aas (iPosterSessions - an aMuze! Interactive system)

Polarization is Important in Type Ia Supernova (SN Ia)

Type Ia Supernovae (SNe Ia), which have been used in cosmological distance measurements as "standardizable candels", are the thermonuclear explosions of white dwarfs. The origin of SNe Ia is believed to involve one or two white dwarfs in a binary system, either the merger of two white dwarf stars (double-degenerate scenario) or the accretion of a white dwarf from a nondegenerate companion star (single-degenerate scenario).

Because the progenitor stars are unobservable at cosmological distance, the understanding of the SNe Ia relies on hydrodynamic, nucleosynthesis, and radiative transfer simulation, which bridges the explosion scenarios to the observable spectra and light curves.

Among the messengers of SNe Ia, the spectropolarimetry is of unique importance, because the three-dimensional geometry of the ejecta is encoded when light scatters through the ejecta. Moreover, as is suggested by hydrodynamic simulations and nearby SNe Ia remnants (an example of SN 1572 is shown in the Figure, false color image taken by Chandra X-ray telescope), SNe Ia are intrinsically 3D events that cannot be accurately modeled under spherical symmetric approximation.

Therefore, modelling the SNe Ia spectropolarimetry signal is critical in understanding the explosion physics of unconfined systems of similar kind.

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Radiative Transfer Simulation

Using an SN Ia ejecta structure from hydrodynamic and nucleosynthesis simulation, the radiative transfer simulation could calculate the observable spectra and polarimetry at different time, therefore providing a bridge to connect the SN Ia explosion models and the observations.

The above figure illustrates the role of radiative transfer simulation in understanding the SN Ia explosion physics, data reproduced from Bulla, et al. (2016).

In the 3D time-dependent radiative transfer program SEDONA (Kasen, et al. (2006)), the gamma-ray energy packets are generated from the decay of radioactive isotopes, then gamma-ray energy packets are converted to optical packets via Compton scattering and photoelectric absorption processes. The optical packets undergo Thomson scattering, bound-free transition, free-free transition, and bound-bound transition processes, finally escape the plasma and form the observable spectra.

The linear polarization effect in SEDONA is produced by the optical packet Thomson scattering process, with a Rayleigh scattering phase matrix. Asymmetric electron density and element structure blocks the polarized light unevenly, result in incomplete cancellation of the electric strokes vector and the observable polarization signal. The circular polarization signal, which is probably due to the magnetic field and has not been observed yet(Wang & Wheeler, 2008), is normally low and set to zero.

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AI's Abilities in Estimating SNe Ia Structures

Our previous project uses a simple 1D time-independent radiative code TARDIS (Kerzendorf, et al, (2014)), to estimate the SN Ia ejecta structure with the help of artificial intelligence (AI)

We firstly use TARDIS to calculate ~100,000 SN Ia spectra with different elemental abundances and density structures, then train a set of deep neural networks to predict the SN Ia structure with the input of simulated spectra. Finally, we input the observed spectra into the neural network to predict the ejecta structure (Chen, et al. (2019), Chen, et al. (2022)). The above figure shows an example of SN2011fe, we notice the AI predicted ejecta structure could generate simulated spectra fit to the observation with high precision.

This example demonstrates the ability of AI in probing a high-dimensionality parameter space such as the SN Ia ejecta structures. However, we notice the further studies of the SN Ia ejecta structures are hindered by the spherical symmetry approximation and the photosphere approximation adopted in TARDIS. Three-dimensional time-dependent computation is becoming important.

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Integral-Based Technique (IBT) to Accelerate in 3D

A simple direct counting technique (DCT), which directly sums the energy of the escaped energy packets within a temporal-directional-frequency bin, is used in multiple radiative transfer codes including SEDONA to retrieve spectropolarimetry signals.

Bulla et al. (2015) proposed the event-based technique (EBT), which introduces virtual packets in the Monte-Carlo radiative transfer calculation to calculate the spectropolarimetry at specified viewing directions.

Based on EBT, I propose the integral-based technique (IBT), which integrates the trajectory of optical packets in each cell to create a equivalent virtual packet.

Apart from the default DCT method, we implement the IBT and the EBT methods into SEDONA, and use a simple DDC10 model to run a 3D time-dependent simulation, in order to compare the precision and computational requirements of the three methods. From the above animation of the spectropolarimetry time sequence and the computation time comparison, we found:

The spectra and polarimetry from both the EBT and the IBT methods shows good signal-to-noise ratio (SNR) that is equivalent to DCT simulation with 100~1000 times more Monte-Carlo quanta.
Enabling IBT calculation increases ~30% of the computation time per viewer, while enabling EBT calculation increases 7-30 times of the computation time.
Because the optical Monte-Carlo packets undergo more scattering events at early phase in SNe Ia, which leads to uncontrolled number of virtual packets in EBT, the EBT calculation is failed at early phase.

The following figure shows the elemental abundances and the density profile of SN Ia ejecta structure model DDC10 (Blondin, et al. (2022)) in 1D, we stretched the model into oval shape to create 3D structure.

The following figure illustrates the mechanism of the EBT and the IBT methods.

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Further Validations of the IBT Polarization Results

Apart from the comparison between the DCT, EBT and IBT calculation results, we designed two other methods to validate the IBT results.

The first validation method is the spherical symmetry. We use a spherical symmetric structure to calculate the spectra which should have zero polarization signal theoretically. The simulation results show the Monte-Carlo noise level is as low as 0.3% in most of the spectropolarimetry data.

The second method is the mirror symmetry. We pick two observation directions of the stretched DDC10 ejecta structure based on the mirror symmetry. Theoretically the Strokers Q parameter should be the same, and the Strokers U parameter should be opposite at this two viewers. The validation results show the polarization signal could reach ~0.3% accuracy in most of the data.

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Future Work

The AI has demonstrative ablities in extracting spectral features and estimating SN Ia structures from the product of complicated radiative transfer simulations.

On the other hand, the newly-developed IBT significantly accelerates the radiative transfer simulation, making it possible to generate a SN Ia 3D structural and spectropolarimetry library. Such a library will support the training of AIs to estimate the 3D structure of SNe Ia from observed spectropolarimetry.

We aim to apply the AI onto ~50 SNe Ia with spectropolarimetry observations before to deduce their 3D ejecta structures, and put direct constraints on their explosion mechanisms and progenitor systems.

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Abstract

We present a new integral-based technique (IBT) for retrieving spectropolarimetry signals from multi-dimensional Monte Carlo supernova radiative transfer simulations. Comparing to the event-based technique (EBT), which utilizes "virtual-packets" to retrieve spectropolarimetry signals (M. Bulla, et al. 2015), the IBT integrates the Monte Carlo quanta over their trajectories to create virtual-packets, and the number of virtual-packets is controlled by the spatial resolution and the simulation time step of the supernova model. We have implemented the IBT into SEDONA, the supernova radiative transfer program developed by (D. Kasen, et al. 2006). We first validate the IBT approach via applying it to idealized supernova models. We then conduct comprehensive comparisons between IBT and EBT, focus on their simulation runtime and result accuracy, in the context of a series of type Ia supernova models with different spatial resolution, elemental abundances, density structures.

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