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Donald C. Warren

Publications and source records attributed to Donald C. Warren.

18 recordsLinked to original sources

The hardest-hit home run?

We present a problem to be assigned or done as an in-class activity in an upper-division undergraduate course on computational physics. The problem involves a home run hit by Mickey Mantle on May 22, 1963, which he famously called ``the hardest ball I ever hit''. Is this home run truly one for the record books, or has it been eclipsed by players in the modern era? Modeling the trajectory of a baseball involves consideration of both wind resistance and the Magnus effect, and is an interesting application of numerical solution of ordinary differential equations. Ultimately, the answer is that Mantle would compare favorably to the most powerful batters currently playing, but to arrive at that conclusion we must reflect on the plausibility of results and sources of uncertainty.

physics.pop-ph

A closer look at parameter identifiability, model selection and handling of censored data with Bayesian Inference in mathematical models of tumour growth

Mathematical models (MMs) are a powerful tool to help us understand and predict the dynamics of tumour growth under various conditions. In this work, we use 5 MMs with an increasing number of parameters to explore how certain (often overlooked) decisions in estimating parameters from data of experimental tumour growth affect the outcome of the analysis. In particular, we propose a framework for including tumour volume measurements that fall outside the upper and lower limits of detection, which are normally discarded. We demonstrate how excluding censored data results in an overestimation of the initial tumour volume and the MM-predicted tumour volumes prior to the first measurements, and an underestimation of the carrying capacity and the MM-predicted tumour volumes beyond the latest measurable time points. We show in which way the choice of prior for the MM parameters can impact the posterior distributions, and illustrate that reporting the highest-likelihood parameters and their 95% credible interval can lead to confusing or misleading interpretations. We hope this work will encourage others to carefully consider choices made in parameter estimation and to adopt the approaches we put forward herein.

q-bio.QM

Numerical simulation of photospheric emission in long gamma-ray bursts: prompt correlations, spectral shapes, and polarizations

We explore the properties of photospheric emission in the context of long gamma-ray bursts (LGRBs) using three numerical models that combine relativistic hydrodynamical simulations and Monte Carlo radiation transfer calculations in three dimensions. Our simulations confirm that the photospheric emission gives rise to correlations between the spectral peak energy and luminosity that agree with the observed Yonetoku, Amati, and Golenetskii correlations. It is also shown that the spectral peak energy and luminosity correlate with the bulk Lorentz factor, as indicated in the literature. On the other hand, synthetic spectral shapes tend to be narrower than those of the observations. The result indicates that an additional physical process that can provide non-thermal broadening is needed to reproduce the spectral features. Furthermore, the polarization analysis finds that, while the degree of polarization is low for the emission from the jet core ($Π< 4~\%$), it tends to increase with the viewing angle outside the core and can be as high as $Π\sim 20-40~\%$ in an extreme case. This suggests that the typical GRBs show systematically low polarization compared to softer, dimmer counterparts (X-ray-rich GRBs and X-ray flashes). Interestingly, our simulations indicate that photospheric emission exhibits large temporal variation in the polarization position angle ($Δψ\sim 90^{\circ}$), which may be compatible with those inferred in observations. A notable energy dependence of the polarization property is another characteristic feature found in the current study. Particularly, the difference in the position angle among different energy bands can be as large as $\sim 90^{\circ}$.

astro-ph.HE

The double detonation of a double degenerate system, from Type Ia supernova explosion to its supernova remnant

Type Ia supernovae (SNe) are believed to be caused by the thermonuclear explosion of a white dwarf (WD), but the nature of the progenitor system(s) is still unclear. Recent theoretical and observational developments have led to renewed interest in double degenerate models, in particular the "helium-ignited violent merger" or "dynamically-driven double-degenerate double-detonation" (D$^6$). In this paper we take the output of an existing D$^6$ SN model and carry it into the supernova remnant (SNR) phase up to 4000 years after the explosion, past the time when all the ejecta have been shocked. Assuming a uniform ambient medium, we reveal specific signatures of the explosion mechanism and spatial variations intrinsic to the ejecta. The first detonation produces an ejecta tail visible at early times, while the second detonation leaves a central density peak in the ejecta that is visible at late times. The SNR shell is off-centre at all times, because of an initial velocity shift due to binary motion. The companion WD produces a large conical shadow in the ejecta, visible in projection as a dark patch surrounded by a bright ring. This is a clear and long-lasting feature that is localized, and its impact on the observed morphology is dependent on the viewing angle of the SNR. These results offer a new way to diagnose the explosion mechanism and progenitor system using observations of a Type Ia SNR.

astro-ph.HE

Examining Two-Dimensional Luminosity-time Correlations for Gamma Ray Burst Radio Afterglows with VLA and ALMA

Gamma-ray burst (GRB) afterglow emission can be observed from sub-TeV to radio wavelengths, though only 6.6\% of observed GRBs present radio afterglows. We examine GRB radio light curves (LCs) to look for the presence of radio plateaus, resembling the plateaus observed in X-ray and optical. We analyze 404 GRBs from the literature with observed radio afterglow and fit 82 GRBs with at least 5 data points with a broken power law (BPL) model, requiring 4 parameters. From these, we find 18 GRBs that present a break feature resembling a plateau. We conduct the first multi-wavelength study of the Dainotti correlation between the luminosity $L_a$ and the rest-frame time of break $T_a^*$ for those 18 GRBs, concluding that the correlation exists and resembles the corresponding correlation in X-ray and optical wavelengths after correction for evolutionary effects. We compare the $T_a^*$ for the radio sample with $T_a^*$ values in X-ray and optical data (Dainotti et al. 2013, 2020b), finding significantly later break times in radio. We propose that this late break time and compatibility in slope suggests either a long-lasting plateau or the passage of a spectral break in the radio band. We also correct the distribution of the isotropic energy $E_{\rm iso}$ vs. the rest-frame burst duration $T^*_{90}$ for evolutionary effects and conclude that there is no significant difference between the $T^*_{90}$ distribution for the radio LCs with a break and those without.

astro-ph.HE

A semi-analytic afterglow with thermal electrons and synchrotron self-Compton emission

We extend previous work on gamma-ray burst (GRB) afterglows involving hot thermal electrons at the base of a shock-accelerated tail. Using a physically-motivated electron distribution based on first-principles simulations, we compute broadband emission from radio to TeV gamma-rays. For the first time, we present the effects of a thermal distribution of electrons on synchrotron self-Compton (SSC) emission. The presence of thermal electrons causes temporal and spectral structure across the entire observable afterglow, which is substantively different from models that assume a pure power-law distribution for the electrons. We show that early-time TeV emission is enhanced by more than an order of magnitude for our fiducial parameters, with a time-varying spectral index that does not occur for a pure power law of electrons. We further show that the X-ray "closure relations" take a very different, also time-dependent, form when thermal electrons are present; the shape traced out by the X-ray afterglows is a qualitative match to observations of the traditional decay phase.

astro-ph.HE

Time to revisit the endpoint dilution assay and to replace TCID$_{50}$ and PFU as measures of a virus sample's infection concentration

The infectivity of a virus sample is measured by the infections it causes, via a plaque or focus forming assay (PFU or FFU) or an endpoint dilution (ED) assay (TCID$_{50}$, CCID$_{50}$, EID$_{50}$, etc., hereafter collectively ID$_{50}$). The counting of plaques or foci at a given dilution intuitively and directly provides the concentration of infectious doses in the undiluted sample. However, it has many technical and experimental limitations. For example, it relies on one's judgement in distinguishing between two merged plaques and a larger one, or between small plaques and staining artifacts. In this regard, ED assays are more robust because one need only determine whether infection occurred. The output of the ED assay, the 50% infectious dose (ID$_{50}$), is calculated using either the Spearman-Karber (SK, 1908,1931) or Reed-Muench (RM, 1938) mathematical approximations. However, these are often miscalculated and their ID$_{50}$ approximation is biased. We propose that the PFU and FFU assays be abandoned, and that the measured output of the ED assay, the ID$_{50}$, be replaced by a more useful measure we coined Specific INfections (SIN). We introduce a free, open-source web-application, midSIN, that computes the SIN concentration in a virus sample from a standard ED assay, requiring no changes to current experimental protocols. We demonstrate that the SIN/mL of a sample reliably corresponds to the number of infections the sample will cause per unit volume, and directly relates to the multiplicity of infection. midSIN estimates are shown to be more accurate and robust than those using the RM and SK approximations. The impact of ED plate design choices (dilution factor, replicates per dilution) on measurement accuracy is also explored. The simplicity of SIN as a measure and the greater accuracy of midSIN make them an easy, superior replacement for the PFU, FFU, and ID$_{50}$ measures.

q-bio.QM

From supernova to supernova remnant: comparison of thermonuclear explosion models

Progress in the three-dimensional modeling of supernovae (SN) prompts us to revisit the supernova remnant (SNR) phase. We continue our study of the imprint of a thermonuclear explosion on the SNR it produces, that we started with a delayed-detonation model of a Chandrasekhar-mass white dwarf. Here we compare two different types of explosion models, each with two variants: two delayed detonation models (N100ddt, N5ddt) and two pure deflagration models (N100def, N5def), where the N number parametrizes the ignition. The output of each SN simulation is used as input of a SNR simulation carried on until 500 yr after the explosion. While all SNR models become more spherical over time and overall display the theoretical structure expected for a young SNR, clear differences are visible amongst the models, depending on the geometry of the ignition and on the presence or not of detonation fronts. Compared to N100 models, N5 models have a strong dipole component, and produce asymmetric remnants. N5def produces a regular-looking, but offset remnant, while N5ddt produces a two-sided remnant. Pure deflagration models exhibit specific traits: a central over-density, because of the incomplete explosion, and a network of seam lines across the surface, boundaries between burning cells. Signatures from the SN dominate the morphology of the SNR up to 100 yr to 300 yr after the explosion, depending on the model, and are still measurable at 500 yr, which may provide a way of testing explosion models.

astro-ph.HE

The maximum energy of shock-accelerated electrons in a microturbulent magnetic field

Relativistic shocks propagating into a medium with low magnetization are generated and sustained by small-scale but very strong magnetic field turbulence. This so-called "microturbulence" modifies the typical shock acceleration process, and in particular that of electrons. In this work we perform Monte Carlo (MC) simulations of electrons encountering shocks with microturbulent fields. The simulations cover a three-dimensional parameter space in shock speed, acceleration efficiency, and peak magnetic field strength. From these, a Markov Chain Monte Carlo (MCMC) method was employed to estimate the maximum electron momentum from the MC-simulated electron spectra. Having estimated this quantity at many points well-distributed over an astrophysically relevant parameter space, an MCMC method was again used to estimate the parameters of an empirical formula that computes the maximum momentum of a Fermi-accelerated electron population anywhere in this parameter space. The maximum energy is well-approximated as a broken power-law in shock speed, with the break occurring when the shock decelerates to the point where electrons can begin to escape upstream from the shock.

astro-ph.HE

3D modeling from the onset of the SN to the full-fledged SNR: Role of an initial ejecta anisotropy on matter mixing

The aim of this work is to bridge the gap between CC SNe and their remnants by investigating how post-explosion anisotropies in the ejecta influence the structure and chemical properties of the remnant at later times. We performed three-dimensional magneto-hydrodynamical simulations starting soon after the SN event and following the evolution of the system in the circumstellar medium (consisting of the wind of the stellar progenitor), for 5000 years, obtaining the physical scenario of a SNR. Here we focused the analysis on the case of a progenitor red supergiant of 19.8 M_sun. We also investigated how a post-explosion large-scale anisotropy in the SN affects the ejecta distribution and the matter mixing of heavy elements in the remnant, during the first 5000 years of evolution. In the case of a spherically symmetric SN explosion without large-scale anisotropies, the remnant roughly keeps memory of the original onion-like layering of ejecta soon after the SN event. Nevertheless, as the reverse shock hits the ejecta, the element distribution departs from a homologous expansion, because of the slowing down of the outermost ejecta layers due to interaction with the reverse shock. In the case of a large-scale anisotropy developed after the SN, we found that the chemical stratification in the ejecta can be strongly modified and the original onion-like layering is not preserved. The anisotropy may cause spatial inversion of ejecta layers, for instance leading to Fe/Si-rich ejecta outside the O shell, and may determine the formation of Fe/Si-rich jet-like features that may protrude the remnant outline. The level of matter mixing and the properties of the jet-like feature are sensitive to the initial physical (density and velocity) and geometrical (size and position) initial characteristics of the anisotropy.

astro-ph.HE

From the supernova to the supernova remnant: the three-dimensional imprint of a thermonuclear explosion

Recent progress in the three-dimensional modeling of supernovae (SN) has shown the importance of asymmetries for the explosion. This calls for a reconsideration of the modeling of the subsequent phase, the supernova remnant (SNR), which has commonly relied on simplified ejecta models. In this paper we bridge SN and SNR studies by using the output of a SN simulation as the input of a SNR simulation carried on until 500~yr. We consider the case of a thermonuclear explosion of a carbon-oxygen white dwarf star as a model for a Type Ia SN; specifically we use the N100 delayed detonation model of Seitenzahl et al 2013. In order to analyze the morphology of the SNR, we locate the three discontinuities that delineate the shell of shocked matter: the forward shock, the contact discontinuity, and the reverse shock, and we decompose their radial variations as a function of angular scale and time. Assuming a uniform ambient medium, we find that the impact of the SN on the SNR may still be visible after hundreds of years. Previous 3D simulations aiming at reproducing Tycho's SNR, that started out from spherically symmetric initial conditions, failed to reproduce structures at the largest angular scales observed in X-rays. Our new simulations strongly suggest that the missing ingredient was the initial asymmetries from the SN itself. With this work we establish a way of assessing the viability of SN models based on the resulting morphology of the SNR.

astro-ph.HE

The photospheric origin of the Yonetoku relation in gamma-ray bursts

Long duration gamma-ray bursts (GRBs), the brightest events since the Big Bang itself, are believed to originate in an ultra-relativistic jet breaking out from a massive stellar envelope. Despite decades of study, there is still no consensus on their emission mechanism. One unresolved question is the origin of the tight correlation between the spectral peak energy Ep and peak luminosity Lp discovered in observations. This Yonetoku relation is the tightest correlation found in the properties of the prompt phase of GRB emission, providing the best diagnostic for the radiation mechanism. Here we present 3D hydrodynamical simulations, and post-process radiation transfer calculations, of photospheric emission from a relativistic jet. Our simulations reproduce the Yonetoku relation as a natural consequence of viewing angle. Although jet dynamics depend sensitively on luminosity, the Ep-Lp correlation holds regardless. This result strongly suggests that photospheric emission is the dominant component in the prompt phase of GRBs.

astro-ph.HE

Synchrotron self-absorption in GRB afterglows: the effects of a thermal electron population

In the standard synchrotron afterglow model, a power law of electrons is responsible for all aspects of photon production and absorption. Recent numerical work has shown that the vast majority of particles in the downstream medium are actually "thermal" particles, which were shock-heated but did not enter the Fermi acceleration process (the name stands in contrast to the nonthermal high-energy tail, rather than connoting a Maxwellian distribution). There are substantial differences at optical and higher energies when these thermal electrons participate in the afterglow, but early work along these lines ignored the radio end of the electromagnetic spectrum. We report here on an extension of previous Monte Carlo simulations of gamma-ray burst afterglows. The model now includes the synchrotron self-absorption (SSA) process and so can simulate afterglows across the entire EM spectrum, and several orders of magnitude in time. In keeping with earlier work, inclusion of the thermal electrons increases the SSA frequency by a factor of 30, and the radio intensity by a factor of 100. Furthermore, these changes happen with no modification to the late optical or X-ray afterglow. Our results provide very strong evidence that thermal electrons must be considered in any multiwavelength model for afterglows.

astro-ph.HE

Nonlinear particle acceleration and thermal particles in GRB afterglows

The standard model for GRB afterglow emission treats the accelerated electron population as a simple power law, $N(E) \propto E^{-p}$ for $p \gtrsim 2$. However, in standard Fermi shock acceleration a substantial fraction of the swept-up particles do not enter the acceleration process at all. Additionally, if acceleration is efficient then the nonlinear backreaction of accelerated particles on the shock structure modifies the shape of the non-thermal tail of the particle spectra. Both of these modifications to the standard synchrotron afterglow impact the luminosity, spectra, and temporal variation of the afterglow. To examine the effects of including thermal particles and nonlinear particle acceleration on afterglow emission, we follow a hydrodynamical model for an afterglow jet and simulate acceleration at numerous points during the evolution. When thermal particles are included, we find that the electron population is at no time well-fitted by a single power law, though the highest-energy electrons are; if the acceleration is efficient, then the power law region is even smaller. Our model predicts hard-soft-hard spectral evolution at X-ray energies, as well as an uncoupled X-ray and optical light curve. Additionally, we show that including emission from thermal particles has drastic effects (factors of 100 and 30, respectively) on the observed flux at optical and GeV energies. This enhancement of GeV emission makes afterglow detections by future $γ$-ray observatories, such as CTA, very likely.

astro-ph.HE

Particle spectra and efficiency in nonlinear relativistic shock acceleration: survey of scattering models

We include a general form for the scattering mean free path in a nonlinear Monte Carlo model of relativistic shock formation and Fermi acceleration. Particle-in-cell (PIC) simulations, as well as analytic work, suggest that relativistic shocks tend to produce short-scale, self-generated magnetic turbulence that leads to a scattering mean free path (mfp) with a stronger momentum dependence than the mfp ~ p dependence for Bohm diffusion. In unmagnetized shocks, this turbulence is strong enough to dominate the background magnetic field so the shock can be treated as parallel regardless of the initial magnetic field orientation, making application to gamma-ray bursts (GRBs), pulsar winds, Type Ibc supernovae, and extra-galactic radio sources more straightforward and realistic. In addition to changing the scale of the shock precursor, we show that, when nonlinear effects from efficient Fermi acceleration are taken into account, the momentum dependence of the mfp has an important influence on the efficiency of cosmic-ray production as well as the accelerated particle spectral shape. These effects are absent in nonrelativistic shocks and do not appear in relativistic shock models unless nonlinear effects are self-consistently described. We show, for limited examples, how the changes in Fermi acceleration translate to changes in the intensity and spectral shape of gamma-ray emission from proton-proton interactions and pion-decay radiation.

astro-ph.HE

Photospheric Emission from Collapsar Jets in 3D Relativistic Hydrodynamics

We explore the photospheric emission from a relativistic jet breaking out from a massive stellar envelope based on relativistic hydrodynamical simulations and post-process radiation transfer calculations in three dimensions. To investigate the impact of three-dimensional (3D) dynamics on the emission, two models of injection conditions are considered for the jet at the center of the progenitor star: one with periodic precession and another without precession. We show that structures developed within the jet due to the interaction with the stellar envelope, as well as due to the precession, have a significant imprint on the resulting emission. Particularly, we find that the signature of precession activity by the central engine is not smeared out and can be directly observed in the light curve as a periodic signal. We also show non-thermal features, which can account for observations of gamma-ray bursts, are produced in the resulting spectra, even though only thermal photons are injected initially and the effect of non-thermal particles is not considered.

astro-ph.HE

Electron and Ion Acceleration in Relativistic Shocks with Applications to GRB Afterglows

We have modeled the simultaneous first-order Fermi shock acceleration of protons, electrons, and helium nuclei by relativistic shocks. By parameterizing the particle diffusion, our steady-state Monte Carlo simulation allows us to follow particles from particle injection at nonthermal thermal energies to above PeV energies, including the nonlinear smoothing of the shock structure due to cosmic-ray (CR) backpressure. We observe the mass-to-charge (A/Z) enhancement effect believed to occur in efficient Fermi acceleration in non-relativistic shocks and we parameterize the transfer of ion energy to electrons seen in particle-in-cell (PIC) simulations. For a given set of environmental and model parameters, the Monte Carlo simulation determines the absolute normalization of the particle distributions and the resulting synchrotron, inverse-Compton, and pion-decay emission in a largely self-consistent manner. The simulation is flexible and can be readily used with a wide range of parameters typical of gamma-ray burst (GRB) afterglows. We describe some preliminary results for photon emission from shocks of different Lorentz factors and outline how the Monte Carlo simulation can be generalized and coupled to hydrodynamic simulations of GRB blast waves. We assume Bohm diffusion for simplicity but emphasize that the nonlinear effects we describe stem mainly from an extended shock precursor where higher energy particles diffuse further upstream. Quantitative differences will occur with different diffusion models, particularly for the maximum CR energy and photon emission, but these nonlinear effects should be qualitatively similar as long as the scattering mean free path is an increasing function of momentum.

astro-ph.HE

Monte Carlo Simulations of Nonlinear Particle Acceleration in Parallel Trans-relativistic Shocks

We present results from a Monte Carlo simulation of a parallel collisionless shock undergoing particle acceleration. Our simulation, which contains parameterized scattering and a particular thermal leakage injection model, calculates the feedback between accelerated particles ahead of the shock, which influence the shock precursor and "smooth" the shock, and thermal particle injection. We show that there is a transition between nonrelativistic shocks, where the acceleration efficiency can be extremely high and the nonlinear compression ratio can be substantially greater than the Rankine-Hugoniot value, and fully relativistic shocks, where diffusive shock acceleration is less efficient and the compression ratio remains at the Rankine-Hugoniot value. This transition occurs in the trans-relativistic regime and, for the particular parameters we use, occurs around a shock Lorentz factor = 1.5. We also find that nonlinear shock smoothing dramatically reduces the acceleration efficiency presumed to occur with large-angle scattering in ultra-relativistic shocks. Our ability to seamlessly treat the transition from ultra-relativistic to trans-relativistic to nonrelativistic shocks may be important for evolving relativistic systems, such as gamma-ray bursts and type Ibc supernovae. We expect a substantial evolution of shock accelerated spectra during this transition from soft early on to much harder when the blast-wave shock becomes nonrelativistic.

physics.space-ph