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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

实验室模拟连续电流与通道光强度关系研究

雷电连续电流是云载荷源向大地转移电荷的一种重要形式,这一过程产生的热效应可能对自然以及人居环境造成严重损害,这种热效应与连续电流波形和转移电荷量有关。在高压实验室电弧放电通道间隙产生了峰值范围为233.8~633.3A的模拟雷电连续电流,利用红光敏感型(探测波长范围200~1000nm,峰值响应600nm)和近红外敏感型(探测波长范围400~1000nm,峰值响应800nm)两种光电探测器同步测量了通道光强度。结果发现,正常通道下测量得到的光强度波形能较好地跟随电流波形的变化,而电弧通道扭曲会导致测量得到的通道光强度波形产生畸变,这种畸变具体表现为光强度波形在持续阶段的凹陷,在所有光强度波形中发生畸变的概率为19.8%。进一步探究了正常通道情况下模拟连续电流与通道光强度的关系,发现在不同光谱响应下,光强度峰值与电流峰值以及光强度-时间积分与电流电荷转移量之间均存在强烈的线性相关性。结果为使用电流与相关光强度关系进行连续电流波形与转移电荷量的准确反演提供了新思路。

基于注意力特征增强的投影图像光度补偿方法

目前,投影补偿算法已经取得了良好的研究成果,但大部分的投影图像色彩补偿研究,忽略了色彩传递函数建模过程中的光学部分,导致对色彩传递函数的建模精确度不高。同时,针对投影图像色彩补偿过程中,出现的加深网络导致提取特征信息丢失的现象,大多数的深度学习网络优化设计较少。基于以上问题,本文提出了一种基于注意力特征增强的投影图像光度补偿方法。该方法通过增加网络深度来提取带有彩色纹理投影表面的特征信息,同时采用深度学习来拟合复杂的复合辐射传递函数,以解决传统光度补偿方法存在的问题,提高了投影图像的质量和色彩,进一步消除了对高质量投影幕的依赖。本文所提方法的投影图像光度补偿结果,在峰值信噪比(PSNR)、均方根误差(RMSE)和结构相似性(SSIM)三项评价指标上,均好于其他对比算法,与CompenNet系列方法相比,本文所提方法在PSNR评价指标上最高提升5717、在RMSE评价指标上最高减少14968,在SSIM评价指标上最高提升2893。

我国区域塌陷的时空演绎特征与影响因素--基于夜间灯光数据的实证研究

区域塌陷问题制约了全国统一大市场建设和新时代区域协调发展。基于夜间灯光数据构建了区域塌陷指数,使用泰尔指数、空间自相关分析和核密度估计法对“十五”时期至“十三五”时期(2001—2020年)我国区域塌陷程度进行实证测度和时空演进分析,并运用地理探测器模型对区域塌陷的影响因素进行识别。结果显示,我国区域塌陷程度总体呈西高东低的梯度格局,且空间集聚特征不断增强。我国区域塌陷指数的区域差异主要源于区域内差异,总体呈倒U形变化。我国区域塌陷的演进趋势存在显著的区域异质性,东部与西部变化相对平稳,中部先“塌陷”后“崛起”,东北塌陷程度升高;南北差距不断扩大,但东西差距仍是主要矛盾。经济、人口、城镇化、行政级别、科技、交通等因素共同影响了我国区域塌陷的空间格局分异。

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.

New Probability Distributions in Astrophysics: XII. Truncation for the Gompertz Distribution

Analytical functions which fit the probability distributions of stars and galaxies can provide insight into how these distributions originate. In order to introduce a truncated version of the Gompertz distribution, we derive its probability density function, its distribution function, its average value, its second moment about the origin, its median, its random generation of values and a maximum likelihood estimator for its two unknown parameters. The astrophysical applications of the Gompertz distribution are the initial mass function for stars, the luminosity function for the galaxies of the Sloan Digital Sky Survey, the photometric maximum of galaxies visible in the GLADE+ catalog and a model for the mean absolute magnitude in the GLADE+ catalog as a function of the redshift.