arXiv subjects

Ehud Nakar

Publications and source records attributed to Ehud Nakar.

At least 19 recordsLinked to original sources

arXiv2026

A spectacular multi-wavelength transient associated with an off-axis relativistic jet

Many of the most luminous extragalactic transients originate from the accretion of material onto a black hole (BH) via core-collapse, stellar mergers, or the tidal disruption of a star. Some produce energetic multi-wavelength emission, displaying short, blue optical flares and bright, long-lived radio afterglows. In rare cases, these have also launched powerful relativistic jets almost exclusively detected on-axis via high-energy emission. Here we report AT 2019ijn, a radio transient discovered in the Very Large Array Sky Survey, associated with a powerful relativistic jet viewed off-axis and accompanied by a luminous ($\nu L_{\nu, opt} \sim 10^{44}$ erg/s) optical transient. Originating from a star-forming dwarf galaxy at z = 0.273, AT 2019ijn's optical flare exhibited a fast rise ($t_{rise, rest} \sim 7$ d) and shallow decline ($t_{dec, rest} > 38$ d), followed a year later by an energetic ($E \sim 2\times10^{52}$ erg) radio counterpart persisting for $>6$ years. These combined properties are unprecedented and preclude known classes of stellar explosion powered by core-collapse. Instead, the implied accretion onto a BH and associated off-axis jet invokes an exotic BH-stellar merger or a jetted tidal disruption event (TDE) by a $10^4 - 10^6 M_\odot$ black hole. Favoring a TDE, this work determines the jet-launching occurrence, with the low redshift allowing constraints on the late-time evolution in contrast to prior events. Upcoming radio sky surveys will offer an unprecedented new window for further discovery of AT 2019ijn-like off-axis relativistic transients.

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arXiv2026

Revisiting GW170817 at milliarcsecond scale: high-precision constraints on jet geometry and $H_0$

The historic detection of gravitational waves from the electromagnetically bright binary neutron star merger GW170817 enabled the first standard siren measurement of Hubble's constant ($H_0$). The accuracy and precision of this measurement depends crucially on how well the merger inclination angle is constrained, given its strong covariance with luminosity distance ($D_L$). Modeling the light-curve of the jet's afterglow provides constraints on inclination, but is highly dependent on the similarly uncertain jet opening angle. Past studies have improved on this by invoking high-resolution radio observations, obtained through very long baseline interferometry (VLBI). We present a Bayesian visibility-plane model-fitting framework that provides a more informed and robust measurement of the viewing geometry of GW170817 and of $H_0$, by including all relevant VLBI data, robustly handling systematic uncertainties and rigorously sampling model parameter space. By fitting new hydrodynamical afterglow models with a continuum of jet geometries, we obtain a viewing angle of $18.^{\circ}3-20.^{\circ}3$ (for a fixed cosmology with $D_L=40.7$ Mpc, as used in most previous analyses). We extend our framework to fit for $D_L$ and $H_0$ directly, and marginalize over an ensemble of plausible peculiar velocity corrections to obtain viewing angle $16.^{\circ}8-19.^{\circ}2$, $D_L=44.0\pm1.6$ Mpc and $H_0=65.5\pm4.4$ km s$^{-1}$ Mpc$^{-1}$. Notably, the peak of our $H_0$ posterior is within $0.5\sigma$ of the early-Universe Planck $H_0$ value, but $1.7\sigma$ from the late-Universe SH0ES measurement. We discuss potential caveats and the implications of this result in the context of the current discrepancy between early and late-Universe measurements of the Hubble constant.

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arXiv2026

Las Cumbres Observatory Gravitational-Wave Follow-up in the Third and Fourth Observing Runs: Strengths and Weaknesses of a Rapid Response Galaxy Targeted Strategy

We present a summary of gravitational-wave (GW) follow-up using the Las Cumbres Observatory global network of telescopes during the third (O3) and fourth (O4) observing runs of the GW detectors. As in O2, we implemented the Gehrels et al. 2016 galaxy-targeted strategy. Here we test its efficacy in O3 and O4 and analyze the Las Cumbres Observatory response time and depth for nine GW alerts that showed a possibility of having an electromagnetic counterpart (GW190425, GW190426_152155, S190510g, GW190728_064510, GW190814, S190822c, GW191216_213338, S240422ed and S250206dm). We find that Las Cumbres Observatory is able to begin observations in response to GW alerts within minutes of the alert, with the observations being deep enough to detect possible GW170817-like kilonovae out to a median distance of 250 Mpc. In this sense a global rapid-response network of telescopes like Las Cumbres is an excellent GW follow-up facility. However, the galaxy-targeted follow-up strategy was much less efficient in O3 and O4 than originally predicted, given the larger than assumed GW localizations. We conclude that coordination between various facilities to include both wide-field and rapid-response capabilities is required to achieve efficient and comprehensive follow-up of GW events.

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arXiv2026

AT2018cow Powered by a Shock in Aspherical Circumstellar Media

We present a quantitative model for the luminous fast blue optical transient AT2018cow in which a shock propagating through an aspherical circumstellar medium (CSM) produces the X-ray and UV/optical/NIR emission. X-rays are emitted from hot post-shock electrons, and soft X-ray photons are reprocessed into optical/UV emission in the cool downstream. This naturally explains two previously puzzling features: (i) the coordinated evolution of the optical and soft X-ray after day 20, (ii) the hard X-ray hump above 10 keV that disappears around day 15 as the Thomson optical depth transitions from $\tau_T \gg1$ to $\tau_T \sim 1$. Our model is over-constrained, and it quantitatively reproduces the bolometric luminosity evolution, soft X-ray spectrum, and time-dependent soft/hard X-ray and soft X-ray/optical luminosity ratios. It also explains additional puzzles: X-ray fluctuations with $\sim4-10$ day timescales arise from a global radiative shock instability, while the NIR excess and the apparent receding blackbody radius result from reprocessed X-rays in matter far from thermodynamic equilibrium. The radio is naturally explained as originating from a shock driven by the same ejecta in the more dilute CSM. The light curve steepening after $\sim 40$ days likely indicates the shock reaches the edge of the dense CSM at $\sim {\rm few} \times 10^{15}$ cm. We infer explosion energy $\sim 1-5 \times 10^{50}$ erg, carried by an ejecta at $\sim 0.1c$ and a mass of $0.01-0.05 M_\odot$, in a dense asymmetric CSM with $\sim 0.3 M_\odot$, embedded in a more dilute CSM.

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arXiv2025

Tidal disruption of a magnetized star

Tidal disruptions of stars by supermassive black holes in galactic centers (TDEs) are now being actively studied both theoretically and observationally. They are observed throughout the electromagnetic spectrum, from radio to gamma-rays. It is still unclear how the emission is produced and, in particular, what is the role of the magnetic field of the disrupted star. There are many ways how magnetic fields might affect the dynamics of a TDE. They are likely responsible for the angular momentum transfer in the accretion disk formed at later stages and thus affect the radiation associated with the disk. Magnetic fields are also an important requirement for the formation of relativistic jets, that are seen in some TDEs. The goal of our study is to connect the field within the star to the fields that develop during the fallback and disk accretion. Using the fluid-dynamic code Athena++, we perform a large-scale three-dimensional adaptive-mesh magnetohydrodynamic simulation of a tidal disruption of a magnetized star. The fallback stream returning to the black-hole vicinity after the disruption contains smooth magnetic fields aligned with the stream lines. Formation of a nozzle shock near the pericenter of the initial orbit leads to a turbulent eccentric disk-like structure where the field is amplified and entangled on the local dynamic time scales up to approximate equipartition. The resulting field is mildly anisotropic and has a typical length several times smaller than the pericenter distance. The properties of the field are consistent with the early stages of turbulent dynamo.

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arXiv2025

X-ray Transmission Through Photoionized Gas with Moderate Thomson Optical Depth

We model the absorption of X-rays by gas obscuring the source and photoionized by it. We consider a broad range of column densities, including both Thomson-thin and Thomson-thick media. For the Thomson thin regime, we derive a simple criterion based on the source luminosity and spectrum, as well as the medium radius and column density, that distinguishes between the following cases: (i) The absorption can be modeled well by a neutral medium; (ii) The radiation ionizes its way through the medium, and no absorption is expected; and (iii) A detailed model is required because the column density inferred from modeling the absorption with a neutral gas is much lower than the actual column density, or because the absorption features cannot be fitted by a neutral absorber. We derive the criterion analytically using a toy model of hydrogen and oxygen and calibrate it for realistic compositions with metallicities in the range $Z/Z_{\odot}=0.01-50$, using \textsc{Cloudy}. We generalize the model to the Thomson-thick regime, where we consider, alongside photoabsorption, electron scattering, Compton heating, Comptonization, and photon degradation. In this case, the emergent spectrum depends on the boundary condition experienced by photons scattered back towards the source. We discuss the effect of a reflective boundary and a reprocessing boundary. We provide simple criteria for the expected absorption state and discuss additional effects that alter the spectrum. The main motivation for our modeling is X-ray emission from supernovae interacting with the circumstellar medium; however, we expect it to be useful for many other applications.

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arXiv2025

GRB 250704B: An Off-axis Short GRB with a Long-Lived Afterglow Plateau

We present a detailed multi-wavelength afterglow study of the short GRB 250704B, extensively monitored in optical and near-infrared bands. Its afterglow displays an unusually long-duration plateau followed by an achromatic break and a steep decline, deviating from canonical GRB afterglows. While long plateaus are often explained by central engine activity, we find that for GRB 250704B, an energy injection model requires unreasonable parameters. The afterglow is better explained by an off-axis power-law structured jet with a narrow core ($\theta_c \approx 0.7^{\circ}$) viewed at a modest angle ($\theta_v \approx 1.9^{\circ}$). A comparison with GRB 170817A shows that both events are consistent with the off-axis structured jet scenario, where the shape of the light curve is governed primarily by the geometry of the jet and the viewing angle rather than the energetics, microphysical parameters, or external density. Our results underscore the importance of incorporating the jet structure in GRB modeling.

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arXiv2025

Early Emission from Double Detonation Type Ia Supernovae

A popular model for Type Ia supernovae (SNe Ia) is the detonation of a CO white dwarf (WD) that is triggered by the prior detonation of a thin surface layer of helium, known as a double detonation (DD). We explore the unique early electromagnetic signatures that are expected from collision of the CO detonation with the He detonation. The three features are (1) a shock breakout flash, (2) a stage of planar shock breakout cooling, and finally (3) shock cooling emission from the thermal energy released by the collision. The planar phase is unique to the unusual density profile of the He-detonated layer in comparison to the steep profile at a stellar edge as is usually considered for shock breakout. The shock cooling emission can be modified by recombination, and we explore these effects. All together, we expect an initial flash dominated by the planar phase of $\sim6\times10^{43}\,{\rm erg\,s^{-1}}$, which lasts ~5 s in the soft X-rays. This is followed by ~12-24 hrs of shock cooling at a luminosity of $3-10\times10^{40}\,{\rm erg\,s^{-1}}$ in the optical/UV. We discuss prospects for detection of this early DD emission with current and upcoming surveys.

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arXiv2025

Monte Carlo simulations of relativistic shock breakout from a stellar wind

We present Monte Carlo simulations of relativistic radiation-mediated shocks (RRMS) in the photon-starved regime, incorporating photon escape from the upstream region--characterized by the escape fraction, $f_{\rm esc}$--under a steady-state assumption. These simulations, performed for shock Lorentz factors $\Gamma_u = 2$, $3.5$, $6$, $10$, and $15$, are applicable to RRMS breakouts in shallowly declining density profiles such as stellar winds. We find that vigorous pair production acts as a thermostat, regulating the downstream temperature to $\sim 100$-$200~{\rm keV}$, largely independent of $f_{\rm esc}$. A subshock forms and strengthens with increasing $f_{\rm esc}$. The escaping spectra peak at $E_p \approx 300$-$600~{\rm keV}$ in the shock frame and deviate from a Wien distribution, exhibiting low-energy flattening ($f_\nu \propto \nu^{0}$) due to free-free emission and high-energy extensions caused by inverse Compton scattering from subshock-heated pairs. While an earlier analytical model reproduces the velocity structure well at $\Gamma_u = 2$, it significantly overestimates the shock width at higher Lorentz factors, particularly for $f_{\rm esc} \gtrsim$ a few $\%$. Based on this finding, we provide updated predictions for breakout observables in wind environments for $\Gamma_u \gtrsim 6$. Notably, the duration of the relativistic breakout becomes largely insensitive to the explosion energy and ejecta mass, typically exceeding analytical predictions by orders of magnitude and capable of producing a $\sim$300 s flash of MeV photons with a radiated energy of $\sim 10^{50}$ erg for an energetic explosion yielding $\Gamma_{bo} \sim 6$. We also discuss limitations of our modelling assumptions and their implications for the predicted breakout observables.

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arXiv2025

The Double Tidal Disruption Event AT 2022dbl Implies That at Least Some "Standard" Optical TDEs are Partial Disruptions

Flares produced following the tidal disruption of stars by supermassive black holes can reveal the properties of the otherwise dormant majority of black holes and the physics of accretion. In the past decade, a class of optical-ultraviolet tidal disruption flares has been discovered whose emission properties do not match theoretical predictions. This has led to extensive efforts to model the dynamics and emission mechanisms of optical-ultraviolet tidal disruptions in order to establish them as probes of supermassive black holes. Here we present the optical-ultraviolet tidal disruption event AT 2022dbl, which showed a nearly identical repetition 700 days after the first flare. Ruling out gravitational lensing and two chance unrelated disruptions, we conclude that at least the first flare represents the partial disruption of a star, possibly captured through the Hills mechanism. Since both flares are typical of the optical-ultraviolet class of tidal disruptions in terms of their radiated energy, temperature, luminosity, and spectral features, it follows that either the entire class are partial rather than full stellar disruptions, contrary to the prevalent assumption, or that some members of the class are partial disruptions, having nearly the same observational characteristics as full disruptions. Whichever option is true, these findings could require revised models for the emission mechanisms of optical-ultraviolet tidal disruption flares and a reassessment of their expected rates.

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arXiv2024

The neutron-star merger delay-time distribution, r-process "knees", and the metal budget of the Galaxy

For a sample of 18 recycled millisecond pulsars (rMSPs) that are in double neutron star (DNS) systems, and 42 rMSPs that are not in DNS pairs, we analyze the distributions of the characteristic age, $\tau_c$, and the time until merger of the double systems, $\tau_{\rm gw}$. Based on the $\tau_c$ distribution of non-DNS rMSPs, we argue that $\tau_c$ is a reasonable estimator of true pulsar age and that rMSPs are active as pulsars for a long (~Hubble) time. Among the DNSs there is an excess of young systems (small $\tau_c$) with short life expectancy (small $\tau_{\rm gw}$) compared to model expectations for the distributions of $\tau_c$ and $\tau_{\rm gw}$ if, at birth, DNSs have a delay-time distribution (DTD) of the form $t^{-1}$ (expected generically for close binaries), or for that matter, from expectations from any single power-law DTD. A two-population DNS model solves the problem: the data are best fit by the combination of a "fast" population with DTD going as $t^{-1.9\pm0.4}$, and a "slow" population of DNSs, with DTD proportional to $t^{-1.1\pm0.15}$. The fast population can be equivalently represented by a DTD with an exponential cutoff beyond t~300 Myr. The fast population completely dominates, by a factor A~10-100, the numbers of DNSs that merge within a Hubble time, and that presumably lead to short gamma-ray bursts and kilonova explosions. With a simple, empirically based, chemical-evolution calculation, we show that the fast/steep kilonova DTD, convolved with the measured star-formation history of the Milky Way's thick-disk population, naturally reproduces the "knee" structure seen in abundance-ratio diagrams of thick-disk stars, for europium and two other r-process elements. As a corollary we show, based again solely on empirical input, that the Milky Way is nearly a "closed box" that has retained at least ~70-90% of the metals produced over the Galaxy's lifetime.

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arXiv2024

Fission and fusion of heavy nuclei induced by the passage of a radiation-mediated shock in BNS mergers

We compute the structure of a Newtonian, multi-ion radiation-mediated shock (RMS) for different compositions anticipated in various stellar explosions. We use a multifluid RMS model that incorporates electrostatic coupling between the different plasma constituents as well as Coulomb friction in a self-consistent manner, and approximates the effect of pair creation and the presence of free neutrons in the shock upstream on the shock structure. We find that under certain conditions a significant velocity separation is developed between different ions in the shock downstream and demonstrate that in fast enough shocks ion-ion collisions may trigger fusion and fission events at a relatively high rate. Our analysis ignores anomalous coupling through plasma microturbulence, that might reduce the velocity spread downstream below the activation energy for nuclear reactions. A rough estimate of the scale separation in RMS suggests that for shocks propagating in BNS merger ejecta the anomalous coupling length may exceed the radiation length, allowing a considerable composition change behind the shock via inelastic collisions of $α$ particles with heavy elements at shock velocities $β_u\gtrsim0.25$. A sufficient abundance of free neutrons in the shock upstream, as expected during the first second after the merger, is also expected to alter the ejecta composition through neutron capture downstream. The resultant change in the composition profile may affect the properties of the early kilonova emission. The generation of microturbulence due to velocity separation can also give rise to particle acceleration that might alter the breakout signal in supernovae and other systems.

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arXiv2024

Stripped-envelope supernova light curves argue for central engine activity

The luminosity of ``stripped-envelope supernovae'', a common type of stellar explosions, has been generally thought to be driven by the radioactive decay of the nickel synthesized in the explosion and carried in its ejecta. Additional possible energy sources have been previously suggested, but these claims have been statistically inconclusive or model-dependent. Here, we analyse the energy budget of a sample of 54 well-observed stripped-envelope supernovae of all sub-types, and present statistically significant, largely model-independent, observational evidence for a non-radioactive power source in most of them (and possibly in all). We consider various energy sources, or alternatively, plausible systematic errors, that could drive this result, and conclude that the most likely option is the existence of a ``central engine'', such as a magnetar (a highly magnetic neutron star) or an accreting neutron star or black hole, operating over hours to days after the explosion. We infer from the observations constraints on the engines, finding that if these are magnetars, then their initial magnetic fields are about $10^{15}\,$G and their initial rotation period is 1--100 ms, implying that stripped-envelope supernovae could be the formative events of magnetars.

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arXiv2023

The Structure and Evolution of Relativistic Jetted Blast Waves

We study, analytically and numerically, the structure and evolution of relativistic jetted blast waves that propagate in uniform media, such as those that generate afterglows of gamma-ray bursts. Similar to previous studies, we find that the evolution can be divided into two parts: (i) a pre-spreading phase, in which the jet core angle is roughly constant, $θ_{c,0}$, and the shock Lorentz factor along the axis, $Γ_a$, evolves as a part of the Blandford-Mckee solution, and (ii) a spreading phase, in which $Γ_a$ drops exponentially with the radius and the core angle, $θ_c$, grows rapidly. Nevertheless, the jet remains collimated during the relativistic phase, where $θ_c(Γ_aβ_a=1)\simeq 0.4θ_{c,0}^{1/3}$. The transition between the phases takes place when $Γ_a\simeq 0.2θ_{c,0}^{-1}$. We find that the "wings" of jets with initial "narrow" structure ($\frac{d \log\,E_{iso}}{d\log\,θ}<-3$ outside of the core, where $E_{iso}$ is isotropic equivalent energy), start evolving during the pre-spreading phase. By the spreading phase these jets evolve to a self-similar profile, which is independent of the initial structure, where in the wings $Γ(θ)\proptoθ^{-1.5}$ and $E_{iso}(θ)\propto θ^{-2.6}$. Jets with initial "wide" structure roughly keep their initial profile during their entire evolution. We provide analytic description of the jet lateral profile evolution for a range of initial structures, as well as the evolution of $Γ_a$ and $θ_c$. For off-axis GRBs, we present a relation between the initial jet structure and the light curve rising phase. Applying our model to GW170817, we find that initially the jet had $θ_{c,0}=0.4-4.5~°$ and wings which are consistent with $E_{iso} \propto θ^{-3}-θ^{-4}$.

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arXiv2023

Constraints on the accretion properties of quasi-periodic erupters from GRMHD simulations

Context: Some apparently quiescent supermassive black holes (BHs) at centers of galaxies show quasi-periodic eruptions (QPEs) in the X-ray band, the nature of which is still unknown. A possible origin for the eruptions is an accretion disk, however the properties of such disks are restricted by the timescales of reccurance and durations of the flares. Aims: In this work we test the possibility that the known QPEs can be explained by accretion from a compact accretion disk with an outer radius $r_{\rm out}\sim 10-40 r_{\rm g}$, focusing on a particular object GSN 069. Methods: We run several 3D GRMHD simulations with the {\tt HARMPI} code of thin and thick disks and study how the initial disk parameters such as thickness, magnetic field configuration, magnetization and Kerr parameter affect the observational properties of QPEs. Results: We show that accretion onto a slowly rotating BH through a small, thick accretion disk with an initially low plasma $\beta$ can explain the observed flare duration, the time between outbursts and the lack of evidence for a variable jet emission. In order to form such a disk the accreting matter should have a low net angular momentum. A potential source for such low angular momentum matter with a quasi periodic feeding mechanism might be a tight binary of wind launching stars.

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arXiv2023

Relativistic Spherical Shocks in Expanding Media

We investigate the propagation of spherically symmetric shocks in relativistic homologously expanding media with density distributions following a power-law profile in their Lorentz factor. That is, $ρ_{ej} \propto t^{-3}γ_{e}(R,t)^{-α}$, where $ρ_{ej}$ is the medium proper density, $γ_{e}$ is its Lorentz factor, $α>0$ is constant and $t$, $R$ are the time and radius from the center. We find that the shocks behavior can be characterized by their proper velocity, $U'=Γ_s'β_s'$, where $Γ_s'$ is the shock Lorentz factor as measured in the immediate upstream frame and $β_s'$ is the corresponding 3-velocity. While generally, we do not expect the shock evolution to be self-similar, for every $α>0$ we find a critical value $U'_c$ for which a self-similar solution with constant $U'$ exists. We then use numerical simulations to investigate the behavior of general shocks. We find that shocks with $U'>U'_c$ have a monotonously growing $U'$, while those with $U'<U'_c$ have a decreasing $U'$ and will eventually die out. Finally, we present an analytic approximation, based on our numerical results, for the evolution of general shocks in the regime where $U'$ is ultra-relativistic.

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arXiv2023

The Iron Yield of Core-collapse Supernovae

We present a systematic analysis of 191 stripped-envelope supernovae (SE SNe), aimed to compute their $^{56}$Ni masses from the luminosity in their radioactive tails ($M_\mathrm{Ni}^\mathrm{tail}$) and/or in their maximum light, and the mean $^{56}$Ni and iron yields of SE SNe and core-collapse SNe. Our sample consists of SNe IIb, Ib, and Ic from the literature and from the Zwicky Transient Facility Bright Transient Survey. To calculate luminosities from optical photometry, we compute bolometric corrections using 49 SE SNe with optical and near-IR photometry, and develop corrections to account for the unobserved UV and IR flux. We find that the equation of Khatami & Kasen for radioactive $^{56}$Ni-powered transients with a single free parameter does not fit the observed peak time-luminosity relation of SE SNe. Instead, we find a correlation between $M_\mathrm{Ni}^\mathrm{tail}$, peak time, peak luminosity, and decline rate, which allows measuring individual $^{56}$Ni masses to a precision of 14%. Applying this method to the whole sample, we find, for SNe IIb, Ib, and Ic, mean $^{56}$Ni masses of $0.066\pm0.006$, $0.082\pm0.009$, and $0.132\pm0.011\,\mathrm{M}_{\odot}$, respectively. After accounting for their relative rates, for SE SNe as a whole we compute mean $^{56}$Ni and iron yields of $0.090\pm0.005$ and $0.097\pm0.007\,\mathrm{M}_{\odot}$, respectively. Combining these results with the recent Type II SN mean $^{56}$Ni mass derived by Rodríguez et al., core-collapse SNe, as a whole, have mean $^{56}$Ni and iron yields of $0.055\pm0.006$ and $0.058\pm0.007\,\mathrm{M}_{\odot}$, respectively. We also find that radioactive $^{56}$Ni-powered models typically underestimate the peak luminosity of SE SNe by 60-70%, suggesting the presence of an additional power source contributing to the luminosity at peak.

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arXiv2023

Analytic Model for Off-Axis GRB Afterglow Images -- Geometry Measurement and Implications for Measuring $H_0$

We present an analytic model for measuring the jet core angle ($θ_c$) and viewing angle ($θ_{obs}$) of off-axis gamma-ray bursts independently of the jet angular structure outside of the core. We model the images of off-axis jets and using this model we show that $θ_{obs}$ and $θ_c$ can be measured using any two of the three following observables: the afterglow light curve, the flux-centroid motion, and the image width. The model is calibrated using 2D relativistic hydrodynamic simulations with a broad range of jet angular structures. We study the systematic errors due to the uncertainty in the jet structure and find that when using the light curve and centroid motion to determine $θ_{obs}$ and $θ_c$, our formulae can be accurate to a level of $5-10\%$ and $30\%$, respectively. In light of the Hubble tension, the systematic error in $\cosθ_{obs}$ in GRBs originating in a binary compact object merger is of special interest. We find that the systematic uncertainty on the measurement of $\cosθ_{obs}$ due to the unknown jet structure is smaller than $1.5\%$ for well-observed events. A similar error is expected if the microphysical parameters evolve at a level that is not easily detected by the light curve. Our result implies that this type of systematic uncertainty will not prevent measurement of $H_0$ to a level of $2\%$ with a sample of well-observed GW events with resolved afterglow image motion. Applying our model to the light curve and centroid motion observations of GW170817 we find $θ_{obs}=19.2\pm 2~°$ (1$σ$) and $θ_c=1.5-4~°$.

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