feature of Type I supernovae, in addition to even late time observations of SNe Ia (Tucker et al. 2020). In the double degenerate scenario, a SN Ia may be triggered via some merger event, either before or after the full disruption of the companion (Pakmor et al. 2010(Pakmor et al. , 2012;;Kashyap et al. 2015;Raskin et al. 2014;Kashyap et al. 2018;Neopane et al. 2022). An increasingly promising theoretical explosion mechanism that may occur in the double degenerate scenario is the double detonation, which was first proposed by Nomoto (1982) (see Townsley et al. 2019, for a history). The double detonation may occur in a carbon/oxygen sub-Chandrasekhar white dwarf that has a helium shell, which may increase in shell mass by accretion from a helium-rich companion. The helium shell detonates atop the primary WD and generates an inward-moving shock that converges within the core, igniting it and leading to a complete detonation of the WD (see Tanikawa et al. 2018;Gronow et al. 2021;Pakmor et al. 2022, for recent 3D simulations). This companion could theoretically be a non-degenerate star, but we focus on the prospect of a double degenerate system for this work in the context of supporting observational evidence.

A variety of studies have shown that the double detonation may indeed be a viable SN Ia channel, as the spectra and light curves around maximum light from explosion models can be satisfactory matches for some observed SNe Ia (Sim et al. 2010;Kromer et al. 2010;Woosley & Kasen 2011;Blondin et al. 2017;Townsley et al. 2019;Shen et al. 2021a). Additionally, the breadth of many observed SNe Ia is also satisfied by theoretical models of double detonations (Polin et al. 2019;Shen et al. 2021b). This is possible due to the variable mass of the sub-Chandrasekhar progenitor and line of sight-dependence in double detonations which allows for a wide range of observational properties, including peak brightness and photospheric velocities (Shen et al. 2021b;Collins et al. 2022). The double detonation progenitor may also vary in composition and thickness of the surface helium layer which determine the production of high velocity, high-mass elements that can have a significant impact on the observables (Woosley & Kasen 2011;Polin et al. 2019;Shen et al. 2021b). It is worth noting that while the double detonation has seen much success in the past decade, there remains some doubt about the scenario, particularly regarding the robustness of the core ignition prior to the complete disruption of the companion (Moll & Woosley 2013;Fenn et al. 2016;Roy et al. 2022).

This wide array of variables is potentially a boon for the double detonation when it comes to explaining the span of most SNe Ia given the broad combinations of peak luminosities, decline rates, and spectral indicators that the candidate scenario can generate. Because of this flexibility, the double detonation may be able to explain the scatter and outliers across the Philips relation. For example, 2011fe and 2011by are a particular set of "twin" SNe that are extremely similar in their optical spectra and light curves, but differ markedly in the UV and have a relatively large peak magnitude difference of 0.33 (Foley & Kirshner 2013;Graham et al. 2015;Foley et al. 2020). This specific contradiction to the standard SN Ia model has been suggested to be from progenitor metallicity differences (Foley et al. 2020), though this is not conclusive and metallicity alone cannot explain all of the other peculiarities observed in the population of SNe Ia. It is possible that some of these may be solved by the right combination of progenitor parameters and observed line of sight in the double detonation scenario. That is, one might be able to change multiple parameters of the underlying system in such a way as to keep something as specific as the maximum light optical spectrum fixed while other features such as the UV and maximum brightness vary.

This flexibility, however, can present a challenge when trying to interpret observables within the traditional one-parameter family model of SNe Ia. To this end, these variations are often characterized as "scatter" about some average one-parameter family. Ultimately, a fully functional model of SNe Ia should resolve this distinction, providing physical explanations for both the general one-parameter variation as well as the departures from it. There is much work to be done in this respect, as the capability to simulate the double detonation scenario continues to mature. Additionally, the need for costly non-local thermodynamic equilibrium (non-LTE) radiative transfer calculations has become more evident, as some observational features, of both the niche and ubiquitous variety, require such calculations (Boyle et al. 2017;Shen et al. 2021a;Collins et al. 2023). This is a significant issue for many supernova models, but it is especially burdensome for the double detonation scenario given its inherent multidimensionality.

Another possible variable affecting the observables of double detonation events is the fate of the donor companion. Given that the double detonation occurs in a tight, likely double degenerate, binary and the primary WD is completely detonated, the donor may be expected to be ejected as a high velocity runaway. While evidence of such a surviving star long eluded observation, a handful of candidates have been identified in recent years using Gaia data (Shen et al. 2018;El-Badry et al. 2023). Alternatively, it may be possible that the donor WD can also be destroyed in the event. Papish et al. (2015) first showed a simulation where a helium companion detonates following the impact from a double detonation, i.e. a "triple detonation". A pair of recent computational studies (Tanikawa et al. 2019;Pakmor et al. 2022) have examined the scenario in which a helium-shelled carbon/oxygen companion undergoes its own double detonation following the initial double detonation, i.e. a "quadruple detonation". These 3dimensional studies show the mechanics of how the core detonation of the primary triggers a delayed detonation of the donor's helium shell, leading to a second double detonation.

The predicted observables from these unique detonations are scant, however. Pakmor et al. (2022) presented 1-dimensional radiative transfer results for their sole 1.05 + 0.7 M ⊙ quadruple detonation model and found that the additional mass and burning yields from the companion detonation had surprisingly little impact on the observables, albeit calculated with an angleaveraged ejecta profile for a low-mass and low-Fe-groupgenerating companion. This result begs the question of how the quadruple detonation scenario fares across various lines of sight for a range of binary mass configurations, particularly those with a relatively high-mass companion.

Some rare objects display overluminous brightnesses so high that they have been labeled "super-Chandrasekhar" due to the inferred ejected mass (Howell et al. 2006;Ashall et al. 2021). Attempts to explain these events have included the explosion of a super-Chandrasekhar WD (Hachinger et al. 2012) and violent merger of a high-mass degenerate binary (Pakmor et al. 2012). Having both stars in a high-mass binary explode presents an interesting candidate for these objects. The number of WD binaries with total masses much above the Chandrasekhar limit are expected to be a fraction of their lower mass counterparts (Nelemans et al. 2001), so these events would likely be rare. It is possible, however, that if a few of these events have been observed, they may have appeared normal enough amongst the breadth of SNe Ia to be automatically assumed to be from a single star detonation. This additional degree of freedom is interesting from the standpoint of observed diversity among SNe Ia. In the double detonation scenario, both the 56 Ni mass and the total ejecta mass are determined by the primary WD mass, and therefore are directly tied. The two star scenario breaks this by allowing explosions with the same 56 Ni mass to have different total ejecta masses depending on the mass of the secondary.

While the conclusion from Pakmor et al. (2022) is extremely interesting, multidimensional analysis across a wider range of progenitor configurations is necessary to evaluate this scenario further. To that end, this work simulates a number of 2D two star explosion models and presents their multi-dimensional synthetic observables. The progenitors used in this work are bare WDs (for the purpose of reduced computational complexity), but approximate the dynamics of triple and quadruple detonations that may otherwise occur when helium shells are considered. We refer to these models as triple and quadruple detonations in this work, despite the exclusion of helium in our calculations. Our models consist of a number of binary mass configurations, including those that produce significant amounts of radioactive material in the companion detonation.

We describe our computational setup and choice of progenitor systems in Section 2. The multi-dimensional light curves and spectra from these two star explosion models are shown in Section 3 and compared to both our previous single star double detonation models and observed SNe Ia. We then discuss the overview of our results in the context of observed SNe Ia in Section 4 before summarizing this work in Section 5.

We use the multiphysics code FLASH (Fryxell et al. 2000) to simulate the detonations in this work, in a similar manner as Boos et al. (2021). We use an adaptive mesh with a minimum cell size of 8 km. We use the Helmholtz EOS and aprox13 nuclear network, along with a burning limiter. 50,000 equal-mass tracer particles are distributed by density within each progenitor. The temperature and density histories from these particles are later used in nucleosynthetic post-processing using MESA and a 205-nuclide network. The significant modifications to our setup from previous work, which involve the change of nuclear network, exclusion of helium shells, and inclusion of the companion WD, are described in Sections 2.1 -2.2.

To generate the spectra from the detonation simulations, we use the Monte Carlo radiative transfer code Sedona (Kasen et al. 2006) under the assumption of LTE. The manner of our radiative transfer calculations are unchanged from that described in Shen et al. (2021b), other than a three-fold reduction of particles and using ejecta out to maximum velocities of 4.5 × 10 9 cm s -1 , rather than the original 3×10 9 cm s -1 . This increase in velocity domain is important for the prediction of the UV region of the spectrum.

In this work, we choose to use the nuclear network aprox13 (Timmes et al. 2000;Fryxell et al. 2000), which To evaluate our additional approximations (the lack of helium shell and reduced nuclear network) of our setup, we conduct a detonation of an isolated, non-shelled WD in our new setup to compare to the true double detonations of Boos et al. (2021). In this comparison simulation, we detonate a 1.00 M ⊙ C/O WD by way of an artificial hotspot within the star. The hotspot is placed where the shock from the helium shell detonation converged in the counterpart model in Boos et al. (2021).

To determine the nuclear burning and observational effects from the lack of helium shell and reduced nuclear network in the simulation, we compare this non-shelled model with the 1.00 M ⊙ core, 0.02 M ⊙ helium shell model from Boos et al. (2021). These models have the same C/O mass and similar central densities. The differences in post-processed yields between the core detonations of these models are shown in Table 1. The 205-nuclide network used in the post-processing is the same for both models. We find that the core nucleosynthetic yields are fairly similar between the two cases. Around 0.02 M ⊙ more 56 Ni is produced in the shelled progenitor using a larger network in the hydrodynamic simulation. This slight increase in burning may be attributable to the minor density enhancement of the core

%RORPHWULF %RORPHWULF %RORPHWULF %RORPHWULF %RORPHWULF %RORPHWULF 8 8 8 8 8 8 % % % % % % 9 9 9 9 9 9 5 5 5 5 5 5 o o o , , , , , , +HOLXPVKHOOHG0 :' %RRVHWDO %DUH0 :'WKLVZRUN 0 'D\VIURP0 B, max Figure 1. Multiband light curves from the detonation of an isolated 1.00 M⊙ WD, compared with that of a double detonation of a thin helium shell 1.02 M⊙ WD (Boos et al. 2021; Shen et al. 2021b). Three lines of sight from each model are shown, where the dotted, solid, and dashed lines represent the model as observed from a southern, equatorial, and northern line of sight, respectively.

from the helium detonation or the more accurate nuclear network.

Figure 1 shows the light curves of these two models for three lines of sight. Despite the lack of a helium shell and use of a less complete nuclear network, the light curves are extremely similar between the two models. The largest deviation is seen in the post peak decline at the northern line of sight in U-band, but for the most part, the light curves are very nearly the same. We note that "north" in this work is defined as the positive zdirection of our simulations.

Figure 2 shows a spectral comparison of these two models at various times around the peak B band time at the line of sight where they disagree the most (42 o north of the equatorial plane). The spectra are very similar at each time, though the UV portion is slightly enhanced at peak B-band time and later in the bare C/O WD case, likely due to the lack of line blanketing from shell ashes. Additionally, there is a lack of latetime suppression around 4100 Å that is not observed at lines of sight south of those shown in Figure 2.

In summary, there is remarkably little difference in the observables between explosions of two progenitors that are nearly identical, save for the presence of a thin helium shell. Thus, we determine that it is practical to model thin shell double detonations without the shell material or detonation, especially for the approximated evaluation of the two star explosion scenario performed in this work.

The details for each of our two star simulations are summarized in Table 2. At initialization, the primary star is placed at the origin of the grid as it was in Boos et al. (2021). The secondary is placed offset from the primary in the positive z-direction, with the central axis of both stars aligned with the axis of symmetry for the simulation. At the time of disruption, the system separation should be such that the donor fills its Roche lobe. Since the binary has no angular momentum in these 2D simulations, a companion initialized at the Roche limit at rest will gain velocity and move towards the primary within the few seconds it takes for the first detonation to influence the companion. So, we initialize the companion WD at a separation slightly below the Roche lobe radius with a velocity (∼ several 10 7 cm s -1 ) away from the primary such that the companion is at the Roche limit with roughly no velocity when the impact shock from the primary detonation is propagating through it. The low-density, domain-filling material outside of the stars (referred to as "fluff"), is slightly changed from the scheme detailed in Boos et al. (2021). The fluff now has a uniform density within a radius that encloses both progenitors, outside of which it declines in a log-linear manner.

Since the helium detonations that generate the converging-shock ignition of the C/O core are not considered in this work, we use artificial hotspots to ignite all of the primary WDs, in addition to most of the companions. The location of these hotspots are informed by the shock convergence points found in previous works that considered helium shells for both double and quadruple detonations. This setup preserves the offcentered interior ignition and asymmetric progression of the core detonation that is characteristic to the double and quadruple detonation. The dynamics leading to each of the ignitions in this scenario is complex in reality, and may be particularly so for the companion helium detonation and subsequent core ignition due to the influence from the accretion and primary WD explosion. However, these dynamics are not the focus of this study; rather we seek to understand how these events may be observed assuming that the two star detonation in this scheme is plausible.

The circular hotspots used in this work are between 200 and 400 km in radius and have a temperature profile that peaks at 2×10 9 K in the center and linearly declines to roughly the local star temperature. We note that the critical hotspot sizes for each of these ignitions were not rigorously investigated in this work (see Seitenzahl et al. 2009 for critical sizes of this hotspot profile) given the relatively modest resolution and uncertain location and condition of the companion ignition. These hotspots are chosen slightly large to ensure ignition, so this study should be viewed as an evaluation of whether such explosions are observationally viable under the assumption that ignition occurs. We leave a thorough exploration into the initiation of the companion core detonation in particular to future works.

At initialization for each of our simulations, a hotspot is placed 100 km from the symmetry axis in the southern hemisphere of the primary, where the shock generated from a helium detonation ignited at the northern pole would otherwise converge and ignite the core (see Figures 2 and 3 of Boos et al. (2021) for a natural C/O core ignition). In some of our simulations, this ultimately leads to an ignition of the companion WD along its southern edge where the impact from the primary ejecta is the strongest, which we label as "direct" ignition cases. If the companion is not directly ignited, we place a hotspot along the symmetry axis in the northern hemisphere of the interior region of the companion Distance between primary origin and companion center at time of companion ignition f Pre-interaction density of the companion at its ignition point core, corresponding to the focus location of the shock created by a helium shell detonation that would be ignited at the southern pole, nearest the primary. Based on Pakmor et al. (2022) and a demonstration simulation with our setup using high-mass helium shells, this second WD ignition would be driven by the combination of shocks from both the companion helium detonation and primary WD detonation. Since the progenitors in this approximated work are bare of helium shells, only the shock from the primary WD detonation exists in our simulations. So, we roughly place the second hotspot in the companion at the position where the shock from a helium detonation would converge (∼ 1 -3 × 10 3 km from the companion center) at the time when the primary ejecta shock intercepts this location. We refer to these models as "interior" ignition cases, which approximate quadruple detonations.

We present two cases that undergo a direct ignition of the companion. The first is a model with a 0.40 M ⊙ helium companion that detonates following the detonation of a 1.00 M ⊙ carbon/oxygen primary. In this case, the helium companion ignites naturally when it is first impacted by the primary ejecta, producing the triple detonation similar to Papish et al. ( 2015 2019), we also find that the direct ignition of the helium companion is sensitive to the separation of the stars. We find a separation threshold of 38.2 × 10 8 cm for our 1.00 + 0.40 M ⊙ system, which is several 10 8 cm lower than the Roche lobe radius for this system. The helium companion ignites at a region of the star that is shocked to a density and temperature of 8.02×10 5 g cm -3 and 1.20×10 9 K, from an original pre-shock state of 2.75 × 10 5 g cm -3 and 3.00 × 10 7 K. This companion is made up of pure helium in the grid simulation, but is post-processed with 0.009 14 N (as in Boos et al. 2021) and elements above Z = 8 are scaled to solar metallicity.

The other direct ignition case is an alternate version of the 1.10 + 1.00 M ⊙ progenitor system that has a slightly smaller separation than its interior ignition counterpart, resulting in a direct ignition at the impact point on the near edge of the carbon/oxygen companion. This simulation has similar dynamics to the helium companion case, however in reality this carbon/oxygen companion may have some helium remaining on its surface when the system is first ignited which may suppress the ability of the primary ejecta impact to directly ignite the companion. For the purpose of this work, we wish to characterize both the interior and direct ignition possibilities. As such, we also consider this direct ignition model as an approximated triple detonation, under the supposition that the companion helium that is not considered in this work would have relatively little effect on the delay or occurrence of the ignition of the companion core.

Additionally, we show the results of a 1.00 + 0.70 M ⊙ binary where the secondary is not ignited and survives the impact from the primary detonation, which gives insight on how the surviving companion may affect the ejecta and observables of a single double detonation. In this simulation, the companion remains near the origin throughout the simulation. In order to perform radiative transfer calculations, we need to remove the bound material from the end-of-simulation ejecta. To that end, we cutoff the ejecta inward of 1,600 km s -1 , removing all of the bound material. We then calculate the mass is present, albeit with varying amounts, at all lines of sight.

The 2D ejecta in velocity space for each of our two star models, in addition to an isolated WD model, are shown in Figure 5. In general, we observe a relatively consistent ejecta structure in the quadruple explosion models where the companion ashes are embedded within the ashes of the primary, similar to what is seen in Tanikawa et al. (2019) and Pakmor et al. (2022). This is most clearly demonstrated in the 2D profiles of 28 Si, which is generated in the outer region of each of the massive progenitors and throughout the 0.70 M ⊙ ashes. In the isolated WD explosion, one clear band of 28 Si can be observed, peaking between 10,000 and 20,000 km s -1 , depending on polar angle. In the two star explosion cases, there are now two prominent bands of 28 Si, each belonging to one of the exploding stars. The velocity extent of these two concentrations are significantly different due to the suppressed expansion of the companion ashes imposed by the surrounding primary ejecta. A similar structure can also be seen in the 56 Ni of our two star explosions models where the 56 Ni from the primary detonation is found outside that of the companion, separated by a relatively narrow layer of predominantly intermediate mass elements that originates from the companion detonation. While the 3D simulations of similar binary star explosions in Tanikawa et al. (2019); Pakmor et al. (2022) show very similar ejecta stratification compared to our models, we find that our ejecta show less prominent asymmetrization, possibly due to multidimensional effects.

In the pair of triple detonation cases where the companion star is directly ignited (1.00 + 0.40 M ⊙ and 1.10 + 1.00 M ⊙ (direct ignition)), rather than via a delayed interior ignition, the ejecta structures are slightly different. Due to the smaller delay between star ignitions, these two models yield significantly increased velocities of the companion ashes at northern latitudes. A similar effect on the ejecta is seen in the triple detonation case from Tanikawa et al. (2019).

We note that a more precise prediction of the final state of the ejecta would demand the inclusion of the shell detonations. Not only will these shell detonations add two additional layers of Si-group material in thinshell cases (Polin et al. 2019;Boos et al. 2021), but they may also affect the timing and location of the core ignition in the companion. The placement of the artificial hotspots used to ignite the companions in this paper were influenced by ignition timings and locations of the core detonations in similar, but shelled, progenitors in Boos et al. (2021), but it is unclear exactly how the interaction between the converging shock from the he-lium shell detonation might interact with the northerlymoving shock from the primary detonation. For example, the companion core detonation may trigger earlier than expected, allowing for more companion ejecta to expand to higher velocities.

The final yields for key isotopes are listed in Table 3. As expected, we find the explosion yields from the primary star to be similar to previous detonation studies of sub-Chandrasekhar WDs (Fink et al. 2010;Shen et al. 2018;Polin et al. 2019;Gronow et al. 2021;Boos et al. 2021). Interestingly, the yields from our interior ignition companion detonations indicate more extensive burning than one would expect given the initial progenitor density. This is demonstrated in the yields from the 1.00 M ⊙ WD across several models, where it has the same initial density profile. When the 1.00 M ⊙ is detonated as the primary, or directly ignited as the companion, it produces 0.55 M ⊙ of 56 Ni. When it explodes as a companion after a interior ignition, however, it produces 0.61

This increased production of radioactive material in the companion is due to the shock induced from the detonation of the primary, which increases the density in the bulk of the companion prior to ignition. A demonstration of this density enhancement can be seen in Figure 6 which shows the density structure of the companion before impact and just before ignition. While some of the outer star material has been spatially disrupted (indicated by the green contour lines in Figure 6), the vast majority of the companion retains its spherical shape due to the low density enhancement relative to the original density of the inner WD. This enhancement also creates a disagreement in the yields between the interior and direct ignition models of the 1.00 M ⊙ companion, as the initiation of the companion detonation in the direct ignition model coincides with the impact of the primary and thus the detonation propagates along the original density structure of the companion. Some of our two star explosion models produce total amounts of 56 Ni that fall within the range of that deduced from normal, observed SNe Ia, with our 1.00 + 0.90 M ⊙ model generating an amount near the expected upper limit (Stritzinger et al. 2006;Scalzo et al. 2014). Both of our 1.10 + 1.00 M ⊙ models, however, produce an amount of radioactive material that exceeds what is expected from normal SNe Ia and is more aligned with that of overluminous Type Ia events.

We split the presentation of our triple and quadruple detonation observables based on their ability to repro-

0.0 2.5 5.0 7.5 10.0 r (10 8 cm) 10 12 14 16 18 20 22 24 z (10 8 cm) 0.75 s 0.0 2.5 5.0 7.5 10.0 r (10 8 cm) 2.90 s 0.0 0.5 1.0 1.5 2.0 2.5 Density (10 7 g/cc)

Figure 6. The qualitative density structure of a 0.90 M⊙ companion before and after the impact of an exploding 1.00 M⊙ primary. The green line indicates the 90% contour for companion material. The first frame is just as the ejecta from the primary detonation is first reaching the companion while the second frame is at companion ignition time. This increase in density leads to enhanced burning in the companion detonation.

duce normal SNe Ia. Our models that look like normal SNe Ia at and around maximum light are shown in Section 3.3.1 and our models that are overluminous, which arise from the 1.10 + 1.00 M ⊙ progenitor system, are shown in Section 3.3.2. Additionally, we show the case where a companion does not detonate in Section 3.3.3.

Light curves for our two star explosion models that have SN Ia-like observables are shown in Figure 7. Each of the models are compared to a single star, thin helium shell double detonation from Shen et al. (2021b) with a similar peak brightness. We also show photometry for a few example observed SNe Ia: 1997E (Hicken et al. 2009), 2011fe (Munari et al. 2013;Tsvetkov et al. 2013), and 1999dq (Stritzinger et al. 2006;Jha et al. 2006;Ganeshalingam et al. 2010). Light curves are corrected for Milky Way reddening as per Schlafly & Finkbeiner (2011).

Overall, the shapes of the light curves of these triple and quadruple detonations are fairly similar to that of double detonations. There are, however, some notable deviations between the one and two star detonations. First, the rise times of the 0.85 + 0.80 M ⊙ and 1.00 + 0.90 M ⊙ are significantly longer than that of their one star counterparts, which is likely due to the increased amount of mass that is encapsulating both concentrations of radioactive ejecta (see Figure 4). This increase in rise time is more consistent with observation than single star double detonations or two star detonations where the companion is low mass (e.g. 1.00 + 0.70 M ⊙ and 1.00 + 0.40 M ⊙ models in Figure 4) (Yao et al. 2019;Miller et al. 2020;Fausnaugh et al. 2023). An additional difference between these sets of models is an imbalance of agreement between different bands. For example, the 0.85 + 0.80 M ⊙ model looks very similar to its counterpart in B, but much less so in bolometric and U. Lastly, there are some disagreements between the models at different lines of sight. This is most apparent in the 1.00 + 0.40 M ⊙ model where the northern line of sight shown is much less luminous in bolometric, U, and B than its counterpart, despite the agreement at the equatorial and southern lines of sight. This can likely be attributed to the ashes of the low mass companion, which contain very little radioactive material, providing predominantly increased opacity at the line of sight that first intersects the companion ashes before that of the primary. With companions of high enough mass (≥ 0.80 M ⊙ ), the companion ashes generate a significant amount of luminosity such that they do not have the luminosity deficit that the low mass companion models have at northern lines of sight.

An apparent delineator between double and quadruple detonations of similar brightnesses is the behavior of the I-band curve. In most of the double detonations in Figure 7, the I-band shows two distinct maxima: one just before the time of the B-band maximum and another ∼ 20 days later. In the quadruple detonation cases, however, the I-band remains fairly flat after rising to a peak and either shows a relatively weak secondary maximum or none at all. This suppression of the secondary peak is also line of sight dependent, with the equatorial and southern viewing angles showing more monotonic evolutions of the I-band.

Spectral comparisons for these models are shown in Figures 89101112where they are compared to thin shell double detonation models with similar peak brightnesses from Shen et al. (2021b). For these progenitor systems with total masses below 2 M ⊙ , we find that the triple and quadruple detonation models mimic the traditional double detonation remarkably well at this epoch, especially given the drastic difference in total ejecta mass. In general, most spectral features and their characteristics that are seen in double detonation models and SN Ia observations are reproduced in these two star explosion models. For example, in Figure 8, much of the optical portion of the spectra before and at maximum light are nearly identical between the double and quadruple detonation models. Similarities are seen throughout a range of progenitor system masses.

The triple and quadruple detonations do, however, have some variations compared to isolated double detonations. One major difference is the enhanced UV in thus have little effect on the spectral features around maximum light. We note that sub-Chandrasekhar detonations across a range of masses are expected to have a non-trivial amount of helium within their ejecta and that this may have an observational signature (Collins et al. 2023). However, the prediction of this signature requires the use of non-LTE.

In Figure 14, we compare the spectra of double and quadruple detonation models at each line of sight at the times corresponding to their respective B-band maxima. In this case, the spectra are very similar at most lines of sight up to ∼6000 Å. There is a slight decrease in Si ii λ6355 velocity in the quadruple detonation model at most lines of sight, except at the northernmost lines of sight where the effect is significant. However, this degree of consistency across viewing angles between the one and two star scenario does not hold across all mass configurations, which we exemplify in Figure 15. Interestingly, the lines of sight for this 0.85 + 0.80 M ⊙ quadruple detonation case are most dissimilar from the double detonation counterpart at southern angles where 8, but for a comparison between a 1.00 M⊙ and 1.00 + 0.70 M⊙ models at a viewing angle of 53 • . the primary intersects the observer's line of sight before the companion. At these angles in some of our models, the spectra of the quadruple detonation models see increased emission between 4000 and 6000 Å beyond maximum light (see B and V light curves for this model in Figure 7). This effect is possibly due to the compacted region of high-mass, radioactive material that is mostly concentrated in the southern regions of the ejecta (see Figure 4). Alternatively, the ejecta density and structure in the north of the quadruple detonation model is less of a departure from the double detonation, leading to more consistent observables from lines of sight in that direction.

Also shown in Figures 14 and 15 are comparisons with observed SNe Ia from Matheson et al. (2008). These observed spectra, along with the following shown in this work, are scaled by a uniform factor at all lines of sight and dereddened for galactic extinction using the SNooPy Python tool for SNe Ia (Burns et al. 2011), using the CCM prescription (Cardelli et al. 1989) and extinction values from Schlafly & Finkbeiner (2011). We find that the two star explosions models fit these observations of SNe Ia about as well as isolated double detonation models do.

We present two models from our 1.10 + 1.00 M ⊙ progenitor system which differ based on the ignition mechanism of the companion; the "interior ignition" case, which is ignited within the core as the primary ejecta shock is passing through it (like most of the other models in this work), and the "direct ignition" case, which sees a natural ignition at the southern edge of the star that is coincident with the primary ejecta impact. The light curves from these models are shown in Figure 16. We find that these two high-mass models reach much higher brightnesses and have significantly flatter light curve shapes post-peak than our previously shown models. The interior and direct ignition cases differ in their light curves due to the different timing in the secondary detonations, and thus nucleosynthetic yields and ejecta structure, as detailed in Section 3.2. We compare these models in Figure 16 to observed overluminous SN Ia, SN 2009dc (Silverman et al. 2011;Taubenberger et al. 2011), which has relatively similar light curve shapes. 8, but for a comparison between the 1.10 M⊙ and 1.00 + 0.90 M⊙ models at a viewing angle of 0 • .

We also show the maximum light spectra at all lines of sight from our two 1.10 + 1.00 M ⊙ cases in Figure 17, where they are compared with observed overluminous SN Ia, SN 2006gz (Hicken et al. 2007). Our two models show an interesting line of sight effect where they are fairly similar at equatorial and southern lines of sight, but show great differences at northern viewing angles. We find a fairly decent match with SN 2006gz at southern lines of sight where there is strong agreement in overall spectral shape and the prominent features at 3800 and 4300 Å. A notable aspect in SN 2006gz that our models do not reproduce is the Si iii λ4560 feature (Hicken et al. 2007). However, we will show in an upcoming work that the production of this line, among others, requires the use of non-LTE for our detonation models. We also find significantly high Si ii λ6355 velocities at northern viewing angles of these high-mass models, in disagreement with SN 2006gz and other overluminous SNe Ia (Ashall et al. 2021). These bright models also share many spectral similarities with the 91T-like class of overluminous SNe Ia, albeit for a much poorer reproduction of the Si ii λ6355 feature. While these models do not generate a complete match to observations of overluminous SNe Ia, they do indicate a potential path towards a mechanism that may produce such events which, like normal SNe Ia, still remain elusive in their origins. A full consideration of the triple and quadruple detonation scenario leading to any class of overluminous SNe Ia would require a greater variety of examined binary configurations than just that from the pair of exploratory models shown in this work. In Figure 18, we show max light spectra from a 1.00 + 0.70 M ⊙ degenerate binary where only the primary detonates. We compare this to the detonation of an isolated, bare 1.00 M ⊙ WD, revealing the effects that the companion's presence has on the observables of such an event. It is shown in Figure 18 that the presence of a 0.70 M ⊙ companion has little effect on the synthetic observables in our setup. The biggest differences are at the northernmost line of sight, as one might expect, but the effect is mostly limited to the near-UV. There is also a modest reduction of the Si ii λ6355 line velocity (∼ 2, 000 km s -1 ) exclusive to this line of sight. At mid and southern latitudes, the spectral features are nearly identical except for a slight decrease in overall luminosity. This slightly decreased luminosity is perhaps attributable to the removal of the 0.04 M ⊙ of bound primary star ash, which is made up of mostly 56 Ni. While it is not considered in this work, the bound material may still effect the observables of the event. For example, the decay of the bound radioactive isotopes may drive a wind, influencing late time observables (Shen & Schwab 2017). In contrast, 0.004 M ⊙ of companion material ends up entrained in the unbound ejecta in our simulation.

One of the attractive features of the double detonation model shown in Shen et al. (2021b) is that it is possible to approximately span the observed range of SNe Ia parameters by varying just the mass of the exploding star and the line of sight. An obvious concern is that including another exploding star might adversely impact this feature. Here we separately address the bolometric Phillips relation, the relations between peak magnitude, (Matheson et al. 2008). Each spectrum is shown at +0.8 days from its respective maximum light time.

color and Si velocity, and, for the first time for our models, the gamma-ray escape time.

We show the bolometric Phillips relation for our new models in Figure 19, along with four thin shell, isolated double detonation models from Boos et al. (2021). In general, the negative relationship between peak bolometric magnitude and decline rate, in addition to the scatter, is reproduced by our two sets of models. When looking at an individual model across all viewing angles, however, the relationship between the two parameters is usually positive. In the isolated double detonations, this trend is strictly positive and effectively linear, but some two star cases show departures from this. For example, the 1.00 + 0.40 M ⊙ model has a sharp turn at the northernmost lines of sight. Additionally, the highest mass two star explosion models have a non-linear rela- %RORPHWULF %RORPHWULF %RORPHWULF %RORPHWULF %RORPHWULF %RORPHWULF 8 8 8 8 8 8 % % % % % % 9 9 9 9 9 9 5 5 5 5 5 5 o o o , , , , , , 0 LQWHULRULJQLWLRQ 0 GLUHFWLJQLWLRQ 61GF 0 'D\VIURP0 B, max Figure 17. Spectra at all lines of sight from our two cases originating from a 1.10 + 1.00 M⊙ binary system, compared with observed luminous SN Ia, SN 2006gz (Hicken et al. 2007). Both model and observed spectra shown are from 2 days before their respective B-band maxima.

tionship between peak magnitude and decline rate as well as a narrower breadth of decline rates. There are a couple regions of the observed bolometric parameter space that our relatively sparse model grid does not directly cover. It is conceivable that models with progenitor masses between those shown here would likely reach that space. For example, models with M bol,max ∼ -18.7 and ∆M bol,15 ∼ 1.0 mag would likely arise from progenitors of ∼ 0.95 M ⊙ . Additionally, a 1.00 M ⊙ progenitor with an exploding companion that has a mass between 0.70 and 0.90 M ⊙ may fill in the high luminosity space at a ∆M bol,15 of ∼ 0.75 mag. Some of our models also lay outside the observed parameter space in Figure 19. The 1.10 + 1.00 M ⊙ models have decline rates that are modestly smaller than observed luminous events. Our low mass cases, including the 0.85 and 0.90 M ⊙ isolated double detonations and most lines of sight from the 0.85 + 0.80 M ⊙ quadru- ple detonation, have peak magnitudes lower than what is observed in normal SNe Ia. It may be possible that events that involve progenitors of this low mass produce peculiar SN Ia or do not actually detonate in reality.

An array of observational correlations for both one and two star explosion models is shown in Figure 20. We use the tool Spextractor ( Papadogiannakis (2019), modified by Burrow et al. (2020)) to calculate the photospheric velocities of our model spectra to be consistent with the methods from Burrow et al. (2020), from which the observational data points plotted in Figure 20 originate. Overall, the two star explosion scenario below 2.0 M ⊙ resides generally within the extent of these observational parameters from the isolated double detonation. The effects from the inclusion of the companion on the Si ii velocities in the two star explosion models relative to their isolated double detonation counterparts depends on the mass of the companion. For example, the 1.00 + 0.70 quadruple detonation M ⊙ model While this work has shown that the triple and quadruple detonation scenario may be observationally viable across a range of binary configurations, more work on the mechanics of two double detonations is needed in order to confidently determine if these events could occur in nature. More precise calculations, particularly those that include the full system in 3D (like Pakmor et al. 2022), may reveal dynamics of the detonation that are relevant to the resulting observables. Given that the helium detonation was not treated in this work, it is unclear to what extent the upward-moving shock from the primary core detonation (see Figure 6) influences the ignition point of the companion core, which is normally triggered solely by the converging shock of its own helium shell. If this factor leads to a shorter delay between core detonations, less primary ash would be able to wrap around the companion before it detonates (see Figure 4). This would limit the amount of primary ash at northern latitudes, influencing the observables with a line of sight dependence. Additionally, a more complete examination of this scenario could show how much helium is remaining on the surface of the companion at the time of the first ignition. If it is shown, for example, that the companion has a very limited amount of helium on its surface for certain mass configurations, then the quadruple detonation may be impossible in those binaries. The explosion modes in two star scenarios may also vary from those that are included in this work (e.g. a helium detonation that travels up the accretion stream, directly to the donor star; Pakmor et al. 2021).

Due to dimensional limitations, we have also only examined the scenario in which the core of the primary is ignited, within its southern hemisphere, along the orbital axis of the system. This corresponds to a double detonation of the primary WD in which its helium shell is also ignited along the orbital axis (at the northern pole of the primary, nearest the companion). This initial helium ignition is expected to be triggered near the impact point of the accretion stream which can have a notable separation from the orbital axis (see Figure 1 in Guillochon et al. 2010). It is very likely that the location of initial helium ignition in the primary would lead to noticeable differences in the formation of the ejecta and observables, if not a major change in detonation dynamics. For example, a helium detonation that begins at the equator (90 • from the implicit and explicit helium ignition locations of this work and Boos et al. 2021, respectively) would ultimately lead to primary ejecta that are directed more strongly away from the companion than those in this work. This would allow the fastest material in the ejecta to expand more freely as opposed to being slowed and compacted by the companion as in this work. It may also affect the timing delay between WD detonations or even the occurrence of a companion detonation. The robustness of the shock-induced ignition of the companion helium shell (or helium core) relative to the shock strength and binary separation is generally unaddressed by this work, but will be explored in detail by an upcoming related work. We note that with cylindrical symmetry, it is not possible to realistically model the scenario where the helium ignition occurs anywhere other than a pole of the primary that is aligned with the central axis of the companion. This work is also idealized in terms of the spherical symmetry of our progenitors at the time of detonation; in reality, the companion and its atmosphere would be substantially deformed by this point which would likely affect its ignition and detonation.

Another limitation of this work is our somewhat limited time domain of the synthetic observables, which are calculated out to around 50 days. We expect there to be much greater differences in the observables between the one and two star explosion scenario at later times when the photosphere moves inwards and reveals more information about the structure at lower velocities. This is especially true for our case involving a detonating 0.40 M ⊙ helium companion that leaves behind 0.16 M ⊙ of unburnt He. In addition to the nebular phase observables, the two star explosion scenario should also impact the long term shape of the supernova remnant.

While observed SN Ia remnants are considered to be fairly symmetric (Lopez et al. 2011), double detonation ejecta are inherently somewhat non-spherical due to the off-centered ignition of the core. The addition of a second doubly-detonating star, as in this work, affects the asymmetry in a complex manner. The innermost ejecta in the quadruple detonation scenario is now much more spherical due to the companion material expansion being suppressed by the presence of relatively dense primary ashes surrounding it. However, the outer ejecta, which consists of the primary star ashes, is now more aspherical primarily due to the companion exploding offcenter to it. It is not directly obvious how a supernova remnant may appear many years after the explosion based on its early ejecta morphology, but recent theoretical work involving a double detonation in a double degenerate system has shown that the original structure of the ejecta can have a lasting impact (Ferrand et al. 2022). Additionally, the previously described assumptions in our setup, in particular the imposed cylindrical symmetry of the calculations, may be leading to an overestimation of the final ejecta asymmetry.

A notable result of the two star explosion scenario compared to isolated sub-Chandrasekhar detonation models is the non-monotonic stratification of core ejecta abundances, which would likely lead to more significant differences in the nebular phase. This is especially interesting in the context of unexplained double-peaked Fe lines observed in the the nebular spectra of some normal SNe Ia (Dong et al. 2015). This feature is indicative of a bimodal distribution of Fe in the supernova ejecta, which is found to have a peak separation of around 5,000 km s -1 (Dong et al. 2015). This is interpreted as the result of a bimodal distribution of 56 Ni generated in the explosion, which would decay to 56 Fe by the nebular phase. As suggested by Pakmor et al. (2022), it may be possible that the quadruple detonation scenario can lead to this conspicuous observational feature. While the models shown in this work are not specifically consistent with the bimodal features detailed in Dong et al. (2015), they demonstrate a method to produce bimodal distributions of high-mass material along a line of sight (see Figure 5) following a SN Ia that may be interpreted as normal at maximum light. It may be that alternative ignition locations (as described above) or lower mass companions (see Pakmor et al. 2022) could produce this bimodal distribution of 56 Fe that is consistent with some SNe Ia.

In our 2D simulations we have determined that two WDs detonating subsequently can generate observables that are remarkably similar to double detonations of a single thin helium-shelled progenitor. Given the work of the past several years that has shown the double detonation as a plausible Type Ia mechanism candidate, this new result suggests that the complete destruction of a WD binary via the triple or quadruple detonation may also be a Type Ia channel, provided the appropriate mass configuration.

Given this, there are several avenues for future work that may elucidate whether these events could occur in nature and how they may be differentiated from other Type Ia explosion mechanisms, including a double detonation of a single star. More "full picture" simulations, like those performed in Tanikawa et al. (2019);Pakmor et al. (2022), could more precisely establish where and when the companion ignition occurs, in addition to exploring higher-dimensional effects that are not accessible in this work. While we showed that the detonation of a thin helium shell has little observational effect in the isolated double detonation scenario, it is possible that the shell ejecta may play a larger role in the quadruple explosion scenario, particularly for the companion shell ejecta that would be compressed. A wider parameter space of progenitor characteristics, including other binary mass configurations and alternative metallicities, would also serve our understanding of the two star explosion scenario and its possible contribution to the scatter of observed SNe Ia. Lastly, the use of non-LTE radiative transfer calculations would improve our interpretation with observation, most notably allowing for an examination of how the two star explosion scenario may affect the Phillips relation (Phillips 1993;Shen et al. 2021a).

The full post-processed yields, ejecta profiles, and synthetic spectra out to ∼50 days for the new detonation models shown in this work can be found on Zenodo (10.5281/zenodo.10515767).

We thank the referee for their helpful comments. S.J.B. acknowledges support from NASA grant HST AR-16156. Financial support for K.J.S. was in part provided by NASA/ESA Hubble Space Telescope programs #15871 and #15918.

Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center and the University of Alabama high performance computing facility.

Software: FLASH (Fryxell et al. 2000;Dubey et al. 2009Dubey et al. , 2013Dubey et al. , 2014, flash.uchicago.edu), flash.uchicago.edu), MESA (Paxton et al. 2011(Paxton et al. , 2013(Paxton et al. , 2015(Paxton et al. , 2018, mesa.sourceforge.net), mesa.sourceforge.net), Sedona (Kasen et al. 2006), yt (yt-project.org), matplotlib (Hunter 2007, matplotlib.org), SNooPy (Burns et al. 2011), Spextractor (github.com/anthonyburrow/ spextractor).