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QuTiP, the Quantum Toolbox in Python, has been at the forefront of open-source quantum software for the last ten years. It is used as a research, teaching, and industrial tool, and has been downloaded millions of times by users around the world. Here we introduce the latest developments in QuTiP v5, which are set to have a large impact on the future of QuTiP and enable it to be a modern, continuously developed and popular tool for another decade and more. We summarize the code design and fundamental data layer changes as well as efficiency improvements, new solvers, applications to quantum circuits with QuTiP-QIP, and new quantum control tools with QuTiP-QOC. Additional flexibility in the data layer underlying all "quantum objects" in QuTiP allows us to harness the power of state-of-the-art data formats and packages like JAX, CuPy, and more. We explain these new features with a series of both well-known and new examples. The code for these examples is available in a static form on GitHub and will be available also in a continuously updated and documented notebook form in the qutip-tutorials package., Comment: 70 pages, 25 figures

The second data release of Type Ia supernovae (SNe Ia) observed by the Zwicky Transient Facility has provided a homogeneous sample of 3628 SNe Ia with photometric and spectral information. This unprecedented sample size enables us to better explore our currently tentative understanding of the dependence of host environment on SN Ia properties. In this paper, we make use of two-dimensional image decomposition to model the host galaxies of SNe Ia. We model elliptical galaxies as well as disk/spiral galaxies with or without central bulges and bars. This allows for the categorisation of SN Ia based on their morphological host environment, as well as the extraction of intrinsic galaxy properties corrected for both cosmological and atmospheric effects. We find that although this image decomposition technique leads to a significant bias towards elliptical galaxies in our final sample of galaxies, the overall results are robust. By successfully modelling 728 host galaxies, we find that the photometric properties of SNe Ia found in disks and in elliptical galaxies, correlate fundamentally differently with their host environment. We identified strong linear relations between light-curve stretch and our model-derived galaxy colour for both the elliptical (16.8$\sigma$) and disk (5.1$\sigma$) subpopulations of SNe Ia. Lower stretch SNe Ia are found in redder environments, which we identify as an age/metallicity effect. Within the subpopulation of SNe Ia found in disk containing galaxies, we find a significant linear trend (6.1$\sigma$) between light-curve stretch and model-derived local $r$-band surface brightness, which we link to the age/metallicity gradients found in disk galaxies. SN Ia colour shows little correlation with host environment as seen in the literature. We identify a possible dust effect in our model-derived surface brightness (3.3$\sigma$), for SNe Ia in disk galaxies., Comment: ZTF SN Ia DR2 release paper. Submitted to A&A (ZTF DR2 Special Issue)

The Zwicky Transient Facility SN Ia Data Release 2 (ZTF SN Ia DR2) contains more than 3,000 Type Ia supernovae (SNe Ia), providing the largest homogeneous low-redshift sample of SNe Ia. Having at least one spectrum per event, this data collection is ideal for large-scale statistical studies of the photometric, spectroscopic and host-galaxy properties of SNe Ia, particularly of the more rare "peculiar" subclasses. In this paper, we first present the method we developed to spectroscopically classify the SNe in the sample, and the techniques we used to model their multi-band light curves and explore their photometric properties. We then show a method to distinguish between the "peculiar" subtypes and the normal SNe Ia. We also explore the properties of their host galaxies and estimate their relative rates, focusing on the "peculiar" subtypes and their connection to the cosmologically useful SNe Ia. Finally, we discuss the implications of our study with respect to the progenitor systems of the "peculiar" SN Ia events., Comment: 19 pages, 13 figures, submitted to Astronomy and Astrophysics

More than 3000 spectroscopically confirmed Type Ia supernovae (SNe Ia) are presented in the Zwicky Transient Facility SN Ia Data Release 2 (ZTF DR2). In this paper, we detail the spectral properties of 482 SNe Ia near maximum light, up to a redshift limit of $z$ $\leq$ 0.06. We measure the velocities and pseudo-equivalent widths (pEW) of key spectral features (Si II $\lambda$5972 and Si II $\lambda$6355) and investigate the relation between the properties of the spectral features and the photometric properties from the SALT2 light-curve parameters as a function of spectroscopic sub-class. We discuss the non-negligible impact of host galaxy contamination on SN Ia spectral classifications, as well as investigate the accuracy of spectral template matching of the ZTF DR2 sample. We define a new subclass of underluminous SNe Ia (`04gs-like') that lie spectroscopically between normal SNe Ia and transitional 86G-like SNe Ia (stronger Si II $\lambda$5972 than normal SNe Ia but significantly weaker Ti II features than `86G-like' SNe). We model these `04gs-like' SN Ia spectra using the radiative-transfer spectral synthesis code tardis and show that cooler temperatures alone are unable to explain their spectra; some changes in elemental abundances are also required. However, the broad continuity in spectral properties seen from bright (`91T-like') to faint normal SN Ia, including the transitional and 91bg-like SNe Ia, suggests that variations within a single explosion model may be able to explain their behaviour.

Type Ia supernova (SN Ia) light curves have a secondary maximum that exists in the $r$, $i$, and near-infrared filters. The secondary maximum is relatively weak in the $r$ band, but holds the advantage that it is accessible, even at high redshift. We used Gaussian Process fitting to parameterise the light curves of 893 SNe Ia from the Zwicky Transient Facility's (ZTF) second data release (DR2), and we were able to extract information about the timing and strength of the secondary maximum. We found $>5\sigma$ correlations between the light curve decline rate ($\Delta m_{15}(g)$) and the timing and strength of the secondary maximum in the $r$ band. Whilst the timing of the secondary maximum in the $i$ band also correlates with $\Delta m_{15}(g)$, the strength of the secondary maximum in the $i$ band shows significant scatter as a function of $\Delta m_{15}(g)$. We found that the transparency timescales of 97 per cent of our sample are consistent with double detonation models, and that SNe Ia with small transparency timescales ($<$ 32 d) reside predominantly in locally red environments. We measured the total ejected mass for the normal SNe Ia in our sample using two methods, and both were consistent with medians of $1.3\ \pm \ 0.3$ and $1.2\ \pm\ 0.2$ solar masses. We find that the strength of the secondary maximum is a better standardisation parameter than the SALT light curve stretch ($x_1$). Finally, we identified a spectral feature in the $r$ band as Fe II, which strengthens during the onset of the secondary maximum. The same feature begins to strengthen at $<$ 3 d post maximum light in 91bg-like SNe. Finally, the correlation between $x_1$ and the strength of the secondary maximum was best fit with a broken line, with a split at $x_1^0\ =\ -0.5\ \pm\ 0.2$, suggestive of the existence of two populations of SNe Ia., Comment: 18 pages, 14 figures

The unprecedented statistics of detected Type Ia supernovae (SNe Ia) brought by the Zwicky Transient Facility enables us to probe the impact of the Large-Scale Structure on the properties of these objects. The goal of this paper is to explore the possible impact of the under-dense part of the large-scale structure on the intrinsic SALT2 light curve properties of SNe Ia and uncover possible biases in SN Ia analyses. With a volume-limited selection of ZTF-Cosmo-DR2 Type Ia supernovae overlapping with the SDSS-DR7 survey footprint, we investigate the distribution of their properties with regard to voids detected in the SDSS-DR7 galaxy sample. We further use Voronoi volumes as proxy for local density environments within the large-scale structure. We find a moderate dependency of the stretch toward the localisation around the void centre and none when considering colour. The local Voronoi volumes mostly affect the fraction of low/high stretch supernovae. With the current statistics available, we consider that the impact of high or low local density environment can be considered as a proxy for the colour of the host galaxy. Under-dense environments should not cause any biases in supernova analyses., Comment: 10 pages, 8 figures. Submitted to A&A

Type Ia supernova (SNIa) are excellent probes of local distance, and the increasing sample sizes of SNIa have driven an increased need to study the associated systematic uncertainties and improve the standardisation methods in preparation for the next generation of cosmological surveys into the dark energy equation-of-state $w$. We aim to probe the potential change in the SNIa standardisation parameter $c$ with redshift and the host-galaxy of the supernova. Improving the standardisation of SNIa brightnesses will require accounting for the relationship between the host and the SNIa, and potential shifts in the SNIa standardisation parameters with redshift will cause biases in the recovered cosmology. Here, we assemble a volume-limited sample of ~3000 likely SNIa across a redshift range of $z = 0.015$ to $z = 0.36$. This sample is fitted with changing mass and redshift bins to determine the relationship between intrinsic properties of SNe Ia and their redshift and host galaxy parameters. We then investigate the colour-luminosity parameter $\beta$ as a further test of the SNIa standardisation process. We find that the changing colour distribution of SNe Ia with redshift is driven by dust at a confidence of $>4\sigma$. Additionally, we show a strong correlation between the host galaxy mass and the colour-luminosity coefficient $\beta$ ($> 4\sigma$), even when accounting for the quantity of dust in a host galaxy.

As Type Ia supernova cosmology transitions from a statistics dominated to a systematics dominated era, it is crucial to understand leftover unexplained uncertainties affecting their luminosity, such as the ones stemming from astrophysical biases. Indeed, SNe Ia are standardisable candles, whose absolute magnitude reach a 0.15~mag scatter once empirical correlations with their lightcurve stretch and colour and with their environment are accounted for. In this paper, we investigate how the standardisation process of SNe Ia depends on environment, to ultimately reduce their scatter in magnitude, focusing on colour standardisation. We use the volume-limited ZTF SN Ia DR2 sample, which offers unprecedented statistics for the low redshift ($z<0.06$) range. We first study the colour distribution, focusing on the effects of dust, to then select a dustless subsample of objects from low stellar mass environments and from the outskirts of their host galaxies. We then look at the colour-residuals relation and its associated parameter $\beta$. Finally, we investigate the colour dependency of the environment-dependent magnitude offsets (steps), to try to disentangle intrinsic and extrinsic colour origin. Our sample probes well the red tail of the colour distribution, up to $c=0.8$. The dustless sample exhibits a significantly lower red tail ($4.6\sigma$) in comparison to the whole sample. This suggests that reddening above $c\geq0.2$ is dominated by host interstellar dust absorption. Looking at the colour-residuals relation, we find it to be linear with lightcurve colour. We show hints of a potential evolution of $\beta$ with host stellar mass at a $2.5\sigma$ level. Finally, unlike recent claims from the literature, we see no evolution of steps as a function of lightcurve colour, suggesting that dust may not be the dominating mechanism responsible for the environmental dependency of SNe Ia magnitude., Comment: 10 pages, 7 figures, submitted to Astronomy and Astrophysics

Understanding Type Ia supernovae (SNe~Ia) and the empirical standardisation relations that make them excellent distance indicators is vital to improving cosmological constraints. SN~Ia ``siblings", i.e. two or more SNe~Ia in the same host or parent galaxy offer a unique way to infer the standardisation relations and their diversity across the population. We analyse a sample of 25 SN~Ia pairs, observed homogeneously by the Zwicky Transient Factory (ZTF) to infer the SNe~Ia light curve width-luminosity and colour-luminosity parameters $\alpha$ and $\beta$. Using the pairwise constraints from siblings, allowing for a diversity in the standardisation relations, we find $\alpha = 0.218 \pm 0.055 $ and $\beta = 3.084 \pm 0.312$, respectively, with a dispersion in $\alpha$ and $\beta$ of $\leq 0.195$ and $\leq 0.923$, respectively, at 95$\%$ C.L. While the median dispersion is large, the values within $\sim 1 \sigma$ are consistent with no dispersion. Hence, fitting for a single global standardisation relation, we find $\alpha = 0.228 \pm 0.029 $ and $\beta = 3.160 \pm 0.191$. We find a very small intrinsic scatter of the siblings sample $\sigma_{\rm int} \leq 0.10$ at 95\% C.L. compared to $\sigma_{\rm int} = 0.22 \pm 0.04$ when computing the scatter using the Hubble residuals without comparing them as siblings. Splitting the sample based on host galaxy stellar mass, we find that SNe~Ia in both subsamples have consistent $\alpha$ and $\beta$. The $\beta$ value is consistent with the value for the cosmological sample. However, we find a higher $\alpha$ by $\sim 2.5 - 3.5 \sigma$. The high $\alpha$ is driven by low $x_1$ pairs, potentially suggesting that the slow and fast declining SN~Ia have different slopes of the width-luminosity relation. We can confirm or refute this with increased statistics from near future time-domain surveys. (abridged), Comment: 12 pages, 7 figures, submitted to A&A

Understanding the impact of the astrophysical environment on Type Ia supernova (SN Ia) properties is crucial to minimize systematic uncertainties in cosmological analyses based on this probe. We investigate the dependence of the SN Ia SALT2.4 light-curve stretch on the distance from their nearest galaxy cluster to study a potential effect of the intracluster medium (ICM) environment on SN Ia intrinsic properties. We use the largest SN Ia sample to date and cross-match it with existing X-ray, Sunyaev-Zel'dovich, and optical cluster catalogs in order to study the dependence between stretch and distance to the nearest detected cluster from each SN Ia. We model the underlying stretch distribution with a Gaussian mixture with relative amplitudes that depend on redshift and cluster-centric distance. We find a significant improvement of the fit quality of the stretch distribution if we include the distance-dependant term in the model with a variation of the Akaike information criterion $\rm{\Delta AIC} = -10.2$. Because of the known correlation between galaxy age and distance from cluster center, this supports previous evidence that the age of the stellar population is the underlying driver of the bimodial shape of the SN Ia stretch distribution. We further compute the evolution of the fraction of quenched galaxies as a function of distance with respect to cluster center from our best-fit model of the SNe Ia stretch distribution and compare it to previous results obtained from $H\alpha$ line measurements, optical broadband photometry, and simulations. We find our estimate to be compatible with these results. The results of this work indicate that SNe Ia searches at high redshift targeted towards clusters to maximize detection probability should be considered with caution as the stretch distribution of the detected sample would be strongly biased towards the old sub-population of SNe Ia., Comment: Accepted in Astronomy & Astrophysics

To get distances, Type Ia Supernovae magnitudes are corrected for their correlation with lightcurve width and colour. Here we investigate how this standardisation is affected by the SN environment, with the aim to reduce scatter and improve standardisation. We first study the SN Ia stretch distribution, as well as its dependence on environment, as characterised by local and global (g-z) colour and stellar mass. We then look at the standardisation parameter $\alpha$, which accounts for the correlation between residuals and stretch, along with its environment dependence and linearity. We finally compute magnitude offsets between SNe in different astrophysical environments after colour and stretch standardisation, aka steps. This analysis is made possible due to the unprecedented statistics of the ZTF SN Ia DR2 volume-limited sample. The stretch distribution exhibits a bimodal behaviour, as previously found in literature. However, we find the distribution means to decrease with host stellar mass at a 9.0$\sigma$ significance. We demonstrate, at the 14.3$\sigma$ level, that the stretch-magnitude relation is non-linear, challenging the usual linear stretch-residuals relation. Fitting for a broken-$\alpha$ model, we indeed find two different slopes between stretch regimes ($x_1<-0.49\pm0.06$): $\alpha_{low}=0.28\pm0.01$ and $\alpha_{high}=0.09\pm0.01$, a $\Delta_{\alpha}=-0.19\pm0.01$ difference. As the relative proportion of SNe Ia in the high-/low-stretch modes evolves with redshift and environment, this implies that a linear $\alpha$ also evolves with redshift and environment. Concerning the environmental magnitude offset $\gamma$, we find it to be greater than 0.14 mag regardless of the considered environmental tracer used (local or global colour and stellar mass), all measured at the $\geq 6\sigma$ level, increased to $\sim0.18\pm0.01$ mag when accounting for the stretch-non linearity., Comment: 15 pages, 9 figures, submitted to Astronomy and Astrophysics

SNe Ia are used to determine the distance-redshift relation and build the Hubble diagram. Neglecting their host-galaxy peculiar velocities (PVs) may bias the measurement of cosmological parameters. The smaller the redshift, the larger the effect is. We use realistic simulations of SNe Ia observed by the Zwicky Transient Facility (ZTF) to investigate the effect of different methods to take into account PVs. We study the impact of neglecting galaxy PVs and their correlations in an analysis of the SNe Ia Hubble diagram. We find that it is necessary to use the PV full covariance matrix computed from the velocity power spectrum to take into account the sample variance. Considering the results we have obtained using simulations, we determine the PV systematic effects in the context of the ZTF DR2 SNe Ia sample. We determine the PV impact on the intercept of the Hubble diagram, $a_B$, which is directly linked to the measurement of $H_0$. We show that not taking into account PVs and their correlations results in a shift of the $H_0$ value of about $1.0$km.s$^{-1}$.Mpc$^{-1}$ and a slight underestimation of the $H_0$ error bar., Comment: 12 pages, 4 figures

The Zwicky Transient Facility (ZTF) was expected to detect more than one strong gravitationally-lensed supernova (glSN) per year, but only one event was identified in the first four years of the survey. This work investigates selection biases in the search strategy that could explain the discrepancy and revise discovery predictions. We present simulations of realistic lightcurves for lensed thermonuclear (glSNIa) and core-collapse supernova (glCCSN) explosions over a span of 5.33 years of the survey, utilizing the actual observation logs of ZTF. We find that the magnitude limit in spectroscopic screening significantly biases the selection towards highly magnified glSNe, for which the detection rates are consistent with the identification of a single object by ZTF. To reach the higher predicted rate of detections requires an optimization of the identification criteria for fainter objects. We find that around 1.36 (3.08) Type Ia SNe (CCSNe) are identifiable with the magnification method per year in ZTF, but when applying the magnitude cut of m < 19 mag, the detection rates decrease to 0.17 (0.32) per year. We compare our simulations with the previously found lensed Type Ia SNe, iPTF16geu and SN Zwicky, and conclude that considering the bias towards highly magnified events, the findings are within expectations in terms of detection rates and lensing properties of the systems. In addition, we provide a set of selection cuts based on simple observables to distinguish glSNe from regular, unlensed, supernovae to select potential candidates for spectroscopic and high-spatial resolution follow-up campaigns. We find optimal cuts in observed colours $g-r$, $g-i$, and $r-i$ as well as in the colour SALT2 fit parameter. The developed pipeline and the simulated lightcurves employed in this analysis can be found in the $LENSIT$ github repository., Comment: 12 pages, 14 figures

Gravitationally lensed Type Ia supernovae (glSNe Ia) are unique astronomical tools for studying cosmological parameters, distributions of dark matter, the astrophysics of the supernovae and the intervening lensing galaxies themselves. Only a few highly magnified glSNe Ia have been discovered by ground-based telescopes, such as the Zwicky Transient Facility (ZTF), but simulations predict the existence of a fainter, undetected population. We present a systematic search in the ZTF archive of alerts from 1 June 2019 to 1 September 2022. Using the AMPEL platform, we developed a pipeline that distinguishes candidate glSNe Ia from other variable sources. Initial cuts were applied to the ZTF alert photometry before forced photometry was obtained for the remaining candidates. Additional cuts were applied to refine the candidates based on their light curve colours, lens galaxy colours, and the resulting parameters from fits to the SALT2 SN Ia template. Candidates were also cross-matched with the DESI spectroscopic catalogue. Seven transients passed all the cuts and had an associated galaxy DESI redshift, which we present as glSN Ia candidates. While superluminous supernovae (SLSNe) cannot be fully rejected, two events, ZTF19abpjicm and ZTF22aahmovu, are significantly different from typical SLSNe and their light curves can be modelled as two-image glSN Ia systems. From this two-image modelling, we estimate time delays of 22 $\pm$ 3 and 34 $\pm$ 1 days for the two events, respectively, which suggests that we have uncovered a population with longer time delays. The pipeline is efficient and sensitive enough to parse full alert streams. It is currently being applied to the live ZTF alert stream to identify and follow-up future candidates while active. This pipeline could be the foundation for glSNe Ia searches in future surveys, like the Vera C. Rubin Observatory's Legacy Survey of Space and Time., Comment: 21 pages, 15 figures

Supernova (SN) H0pe is a gravitationally lensed, triply-imaged, Type Ia SN (SN Ia) discovered in James Webb Space Telescope imaging of the PLCK G165.7+67.0 cluster of galaxies. Well-observed multiply-imaged SNe provide a rare opportunity to constrain the Hubble constant ($H_0$), by measuring the relative time delay between the images and modeling the foreground mass distribution. SN H0pe is located at $z=1.783$, and is the first SN Ia with sufficient light curve sampling and long enough time delays for an $H_0$ inference. Here we present photometric time-delay measurements and SN properties of SN H0pe. Using JWST/NIRCam photometry we measure time delays of $\Delta t_{ab}=-116.6^{+10.8}_{-9.3}$ and $\Delta t_{cb}=-48.6^{+3.6}_{-4.0}$ observer-frame days relative to the last image to arrive (image 2b; all uncertainties are $1\sigma$), which corresponds to a $\sim5.6\%$ uncertainty contribution for $H_0$ assuming $70 \rm{km s^{-1} Mpc^{-1}}$. We also constrain the absolute magnification of each image to $\mu_{a}=4.3^{+1.6}_{-1.8}$, $\mu_{b}=7.6^{+3.6}_{-2.6}$, $\mu_{c}=6.4^{+1.6}_{-1.5}$ by comparing the observed peak near-IR magnitude of SN H0pe to the non-lensed population of SNe Ia., Comment: Accepted in ApJ

Observing a supernova explosion shortly after it occurs can reveal important information about the physics of stellar explosions and the nature of the progenitor stars of supernovae (SNe). When a star with a well-defined edge explodes in vacuum, the first photons to escape from its surface appear as a brief shock-breakout flare. The duration of this flare can extend to at most a few hours even for nonspherical breakouts from supergiant stars, after which the explosion ejecta should expand and cool. Alternatively, for stars exploding within a distribution of sufficiently dense optically thick circumstellar material, the first photons escape from the material beyond the stellar edge, and the duration of the initial flare can extend to several days, during which the escaping emission indicates photospheric heating. The difficulty in detecting SN explosions promptly after the event has so far limited data regarding supergiant stellar explosions mostly to serendipitous observations that, owing to the lack of ultraviolet (UV) data, were unable to determine whether the early emission is heating or cooling, and hence the nature of the early explosion event. Here, we report observations of SN 2023ixf in the nearby galaxy M101, covering the early days of the event. Using UV spectroscopy from the Hubble Space Telescope (HST) as well as a comprehensive set of additional multiwavelength observations, we trace the photometric and spectroscopic evolution of the event and are able to temporally resolve the emergence and evolution of the SN emission.

Supernovae (SNe) that have been multiply-imaged by gravitational lensing are rare and powerful probes for cosmology. Each detection is an opportunity to develop the critical tools and methodologies needed as the sample of lensed SNe increases by orders of magnitude with the upcoming Vera C. Rubin Observatory and Nancy Grace Roman Space Telescope. The latest such discovery is of the quadruply-imaged Type Ia SN 2022qmx (aka, "SN Zwicky") at $z=0.3544$. SN Zwicky was discovered by the Zwicky Transient Facility (ZTF) in spatially unresolved data. Here we present follow-up Hubble Space Telescope observations of SN Zwicky, the first from the multi-cycle "LensWatch" program. We measure photometry for each of the four images of SN Zwicky, which are resolved in three WFC3/UVIS filters (F475W, F625W, F814W) but unresolved with WFC3/IR~F160W, and present an analysis of the lensing system using a variety of independent lens modeling methods. We find consistency between lens model predicted time delays ($\lesssim1$ day), and delays estimated with the single epoch of HST colors ($\lesssim3.5$ days), including the uncertainty from chromatic microlensing ($\sim1$-$1.5$ days). Our lens models converge to an Einstein radius of $\theta_E=(0.168^{+0.009}_{-0.005})\prime\prime$, the smallest yet seen in a lensed SN system. The "standard candle" nature of SN Zwicky provides magnification estimates independent of the lens modeling that are brighter than predicted by $\sim1.7^{+0.8}_{-0.6}$mag and $\sim0.9^{+0.8}_{-0.6}$mag for two of the four images, suggesting significant microlensing and/or additional substructure beyond the flexibility of our image-position mass models.

The observed magnifications and light curves of the quadruply-imaged iPTF16geu supernova (SN) offers a unique opportunity to study a lens system with a variety of independent constraints. The four observed positions can be used to constrain the macrolens model. The magnifications and light curves at the four SN positions are more useful to constrain microlensing models. We define the macrolens model as a combination of a baryonic component that traces the observed light distribution, and a dark matter halo component. We constrain the macrolens model using the positional constraints given by the 4 observed images, and compare it with the best model obtained when magnification constraints are included. We find that the magnification can not be explained by a macrolens model alone, and that contributions from substructures such as microlenses are needed to explain the observed magnifications. We consider microlens models based on the inferred stellar mass from the baryonic component of the macrolens model, and use the observed magnification and light curves to constrain the contribution from microlenses. We compute the likelihood of a variety of macro+micro lens models where we vary the dark matter halo, baryonic component, and microlens configurations. We use information about the position, magnification and, for the first time, the lightcurves of the four observed SN images. We combine macrolens and microlens models in order to reproduce the observations; the four SN positions, magnifications, and lack of fluctuations in the light curves. After marginalizing over the model parameters, we find that larger stellar surface mass densities are preferred. This result suggests that the mass of the baryonic component is dominated by its stellar component. We conclude that microlensing from the baryonic component suffices to explain the observed flux ratios and light curves., Comment: 21 pages and 30 figures

Type Ia supernovae (SNe~Ia) in the nearby Hubble flow are excellent distance indicators in cosmology. The Zwicky Transient Facility (ZTF) has observed a large sample of supernovae from an untargeted, rolling survey, reaching $20.8, 20.6, 20.3$ mag in $g$ $r$, and $i$-band, respectively. With a FoV of 47 sq.deg, ZTF discovered $>$ 3000 SNe~Ia in a little over 2.5 years. Here, we report on the sample of 761 spectroscopically classified SNe~Ia from the first year of operations (DR1). The sample has a median redshift $\bar z =$ 0.057, nearly a factor of two higher than the current low-$z$ sample. Our sample has a total of 934 spectra, of which 632 were obtained with the robotic SEDm on Palomar P60. We assess the potential for precision cosmology for a total of 305 SNe with redshifts from host galaxy spectra. The sample is already comparable in size to the entire combined literature low-$z$ anchor sample. The median first detection is 13.5 days before maximum light, about 10 days earlier than the median in the literature. Furthermore, six SNe from our sample are at $D_L < 80$ Mpc, for which host galaxy distances can be obtained in the JWST era, such that we have calibrator and Hubble flow SNe observed with the same instrument. In the entire duration of ZTF-I, we have observed nearly fifty SNe for which we can obtain calibrator distances, key for percent level distance scale measurements., Comment: 16 pages, 9 figures, accepted for publication in MNRAS. Data and associated information for the sample can be found at https://github.com/ZwickyTransientFacility/ztfcosmodr

We describe the development of a broadband magneto-optical spectrometer with femtosecond temporal resolution. The absorption spectrometer is based on a white-light supercontinuum (ca. 320 - 750 nm) using shot-to-shot temporal and spectral referencing at 1 kHz. Static and transient absorption spectra using circularly polarised light are collected in a magnetic field. The difference spectra with respect to the external field direction give the static and transient magneto-optical Faraday rotation (magnetic optical rotary dispersion) and ellipticity (magnetic circular dichroism) spectra. An achromatic quarter-wave plate is used and the impact of the deviation from ideal retardance on the spectra is discussed. Results from solution-based and thin-film samples are used to demonstrate the performance and wide applicability of the instrument. The sensitivities for the static and time-resolved data were found to be 5 and 0.4 mdeg, respectively. The method presents a simple way to measure magneto-optical spectra using a transient absorption spectrometer and an electromagnet., Comment: The following article has been submitted to Review of Scientific Instruments

We present optical and near-infrared (NIR, $YJH$-band) observations of 42 Type Ia supernovae (SNe Ia) discovered by the untargeted intermediate Palomar Transient Factory (iPTF) survey. This new data-set covers a broad range of redshifts and host galaxy stellar masses, compared to previous SN Ia efforts in the NIR. We construct a sample, using also literature data at optical and NIR wavelengths, to examine claimed correlations between the host stellar masses and the Hubble diagram residuals. The SN magnitudes are corrected for host galaxy extinction using either a global total-to-selective extinction ratio, $R_V$=2.0 for all SNe, or a best-fit $R_V$ for each SN individually. Unlike previous studies which were based on a narrower range in host stellar mass, we do not find evidence for a "mass-step", between the color- and stretch-corrected peak $J$ and $H$ magnitudes for galaxies below and above $\log(M_{*}/M_{\odot}) = 10$. However, the mass-step remains significant ($3\sigma$) at optical wavelengths ($g,r,i$) when using a global $R_V$, but vanishes when each SN is corrected using their individual best-fit $R_V$. Our study confirms the benefits of the NIR SN Ia distance estimates, as these are largely exempted from the empirical corrections dominating the systematic uncertainties in the optical., Comment: 20 pages, 13 figures. Submitted to ApJ. Comments are welcome!

We present the bolometric lightcurve, identification and analysis of the progenitor candidate, and preliminary modelling of AT2016jbu (Gaia16cfr). We find a progenitor consistent with a $\sim$22--25~$M_{\odot}$ yellow hypergiant surrounded by a dusty circumstellar shell, in agreement with what has been previously reported. We see evidence for significant photometric variability in the progenitor, as well as strong H$\alpha$ emission consistent with pre-existing circumstellar material. The age of the environment as well as the resolved stellar population surrounding AT2016jbu, support a progenitor age of $>$10 Myr, consistent with a progenitor mass of $\sim$22~$M_{\odot}$. A joint analysis of the velocity evolution of AT2016jbu, and the photospheric radius inferred from the bolometric lightcurve shows the transient is consistent with two successive outbursts/explosions. The first outburst ejected material with velocity $\sim$650$kms^{-1}$, while the second, more energetic event, ejected material at $\sim$4500$kms^{-1}$. Whether the latter is the core-collapse of the progenitor remains uncertain. We place a limit on the ejected $^{56}$Ni mass of $<$0.016$M_{\odot}$. Using the BPASS code, we explore a wide range of possible progenitor systems, and find that the majority of these are in binaries, some of which are undergoing mass transfer or common envelope evolution immediately prior to explosion. Finally, we use the SNEC code to demonstrate that the low-energy explosion within some of these binary systems, together with sufficient CSM, can reproduce the overall morphology of the lightcurve of AT2016jbu., Comment: 23 pages, 15 figures, accepted for publication in MNRAS

We present the results from a high cadence, multi-wavelength observation campaign of AT 2016jbu (aka Gaia16cfr), an interacting transient. This dataset complements the current literature by adding higher cadence as well as extended coverage of the lightcurve evolution and late-time spectroscopic evolution. Photometric coverage reveals that AT 2016jbu underwent significant photometric variability followed by two luminous events, the latter of which reached an absolute magnitude of M$_V\sim$-18.5 mag. This is similar to the transient SN 2009ip whose nature is still debated. Spectra are dominated by narrow emission lines and show a blue continuum during the peak of the second event. AT 2016jbu shows signatures of a complex, non-homogeneous circumstellar material (CSM). We see slowly evolving asymmetric hydrogen line profiles, with velocities of 500km$s^{-1}$ seen in narrow emission features from a slow moving CSM, and up to 10,000km$s^{-1}$ seen in broad absorption from some high velocity material. Late-time spectra ($\sim$+1 year) show a lack of forbidden emission lines expected from a core-collapse supernova and are dominated by strong emission from H, He i and Ca ii. Strong asymmetric emission features, a bumpy lightcurve, and continually evolving spectra suggest an inhibit nebular phase. We compare the evolution of H$\alpha$ among SN 2009ip-like transients and find possible evidence for orientation angle effects. The light-curve evolution of AT 2016jbu suggests similar, but not identical, circumstellar environments to other SN 2009ip-like transients., Comment: 27 pages, 21 figures, accepted for publication in MNRAS

We report the results from spectroscopic observations of the multiple images of the strongly lensed Type Ia supernova (SN Ia), iPTF16geu, obtained with ground based telescopes and the Hubble Space Telescope (HST). From a single epoch of slitless spectroscopy with HST, we can resolve spectra of individual lensed supernova images for the first time. This allows us to perform an independent measurement of the time-delay between the two brightest images, $\Delta t = 1.4 \pm 5.0$ days, which is consistent with the time-delay measured from the light-curves. We also present measurements of narrow emission and absorption lines characterizing the interstellar medium in the host galaxy at z=0.4087, as well as in the foreground lensing galaxy at z=0.2163. We detect strong Na ID absorption in the host galaxy, indicating that iPTF16geu belongs to a subclass of SNe Ia displaying "anomalously" large Na ID column densities in comparison to the amount of dust extinction derived from their light curves. For the deflecting galaxy, we refine the measurement of the velocity dispersion, $\sigma = 129 \pm 4$ km/s, which significantly constrains the lens model. Since the time-delay between the SN images is negligible, we can use unresolved ground based spectroscopy, boosted by a factor ~70 from lensing magnification, to study the properties of a high-z SN Ia with unprecedented signal-to-noise ratio. The spectral properties of the supernova, such as pseudo-Equivalent widths of several absorption features and velocities of the Si II-line indicate that iPTF16geu, besides being lensed, is a normal SN Ia, indistinguishable from well-studied ones in the local universe, providing support for the use of SNe Ia in precision cosmology. We do not detect any significant deviations of the SN spectral energy distribution from microlensing of the SN photosphere by stars and compact objects in the lensing galaxy., Comment: 10 pages, 10 figures. Comments are welcome!

In 2016, the first strongly lensed Type Ia supernova, iPTF16geu at redshift $z=0.409$ with four resolved images arranged symmetrically around the lens galaxy at $z=0.2163$, was discovered. Here, refined observations of iPTF16geu, including the time delay between images, are used to decrease uncertainties in the lens model, including the the slope of the projected surface density of the lens galaxy, $\Sigma\propto r^{1-\eta}$, and to constrain the universal expansion rate $H_0$. Imaging with HST provides an upper limit on the slope $\eta$, in slight tension with the steeper density profiles indicated by imaging with Keck after iPTF16geu had faded, potentially due to dust extinction not corrected for in host galaxy imaging. Since smaller $\eta$ implies larger magnifications, we take advantage of the standard candle nature of Type Ia supernovae constraining the image magnifications, to obtain an independent constraint of the slope. We find that a smooth lens density fails to explain the iPTF16geu fluxes, regardless of the slope, and additional sub-structure lensing is needed. The total probability for the smooth halo model combined with star microlensing to explain the iPTF16geu image fluxes is maximized at $12\,\%$ for $\eta\sim 1.8$, in excellent agreement with Keck high spatial resolution data, and flatter than an isothermal halo. It also agrees perfectly with independent constraints on the slope from lens velocity dispersion measurements. Combining with the observed time delays between the images, we infer a lower bound on the Hubble constant, $H_0 \gtrsim 40\,{\rm km \ s^{-1} Mpc^{-1}}$ at $68.3\,\%$ confidence level., Comment: 12 pages, 9 figures. Expanded version with improved constraints accepted for publication in MNRAS

We report lensing magnifications, extinction, and time-delay estimates for the first resolved, multiply-imaged Type Ia supernova iPTF16geu, at $z = 0.409$, using $Hubble\,Space\,Telescope$ ($HST$) observations in combination with supporting ground-based data. Multi-band photometry of the resolved images provides unique information about the differential dimming due to dust in the lensing galaxy. Using $HST$ and Keck AO reference images taken after the SN faded, we obtain a total lensing magnification for iPTF16geu of $\mu = 67.8^{+2.6}_{-2.9}$, accounting for extinction in the host and lensing galaxy. As expected from the symmetry of the system, we measure very short time-delays for the three fainter images with respect to the brightest one: -0.23 $\pm$ 0.99, -1.43 $\pm$ 0.74 and 1.36 $\pm$ 1.07 days. Interestingly, we find large differences between the magnifications of the four supernova images, even after accounting for uncertainties in the extinction corrections: $\Delta m_1 = -3.88^{+0.07}_{-0.06}$, $\Delta m_2 = -2.99^{+0.09}_{-0.08}$, $\Delta m_3 = -2.19^{+0.14}_{-0.15}$ and $\Delta m_4 = -2.40^{+0.14}_{-0.12}$ mag, discrepant with model predictions suggesting similar image brightnesses. A possible explanation for the large differences is gravitational lensing by substructures, micro- or millilensing, in addition to the large scale lens causing the image separations. We find that the inferred magnification is insensitive to the assumptions about the dust properties in the host and lens galaxy., Comment: 18 pages, 8 figures accepted to MNRAS

We present the best 265 sampled R-band light curves of spectroscopically identified Type Ia supernovae (SNe) from the Palomar Transient Factory (PTF; 2009-2012) survey and the intermediate Palomar Transient Factory (iPTF; 2013-2017). A model-independent light curve template is built from our data-set with the purpose to investigate average properties and diversity in our sample. We searched for multiple populations in the light curve properties using machine learning tools. We also utilised the long history of our light curves, up to 4000 days, to exclude any significant pre- or post- supernova flares. From the shapes of light curves we found the average rise time in the R band to be $16.8^{+0.5}_{-0.6}$ days. Although PTF/iPTF were single-band surveys, by modelling the residuals of the SNe in the Hubble-Lema\^{i}tre diagram, we estimate the average colour excess of our sample to be $<$E$($B$-$V$)> \approx 0.05(2)$ mag and thus the mean corrected peak brightness to be $M_R = -19.02\pm0.02$ $+5 \log( {\rm H}_0 [{\rm km} \cdot{\rm s}^{-1} {\rm Mpc}^{-1}]/70)$ mag with only weakly dependent on light curve shape. The intrinsic scatter is found to be $\sigma_R = 0.186 \pm 0.033$ mag for the redshift range $0.05

Key information about the progenitor system and the explosion mechanism of Type Ia supernovae (SNe~Ia) can be obtained from early observations, within a few days from explosion. iPTF16abc was discovered as a young SN~Ia with excellent early time data. Here, we present photometry and spectroscopy of the SN in the nebular phase. A comparison of the early time data with a sample of SNe~Ia shows distinct features, differing from normal SNe~Ia at early phases but similar to normal SNe~Ia at a few weeks after maximum light (i.e. the transitional phase) and well into the nebular phase. The transparency timescales ($t_0$) for this sample of SNe~Ia range between $\sim$ 25 and 41 days indicating a diversity in the ejecta masses. $t_0$ also weakly correlates with the peak bolometric luminosity, consistent with the interpretation that SNe with higher ejecta masses would produce more $^{56}$Ni. Comparing the $t_0$ and the maximum luminosity, L$_{max}$\, distribution of a sample of SNe~Ia to predictions from a wide range of explosion models we find an indication that the sub-Chandrasekhar mass models span the range of observed values. However, the bright end of the distribution can be better explained by Chandrasekhar mass delayed detonation models, hinting at multiple progenitor channels to explain the observed bolometric properties of SNe~Ia. iPTF16abc appears to be consistent with the predictions from the M$_{ch}$ models., Comment: 13 pages, 8 figures, accepted for publication in MNRAS

We report the discovery of a multiply-imaged gravitationally lensed Type Ia supernova, iPTF16geu (SN 2016geu), at redshift $z=0.409$. This phenomenon could be identified because the light from the stellar explosion was magnified more than fifty times by the curvature of space around matter in an intervening galaxy. We used high spatial resolution observations to resolve four images of the lensed supernova, approximately 0.3" from the center of the foreground galaxy. The observations probe a physical scale of $\sim$1 kiloparsec, smaller than what is typical in other studies of extragalactic gravitational lensing. The large magnification and symmetric image configuration implies close alignment between the line-of-sight to the supernova and the lens. The relative magnifications of the four images provide evidence for sub-structures in the lensing galaxy., Comment: Matches published version

We present photometry and time-series spectroscopy of the nearby type Ia supernova (SN Ia) SN 2015F over $-16$ days to $+80$ days relative to maximum light, obtained as part of the Public ESO Spectroscopic Survey of Transient Objects (PESSTO). SN 2015F is a slightly sub-luminous SN Ia with a decline rate of $\Delta m15(B)=1.35 \pm 0.03$ mag, placing it in the region between normal and SN 1991bg-like events. Our densely-sampled photometric data place tight constraints on the epoch of first light and form of the early-time light curve. The spectra exhibit photospheric C II $\lambda 6580$ absorption until $-4$ days, and high-velocity Ca II is particularly strong at $<-10$ days at expansion velocities of $\simeq$23000\kms. At early times, our spectral modelling with syn++ shows strong evidence for iron-peak elements (Fe II, Cr II, Ti II, and V II) expanding at velocities $>14000$ km s$^{-1}$, suggesting mixing in the outermost layers of the SN ejecta. Although unusual in SN Ia spectra, including V II in the modelling significantly improves the spectral fits. Intriguingly, we detect an absorption feature at $\sim$6800 \AA\ that persists until maximum light. Our favoured explanation for this line is photospheric Al II, which has never been claimed before in SNe Ia, although detached high-velocity C II material could also be responsible. In both cases the absorbing material seems to be confined to a relatively narrow region in velocity space. The nucleosynthesis of detectable amounts of Al II would argue against a low-metallicity white dwarf progenitor. We also show that this 6800 \AA\ feature is weakly present in other normal SN Ia events, and common in the SN 1991bg-like sub-class., Comment: Accepted for publication in MNRAS

When a star passes within the tidal radius of a supermassive black hole, it will be torn apart. For a star with the mass of the Sun ($M_\odot$) and a non-spinning black hole with a mass $<10^8 M_\odot$, the tidal radius lies outside the black hole event horizon and the disruption results in a luminous flare. Here we report observations over a period of 10 months of a transient, hitherto interpreted as a superluminous supernova. Our data show that the transient rebrightened substantially in the ultraviolet and that the spectrum went through three different spectroscopic phases without ever becoming nebular. Our observations are more consistent with a tidal disruption event than a superluminous supernova because of the temperature evolution, the presence of highly ionised CNO gas in the line of sight and our improved localisation of the transient in the nucleus of a passive galaxy, where the presence of massive stars is highly unlikely. While the supermassive black hole has a mass $> 10^8 M_\odot$, a star with the same mass as the Sun could be disrupted outside the event horizon if the black hole were spinning rapidly. The rapid spin and high black hole mass can explain the high luminosity of this event., Comment: Modified after proofs to match published version as much as possible. 56 pages, 12 figures, 2 tables, including Methods and Supplementary Information. A photometry file is linked here as ancillary file. All data (photometry and spectra) are also publicly available from WISeREP

Temporal variability of narrow absorption lines in high-resolution spectra of Type Ia supernovae (SNe Ia) is studied to search for circumstellar matter. Time series which resolve the profiles of absorption lines such as Na I D or Ca II H&K are expected to reveal variations due to photoionisation and subsequent recombination of the gases. The presence, composition, and geometry of circumstellar matter may hint at the elusive progenitor system of SNe Ia and could also affect the observed reddening law. To date, there are few known cases of time-varying Na I D absorption in SNe Ia, all of which occurred during relatively late phases of the supernova evolution. Photoionisation, however, is predicted to occur during the early phases of SNe Ia, when the supernova peaks in the ultraviolet. We therefore attempt to observe early-time absorption-line variations by obtaining high-resolution spectra of SNe before maximum light. We have obtained photometry and high-resolution spectroscopy of SNe Ia 2013gh and iPTF 13dge, to search for absorption- line variations. Furthermore, we study interstellar absorption features in relation to the observed photometric colours of the SNe. Results. Both SNe display deep Na I D and Ca II H&K absorption features. Furthermore, small but significant variations are detected in a feature of the Na I D profile of SN 2013gh. The variations are consistent with either geometric effects of rapidly moving or patchy gas clouds or photoionisation of Na I gas at R \approx 1019 cm from the explosion. Our analysis indicates that it is necessary to focus on early phases to detect photoionisation effects of gases in the circumstellar medium of SNe Ia. Different absorbers such as Na I and Ca II can be used to probe for matter at different distances from the SNe., Comment: accepted for publication in A&A

Quantum mechanical effects induced by the miniaturization of complementary metal-oxide-semiconductor (CMOS) technology hamper the performance and scalability prospects of field-effect transistors. However, those quantum effects, such as tunnelling and coherence, can be harnessed to use existing CMOS technology for quantum information processing. Here, we report the observation of coherent charge oscillations in a double quantum dot formed in a silicon nanowire transistor detected via its dispersive interaction with a radio-frequency resonant circuit coupled via the gate. Differential capacitance changes at the inter-dot charge transitions allow us to monitor the state of the system in the strong-driving regime where we observe the emergence of Landau-Zener-St{\"u}ckelberg-Majorana interference on the phase response of the resonator. A theoretical analysis of the dispersive signal demonstrates that quantum and tunnelling capacitance changes must be included to describe the qubit-resonator interaction. Furthermore, a Fourier analysis of the interference pattern reveals a charge coherence time, $T_2\approx 100$~ps. Our results demonstrate charge coherent control and readout in a simple silicon transistor and open up the possibility to implement charge and spin qubits in existing CMOS technology.