scholarly journals A Physical Model for the Quasar Luminosity Function Evolution between Cosmic Dawn and High Noon

2021 ◽  
Vol 923 (1) ◽  
pp. 110
Author(s):  
Keven Ren ◽  
Michele Trenti
Keyword(s):  
Duty Cycle ◽  
Free Parameter ◽  
Luminosity Function ◽  
Mass Function ◽  
Model Parameters ◽  
Data Sets ◽  
Mass Relation ◽  
Semiempirical Model ◽  
Number Density ◽  
Model Predictions

Abstract Modeling the evolution of the number density distribution of quasars through the quasar luminosity function (QLF) is critical to improving our understanding of the connection between black holes, galaxies, and their halos. Here we present a novel semiempirical model for the evolution of the QLF that is fully defined after the specification of a free parameter, the internal duty cycle, ε DC, along with minimal other assumptions. All remaining model parameters are fixed upon calibration against the QLF at two redshifts, z = 4 and z = 5. Our modeling shows that the evolution at the bright end results from the stochasticity in the median quasar luminosity versus halo mass relation, while the faint end shape is determined by the evolution of the halo mass function (HMF) with redshift. Additionally, our model suggests the overall quasar density is determined by the evolution of the HMF, irrespective of the value of ε DC. The z ≥ 4 QLFs from our model are in excellent agreement with current observations for all ε DC, with model predictions suggesting that observations at z ≳ 7.5 are needed to discriminate between different ε DC. We further extend the model at z ≤ 4, successfully describing the QLF between 1 ≤ z ≤ 4, albeit with additional assumptions on Σ and ε DC. We use the existing measurements of quasar duty cycle from clustering to constrain ε DC, finding ε DC ∼ 0.01 or ε DC ≳ 0.1 dependent on observational data sets used for reference. Finally, we present forecasts for future wide-area surveys with promising expectations for the Nancy Grace Roman Telescope to discover N ≳ 10, bright, m UV < 26.5 quasars at z ∼ 8.

scholarly journals Virial Halo Mass Function in the Planck Cosmology

2021 ◽  
Vol 922 (1) ◽  
pp. 89
Author(s):  
Masato Shirasaki ◽  
Tomoaki Ishiyama ◽  
Shin’ichiro Ando
Keyword(s):  
Luminosity Function ◽  
Mass Function ◽  
Number Density ◽  
Baseline Model ◽  
Wide Range ◽  
Halo Masses ◽  
Number Counts ◽  
Mass Functions ◽  
Analytic Prediction ◽  
Fitting Parameters

Abstract We study halo mass functions with high-resolution N-body simulations under a ΛCDM cosmology. Our simulations adopt the cosmological model that is consistent with recent measurements of the cosmic microwave backgrounds with the Planck satellite. We calibrate the halo mass functions for 108.5 ≲ M vir/(h −1 M ⊙) ≲ 1015.0–0.45 z , where M vir is the virial spherical-overdensity mass and redshift z ranges from 0 to 7. The halo mass function in our simulations can be fitted by a four-parameter model over a wide range of halo masses and redshifts, while we require some redshift evolution of the fitting parameters. Our new fitting formula of the mass function has a 5%-level precision, except for the highest masses at z ≤ 7. Our model predicts that the analytic prediction in Sheth & Tormen would overestimate the halo abundance at z = 6 with M vir = 108.5–10 h −1 M ⊙ by 20%–30%. Our calibrated halo mass function provides a baseline model to constrain warm dark matter (WDM) by high-z galaxy number counts. We compare a cumulative luminosity function of galaxies at z = 6 with the total halo abundance based on our model and a recently proposed WDM correction. We find that WDM with its mass lighter than 2.71 keV is incompatible with the observed galaxy number density at a 2σ confidence level.

scholarly journals Evolution of the Cluster X-Ray Luminosity Function

1980 ◽  
Vol 92 ◽  
pp. 231-231
Author(s):  
Stephen C. Perrenod
Keyword(s):  
Power Law ◽  
Luminosity Function ◽  
Mass Function ◽  
Mass Relation ◽  
Clusters Of Galaxies ◽  
Supply Rate ◽  
X Ray ◽  
Abell Clusters ◽  
Number Counts ◽  
Gas Supply

I predict the evolution of the X-ray luminosity function of clusters of galaxies. Predominantly, I treat the assumption that galaxies form first, then cluster purely due to gravitation. I show that the richness distribution of Abell clusters favors this scenario, rather than the protocluster hypothesis. The luminosity function is produced by combining a generalized (for all Ω) Press-Schechter evolutionary mass function for clusters (derived herein) with a power law X-ray luminosity-mass relation; a power law relation is supported by observations of low-redshift clusters.I find very steep evolution in the luminosity function, and thus in the source counts, for large Ω, and moderate evolution for small Ω. For a variety of models for the gas supply rate to the intracluster medium, the evolution of the luminosity function does not vary greatly. Thus it appears that the Ω, dependence will dominate and that number counts of X-ray clusters will yield cosmological information. The power of a test of Ω with an evolving luminosity function is considerably enhanced relative to a test which involves solely global cosmological effects on a non-evolving population. This occurs because of the well-known result that, at late times, clustering tends to proceed slowly for universes of small Ω and rapidly for large Ω.

scholarly journals Kernel Density Estimation in the Study of Star Clusters

2016 ◽  
Vol 25 (3) ◽  
Author(s):  
Anton F. Seleznev
Keyword(s):  
Luminosity Function ◽  
Open Cluster ◽  
Cluster Structure ◽  
Star Clusters ◽  
Kernel Estimator ◽  
Mass Function ◽  
Number Density ◽  
Density Profiles ◽  
Density Maps ◽  
Technical Details

AbstractThe kernel estimator method is used to evaluate the surface and spatial star number density in star clusters. Both density maps and radial density profiles are plotted. These estimates are used to derive the cluster size, the number of cluster stars and the cluster mass, and to study the cluster structure. The kernel estimator is also used to plot the luminosity function, mass function, the velocity distribution, and Hess diagrams for star clusters. The advantages of the kernel estimator method and technical details of its use are illustrated by modern results for the open cluster NGC 4337.

scholarly journals Combining high-z galaxy luminosity functions with Bayesian evidence

2019 ◽  
Author(s):  
Nicolas J F Gillet ◽  
Andrei Mesinger ◽  
Jaehong Park
Keyword(s):  
Galaxy Formation ◽  
Luminosity Function ◽  
Star Formation Rate ◽  
Formation Rate ◽  
Mass Function ◽  
Data Sets ◽  
Bayesian Data Analysis ◽  
Luminosity Functions ◽  
Bayesian Evidence ◽  
Galaxy Model

Abstract Galaxy formation during the first billion years of our Universe remains a challenging problem at the forefront of astrophysical cosmology. Although these $z\,\,{\gtrsim}\,\,6$ galaxies are likely responsible for the last major phase change of our Universe, the epoch of reionization (EoR), detailed studies are possible only for relatively rare, bright objects. Characterizing the fainter galaxies which are more representative of the population as a whole is currently done mainly through their non-ionizing UV luminosity function (LF). Observing the faint end of the UV LFs is nevertheless challenging, and current estimates can differ by orders of magnitude. Here we propose a methodology to combine disparate high-z UV LF estimates in a Bayesian framework: Bayesian Data-analysis Averaging (BDA). Using a flexible, physically-motivated galaxy model, we compute the relative evidence of various z = 6 UV LFs within the magnitude range −20 ≤ MUV ≤ −15 which is common to the data sets. Our model, based primarily on power-law scalings of the halo mass function, naturally penalizes systematically jagged points as well as misestimated errors. We then use the relative evidence to weigh the posteriors obtained from disparate LF data sets during the EoR, 6 ≤ z ≤ 10. The resulting LF posteriors suggest that the star formation rate density (SFRD) integrated down to a UV magnitude of -17 represent $60.9^{+11.3}_{-9.6}\%$ / $28.2^{+9.3}_{-10.1}\%$ / $5.7^{+4.5}_{-4.7}\%$ of the total SFRD at redshifts 6 / 10 / 15. The BDA framework we introduce enables galaxy models to leverage multiple, analogous LF estimates when constraining their free parameters.

scholarly journals Theory and Applications of the Unit Gamma/Gompertz Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1850
Author(s):  
Rashad A. R. Bantan ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Stochastic Ordering ◽  
Real Data ◽  
Rate Function ◽  
The Other ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Gompertz Distribution ◽  
Probability And Statistics ◽  
Analytical Behavior

Unit distributions are commonly used in probability and statistics to describe useful quantities with values between 0 and 1, such as proportions, probabilities, and percentages. Some unit distributions are defined in a natural analytical manner, and the others are derived through the transformation of an existing distribution defined in a greater domain. In this article, we introduce the unit gamma/Gompertz distribution, founded on the inverse-exponential scheme and the gamma/Gompertz distribution. The gamma/Gompertz distribution is known to be a very flexible three-parameter lifetime distribution, and we aim to transpose this flexibility to the unit interval. First, we check this aspect with the analytical behavior of the primary functions. It is shown that the probability density function can be increasing, decreasing, “increasing-decreasing” and “decreasing-increasing”, with pliant asymmetric properties. On the other hand, the hazard rate function has monotonically increasing, decreasing, or constant shapes. We complete the theoretical part with some propositions on stochastic ordering, moments, quantiles, and the reliability coefficient. Practically, to estimate the model parameters from unit data, the maximum likelihood method is used. We present some simulation results to evaluate this method. Two applications using real data sets, one on trade shares and the other on flood levels, demonstrate the importance of the new model when compared to other unit models.

scholarly journals Bayesian Inference of Species Trees using Diffusion Models

2020 ◽  
Vol 70 (1) ◽  
pp. 145-161 ◽  
Author(s):  
Marnus Stoltz ◽  
Boris Baeumer ◽  
Remco Bouckaert ◽  
Colin Fox ◽  
Gordon Hiscott ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Numerical Algorithms ◽  
Diffusion Models ◽  
Model Parameters ◽  
Data Sets ◽  
Species Trees ◽  
Computationally Efficient ◽  
Data Set ◽  
Snp Data ◽  
Binary Markers

Abstract We describe a new and computationally efficient Bayesian methodology for inferring species trees and demographics from unlinked binary markers. Likelihood calculations are carried out using diffusion models of allele frequency dynamics combined with novel numerical algorithms. The diffusion approach allows for analysis of data sets containing hundreds or thousands of individuals. The method, which we call Snapper, has been implemented as part of the BEAST2 package. We conducted simulation experiments to assess numerical error, computational requirements, and accuracy recovering known model parameters. A reanalysis of soybean SNP data demonstrates that the models implemented in Snapp and Snapper can be difficult to distinguish in practice, a characteristic which we tested with further simulations. We demonstrate the scale of analysis possible using a SNP data set sampled from 399 fresh water turtles in 41 populations. [Bayesian inference; diffusion models; multi-species coalescent; SNP data; species trees; spectral methods.]

MASS FUNCTION OF HALOS: A NEW ANALYTICAL APPROACH

2004 ◽  
Vol 13 (07) ◽  
pp. 1345-1349 ◽  
Author(s):  
JOSÉ A. S. LIMA ◽  
LUCIO MARASSI
Keyword(s):  
Power Law ◽  
Free Parameter ◽  
Analytical Approach ◽  
Mass Function ◽  
New Method ◽  
Power Law Distribution ◽  
The Press ◽  
The Universe ◽  
Special Case

A generalization of the Press–Schechter (PS) formalism yielding the mass function of bound structures in the Universe is given. The extended formula is based on a power law distribution which encompasses the Gaussian PS formula as a special case. The new method keeps the original analytical simplicity of the PS approach and also solves naturally its main difficult (the missing factor 2) for a given value of the free parameter.

scholarly journals The seven sisters DANCe

2018 ◽  
Vol 612 ◽  
pp. A70 ◽  
Author(s):  
J. Olivares ◽  
E. Moraux ◽  
L. M. Sarro ◽  
H. Bouy ◽  
A. Berihuete ◽  
...  
Keyword(s):  
Spatial Distribution ◽  
Model Comparison ◽  
Precise Determination ◽  
Model Parameters ◽  
Data Sets ◽  
Adequate Model ◽  
Comparison Results ◽  
Bayesian Evidence ◽  
Mass Segregation

Context. Membership analyses of the DANCe and Tycho + DANCe data sets provide the largest and least contaminated sample of Pleiades candidate members to date. Aims. We aim at reassessing the different proposals for the number surface density of the Pleiades in the light of the new and most complete list of candidate members, and inferring the parameters of the most adequate model. Methods. We compute the Bayesian evidence and Bayes Factors for variations of the classical radial models. These include elliptical symmetry, and luminosity segregation. As a by-product of the model comparison, we obtain posterior distributions for each set of model parameters. Results. We find that the model comparison results depend on the spatial extent of the region used for the analysis. For a circle of 11.5 parsecs around the cluster centre (the most homogeneous and complete region), we find no compelling reason to abandon King’s model, although the Generalised King model introduced here has slightly better fitting properties. Furthermore, we find strong evidence against radially symmetric models when compared to the elliptic extensions. Finally, we find that including mass segregation in the form of luminosity segregation in the J band is strongly supported in all our models. Conclusions. We have put the question of the projected spatial distribution of the Pleiades cluster on a solid probabilistic framework, and inferred its properties using the most exhaustive and least contaminated list of Pleiades candidate members available to date. Our results suggest however that this sample may still lack about 20% of the expected number of cluster members. Therefore, this study should be revised when the completeness and homogeneity of the data can be extended beyond the 11.5 parsecs limit. Such a study will allow for more precise determination of the Pleiades spatial distribution, its tidal radius, ellipticity, number of objects and total mass.

scholarly journals Statistical Properties of Kerr BH Flywheel Model of QSOs/AGNs

2000 ◽  
Vol 195 ◽  
pp. 417-418
Author(s):  
S. Nitta
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Kerr Black Hole ◽  
Mass Function ◽  
Initial Mass Function ◽  
Number Density ◽  
Disk System ◽  
The Press ◽  
The Individual ◽  
Density Population

The aim of this work is to demonstrate the properties of the magnetospheric model around Kerr black holes, so-called the “flywheel” (rotation powered) model. The fly-wheel engine of the BH accretion disk system is applied to the statistics of QSOs/AGNs. Nitta, Takahashi, & Tomimatsu clarified the individual evolution of the Kerr black-hole fly-wheel engine, which is parameterized by black-hole mass, initial Kerr parameter, magnetic field near the horizon, and a dimensionless small parameter. We impose a statistical model for the initial mass function of an ensemble of black holes using the Press-Schechter formalism. With the help of additional assumptions, we can discuss the evolution of the luminosity function and the spatial number density (population) of QSOs/AGNs. The result explains well the decrease of very bright QSOs and decrease of population after z ~ 2.

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