Legendre-Jacobi’s Elliptic Integrals Shed Light on the Luminosity Distance in Cosmology

This article concerns the integral related to the transverse comoving distance and, in turn, to the luminosity distance both in the standard non-flat and flat cosmology. The purpose is to determine a straightforward mathematical formulation for the luminosity distance as function of the transverse comoving distance for all cosmology cases with a non-zero cosmological constant by adopting a different mindset. The applied method deals with incomplete elliptical integrals of the first kind associated with the polynomial roots admitted in the comoving distance integral according to the scientific literature. The outcome shows that the luminosity distance can be obtained by the combination of an analytical solution followed by a numerical integration in order to account for the redshift. This solution is solely compared to the current Gaussian quadrature method used as basic recognized algorithm in standard cosmology.

The CMB Luminosity Distance and Cosmological Redshifts

We will outline the relationship between luminosity distance and cosmological redshifts, demonstrating that it is consistent with a new cosmological model recently proposed by Haug and Tatum [1] , which appears to resolve the Hubble tension within the Rh=ctcosmology.

Luminos Fusion数字胃肠机四例故障维修

Luminos Fusion（德国Siemens公司）是一款经济型数字胃肠机,该设备在医院使用较多,经常因位置检测电位器故障,造成床体无法正常运动或倾斜,或因缩光器故障造成机器不能正常曝光的现象,就日常使用中遇到的4例故障进行总结分析,供同行参考。1故障案例一1.1故障现象开机正常,当患者到检查床上后,运动床板时常报错。错误代码＂Err40266/32.

Gamma-ray luminosity function of gamma-ray bright AGNs

Detection of γ-ray emissions from a class of active galactic nuclei （viz blazars）, has been one of the important findings from the Compton Gamma-Ray Observatory （CGRO）. However, their γ-ray luminosity function has not been well determined. Few attempts have been made in earlier works, where BL Lacs and Flat Spectrum Radio Quasars （FSRQs） have been considered as a single source class. In this paper, we investigated the evolution and γ-ray luminosity function of FSRQs and BL Lacs separately. Our investigation indicates no evolution for BL Lacs, however FSRQs show significant evolution. Pure luminosity evolution is assumed for FSRQs and exponential and power law evolution models are examined. Due to the small number of sources, the low luminosity end index of the luminosity function for FSRQs is constrained with an upper limit. BL Lac luminosity function shows no signature of break. As a consistency check, the model source distributions derived from these luminosity functions show no significant departure from the observed source distributions.

Operation of the jet feedback mechanism (JFM) in intermediate luminosity optical transients (ILOTs)

We follow the premise that most intermediate luminosity optical transients （ILOTs） are powered by rapid mass accretion onto a main sequence star, and study the effects of jets launched by an accretion disk. The disk is formed due to large specific angular momentum of the accreted mass. The two opposite jets might expel some of the mass from the reservoir of gas that feeds the disk, and therefore reduce and shorten the mass accretion process. We argue that by this process ILOTs limit their luminosity and might even shut themselves off in this negative jet feedback mechanism （JFM）. The group of ILOTs is a new member of a large family of astrophysical objects whose activity is regulated by the operation of the JFM.

Measurement of the Dark Matter Velocity Dispersion with Galaxy Stellar Masses, UV Luminosities, and Reionization

The root-mean-square of non-relativistic warm dark matter particle velocities scales as vhrms(a)=vhrms(1)/a , where a is the expansion parameter of the universe. This velocity dispersion results in a cut-off of the power spectrum of density fluctuations due to dark matter free-streaming. Let kfs (teq) be the free-streaming comoving cut-off wavenumber at the time of equal densities of radiation and matter. We obtain , and , at 68% confidence, from the observed distributions of galaxy stellar masses and rest frame ultra-violet luminosities. This result is consistent with reionization. From the velocity dispersion cut-off mass we obtain the limits vhrms(1)kfs (teq) >1.5 Mpc-1. These results are in agreement with previous measurements based on spiral galaxy rotation curves, and on the formation of first galaxies and reionization. These measured parameters determine the temperature-to-mass ratio of warm dark matter. This ratio happens to be in agreement with the no freeze-in and no freeze-out warm dark matter scenario of spin 0 dark matter particles decoupling early on from the standard model sector. Spin 1/2 and spin 1 dark matter are disfavored if nature has chosen the no freeze-in and no freeze-out scenario. An extension of the standard model of quarks and leptons, with scalar dark matter that couples to the Higgs boson that is in agreement with all current measurements, is briefly reviewed. Discrepancies with limits on dark matter particle mass that can be found in the literature are addressed.

The galaxy luminosity function in the LAMOST Complete Spectroscopic Survey of Pointing Area at the Southern Galactic Cap

We present optical luminosity functions(LFs) of galaxies in the0.1 g,0.1 r,0.1 i bands, calculated using data in40 deg2 sky area of the LAMOST Complete Spectroscopic Survey of Pointing Area(LaCoSSPAr) in the Southern Galactic Cap. Redshifts for galaxies brighter than r = 18.1 were obtained mainly with LAMOST. In each band, LFs derived using both parametric and non-parametric maximum likelihood methods agree well with each other. In the0.1 r band, our fitting parameters of the Schechter function are φ*=(1.65 ± 0.36) × 10-2 h3 Mpc-3, M*=-20.69 ± 0.06 mag and α =-1.12 ± 0.08,which agree with previous studies. Separate LFs are also derived for emission line galaxies and absorption line galaxies. The LFs of absorption line galaxies show a dip at0.1 r 18.5 and can be fitted well by a double-Gaussian function, suggesting a bimodality in passive galaxies.

Luminosity Limit of Super-Eddington Accretion onto Black Holes

The luminosity limit is derived for the super-Eddington accretion by obtaining the self-similar solution.The maximum luminosity is about 4.0×10^(37) erg/s(M/M_(⊙))or so(significantly less than the Eddington luminosity)due to photon trapping although the accretion rate is super-Eddington.The radiation spectrum is found to be universal as F_(v) α v^(-1).

DOES THE RADIO LUMINOSITY OF PULSAR GROW UP IN ITS LATER STAGE?

In usual statistical analyses,because of diversities of proper parameters of pulsars,some interesting features might be smeared.In order to remove these diversities,we use the mean values for all quantities of pulsars,instead of values of individual one to do statistical analyses.Logp/p3-logτand LogL-logτhave been plotted.The most interesting feature is that the radio luminosity of pulsar evidently appears to regrow up after its initial dropping.This feature is difficult to understand in usual models.Two tentatlive interpretations have been given.

The X-ray Background (Deep Fields, Luminosity Functions and Type-Ⅱ Quasars)

Deep X ray surveys have shown that the cosmic X ray background (XRB) is largely due to the accretion onto supermassive black holes, integrated over the cosmic time. These surveys have resolved more than 80% of the 0.1-10keV X ray background into discrete sources. Optical spectroscopic identifications show that the sources producing the bulk of the X ray background are a mixture of obscured (type 1) and unobscured (type 2) AGNs, as predicted by the XRB population synthesis models. A class of highly luminous type 2 AGN, so called QSO 2s, has been detected in the deepest Chandra and XMM Newton surveys. The new Chandra AGN redshift distribution peaks at much lower redshifts (z≈0.7) than that based on ROSAT data, indicating that Seyfert galaxies peak at significantly lower redshifts than QSOs.

Long-period eclipsing binaries:towards the true mass-luminosity relation.I.the test sample,observations and data analysis

The mass-luminosity relation is a fundamental law of astrophysics.We have suggested that the currently used mass-luminosity relation is not correct for the M/M⊙>2.7 range of mass since it was created utilizing double-lined eclipsing binaries,where the components are synchronized and consequently change each other's evolutionary path.To exclude this effect,we have started a project to study longperiod massive eclipsing binaries in order to construct radial velocity curves and determine masses for the components.We outline our project and present the selected test sample together with the first HRS/SALT spectral observations and the software package,FITTING BINARY STARS(FBS),that we developed for the analysis of our spectral data.As the first result,we present the radial velocity curves and best-fit orbital elements for the two components of the FP Car binary system from our test sample.

Dependence of the GRB Lag-Luminosity Relation on Redshift in the Source Frame

The lag-luminosity relation for gamma-ray bursts (GRBs) is an anti-correlation between the time lag, ?lag, which represents the delay between the arrival of hard and soft photons, and the isotropic peak luminosity, L. In this paper, we use a sample of 43 Swift bursts, which was taken from Ukwatta et al., to investigate whether this relation depends on redshift. Both the z-correction and the k-correction are taken into account. Our analysis consists of binning the data in redshift, z, then applying a fit of the form: for each bin, where ?lag0 is the time-lag in the burst’s source frame, and is the corresponding mean value for the entire sample. The goal is to see whether the two fitting parameters, A and B, evolve in a systematic way with z. Our results indicate that both the normalization, A, and the slope, B, seem to vary in a systematic way with redshift. We note that although good best-fits were obtained, with reasonable values for both the linear regression coefficient, r, and the reduced chi-squared, the data showed large scatter. Also, the number of GRBs in the sample studied is not large, and thus our conclusions are only tentative at this point. A flat universe with M = 0.27, ?? = 0.73, and a Hubble constant, H0 = 70 km.s-1.Mpc-1 is assumed.

Standard and Truncated Luminosity Functions for Stars in the Gaia Era

The luminosity function (LF) for stars is here fitted by a Schechter function and by a Gamma probability density function. The dependence of the number of stars on the distance, both in the low and high luminosity regions, requires the inclusion of a lower and upper boundary in the Schechter and Gamma LFs. Three astrophysical applications for stars are provided: deduction of the parameters at low distances, behavior of the average absolute magnitude with distance, and the location of the photometric maximum as a function of the selected flux. The use of the truncated LFs allows modeling the Malmquist bias.

The Luminosity Function of Galaxies as Modeled by a Left Truncated Beta Distribution

A first new luminosity function of galaxies can be built starting from a left truncated beta probability density function, which is characterized by four parameters. In the astrophysical conversion, the number of parameters increases by one, due to the addition of the overall density of galaxies. A second new galaxy luminosity function is built starting from a left truncated beta probability for the mass of galaxies once a simple nonlinear relationship between mass and luminosity is assumed;in this case the number of parameters is six because the overall density of galaxies and a parameter that regulates mass and luminosity are added. The two new galaxy luminosity functions with finite boundaries were tested on the Sloan Digital Sky Survey (SDSS) in five different bands;the results produce a “better fit” than the Schechter luminosity function in two of the five bands considered. A modified Schechter luminosity function with four parameters has been also analyzed.

Fabrication of Binary Diffractive Lenses and the Application to LED Lighting for Controlling Luminosity Distribution

We designed and fabricated two types of binary diffractive lenses using Electron beam lithography (EBL) on optical films film for controlling LED light. In the case of the binary diffractive convex lens with 2-mm focal length, it is possible to control the luminous intensity distribution. To improve the diffraction efficiency and realize a thin LED light source, the binary diffractive lenses with 100-μm-order focal length are effective. Furthermore we fabricated and characterized the binary diffractive concave lenses for application in LED lighting. It is found that white-light LEDs are strongly diffused by using the binary diffractive concave lenses.

Optical Luminosity Function of the QSOs Observed with the Sloan Digital Sky Survey Data Release Seven (SDSS DR7)

We have determined the Optical Luminosity Function (OLF) of a sample of 80946 Quasi Stellar Objects (QSOs) taken from the Sloan Digital Sky Survey Data Release Seven (SDSS DR7) with redshift range??0.3 z Mi < -22.5. The Monte Carlo Technique of numerical integration is used. The sample of QSOs is divided into seven sub-samples with redshift in the ranges: 0.30 z z z < 1.05,?1.05 z z z < 1.80, and 1.80 z < 2.05. Each redshift interval is binned in absolute magnitude with bin width ΔMi = -0.5. A flat universe with cosmological parameters Ωm = 0.3, Ω∧ = 0.7, and Hubble constant Ho = 70.0 km·s-1·Mpc-1 is used. From the optical luminosity function a clear evidence of AGN downsizing is observed, i.e. the number density of the less luminous AGNs peaks at lower redshift than the number density of the more luminous AGNs.

Schechter Function Model for the QSO Luminosity Function from the SDSS DR7

A study of the optical luminosity function of Quasi Stellar Objects (QSOs) and its evolution with redshift is carried out using the data from the Sloan Digital Sky Survey Data Release Seven (SDSS DR7). It is shown that the observed QSO luminosity function is well fitted by a Schechter function model of the form , where is the break or characteristic luminosity with luminosity evolution characterized by a second order polynomial in red shift. The best fit parameters are determined by using the Levenberg-Marquardt method of nonlinear least square fit.

New Probability Distributions in Astrophysics: X. Truncation and Mass-Luminosity Relationship for the Frèchet Distribution

The Frèchet distribution has aided the modelling of scientific data in many contexts. We demonstrate how it can be adapted to model astrophysical data. We analyze the truncated version of the Frèchet distribution deriving the probability density function (PDF), the distribution function, the average value, the rth moment about the origin, the median, the random generation of values and the maximum likelihood estimator, which allows us to derive the two unknown parameters. This first PDF in the regular and truncated version is then applied to model the mass of the stars. A canonical transformation from the mass to the luminosity allows us to derive a new PDF, which is derived in its regular and truncated version. Finally, we apply this new PDF model on the distribution in luminosity of NGC 2362.

Progenitor-age dependence of type Ia supernova luminosity and its cosmological implication

Empirically standardised peak luminosity of Type Ia supernovae(SNe Ia)as a standard candle has become one of the most powerful probes of the expansion history of the late universe.Although the existence of such a consistent peak luminosity could be interpreted as a consequence of the fixed critical Chandrasekhar mass at which a carbon-oxygen white dwarf explodes,there is growing evidence for a more complex environmental dependence to the SN Ia luminosity beyond the current understanding of the SN Ia physics.

Measurement of integrated luminosity of data collected at 3.773 GeV by BESIII from 2021 to 2024

We present a measurement of the integrated luminosity of e^(+)e^(-)collision data collected by the BESIII detector at the BEPCII collider at a center-of-mass energy of Ecm=3.773 GeV.The integrated luminosities of the datasets taken from December 2021 to June 2022,from November 2022 to June 2023,and from October 2023 to February 2024 were determined to be 4.995±0.019 fb^(-1),8.157±0.031 fb^(-1),and 4.191±0.016 fb^(-1),respectively,by analyzing large angle Bhabha scattering events.The uncertainties are dominated by systematic effects,and the statistical uncertainties are negligible.Our results provide essential input for future analyses and precision measurements.