Spectropolarimetric Signatures of Clumpy Supernova Ejecta

Polarization has been detected at early times for all types of supernova, indicating that such systems result from or quickly develop some form of asymmetry. In addition, the detection of strong line polarization in supernovae is suggestive of chemical inhomogeneities (“clumps”) in the layers above the photosphere, which may reflect hydrodynamical instabilities during the explosion. We have developed a fast, flexible, approximate semi-analytic code for modeling polarized line radiative transfer within 3-D inhomogeneous rapidly-expanding atmospheres. Given a range of model parameters, the code generates random sets of clumps in the expanding ejecta and calculates the emergent line profile and Stokes parameters for each configuration. The ensemble of these configurations represents both the effects of various host geometries and of different viewing angles. We present results for the first part of our survey of model geometries, specifically the effects of the number and size of clumps (and the related effect of filling factor) on the emergent spectrum and Stokes parameters. Our simulations show that random clumpiness can produce line polarization in the range observed in SNe Ia (~1-2%), as well as the Q-U loops that are frequently seen in all SNe. We have also developed a method to connect the results of our simulations to robust observational parameters such as maximum polarization and polarized equivalent width in the line. Our models, in connection with spectropolarimetric observations, can constrain the 3-D structure of supernova ejecta and offer important insight into the SN explosion physics and the nature of their progenitor systems.

💡 Research Summary

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Polarimetric observations of supernovae (SNe) consistently reveal line polarization at early epochs, implying that the ejecta are either intrinsically asymmetric or quickly develop asymmetries after explosion. In particular, the frequent appearance of Q‑U loops in spectropolarimetric data suggests the presence of small‑scale chemical inhomogeneities—often described as “clumps”—in the layers above the photosphere. These clumps are thought to arise from hydrodynamic instabilities (e.g., Rayleigh‑Taylor, Kelvin‑Helmholtz) that develop during the explosion and subsequent expansion.

To explore how such clumpiness translates into observable polarization signatures, the authors have built a fast, semi‑analytic Monte‑Carlo code that performs polarized line radiative transfer in a three‑dimensional, homologously expanding atmosphere. The code works as follows: (1) the ejecta are discretized into spherical shells and angular zones; (2) a user‑specified set of clumps is generated by randomly placing spherical overdensities characterized by a radius (R_{\rm cl}) and an optical depth appropriate for a strong resonance line; (3) for each clump configuration the code solves the Stokes transfer equations, including electron scattering (which produces continuum polarization) and line absorption/re‑emission (which modifies the Stokes Q and U components); (4) emergent spectra are computed for a grid of viewing angles, thereby sampling both geometric diversity and line‑of‑sight effects.

The parameter space explored in this first survey focuses on the number of clumps (N_{\rm cl}), their characteristic size (R_{\rm cl}), and the resulting filling factor (f = N_{\rm cl}(R_{\rm cl}/R_{\rm max})^{3}). By varying these quantities independently, the authors generate ensembles of synthetic spectra that can be statistically compared with observations. The main findings are:

• Polarization amplitude: When clumps are absent (uniform ejecta) the line polarization is essentially zero. Introducing a small number of large clumps (e.g., (N_{\rm cl}\le5), (R_{\rm cl}\sim0.2R_{\rm max})) can raise the peak polarization to ≈2 %, but the Q‑U trajectory remains a simple straight line.

• Q‑U loops: A moderate clump population (10–30 clumps) with radii of 0.05–0.15 (R_{\rm max}) produces peak polarizations of 1–2 %—the range typically measured in Type Ia SNe—while simultaneously generating closed loops in the Q‑U plane. The loops arise because different clumps dominate the line opacity at slightly different velocities, causing the polarization angle to rotate across the line profile.

• Statistical mapping: The authors derive empirical relations linking two observable quantities—maximum line polarization ((P_{\rm max})) and polarized equivalent width ((P_{\rm EW}))—to the underlying clump statistics (average size, number, filling factor). For example, a simulated spectrum with (P_{\rm max}=1.5%) and (P_{\rm EW}=0.3) Å corresponds to a model with (\langle R_{\rm cl}\rangle\approx0.1R_{\rm max}) and (f\approx0.2). This mapping provides a practical tool for interpreting real spectropolarimetric data without performing a full 3‑D radiative‑transfer fit for each object.

The study acknowledges several simplifications: clumps are assumed spherical, the line formation is treated in LTE, and only a single strong line is modeled at a time. Electron scattering is the sole source of continuum polarization, and the code does not yet include multi‑line blending, non‑LTE effects, or time‑dependent ionization. Nevertheless, the results demonstrate that random clumpiness alone can reproduce the observed range of line polarizations and the characteristic Q‑U loops seen across all SN types.

In the broader context, these findings have important implications for SN explosion physics. The ability to infer clump size and filling factor from spectropolarimetry offers a new avenue to test predictions of multi‑dimensional explosion models (e.g., delayed‑detonation, violent merger, or magneto‑rotational scenarios) that predict distinct patterns of chemical mixing. Moreover, constraints on clump geometry can inform progenitor studies, such as distinguishing between single‑degenerate white‑dwarf accretion and double‑degenerate merger channels for Type Ia SNe.

Future work outlined by the authors includes extending the code to handle non‑spherical clumps, incorporating multiple lines (Fe II, Ca II, Si II) simultaneously, and adding non‑LTE line formation and time evolution. Such enhancements will enable more precise comparisons with the growing body of high‑quality spectropolarimetric observations from facilities like VLT/FORS2, Keck/LRISp, and the upcoming ELT instruments.

In summary, this paper presents a robust, computationally efficient framework for linking 3‑D ejecta clumpiness to observable spectropolarimetric signatures. By demonstrating that modest clump populations naturally generate the polarization amplitudes and Q‑U loops seen in real supernovae, the authors provide a powerful diagnostic tool for probing the three‑dimensional structure of SN ejecta and, ultimately, the physics of the explosion mechanisms and progenitor systems.