Supernova explosions and Nucleosynthesis

I) Explosive nucleosynthesis in core collapse SNe

Click to enlarge

Core-collapse supernovae (CCSNe), the death of massive stars, are one of the most drastic explosions in the Universe. However, the mechanism of CCSNe has not been understood theoretically even by recent supercomputing efforts. Multi-dimensional effects would be the keys ot understand the mechanism. Therefore, 3-D simulations of CCSNe are highly desired although they are typically very challenging. For example, hydrodynamical instabilities affect not only the feasibility of the explosion but also the mixing of the ejected matter, which is partly composed of newly-synthesized heavy elements (e.g., radioactive56Ni and even heavier metals) born in the explosive nucleosynthesis. Actually, observations of SN1987A (the most frequently observed SN) imply that some 56Ni synthesized is conveyed into outer layer of the star by the mixing in contrast with sample spherical (i.e. 1-D) estimations. 

Most of previous simulations considering the hydrodynamc mixing in core-collapse supernova envelops failed to reproduce fast moving 56Ni beyond 2000 km/s, as suggested by observations of SN1987A. However in these simulations the large scale asymmetries, which are generated naturally from hydrodynamic instabilities during the explosion phase of core-collapse supernova, are often neglected. The explosion is usually assumed to be spherically symmetric, and small scale perturbations are added artificially after the explosion to break the symmetry. The presence of the large scale asymmetries should help facilitating mixing processes to convey 56Ni to the outer layers of the exploding star. Thus, our group is interested in performing state-of-the-art long-time 3D core-collapse supernova simulations which follow the complete time evolution from the onset of the explosion until late times. These simulations are extremely computationally challenging because vast length- and timescales must be resolved in the simulations. However, recent development in high performance computing has made these simulations become feasible.

CCSNe play an important role as factories of heavy elements, e.g., "Gold". If rapid neutron capture process (r-process) occurs in CCSNe, heavy elements including Gold could be synthesized. However, the specific type(s) of CCSNe that can realize the r-process, or whether CCSNe are resposible for the creation of r-process elements in the first place are not clear. Recently, the Radioactive Isotope Beam Factory (RIBF) facility in RIKEN are starting to unveil the important features of unstable nuclei related to r-process. Our group tries to figure out the mechanism of CCSNe and the origin of heavy elements using state-of-the-art numerical simulations and the most up-to-date experimental results obtained by RIBF.

The calculated dynamics of the outburst of a star (shock breakout and supernova), as if it would be visible to an observer.

Phenomenon of supernovae in most cases should start with a bright flash, caused by a shock wave emerging from the surface of the progenitor stars after the phase of collapse of thermonuclear explosion in their interiors. The detection of such outbursts associated with the supernova shock breakout can be used to obtain information about the explosion properties and pre-supernova parameters, which is necessary to understand the physical processes that underlie this phenomenon.

Study of supernova shock breakouts has become particularly timely owing to the recent detections of this phenomenon by the SWIFT and GALEX missions. The number of future/ongoing wide and/or deep-field surveys capable of observing shock breakouts is also increasing dramatically, including PTF, LOSS, CRTS, KWFC, Skymapper, DES, Pan-STARS and Subaru/HSC, LSST.

Shock propagation at the epoch of shock breakout cannot be considered as adiabatic, which makes it difficult to construct analytical solutions. This necessitates the usage of numerical calculations of the process in which radiative transport plays a very important role. Our group approaches this problem using multi-group radiation hydrodynamics codes STELLA and RADA that allow us to calculate shock breakout for compact pre-supernovae and take into account a number of relativistic effects

Supernova Remnants

Simulated image of a SNR, as would be observed in X-rays, 500 yr after a N100 explosion. Left: starting from (effectively 1D) spherically symmetric initial conditions, right: starting from realistic (fully 3D) realistic initial conditions. The morphology of the SNR bears the imprint of the explosion. Morphology of a D6 SNR up to 2000 yr. Shown is the projection of the density squared, which is a proxy for the thermal X-ray emission in the shocked region. The presence of a surviving WD companion affects the development of the SNR up to late ages.

After the explosion of a star as a supernova, a supernova remnant (SNR) is formed by the interaction of stellar ejecta with the interstellar medium. Young SNRs are characterized by strong shocks that heat and ionize the gas, generate magneto-hydrodynamic turbulence, and accelerate particles to relativistic energies. They radiate at all wavelengths, especially in the X-ray domain, where spectro-imaging observations can provide a wealth of information on the shock dynamics and the explosion physics.

I) Particle acceleration and the origin of cosmic rays

Our research activities also involve the study of cosmic rays (CRs) with a Galactic origin, especially on their very probable link with supernova remnants (SNRs), using the latest numerical techniques and sometimes also analysis of observation data from space telescopes. SNRs are objects known to emit very energetic photons in X-ray and Gamma-ray, that must be produced by local populations of high-energy particles. Existence of strong collision-less (magnetic) shocks have been confirmed in SNRs, which can indeed accelerate charged particle locally to relativistic energies via the Nonlinear Diffusive Shock Acceleration (NL-DSA) mechanism with very appreciable efficiencies. Unfortunately, the confirmation of CR production at SNRs and their shocks is a very nontrivial task since CRs are deflected by the magnetic field in Milky Way and hence cannot be measured directly from their sources. However, many SNRs can be observed across the whole frequency spectrum, spanning from radio to TeV gamma-ray energies. A good understanding of the multi-wavelength emission from these cosmic accelerators is absolutely key to unravel the long-standing puzzle of Galactic CR origin.

Because of the tight coupling between the plasma and the particles in NL-DSA, and the wide range of space-, time- and energy-scales involved, we mostly rely on numerical simulations, that couple hydrodynamic and kinetic approaches. Our group performs 1-D (with micro-physics) and global multi-D hydrodynamical simulations to study the dynamics, particle acceleration, broadband emission and neutrino production for various types of SNRs. Our results can be directly compared with current and future observations from radio to TeV energies to accurately quantify the contribution of SNRs to the production of CRs within Milky Way and in other galaxies similar to ours. Meanwhile, we have started to tie our code to dedicated multi-D simulations of SN explosions and nucleosynthesis, that will provide us a consistent evolutionary picture of the very last stages of stellar evolution and their contributions to chemical enrichment of the interstellar space. We have been performing simulations of the evolution and emission from young supernova remnants in 3D, for the first time including both the development of Rayleigh-Taylor instabilities and efficient particle acceleration. The simulations are post-processed at a given age to compute both the thermal emission from the shocked plasma (in the X-ray band), that is out of ionization equilibrium, and the non-thermal emission from the accelerated particles (in the radio to X-ray band), that depends on the fate of the magnetic field. This uniquely enables us to produce realistic synthetic maps, as observed in projection. This allows us to assess the impact of CRs on the morphology of the remnant.

II) From the supernova engine to the supernova remnant

Another very interesting question is to what extent and for how long the SNR bears the signature of the initial explosion. Type Ia SNe are believed to mark the thermonuclear explosion of a white dwarf (WD). Despite their importance in cosmology, their explosion mechanism is still unclear. It is unknown whether they are produced by single-degenerate progenitors, via accretion, or by double-generate progenitors, via mergers – or a mixture of both, or other mechanisms. Recent progress in the simulation of SNe has shown the importance of turbulence and asymmetries in successful explosions, which prompts us to revisit the subsequent phase, the remnant phase. Can we use the SNR morphology as a probe of the explosion mechanism? Recent work by Orlando et al has shown the interest of this approach for a core-collapse SNR like Cas A. We have been arguing for the case of a Type Ia SNR like Tycho. First, we have run 3D simulations of a SNR starting from the output of a 3D simulation of a canonical SN model, the thermonuclear explosion of a Chandrasekhar-mass carbon-oxygen WD (model N100). By analyzing the wavefronts we were able to quantify the imprint of the explosion on the remnant over time. Assuming a uniform ambient medium, we found that the impact of the SN on the SNR may still be visible after hundreds of years. The newly simulated maps look more realistic than in previous works based on spherically symmetric ejecta profiles. Second, we have made a comparative study of four different explosion models, still for a single WD of Chandrasekhar-mass, but with different levels of asymmetry. These were obtained by varying the number of ignition points (N100 vs N5) and the propagation of the flame (ddt = deflagration to detonation transition, def = pure deflagration). We observed that N100 models produce different remnants than N5 models: the latter produce asymmetric remnants, an asymmetric shell for N5ddt, a regular but off-set shell for N5def; and that ddt models produce different remnants than def models: the latter show a peaked remnant at the centre and large-scale plumes at the edge. Third, we considered a different kind of model, where the primary WD explodes via a double detonation, despite being of sub-Chandrasekhar mass, while the secondary WD survives and is ejected away. This has been called a dynamically-driven double-degenerate double-detonation or D6. We simulated in 3D for the first time the evolution of a D6 SNR for thousands of years after the explosion. Assuming a uniform ambient medium, we revealed specific signatures of the progenitor system and explosion mechanism. In particular the companion WD produces a large and lasting conical shadow in the ejecta. Our work shows the intrinsic diversity of thermonuclear SNe and their remnants, and offers new perspectives for the interpretation of observations of young nearby SNRs. The combination of 3D simulations and spatially resolved spectroscopic observations of SNRs will enable us to better constrain explosion mechanism(s).

Recent publications

1. Ferrand, Warren, Ono, Nagataki, Röpke, Seitenzahl, “From supernova to supernova remnant: the three-dimensional imprint of a thermonuclear explosion”, ApJ, 877, 136, 2019
2. Ferrand, Warren, Ono, Nagataki, Röpke, Seitenzahl, Lach, Iwasaki, Sato, “From Supernova to Supernova Remnant: comparison of thermonuclear explosion models”, ApJ, 906, id. 93, 2021
3. Ferrand, Tanikawa, Warren, Nagataki, Safi-Harb, Decourchelle, “The double detonation of a double degenerate system, from Type Ia supernova explosion to its supernova remnant”, ApJ, 930, id. 92, 2022
4. Online gallery of interactive 3D models (link to Ferrand's personal page)
   

Neutron Star Mergers and r-process Nucleosynthesis

Combined abundance pattern (mass fraction as function of mass number) of elements synthesized in outflows of binary neutron-star and neutron-star black-hole mergers and their remnants as resulting in some of our simulations (colored symbols). The remarkable similarity to the r-process pattern observed in our Sun (black circles) suggests neutron-star mergers as a possible source of these elements.

The mergers of two neutron stars or of a neutron star with a black hole are spectacular and very energetic events that have been intensively studied already for several decades, even despite the lack of a single direct observation up to the present day. However, after the recent discovery of binary black-hole mergers by the gravitational-wave detector LIGO, and therefore the first direct proof of the existence of gravitational waves, there is ample reason to expect also the first observations of neutron-star mergers very soon. One of the aspects that makes these events so fascinating and that is studied in our group is that during and after a neutron-star merger a substantial amount of matter from the newly disrupted neutron star(s) can be expelled into the interstellar medium. If this outflow material is massive enough and has a sufficiently high neutron density, the rapid-neutron-capture (r-) process could be activated. This, in turn, could mean that not (only) core-collapse supernovae but (also) neutron-star mergers are siginificant sources of the heaviest elements in our Universe. Another long-standing puzzle connected with neutron-star mergers is represented by the question if these events are viable central engines of short gamma-ray burst (sGRB), which are regularly observed by telescopes but whose origin is still unidentified. We study these questions by means of neutrino-hydrodynamics simulations, i.e. by solving numerically the time-dependent equations describing the motion of the neutron-star fluid and the transport of neutrinos. The latter type of equations are numerically cumbersome but are of major importance to properly follow the composition and energetic properties of the remnant of the neutron-star merger.

Explosion Mechanism of Gamma-ray Bursts

I) 3-D general-relativistic magnetohydrodynamics

An example of 3-D GRMHD simulation on formation of a relativistic jet using YAMATO code The rapidly rotating black hoke is driving a relativistic jet with a help of magnetic fields (white curves). Colors represent density contours.

It is an observational fact that some gamma-ray bursts (GRBs) happen together with CC-SNe. The explosion energy of these supernovae can be ten times larger than that of normal core-collapse supernovae. Therefore, the central engine of GRBs should be entirely different from normal core-collapse supernovae, although its detailed mechanism is still poorly understood. We are challenging ourselves to understand the explosion mechanism with help of super-computing power, the developing the state-of-the-art General Relativisitic Magneto-Hydro Dynamic (GRMHD) code, a.k.a. the YAMATO code (YAMATO "大和" is the histric name of "JAPAN").

We are particularly interested in the mechanism of energy extraction from a rotating black hole which is expected to form as a result of the core-collapse of a rapidly rotating massive star. In principle, according to general relativity, it is possible to extract rotational energy from a rotating black hole. We are investigating whether this effect is self-sufficient to drive the most powerful explosions in the Universe (GRBs + CC-SNE).

1. S. Nagataki, "Rotating BHs as Central Engine of Long GRBs: Faster is Better", PASJ 63, 1243-1249, 2011
2. S. Nagataki, "Development of General Relativistic Magnetohydrodynamic Code and its Application to Central Engine of Long Gamma-Ray Bursts", ApJ 704-950, 2009

II) GRB jet propagation in progenitor stars

A grand challenge in the GRB jet is to construct a self-consistent theory that is responsible for the generation, acceleration, and collimation of the relativistic jet. The interaction of the relativistic jet with the progenitor star and interstellar medium is very important to reveal global dynamics and structure of the GRB jet. The hydrodynamical structure of the relativistic jet is also important in order to produce GRB emission. Our group investigates the physics of the propagation of the relativistic jet in the progenitor star through 3-D numerical simulations. The basic property of the propagation of the relativistic jet through the ambient medium is useful for understanding the jet dynamics in other systems such as AGNs and microquasars.

III) Multi-fluid simulations of relativistic outflows

It is now well recognized that magnetic fields play a very important role in many astrophysical phenomena and in particular in those involving relativistic outflows. The magnetic fields are likely to be involved in launching, powering and collimation of such outflows. The dynamics of relativistic magnetized plasma can be studied using diverse mathematical frameworks. The most developed one so far is the single fluid ideal relativistic Magnetohydrodynamics (RMHD). The framework of resistive RMHD allows to incorporate this magnetic dissipation but the inevitably phenomenological nature of its Ohm's law puts constraints on its robustness. At the other extreme is the particle dynamics, describling the motion of individual charges in their collective electromagnetic field. The numerical stability considerations require particle-in-cell (PIC) codes to resolve the scales of plasma oscillations. The accuracy considerations can be even more demanding, pushing toward the particle gyration scales.

Somewhere in between lies the multi-fluid approximation, where plasma is modeled as a collection of several inter-penetrating charged and neutral fluids, coupled via macroscopic electromagnetic field and inter-fluid friction. Undoubtedly, this approach is not as comprehensive in capturing the microphysics of collisionless plasma as the particle dynamics (and kinetics) simulations. However, it does this better than the single-fluid MHD treatment. The ability of two-fluid approach to decribe accurately the magnetic reconnection phenomenon is probably the most important advacate for this method. The inter-fluid friction term is analogous to resistivity. In the absence of extact analytic solutions of equations with non-vanishing inter-fluid friction term, we are force to try problems for which this term is expected to be of critical significance. This important problem merits a comprehensive study, which we are planning to carry out in the near future.

Recent publications

1. Barkov M, Komissarov S., Korolev V., Zankovich A., "A multi-dimensional numerical shecme for two-fluid Relativistic MHD", MNRAS, 438, 704-716, 2014
   

Emission Mechanisms of Gamma-ray Bursts

I) Photospheric emission and Monte Carlo simulations

Example of emission spectrum from a relativistic jet obtained by performing a Monte Carlo simulation of radiative transfer. Jets having a stratified structure can successfully reproduce the typical spectrum of GRBs.

Gamma-ray burst is the most luminous phenomena in the Universe. It is believed to be induced by an ultra-relativistic jets originating from a compact objects. However, exactly how the gamma-rays are produced within the jet is still under hot debates. Recently, the so-called "photospheric emission model" is considered to be one of the most promissing candidates for GRB emission mechanism. In this model, the gamma-rays are emitted from the jet when it becomes transparent to radiation. Since the interaction with the jet material plays an important role in determining the properties of the emitted gamma-rays, detailed radiative transfer calculations are essential to model the GRB phorospheric emission.

In our group, we approach this problem by performing Monte Carlo simulations that solve the propagation of gamma-rays within the jet. We are particularly interested in how the hydrodynamical structure of the GRB jet influences the properties of the resultant emission, including its spectrum, polarization and light curves. Starting from a series of toy models of jet structures, we are investigating the conditions udner which the photosheric emission can successfully reproduce the observed characteristics of GRBs.

II) Jitter radiation model

Explorations of physical processes related to random and small-scale magnetic fields are exciting and can be highly related to GRB emission. Jitter radiation, which involves relativistic electrons radiating in random and small-scale magnetic fields, can be applied to explain high-energy emission of AGNs and GRBs. We also explore the possibility that high polarization degree discovered in some GRBs in high-energy can be reproduced by the jitter polarization process. Compton scattering of jitter photons can be also applied to explain the GeV emission of some special classes of GRBs.

III) Novel radiation mechanisms

Our group also investigate more general radiation mechanisms than the jitter radiation. In the emission regions of GRBs, we can expect turbulent electromagnetic fields which are generated by some plasma instabilities. The radiation spectra from accelerated electrons in such turbulences have not been fully investigated. We employ first principle numerical method to clarify them. We have found novel emission spectrum in the intermediate regime between synchrotron regime and jitter regime. Also, we have clarify the general properties of radiation spectra for the Langmuir turbulences. The radiation properties for more general turbulences are going to be investigated.

IV) Optical observations of GRBs

Follow-up observation of GRBs is another interesting research topic carried out in our group. Multi-wavelength observations are more than essential to understand the mysterious phenomenon of GRBs. We regularly perform ground-based optical follow-up observations of GRBs detected in X-ray, mostly by the Swift satellite. In addition, observations are forged with theoretical explanations for GRB host galaxies in our group to revearl the true identify of GRB central engine.

Gamma-ray Burst as Cosmological Tool

GRBs are the farthest and the most powerful objects ever observed in the universe and therefore can be useful probes for testing cosmological models. To this end, it is crucial to understand if they can be considered as standard candles (astronomical objects whose luminosity is known or can be derived from other distance-independent observables). At first sight, GRBs seem to be far from standard candles, with their energies spanning over 8 orders of magnitude. However, discovering universal relations among the observables properties of GRBs plays a  crucial role  in determining whether they  can be considered standard candles and can provide insight intor the processes responsible for GRBs.

Within this framework, Dainotti et al. (2008) discovered a new correlation for long GRBs between the  X-ray luminosity at the end of the plateau phase, L_x and its duration, T^*_a (see figure).  This correlation has been updated (Dainotti et al. 2010) used as possible redshift estimator (Dainotti et al. 2011a), applied as cosmological tool (Cardone et al. 2009;2010) recently corrected for selection effects (Dainotti et al. 2013a). Caveats on the use correlations not corrected by selection effects has been presented (Dainotti et al. 2013b) showing how we can commit errors on the evaluation of the cosmological parameters. Nowadays, the challenge is the user of the intrinsic correlation to explain the most plausible theoretical models and to apply as a cosmological tool.

Other topics

I) Ultra high-energy cosmic rays

We are also interested in the origin(s) of ultra high-energy cosmic rays (UHECR) and high-energy neutrinos, cosmic particles that are often thought to come from extra-galactic space at extreme distances. Along with construction of theoretical models, we also try to find clues from data gathered by the latest astro-particle experiments. Several individuals of our team are team members of Telescope Array at Utah that studies very high-energy CRs hitting our atmosphere from outer space.

The members contribute to the operation of the Telescope Array (TA) detectors. TA found evidence for a cluster of the cosmic rays with energies greater than 57 EeV. To accelerate the data collection speed for elucidating this new prospect, the TAx4 experiment was started. Recently our member contributed to the design, construction, calibration and the data acquisition of the surface detectors of the TAx4 experiment. The surface detectors of the TAx4 experiment started to collect cosmic ray events from 2019. We are analyzing the data to study the origins of the events.

UHECR nuclei are expected to interact with the background photons in intergalactic space. The photo-absorption of UHECR nuclei can be an important process to interpret the observables such as energy spectra and compositions of UHECRs. The Photo-Absorption of Nuclei and Decay Observation for Reactions in Astrophysics (PANDORA) project is a joint project among three experimental facilities with nuclear theories and astrophysical simulations. Some members are involved in this project and study the impact of the measurements and nuclear theories on the interpretation of UHECRs.

Currently, a few of us are also involved in activities of the Cherenkov Telescope Array (CTA), a near-future international ground-based observatory for very high energy (VHE) gamma-rays. We are performing theoretical and numerical calculations to help the team make plans for future observations of various high-energy astrophysical objects using CTA.

II) Pulsar

Pulsar is a rapidly rotating and strongly magnetized neutron star which emits radiation beam in a rotation period. The word "pulsar" is a contraction of "pulsating star". Today, more than 2000 pulsars are detected,  some of them are one of the brightest source in our galaxy. In addition, young pulsar is  usually surrounded by luminous synchrotron nebula e.g. Crab nebula. For most pulsars, the activity  is drived by rotationing neutron star (Rotation powered pulsar). For simlicity, it is just a rotating magnet, which is known as a high-power unipolar dynamo.  And therefore, the plasma in magnetosphere is highly accelerated. The rotation energy of pulsar  is released by electro-magnetic wave (Beam) and outflow of high energy plasma (Pulsar wind). But detailed radiation mechanism or structure of magnetosphere have been still controversial. To solve this problem, we have been tried global simulation for global pulsar magnetosphere. The simulation includes inertia of accelerated plasma and pair creation process (photon collision and magnetic pair creation). 

III) Interaction of the Stellar Wind with the Pulsar

The structure formed by the shocked winds of a massive star and a non-accreting pulsar in a binary system suffers periodic and random variations of orbital and non-linear dynamical origins. The characterization of the evolution of the wind interaction region is necessary for understanding the rich phenomenology of Galactic Gamma-ray binaries. For the first time, we simulate in 3 dimensions the interaction of isotropic stellar and relativistic pulsar winds along one full orbit, on scales well beyond the binary size. Previously only the Kelvin-Helmholtz instability, discussed in the past, we find that the Richtmyer-Meshkov and the Rayleigh-Taylor instabilities are very likely acting together in the shocked flow evolution. Simulations in 3 dimensions confirm that the interaction of stellar and pulsar winds yields structures that evolve non-linearly and become strongly entangled. The evolution is accompanied by strong kinetic energy dissipation, rapid changes in flow orientation and speed, and turbulent motion. The results of this work confirm our prediction for the loss of the coherence of the whole shocked structure on large scales.

animation of the simulation
https://youtu.be/4Xu1ZHl0nkk
https://youtu.be/adtMPuERsoc
https://youtu.be/U1WOyUaPk98

A mysterious X-ray-emitting object has been detected moving away from the high-mass gamma-ray binary PSR B1259-63, which contains a non-accreting pulsar and a Be star whose winds collide forming a complex interaction structure. Given the strong eccentricity of this binary, the interaction structure should be strongly anisotropic, which together with the complex evolution of the shocked winds, could explain the origin of the observed moving X-ray feature. We proposed that a fast outflow made of a pulsar-stellar wind mixture is always present moving away from the binary in the apastron direction, with the injection of stellar wind occurring at orbital phases close to periastron passage. This outflow periodically loaded with stellar wind would move with a high speed, and likely host non-thermal activity due to shocks, on scales similar to those of the observed moving X-ray object. Such an outflow is thus a very good candidate to explain this X-ray feature. This, if confirmed, would imply pulsar-to-stellar wind thrust ratios of 0.1, and the presence of a jet-like structure on the larger scales, up to its termination in the interstellar medium. 

Recent publications

1. Bosch-Ramon, Barkov, & Perucho, "Orbital evolution of colliding star and pulsar winds in 2D and 3D effects of dimensionality, EoS, resolution, and grid size", 2015, A&A, 577, A89
   
2. Barkov & Bosch-Ramon, "The origin of the X-ray-emitting object moving away from PSR B1259-63", 2016, MNRAS, 456, L64
   

IV) Type-I X-ray Burst

Several X-ray burst light curves with different equation of states and their comparison with the observed light curves of regular burster GS 1826-24.

Recent publications

1. Akira Dohi, Nobuya Nishimura, Masa-aki Hashimoto, Yasuhide Matsuo, Tsuneo Noda, and Shigehiro Nagataki, "Effects of Nuclear Equation of State on Type-I X-ray Bursts: Interpretation of the X-ray Bursts from GS 1826-24", ApJ 923, 64, 2021
   
2. Akira Dohi, Nobuya Nishimura, Hajime Sotani, Tsuneo Noda, Helei Liu, Shigehiro Nagataki, and Masa-aki Hashimoto, "Impacts of the direct URCA and Superfluidity inside a Neutron Star on Type-I X-Ray Bursts and X-Ray Superbursts", ApJ 937, 124, 2022