First Cosmology Results Using Type Ia Supernovae from the Dark Energy Survey: Photometric Pipeline and Light-curve Data Release

The DES-SN performed a deep, time-domain survey in four optical bands (griz) with an average cadence of 7 days per filter covering ∼27 deg² over 5 annual campaigns from 2013 to 2018 using the Dark Energy Camera (DECam: Flaugher et al. 2015). DECam exposure processing (Morganson et al. 2018), DiffImg, and automated artifact rejection (Goldstein et al. 2015) were run on a nightly basis.

DES-SN observed in eight "shallow" and in two "deep" fields, with the shallow and deep fields having typical nightly point-source depths of 23.5 and 24.5 mag, respectively. Multiple exposures are taken each night with 3, 3, 5, and 11 (1, 1, 1, and 2) exposures taken in griz for the deep (shallow) fields (See D'Andrea et al. 2018). Images used in this analysis were taken during the first three years of DES-SN, from 2013 September to 2016 February, in which we discovered roughly ∼12,000 transients. Among these transients, ∼3000 were identified as likely SNe Ia based on their light curves and 251 were spectroscopically confirmed (D'Andrea et al. 2018).

2.2.1. FirstCut

2.2.2. Additional Image Preparation

Calibrated tertiary standard star magnitudes from Burke et al. (2018) are used for the DES-SN internal calibration of each DES-SN image. Approximately 50 tertiary standard stars lie within each DECam CCD image. Burke et al. (2018) have determined grizY magnitudes in the AB system of these standard stars using the "Forward Global Calibration Method" (FGCM). The FGCM "forward" computes the fraction of photons observed for each star over repeated exposures by utilizing measurement of the instrument transmission function, precipitable water vapor, observing conditions, and a model of the stellar source. In addition, using the passband transmission (instrument+atmosphere) versus wavelength and the spectral energy distribution (SED) of the source, corrections are applied to the stellar catalog fluxes (as well as to the final SN fluxes). These SED-dependent "chromatic corrections" account for differences between SED and the mean stellar SED, and between atmospheric transmission of each exposure and the mean atmospheric transmission. This correction extends the FGCM calibration precision to be valid over a wide color range (−1 ≲ g − i ≲ 3). We refer the reader to Li et al. (2016) for more detail. The implications on cosmological measurements due to these corrections are discussed in Lasker et al. (2018).

We use PSF-fitted photometry of the tertiary standard stars to determine the zero-point of each image. As discussed above, the sky background in the FirstCut images was subtracted using PCA over the entire exposure. However, at the specific locations of transient objects we check for residual nonzero sky background. Residual sky often occurs when the moon is bright, causing large sky gradients that are not captured with PCA. We apply a second method of local sky background and sky uncertainty estimation using concentric apertures of 40 and 60 pixels following Jones et al. (2015) and the resulting sky and uncertainty are calculated in the same manner for each tertiary standard star as well as for the SN.

Biases are induced in PSF-fitted flux measurements when the astrometric solution of a source is incorrect or is uncertain (Rest et al. 2014). These biases are smaller for stars than for SNe because the stars have higher signal-to-noise ratios (S/Ns) and their positions are better constrained. When computing photometric magnitudes, in the limit of high S/N and a correct PSF model, there is no astrometrically induced flux bias if the astrometric solution and uncertainty are the same for both the stars and the SN itself. The bias in the zero-point and the bias in the SN flux will cancel. Here, we discuss the expected photometric biases in the real SNe data set; in the fake data set this is more subtle and is discussed in Section 4.3.

There are fundamental differences between stars and the SNe that must be accounted for. The stars may have measurable proper motion while the SNe do not. Additionally, the centroids of SNe have larger uncertainty because there are fewer epochs to constrain the position and the S/N is lower. Therefore, in modeling the SNe, we fix the location of the SN in R.A. and decl. across all images (Section 3). While the SN position is fixed ("fixed-position photometry"), we determine the position of the stars for each image in order to account for stellar proper motions ("variable-position"). Proper motions of the standard stars, which are estimated by linear fits to the positions over 3 yr of observations, have an rms of ∼10 mas per year.

In order to be consistent in the application of the stellar position in the photometry, Rest et al. (2014) and Scolnic et al. (2017) run fixed-position photometry on both the stars and SNe. In our pipeline we apply fixed-position photometry to the SN but we apply variable-position photometry on the stars, and this inconsistency causes a small 1–2 mmag bias toward fainter SN flux measurements but has the benefit of accounting for stellar proper motions. These small biases are not corrected for, but rather are incorporated into the systematic uncertainty budget as they are subdominant to the total calibration uncertainties of the systematic error budget described in B18-SYS.

Millions of tertiary standard star measurements are taken over the course of DES-SN. Following A13, the uncertainty used in the stellar photometry fits does not include source Poisson noise. The 1σ scatter in the recovered stellar magnitudes (hereafter "repeatability") is plotted in Figure 2. For the brightest stars (<17 mag), the photometric uncertainties after including Poisson noise analytically are 1 mmag, but the observed measurement scatter is >5 mmag (Figure 2) in each band. This floor, after subtracting out the mean photometric uncertainty, is added in quadrature to all flux uncertainties.

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In order to demonstrate the size of the chromatic corrections applied to the tertiary standards in the SN fields, we compare the uncorrected individual exposure (nightly) stellar photometry with the FGCM chromatically corrected stellar catalog magnitudes (Figure 3). Differences are up to 4 mmag over the color range of the tertiary standards ($0.25\lt g-i\lt 2$ mag).

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As in H08 and A13, SMP uses a time series of image stamps from the data located at the position of the SN. We assume that the DECam pixel fluxes can be modeled from a temporally varying SN flux and a temporally constant galaxy model that is modeled as a grid of pixels. In order to facilitate model comparisons to all images simultaneously, all data images are scaled to a common zero-point of 31.00 mag.⁵³ Following H08 and A13, the model is resampled to compare with the data set and the data are never resampled to avoid correlated noise. A visual representation of the model is shown in Figure 1. The "Model" images shown on the right-hand side of Figure 1 are compared to data, and to constrain our model we minimize the following:

$$\begin{eqnarray}&&{\chi }^{2}=\displaystyle \sum _{{ij},n}\displaystyle \frac{{({S}_{{ij},n}-{D}_{{ij},n})}^{2}}{{\sigma }_{{\mathrm{sky}}_{n}}^{2}},\end{eqnarray} \tag{ 1 }$$

for each pixel labeled with indices i and j, and exposure n. ${S}_{{ij},n}$ are the modeled pixel fluxes and ${D}_{{ij},n}$ are the data pixel fluxes. Equation (1) is weighted by the precomputed variance in the sky counts (${\sigma }_{{\mathrm{sky}}_{n}}^{2}$) as motivated by A13 to preserve statistical optimality for faint sources and avoid potential biases due to inaccuracy of the PSF model. However, because the denominator of Equation (1) does not include all sources of noise, we modify the photometric uncertainties output by SMP using both the analytical expectations of source and galaxy noise (Section 3.4), and we correct our uncertainties using results on fake SNe (Section 5).

For our model ${S}_{{ij},n}$, we define a temporally varying SN flux for each exposure n (F_n) and a temporally constant grid of fluxes (g_ij) of size N × N (N = 30). The SN and host galaxy fluxes per pixel are defined as follows:

$$\begin{eqnarray}\begin{array}{rcl}{\mathrm{FSN}}_{{ij},n} & = & {{\boldsymbol{F}}}_{{\boldsymbol{n}}}\displaystyle \sum _{{k}_{i}{k}_{j}}{\tilde{\mathrm{PSF}}}_{{k}_{i},{k}_{j},n}\\ & & \quad \times \ {e}^{2i\pi {k}_{i}({\bar{{\boldsymbol{SN}}}}_{{\boldsymbol{i}}}-{i}_{0})/N}\,{e}^{2i\pi {k}_{j}({\bar{{\boldsymbol{SN}}}}_{{\boldsymbol{j}}}-{j}_{0})/N},\end{array}\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{\mathrm{FGAL}}_{{ij},n}=\displaystyle \sum _{{k}_{i}{k}_{j}}{\tilde{\mathrm{PSF}}}_{{k}_{i},{k}_{j},n}\ {\tilde{{\boldsymbol{g}}}}_{{{\boldsymbol{k}}}_{{\boldsymbol{i}}},{{\boldsymbol{k}}}_{{\boldsymbol{j}}}}{e}^{-2i\pi {k}_{i}/N}\,{e}^{-2i\pi {k}_{j}/N},\end{eqnarray} \tag{ 3 }$$

and the model image ${S}_{{ij},n}$ is defined as

$$\begin{eqnarray}&&{S}_{{ij},n}={\mathrm{FSN}}_{{ij},n}+{\mathrm{FGAL}}_{{ij},n},\end{eqnarray} \tag{ 4 }$$

where ${\tilde{\mathrm{PSF}}}_{{ij},n}$ is the Fourier transform of the PSF evaluated at the location of the SN. We vary the SN sky position in Fourier space, where the SN point source is represented by a plane wave at ${\bar{\mathrm{SN}}}_{i}$, ${\bar{\mathrm{SN}}}_{j}$ in pixel coordinates relative to the center of the galaxy model (i₀ and j₀), which is defined to be the DiffImg SN position. This formalism allows us to model the SN position at subpixel locations in Fourier space and to evaluate the likelihood in real space. The floated parameters in our fits are designated in bold font in Equations (2) and (3); these parameters are F_n, g_ij, ${\bar{\mathrm{SN}}}_{i}$, and ${\bar{\mathrm{SN}}}_{j}$.

We adopt a galaxy model on a grid of pixels with the same 027 pixel scale as the DECam images. The reference center of each data stamp is the position of the SN as determined by DiffImg. This position is an average of all epochs for which there was a DiffImg detection. The reference center is at a subpixel location, so as to facilitate comparison of our model with the data, we shift the galaxy model and the SN model for each exposure by the difference of the center image pixel and the reference center.

In order to avoid degeneracies between the galaxy model and the SN flux, we fix the model SN flux at zero for epochs outside the observer frame range ${\rm{\Delta }}{\mathrm{MJD}}_{\mathrm{peak}}\gt 300$ days or ${\rm{\Delta }}{\mathrm{MJD}}_{\mathrm{peak}}\lt -60$ days, where MJD_peak is the derived date of peak flux from an initial light-curve fit of DiffImg photometry and ${\rm{\Delta }}{\mathrm{MJD}}_{\mathrm{peak}}={\mathrm{MJD}}_{\mathrm{exposure}}-{\mathrm{MJD}}_{\mathrm{peak}}$. We find that any residual SN flux beyond 300 days contributes to negligible biases in photometry (<0.01%).

We utilize a Markov Chain Monte Carlo Metropolis Hastings algorithm (Metropolis et al. 1953; Hastings 1970) to sample the likelihood and we assume flat priors on each of our model parameters with the exception of the SN R.A. and decl. for which we assume a top-hat prior with radius 2 pixels that is centered at the location of the DiffImg fit sky position. For our model image stamps, we adopt a radius of 13 pixels (3.5 arcsec) around ${i}_{0},{j}_{0}$, inside of which we compute χ² from Equation (1) using only pixels that fall entirely within the predefined radius. For each filter, we have a total of ∼500 galaxy model parameters and anywhere from 25 to 500 SN flux parameters; one for SN flux in each exposure that falls within our defined MJD range over which we fit SN fluxes. For our sampling algorithm, we do not employ more complicated algorithms such as emcee because the computation requirements of our likelihood and the number of parameters make running the required 2N walkers intractable. Instead, during the first 100,000 steps we optimize our steps in each parameter to achieve between a 25% and 75% acceptance rate. We employ a Geweke Diagnostic (Geweke 1992) test to ensure that our chains for the SN fluxes have sufficiently sampled the posterior space. Our chains can run up to 2,000,000 steps. The galaxy model, which is represented as a grid of delta functions in Fourier space, has power on all scales that can lead to poor convergence. For this reason we do not explicitly check for convergence of g_ij, but rather we ensure convergence of the ${\mathrm{FGAL}}_{{ij},n}$ pixels in a 1'' aperture centered at the location of the SN.

The SMP fits are performed separately in each band. While there could be added benefit in measuring the SN position by fitting all bands simultaneously, atmospheric refraction causes the position of the SN to be color dependent, which is not accounted for in this work. A total of 41,004 jobs were run independently in order to produce griz light curves for the 251 SNe in the spectroscopic sample and 10,000 fakes. Each job utilized a single FNAL processor and could take anywhere from 5 to 48 hr to fit, with the latter occurring for deep-field z-band fits with up to 750 exposures. The vast majority of the computation time is in the convolution of the galaxy model with the PSF for each exposure. To improve fitting speed, the PSFs were stored in Fourier space and the galaxy model (g_ij) is transformed to Fourier space and subsequently convolved with the PSF requiring only n + 1 Fourier transforms. After fitting, we evaluate the best fit F_n for each exposure n by taking the mean of the MCMC chain. The error on F_n is the standard deviation of the MCMC chain. For observation sequences with multiple back-to-back exposures, we report the weighted average flux and uncertainty among the individual exposures.

Here we describe the treatment of the statistical uncertainties within SMP to which an additional empirically observed dependence on host galaxy surface brightness is included in Section 4.4. There has been debate about the proper way to include Poisson noise of the host galaxy and source in the photometry fits (H08 and A13). H08 weight their fits according to expected photon statistics, which includes the Poisson noise of the host galaxy. A13 exclude the noise contribution of the host galaxy and source in the fitting process. We have chosen the latter method (shown in Equation (1)) and correct our output uncertainties using expected photon statistics after the fitting process following:

$$\begin{eqnarray}&&{\sigma }_{\mathrm{stat}}^{2}={\sigma }_{{\mathtt{SMP}}\mathrm{fit}}^{2}+{\sigma }_{\mathrm{source}}^{2}+{\sigma }_{\mathrm{hostgal}}^{2},\end{eqnarray} \tag{ 5 }$$

where ${\sigma }_{{\mathtt{SMP}}\mathrm{fit}}$ is the uncertainty derived from the SMP Monte Carlo chains that were computed using only the sky uncertainty, σ_source is the Poisson noise of the SN, and σ_hostgal is the host galaxy Poisson noise. The host galaxy photon variance on exposure n is approximated by

$$\begin{eqnarray}&&{\sigma }_{\mathrm{hostgal},n}^{2}=\displaystyle \frac{{\displaystyle \sum }_{{ij}}{\mathrm{fgal}}_{{ij},n}\times {\mathrm{PSF}}_{{ij},n}^{2}}{{\displaystyle \sum }_{{ij}}{\mathrm{PSF}}_{{ij},n}^{2}}\times \mathrm{NEA},\end{eqnarray} \tag{ 6 }$$

where ${\mathrm{fgal}}_{{ij},n}$ is ${\mathrm{FGAL}}_{{ij},n}$ expressed in photoelectrons following:

$$\begin{eqnarray}&&{\mathrm{fgal}}_{{ij},n}={\mathrm{FGAL}}_{{ij},n}\times {10}^{({{ZP}}_{n}-31)/2.5}\times {\mathrm{Gain}}_{n},\end{eqnarray} \tag{ 7 }$$

and the noise equivalent area is $\mathrm{NEA}\equiv 1/{\sum }_{{ij}}{\mathrm{PSF}}_{{ij},n}^{2}$. Equation (5) corresponds to our analytic expectation of the photometric uncertainties. Finally, we report the weighted average uncertainty among the individual back-to-back exposures. Below we test the accuracy of our photometric extraction and correct σ_stat for underestimation of the measurement noise.

The insertion of fake SNe at the image level and the subsequent analysis of their measured fluxes is an important test of the photometric pipeline. It allows us to quantify measurement biases, compare SMP uncertainties to the measured minus true flux differences and determine uncertainty corrections, and optimize SMP cuts to reject flux outliers. We simulate a sample of SN Ia light curves and insert light-curve fluxes onto DES-SN images using the measured PSF. Because we insert an entire sample of SN Ia light curves, we are able to characterize biases in photometry as well as the propagation of these photometry biases to biases in measured distances. A13 moved nearby stars in their images to locations near host galaxies and treated them as fake transients, which preserves the true PSF for each star, but it is difficult to trace photometry biases to distance biases given that they have limited statistics of fake stars and do not model a sample of fake SNe light-curve magnitudes. Additionally, A13 did not account for a position-dependent PSF when moving stars, whereas the method described here does.

Fake SN light-curve fluxes are generated using the SuperNova ANAlysis software package (Kessler et al. 2009) in a ΛCDM cosmology (Ω_M = 0.3). Light-curve fluxes are overlaid as PSF sources onto the DECam images and processed with the DiffImg pipeline. A detailed description of the simulation used for the fakes can be found in Section 2 of Kessler et al. (2018), but here we provide a brief summary. The fake SNe span a wide magnitude range (from 19th mag to well below the detection limit) and redshift range (0.1 < z < 1.2). K15 overlay fluxes onto the CCD image near real galaxies with SN locations chosen with a probability proportional to the host surface brightness density. The SN flux is distributed over nearby pixels using the PSF determined with PSFEx, and the flux in each pixel is varied by random Poisson noise. Since we use a scaling of the modeled PSF to insert the fake transient, rather than the real PSF (i.e., moving real stars in the image), we separately check for potential PSF modeling errors that are not included as a part of the analysis of the fakes.

K15 inserted 100,000 fake SN light curves into the first 3 yr of DES-SN images. These fakes were used to monitor image quality and ∼40,000 fake SNe Ia were "discovered" by DiffImg. However because SMP is computationally expensive, for this first DES-cosmology analysis, only on a subset of 10,000 fake SN light curves were processed by SMP.

In order to reduce the number of photometric outliers, exposure quality requirements (cuts) were optimized on the sample of fake SNe. We denote the fraction of 5σ flux outliers (η_5σ) when comparing the SMP fit flux (F_n) to the true fake flux (F_True). We remove exposures with poor data-model agreement (χ²/ndof >1.2) and with poor seeing conditions (PSF_FWHM > 2.75 arcsec). To make additional improvements we also place conservative cuts based on zero-point and sky level to remove the poorest quality images. These cuts retain 94% of all exposures and reduce η_5σ from 6 × 10⁻⁴ to 2 × 10⁻⁴.

Comparing the input photometry to the recovered photometry (${\rm{\Delta }}F={F}_{n}-{F}_{\mathrm{True}}$), we measure photometric biases <0.5% over 19th to 24th magnitude. As shown in panel (a) of Figure 4, there is a slight bias in the deep fields for ${\rm{\Delta }}F/{F}_{\mathrm{True}}$ of −0.3% at faint magnitudes, which is included in the systematic error budget of B18-SYS.

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There are three key differences between the analysis of the DES-SN data set and that of the fake SNe. First, the astrometric solution used to insert fakes (K15) is the same solution that is used to model the fakes within SMP. Astrometric uncertainty is not simulated in the fake point sources. Second, K15 use zero-points that were fit using aperture photometry to insert fake fluxes onto images, while SMP uses PSF fitting. In order to assess the accuracy of SMP, we correct for the zero-point difference between the K15 and SMP. Thus, our results presented here are insensitive to incorrect modeling of the zero-point. B18-SYS discuss an independent method for validating the zero-point and internal calibration uncertainties. Third, the analysis of the fakes uses the same PSF model that was used to insert the fakes. Inaccuracies of the PSF model are not simulated in the fakes, and thus in Section 6 we perform a cross-check of our PSF model.

If the SMP flux uncertainties are accurate, then rms $({\rm{\Delta }}F/{\sigma }_{\mathrm{stat}})=1$. However, we observe that the rms of the fakes is slightly above unity as shown in panel (b) of Figure 4. To characterize the excess scatter, we examine the dependence of the rms on the local host galaxy local surface brightness (m_SB).

We find that there is an underestimation of photometric uncertainties for SNe located in galaxies with high local surface brightness, as was seen previously in DiffImg (K15). A scale correction (S) is computed from the fakes as shown in Figure 5 that is required to bring rms of recovered fake fluxes as a function of m_SB to unity. This dependence (hereafter the Host SB dependence) has been seen in the past (K15, Scolnic et al. 2017). The source of the Host SB dependence is unclear because we include host galaxy Poisson noise in our SMP uncertainty calculation (see Section 3.4). In SMP, we find no significant bias in ${\rm{\Delta }}F/{\sigma }_{\mathrm{stat}}$ as a function of m_SB.

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The inset of Figure 5 shows the results of SMP run on two example host galaxies, one bright and one faint. For the bright host galaxy, visibly poorer χ² distributions are seen across the image stamp and structure can be seen in the residual stamp.

To account for the increased scatter as a function of host galaxy surface brightness, K15 scaled their output SN flux uncertainties. In SMP we apply the same method of scaling our SN flux uncertainties with multiplicative corrections (S). The SMP light-curve photometric uncertainties (σ_F) are given by

$$\begin{eqnarray}&&{\sigma }_{F}={\sigma }_{\mathrm{stat}}\times S,\end{eqnarray} \tag{ 8 }$$

where σ_stat was defined as the coadded measurement uncertainty and S is the function of m_SB, bandpass, and field shown in Figure 5.

The host SB dependence was first quantified for DiffImg photometry in K15 and the excess scatter is also seen in the SMP results. Because the host SB dependence is not unique to difference imaging photometry, we conclude it does not result from the use of SWarp (Bertin et al. 2002), which is used to coadd exposures, nor is it from hotPants (Becker 2015). Because the size of the dependence is similar in all bands, chromatic refraction likely plays a subdominant role in the host SB dependence. The source of this additional scatter is likely due to a number of confounding sources similar to the photometric repeatability floor for the stars. Atmospheric distortions contribute a chromatic increase in flux scatter and astrometric errors could introduce unmodeled uncertainty in the host galaxy itself. With improvements to the astrometric solution expected in the coming analysis of the full DES-SN 5 yr data set, we will be able to examine the dependence on astrometric quality.

DiffImg was designed for DES-SN as a rapid transient identification and SMP was designed as a precision photometric tool to be used for cosmology. Because they have been optimized for different purposes, it is difficult to make a direct comparison. We find that the fraction of catastrophic photometric outliers (η_5σ) occurs at 0.02% for SMP in comparison with 0.08% for the DiffImg pipeline. In addition, we compare the overall size of our photometric errors and find that the uncertainties output by the SMP pipeline are slightly smaller than those of DiffImg (Figure 8).

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A number of improvements can be made to our photometric pipeline and analysis of the fake SNe. There are two main aspects of our fakes analysis that inhibit our ability to characterize the full extent of our photometric pipeline. First, we know the precise PSF of our fake SNe because we use the same PSF to overlay the point source and do the SMP fitting. In the future we will vary the PSF and calculate the impact on photometric repeatability, biases and the host SB dependence. Second, the method by which the fakes are inserted onto the images is not representative of the true astrometric uncertainty because the fakes are inserted and modeled in SMP using the same astrometric solution. In the future we will vary the location of the fake point source on each exposure by the astrometric uncertainty. The ability to simulate both of these effects will facilitate the tracing of photometric biases due to the PSF and astrometry all the way to cosmological parameters.

For future stage IV surveys in which calibration uncertainty in the filter zero-points approaches the <4 mmag level, current photometric errors (3 mmag) will need to be reduced. Additionally, as the measurement uncertainties on SN fluxes improve, it will become ever more important to understand the source of the host SB dependence. While Kessler et al. (2018) show that the host SB dependence has little effect on the DES-SN detection efficiency of SNe Ia, more general transient searches for faint nearby sources (e.g., Kilonovae) on bright galaxies could also be significantly affected.

The host SB dependence may be mitigated in future DES-SN analyses with upcoming improvements to the astrometric solution and DES image processing pipelines, which will include the tree ring effect noted in Plazas et al. (2014). As we do not expect the dependence to fully disappear, and to facilitate more accurate simulations of the SMP pipeline, we will also investigate applying a series of additive flux uncertainty floors dependent not only on m_SB, but also on observing conditions. Lastly, we will also investigate the effects of better galaxy modeling and resampling tools such as GALSIM (Rowe et al. 2015).