Accounting for Selection Bias and Redshift Evolution in GRB Radio Afterglow Data

Gamma-ray Bursts (GRBs) are highly energetic events that can be observed at extremely high redshift. However, inherent bias in GRB data due to selection effects and redshift evolution can significantly skew any subsequent analysis. We correct for important variables related to the GRB emission, such as the burst duration, T90*, the prompt isotropic energy, Eiso, the rest-frame end time of the plateau emission, Ta,radio*, and its correspondent luminosity La,radio, for radio afterglow. In particular, we use the Efron–Petrosian method presented in 1992 for the correction of our variables of interest. Specifically, we correct Eiso and T90* for 80 GRBs, and La,radio and Ta,radio* for a subsample of 18 GRBs that present a plateau-like flattening in their light curve. Upon application of this method, we find strong evolution with redshift in most variables, particularly in La,radio, with values similar to those found in past and current literature in radio, X-ray and optical wavelengths, indicating that these variables are susceptible to observational bias. This analysis emphasizes the necessity of correcting observational data for evolutionary effects to obtain the intrinsic behavior of correlations to use them as discriminators among the most plausible theoretical models and as reliable cosmological tools.

The isotropic energy function and formation rate of short gamma-ray bursts

Gamma-ray bursts (GRBs) are brief, intense, gamma-ray flashes in the universe, lasting from a few milliseconds to a few thousand seconds. For short gamma-ray bursts (sGRBs) with duration less than 2 seconds, the isotropic energy (E iso) function may be more scientifically meaningful and accurately measured than the luminosity (L p) function. In this work we construct, for the first time, the isotropic energy function of sGRBs and estimate their formation rate. First, we derive the L p – E p correlation using 22 sGRBs with known redshifts and well-measured spectra and estimate the pseduo redshifts of 334 Fermi sGRBs. Then, we adopt the Lynden-Bell c − method to study isotropic energy functions and formation rate of sGRBs without any assumption. A strong evolution of isotropic energy E iso ∝ (1+z)5.79 is found, which is comparable to that between L p and z. After removing effect of the cosmic evolution, the isotropic energy function can be reasonably fitted by a broken power law, which is ϕ ( E iso , 0 ) ∝ E iso , 0 − 0.45 for dim sGRBs and ϕ ( E iso , 0 ) ∝ E iso , 0 − 1.11 for bright sGRBs, with the break energy 4.92 × 1049 erg. We obtain the local formation rate of sGRBs is about 17.43 events Gpc−3 yr−1. If assuming a beaming angle is 6° to 26°, the local formation rate including off-axis sGRBs is estimated as ρ 0,all = 155.79 – 3202.35 events Gpc−3 yr−1.

Intensity and anisotropies of the stochastic gravitational wave background from merging compact binaries in galaxies

We investigate the isotropic and anisotropic components of the Stochastic Gravitational Wave Background (SGWB) originated from unresolved merging compact binaries in galaxies. We base our analysis on an empirical approach to galactic astrophysics that allows to follow the evolution of individual systems. We then characterize the energy density of the SGWB as a tracer of the total matter density, in order to compute the angular power spectrum of anisotropies with the Cosmic Linear Anisotropy Solving System (CLASS) public code in full generality. We obtain predictions for the isotropic energy density and for the angular power spectrum of the SGWB anisotropies, and study the prospect for their observations with advanced Laser Interferometer Gravitational-Wave and Virgo Observatories and with the Einstein Telescope. We identify the contributions coming from different type of sources (binary black holes, binary neutron stars and black hole-neutron star) and from different redshifts. We examine in detail the spectral shape of the energy density for all types of sources, comparing the results for the two detectors. We find that the power spectrum of the SGWB anisotropies behaves like a power law on large angular scales and drops at small scales: we explain this behavior in terms of the redshift distribution of sources that contribute most to the signal, and of the sensitivities of the two detectors. Finally, we simulate a high resolution full sky map of the SGWB starting from the power spectra obtained with CLASS and including Poisson statistics and clustering properties.

HVSR analysis of a layered saturated half-space using diffuse-field theory

SUMMARY The recently constructed diffuse field theory from isotropic energy equipartition has been well developed in elasticity for full-wave interpretation of horizontal-to-vertical ratio (HVSR), which links the signal autocorrelation with the imaginary part of Green's function. Here, the theory is extended to the saturated layered medium within the framework of Biot's theory to account for the offshore environment. The imaginary parts of Green's functions are obtained using direct stiffness method accompanied with Fourier–Hankel transform. In particular, the upgoing wave amplitudes are modified to tackle the overflow during wavenumber integral and allow for fast calculations. After validating the method from the perspectives of Green's function calculation, emphasis is laid on evaluating the inaccuracies of HVSR calculation induced by model misuses in the lack of prior geological and geotechnical information. The numerical results considering the effects of layer sequence, impedance ratio, porosity and drainage condition show that the predominant frequency of the one-phase medium is slightly less than the two-phase medium with the maximum shift no more than 0.1 Hz, while their amplitude differences can be prominent as impedance ratio and porosity increase, with the maximum difference up to 29 per cent. The shallowest soft layer has the dominant effects on HVSR amplitudes, whereas the buried low-velocity layer at depth over one-wavelength contributes little to the peak amplitude. Finally, the method is applied to a realistic case at Mirandola, Northorn Italy, which suffered extensive liquefaction-induced damages in 2012 Emilia earthquake. The well identified pattern of the experimental HVSR using the two-phase medium model illustrates the application potential of our method to further assist the subsurface geology retrieval.

Violation of the Dominant Energy Condition in Geometrodynamics

It is shown that in Einstein’s theory and in the theory of gravity with Logunov constraints, there is a field-theoretical model of dark energy that is consistent with the observational data indicating that the Hubble value increases over time. In the developed model of dark energy, the isotropic energy dominant condition is violated. It solves the problem of the cosmological singularity and the singularity of “black holes”. The compact configuration of the scalar field can generate a flux of particles by the pairs of particles production mechanism from the vacuum by a field of barrier and in the process of transformation of thermal energy (Hawking radiation) and acceleration energy into radiation. The scalars can play the role of the so-called “black holes” with no singularity inside themselves.

On the cosmological evolution of long gamma-ray burst properties

ABSTRACT We examine the relationship between a number of long gamma-ray burst (lGRB) properties (isotropic emitted energy, luminosity, intrinsic duration, jet opening angle) and redshift. We find that even when accounting for conservative detector flux limits, there appears to be a significant correlation between isotropic equivalent energy and redshift, suggesting cosmological evolution of the lGRB progenitor. Analysing a sub-sample of lGRBs with jet opening angle estimates, we find the beaming-corrected lGRB emitted energy does not correlate with redshift, but jet opening angle does. Additionally, we find a statistically significant anticorrelation between the intrinsic prompt duration and redshift, even when accounting for potential selection effects. We also find that, for a given redshift, isotropic energy is positively correlated with intrinsic prompt duration. None of these GRB properties appear to be correlated with galactic offset. From our selection-effect-corrected redshift distribution, we estimate a co-moving rate density for lGRBs, and compare this to the global cosmic star formation rate (SFR). We find the lGRB rate mildly exceeds the global star formation rate between a redshift of 3 and 5, and declines rapidly at redshifts above this (although we cannot constrain the lGRB rate above a redshift of about 6 due to sample incompleteness). We find the lGRB rate diverges significantly from the SFR at lower redshifts. We discuss both the correlations and lGRB rate density in terms of various lGRB progenitor models and their apparent preference for low-metallicity environments.

A polyconvex extension of the logarithmic Hencky strain energy

Adapting a method introduced by Ball, Muite, Schryvers and Tirry, we construct a polyconvex isotropic energy function [Formula: see text] which is equal to the classical Hencky strain energy [Formula: see text] in a neighborhood of the identity matrix 𝟙; here, [Formula: see text] denotes the set of [Formula: see text]-matrices with positive determinant, [Formula: see text] denotes the deformation gradient, [Formula: see text] is the corresponding stretch tensor, [Formula: see text] is the principal matrix logarithm of [Formula: see text], [Formula: see text] is the trace operator, [Formula: see text] is the Frobenius matrix norm and [Formula: see text] is the deviatoric part of [Formula: see text]. The extension can also be chosen to be coercive, in which case Ball’s classical theorems for the existence of energy minimizers under appropriate boundary conditions are immediately applicable. We also generalize the approach to energy functions [Formula: see text] in the so-called Valanis–Landel form [Formula: see text] with [Formula: see text], where [Formula: see text] denote the singular values of [Formula: see text].

GRB 171205A/SN 2017iuk: A local low-luminosity gamma-ray burst

Context. Gamma-ray bursts (GRBs) occurring in the local Universe constitute an interesting sub-class of the GRB family, since their luminosity is on average lower than that of their cosmological analogs. Attempts to understand in a global way this peculiar behaviour is still not possible, since the sample of low redshift GRBs is small, and the properties of individual objects are too different from each other. In addition, their closeness (and consequently high fluxes) make these sources ideal targets for extensive follow-up even with small telescopes, considering also that these GRBs are conclusively associated with supernova (SN) explosions. Aims. We aim to contribute to the study of local bursts by reporting the case of GRB 171205A. This source was discovered by Swift Burst Alert Telescope (BAT) on 2017, December 5 and soon associated with a low redshift host galaxy (z = 0.037), and an emerging SN (SN 2017iuk). Methods. We analyzed the full Swift dataset, comprising the UV-Optical Telescope (UVOT), X-ray Telescope (XRT) and BAT data. In addition, we employed the Konus-Wind high energy data as a valuable extension at γ-ray energies. Results. The photometric SN signature is clearly visible in the UVOT u, b and ν filters. The maximum emission is reached at ∼13 (rest frame) days, and the whole bump resembles that of SN 2006aj, but lower in magnitude and with a shift in time of +2 d. A prebump in the ν-band is also clearly visible, and this is the first time that such a feature is not observed achromatically in GRB–SNe. Its physical origin cannot be easily explained. The X-ray spectrum shows an intrinsic Hydrogen column density NH,int = 7.4+4.1−3.6 × 1020 cm−2, which is at the low end of the N H, int, even considering just low redshift GRBs. The spectrum also features a thermal component, which is quite common in GRBs associated with SNe, but whose origin is still a matter of debate. Finally, the isotropic energy in the γ-ray band, Eiso = 2.18+0.63−5.0 × 1049 erg, is lower than those of cosmological GRBs. Combining this value with the peak energy in the same band, Ep = 125+141−37 keV, implies that GRB 171205A is an outlier of the Amati relation, as are some other low redshift GRBs, and its emission mechanism should be different from that of canonical, farther away GRBs.