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S. Taubenberger

Publications and source records attributed to S. Taubenberger.

At least 37 records · Page 2Linked to original sources

Uniform Recalibration of Common Spectrophotometry Standard Stars onto the CALSPEC System using the SuperNova Integral Field Spectrograph

We calibrate spectrophotometric optical spectra of 32 stars commonly used as standard stars, referenced to 14 stars already on the HST-based CALSPEC flux system. Observations of CALSPEC and non-CALSPEC stars were obtained with the SuperNova Integral Field Spectrograph over the wavelength range 3300 A to 9400 A as calibration for the Nearby Supernova Factory cosmology experiment. In total, this analysis used 4289 standard-star spectra taken on photometric nights. As a modern cosmology analysis, all pre-submission methodological decisions were made with the flux scale and external comparison results blinded. The large number of spectra per star allows us to treat the wavelength-by-wavelength calibration for all nights simultaneously with a Bayesian hierarchical model, thereby enabling a consistent treatment of the Type Ia supernova cosmology analysis and the calibration on which it critically relies. We determine the typical per-observation repeatability (median 14 mmag for exposures >~ 5 s), the Maunakea atmospheric transmission distribution (median dispersion of 7 mmag with uncertainty 1 mmag), and the scatter internal to our CALSPEC reference stars (median of 8 mmag). We also check our standards against literature filter photometry, finding generally good agreement over the full 12-magnitude range. Overall, the mean of our system is calibrated to the mean of CALSPEC at the level of ~ 3 mmag. With our large number of observations, careful crosschecks, and 14 reference stars, our results are the best calibration yet achieved with an integral-field spectrograph, and among the best calibrated surveys.

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HOLISMOKES -- VII. Time-delay measurement of strongly lensed Type Ia supernovae using machine learning

The Hubble constant ($H_0$) is one of the fundamental parameters in cosmology, but there is a heated debate around the $>$4$σ$ tension between the local Cepheid distance ladder and the early Universe measurements. Strongly lensed Type Ia supernovae (LSNe Ia) are an independent and direct way to measure $H_0$, where a time-delay measurement between the multiple supernova (SN) images is required. In this work, we present two machine learning approaches for measuring time delays in LSNe Ia, namely, a fully connected neural network (FCNN) and a random forest (RF). For the training of the FCNN and the RF, we simulate mock LSNe Ia from theoretical SN Ia models that include observational noise and microlensing. We test the generalizability of the machine learning models by using a final test set based on empirical LSN Ia light curves not used in the training process, and we find that only the RF provides a low enough bias to achieve precision cosmology; as such, RF is therefore preferred over our FCNN approach for applications to real systems. For the RF with single-band photometry in the $i$ band, we obtain an accuracy better than 1\% in all investigated cases for time delays longer than 15 days, assuming follow-up observations with a 5$σ$ point-source depth of 24.7, a two day cadence with a few random gaps, and a detection of the LSNe Ia 8 to 10 days before peak in the observer frame. In terms of precision, we can achieve an approximately 1.5-day uncertainty for a typical source redshift of $\sim$0.8 on the $i$ band under the same assumptions. To improve the measurement, we find that using three bands, where we train a RF for each band separately and combine them afterward, helps to reduce the uncertainty to $\sim$1.0 day. We have publicly released the microlensed spectra and light curves used in this work.

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HOLISMOKES -- V. Microlensing of type II supernovae and time-delay inference through spectroscopic phase retrieval

We investigate strongly gravitationally lensed type II supernovae (LSNe II) for time-delay cosmography incorporating microlensing effects, which expands on previous microlensing studies of type Ia supernovae (SNe Ia). We use the radiative-transfer code ${\rm \small TARDIS}$ to recreate five spectra of the prototypical SN 1999em at different times within the plateau phase of the light curve. The microlensing-induced deformations of the spectra and light curves are calculated by placing the SN into magnification maps generated with the code ${\rm \small GERLUMPH}$. We study the impact of microlensing on the color curves and find that there is no strong influence on them during the investigated time interval of the plateau phase. The color curves are only weakly affected by microlensing due to the almost achromatic behavior of the intensity profiles. However, the lack of non-linear structure in the color curves makes time-delay measurements difficult given the possible presence of differential dust extinction. Therefore, we further investigate SN phase inference through spectral absorption lines under the influence of microlensing and Gaussian noise. As the spectral features shift to longer wavelengths with progressing time after explosion, the measured wavelength of a specific absorption line provides information on the epoch of the SN. The comparison between retrieved epochs of two observed lensing images then gives the time delay of the images. We find that the phase retrieval method using spectral features yields accurate delays with uncertainties $\small {\lesssim}$2 days, making it a promising approach.

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HOLISMOKES. VI. New galaxy-scale strong lens candidates from the HSC-SSP imaging survey

We have carried out a systematic search for galaxy-scale strong lenses in multiband imaging from the Hyper Suprime-Cam (HSC) survey. Our automated pipeline, based on realistic strong-lens simulations, deep neural network classification, and visual inspection, is aimed at efficiently selecting systems with wide image separations (Einstein radii ~1.0-3.0"), intermediate redshift lenses (z ~ 0.4-0.7), and bright arcs for galaxy evolution and cosmology. We classified gri images of all 62.5 million galaxies in HSC Wide with i-band Kron radius >0.8" to avoid strict pre-selections and to prepare for the upcoming era of deep, wide-scale imaging surveys with Euclid and Rubin Observatory. We obtained 206 newly-discovered candidates classified as definite or probable lenses with either spatially-resolved multiple images or extended, distorted arcs. In addition, we found 88 high-quality candidates that were assigned lower confidence in previous HSC searches, and we recovered 173 known systems in the literature. These results demonstrate that, aided by limited human input, deep learning pipelines with false positive rates as low as ~0.01% can be very powerful tools for identifying the rare strong lenses from large catalogs, and can also largely extend the samples found by traditional algorithms. We provide a ranked list of candidates for future spectroscopic confirmation.

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Photometric Redshift Estimation with a Convolutional Neural Network: NetZ

The redshifts of galaxies are a key attribute that is needed for nearly all extragalactic studies. Since spectroscopic redshifts require additional telescope and human resources, millions of galaxies are known without spectroscopic redshifts. Therefore, it is crucial to have methods for estimating the redshift of a galaxy based on its photometric properties, the so-called photo-$z$. We developed NetZ, a new method using a Convolutional Neural Network (CNN) to predict the photo-$z$ based on galaxy images, in contrast to previous methods which often used only the integrated photometry of galaxies without their images. We use data from the Hyper Suprime-Cam Subaru Strategic Program (HSC SSP) in five different filters as training data. The network over the whole redshift range between 0 and 4 performs well overall and especially in the high-$z$ range better than other methods on the same data. We obtain an accuracy $|z_\text{pred}-z_\text{ref}|$ of $σ= 0.12$ (68% confidence interval) with a CNN working for all galaxy types averaged over all galaxies in the redshift range of 0 to $\sim$4. By limiting to smaller redshift ranges or to Luminous Red Galaxies (LRGs), we find a further notable improvement. We publish more than 34 million new photo-$z$ values predicted with NetZ here. This shows that the new method is very simple and fast to apply, and, importantly, covers a wide redshift range limited only by the available training data. It is broadly applicable and beneficial to imaging surveys, particularly upcoming surveys like the Rubin Observatory Legacy Survey of Space and Time which will provide images of billions of galaxies with similar image quality as HSC.

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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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The Twins Embedding of Type Ia Supernovae II: Improving Cosmological Distance Estimates

We show how spectra of Type Ia supernovae (SNe Ia) at maximum light can be used to improve cosmological distance estimates. In a companion article, we used manifold learning to build a three-dimensional parameterization of the intrinsic diversity of SNe Ia at maximum light that we call the "Twins Embedding". In this article, we discuss how the Twins Embedding can be used to improve the standardization of SNe Ia. With a single spectrophotometrically-calibrated spectrum near maximum light, we can standardize our sample of SNe Ia with an RMS of $0.101 \pm 0.007$ mag, which corresponds to $0.084 \pm 0.009$ mag if peculiar velocity contributions are removed and $0.073 \pm 0.008$ mag if a larger reference sample were obtained. Our techniques can standardize the full range of SNe Ia, including those typically labeled as peculiar and often rejected from other analyses. We find that traditional light curve width + color standardization such as SALT2 is not sufficient. The Twins Embedding identifies a subset of SNe Ia including but not limited to 91T-like SNe Ia whose SALT2 distance estimates are biased by $0.229 \pm 0.045$ mag. Standardization using the Twins Embedding also significantly decreases host-galaxy correlations. We recover a host mass step of $0.040 \pm 0.020$ mag compared to $0.092 \pm 0.024$ mag for SALT2 standardization on the same sample of SNe Ia. These biases in traditional standardization methods could significantly impact future cosmology analyses if not properly taken into account.

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The Twins Embedding of Type Ia Supernovae I: The Diversity of Spectra at Maximum Light

We study the spectral diversity of Type Ia supernovae (SNe Ia) at maximum light using high signal-to-noise spectrophotometry of 173 SNe Ia from the Nearby Supernova Factory. We decompose the diversity of these spectra into different extrinsic and intrinsic components, and we construct a nonlinear parameterization of the intrinsic diversity of SNe Ia that preserves pairings of "twin" SNe Ia. We call this parameterization the "Twins Embedding". Our methodology naturally handles highly nonlinear variability in spectra, such as changes in the photosphere expansion velocity, and uses the full spectrum rather than being limited to specific spectral line strengths, ratios or velocities. We find that the time evolution of SNe Ia near maximum light is remarkably similar, with 84.6% of the variance in common to all SNe Ia. After correcting for brightness and color, the intrinsic variability of SNe Ia is mostly restricted to specific spectral lines, and we find intrinsic dispersions as low as ~0.02 mag between 6600 and 7200 A. With a nonlinear three-dimensional model plus one dimension for color, we can explain 89.2% of the intrinsic diversity in our sample of SNe Ia, which includes several different kinds of "peculiar" SNe Ia. A linear model requires seven dimensions to explain a comparable fraction of the intrinsic diversity. We show how a wide range of previously-established indicators of diversity in SNe Ia can be recovered from the Twins Embedding. In a companion article, we discuss how these results an be applied to standardization of SNe Ia for cosmology.

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HOLISMOKES -- II. Identifying galaxy-scale strong gravitational lenses in Pan-STARRS using convolutional neural networks

We present a systematic search for wide-separation (Einstein radius >1.5"), galaxy-scale strong lenses in the 30 000 sq.deg of the Pan-STARRS 3pi survey on the Northern sky. With long time delays of a few days to weeks, such systems are particularly well suited for catching strongly lensed supernovae with spatially-resolved multiple images and open new perspectives on early-phase supernova spectroscopy and cosmography. We produce a set of realistic simulations by painting lensed COSMOS sources on Pan-STARRS image cutouts of lens luminous red galaxies with known redshift and velocity dispersion from SDSS. First of all, we compute the photometry of mock lenses in gri bands and apply a simple catalog-level neural network to identify a sample of 1050207 galaxies with similar colors and magnitudes as the mocks. Secondly, we train a convolutional neural network (CNN) on Pan-STARRS gri image cutouts to classify this sample and obtain sets of 105760 and 12382 lens candidates with scores pCNN>0.5 and >0.9, respectively. Extensive tests show that CNN performances rely heavily on the design of lens simulations and choice of negative examples for training, but little on the network architecture. Finally, we visually inspect all galaxies with pCNN>0.9 to assemble a final set of 330 high-quality newly-discovered lens candidates while recovering 23 published systems. For a subset, SDSS spectroscopy on the lens central regions proves our method correctly identifies lens LRGs at z~0.1-0.7. Five spectra also show robust signatures of high-redshift background sources and Pan-STARRS imaging confirms one of them as a quadruply-imaged red source at z_s = 1.185 strongly lensed by a foreground LRG at z_d = 0.3155. In the future, we expect that the efficient and automated two-step classification method presented in this paper will be applicable to the deeper gri stacks from the LSST with minor adjustments.

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HOLISMOKES -- III. Achromatic Phase of Strongly Lensed Type Ia Supernovae

To use strongly lensed Type Ia supernovae (LSNe Ia) for cosmology, a time-delay measurement between the multiple supernova (SN) images is necessary. The sharp rise and decline of SN Ia light curves make them promising for measuring time delays, but microlensing can distort these light curves and therefore add large uncertainties to the measurements. An alternative approach is to use color curves where uncertainties due to microlensing are significantly reduced for a certain period of time known as the achromatic phase. In this work, we investigate in detail the achromatic phase, testing four different SN Ia models with various microlensing configurations. We find on average an achromatic phase of around three rest-frame weeks or longer for most color curves but the spread in the duration of the achromatic phase (due to different microlensing maps and filter combinations) is quite large and an achromatic phase of just a few days is also possible. Furthermore, the achromatic phase is longer for smoother microlensing maps, lower macro-magnifications and larger mean Einstein radii of microlenses. From our investigations, we do not find a strong dependency on the model or on asymmetries in the SN ejecta. Further, we find that three independent LSST color curves exhibit features such as extreme points or turning points within the achromatic phase, which make them promising for time-delay measurements. These curves contain combinations of rest-frame bands $u$, $g$, $r$, and $i$ and to observe them for typical LSN Ia redshifts, it would be ideal to cover (observer-frame) filters $r$, $i$, $z$, $y$, $J$, and $H$.

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Strong Dependence of Type Ia Supernova Standardization on the Local Specific Star Formation Rate

As part of an on-going effort to identify, understand and correct for astrophysics biases in the standardization of Type Ia supernovae (SNIa) for cosmology, we have statistically classified a large sample of nearby SNeIa into those located in predominantly younger or older environments. This classification is based on the specific star formation rate measured within a projected distance of 1kpc from each SN location (LsSFR). This is an important refinement compared to using the local star formation rate directly as it provides a normalization for relative numbers of available SN progenitors and is more robust against extinction by dust. We find that the SNeIa in predominantly younger environments are DY=0.163\pm0.029 mag (5.7 sigma) fainter than those in predominantly older environments after conventional light-curve standardization. This is the strongest standardized SN Ia brightness systematic connected to host-galaxy environment measured to date. The well-established step in standardized brightnesses between SNeIa in hosts with lower or higher total stellar masses is smaller at DM=0.119\pm0.032 mag (4.5 sigma), for the same set of SNeIa. When fit simultaneously, the environment age offset remains very significant, with DY=0.129\pm0.032 mag (4.0 sigma), while the global stellar mass step is reduced to DM=0.064\pm0.029 mag (2.2 sigma). Thus, approximately 70% of the variance from the stellar mass step is due to an underlying dependence on environment-based progenitor age. Standardization using only the SNeIa in younger environments reduces the total dispersion from 0.142\pm0.008 mag to 0.120\pm0.010 mag. We show that as environment ages evolve with redshift a strong bias on measurement of the dark energy equation of state parameters can develop. Fortunately, data to measure and correct for this effect is likely to be available for many next-generation experiments. [abstract shorten]

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HOLISMOKES -- IV. Efficient mass modeling of strong lenses through deep learning

Modelling the mass distributions of strong gravitational lenses is often necessary to use them as astrophysical and cosmological probes. With the high number of lens systems ($>10^5$) expected from upcoming surveys, it is timely to explore efficient modeling approaches beyond traditional MCMC techniques that are time consuming. We train a CNN on images of galaxy-scale lenses to predict the parameters of the SIE mass model ($x,y,e_x,e_y$, and $θ_E$). To train the network, we simulate images based on real observations from the HSC Survey for the lens galaxies and from the HUDF as lensed galaxies. We tested different network architectures, the effect of different data sets, and using different input distributions of $θ_E$. We find that the CNN performs well and obtain with the network trained with a uniform distribution of $θ_E$ $>0.5"$ the following median values with $1σ$ scatter: $Δx=(0.00^{+0.30}_{-0.30})"$, $Δy=(0.00^{+0.30}_{-0.29})" $, $Δθ_E=(0.07^{+0.29}_{-0.12})"$, $Δe_x = -0.01^{+0.08}_{-0.09}$ and $Δe_y = 0.00^{+0.08}_{-0.09}$. The bias in $θ_E$ is driven by systems with small $θ_E$. Therefore, when we further predict the multiple lensed image positions and time delays based on the network output, we apply the network to the sample limited to $θ_E>0.8"$. In this case, the offset between the predicted and input lensed image positions is $(0.00_{-0.29}^{+0.29})"$ and $(0.00_{-0.31}^{+0.32})"$ for $x$ and $y$, respectively. For the fractional difference between the predicted and true time delay, we obtain $0.04_{-0.05}^{+0.27}$. Our CNN is able to predict the SIE parameters in fractions of a second on a single CPU and with the output we can predict the image positions and time delays in an automated way, such that we are able to process efficiently the huge amount of expected lens detections in the near future.

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HOLISMOKES -- I. Highly Optimised Lensing Investigations of Supernovae, Microlensing Objects, and Kinematics of Ellipticals and Spirals

We present the HOLISMOKES programme on strong gravitational lensing of supernovae as a probe of supernova (SN) physics and cosmology. We investigate the effects of microlensing on early-phase SN Ia spectra using four different SN explosion models, and find that within 10 rest-frame days after SN explosion, distortions of SN Ia spectra due to microlensing are typically negligible ($<$1% distortion within the 1$σ$ spread, and $\lesssim$10% distortion within the 2$σ$ spread). This shows great prospects of using lensed SNe Ia to obtain intrinsic early-phase SN spectra for deciphering SN Ia progenitors. As a demonstration of the usefulness of lensed SNe Ia for cosmology, we simulate a sample of mock lensed SN Ia systems that are expected to have accurate and precise time-delay measurements in the era of the Rubin Observatory Legacy Survey of Space and Time (LSST). Adopting realistic yet conservative uncertainties on their time-delay distances and lens angular diameter distances (of 6.6% and 5%, respectively), we find that a sample of 20 lensed SNe Ia would allow a constraint on the Hubble constant ($H_0$) with 1.3% uncertainty in the flat $Λ$CDM cosmology. We find a similar constraint on $H_0$ in an open $Λ$CDM cosmology, while the constraint degrades to $3\%$ in a flat $w$CDM cosmology. We anticipate lensed SNe to be an independent and powerful probe of SN physics and cosmology in the upcoming LSST era.

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SN 2017ivv: two years of evolution of a transitional Type II supernova

We present the photometric and spectroscopic evolution of the Type II supernova (SN II) SN 2017ivv (also known as ASASSN-17qp). Located in an extremely faint galaxy (M$_r=-10.3$ mag), SN 2017ivv shows an unprecedented evolution during the two years of observations. At early times, the light curve shows a fast rise ($\sim6-8$ days) to a peak of ${\rm M}^{\rm max}_{g}= -17.84$ mag, followed by a very rapid decline of $7.94\pm0.48$ mag per 100 days in the $V-$band. The extensive photometric coverage at late phases shows that the radioactive tail has two slopes, one steeper than that expected from the decay of $^{56}$Co (between 100 and 350 days), and another slower (after 450 days), probably produced by an additional energy source. From the bolometric light curve, we estimated that the amount of ejected $^{56}$Ni is $\sim0.059\pm0.003$ M$\odot$. The nebular spectra of SN 2017ivv show a remarkable transformation that allows the evolution to be split into three phases: (1) H$α$ strong phase ($<200$ days); (2) H$α$ weak phase (between 200 and 350 days); and (3) H$α$ broad phase ($>500$ days). We find that the nebular analysis favours a binary progenitor and an asymmetric explosion. Finally, comparing the nebular spectra of SN 2017ivv to models suggests a progenitor with a zero-age main-sequence mass of 15 -- 17 \Msun.

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An in-depth reanalysis of the alleged type Ia supernova progenitor Henize 2-428

The nucleus of the planetary nebula Hen2-428 is a short orbital-period (4.2h), double-lined spectroscopic binary, whose status as a potential supernova type Ia progenitor has raised some controversy in the literature. With the aim of resolving this debate, we carried out an in-depth reanalysis of the system. Our approach combines a refined wavelength calibration, thorough line-identifications, improved radial-velocity measurements, non-LTE spectral modeling, as well as multi-band light-curve fitting. Our results are then discussed in view of state-of-the-art stellar evolutionary models. Besides systematic zero-point shifts in the wavelength calibration of the OSIRIS spectra which were also used in the previous analysis of the system, we found that the spectra are contaminated with diffuse interstellar bands. Our Voigt-profile radial velocity fitting method, which considers the additional absorption of these diffuse interstellar bands, reveals significantly lower masses ($M_1=0.66\pm0.11M_\odot$ and $M_2=0.42\pm0.07M_\odot$) than previously reported and a mass ratio that is clearly below unity. Our spectral and light curve analyses lead to consistent results, however, we find higher effective temperatures and smaller radii than previously reported. Moreover, we find that the red-excess that was reported before to prove to be a mere artifact of an outdated reddening law that was applied. Our work shows that blends of HeII 5412A with diffuse interstellar bands have led to an overestimation of the previously reported dynamical masses of Hen2-428. The merging event of Hen2-428 will not be recognised as a supernova type Ia, but most likely leads to the formation of a H-deficient star. We suggest that the system was formed via a first stable mass transfer episode, followed by common envelope evolution, and it is now composed of a post-early AGB star and a reheated He-core white dwarf.

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The SNEMO and SUGAR Companion Datasets

The Nearby Supernova Factory has made spectrophotometric observations of Type Ia supernovae since $2004$. This work presents an interim version of the data produced, including $210$ supernovae observed between $2004$ and $2013$.

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The rise and fall of an extraordinary Ca-rich transient -- The discovery of ATLAS19dqr/SN 2019bkc

This work presents the observations and analysis of ATLAS19dqr/SN 2019bkc, an extraordinary rapidly evolving transient event located in an isolated environment, tens of kiloparsecs from any likely host. Its light curves rise to maximum light in $5-6$ d and then display a decline of $Δm_{15} \sim5$ mag. With such a pronounced decay, it has one of the most rapidly evolving light curves known for a stellar explosion. The early spectra show similarities to normal and `ultra-stripped' type Ic SNe, but the early nebular phase spectra, which were reached just over two weeks after explosion, display prominent calcium lines, marking SN 2019bkc as a Ca-rich transient. The Ca emission lines at this phase show an unprecedented and unexplained blueshift of 10,000 -- 12,000 km/s. Modelling of the light curve and the early spectra suggests that the transient had a low ejecta mass of $0.2 - 0.4$ M$_\odot$ and a low kinetic energy of $ (2-4)\times 10^{50}$ erg, giving a specific kinetic energy $\sim1$ [$10^{51}$ erg]/M$_\odot$. The origin of this event cannot be unambiguously defined. While the abundance distribution used to model the spectra marginally favours a progenitor of white dwarf origin through the tentative identification of \ArII, the specific kinetic energy, which is defined by the explosion mechanism, is found to be more similar to an ultra-stripped core-collapse events. SN 2019bkc adds to the diverse range of physical properties shown by Ca-rich events.

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SUGAR: An improved empirical model of Type Ia Supernovae based on spectral features

Type Ia Supernovae (SNe Ia) are widely used to measure the expansion of the Universe. Improving distance measurements of SNe Ia is one technique to better constrain the acceleration of expansion and determine its physical nature. This document develops a new SNe Ia spectral energy distribution (SED) model, called the SUpernova Generator And Reconstructor (SUGAR), which improves the spectral description of SNe Ia, and consequently could improve the distance measurements. This model is constructed from SNe Ia spectral properties and spectrophotometric data from The Nearby Supernova Factory collaboration. In a first step, a PCA-like method is used on spectral features measured at maximum light, which allows us to extract the intrinsic properties of SNe Ia. Next, the intrinsic properties are used to extract the average extinction curve. Third, an interpolation using Gaussian Processes facilitates using data taken at different epochs during the lifetime of a SN Ia and then projecting the data on a fixed time grid. Finally, the three steps are combined to build the SED model as a function of time and wavelength. This is the SUGAR model. The main advancement in SUGAR is the addition of two additional parameters to characterize SNe Ia variability. The first is tied to the properties of SNe Ia ejecta velocity, the second is correlated with their calcium lines. The addition of these parameters, as well as the high quality the Nearby Supernova Factory data, makes SUGAR an accurate and efficient model for describing the spectra of normal SNe Ia as they brighten and fade. The performance of this model makes it an excellent SED model for experiments like ZTF, LSST or WFIRST.

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