We evolve stellar models with zero-age main sequence (ZAMS) mass of $M_{\rm ZAMS} \gtrsim 18 M_\odot$ under the assumption that they experience an enhanced mass-loss rate when crossing the instability strip at high luminosities and conclude that most of them end as type Ibc supernovae (SNe Ibc) or dust-obscured SNe II. We explore what level of enhanced mass-loss rate during the instability strip would be necessary to explain the `red supergiant (RSG) problem'. This problem refers to the dearth of observed core-collapse supernovae progenitors with $M_{\rm ZAMS} \gtrsim 18 M_\odot$. Namely, we examine what enhanced mass loss rate could make it possible for all these stars actually to explode as CCSNe. We find that the mass-loss rate should increase by a factor of at least about ten. We reach this conclusion by analyzing the hydrogen mass in the stellar envelope and the optical depth of the dusty wind at the explosion, and crudely estimate that under our assumptions only about a fifth of these stars explode as unobscured SNe II and SNe IIb. About 10-15 per cent end as obscured SNe II that are infrared-bright but visibly very faint, and the rest, about 65-70 per cent, end as SNe Ibc. However, the statistical uncertainties are still too significant to decide whether many stars with $M_{\rm ZAMS} \gtrsim 18M_\odot$ do not explode as expected in the neutrino driven explosion mechanism, or whether all of them explode as CCSNe, as expected by the jittering jets explosion mechanism.
We calculate the properties of 135 stellar supernovae using data from the Open Supernova Catalog. We generate temperatures, radii, luminosities, and expansion velocities using a spherically symmetric optically thick fireball model. These modeled parameters reveal trends that are common across different types of supernovae. We have identified distinct phases that appear across Type Ia, II, II P, and IIb supernovae. We note that there is a long period of reasonable continuous growth (Phase 1), giving credence to our simple model of an optically thick fireball. The modeled radius reaches a maximu…
Understanding the link between massive ($\gtrsim 30$ M$_{\odot{}}$) stellar black holes (BHs) and their progenitor stars is a crucial step to interpret observations of gravitational-wave events. In this paper, we discuss the final fate of very massive stars (VMSs), with zero-age main sequence (ZAMS) mass $>150$ M$_{\odot}$, accounting for pulsational pair-instability supernovae (PPISNe) and for pair-instability supernovae (PISNe). We describe an updated version of our population synthesis code SEVN, in which we added stellar evolution tracks for VMSs with ZAMS mass up to $350 $M$_{\odot{}}$ an…
The single-degenerate channel is widely accepted as the progenitors of type Ia supernovae (SNe Ia). Following the work of Meng, Chen and Han (2009), we reproduced the birth rate and age of supernovae like SN 2006X by the single-degenerate model (WD + MS) with an optically thick wind, which may imply that the progenitor of SN 2006X is a WD + MS system.
Two main physical mechanisms are used to explain supernova explosions: thermonuclear explosion of a white dwarf(Type Ia) and core collapse of a massive star (Type II and Type Ib/Ic). Type Ia supernovae serve as distance indicators that led to the discovery of the accelerating expansion of the Universe. The exact nature of their progenitor systems however remain unclear. Radio emission from the interaction between the explosion shock front and its surrounding CSM or ISM provides an important probe into the progenitor star's last evolutionary stage. No radio emission has yet been detected from T…
We present near-infrared synthetic spectra of a delayed-detonation hydrodynamical model and compare them to observed spectra of four normal type Ia supernovae ranging from day +56.5 to day +85. This is the epoch during which supernovae are believed to be undergoing the transition from the photospheric phase, where spectra are characterized by line scattering above an optically thick photosphere, to the nebular phase, where spectra consist of optically thin emission from forbidden lines. We find that most spectral features in the near-infrared can be accounted for by permitted lines of Fe II an…
When a core-collapse supernova explodes in a binary star system, the ejecta might encounter an overdense shell, where the stellar winds of the two stars previously collided. In this work, we investigate effects of such interactions on supernova light curves on time-scales from the early flash ionization signatures to approximately one year after the explosion. We construct a model of the colliding-wind shell in an orbiting binary star system and we provide an analytical expression for the shell thickness and density, which we calibrate with three-dimensional adaptive mesh refinement hydrodynam…
Neutron stars receive velocity kicks at birth in supernovae. Those formed in electron-capture supernovae from super asymptotic giant branch stars -- the lowest mass stars to end their lives in supernovae -- may receive significantly lower kicks than typical neutron stars. Given that many massive stars are members of wide binaries, this suggests the existence of a population of low-mass ($1.25 < M_\mathrm{psr} / $M$_\odot < 1.3$), wide ($P_\mathrm{orb} \gtrsim 10^{4}$\,day), eccentric ($e \sim 0.7$), unrecycled ($P_\mathrm{spin} \sim 1$\,s) binary pulsars. The formation rate of such binaries is…
WTP19aalnxx: Discovery of a bright mid-infrared transient in the emerging class of low luminosity supernovae revealed by delayed circumstellar interaction
Single Degenerate model is the most widely accepted progenitor model of type Ia supernovae (SNe Ia), in which a carbon-oxygen white dwarf (CO WD) accretes hydrogen-rich material from a main sequence or a slightly evolved star (WD +MS) to increase its mass, and explodes when its mass approaches the Chandrasekhar mass limit. During the mass transfer phase between the two components, an optically thick wind may occur and the material lost as the wind may exist as circumstellar material (CSM). Searching the CSM around progenitor star is helpful to discriminate different progenitor models of SNe Ia…
It has recently been proposed that one sub-class of type Ia supernovae (SNe Ia) is sufficiently both distinct and common to be classified separately from the bulk of SNe Ia, with a suggested class name of "type Iax supernovae" (SNe Iax), after SN 2002cx. We show that the population properties of this class can be understood if the events originate from helium double-detonation sub-Chandrasekhar mass explosions, in which a carbon--oxygen white dwarf (CO WD) accumulates a helium layer from a non-degenerate helium star. We have incorporated detailed binary evolution calculations for the progenito…
There is currently a severe discrepancy between theoretical models of dust formation in core-collapse supernovae (CCSNe), which predict $\gtrsim 0.01$ M$_\odot$ of ejecta dust forming within $\sim 1000$ days, and observations at these epochs, which infer much lower masses. We demonstrate that, in the optically thin case, these low dust masses are robust despite significant observational and model uncertainties. For a sample of 11 well-observed CCSNe, no plausible model reaches carbon dust masses above $10^{-4}$ M$_\odot$, or silicate masses above $\sim 10^{-3}$ M$_\odot$. Optically thick model…
Using the Boltzmann-radiation-hydrodynamics code, which solves the Boltzmann equation for neutrino transport, we present the results of the simulations with the nuclear equations of state (EOSs) of Lattimer and Swesty (LS) and Furusawa and Shen (FS). We extend the simulation time of the LS model and conduct thorough investigations, though our previous paper briefly reported some of the results. Only the LS model shows the shock revival. This seems to originate from the nuclear composition: the different nuclear composition results in the different energy loss by photodissociation and hence the…
Analytical modeling of polarization signals arising from confined circumstellar material in Type II supernovae
University of Turku（图尔库大学）；Aalto University Metsähovi Radio Observatory（阿尔托大学梅萨霍维射电天文台）；Aalto University Department of Electronics and Nanoengineering（阿尔托大学电子与纳米工程系）；Kyoto University（京都大学）；The University of Tokyo（东京大学）
SPIRITS---SPitzer InfraRed Intensive Transients Survey---is an ongoing survey of nearby galaxies searching for infrared (IR) transients with Spitzer/IRAC. We present the discovery and follow-up observations of one of our most luminous ($M_{[4.5]} = -17.1\pm0.4$ mag, Vega) and red ($[3.6] - [4.5] = 3.0 \pm 0.2$ mag) transients, SPIRITS 15c. The transient was detected in a dusty spiral arm of IC 2163 ($D\approx35.5$ Mpc). Pre-discovery ground-based imaging revealed an associated, shorter-duration transient in the optical and near-IR (NIR). NIR spectroscopy showed a broad ($\approx 8400$ km s$^{-…
We present the mid-infrared (MIR) light curves (LC) of 10 superluminous supernovae (SLSNe) at $z<0.12$ based on WISE data at 3.4 and 4.6 $μ$m. Three of them, including PS15br, SN 2017ens, and SN 2017err show rebrightening which started at 200--400 days and ended at 600--1000 days, indicating the presence of dust. In four of the left seven SLSNe, dust emission was detected with monochromatic luminosities of $10^7\sim10^8\ L_\odot$ at epochs of 100--500 days based on MIR colors $W1-W2\sim1$. Among the three SLSNe which show rebrightening, we further analysed PS15br and SN 2017ens. We modeled the…
The most massive stars on the asymptotic giant branch (AGB), so called super-AGB stars, are thought to produce supernovae (SNe) triggered by electron captures in their degenerate O+Ne+Mg cores. Super-AGB stars are expected to have slow winds with high mass-loss rates, so their wind density is high. The explosions of super-AGB stars are therefore presumed to occur in this dense wind. We provide the first synthetic light curves (LCs) for such events by exploding realistic electron-capture supernova (ecSN) progenitors within their super-AGB winds. We find that the early LC, i.e. before the recomb…
The interaction of a supernova with a circumstellar medium (CSM) can dramatically increase the emitted luminosity by converting kinetic energy to thermal energy. In 'superluminous' supernovae (SLSNe) of Type IIn -- named for narrow hydrogen lines in their spectra -- the integrated emission can reach $\sim 10^{51}$ erg, attainable by thermalising most of the kinetic energy of a conventional SN. A few transients in the centres of active galaxies have shown similar spectra and even larger energies, but are difficult to distinguish from accretion onto the supermassive black hole. Here we present a…
Fast neutrino-flavor conversion (FFC) is a possible game-changing ingredient in core-collapse supernova (CCSN) theory. In this paper, we examine the impact of FFC on explosive nucleosynthesis by including the effects of FFC in conjunction with asymmetric neutrino emission into nucleosynthetic computations in a parametric way. We find that the ejecta compositions are not appreciably affected by FFC for elements lighter than Co, while the compositions are influenced by FFC for the heavier elements. We also find that the role of FFC varies depending on the asymmetric degree of neutrino emission (…
It has recently been proposed that one sub-class of type Ia supernovae (SNe Ia) is sufficiently both distinct and common to be classified separately from the bulk of SNe Ia, with a suggested class name of "type Iax supernovae" (SNe Iax), after SN 2002cx. However, their progenitors are still uncertain. We study whether the population properties of this class might be understood if the events originate from a subset of sub-Chandrasekhar mass explosions. In this potential progenitor population, a carbon--oxygen white dwarf (CO WD) accumulates a helium layer from a non-degenerate helium star; igni…
We study properties of early radio emission from stripped-envelope supernovae (those of type IIb/Ib/Ic). We suggest there is a sub-class of stripped-envelope supernovae in their radio properties, including optically well-studied type Ic supernovae (SNe Ic) 2002ap and 2007gr, showing a rapid rise to a radio peak within ~ 10 days reaching to a low luminosity (at least an order of magnitude fainter than a majority of SNe IIb/Ib/Ic). They show a decline after the peak shallower than others while the spectral index is similar. We show that all these properties are naturally explained if the circums…
Stripped-envelope supernovae (Types IIb, Ib, and Ic) that show little or no hydrogen comprise roughly one-third of the observed explosions of massive stars. Their origin and the evolution of their progenitors are not yet fully understood. Very massive single stars stripped by their own winds ($\gtrsim 25-30 M_{\odot}$ at solar metallicity) are considered viable progenitors of these events. However, recent 1D core-collapse simulations show that some massive stars may collapse directly into black holes after a failed explosion, with a weak or no visible transient. In this letter, we estimate the…
We present a spectroscopic analysis of the H-alpha profiles of hydrogen-rich type II supernovae. A total of 52 type II supernovae having well sampled optical light curves and spectral sequences were analyzed. Concentrating on the H-alpha P-Cygni profile we measure its velocity from the FWHM of emission and the ratio of absorption to emission (a/e) at a common epoch at the start of the recombination phase, and search for correlations between these spectral parameters and photometric properties of the V-band light curves. Testing the strength of various correlations we find that a/e appears to b…
We study the spectroscopic evolution of superluminous supernovae (SLSNe) later than 100 days after maximum light. We present new data for Gaia16apd and SN2017egm, and analyse these with a larger sample comprising 41 spectra of 12 events. The spectra become nebular within 2-4 $e$-folding times after light curve peak, with the rate of spectroscopic evolution correlated to the light curve timescale. Emission lines are identified with well-known transitions of oxygen, calcium, magnesium, sodium and iron. SLSNe are differentiated from other Type Ic SNe by a prominent O I $λ$7774 line and higher-ion…
Double peaked light curves are observed for some Type Ic supernovae (SNe Ic) including LSQ14efd, iPTF15dtg and SN 2020bvc. One possible explanation of the first peak would be shock-cooling emission from massive extended material around the progenitor, which is produced by mass eruption or rapid expansion of the outermost layers of the progenitor shortly before the supernova explosion. We investigate the effects of such circumstellar matter (CSM) on the multi-band optical light curves of SNe Ic using the radiation hydrodynamics code STELLA. Two different SNe Ic progenitor masses at the pre-SN s…
Binary Chandrasekhar-mass white dwarfs accreting mass from non-degenerate stellar companions through the single-degenerate channel have reigned for decades as the leading explanation of Type Ia supernovae. Yet, a comprehensive theoretical explanation has not yet emerged to explain the expected properties of the canonical near-Chandrasekhar-mass white dwarf model. A simmering phase within the convective core of the white dwarf leads to the ignition of one or more flame bubbles scattered across the core. Consequently, near-Chandrasekhar-mass single-degenerate SNe Ia are inherently stochastic, an…
The nucleosynthetic site of the rapid ($r$) neutron-capture process is currently being debated. The direct detection of the neutron star merger GW170817, through gravitational waves and electromagnetic radiation, has confirmed such events as important sources of the $r$-process elements. However, chemical evolution models are not able to reproduce the observed chemical abundances in the Milky Way when neutron star mergers are assumed to be the only $r$-process site and realistic time distributions of such events are taken into account. Now for the first time, we combine all the available obser…
It is recognized that some core-collapse supernovae (SNe) show a double-peaked radio light curve within a few years since the explosion. A shell of circumstellar medium (CSM) detached from the SN progenitor has been considered to play a viable role in characterizing such a re-brightening of radio emission. Here, we propose another mechanism that can give rise to the double-peaked radio light curve in core-collapse SNe. The key ingredient in the present work is to expand the model for the evolution of the synchrotron spectral energy distribution (SED) to a generic form, including fast and slow …
Recent studies of low redshift type Ia supernovae (SNIa) indicate that half explode from less than Chandrasekhar mass white dwarfs, implying ignition must proceed from something besides the canonical criticality of Chandrasekhar mass SNIa progenitors. We show that $1-100$ PeV mass asymmetric dark matter, with imminently detectable nucleon scattering interactions, can accumulate to the point of self-gravitation in a white dwarf and collapse, shedding gravitational potential energy by scattering off nuclei, thereby heating the white dwarf and igniting the flame front that precedes SNIa. We combi…
The progenitor stars of several Type IIb supernovae (SNe) show indications for extended hydrogen envelopes. These envelopes might be the outcome of luminous energetic pre-explosion events, so-called precursor eruptions. We use the Palomar Transient Factory (PTF) pre-explosion observations of a sample of 27 nearby Type IIb SNe to look for such precursors during the final years prior to the SN explosion. No precursors are found when combining the observations in 15-day bins, and we calculate the absolute-magnitude-dependent upper limit on the precursor rate. At the 90% confidence level, Type IIb…
We present numerical simulations that include 1-D Eulerian multi-group radiation-hydrodynamics, 1-D non-LTE radiative transfer, and 2-D polarised radiative transfer for super-luminous interacting supernovae (SNe). Our reference model is a ~10Msun inner shell with 10^51erg ramming into a ~3Msun cold outer shell (the circumstellar-medium, or CSM) that extends from 10^15cm to 2x10^16cm and moves at 100km/s. We discuss the light curve evolution, which cannot be captured adequately with a grey approach. In these interactions, the shock-crossing time through the optically-thick CSM is much longer th…
Employing Eggleton's stellar evolution code with an optically thick wind assumption, we have systematically studied the WD + He star channel of Type Ia supernovae (SNe Ia), in which a carbon-oxygen WD accretes material from a He main-sequence star or a He subgiant to increase its mass to the Chandrasekhar mass. We mapped out the parameter spaces for producing SNe Ia. According to a detailed binary population synthesis approach, we find that the Galactic SN Ia birthrate from this channel is $\sim$$0.3\times 10^{-3} {\rm yr}^{-1}$, and that this channel can produce SNe Ia with short delay times …
Employing Eggleton's stellar evolution code with the optically thick wind assumption, we systematically studied the He star donor channel of type Ia supernovae (SNe Ia), in which a carbon-oxygen white dwarf (WD) accretes material from a He main-sequence star or a He subgiant to increase its mass to the Chandrasekhar mass. We mapped out the initial parameters for producing SNe Ia in the orbital period--secondary mass plane for various WD masses from this channel. Based on a detailed binary population synthesis approach, we find that this channel can produce SNe Ia with short delay times (\sim10…
The nature of type Ia supernovae (SNe Ia) is still unclear. Employing Eggleton's stellar evolution code with the optically thick wind assumption, we systematically studied the He star donor channel of SNe Ia, in which a carbon-oxygen white dwarf accretes material from a He main-sequence star or a He subgiant to increase its mass to the Chandrasekhar mass. We mapped out the initial parameters for producing SNe Ia in the orbital period--secondary mass plane for various WD masses from this channel. According to a detailed binary population synthesis approach, we find that this channel can produce…
We present an analysis of the diversity of V-band light-curves of hydrogen-rich type II supernovae. Analyzing a sample of 116 supernovae, several magnitude measurements are defined, together with decline rates at different epochs, and time durations of different phases. It is found that magnitudes measured at maximum light correlate more strongly with decline rates than those measured at other epochs: brighter supernovae at maximum generally have faster declining light-curves at all epochs. We find a relation between the decline rate during the 'plateau' phase and peak magnitudes, which has a …
Recurrent novae are binaries harboring a very massive white dwarf (WD), as massive as the Chandrasekhar mass, because of their short recurrence periods of nova outbursts of 10-100 years. Thus, recurrent novae are considered as candidates of progenitors of Type Ia supernovae (SNe Ia). In fact, the SN Ia PTF11kx showed evidence that its progenitor is a symbiotic recurrent nova. The binary parameters of recurrent novae have been well determined, especially for the ones with frequent outbursts, U Sco and RS Oph, which provide useful information on the elementary processes in binary evolution towar…
We study the populations of massive stars in the Carina region and their energetic feedback and ejection of $^{26}$Al. We did a census of the stellar populations in young stellar clusters within a few degrees of the Carina Nebula. For each star we estimated the mass, based on the spectral type and the host cluster age. We used population synthesis to calculate the energetic feedback and ejection of $^{26}$Al from the winds of the massive stars and their supernova explosions. We used 7 years of INTEGRAL observations to measure the $^{26}$Al signal from the region. The INTEGRAL $^{26}$Al signal …
Context: The nature of type Ia supernovae (SNe Ia) is still unclear. Metallicities may have an important effect on their properties. Aims: In this paper, we study the He star donor channel towards SNe Ia comprehensively and systematically at various metallicities. Methods: Employing Eggleton's stellar evolution code with the optically thick wind assumption, we calculated about 10 000 WD + He star systems and obtained SN Ia production regions of the He star donor channel with metallicities Z=0.03, 0.02, 0.004 and 0.0001. According to a detailed binary population synthesis approach, we also obta…
Mass loss through stellar winds plays a dominant role in the evolution of massive stars. In particular the mass-loss rates of very massive stars (VMSs, $> 100\,M_{\odot}$) are highly uncertain. Such stars display Wolf-Rayet spectral morphologies (WNh) whilst on the main-sequence. Metal-poor VMSs are progenitors of gamma-ray bursts and pair instability supernovae. In this study we extended the widely used stellar wind theory by Castor, Abbott & Klein from the optically thin (O star) to the optically thick main-sequence (WNh) wind regime. In particular we modify the mass-loss rate formula in a w…
Based mostly on stellar models which do not include rotation, CO white dwarfs which accrete helium at rates of about $\sim 10^{-8}~\mathrm{M}_\odot/\mathrm{yr}$ have been put forward as candidate progenitors for a number of transient astrophysical phenomena, including supernovae of Type Ia, and the peculiar and fainter Type Iax supernovae. Here we study the impact of accretion-induced spin-up including the subsequent magnetic field generation, angular momentum transport, and viscous heating on the white dwarf evolution up to the point of helium ignition. We resolve the structure of the helium …
Type Ia supernovae (SNe Ia) play an important role in astrophysics, especially in the study of cosmic evolution. There are several progenitor models for SNe Ia proposed in the past years. In this paper, we have carried out a detailed study of the He star donor channel, in which a carbon-oxygen white dwarf (CO WD) accretes material from a He main sequence star or a He subgiant to increase its mass to the Chandrasekhar mass. Employing Eggleton's stellar evolution code with an optically thick wind assumption, and adopting the prescription of Kato & Hachisu (2004) for the mass accumulation efficie…
Manganese (Mn) abundances are sensitive probes of the progenitors of Type Ia supernovae (SNe). In this work, we present a catalog of manganese abundances in dwarf spheroidal satellites of the Milky Way, measured using medium-resolution spectroscopy. Using a simple chemical evolution model, we infer the manganese yield of Type Ia SNe in the Sculptor dwarf spheroidal galaxy (dSph) and compare to theoretical yields. The sub-solar yield from Type Ia SNe ($\mathrm{[Mn/Fe]}_{\mathrm{Ia}}=-0.30_{-0.03}^{+0.03}$ at $\mathrm{[Fe/H]}=-1.5$ dex, with negligible dependence on metallicity) implies that sub…
I review various phenomena associated with mass-accreting white dwarfs (WDs) in relation to progenitors of type Ia supernovae (SNe Ia). The WD mass can be estimated from light curve analysis in multiwavelength bands based on the optically thick wind theory. In the single degenerate scenario of SNe Ia, two main channels are known, i.e., WD + main sequence (MS) channel and WD + red giant (RG) channel. In each channel, a typical binary undergoes three evolutional stages before explosion, i.e., the wind phase, supersoft X-ray source (SSS) phase, and recurrent nova phase in order of time because th…
Infrared (IR) observations of core collapse supernovae (CCSNe) have been used to infer the mass of dust that has formed in their ejecta. A plot of inferred dust masses versus supernova (SN) ages shows a trend of increasing dust mass with time, spanning a few decades of observations. This trend has been interpreted as evidence for the slow and gradual formation of dust in CCSNe. Observationally, the trend exhibits a $ t^2$ behavior, exactly what is expected from an expanding optically thick ejecta. In this case, the observed dust resides in the infrared (IR)-thin "photosphere" of the ejecta, an…
The single-degenerate (SD) model is one of the principal models for the progenitors of type Ia supernovae (SNe Ia), but some of the predictions in the most widely studied version of the SD model, i.e. the optically thick wind (OTW) model, have not been confirmed by observations. Here, we propose a new version of the SD model in which a common envelope (CE) is assumed to form when the mass-transfer rate between a carbon-oxygen white dwarf (CO WD) and its companion exceeds a critical accretion rate. The WD may gradually increase its mass at the base of the CE. Due to the large nuclear luminosity…
We present optical and near-infrared (IR) photometry and near-IR spectroscopy of SN 2004am, the only optically detected supernova (SN) in M 82. These demonstrate that SN 2004am was a highly reddened type II-P SN similar to the low luminosity type II-P events such as SNe 1997D and 2005cs. We show that SN 2004am was located coincident with the obscured super star cluster M 82-L, and from the cluster age infer a progenitor mass of 12 +7/-3 Msun. In addition to this, we present a high spatial resolution Gemini-N K-band adaptive optics image of the site of SN 2008iz and a second transient of uncert…
(abridged) The strong winds of Wolf-Rayet (WR) stars are important for the mechanical and chemical feedback of the most massive stars and determine whether they end their lives as neutron stars or black holes. In this work we investigate theoretically the mass-loss properties of H-free WR stars of the nitrogen sequence (WN stars). We connect stellar structure models for He stars with wind models for optically-thick winds and assess how both types of models can simultaneously fulfill their respective sonic-point conditions. Fixing the outer wind law and terminal wind velocity, we obtain unique …
Type Ia supernovae (SNe Ia) often show high-velocity absorption features (HVFs) in their early phase spectra; however the origin of the HVFs is unknown. We show that a near-Chandrasekhar-mass white dwarf (WD) develops a silicon-rich layer on a carbon-oxygen (CO) core before it explodes as an SN Ia. We calculated the nuclear yields in successive helium shell flashes for 1.0 $M_\odot$, 1.2 $M_\odot$, and 1.35 $M_\odot$ CO WDs accreting helium-rich matter with several mass-accretion rates ranging from $1 \times 10^{-7}~M_\odot$ yr$^{-1}$ to $7.5 \times 10^{-7}~M_\odot$ yr$^{-1}$. For the $1.35~M_…
