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The study of supernovae works in two extremes: the very general (treating all SNe Ia as the same and correcting for, or smoothing out, their differences), and the very specific: detailed observations of individual objects and probing the physics which leads to these observations. Supernova cosmology as a necessity tends towards the former, but the latter are not to be discounted for the value they add to our understanding. From a cosmology perspective, the better we understand the systematic effects which lead to diversity, or physical processes behind observations, the better we can standardise objects. The homogeneity of Ia samples for cosmology has immense power as a statistical sample for placing on a Hubble diagram and constraining cosmological parameters (Sections 1.3.1 and 2.2), and yet the knowledge gained of individual supernovae as astronomical objects and former stars is vital to our knowledge of their explosion mechanisms, progenitors, and astrophysics in general. This knowledge will aid our analyses of supernovae into the future, including for cosmology, by allowing us to examine, estimate, and reduce systematic uncertainties.

In this section, we provide an overview of the physics of type Ia supernovae, and the questions currently relevant to their study, to give context to discussions of their standardisation in Section 2.2.

§2.1 Supernovae: an overview 21

Observables: lightcurves and power sources

Without their uniformity, SNe Ia would not occupy their place as a powerful cosmological probe, and as precise distance indicators. The simplicity of this consistency is alluring, and founded on a sound theoretical basis: the hard limit of the Chandrasekhar mass. This seemingly places all SNe Ia at the same mass when they explode, resulting in remarkable homogeneity within SN Ia populations. The reality is slightly more subtle, and this view is an approximation. Like many approximations, it has served us well in cosmology: as a stepping stone to improve upon.

The Chandrasekhar limit (Chandrasekhar, 1931) at approximately ∼1.4 M⊙ is a theoretically

calculated maximum mass of a white dwarf. Being extremely dense (around a million times more dense than water), their extreme inward gravitational force is balanced by electron degeneracy pressure. Electrons are fermions, not able to multiply occupy the same state by the Pauli exclusion principle; consequently the higher energy electrons result in strong outward pressure exerted. However, at the Chandrasekhar mass, this pressure is no longer sufficient to counteract gravitational collapse. The star either undergoes collapse into a neutron star, or if fusion is triggered by an increase in mass (e.g. accretion of material in a binary system), it can explode as a type Ia supernova. We explore the commonly proposed scenarios for the circumstances in which this explosion takes place or is triggered, reviewed in Hillebrandt et al. (2013); Ruiz-Lapuente (2014); Maeda & Terada (2016).

Observational signatures have long established that SNe Ia explode as runaway thermonuclear explosions of a CO WD in a binary system with another star. The chemical compositions of SN Ia progenitor systems have been discerned from the evolution of spectral lines, as a function of velocity, which signal the nature of the ejecta (e.g. Branch et al., 1995). Spectra of SNe Ia are characterised by P-Cygni absorption lines superimposed on a blackbody continuum at early times, supporting a layered ejecta with iron-peak elements in the centre and intermediate mass elements such as silicon and sulfur on the outside (Stehle et al., 2005; Mazzali et al., 2007). The spectrum at late times (in the nebular phase) exhibits only forbidden lines from iron-peak elements with no continuum. As with SN Ia spectra, the lightcurves of type Ia supernovae can be understood in terms of the physical mechanisms driving the explosion, in particular the radioactive decay of 56_{Ni. The decay of} 56_Ni→56_Co→56_{Fe entirely powers the luminosity of SNe Ia, starting from the thermonuclear detonation} at the centre of a white dwarf, initiating the synthesis of iron-peak elements in the dense centre of the WD (e.g. Kuchner et al., 1994; Howell, 2011; Hillebrandt et al., 2013). Over an average of∼18 days, the pre-explosion supernova rises steeply in luminosity; while the amount of energy deposited in this stage is enormous, the centre of the WD is optically thick, and the radiation is mostly bound within the ejecta. As the density of the ejecta decreases, more energy is released outward, and the lightcurve reaches its maximum: at this point, the outward radiation matches the energy deposited by radioactive decay, and the slow decline of the lightcurve begins. The slope of the post-maximum decline in luminosity is tied to the half-life of56_{Ni decay.}

The standardisability of SN Ia lightcurves is the cornerstone of their use in cosmology. Applying corrections to luminosity for ‘stretch’ or slowness-to-fade (Phillips, 1993) is the next step in under- standing the brightnesses of supernovae, after the initial approximation of constant brightness due to the Chandrasekhar mass. The stretch-luminosity relation, or Phillips relation, is grounded physically in the physical size of a WD at time of detonation; in simple terms, the more massive it is, the more luminous, and the more time it takes to undergo the same decline in magnitude. Recently, this has been examined in terms of ejected mass (i.e. total mass) by studying bolometric lightcurves (e.g. Scalzo et al., 2014; Piro & Nakar, 2014), in relation to observed decline rate and 56_{Ni mass lost. Developments in} homogenising SN Ia lightcurves will be detailed in Section 2.2, from the first uses of supernovae as distance indicators, to current best methods.

Progenitor channels and explosion mechanisms

The more uncertain factors in this picture are the identity of the other star and the mode of detonation. The WD may merge with another WD in thedouble degeneratescenario, or accrete from main sequence or red giant star in thesingle degeneratescenario, or accrete from an asymptotic giant branch (AGB) star in thecore degeneratescenario. The paths through which the explosion can start also vary between deflagration and detonation models, or a combination; these are linked intrinsically to whether a WD has reached Chandrasekhar mass at explosion. Deflagration is thought to begin as a runaway flame near the centre of a WD as it reaches Chandrasekhar mass. Neither deflagration nor detonation by itself is sufficient to explain observations, particularly luminosities, and the correct amount of iron-peak elements produced (primarily56_{Ni), i.e. amounts produced are too low and too high respectively. Proposed hybrid} explanations includedelayed detonation, where the explosion mechanism turns from deflagation to detonation at a critical density; if it fails to do so it results in afailed deflagration. Ignition may occur when two CO WDs combine in aviolent merger, at or above Chandrasekhar mass (e.g. Pakmor et al., 2012). Alternatively, if the companion star has a helium shell, unstable triple-alpha reactions detonate at the surface and propagate inward to trigger a second detonation within the WD, in the double detonation model (Woosley & Weaver, 1994; Fink et al., 2010). In thespin-up spin-down scenario (Justham, 2011; Di Stefano & Kilic, 2012), where Roche lobe accretion from a donor star accelerates the spinning of the WD; the increased angular momentum allows the WD to exceed Chandrasekhar mass, and it detonates when it slows (e.g. due to magnetic braking). These competing models are explored and tested through a combination of theory and observations (binary population synthesis, modelling ejected (hence total initial) mass, nucleosynthesis codes, explosion simulation codes, spectral synthesis codes). Diversity and subclasses

The notion that type Ia SNe can be further subdivided was introduced in the early 1990s and supported by two anomalous Ias, SN 1991bg (Filippenko et al., 1992a; Leibundgut et al., 1993) and SN 1991T (Phillips et al., 1992; Filippenko et al., 1992b). The close occurrence of two outliers within a short period prompted questions of whether Ias were as homogeneous as they appeared, and what a typical Ia looks like; Branch et al. (1993) studied SNe Ia discovered up until then, using optical spectra to separate them into those resembling SN 1981B and a few similar SNe Ia, and the remainder, coined ‘peculiar’ Ias. The former category of spectroscopically normal (now often referred to as ‘Branch-normal’) Ias, later were parametrised using lightcurve fitters (Section 2.2.3) and used for cosmology fits. These subcollections of Ias are separated primarily by absolute peak magnitude, and decline rate: the quantity ∆m15(B) (the dimming inBband in the 15 days since peak). The separation of several subpopulations is shown in Figure 2.2 (Maeda & Terada, 2016, figure 1). Apart from normal Ias, the following subclasses of SNe Ia had been identified: ‘91bg’-like, ‘91T’-like, ‘Iax’, ‘Ia-CSM’, as well as overluminous SNe Ia exceeding even the brightness of 91T-like Ias. The label ‘Iax’ (Foley et al., 2013) was applied to fainter SNe Ia appearing like SN 2002cx (the first in the class), revealing a bluer continuum, Fe lines at higher ionization, lower line velocities than typical Ias, and not following the same Phillips relation (Phillips, 1993) between peak magnitude and decline ∆m15 (discussed more in Section 2.2.3). The Ia-CSMs (Silverman et al., 2013; Inserra et al., 2016) showed evidence of interaction with their circumstellar material (CSM), spectroscopically appearing like IIns (due to hydrogen from the CSM) with strong Balmer emission lines and a blue continuum, but show signatures of Ia ejecta expanding into dense CSM.

For a long time, efforts to connect the above progenitor models and explosion mechanisms to ob- servations and simulations have been motivated by the hope of explaining a majority of observed SNe Ia with one answer. Particularly in the last decade, the number and quality of SN Ia data have shown this to simply not be possible: the range and variation over the collection of SN Ia observations have pointed the insufficiency of any single progenitor channel in explaining all observed Ias.

Significant developments have occurred in recent years: surveys have developed into more coordi- nated and automated operations and are thus more productive (Section 2.4), and supernovae have been discovered and followed up sooner, yielding better sampled lightcurves and spectroscopy at earlier