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Type Ia supernovae (SNe Ia) constitute an historical probe to derive cosmological parameters through the fit of the Hubble-Lema\^itre diagram, i.e. SN Ia distance modulus versus their redshift. In the era of precision cosmology, realistic simulation of SNe Ia for any survey entering in an Hubble-Lema\^itre diagram is a key tool to address observational systematics, like Malmquist bias. As the distance modulus of SNe Ia is derived from the fit of their light-curves, a robust simulation framework is required. In this paper, we present the performances of the simulation framework skysurvey to reproduce the the Zwicky Transient Facility (ZTF) SN Ia DR2 covering the first phase of ZTF running from April 2018 up to December 2020. The ZTF SN Ia DR2 sample correspond to almost 3000 classified SNe Ia of cosmological quality. First, a targeted simulation of the ZTF SN Ia DR2 was carried on to check the validity of the framework after some fine tuning of the observing conditions and instrument performance. Then, a realistic simulation has been run using observing ZTF logs and ZTF SN Ia DR2 selection criteria on simulated light-curves to demonstrate the ability of the simulation framework to match the ZTF SN Ia DR2 sample. Furthermore a redshift dependency of SALT2 light-curve parameters (stretch and colour) was conducted to deduce a volume limited sample, i.e. an unbiased SNe Ia sample, characterized with $z_{lim} \leq 0.06$. This volume limited sample of about 1000 SNe Ia is unique to carry on new analysis on standardization procedure with a precision never reached (those analysis are presented in companion papers)., Comment: 10 pages, 10 figures. Submitted to A & A

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

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.

We present an in-depth study of the late-time near-infrared plateau in Type Ia supernovae (SNe Ia), which occurs between 70-500 d. We double the existing sample of SNe Ia observed during the late-time near-infrared plateau with new observations taken with the Hubble Space Telescope, Gemini, New Technology Telescope, the 3.5m Calar Alto Telescope, and the Nordic Optical Telescope. Our sample consists of 24 nearby SNe Ia at redshift < 0.025. We are able to confirm that no plateau exists in the Ks band for most normal SNe Ia. SNe Ia with broader optical light curves at peak tend to have a higher average brightness on the plateau in J and H, most likely due to a shallower decline in the preceding 100 d. SNe Ia that are more luminous at peak also show a steeper decline during the plateau phase in H. We compare our data to state-of-the-art radiative transfer models of nebular SNe Ia in the near-infrared. We find good agreement with the sub-Mch model that has reduced non-thermal ionisation rates, but no physical justification for reducing these rates has yet been proposed. An analysis of the spectral evolution during the plateau demonstrates that the ratio of [Fe II] to [Fe III] contribution in a near-infrared filter determines the light curve evolution in said filter. We find that overluminous SNe decline slower during the plateau than expected from the trend seen for normal SNe Ia, Comment: 17 pages, 8 figures, Accepted for publication in MNRAS

A thermonuclear explosion triggered by a helium-shell detonation on a carbon-oxygen white dwarf core has been predicted to have strong UV line blanketing at early times due to the iron-group elements produced during helium-shell burning. We present the photometric and spectroscopic observations of SN 2016dsg, a sub-luminous peculiar Type I SN consistent with a thermonuclear explosion involving a thick He shell. With a redshift of 0.04, the $i$-band peak absolute magnitude is derived to be around -17.5. The object is located far away from its host, an early-type galaxy, suggesting it originated from an old stellar population. The spectra collected after the peak are unusually red, show strong UV line blanketing and weak O I $\lambda$7773 absorption lines, and do not evolve significantly over 30 days. An absorption line around 9700-10500 \AA is detected in the near-infrared spectrum and is likely from the unburnt helium in the ejecta. The spectroscopic evolution is consistent with the thermonuclear explosion models for a sub-Chandrasekhar mass white dwarf with a thick helium shell, while the photometric evolution is not well described by existing models., Comment: accepted for publication in ApJ

[Abridged] We classify AT 2020zso as a TDE based on the blackbody evolution inferred from UV/optical photometric observations, and spectral line content and evolution. We identify transient, double-peaked Bowen (N III), He I, He II and Halpha emission lines. We model medium resolution optical spectroscopy of the He II (after careful deblending of the N III contribution) and Halpha lines during the rise, peak and early decline of the light curve using relativistic, elliptical accretion disk models. We find that the spectral evolution before peak can be explained by optical depth effects consistent with an outflowing, optically thick Eddington envelope. Around peak the envelope reaches its maximum extent (approximately 10^15 or 3000-6000 gravitational radii for an inferred black hole mass of 5-10 10^5) and becomes optically thin. The Halpha and He II emission lines at and after peak can be reproduced with a highly inclined (i=85+-5 degrees), highly elliptical (e=0.97+-0.01) and relatively compact (Rin = several 100 Rg and Rout = several 1000 Rg ) accretion disk. Overall, the line profiles suggest a highly elliptical geometry for the new accretion flow, consistent with theoretical expectations of newly formed TDE disks. We quantitatively confirm, for the first time, the high inclination nature of a Bowen (and X-ray dim) TDE, consistent with the unification picture of TDEs where the inclination largely determines the observational appearance. Rapid line profile variations rule out the binary SMBH hypothesis as the origin of the eccentricity; these results thus provide a direct link between a TDE in an AGN and the eccentric accretion disk. We illustrate for the first time how optical spectroscopy can be used to constrain the black hole spin, through (the lack of) disk precession signatures (changes in inferred inclination) - and rule out high black hole spin values (a < 0.8)., Comment: 20 pages, 15 figures and 5 tables. Accepted for publication in A&A. The spectra will be made publicly available through WISErep

The division between stripped-envelope supernovae (SE-SNe) and superluminous supernovae (SLSNe) is not well defined in either photometric or spectroscopic space. While a sharp luminosity threshold has been suggested, there remains an increasing number of transitional objects that reach this threshold without the spectroscopic signatures common to SLSNe. In this work we present data and analysis on four SNe transitional between SE-SNe and SLSNe; the He-poor SNe 2019dwa and 2019cri, and the He-rich SNe 2019hge and 2019unb. Each object displays long-lived and variable photometric evolution with luminosities around the SLSN threshold of $M_r < -19.8$ mag. Spectroscopically however, these objects are similar to SE-SNe, with line velocities lower than either SE-SNe and SLSNe, and thus represent an interesting case of rare transitional events., Comment: Accepted for publication in MNRAS

In most strategy research, the focus is on ready-made models provided by the teacher or a textbook. However, in this research project the effects are described of an experimental program in primary maths education, concerning the construction and use of models by pupils in guided co-construction. Learning how to construct models is said to enhance the occurrence of transfer. Therefore, pupils in the experimental condition were expected to show a larger amount of transfer of the learned material than pupils in the control condition. In a field experiment, in which 239 grade-5 pupils were involved, this hypothesis was tested. In a series of experimental lessons, pupils were taught to design models as a tool in the learning of percentages. The scores on the transfer test of pupils in the experimental condition were compared to the scores of their counterparts in the control group, which was based on the teachers' strategy of directly providing ready-made models to the pupils. The conclusion, then, is that children in the experimental condition significantly outperform children in the control condition in terms of transfer. (Contains 35 references.) (Author/ASK)

A program designed to help teachers in the Netherlands put a form of mixed ability teaching into practice was evaluated for its implementation and effects. Implemented with 14-year-old students, the program consisted of whole class instruction by teachers, followed by guidance of small groups and individuals. Cooperative learning in small groups, mathematics set in real life situations, and different levels in the learning process were features of the program. The program was compared with a more traditional program for pre-test and post-test results. Antecedents were measured by a pretest and attitude scale. Processes were measured by a student questionnaire, the PERception of the Curriculum In Action (PERCIA)-scale. Outcomes were measured by a parallel version of the pre-test for learning results in the cognitive domain. Implementation of this program had a positive effect on learning results. Differences in implementation found in various classes had a significant effect on learning results. Teacher training and guidance can reduce variations in implementation, although class composition remains an important factor. (SLD)