## Abstract

Spectropolarimetry is one of the most powerful methods to study the multi-dimensional geometry of supernovae (SNe). We present a brief summary of the spectropolarimetric observations of stripped-envelope core-collapse SNe. Observations indicate that stripped-envelope SNe generally have a non-axisymmetric ion distribution in the ejecta. Three-dimensional clumpy geometry nicely explains the observed properties. A typical size of the clumps deduced from observations is relatively large: 25% of the photosphere. Such a large-scale clumpy structure is similar to that observed in Cassiopeia A, and suggests that large-scale convection or standing accretion shock instability takes place at the onset of the explosion.

This article is part of the themed issue ‘Bridging the gap: from massive stars to supernovae’.

## 1. Introduction

Core-collapse supernovae (SNe) are the explosions of massive stars. SNe mark the end points of stellar evolution and form compact objects, i.e. neutron stars and black holes. In addition, SNe play important roles in the chemical and dynamical evolution of galaxies. The detailed explosion mechanism of SNe, however, has remained unsolved for a long time (see [1–3] for reviews). It is widely accepted that a SN explosion does not successfully occur in one-dimensional (1D) simulations [4–7]. Therefore, multi-dimensional effects are thought to be essential for successful explosions. In this circumstance, many multi-dimensional numerical simulations have been performed, capturing multi-dimensional effects such as convection [8–10] and standing accretion shock instability (SASI) [11–18]. It is remarkable that some successful explosions have been reported by two-dimensional (2D) or three-dimensional (3D) simulations [19–29].

In order to obtain a link between numerical simulations and actual observations, it is important to deduce the multi-dimensional geometry from observed SNe. This is challenging especially for extragalactic SNe, which are observed as point sources. Polarization is a powerful method to study the multi-dimensional geometry of SNe (see [30] for a review) because polarization is sensitive to deviation from the spherical symmetry. From the spherical symmetric SN ejecta, no polarization would be observed since polarization vectors are cancelled out (figure 1).

Non-zero continuum polarization would be observed when the photosphere deviates from spherical symmetry [34–38]. In addition, even when the photosphere is spherical, non-zero line polarization would be observed if the ion distribution is not spherically symmetric (figure 1 [32,39]). Therefore, line polarization can be used as a probe of multi-dimensional element distribution in the SN ejecta.

In this paper, we focus on stripped-envelope core-collapse SNe (SNe of types Ib and Ic) with which we can obtain a close insight into the explosion mechanism, owing to the absence of a large hydrogen envelope. In §2, we present a brief summary of spectropolarimetric observations of stripped-envelope SNe. In §3, we show modelling of line polarization to obtain a link between multi-dimensional geometry and observed data. In §4, we discuss implications from spectropolarimetric observations and modelling.

## 2. Spectropolarimetric observations

Figure 2 shows an example of spectropolarimetric data of stripped-envelope SNe (type Ib SN 2009jf, [40]). What can be observed with spectropolarimetry is the sum of the intrinsic and interstellar polarization (ISP). However, since the ISP has a smooth wavelength dependence [42], the line polarization features detected at the wavelengths of the strong absorption lines (e.g. HeI, OI and CaII) are certainly intrinsic. When the polarization data are plotted in the Stokes *Q*–*U* diagram (figure 2*b*), the data show a loop. This indicates that the polarization angle varies as a function of the Doppler velocities.

Figure 3 shows the line polarization of six stripped-envelope SNe with high-quality data: type Ib SNe 2005bf [43,44], 2008D [45], 2009jf [40], type Ic SNe 2002ap [46–48], 2007gr [49] and 2009mi [40]. The degree of line polarization is shown as a function of the fractional depth (FD) of the absorption. The filled and open symbols show the line polarization of the CaII and FeII lines, respectively. The FD of an absorption is given by FD =(*f*_{cont}−*f*_{abs})/*f*_{cont}, where *f*_{abs} and *f*_{cont} are the flux at the absorption minimum and at the continuum near the absorption line, respectively.

The properties of line polarization in stripped-envelope SNe can be summarized as follows.

(i) Non-zero line polarization is commonly observed [40,43–52].

(ii) Polarization data in the Stokes

*Q*–*U*diagram (figure 2*b*) show a loop [40,43,45,50–52].(iii) The degree of line polarization ranges approximately from 0.2% to 3% (figure 3), and it tends to be higher for stronger lines.

## 3. Spectropolarimetric modelling

We perform spectropolarimetric modelling to connect the observed polarization and explosion geometry. We use a Monte Carlo line transfer code 53, which computes the polarization spectra for arbitrary line optical depth distributions by taking into account the electron and line scattering. In the calculation, we treat only a *single* line at a *single* epoch rather than modelling the time evolution of full spectra (see [39] for a similar strategy). In figure 4, we show examples of the calculation for a 2D bipolar model (*a*,*b*), a 3D clumpy model with a clump size of 50% of the photosphere (*c*,*d*) and another 3D clumpy model with a clump size of 12.5% of the photosphere (*e*,*f*).

When the optical depth distribution has a 2D axisymmetric structure such as bipolar blobs or a torus, the polarization always shows a straight line in the *Q*–*U* diagram (figure 4*a*,*b*). Therefore, a purely axisymmetric distribution cannot reproduce the loop in the *Q*–*U* diagram that is commonly observed in stripped-envelope SNe (figure 2*b*).

On the contrary, 3D clumpy structures naturally reproduce the loop in the *Q*–*U* diagram (figure 4*c*,*d*). In 3D clumpy models, different portions of the photosphere are hidden for different Doppler velocities. Since the distribution of the clumps does not have a common symmetric axis, the position angle of the polarization can change depending on the Doppler velocities. This produces a loop in the *Q*–*U* diagram.

If the size of the clumps is too small, however, such a structure cannot produce the polarization degree of 0.5%, which is commonly observed (figure 3). As shown in figure 4*e*,*f*, models with many small clumps show a low polarization level (0.5%). In such models, the photospheric disc is hidden by many small clumps, and the remaining polarization vectors tend to be cancelled out [39]. As is also clear from figure 1, in order to produce a large enough polarization degree, a typical size of the clumps should be 25% of the size of the photosphere.

## 4. Discussion

Implications from observations and modelling of SN line polarization can be summarized as follows. (i) The element distribution in the SN ejecta is not completely 2D axisymmetric. (ii) A 3D clumpy component is present. (iii) The typical size of the clumps is relatively large, i.e. of the photosphere. It is interesting to note that such a large-scale clumpy structure is also seen in the element distribution of Cassiopeia A [54–57].

One possible scenario to produce a clumpy structure in the ejecta is the Rayleigh–Taylor (RT) instability developed during the shock propagation in the stellar envelope. However, the RT instability tends to produce small fingers in many directions, which does not effectively produce the polarization. A relatively large-scale structure required for polarization is more in favour of large-scale convection or SASI. In fact, numerical simulations show that, if the large-scale convection or SASI takes place at the onset of the explosion, the resultant element distribution at the later phase retains an imprint of the large-scale asymmetry in addition to the small-scale structures added by the RT instability [58–61].

More and more long-term simulations from the onset of the explosion to shock breakout become available (e.g. [61,62]), and thus full radiative transfer modelling for polarization (e.g. [38,63]) using such results will enable direct mapping of explosion models and observables. From the observational side, the number of SNe with a good time series of polarization is increasing [51,64]. The combination of these models and observations will place further constraints on the explosion mechanism of core-collapse SNe.

## Data accessibility

Data shown in this paper will be provided upon request.

## Competing interests

I declare I have no competing interests.

## Funding

This research was supported by a Grant-in-Aid for Scientific Research from JSPS (15H02075, 16H02183) and MEXT (17H06357, 17H06363).

## Footnotes

One contribution of 9 to a Theo Murphy meeting issue ‘Bridging the gap: from massive stars to supernovae’.

- Accepted June 16, 2017.

- © 2017 The Author(s)

Published by the Royal Society. All rights reserved.