First Cosmology Results using Type Ia Supernova from the Dark Energy Survey: Simulations to Correct Supernova Distance Biases
R. Kessler, D. Brout, C. B. D'Andrea, T. M. Davis, S. R. Hinton, A. G. Kim, J. Lasker, C. Lidman, E. Macaulay, A. Möller, M. Sako, D. Scolnic, M. Smith, M. Sullivan, B. Zhang, P. Andersen, J. Asorey, A. Avelino, J. Calcino, D. Carollo, P. Challis, M. Childress, A. Clocchiatti, S. Crawford, A. V. Filippenko, R. J. Foley, K. Glazebrook, J. K. Hoormann, E. Kasai, R. P. Kirshner, G. F. Lewis, K. S. Mandel, M. March, E. Morganson, D. Muthukrishna, P. Nugent, Y.-C. Pan, N. E. Sommer, E. Swann, R. C. Thomas, B. E. Tucker, S. A. Uddin, T. M. C. Abbott, S. Allam, J. Annis, S. Avila, M. Banerji, K. Bechtol, E. Bertin, D. Brooks, E. Buckley-Geer, D. L. Burke, A. Carnero Rosell, M. Carrasco Kind, J. Carretero, F. J. Castander, M. Crocce, L. N. da Costa, C. Davis, J. De Vicente, S. Desai, H. T. Diehl, P. Doel, T. F. Eifler, B. Flaugher, P. Fosalba, J. Frieman, J. Garcia-Bellido, E. Gaztanaga, D. W. Gerdes, D. Gruen, R. A. Gruendl, G. Gutierrez, W. G. Hartley, D. L. Hollowood, K. Honscheid, D. J. James, M. W. G. Johnson, M. D. Johnson, E. Krause, K. Kuehn, N. Kuropatkin, O. Lahav, T. S. Li, M. Lima, J. L. Marshall, P. Martini, F. Menanteau, C. J. Miller, R. Miquel, B. Nord, A. A. Plazas, A. Roodman, E. Sanchez, V. Scarpine, R. Schindler, M. Schubnell, S. Serrano, I. Sevilla-Noarbe, M. Soares-Santos, et al. (6 additional authors not shown)
aa r X i v : . [ a s t r o - ph . C O ] M a y MNRAS , 1–18 (2015) Preprint 13 May 2019 Compiled using MNRAS L A TEX style file v3.0
First Cosmology Results using Type Ia Supernova fromthe Dark Energy Survey: Simulations to CorrectSupernova Distance Biases
R. Kessler , , D. Brout , C. B. D’Andrea , T. M. Davis , S. R. Hinton , A. G. Kim ,J. Lasker , , C. Lidman , E. Macaulay , A. M¨oller , , M. Sako , D. Scolnic , M. Smith ,M. Sullivan , B. Zhang , , P. Andersen , , J. Asorey , A. Avelino , J. Calcino , D. Carollo ,P. Challis , M. Childress , A. Clocchiatti , S. Crawford , , A. V. Filippenko , , R. J. Foley ,K. Glazebrook , J. K. Hoormann , E. Kasai , , R. P. Kirshner , , G. F. Lewis , K. S. Mandel ,M. March , E. Morganson , D. Muthukrishna , , , P. Nugent , Y.-C. Pan , , N. E. Sommer , ,E. Swann , R. C. Thomas , B. E. Tucker , , S. A. Uddin , T. M. C. Abbott , S. Allam ,J. Annis , S. Avila , M. Banerji , , K. Bechtol , E. Bertin , , D. Brooks , E. Buckley-Geer ,D. L. Burke , , A. Carnero Rosell , , M. Carrasco Kind , , J. Carretero , F. J. Castander , ,M. Crocce , , L. N. da Costa , , C. Davis , J. De Vicente , S. Desai , H. T. Diehl , P. Doel ,T. F. Eifler , , B. Flaugher , P. Fosalba , , J. Frieman , , J. Garc´ıa-Bellido , E. Gaztanaga , ,D. W. Gerdes , , D. Gruen , , R. A. Gruendl , , G. Gutierrez , W. G. Hartley , ,D. L. Hollowood , K. Honscheid , , D. J. James , M. W. G. Johnson , M. D. Johnson ,E. Krause , K. Kuehn , N. Kuropatkin , O. Lahav , T. S. Li , , M. Lima , , J. L. Marshall ,P. Martini , , F. Menanteau , , C. J. Miller , , R. Miquel , , B. Nord , A. A. Plazas ,A. Roodman , , E. Sanchez , V. Scarpine , R. Schindler , M. Schubnell , S. Serrano , ,I. Sevilla-Noarbe , M. Soares-Santos , F. Sobreira , , E. Suchyta , G. Tarle , D. Thomas ,A. R. Walker , Y. Zhang (DES Collaboration) Affiliations are in Appendix B.
Accepted XXX. Received YYY
ABSTRACT
We describe catalog-level simulations of Type Ia supernova (SN Ia) light curves inthe Dark Energy Survey Supernova Program (DES-SN), and in low-redshift samplesfrom the Center for Astrophysics (CfA) and the Carnegie Supernova Project (CSP).These simulations are used to model biases from selection effects and light curveanalysis, and to determine bias corrections for SN Ia distance moduli that are usedto measure cosmological parameters. To generate realistic light curves, the simulationuses a detailed SN Ia model, incorporates information from observations (PSF, skynoise, zero point), and uses summary information (e.g., detection efficiency vs. signal tonoise ratio) based on 10,000 fake SN light curves whose fluxes were overlaid on imagesand processed with our analysis pipelines. The quality of the simulation is illustrated bypredicting distributions observed in the data. Averaging within redshift bins, we finddistance modulus biases up to 0 .
05 mag over the redshift ranges of the low- z and DES-SN samples. For individual events, particularly those with extreme red or blue color,distance biases can reach 0 . https://des.ncsa.illinois.edu/releases/sn . Key words: techniques – cosmology – supernovae c (cid:13) DES Collaboration
Since the discovery of cosmic acceleration (Riess et al. 1998;Perlmutter et al. 1999) using a few dozen Type Ia super-novae (SNe Ia), surveys have been collecting larger SN Iasamples and improving the measurement precision of thedark energy equation of state parameter ( w ). This improve-ment is in large part due to the use of rolling surveys todiscover and measure large numbers of SN Ia light curvesin multiple passbands with the same instrument. The mostrecent Pantheon sample (Scolnic et al. 2018b) includes morethan 1,000 spectroscopically confirmed SNe Ia from low andhigh redshift surveys. Compared to the 20th century sam-ple used to discover cosmic acceleration, the Pantheon sam-ple has more than a 20-fold increase in statistics and muchhigher quality light curves.In addition to improving statistics and light curve qual-ity, reducing systematic uncertainties is equally important.While most of the attention is on calibration, which is thelargest source of systematic uncertainty, significant effortover more than a decade has gone into making robust simu-lations that are used to correct for the redshift-dependentdistance-modulus bias ( µ -bias) arising from selection ef-fects. Selection effects include several sources of experimen-tal inefficiencies: instrumental magnitude limits resultingin Malmquist bias, detection requirements from an image-subtraction pipeline used to discover transients, target selec-tion for spectroscopic follow-up, and cosmology-analysis re-quirements. These selection effects introduce average µ -biasvariations reaching ∼ .
05 mag at the high-redshift range ofa survey. (e.g., see Fig. 5 in Betoule et al. (2014) and Fig. 6in Scolnic et al. (2018b)), and the µ -bias averaged in specificcolor ranges can be an order of magnitude larger.In addition to sample selection, the µ -bias depends onthe parent populations of the SN Ia stretch and color, andalso on intrinsic brightness variations, hereafter called ‘in-trinsic scatter,’ in both the absolute magnitude and in thecolors. For precision measurements of cosmological param-eters, simulations are essential to determine µ -bias correc-tions, and these simulations require accurate models of SNlight curves and sample selection.The main focus of this paper is to describe our sim-ulations of spectroscopically confirmed SNe Ia from threeseasons of the Dark Energy Survey Supernova Program(DES-SN), and the associated low- z sample. The com-bination of these two samples, called DES-SN3YR , isused to measure cosmological parameters presented inDES Collaboration et al. (2019). All simulations were per-formed with the public “SuperNova ANAlysis” (
SNANA ) soft-ware package (Kessler et al. 2009a). In addition to SNe Ia,a variety of source models can be supplied to the
SNANA sim-ulation, including core collapse (CC) SNe, kilonovae (KN),or any rest-frame model described by a time-dependent se-quence of spectral energy distributions.The
SNANA simulations are performed at the “cataloglevel,” which means that rather than simulating SN lightcurves on images, light curve fluxes and uncertainties arecomputed from image properties. The simulation inputs in-clude a rest-frame source model, volumetric rate versus red-shift, cosmological parameters (e.g., Ω M , w ), telescope trans- https://snana.uchicago.edu mission in each passband, calibration reference, observingand image properties from a survey, and random numbersto generate Poisson fluctuations. The simulated light curvesare treated like calibrated light curves from a survey, andare thus analyzed with the same software as for the data.The SNANA simulation is ideally suited for rollingsearches in which the same instrument is used for bothdiscovery and for measuring light curves. Surveys withrolling searches include the Supernova Legacy Survey(SNLS; Astier et al. 2006), the Sloan Digital Sky Survey-II (SDSS-II; Frieman et al. 2008; Sako et al. 2018), thePanoramic Survey Telescope and Rapid Response System(PS1; Kaiser et al. 2002), and DES. The low- z sample, how-ever, is based on follow-up observations from independentsearch programs (Hicken et al. 2009, 2012; Contreras et al.2010; Folatelli et al. 2010, CFA, CSP), and the observingproperties of the search are not available to perform a propersimulation. The low- z simulation, therefore, requires addi-tional assumptions and approximations.Simulated corrections first appeared in the SNLScosmology analysis (Astier et al. 2006). Kessler et al.(2009b) analyzed several samples (low- z , SDSS-II, SNLS,ESSENCE), which led to a more general SNANA framework tosimulate µ -bias corrections for arbitrary surveys. The heartof this framework is a set of two libraries. First, an observa-tion library where each observation date includes a charac-terization of the point spread function (PSF), sky and read-out noise, template noise, zero point, and gain. Second, ahost-galaxy library includes magnitudes and surface profiles,and is used to compute Poisson noise and to model the localsurface brightness. For a specified light curve model, theselibraries are used to convert top-of-the-atmosphere modelmagnitudes into observed fluxes and uncertainties.After a survey has completed, assembling the librariesis a relatively straightforward exercise, and SNANA sim-ulations have been used in numerous cosmology analy-ses (Kessler et al. 2009b; Conley et al. 2011; Betoule et al.2014; Rest et al. 2014; Scolnic et al. 2014b, 2018b). Be-fore a survey has started, predicting the libraries is oneof the critical tasks for making reliable forecasts. Suchpre-survey forecasts with the
SNANA simulation have beenmade for LSST (LSST Science Collaboration et al. 2009;Kessler et al. 2010b), DES-SN (Bernstein et al. 2012), andWFIRST (Hounsell et al. 2018).While our main focus is to describe the DES-SN3YR simulation of SNe Ia, and how a large ( ∼ events) simu-lated bias-correction sample is used to model biases in themeasured distance modulus, it is worth noting other applica-tions from the flexibility in SNANA . First, these simulationsare used to generate 100 data-sized
DES-SN3YR valida-tion samples that are processed with the same bias correc-tions and cosmology analysis used on the data. This vali-dation test is used to accurately check for w -biases at the ∼ .
01 level, and to compare the spread in w values withthe fitted uncertainty (Brout et al. 2019b). The validationand bias-correction samples are generated with the samecode and options, but are used for different tasks. Other Large Synoptic Survey Telescope: Wide Field Infrared Space Telescope: https://wfirst.gsfc.nasa.gov
MNRAS , 1–18 (2015) imulations to Correct SN Ia Distance Biases applications include CC simulations for a classification chal-lenge (Kessler et al. 2010a), CC simulations for a PS1 cos-mology analysis using photometrically identified SNe Ia(Jones et al. 2017, 2018), simulating the KN search efficiency(Soares-Santos et al. 2016; Doctor et al. 2017), and makingKN discovery predictions for 11 past, current, and futuresurveys (Scolnic et al. 2018a).In this work we describe the simulation from a sci-entific perspective without instructions on implementation.For implementation, we refer to the manual available fromthe SNANA homepage, and recommend contacting commu-nity members familiar with the software. This simulationis possible because of extensive publicly available resources.When using this simulation in a publication, we recommendthe added effort of referencing the relevant underlying con-tributions, such as the source of models or data samples usedto make templates.The organization of this paper is as follows. The
DES-SN3YR sample is described in §
2. An overview of the sim-ulation method is in §
3, and fake SN light curves overlaidon images is described in §
4. Modeling is described in § § § § µ -biases are described in §
9. We con-clude in §
10, and present additional simulation features inthe Appendix.
Here we describe the data samples that are simulated for thecosmology analysis in DES Collaboration et al. (2019) andBrout et al. (2019b). After selection, this sample includes207 spectroscopically confirmed SNe Ia from the first threeseasons (2013 August through 2016 February) of DES-SN(Diehl et al. 2016), and 122 low- z ( z < .
1) SNe Ia fromCFA3 (Hicken et al. 2009), CFA4 (Hicken et al. 2012), andCSP (Contreras et al. 2010; Folatelli et al. 2010). This com-bined sample of 329 SNe Ia is called “
DES-SN3YR .”The DES-SN sample was acquired in rolling searchmode using the 570 Megapixel Dark Energy Camera (DE-Cam; Flaugher et al. (2015)) mounted on the 4-m Blancotelescope at the Cerro Tololo Inter-American Observatory(CTIO). Ten 2.7 deg fields were observed in g, r, i, z broad-band filters, with a cadence of roughly 1 week in each band.Defining single-visit depth as the magnitude where the de-tection efficiency is 50%, eight of these fields have an aver-age single-visit depth of ∼ . ∼ . DiffImg ) described in Kessler et al. (2015), and the spec-troscopic selection is described in D’Andrea et al. (2018).The instrumental photometric precision from
DiffImg is lim-ited at the 2% level, and therefore a separate and more accu-rate “Scene Model Photometry (
SMP )” pipeline (Brout et al.2019a) is used to measure the light curve fluxes and un-certainties for the cosmology analysis. For each event,
SMP simultaneously fits a 30 ×
30 pixel-grid flux model to eachobservation, where the model includes a time-independent galaxy flux and a time-dependent source flux, each convolvedwith the PSF.In addition to SN Ia light curves, the DES-SN datainclude other ‘meta-data’ for monitoring, calibration (e.g.,telescope transmissions) and analysis. An important meta-data product for simulations is from the fluxes of ∼ , § DiffImg .The low- z sample includes redshifts, light-curve fluxes,flux uncertainties, and filter transmission functions. Thephotometry, however, is not from a rolling search but is fromfollow-up programs that target SNe Ia discovered from othersearch programs such as LOSS (Ganeshalingam et al. 2013).Since the observation information from the search programsis not available, the resulting observation library is an ap-proximation based on several assumptions ( § The primary goal of our simulation is to provide in-puts to the ‘BEAMS with Bias Correction’ (BBC) method(Kessler & Scolnic 2017), which is the stage in our cosmol-ogy analysis that produces a bias-corrected SN Ia Hubble di-agram ( § SALT-II light curve model,in the same way as for the data, to produce three parametersfor each event: amplitude ( x ), stretch ( x ), and color ( c ).A statistical comparison of the fitted and true parameters isused to determine a bias correction for each parameter ona 5-dimensional (5D) grid of { z, x , c, α, β } , where z is theredshift, x and c are SALT-II -fitted parameters, and α and β are SALT-II standardization parameters ( § SALT-II parametersfrom the data, and these corrected parameters are used todetermine a bias-corrected distance modulus.A schematic illustration of the
SNANA simulation isshown in Fig. 1. The left column illustrates the generationof the source spectral energy distribution (SED), and as-trophysical effects. These effects include host galaxy extinc-tion, redshifting, cosmological dimming, lensing magnifica-tion, peculiar velocity, and Milky Way extinction. The out-put of this column is a true magnitude at the top of theatmosphere.The middle column of Fig. 1 illustrates the instrumentalsimulation, where the true magnitude is converted into anobserved number of CCD counts, hereafter denoted ‘flux,’and the uncertainty on the flux. The observation information(PSF, sky noise, zero point) and host galaxy profile are usedto compute the Poisson noise.The right column in Fig. 1 illustrates the simulationof the trigger that selects events for analysis. Epochs thatresult in a detection, which is roughly a 5 σ excess on thesubtracted image ( § MNRAS , 1–18 (2015)
DES Collaboration
The noise and trigger models in Fig. 1 each have inputsbased on analyzing artificial light curves overlaid on CCDimages. These fakes are described next in § Ideally, simulated bias corrections would be based on SN Ialight curve fluxes overlaid onto CCD images and processedwith exactly the same software as the data. The CPUresources for so many image-based simulations, however,would be enormous. Kessler et al. (2015) estimates that
SNANA simulations are × faster than image-based sim-ulations, while still producing realistic light curve fluxesand uncertainties. Although we do not perform image-basedsimulations for bias corrections, we use image simulationsto inform the SNANA simulation. Specifically, 10,000 fakeSN light curves were overlaid on DES-SN images and pro-cessed through the same pipelines as the data, includingdifference-imaging (
DiffImg ; Kessler et al. 2015) and pho-tometry (Brout et al. 2019a) pipelines. For
DiffImg , thesefakes are used to measure the detection efficiency versussignal-to-noise ratio (SNR), which is needed for the trig-ger model in Fig. 1. For the photometry pipeline, fakes areused to measure the rms scatter between measured and truefluxes, and the rms is used to determine scale factors for theSN flux uncertainties (noise model in Fig. 1).Prior to the start of DES operations, the fake light curvefluxes were computed from the
SNANA simulation using thepopulation of stretch and color ( § § . < z < .
4) is described by a polynomial function of redshift, andwas tuned to acquire good statistics over the full redshiftrange and thus span the full range of SN magnitudes. Eachfake location is selected on top of a random galaxy as de-scribed in § ∼ ∼ .
001 mag uncertainties for real sources, and thus the as-trometric precision is adequate for the fakes.Since the goal with fakes is to characterize single-epochfeatures of the CPU intensive image-processing pipelines,and to input these features into the much faster
SNANA sim-ulation, the choice of SN light curve model does not matteras long as the fake model magnitudes span the same rangeas the data. The resulting
SNANA simulation can be used tosimulate arbitrary light curve models and redshift depen- dence. For example, to evaluate systematic uncertainties inthis analysis, we simulate SNe Ia with different models of in-trinsic scatter and with different populations of stretch andcolor.While this seemingly large sample of SN fakes is usedto characterize image-processing features, these fakes can-not be used to compute µ -bias corrections for two reasons.First, the light curve model used to generate fakes is delib-erately different from reality for practical reasons explainedabove. Second, 10,000 fakes is more than an order of mag-nitude smaller than what is needed for the bias-correctionsample used in the BBC method (Kessler & Scolnic 2017).In addition, even if an accurate SN Ia model were used togenerate fakes, the resulting efficiency and bias correctionswould be valid only for that particular SN Ia model, and notapplicable to other SN Ia models, nor to transient modelssuch as CC SNe or KNe. Here we describe the simulation components under “SourceModel” in Fig. 1. This includes the generation of the SN IaSED as a function of time, how the SEDs are altered as thelight travels from the source to Earth, and how each SED istransformed into a model magnitude above the atmosphere.
To simulate SNe Ia, we use the
SALT-II
SED model de-scribed in Guy et al. (2010), and the trained model fromthe Joint Lightcurve Analysis (Betoule et al. 2014). The un-derlying model is a rest-frame SED with wavelengths span-ning 2000 ˚A to 9200 ˚A, and rest-frame epochs spanning − < T rest < +50 days with respect to the epoch of peakbrightness. For each event there are four SN-dependent pa-rameters generated by the simulation:(i) time of peak brightness, t , randomly selected between2 months before the survey begins and one month after thesurvey ends.(ii) SALT-II color parameter, c .(iii) SALT-II stretch parameter, x .(iv) CMB frame redshift, z cmb , true , selected from the ratemodel in § § § § T rest . For light curvefitting we use epochs satisfying − < T rest <
45 days, butwe simulate epochs outside this T rest range to account foruncertainty in the fitted t , which increases the true T rest range.The SALT-II amplitude parameter, x , is computed us-ing the estimator in Tripp (1998),log ( x ) = − . µ model + µ lens − αx + βc − M ) , (1) MNRAS000
45 days, butwe simulate epochs outside this T rest range to account foruncertainty in the fitted t , which increases the true T rest range.The SALT-II amplitude parameter, x , is computed us-ing the estimator in Tripp (1998),log ( x ) = − . µ model + µ lens − αx + βc − M ) , (1) MNRAS000 , 1–18 (2015) imulations to Correct SN Ia Distance Biases Figure 1.
Flow chart of
SNANA simulation. where µ model is the distance modulus ( § µ lens is due to lensing magnifica-tion ( § α and β are SALT-II standardization parame-ters ( § M = − .
365 is a reference magnitude. It iswell known that M is degenerate with the Hubble constant( H ), and that their values have no impact in the SN Iaanalysis of cosmological parameters. However, the qualityof the simulation depends on predicting accurate observer-frame magnitudes, and therefore M + 5 log ( H ) must bewell determined. The SALT-II
SED is redshifted using theheliocentric redshift ( z hel , true ), which is transformed from z cmb , true using the sky coordinates from the observation li-brary. z hel , true also includes a random host-galaxy peculiarvelocity described in § Before redshifting the
SALT-II
SED, intrinsic scatter is ap-plied as spectral variations to the SED. To evaluate sys-tematic uncertainties in the bias corrections, two differ-ent models are used that approximately span the rangeof possibilities in current data samples. First is the ‘G10’model (Guy et al. 2010) from the
SALT-II training pro-cess. Roughly 75% of the scatter is coherent among all wave-lengths and epochs, while the remaining 25% of the scatterresults from color variations that are not correlated with lu-minosity. The second model, ‘C11,’ is based on broadband(
UBV RI ) covariances found in Chotard et al. (2011). Only25% of the scatter is coherent, while the remaining scatter re-sults from color variations. Details of these models are given in Kessler et al. (2013), and both models result in 0 .
13 magintrinsic scatter on the Hubble diagram. SALT-II
Model Parameters
While the
SALT-II
SED and color law model parametersfrom the training process are fixed for each SN, there are afew parameters that are determined outside the training pro-cess. To simulate validation data samples, the standardiza-tion parameters are: α = 0 . β G10 = 3 .
1, and β C11 = 3 . § µ -bias simu-lations are defined on a 2 × µ -bias as a function of α and β ; this is describedin § x ) and color ( c ),we use the asymmetric Gaussian parametrization fromScolnic & Kessler (2016, hereafter SK16). For DES-SNstretch & color, we use the high- z G10 and C11 rows fromTable 1 of SK16. For the low- z sample we use the color pop-ulation parameters from the low- z row of Table 1 of SK16.The stretch population is double-peaked, and we use theparametrization from Appendix C of Scolnic et al. (2018b).While we account for the color and stretch population differ-ences between low- z and DES-SN, the redshift dependence This 0.13 mag scatter is larger than typical fitted σ int valuesof 0.1 mag because of SALT-II model uncertainties; see § , 1–18 (2015) DES Collaboration of the population has not been quantified and therefore isnot included in our simulations.
The luminosity distance ( D L ) for a flat universe is computedas D L = (1 + z hel , true ) cH Z z cmb , true dz/E ( z ) (2) E ( z ) = (cid:2) Ω Λ (1 + z ) w ) + Ω M (1 + z ) (cid:3) / , where Ω M is today’s matter density, Ω Λ is today’s dark en-ergy density, and w is the dark energy equation of stateparameter. Note that both the CMB and heliocentric red-shifts are used to compute D L , but the 1 + z hel , true pre-factor is an approximation: the exact pre-factor is 1 + z obs ,where z obs is the measured redshift (Davis et al. 2011). How-ever, we do not simulate Earth’s motion around our Sun,nor the local SN motion within its host galaxy, and there-fore z obs = z hel , true . The error on D L from ignoring localmotions is less than 10 − . To compute E ( z ) in our simu-lations we set H = 70 km / s, Ω Λ = 0 .
7, Ω M = 0 . w = −
1. The distance modulus ( µ model in Eq. 1) is definedas µ model = 5 log ( D L /
10 pc).Weak lensing effects are described by the µ lens term inEq. 1, and modeled as follows: • . < z < . κ ) distribution is de-termined from a 900 deg patch of the MICECAT N -bodysimulation (Crocce et al. 2015). Galaxies are from a halooccupation distribution and a sub-halo abundance matchingtechnique (Carretero et al. 2015). The lensing distribution isdetermined from µ lens = 5 log (1 − κ ) (shear contributionis negligible and ignored). • z < . µ lens at z = 0 . µ lens , . ), the lensing at lower redshiftsis computed as µ lens ,z = µ lens , . × z/ . . (3)As a crosscheck, this z -scale approximation works wellwithin the MICECAT redshift range: e.g., µ lens , . ≃ µ lens , . × (0 . / . µ lens dis-tribution is approximately 0 . × z . For systematic studies,the simulation includes an option to scale the width of thedistribution to increase or decrease the scatter.To properly select from the asymmetric µ lens distribu-tion, instead of a Gaussian approximation, the lensing mag-nification probability is defined as a 2-dimensional functionof redshift and µ lens . For each simulated redshift, a ran-dom µ lens is selected from the µ lens probability distribution.While our lensing model accounts for large scale structure onaverage, it does not account for correlations between eventswith small angular separations. This H value was used in the SN Ia model training, which de-termines the absolute brightness M , and therefore the simulated H should not be updated with more recent measurements. https://cosmohub.pic.es The generated CMB-frame redshift, z cmb , true , is transformedto the heliocentric frame, z hel , true , using the sky coordinatesfrom the observation library. The redshift observed in theheliocentric frame is z hel , obs = (1 + z hel , true )(1 + v pec /c − v pec , cor /c ) − δz noise = (1 + z hel , true )(1 − v pec , err /c ) − δz noise , where v pec is a peculiar velocity randomly chosen from aGaussian profile with σ vpec = 300 km/sec, and δz noise is ameasurement error. For DES-SN and low- z , δz noise is drawnfrom a Gaussian with σ z = 10 − .While the peculiar velocity model is the same for low- z and DES-SN, corrections are modeled only for the low- z sample. The simulated low- z correction simply reduces the v pec scatter without applying real corrections. Following thePantheon analysis (Scolnic et al. 2018b), v pec , cor = v pec + v pec , err where v pec , err is a randomly selected error from aGaussian profile with a 250 km/sec sigma. Finally, z hel , obs is transformed back to the CMB frame redshift, z cmb , obs .Peculiar velocity corrections for DES-SN can be computedin principle, but such corrections on a high-redshift sampleare negligible and were thus ignored. For each simulated event the Galactic extinction pa-rameter, E ( B − V ), is computed from the maps inSchlegel et al. (1998). Following a stellar analysis from SDSS(Schlafly & Finkbeiner 2011), we scale the E ( B − V ) valuesby 0.86. We assume the reddening law derived in Fitzpatrick(1999), and with A V defined as the extinction at 5500 ˚A, R V ≡ A V /E ( B − V ) = 3 . The redshift distribution of SNe Ia is generated froma co-moving volumetric rate, R ( z ), measured by SNLS(Perrett et al. 2012): R ( z ) = 1 . × − (1 + z ) . yr − Mpc − , (6)and is valid up to redshift z < Here we describe the simulation components under ‘NoiseModel’ in Fig. 1. There are two steps needed to simulate fluxand noise. First, an observation library is needed to char-acterize observing conditions ( § § An observation library is a collection of sky locations, eachspecified by right ascension (RA) and declination (Dec),along with a list of observations for each location. For a
MNRAS000
MNRAS000 , 1–18 (2015) imulations to Correct SN Ia Distance Biases small survey area, a single sky location may be adequate,particularly for making forecasts. For a proper simulation,however, many sky locations should be used with either ran-dom sampling or a grid. For DES-SN we use ∼ randomsky locations covering 27 deg , which averages over densityfluctuations to achieve a representative sample for a homo-geneous universe. For simulations with more than 10 gen-erated events, the library sky locations and observations arere-used with SNe that have a different set of randomly cho-sen properties. Since ∼
1% of the DES-SN events occur inthe overlap between two adjacent fields, and thus have dou-ble the number of observations, the simulation includes amechanism to handle overlapping fields.The exposure information for each sky location is de-fined as follows: • MJD is the modified Julian date. • FILTER is the filter passband. • GAIN is the number of photoelectrons per ADU . • SKYSIG is the sky noise, including read noise. • σ PSF = p NEA / π is an effective Gaussian σ for the PSF,and NEA is the noise-equivalent area defined as
NEA = (cid:20) π Z [PSF( r )] rdr (cid:21) − . (7)For a PSF-fitted flux, the fitted flux variance is the sky noiseper pixel multiplied by NEA . • ZPTADU is the zero point (ADU), and includes telescopeand atmospheric transmission.Many of the DES-SN visits include multiple exposures:two z -band exposures in each of the 8 shallow fields, and the2 deep fields include 3, 3, 5, 11 exposures for g, r, i, z -bands,respectively. During the survey, DiffImg performs the searchon co-added exposures. In the analysis,
SMP determines theflux for each individual exposure, and the fluxes are co-addedat the catalog level. The co-adding for both
DiffImg and
SMP are treated the same in the simulation by co-adding theobservation library information as follows:
MJD = hX MJD i i /N expose SKYSIG = qX SKYSIG i σ PSF = hX σ PSF i i /N expose ZPTADU = 2 . × log hX (0 . · ZPTADU i ) i , (8)where N expose is the number of exposures and each sum in-cludes i = 1 , N expose . ZPTADU is an approximation assumingthe same
GAIN for each exposure; the DES
GAIN variationsare a few percent.The randomly selected time of peak brightness ( t , § MJD -overlap in the observation sequence. ADU: Analog to Digital Unit. shallow g, r, i include one exposure per visit. z Sample
The low- z sample does not include the observation proper-ties (PSF, sky noise, zero point) from their image-processingpipelines. Therefore we construct an approximate libraryfrom the low- z light curves, using their sky locations, ob-servation dates, and SNR. There is not enough light curveinformation to uniquely determine the observation proper-ties, and therefore we use three assumptions: (1) fix each GAIN to unity, (2) fix each PSF to 1 ′′ (FWHM), and (3) usea previously determined set of broadband sky magnitudes,and interpolate the sky magnitude to the central wavelengthof each simulated filter. For ground-based surveys we use theaverage sky mags in ugrizY passbands from a simulation ofLSST (Delgado et al. 2014). The ZPTADU parameter is ad-justed numerically so that the calculated SNR matches theobserved SNR.Another subtlety is that the low- z sample was collectedover decades, and thus for a randomly selected explosiontime there is little chance that the simulated light curvewould overlap the observation dates. To generate low- z lightcurves more efficiently, the measured time of peak brightness( t ) for each light curve is used for the corresponding sky lo-cation, thus ensuring a light curve will be generated. OtherSN properties (redshift, color, stretch, intrinsic scatter) arerandomly selected in the same way as for the DES-SN sim-ulation. Host galaxies are used for two purposes in the
SNANA simula-tions of DES-SN. First, fakes are generated to be overlaid ontop of galaxies in real CCD images. Second, to simulate biascorrections and validation samples in the analysis, the localsurface brightness from the host is used to add Poisson noiseand anomalous scatter (Fig. 2) in the light curve fluxes. Wedo not simulate low- z host galaxies because the cadence li-brary is constructed from observed SNR that should alreadyinclude Poisson noise from the host. While anomalous scat-ter in the low- z sample may be present, the local surfacebrightness information is not available to study this effect. For DES-SN the
SNANA simulation uses a host galaxylibrary (
HOSTLIB ), where each galaxy is described by (1) he-liocentric redshift, z HOST , hel , (2) coordinates of the galaxycenter, (3) observer-frame magnitudes in the survey band-passes, and (4) S´ersic profile with index n = 0 . HOSTLIB can be created from data or from an astro-physical simulation. Our DES-SN simulation uses a galaxycatalog derived from the DES science verification (SV) data,as described in Gupta et al. (2016). Eventually this galaxycatalog will be updated using a much deeper co-add fromthe full DES data set.There are two caveats about this
HOSTLIB . First, z HOST , hel are photometric redshifts (photo- z ). Extremephoto- z outliers are rejected by requiring the absolute r and i band magnitudes ( M r,i ) to satisfy − < M r,i < −
16, where M r,i = m r,i − µ phot , m r,i are the observed magnitues, and It would be a valuable community contribution to use publicsurvey data (e.g., PS1, SDSS, DES) and determine the local sur-face brightness for each low- z event.MNRAS , 1–18 (2015) DES Collaboration µ phot is the distance modulus computed from the photo- z .The second caveat is that the measured half-light radii werescaled by a factor of 0.8 to obtain better data-simulationagreement in the surface brightness distribution ( § HOSTLIB event satisfying | z SN , hel − z HOST , hel | < .
01 + 0 . z SN , (9)where z SN , hel and z HOST , hel are the heliocentric redshifts forthe SN and host galaxy, respectively. The SN redshift isupdated to z HOST , hel , the CMB-frame redshift ( z cmb , true ) iscomputed from z HOST , hel , and the resulting z cmb , true is usedto update the distance modulus and light curve magnitudes.To avoid multiple fakes around a single galaxy, each HOSTLIB event can be used only once. The SN coordinates are chosennear the host, weighted by the S´ersic profile.To simulate samples for the analysis, the redshift match-ing between the SN and the host is the same as for fakes(Eq. 9). However, the generated SN redshift (from ratemodel) and its coordinates (from cadence library) are pre-served. A random location near the host is selected fromthe S´ersic profile, and is used to determine the local surfacebrightness and to add Poisson noise to the light curves. ThePoisson noise variance is computed by integrating the host-galaxy flux over the noise equivalent area (Eq. 7). In thisimplementation of the DES-SN simulation, the host-galaxyspatial distribution is homogeneous on all scales. Large-scalestructure can be incorporated as explained in the Appendix.
Here we describe how a true source magnitude at the top ofthe atmosphere, m true , is used to determine the instrumentalflux and its uncertainty. The flux unit for this discussion isphotoelectrons, but the simulation uses the GAIN to properlydigitize the signals in ADU.The true flux is given by F true = 10 . m true − ZPTpe ) , (10)where ZPTpe = ZPTADU + 2 . ( GAIN ) is the zero point inunits of photoelectrons.The true Poisson noise for the measured flux is givenby σ = [ F true + ( NEA · b ) + σ ] ˆ S , (11)where • F true is the true flux; • NEA is the noise equivalent area (Eq. 7); • b is the background per unit area (includes sky andCCD read noise); • σ host is Poisson noise from the underlying host galaxy( § • ˆ S sim is an empirically determined scale ( § NEA , b , and σ PSF are obtained from the observation library( § S sim is determined from analyzing the fakes ( § SMP ) be-havior that cannot be computed from first principles, mainlythe anomalous flux scatter from bright galaxies. Because of the large number of reference images used in
SMP , we do notinclude an explicit template noise term.For PSF-fitted fluxes, the noise estimate in Eq. 11 isan approximation that is more accurate for sky-dominatednoise, or as F true / ( NEA · b ) becomes smaller. In principleEq. 11 is also accurate for bright events with high SNR,but brighter SNe are associated with brighter galaxies thatintroduce anomalous flux scatter. In § σ Ftrue ) is used to select a ran-dom fluctuation on the true flux ( F true ), resulting in theobserved flux, F . The measured uncertainty for data is notthe true uncertainty, but rather an approximation based onthe observed flux. In the simulation, the measured uncer-tainty, σ F , is computed from the observed flux by substitut-ing F true → F in Eq. 11: σ F = p σ + ( F − F true ) ( F > , (12) σ F = p σ − F true ( F < . (13)In the case where F < F = 0)because σ F is dominated by sky noise which is determinedfrom a CCD region well away from the SN. ˆ S sim ) An accurate description of the uncertainty is important inorder to model selection cuts on quantities related to SNRand chi-squared from light curve fitting. With ˆ S sim = 1, thecalculated flux uncertainty, σ Ftrue in Eq. 11, is an approx-imation for PSF-fitting, and it does not account for all ofthe details in the
SMP pipeline. We correct the simulated un-certainty to match the observed flux scatter in the fakes,which we interpret to be the true scatter in the data. Theuncertainty correction, ˆ S sim , is defined asˆ S sim ( ~ O ) = rms[( F true − F SMP ) /σ ′ F ] fake rms[( F true − F sim ) /σ ′ F ] sim , (14)where F true is the true flux, F SMP is the fake flux determinedby
SMP , and F sim = F true + N (0 , σ F ) is the simulated fluxwith ˆ S sim = 1.The σ ′ F term in both denominators is a common refer-ence so that the ∆ F/σ ′ F ratios in Eq. 14 are ∼ unity, whichsignificantly improves the sensitivity in measuring the ˆ S sim map. σ ′ F is the naively expected uncertainty computed fromEq. 11 with ˆ S sim = 1, F true → F , and σ host computed us-ing the approximation of a constant local surface brightnessmagnitude over the entire noise-equivalent area. This σ host approximation can be used with photometry that does notinclude a detailed model of the host galaxy profile, and sim-ulation tests have shown that this approximation does notdegrade the determination of ˆ S sim ( ~ O ).The numerator includes information from the fakes and SMP pipeline. The argument ~ O indicates an arbitrary depen-dence on observed image properties. For the DES-SN3YR analysis we use a 1-dimensional map with ~ O = { m SB } ,where m SB is the local surface brightness magnitude. Beforedetermining ˆ S sim , it is important that the simulated distri-butions in redshift, color, and stretch ( § MNRAS000
SMP , and F sim = F true + N (0 , σ F ) is the simulated fluxwith ˆ S sim = 1.The σ ′ F term in both denominators is a common refer-ence so that the ∆ F/σ ′ F ratios in Eq. 14 are ∼ unity, whichsignificantly improves the sensitivity in measuring the ˆ S sim map. σ ′ F is the naively expected uncertainty computed fromEq. 11 with ˆ S sim = 1, F true → F , and σ host computed us-ing the approximation of a constant local surface brightnessmagnitude over the entire noise-equivalent area. This σ host approximation can be used with photometry that does notinclude a detailed model of the host galaxy profile, and sim-ulation tests have shown that this approximation does notdegrade the determination of ˆ S sim ( ~ O ).The numerator includes information from the fakes and SMP pipeline. The argument ~ O indicates an arbitrary depen-dence on observed image properties. For the DES-SN3YR analysis we use a 1-dimensional map with ~ O = { m SB } ,where m SB is the local surface brightness magnitude. Beforedetermining ˆ S sim , it is important that the simulated distri-butions in redshift, color, and stretch ( § MNRAS000 , 1–18 (2015) imulations to Correct SN Ia Distance Biases Deep-g Shallow-gDeep-r Shallow-r S s i m Deep-i Shallow-iSB mag Deep-z SB mag Shallow-z
Figure 2.
Simulated uncertainty scale, ˆ S sim , as a function oflocal surface brightness mag (SB mag). Each panel indicates theset of fields and passband. Left panels are for the deep SN fields(depth per visit ∼ . ∼ . match the distributions for the fakes. After this tuning, ˆ S sim versus m SB is shown in Fig. 2. For m SB values outside thedefined range of the map, ˆ S sim is computed from the closest m SB value in the map. This m SB -dependence has been seenpreviously in the difference-imaging pipeline (Kessler et al.2015; Doctor et al. 2017), and it persists in the SMP pho-tometry. After applying the corrections in Fig. 2, the fluxuncertainties for the fakes and simulations agree to within5% over the entire m SB range.The impact of the uncertainty corrections is shown inFig. 3, which compares the maximum SNR distribution ineach band for fakes and the simulation. Compared to simu-lations with no correction, simulations with corrections showmuch better agreement with the fakes.While Eq. 14 describes the simulated correction, thereis an analogous correction for the data uncertainty producedby SMP : σ SMP → σ SMP × ˆ S SMP , whereˆ S SMP ( ~ O ) = rms[( F true − F SMP ) /σ ′ F ] fake h σ SMP /σ ′ F i fake . (15)The observed scatter in the fakes is a common reference forboth the data and simulations, and therefore the numer-ator (Eq. 15) is the same as for the simulated correction(Eq. 14). The denominator, h σ SMP /σ ′ F i fake , specifies an aver-age within each ~ O bin. This ˆ S SMP correction is applied to thedata uncertainties, including fakes, while ˆ S sim is applied tothe simulated noise and uncertainty. More details of ˆ S SMP aregiven in Brout et al. (2019a).
Here we describe the simulation components under ‘Trig-ger Model’ in Fig. 1. Ideally, every DECam pixel would becontinuously monitored for transient activity. However, stor-ing light curves near every pixel is impractical with today’s g FakesSim (no corr) g FakesSim (+corr) r ri E n t r i e s i SNRMAX z SNRMAX z Figure 3.
Distribution of maximum SNR in the DES band la-beled on each panel. Filled circles are for the fakes processedthrough the
SMP pipeline; histogram is the simulation. Left panelsare before applying the ˆ S sim scale; right panels are after applyingthe ˆ S sim scale from Fig. 2. computing, and therefore a ‘trigger’ is used to select candi-dates for analysis. Here we describe the trigger simulationfor the DES-SN and low- z samples. For a general survey,the simulation of the trigger consists of three stages: 1) de-tecting PSF-shaped objects above threshold, 2) matchingmultiple objects, from different bands and nights, to formcandidates, and 3) selection for spectroscopic classification.All three stages are modeled for DES-SN. For low- z , how-ever, we do not have information to simulate the first twotrigger stages and therefore all three trigger stages are em-pirically combined in the third stage.The total efficiency ( E TOT ) can be described by E TOT = E ~ SNR × E spec , (16)where E ~ SNR includes the first two trigger stages and de-pends on the SNR for each epoch ( ~ SNR ), and E spec de-scribes the spectroscopic selection in the third stage. Wedo not explicitly define E ~ SNR , but instead model the effi-ciency vs. SNR for each epoch. E spec , however, is explicitlydescribed by a smooth function of magnitude at peak bright-ness. Another subtlety here is that E ~ SNR is valid for arbi-trary transient source models, while E spec is valid only forSNe Ia and only if the first two trigger stages are satisfied. For the first trigger stage, fakes are used to characterize thedetection efficiency versus SNR in each filter, as shown inFig. 8 of Kessler et al. (2015). The efficiency reaches 50%around SNR ∼
5. Since these efficiency curves are intendedfor simulations, we do not use the measured SNR, but in-stead the fake SNR is calculated from the true flux (Eq. 10)and noise (Eq. 11) with ˆ S sim = 1. These efficiency curvesare therefore determined as a function of a calculated SNRquantity that is calculated in exactly the same way in thesimulation.In the second trigger stage, a candidate requires two MNRAS , 1–18 (2015) DES Collaboration detections on separate nights within 30 days. Thus a single-night detection in all four bands ( g, r, i, z ) will not trigger acandidate. However, a single-band detection on two separatenights will trigger a candidate.The third trigger stage, spectroscopic selection effi-ciency ( E spec ), is the most subtle. While the selection al-gorithm was designed to exclude human decisions as muchas possible (D’Andrea et al. 2018), we are not able to simu-late the selection algorithm because we have eight frequentlyused telescopes, inefficiencies due to weather and schedul-ing, spectral classification uncertainty, and a small amountof human decision making.Ideally we would compute E spec as a ratio of spectro-scopically confirmed events (numerator) to photometricallyidentified events (denominator). A data-derived E spec anal-ysis is under development and described in D’Andrea et al.(2018), but here we use simulations to predict the denomi-nator. A caveat is that a simulation used to determine E spec needs the population parameters for stretch and color ( § E spec . Rather than performing an iterative procedure withDES-SN data, we use the population parameters from exter-nal data sets as described in SK16, who show that varyingthe external E spec functions has a negligible effect on thepopulation parameters.Without a well-defined algorithm to compute E spec , weuse an empirical model where E spec depends on the i -bandmagnitude at the epoch of peak brightness, i peak . The basicidea is to compare the i peak distribution between data anda simulated sample passing the first two trigger stages (i.e.,with E spec = 1). We define E spec ( i peak ) to be a smooth curvefit to the data/sim ratio as a function of i peak (solid curve inFig. 4), where i peak is computed from the best-fit SALT-II model. The data/sim ratio is fit to a sigmoid function, E spec ( i peak ) = s [1 + e ( s i peak − s ) ] − , (17)where s , s , s are floated parameters determined with em-cee (Foreman-Mackey et al. 2013) and the data uncertain-ties are modeled using a Poisson distribution. For the cos-mology analysis, E spec can be arbitrarily scaled (boundedbetween 0 and 1) without affecting the µ -bias determina-tion, and thus to generate events most efficiently we havescaled E spec to have a maximum efficiency of 1.There is a subtle caveat in the DiffImg trigger mod-eling related to bright galaxies. As illustrated in Figure 7of Doctor et al. (2017), image-subtraction artifacts result inan anomalous decrease in detection efficiency as the localsurface brightness increases. Here the term ‘anomalous’ in-dicates an efficiency loss that is much greater than expectedfrom the increased Poisson noise from the host galaxy. WhileFig. 2 shows how the
SNANA simulation models anomalousscatter, the simulation does not model the anomalous de-tection inefficiency. Studies with fakes have shown that thisbright-galaxy anomaly does not reduce the trigger efficiencyfor nearby SNe Ia on bright galaxies. The reason is that thereare a few dozen opportunities to acquire detections, and itis very unlikely to fail the 2-detection trigger requirement. z Trigger
As explained in Betoule et al. (2014) and Scolnic et al.(2014b), there is evidence that the low- z search is magni- i peak E s pe c ( da t a / s i m r a t i o ) DES-SN
Figure 4. E spec vs. i peak for DES-SN sample. Filled circles aredata/sim ratios, with error bars from Poisson uncertainties on thebest-fit model curve. The simulation includes the first two triggerstages ( E spec = 1), uses the G10 scatter model, and is scaledto match the data statistics for the brightest events. Smoothsolid curve is a fit that defines E spec in the simulation, and max E spec = 1 is an arbitrary normalization. B peak CFA3 E s pe c ( da t a / s i m r a t i o ) B peak CFA4 B peak CSP
Figure 5. E spec vs. B peak for each low- z sample. Filled circlesare the data/sim ratio with E spec = 1 in the simulation. Smoothcurve is a fit that defines E spec in the simulation. tude limited because of the decreasing number of events withredshift, and because higher redshift events are bluer. Onthe other hand, many low- z searches target a specific list ofgalaxies, suggesting a volume-limited sample. We thereforesimulate both assumptions for evaluating systematic uncer-tainties.For the magnitude-limited assumption, we incorporateall trigger stages into a single E spec function of B -band mag-nitude at the time of peak brightness ( B peak ). Following therecipe for the DES-SN simulation, we simulate a low- z sam-ple with E ~ SNR = 1 and define E spec to be the data/simratio vs. B peak (Fig. 5). The fitted B peak function is a one-sided Gaussian as described in Appendix C of Scolnic et al.(2018b). Describing E spec as a function of V or R band alsoworks well, so the choice of B band is arbitrary.For the volume-limited assumption, which is used asa systematic uncertainty in Brout et al. (2019b), we set E TOT = 1 and interpret the redshift evolution of stretchand color to be astrophysical effects instead of artifacts fromMalmquist bias. To match the low- z data, the low- z simula-tion is tuned using redshift-dependent stretch and color pop-ulations: x → x + 25 z and c → c − z . There is no physicalmotivation for this redshift dependence, and therefore thisis a conservative assumption for the systematic uncertainty. MNRAS , 1–18 (2015) imulations to Correct SN Ia Distance Biases Here we qualitatively validate the simulations by comparingsimulated distributions with data. While we do not quantifythe data-simulation agreement here (e.g., via χ ), such quan-titative comparisons are used to assess systematic uncertain-ties in Brout et al. (2019b). To limit statistical uncertaintiesin these comparisons, very large simulations are generatedand the distributions are scaled to match the statistics of thedata. Recall that the tuned distributions are E spec ( i peak ) andthe populations for stretch and color; all other inputs to thesimulation are from measurements.We apply light-curve fitting and selection requirements(cuts) that depend on SALT-II fitted parameters, SNR, andlight curve sampling ( § i peak distribution for data andsimulation are guaranteed to match because of the methodfor determining E spec in § E ( B − V ) and maximum gap between observations, are alsoin excellent agreement, and this agreement validates thechoice of random sky locations in the cadence library. Thedouble peak structure of E ( B − V ) is from the large skyseparations between groups of fields.The middle column of Fig. 6 compares the maximumSNR in each band, and these are the most difficult distri-butions to predict with the simulation. The comparisonslook good, except for a slight excess in the simulation forSNR > <
24, For fainter hosts beyond thedetection limit the agreement is much poorer, and is likelydue to Malmquist bias for the limited co-add depth used inthis analysis. Note that the poor agreement for faint hosts re-sults in relatively small ˆ S sim errors because ˆ S sim → S sim corrections is smaller.Figure 7 shows data/simulation comparisons for thelow- z sample. The B peak distributions are forced to matchbecause of the method for determining E spec . The compar-isons for redshift, E ( B − V ) and minimum T rest show ex-cellent agreement. The comparisons for maximum gap be-tween observations (rest-frame) and maximum B -band SNRindicate a slight discrepancy. The SNR agreement is poorercompared to DES-SN because we do not have the obser-vation information for the low- z sample, and thus rely onapproximations ( § SALT-II light curve fits onthe simulations, and Fig. 7 of Brout et al. (2019b) showsdata/simulation comparisons for the
SALT-II parameters( m B , x , c ) and their uncertainties. The excellent agree-ment in these distributions adds confidence in our µ -biaspredictions. In one of our
DES-SN3YR cosmology analyses (Brout et al.2019b), we use the BBC method (Kessler & Scolnic 2017) inwhich µ -bias is characterized as a 5-dimensional function of { z, x , c, α, β } . The first three parameters are observed, and { α, β } are determined from the BBC fit. Here we illustrate µ -bias as a function of redshift for a variety of sub-samples,and also compare µ -bias for the two intrinsic scatter models(G10,C11) from § µ -bias isnot a correction for the SN magnitude, but is a correction forfitted light curve parameters (describing the stretch, colorand brightness) along with a correction for the impact ofintrinsic scatter in which brighter events are preferentiallyselected in a magnitude-limited survey.The true distance modulus is defined as µ true , and themeasured distance modulus ( µ ) is determined in the analysisfrom Tripp (1998), µ = − . x ) + αx − βc + M , (18)where { x , x , c } are fitted SALT-II light-curve parameters, α and β are the standardization parameters, and M is anoffset so that µ = µ true when the true values of { x , x , c } true are used in Eq. 18. The distance modulus bias is defined as µ -bias ≡ µ − µ true . The BBC method applies a µ -bias correctionfor each event, and determines the following parameters ina fit to the entire sample: α, β, M , and a weighted-averagebias-corrected distance modulus in discrete redshift bins.We implement the BBC procedure on a simulated DES-SN3YR data sample with 3 × events after applying thecuts from §
8. The µ -bias thus has contributions from the DiffImg trigger, spectroscopic selection, and analysis cuts.We use a large ‘bias-correction’ sample with 1 . × eventsafter the same cuts. Samples are generated with both theG10 and C11 intrinsic scatter model, and the bias-correctionsample with the correct intrinsic scatter model is used on thedata; the effect of using the incorrect model is discussed inBrout et al. (2019b).To account for a µ -bias dependence on α and β , wegenerate the bias-correction sample on a 2 × α × β and use this grid for interpolation within the BBC fit.The grid values are α = { . , . } , β G10 = { . , . } , and β C11 = { . , . } .The BBC-fitted values of α and β are un-biased withintheir 5% statistical uncertainties, and fitting with optional z -dependent slope parameters, dα/dz and dβ/dz are bothconsistent with zero. M does not contribute to µ -bias andtherefore the µ -bias is caused by the fitted light curve param-eters { x , x , c } . The µ -bias versus redshift from the BBC fitis shown in Figs. 8-9 for the low- z and DES-SN samples, re-spectively. The filled circles correspond to the G10 intrinsicscatter model, and open circles correspond to C11.The average µ -bias (left panels) is zero at the lower endof the redshift range. At higher redshifts, µ -bias depends onthe intrinsic scatter model, reaching ∼ .
05 mag at the high-redshift range. The middle and right panels of Figs. 8-9 showthat µ -bias is much larger within restricted color ranges,reaching up to 0 . c > .
06) events. Allpanels show a µ -bias difference between the G10 and C11models, and this difference is largely due to the differentparent color populations (Scolnic et al. 2014a): the C11 colorpopulation has a sharp cut-off on the blue side, while the G10population has a tail extending bluer than in the C11 model.These µ -bias differences, along with differences in fitted α and β , are incorporated into the systematic uncertainty inBrout et al. (2019b).The large µ -bias for red events at higher redshift is be-cause most of these events are intrinsically blue, which are MNRAS , 1–18 (2015) DES Collaboration i peak DES
RedshiftE(B - V)max rest-frame gap (days) log (SNRMAX) DES: maximum SNR g log (SNRMAX) r log (SNRMAX) i log (SNRMAX) z magSB DES: local surface mag g magSB r magSB i magSB z Figure 6.
Comparison of data (black dots) and simulation with G10 scatter model (red histogram) for distributions in the DES-SNsample, where the simulation is scaled to have the same number of events as the data. Left column shows i peak , CMB redshift, Galacticextinction, and maximum gap between observations (rest frame). Middle column shows log of maximum SNR in each band. Right columnshows local surface mag in each band. B peak Low Redshift (CFA,CSP) E n t r i e s RedshiftE(B - V) E n t r i e s max rest-frame gap (days)Max SNR, B-band E n t r i e s min T rest (days) Figure 7.
Data/simulation comparisons for distributions inthe low- z sample, using the G10 intrinsic scatter model andmagnitude-limited selection model. bright enough to be detected, but have poorly measuredcolors. Intrinsically red events are fainter and thus tend tobe excluded at higher redshifts. To illustrate the size of thecolor uncertainties for the DES-SN sample, we computedthe rms on measured color minus true color, rms(∆ c ), andthe rms of the true color population, rms( c true ). The ratio isrms(∆ c ) / rms( c true ) ∼ .
5. Therefore the typical differencebetween measured and true color is 50% of the size of theintrinsic color distribution. For redshifts z > . -0.5-0.4-0.3-0.2-0.100.10.20.30.40.5 0.025 0.05 0.075 -0.5-0.4-0.3-0.2-0.100.10.20.30.40.5 0.025 0.05 0.075 -0.5-0.4-0.3-0.2-0.100.10.20.30.40.5 0.025 0.05 0.075 Low-z Simulations redshiftAll m - b i a s G10C11 redshiftc < - > Figure 8.
For the magnitude-limited low- z simulation, µ -biasvariance-weighted average vs. redshift for all events satisfying se-lection requirements from Brout et al. (2019b) (left panel), blueevents with fitted c < − .
06 (middle panel), and red events withfitted c > .
06 (right panel). Filled circles are with simulationsusing the G10 intrinsic scatter model; open circles are for the C11model.
As described in § µ -bias dependence on { α, β } . This de-pendence is shown in Fig. 10 for DES-SN. Comparing sim-ulations for α = 0 .
10 and α = 0 .
24 (nominal α ≃ . µ -bias difference reaches 0 .
03 mag at high redshift, and issimilar for the two intrinsic scatter models (G10 and C11).The right panel in Fig. 10 shows the µ -bias difference with β values differing by ∼
1; the maximum µ -bias difference is0.01 mag, and is similar for both intrinsic scatter models.We end this section by illustrating the contributions to µ -bias for red events ( c > .
06) in the right panel of Fig. 9,where µ -bias reaches ∼ . MNRAS000
06) in the right panel of Fig. 9,where µ -bias reaches ∼ . MNRAS000 , 1–18 (2015) imulations to Correct SN Ia Distance Biases -0.5-0.4-0.3-0.2-0.100.10.20.30.40.5 0.2 0.4 0.6 0.8 -0.5-0.4-0.3-0.2-0.100.10.20.30.40.5 0.2 0.4 0.6 0.8 -0.5-0.4-0.3-0.2-0.100.10.20.30.40.5 0.2 0.4 0.6 0.8 DES Simulations redshiftAll m - b i a s G10C11 redshiftc < - > Figure 9.
Same as Fig. 8, but for DES-SN. -0.05-0.04-0.03-0.02-0.0100.010.020.030.040.05 0.2 0.4 0.6 0.8 -0.05-0.04-0.03-0.02-0.0100.010.020.030.040.05 0.2 0.4 0.6 0.8 redshift m b i a s ( a ) - m b i a s ( a ) G10 ( a a C11 ( a a redshift m b i a s ( b ) - m b i a s ( b ) G10 ( b b C11 ( b b Figure 10.
For the DES-SN sample, left panel shows µ -biasdifference vs. redshift between α = 0 .
10 and α = 0 .
24. Right panelshows µ -bias difference between different β values: { . , . } forG10 intrinsic scatter model (filled circles), and { . , . } for C11(open circles). While high-redshift bias is often associated with Malmquistbias, we show that µ -bias is primarily associated with intrin-sic scatter and light-curve fitting. We begin with an idealDES-SN simulation that has no intrinsic scatter, and per-form light-curve fits in which only the amplitude x is floatedwhile stretch and color ( x , c ) are assumed to be perfectlyknown. Defining m = − . x ), µ -bias and m -bias arethe same. The resulting µ -bias is shown by the dashed curvein Fig. 11a; this bias is only ∼ .
01 mag, a very small frac-tion of the µ -bias in Fig. 9. While there may be selectionbias in the 2 detections contributing to the trigger ( § x are un-biased.The solid curve in Fig. 11a shows µ -bias with the G10intrinsic scatter model, and still fitting only for x . In thiscase, µ -bias increases considerably to about 0.1 mag at thehighest redshift, and is a result of the strong brightness cor-relations among epochs and passbands. While the true in-trinsic scatter variations average to zero, magnitude-limitedobservations preferentially select positive brightness fluctu-ations, which lead to non-zero µ -bias.Figure 11b shows the same simulations, but with lightcurve fits that float all three parameters ( x , x , c ). Com-pared with Fig. 11a, the µ -bias is much larger, mainly be- -0.4-0.3-0.2-0.100.10.20.30.4 0.2 0.4 0.6 0.8 -0.4-0.3-0.2-0.100.10.20.30.4 0.2 0.4 0.6 0.8 DES Simulations (c > (a) fit x fix x ,c = trueRedshift m - b i a s IDEALG10 (b) fit x , x , cRedshift IDEALG10
Figure 11.
For the simulated DES-SN sample, (a) shows µ -bias vs. redshift for light curve fits that float x only, while fixingstretch and color to their true values. (b) shows µ -bias vs. redshiftfor nominal light curve fits. Dashed line is for the ideal simulationdefined as having no intrinsic scatter; solid line uses G10 intrinsicscatter model. cause of the bias in fitted color. Although this µ -bias test isshown only for the the red events in Fig. 9, similar trendsexist in all color ranges.The statistical uncertainties on these µ -bias correc-tions are negligible. Systematic uncertainties in Brout et al.(2019b) are thus determined from changing input assump-tions such as the color and stretch populations, model ofintrinsic scatter, and the value of the flux-uncertainty scale,ˆ S sim .
10 CONCLUSION
The
SNANA simulation program has been under active de-velopment for a decade, and has been used in severalcosmology analyses to accurately simulate SN Ia lightcurves and determine bias corrections for the distance mod-uli. This work focuses on simulated bias corrections forthe
DES-SN3YR sample, which combines spectroscopi-cally confirmed SNe Ia from DES-SN and low-redshift sam-ples. Files used to make these corrections are available at https://des.ncsa.illinois.edu/releases/sn .The DES-SN simulation includes three categories of de-tailed modeling: (1) source model including the rest-frameSN Ia SED, cosmological dimming, weak lensing, peculiarvelocity, and Galactic extinction, (2) noise model account-ing for observation properties (PSF, sky noise, zero point),host galaxy, and information derived from 10,000 fake SNlight curves overlaid on images and run through our image-processing pipelines, (3) trigger model of single-visit detec-tions, candidate logic, and spectroscopic selection efficiency.The low- z sample, however, does not include observationproperties, and thus approximations are used to simulatethis sample. The quality of the simulation is illustrated bypredicting observed distributions (Figs. 6-7), and bias cor-rections on the distance moduli are shown in Figs. 8-9.The reliability of the bias corrections is only as good asthe underlying assumptions in the simulation. To properlypropagate bias correction uncertainties into systematic un-certainties on cosmological parameters, Brout et al. (2019a) MNRAS , 1–18 (2015) DES Collaboration evaluate uncertainties for each of the 3 modeling categoriesabove (source, noise, trigger). In addition to explicit assump-tions such as those associated with the
SALT-II model, oneshould always be aware of the implicit assumptions such assimulating SN properties (e.g., α , β ) that are independentof redshift and host galaxy properties.The simulations presented here are used to correct SN Iadistance biases in the DES-SN3YR sample (Brout et al.2019b), and these bias-corrected distances are used tomeasure cosmological parameters (DES Collaboration et al.2019). These simulations also serve as a starting point forthe analysis of the full DES 5-year photometrically classifiedsample, which will be significantly larger than the
DES-SN3YR sample.
11 ACKNOWLEDGEMENTS
This work was supported in part by the Kavli Institute forCosmological Physics at the University of Chicago throughgrant NSF PHY-1125897 and an endowment from the KavliFoundation and its founder Fred Kavli. This work wascompleted in part with resources provided by the Univer-sity of Chicago Research Computing Center. R.K. is sup-ported by DOE grant DE-AC02-76CH03000. D.S. is sup-ported by NASA through Hubble Fellowship grant HST-HF2-51383.001 awarded by the Space Telescope Science In-stitute, which is operated by the Association of Universi-ties for Research in Astronomy, Inc., for NASA, under con-tract NAS 5-26555. The U.Penn group was supported byDOE grant DE-FOA-0001358 and NSF grant AST-1517742.A.V.F.’s group at U.C. Berkeley is grateful for financial as-sistance from NSF grant AST-1211916, the Christopher R.Redlich Fund, the TABASGO Foundation, and the MillerInstitute for Basic Research in Science.Funding for the DES Projects has been provided bythe U.S. Department of Energy, the U.S. National Sci-ence Foundation, the Ministry of Science and Education ofSpain, the Science and Technology Facilities Council of theUnited Kingdom, the Higher Education Funding Council forEngland, the National Center for Supercomputing Applica-tions at the University of Illinois at Urbana-Champaign, theKavli Institute of Cosmological Physics at the Universityof Chicago, the Center for Cosmology and Astro-ParticlePhysics at the Ohio State University, the Mitchell Institutefor Fundamental Physics and Astronomy at Texas A&MUniversity, Financiadora de Estudos e Projetos, Funda¸c˜aoCarlos Chagas Filho de Amparo `a Pesquisa do Estado do Riode Janeiro, Conselho Nacional de Desenvolvimento Cient´ı-fico e Tecnol´ogico and the Minist´erio da Ciˆencia, Tecnologiae Inova¸c˜ao, the Deutsche Forschungsgemeinschaft and theCollaborating Institutions in the Dark Energy Survey.The Collaborating Institutions are Argonne NationalLaboratory, the University of California at Santa Cruz,the University of Cambridge, Centro de InvestigacionesEnerg´eticas, Medioambientales y Tecnol´ogicas-Madrid, theUniversity of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh, the Ei-dgen¨ossische Technische Hochschule (ETH) Z¨urich, FermiNational Accelerator Laboratory, the University of Illi-nois at Urbana-Champaign, the Institut de Ci`encies del’Espai (IEEC/CSIC), the Institut de F´ısica d’Altes Ener- gies, Lawrence Berkeley National Laboratory, the Ludwig-Maximilians Universit¨at M¨unchen and the associated Ex-cellence Cluster Universe, the University of Michigan, theNational Optical Astronomy Observatory, the University ofNottingham, The Ohio State University, the University ofPennsylvania, the University of Portsmouth, SLAC NationalAccelerator Laboratory, Stanford University, the Universityof Sussex, Texas A&M University, and the OzDES Member-ship Consortium.Based in part on observations at Cerro Tololo Inter-American Observatory, National Optical Astronomy Obser-vatory, which is operated by the Association of Universi-ties for Research in Astronomy (AURA) under a cooperativeagreement with the National Science Foundation.The DES data management system is supported bythe National Science Foundation under Grant NumbersAST-1138766 and AST-1536171. The DES participants fromSpanish institutions are partially supported by MINECOunder grants AYA2015-71825, ESP2015-66861, FPA2015-68048, SEV-2016-0588, SEV-2016-0597, and MDM-2015-0509, some of which include ERDF funds from the Euro-pean Union. IFAE is partially funded by the CERCA pro-gram of the Generalitat de Catalunya. Research leading tothese results has received funding from the European Re-search Council under the European Union’s Seventh Frame-work Program (FP7/2007-2013) including ERC grant agree-ments 240672, 291329, and 306478. We acknowledge sup-port from the Australian Research Council Centre of Excel-lence for All-sky Astrophysics (CAASTRO), through projectnumber CE110001020, and the Brazilian Instituto Nacionalde Ciˆencia e Tecnologia (INCT) e-Universe (CNPq grant465376/2014-2).This manuscript has been authored by Fermi ResearchAlliance, LLC under Contract No. DE-AC02-07CH11359with the U.S. Department of Energy, Office of Science, Of-fice of High Energy Physics. The United States Governmentretains and the publisher, by accepting the article for pub-lication, acknowledges that the United States Governmentretains a non-exclusive, paid-up, irrevocable, world-wide li-cense to publish or reproduce the published form of thismanuscript, or allow others to do so, for United States Gov-ernment purposes.
APPENDIX A: ADDITIONAL SIMULATIONFEATURES FOR FUTURE ANALYSIS
The focus of this work has been on simulating bias correc-tions and validation samples for the
DES-SN3YR
SN Iacosmology analysis. Here we describe additional features ofthe
SNANA simulation that have been developed for futurework, but are beyond the current scope of the
DES-SN3YR analysis. This future work includes extending the cosmologyanalysis to photometrically identified SNe Ia, more detailedsystematics studies, determining the efficiency for Bayesiancosmology fitting methods (e.g., Rubin et al. 2015), deter-mining the efficiency for SN rate studies, and optimizingfuture surveys. We end with a summary of missing featuresthat would be useful to add for future analysis work.
MNRAS000
MNRAS000 , 1–18 (2015) imulations to Correct SN Ia Distance Biases A1 SED Time Series
The
SALT-II light curve model, which is designed for SN Iacosmology analyses, is a rather complex semi-analyticalmodel. Most transient models, however, are much simpler. Inaddition to specialized SN Ia models, the SNANA simulationworks with arbitrary collections of SED time series. Eachevent can be generated from a random SED time series, orcomputed from parametric interpolation. For example, sup-pose a set of N p parameters, ~P = { p , p , ...p N p } , describeseach SED time series. Each parameter ( p i ) can be drawnfrom a Gaussian distribution (or asymmetric Gaussian) anda full covariance matrix to induce correlations. The SEDs onthe parameter grid are interpolated to the generated ~P .Examples include CC simulations to model con-tamination in photometrically identified SN Ia samples(Kessler et al. 2010a; Rodney et al. 2012; Kessler & Scolnic2017; Jones et al. 2017), and simulating Kilonovae(Barnes & Kasen 2013) to model the search efficiency(Soares-Santos et al. 2016; Doctor et al. 2017), and topredict discovery rates (Scolnic et al. 2018a).An SED time series can also be useful for modelingSNe Ia. Examples include systematic studies on training the SALT-II model with simulated spectra (Hsiao et al. 2007;Mosher et al. 2014), and simulating spectra from SN Ia ex-plosion models (Diemer et al. 2013; Kessler et al. 2013).
A2 Light Curve Library for Galactic Transients
Galactic transients can potentially contribute contamina-tion in a photometrically identified SN Ia sample. To modelgalactic transients, the simulation reads a pre-computed‘light curve library’ of transient magnitudes versus time. Thelight curves can be recurring or non-recurring. For recurringand long-lived non-recurring transients, the library specifiessource magnitudes at epochs to use as templates for image-subtraction, and the simulation accounts for source signal inthe templates. The subtracted fluxes can therefore be pos-itive or negative. To detect negative fluxes with SNR < | SNR | . Each library light curve is overlaid on thesurvey time window, and overlapping observations in thecadence library are converted into a measured flux and un-certainty. Readers are cautioned that this model is relativelynew, and has not yet been used in a publication. A3 Characterization of Detection Efficiency
For the
DES-SN3YR analysis, the DES detection efficiencywas adequately characterized as a function of SNR. In thenext cosmology analysis with a much larger photometricsample, we may need a more accurate description. In partic-ular, we may need to characterize the efficiency of a machinelearning (ML) requirement in
DiffImg that was used to re-ject image-subtraction artifacts (Goldstein et al. 2015). The
SNANA data file structure includes a ‘
PHOTPROB ’ entry for eachepoch, which is intended to store information such as an MLscore. The simulation can generate ML scores (between 0 SN Ia models in
SNANA include
SALT-II (Guy et al. 2010),
MLCS2k2 (Jha et al. 2007), and
SNOOPY (Burns et al. 2011). and 1) based on an input probability map that depends onSNR and/or m SB . The input ML map should be generatedfrom fakes processed through the same pipeline as the data.Since ML scores describe imaging data near the source, thesescores are likely to be correlated among different epochs. Areduced correlation (0 to 1) can be provided to introduceML correlations.While we have been characterizing anomalous effects asa function of m SB , we have begun exploring the dependenceon m − m SB , where m is the source magnitude. This source-to-galaxy flux ratio can be used to describe the detectionefficiency or the ML map. A4 Characterization of Flux-Uncertainty Scale In § S sim , was defined as afunction of 1 parameter: m SB . In future work we plan toinvestigate if ˆ S sim depends on other parameters. The addi-tional ˆ S sim -dependent parameters in the simulation are: (1)SNR, (2) PSF, (3) MJD, (4) sky noise, (5) zero points, (6)galaxy magnitude, and (7) SN-host separation. Additionalparameters, such as the source-to-galaxy flux ratio, can beadded with minor code modifications. A5 Rate Models
The following rate models can be used in the
SNANA simula-tion: • R ( z ) = α (1+ z ) β with user-specified α, β . Multiple R ( z )functions can be defined, each in a different redshift range. • R ( z ) = A · R z ∞ dz ′ SFR( z ′ )+ B · SFR( z ) where SFR is thestar formation rate, A is the amplitude of the delayed com-ponent, and B is the amplitude of the prompt component(Scannapieco & Bildsten 2005; Mannucci et al. 2006). • CC R ( z ) measured with HST (Strolger et al. 2015). • Star formation R ( z ) from Madau & Dickinson (2014),where user defines R (0). A6 Redshift Dependent Input Parameters
Since redshift evolution is a concern in cosmology analy-ses, any simulation-input parameter can be given a redshiftdependence: P → P + p z + p z + p z , where P is a user-specified simulation parameter and p , , are user-definedparameters. If a 3rd-order polynomial is not adequate, thesimulation can read an explicit P ( z ) map in arbitrary red-shift bins. A7 Population Parametrization
The
SALT-II color and stretch populations are described bytwo asymmetric Gaussian profiles. The probability for coloris defined as P ( c ) ∝ exp[ − ( c − ¯ c ) / σ ] ( c ≥ ¯ c ) (A1) P ( c ) ∝ exp[ − ( c − ¯ c ) / σ − ] ( c < ¯ c ) (A2)and similarly for P ( x ). A second asymmetric Gaussiancan be added, as described in Appendix C of Scolnic et al.(2018b) for the low- z stretch distribution. MNRAS , 1–18 (2015) DES Collaboration
A8 Inhomogeneous Distributions
The
DES-SN3YR simulations assume an isotropic and ho-mogeneous universe on all distance scales because of therandom selection of sky coordinates in the observation li-brary ( § z ) galaxy lo-cations. For each such galaxy, the RA, DEC and redshift areused to create an entry in the observation library.Another application is to simulate transients corre-sponding to a posterior from a gravitational wave (GW)event found by the Large Interferometer Gravity Wave Ob-servatory (Singer et al. 2016b,a, LIGO). Drawing randomevents from the posterior described by RA, DEC and dis-tance, each event corresponds to an entry in the observationlibrary. A9 Host Galaxy Library Features
A host-galaxy library (
HOSTLIB ) was defined in § HOSTLIB features include: • mis-matched host redshift model for photometricallyidentified sample (Jones et al. 2017), • a weight map to assign SN magnitude offsets based onhost-galaxy mass, or other properties such as specific starformation rate, • photometric galaxy redshift ( ZPHOT ) and Gaussian un-certainty (
ZPHOTERR ), which must be computed externallyfrom broadband filters, • brightness distribution described with arbitrary sum ofS´ersic profiles, each with its own index, • correlation of host and SN properties by including SALT-II color and stretch for each
HOSTLIB event.
A10 Generating Spectra
Ideally the modeling of spectroscopic selection would includean analysis of simulated spectra, but instead we empiricallymodel this efficiency as a function of peak magnitude. Tobegin the effort on modeling spectroscopic selection, the
SNANA simulation was enhanced to generate spectra for theWFIRST simulation study in Hounsell et al. (2018). Spectraare characterized by their SNR versus wavelength. They canbe generated at specific dates in the observation library, ora random date can be selected in time windows with respectto peak brightness. This time-window can be specified in ei-ther the rest-frame or observer-frame, although the formeris more difficult to carry out in practice. Spectral slices canalso be integrated and stored as broadband fluxes.Finally, a high-SNR (low- z ) spectrum can be simulatedat arbitrary redshift to examine the expected SNR degrada-tion versus distance. A11 Missing Features
We finish this section with a few features that are not in-cluded in the simulation, but might be useful in future anal-yses: • peculiar velocity covariances (currently all v pec are un-correlated), • galactic E ( B − V ) covariance (currently all extinctionsare uncorrelated), • spectral PCA coefficients in the HOSTLIB to model hostcontamination in spectra, • probability distribution for host-galaxy photometricredshifts (instead of Gaussian-error approximation), • anomalous detection inefficiency from bright galaxies, • weak lensing magnification model ( § APPENDIX B: AUTHOR AFFILIATIONS Department of Astronomy and Astrophysics, Universityof Chicago, Chicago, IL 60637, USA Kavli Institute for Cosmological Physics, University ofChicago, Chicago, IL 60637, USA Department of Physics and Astronomy, University ofPennsylvania, Philadelphia, PA 19104, USA School of Mathematics and Physics, University of Queens-land, Brisbane, QLD 4072, Australia Lawrence Berkeley National Laboratory, 1 CyclotronRoad, Berkeley, CA 94720, USA The Research School of Astronomy and Astrophysics,Australian National University, ACT 2601, Australia Institute of Cosmology and Gravitation, University ofPortsmouth, Portsmouth, PO1 3FX, UK ARC Centre of Excellence for All-sky Astrophysics(CAASTRO), Sydney, Australia School of Physics and Astronomy, University of Southamp-ton, Southampton, SO17 1BJ, UK University of Copenhagen, Dark Cosmology Centre,Juliane Maries Vej 30, 2100 Copenhagen O Korea Astronomy and Space Science Institute, Yuseong-gu, Daejeon, 305-348, Korea Harvard-Smithsonian Center for Astrophysics, 60 GardenSt., Cambridge, MA 02138, USA INAF, Astrophysical Observatory of Turin, I-10025 PinoTorinese, Italy Millennium Institute of Astrophysics and Departmentof Physics and Astronomy, Universidad Cat´olica de Chile,Santiago, Chile South African Astronomical Observatory, P.O.Box 9,Observatory 7935, South Africa Space Telescope Science Institute, 3700 San MartinDrive, Baltimore, MD 21218, USA Department of Astronomy, University of California,Berkeley, CA 94720-3411, USA Miller Senior Fellow, Miller Institute for Basic Researchin Science, University of California, Berkeley, CA 94720,USA Santa Cruz Institute for Particle Physics, Santa Cruz,CA 95064, USA Centre for Astrophysics & Supercomputing, SwinburneUniversity of Technology, Victoria 3122, Australia Department of Physics, University of Namibia, 340Mandume Ndemufayo Avenue, Pionierspark, Windhoek,Namibia Harvard-Smithsonian Center for Astrophysics, 60 GardenSt., Cambridge, MA 02138,USA
MNRAS , 1–18 (2015) imulations to Correct SN Ia Distance Biases Gordon and Betty Moore Foundation, 1661 Page MillRoad, Palo Alto, CA 94304,USA Sydney Institute for Astronomy, School of Physics, A28,The University of Sydney, NSW 2006, Australia Institute of Astronomy and Kavli Institute for Cosmol-ogy, Madingley Road, Cambridge, CB3 0HA, UK National Center for Supercomputing Applications, 1205West Clark St., Urbana, IL 61801, USA Institute of Astronomy, University of Cambridge, Mad-ingley Road, Cambridge CB3 0HA, UK Division of Theoretical Astronomy, National Astronom-ical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo181-8588, Japan Institute of Astronomy and Astrophysics, AcademiaSinica, Taipei 10617, Taiwan Observatories of the Carnegie Institution for Science, 813Santa Barbara St., Pasadena, CA 91101, USA Cerro Tololo Inter-American Observatory, NationalOptical Astronomy Observatory, Casilla 603, La Serena,Chile Fermi National Accelerator Laboratory, P. O. Box 500,Batavia, IL 60510, USA Kavli Institute for Cosmology, University of Cambridge,Madingley Road, Cambridge CB3 0HA, UK LSST, 933 North Cherry Avenue, Tucson, AZ 85721,USA CNRS, UMR 7095, Institut d’Astrophysique de Paris,F-75014, Paris, France Sorbonne Universit´es, UPMC Univ Paris 06, UMR 7095,Institut d’Astrophysique de Paris, F-75014, Paris, France Department of Physics & Astronomy, University CollegeLondon, Gower Street, London, WC1E 6BT, UK Kavli Institute for Particle Astrophysics & Cosmology,P. O. Box 2450, Stanford University, Stanford, CA 94305,USA SLAC National Accelerator Laboratory, Menlo Park, CA94025, USA Centro de Investigaciones Energ´eticas, Medioambientalesy Tecnol´ogicas (CIEMAT), Madrid, Spain Laborat´orio Interinstitucional de e-Astronomia - LIneA,Rua Gal. Jos´e Cristino 77, Rio de Janeiro, RJ - 20921-400,Brazil Department of Astronomy, University of Illinois atUrbana-Champaign, 1002 W. Green Street, Urbana, IL61801, USA Institut de F´ısica d’Altes Energies (IFAE), The BarcelonaInstitute of Science and Technology, Campus UAB, 08193Bellaterra (Barcelona) Spain Institut d’Estudis Espacials de Catalunya (IEEC), 08034Barcelona, Spain Institute of Space Sciences (ICE, CSIC), Campus UAB,Carrer de Can Magrans, s/n, 08193 Barcelona, Spain Observat´orio Nacional, Rua Gal. Jos´e Cristino 77, Riode Janeiro, RJ - 20921-400, Brazil Department of Physics, IIT Hyderabad, Kandi, Telan-gana 502285, India Department of Astronomy/Steward Observatory, 933North Cherry Avenue, Tucson, AZ 85721-0065, USA Jet Propulsion Laboratory, California Institute of Tech-nology, 4800 Oak Grove Dr., Pasadena, CA 91109, USA Instituto de Fisica Teorica UAM/CSIC, UniversidadAutonoma de Madrid, 28049 Madrid, Spain Department of Astronomy, University of Michigan, AnnArbor, MI 48109, USA Department of Physics, University of Michigan, AnnArbor, MI 48109, USA Department of Physics, ETH Zurich, Wolfgang-Pauli-Strasse 16, CH-8093 Zurich, Switzerland Center for Cosmology and Astro-Particle Physics, TheOhio State University, Columbus, OH 43210, USA Department of Physics, The Ohio State University,Columbus, OH 43210, USA Harvard-Smithsonian Center for Astrophysics, Cam-bridge, MA 02138, USA Australian Astronomical Optics, Macquarie University,North Ryde, NSW 2113, Australia Departamento de F´ısica Matem´atica, Instituto de F´ısica,Universidade de S˜ao Paulo, CP 66318, S˜ao Paulo, SP,05314-970, Brazil George P. and Cynthia Woods Mitchell Institute forFundamental Physics and Astronomy, and Department ofPhysics and Astronomy, Texas A&M University, CollegeStation, TX 77843, USA Department of Astronomy, The Ohio State University,Columbus, OH 43210, USA Instituci´o Catalana de Recerca i Estudis Avan¸cats,E-08010 Barcelona, Spain Brandeis University, Physics Department, 415 SouthStreet, Waltham MA 02453 Instituto de F´ısica Gleb Wataghin, Universidade Estad-ual de Campinas, 13083-859, Campinas, SP, Brazil Computer Science and Mathematics Division, Oak RidgeNational Laboratory, Oak Ridge, TN 37831
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