Classification Scheme (Background)

We here discuss the photometric classification technique presented in González-Gaitán et al. 2014 (G14) that this project is based on.

Important

G14 relies on the SiFTO light-curve fitter. We here instead apply the sncosmo package. In their default setup, these two packages are very different, but we intentionally implement sncosmo in a way that mimics the SiFTO approach. See the Implementation section for more details.

Background

Despite being surprisingly homogeneous, type Ia Supernovae (SNe Ia) are in fact a heterogeneous collection of events who’s variety is well parameterized by empirical descriptions such as stretch and color. Although prevalent theories attribute supernova explosions as being the thermonuclear runaway of an exploding CO white dwarf, modeling efforts have seen little progress in providing a definitive explanation. The goal of classification is to provide a framework from which we can further build and explore theoretical explanations.

Sub-types of Type Ia SNe include:

  • SN 1991T-like (Filippenko+ 1992a; Phillips+ 1992; Maza+ 1994)
  • SN 1991bg-like (Filippenko+ 1992b; Leibundgut+ 1993; Hamuy+ 1994)
  • 2002cx-like SNe or “SNe Iax” (e.g. Li+ 2003; Foley+ 2013)
  • super-Chandrasekhar mass candidates (e.g. Howell+ 2006; Scalzo+ 2012)
  • SN 2000cx-like (Li+ 2001; Candia+ 2003; Silverman+ 2013a)
  • SN 2006bt-like (Foley+ 2010b)
  • SNe Ia with possible circumstellar material (CSM) interactions (Hamuy 2003; Dilday+ 2012; Silverman+ 2013b)
  • Ca-rich SNe (Perets+ 2010, 2011b; Valenti+ 2013a; Kasliwal+ 2012)

Note

See Gal-Yam 2017 for a comprehensive discussion.

We are primarily focused on the identification of SN 1991-bg like objects (91bgs). These tend to be around 1.1 mag fainter and decline notably faster than normal Ia’s. Their redder colors and more prevalent Ti lines also indicate that they are cooler. Since 91bgs are cooler, the recombination of Fe III to Fe II also occurs sooner causing the peak brightness in the redder bands to happen sooner than in the bluer bands.

González-Gaitán et al. 2014 (G14) puts forth a classification technique by which 91bg and a few other peculiar SNe can be identified (described below). This approach is compared against existing approaches (SNID and GELATO2) and found to be in good agreement.

The Original Data Set

G14 focuses on low-redshift SN samples (z < 0.1). In addition to a few targets picked from the literature, the data is primarily taken from:

  • The Caĺan/Tololo survey (Hamuy et al. 1996a)
  • The Carnegie Supernova Project (CSP)
  • The Center for Astrophysics (CfA) (Hicken et al. 2009, 2012)
  • The Lick Observatory Supernova Search (Ganeshalingam et al. 2010)

No initial cuts are applied to the data.

The General Approach

91bg’s can be photometrically distinguished from normal Ia’s by the morphology of their light-curve - particularly in then redder bands (as described above). To identify 91bg like objects, the photometry for each target is first split into the red and blue bands as separated by 5500 angstroms in the rest frame. Both data sets are then fit using two light-curve models: one representing normal Ia’s and one representing 91bg’s. Using the resulting chi-squared values, targets are classified based on their position in the following phase space:

\[x \def \chi^2_{blue}(Ia) - \chi^2_{blue}(91bg) y \def \chi^2_{red}(Ia) - \chi^2_{red}(91bg)\]

By construction of the above coordinates, we expect 91bg’s to fall in the upper right (first) quadrant while type Ia’s should fall in the lower left (third) quadrant.

In principle there is no physical reason why the quadrants should be separated by intersecting lines at \((0, 0)\). To determine where in this phase space we should draw the boundaries separating each classification, we use whatever boundaries are found to maximize the figure of merit (FOM) which is given by:

\[FOM = \frac{N_{true}}{N_{total}} \times \frac{N_{true}}{N_{true} + N_{false}}\]

Where each term is defined as the following:

  • \(N_{total}\) is the total number of objects with a given type (i.e. the “truth”)
  • \(N_{true}\) is the number object correctly classified as a given type
  • \(N_{false}\) is the number of objects falsely classified a given type

Here “a given type” refers to 91bg-like.

The added work of fitting red and blue bands independently could be avoided and a chi-squared for all bands could be used. Although this works, it does not work as well since there may be some normal SNe with lower stretch or redder colors. It is also possible to use a simple cut on the fitted color and/or stretch values (using either the normal or 91bg template). However, this suffers from a similar problem where highly reddened, normal Ia’s at low stretch would look like Ia’s.

Some Additional Details

  • The normal Ia template used in G14 is the Hsiao+ 2007 template
  • The 91bg template is the Nugent+ 2002 template
  • Data cuts were implemented as follows:
    1. Exclude targets without observations in at least two filters, each with at least one data point between -15 and 0 days and one between 0 and 25 days.
    2. Data past 85 days was ignored
    3. If observations are available in duplicate filters (e.g. the same filter from different surveys) the filter with the most data points is used.