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Simulations of the WFIRST Supernova Survey and Forecasts of Cosmological Constraints

R. Hounsell, D. Scolnic, R. J. Foley, R. Kessler, V. Miranda, A. Avelino, R. C. Bohlin, A. V. Filippenko, J. Frieman, S. W. Jha, P. L. Kelly, R. P. Kirshner, K. Mandel, A. Rest, A. G. Riess, S. A. Rodney, L. Strolger

arXiv:1702.01747v2astro-ph.IM

TL;DR

The paper addresses how WFIRST can optimize Type Ia supernova observations for dark-energy constraints under realistic statistical and systematic uncertainties. It simulates WFC light curves and IFC spectra across 11 survey strategies and propagates those uncertainties into FoM predictions. WFC-focused strategies perform best, while further systematic-error work is needed to optimize IFC use.

  • Problem

    WFIRST needs realistic supernova-survey simulations to determine how instrument time allocations and systematic uncertainties affect dark-energy constraints.

  • Method

    The study uses open-source tools to simulate WFC light curves and IFC spectra across 11 strategies, then propagates statistical and systematic uncertainties into DETF FoM forecasts.

  • Results

    WFC-focused strategies are the most successful among those investigated, while some imaging and SDT strategies have lower utility because of shallow exposures, selection losses, and contamination.

  • Takeaways & Limitations

    The WFIRST supernova survey could increase the current FoM by more than an order of magnitude and inform final mission design and implementation.

  • Takeaways & Limitations

    The simulated survey strategies are not fully optimized, and uncertain systematic effects and mission overheads still require further evaluation.

Abstract

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The Wide Field InfraRed Survey Telescope (WFIRST) was the highest ranked large space-based mission of the 2010 New Worlds, New Horizons decadal survey. It is now a NASA mission in formulation with a planned launch in the mid-2020s. A primary mission objective is to precisely constrain the nature of dark energy through multiple probes, including Type Ia supernovae (SNe Ia). Here, we present the first realistic simulations of the WFIRST SN survey based on current hardware specifications and using open-source tools. We simulate SN light curves and spectra as viewed by the WFIRST wide-field channel (WFC) imager and integral-field channel (IFC) spectrometer, respectively. We examine 11 survey strategies with different time allocations between the WFC and IFC, two of which are based upon the strategy described by the WFIRST Science Definition Team, which measures SN distances exclusively from IFC data. We propagate statistical and, crucially, systematic uncertainties to predict the Dark Energy Task Force figure of merit (FoM) for each strategy. Of the strategies investigated, we find the most successful to be WFC-focused. However, further work in constraining systematics is required to fully optimize the use of the IFC. Even without improvements to other cosmological probes, the WFIRST SN survey has the potential to increase the FoM by more than an order of magnitude from the current values. Although the survey strategies presented here have not been fully optimized, these initial investigations are an important step in the development of the final hardware design and implementation of the WFIRST mission.

1. INTRODUCTION

WFIRST is designed to probe dark energy and cosmological growth using multiple observations, including Type Ia supernovae. This paper develops realistic simulations to compare WFIRST supernova strategies while accounting for statistical and systematic uncertainties.

  • Cosmological framework: The survey assesses dark-energy equation-of-state constraints in the w0–wa plane using the DETF figure of merit.The FoM is defined from the inverse area enclosed by the 95% confidence contour.
  • Motivation: WFIRST is a Stage 4 mission intended to improve dark-energy constraints through larger samples and reduced systematic uncertainties.The Dark Energy Task Force target is a tenfold gain over Stage 2 experiments, corresponding to FoM ≥320.
  • Supernova constraints: Type Ia supernovae are critical to combining Stage 3 and Stage 4 probes, but their distances require color, shape, bias, and systematic corrections.These corrections standardize brightness and address selection effects, especially at higher redshifts.
  • Systematic uncertainties: The SDT baseline assumes independent systematic uncertainties in redshift bins, whereas calibration and other effects can correlate across broader redshift ranges.The paper motivates more realistic uncertainty modeling through detailed survey simulations.
  • Study contribution: Using SNANA and other open-source tools, the study creates the first realistic WFIRST supernova simulations to compare survey strategies and their scientific impact.The simulations are also intended as a reference for future work and mission planning.

2. WFIRST HARDWARE

WFIRST’s wide-field instrument combines WFC imaging and IFC spectroscopy for supernova observations. The hardware simulation models their filters, detectors, fields of view, spectral coverage, and relevant detector effects.

  • Instrument overview: The WFI includes a WFC imager with grism capability and an IFC containing two integral-field units.The IFC-S is designed for supernova observations, while the larger IFC-G supports galaxy observations.
  • Wide Field Channel: The WFC uses 18 H4RG detectors in a 6 × 3 array, producing a 0.281 deg2 field of view.Its seven imaging filters span approximately 0.44–2.0 µm.
  • Wide Field Channel: The WFC’s imaging system has approximately 0.11′′ pixel resolution, and inter-pixel capacitance redistributes charge between neighboring pixels.The simulations account for this effect because it can alter PSF width and cosmic-ray or hot-pixel impacts.
  • Wide Field Channel: The WFC grism covers 1.00–1.89 µm at resolving power λ/∆λ ≈435–865, but grism observations are not analyzed in this paper.The study focuses on imaging and integral-field spectroscopy instead.
  • Integral Field Channel: The IFC-S provides a 3.00′′ × 3.15′′ field with 0.42–2.0 µm wavelength coverage and spectral resolution λ/∆λ ≈70–225.It uses 352 spectral bins and is the IFC component intended for supernova observations.

3. AN OUTLINE OF THE SDT SN SURVEY STRATEGY

The SDT strategy combines three-tier WFC imaging for discovery with scheduled IFC-S spectroscopy for classification and distance measurement across a two-year, five-day-cadence survey. Its design allocates observing time by tier and redshift, while simulations incorporate operational overheads and systematic-uncertainty considerations.

  • Observing sequence: WFC imaging discovers candidates, while IFC-S observations provide classification and spectrophotometry for distance measurements at roughly five rest-frame days.The IFC-S sequence includes short, medium, and long exposures, with synthetic broadband photometry derived from the spectra in the simulation implementation.
  • Survey design: The SN survey spans two years with 146 visits at a five-day cadence, allocating 8 hours per visit to WFC discovery and 22 hours to IFC-S observations.Each 30-hour visit contributes to a total survey time of 4380 hours, or six months.
  • Survey design: The strategy uses three WFC imaging tiers with progressively greater depth and smaller area: 27.44, 8.96, and 5.04 deg2 for shallow, medium, and deep surveys, respectively.The tiers target z < 0.4, 0.4 ≤ z < 0.8, and z ≤ 1.7, using Y+J for the shallow tier and J+H for the other two.
  • Operational assumptions: The SDT strategy’s exposure and depth estimates omit the 42 s slew-and-settle overhead, whereas these simulations include it and identify the overhead as uncertain and underestimated.The authors note that current mission estimates are almost twice the quoted 42 s value, so the overhead remains a significant performance uncertainty.
  • Detection and classification: Candidate selection progressively removes objects using discovery-band SNR, flux evolution, and color consistency before scheduling later IFC-S exposures.Detected objects require SNR ≥4 in both discovery bands within one epoch; surviving candidates proceed to short and then medium IFC-S observations.
  • Systematic uncertainties: The SDT systematic model assumes redshift-bin uncertainties, but correlated calibration and SN-color uncertainties span broader redshift ranges, so the model is not used in the analysis.The assumed functional form also drives the broad, flat redshift distribution shown for the SDT strategy.

4. SIMULATION AND ANALYSIS TOOLS

The paper builds realistic WFIRST supernova simulations with SNANA and related open-source tools, modeling observations, noise, supernova populations, selection, and cosmological distance inference.

  • Simulation framework: Realistic WFIRST simulations combine observatory, survey, physical-Universe, and analysis inputs to evaluate supernova strategies and cosmological impact.The framework uses image properties rather than images and incorporates survey cadence, exposure times, selection requirements, spectral models, rates, and cosmological assumptions.
  • Instrument simulation: SNANA simulations model WFC light curves and IFC-S spectra, with IFC-S data represented through 52 synthetic filters formed from 352 spectral elements.This extends SNANA beyond broadband light curves while preserving the IFC-S wavelength-bin information needed for the analysis.
  • Noise modeling: The simulations include zodiacal, thermal, dark-current, read, and host-galaxy noise, while template noise is coherent across exposures and especially important for IFC-S observations.Host-galaxy Poisson noise is included where possible; its omission from IFC-S spectrophotometry is judged negligible for WFC observations but remains an implementation boundary.
  • Supernova populations: Supernova populations use redshift-dependent volumetric rates, SALT2 spectral models, and an external low-redshift anchor of 800 simulated SNe Ia.The rate model includes SNe Ia and core-collapse events, while the low-redshift sample is modeled after the Foundation survey.
  • Cosmology analysis: BBC distance fitting corrects fitted color, stretch, and magnitude parameters for selection and contamination biases before constructing a redshift-binned Hubble diagram.The reported distance uncertainties include fitted-parameter statistics, lensing, peculiar velocities, and intrinsic scatter; fixing the CC likelihood parameter makes contamination estimates conservative.

5. SIMULATED STRATEGIES

The study compares WFC-plus-IFC and imaging-only WFIRST strategies under a fixed six-month observing allocation, using simulated selection and classification to assess sample quality.

  • Strategy set: The simulated strategies include SDT, SDT* and SDT* Highz configurations using both WFC and IFC-S, alongside Imaging, Imaging:Lowz, and Imaging:Highz configurations using imaging only.Across strategies, the analysis preserves cadence, tier depth, IFC-S operation, and WFIRST filter bandpasses rather than fully optimizing them.
  • Survey constraints: All strategies account for 42 seconds of slew-and-settle time per exposure while satisfying the six-month total observing-time constraint.When components are added or removed, remaining tier areas are generally rescaled to account for the time change.
  • SDT and SDT* selection: SDT* efficiency remains relatively flat with redshift, whereas the SDT methodology falls rapidly at high redshift.Spectroscopic classification subsequently reduces SDT* efficiency to approximately 82%, while the combined photometric and spectroscopic sample reaches approximately 99% purity.
  • SDT and SDT* selection: The SDT* sample contains only 475 SNe at z < 0.6, or 39% of the 1,230 low-redshift SNe Ia expected in the SDT report.The deficit is attributed primarily to low signal-to-noise in the shallow tier and the decision not to follow low-redshift events from deeper tiers.

5.2. SDT* Highz

The SDT* Highz strategy removes the shallow tier and reallocates time to the medium tier, expanding its redshift coverage and increasing the final classified SN Ia sample.

  • 5.2. SDT* Highz: Reallocating shallow-tier time to the medium tier produces 24% more SNe Ia in the final classified sample than the SDT* strategy.The modified medium tier covers 0.1 ≤ z < 0.8 instead of 0.4 ≤ z < 0.8, while the deep tier remains unchanged.

5.3. SDT Imaging

The SDT Imaging strategy evaluates a worst-case scenario in which IFC-S data are unusable and only existing WFC imaging data are used.

  • 5.3. SDT Imaging: The imaging-only simulation produces 1.24 times more SNe Ia than the possible SDT* sample, but only approximately 76% lie within 0.1 ≤ z ≤ 1.7.Only two SNe Ia are detected at z < 0.5, attributed to insufficient signal-to-noise for low-redshift shallow-tier events.
  • 5.3. SDT Imaging: The SDT Imaging case is explicitly a worst-case and unlikely scenario, and the analysis excludes WFC discovery-filter failure because the mission would lose self-reliant SN discovery.It nevertheless indicates the usefulness of limited imaging-only data.

5.4. Imaging:Allz

The Imaging:Allz strategy reallocates IFC-S time to WFC imaging, substantially increasing the SN sample and extending coverage to higher redshift than SDT*.

  • 5.4. Imaging:Allz: The strategy uses four filters in the shallow and medium tiers and Y JHF in the deep tier, with tier areas increased to compensate for removing IFC-S.The filters span the rest-frame optical and NIR wavelength range represented by the spectral models.
  • 5.4. Imaging:Allz: A factor of ∼4.7 increase in the final SN sample over the possible SDT* results from reallocating IFC-S time, removing IFC selection criteria, and adding filters.This is the first scenario exceeding SDT requirements in every 0.1 redshift bin.
  • 5.4. Imaging:Allz: The simulated Imaging:Allz and SDT* samples are compared using BBC-fitted Hubble diagrams against the ΛCDM model.The comparison also shows a wCDM model with w = −1.05 and binned Hubble residuals.
  • 5.4. Imaging:Allz: Imaging:Allz covers 0.0 ≤z ≤3.0, while SDT* covers 0.1 ≤z ≤1.7.Within the shared range, SDT* distance uncertainties are on average ∼2.4 times worse than Imaging:Allz; above z > 2.0, Imaging:Allz uncertainties are larger.

5.7. Imaging:Lowz+

The Imaging:Lowz+ and related imaging strategies increase SN yields through tier-area and filter reallocations, but low-z-focused designs provide limited high-redshift coverage.

  • 5.7. Imaging:Lowz+: Alternative two-tier imaging designs produce ∼2.5 and ∼2.3 times more SNe Ia than SDT* while retaining only ∼5% of samples at z ≥1.2.These designs use different filter sets and tier-area reallocations.
  • 5.7. Imaging:Lowz+: A factor of ∼6.5 times greater SN yield than SDT* comes from using medium and deep tiers with redistributed IFC-S and shallow-tier time.This strategy is the second scenario exceeding SDT requirements per 0.1 redshift bin and provides a more complete required-range sample.
  • 5.7. Imaging:Lowz+: Low-z strategies lose SNe at z ≥1.3 because removing the long-exposure deep tier and redder bands limits high-redshift detection.By contrast, Imaging:Highz and Imaging:Allz produce significantly more SNe per 0.1 redshift bin than SDT*.
  • 5.7. Imaging:Lowz+: The shallow tier is inefficient because short exposures produce low-SNR objects and poor filter selection provides minimal rest-frame coverage.Slew-and-settle time further reduces the shallow tier’s utility relative to the SDT report.
  • 5.7. Imaging:Lowz+: The Imaging:Highz* design yields ∼2.4 times better statistical precision per redshift bin than SDT* in the relevant redshift ranges.Many imaging-only scenarios extend beyond z > 2, although the SN rate is more uncertain there.

6. SYSTEMATIC UNCERTAINTIES

The analysis propagates statistical and systematic uncertainties through covariance modeling and cosmological fits, while identifying calibration and unmodeled detector effects as important limitations.

  • 6. SYSTEMATIC UNCERTAINTIES: The first WFIRST SN systematic-uncertainty analysis quantifies effects beyond ad hoc uncertainty functions and evaluates their impact on the FoM.The study includes both current and optimistic assumptions.
  • 6. SYSTEMATIC UNCERTAINTIES: The total covariance is modeled as Ctot = Dstat + Csys, with Csys derived by perturbing each systematic by 1σ and measuring BBC distance-modulus changes.The statistical component is diagonal, while systematic contributions depend on each SN’s sensitivity to each uncertainty.
  • 6. SYSTEMATIC UNCERTAINTIES: CosmoMC* combines the derived distances and covariance matrix with CMB and BAO constraints to calculate the FoM and its response to scaled systematics.Systematic effects are varied from zero to 12 times their current constraints.
  • 6. SYSTEMATIC UNCERTAINTIES: Calibration choices affect survey design: if ground-to-space relative calibration is accurate to 1–2 mmag, dropping the shallow tier may benefit the survey, whereas suboptimal calibration may require a low-z survey.That low-z survey would require a strategy outside those studied here.
  • 6. SYSTEMATIC UNCERTAINTIES: The systematic inventory is incomplete because pixel-level calibration, subpixel sensitivity, and persistence uncertainties are omitted or assumed to average out.Subpixel and persistence effects may introduce redshift-dependent biases as host galaxies become less resolved at high redshift.
  • 6. SYSTEMATIC UNCERTAINTIES: For SDT*, wavelength-dependent calibration is the largest uncertainty, with a current IFC-S estimate of 50 mmag per 7000 ˚A and an expected reduction of over a factor of 10 by launch.The resulting optimistic FoM is correspondingly much larger.

7. COMPARISON OF SIMULATED SURVEY STRATEGIES

The simulated strategies span a wide range of statistical precision, but systematic uncertainties narrow total-FoM differences and favor imaging-focused designs. Low-redshift coverage and carefully chosen selection criteria materially affect the resulting supernova samples and cosmological constraints.

  • FoMstat spans 211–704, whereas FoMtot,curr spans only 86–169 across strategies, indicating that systematic uncertainties compress the total-performance range.Many WFC-focused strategies have comparable current-systematics FoM values, consistent with becoming systematics limited.
  • Modifying selection criteria increases low-redshift SNe Ia by ∼300% and SNe at 0.1 ≤z ≤1.7 by ∼31%, but the shallow tier still reaches only ∼39% of the SDT low-redshift fraction.Moving exposure time from the shallow to medium tier further increases the sample by 460 and 923 SNe Ia relative to SDT* and SDT, respectively.
  • Imaging:Allz achieves FoMtot,opt = 388 and FoMstat = 622 while producing more than five times as many SNe Ia as any IFC-S strategy.This three-tier imaging strategy uses four broadband filters, but zero-point uncertainties remain among its largest systematic uncertainties.
  • FoMstat reaches ∼86% of its full-sample value by z = 1.5 and stops increasing past z ≈2.0, while cutting below z = 0.4 reduces it by ∼79%.The comparison shows that low-redshift data, including Foundation-like observations, are important, whereas many additional very-high-redshift SNe contribute little.
  • The SDT* Highz strategy is the most successful IFC-focused option, while IFC-focused strategies are otherwise least successful after excluding SDT Imaging and Imaging:Lowz.The SDT* modification is superior to the SDT report strategy because their final systematic uncertainties are essentially equivalent.
  • Among the investigated strategies, Imaging:Allz, Imaging:Highz*, and Imaging:Highz+ have similar top FoMtot,opt values, leaving no obvious optimal strategy.Imaging-only strategies constrain dark energy as well as, and sometimes better than, the current IFC-focused strategies.

8. DISCUSSION AND FUTURE WORK

The discussion presents the strategies as reference options for future optimization while identifying unresolved calibration, redshift, scheduling, and modeling issues. Hybrid WFC–IFC observations may retain imaging-focused performance while supplying spectra useful for calibration and systematic characterization.

  • The proposed strategies are reference options for increasing both the number and redshift range of detected SNe Ia, not fully optimized final designs.Future optimization may trade survey depth against area, adjust cadence, and modify the redshift distribution.
  • The analysis assumes perfectly known SN or host-galaxy redshifts, although real redshift uncertainties affect exposure choices, classification precision, biases, and cosmological constraints.A complete assessment depends on the available redshift catalogs, ground-based resources, survey strategy, and post-survey resources.
  • Grism spectroscopy appears effective for classification only with longer exposures than IFC-focused strategies, so more extensive simulations are needed before judging its survey utility.Using both IFC-S and WFC imaging at the current five-day cadence would also require considerable scheduling resources.
  • A hybrid WFC-focused strategy obtaining IFC-S spectra in parallel could provide vital calibration and population-drift information from only 10–15% of SN Ia spectra.The spectra could also improve the SALT2 SED model and help explore unknown systematics.
  • The underlying SED-model training sample is an important limitation because the model uncertainty depends on maintaining a common rest-frame wavelength range across redshifts.The analysis discusses substantially different usable redshift ranges for the extended and nominal SALT2 spectral models.
  • The redshift distribution requires further optimization because increasing the fraction of SNe Ia above z > 1.2 does not necessarily produce the same fractional increase in FoM.The analysis also notes that future external BAO and CMB constraints could affect the impact of Stage 4 supernova constraints.

9. CONCLUSION

The simulations compare 11 WFIRST supernova survey strategies while propagating statistical and systematic uncertainties into FoMtot,opt. WFC-focused strategies generally perform best, but IFC-focused approaches retain possible calibration and spectral-diversity advantages whose value depends on better-constrained systematics.

  • Survey design: 42 s slew-and-settle overheads drastically reduce the efficiency of the SDT strategy’s low-redshift, wide-area tier.Optimal survey design depends strongly on the uncertain overhead values.
  • SDT variants: FoMtot,opt rises from 158 for the SDT strategy to 216 with SDT* selection criteria and 236 for the SDT* Highz scenario.The SDT simulation selects too few SNe Ia because of low selection efficiency, underestimated noise, and strict classification; the Highz variant reallocates shallow-tier time to the medium tier.
  • Imaging-only strategies: Imaging-only strategies often produce significantly more final-sample SNe Ia than the SDT strategy.Their designs add filters and reallocate time after removing IFC-S and/or discovery tiers.
  • Strategy comparison: WFC-focused strategies are more successful than IFC-focused strategies, although no single strategy is a clear winner.Imaging:Allz, Imaging:Highz*, and Imaging:Highz+ have similar current and optimistic FoM values.
  • IFC-focused strategies: IFC-focused strategies may enable stacked low-SNR spectra, improved calibration against SED evolution, and more information about population-drift systematics.A parallel imaging survey could mitigate some IFC concerns, but its power relative to an optimized imaging-only survey remains unassessed.
  • Scope and outlook: The strategies are not fully optimized, so future work will continue optimizing WFIRST to identify a more successful strategy.The study establishes reproducible baseline strategies and provides broader understanding for mission design and risk mitigation.

A. IFC-S EXTENDED TABLE:

The appendix lists the IFC-S spectral bins used in the simulations, covering wavelengths from 0.42 to 2.1 µm with associated wavelength ranges and FWHM information.

  • IFC-S bin table: The extended table provides every IFC-S bin between 0.42 and 2.1 µm, including minimum and maximum wavelength ranges and FWHM.A machine-readable version is available online.

B. HOST-GALAXY SURFACE BRIGHTNESS LIBRARY

The host-galaxy surface-brightness library combines CANDLES measurements with fitted galaxy SED models to generate synthetic WFIRST photometry. Simulations approximate SN locations at host-galaxy centers using a fixed Sérsic profile and magnitude offset.

  • Library construction: CANDLES measurements at approximately 40 SN sites provide HST photometry used to fit redshifted and warped galaxy SED models.The fitted SEDs generate synthetic photometry in WFIRST filters.
  • Simulation approximation: The simulations place each SN at its host-galaxy center with a Sérsic profile index of 0.5 and a slight magnitude offset.Figure 17 compares this approximation with CANDLES data, finding it imperfect but usable throughout the study.

C. PHOTOMETRIC CUTS IN THE IFC-S DATA

The IFC-S analysis applies iterative color and flux-rise cuts to imaging data for SN selection. Because individual photometric uncertainties were excluded when defining the ranges, the resulting cuts are restrictive and the SDT* method is considered more representative of the intended procedure.

  • Cut criteria: The photometric cuts examine SN color and flux between successive epochs.The SDT report specifies these cuts for imaging data used in SN discovery.
  • Cut construction: IFC-S-focused simulations define acceptable color and flux-rise ranges iteratively from the full simulated SN sample.The cuts incorporate photometric and intrinsic scatter and are illustrated for the SDT shallow tier in Figure 18.
  • Caveat: Excluding individual photometric uncertainties makes the color and rise ranges restrictive, while SDT* is likely more representative of the originally intended selection.The authors note that the intended procedure was not explicitly stated.

D. MEASURING THE POPULATION DRIFT

The study evaluates whether WFIRST spectroscopy can measure SN Ia ejecta velocities to address redshift-dependent color effects in distance estimates. Realistic IFC-S measurements show substantial velocity uncertainty, limiting their usefulness at the current survey design.

  • Velocity measurements: The Si II λ6355 feature is accessible in all IFC-S spectra and grism spectra at z > 1.2, enabling the ejecta-velocity measurement across the relevant sample.
  • Velocity measurements: 1000 km s−1 is the typical velocity uncertainty, with a ∼5% failure rate and a ∼500 km s−1 low bias.The bias can be corrected using higher-resolution spectra or simulations.
  • Velocity measurements: 0.10 mag distance-modulus uncertainty propagates from the measured ejecta velocities, comparable to the total distance uncertainty.The uncertainty is attributed to the low resolution and low SNR of the IFC-S spectra.
  • Velocity measurements: 800 km s−1 is the grism uncertainty at matched binned SNR, indicating that low SNR causes most of the measurement uncertainty.
  • Survey-design implications: SNR > 20 is required for ejecta velocities to improve distance estimates, exceeding the current SDT design.Higher resolution or higher SNR would also improve spectral classification, but requires additional exposure time per SN.
  • Alternative spectral indicators: Flux-ratio uncertainties of generally 20% propagate into a ∼0.4 mag distance-modulus uncertainty, ruling out their use with IFC-S at the current SNR.
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