter Rotation ◽  
Taylor Couette

AbstractStrongly turbulent Taylor–Couette flow with independently rotating inner and outer cylinders with a radius ratio of $\eta = 0. 716$ is experimentally studied. From global torque measurements, we analyse the dimensionless angular velocity flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)$ as a function of the Taylor number $\mathit{Ta}$ and the angular velocity ratio $a= \ensuremath{-} {\omega }_{o} / {\omega }_{i} $ in the large-Taylor-number regime $1{0}^{11} \lesssim \mathit{Ta}\lesssim 1{0}^{13} $ and well off the inviscid stability borders (Rayleigh lines) $a= \ensuremath{-} {\eta }^{2} $ for co-rotation and $a= \infty $ for counter-rotation. We analyse the data with the common power-law ansatz for the dimensionless angular velocity transport flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)= f(a)\hspace{0.167em} {\mathit{Ta}}^{\gamma } $, with an amplitude $f(a)$ and an exponent $\gamma $. The data are consistent with one effective exponent $\gamma = 0. 39\pm 0. 03$ for all $a$, but we discuss a possible $a$ dependence in the co- and weakly counter-rotating regimes. The amplitude of the angular velocity flux $f(a)\equiv {\mathit{Nu}}_{\omega } (\mathit{Ta}, a)/ {\mathit{Ta}}^{0. 39} $ is measured to be maximal at slight counter-rotation, namely at an angular velocity ratio of ${a}_{\mathit{opt}} = 0. 33\pm 0. 04$, i.e. along the line ${\omega }_{o} = \ensuremath{-} 0. 33{\omega }_{i} $. This value is theoretically interpreted as the result of a competition between the destabilizing inner cylinder rotation and the stabilizing but shear-enhancing outer cylinder counter-rotation. With the help of laser Doppler anemometry, we provide angular velocity profiles and in particular identify the radial position ${r}_{n} $ of the neutral line, defined by $ \mathop{ \langle \omega ({r}_{n} )\rangle } \nolimits _{t} = 0$ for fixed height $z$. For these large $\mathit{Ta}$ values, the ratio $a\approx 0. 40$, which is close to ${a}_{\mathit{opt}} = 0. 33$, is distinguished by a zero angular velocity gradient $\partial \omega / \partial r= 0$ in the bulk. While for moderate counter-rotation $\ensuremath{-} 0. 40{\omega }_{i} \lesssim {\omega }_{o} \lt 0$, the neutral line still remains close to the outer cylinder and the probability distribution function of the bulk angular velocity is observed to be monomodal. For stronger counter-rotation the neutral line is pushed inwards towards the inner cylinder; in this regime the probability distribution function of the bulk angular velocity becomes bimodal, reflecting intermittent bursts of turbulent structures beyond the neutral line into the outer flow domain, which otherwise is stabilized by the counter-rotating outer cylinder. Finally, a hypothesis is offered allowing a unifying view and consistent interpretation for all these various results.

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