Department of Physics and Astronomy
Research project in Physics, 5 credits
Lightcurves of super-Chandrasekhar mass supernovae
Amanda Byström Supervisor: Joel Johansson
Spring semester 2020
Abstract
20 supernovae that spectroscopically match the peculiar, superluminous type Ia supernova 2003fg are studied in this project. SN2003fg is thought to have erupted at a super-Chandrasekhar mass, thus breaching the theo- retical mass limit for a white dwarf. By analysing the lightcurves of these 20 supernovae, this work aims to understand what the progenitor binary systems from which the supernovae erupt looked like. A lightcurve fit- ting using the software snpy is performed for each supernova. Using the produced models, time of maximum luminosity, stretch and maximum magnitudes in the g-, r- and i-bands are found. It is found that sublumi- nous supernovae might be a sign of circumstellar material surrounding the progenitor star, though some of the supernovae were superluminous and some adhered to Phillip’s relationship. Substructures were found in the lightcurves, as the sampled supernovae showed clearly different behaviours in each of the three bands.
1 Introduction
A supernova (SN) is an explosion of a star that can be as bright as a minor galaxy. There are several mechanisms that can produce these violent explosions, and thus there are several types of SNe. These types are morphologically based on the spectra and lightcurves of the SNe, and as more and more SNe are discovered and observed, astrophysicists are identifying an increasing amount of SN subclasses.
A well-studied SN type is type Ia. They are known to occur in a binary system, in which at least one of the components is a white dwarf (WD). What the companion looks like is a debated topic. Either way, the WD can accrete mass from its companion if the companion fills its Roche lobe. When the WD gains enough mass to breach the theoretically highest WD mass possible, the so called Chandrasekhar mass limit of 1.44M , the electron degeneracy pressure within the star cannot withhold the gravitational pressure any longer. The star contracts, causing core carbon and oxygen to fuse, producing the Nickel-56 isotope. The decay of this isotope is what fuels the thermonuclear explosion of the WD; this thermonuclear explosion is what is called a SN.
Two parameters that are of interest when examining type Ia SNe are maxi- mum brightness (and the time of this maximum brightness, called Tmax, mea- sured in days) and the decline rate after the maximum brightness typically parametrized by ∆m15 (see eq. (1) in section 3) or stretch. stretch is dimen- sionless. The higher stretch, the slower it takes for the luminosity of the SN to fade, making its lightcurve look stretched; hence the parameter name. For type Ia SNe, there is a relationship between stretch and absolute magnitude at Tmax, i.e. peak M ; the higher this M , the higher stretch (Phillips 1993). This relationship will in this work be called Phillip’s relationship.
The lightcurves and magnitudes of these SNe are fairly homogeneous. Thus, Ia SNe are often used as standard candles for astronomical measurements. How- ever, since the 1990’s, astrophysicists have found that there are two subclasses of type Ia SNe; one is more luminous, and the latter is less so. With the Phillip’s relationship, they have been able to reconcile the magnitude differences, so that the lightcurves of these SNe indeed match, reducing the spread in peak magnitudes and allowing even strange SNe to be used as yardsticks. With the advent of surveys such as the Palomar Transient Factory (PTF), a zoo of Ia SNe have been discovered, with many more distinctions than just peak brightness (Taubenberger 2017).
One such newly discovered SN class is the 03fg-like SNe. SN2003fg (03fg for short) was a SN at redshift z = 0.2440 that did not obey Phillip’s relationship;
it was too bright for its stretch. Since the decay of Ni-56 is exclusively what fuels a type Ia SN, 1.3M of this nickel isotope is the only thing that can explain its luminosity being 2.2 times higher than a normal type Ia SN. This is not reconcilable with the progenitor WD exploding at 1.44 M . Also, the ejecta of this SN had a low kinematic energy; since the kinematic energy is the thermonuclear burning energy minus the binding energy of the WD, a low kinematic energy means a high WD binding energy; this in turn means a large mass. The calculated mass for 03fg is 2.1M (Howell et al. 2006). Because of this, these 03fg-like SNe are sometimes also called super-Chandrasekhar (SC) mass SNe. Theoretical calculations also show that the mass of SN2007if, a well- studied 03fg-like SN, must be larger than Chandrasekhar to explain its 03fg-like
behaviour (Scalzo et al. 2010).
The main question then is how these SNe can breach the Chandrasekhar mass limit. These 03fg-like SNe are most often found at redshifts where the amount of younger stellar populations is thought to be higher than at lower red- shifts (Howell et al. 2006), together with blue, low-mass, star forming galaxies.
In these young populations, the likelihood of the companion star being another WD is higher than in older, ’dead’ populations. In such a so-called double- degenerate (DD) binary system, the explosion of one of the WD’s can trigger the second one, causing an explosion of a system in which the total mass can be up to 2.88M . Another possible explanation for the super-Chandrasekhar mass is the rotation of the WD. This rotation would increase as the WD accretes mass from its companion; i.e. a transfer of angular momentum would automat- ically come with mass transfer. If the rotation is rapid enough, the WD could be dynamically stable up to 2.88M (Yoon & Langer 2005).
A third, possible explanation is that the WD is surrounded by a circumstellar medium (CSM). If the binary system is single-degenerate (SD), i.e. only one of the stars is a WD, the system should be veiled in a dense CSM. In the DD scenario, the CSM is expected to be much thinner. If a CSM surrounds the system, it would be detectable by creating an echo in the light either in the near-infrared (NIR) or in the visual, because the interaction of SN ejecta and the CSM would release energy, making the SN more luminous. SN2012dn has shown a NIR excess (though normal type Ia luminosity in the visual, because the echo is hid within the normal light) in accordance with it being surrounded by a CSM. The large amount of CSM suggests that SN2012dn was part of a SD binary system. SN2009dc on the other hand probably did not have a large CSM. This suggests two kinds of 03fg-like SNe; those brighter from a clean environment, and those fainter from a dusty environment (Nagao, Maeda &
Yamanaka 2017).
Within the redder bands, especially the i-band, type Ia SNe lightcurves tend to show some peculiarities. Most of these lightcurves have two magnitude peaks;
one at maximum brightness, and a second one about 1-2 months later. However, about 11% of normal SNe lack this later hump (Takanashi et al. 2008). 03fg-like SNe were shown by Ashall et al. (2020) to not, in general, exhibit this second peak. They also showed that it takes a longer time for these SNe to rise to the first magnitude peak in the i-band, than for normal SNe Ia, so that the slope is less steep and that Tmax appears later in comparison.
1.1 Aim
The aim of this work is to analyse the lightcurves of 03fg-like SNe in the g, r and i-bands to find their Tmax, stretch and peak magnitudes in all three bands. These parameters will be used to examine if the sampled SNe adhere to the Phillip’s relation and what their lightcurves tend to look like in each band.
This will hopefully shed light on the progenitors of 03fg-like SNe.
2 Observations
In this work, 20 03fg-like SNe are examined. They were all observed with the Palomar 48-inch telescope during the survey Palomar Transient Factory. Out of a large sample of ∼ 2000 SNe Ia, these 20 were chosen to be studied since they matched SN2003fg spectroscopically (an example of a spectroscopic match is shown below); this shows the rarity of these SNe. The spectroscopic matching was performed with the software SN ID (Blondin & Tonry 2007).
Figure 1: A spectroscopic match found using the software SN ID, showing that the SN iPTF15doz (in black) matches SN 2007if, a well-studied 03fg-like SN, well.
Three well-studied SC-SNe in literature are SN2007if, SN2009dc and SN2012dn (Taubenberger 2017). They have been included in this work as references, since they show 03fg-like features such as e.g. high stretch, low ejecta velocities and large luminosities.
3 Analysis
The SN lightcurves were analyzed, from which we find time of peak brightness Tmax, stretch s and absolute magnitude M at Tmax, the peak magnitude. For this, the software SNooPy (henceforth abbreviated snpy ) (Burns et al. 2011), has been used to model lightcurves of each SN based on lightcurve data in three filters (see next page). The model used is the so-called max model. This model is designed to suit normal type Ia SNe, and fits the maximum magnitude of an observed lightcurve. It is defined by Carnegie Science (2015) as:
mX(t) = TY(t0, ∆m15) + mY + RXE(B − V )gal+ KX,Y (1)
In the equation above, we have the parameter ∆m15 defined by Phillips et al.
(1999). It is the decline in the B-filter magnitude from Tmax to 15 days later.
It is sometimes used alongside, or instead of, the stretch parameter. mX(t) and mY is the peak apparent magnitude of filter X and Y respectively, where the former is observed. The argument t is observed time relative to B maximum and t0 is the de-redshifted time relative to B maximum. RX is the absorption in filter X, and E(B − V )gal is reddening due to Galactic dust. The last term, KX,Y, is cross-band K-correction from restframe X to observed filter Y . Cross- filter K-corrections are used when operating at high redshifts. They are used to transform the observed band, that gets redshifted along with the SN, to rest-frame optical light (Nugent, Kim & Perlmutter 2002).
Lightcurves in the filters g and r (effective wavelength midpoints are 4750 and 6580 Å respectively) were fitted using the max model. Since the redshifts are quite small for the sampled SNe, observed g- and r-bands were fit to restframe templates. When snpy performs the fitting, it calculates Tmax and stretch, together with statistical and systematic errors. The software retrieves a redshift z from the photometry file (which has been computed using SN ID fits or galaxy emission or absorption lines when available). It also presents the peak apparent restframe magnitude (i.e. apparent magnitude at t = Tmax) in each filter used, together with errors. Within snpy, it is also possible to calculate the distance modulus of a SN; this is subtracted from the given apparent magnitude, to get the maximum absolute magnitudes of the SNe. The final lightcurve model and its corresponding parameters are corrected for extinction due to gas in the Milky Way (Burns et al. 2011).
If only the g-filters are used to calculate stretch, stretchgcan be calculated.
While this fitting is done, Tmax is held fixed as the value found by using both g- and r-bands. The computation of stretchg is a way to check if the SNe behave the same in both g- and r-band, and if a global stretch can be applied to lightcurves in both filters.
Since we know that 03fg-like SNe behave differently in the i-band (effective wavelength 8060 Å) compared to normal type Ia SNe, it is of interest to also fit i- band lightcurves. We calculate peak Miby redoing the process described above, but this time, apart from the same g- and r-bands as previously, all available i-filters of sufficiently high quality are also used. Once again, snpy presents a peak apparent magnitude, from which the distance modulus is subtracted to get the peak absolute magnitude Mi. This way, the Phillip’s relationship can be examined for this band as well, without it sullying the results given by the other two, more normal, bands.
3.1 Computed parameters
Table 1 and Table 2 show time of maximum luminosity Tmax, stretch stretch and stretchg, redshift z, and maximum absolute magnitude M in the g-, r- and i-bands (if available), for all 20 SNe. The presented errors are the statis- tical ones. The SNe have been divided into two categories in the tables: the first category, i.e. SN2007if, SN2009dc and SN2012dn are well-studied SC-SNe in the literature; the second category are SNe that were observed during the survey Palomar Transient Factory (prefix ’PTF’), and those with prefix ’iPTF’
were observed during the Intermediate Palomar Transient Factory, which was a survey that succeeded the PTF.
Table 1: The supernovae and their time of maximum luminosity Tmax, param- eters stretch and stretchg as well as redshift z.
Supernova Tmax[MJD] stretch stretchg z
SN2007if 1345.057 ± 0.967 1.433 ± 0.029 1.500 ± 0.000 0.0742 SN2009dc 1946.257 ± 0.831 1.449 ± 0.056 1.460 ± 0.025 0.0214 SN2012dn 133.398 ± 0.177 1.308 ± 0.014 1.256 ± 0.015 0.0102 PTF09dnp 55069.690 ± 0.000 1.079 ± 0.087 1.344 ± 0.206 0.0373 PTF10abjp 55523.290 ± 2.254 1.421 ± 0.058 1.339 ± 0.220 0.1100 PTF10gbq 55303.225 ± 2.272 1.668 ± 0.038 1.700 ± 0.000 0.1000 PTF11all 55598.000 ± 0.000 1.000 ± 0.000 1.381 ± 0.277 0.1900 PTF11jgq 55782.251 ± 0.312 1.191 ± 0.052 1.103 ± 0.265 0.1290 PTF11mkx 55836.498 ± 0.323 1.189 ± 0.024 1.189 ± 0.033 0.0550 PTF11pdl 55857.752 ± 0.000 1.000 ± 0.000 1.000 ± 0.000 0.2630 PTF12dst 56048.975 ± 2.194 1.322 ± 0.100 2.020 ± 0.221 0.1920 iPTF13dhs 56556.548 ± 0.436 1.266 ± 0.034 1.283 ± 0.071 0.1710 iPTF14flj 56921.806 ± 0.910 1.000 ± 0.000 1.087 ± 0.184 0.1803 iPTF14gkg 56939.440 ± 0.305 1.189 ± 0.049 1.092 ± 0.067 0.1100 iPTF15doz 57342.019 ± 0.341 1.342 ± 0.034 1.497 ± 0.064 0.1100 iPTF15eod 57346.114 ± 0.379 1.573 ± 0.025 1.549 ± 0.031 0.0340 iPTF15eue 57390.000 ± 0.070 2.000 ± 0.000 2.000 ± 0.014 0.2600 iPTF16arh 57531.474 ± 0.205 0.950 ± 0.052 1.010 ± 0.056 0.0740 iPTF16bcl 57548.255 ± 0.625 1.269 ± 0.129 1.455 ± 0.116 0.1500 iPTF16gnw 57655.320 ± 3.829 1.400 ± 0.000 1.400 ± 0.000 0.1120
In Table 1, for all SNe, the systematic error is ±0.340 days, ±0.030 and ±0.030 for Tmax, stretch and stretchg, respectively. In Table 2 below, the systematic error is ±0.014 mag for Mg and ±0.022 mag for Mrand Mi.
Table 2: The supernovae and their maximum absolute magnitudes in the g, r and i-bands, with g being the bluest and i the reddest.
Supernova Mg Mr Mi
SN2007if -20.299 ± 0.044 -20.129 ± 0.032 -19.872 ± 0.045 SN2009dc -19.783 ± 0.021 -19.627 ± 0.025 -19.740 ± 0.049 SN2012dn -18.790 ± 0.010 -18.972 ± 0.009 -18.644 ± 0.019 PTF09dnp -18.927 ± 0.040 -19.026 ± 0.049 -18.944 ± 0.071 PTF10abjp -19.780 ± 0.197 -19.668 ± 0.046 -19.716 ± 0.199 PTF10gbq -19.525 ± 0.121 -19.201 ± 0.049 -19.108 ± 0.075 PTF11all -19.637 ± 0.088 -19.202 ± 0.076 -18.729 ± 0.092 PTF11jgq -19.484 ± 0.026 -19.329 ± 0.032 -18.791 ± 0.041 PTF11mkx -19.332 ± 0.027 -19.577 ± 0.030 -19.052 ± 0.039 PTF11pdl -19.580 ± 0.042 -19.359 ± 0.073 No data PTF12dst -19.903 ± 0.070 -19.633 ± 0.045 -19.014 ± 0.030 iPTF13dhs -19.644 ± 0.046 -19.559 ± 0.016 -19.167 ± 0.089 iPTF14flj -19.896 ± 0.038 -19.562 ± 0.079 -18.790 ± 0.135 iPTF14gkg -19.546 ± 0.010 -19.276 ± 0.072 -18.432 ± 0.091 iPTF15doz -19.727 ± 0.023 -19.553 ± 0.025 -18.905 ± 0.040 iPTF15eod -18.824 ± 0.013 -19.012 ± 0.022 -18.700 ± 0.034 iPTF15eue -21.409 ± 0.065 -20.939 ± 0.046 No data iPTF16arh -19.520 ± 0.061 -19.398 ± 0.039 -18.970 ± 0.114 iPTF16bcl -19.754 ± 0.021 -19.563 ± 0.032 No data iPTF16gnw -19.274 ± 0.173 -19.122 ± 0.123 No data
Mean value -19.632 -19.485 -19.098
4 Results
4.1 Phillip’s relationship
In figures 2, 3 and 4, Mg, Mr and Mi respectively are shown as a function of stretch for each sampled SN. The values used are those presented in Table 2 and Table 1, respectively. The errors presented in the plots are the statistical ones.
The grey marks are the peak magnitudes and stretches of normal, Chan- drasekhar mass type Ia SNe taken from Krisciunas et al. (2017). These SNe are known to obey Phillip’s relationship. They have all been corrected for redden- ing due to extragalactic extinction (on top of the Milky Way extinction, that the sampled SNe also have been corrected for). The figures below confirm that some of the 20 studied SNe also obey this relationship. Some do not however;
for example, SN2012dn seems to, in all filters (but in g the most), exhibit a less bright peak magnitude than expected by its high stretch.
Figure 2: Phillip’s relation in g-band. Note iPTF15eue in the upper left corner.
Figure 3: Phillip’s relation in r-band. Note iPTF15eue in the upper left corner.
Figure 4: Phillip’s relation in i-band.
4.2 Lightcurves
Figures 5 and 6 show the lightcurve data and corresponding models for all 20 SNe, in the g- and r-bands respectively. In the legends, the prefix (i)PTF for all Palomar SNe have been omitted; but they are given in the same order as in Table 1-2. The plots are all centered along the t-axis on t = 0, which corresponds to Tmax, so that differences in magnitudes (along the abscissa) can be analyzed, both in data and models. The errors in the data points are the same errors given in Table 1.
If the peak magnitudes of each SNe is subtracted from the data shown in Fig 5-6, we get Fig. 7-8; normalized in both flux and Tmax, allowing us to make comparisons between the lightcurve behaviours of the SNe. However, the SNe don’t exactly match up at (0,0). This is due to the fact that the models, and thus the calculated Mpeak values, have been corrected for extinction from the Milky Way. This has not been subtracted from the data points however. The colors and markers are the same for each SN in all four figures.
Plots for the lightcurve data and models in the i-band have not been included in this section. This is because the discrepancy between the normal Ia SNe i- band behaviour is so different from the 03fg-like SNe behaviour (see e.g. Fig.
9-10).
Figure 5: Measured absolute g-band magnitudes are plotted with their corre- sponding modeled lightcurves.
Figure 6: Measured absolute r-band magnitudes are plotted with their corre- sponding modeled lightcurves.
Figure 7: Measured absolute g-band magnitudes where peak magnitude has been subtracted.
Figure 8: Measured absolute r-band magnitudes where peak magnitude has been subtracted. Note PTF10abjp (red dots) having the seemingly slowest decline rate, suggesting a large stretchr (see section 5.3).
Figure 9: PTF11jgq: Model and data shows hump in the i-band.
Figure 10: SN2012dn: Model shows hump in the i-band, but not data.
Figures 9 and 10 exemplify the fitting of 03fg-like SNe in the i-band. For both plots, the magnitude is apparent magnitude. For the first example, PTF11jgq, the fitting is one of the best in the sample; both the data and the model display a second bump in brightness after Tmax, and Tmax appears approximately at the same time. However, most SNe resemble the fitting of SN2012dn, where the model predicts a second bump, which is not seen in the observations. Only 16 SNe had data in the i-band. Out of these only three exhibited the second peak and two showed a plateau after the peak magnitude.
5 Discussion
5.1 Modelling the SNe
Before this work was begun, it was known that 03fg-like SNe behave differently than normal type Ia SNe; something that could introduce errors into this work is then that the max model, designed to fit normal type Ia SNe, were used for the 03fg-like fits. However, applying this model could be interesting anyway, because then differences in the theoretical and observed behaviour of the sampled SNe could be found by looking at Fig. 5-6. Unfortunately, due to the small amount of data points for most SNe, drawing solid conclusions about model vs. data differences is hard based on these figures alone.
Most SNe had quite similar stretch and stretchg. However, in SN2007if, SN2012dn, PTF11all, PTF12dst and iPTF15doz, i.e. a fourth of the sam- ple, the values for the two parameters were incompatible after taking the er- rors into account. The biggest difference was displayed by PTF12dst, with stretch = 1.322 ± 0.100 and stretchg = 2.020 ± 0.221. The reason for these large discrepancies is probably that for this particular SN, the g- and r-band behaves differently, something that the max model does not take into account.
The same goes for the other four SNe with incommensurable stretch values for different bands.
5.2 Phillip’s relationship
Looking at Fig. 2-4, there are three different trends within the sample: either the SNe adhere to Phillip’s relationship, or they lie above or under the expected relationship curve. Thus, even though all of the SNe in this sample match each other spectroscopically, they show quite different behaviours within their lightcurve declines.
None of the SNe in this sample have had a extinction correction due to extragalactic reddening (only that due to the Milky Way). Thus, there is a possibility that the peak magnitudes calculated are not the true ones; they are only a lower bound. Doing an extinction correction might thus eradicate, or at least minimise, the SN group lying below Phillip’s trend, possibly leaving the group above and on top of the trend. However, no such explanation exists for the strong luminosities of the SNe above the Phillip’s curve. In fact, because of the previous reasoning, they might be even brighter than calculated in this work. To more thoroughly investigate if there are subclasses within the 03fg-like SNe that do or do not adhere to Phillip’s relation (remembering that 03fg was overluminous), extragalactic extinction corrections must be done first.
The values in Table 2 indicate that the 03fg-like SNe cause problems, if they are used as standard candles; the range in magnitudes is ∼ 3 mag, and since some of these SNe do not follow Phillip’s relation, there is no way of reconciling the magnitude differences by studying the stretch (as is done with normal SNe Ia, which can also vary in magnitude). This means that astrophysicists need to find features of super- or subluminous 03fg-like SNe that makes it possible to exclude them from a sample of SNe that are used as distance indicators. Luckily, their contribution to SNe Ia populations is small; in preparation for this study, a large sample of ∼ 2000 SNe Ia were examined, and out of these, only ∼ 30 03fg-like SNe were identified. So, even though it is important to be aware that these SNe might sully samples, the likelihood of them doing so is perhaps small.
5.3 Different behaviours for different bands
It seems like the SNe in this sample are brighter in the bluer ends of the spectrum than the redder; the lowest absolute magnitude occurs in the g-band, and the highest in the i-band. These intrinsically bluer colors imply that the 03fg-like SN explosions are very hot, since most of the released energy is released in the shorter wavelength range of the electromagnetic spectrum.
Looking at Fig. 7-8, we see that within a certain band, these SNe behave the same. In the g-band (Fig. 7), the magnitude rise and decline is almost quadratic and symmetric around t = Tmax, and then after an abrupt discontinuity that occurs at approximately 20 days after peak magnitude, the magnitude decline behaves linearly. In the r-band (Fig. 8), the behaviour is clearly different. The rise to peak magnitude is approximately as fast as in the g-band, but then the decline is slower and does not show any breaks.
There is another distinction between the r-band and the g-band; the differ- ence in magnitude decline. For example, PTF10abjp (red dots) has the slowest decline of all the SNe, while e.g. SN2012dn (black left-pointing triangles) is quite close in behaviour to PTF11mkx (blue circles) and PTF11jgq (turquoise diamonds). PTF10abjp has the highest stretch of these four SNe, but right un- derneath it lies PTF10gbq, which has an even higher stretch. This means that
the magnitude declines that we see in these figures is not the global stretch, presented in Table 1, but rather a stretch for each band. This means that even though PTF10abjp does not have the highest stretch, it has (one of; some SNe do not have enough data points to draw a definite conclusion) the largest stretchr. Also, the spread in stretchr is larger than the spread in stretchg.
Not only do these SNe behave different in their lightcurve declines, but they also show different behaviours in the i-band. Some of the SNe exhibit a second peak maximum in the i-band, which others do not (exemplified in Fig. 9-10).
Takanashi et al. (2008) showed that 89 % of normal SNe Ia show this second hump, while for the sample in this work, only 19 % of the SNe show it (exluding the two that only exhibited a plateau). Ashall et al. (2020) showed that 03fg- like SNe have a slow rise to peak maximum in the i-band compared to normal SNe Ia; a maximum which also occurs later for the former than for the latter (see Introduction). This is a behaviour that SN2012dn exhibits, compared to a normal SN Ia model based on it (see Fig. 9). However, PTF11jgq does not show any of the special lightcurve features that SN2012dn exhibits; it behaves just like a normal SN Ia and thus, like its model (see Fig. 8). This despite the fact that both SNe match SN2003fg spectroscopically.
5.4 Possible clues to the SNe progenitors
Of all the studied SNe, only PTF11pdl and iPTF15eue occurred at redshifts around the same value as SN2003fg (z = 0.244); i.e. z = 0.263 and z = 0.260, respectively. At these redshifts, the stellar birth environments are expected to in general be younger (i.e. bluer, lower mass, for example) than otherwise.
In these environments, the probability of encountering a DD binary system is higher; thus, the chance that these two SNe came from a DD progenitor system is the highest for all studied SNe.
SN2012dn is thought to come from a SD progenitor system, surrounded by thick CSM. What is interesting to note, is that it lies the farthest below Phillip’s relationship in the bluest band (Fig. 2), and then it creeps upwards as the bands get redder; in the reddest i-band, it lies very close to the normal type Ia SNe.
This could be a feature common to those SNe with a progenitor that had a thick CSM, considering that a thick CSM causes a NIR light excess. SN2009dc is on the other hand thought to have originated in a CSM-poor environment, thus belonging to the SC-SN group of bright SNe from a dust-free environment. It is consistent with the extrapolation of Phillip’s relation in all bands, which we see by examining Fig 2-4.
This suggests that the Phillip’s relation need to be reevaluated for 03fg-like SNe of both the bright kind from a clean environment and the faint kind from a dusty environment, since it seems like their magnitude vs. stretch relationships are different. Of course, this requires checking the CSM for all the 03fg-like SNe studied in this work, which is an interesting future study. Hopefully, learning how SN birth environments affect their stretch and absolute magnitudes could help us identify 03fg-like SNe.
5.5 Recommendations
For future analysis of the studied SNe, their ejecta velocities need to be exam- ined (by looking at the temporal evolution of spectral features), to find their kinematic energies. That way, it is possible to find the WD binding energy and thus the mass of the progenitor WD of each SNe. Also, their Nickel-56 amounts should be examined, since the decay of this isotope is what fuels the SN; if this isotope amount is abnormally large, that also indicates a SC mass of the progen- itor star. Furthermore, the sampled SNe should be corrected for extragalactic extinction, to see how that would affect their adherence to Phillip’s relationship.
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