Type One-A Supernova Explosions in Binary Systems: A Review. Zheng-Wei Liu A Puke(TM) Audiopaper

Research in Astronomy and Astrophysics.
Type One-A Supernova Explosions in Binary Systems: A Review.
Zheng-Wei Liu and others.
Yunnan Observatories, Chinese Academy of Sciences, Kunming, China;
Abstract Type One-A supernovae, SNe One-A, play a key role in the fields of astrophysics and cosmology. It is widely accepted that SNe One-a arise from thermonuclear explosions of white dwarfs, WD’s in binary systems.
We can distinguish two kinds of supernovae, corresponding to two kinds of star death: Type one-a, thought to be the thermonuclear explosions of accreting white dwarf stars, and all the rest, Type two, one-b, one-c and so on), which happen when the iron core of a massive star collapses to a neutron star or black hole. Observationally, Type one is defined by a lack of hydrogen lines in its spectrum, lines that Type two has.
However, there is no consensus on the fundamental aspects of the nature of SN One-a progenitors and their actual explosion mechanism. This a fundamental limit in our understanding of these important astrophysical objects. In this review, we outline the diversity of SNe One-a and the proposed progenitor models and explosion mechanisms. We discuss the recent theoretical and observational progress in addressing the SN One-a progenitor and explosion mechanism in terms of the observables at various stages of the explosion, including rates and delay times, pre-explosion companion stars, ejecta, companion interaction, early excess emission, early radio, X-ray emission from circumstellar material (CSM) interaction, surviving companion stars, late-time spectra and photometry, polarization signals, and supernova remnant properties, etc. Despite the efforts from both the theoretical and observational side, the questions of how the WD’s reach an explosive state and what progenitor systems are more likely to produce SNe One-a remain open. No single published model is able to consistently explain all observational features and the full diversity of SNe One-a. This may indicate that either a new progenitor paradigm or the improvement of current models is needed if all SNe one-a arise from the same origin. An alternative scenario is that different progenitor channels and explosion mechanisms contribute to SNe One-a. In the next decade, the ongoing campaigns with the James Webb Space Telescope, Gaia and the Zwicky Transient Facility, and upcoming extensive projects with the Vera C Rubin Observatory Legacy Survey of Space and Time and the Square Kilometre Array will allow us to conduct not only studies of individual SNe One-a in unprecedented detail but also systematic investigations for different subclasses of SNe One-a. This will advance theory and observations of SNe One-a sufficiently far to gain a deeper understanding of their origin and explosion mechanism.Show more

One. INTRODUCTION.
Supernovae (SNe) are highly energetic explosions of some stars, that are so bright that they can outshine an entire galaxy. Their typical bolometric luminosities reach the order of ten to the forty three ergs per second, which is about ten billion times the solar luminosity. SNe play an important role in the fields of astrophysics and cosmology because they have been used as cosmic distance indicators, and they are heavy-element factories, especially for intermediate mass and iron-group elements, kinetic-energy sources, and cosmic-ray accelerators in galaxy evolution. SNe are also key players in the formation of new-generation stars by triggering the collapse of molecular clouds. SNe are generally classified into two main categories according to their spectroscopic features, Type One and Type Two SNe.

Type One SNe have no hydrogen, H, lines in their spectra whereas Type two SNe contain obvious H lines. Type One-a SNe, SNe Ione-a are a subclass of Type One which exhibit strong singly ionized silicon, Si, absorption, Si two at 6150, 5800 and 4000 Angstroms feature in their spectra.
SNe One-a are widely thought to be thermonuclear explosions of white dwarfs (WDs) in binary systems, Hoyle and Fowler 1960. They have been found to occur in all galaxy types. Their typical peak luminosity in the B-band is about MB equals minus 19.5 magnitudes, and the typical kinetic energy is around ten to the fifty one ergs, or equivalently, ten to the forty four Joules.
The light curves of SNe One-a are powered by the Compton scattering of gamma rays produced by the radioactive decay of Nickel 56 to Cobalt 56 to Iron 56, with respective half-life times of 6.1 and 77 days SNe One-a have been successfully used as cosmic distance indicators to constrain cosmological parameters, which has led to the discovery of the accelerating expansion of the Universe, a breakthrough rewarded with the 2011 Nobel Prize in physics. Despite their importance and far-reaching implications, the specific progenitor systems as well as the explosion mechanism of SNe One-a remains enigmatic.
This affects the reliability of necessary assumptions such as those of universality of their calibration as distance indicators. Recently, it was found that the local measurements of the Hubble constant H sub zero, based on SNe one-a is inconsistent with the value inferred from the cosmic microwave background radiation observed by the Planck satellite assuming a Capital Lambda CDM cosmological world model.

To determine whether this so-called “H sub zero tension” hints to new physics, it is critical to improve our understanding of SNe One-a and, more specifically, their progenitors and explosion mechanisms.

Two. THE DIVERSITY OF SNe One-a.
A large fraction of observed SNe one-a, around seventy percent, is found to show remarkable homogeneity and quantifiable heterogeneity, and they exhibit a clear empirical relationship between light curve width and peak luminosity, meaning the so-called “Phillips relation”, sometimes known as the width–luminosity relation, WLR. These SNe one-a are usually referred to as “normal SNe one-a”, and they have long been used as standard candles for measuring cosmological distances.
However, an increasing number of SNe one-a has been observed that does not follow the Phillips relation, see Figure one, and they are diverse in their observational characteristics such as light curveshape, peak luminosity and spectral features.
For these reasons, SNe one-a have been classified into different sub-classes diverging from normal events, which include 1991T-likes 1991bg-likes, SNe One-ax, meaning, SN 2002cx-likes, 2002es-likes, Carich Objects, meaning SN 2005E-like, super-Chandrasekhar objects, meaning SN 2003fg-likes; SNe One-a-CSM and fast decliners. The diversity of SNe One-a has recently been reviewed by Taubenberger in 2017, and so we only skim the surface here.

1991T-like objects form a luminous, slow-declining subclass of SNe One-a, named after the well-observed SN 1991T.
Their optical spectra at pre-maximum phases show extremely weak Calcium Two H and K and Silicon two wavelength 6355 and strong Iron three absorption features. 91T-like SNe are expected to be on average zero point two to zero point five magnitudes more luminous than normal SNe One-a with similar decline rate.
1991T-like SNe are found preferentially in late-type galaxies, suggesting that they are likely associated with young stellar populations. It has been suggested that 1991T-like SNe could contribute two to nine percent to all SNe One-a in the local Universe.
1991bg-like objects are a cool, subluminous, and fast-declining subclass of SNe One-a with low ejecta velocity.
Typically, they are fainter than normal SNe One-a in optical band up to 2.5 magnitudes.
Their spectra at maximum light show strong Titanium two absorption, indicating a relatively cool photosphere. 1991bg-like SNe are found preferentially in early-type, meaning, passive galaxies.
Only few 1991bg-like SNe have been found in spiral galaxies. This suggests old stellar populations for the progenitors of 1991bg-like SNe. There is no agreement about the rates of 1991bglike SNe in the literature, estimates range from six to fifteen percent of all SNe One-a.
SNe One-a-x are proposed as a hot, sublumious, subclass of SNe One-a. SNe One-ax are fainter than normal SNe One-a and highly skewed to late-type galaxies. Their explosion ejecta are characterized by low expansion velocities and show strong mixing features. Their maximum-light spectra show similar features to those of 1991T-like SNe, which are characterized by weak Silicon two wavelength 6355 Angstrom features and dominated by Iron three lines. In addition, strong Helium lines are identified in spectra of two events, meaning, SN 2004cs and SN 2007J. The late-time spectra of SNe One-a-x are dominated by narrow permitted Iron two. It has been suggested that they contribute about one third of total SNe One-a.
2002es-like objects are another cool, rapidly fading, subluminous subclass of SNe One-a which have a peak luminosity and ejecta velocity around 6000 kilometers per second, similar to SN 2002cx.
Their spectra at near maximum light phases share some characteristics in common with the subluminous 1991bg-like SNe, which are clearly characterized by strong Titanium two, Silicon two, and Oxygen two absorption features.
However, 2002es-like SNe do not have the fast-declining light curves characteristic of 1991bg-like events. White suggested in 2015, that 2002es-like events tend to explode preferentially, but not exclusively, in massive, early-type galaxies
Ganeshalingam in 2012 suggested that SN 2002es-like objects should account for around two point five percent of all SNe One-a.

Calcium-rich objects, Ca-rich, constitute a peculiar subclass of SNe One-a with SN 2005E as a prototype. Ca-rich SNe are primarily characterized by peak magnitudes of minus 14 to minus 16.5 magnitudes, rapid photometric evolution with typical rise times of 12 to 15 days, and strong Calcium features in nebular phase spectra. They exhibit low ejecta and Nickel 56 masses of less than a half Solar mass, and less than a tenth of a solar mass, respectively. The majority of Calcium-rich SNe has been observed in early type galaxies and the inferred rates of such SNe are likely in the range of five to twenty percent of the normal SN One-a rates.
Super-Chandrasekhar objects are sometimes known as SN 2003fg-like SNe.
They are referred to as “super-Chandrasekhar SNe” because a differentially rotating WD with a super-Chandrasekhar mass of around two solar masses was used to interpret the observations of SN 2003fg. The main features of this subtype are summarized by Ashall in a 2021 article: They are generally characterized by high luminosities, B-band peak absolute magnitudes of minus 19 to minus 21 magnitudes, broad light curves, delta m 15 B less than 1.3 magnitudes, defined as the decline in the B-band magnitude light curve from peak to 15 days later, and relatively low ejecta velocities.
To repeat, the quantity delta M 15 B is the decline in the B-band magnitude light curve from peak to 15 days later.
This is puzzling for a theoretical explanation: the first two properties point to a powerful explosion which seems to be at odds with the low ejecta velocities. They have only one i-band maximum which peaks after the epoch of the B-band maximum, but with weak (or without) i-band secondary maximum.
Their maximum-light spectra do not show a Titanium two feature; in addition, their nebular-phase spectra are characterized by a low ionization state. Super-Chandrasekhar SNe seem to be preferentially found in low-mass galaxies, indicating that they prefer a low-metallicity environment.

They seem to make up a small fraction of SNe One-a, but their exact rates are still unknown
SNe One-a-CSM are a subclass named after the discovery of SN 2002ic, although there is still a debate on whether these objects are SNe One-a or in fact core-collapse SNe.
A list of several common features of SNe One-a-CSM has been compiled by Silverman in a 2013 article. They have a range of R-band peak absolute magnitudes of MR minus 19 to minus 21.3 magnitudes, and they exhibit narrow hydrogen emission features in their spectra.

The presence of narrow H lines is thought to arise from circumstellar material, CSM, which is strongly indicative of mass loss, or outflows, of the progenitor system prior to the SN explosion.
An initial systematic study of this subclass has been presented by Silverman in a 2013 article, and it has been recently updated by Sharma in 2023. SNe One-a-CSM are preferentially found in late-type spirals and irregular galaxies, indicating the origin from a relatively young stellar population.
The rate of SNe One-a CSM is estimated to be no more than a few per cent of the SN one-a rates.
Fast decliners are rare and the extremely rapidly declining SNe. So far, this class includes SN 1885A, SN 1939B, SN 2002bj, SN 2005ek, SN 2010X.
Whether these peculiar objects arise from thermonuclear explosions of WD’s or core-collapse explosions of massive stars remains open.
There is no conclusion on whether or not all of these objects actually belong to the same class of events

Three. PROGENITORS AND EXPLOSION MECHANISMS.
It is widely accepted that SNe One-a arise from thermonuclear explosions of white dwarfs, WD’s in binary systems, Hoyle and Fowler 1960. However, there is no consensus on the fundamental aspects of the nature of SN One-a progenitors and their explosion mechanism from both, the theoretical and observational side.

In this section, potential progenitor models and explosion mechanisms of SNe One-a are briefly summarized.
Three point one. Progenitor scenarios.
Three point one, point one. Single-degenerate scenario.
In the single-degenerate (SD) scenario, a WD accretes hydrogen-rich or helium-rich material from a nondegenerate companion star through Roche-lobe overflow, RLOF, or stellar wind until its mass approaches the Chandrasekhar-mass, around one point four solar masses, at which point a thermonuclear explosion ensues.
The companion star could be either a main-sequence, MS, star, a subgiant, SG, a red giant, RG, an asymptotic giant-star, AGB, or a Helium star.
It has been suggested that a Chandrasekhar-mass WD can undergo a deflagration, or a detonation or a delayed detonation to lead to a SN one-a explosion
In the SD scenario, SNe One-a are thought to arise from Chandrasekhar-mass WD’s, double detonation explosions of sub-Chandrasekhar mass WD’s could happen when accreting from a Helium-star companion, the homogeneity of the majority of SNe One-a therefore can be well explained by this scenario. A schematic illustration of main binary evolutionary paths for producing SNe One-a in the SD scenario is given in Figure two.
One of the key questions in the SD scenario is how the WD retains the accreted companion material and grows in mass to approach the Chandrasekhar limit, meaning the mass-retention efficiency of onto the WD. The SD scenario requires that the WD accretes material at a relatively narrow range of accretion rates of a few times ten to the minus eight or seven times the mass of the sun per year, to allow steady burning of accreted material, which causes difficulties for explaining the observed nearby SN one-a rate, see Section four. Moreover, some recent observations seem to pose a challenge to the SD scenario, see Section five, such as the missing of surviving companion stars in supernova remnants, SNR’s.

The absence of swept-up Hydrogen, Helium in their late spectra and low X-ray flux from nearby elliptical galaxies.
In addition, although the SD scenario makes the explosion rather homogeneous, it turns out to be difficult to cover the observed ranges in brightness and decline rates in this scenario. However, to conclude whether the SD scenario is promising for producing the majority of SNe One-a requires comparing a full range of predicted observational consequences from this scenario with the observations of SNe One-a.
A number of candidate progenitors have been suggested for the SD scenario, including cataclysmic variable stars like classic novae, recurrent novae and dwarf novae, supersoft X-ray sources, symbiotic systems and WD plus hot-subdwarf binaries.
In the SD scenario, a WD accretes and retains companion matter that carries angular momentum. As a consequence the WD spins with a short period which leads to an increase of the critical explosion mass. If the critical mass is higher than the actual mass of the WD, the SN explosion could only occur after the WD increases the spin period with a specific spin down timescale. This scenario is known as the “spin-up, spin-down model”.
In this model, if the spin down timescale is longer than about one million years, the CSM around the progenitor system could become diffuse and reach a density similar to that of the ISM. This could explain the lack of radio and X-ray emission from SNe One-a in agreement with the current radio and X-ray observations.
Also, the H rich or Helium-rich companion star, meaning, MS, subgiant, RG and Helium stars, may shrink rapidly before the SN one-a explosion occurs by exhausting most of its Hydrogen-rich or Helium-rich envelope during a long spin-down, greater than one hundred million year phase to become a WD or a hot subdwarf star.

This would explain the non-detection of a pre-explosion companion star in SNe One-a and the absence of swept-up Hydrogen, Helium in their late spectra.
However, no, or weak, interaction signature of shocked gas is predicted in this scenario, which makes it difficult to explain the early excess luminosity seen in some SNe One-a such as iPTF14atg and SN 2012cg.

The exact spin down timescale of the WD in this model is uncertain, but it is a key to the success of the model.
Three point one point two. Double-degenerate scenario.
In the original double-degenerate, DD, scenario, two carbon-oxygen, CO, WD’s in a binary system are brought into contact by the emission of gravitational wave radiation and merge via tidal interaction into one single object, triggering a SN One-a explosion if the combined mass exceeds the Chandrasekhar-mass limit.

There are a number of evolutionary paths that can lead to SN one-a explosions in the DD scenario, see Figure two.
The key question of the original DD scenario is whether the merger of two WD’s could successfully lead to an SN one-a explosion.
Different calculations have predicted that the merger of two White Dwarves would likely cause the formation of neutron stars through accretion-induces collapse, AIC, rather than SN one-a explosions.
The accretion from the secondary WD onto the primary WD during the merger process may lead to burning in the outer layers of the WD rather than central burning, which would turn the original carbon-oxygen WD into an oxygen-neon-magnesium, O-Ne-Mg WD. A Chandrasekhar-mass One WD is thought to be prone to collapse into a neutron star via AIC. However, there are possibilities to avoid AIC after the merger of two CO WD’s. For instance, Yoon, in 2007 concluded that the merger of two Carbon-Oxygen White Dwarves could avoid off-center C-burning and explode as an SN one-a in the thermal evolution phase if the rotation of the WD’s is taken into account.
In the past decades, a number of numerical simulations have investigated the merger of two WD’s
More importantly, some recent theoretical studies have shown that the merger of two WD’s can eventually trigger an SN one-a explosion in ways that are different from the original DD scenario. For instance, a carbon detonation can be directly triggered by the interaction of the debris of the secondary WD with the primary WD during the violent merger phase of two CO WD’s to eventually trigger an SN one-a explosion, meaning the “violent merger model”.
If the secondary WD in a DD binary system is a pure Helium White Dwarf, an initial Helium detonation could be triggered by accumulating a Helium shell on top of the primary Carbon-Oxygen White Dwarf through stable mass transfer, eventually triggering the C-core detonation near the center to successfully cause an SN one-a.
This corresponds to the sub-Chandrasekhar-mass double detonation scenario.
In addition, unstable mass transfer could also lead to the presence of Helium in the surface layers of the primary CO WD if the secondary WD is either a Helium WD or a hybrid Helium Carbon Oxygen White Dwarf, which could successfully give rise to an SN one-a during the coalescence itself through the double detonation mechanism, meaning the Helium-ignited violent merger model described in Section three point two point five.

There are some evidences in favor of the DD scenario, see Sections 4 and 5 for a detailed discussion.
Binary population synthesis, BPS, calculations have shown that the predicted SN one-a rates and delay times from the DD scenario could well reproduce those inferred from the observations

In addition, the non-detection of pre-explosion companion stars in normal SNe One-a the lack of radio and X-ray emission around peak brightness the absence of a surviving companion star in SN one-a remnants, and the fact that no signatures of the swept-up Hydrogen, Helium have been detected in the nebular spectra of SNe One-a and the lack of X-ray flux, meaning supersoft X-ray sources, expected for accreting WD’s seem to favour the DD scenario. Also, it has been suggested that some super luminous SNe One-a that have ejecta masses of greater then two solar masses may arise from the merger of two WD’s

However, the DD scenario predicts a relatively wide range of explosion masses and thus makes it difficult to explain the observed homogeneity of the majority of SNe One-a.
Double WD’s, DWD’s are the primary targets of some upcoming space gravitational-wave missions and observatories such as the Laser Interferometer Space Antenna, LISA, Tianqin and Taiji.
Searches for DWDs have been carried out by different surveys like the dedicated ESO Supernovae type One-a Progenitor survey, SPY. The Sloan Digital Sky Survey, SDSS, the SWARMS survey, the Extremely Low Mass, ELM, survey, the Kepler-K2 survey, and the large all-sky survey Gaia, Gaia Collaboration.
However, to date, only about 150 DWD systems have been detected with detailed orbital parameters.
A comprehensive list of close DWD systems, periods below 35 days, containing two low-mass WD’s are given by Schreiber in a 2022 article.
Only a few DWD’s have been reported to be possible SN one-a progenitors that would merge in a Hubble time, including two systems with sub-Chandrasekhar total masses obtained by SPY (WD2020 dash 425 and HE2209 dash 1444, two super-Chandrasekhar progenitor candidates composed of a WD and a hot sub-dwarf, KPD 1930 plus 2752 and HD 265435; CD minus 30, 11223, Henize 2 dash 428 system, 458 Vulpeculae, SBS 1150 plus 599A and GD 687.
Besides, Kawka in 2017 suggested that NLTT 12758 is a super-Chandrasekhar DWD system, but it would merge in a timescale longer than the Hubble time.

Three point one point three. Other proposed progenitor scenarios.

Some subtypes of the SD model and other possible progenitor scenarios have been proposed for SNe One-a, including:
One. The CE wind model, in which the SD models are assumed to drive CE winds rather than optical thick winds when the mass transfer rate exceeds the critical accretion rate
Two. The hybrid C-O-Ne WD model, in which a hybrid carbon-oxygen-neon, C-O-Ne, WD with a mass of greater than around one point three solar masses, accretes material from its companion star to approach the Chandrasekhar-mass limit and explodes as faint SNe One-a.
Three. The M dwarf donor model, in which the WD accretes material from an M-dwarf star so that it approaches the Chandrasekhar-mass limit and triggers an SN one-a explosion.
Four. The core-degenerate model, in which an SN One-a is produced from the merger of a COWD with the core of an AGB companion star during a common envelope, CE, evolution.
Five. The triple channel, in which thermonuclear explosions in triple-star systems are triggered through both the SD and DD channels.
Six. The single-star model, in which AGB stars or Helium stars with a highly degenerate CO core near the Chandrasekhar mass ignite carbon at the center to subsequently cause an SN one-a explosion if they have lost their H-rich or Helium-rich envelopes.
Note that this list may not be complete and that new channels may still be proposed.
Ultimately, the question of SN one-a progenitor systems has to be settled by observations.
For a coarse and sketchy overview of the different progenitor scenarios of SNe One-a, we compile the different characteristics in Table one. We would like to caution here, that usually the arguments to be made in favor or against specific scenarios are more complex than what can be listed in a table. Therefore we emphasize that they are only intended for a quick overview. The main benefit of our table is to highlight open research questions that are marked with “unclear”.
Three point two. Explosion models.
The explosion mechanism depends mainly on the question of whether the WD explodes near the Chandrasekhar mass, or at a mass below this limit the “sub-Chandrasekhar mass” explosion scenario.

To provide clues on the yet poorly understood origin and explosion mechanism of SNe One-a, one needs to compare the observational features predicted by different explosion mechanism in the context of the progenitor models discussed in Section three point one with the observations.
A number of explosion models have been proposed to cover various progenitor scenarios of explosion.
SNe One-a, including near Chandrasekhar-mass deflagrations, near Chandrasekhar-mass delayed detonations, gravitationally-confined detonations, sub-Chandrasekhar-mass double detonations, and violent mergers.
A schematic overview of various SN One-a explosion models proposed in the framework of either Chandrasekhar-mass or sub-Chandrasekhar-mass explosion is shown in Figure three.
Section three point two point one. Chandrasekhar-mass pure deflagrations.

Near Chandrasekhar-mass explosions in the SD scenario have long been proposed as a potential model for SNe One-a because they could reproduce some observational features such as the light curves and spectra.
Moreover, Yamaguchi and others in 2015 suggested that the detection of strong K-shell emission from stable Iron peak elements in SN one-a remnant 3C 397 requires electron captures at high density that can only be achieved by a near-Chandrasekhar mass explosion. In such a configuration, a supersonic prompt detonation would turn essentially the entire star into iron-group elements which is inconsistent with the observed features of SNe One-a:
To produce the intermediate-mass elements, IME, such as Silicon and Sulphur, observed in their spectra, burning must start out as a subsonic deflagration. The WD then expands prior to being incinerated. Compared with a prompt detonation, this reduces the production of Nickel 56 and can in principle increase the IME yields. The outward propagation of the subsonic deflagration flame leads to Rayleigh-Taylor instabilities that generate turbulence at the contact between hot ashes and cold fuel. This enlarges the surface area of the burning front and accelerates it.

One of commonly used near Chandrasekhar-mass explosion models is the so-called “W7 model” of Nomoto from 1984. The W7 model is a one-dimensional, 1D, pure deflagration explosion of a Chandrasekhar mass WD, in which a parametrized description was used for the turbulent burning process. To avoid free parameters in the model, multidimensional simulations, for an example, see top panels of Figure four, have been carried out.

The result of these simulations is that pure deflagrations are not able to reproduce the majority of normal SNe One-a.
In the framework of the the Chandrasekhar-mass deflagration model, it is difficult to produce the canonical half solar mass nickel 56 for normal SNe One-a, because the flame ultimately cannot catch up with the expansion of the WD and much of its material remains unburned. Enhancing the burning efficiency with multi-spot ignitions had only limited success.

Moreover, the ignition process itself is rather uncertain and multi-spot ignition does not seem very likely according to the simulations of Nonaka from a 2012 article.
However, off-center ignited weak deflagration models have been suggested to explain the particular sub-class of SNe One-ax

Figure four presents an example of a 3D explosion simulation for a Chandrasekhar-mass pure deflagration model from Lach in 2022. In the weak pure deflagration model of Chandrasekhar mass WD’s, sometimes known as the “failed detonation model”, an off-center ignited pure deflagration of a Chandrasekhar-mass CO WD, or hybrid CONe WD, fails to completely unbind the entire WD, leaving behind a bound WD remnant.

It has been shown that pure deflagrations in near-Chandrasekhar-mass CO WD’s and hybrid CONe WD’s can respectively reproduce the observational light curves and spectra of brighter SNe One-ax such as SN 2005hk, and, less confidently, the faint Iax event SN 2008ha have shown that the maximum light polarization signal observed in SN 2005hk can be explained in the context of a weak deflagration explosion of a Chandrasekhar-mass WD if asymmetries caused by both the SN explosion itself and the ejecta-companion interaction are considered.
Therefore, the weak deflagration explosion of a Chandrasekhar-mass WD seems to be a potential model for SNe One-ax, at least the brighter members of this sub-class.
Interestingly, the weak pure deflagration model of Chandrasekhar-mass WD’s predicts the existence of a surviving bound WD remnant which is significantly heated by the explosion and highly enriched by heavy elements from SN ejecta. Searches for such surviving WD remnants would be very helpful for assessing the validity of this explosion model.

Section three point two point two. Chandrasekhar-mass delayed detonations.

Besides pure deflagration models, pure detonations of near-Chandrasekhar-mass WD’s have also been proposed for SNe One-a. As already mentioned, the first numerically studied pure detonation model of a near-Chandrasekhar mass WD in hydrostatic equilibrium showed that this model produces too much Nickel 56 and too little IME’s to explain the observations of normal SNe One-a.
This conflict indicates that an expansion of the WD is needed prior to the detonation in order to reduce the production of Nickel 56 and to increase that of IME’s.
To achieve this, the “delayed detonation model” of a near Chandrasekhar-mass WD was proposed by Khokhlov in 1989: The WD expands first due to an initial deflagration and causes the subsequent detonation to burn at relatively low fuel densities, reducing the production of Nickel 56 and enhancing the yields of IME’s compared with the earlier pure detonation models. This therefore makes the delayed detonation model more favorable for explaining normal SNe One-a.

Figure four shows an example of 3D explosion simulations for a Chandrasekhar-mass delayed detonation model, meaning a gravitationally confined detonation model.
Several scenarios for the transition from the initial deflagration to a subsequent detonation have been proposed for SNe One-a such as the deflagration to detonation transition model, or DDT; the pulsating delayed detonation model, PDD; gravitationally confined detonation model, GCD, and the pulsational reverse detonation model.
Despite substantial effort, none of the simulations could demonstrate from first principles that the transition of the deflagration to a detonation really occurs.

Section three point two point three. sub-Chandrasekhar-mass double-detonations.
Sub-Chandrasekhar mass WD’s can be ignited through a double detonation mechanism to give rise to thermonuclear explosions in the context of either the SD or DD progenitor scenario.
The initial detonation in this model is triggered by accumulating a Helium shell on top of the primary WD through either stable mass transfer, meaning the sub-Chandrasekhar mass double-detonation model; or unstable mass-transfer, meaning the so-called D6 model; from a secondary in a binary system.

In the sub-Chandrasekhar-mass double-detonation scenario, shown in figure three, the WD accretes material from a Helium-burning star or a Helium WD companion via stable mass-transfer to accumulate a Helium-layer on its surface. If the Helium shell reaches a critical mass of around zero point zero two, to zero point two Solar masses, which is, however, quite uncertain, an initial detonation of the Helium shell is triggered and eventually ignites a second detonation in the core. This leads to a thermonuclear explosion of the entire sub-Chandrasekhar mass WD.

On the one hand, several binary systems composed of a WD and a Helium-rich companion star have been detected observationally, for example KPD 1930 plus 2752, V445 Pup, HD 49798, and others; which seems to support this scenario. For example, CD minus thirty, 11223 is a binary system containing a WD and a sub-dwarf-B, sdB, star, in which the WD mass is MWD equals zero point seven six solar masses, the companion mass is MsdB equal to zero point five one solar masses, and the orbital period is only Porb around one point two hours.
Venneset and others suggested that CD minus thirty, 11223 will likely explode as a SN One-a via the sub-Chandrasekhar double-detonation mechanism during its future evolution. Very recently, Kupfer in 2022 predicted that PTF1 J2238 plus 7430 would lead to a thermonuclear explosion in the context of the sub-Chandrasekhar double-detonation scenario with a thick Helium shell of around zero point seventeen solar masses.
On the other hand, different studies in the literature have shown that the sub-Chandrasekhar-mass double detonation models with a thick Helium shell zero point one to zero point two solar masses, produce an outer layer of SN ejecta enriched with titanium, Ti, chromium, Cr, and nickel, Ni, leading to predicted spectra and light curves that are inconsistent with the observations of SNe One-a.
However, numerous complications remain to be solved in such a model, and both the production of IGEs in the outer layers and the predicted observables, such as spectra and color, are rather sensitive to the total mass, the thermal and the chemical conditions of the Helium shell, and to details of the treatment of radiative transfer modeling.

For instance, Kromer showed that pollution of the Helium shell with carbon 12 helps to bring the predicted observables into better agreement with observations of normal SNe One-a. More recently, some updated simulations have shown that double detonations of sub-Chandrasekhar mass WD’s with a thin and C-polluted Helium shell holds promise for explaining SNe One-a, including normal SNe One-a and peculiar objects.
Figure five shows an example of the sub-Chandrasekhar-mass double-detonation simulation of a one solar mass CO WD with a thin Helium shell of zero point zero sixteen solar masses from have suggested that the sub-Chandrasekhar-mass double-detonation scenario might be viable for producing spectroscopically normal SNe One-a if the Helium layer is sufficiently thin, around one hundredth of a solar mass, and modestly enriched with core material. This indicates that double detonations of sub-Chandrasekhar-mass WD’s may contribute the bulk of observed SNe One-a. However, the exact critical Helium shell mass required for successfully initiating double detonations of the entire sub-Chandrasekhar mass WD remains uncertain. In addition, the exact Helium retention efficiency of the accreting WD in the progenitor system is still poorly constrained.

Section three point one point four. Carbon-ignited violent mergers.
The “C-ignited violent merger model” of figure three is one of the modern versions of the DD scenario. In this model, unstable dynamical accretion of material from the secondary, less massive, WD on to the primary WD causes compressional heating sufficient to directly trigger a detonation of a CO core in primary WD, producing an SN one-a.
While the original DD scenario assumes an explosion of a merged object exceeding the Chandrasekhar mass limit, in the violent merger model the explosion triggers already during the merger process before the two stars are completely disrupted.
Therefore it proceeds in sub-Chandrasekhar mass WD’s. This scenario avoids the problem of a potential collapse to a neutron star in an AIC.

It has been shown that the violent mergers of two CO WD’s that involve a single carbon detonation in the primary star can generally explain the observational properties of a sub luminous SNe One-a, such as 1991bg-like events SN 2010lp and the SN 2002es-like event iPTF14atg.

However, the triggering of the detonation during the violent merger phase is still poorly constrained.

Section three point two point five. Helium-ignited violent mergers.
The Helium-ignited violent merger model, or “dynamically driven double-degenerate double-detonation” (D6) model, is another modern version of sub-Chandrasekhar explosions in the DD scenario, in which SNe One-a are produced through the double detonation mechanism during the merger of two WD’s, see Figure three. In the D6 model, an initial Helium detonation triggers on the surface of a heavier CO WD primary due to unstable dynamical Helium accretion from the less massive secondary which could be either another CO WD with thin surface Helium layers, a Helium WD, or a hybrid Helium-CO WD. Via a double-detonation mechanism, the initial Helium detonation initiates into a detonation of CO core, producing an SN one-a, shown in figure six.

Because the Helium detonation in this model proceeds in a dynamic stage and not in a massive
Helium layer at hydrostatic equilibrium conditions, the impact of the Helium detonation products on the observables is reduced compared to the classical sub-Chandrasekhar mass double detonation scenario. For instance, it has been shown that the double detonation explosion in the violent merger of two COWD’s with masses ofzero point nine and one point one solar masses can closely resemble normal SNe One-a, indicating that the D6 model has the potential to explain the bulk of normal SNe One-a.

Interestingly, the secondary WD may survive from the explosion in the D6 model and become a hypervelocity WD with a velocity of greater than around 1000 kilometers per second, suggested that three hypervelocity runaway stars with a velocity of greater than around 1000 kilometers per second detected in the Gaia survey are likely to be WD companions that survived the D6 SNe One-a scenario.

However, the fate of the secondary WD in this model is rather unclear.

Recent investigations of the fate of secondary WD’s with self-consistent 3D hydrodynamical simulations, have confirmed that the primary WD can explode as an SN one-a. But there is a large uncertainty on the question of whether the secondary WD detonates or not. In contrast, others claim that an initial Helium detonation does not ignite a carbon detonation in the underlying WD.

Section three point two point six. Other proposed explosion models.
In the framework of either Chandrasekhar-mass or sub-Chandrasekhar-mass explosion, some other possible explosion models have been proposed for SNe One-a, including:
One. The core-degenerate model, in which the WD merges with the core of an AGB star during the CE phase, triggering a thermonuclear explosion inside the envelope.
Two. Tidal disruptions, in which the tidal interaction of a WD with a black hole triggers a thermonuclear explosion.
Three. Head-on collisions of two WD’s, in which two WD’s collide in a binary or triple-star system, leading to a thermonuclear explosion due to the resultant shock compression.
Four. The spiral instability model, in which a spiral mode instability in the accretion disk forms during the merger of two WD’s and leads to a detonation on a dynamical timescale resulting a SN one-a.
In Table 2, we present an overview of the main characteristics of different explosion mechanisms of SNe One-a. Again, the same cautionary remark as for Table 1 applies.

Four. RATES AND DELAY TIMES.
The observationally-inferred SN one-a rate in our Galaxy is about 2.84 plus or minus zero point six times ten per thousand years.

The observed delay-time distribution of SNe One-a, DTD’s, meaning the distribution of durations between star formation and SN one-a explosion, covers a wide range from around ten mega years to ten giga-years.

By comparing the expected rates and DTD’s of SNe One-a from BPS calculations for different proposed progenitor models with those inferred from the observation, several studies attempted to place constraints on the nature of SN one-a progenitor systems

In summary, no single proposed progenitor model is able to consistently reproduce both the observed SN one-a rates and the DTD’s, see Figure seven. The DD progenitor model generally predicts a broad range of delay times that follow an inverse t power-law, which is similar to the overall behavior of the observed DTD. But a sharp decrease of SN one-a rates for delay times shorter than 200Myr is seen in the DD model.
This is inconsistent with a significant detection of prompt SNe One-a with delay times of t bounded by 35 to 200 mega years.

BPS calculations have predicted that SD models with a MS or a RG donor mainly contribute to intermediate delay times of a hundred million to a billion years, and long delay times of greater than 3 Giga-years, respectively.

SD models with a Helium star donor are expected to contribute to delay times shorter than a hundred mega years.
The SD scenario generally tends to predict much lower SN one-a rates than those of the DD scenario
However, a large variation of the results among different BPS studies is seen.
One should always keep in mind that there are significant uncertainties in the theoretical predictions of SN one-a rates and delayed times from BPS calculations. On the one hand, constraints on the mass-retention efficiencies in the SD scenario are still rather weak yet studies show that there is a significant impact of the mass-retention efficiencies on BPS results such as rates and DTD’s.
On the other hand, the predictions of BPS calculations sensitively rely on the assumed parameters in specific BPS codes such as the CE evolution, star-formation rate and initial mass function. However, to date, strong constraints on these parameters, for example the CE efficiency, are still lacking. This limits the predictive power of the BPS results.

Section five. OBSERVABLES OF THERMONUCLEAR SUPERNOVAE.
The approach to compare the observational features predicted by different progenitor models with observations has long been used to provide important clues to the yet poorly understood origin and explosion mechanism of SNe One-a. Over the past decades, substantial effort in modeling SNe One-a aimed at the prediction of optical observables light curves and spectra;
The main goal was to distinguish between explosions of Chandrasekhar mass and sub-Chandrasekhar mass WD explosions as well as different mechanisms of thermonuclear combustion in these events. Despite all efforts, degeneracies make it difficult to draw firm conclusions.
Besides optical light curves and spectra predicted by radiative transfer calculations in the context of different explosion mechanisms, certain other observational signatures are also expected to be indicative for different progenitor scenarios, including the detection of pre-explosion companions, H, Helium lines in SN one-a late-time spectra caused by material stripped from the companion during its interaction with the SN ejecta, early excess emission due to the ejecta–companion interaction, narrow absorption signatures of circumstellar material, CSM, radio and X-ray emission from CSM interactions, surviving companion Stars, and WD remnants, polarization signals, SN remnant, SNR, morphology, etc.
In this section, we will give a detailed overview to the observables predicted for different phases, from the pre-explosion phase to the SNR phase, of SNe One-a from currently proposed progenitor scenarios and their comparisons with the observations. In particular, we focus on the question of how a binary companion star in the SD scenario shapes the observables of SNe One-a.

Section five point one. Pre-explosion companion stars.
The companion stars in potential progenitor models of SNe One-a fall into two categories
One. Nondegenerate companion stars (MS, SG, RG, AGB or Heburning stars) in the SD scenario;
Two. WD companions in the DD scenario. Becuase a non-degenerate companion star is much brighter than a WD, a luminous source is expected to be detected in pre-explosion images at position of the SNe One-a if they are generated from the SD progenitor scenario. Therefore, analyzing pre-explosion images from the SN position provides a direct way to test the SD progenitor scenario.

On the theoretical side, Han in 2008 has comprehensively addressed the pre-explosion observable properties, luminosities, effective temperatures, masses, surface gravity, orbital and spin velocities, of MS companion stars at the moment of SN one-a explosion by performing BPS calculations for the WD + MS progenitor model.
Following this work, Liu in 2015, extended the calculations to present pre-explosion properties of different non-degenerate companion stars, including the MS, SG, RG companions in the SD scenario, and the Helium-burning companion stars from both the SD and sub-Chandrasekhar mass double-detonation scenarios. Wong in 2021 also made predictions for the properties of the Helium-star donors at the time of explosion for a set of progenitor systems involving a CO WD and a Helium star.

On the observational side, different studies have attempted to search for the expected non-degenerate companion stars by analyzing pre-explosion images at the SN position, for example, those taken by the Hubble Space Telescope, HST.
To date, however, no progenitor companion star has been firmly detected in the analysis of pre explosion images of normal SNe One-a
But there are some possible pre-explosion detections recently reported in several SNe One-ax.
For instance, in 2014 McCully detected a blue luminous source in pre-explosion image of an SN one-ax event, SN 2012Z.
As shown in Figure eight, the properties of this pre-explosion luminous source, SN 2012Z minus S1, have been found to be consistent with those of a Helium-star companion to the exploding WD.
Interestingly, latetime observations taken about 1400 days after the explosion by the HST have shown that SN 2012Z is brighter than the normal SN 2011fe by a factor of two at this epoch.
Comparing with theoretical models, this suggests the excess flux to be a composite of several sources: the shock-heated companion, a bound WD remnant that could drive a wind, and light from the SN ejecta due to radioactive decay.
Analyzed pre-explosion HST images of another SN one-ax, SN 2014dt, but no source could be detected in this case.

Section five point two. Ejecta–companion interaction.

After the explosion in the SD scenario, the ejecta expand freely for a few minutes to hours before hitting the non-degenerate companion star, engaging into ejecta– companion interaction. The effect of a SN explosion on a nearby companion star has been studied since the 1970’s
There are several ways in which the SN blast wave can modify the properties of companion stars during the ejecta-companion interaction, giving rise to observables that can be used to constrain SN one-a progenitors.
First, the SN ejecta significantly interact with the companion star after the explosion, stripping some H-rich and Helium-rich material from its surface. This effect is caused either by the direct transfer of momentum or by the conversion of the blast kinetic energy into internal heat, meaning, by evaporation, ablation. As a consequence, some H, Helium lines caused by the stripped material may be present in late-time spectra of SNe One-a.
Second, the shock heating injects thermal energy into the companion star during the interaction, leading to a dramatic expansion of the surviving companion star so that it displays signatures that are different from a star without experiencing the ejecta–companion interaction. For example, it could become more luminous and have a lower surface gravity.
Third, radiative diffusion from shock-heated ejecta during the interaction is expected to produce an early excess in optical, UV or X-ray emission, see Kasen 2010.
Fourth, the surface of a companion star may be enriched with heavy elements, for example, Nickel, Iron or Calcium, deposited by the SN One-a ejecta, which might be detectable in the spectra of a surviving companion star.
Finally, the companion star survives from the explosion and retains its pre-explosion orbital velocity after the SN explosion, which leads a high peculiar velocity compared with other stars in the vicinity.

The typical pre-explosion orbital velocities of the Hydrogen rich and Helium-rich companions in the SD Chandrasekhar mass scenario are eighty to two eighty kilometers per second, and around two fifty to five hundred kilometers per second, respectively.
The Helium star companions in the sub-Chandrasekhar mass double detonation scenario and the Helium WD, or the CO WD which transfers its outer Helium layers, companions in the D6 model are respectively expected to have pre-explosion orbital velocities of around four hundred to one thousand kilometers per second and greater than a thousand kilometers per second.

Section five point two point one. Searches for stripped hydrogen and helium.

The earliest study of the effect of a SN explosion on a companion star was done by Colgate in 1970. Helium suggested that the companion star receives a kick that is mainly caused by the evaporation from the stellar surface, meaning the ablation, although there is also a small kick from the direct collision with the SN ejecta. Cheng in 1974 further investigated the impact of a SN shell onto a two point eight two and twenty solar mass MS companion star for various binary separations, SN shell masses, and velocities. Helium concluded that the MS companion star could survive from the interaction with SN shell. Upon these two works, several analytical models were developed to estimate the amount of stripped H mass and the kick velocity received by the companion star during the ejecta–companion interaction for MS companion stars with an n equals three and and n equals two thirds polytrope, which is appropriate for a low-mass MS, and for RG companion stars.

To test the analytic prescription of Wheeler from 1975, several numerical simulations were performed for low-mass MS companions and RG stars.
In particular, Livne suggested in 1992 that almost the entire envelope of a RG star could be stripped off by the SN blast, imparting a velocity to the stripped material around a thousand kilometers per second, much smaller than that of SN ejecta, of around ten thousand kilometers per second. Following the 1975 work of Wheeler, Meng in 2007 semi-analytically estimated the amount of stripped Hydrogen mass due to SN One-a explosions by adopting the binary and companion properties constructed with detailed binary evolution calculations. However, they underestimated the total stripped companion masses because of neglecting the effect of the ablation on the companion surface.
More recently, updated two-dimensional 2D and 3D simulations with grid-based or smoothed particle hydrodynamics, SPH, methods have been presented that investigate the details of the interaction between SN one-a ejecta and the companion star.

For instance, Marietta performed high-resolution 2D simulations in 2000 to comprehensively study the interaction of SN one-a ejecta in a variety of plausible progenitor systems with MS, SG and RG companions. However, they assumed the structure of single MS, SG, RG stars for the companion in their simulations.
The 2000 study of Marietta for MS companion stars was updated to 3D simulations with the smoothed particle hydrodynamics (SPH) method by Pakmor in 2008, in which they considered the effect of pre-explosion mass transfer on the structures of a companion star at the moment of SN explosion. However, they computed their companion star models by constantly removing mass while evolving a single MS star to mimick the detailed mass transfer processes in a binary system. This makes their MS star model much more compact than one constructed from a full binary evolution calculation.

Therefore, they predicted a small amount of stripped H masses of one to six percent of a solar mass for MS donor model. Liu further developed the work of Pakmor by adopting more realistic companion star models constructed from detailed, state-of-the-art binary evolution calculations.
They also extended simulations to cover different companion stars, MS, SG and Helium-star, and a range of binary separations and explosion energies.
Pan in 2012 employed adaptive mesh refinement, AMR, simulations to study the ejecta, companion interaction for MS, RG and Helium-star companions with different binary separations and explosion energies.
In their simulations, however, they did not follow the full binary evolution but used initial conditions with a constant mass-loss rate when constructing their companion stars.
The main results of ejecta–companion interaction of SNe One-a in the literature can be summarized as follows.
One. 2D or 3D hydrodynamical simulations have predicted that about 5 per cent to 30 per cent of the companion mass, meaning greater than around ten percent of a solar mass can be stripped off from the outer layers of a MS or SG companion star, see top panel of figure ten. For RG companions, almost the entire envelope is removed by SN one-a blast wave. In the case of a Helium companion star, about one to three per cent of the mass is lost in the interaction.
Two. The SN impact affects not only the companion star, but also the SN ejecta themselves. The presence of a companion star strongly breaks the symmetry of the SN one-a ejecta after the interaction.
The stripped companion material is largely confined to the downstream region behind the companion star, creating a hole in the SN debris with an opening angle of about thirty to a hundred and fifteen degrees.
Three. Depending on the different stellar types, the companion stars receive kick velocities of a few ten kilometers per second to one hundred kilometers per second , which are lower that their pre-explosion orbital velocities. This indicates that the surviving companion star should move with a velocity which is largely determined by its pre-explosion orbital velocity.
Four. The characteristic velocities of stripped companion material for the MS, SG, RG and Helium star companions are five hundred to eight hundred kilometers per second , less than around nine hundred kilomeers per seonc, four to seven hundred kilometers per second, and eight hundred to a thousand kilometers per second respectively, which are slower than the maximum velocity of SN one-a ejecta, ten thousand kilometers per second, by about one order of magnitude.
This implies that Hydrogen, Helium lines caused by stripped companion material become visible only at late-times when the photosphere recedes and moves to low velocity regions, revealing the inner SN one-a ejecta.
Five. For a given companion model, the amount of stripped companion mass and kick velocity received by the companion star during the interaction decrease as the binary separation increases, which can be fitted by power-law relations.
Six. The dependence of the amount of stripped mass and kick velocity on the explosion energy is in agreement with linear relations. Both quantities increase as the explosion energy increases.
Seven. The companion star is generally expected to survive the explosion and becomes a runaway or hypervelocity star. However, whether a Helium WD companion in the double-detonation model would survive the explosion is still unclear.
Eight. The companion surface could be enriched with heavy elements, contamination, from the low-expansion velocity tail of SN one-a ejecta, which provides a way to observationally identify the surviving companion stars in SNRs. However, the exact level of contamination is still rather uncertain in current models because of uncertainties of mixing of the contaminants in the envelope.
One of the key questions of the SD scenario is whether the signatures of swept-up H or Helium due to the interaction can be detected in late-time spectra of SNe One-a.
On the theoretical side, by performing the 1D parameterized spherically symmetric radiative transfer calculations, Mattila concluded in 2005 that Balmer lines should be detectable in SN one-a nebular spectra if the stripped H masses are greater than around three percent of a solar mass.

In their models, they artificially added some uniform density solar-abundance material with a low expansion velocity of a thousand kilometers per second at the center of SN one-a ejecta of the W7 model from Nomoto 1984. Recently for the first time were performed, 3D Monte Carlo simulations with a non-local thermodynamic equilibrium, NLTE, radiative transport code to determine the signatures of stripped companion material in nebular spectra of SNe One-a as a function of viewing angle. In this study, more realistic distributions of stripped companion material and post-explosion SN One-a ejecta structures were adopted based on 2D hydrodynamical simulations of the ejecta–companion interaction.
However, the Sobolev approximation as well as the simplified treatment on line overlap and multiple scattering causing some uncertainties in the results. Extension of previous calculations with a set of 1D NLTE steady-state radiative transfer simulations by covering a broader parameter space, a large range of masses for the ejecta, Nickel 56, and stripped material, and computing line overlap and line blanketing explicitly. These models adopted a 1D parameterized spherically symmetric SN ejecta structure.

In summary, all radiative transfer calculations in the literature for SNe One-a with stripped companion material have concluded that the ejecta-companion interaction in the SD scenario produces significant and detectable signatures of stripped Hydrogen, Helium in late-time spectra. They further provided the dependence of line luminosities from stripped H-Helium-rich material on the amount of stripped H-Helium mass.
This indicates that searching for Hydrogen-Helium emission due to stripped companion material in late-time spectra of SNe One-a is promising for identifying the SD or DD nature of the progenitor system.
On the observational side, a series of observations have attempted to search for narrow, low-velocity H, Helium emission lines expected to be caused by swept-up H, Helium in late-time spectra of SNe One-a. But to date, no strong evidence for such H, Helium emission has been found in late-time spectra of most SNe One-a, even for the nearby SNe One-a with very high quality observations, meaning, SN 2011fe and SN 2014J.

A detection was reported only for two fast-declining, sub-luminous events, SN 2018cqj and ASASSN 18tb.
However, the H alpha emission lines detected in SN 2018cqj and ASASSN-18tb have been suggested to be caused by either CSM interaction or by H material stripped from a companion star.
Furthermore, by analyzing late-time spectra of SNe One-a, one can convert the line luminosity limits to limits on the mass of H, Helium in SN one-a progenitors based on the current radiative transfer calculations for stripped companion material.

Statistical limits on stripped H, Helium mass by analyzing a number of SN one-a late-time spectra have been given by Tucker in 2020, and they are summarized in Figure eleven. Comparing these statistical limits from the observation with the stripped H, Helium masses derived from numerical simulations, we can examine the validity of SD scenario for SNe One-a. As shown in Figure eleven, the observational constraints on the swept-up H, Helium masses are generally much lower than those from theoretical predictions, which poses a serious challenge for the SD scenario.
Current radiative transfer simulations for SNe One-a with stripped material are still afflicted with uncertainties, because they either simply assume parameterized spherically-symmetric SN ejecta, or the treat line overlap and multiple scattering in an approximate way.
For stricter predictions of the strength of H and Helium lines in late-epoch spectra, multi-dimensional NLTE radiative transfer calculations are needed that use the output ejecta model from 3D impact simulations and treat line overlap and multiple scatterings in detail. Moreover, there are some other possibilities that may explain to the lack of H-He emission in late-time spectra. For instance, the “spin-up, spin-down” model may lead to a compact companion star whose H, He-rich envelope has been stripped before the explosion, causing the absence of stripped H, Helium material during the interaction.

Section five point two point two. Early excess emission.
Different progenitor models and explosion mechanisms of SNe One-a may produce distinct early light curves. Therefore, early light curves of SNe One-a have been thought to play an important role in constraining their progenitor systems and explosion mechanism. For example, Nugent used the early light curves of the nearby SN 2011fe to constrain the radius of its exploding star, confirming that it must have been a WD. In the literature, different mechanisms have been proposed to cause an excess emission, meaning a “bump”, in early light curves of SNe One-a within the days following explosion, which will be described in detail below.
Companion interaction: Kasen (2010) predicted that the shock caused by the ejecta–companion interaction significantly heats SN one-a ejecta to high temperatures, which causes a strong excess emission during the first few days after the explosion that is observable in the light curves within certain viewing angles in the SD scenario. This early-time excess emission is expected to be brightest in the ultraviolet (UV) wavelengths and becomes subordinate at longer optical wavelengths.
However, it can still cause a blue color evolution in the optical light curve. By applying BPS results to the analytical models presents the distributions of expected early UV emission for different SD progenitor systems. Because the DD scenario does not predict such early UV emission, detecting early strong UV emission within the days following explosion has long been considered a smoking gun for the SD scenario of SNe One-a.

For a given explosion model, early UV emission caused by the ejecta– companion interaction is strongly dependent on the ratio of binary separation to companion radius, assuming RLOF, at the moment of SN explosion. Therefore, the properties of this early UV emission are expected to provide a clue to the types of non-degenerate companions.

Sub-Chandrasekhar-mass double-detonations: The burning of the initial Helium shell in sub-Chandrasekhar-mass double-detonation explosions can leave heavy, radioactive material in the outermost ejecta. A more massive Helium shell is expected to produce more radioactive material.
The decay of this heavy, radioactive material could create an excess luminosity in the early light curves of SNe One-a.
This may produce the early gamma emissions detected in SN 2014J Nickel-shell models: Piro and Nakar in 2013 suggested that the location of Nickel 56 in SN one-a ejecta could have noticeable impact on early-time light curves of SNe One-a.
Further investigation showed how the distribution of Nickel 56 in the outer layers of the ejecta shapes early light curves of SNe One-a. More recently, comprehensive predictions of early-time curves of SNe One-a from a series of models containing Nickel 56 shells with different masses and widths in outer layers of SN one-a ejecta. They have shown that a Nickel 56 shell in outer SN one-a ejecta will lead to an early excess luminosity at a few days after the explosion.

CSM interaction: The presence of CSM is expected in different progenitor scenarios, which can also significantly affect early light curves of SNe One-a.
The presence of CSM can lead to a significant shock cooling emission during the first few days after the explosion, which can affect the early-time rise of the light curves of SNe One-a.
Depending on the degree of mixing of Nickel 56 in the exploding WD and the detailed configurations of the CSM, this shock cooling emission can lead to early-time signatures, such as the early colour evolution, similar to those caused by the eject