SearcharxivSearch

arXiv subjects

D. Fouchez

Publications and source records attributed to D. Fouchez.

At least 19 recordsLinked to original sources

Study of the anisotropy of cosmic expansion on ZTF type Iasupernovae simulations

The cosmological principle assumes the isotropy of the Universe at large scales. It is a foundational assumption in the $\Lambda$CDM model, which is the current standard model of cosmology. Recent tensions give legitimacy to investigating the possibility of anisotropies in the Universe. The large sky coverage achieved by the Zwicky Transient Facility survey (ZTF) allows us to test the veracity of the cosmological principle using observations of Type Ia supernovae (SNe Ia). In this article, we develop a methodology to measure potential anisotropies in the Hubble constant $H_0$. We test our method on realistic simulations of the second data release (DR2) of ZTF SNe Ia in which we introduce a dipole. We develop an unbiased method both to introduce a dipole in the simulations and to recover it. We test a potential $H_0$ dependency of our method while varying the dipole amplitude. We analyse the impact of introducing large-scale structures in the simulations and the efficiency of using a volume-limited sample, which is an unbiased subsample of the ZTF SNe Ia sample. Finally, we build an error model applied to the recovered dipole amplitude ($\Delta H_0$) and its direction ($\alpha_0$, $\delta_0$). Our analysis allows us to recover a dipole with an error on the amplitude of $0.33\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$, and uncertainties of $3.4^\circ$ and $6.1^\circ$ on the right ascension and declination, respectively, for an initial dipole amplitude of $\Delta H_0 = 3\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$. The resulting dipole is independent of the chosen $H_0$ value and sky coverage. This paper paves the way for a future precise ZTF dipole investigation.

astro-ph.CO

ZTF SNe Ia DR2: Towards cosmology-grade ZTF supernova light curves using scene modeling photometry

The Zwicky Transient Facility (ZTF) is conducting a wide-field survey of the northern sky in three optical bands and the collaboration cosmology working group has released 3628 spectroscopically confirmed Type Ia supernovae (SNe Ia) discovered during its first 2.5 years of operation. This "ZTF SN Ia DR2" sample is the largest SN Ia dataset to date. Fully exploiting this dataset to improve understanding of the properties of dark energy requires a photometric accuracy of O(0.1%). This can be achieved using Scene Modeling Photometry (SMP), which is optimal to extract a transient signal (SN) from a complex background (its host), while ensuring a common flux estimator with nearby stars used as calibration reference. In this paper, we present the status of the SMP development and use it to assess the precision and accuracy of the ZTF SN Ia DR2 force photometry light curves. We reach a repeatability of the star observations better than 1%. However, we have identified a new sensor effect, dubbed "pocket-effect", which distorts the Point Spread Function (PSF) in a flux-dependent manner leading to non-linearities in the photometry of a few percent. Correcting for this effect requires time- and sensor-dependent corrections to be applied at the pixel level, which is currently under development. This effects affects all light curve releases to date -- both from forced photometry and scene modelling preventing ZTF SN Ia DR2 to be used for accurate cosmological inference. Comparing the SMP and forced photometry measurements, we find that stretch and color estimated from both processings are consistent, aside from a 10 mmag shift in color. This assess the robustness of results presented as part of the the ZTF SN Ia DR2 release. The absolute calibration however shifts by 90 mmag. A reprocessing of the full ZTF SN Ia DR2 dataset using the SMP method is currently in progress.

astro-ph.CO

An Agnostic Approach to Building Empirical Type Ia Supernova Light Curves: Evidence for Intrinsic Chromatic Flux Variation Using Nearby Supernova Factory Data

We present a new empirical Type Ia supernova (SN Ia) model with three chromatic flux variation templates: one phase dependent and two phase independent. No underlying dust extinction model or patterns of intrinsic variability are assumed. Implemented with Stan and trained using spectrally binned Nearby Supernova Factory spectrophotometry, we examine this model's 2D, phase-independent flux variation space using two motivated basis representations. In both, the first phase-independent template captures variation that appears dust-like, while the second captures a combination of effectively intrinsic variability and second-order dust-like effects. We find that approximately 13% of the modeled phase-independent flux variance is not dust-like. Previous empirical SN Ia models either assume an effective dust extinction recipe in their architecture, or only allow for a single mode of phase-independent variation. The presented results demonstrate such an approach may be insufficient, because it could "leak" noticeable intrinsic variation into phase-independent templates.

astro-ph.HE

ZTF SN Ia DR2: Exploring SN Ia properties in the vicinity of under-dense environments

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.

astro-ph.CO

ZTF SN Ia DR2: Evidence of Changing Dust Distributions With Redshift Using Type Ia Supernovae

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.

astro-ph.CO

ZTF SN Ia DR2: Study of Type Ia Supernova lightcurve fits

Type Ia supernova (SN Ia) cosmology relies on the estimation of lightcurve parameters to derive precision distances that leads to the estimation of cosmological parameters. The empirical SALT2 lightcurve modeling that relies on only two parameters, a stretch x1, and a color c, has been used by the community for almost two decades. In this paper we study the ability of the SALT2 model to fit the nearly 3000 cosmology-grade SN Ia lightcurves from the second release of the Zwicky Transient Facility (ZTF) cosmology science working group. While the ZTF data was not used to train SALT2, the algorithm is modeling the ZTF SN Ia optical lightcurves remarkably well, except for lightcurve points prior to -10 d from maximum, where the training critically lacks statistics. We find that the lightcurve fitting is robust against the considered choice of phase-range, but we show the [-10; +40] d range to be optimal in terms of statistics and accuracy. We do not detect any significant features in the lightcurve fit residuals that could be connected to the host environment. Potential systematic population differences related to the SN Ia host properties might thus not be accountable for by the addition of extra lightcurve parameters. However, a small but significant inconsistency between residuals of blue- and red-SN Ia strongly suggests the existence of a phase-dependent color term, with potential implications for the use of SNe Ia in precision cosmology. We thus encourage modellers to explore this avenue and we emphasize the importance that SN Ia cosmology must include a SALT2 retraining to accurately model the lightcurves and avoid biasing the derivation of cosmological parameters.

astro-ph.CO

ZTF SN Ia DR2: Colour standardisation of Type Ia Supernovae and its dependence on environment

As type Ia supernova (SN Ia) cosmology transitions from a statistics-dominated to a systematics-dominated era, it is crucial to understand the remaining unexplained uncertainties that affect their luminosity, such as those stemming from astrophysical biases. SNe Ia are standardisable candles whose absolute magnitude reaches a scatter of 0.15 mag when empirical correlations with their light-curve stretch and colour and with their environment are accounted for. We investigate the dependence of the standardisation process of SNe Ia on the astrophysical environment, focusing on colour standardisation. We used the volume-limited ZTF SN Ia DR2 sample, which offers unprecedented statistics for the low-redshift ($z < 0.06$) range. We first studied the colour distribution, to then select a dustless subsample of objects. We then examined the colour-residual relation and its associated parameter $\beta$. Finally, we investigated the colour dependence of the environment-dependent magnitude offsets (steps) to separate their intrinsic and extrinsic components. Our sample of nearly 1,000 SNe probes the red tail of the colour distribution up to $c = 0.8$. The dustless sample exhibits a significantly shorter red tail ($4.3\sigma$) than the whole sample, but the distributions around $c\sim0$ are similar for both samples. This suggests that the reddening above $c\geq0.2$ is dominated by interstellar dust absorption of the host. The colour-residual relation is linear with SN colour. We found indications of a potential evolution of $\beta$ with the stellar host mass, with $\beta\sim3.6$ for low-mass galaxies, compared to $\beta=3.05\pm0.06$ for the full sample. Finally, in contrast to recent claims from the literature, we found no evolution of steps as a function of SN colour. This suggests that dust may not be the dominating mechanism for the dependence on the environment of the magnitude of SNe Ia.

astro-ph.CO

ZTF SN Ia DR2: Impact of the galaxy cluster environment on the stretch distribution of Type Ia supernovae

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.

astro-ph.CO

ZTF SN Ia DR2: Environmental dependencies of stretch and luminosity of a volume limited sample of 1,000 Type Ia Supernovae

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 9.2$\sigma$ significance. We demonstrate, at the 13.4$\sigma$ 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 ($x_1<-0.48\pm0.08$): $\alpha_{low}=0.27\pm0.01$ and $\alpha_{high}=0.08\pm0.01$, 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 0.12 mag regardless of the considered environmental tracer used (local or global colour and stellar mass), all measured at the $\geq 5\sigma$ level, increased to $\sim0.17\pm0.01$ mag when accounting for the stretch-non linearity.

astro-ph.CO

ZTF SN Ia DR2: Peculiar velocities impact on the Hubble diagram

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.

astro-ph.CO

CNN photometric redshifts in the SDSS at $r\leq 20$

We release photometric redshifts, reaching $\sim$0.7, for $\sim$14M galaxies at $r\leq 20$ in the 11,500 deg$^2$ of the SDSS north and south galactic caps. These estimates were inferred from a convolution neural network (CNN) trained on $ugriz$ stamp images of galaxies labelled with a spectroscopic redshift from the SDSS, GAMA and BOSS surveys. Representative training sets of $\sim$370k galaxies were constructed from the much larger combined spectroscopic data to limit biases, particularly those arising from the over-representation of Luminous Red Galaxies. The CNN outputs a redshift classification that offers all the benefits of a well-behaved PDF, with a width efficiently signaling unreliable estimates due to poor photometry or stellar sources. The dispersion, mean bias and rate of catastrophic failures of the median point estimate are of order $σ_{\rm MAD}=0.014$, <$Δz_{\rm norm}$>$=0.0015$, $η(|Δz_{\rm norm}|>0.05)=4\%$ on a representative test sample at $r<19.8$, out-performing currently published estimates. The distributions in narrow intervals of magnitudes of the redshifts inferred for the photometric sample are in good agreement with the results of tomographic analyses. The inferred redshifts also match the photometric redshifts of the redMaPPer galaxy clusters for the probable cluster members. The CNN input and output are available at: https://deepdip.iap.fr/treyer+2023.

astro-ph.CO

Bump Morphology of the CMAGIC Diagram

We apply the color-magnitude intercept calibration method (CMAGIC) to the Nearby Supernova Factory SNe Ia spectrophotometric dataset. The currently existing CMAGIC parameters are the slope and intercept of a straight line fit to the first linear region in the color-magnitude diagram, which occurs over a span of approximately 30 days after maximum brightness. We define a new parameter, $ω_{XY}$, the size of the ``bump'' feature near maximum brightness for arbitrary filters $X$ and $Y$. We find a significant correlation between the slope of the first linear region, $β_{XY, 1}$, in the CMAGIC diagram and $ω_{XY}$. These results may be used to our advantage, as they are less affected by extinction than parameters defined as a function of time. Additionally, $ω_{XY}$ is computed independently of templates. We find that current empirical templates are successful at reproducing the features described in this work, particularly SALT3, which correctly exhibits the negative correlation between slope and bump size seen in our data. In 1-D simulations, we show that the correlation between the size of the bump feature and $β_{XY, 1}$ can be understood as a result of chemical mixing due to large-scale Rayleigh-Taylor instabilities.

astro-ph.SR

A Probabilistic Autoencoder for Type Ia Supernovae Spectral Time Series

We construct a physically-parameterized probabilistic autoencoder (PAE) to learn the intrinsic diversity of type Ia supernovae (SNe Ia) from a sparse set of spectral time series. The PAE is a two-stage generative model, composed of an Auto-Encoder (AE) which is interpreted probabilistically after training using a Normalizing Flow (NF). We demonstrate that the PAE learns a low-dimensional latent space that captures the nonlinear range of features that exists within the population, and can accurately model the spectral evolution of SNe Ia across the full range of wavelength and observation times directly from the data. By introducing a correlation penalty term and multi-stage training setup alongside our physically-parameterized network we show that intrinsic and extrinsic modes of variability can be separated during training, removing the need for the additional models to perform magnitude standardization. We then use our PAE in a number of downstream tasks on SNe Ia for increasingly precise cosmological analyses, including automatic detection of SN outliers, the generation of samples consistent with the data distribution, and solving the inverse problem in the presence of noisy and incomplete data to constrain cosmological distance measurements. We find that the optimal number of intrinsic model parameters appears to be three, in line with previous studies, and show that we can standardize our test sample of SNe Ia with an RMS of $0.091 \pm 0.010$ mag, which corresponds to $0.074 \pm 0.010$ mag if peculiar velocity contributions are removed. Trained models and codes are released at \href{https://github.com/georgestein/suPAErnova}{github.com/georgestein/suPAErnova}

astro-ph.CO

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.

astro-ph.IM

Photometric Redshift Estimation with Convolutional Neural Networks and Galaxy Images: A Case Study of Resolving Biases in Data-Driven Methods

Deep Learning models have been increasingly exploited in astrophysical studies, yet such data-driven algorithms are prone to producing biased outputs detrimental for subsequent analyses. In this work, we investigate two major forms of biases, i.e., class-dependent residuals and mode collapse, in a case study of estimating photometric redshifts as a classification problem using Convolutional Neural Networks (CNNs) and galaxy images with spectroscopic redshifts. We focus on point estimates and propose a set of consecutive steps for resolving the two biases based on CNN models, involving representation learning with multi-channel outputs, balancing the training data and leveraging soft labels. The residuals can be viewed as a function of spectroscopic redshifts or photometric redshifts, and the biases with respect to these two definitions are incompatible and should be treated in a split way. We suggest that resolving biases in the spectroscopic space is a prerequisite for resolving biases in the photometric space. Experiments show that our methods possess a better capability in controlling biases compared to benchmark methods, and exhibit robustness under varying implementing and training conditions provided with high-quality data. Our methods have promises for future cosmological surveys that require a good constraint of biases, and may be applied to regression problems and other studies that make use of data-driven models. Nonetheless, the bias-variance trade-off and the demand on sufficient statistics suggest the need for developing better methodologies and optimizing data usage strategies.

astro-ph.IM

SNIa-Cosmology Analysis Results from Simulated LSST Images: from Difference Imaging to Constraints on Dark Energy

The Vera Rubin Observatory Legacy Survey of Space and Time (LSST) is expected to process ${\sim}10^6$ transient detections per night. For precision measurements of cosmological parameters and rates, it is critical to understand the detection efficiency, magnitude limits, artifact contamination levels, and biases in the selection and photometry. Here we rigorously test the LSST Difference Image Analysis (DIA) pipeline using simulated images from the Rubin Observatory LSST Dark Energy Science Collaboration (DESC) Data Challenge (DC2) simulation for the Wide-Fast-Deep (WFD) survey area. DC2 is the first large-scale (300 deg$^2$) image simulation of a transient survey that includes realistic cadence, variable observing conditions, and CCD image artifacts. We analyze ${\sim}$15 deg$^2$ of DC2 over a 5-year time-span in which artificial point-sources from Type Ia Supernovae (SNIa) light curves have been overlaid onto the images. We measure the detection efficiency as a function of Signal-to-Noise Ratio (SNR) and find a $50\%$ efficiency at $\rm{SNR}=5.8$. The magnitude limits for each filter are: $u=23.66$, $g=24.69$, $r=24.06$, $i=23.45$, $z=22.54$, $y=21.62$ $\rm{mag}$. The artifact contamination is $\sim90\%$ of detections, corresponding to $\sim1000$ artifacts/deg$^2$ in $g$ band, and falling to 300 per deg$^2$ in $y$ band. The photometry has biases $<1\%$ for magnitudes $19.5 < m <23$. Our DIA performance on simulated images is similar to that of the Dark Energy Survey pipeline applied to real images. We also characterize DC2 image properties to produce catalog-level simulations needed for distance bias corrections. We find good agreement between DC2 data and simulations for distributions of SNR, redshift, and fitted light-curve properties. Applying a realistic SNIa-cosmology analysis for redshifts $z<1$, we recover the input cosmology parameters to within statistical uncertainties.

astro-ph.CO

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.

astro-ph.CO

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.

astro-ph.CO