arXiv subjects

R. Pain

Publications and source records attributed to R. Pain.

At least 37 records · Page 2Linked to original sources

arXiv2015

Improving Cosmological Distance Measurements Using Twin Type Ia Supernovae

We introduce a method for identifying "twin" Type Ia supernovae, and using them to improve distance measurements. This novel approach to Type Ia supernova standardization is made possible by spectrophotometric time series observations from the Nearby Supernova Factory (SNfactory). We begin with a well-measured set of supernovae, find pairs whose spectra match well across the entire optical window, and then test whether this leads to a smaller dispersion in their absolute brightnesses. This analysis is completed in a blinded fashion, ensuring that decisions made in implementing the method do not inadvertently bias the result. We find that pairs of supernovae with more closely matched spectra indeed have reduced brightness dispersion. We are able to standardize this initial set of SNfactory supernovae to 0.083 +/- 0.012 magnitudes, implying a dispersion of 0.072 +/- 0.010 magnitudes in the absence of peculiar velocities. We estimate that with larger numbers of comparison SNe, e.g, using the final SNfactory spectrophotometric dataset as a reference, this method will be capable of standardizing high-redshift supernovae to within 0.06-0.07 magnitudes. These results imply that at least 3/4 of the variance in Hubble residuals in current supernova cosmology analyses is due to previously unaccounted-for astrophysical differences among the supernovae

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arXiv2015

Measuring cosmic bulk flows with Type Ia Supernovae from the Nearby Supernova Factory

Context. Our Local Group of galaxies appears to be moving relative to the cosmic microwave background with the source of the peculiar motion still uncertain. While in the past this has been studied mostly using galaxies as distance indicators, the weight of type Ia supernovae (SNe Ia) has increased recently with the continuously improving statistics of available low-redshift supernovae. Aims. We measured the bulk flow in the nearby universe ($0.015 < z < 0.1$) using 117 SNe Ia observed by the Nearby Supernova Factory, as well as the Union2 compilation of SN Ia data already in the literature. Methods. The bulk flow velocity was determined from SN data binned in redshift shells by including a coherent motion (dipole) in a cosmological fit. Additionally, a method of spatially smoothing the Hubble residuals was used to verify the results of the dipole fit. To constrain the location and mass of a potential mass concentration (e.g., the Shapley supercluster) responsible for the peculiar motion, we fit a Hubble law modified by adding an additional mass concentration. Results. The analysis shows a bulk flow that is consistent with the direction of the CMB dipole up to $z \sim 0.06$, thereby doubling the volume over which conventional distance measures are sensitive to a bulk flow. We see no significant turnover behind the center of the Shapley supercluster. A simple attractor model in the proximity of the Shapley supercluster is only marginally consistent with our data, suggesting the need for another, more distant source. In the redshift shell $0.06 < z < 0.1$, we constrain the bulk flow velocity to $< 240~\textrm{km s}^{-1}$ (68% confidence level) for the direction of the CMB dipole, in contradiction to recent claims of the existence of a large-amplitude dark flow.

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arXiv2015

The DICE calibration project: design, characterization, and first results

We describe the design, operation, and first results of a photometric calibration project, called DICE (Direct Illumination Calibration Experiment), aiming at achieving precise instrumental calibration of optical telescopes. The heart of DICE is an illumination device composed of 24 narrow-spectrum, high-intensity, light-emitting diodes (LED) chosen to cover the ultraviolet-to-near-infrared spectral range. It implements a point-like source placed at a finite distance from the telescope entrance pupil, yielding a flat field illumination that covers the entire field of view of the imager. The purpose of this system is to perform a lightweight routine monitoring of the imager passbands with a precision better than 5 per-mil on the relative passband normalisations and about 3Å on the filter cutoff positions. The light source is calibrated on a spectrophotometric bench. As our fundamental metrology standard, we use a photodiode calibrated at NIST. The radiant intensity of each beam is mapped, and spectra are measured for each LED. All measurements are conducted at temperatures ranging from 0°C to 25°C in order to study the temperature dependence of the system. The photometric and spectroscopic measurements are combined into a model that predicts the spectral intensity of the source as a function of temperature. We find that the calibration beams are stable at the $10^{-4}$ level -- after taking the slight temperature dependence of the LED emission properties into account. We show that the spectral intensity of the source can be characterised with a precision of 3Å in wavelength. In flux, we reach an accuracy of about 0.2-0.5% depending on how we understand the off-diagonal terms of the error budget affecting the calibration of the NIST photodiode. With a routine 60-mn calibration program, the apparatus is able to constrain the passbands at the targeted precision levels.

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arXiv2015

PESSTO : survey description and products from the first data release by the Public ESO Spectroscopic Survey of Transient Objects

The Public European Southern Observatory Spectroscopic Survey of Transient Objects (PESSTO) began as a public spectroscopic survey in April 2012. We describe the data reduction strategy and data products which are publicly available through the ESO archive as the Spectroscopic Survey Data Release 1 (SSDR1). PESSTO uses the New Technology Telescope with EFOSC2 and SOFI to provide optical and NIR spectroscopy and imaging. We target supernovae and optical transients brighter than 20.5mag for classification. Science targets are then selected for follow-up based on the PESSTO science goal of extending knowledge of the extremes of the supernova population. The EFOSC2 spectra cover 3345-9995A (at resolutions of 13-18 Angs) and SOFI spectra cover 0.935-2.53 micron (resolutions 23-33 Angs) along with JHK imaging. This data release contains spectra from the first year (April 2012 - 2013), consisting of all 814 EFOSC2 spectra and 95 SOFI spectra (covering 298 distinct objects), in standard ESO Phase 3 format. We estimate the accuracy of the absolute flux calibrations for EFOSC2 to be typically 15%, and the relative flux calibration accuracy to be about 5%. The PESSTO standard NIR reduction process does not yet produce high accuracy absolute spectrophotometry but the SOFI JHK imaging will improve this. Future data releases will focus on improving the automated flux calibration of the data products.

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arXiv2014

Confirmation of a Star Formation Bias in Type Ia Supernova Distances and its Effect on Measurement of the Hubble Constant

Previously we used the Nearby Supernova Factory sample to show that SNe~Ia having locally star-forming environments are dimmer than SNe~Ia having locally passive environments.Here we use the \constitution\ sample together with host galaxy data from \GALEX\ to independently confirm that result. The effect is seen using both the SALT2 and MLCS2k2 lightcurve fitting and standardization methods, with brightness differences of $0.094 \pm 0.037\ \mathrm{mag}$ for SALT2 and $0.155 \pm 0.041\ \mathrm{mag}$ for MLCS2k2 with $R_V=2.5$. When combined with our previous measurement the effect is $0.094 \pm 0.025\ \mathrm{mag}$ for SALT2. If the ratio of these local SN~Ia environments changes with redshift or sample selection, this can lead to a bias in cosmological measurements. We explore this issue further, using as an example the direct measurement of $H_0$. \GALEX{} observations show that the SNe~Ia having standardized absolute magnitudes calibrated via the Cepheid period--luminosity relation using {\textit{HST}} originate in predominately star-forming environments, whereas only ~50% of the Hubble-flow comparison sample have locally star-forming environments. As a consequence, the $H_0$ measurement using SNe~Ia is currently overestimated. Correcting for this bias, we find a value of $H_0^{corr}=70.6\pm 2.6\ \mathrm{km\ s^{-1}\ Mpc^{-1}}$ when using the LMC distance, Milky Way parallaxes and the NGC~4258 megamaser as the Cepheid zeropoint, and $68.8\pm 3.3\ \mathrm{km\ s^{-1}\ Mpc^{-1}}$ when only using NGC~4258. Our correction brings the direct measurement of $H_0$ within $\sim 1\,σ$ of recent indirect measurements based on the CMB power spectrum.

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arXiv2014

Type Ia Supernova Distance Modulus Bias and Dispersion From K-correction Errors: A Direct Measurement Using Lightcurve Fits to Observed Spectral Time Series

We estimate systematic errors due to K-corrections in standard photometric analyses of high redshift Type Ia supernovae. Errors due to K-correction occur when the spectral template model underlying the lightcurve fitter poorly represents the actual supernova spectral energy distribution, meaning that the distance modulus cannot be recovered accurately. In order to quantify this effect, synthetic photometry is performed on artificially redshifted spectrophotometric data from 119 low-redshift supernovae from the Nearby Supernova Factory, and the resulting lightcurves are fit with a conventional lightcurve fitter. We measure the variation in the standardized magnitude that would be fit for a given supernova if located at a range of redshifts and observed with various filter sets corresponding to current and future supernova surveys. We find significant variation in the measurements of the same supernovae placed at different redshifts regardless of filters used, which causes dispersion greater than $\sim0.05$ mag for measurements of photometry using the Sloan-like filters and a bias that corresponds to a $0.03$ shift in $w$ when applied to an outside data set. To test the result of a shift in supernova population or environment at higher redshifts, we repeat our calculations with the addition of a reweighting of the supernovae as a function of redshift and find that this strongly affects the results and would have repercussions for cosmology. We discuss possible methods to reduce the contribution of the K-correction bias and uncertainty.

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arXiv2014

A metric space for type Ia supernova spectra

We develop a new framework for use in exploring Type Ia Supernova (SN Ia) spectra. Combining Principal Component Analysis (PCA) and Partial Least Square analysis (PLS) we are able to establish correlations between the Principal Components (PCs) and spectroscopic/photometric SNe Ia features. The technique was applied to ~120 supernova and ~800 spectra from the Nearby Supernova Factory. The ability of PCA to group together SNe Ia with similar spectral features, already explored in previous studies, is greatly enhanced by two important modifications: (1) the initial data matrix is built using derivatives of spectra over the wavelength, which increases the weight of weak lines and discards extinction, and (2) we extract time evolution information through the use of entire spectral sequences concatenated in each line of the input data matrix. These allow us to define a stable PC parameter space which can be used to characterize synthetic SN Ia spectra by means of real SN features. Using PLS, we demonstrate that the information from important previously known spectral indicators (namely the pseudo-equivalent width (pEW) of Si II 5972 / Si II 6355 and the line velocity of S II 5640 / Si II 6355) at a given epoch, is contained within the PC space and can be determined through a linear combination of the most important PCs. We also show that the PC space encompasses photometric features like B or V magnitudes, B-V color and SALT2 parameters c and x1. The observed colors and magnitudes, that are heavily affected by extinction, cannot be reconstructed using this technique alone. All the above mentioned applications allowed us to construct a metric space for comparing synthetic SN Ia spectra with observations.

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arXiv2014

Extending the supernova Hubble diagram to z~1.5 with the Euclid space mission

We forecast dark energy constraints that could be obtained from a new large sample of Type Ia supernovae where those at high redshift are acquired with the Euclid space mission. We simulate a three-prong SN survey: a z<0.35 nearby sample (8000 SNe), a 0.2<z<0.95 intermediate sample (8800 SNe), and a 0.75<z<1.55 high-z sample (1700 SNe). The nearby and intermediate surveys are assumed to be conducted from the ground, while the high-z is a joint ground- and space-based survey. This latter survey, the "Dark Energy Supernova Infra-Red Experiment" (DESIRE), is designed to fit within 6 months of Euclid observing time, with a dedicated observing program. We simulate the SN events as they would be observed in rolling-search mode by the various instruments, and derive the quality of expected cosmological constraints. We account for known systematic uncertainties, in particular calibration uncertainties including their contribution through the training of the supernova model used to fit the supernovae light curves. Using conservative assumptions and a 1-D geometric Planck prior, we find that the ensemble of surveys would yield competitive constraints: a constant equation of state parameter can be constrained to sigma(w)=0.022, and a Dark Energy Task Force figure of merit of 203 is found for a two-parameter equation of state. Our simulations thus indicate that Euclid can bring a significant contribution to a purely geometrical cosmology constraint by extending a high-quality SN Hubble diagram to z~1.5. We also present other science topics enabled by the DESIRE Euclid observations

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arXiv2014

Cosmological Parameter Uncertainties from SALT-II Type Ia Supernova Light Curve Models

We use simulated SN Ia samples, including both photometry and spectra, to perform the first direct validation of cosmology analysis using the SALT-II light curve model. This validation includes residuals from the light curve training process, systematic biases in SN Ia distance measurements, and the bias on the dark energy equation of state parameter w. Using the SN-analysis package SNANA, we simulate and analyze realistic samples corresponding to the data samples used in the SNLS3 analysis: 120 low-redshift (z < 0.1) SNe Ia, 255 SDSS SNe Ia (z < 0.4), and 290 SNLS SNe Ia (z <= 1). To probe systematic uncertainties in detail, we vary the input spectral model, the model of intrinsic scatter, and the smoothing (i.e., regularization) parameters used during the SALT-II model training. Using realistic intrinsic scatter models results in a slight bias in the ultraviolet portion of the trained SALT-II model, and w biases (winput - wrecovered) ranging from -0.005 +/- 0.012 to -0.024 +/- 0.010. These biases are indistinguishable from each other within uncertainty; the average bias on w is -0.014 +/- 0.007.

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arXiv2014

Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples

We present cosmological constraints from a joint analysis of type Ia supernova (SN Ia) observations obtained by the SDSS-II and SNLS collaborations. The data set includes several low-redshift samples (z<0.1), all 3 seasons from the SDSS-II (0.05 < z < 0.4), and 3 years from SNLS (0.2 <z < 1) and totals \ntotc spectroscopically confirmed type Ia supernovae with high quality light curves. We have followed the methods and assumptions of the SNLS 3-year data analysis except for the following important improvements: 1) the addition of the full SDSS-II spectroscopically-confirmed SN Ia sample in both the training of the SALT2 light curve model and in the Hubble diagram analysis (\nsdssc SNe), 2) inter-calibration of the SNLS and SDSS surveys and reduced systematic uncertainties in the photometric calibration, performed blindly with respect to the cosmology analysis, and 3) a thorough investigation of systematic errors associated with the SALT2 modeling of SN Ia light-curves. We produce recalibrated SN Ia light-curves and associated distances for the SDSS-II and SNLS samples. The large SDSS-II sample provides an effective, independent, low-z anchor for the Hubble diagram and reduces the systematic error from calibration systematics in the low-z SN sample. For a flat LCDM cosmology we find Omega_m=0.295+-0.034 (stat+sys), a value consistent with the most recent CMB measurement from the Planck and WMAP experiments. Our result is 1.8sigma (stat+sys) different than the previously published result of SNLS 3-year data. The change is due primarily to improvements in the SNLS photometric calibration. When combined with CMB constraints, we measure a constant dark-energy equation of state parameter w=-1.018+-0.057 (stat+sys) for a flat universe. Adding BAO distance measurements gives similar constraints: w=-1.027+-0.055.

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arXiv2014

Type Ia supernova bolometric light curves and ejected mass estimates from the Nearby Supernova Factory

We present a sample of normal type Ia supernovae from the Nearby Supernova Factory dataset with spectrophotometry at sufficiently late phases to estimate the ejected mass using the bolometric light curve. We measure $^{56}$Ni masses from the peak bolometric luminosity, then compare the luminosity in the $^{56}$Co-decay tail to the expected rate of radioactive energy re- lease from ejecta of a given mass. We infer the ejected mass in a Bayesian context using a semi-analytic model of the ejecta, incorporating constraints from contemporary numerical models as priors on the density structure and distribution of $^{56}$Ni throughout the ejecta. We find a strong correlation between ejected mass and light curve decline rate, and consequently $^{56}$Ni mass, with ejected masses in our data ranging from 0.9-1.4 $M_\odot$. Most fast-declining (SALT2 $x_1 < -1$) normal SNe Ia have significantly sub-Chandrasekhar ejected masses in our fiducial analysis.

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arXiv2014

Type Ia Supernova Hubble Residuals and Host-Galaxy Properties

Kim et al. (2013) [K13] introduced a new methodology for determining peak-brightness absolute magnitudes of type Ia supernovae from multi-band light curves. We examine the relation between their parameterization of light curves and Hubble residuals, based on photometry synthesized from the Nearby Supernova Factory spectrophotometric time series, with global host-galaxy properties. The K13 Hubble residual step with host mass is $0.013\pm 0.031$ mag for a supernova subsample with data coverage corresponding to the K13 training; at $\ll 1σ$, the step is not significant and lower than previous measurements. Relaxing the data coverage requirement the Hubble residual step with host mass is $0.045\pm 0.026$ mag for the larger sample; a calculation using the modes of the distributions, less sensitive to outliers, yields a step of 0.019 mag. The analysis of this article uses K13 inferred luminosities, as distinguished from previous works that use magnitude corrections as a function of SALT2 color and stretch parameters: Steps at $>2σ$ significance are found in SALT2 Hubble residuals in samples split by the values of their K13 $x(1)$ and $x(2)$ light-curve parameters. $x(1)$ affects the light-curve width and color around peak (similar to the $Δm_{15}$ and stretch parameters), and $x(2)$ affects colors, the near-UV light-curve width, and the light-curve decline 20 to 30 days after peak brightness. The novel light-curve analysis, increased parameter set, and magnitude corrections of K13 may be capturing features of SN~Ia diversity arising from progenitor stellar evolution.

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arXiv2013

Two superluminous supernovae from the early universe discovered by the Supernova Legacy Survey

We present spectra and lightcurves of SNLS 06D4eu and SNLS 07D2bv, two hydrogen-free superluminous supernovae discovered by the Supernova Legacy Survey. At z = 1.588, SNLS 06D4eu is the highest redshift superluminous SN with a spectrum, at M_U = -22.7 is one of the most luminous SNe ever observed, and gives a rare glimpse into the restframe ultraviolet where these supernovae put out their peak energy. SNLS 07D2bv does not have a host galaxy redshift, but based on the supernova spectrum, we estimate it to be at z ~ 1.5. Both supernovae have similar observer-frame griz lightcurves, which map to restframe lightcurves in the U-band and UV, rising in ~ 20 restframe days or longer, and declining over a similar timescale. The lightcurves peak in the shortest wavelengths first, consistent with an expanding blackbody starting near 15,000 K and steadily declining in temperature. We compare the spectra to theoretical models, and identify lines of C II, C III, Fe III, and Mg II in the spectrum of SNLS 06D4eu and SCP 06F6, and find that they are consistent with an expanding explosion of only a few solar masses of carbon, oxygen, and other trace metals. Thus the progenitors appear to be related to those suspected for SNe Ic. A high kinetic energy, 10^52 ergs, is also favored. Normal mechanisms of powering core- collapse or thermonuclear supernovae do not seem to work for these supernovae. We consider models powered by 56Ni decay and interaction with circumstellar material, but find that the creation and spin-down of a magnetar with a period of 2ms, magnetic field of 2 x 10^14 Gauss, and a 3 solar mass progenitor provides the best fit to the data.

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arXiv2013

Evidence of Environmental Dependencies of Type Ia Supernovae from the Nearby Supernova Factory indicated by Local Hα

(Abridged) We study the host galaxy regions in close proximity to Type Ia supernovae (SNe Ia) to analyze relations between the properties of SN Ia events and environments most similar to where their progenitors formed. We focus on local Hα emission as an indicator of young environments. The Nearby Supernova Factory has obtained flux-calibrated spectral timeseries for SNe Ia using integral field spectroscopy, allowing the simultaneous measurement of the SN and its immediate vicinity. For 89 SNe Ia we measure Hα emission tracing ongoing star formation within a 1 kpc radius around each SN. This constitutes the first direct study of the local environment for a large sample of SNe Ia also having accurate luminosity, color and stretch measurements. We find that SNe Ia with local Hα emission are redder by 0.036+/-0.017 mag, and that the previously-noted correlation between stretch and host mass is entirely driven by the SNe Ia coming from passive regions. Most importantly, the mean standardized brightness for SNe Ia with local Hα emission is 0.094+/-0.031 mag fainter than for those without. This offset arises from a bimodal structure in the Hubble residuals, that also explains the previously-known host-mass bias. We combine this bimodality with the cosmic star-formation rate to predict changes with redshift in the mean SN Ia brightness and the host-mass bias. This change is confirmed using high-redshift SNe Ia from the literature. These environmental dependences point to remaining systematic errors in SNe Ia standardization. The observed brightness offset is predicted to cause a significant bias in measurements of the dark energy equation of state. Recognition of these effects offers new opportunities to improve SNe Ia as cosmological probes - e.g. SNe Ia having local Hα emission are more homogeneous, having a brightness dispersion of 0.105+/-0.012 mag.

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arXiv2013

Photometry of supernovae in an image series : methods and application to the Supernova Legacy Survey (SNLS)

We present a technique to measure lightcurves of time-variable point sources on a spatially structured background from imaging data. The technique was developed to measure light curves of SNLS supernovae in order to infer their distances. This photometry technique performs simultaneous PSF photometry at the same sky position on an image series. We describe two implementations of the method: one that resamples images before measuring fluxes, and one which does not. In both instances, we sketch the key algorithms involved and present the validation using semi-artificial sources introduced in real images in order to assess the accuracy of the supernova flux measurements relative to that of surrounding stars. We describe the methods required to anchor these PSF fluxes to calibrated aperture catalogs, in order to derive SN magnitudes. We find a marginally significant bias of 2 mmag of the after-resampling method, and no bias at the mmag accuracy for the non-resampling method. Given surrounding star magnitudes, we determine the systematic uncertainty of SN magnitudes to be less than 1.5 mmag, which represents about one third of the current photometric calibration uncertainty affecting SN measurements. The SN photometry delivers several by-products: bright star PSF flux mea- surements which have a repeatability of about 0.6%, as for aperture measurements; we measure relative astrometric positions with a noise floor of 2.4 mas for a single-image bright star measurement; we show that in all bands of the MegaCam instrument, stars exhibit a profile linearly broadening with flux by about 0.5% over the whole brightness range.

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arXiv2013

Host Galaxies of Type Ia Supernovae from the Nearby Supernova Factory

We present photometric and spectroscopic observations of galaxies hosting Type Ia supernovae (SNe Ia) observed by the Nearby Supernova Factory (SNfactory). Combining GALEX UV data with optical and near infrared photometry, we employ stellar population synthesis techniques to measure SN Ia host galaxy stellar masses, star-formation rates (SFRs), and reddening due to dust. We reinforce the key role of GALEX UV data in deriving accurate estimates of galaxy SFRs and dust extinction. Optical spectra of SN Ia host galaxies are fitted simultaneously for their stellar continua and emission lines fluxes, from which we derive high precision redshifts, gas-phase metallicities, and Halpha-based SFRs. With these data we show that SN Ia host galaxies present tight agreement with the fiducial galaxy mass-metallicity relation from SDSS for stellar masses log(M_*/M_Sun)>8.5 where the relation is well-defined. The star-formation activity of SN Ia host galaxies is consistent with a sample of comparable SDSS field galaxies, though this comparison is limited by systematic uncertainties in SFR measurements. Our analysis indicates that SN Ia host galaxies are, on average, typical representatives of normal field galaxies.

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arXiv2013

Host Galaxy Properties and Hubble Residuals of Type Ia Supernovae from the Nearby Supernova Factory

We examine the relationship between Type Ia Supernova (SN Ia) Hubble residuals and the properties of their host galaxies using a sample of 115 SNe Ia from the Nearby Supernova Factory (SNfactory). We use host galaxy stellar masses and specific star-formation rates fitted from photometry for all hosts, as well as gas-phase metallicities for a subset of 69 star-forming (non-AGN) hosts, to show that the SN Ia Hubble residuals correlate with each of these host properties. With these data we find new evidence for a correlation between SN Ia intrinsic color and host metallicity. When we combine our data with those of other published SN Ia surveys, we find the difference between mean SN Ia brightnesses in low and high mass hosts is 0.077 +- 0.014 mag. When viewed in narrow (0.2 dex) bins of host stellar mass, the data reveal apparent plateaus of Hubble residuals at high and low host masses with a rapid transition over a short mass range (9.8 <= log(M_*/M_Sun) <= 10.4). Although metallicity has been a favored interpretation for the origin of the Hubble residual trend with host mass, we illustrate how dust in star-forming galaxies and mean SN Ia progenitor age both evolve along the galaxy mass sequence, thereby presenting equally viable explanations for some or all of the observed SN Ia host bias.

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arXiv2013

Standardizing Type Ia Supernova Absolute Magnitudes Using Gaussian Process Data Regression

We present a novel class of models for Type Ia supernova time-evolving spectral energy distributions (SED) and absolute magnitudes: they are each modeled as stochastic functions described by Gaussian processes. The values of the SED and absolute magnitudes are defined through well-defined regression prescriptions, so that data directly inform the models. As a proof of concept, we implement a model for synthetic photometry built from the spectrophotometric time series from the Nearby Supernova Factory. Absolute magnitudes at peak $B$ brightness are calibrated to 0.13 mag in the $g$-band and to as low as 0.09 mag in the $z=0.25$ blueshifted $i$-band, where the dispersion includes contributions from measurement uncertainties and peculiar velocities. The methodology can be applied to spectrophotometric time series of supernovae that span a range of redshifts to simultaneously standardize supernovae together with fitting cosmological parameters.

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