The luminosity functions of kilonovae from binary neutron star mergers under different equation of states

Kilonovae produced by mergers of binary neutron stars (BNSs) are important transient events to be detected by time domain surveys with the alerts from the ground-based gravitational wave detectors. The observational properties of these kilonovae depend on the physical processes involved in the merging processes and the equation of state (EOS) of neutron stars (NSs). In this paper, we investigate the dependence of kilonova luminosities on the parameters of BNS mergers, and estimate the distribution functions of kilonova peak luminosities (KLFs) at the u, g, r, i, y, and z bands as well as its dependence on the NS EOS, by adopting a comprehensive semi-analytical model for kilonovae (calibrated by the observations of GW170817), a population synthesis model for the cosmic BNSs, and the ejecta properties of BNS mergers predicted by numerical simulations. We find that the kilonova light curves depend on both the BNS properties and the NS EOS, and the KLFs at the considered bands are bimodal with the bright components mostly contributed by BNS mergers with total mass $\lesssim 3.2M_\odot$/$2.8M_\odot$ and fainter components mostly contributed by BNS mergers with total mass $\gtrsim 3.2M_\odot$/$2.8M_\odot$ by assuming a stiff/soft (DD2/SLy) EOS. The emission of the kilonovae in the KLF bright components is mostly due to the radiation from the wind ejecta by the remnant discs of BNS mergers, while the emission of the kilonovae in the KLF faint components is mostly due to the radiation from the dynamical ejecta by the BNS mergers.Comment: 28 pages, 16 figures, to appear in MNRA

Existence of Positive Periodic Solutions for n

In this paper we consider the existence, multiplicity, and nonexistence of positive periodic solutions for n-dimensional nonautonomous functional differential system x'(t)=H(t,x(t))-λB(t)F(x(t-τ(t))), where hi are ω-periodic in t and there exist ω-periodic functions αi,βi∈C(R,R+) such that αi(t)≤(hi(t,x)/xi)≤βi(t),∫0ω‍αi(t)dt>0, for x∈R+n all with xi>0, and t∈R, limxi→0+(hi(t,x)/xi) exist for t∈R; bi∈C(R,R+) are ω-periodic functions and ∫0ω‍bi(t)dt>0;fi∈C(R+n,R+), fi(x)>0 for x >0; τ∈(R,R) is an ω-periodic function. We show that the system has multiple or no positive ω-periodic solutions for sufficiently large or small λ>0, respectively

Gravitational lensing of gravitational waves: A statistical perspective

In this paper, we study the strong gravitational lensing of gravitational waves (GWs) from a statistical perspective, with particular focus on the high frequency GWs from stellar binary black hole coalescences. These are most promising targets for ground-based detectors such as Advanced Laser Interferometer Gravitational Wave Observatory (aLIGO) and the proposed Einstein Telescope (ET) and can be safely treated under the geometrical optics limit for GW propagation. We perform a thorough calculation of the lensing rate, by taking account of effects caused by the ellipticity of lensing galaxies, lens environments, and magnification bias. We find that in certain GW source rate scenarios, we should be able to observe strongly lensed GW events once per year ($\sim1~\text{yr}^{-1}$) in the aLIGO survey at its design sensitivity; for the proposed ET survey, the rate could be as high as $\sim80~\text{yr}^{-1}$. These results depend on the estimate of GW source abundance, and hence can be correspondingly modified with an improvement in our understanding of the merger rate of stellar binary black holes. We also compute the fraction of four-image lens systems in each survey, predicting it to be $\sim30$ per cent for the aLIGO survey and $\sim6$ per cent for the ET survey. Finally, we evaluate the possibility of missing some images due to the finite survey duration, by presenting the probability distribution of lensing time delays. We predict that this selection bias will be insignificant in future GW surveys, as most of the lens systems ($\sim90$ per cent) will have time delays less than $\sim1$ month, which will be far shorter than survey durations.Comment: 10 pages, 5 figures, 1 table. Revised to match version published in MNRA

A High-Performance Liquid Chromatography:Chemiluminescence Method for Potential Determination of Vardenafil in Dietary Supplement

A flow method of high-performance liquid chromatography (HPLC) seperation and chemiluminescence (CL) detection for sensitive vardenafil analysis in dietary supplements was developed. The vardenafil separation was achieved on a C18 column at 30°C using ethanol-H3PO4 and ethylenediaminetetraacetic acid disodium salt (Na2EDTA) aqueous solution (25 : 75, v/v%) as mobile phase. The followed continuous CL detection was conducted based on the strong CL enhancement by the presence of vardenafil to luminol-K3Fe(CN)6 reaction in alkaline medium. At the flow rate of 0.8 mL/min, the vardenafil retention time (tR) was 6.4 min. Factors that affected the HPLC resolution and CL detection were studied and optimized. The calibration curve obtained for vardenafil standard was linear in concentration range of 8.0 × 10−7 ~ 1.0 × 10−4 mol/L. The relative standard deviations (RSD) of intraday and interday precision were less than 3.5%. The proposed method was applied to the vardenafil determination in oral liquid, wine, and capsule samples

The Age-Redshift Relation For Luminous Red Galaxies Obtained From the Full Spectrum Fitting and Its Cosmological Implications

The relative age of galaxies at different redshifts can be used to infer the Hubble parameter and put constraints on cosmological models. We select 23,883 quiescent luminous red galaxies (LRGs) from the SDSS DR7 and divide them into four sub-samples according to their velocity dispersions and each sub-sample is further divided into 12 redshift bins. The spectra of the LRGs in each redshift and velocity bin are co-added in order to obtain a combined spectrum with relatively high $S/N$. Adopting the GalexEV/SteLib model, we estimate the mean ages of the LRGs from these combined spectra by the full-spectrum fitting method. We check the reliability of the estimated age by using Monte-Carlo simulations and find that the estimates are robust and reliable. Assuming that the LRGs in each sub-sample and each redshift bin were on average formed at the same time, the Hubble parameter at the present time $H_0$ is estimated from the age--redshift relation obtained for each sub-sample, which is compatible with the $H_0$ value measured by other methods. We demonstrate that a systematic bias (up to $\sim 20$) may be introduced to the $H_0$ estimation because of recent star formation in the LRGs due to the later major mergers at z\la 0.4, but this bias may be negligible for those sub-samples with large velocity dispersions. Using the age--redshift relations obtained from the sub-sample with the largest velocity dispersion or the two sub-samples with high velocity dispersions, we find H_0= 65^{+7}_{-3}\kmsmpc or H_0= 74^{+5}_{-4}\kmsmpc by assuming a spatially flat $\Lambda$CDM cosmology. With upcoming surveys, such as the Baryon Oscillation Spectroscopic Survey (BOSS), even larger samples of quiescent massive LRGs may be obtained, and thus the Hubble parameter can be measured with high accuracy through the age--redshift relation.Comment: 13 pages, 7 figures, accepted for publication in AP