Introduction

Both the progenitor configuration and the explosion mechanism of thermonuclear supernovae (Type Ia SNe) are still heavily debated, despite the intense and extensive studies that such events have received for 50+ yr (see. e.g., Maoz et al. 2014;Branch & Wheeler 2017;Livio & Mazzali 2018, for reviews). It has been recognized decades ago that SNe Ia are produced by thermonuclear explosions of carbon-oxygen white dwarfs (C/O WDs). It is also known that the WD must Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

be in a binary system to be able to reach the physical state that leads to explosion. There are, however, many possible configurations for such a binary system (see, e.g., Figure 2 in Liu et al. 2023). They are usually categorized by the number of WDs in the system: a single-degenerate (SD) configuration contains only one WD, while double-degenerate (DD) systems consist of two WDs (Livio & Mazzali 2018). In addition, the core-degenerate scenario was also proposed (Livio & Riess 2003), in which the WD and the degenerate core of an AGB star rapidly merge during a common-envelope phase. Merging also plays a key role in the DD scenario, although an interesting possibility of a direct WD-WD collision induced by a third body was also considered as an alternative scenario (Thompson 2011). A detailed review of the pros and cons of all these possible progenitor configurations can be found in, e.g., Livio & Mazzali (2018). For further discussion, including a detailed list of references, we refer to Liu et al. (2023).

There are also several possibilities for the explosion mechanism. The key parameter is the mass of the exploding WD, i.e., whether it is close to the Chandrasekhar mass or significantly below it (near-Chandra, or sub-Chandra models, respectively). Liu et al. (2023) gives a detailed summary of the relevant explosion mechanisms, see their Figure 3 and Table 2.

The high degree of homogeneity of the observables of SNe Ia, including light curves (LCs) and spectra, can be explained relatively easily by having ∼0.5 M e of 56 Ni surrounded by a layer consisting of mostly 28 Si, 12 C and 16 O and expanding homologously with » v 20,000 max km s -1 (e.g., Hoeflich 2017). Such an ejecta configuration can be produced by a variety of progenitor systems and explosion mechanisms, involving WDs having either near-Chandra or sub-Chandra masses. Historically, SNe Ia have been thought to arise from the explosion of near-Chandra WDs for many decades. More recent studies found, however, that ejecta masses derived directly from photometric observations (Scalzo et al. 2014a(Scalzo et al. , 2014b(Scalzo et al. , 2019;;Könyves-Tóth et al. 2020) resulted in a significant fraction of sub-Chandra masses, which actually turned out to be more numerous than near-Chandra events among the normal SNe Ia (excluding 91T-like and super-Chandra SNe).

Nebular spectroscopy is another powerful tool for constraining ejecta masses. Recent analyses of SNe Ia nebular spectra, both in the optical and near-infrared, compared the observed strength of (forbidden) emission lines of iron peak elements (mostly Ni and Fe) with the theoretical predictions to reveal the possible progenitor systems and explosion types. These studies suggested a mixed population of sub-Chandra and near-Chandra progenitors for the observed events. For example, Maguire et al. (2018), Diamond et al. (2018) and Dhawan et al. (2018) found consistency with near-Chandra delayed-detonation models, while Flörs et al. (2018Flörs et al. ( , 2020) ) preferred mostly sub-Chandra explosions. Most recently, Liu et al. (2023b) found that ∼67% of their sample (24 out of 36 SNe) is consistent with sub-Chandra explosion models.

On the other hand, to explain the ionization balance in latetime SN Ia spectra, the presence of neutron-rich Fe-group elements (like 55 Mn and 57 Fe, 58 Ni) is needed (e.g., Livio & Mazzali 2018). The production of such species and their corresponding decay chains ( 57 Ni → 57 Co → 57 Fe, or 55 Co → 55 Fe → 55 Mn) require high central densities, i.e., near-Chandra masses for the exploding WDs (e.g., Seitenzahl et al. 2013). However, this does not rule out sub-Chandra explosions, because those are also capable of producing (at least some fraction of) such neutron-rich isotopes (see, e.g., Shen et al. 2018).

There are also other theoretical arguments that favor near-Chandra, or even super-Chandra WDs at the moment of explosion. In the SD scenario the accreting WD must gain angular momentum as well, resulting in a rapidly spinning, highly magnetized object. Such a WD may significantly exceed the Chandrasekhar mass due to centrifugal forces and magnetic pressure. It must lose its angular momentum in order to reach central density of ∼3 × 10 9 g cm -3 to explode. Such spin-up/ spin-down models might explain the existence of Ia-like super-Chandra explosions, but it is uncertain what fraction of the near-Chandra events they represent in reality (see Branch & Wheeler 2017, and references therein). Another possibility is the violent merger scenario, arising from DD systems, where the merger of two sub-Chandra C/O WDs could lead to a super-Chandra explosion (e.g., Pakmor et al. 2012Pakmor et al. , 2013)).

Motivated by the observational findings mentioned above, a considerable number of Ia explosion models that involve sub-Chandra (0.9  M  1.2 M e , Blondin et al. 2017;Shen et al. 2018;Polin et al. 2019) WDs have been published recently (see, e.g., Liu et al. 2023, and references therein). Their common feature is the capability of modeling the ignition of the thermonuclear explosion self-consistently, without the need for an artificial triggering or a by-hand implementation of the deflagration-to-detonation transition, either via double-detonation (DuDe, i.e., triggering the explosion of the C/O WD by the detonation of a ∼0.01 M e He layer on top of the WD), or by the "dynamically driven DD double-detonation" (D 6 , i.e., He-detonation caused by the merging of a C/O and a He-C/O WD) mechanism. Confronting the predictions of these models with the observations may advance our understanding about the true nature of these exotic explosions.

The goal of the present paper is the continuation of the work by Könyves-Tóth et al. (2020), hereafter referred as KTR20, by extending the photometric sample of SNe Ia with more wellobserved objects, to derive constraints on the physical properties of SNe Ia, especially the ejecta mass, by combining photometric and spectroscopic data. In Section 2 we describe the new observational data used in this paper. In Section 3 we present the applied methods for distance determination, while Section 4 contains the details about the construction of the bolometric light curves. The method of inferring the physical parameters from the observations is described in Section 5. The results are presented and discussed in Section 6, while in Section 7 we summarize our conclusions.

Data

In this section we present the observational data, the instruments utilized for the present study and the applied data reduction methods.

Observations

We carried out photometric observations of 28 Type Ia SNe between 2019 and 2023 from the Piszkéstető mountain station of Konkoly Observatory, Hungary in order to continue the photometric study of SNe Ia presented in KTR20. Our selection criteria for the sample SNe were the following:

1. decl. above -15°, in order to be observable from Piszkéstető station. 2. Low redshift, i.e., 0 < z < 0.1. The minimum redshift in the sample is z = 0.003, while the maximum is z = 0.07. 3. Pre-maximum discovery date in order to get reliable estimates on the rise time of the LCs. 4. Follow-up observations up to at least 40 days after maximum light.

From the overall sample of 28 objects, 21 exploded in spiral galaxies, 3 in lenticular galaxies, 3 in ellipticals and 1 host has unknown morphology.

The data were taken using the 0.8 m Ritchy-Chrétien (RC80) telescope of Konkoly Observatory, manufactured by the AstroSysteme Austria. RC80 is equipped with a 2048 × 2048 back-illuminated FLI PL230 CCD chip that has 0 55 pixel scale and Johnson-Cousins BV and Sloan griz filters. This instrument is appropriate to obtain photometry for nearby (z < 0.1) Type Ia SNe with acceptable photometric signal-tonoise of 10.

There is an identical telescope, called BRC80, located at Baja Observatory of the University of Szeged, Hungary. Photometric data for two objects in the sample (SN 2021afsj and SN 2022fw) were obtained with this instrument. In the case of two other SNe (SN 2019bkh and SN 2019np) we also used some frames taken with the 0.6/0.9 m Schmidt telescope of the Piszkéstető Observatory using Johnson-Cousins BVRI filters, in order to extend the pre-maximum coverage of their LCs. The technical details of the Schmidt telescope can be found in KTR20, Section 2.

The basic data of the studied SNe Ia are collected in Table 1. The total (Milky Way plus host) reddenings (E(B -V ) tot ) and the luminosity distances (D L ) were derived by fitting the SN LCs with MLCS2k2 and SALT3 (see Section 3 for details). The color-combined gri images of the studied SNe are displayed in Figures 1 and 2.

Reduction and Photometry

The basic data reduction steps (bias, dark and flatfield corrections) were done in the standard way using the appropriate tasks in IRAF 20 (Image Reduction and Analysis Facility). The frames were then registered and mediancombined to produce a single frame in each filter (see, e.g., Vinkó et al. 2018).

Except in a few cases, when the supernova occurred so far away from its host galaxy that it was unaffected by the host galaxy background, we applied image subtraction photometry to separate the light of the host galaxy from the light of the transient. Since we do not have images with the RC80 telescope taken before or sufficiently late after explosion, we used frames from the PanSTARRS-1 (PS1) imaging archive (Flewelling et al. 2020) for the image subtraction process. Before subtracting the PS1 images, we applied the IRAF geomap, gregister, psfmatch and linmatch tasks to crop, rotate, and scale the PS1 images to match the reduced RC80 frames. After removing the host from the frames, we determined the apparent magnitude of the SN and multiple local comparison stars in each filter via aperture photometry. We used the cataloged PS1 magnitudes of the comparison stars for transforming the instrumental magnitudes to the standard system in the standard way, including color terms in the transformation. For the B and V data the g PS1 and r PS1 magnitudes of the comparison stars were transformed into Johnson-Cousins B and V magnitudes based on the formulae given by Tonry et al. (2012).

Finally, the uncertainties of the obtained magnitudes were calculated as the squared sum of the photometric errors given by IRAF, and the fitting errors from the standard transformation.

All photometric data can be found online in the following GitHub repository: https://github.com/borazso/PiszkeSN.

Spectroscopy

In order to determine expansion velocities (see Section 5.1), we used spectra obtained with the instruments at Las Cumbres Observatory (LCO) and McDonald Observatory (Table 2).

The LCO spectra were taken with the FLOYDS spectrographs mounted on the LCO 2 m telescopes, via the Global Supernova Project (GSP). The spectra were reduced by a custom pipeline using IRAF tasks (Valenti et al. 2014). Additional data were taken with the Low Resolution Spectrograph 2 (LRS2) on the 10 m Hobby-Eberly Telescope (HET) at McDonald Observatory (Chonis et al. 2016). Since the Si II λ6355 line, which was used for the velocity measurements, falls within the wavelength coverage of the blue arm (LRS2-B, 20 IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation http://iraf.noirlab.edu. 3640-6970 Å), we used spectra taken with LRS2-B. The spectra were extracted from the IFU data cubes by the Panaceafoot_0 pipeline. The extracted spectra were then corrected for redshift and telluric lines using Python scripts and IRAF tasks.

Public Databases

We collected additional data to supplement our observations from two sources. We used public photometry from the Zwicky Transient Facility (ZTF) (Bellm et al. 2019) for 7 SNe (SN 2019bkh, SN 2019ein, SN 2020fob, SN 2020hvq, SN 2020tug, SN 2020uxz, SN 2021ytp), where the RC80 LCs did not cover the pre-maximum phases. Since our goal is to determine the physical parameters of these supernovae, wide phase coverage of the LCs is crucial. Additionally, some physical parameters of the explosion can only be determined by examining the late-time tail of the light-curve. Therefore in the case of 3 SNe (SN 2019ein, SN 2020tug, SN 2020uxz), we used the public ZTF photometry to extend their LCs into later phases. The downloaded ZTF data can be found in the GitHub repositoryfoot_1 of this paper. We also collected all available public spectra for our sample SNe from the Transient Name Server (TNS). 23 All spectroscopic data are shown in Table 2. Details on determining the expansion velocities from these spectra are given in Section 5.1.

Distance Estimates

In this section, we describe our methods to estimate the distances and reddenings of our sample SNe Ia by applying two different techniques and codes: SALT3 (see Section 3.1) and MLCS2k2 (Section 3.2).

SALT3

In the present paper we utilized the SALT3 code, which is the improved version of SALT2 (Spectral Adaptive Lightcurve Template; Guy et al. 2005Guy et al. , 2007Guy et al. , 2010;;Betoule et al. 2014).

In SALT3 the spectral flux of the supernova is expressed as a function of wavelength (λ) and the rest-frame phase (p) as

where M 0 , M 1 , and CL are the calibrated template vectors, while the fitting parameters are the flux normalization x 0 , the stretch parameter x 1 and the color parameter c.

Here we adopt the most recent template vectors by Kenworthy et al. (2021), which were trained with ∼1200 spectra covering the wavelength range of 2000 and 11000 Å. This sample is more than an order of magnitude larger compared to the training sets of previous version of the code, thus, SALT3 has lower uncertainties than, e.g., SALT2.4 (Taylor et al. 2023). In 2022, the SALT3 code was extended further into the near-infrared by Pierel et al. (2022).

In the SALT3 framework the luminosity distances to SNe Ia can be derived in two main steps. First, the three free parameters (x 0 , x 1 , and c) are found from fitting Equation (1) to a particular SN Ia light curve. Second, their best-fit values are substituted into the Tripp-equation (Tripp 1998) to get the distance modulus μ:

where m B is the rest-frame B-band peak magnitude of the SN (2022). We find m 0 = 10.607 by matching our best-fit m B values to those of the Pantheon+SH0ESfoot_3 SNe Ia sample (Riess et al. 2022). Note that we ignore second-order terms in Equation (2), like the mass-step δμ host (Betoule et al. 2014;Brout et al. 2019), or the bias correction δμ bias (Kessler et al. 2019), because for our low-z sample their values are smaller than the typical uncertainty of our distance modulus estimates (∼0.1 mag).

The fitting was done with the SNcosmofoot_4 python library (Barbary et al. 2016), adopting Milky Way extinction estimates provided by the NASA/IPAC Infrared Science Archive (Schlegel et al. 1998;Schlafly & Finkbeiner 2011), and redshift information from the NASA Extragalactic Database (NED). 26 The best-fit values of t 0 , x 0 , x 1 and c for each supernova can be found in the GitHub repository of this paper (see above). The final luminosity distances (via μ from Equation (2)) are shown in Table 1.

MLCS2k2

Even though SALT3 provides accurate relative distances to SNe Ia via Equation (2), which are now tied to Cepheid-based absolute distances (Riess et al. 2022), the construction of the bolometric LCs require information about the extinction due to dust in the host galaxy of each SN. Since the SALT3 flux model (Equation (1)) incorporates the effect of dust extinction into the color parameter, it does not give a direct prediction of the dust extinction occurred in the host. Thus, we utilized the Multi-Color Light Curve Shape Method (MLCS2k2; Riess et al. 1995Riess et al. , 1996;;Jha et al. 2007) to overcome this difficulty.

Since MLCS2k2 was calibrated to Johnson-Cousins UBVRI photometry (Jha et al. 2007) we applied this code only to our Johnson B-and V-band data (after correcting them to Milky Way extinction, as above), and fixed both the distance modulus and the moment of the B-band maximum light from the results of our SALT3 fitting. This way we got reasonable estimates on the host galaxy extinction value A V , from which we inferred the E(B -V ) host reddening and the extinction in other passbands using the Milky Way reddening law parameter R V = 3.1. Finally, the total reddening was calculated as 1). The best-fit MLCS2k2 parameters can be found in the GitHub repositoryfoot_7 of this paper.

Bolometric Light Curves and their Modeling

In this section we briefly describe the construction of the bolometric LCs and the fitting of the radiation-diffusion Arnett models.

Bolometric Light Curve Construction

The bolometric LCs were constructed with the same methodology as in KTR20: briefly, after correcting the BVgri magnitudes (the z-band data were omitted due to their higher uncertainties) to the effect of dust extinction (both in the Milky Way and the host galaxy, see Table 1), the magnitudes were converted to flux densities, then corrected for distance and redshift. The resulting rest-frame absolute flux densities were then integrated along the wavelength axis by applying the trapezoidal rule. The missing UV-and IR-fluxes were approximated in a similar way as in KTR20, by assuming a linear decrease in flux from the wavelength of the B filter down to 1900 Å, and estimating the IR contribution by fitting a Rayleigh-Jeans tail to the i-band flux, then integrating it from the wavelength of the i-band filter to infinity. This method was extensively tested by KTR20 concluding that this technique gives a reliable representation of the true bolometric flux/ luminosity, and the relative uncertainty of the derived fluxes does not exceed ∼10%.

As mentioned above, in those cases when our observations did not cover the pre-maximum phases, we extended the LCs with public ZTF photometry. Since ZTF data are available only in g-and r-bands, applying the trapezoidal integration method leads to higher uncertainties in the resulting pseudo-bolometric fluxes. Thus, we tested the effect of omitting bands other than g and r from the integration using the high-cadence data of SN 2021hpr. We found that restricting the data only to g and r (but doing the correction for the missing bands as above) underestimates the integrated flux by only ∼2.8% during the pre-maximum phases compared to the case when the full BVgri data are integrated. The difference increases up to ∼8% around maximum light, then drops back to ∼2.5% later than +5 days from maximum. Since pre-maximum data are important to constrain the physical parameters of the light curve model, motivated by these experiments we decided to use the ZTFbased quasi-bolometric data in the final LCs, but assigned 50% larger error bars to those points in order to represent their higher uncertainty.

Model Fitting

The bolometric LCs were modeled applying the Monte-Carlo based Minim code (Chatzopoulos et al. 2013), which fits the radiation-diffusion model of Arnett (1982) to the quasibolometric LC of the SN. The following assumptions were adopted for the Arnett-model:

1. spherically symmetric, homologously expanding ejecta, 2. spatially constant density profile, 3. constant optical opacity, both spatially and temporally, 4. centrally located radioactive heating source, 5. radiation pressure being dominant, 6. the spatial temperature profile being fixed to the "radiative-zero" solution, 7. separation of the spatial and temporal part of the energy equation.

The Minim code uses the Price-algorithm in order to localize the absolute minimum of the χ 2 surface in the parameter space within pre-selected parameter bounds. The detailed description of the code and its method to estimate the uncertainties of each fitted parameter values can be found in Chatzopoulos et al. (2013).

The SNe Ia LCs were fitted with the usual model of radioactive decay of 56 Ni → 56 Co → 56 Fe by optimizing the following four parameters (e.g., KTR20):

1. t 0 : the moment of the explosion with respect to the date of maximum brightness in the B-band (in days), 2. t LC : the LC timescale, similar to the rise time to maximum (in days), 3. t γ : the timescale of the gamma-ray leaking (in days), 4. M Ni : the initial nickel-mass (in M e ).

The best-fit model parameters are given in the first 4 columns of Table 3.

Physical Parameters

To determine the physical parameters for each SN, such as the ejecta mass (M ej ) or the opacity (κ), we used an improved version of the method presented in Li et al. (2019) and KTR20 (see Equations (3) and (4)). In the present paper the expansion velocity v exp was estimated directly from spectra taken near maximum light (described in Section 5.1). By using the timescales t γ and t LC provided by the Minim code, we calculate the ejecta mass as

and the average opacity in the ejecta as

where κ γ = 0.025 cm 2 g -1 is the opacity for gamma-ray photons (Guttman et al. 2024), β = 13.8 is an integration constant related to the density distribution of the ejecta (Arnett 1982), and v exp is the expansion velocity of the SN. Furthermore, the kinetic energy of the expanding ejecta (assuming homologous expansion of a constant density sphere) can be expressed as

. 5 kin ej exp 2

Expansion Velocities

The expansion velocity, v exp , appearing in Equations (3)-( 5), was estimated from optical spectra taken near maximum light (see Section 2.3): we used the Doppler-shift of the absorption minimum of the Si II λ6355 feature in each available spectrum to measure the expansion velocity at the given phase. After correcting the spectra for the redshift of the host galaxy, the observed wavelength of the Si II feature was measured by fitting the absorption component with a single Gaussian function near the core, then taking the center of the fitted profile as the observed wavelength (λ obs ). The Doppler-shift of λ obs from the rest-frame position, λ 0 = 6355 Å, gives the Si II velocity (v Si II ). In this paper we adopted v Si II measured at maximum light as an estimate for v exp .

For those SNe that had available spectra taken close to maximum, the determination of v exp was relatively easy. However, this was not the case for most of our sample SNe. In these cases we had to interpolate between the v Si II values measured at different phases in order to get the velocity near maximum light. The interpolation was done using a pre-defined set of exponential functions fitted to the measured v Si II velocities of the well-observed SN 2019ein (a high-velocity SN Ia) and SN 2011fe (a normal velocity SN Ia).

For SN 2019ein we used the spectra listed in Table 2, while for SN 2011fe we collected the spectra from Pereira et al. (2013). First, the measured velocities of these two SNe as a function of time were fitted with exponential functions. Then, 100 other exponentials were computed to model the temporal evolution of the velocity within the range defined by SN 2011fe and SN 2019ein (plotted with gray dotted curves in Figure 3). The parameters of these exponentials were computed starting from 90% of the parameters of SN 2011fe, extending up to 110% of the parameters of SN 2019ein.

To estimate the velocity at the moment of maximum light for a given SN, first, we plotted the measured velocities against phase, then looked for the best-fitting pre-defined exponential that was closest to the measured velocities. Then, using the parameters of this exponential we inferred its value at zero phase, i.e., at the moment of maximum light in the B-band (see the blue dashed curve in Figure 3 as an example for SN 2021hpr).

This method worked well in those cases when only 1 or 2 spectra were available. However, for SNe with multiple spectra available, we found that some of them showed a velocity evolution that was slightly different from the pre-defined exponential functions. Thus, in those cases we preferred fitting the measured velocities with another exponential function and using this best-fit exponential to estimate the velocity at maximum light. This fitting introduces a small (∼200 km s -1 ) error and so the uncertainty of the Si II velocity at maximum light comes in most part from the uncertainty of how well we can find the line minima in the individual spectra.

Figure 4 summarizes the measured velocities (colored symbols) as well as their best-fitting exponential functions (dotted curves). The two solid curves represent SN 2011fe and SN 2019ein.

Classification of the Sample SNe Into Subtypes

One of the most important parameters of a SN Ia is its color, which is especially interesting in the early phases: it can be a good tracer of the presence of interaction with a companion star (Kasen 2010), double detonation explosion (Polin et al. 2019), or 56 Ni-mixing near the surface (Magee & Maguire 2020).

After correcting for Milky Way and host galaxy extinction, we constructed the (B -V ) 0 color curves of our sample, and estimated the color at the moment of maximum light by fitting a quadratic function to their color evolution.

Many studies have been proposed to further divide SNe Ia into several subclasses based on their spectroscopic and photometric properties; see, e.g., Benetti et al. (2005), Branch et al. (2006Branch et al. ( , 2009)), Wang et al. (2009), Stritzinger et al. (2018). The Stritzinger et al. (2018) classification separates SNe Ia based on their early (4-5 days after explosion) color evolution: SNe showing (B -V ) 0 0.2 mag at around +2 days belong to the early red group, while objects showing (B -V ) 0 < 0.05 mag are considered as the members of the early blue group. According to Benetti et al. (2005), early red SNe Ia are often associated with Branch Core Normal (CN) and Cool (CL) types showing low velocity gradient (LVG), while early blue objects are usually classified as LVG Shallow Silicon (SS), also known as SNIa-91T subtype. The Wang et al. (2009) scheme separates SNe Ia based on their v Si II velocity at maximum light: High Velocity (HV) SNe have v Si II  12,000 km s -1 , while Normal Velocity (NV) SNe show v Si II ≈ 10,600 km s -1 (see also Branch & Wheeler 2017, for further details and references). The Si II velocity has also been found by Wang et al. (2013) to be connected to the environment of SNe Ia, with HV events originating from younger, more metal-rich surroundings than NV events.

By using the estimated v exp at maximum and the early (B -V ) 0 color curves, we determined the Wang et al. (2009) and Stritzinger et al. (2018) subtypes for the sample SNe where it was possible. Unfortunately, only 7 objects (SNe 2019ein, 2020rqk, 2020tug, 2020uxz, 2021hpr, 2021rhu, 2022fw) had photometry taken at sufficiently early phases to determine their Stritzinger et al. (2018) group. 5 SNe out of 7 (SNe 2019ein, 2020uxz, 2021hpr, 2021rhu and 2022fw) were found to be consistent with the criteria for the early red subgroup, and the remaining 2 (SNe 2020rqk and 2020tug) belong to the early blue subgroup. Applying the Wang et al. (2009) classification, most SNe in our sample were found to be of normal velocity (NV) type, and only 6 of them (SNe 2019cth, 2019ein, 2020hvq, 2021wuf, 2021ytp and 2022hrs) belonged to the high velocity (HV) group. It was, however, recently argued that SN 2021hpr may be a transitional object between the Wang NV and HV objects being at the lower end of the HV regime (Zhang et al. 2022).

Ejecta Masses

Finally, from Equations (3)-( 5) we inferred the ejecta masses, ejecta opacities and kinetic energies of each SNe Ia in our sample. The results are summarized in Table 3.

Discussion

In this section we present constraints and correlations between the physical parameters and progenitor systems of the studied SNe Ia, and discuss their implications for the explosion mechanisms.

Comments on Individual Objects

In this subsection we discuss and compare our results with those obtained by others for some individual SNe in our sample. The objects listed here are the ones that either had published results that were comparable to our work, or they were found to have some peculiarities during our analysis. (2020) also estimated a nickel mass of 0.33 M e , which, again, is lower than our result, but it was based on spectral modeling instead of photometry. Contrary to Xi et al. (2022), they argue that this event is a product of the delayed-detonation scenario. Our estimated ejecta mass for SN 2019ein is 1.12 ± 0.18 M e , which is consistent with a sub-Chandra explosion, but because of the relatively high uncertainty of the ejecta mass, the possibility for a Chandrasekhar-mass delayed-detonation explosion cannot be excluded. 2. SN 2019cth: SN 2019cth was a 91T-like event, but with low maximum luminosity and low nickel mass, contrary to the expectations. The reason for the inconsistency could be due to the poor phase coverage of our data around maximum light. The uncertainty of the nickel mass is also significant: the value given by the Minim fitting (0.64 ± 0.08 M e ) is significantly higher than the one calculated by the method of Khatami & Kasen (2019) (0.46 ± 0.01 M e ). Thus, the parameters for this object listed in Table 3 should be considered with caution. 3. SN 2019np: Sai et al. (2022) also applied the Minim code and the Arnett-model to fit the quasi-bolometric light curve of SN 2019np, which resulted in a nickel mass of 0.66 ± 0.05 M e . This value is slightly lower than our M Ni = 0.75 ± 0.05 M e . From spectroscopy Sai et al.

(2022) estimated the ejecta velocity as ∼10,200 km s -1 at B-band maximum, which agrees with our value within the errors. On the other hand, they estimated a high ejecta mass of ∼1.34 ± 0.12 M e compared to our value of ∼1.01 ± 0.08 M e . However, inserting their reported v exp and t γ values into Equation (3), we get an ejecta mass of ∼0.9 M e . Thus, we believe that the ejecta mass reported by Sai et al. (2022) is an overestimate, if we use their parameters at face value. They also found extra light in the early phases of the light curve, and attribute it to nickel-mixing. Our data were not taken early enough to confirm their finding. 4. SN 2020hvq: This SN appeared right in the dust lane of the edge-on galaxy UGC 10561 (see Figure 1). Our data on SN 2020hvq extend well beyond +80 days, but the Minim code could not fit the tail beyond +60 days well. This may have resulted in an overestimate of the t γ value. The best-fit t γ ∼ 50 days is not extremely long, but coupled with the relatively high expansion velocity, » v 13,900 exp km s -1 , gives a very high ejecta mass of M ej ≈ 3 M e . Such a high ejecta mass is inconsistent with not only the current explosion models for SNe Ia, but also with the t LC parameter (∼10.6 days) that would imply M ej ≈ 1.2 M e according to the method by KTR20. The long t γ could be due to some extra light in the late-phase photometry, either by the insufficient subtraction of host galaxy background from our frames, a light echo on significant dust content in the host around the line of sight, or a late-time circumstellar interaction (Terwel et al. 2024). Because SN 2020hvq is a significant outlier in our sample, it was excluded from further analysis. 5. SN 2020tug: Similar to SN 2019cth, this object lacked near-maximum observations in our data, thus, the estimated nickel mass may be more uncertain. 6. SN 2021dov: SN 2021dov is a 91T-like SN Ia, which showed the highest maximum luminosity in our sample (∼2 × 10 43 erg s -1 ). As expected, this implies a high nickel mass of ∼1.2 M e . However, the inferred ejecta mass was found to be unexpectedly low, 0.93 ± 0.15 M e .

Since the condition M Ni > M ej is unphysical, we suspect that in this case some of the initial assumptions, probably the centrally located powering source, of the Arnettmodel fails (see Section 6.5 for further discussion).

Significant interaction with a H-poor CSM that increases the maximum luminosity beyond the radioactive heating, or a non-spherically expanding ejecta are also possible explanations. Note that KTR20 also found a similar

outlier (SN 2017erp) in their sample, which showed M Ni ≈ M ej . 7. SN 2021hpr: Lim et al. (2023) observed excess light in the early LC, and attributed this to the shock-heated cooling emission (SHCE) that arises from interaction with a companion star. Using the SHCE model along with delayed-detonation models, they were able to fit the early LC adequately. While the double-detonation model of Polin et al. (2019) also predicts extra light in the early LC, Lim et al. (2023) found that it does not fit the observations as well as the SHCE model. SN 2021hpr is the third SN Ia discovered in NGC 3147 during the last half-century. A study of SN 2021hpr and its siblings were presented by Barna et al. (2023), who also used the data from the RC80 and BRC80 telescopes, but performed their own independent analysis. Their estimated nickel mass (0.44 ± 0.14 M e ) is lower than the value given in Table 3 (0.67 ± 0.05 M e ), but their expansion velocity (11,200 ± 1200 km s -1 ), and ejecta mass (1.12 ± 0.28 M e ) are both in agreement with our values (see Table 3). The disagreement in the nickel mass can be traced back to their lower adopted extinction and distance modulus. 8. SN 2021rhu: SN 2021rhu was a sub-luminous and very red event near maximum compared to the other SNe in our sample. According to Harvey et al. (2023), it may represent a transitional object between normal and 91bglike SNe Ia, i.e., a 86G-like object. By modeling its spectra, Harvey et al. (2023) found that a delayeddetonation scenario is more likely than a doubledetonation explosion. In this paper, we estimate a nickel mass of ∼0.45 M e , which is close to the calculated ∼0.74 M e ejecta mass. The low ejecta mass is a consequence of the low t γ value (∼31 days), which is one of the lowest in our sample. Since the low t γ and M ej values seem to be relatively well-constrained and consistent with SN 2021rhu being a lower mass object, we speculate that the too low ejecta mass might be due to the failure of the Arnett-model, e.g., because of the unusual Ni-distribution (see Section 6.5). 9. SN 2022hrs: A SALT3 fitting of the BVri LC of SN 2022 hrs taken by 0.4 m LCO telescopes was recently published by Risin et al. (2023). They got significantly lower Ni-mass (∼0.16 M e ) compared to our result (∼0.6 M e , Table 3). The disagreement is probably due to their different methodology: they used the best-fit LC amplitude provided by SALT3 to estimate the Ni-mass, while our result was inferred from the quasi-bolometric luminosities. Nevertheless, their result seems to be an underestimate compared the usual range of nickel masses in SNe Ia (0.3-1.1 M e ). 10. SN 2022ydr: Our observations of SN 2022ydr lack adequate coverage in the pre-maximum period, and the observations only extend until ∼30 days after maximum. This can cause an uncertain fitting of the t γ parameter, which in turn may lead to the low ejecta mass estimate of ∼0.49 ± 0.12 M e , making it the only object in our sample that lies significantly below the sub-Chandra explosion models. SN 2022ydr was of a Ia-91bg subtype, and accordingly it had the lowest maximum luminosity

∼0.55 × 10 43 erg s -1 ), which is reflected in the relatively low (∼0.24 M e ) nickel mass with respect to the rest of the sample. Compared to most 91bg-like SNe, the Nimass of SN 2022ydr is a bit higher, but not unprecedented. For example, Sullivan et al. (2011) used Arnett's rule to estimate ∼0.2 M e of 56 Ni for SN 2007au that had a peak luminosity similar to that of SN 2022ydr. It is possible that these higher-mass 91bg-like SNe Ia belong to a transitional group between 91bg and normal SNe Ia (Li et al. 2022). Another possibility is that at such low nickel masses the Arnett model might overestimate M Ni . 11. SN 2023bee: SN 2023bee was found to have excess blue light in the early part of the light-curve (Hosseinzadeh et al. 2023), which is most probably due to companion interaction (Kasen 2010).

Comparison with Other Works

In this subsection, we compare our methods and results to those given by previous publications. Khatami & Kasen (2019) Instead of fitting the entire bolometric LC, Khatami & Kasen (2019) used only the maximum bolometric luminosity and the LC rise time to constrain the nickel mass. By using their method, we re-calculated the 56 Ni masses for the objects in our sample. Comparison of the nickel masses derived with the two different methods can be seen in Figure 5, which shows that the two methods give similar results, consistently with Bora et al. (2022). The consistency between the results from two different approaches that constrain the initial Ni-mass suggests that systematic errors of the estimated Ni-masses are not severe. It may strengthen the validity and applicability of the Arnettmodel for most of the SNe Ia in the present sample.

Comparison with

Comparison with KTR20

As mentioned in Section 5, in the present paper we estimated the physical parameters of the studied SNe Ia similar to KTR20, except that the expansion velocities were inferred

Table 2 (Continued) SN Date Phase v exp. Source (YYYY-MM-DD) ( days) ( km s -1 ) 2022-11-17 -5.33 12997 (45) HET 2022-11-23 +0.65 10827 (194) LCO GSP SN 2023bee 2023-02-01 -17.80 23658 (1763) TNS: LiONS (Zhai et al. 2023) 2023-02-02 -16.81 22207 (1941) TNS: Global SN Project (Hosseinzadeh et al. 2023) 2023-02-11 -7.87 12150 (40) HET 2023-02-16 -2.90 11461 (45) LCO GSP 2023-02-17 -1.91 11444 (358) HET 10 Publications of the Astronomical Society of the Pacific, 136:094201 (29pp), 2024 September Bora et al.

Table 3 Best-fit Physical Parameters of the Sample SNe SN t 0 M Ni t LC t γ v exp M ej κ E kin. M Ni KK19 Expl. (days) ( M e ) ( days) ( days) ( km s -1 ) ( M e ) ( cm 2 g -1 ) ( 10 51 erg) ( M e ) Model SN 2019bkh -16.4 (1.4) 0.70 (0.05) 12.40 (1.14) 43.80 (3.75) 10573 (383) 1.34 (0.33) 0.09 (0.04) 0.90 (0.22) 0.66 (0.01) Both SN 2019cth -19.4 (0.3) 0.64 (0.08) 19.57 (1.21) 36.64 (1.27) 13644 (81) 1.56 (0.13) 0.26 (0.05) 1.75 (0.14) 0.46 (0.01) Near-M Ch SN 2019ein -15.6 (0.4) 0.44 (0.05) 13.41 (0.32) 32.72 (1.14) 12927 (583) 1.12 (0.18) 0.16 (0.04) 1.12 (0.18) 0.41 (0.01) Both SN 2019np -17.9 (0.4) 0.75 (0.05) 16.21 (1.11) 41.28 (0.23) 9760 (350) 1.01 (0.08) 0.20 (0.05) 0.58 (0.05) 0.62 (0.01) Sub-M Ch SN 2020enm -13.2 (2.2) 0.65 (0.06) 10.93 (1.23) 40.79 (0.82) 9449 (937) 0.93 (0.22) 0.09 (0.05) 0.50 (0.12) 0.59 (0.02) Sub-M Ch SN 2020fob -12.1 (1.9) 0.26 (0.05) 8.26 (1.33) 37.20 (3.92) 10164 (933) 0.89 (0.35) 0.06 (0.05) 0.55 (0.22) 0.27 (0.01) Both SN 2020hvq -15.3 (0.5) 0.40 (0.05) 10.62 (0.83) 50.00 (2.33) 13881 (945) 3.01 (0.69) 0.04 (0.02) 3.48 (0.80) 0.42 (0.01) Neither SN 2020rqk -15.9 (0.1) 0.59 (0.05) 12.95 (0.40) 36.61 (1.17) 9602 (887) 0.77 (0.19) 0.16 (0.06) 0.43 (0.11) 0.57 (0.02) Sub-M Ch SN 2020tug -15.8 (1.0) 0.70 (0.05) 11.06 (2.41) 41.69 (1.75) 9485 (864) 0.98 (0.26) 0.09 (0.07) 0.53 (0.14) 0.83 (0.01) Both SN 2020ue -12.6 (0.4) 0.34 (0.05) 9.57 (0.71) 34.45 (0.75) 11135 (588) 0.92 (0.14) 0.09 (0.03) 0.68 (0.10) 0.35 (0.01) Sub-M Ch SN 2020uxz -17.7 (0.1) 0.63 (0.05) 14.39 (1.00) 43.60 (2.90) 10315 (190) 1.26 (0.22) 0.13 (0.04) 0.81 (0.14) 0.59 (0.01) Both SN 2021accx -14.9 (1.0) 0.66(0.05) 11.62 (1.43) 40.68 (1.97) 10008 (438) 1.04 (0.19) 0.10 (0.05) 0.62 (0.12) 0.61 (0.01) Both SN 2021afsj -15.6 (0.5) 0.64 (0.05) 12.79 (0.95) 38.28 (1.13) 9653 (1502) 0.85 (0.32) 0.14 (0.10) 0.48 (0.18) 0.59 (0.01) Sub-M Ch SN 2021dov -17.0 (0.6) 1.19 (0.09) 14.59 (1.35) 39.42 (2.03) 9779 (286) 0.93 (0.15) 0.17 (0.06) 0.53 (0.09) 1.08 (0.01) Sub-M Ch SN 2021gtp -15.4 (0.7) 0.69 (0.06) 12.80 (1.34) 37.64 (1.54) 10880 (1654) 1.05 (0.40) 0.13 (0.10) 0.74 (0.29) 0.66 (0.02) Both SN 2021hiz -16.7 (0.2) 0.59 (0.05) 14.98 (0.46) 37.38 (1.01) 9804 (523) 0.84 (0.14) 0.20 (0.06) 0.48 (0.08) 0.51 (0.01) Sub-M Ch SN 2021hpr -17.0 (0.1) 0.67 (0.05) 13.97 (0.27) 39.96 (0.68) 11132 (560) 1.24 (0.17) 0.14 (0.03) 0.92 (0.12) 0.62 (0.01) Both SN 2021rhu -14.5 (0.1) 0.45 (0.05) 13.81 (0.73) 30.64 (2.79) 11206 (477) 0.74 (0.20) 0.22 (0.09) 0.56 (0.15) 0.37 (0.01) Sub-M Ch SN 2021ucm -16.1 (3.2) 0.76 (0.12) 13.94 (3.50) 42.58 (2.98) 11137 (719) 1.41 (0.38) 0.12 (0.10) 1.05 (0.28) 0.70 (0.07) Both SN 2021wuf -15.1 (0.9) 0.72 (0.09) 12.33 (1.59) 35.09 (1.47) 12547 (2528) 1.21 (0.59) 0.12 (0.12) 1.14 (0.56) 0.56 (0.01) Both SN 2021yrf -15.0 (0.6) 0.55 (0.05) 11.91 (0.78) 37.27 (1.53) 11391 (1771) 1.13 (0.44) 0.11 (0.08) 0.88 (0.34) 0.52 (0.01) Both SN 2021ytp -13.1 (0.8) 0.64 (0.06) 11.28 (1.08) 27.33 (1.69) 13894 (328) 0.90 (0.15) 0.15 (0.06) 1.04 (0.18) 0.56 (0.05) Sub-M Ch SN 2022aaiq -14.5 (1.2) 0.49 (0.06) 9.02 (1.59) 53.29 (3.06) 9347 (349) 1.55 (0.29) 0.04 (0.02) 0.81 (0.15) 0.52 (0.01) Near-M Ch SN 2022fw -16.4 (0.6) 0.71 (0.07) 12.59 (1.26) 45.54 (2.11) 9551 (355) 1.18 (0.20) 0.10 (0.04) 0.65 (0.11) 0.69 (0.02) Both SN 2022 hrs -15.3 (0.2) 0.60 (0.05) 12.37 (0.35) 39.29 (1.31) 12349 (1257) 1.47 (0.40) 0.10 (0.04) 1.35 (0.36) 0.58 (0.01) Both SN 2022ydr -13.9 (1.0) 0.24 (0.05) 13.02 (1.28) 27.95 (1.60) 10010 (649) 0.49 (0.12) 0.27 (0.14) 0.29 (0.07) 0.19 (0.01) Neither SN 2022zut -20.3 (1.6) 0.61 (0.06) 15.14 (1.72) 47.88 (4.55) 11332 (497) 1.84 (0.51) 0.11 (0.06) 1.42 (0.39) 0.62 (0.03) Near-M Ch SN 2023bee -17.1 (0.5) 0.82 (0.05) 13.25 (0.79) 45.14 (1.61) 11074 (829) 1.56 (0.35) 0.10 (0.04) 1.15 (0.25) 0.79 (0.02) Near-M Ch

Note. The first 4 columns list the best-fit parameters given by Minim, then the expansion velocities, the ejecta masses, the calculated opacities, kinetic energies (see Section 5), nickel masses from the method of Khatami & Kasen (2019), and the consistency with near-Chandra and/or sub-Chandra explosion models are shown. Publications of the Astronomical Society of the Pacific, 136:094201 (29pp), 2024 September Bora et al. Publications of the Astronomical Society of the Pacific, 136:094201 (29pp), 2024 September Bora et al. from the Doppler shift of the Si II λ6355 feature in the available spectra. For comparison, we also derived the physical parameters for the whole sample with the method of KTR20, i.e., without using spectroscopic velocities. After comparing the two sets of parameters taken with and without spectroscopic velocities, we found that the v exp and E kin parameters are significantly different. This is not surprising given the very approximate methodology used by KTR20 for estimating the velocities without spectroscopy. Thus, our new velocities and kinetic energies are more reliable than those obtained by KTR20 for their sample. Note also that Scalzo et al. (2019) revealed practically no correlation between their expansion velocities (inferred directly from the kinetic energy provided by explosion models) and v Si II , thus, they concluded that v Si II is not a good proxy for estimating the kinetic energy of the bulk ejecta.

On the other hand, the ejecta masses (M ej ), and opacities (κ) given by the two methods are in good agreement, as seen in Figure 6. We also compare the nickel masses and ejecta masses between our sample and that of KTR20 in Figure 7 (note that in Figure 6 the objects are the same, but the methods are different, while in Figure 7 we show the results of two different methods being applied to two different samples).

Figure 7 demonstrates that the two samples have similar distributions of both the ejecta masses and the nickel masses, even though different methods were applied to different samples. This shows that in spite of not using spectral information, the ejecta masses estimated by KTR20 are realistic, and their method is useful for estimating the ejecta mass in cases where getting near-maximum spectra is not possible. It is important to note that in their analysis, KTR20 set an upper limit of 1.4 M e for the ejecta mass and a lower limit of 10,000 km s -1 for v exp . Our method does not have these limits, so the distribution of ejecta masses can be wider, as seen in Figure 7. Other than that, we found good agreement between the two distributions: SNe in the KTR20 sample were found to have a mean M ej of ∼1.07 M e and standard deviation of 0.15 M e , which is consistent with those of our sample, ∼1.12 M e and 0.30 M e , respectively.

Comparison with Scalzo et al. (2019)

Previously, ejecta masses for SNe Ia were also inferred by Scalzo et al. (2010Scalzo et al. ( , 2012)), and Scalzo et al. (2014a). They used a method that was purely photometric, without any spectroscopic information, similar to KTR20. Their theoretical approach was based on a combination of several theoretical Ia explosion models, and they applied a different formalism than KTR20 and we did in the present paper. Scalzo et al. (2014a) estimated the 56 Ni and ejecta masses for their sample containing 19 SNe Ia, and concluded that about 50% of their sample SNe arose from the explosion of sub-Chandra WDs (see also Scalzo et al. 2014b). Their method was further applied on a larger sample (∼45 SNe) and reached a similar conclusion (Scalzo et al. 2019).

Taking into account the uncertainties, 22 out of 27 SNe (81%) in our sample are consistent with sub-Chandra WD masses, but 13 of them are also consistent with both sub-Chandra and near-Chandra masses (see Table 3). This leaves 9 SNe (33%) in our sample whose ejecta masses are consistent with only sub-Chandra WDs. If we take the inferred ejecta masses at their face value, 11 out of 27 SNe (41%) fall within the mass range of sub-Chandra explosion, i.e., between 0.9 and 1.2 M e . This is somewhat lower than the value found by Scalzo et al. (2019), but the uncertainties of the inferred ejecta masses, or the minor differences between the methodologies could explain the differences. Nevertheless, our results are consistent with the previous conclusions that a significant fraction (∼50%) of SNe Ia produce sub-Chandra ejecta masses after explosion.

Correlations between the Parameters

In this section we examine the correlation between the inferred physical parameters using p-values and Pearson correlation coefficients, which are presented in Figures 8, 9 and 12. In Figure 8 we show the correlation between the SALT3 x 1 parameter and the initial nickel mass (left panel) and the ejecta mass (right panel). The best-fitting linear equations are

117 0.022 0.659 0.027 , 6 Ni 1 Figure 3. Visualization of the method we used to estimate v exp for SN 2021hpr. The high-and low velocity bounds are defined by SN 2019ein (black symbols and thick curve) and SN 2011fe (red symbols and thick curve). Among the interpolated velocity curves (thin dotted curves) the best-fit curve for SN 2021hpr (blue dashed curve) is used to estimate the velocity at maximum (orange symbol).

and ( )• ( ) ( ) =  +  M x 0.140 0.057 1.258 0.055 . 7 ej 1

Both of these fittings agree well with those of Scalzo et al. (2019) within the errors, and show that the light curve decline rate (measured by the SALT3 x 1 parameter) correlates with the initial mass of the radioactive nickel synthesized in the explosion, as well as with the ejecta mass: lower decline rates (more positive x 1 ) correspond to higher M Ni and M ej .

Similar correlation can be seen between M ej and the timescale of the gamma-ray leakage (t γ ), as shown in Figure 9 (left panel). This relation illustrates that in more massive ejecta it takes longer for the gamma-photons to diffuse out, therefore t γ is a good indicator of progenitor mass (see also KTR20, but see Section 6.5 for caveats). The correlation with the expansion velocities (Figure 9

2 is expected, but, because of the presence of the » g M t ej 2 dependency, the correlation with the velocities looks smeared. In Figure 10 we show the relation between the ejecta mass and the optical opacity. The dotted line indicates the expected dependency from Equation (4) using the mean values for t LC and v exp (12.81 days and 10,929 km s -1 , respectively) inferred from our sample.

Comparison with Explosion Models

In this subsection we examine if our results are consistent with recently published explosion models.

First, we compare our estimated ejecta and nickel masses to the predictions of various detonation models in Figure 11 As Figure 11 illustrates, the majority of objects in our observational sample (22 out of 27) are consistent with the current sub-M Ch models, including the thin He-shell double detonation models in SD progenitors. Even though some of the calculated ejecta masses are below 0.9 M e , which is the lowmass cutoff of the current sub-Chandra models that produce enough 56 Ni to be consistent with observed SNe Ia, the uncertainties of the inferred ejecta masses still make them consistent with the models (i.e., their difference from the cutoff mass is less than 1σ). Moreover, the DD models of Tanikawa et al. (2019), involving two merging WDs in a DD configuration, are also consistent with the observations, at least in the nickel mass range of 0.5-0.7 M e , but this is a bit uncertain since those models do not extend significantly below ∼1 M e ejecta mass, unlike the SNe in our observational sample. The Tanikawa et al. (2019) models above ∼1 M e are TD and QD explosions, where the companion WD also explodes, resulting in higher ejected masses. Overall, sub-Chandra detonations as well as DD models seem to be consistent with the majority of our observational sample.

There is only 1 object (the 91bg-like SN 2022ydr) that seems to be significantly below the cutoff mass, i.e., inconsistent with the current explosion models. Since all of these events are spectroscopically confirmed SNe Ia, this inconsistency is likely due to either some difficulties with the observations, or the failure of the Arnett-model for this particular object (see Section 6.5).

On the other hand, Figure 11 shows that more than 50% of the SNe (17 out of 27) also fall within the mass range of near-DDC models (1.2  M ej  1.5 M e ) if their errorbars are taken into account. However, only 4 of them exceed 1.2 M e significantly, as the others have uncertainties that extend below 1.2 M e . The near-Chandra models, plotted with red dashed and dotted lines in Figure 11, have the same M ej ≈ 1.44 M e in general, and they show practically no correlation between their M ej and M Ni .

It is important to note that due to the uncertainties of the calculated ejecta masses, a significant fraction of our sample (13/27, 48%) are consistent with both the near-Chandra and sub-Chandra explosion scenarios, so it is not possible to distinguish between these two possibilities in those cases.

These fractions can also be estimated using the Gaussian Probability Density Function (PDF) shown in the bottom panel of Figure 7. Integrating the PDF below 0.9 M e , between 0.9 and 1.2 M e , between 1.2 and 1.5 M e and above 1.5 M e , corresponding to below-sub-Chandra, sub-Chandra, near-Chandra and super-Chandra mass regimes, respectively, we got the probabilities for these regimes as 0.32, 0.33, 0.20, and 0.15, respectively. These are also indicated in the legend of 17 Publications of the Astronomical Society of the Pacific, 136:094201 (29pp), 2024 September Bora et al.

Figure 7. Again, since the uncertainties seem to be higher than the mass difference between the sub-Chandra, and near-Chandra channels, it is difficult to draw a definite conclusion, but it seems to be slightly more probable (at least in the present sample) that a SN belongs to the sub-Chandra mass regime instead of being a near-Chandra event.

As seen in Figure 11, the range of the inferred Ni-masses is fully consistent with the ones predicted by both the near-Chandra and sub-Chandra models. For the former, where the ejecta masses are the same (M Ch ), the differences in the Nimasses can be achieved by the number of ignition sparks and the implementation of the deflagration-to-detonation transition (e.g., Seitenzahl et al. 2013). On the contrary, in sub-Chandra explosions the synthesized Ni-mass is connected with the mass of the WD (and partly with the details of the ignition mechanism), which is reflected by the slope of the lines representing the sub-Chandra models in Figure 11. The fact that most of the inferred ejecta masses also seem to show a similar trend suggests that those SNe (or at least some of them) might also be produced by sub-Chandra explosions, but the uncertainties of the inferred ejecta masses prevent making a definite conclusion at the moment.

In Figure 12 we plot the correlation between the inferred bolometric luminosity and the reddening-corrected (B -V ) 0 color at the moment of maximum light. We compare these data with the results of two explosion models given by Blondin et al. (2017): we plot the results of the central detonation sub- (Fink et al. 2010;Seitenzahl et al. 2013;Blondin et al. 2017;Polin et al. 2019;Tanikawa et al. 2019;Gronow et al. 2021). The blue, gray and red colors code the 91T-, normal-and 91bg subtypes respectively. SNe from this paper are plotted with filled circles, while hollow circles represent the objects from KTR20.

Chandra scenario with a dotted curve, while the dashed curve shows the same from the Chandrasekhar-mass delayeddetonation model. It can be seen that the models follow the observed trend of most SNe Ia having (B -V ) 0 ≈ 0.0 mag around maximum, with the fainter events being redder. However, considering just the luminosity and the color at the moment of maximum is not enough to differentiate between these two explosion scenarios, as they both fit our observed sample relatively well. Our observations also show brighter and bluer events than those predicted by the Blondin et al. (2017) models.

Overall, we conclude that the predictions of current sub-Chandra models are consistent with the ejecta and nickel masses measured from observations for most SNe Ia in our sample. Due to the uncertainties of the inferred masses, the conventional delayed-detonation models are also compatible with many of the SNe in our sample, but those models have difficulties explaining the significant number of sub-Chandra ejecta masses.

Concerns and Caveats Regarding the Methodology

The Arnett-model as well as similar semi-analytic LC models have been widely used for inferring ejecta parameters of various types of SNe, even though such a model is (of course) far from being perfect, and suffers from several issues. Regarding the ejecta mass, one of the most serious, well-known issues is the degeneracy between M ej and the optical opacity κ, as seen in Equation (4): from the t LC timescale, representing the pre-maximum part of the LC, both κ and v exp must also be known to calculate M ej . κ, however, is treated very approximately within the framework of the Arnett-model: it is assumed to be constant both in space (within the ejecta) and in time (i.e., no evolution), neither of which is expected to be true in reality. Thus, κ should be considered only as a technical, rather than a self-consistent physical parameter, which characterizes the timescale of the diffusion of photons within a spherical, constant-density, homologously expanding ejecta.

Despite this well-known caveat, it is somewhat surprising that applying physically motivated estimates for κ, like the expected Thompson-scattering opacity of a metal-dominated plasma (κ ∼ 0.1 cm 2 g -1 ), one can get quite reasonable ejecta mass estimates for SNe Ia from observationally inferred t LC parameters. In order to verify this statement using the present sample, we explored two alternative ways in deriving the ejecta masses. As a first experiment, we calculated ejecta masses from Equation (4) assuming κ = 0.1 cm 2 g -1 and = v 10,000 exp km s -1 . Second, we substituted v exp into Equation (3) with the kinetic energy E kin taken from Equation (5), expressed M ej , and assumed E kin = 10 51 erg as a uniform value for the whole sample. The results of these experiments are plotted as histograms and Gaussian PDFs in Figure 13, together with the distribution of the original M ej values listed in Table 3.

It is seen that, despite the over-simplifying assumptions used in these experiments, either the constant opacity and expansion velocity, or the kinetic energy that are uniform for the whole Ia sample, the resulting ejecta masses are close to the ones estimated from the gamma-ray leaking timescales, even though the peaks of their distributions are shifted to somewhat higher values. The mean ejecta mass from the uniform opacity assumption is 〈M ej 〉 = 1.32 M e with a standard deviation of 0.47 M e , while from the uniform kinetic energy assumption these are 〈M ej 〉 = 1.26 M e and 0.18 M e . It is seen that using such kind of physically motivated assumptions one can get slightly different ejecta masses than by using the data-driven method we preferred in this paper, which makes as minimal assumptions as possible within the framework of the Arnettmodel. Still, even if we adopted any of the results from the above experiments, a non-negligible fraction of the sample (∼7% in the uniform opacity model, or ∼19% in the uniform kinetic energy model) would be consistent only with sub-Chandra explosions (see Table 4). However, the uniform opacity model would also predict that ∼26% of the sample is consistent only with near-Chandra explosions, with ∼22% of the sample being super-Chandra (M ej > 1.5 M e ). In the fixed kinetic energy model the fraction of only near-Chandra explosions is higher (∼30%). The number of SNe that are consistent with both explosion channels are nearly the same (40%-50%), regardless of the adopted LC interpretation. Thus, it seems that the Arnett-models that relate the timescales of the SN bolometric LCs to the basic physical parameters of the ejecta are consistent with the observations only if a fraction of the observed SNe Ia are produced by sub-Chandra progenitors. While discussing the physics of SNe Ia, Livio & Mazzali (2018) argued that ejecta mass estimates based on the Arnettmodel are sensitive only to the opaque mass. Since the optical opacity is mostly sensitive to the Fe-group elements, such a method can recover only the mass rich of Fe-group elements. They concluded that "It would therefore not be surprising for Scalzo et al. to find masses that are proportional to the nickel mass." This argument, however, assumes that the ejecta mass We show the ejecta masses obtained with κ γ = 0.025 cm 2 g -1 (solid blue), κ γ = 0.028 cm 2 g -1 (dashed green), and κ γ = 0.03 cm 2 g -1 (dotted red). Bottom panel: Gaussian distributions of the different masses, constructed the same way as in Figure 7.

estimate is based on the optical (average) opacity, like in Equation (4). It is emphasized that the ejecta mass estimates that are based on the gamma-ray transparency timescale (t γ ) that we use in this paper (and also the numerous previous studies discussed in Section 6), is much less affected by the uncertainty of the gamma-ray opacity, κ γ , which is constrained much better and it is less sensitive to the actual chemical composition of the ejecta than the optical opacity.

In this study we have adopted κ γ = 0.025 cm 2 g -1 from Guttman et al. (2024), who derived the value from a semianalytic method. Some previous works used κ γ = 0.03 cm 2 g -1 from Wheeler et al. (2015) but this value goes back to Colgate et al. (1980) who inferred κ γ = 0.028 cm 2 g -1 using a multiplescattering Monte Carlo gamma-ray transport code developed at Los Alamos. It is seen that these values are in good agreement with each other. Still, because κ γ appears in the denominator in Equation (3), the inferred M ej masses are sensitive to the adopted value of this parameter. In order to test the effect of the adopted gamma-ray opacity on the final results, we have recalculated the ejecta masses from Equation (3) using κ γ = 0.028 and 0.03 cm 2 g -1 .

The results are shown in Figure 14, where the histograms and PDFs of the inferred M ej values corresponding to the different adopted gamma-ray opacities are plotted together. It is seen that adopting a slightly higher gamma-ray opacity decreases the inferred ejecta masses (Table 4), as expected. This can be considered as a systematic uncertainty of the calculated ejecta masses. However, the range of the potential gamma-ray opacity values is small enough that this systematic uncertainty is not severe. Indeed, as Table 4 shows, adopting κ γ = 0.03 cm 2 g -1 would decrease only the number of systems that are consistent only with the near-Chandra scenario, but the fraction of sub-Chandra SNe would be nearly the same. It is true, however, that the higher gamma-ray opacity would significantly increase the fraction of SNe that have too low ejecta masses, hence they would become inconsistent even with the sub-Chandra explosion models. Still, regardless of the adopted gamma-ray opacity value, the majority of the SNe in our sample are consistent with both explosion channels. These calculations confirm that the ejecta masses inferred from the gamma-ray transparency timescales measured at late phases suggest that more SNe Ia may be due to sub-Chandra explosions than what could be estimated from the nearmaximum LCs. The key parameter behind this conclusion is clearly the gamma-ray opacity, which is much better constrained than the optical (electron scattering) opacity.

The expansion velocity parameter, v exp , is also problematic. In the original paper Arnett (1982) used the term "scaling velocity," v sc , to emphasize that it is more like a parameter describing the homologous expansion of a constant-density sphere instead of being an actually observed velocity. However, he also argued that "... if we take v sc from the photospheric fluid velocity near maximum light, this value is not far from the uniform-density estimate." This note was the main motivation for us to assign the observed v Si II at maximum to the expansion velocity in our calculations.

In order to test whether the observed v Si II velocities were valid expansion velocities in the Arnett-model, we inferred the expected expansion velocity as a function of t γ from Equation (3) by assuming a fixed ejecta mass, and compared them with the observed velocities (see Figure 15). It is seen that most of the observed points fall within the two theoretical curves corresponding to M ej = 0.9 and 1.5 M e . Thus, using the observed v Si II velocity and t γ values one can get reasonable estimates for the ejecta mass via Equation (3).

Still, the question remains whether v Si II gave the total ejecta mass when inserting it into Equation (3). In other words: is it possible that v Si II probes only the inner, optically thick part of the ejecta at the moment of maximum light, resulting in a mass that is systematically lower than the true M ej ? This is a nontrivial problem, because the Arnett-model assumes a constant density ejecta, while real SNe Ia have different density profiles. The detailed investigation of this issue will be the subject of a subsequent paper (J. Vinkó et al. 2024, in preparation), but a quick analytic estimate is given here. Following Magee et al. (2020), we used the exponential density profile of a fiducial SN Ia having M ej = 1.44 M e and E kin = 10 51 erg to calculate the velocity at the photosphere via the usual condition of Note. First column: method for calculating M ej . 2nd and 3rd columns: the mean and the standard deviation of the masses inferred by each method. Next columns: the percentage of SNe that are consistent with only sub-Chandra, only near-Chandra, both or neither explosion models. See Section 6.5 for explanation.

τ(v ph ) = 2/3, where τ(v ph ) is the optical depth of the ejecta at v ph . After that, the mass above v ph , which is optically thin and may not contribute to the photon diffusion, was determined by integrating the density profile between v ph and = v 30,000 max km s -1 (Magee et al. 2020). Adopting » t 18 max days as the moment of maximum light after explosion, we got v ph = 11,571 km s -1 and 13,238 km s -1 for κ = 0.1 and 0.2 cm 2 g -1 , respectively. The masses above these photospheric velocities are ΔM ej ≈ 0.20 and 0.13 M e , respectively. It is seen that even though the mass probed by the Arnett-model is 1.44-0.20 = 1.24 M e , i.e., ∼14% lower than M Ch , it would still be within the range of the near-Chandra explosions. Thus, it is not likely that the significant fraction of the sub-Chandra ejecta masses given by the Arnett-model are simply due to the systematically low velocities inserted into Equation (3).

Yet another important restriction of the Arnett-model is the assumption of a centrally localized heating source, i.e., the spatial distribution of 56 Ni is strongly peaked at the center. This may be a fair assumption for a fiducial SN Ia model having M Ch mass and ∼0.6 M e (i.e., ∼40% mass fraction) of 56 Ni. However, it can be expected to break down in several cases: (i) when M Ni  1.0 M e , i.e., the majority of the ejecta mass consists of radioactive Ni, (ii) when M ej = M Ch , i.e., for sub-Chandra explosions, and (iii) when 56 Ni has a more extended distribution for other reasons, e.g., off-center ignition (Seitenzahl et al. 2013;Magee et al. 2020). If the radioactive heating is not centrally localized, the photon diffusion timescale may get shorter, and some of the gamma-rays produced by the radioactive decay may start to leak out from the expanding ejecta earlier than expected for a centrally located heating source. These effects may result in shorter t LC and t γ timescales for the observed light curve, which, in the formalism of the Arnett-model, gives an ejecta mass that is lower than in reality.

This caveat may explain the presence of SNe having ejecta masses significantly less than the lower limit of sub-Chandra Ia models (0.9 M e ), which otherwise have "normal" nickel masses in the observed sample (Figure 11). This may also be the explanation for those objects having M Ni  M ej (SN 2021dov or SN 2017erp in KTR20). Since it is certainly a limitation for the applicability of the Arnett-model to real data, the resulting too low ejecta masses or the cases when M Ni /M ej ≈ 1 should be treated with caution.

Even though these undeniable caveats exist, we believe that radiation-diffusion (Arnett-) models can still give us reliable constraints on the global physical properties of SNe Ia if the photometry extends well beyond maximum light into the regime when the ejecta becomes semi-transparent to gammarays, and there is near-maximum spectroscopy available.

Summary

We presented multicolor photometry of 28 nearby Type Ia supernovae taken during the first 4 yr of operation of the RC80 and BRC80 telescopes at Piszkéstető station of Konkoly Observatory and Baja Observatory of University of Szeged, Hungary. Using the multicolor light curve fitting codes SALT3 and MLCS2k2, we determined luminosity distances as well as total dust extinctions to the sample SNe, which we used to construct their pseudo-bolometric LCs. Fitting the bolometric LCs with the Arnett-model yielded the mass of the radioactive nickel synthesized during the explosion along with the important timescales of t LC , and t γ , which can be used to estimate the ejecta mass if the photospheric velocity is known. After collecting previously unpublished optical spectra taken by LCO telescopes and the HET, supplemented by public spectra downloaded from the TNS, we measured the velocities of the Si II λ6355 feature and determined the v Si II velocities at the moment of maximum for all of our sample SNe.

Via Equations (3)-( 5) we calculated the ejecta masses, optical opacities and kinetic energies for the sample SNe. We found that based on the inferred ejecta masses, ∼48% of the sample SNe are consistent with both sub-Chandra and near-Chandra explosion models. Our results suggest that ∼33% of the sample can be explained by only sub-Chandra progenitors. This is a somewhat lower value than appeared earlier in the literature (Scalzo et al. 2014a(Scalzo et al. , 2014b(Scalzo et al. , 2019;;Könyves-Tóth et al. 2020;Liu et al. 2023b), but together with the events that are consistent with both explosion channels, this could be as high as 81%. The fraction of near-Chandra events was found to be in between ∼15% and 63%, but this estimate may suffer from low-number statistics and can also be affected by the adopted value of the gamma-ray opacity. If we used κ γ = 0.03 cm 2 g -1 instead of 0.025, the maximum fraction of near-Chandra SNe Ia would decrease down from 63% to ∼41% at best. After comparing our results with multiple types of recent explosion models, we revealed that significant differences between the predictions of near-Chandra and sub-Chandra models cannot be seen in the color-luminosity relation around maximum (see Figure 12). We showed that the ejecta mass can be a useful constraint to confront the predictions of various explosion models with the observations. From the results presented in this paper it seems that the majority of the studied SNe Ia are consistent with either the sub-Chandra or the near-Chandra explosion models, but the accuracy of the current photometric mass estimates are not high enough to clearly distinguish between these two possibilities.