Going Forward with the Nancy Grace Roman Space Telescope Transient Survey: Validation of Precision Forward-Modeling Photometry for Undersampled Imaging
David Rubin, Aleksandar Cikota, Greg Aldering, Andy Fruchter, Saul Perlmutter, Masao Sako
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Going Forward with the
Nancy Grace Roman Space Telescope
Transient Survey:Validation of Precision Forward-Modeling Photometry for Undersampled Imaging
David Rubin,
1, 2
Aleksandar Cikota,
2, 3
Greg Aldering, Andy Fruchter, Saul Perlmutter,
2, 5 and Masao Sako Department of Physics and Astronomy, University of Hawai‘i at M¯anoa, Honolulu, Hawai‘i 96822 E.O. Lawrence Berkeley National Laboratory, 1 Cyclotron Rd., Berkeley, CA, 94720, USA European Southern Observatory, Alonso de Cordova 3107, Vitacura, Casilla 19001, Santiago de Chile, Chile Space Telescope Science Institute, 3700 San Martin Drive Baltimore, MD 21218, USA Department of Physics, University of California Berkeley, Berkeley, CA 94720, USA Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA
Submitted to PASPABSTRACTThe
Nancy Grace Roman Space Telescope ( Roman ) is an observatory for both wide-field observationsand coronagraphy that is scheduled for launch in the mid 2020’s. Part of the planned survey is a deep,cadenced field or fields that enable cosmological measurements with type Ia supernovae (SNe Ia).With a pixel scale of 0 . (cid:48)(cid:48)
11, the Wide Field Instrument will be undersampled, presenting a difficultyfor precisely subtracting the galaxy light underneath the SNe. We use simulated data to validatethe ability of a forward-model code (such codes are frequently also called “scene-modeling” codes) toperform precision supernova photometry for the
Nancy Grace Roman Space Telescope
SN survey. Oursimulation includes over 760,000 image cutouts around SNe Ia or host galaxies ( ∼
10% of a full-scalesurvey). To have a realistic 2D distribution of underlying galaxy light, we use the VELA simulatedhigh-resolution images of galaxies. We run each set of cutouts through our forward-modeling code whichautomatically measures time-dependent SN fluxes. Given our assumed inputs of a perfect model ofthe instrument PSFs and calibration, we find biases at the millimagnitude level from this method infour red filters ( Y J H F Roman inter-filter calibrationrequirement for a cutting-edge measurement of cosmological parameters using SNe Ia. Simulated datain the bluer Z
087 filter shows larger ∼ Keywords:
Surveys, IR telescopes, Space telescopes, Dark energy, Type Ia supernovae INTRODUCTIONThe
Nancy Grace Roman Space Telescope ( Roman ) is an observatory for both wide-field observations and coronag-raphy that is scheduled for launch in the mid 2020’s. The Wide Field Instrument (WFI) covers 0.281 square degreesand performs both imaging and low-resolution slitless spectroscopy. One of the primary science objectives of the
Ro-man mission is to investigate the expansion history of the Universe using thousands of Type Ia Supernovae (SNe Ia).Although the
Roman supernova survey strategy is not yet finalized, the survey is planed to have two components: a ∼ ∼ ◦ from the previous visit (two full rotationsover two years) to keep the solar panels pointed at the Sun. Corresponding author: David [email protected] a r X i v : . [ a s t r o - ph . I M ] F e b Rubin and Cikota et al.
Table 1.
Filter-dependent simulation quantitiesFilter Z Y J H F − /pix/s) 0.349 0.384 0.376 0.365 0.381Exposure Time (s) 300 300 300 300 600Read Noise (e − ) 8.3 8.3 8.3 8.3 6.9Fitted PSF FWHM (”) 0 . (cid:48)(cid:48)
127 0 . (cid:48)(cid:48)
130 0 . (cid:48)(cid:48)
136 0 . (cid:48)(cid:48)
150 0 . (cid:48)(cid:48) Figure 1.
Forward modeling an example simulated SN in Y each column ) consists of only one unditheredexposure per filter; subpixel sampling is provided by a ∼ ◦ rotation between subsequent epochs. The top row of panels showsa set of cutouts around the SN; only epochs with SN light are shown. The next row of panels shows the model inferred fromthis data and 49 reference epochs without the SN. The galaxy model is an analytic function, parameterized with a 2D setof spline nodes. For each image, the galaxy model is sampled at high resolution (11 × oversampling, across each pixel, thenconvolved with the PSF and the pixel and sampled at the native pixel scale. This accuracy is sufficient for ∼ − accuracyin representing the spline. The image-dependent SN light (also convolved by the PSF and the pixel and sampled at the nativescale) and background are added to this galaxy model. The next row of panels show the residuals where the SN models are notsubtracted. Finally, the bottom row of panels show the residuals when the modeled SN and modeled galaxy are subtracted. To balance field of view, read noise, and PSF sampling, the pixel scale of the WFI was set at 0 . (cid:48)(cid:48)
11, leaving theimaging PSF undersampled (Table 1). This undersampling is not mitigated by the SN survey strategy, since much ofthe survey will likely only have one (undithered) exposure per filter per epoch in order to minimize overheads and readnoise. Undersampled, undithered imaging poses a challenge for photometry methods based on image resampling (e.g.,Alard & Lupton 1998). Much existing undersampled photometry is thus done with codes that use forward modeling(e.g., Suzuki et al. 2012; Hayden et al. submitted). Forward modeling (called “scene modeling” by Holtzman et al.2008) bypasses image resampling to model each image as observed. Figure 1 shows an example and Figure 2 showsthe recovered high-resolution galaxy model.The gold standard for validating forward-model results is to inject simulated SNe into real survey data (Holtzmanet al. 2008; Suzuki et al. 2012; Astier et al. 2013; Brout et al. 2019). As we have no
Roman data to validate with,we are left with two choices for test data: inject simulated SNe into images from the
Hubble Space Telescope
WideField Camera 3 IR channel (
HST
WFC3 IR, which has similar filters with a similar pixel scale of 0 . (cid:48)(cid:48) HST data will confound
HST calibrationuncertainties with forward-model problems. Of particular worry are thermal variations due to the
HST ’s low orbit(B´ely et al. 1993), PSF spatial variations (Anderson 2016), and detector effects (e.g., Zhou et al. 2017).In Section 2 we very briefly outline the assumptions and requirements for our forward modeling algorithm and how itmay interface with the
Roman pipeline and cosmology analysis. In Section 3 we describe the WFI mock observations The ground-based SuperNova Legacy Survey developed a similar sort of code that used resampled and aligned images (Astier et al. 2006;Guy et al. 2010). The goal in that work was to avoid image subtraction and take the time-variable PSF into account. orward Modeling for
Roman
SNe High-Resolution Model
High-Resolution Model,Convolved with PSF and Pixel
Figure 2.
Recovered galaxy model from Figure 1. The left panel shows the recovered high-resolution galaxy model G (fromEquation 1), sampled at 11 × the native resolution (i.e., 0 . (cid:48)(cid:48) right panel shows G convolved with the PSF and the pixel(the PSF has the same orientation), also at 11 × the native resolution. Most of the unphysical high-frequency power visible inthe left panel is suppressed. Note that the convolution with the pixel ensures that the total galaxy flux is not dependent on thealignment with the pixels in a given epoch. which we generate and use to test the forward modeling algorithm. In Section 4 we explain the forward-modelingassumptions in detail, and in Section 5 we present and discuss the results. Section 6 summarizes our conclusions. FORWARD-MODEL INPUTS AND OUTPUTSFigure 3 shows a conceptual overview of the
Roman
SN cosmological data-processing flowchart and how this workfits in. The downlinked data will be processed into calibrated images (top of Figure 3). Mosby et al. (2020) discussesthe performance of the IR detectors in detail. In short, there are eighteen Teledyne HAWAII 4RG detectors (with 10micron 4k by 4k pixels) that non-destructively read out every 2.825 seconds. These multiple readouts enable lowerread noise than is possible with one read, enable rejecting cosmic-ray hits during a single exposure (visible as jumps incharge vs. readouts), and possibly provide better control of pointing drifts and detector effects (Rauscher et al. 2019).(To lower the required bandwidth, averaged groups or other linear combinations of readouts will be downlinked.)We assume for this work that the calibration process produces 2D images with known astrometric and photometriccalibration. We acknowledge the possibility that we may need to go back earlier in the process (for example by fittingthe readouts directly); this will have to be explored with better simulations of the detectors (and ultimately exploredwith real data).After the images are calibrated, we assume further processing generates a PSF model. This PSF model will haveto take focal-plane position and effective wavelength into account (and possibly temporal or thermal variations asdiscussed above for
HST ). Depending on the linearity calibration (Choi & Hirata 2020), it may also have to take fluxinto account.The transients in each image will have to be found and assessed. This will require a highly automated process;a 20 deg survey with a five-day cadence is equivalent to searching more than 3,000 WFC3 IR pointings per day.Hayden et al. (submitted) demonstrated an automated transient classifier for WFC3 IR data with near-human levelsof performance (as noted above, WFC3 IR has similar pixel scale and wavelength coverage), so the search process isfeasible, even for these large data sets.With a series of calibrated images, a PSF model, and transient detections, the forward-modeling code can run. Wedescribe this in more detail in Section 4. This step produces calibrated fluxes. The slitless spectroscopy will also needa separate forward-model code appropriate for 3D reconstruction (two dimensions on the sky plus wavelength). Thisis a fundamentally harder problem (because of the increase in dimensionality, the increase in data volume, and thespatial/spectral degeneracy of a slitless spectrograph observing a complex scene). Ryan et al. (2018) demonstratesthis concept on WFC3 IR data.The lower half of Figure 3 outlines the steps involved in going from these calibrated imaging and spectroscopic fluxesto SN distances and cosmological results. We do not elaborate here, as many of the steps will be similar to othersurveys (e.g., Scolnic et al. 2018). Rubin and Cikota et al.
PhotometryThis work SpectroscopyATELs, External Followup, and Archival Observations Multi-Probe Cosmological AnalysisUpdate Galaxy Catalog
Galaxy Catalog
External SN Measurements
External LightcurvesExternal SN Spectroscopy
External Galaxy Measurements
External ImagingExternal Galaxy Spectroscopy
Roman Images CalibrationAstrometric Refinement PSF DeterminationImaging Forward Modeling Prism Forward ModelingSpectroscopic and Photometric Classification and EfficiencyTraining SED Model (both SNe Ia and CC SNe) SN Distances and Cosmological AnalysisTransient Detection (including blinded recovery of simulated SNe)
Flat-fielded images ("flt") or possibly raw. Includes uncertainties, associated calibration files, world coordinate system, bad-pixel masking, persistence masking, model of detector effectsCalibrated Images Time, position, flux, and wavelength-dependent PSF models
Fast spectroscopyFast photometry
High Accuracy PhotometryUpdated world coordinate system List of Transients (coordinates, dates)
Photometry
High Accuracy S pectra Spectra
List of selected SNe Ia appropriate for cosmologyand/orSpitzer, Euclid, Vera C. Rubin Observatory, Hyper Suprime-Cam, Prime Focus Spectrograph, Dark Energy Spectroscopic Instrument, 4-metre Multi-Object Spectrograph Telescope, ...
Figure 3.
Conceptual
Roman
SN cosmological data-processing flowchart. The red dashed square denotes the photometrycomponent, which is described and validated in this work. We show each step as a single box, but many surveys use more thanone semi-independent analyses of the same data as a cross-check (e.g., Guy et al. 2010).3.
SIMULATED DATA GENERATIONTo create mock observations, we use galaxies from the VELA Cosmological Simulation (Snyder 2018; Simons et al.2019). The dataset spans the cosmic time evolution of 35 galaxies over 10–50 timesteps with cosmological scalefactors between 0.05 and 0.5 (redshift 1 to 19), each with approximately 20 viewing angles. The simulated spatiallydependent galaxy SEDs are integrated over
Roman filters (and other existing and proposed observatories), makingsimulated images. These simulated images are high resolution (oversampled by a factor ∼
15 compared to
Roman pixels), and are much larger than a PSF (800 by 800 oversampled pixels or ∼
50 by 50 native pixels), making themperfect for precision tests of galaxy subtraction. The stellar mass distribution is also similar to SN Ia hosts. Weadd the time-dependent Type Ia SN fluxes and reproject the high-resolution images onto the WFI detector pixels atdifferent telescope orientations (depending on the position relative to the Sun) for 74 time epochs in a range of 1 year(which is designed to fit well within the two-year planned
Roman survey).3.1.
Supernova light curves
So that our light curves would be reasonably realistic, we generated a sample of SN Ia fluxes using the SALT2-Extended model in the SNCosmo Python package (Barbary 2014). SALT2 is a two-parameter (light-curve shape x and light-curve color c ) spectro-temporal model (Guy et al. 2007) that was extended into the UV and NIR with the orward Modeling for Roman
SNe To ensure good sampling of redshift, we assumed a random uniform redshift distributionof the SN sample between z = 0 . − . − . x + 3 . c + ∆ m mag, where x and c are drawn from random normal distributions centeredaround 0 with standard deviations of 1 and 0.1, respectively. ∆ m is also assumed to be Gaussian, with a standarddeviation of (cid:112) . + (0 . z ) . The 0 . z is the magnitude dispersion due to the weak gravitational lensing of galaxyhalos along the line of sight J¨onsson et al. (2010). Finally, we calculated the integrated flux of the SNe in the five Roman bands ( Z Y J H F Supernova positions
We assume that SNe Ia are distributed following the optical light of the galaxy (Anderson et al. 2015), and convolvethe high resolution Y
106 VELA image by a Gaussian with a 1 kpc radius before choosing locations to plant SNe.3.3.
Point spread functions
We use point-spread functions (PSFs) generated by WebbPSF (Perrin et al. 2014). We convolve the PSFs withsquare 0 . (cid:48)(cid:48)
11 pixels with uniform sensitivity. As described in Section 2, we assume that detector effects such as countnonlinearity, count-rate nonlinearity, and inter-pixel capacitance have been perfectly calibrated and can be neglected.We also assume that the dependence of the PSFs on the spectral energy distribution (SED) of the source is negligible. All of these simplifying assumptions are in keeping with our philosophy for this work of focusing on the “Photometry”box in Figure 3. 3.4.
Reprojection
With a full set of oversampled live-SN and reference images in hand, we use
Astropy reproject exact to rotatethe oversampled data to match the rotation angle for each epoch and give each epoch and filter a random sub-pixeldither offset. This procedure technically convolves the images by each oversampled pixel twice: once when generatingthe data, and once when rotating the data. We use 30 × oversampled images (pixel doubling the 15 × oversampledVELA images), so this limits the accuracy of our simulations to O (30 − ) ≈ . . (cid:48)(cid:48)
11 resolution. Figure 4 shows a randomly selected set ofsimulated images (near maximum light for the SNe) before the addition of noise.WebbPSF defines the PSF as the PSF at exactly the sampled locations. The image-reprojecting code effectivelydefines the PSF as convolved with the subpixel (in the sense that adding together all the subpixels of a pixel of thePSF should exactly equal the PSF convolved with the pixel). We sample the PSFs at very high resolution ( ∼ × )and integrate over each subpixel to ensure that the pixel convolution is done with high accuracy. Such definitionconsiderations will need to be kept in mind as the Roman software stack is built.3.5.
Sources of Noise
It is likely that the
Roman
SN survey will consist of tiers (Spergel et al. 2015; Hounsell et al. 2018; Rubin 2020),with each “wedding cake” layer trading area on the sky against depth. The deepest tier will likely have ∼
300 secondexposure times and reach redshift ∼ (cid:46)
100 exposure times andreach redshift ∼ z = 1VELA images (the angular scale is only about 12% different between z = 0 . z (cid:46) . Z Y J H F More than one version of SALT2-Extended has been trained. We use the SNCosmo version, not the published one (Pierel et al. 2018); theSNCosmo version seems to have more accurate rest-frame UV fluxes. In practice, one can use an iterative process of generating a PSF, measuring photometry, estimating the SED from a light-curve fit, andre-estimating the PSF (Suzuki et al. 2012). We neglect this iteration for simplicity. For sufficiently well sampled images, even simplerapproximation suffices: using a single PSF for all SEDs and modifying the filter bandpass instead of the PSF (e.g., Guy et al. 2010; Suzukiet al. 2012).
Rubin and Cikota et al.
Figure 4.
A randomly selected set of postage stamps from our simulations near maximum light for each supernova before theaddition of noise. The color channels are Z
087 (blue), J
129 (green), and F
184 (red). The subpixel positions are different foreach filter, so we resample the Z
087 and F
184 images to match the J
129 so that the colors align. The VELA galaxies arequalitatively similar to real SN host galaxies (e.g., Figure 2 of Riess et al. 2007). Some of the VELA viewing angles are alignedby angular momentum axis, giving a similar orientation for some galaxies in this figure.
It is also possible that the R
062 filter or the proposed K band could be used, but these were too recent to be in theVela simulations, so they are not included here. In addition to Poisson noise from the scene (SN + host galaxy), weinclude zodiacal (based on the model of Aldering 2002) and thermal background (Rubin 2020) given in Table 1. Forread noise, we assume 106 reads for the 300 s exposures and 212 reads for 600 s, using 20 electrons per read with a orward Modeling for Roman
SNe
75 electron floor, giving values also displayed in Table 1 (Garnett & Forrest 1993; Vacca et al. 2004; Rauscher et al.2007). Some forward-modeling codes for ground-based data (e.g., Astier et al. 2013) use only the sky noise (not the sourcePoisson noise or detector noise) to eliminate biases that would otherwise by caused by by using noisy observationsto estimate the Poisson noise. Our photometry is in an even more complex regime: SN Poisson noise, galaxy+skyPoisson noise, and detector noise all matter. We assume that the up-the-ramp readouts have been accurately fit,yielding count-rates with known, Gaussian-distributed uncertainties. As discussed in Section 2, we may have toforward model starting with the original detector readouts (which will be read-noise-limited for these faint sources)for satisfactory performance.If the SN survey takes place over two years, with visits to the SN field(s) every five days, then there will be 146 visits.If a SN goes off at a random epoch, and every image taken after explosion at that location is considered contaminatedwith SN light, then the number of references will vary up to about 140 (assuming an absolute minimum of ∼ ∼
70 on average. (Including lost epochs due to chip gaps, these numbers are ∼
124 and ∼ PHOTOMETRYFollowing Suzuki et al. (2012), we performed photometry of the SNe Ia in the WFI mock observations using aforward-model code (the same one used by Hayden et al. submitted and Ori et al. in prep.). This code fits analytic2D-spline galaxy models (one independent model for each filter) which are convolved with PSFs (including convolutionwith the pixel) and resampled to match the images. As in Suzuki et al. (2012), the modeling uses 0 . (cid:48)(cid:48)
01 subpixels (11 × oversampling). Our minimizer of choice is Levenberg-Marquardt (Levenberg 1944; Marquardt 1963).The flux of image i on a pixel x, y near the SN location is modeled as the sum of galaxy light G ( α, δ ), backgroundlight s i , and SN light ( F i , which is zero for epochs before explosion or ∼ α and declination δ ). These must be mappedto the 11 × oversampled pixel coordinates with WCS functions A i : x × , y × → α and D i : x × , y × → δ . In ourcode, this is done using Astropy all pix2world . These α and δ values are slightly adjusted with ∆ α i and ∆ δ i valuesfor each image (it remains to be seen if the Roman
WCS solution will be good enough to avoid these adjustments).The 11 × oversampled galaxy model is convolved with the PSF and the pixel (also 11 × oversampled), then thishigh-resolution model is sampled every 11 subpixels (including at x, y ). Thus, G i ( x, y ) = G ( A i ( x × , y × ) + ∆ α i , D i ( x × , y × ) + ∆ δ i ) ⊗ PSF i ( x × , y × ) | x,y . (1)The SN coordinates are also stored in sky coordinates ( α SN , δ SN ), but the PSF is in pixels. To convert, we need theinverse of the above WCS transform ( Astropy all world2pix ): X i : α SN , δ SN → x SN i and Y i : α SN , δ SN → y SN i . Theseare also adjusted with ∆ α i and ∆ δ i , giving x SN i , y SN i = X i ( α SN + ∆ α i , δ SN + ∆ δ i ) , Y i ( α SN + ∆ α i , δ SN + ∆ δ i ) . (2)Finally, we can combine both models with the image-dependent, spatially flat sky s i , giving the model M i ( x, y ): M i ( x, y ) = G i ( x, y ) + F i A ( x, y ) PSF i ( x − x SN i , y − y SN i ) + s i (3)We assume (as is true for WFC3 IR) that the flat fielding preserves surface brightness, but point-source fluxes arescaled down proportional to the pixel area on the sky A ( x, y ). Thus the SN model fluxes must also be scaled downto match the data. The galaxy model goes to zero at the edge of the circular fit patch (thus breaking the degeneracybetween sky and galaxy light). Note that both the galaxy model and the SN require convolution with the PSF, but wedo not insert the SN as a Dirac delta function into the 11 × oversampled galaxy model, as the SN may land with light As most of the noise in the simulated observations is Poisson noise, we take a simple quadrature sum of the read noise and Poisson noise,without the (cid:112) / Rubin and Cikota et al. split between subpixels, broadening the PSF. Finally, we note that other extensions of the formalism (e.g., modifyingthe PSF shape as a function of image counts, Choi & Hirata 2020) are straightforward, but we do not consider thesehere.There are many possible choices for the galaxy basis functions (Thevenaz et al. 2000). The general considerations forthe galaxy basis functions are that they should be flexible enough to model real galaxies accurately, without being soflexible that the model is poorly constrained, amplifying noise. Holtzman et al. (2008), Astier et al. (2013), and Broutet al. (2019) used a grid of squares of constant surface brightness. Smooth parameterizations are also used; Rodetet al. (2008) used Gaussians and Bongard et al. (2011) used sinc interpolation of a uniform grid. We want to maintaina smoother model for the undersampled data than a pixelized model or even Gaussians, and want a faster falloff thansinc interpolation (for a smaller modeled patch), so we use 2D splines. Suzuki et al. (2012) and Rubin et al. (2013)also used 2D splines, but added greater flexibility in the galaxy radial direction, giving an overall smoother modelto reduce noise for SNe with limited numbers of references. Here, we have many reference epochs, so we simply use2D splines with a uniform grid. Initially, we experimented with the spline node spacing. In the end, we settled on 2nodes per PSF FWHM, effectively building an approximately Nyquist-sampled model. In other words, the spline-nodespacing for J
129 was 0.62 pixels or 0 . (cid:48)(cid:48)
068 (Table 1). RESULTS AND DISCUSSIONWe run several sets of analyses to investigate the results of the photometry. Our first result is that our spline-nodespacing is sufficient. It is common in ground-based forward modeling to plot results against local galaxy surfacebrightness (e.g., Brout et al. 2019). However, the galaxy-light Laplacian (second derivative) is the better quantity formost types of modeling errors, as smooth galaxy gradients generally do not cause problems. (For ground-based work,the host galaxy is frequently poorly resolved, and the local surface brightness correlates with the Laplacian.) Figure 5shows the second derivative for a typical galaxy. For each band, Figure 6 shows the noise-free residuals plotted againstthe local second derivative of the host-galaxy light; no trends are seen. Galaxy Convolved by PSF and Pixel,Inverse Hyperbolic Sine Scale Laplacian,Linear Scale
Figure 5.
Visualization of the second derivative (Laplacian) for a galaxy. The left panel shows the central area around aVELA simulated galaxy, convolved with the PSF and the pixel. To better show faint features, this panel uses inverse hyperbolicsine scaling. The right panel shows the second derivative of the left panel. The largest deviations from zero are in a smallregion of the galaxy around the core. It is these regions that most require spatial flexibility in a galaxy model.
Next, we search for biases and check the uncertainties by plotting distributions of pulls: (recovered flux − true flux)/(recovered flux uncertainty). Figure 7 shows summary statistics, binned in AB magnitude: zero-point − . (true flux). In general, the forward-model code has better performance in the redder filters withbetter sampling. The mildly underestimated ( (cid:46) For a simple comparison, we also perform photometry using a simple image-resampling code for the host-galaxy subtraction. For each imagewith SN light in it, we take each reference image and resample it to the pixels of that live-SN image. We use a square kernel with a sizeof 0.3 pixels (frequently called the pixfrac). After subtracting the references, we perform PSF photometry on the subtracted images. Weonly perform this test with the noise-free images to better examine the differences with forward modeling. This is an extremely simplisticresampling compared to more accurate procedures, e.g., Rowe et al. (2011) or Fruchter (2011). Unsurprisingly, it gives results that aremuch poorer than the forward model, with large negative slopes visible in all panels indicating over-smoothed galaxy models. orward Modeling for
Roman
SNe M e a n R e s i d u a l f o r E a c h S N ± R M S R e s i d u a l ( e / s ) Z Y J H F Figure 6.
For each band, for each simulated SN, we show the mean flux residual (recovered flux − true flux) over the wholelight curve (blue points) plotted against the second derivative of the galaxy flux at the SN location. As illustrated in Figure 5,the second derivative is close to zero over much of the galaxy after convolution with the PSF and the pixel. The error bar oneach point shows the RMS across epochs for that SN. To search for any possible trends with the highest sensitivity, we usethe forward-model runs on the images that have no noise added. The typical flux at maximum light in this redshift range is 3e − /s for the four bluest bands and 1.5 e − /s for F − .
03 to 0.03 e − /s (roughly ±
1% of peak flux). Any trends withgalaxy second derivative would indicate that the photometry may need a more flexible galaxy model (e.g., spacing the splinenodes closer together).
Figure 8 shows observed flux regressed on true flux. We use both images with noise (top panel) and imageswithout noise (bottom panel). For the images without noise only small biases ( ∼ ∼ Z
087 but the other filters are generally consistent with unitymean scaling between true and observed fluxes.Finally, we fit light curves using SALT2-Extended; Figure 9 shows these results. Any biases seem to be at thefew mmag level or smaller. Figure 10 shows the sensitivity of our distance moduli to the calibration of each filter asa function of redshift. Our constraints on the cosmological bias are thus expected from the accuracy on the inputphotometry, but this test still uniquely measures any correlated effects of host-galaxy subtraction on the full lightcurves. SUMMARYWe validate a forward-model code for performing SN photometry in simulated undersampled images for the
Roman transient survey. As there are no real images to inject simulated SNe into, we use the VELA simulated galaxy images,which are generated in the
Roman filters over a similar redshift range as the SN survey. We create 762,570 simulatedpostage stamps around the locations of 2,061 simulated SNe ( ∼
10% of the anticipated full survey). We describe theassumptions of our forward-model code and validate those assumptions first with noise-free images, and then withimages that have noise added. Finally, we fit our simulated light curves and show that we can recover SN distancemoduli with biases limited to less than a few mmags.0
Rubin and Cikota et al.
24 25 26 27 28 29 300.200.150.100.050.000.05 P u ll C e n t r a l V a l u e Z Z
087 at Max. Y Y
106 at Max. J J
129 at Max. H H
158 at Max. F F
184 at Max.
MeanMedian24 25 26 27 28 29 30AB Magnitude Bin0.900.951.001.051.101.151.201.25 P u ll D i s p e r s i o n Z Y J H F Standard DeviationNormalized Median Absolute Deviation
Figure 7.
Summary statistics for pulls: (recovered flux − true flux)/recovered flux uncertainty. The results are binned inAB magnitude and separate results are shown for each filter (left to right is Z
087 to F top panel shows centralvalues (mean with red dots, median with blue triangles). In general, there is no evidence for biases (offsets from zero) exceptin the Z
087 filter in the middle of the magnitude range ( ∼ bottom panel shows dispersions (standard deviation with red dots, the normalizedmedian absolute deviation with blue triangles). The uncertainties on the NMAD are computed with bootstrap resampling. Ifall uncertainties are correct and Gaussian, the dispersion values should be unity. There is evidence of mildly underestimated(by (cid:46) ∼ orward Modeling for Roman
SNe
24 25 26 27 28 29True AB Magnitude Bin0.960.970.980.991.001.011.02 S c a li n g f r o m T r u e F l u x t o O b s e r v e d F l u x Z Y J H F
24 25 26 27 28 29True AB Magnitude Bin0.960.970.980.991.001.011.02 S c a li n g f r o m T r u e F l u x t o O b s e r v e d F l u x Z Y J H F Figure 8.
Average scaling on true flux to match observed flux, binned by AB magnitude and separated by filter. The toppanel shows the results from the images with noise added. A small consistent bias is seen in the Z
087 filter (leftmost point ineach bin). The bottom panel shows the results from images without noise added. The brightest three magnitude bins showa slight bias (probably due to the way the data were generated as discussed in Section 3). The faintest magnitude bins show alarger (but still small) bias. Rubin and Cikota et al. C e n t r a l V a l u e o f ( F i t T r u e ) D i s t a n c e M o d u l u s Mean: 0.0020 ± 0.0014Median: 0.0028 ± 0.0017MeanMedian0.8 1.0 1.2 1.4 1.6 1.8 2.0Redshift Bin0.020.040.060.080.10 D i s p e r s i o n o f ( F i t T r u e ) D i s t a n c e M o d u l u s Standard DeviationNormalized Median Absolute Deviation
Figure 9.
Summary statistics on recovered distance modulus compared to true distance modulus for each SN. The top panel shows the mean (blue circles) and median (red triangles) in bins of redshift. The blue and red lines show the result over allredshifts. No strong evidence of bias is seen. The bottom panel shows the dispersion in each bin (blue dots for the mean, andred triangles for the normalized median absolute deviation). The increase as a function of redshift is due to a combination ofthe lower signal to noise, and the loss of red rest-frame wavelength coverage. orward Modeling for
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SNe ( D i s t a n c e M o d l u s ) / ( Z e r o p o i n t ) Z Y J H F Figure 10.
Sensitivity of the distance modulus of each SN to the calibration of each filter, plotted as a function of the redshiftof each SN. As in Amanullah et al. (2010), this is computed by scaling the calibration for each filter in turn, refitting the SN withSALT2, and computing a new distance modulus. The distance modulus difference divided by the size of the shift in magnitudesgives the derivative. We do not propagate these calibration changes into the training of SALT2, which will change the resultsin detail (Guy et al. 2010). The sum of all the derivatives should be 1 (moving the calibration of each filter by 1 magnitudeshould move the distance modulus by 1 magnitude), and Amanullah et al. (2010) note that unstable light-curve fits frequentlyreveal themselves as deviations from 1. We exclude three such SNe from this plot which show up as outliers. For the five-bandlight-curves considered in this work, the sensitivity of the distance moduli to the calibration of any one filter is (cid:46)
1. Limitingthe wavelength range or number of bands will significantly increase the sensitivity to calibration, resulting in much larger valuesthan those shown here. For example, with just rest-frame B and V data (and using 3.1 for the slope of the color-magnituderelation), the distance moduli scale as m B − . m B − m V ) = 3 . m V − . m B . ACKNOWLEDGMENTSWe thank Susana Deustua for careful feedback. This work was supported by NASA through grant NNG16PJ311I(Perlmutter
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Science Investigation Team). The technical support and advanced computing resources from theUniversity of Hawai‘i Information Technology Services Cyberinfrastructure are gratefully acknowledged. This workwas also partially supported by the Office of Science, Office of High Energy Physics, of the U.S. Department of Energy,under contract no. DE-AC02-05CH11231. This research used resources of the National Energy Research ScientificComputing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Departmentof Energy under Contract No. DE-AC02-05CH11231.
Software:
Astropy (Astropy Collaboration et al. 2013), Mathematica (Wolfram Research Inc. 2020), Matplotlib(Hunter 2007), Numpy (Harris et al. 2020), Python (Van Rossum & Drake 2009), SciPy (Virtanen et al. 2020), SNCosmo(Barbary 2014) REFERENCES