Literature Search¶
Notes are provided for a small subset of papers relevant to this project. This page is intended as a quick reference sheet for the developers.
Properties of 91bg-like SNe¶
Comparative Analysis of Peculiar Type Ia 1991bg-like Supernovae Spectra (Doull+ 2011)¶
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TLDR: Several 91bg-like spectra are fit with SYNOW and common ions are identified.
Several 91bg-like spectra are selected according to the Branch 2006 sub-typing method and are fit with the SYNOW spectral fitter. These SNe have an unusually deep and wide absorption around 4200 A and very strong Si II at 5972 A. Nine Ions fit most of the observed features well at all epochs: O I, Na I, Mg II, Si II, S II, Ca II, Ti II, Cr II, and Fe II. At early times Ca I also seems to play a role.
The 4200 A absorption feature is well fit by a combination of Ti II and Mg II. This is indicative of a cooler temperature. As the spectra evolve to around 20 days, the absorptions and emissions become more extreme, and the photosphere velocity begins to decrees. For phases beyond this, assumptions of the SYNOW fitter begin to play a noticeable effect.
Some of the spectral diversity may be due to differences in viewing angle on an asymmetric explosion (see Maeda+ 2010). The spectral similarities indicate SNe are a continuous distribution and it is possible the heterogeneity of SNe Ia is not due to fundamental differences in the underlying physical mechanism. Instead, there may be a set of primary, stable parameters for the explosion followed by secondary sets of slightly less stable parameters.
This explanation would explain the structure we see in Branch style W-W plots. The most stable parameters would result in the highest density regions with the most common SNe Ia (the core-normals). The lowest density regions would contain SNe Ia with less stable parameters. The SNe in between would be transition regions.
The Extremes of Thermonuclear Supernovae (Taubenberger 2017)¶
This paper provides an overview of peculiar SNe, and is fairly expansive. For our purposes here, we pull out a few useful references.
There is agreement in the literature that SN 1991bg-like SNe tend to be found in massive elliptical (S0 type) galaxies with low star-formation rates (\(~10^{−9} M_\odot yr^{−1}\); Howell, 2001; Neill+, 2009; González-Gaitán+, 2011). However, there is significant disagreement when it comes to rate of 91bg-like events. Recent rate estimates using SNe observed by the Lick Observatory Supernova Search (LOSS) range from 11 to 15% of the SNe Ia population (Ganeshalingam+ 2010, Li, Leaman+ 2011). Alternatively, González-Gaitán+ (2011) and Silverman+ (2012) estimated 91bg-like SNe make up a mor modest 6 to 9%. However, González-Gaitán+ (2011) does note that their estimates increase dramatically with the inclusion of transitional 86G-like SNe.
Evidence for a Spectroscopic Sequence among Type Ia Supernovae (Nugent+ 1995)¶
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TLDR: The continuity of photometric properties in SNe Ia is equally present in spectroscopic observations.
Although heterogeneous, SNe tend to follow a continuous distribution of photometric properties instead of falling into well defined subgroups. Using a sample of sixe SNe, it is shown that this continuity is equally well represented in spectroscopic observations. Synthetic spectra also indicate that these differences are primarily due to variations in temperature, which is driven by the \(^{56}\text{Ni}\) mass.
SNe Classification¶
A list of machine learning classifiers:
- Richards+ 2012
- Ishida & de Souza 2013
- Karpenka+ 2013
- Varughese+ 2015
- Lochner+ 2016
- Möller+ 2016
- Dai+ 2018
- muthukrishna+ 2019
- Pasquet+ 2019
We note that Pasquet+ 2019 performed well when trained on and tested against data from the Supernova Classification Challenge (Kessler+ 2010a) but performed notably worse when applied to the SDSS SN sample due to the training sample not being as representative.
Quantitative Classification of Type I Supernovae Using Spectroscopic Features at Maximum Brightness (Fengwu+ 2006)¶
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TLDR: A quantitative definition of what feature strengths indicate a Ia, Ib, and Ic.
The evolution of SNe classification is based on unquantified spectroscopic qualities near peak luminosity. As a quick recap on the evolution of Type I classification:
- Minkowski (1941): Introduces type I/II
- Wheeler & Levreault (1985) and Elias+ (1985): Introduces type Ib
- Wheeler & Harkness (1990): Introduces type Ic
Fengwu+ presents a quantified set of classification criteria based on the depths of spectroscopic features. The boundaries of each classification are selected to represent the classifications of objects already available in the literature. The chosen SNe sample includes:
- 3 SNe 2002cx-like
- 1 SN 1991T- like
- 21 SNe 1991bg-like
- 8 SNe 1999aa-like
- the unclassified peculiar object SN2000cx
- 12 SNe Ib
- 19 SNe Ic
- 4 SNe Ib/c
Classifications are based on the depths of the Si II (6150 A) and O I (7774 A) features relative to the pseudo-continuum. The steps of determining these values include 1. Smoothing the spectra to eliminate narrow features, 2. identifying the boundaries of the features, 3. removing non-intrinsic features, and 4. measuring the feature depths.
The spectra are smoothed to eliminate narrower features using the prescription of Savitzky & Golay 1964. In general, SNe should not have strong, intrinsic narrow features due to their high ejecta velocity. This process helps increase the size of the usable data set by improving the precision of measurements performed on low SNR spectra that would otherwise have to be dropped. The window size \(w\) and polynomial order \(o\) of the smoothing function are determined using the average wavelength interval \(\Delta \lambda\) as
After smoothing the spectra, the boundaries for both features are determined by eye. Identifying the feature boundaries can be difficult since the high ejecta velocity (broad feature widths) causes some features to blend together (e.g. Si II 6355 with He I 6678). THe paper argues that the sample size is small enough, and the inspection duration is quick enough, that the introduction of human bias is negligible so long as only one person is used.
Non-intrinsic features that overlap with the features we are interested in are replaced with a pseudo continuum (linear interpolation) between the contaminating feature’s start and end points. Since the paper is interesting in feature depth and not width, the effects of this de-resolution are negligible.
Finally, a pseudo-continuum is adopted for the Si II and O I features in the same way as for the contaminating features. If the spectrum is visually determined to not be smooth enough within the feature, the spectrum withing the feature is smoothed using a 9th degree polynomial. The line depth is then calculated as:
The paper finds that peculiar Type Ia’s generally have shallower Si II 6355 lines. The same cannot be said for O I 7774, where the normal and combined peculiar SNe follow a similar range and distribution. However, the 91bg and 99aa objects are distinguishable by O I. This indicates an intrinsic diversity of O I optical depths in SNe Ia photospheres.
Although the paper struggles to confidently distinguishing the normal and peculiar subsets, they are able to find significant differences between SNe Ib and Ic using the ratio r = a(6150) / a(7774). The Ib and Ic populations are entirely separated by a line near \(r=1\).
The concluded classification criteria is as follows:
- SNe Ia (including normal Ia, Ia-1991bg and Ia-1999aa): a(6150 A) > 0.35
- SNe Ib: a(6150 A) < 0.35 and a(6150) / a(7774) > 1
- SNe Ic (except for Ic-BL): a(6150)<0.35 and a(6150) / a(7774) < 1
Comparative Direct Analysis of Type Ia Supernova Spectra II. Maximum Light (Branch+ 2006)¶
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TLDR: SNe Ia are subclassed into shallow silicon, core-normal, broad line, and cool groups based on the strength 5750 A vs 6100 A.
This paper identifies classifications of SNe Ia using the width of the 5750 and 6100 features (usually attributed to Si ii at 5972 and 6355). To simplify the process of feature comparison, spectra are first tilted by multiplying the flux by \(\lambda^\alpha\) where \(\alpha\) is chosen such that the peak flux near 4600 and 6300 A are equal. The Equivalent widths are then plotted for the feature at 5750 A vs the feature at 6100 A. After applying a nearest neighbor algorithm, four groups emerged: shallow silicon, core-normal, broad line, and cool (which includes SN 1991bg).
Broad-line SNe Ia have absorption features at 6100 A absorptions that are broader and deeper than core-normal SNe Ia. However, SNe in this category do not appear to follow a simple one-dimensional sequence based on their distance from the core-normal population.
The shallow silicon group are not (necessarily) very different from the core normal group. Other than a narrower Si feature, they look remarkably similar. The primary reason for the spectroscopic differences seems to be the lower temperature, as indicated by low temperature ion signatures (e.g. Ti). Otherwise, they have the same ions evident in their spectra, just at very different optical depths. This aligns with their lower temperatures since “as noted by Hatano+ (2002) and Ho Flich+ (2002), there is a temperature threshold below which, owing to abrupt changes in key ionization ratios, line optical depths change abruptly (Hatano+ 1999).”
The core-normal subgroup have a very high degree of similarity, suggesting a standard, common physical mechanism involving no large inhomogeneities near the characteristic photosphere velocity of 12,000 km/s.