Rm Iso Research Articles

Radiation and outflow properties of super-Eddington accretion flows around various mass classes of black holes: Dependence on the accretion rates

Abstract We perform axisymmetric two-dimensional radiation-hydrodynamic simulations of super-Eddington accretion flow and outflow around black holes to examine the properties of radiation and outflow as functions of the black hole mass and the accretion rate on to the black hole ($\dot{M}_{\rm BH}$). We find that the $\dot{m}_{\rm BH} ({\equiv} \dot{M}_{\rm BH}c^2 /L_{\rm Edd})$ dependence of $L_{\rm rad}/L_{\rm Edd}$ and $L_{\rm mech}/L_{\rm Edd}$ found for a stellar-mass black hole can apply to the high-mass cases, where $L_{\rm rad}$ is the radiation luminosity, $L_{\rm mech}$ is the mechanical luminosity, c is the speed of light, and $L_{\rm Edd}$ is the Eddington luminosity. Such universalities can appear in the regime in which electron scattering opacity dominates over absorption opacity. Further, the normalized isotropic mechanical luminosity $L_{\rm mech}^{\rm ISO}/L_{\rm Edd}$ (evaluated by normalized density and velocity at $\theta =10^\circ$) exhibits a broken power-law relationship with ${\dot{m}}_{\rm BH}$; $L_{\rm mech}^{\rm ISO}/ L_{\rm Edd} \propto {\dot{m}}_{\rm BH}^{2.7}$ (or $\propto {\dot{m}}_{\rm BH}^{0.7}$) below (above) ${\dot{m}}_{\rm BH}\sim 400$. This is because the radial velocity stays nearly constant (or even decreases) below (above) the break with increase of $\dot{m}_{\rm BH}$. We also find that the luminosity ratio is $L_{\rm mech}/L_{\rm rad}^{\rm ISO} \sim 0.05$ at ${\dot{m}}_{\rm BH} \sim 100$, which is roughly consistent with the observations of NLS1, 1H 0323+103.

Constraints from Fermi observations of long gamma-ray bursts on cosmological parameters

ABSTRACT In this paper, we compile a Fermi sample of the long gamma-ray bursts (GRB) observations from 15 years of GBM catalogue with identified redshift, in which the GOLD sample contains 123 long GRBs at $z\le 5.6$ and the FULL sample contains 151 long GRBs with redshifts at $z\le 8.2$. The Amati relation (the $E_{\rm p,i}$–$E_{\rm iso}$ correlation) is calibrated at $z\lt 1.4$ by a Gaussian Process from the latest observational Hubble data with the cosmic chronometers method so that GRBs at high-redshift $z\ge 1.4$ can be used to constrain cosmological models via the Markov chain Monte Carlo (MCMC) method. From the cosmology-independent GRBs with the GOLD sample at $z\ge 1.4$ and the Pantheon + sample of type Ia supernovae (SNe Ia) at $0.01\lt z\le 2.3$, we obtain $\Omega _{\rm m} = 0.354\pm 0.018, H_0 = 73.05\pm 0.2\, \rm {km\,s^{-1}\,Mpc^{-1}}$ for the flat Lambda cold dark matter ($\Lambda$CDM) model; $w_0 = -1.22^{+0.18}_{-0.15}$ for the flat wCDM model; and $w_{a} = -1.12^{+0.45}_{-0.83}$ for the flat Chevallier–Polarski–Linder model at the 1$\sigma$ confidence level. Our results with the GOLD and FULL sample are almost identical, which are more stringent than the previous results with GRBs.

GRB 221009A afterglow from a shallow angular structured jet

ABSTRACT Exceptionally bright gamma-ray burst (GRB) afterglows can reveal the angular structure of their jets. GRB jets appear to have a narrow core (of half-opening angle θc), beyond which their kinetic energy drops as a power-law with angle θ from the jet’s symmetry axis, $E_{\mathrm{ k},\rm iso}(\theta)\propto [1+(\theta /\theta _\mathrm{ c})^2]^{-a/2}$. The power-law index a reflects the amount of mixing between the shocked jet and confining medium, which depends on the jet’s initial magnetization. Weakly magnetized jets undergo significant mixing, leading to shallow (a ≲ 2) angular profiles. We use the exquisite multiwaveband afterglow observations of GRB 221009A to constrain the jet angular structure using a dynamical model that accounts for both the forward and reverse shocks, for a power-law external density profile, next ∝ R−k. Both the forward shock emission, that dominates the optical and X-ray flux, and the reverse shock emission, that produces the radio afterglow, require a jet with a narrow core (θc ≈ 0.021) and a shallow angular structure (a ≈ 0.8) expanding into a stellar wind (k ≈ 2). Moreover, these data appear to favour a small fraction (ξe ≈ 10−2) of shock heated electrons forming a power-law energy distribution in both shocks.

GRB 201015A and the nature of low-luminosity soft gamma-ray bursts

ABSTRACT GRB 201015A is a peculiarly low luminosity, spectrally soft gamma-ray burst (GRB), with T90 = 9.8 ± 3.5 s (time interval of detection of 90 per cent of photons from the GRB), and an associated supernova (likely to be type Ic or Ic-BL). GRB 201015A has an isotropic energy $E_{\gamma , \rm iso}$$= 1.75 ^{+0.60} _{-0.53} \times 10^{50}$ erg, and photon index $\Gamma = 3.00 ^{+0.50} _{-0.42}$ (15–150 keV). It follows the Amati relation, a correlation between $E_{\gamma , \rm iso}$ and spectral peak energy Ep followed by long GRBs. It appears exceptionally soft based on Γ, the hardness ratio of HR = 0.47 ± 0.24, and low-Ep, so we have compared it to other GRBs sharing these properties. These events can be explained by shock breakout, poorly collimated jets, and off-axis viewing. Follow-up observations of the afterglow taken in the X-ray, optical, and radio reveal a surprisingly late flattening in the X-ray from t = (2.61 ± 1.27) × 104 s to $t = 1.67 ^{+1.14} _{-0.65} \times 10^6$ s. We fit the data to closure relations describing the synchrotron emission, finding the electron spectral index to be $p = 2.42 ^{+0.44} _{-0.30}$ and evidence of late-time energy injection with coefficient $q = 0.24 ^{+0.24} _{-0.18}$. The jet half opening angle lower limit (θj ≥ 16°) is inferred from the non-detection of a jet break. The launch of SVOM and Einstein Probe in 2023 should enable detection of more low-luminosity events like this, providing a fuller picture of the variety of GRBs.

A halo of trapped interstellar matter surrounding the Solar system

ABSTRACT This paper shows that gravitating bodies travelling through the Galaxy can trap lighter interstellar particles that pass nearby with small relative velocities onto temporarily bound orbits. The capture mechanism is driven by the Galactic tidal field, which can decelerate infalling objects to a degree where their binding energy becomes negative. Over time, trapped particles build a local overdensity – or ‘halo’– that reaches a steady state as the number of particles being captured equals that being tidally stripped. This paper uses classical stochastic techniques to calculate the capture rate and the phase-space distribution of particles trapped by a point-mass. In a steady state, bound particles generate a density enhancement that scales as δ(r) ∼ r−3/2 (a.k.a ‘density spike’) and follow a velocity dispersion profile σh(r) ∼ r−1/2. Collision-less N-body experiments show excellent agreement with these theoretical predictions within a distance range r ≳ rϵ, where $r_\epsilon \simeq 0.8\, \exp [-V_\star ^2/(2\sigma ^2)]\, Gm_\star /\sigma ^2$ is the thermal critical radius of a point-mass m⋆ moving with a speed V⋆ through a sea of particles with a velocity dispersion σ. Preliminary estimates that ignore collisions with planets and Galactic substructures suggest that the Solar system may be surrounded by a halo that contains the order of $N^{\rm ISO}(\lt 0.1\, {\rm pc})\sim 10^7$ energetically bound ‘Oumuamua-like objects, and a dark matter mass of $M^{\rm DM}(\lt 0.1\, {\rm pc})\sim 10^{-13}M_\odot$. The presence of trapped interstellar matter in the Solar system can affect current estimates on the size of the Oort Cloud, and leave a distinct signal in direct dark matter detection experiments.

Outliers in the Ep,z – Eγ relation of Fermi-GBM long-duration gamma-ray bursts

ABSTRACT Long gamma-ray bursts (GRBs) are typically associated with massive star core collapse, while the short GRBs are associated with compact binary mergers. However, recent evidence indicates that some peculiar long-duration bursts may correspond to compact binary mergers origins. In this paper, we use the data of the Fermi Gamma-ray Burst Monitor to search for peculiar long-duration bursts which may be from compact binary mergers based on outlier events in the $E_{p,z}\!-\!E_{\gamma ,\rm iso}$ relation. We obtained 10 outlier events by systematically analysing bursts with $T_{90}\gt 4.2 \rm \ s$ from 2008 August to 2021 July. In order to determine whether these outlier events were from compact binary mergers, we analysed their properties, including spectral lag, hardness ratio, and energy-hardness parameter. Based on the distributions of T90 − HR and T90 − Ep, we calculated the probability of outlier events belonging to the short GRBs. Our analysis indicates that GRB 120304B is likely to arise from the merger of a neutron star and a massive white dwarf. GRB 150210A is likely to arise from massive star core collapse. The other eight GRBs are fuzzy bursts that have both long and short GRBs properties. Additionally, we find that outlier samples have relatively high Ep and low fluences.

The origins and impact of outflow from super-Eddington flow

Abstract It is widely believed that super-Eddington accretion flow can produce powerful outflow, but where does this originate and how much mass and energy are carried away in which directions? To answer these questions, we perform a new large-box, two-dimensional radiation hydrodynamic simulation, paying special attention lest the results should depend on the adopted initial and boundary conditions. We achieve a quasi-steady state at an unprecedentedly large range, r = 2–600rS (with rS being the Schwarzschild radius), from the black hole. The accretion rate onto the central 10 M⊙ black hole is $\dot{M}_{\rm BH} \sim 180 L_{\rm Edd}/c^{2}$, whereas the mass outflow rate is ${\dot{M}}_{\rm outflow} \sim 24 L_{\rm Edd}/c^2$ (where LEdd and c are the Eddington luminosity and the speed of light, respectively). The ratio ${\dot{M}}_{\rm outflow}/{\dot{M}}_{\rm BH} \sim 0.14$ is much less than previously reported. By careful inspection we find that most of the outflowing gas reaching the outer boundary originates from the region at R ≲ 140rS, while gas at 140–230rS forms failed outflow. Therefore, significant outflow occurs inside the trapping radius ∼450rS. The mechanical energy flux (or mass flux) reaches its maximum in the direction of ∼15° (∼80°) from the rotation axis. The total mechanical luminosity is Lmec ∼ 0.16LEdd, while the isotropic X-ray luminosity varies from $L_{\rm X}^{\rm ISO}\sim 2.9 L_{\rm Edd}$ (for a face-on observer) to ∼2.1LEdd (for a nearly edge-on observer). The power ratio is $L_{\rm mec}/L_{\rm X}^{\rm ISO}\sim 0.05$–0.08, in good agreement with observations of ultra-luminous X-ray sources surrounded by optical nebulae.

How are gamma-ray burst radio afterglows populated?

ABSTRACT We systematically analyse two GRB samples with radio-loud and radio-quiet afterglows, respectively. It is interestingly found that the radio-selected GRB samples exhibit a clear dichotomy in terms of their distributions of intrinsic durations (Tint), isotropic energies in γ-rays (Eγ, iso), the circum-burst medium density (n), the spectral radio peak luminosity (Lν, p) and flux densities (Fhost) of host galaxies. On average, the values of Tint, Eγ, iso, n, Lν, p, and Fhost of radio-quiet GRBs are relatively smaller than those of radio-loud ones. However, the redshifts and host flux densities of both samples are similarly distributed. In addition, a positive power-law correlation of $L_{\nu ,p}\propto E_{\gamma ,\rm iso}^{0.41\pm 0.04}$ is found for the radio-loud sample, especially in accord with the supernova-associated GRBs, which is marginally consistent with that of the radio-quiet GRB sample. A negative correlation between Tint and z is confirmed to similarly hold for both radio-loud and radio-quiet GRBs. The dividing line between short and long GRBs in the rest frame is at Tint ≃1 s. Consequently, we propose that the radio-selected GRBs could be originated from distinct progenitors and central engines, together with environments.

A numerical jet model for the prompt emission of gamma–ray bursts

Abstract Gamma-ray bursts (GRBs) are known to be highly collimated events, and are mostly detectable when they are seen on-axis or very nearly on-axis. However, GRBs can be seen from off-axis angles, and the recent detection of a short GRB associated to a gravitational wave event has conclusively shown such a scenario. The observer viewing angle plays an important role in the observable spectral shape and the energetic of such events. We present a numerical model which is based on the single-pulse approximation with emission from a top-hat jet and has been developed to investigate the effects of the observer viewing angle. We assume a conical jet parametrized by a radius Rjet, half-opening angle θjet, a comoving-frame emissivity law and an observer viewing angle θobs, and then study the effects for the conditions θobs < θjet and θobs > θjet. We present results considering a smoothly broken power-law emissivity law in jet comoving frame, albeit the model implementation easily allows to consider other emissivity laws. We find that the relation $E^{\rm i}_{\rm p}\propto E_{\rm iso}^{0.5}$ (Amati relation) is naturally obtained from pure relativistic kinematic when $\Gamma \gtrsim 10$ and θobs < θjet; on the contrary, when θobs > θjet it results $E^{\rm i}_{\rm p}\propto E_{\rm iso}^{0.25}$. Using data from literature for a class of well-know sub-energetic GRBs, we show that their position in the $E^{\rm i}_{\rm p}-E_{\rm iso}$ plane is consistent with event observed off-axis. The presented model is developed as a module to be integrated in spectral fitting software package XSPEC and can be used by the scientific community.

Constraints on the emitting region of the gamma-rays observed in GW170817

The gravitational waves from the neutron star merger event GW170817 were accompanied by an unusually weak short GRB 170817A, by an optical/IR macronova/kilonova and by a long lasting radio to X-rays counterpart. While association of short GRBs with mergers was predicted a long time ago, the luminosity of this prompt {\gamma}-ray emission was weaker by a few orders of magnitude than all known previous sGRBs and it was softer than typical sGRBs. This raise the question whether the {\gamma}-rays that we have seen were a regular sGRB viewed off-axis. We revisit this question following recent refined analyses of the {\gamma}-ray signal and the VLBI observations that revealed the angular structure of the relativistic outflow: observing angle of $\sim\,20^\circ$, a narrow jet with core $\lesssim5^\circ$ and $E_{\rm iso}>10^{52}\,{\rm ergs}$. We show here that: (i) The region emitting the observed $\gamma$-rays must have been moving with a Lorentz factor $\Gamma\gtrsim5$; (ii) The observed {\gamma}-rays were not "off-axis" emission (viewing angle $>1/\Gamma$) emerging from the core of the jet, where a regular sGRB was most likely produced; (iii) The $\gamma$-ray emission region was either "on-axis" (at an angle $<1/\Gamma$) or if it was "off-axis" then the observing angle must have been small ($<5^\circ$) and the on-axis emission from this region was too faint and too hard to resemble a regular sGRB.

Frustration of square cupola in Sr(TiO) Cu4(PO4)4

The structural and magnetic properties of the square-cupola antiferromagnet Sr(TiO)Cu$_{4}$(PO$_{4}$)$_{4}$ are investigated via x-ray diffraction, magnetization, heat capacity, and $^{31}$P nuclear magnetic resonance experiments on polycrystalline samples, as well as density-functional band-structure calculations. The temperature-dependent unit cell volume could be described well using the Debye approximation with the Debye temperature of $\theta_{\rm D} \simeq $ 550~K. Magnetic response reveals a pronounced two-dimensionality with a magnetic long-range-order below $T_{\rm N} \simeq 6.2$~K. High-field magnetization exhibits a kink at $1/3$ of the saturation magnetization. Asymmetric $^{31}$P NMR spectra clearly suggest strong in-plane anisotropy in the magnetic susceptibility, as anticipated from the crystal structure. From the $^{31}$P NMR shift vs bulk susceptibility plot, the isotropic and axial parts of the hyperfine coupling between $^{31}$P nuclei and the Cu$^{2+}$ spins are calculated to be $A_{\rm hf}^{\rm iso} \simeq 6539$ and $A_{\rm hf}^{\rm ax} \simeq 952$~Oe/$\mu_{\rm B}$, respectively. The low-temperature and low-field $^{31}$P NMR spectra indicate a commensurate antiferromagnetic ordering. Frustrated nature of the compound is inferred from the temperature-dependent $^{31}$P NMR spin-lattice relaxation rate and confirmed by our microscopic analysis that reveals strong frustration of the square cupola by next-nearest-neighbor exchange couplings.

Hard X-ray spectral investigations of gamma-ray bursts 120521C and 130606A at high-redshift z ∼ 6

This study presents the temporal and spectral analysis of the prompt emission of two high-redshift gamma-ray bursts (GRBs), 120521C at $z\sim6$ and 130606A at $z\sim5.91$, which were performed using the Swift-XRT/BAT and the Suzaku-WAM simultaneously. Based on follow-up XRT observations, the longest durations of the prompt emissions were approximately $80$ s (120521C) and $360$ s (130606A) in the rest frame of each GRB, which are categorized as long-duration GRBs, but are insufficiently long compared with the predicted duration of GRBs that originate from first-generation stars. Because of the wide bandpass of the instruments covering the ranges of 15 keV--5 MeV (BAT-WAM) and 0.3 keV--5.0 MeV (XRT-BAT-WAM), we successfully determined the $\nu F_{\nu}$ peak energies $E_{\rm peak}^{\rm src}$ of $682^{+845}_{-207}$ keV and $1209^{+553}_{-304}$ keV in the rest frame, and the isotropic-equivalent radiated energies $E_{\rm iso}$ of $(8.25^{+2.24}_{-1.96})\times10^{52}$ erg and $(2.82^{+0.17}_{-0.71})\times10^{53}$ erg, respectively. These obtained characteristic parameters are in accordance with the well-known relation between $E_{\rm peak}^{\rm src}$ and $E_{\rm iso}$ (Amati relation). In addition, we examined the relations between $E_{\rm peak}^{\rm src}$ and the 1-s peak luminosity, $L_{\rm p}$, or the geometrical corrected radiated energy, $E_{\gamma}$, and confirmed the $E_{\rm peak}^{\rm src}$-$L_{\rm p}$ (Yonetoku) and $E_{\rm peak}^{\rm src}$-$E_{\gamma}$ (Ghirlanda) relations. The results implied that these high-redshift GRBs at $z\sim6$, expected as having radiated from the reionization epoch, have similar properties as that of X-ray prompt emission with low-redshift GRBs.

Giant thermal vibrations in the framework compoundsBa1−xSrxAl2O4

Synchrotron X-ray diffraction (XRD) experiments were performed on the network compounds Ba1-xSrxAl2O4 at temperatures between 15 and 800 K. The ferroelectric phase of the parent BaAl2O4 is largely suppressed by the Sr-substitution and disappears for $x\geq0.1$. Structural refinements reveal that the isotropic atomic displacement parameter ($B_{\rm iso}$) in the bridging oxygen atom for $x\geq0.05$ is largely independent of temperature and retains an anomalously large value in the adjacent paraelectric phase even at the lowest temperature. The $B_{\rm iso}$ systematically increases as $x$ increases, exhibiting an especially large value for $x\geq0.5$. According to previous electron diffraction experiments for Ba1-xSrxAl2O4 with $x\geq0.1$, strong thermal diffuse scattering occurs at two reciprocal points relating to two distinct soft modes at the M- and K-points over a wide range of temperatures below 800 K [Y. Ishii et al., Sci. Rep. 6, 19154 (2016)]. Although the latter mode disappears at approximately 200 K, the former does not condense, at least down to 100 K. On the contrary, it still survives at low-temperature. The anomalously large $B_{\rm iso}$ observed in this study is ascribed to these soft modes existing in a wide temperature range.

RIESZ PROJECTIONS FOR A NON-HYPONORMAL OPERATOR

J. G. Stampfli proved that if a bounded linear operator $T$ on a Hilbert space $\mathscr H$ satisfies ($G_1$) property, then the Riesz projection $P_{\lambda}$ associated with $\lambda\in{\rm iso}\sigma(T)$ is self-adjoint and $P_{\lambda}\mathscr{H}=(T - \lambda)^{-1}(0)=(T^{*} - \bar{\lambda})^{-1}(0)$. In this note we show that Stampfli's result is generalized to an nilpotent extension of an operator having ($G_1$) property.

Measuring dark energy with theEiso–Epcorrelation of gamma-ray bursts using model-independent methods

In this paper, we use two model-independent methods to standardize long gamma-ray bursts (GRBs) using the $E_{\rm iso}-E_{\rm p}$ correlation, where $E_{\rm iso}$ is the isotropic-equivalent gamma-ray energy and $E_{\rm p}$ is the spectral peak energy. We update 42 long GRBs and try to make constraint on cosmological parameters. The full sample contains 151 long GRBs with redshifts from 0.0331 to 8.2. The first method is the simultaneous fitting method. The extrinsic scatter $\sigma_{\rm ext}$ is taken into account and assigned to the parameter $E_{\rm iso}$. The best-fitting values are $a=49.15\pm0.26$, $b=1.42\pm0.11$, $\sigma_{\rm ext}=0.34\pm0.03$ and $\Omega_m=0.79$ in the flat $\Lambda$CDM model. The constraint on $\Omega_m$ is $0.55<\Omega_m<1$ at the 1$\sigma$ confidence level. If reduced $\chi^2$ method is used, the best-fit results are $a=48.96\pm0.18$, $b=1.52\pm0.08$ and $\Omega_m=0.50\pm0.12$. The second method is using type Ia supernovae (SNe Ia) to calibrate the $E_{\rm iso}-E_{\rm p}$ correlation. We calibrate 90 high-redshift GRBs in the redshift range from 1.44 to 8.1. The cosmological constraints from these 90 GRBs are $\Omega_m=0.23^{+0.06}_{-0.04}$ for flat $\Lambda$CDM, and $\Omega_m=0.18\pm0.11$ and $\Omega_{\Lambda}=0.46\pm0.51$ for non-flat $\Lambda$CDM. For the combination of GRB and SNe Ia sample, we obtain $\Omega_m=0.271\pm0.019$ and $h=0.701\pm0.002$ for the flat $\Lambda$CDM, and for the non-flat $\Lambda$CDM, the results are $\Omega_m=0.225\pm0.044$, $\Omega_{\Lambda}=0.640\pm0.082$ and $h=0.698\pm0.004$. These results from calibrated GRBs are consistent with that of SNe Ia. Meanwhile, the combined data can improve cosmological constraints significantly, comparing to SNe Ia alone. Our results show that the $E_{\rm iso}-E_{\rm p}$ correlation is promising to probe the high-redshift universe.

Neutron-Star-Black-Hole Binaries Produced by Binary-Driven Hypernovae.

Binary-driven hypernovae (BdHNe) within the induced gravitational collapse paradigm have been introduced to explain energetic (E_{iso}≳10^{52} erg), long gamma-ray bursts (GRBs) associated with type Ic supernovae (SNe). The progenitor is a tight binary composed of a carbon-oxygen (CO) core and a neutron-star (NS) companion, a subclass of the newly proposed "ultrastripped" binaries. The CO-NS short-period orbit causes the NS to accrete appreciable matter from the SN ejecta when the CO core collapses, ultimately causing it to collapse to a black hole (BH) and producing a GRB. These tight binaries evolve through the SN explosion very differently than compact binaries studied in population synthesis calculations. First, the hypercritical accretion onto the NS companion alters both the mass and the momentum of the binary. Second, because the explosion time scale is on par with the orbital period, the mass ejection cannot be assumed to be instantaneous. This dramatically affects the post-SN fate of the binary. Finally, the bow shock created as the accreting NS plows through the SN ejecta transfers angular momentum, braking the orbit. These systems remain bound even if a large fraction of the binary mass is lost in the explosion (well above the canonical 50% limit), and even large kicks are unlikely to unbind the system. Indeed, BdHNe produce a new family of NS-BH binaries unaccounted for in current population synthesis analyses and, although they may be rare, the fact that nearly 100% remain bound implies that they may play an important role in the compact merger rate, important for gravitational waves that, in turn, can produce a new class of ultrashort GRBs.

Model-independent distance calibration of high-redshift gamma-ray bursts and constrain on the ΛCDM model

Gamma-ray bursts (GRBs) are luminous enough to be detectable up to redshift $z\sim 10$. They are often proposed as complementary tools to type-Ia supernovae (SNe Ia) in tracing the Hubble diagram of the Universe. The distance calibrations of GRBs usually make use one or some of the empirical luminosity correlations, such as $\tau_{\rm lag}-L$, $V-L$, $E_p-L$, $E_p-E_{\gamma}$, $\tau_{\rm RT}-L$ and $E_p-E_{\rm iso}$ relations. These calibrating methods are based on the underling assumption that the empirical luminosity correlations are universal over all redshift range. In this paper, we test the possible redshift dependence of six luminosity correlations by dividing GRBs into low-$z$ and high-$z$ classes according to their redshift smaller or larger than 1.4. It is shown that the $E_p-E_{\gamma}$ relation for low-$z$ GRBs is consistent with that for high-$z$ GRBs within $1\sigma$ uncertainty. The intrinsic scatter of $V-L$ relation is too larger to make a convincing conclusion. For the rest four correlations, however, low-$z$ GRBs differ from high-$z$ GRBs at more than $3\sigma$ confidence level. As such, we calibrate GRBs using the $E_p-E_{\gamma}$ relation in a model-independent way. The constraint of high-$z$ GRBs on the $\Lambda$CDM model gives $\Omega_M=0.302\pm 0.142(1\sigma)$, well consistent with the Planck 2015 results.

A TIGHTLiso–Ep,z–Γ0CORRELATION OF GAMMA-RAY BURSTS

We select a sample of 34 gamma-ray bursts (GRBs) whose $\Gamma_0$ values are derived with the onset peaks observed in the afterglow lightcurves (except for GRB 060218 whose $\Gamma_0$ is estimated with its radio data), and investigate the correlations among $\Gamma_0$, the isotropic peak luminosity ($L_{\rm iso}$), and the peak energy ($E_{\rm p,z}$) of the $\nu f_\nu$ spectrum in the cosmological rest frame. An analysis of pair correlations among these observables well confirms the results reported by the previous papers. More interestingly, a tight correlation among $L_{\rm iso}$, $E_{\rm p,z}$, and $\Gamma_0$ is found from a multiple regression analysis, which takes the form of $L_{\rm iso} \propto E_{\rm p,z}^{1.34\pm 0.14} \Gamma_0^{1.32\pm 0.19}$ or $E_{\rm p,z} \propto L_{\rm iso}^{0.55\pm 0.06}\Gamma_0^{-0.50\pm 0.17}$. Nine other GRBs whose $\Gamma_0$ are derived via the pair production opacity constraint also follow such a correlation. Excluding GRB 060218, the $L_{\rm iso}-E_{\rm p,z}-\Gamma_0$ correlation is valid, and it even holds in the jet co-moving frame. However, GRB 060218 deviates the $L^{'}_{\rm iso}-E^{'}_{\rm p}$ relation of typical GRBs in the jet co-moving frame with $3\sigma$. We argue that the $L_{\rm iso} - E_{\rm p, z} - \Gamma_0$ correlation may be more physical than the $L_{\rm iso} - E_{\rm p,z}$ correlation, since physically the relationship between the observed $L_{\rm iso}$ and $E_{\rm p,z}$ not only depends on radiation physics, but also depends on the bulk motion of the jet. We explore the possible origins of this correlation and discuss its physical implications for understanding GRB jet composition and radiation mechanism.

ANGULAR MOMENTUM ROLE IN THE HYPERCRITICAL ACCRETION OF BINARY-DRIVEN HYPERNOVAE

The induced gravitational collapse (IGC) paradigm explains a class of energetic, $E_{\rm iso}\gtrsim 10^{52}$~erg, long-duration gamma-ray bursts (GRBs) associated with Ic supernovae, recently named binary-driven hypernovae (BdHNe). The progenitor is a tight binary system formed of a carbon-oxygen (CO) core and a neutron star companion. The supernova ejecta of the exploding CO core triggers a hypercritical accretion process onto the neutron star, which reaches in a few seconds the critical mass, and gravitationally collapses to a black hole emitting a GRB. In our previous simulations of this process we adopted a spherically symmetric approximation to compute the features of the hypercritical accretion process. We here present the first estimates of the angular momentum transported by the supernova ejecta, $L_{\rm acc}$, and perform numerical simulations of the angular momentum transfer to the neutron star during the hyperaccretion process in full general relativity. We show that the neutron star: i) reaches in a few seconds either mass-shedding limit or the secular axisymmetric instability depending on its initial mass; ii) reaches a maximum dimensionless angular momentum value, $[c J/(G M^2)]_{\rm max}\approx 0.7$; iii) can support less angular momentum than the one transported by supernova ejecta, $L_{\rm acc} > J_{\rm NS,max}$, hence there is an angular momentum excess which necessarily leads to jetted emission.

Statistical analysis of the parameters of gamma-ray bursts with known redshifts and peaked optical light curves

We present the statistical analysis of the properties of gamma-ray bursts with measured host galaxy redshifts and peaked optical light curves in proper frames of reference. The optical transients are classified by comparing the time lag of the optical peak relative to the GRB trigger with the duration of the gamma-ray emission itself. The results of the correlation analysis of all possible pairs of energy, spectral, and temporal characteristics of both gamma-ray and optical emissions are given. We specify the pairs of the parameters with correlation coefficients greater than 50 % at significance levels better than 1 %. The following empirical relations, obtained for the first time, are specifically discussed: a correlation between the peak optical afterglow $R$ band luminosity and redshift $L_{R} \propto (z+1)^{5.39 \pm 0.74}$ and a correlation between the peak luminosity of the prompt optical emissions and the time of the peak $L_{R} \propto T_{\rm peak}^{-3.85 \pm 1.22}$. We also analyze the similarity of the relationships between the peak optical luminosity and the isotropic equivalent of the total energy of gamma-ray bursts for afterglows ($L_{R} \propto E_{\rm iso}^{1.06 \pm 0.22}$) and for prompt optical emissions ($L_{R} \propto E_{\rm iso}^{1.59 \pm 0.21}$).