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M. Bulla

Publications and source records attributed to M. Bulla.

At least 37 records · Page 2Linked to original sources

Science with a small two-band UV-photometry mission I: Mission description and follow-up observations of stellar transients

This is the first in a collection of three papers introducing the science with an ultra-violet (UV) space telescope on an approximately 130~kg small satellite with a moderately fast re-pointing capability and a real-time alert communication system approved for a Czech national space mission. The mission, called Quick Ultra-Violet Kilonova surveyor - QUVIK, will provide key follow-up capabilities to increase the discovery potential of gravitational wave observatories and future wide-field multi-wavelength surveys. The primary objective of the mission is the measurement of the UV brightness evolution of kilonovae, resulting from mergers of neutron stars, to distinguish between different explosion scenarios. The mission, which is designed to be complementary to the Ultraviolet Transient Astronomy Satellite - ULTRASAT, will also provide unique follow-up capabilities for other transients both in the near- and far-UV bands. Between the observations of transients, the satellite will target other objects described in this collection of papers, which demonstrates that a small and relatively affordable dedicated UV-space telescope can be transformative for many fields of astrophysics.

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Spectropolarimetry of Type II supernovae (II) Intrinsic supernova polarization and its relations with the photometric/spectroscopic properties

The explosion processes of supernovae (SNe) are imprinted in their explosion geometries. Here, we study the intrinsic polarization of 15 hydrogen-rich core-collapse SNe and explore the relation with the photometric and spectroscopic properties. Our sample shows diverse properties of the continuum polarization. The polarization of most SNe has a low degree at early phases but shows a sudden rise to $\sim 1$ \% degree at certain points during the photospheric phase as well as a slow decline during the tail phase, with a constant polarization angle. The variation in the timing of peak polarisation values implies diversity in the explosion geometry: some SNe have aspherical structures only in their helium cores, while in other SNe these reach out to a significant part of the outer hydrogen envelope with a common axis from the helium core to the hydrogen envelope. Other SNe show high polarization from early phases and a change of the polarization angle around the middle of the photospheric phase. This implies that the ejecta are significantly aspherical to the outermost layer and have multi-directional aspherical structures. Exceptionally, the Type~IIL SN~2017ahn shows low polarization at both the photospheric and tail phases. Our results show that the timing of the polarization rise in Type~IIP SNe is likely correlated with their brightness, velocity and the amount of radioactive Ni produced: brighter SNe with faster ejecta velocity and a larger $^{56}$Ni mass have more extended-aspherical explosion geometries. In particular, there is a clear correlation between the timing of the polarization rise and the explosion energy, that is, the explosion asphericity is proportional to the explosion energy. This implies that the development of a global aspherical structure, e.g., a jet, might be the key to realising an energetic SN in the mechanism of SN explosions.

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Optimising the observation of optical kilonovae with medium size telescopes

We consider the optimisation of the observing strategy (cadence, exposure time and filter choice) using medium size (2-m class) optical telescopes in the follow-up of kilonovae localised with arcminute accuracy to be able to distinguish among various kilonova models and viewing angles. To develop an efficient observation plan, we made use of the synthetic light curves obtained with the Monte Carlo radiative transfer code POSSIS for different kilonova models and as a function of different viewing angles and distances. By adding the appropriate photon counting noise to the synthetic light curves, we analysed four alternative sequences having the same total time exposure of 8 hours, with different time windows (0.5, 1, 2, 4 h), each with $i$, $r$, and $u$ filters, to determine the observing sequence that maximises the chance of a correct identification of the model parameters. We suggest to avoid $u$ filter and to avoid the use of colour curves. We also found that, if the error on distance is $\le$ 2%, 0.5, 1, 2-hour time window sequences are equivalent, so we suggest to use 2-hour one, because it has 1 day cadence, so it can be easily realised. When the distance of the source is unknown, 0.5 h time window sequence is preferable.

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JWST detection of heavy neutron capture elements in a compact object merger

The mergers of binary compact objects such as neutron stars and black holes are of central interest to several areas of astrophysics, including as the progenitors of gamma-ray bursts (GRBs), sources of high-frequency gravitational waves and likely production sites for heavy element nucleosynthesis via rapid neutron capture (the r-process). These heavy elements include some of great geophysical, biological and cultural importance, such as thorium, iodine and gold. Here we present observations of the exceptionally bright gamma-ray burst GRB 230307A. We show that GRB 230307A belongs to the class of long-duration gamma-ray bursts associated with compact object mergers, and contains a kilonova similar to AT2017gfo, associated with the gravitational-wave merger GW170817. We obtained James Webb Space Telescope mid-infrared (mid-IR) imaging and spectroscopy 29 and 61 days after the burst. The spectroscopy shows an emission line at 2.15 microns which we interpret as tellurium (atomic mass A=130), and a very red source, emitting most of its light in the mid-IR due to the production of lanthanides. These observations demonstrate that nucleosynthesis in GRBs can create r-process elements across a broad atomic mass range and play a central role in heavy element nucleosynthesis across the Universe.

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GRANDMA and HXMT Observations of GRB 221009A -- the Standard-Luminosity Afterglow of a Hyper-Luminous Gamma-Ray Burst

GRB 221009A is the brightest Gamma-Ray Burst (GRB) detected in more than 50 years of study. In this paper, we present observations in the X-ray and optical domains after the GRB obtained by the GRANDMA Collaboration (which includes observations from more than 30 professional and amateur telescopes) and the Insight-HXMT Collaboration. We study the optical afterglow with empirical fitting from GRANDMA+HXMT data, augmented with data from the literature up to 60 days. We then model numerically, using a Bayesian approach, the GRANDMA and HXMT-LE afterglow observations, that we augment with Swift-XRT and additional optical/NIR observations reported in the literature. We find that the GRB afterglow, extinguished by a large dust column, is most likely behind a combination of a large Milky-Way dust column combined with moderate low-metallicity dust in the host galaxy. Using the GRANDMA+HXMT-LE+XRT dataset, we find that the simplest model, where the observed afterglow is produced by synchrotron radiation at the forward external shock during the deceleration of a top-hat relativistic jet by a uniform medium, fits the multi-wavelength observations only moderately well, with a tension between the observed temporal and spectral evolution. This tension is confirmed when using the extended dataset. We find that the consideration of a jet structure (Gaussian or power-law), the inclusion of synchrotron self-Compton emission, or the presence of an underlying supernova do not improve the predictions, showing that the modelling of GRB22109A will require going beyond the most standard GRB afterglow model. Placed in the global context of GRB optical afterglows, we find the afterglow of GRB 221009A is luminous but not extraordinarily so, highlighting that some aspects of this GRB do not deviate from the global known sample despite its extreme energetics and the peculiar afterglow evolution.

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Polarimetry of Hydrogen-Poor Superluminous Supernovae

We present linear polarimetry for seven hydrogen-poor superluminous supernovae (SLSNe-I). For SN 2017gci, for which we present two epochs of spectropolarimetry at +3 d and +29 d post-peak in rest frame, accompanied by four epochs of imaging polarimetry up to +108 d. The spectropolarimetry at +3 d shows increasing polarisation degree P towards the redder wavelengths and exhibits signs of axial symmetry, but at +29 d P=0 throughout the spectrum implying that the photosphere of SN 2017gci evolved from a slightly aspherical configuration to a more spherical one in the first month post-peak. However, an increase of P to 0.5% at +55 d accompanied by a different orientation of the axial symmetry compared to +3 d implies the presence of additional sources of polarisation at this phase. The increase in polarisation is possibly caused by interaction with circumstellar matter as already suggested by a knee in the light curve and a possible detection of broad Ha emission. We also analysed the sample of all 16 SLSNe-I with polarimetry to date. The data taken during the early spectroscopic phase show consistently low P indicating spherical photospheres. No clear relation between the polarimetry and spectral phase was seen when the spectra resemble Type Ic SNe during the photospheric and nebular phases. The light curve decline rate also shows no clear relation with the polarisation properties. While only slow-evolving SLSNe-I have shown non-zero P, the fast-evolving ones have not been observed at sufficiently late times to conclude that none of them exhibit changing P. However, the four SLSNe-I with increasing polarisation degree also have irregular light curve declines. For up to half of them, the photometric, spectroscopic and polarimetric properties are affected by CSM interaction. As such CSM interaction clearly plays an important role in understanding the polarimetric evolution of SLSNe-I.

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Hubble constant and nuclear equation of state from kilonova spectro-photometric light curves

The merger of two compact objects of which at least one is a neutron star is signalled by transient electromagnetic emission in a kilonova (KN). This event is accompanied by gravitational waves and possibly other radiation messengers such as neutrinos or cosmic rays. The electromagnetic emission arises from the radioactive decay of heavy $r-$process elements synthesized in the material ejected during and after the merger. In this paper we show that the analysis of KNe light curves can provide cosmological distance measurements and constrain the properties of the ejecta. In this respect, MAAT, the new Integral Field Unit in the OSIRIS spectrograph on the $10.4$ m Gran Telescopio CANARIAS (GTC), is well suited for the study of KNe by performing absolute spectro-photometry over the entire 3600-10000 Angstron spectral range. Here, we study the most representative cases regarding the scientific interest of KNe from binary neutron stars, and we evaluate the observational prospects and performance of MAAT on the GTC to do the following: a) study the impact of the equation of state on the KN light curve, and determine to what extent bounds on neutron star (NS) radii or compactness deriving from KN peak magnitudes can be identified and b) measure the Hubble constant, $H_0$, with precision improved by up to 40$\%$, when both gravitational wave data and photometric-light curves are used. In this context we discuss how the equation of state, the viewing angle, and the distance affect the precision and estimated value of $H_0$.

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SN 2018bsz: a Type I superluminous supernova with aspherical circumstellar material

We present a spectroscopic analysis of Type I superluminous supernova (SLSN-I), SN 2018bsz. While it closely resembles SLSNe-I, the multi-component H$α$ line appearing at $\sim30$ d post-maximum is the most atypical. The H$α$ is characterised by two emission components, one at $+3000$ km/s and a second at $-7500$ km/s, with a third, near-zero velocity component appearing after a delay. The blue and central components can be described by Gaussian profiles of intermediate width, but the red component is significantly broader and Lorentzian. The blue component evolves towards lower velocity before fading at $100$ d post-peak, concurrently with a light curve break. Multi-component profiles are observed in other hydrogen lines including Pa$β$, and in lines of Ca II and He I. Spectropolarimetry obtained before (10.2 d) and after (38.4 d) the appearance of the H lines show a large shift on the Stokes $Q$ -- $U$ plane consistent with SN 2018bsz undergoing radical changes in its geometry. Assuming the SN is almost unpolarised at 10.2 d, the continuum polarisation at 38.4 d reaches $P \sim1.8\%$ implying a highly asymmetric configuration. We propose that the observed evolution of SN 2018bsz can be explained by highly aspherical CSM. After the SN explosion, the CSM is quickly overtaken by the ejecta, but as the photosphere starts to recede, the different CSM regions re-emerge producing the peculiar line profiles. Based on the first appearance of H$α$, we can constrain the distance of the CSM to be less than $430$ AU, or even lower ($<87$ AU) if the pre-peak plateau is related to an eruption that created the CSM. The presence of CSM has been inferred for other SLSNe-I. However, it is not clear whether the rare properties of SN 2018bsz can be generalised for SLSNe-I or whether they are the result of an uncommon evolutionary path, possibly involving a binary companion.

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Constraining Neutron-Star Matter with Microscopic and Macroscopic Collisions

Interpreting high-energy, astrophysical phenomena, such as supernova explosions or neutron-star collisions, requires a robust understanding of matter at supranuclear densities. However, our knowledge about dense matter explored in the cores of neutron stars remains limited. Fortunately, dense matter is not only probed in astrophysical observations, but also in terrestrial heavy-ion collision experiments. In this work, we use Bayesian inference to combine data from astrophysical multi-messenger observations of neutron stars and from heavy-ion collisions of gold nuclei at relativistic energies with microscopic nuclear theory calculations to improve our understanding of dense matter. We find that the inclusion of heavy-ion collision data indicates an increase in the pressure in dense matter relative to previous analyses, shifting neutron-star radii towards larger values, consistent with recent NICER observations. Our findings show that constraints from heavy-ion collision experiments show a remarkable consistency with multi-messenger observations and provide complementary information on nuclear matter at intermediate densities. This work combines nuclear theory, nuclear experiment, and astrophysical observations, and shows how joint analyses can shed light on the properties of neutron-rich supranuclear matter over the density range probed in neutron stars.

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Evidence for multiple origins of fast declining Type II supernovae from spectropolarimetry of SN 2013ej and SN 2017ahn

The origin of the diverse light-curve shapes of Type II supernovae (SNe), and whether they come from similar or distinct progenitors, has been actively discussed for decades. Here we report spectropolarimetry of two fast declining Type II (Type IIL) SNe: SN 2013ej and SN 2017ahn. SN 2013ej exhibited high continuum polarization from very soon after the explosion to the radioactive tail phase with time-variable polarization angles. The origin of this polarimetric behavior can be interpreted as the combination of two different aspherical structures, namely an aspherical interaction of the SN ejecta with circumstellar matter (CSM) and an inherently aspherical explosion. Aspherical explosions are a common feature of slowly declining Type II (Type IIP) SNe. By contrast, SN 2017ahn showed low polarization not only in the photospheric phase but also in the radioactive tail phase. This low polarization in the tail phase, which has never before been observed in other Type IIP/L SNe, suggests that the explosion of SN 2017ahn was nearly spherical. These observations imply that Type IIL SNe have, at least, two different origins: they result from stars that have different explosion properties and/or different mass-loss processes. This fact might indicate that 13ej-like Type IIL SNe originate from a similar progenitor to those of Type IIP SNe accompanied by an aspherical CSM interaction, while 17ahn-like Type IIL SNe come from a more massive progenitor with less hydrogen in its envelope.

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Detectability of kilonovae in optical surveys: $post$-$mortem$ examination of the LVC O3 run follow-up

The detection of the binary neutron star merger GW170817 and the associated electromagnetic (EM) counterpart, the "kilonova" (kN) AT2017gfo, opened a new era in multi-messenger astronomy. However, despite many efforts, it has been proven very difficult to find additional EM counterparts to the many LIGO/Virgo compact binary merger candidates since then. We explore the sensitivity of ongoing optical surveys searching for kNe and propose ways to optimize the choices of filters and survey depth to boost the detection efficiency for these faint and fast-evolving transients. In particular, we use kN models to explore the dependence on ejecta mass, geometry, viewing angle, wavelength coverage and source distance. Considering that the O3 LIGO/Virgo binary neutron star merger candidates were at distances about 5 times further than GW170817, we find that efficient $gri$ counterpart search would require reaching a limiting magnitude $m_{\rm lim}=$ 23 mag, given the model phase-space. We conclude that kN searches during O3 were generally too shallow to observe optical counterparts, even under optimistic assumptions, thus providing a plausible explanation for the lack of detections.

astro-ph.HE↗

Polarized kilonovae from black hole-neutron star mergers

We predict linear polarization for a radioactively-powered kilonova following the merger of a black hole and a neutron star. Specifically, we perform 3-D Monte Carlo radiative transfer simulations for two different models, both featuring a lanthanide-rich dynamical ejecta component from numerical-relativity simulations while only one including an additional lanthanide-free disk wind component. We calculate polarization spectra for nine different orientations at 1.5, 2.5 and 3.5 d after the merger and in the $0.1-2\,μ$m wavelength range. We find that both models are polarized at a detectable level 1.5 d after the merger while show negligible levels thereafter. The polarization spectra of the two models are significantly different. The model lacking a disk wind shows no polarization in the optical, while a signal increasing at longer wavelengths and reaching $\sim1\%-6\%$ at $2\,μ$m depending on the orientation. The model with a disk-wind component, instead, features a characteristic "double-peak" polarization spectrum with one peak in the optical and the other in the infrared. Polarimetric observations of future events will shed light on the debated neutron richness of the disk-wind component. The detection of optical polarization would unambiguously reveal the presence of a lanthanide-free disk-wind component, while polarization increasing from zero in the optical to a peak in the infrared would suggest a lanthanide-rich composition for the whole ejecta. Future polarimetric campaigns should prioritize observations in the first $\sim48$ hours and in the $0.5-2\,μ$m range, where polarization is strongest, but also explore shorter wavelengths/later times where no signal is expected from the kilonova and the interstellar polarization can be safely estimated.

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Comparing inclination dependent analyses of kilonova transients

The detection of AT2017gfo proved that binary neutron star mergers are progenitors of kilonovae. Using a combination of numerical-relativity and radiative-transfer simulations, the community has developed sophisticated models for these transients for a wide portion of the expected parameter space. Using these simulations and surrogate models made from them, it has been possible to perform Bayesian inference of the observed signals to infer properties of the ejected matter. It has been pointed out that combining inclination constraints derived from the kilonova with gravitational-wave measurements increases the accuracy with which binary parameters can be measured and allows a more accurate inference of the Hubble Constant. In order to not introduce biases, constraints on the inclination angle for AT2017gfo should be insensitive to the employed models. In this work, we compare different assumptions about the ejecta and radiative reprocesses used by the community and we investigate their impact on the parameter inference. While most inferred parameters agree, we find disagreement between posteriors for the inclination angle for different geometries that have been used in the literature. According to our study, the inclusion of reprocessing of the photons between different ejecta types improves the modeling fits to AT2017gfo and in some cases affects the inferred constraints. Our study motivates the inclusion of large $\sim$ 1 mag uncertainties in the kilonova models employed for Bayesian analysis to capture yet unknown systematics, especially when inferring inclination angles, although smaller uncertainties seem appropriate to capture model systematics for other parameters. We also use this method to impose soft constraints on the ejecta geometry of the kilonova AT2017gfo.

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ZTF Early Observations of Type Ia Supernovae II: First Light, the Initial Rise, and Time to Reach Maximum Brightness

While it is clear that Type Ia supernovae (SNe) are the result of thermonuclear explosions in C/O white dwarfs (WDs), a great deal remains uncertain about the binary companion that facilitates the explosive disruption of the WD. Here, we present a comprehensive analysis of a large, unique data set of 127 SNe$\,$Ia with exquisite coverage by the Zwicky Transient Facility (ZTF). High-cadence (six observations per night) ZTF observations allow us to measure the SN rise time and examine its initial evolution. We develop a Bayesian framework to model the early rise as a power law in time, which enables the inclusion of priors in our model. For a volume-limited subset of normal SNe$\,$Ia, we find that the mean power-law index is consistent with 2 in the $r_\mathrm{ZTF}$-band ($α_r = 2.01\pm0.02$), as expected in the expanding fireball model. There are, however, individual SNe that are clearly inconsistent with $α_r=2$. We estimate a mean rise time of 18.9$\,$d (with a range extending from $\sim$15 to 22$\,$d), though this is subject to the adopted prior. We identify an important, previously unknown, bias whereby the rise times for higher-redshift SNe within a flux-limited survey are systematically underestimated. This effect can be partially alleviated if the power-law index is fixed to $α=2$, in which case we estimate a mean rise time of 21.7$\,$d (with a range from $\sim$18 to 23$\,$d). The sample includes a handful of rare and peculiar SNe$\,$Ia. Finally, we conclude with a discussion of lessons learned from the ZTF sample that can eventually be applied to observations from the Vera C. Rubin Observatory.

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The Spectacular Ultraviolet Flash From the Peculiar Type Ia Supernova 2019yvq

Early observations of Type Ia supernovae (SNe$\,$Ia) provide essential clues for understanding the progenitor system that gave rise to the terminal thermonuclear explosion. We present exquisite observations of SN$\,$2019yvq, the second observed SN$\,$Ia, after iPTF$\,$14atg, to display an early flash of emission in the ultraviolet (UV) and optical. Our analysis finds that SN$\,$2019yvq was unusual, even when ignoring the initial flash, in that it was moderately underluminous for an SN$\,$Ia ($M_g \approx -18.5\,$mag at peak) yet featured very high absorption velocities ($v \approx 15,000\,\mathrm{km\,s}^{-1}$ for Si II $λ$6355 at peak). We find that many of the observational features of SN$\,$2019yvq, aside from the flash, can be explained if the explosive yield of radioactive $^{56}\mathrm{Ni}$ is relatively low (we measure $M_{^{56}\mathrm{Ni}} = 0.31 \pm 0.05\,M_\odot$) and it and other iron-group elements are concentrated in the innermost layers of the ejecta. To explain both the UV/optical flash and peak properties of SN$\,$2019yvq we consider four different models: interaction between the SN ejecta and a nondegenerate companion, extended clumps of $^{56}\mathrm{Ni}$ in the outer ejecta, a double-detonation explosion, and the violent merger of two white dwarfs. Each of these models has shortcomings when compared to the observations; it is clear additional tuning is required to better match SN$\,$2019yvq. In closing, we predict that the nebular spectra of SN$\,$2019yvq will feature either H or He emission, if the ejecta collided with a companion, strong [Ca II] emission, if it was a double detonation, or narrow [O I] emission, if it was due to a violent merger.

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Observational constraints on the optical and near-infrared emission from the neutron star-black hole binary merger S190814bv

On 2019 August 14, the LIGO and Virgo interferometers detected a high-significance event labelled S190814bv. Preliminary analysis of the GW data suggests that the event was likely due to the merger of a compact binary system formed by a BH and a NS. ElectromagNetic counterparts of GRAvitational wave sources at the VEry Large Telescope (ENGRAVE) collaboration members carried out an intensive multi-epoch, multi-instrument observational campaign to identify the possible optical/near infrared counterpart of the event. In addition, the ATLAS, GOTO, GRAWITA-VST, Pan-STARRS and VINROUGE projects also carried out a search on this event. Our observations allow us to place limits on the presence of any counterpart and discuss the implications for the kilonova (KN) possibly generated by this NS-BH merger, and for the strategy of future searches. Altogether, our observations allow us to exclude a KN with large ejecta mass $M\gtrsim 0.1\,\mathrm{M_\odot}$ to a high ($>90\%$) confidence, and we can exclude much smaller masses in a subsample of our observations. This disfavours the tidal disruption of the neutron star during the merger. Despite the sensitive instruments involved in the campaign, given the distance of S190814bv we could not reach sufficiently deep limits to constrain a KN comparable in luminosity to AT 2017gfo on a large fraction of the localisation probability. This suggests that future (likely common) events at a few hundreds Mpc will be detected only by large facilities with both high sensitivity and large field of view. Galaxy-targeted observations can reach the needed depth over a relevant portion of the localisation probability with a smaller investment of resources, but the number of galaxies to be targeted in order to get a fairly complete coverage is large, even in the case of a localisation as good as that of this event.

astro-ph.SR↗

White dwarf deflagrations for Type Iax supernovae: Polarisation signatures from the explosion and companion interaction

Growing evidence suggests that Type Iax supernovae might be the result of thermonuclear deflagrations of Chandrasekhar-mass white dwarfs in binary systems. We carry out Monte Carlo radiative transfer simulations and predict spectropolarimetric features originating from the supernova explosion and subsequent ejecta interaction with the companion star. Specifically, we calculate viewing-angle dependent flux and polarisation spectra for a 3D model simulating the deflagration of a Chandrasekhar-mass white dwarf and, for a second model, simulating the ejecta interaction with a main-sequence star. We find that the intrinsic signal is weakly polarised and only mildly viewing-angle dependent, owing to the overall spherical symmetry of the explosion and the depolarising contribution of iron-group elements dominating the ejecta composition. The interaction with the companion star carves out a cavity in the ejecta and produces a detectable, but modest signal that is significant only at relatively blue wavelengths ($\lesssim$ 5000 $\unicode{x212B}$). In particular, increasingly fainter and redder spectra are predicted for observer orientations further from the cavity, while a modest polarisation signal $P\sim0.2$ per cent is found at blue wavelengths for orientations 30$^\circ$ and 45$^\circ$ away from the cavity. We find a reasonable agreement between the interaction model viewed from these orientations and spectropolarimetric data of SN 2005hk and interpret the maximum-light polarisation signal seen at blue wavelengths for this event as a possible signature of the ejecta-companion interaction. We encourage further polarimetric observations of SNe Iax to test whether our results can be extended and generalised to the whole SN Iax class.

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Monte Carlo radiative transfer for the nebular phase of Type Ia supernovae

We extend the range of validity of the ARTIS 3D radiative transfer code up to hundreds of days after explosion, when Type Ia supernovae are in their nebular phase. To achieve this, we add a non-local thermodynamic equilibrium (non-LTE) population and ionisation solver, a new multi-frequency radiation field model, and a new atomic dataset with forbidden transitions. We treat collisions with non-thermal leptons resulting from nuclear decays to account for their contribution to excitation, ionisation, and heating. We validate our method with a variety of tests including comparing our synthetic nebular spectra for the well-known one-dimensional W7 model with the results of other studies. As an illustrative application of the code, we present synthetic nebular spectra for the detonation of a sub-Chandrasekhar white dwarf in which the possible effects of gravitational settling of Ne22 prior to explosion have been explored. Specifically, we compare synthetic nebular spectra for a 1.06 M$_\odot$ white dwarf model obtained when 5.5 Gyr of very-efficient settling is assumed to a similar model without settling. We find that this degree of Ne22 settling has only a modest effect on the resulting nebular spectra due to increased Ni58 abundance. Due to the high ionisation in sub-Chandrasekhar models, the nebular [Ni II] emission remains negligible, while the [Ni III] line strengths are increased and the overall ionisation balance is slightly lowered in the model with Ne22 settling. In common with previous studies of sub-Chandrasekhar models at nebular epochs, these models overproduce [Fe III] emission relative to [Fe II] in comparison to observations of normal Type Ia supernovae.

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