ZTF Early Observations of Type Ia Supernovae. I. Properties of the 2018 Sample

The ZTF camera is mounted on the 48 inch Samuel Oschin Telescope (P48) at Palomar Observatory (Dekany et al. 2016). At a limiting magnitude of r ∼ 20.5 mag, three custom filters (g_ZTF, r_ZTF, and i_ZTF; hereafter g, r, and i) are designed to maximize throughput by avoiding major skylines at Palomar (Bellm et al. 2019b). ZTF divides its observing time between public surveys (40%), partnership surveys (40%), and Caltech surveys (20%). Bellm et al. (2019a) provide details of the ZTF surveys. In brief, 85% of the public time was allocated to a "Northern Sky Survey" with a cadence of three days in g and r, and the remaining 15% to a "Galactic Plane Survey" with two visits to the Galactic plane (one g + one r) every night. The bulk of the partnership time in 2018 (May–December) was dedicated to two experiments, including an extragalactic high-cadence experiment covering ∼2500 deg² with six visits (three g + three r) every night, and a lower-cadence, wide-field i-band survey. The Caltech time was conducted in a one-day cadence in both g and r with a total footprint of ∼3000 deg². Each night's schedule is arranged by the survey scheduler (Bellm et al. 2019a) to optimize volumetric survey speed (Bellm 2016). In this work, we only focus on the g- and r-band observations within the partnership high-cadence fields.

The current ZTF alert distribution system (Patterson et al. 2019) generates a source packet once a transient ²³ is detected. By definition, a "detection" means that the observed flux is five times larger than the flux uncertainty (see Masci et al. 2019, Section 6). For each transient the alert packet includes a rolling 30 days history of detections and non-detections.

Following the association of all alerts generated at the same position, the GROWTH "Marshal" (Kasliwal et al. 2019) compiles a complete historical record of variability, which is further used to aggregate and visualize follow-up observations.

The sample selection process is summarized in Table 1. In total, there were 336 SNe Ia classified in the partnership fields in 2018, 247 of which were observed as part of the high-cadence partnership survey. ²⁴ For the sample of 247 SNe with high-cadence observations, we performed a preliminary fit to their light curves using the SALT2 software package (Guy et al. 2007) implemented in the sncosmo Python package (Barbary et al. 2016) ²⁵ to estimate the time of maximum light. The sample was further reduced to include only those sources with more than one detection in either the g or r band obtained at least five days before the SALT2-estimated time of B-band maximum, t_B,max. This resulted in a selection of 191 SNe.

Table 1. Steps in Sample Selection

Step	Criteria	Total # SNe
1	Spectroscopically classified SNe Ia observed by the ZTF partnership survey	336
2	Observed by the high-cadence fields	247
3	At least one detection on the Marshal light curve earlier than 5 days prior to ${t}_{B,\max }$	191
4	Remove observations where the reference images are obtained after tB,max − 25 days	154
Extract forced PSF photometry light curves
5	Before ${t}_{B,\max }$, the target must be detected in both g and r over at least five nights	140
6	The first 3σ detection in both g and r must be earlier than tB,max − 10(1 + z)	129
7	Must be detected at least once in both g and r in [tB,max, tB,max + 20(1 + z)]	127

Download table as:  ASCIITypeset image

Note that although the 191 SNe were all discovered in the partnership high-cadence fields, some of them also have observations during the public or Caltech time. We retained those observations in the following analysis.

The ZTF Science Data System (ZSDS) constructed reference images for each field and filter by taking the stack-average of 15–40 historical images ²⁶ (Masci et al. 2019). Observations for each target could be covered by multiple fields. To ensure that the reference images do not contain contamination from SN flux, we need to treat each field (with specific CCD-quadrant therein) for a given filter separately. Hereafter we use "fcqf ID," defined by

$$\begin{eqnarray}\begin{array}{rcl}(\mathrm{fcqf}\,\mathrm{ID}) & = & (\mathrm{field}\,\mathrm{ID})\times 10000+(\mathrm{CCD}\,\mathrm{ID})\times 100\\ & & +(\mathrm{quadrant}\,\mathrm{ID})\times 10+(\mathrm{filter}\,\mathrm{ID})\end{array}\end{eqnarray} \tag{ 1 }$$

as an identifier of the reference images.

We grouped observations by fcqf ID, and excluded those where the time of the latest exposure used to create the reference product was within 25 days of ${t}_{B,\max }$ (in the SN rest frame). Since the typical rise time of SNe Ia is 17 days (Firth et al. 2015), 25 days is a conservative choice. For each target, we further required that the remaining number of observations in both g and r must be no less than 35. 154 SNe met this criterion.

The position of ZTF transients reported on the GROWTH Marshal is based on the initial detection of the source, which is often at low signal-to-noise ratio (S/N). As the first step of forced-PSF photometry, we need to determine the position of the transient more accurately. To this end, for each SN, we obtained the coordinates in all epochs where the SN is detected using Kowalski, ²⁷ a ZTF database system. The typical scatter in both R.A. and decl. is ∼0088 (0.09 pixel size). This uncertainty is small, and thus we do not incorporate it into the PSF modeling. We took the median R.A. and decl. as the true position of each SN.

The pixel scale of the ZTF camera is 1012 pixel⁻¹. The typical seeing-limited FWHM of the PSF is ∼2'' pixel⁻¹. Figure 2 shows an example of the point-source cutouts of a difference image and its normalized PSF-model template. The PSF is normalized such that the sum of all pixel response values is equal to 1. These images are available at the NASA/IPAC Infrared Science Archive (IRSA). ²⁸

Zoom In Zoom Out Reset image size

The difference image PSF is a product of the ZOGY image subtraction algorithm (Zackay et al. 2016). ZOGY generates this by combining the input PSF templates from the science and reference images prior to subtraction. The science and reference image PSF templates were generated using an automated version of the classic DAOPhot/AllStar software (Stetson 1987), with further optimizations for ZTF (Masci et al. 2019; Sections 3.5 and 4). A linearly spatially varying PSF model consisting of a Gaussian core modulated by corrections is fit to a set of pre-filtered (uncontaminated and unsaturated) stars in the science and reference images separately. Only PSF estimates at the center of the science and reference CCD-quadrants are used for input to ZOGY. Prior to use in ZOGY, the PSF templates are further regularized to suppress pixel outliers in their outer regions. ZOGY then combines the PSFs using a Fourier inversion method to generate a single PSF template for the difference image. This single PSF therefore represents an effective PSF for the entire quadrant image. Its spatial variation on quadrant scales (inherent in the science and reference images) is <1%. This is not significant enough to impact the accuracy of our PSF-fit photometry in our magnitude range of interest (≳17 mag), where measurements are dominated by sky background noise.

Hereafter we denote the pixel values of model image and difference image by x_i and ${y}_{i}^{{\prime} }$, respectively. x is unitless and y' has the unit of detector data number (DN), which is analogous to analog digital units (ADU). We estimate the background noise σ_bkg (in the unit of DN) from all pixels inside an annulus centered at the location of the target, with an inner radius r_in = 10 pixels and an outer radius r_out = 15 pixels (indicated by the dashed green circles in Figure 2). Thus, σ_bkg = 0.5 ×[(the 84th percentile of ${{\rm{y}}}_{\mathrm{bkg}}^{{\prime} }$) − (the 16th percentile of ${{\rm{y}}}_{\mathrm{bkg}}^{{\prime} }$)]. Ideally the median of all pixels in this background annulus should be around zero, i.e., median($y{{\prime} }_{\mathrm{bkg}})\approx 0$, assuming that image subtraction is perfect. However, it was found that the background level is sometimes far from zero in regions close to the center of galaxies. Therefore, we subtracted the local background from y' to get a more robust estimate of the excess flux relative to background: ${y}_{i}=y{{\prime} }_{i}-\mathrm{median}(y{{\prime} }_{\mathrm{bkg}})$. The y thus derived also has units of DN.

In ZSDS, image subtraction is performed using the ZOGY algorithm (Zackay et al. 2016). The PSF template image (left panel of Figure 2) is generated such that the difference image (right panel of Figure 2) can be modeled by the PSF image multiplied by a number m, plus some random noise , i.e., y = mx + . Here, m is the PSF-fit flux in the unit of DN, and is a noise term: $\epsilon \sim { \mathcal N }(0,{\sigma }^{2})$. The statistical pixel uncertainty for y_i is

$$\begin{eqnarray}&&{\sigma }_{i}^{2}=\displaystyle \frac{{y}_{i}}{\mathrm{gain}}+{\sigma }_{\mathrm{bkg}}^{2}\end{eqnarray} \tag{ 2 }$$

where the gain is the electronic detector-gain (in the unit of electron per DN).

Although our task is simply to fit a straight line to a set of (x_i , y_i ) pairs, there is no consensus on how to derive the best measurement of m (see Hogg et al. 2010 or Sharma 2017 (Section 2) for a recipe on this problem). The commonly adopted maximum likelihood estimate has the advantage of being fast, but is only optimal for the background-dominated-noise limit (Zackay et al. 2016). In principle we expect measurements of intra-night observations to be consistent with each other, but we found that our initially adopted maximum likelihood method did not provide such a result. Instead, a Bayesian method was attempted whereby we implemented a Markov chain Monte Carlo (MCMC) fit, which was found to give the smallest variance of intra-night observations in the same band. Therefore, we adopted the MCMC approach, and utilized emcee, which is an affine-invariant MCMC ensemble sampler that uses multiple walkers to sample the posterior probability distribution (Goodman & Weare 2010; Foreman-Mackey et al. 2013).

Assuming that the uncertainties in Equation (2) are underestimated by a constant systematic factor σ₀, the probability of y_i given (x_i , σ_i , m, σ₀) is

$$\begin{eqnarray}&&\begin{array}{l}p({y}_{i}| m,{\sigma }_{0},{x}_{i},{\sigma }_{i})\\ \quad =\,\displaystyle \frac{1}{\sqrt{2\pi ({\sigma }_{i}^{2}+{\sigma }_{0}^{2})}}\exp \left(-\displaystyle \frac{{\left({y}_{i}-{{mx}}_{i}\right)}^{2}}{2({\sigma }_{i}^{2}+{\sigma }_{0}^{2})}\right).\end{array}\end{eqnarray} \tag{ 3 }$$

From (3) it follows that the log-likelihood is

$$\begin{eqnarray}&&\mathrm{ln}{ \mathcal L }=\displaystyle \sum _{i}^{N}\left[\mathrm{ln}\left(\displaystyle \frac{1}{\sqrt{2\pi ({\sigma }_{i}^{2}+{\sigma }_{0}^{2})}}\right)-{\left(\displaystyle \frac{{y}_{i}-{{mx}}_{i}}{2({\sigma }_{i}^{2}+{\sigma }_{0}^{2})}\right)}^{2}\right].\end{eqnarray} \tag{ 4 }$$

We only include the central 7 × 7 cutout (indicated by the dotted red square in Figure 2) in the fit, so N = 49 is the number of pixels that were taken into consideration.

The posterior probability distribution function of the model parameters (m, σ₀) for each observation can be obtained from the following equation according to Bayes' theorem:

$$\begin{eqnarray}&&\begin{array}{l}p(m,{\sigma }_{0}| {\{{y}_{i}\}}_{i=1}^{N},{x}_{i},{\sigma }_{i})\\ \quad =\,\displaystyle \frac{1}{Z}p({\{{y}_{i}\}}_{i=1}^{N}| m,{\sigma }_{0},{x}_{i},{\sigma }_{i})p(m,{\sigma }_{0})\end{array}\end{eqnarray} \tag{ 5 }$$

where Z is a normalization factor and p(m, σ₀) is the prior.

We adopted wide and flat priors: (i) m was uniformly distributed in the range [−10⁶, 10⁶]; (ii) σ₀ was logarithmically uniformly distributed in the range [e⁻¹⁰, e¹⁰]. The two-dimensional parameter space was investigated using 250 walkers. All models were run to convergence as determined by the evolution of the autocorrelation of the individual MCMC chains (see https://emcee.readthedocs.io/en/latest/tutorials/autocorr/). A demonstration of this step is given in Figure 3.

Zoom In Zoom Out Reset image size

We obtained the posterior probability distributions for m and σ₀ as the output from the MCMC fitting, and marginalized over σ₀ to estimate the slope, m. Throughout this paper, we take the median value of the distribution as the measured flux, f_mcmc, whereas the uncertainty on this value, ${\sigma }_{{f}_{\mathrm{mcmc}}}$, was estimated as half of the difference between the 84th and 16th percentiles of the marginalized posterior of m. Both f_mcmc and ${\sigma }_{{f}_{\mathrm{mcmc}}}$ have units of DN.

A small fraction of the ZTF data were acquired through intermittent cloud cover or featured extremely high backgrounds due to the proximity of the full moon. This affects the resulting photometric calibration. Therefore, several cuts were applied to ensure the quality of our photometric measurements.

• 1.  
  We removed data points with non-zero values of infobits. This keyword is a 16-bit integer that encodes the status of processing and instrumental calibration steps for the science image; specific operations that fail to meet predefined quality criteria are assigned to individual bits [0...15]. These bits can be "AND'ed" with a template bit-string to reject science images that failed specific calibration steps.
• 2.  
  We removed data points with scisigpix >25. scisigpix is a robust estimate of spatial noise-sigma per pixel in the input science image; this is based on half the "84.13 − 15.86" percentile difference in pixel values.
• 3.  
  We removed data points with seeing >4'', where seeing captures the FWHM of the point source.
• 4.  
  We removed the observation if there was any pixel in the central 7 × 7 cutout with ${y}_{i}\lt -500$. Typically, pixels with negative values of several hundreds are caused by saturation in the reference image, and thus should be removed in the fitting. It is difficult to define a threshold to mask out those bad pixels, so we choose to remove the observations instead.

infobits and seeing are in the header of every science image product in the archive as well as in IRSA's science image metadata database (DB) table. However, scisigpix is internal and not propagated to any publicly visible product, but it can be estimated directly from the science images.

Note that while alternative prescriptions to flag observations may be adopted, we found the above cuts to be adequate to remove most of the non-photometric data in our sample. The flagged "bad" observations are not included in the table of final light curves accompanying this paper.

A baseline correction was applied to f_mcmc to correct for any residual offset in the "history" of the light curve. We chose to define any data earlier than T_before days prior to t_B,max (in the rest frame) to be the "history" where T_before = 20. We visually inspected the light curves to make sure that no supernova flux was included in the baseline. For six targets (ZTF18aaykjei, ZTF18abhpgje, ZTF18abdpvnd, ZTF18aaytovs, ZTF18abddmrf, and ZTF18aawpcel) where the rest-frame rise time is obviously longer than 20 days, we adjusted the value of T_before to 25. Note that these objects are peculiar SNe with longer rise time than normal SNe Ia (see Table 2 and Section 5). Since the reference images for different fcqf ID (Equation (1)) were created by different observations, the baseline level should be determined separately for every possible combination of field and filter. For example, Figure 4 shows the light curve of ZTF18aazblzy, a normal SN Ia in our sample at redshift z = 0.0653. The lower panels show the number of observations in each fcqf ID in the baseline region (N_base), the offset level C, as well as the reduced chi-square statistic (${\chi }_{\nu }^{2}$):

$$\begin{eqnarray}&&{\chi }_{\nu }^{2}=\displaystyle \frac{1}{\nu }\displaystyle \sum _{i=1}^{{N}_{\mathrm{base}}}\displaystyle \frac{{\left(C-{f}_{\mathrm{mcmc},i}\right)}^{2}}{{\sigma }_{{f}_{\mathrm{mcmc}},i}^{2}}\end{eqnarray} \tag{ 6 }$$

where ν = N_base − 1 is the degree of freedom and C is calculated as the weighted mean of all f_mcmc measurements in the baseline.

Zoom In Zoom Out Reset image size

Figure 5 shows the distribution of ${\chi }_{\nu }^{2}$ versus C for all targets in our sample. Although we may expect C ≈ 0, a non-zero historical baseline level can occur if

• (i)  
  The reference image is contaminated by residual flux from the actual transient being measured, i.e., the input images used to construct the reference inadvertently included epochs containing significant transient flux. (This is unlikely because we applied selection step 4 in Table 1.)
• (ii)  
  The reference image is contaminated by an instrumental artifact that was not properly masked (or detected as an outlier) prior to co-addition.
• (iii)  
  There are systematic residuals from persistently inaccurate gain-matching between the science and reference images. This is usually triggered by imperfect flat-fielding of the science images used to construct the reference image, i.e., the reference image exhibits a spatial variation in its photometric gain. This systematic spatial variation will persist (be imprinted) in all subtraction images constructed using this reference image. If the gain-mismatch between science and reference images at the location of the transient is significant, this will also lead to inflated ${\chi }_{\nu }^{2}$ values since measurements relative to the baseline will be noisier (inflated by a hidden systematic gain factor) than those represented by the individual-epoch measurement uncertainties (${\sigma }_{{f}_{\mathrm{mcmc}},i}$).

A sufficient number of historical measurements is required for robust estimates of C and ${\chi }_{\nu }^{2}$. Large absolute values of C or large values of ${\chi }_{\nu }^{2}$ should be considered as "red flags" suggesting further analysis and visual examination of the images, particularly the reference image to search for the systematic described in case (iii) above. We mitigate this systematic by subtracting the baseline C from the measured f_mcmc, and if ${\chi }_{\nu }^{2}\gt 1$ we multiply the raw ${\sigma }_{{f}_{\mathrm{mcmc}}}$ by $\sqrt{{\chi }_{\nu }^{2}}$. The photometric uncertainties thus derived should be considered as a conservative estimate. For others who would like to model these light curves in the future, it is also advised to perform such a baseline validation and uncertainty scaling, or to remove observations associated with ${\chi }_{\nu }^{2}\gtrsim 4$ or $| C| \gtrsim 15$ from the sample. In the light curves accompanying this paper we provide our measurements of C and $\sqrt{{\chi }_{\nu }^{2}}$, and set the values of these columns to −999 if the corresponding fcqf ID has N_base < 30.

Zoom In Zoom Out Reset image size

With the knowledge of the zero-point magnitude (zp) of the difference image provided by ZSDS, the zero-point flux in the unit of DN (f₀) can be calculated:

$$\begin{eqnarray}&&{f}_{0}={10}^{0.4\times \mathrm{zp}}\end{eqnarray} \tag{ 7a }$$

$$\begin{eqnarray}&&{\sigma }_{{f}_{0}}={f}_{0}\displaystyle \frac{\mathrm{ln}(10)}{2.5}{\sigma }_{\mathrm{zp}}.\end{eqnarray} \tag{ 7b }$$

Thus, the dimensionless flux ratio is

$$\begin{eqnarray}&&{f}_{\mathrm{ratio}}={f}_{\mathrm{mcmc}}/{f}_{0}\end{eqnarray} \tag{ 8a }$$

$$\begin{eqnarray}&&{\sigma }_{{f}_{\mathrm{ratio}}}=\sqrt{{\left(\displaystyle \frac{{\sigma }_{{f}_{\mathrm{mcmc}}}}{{f}_{0}}\right)}^{2}+{\left(\displaystyle \frac{{f}_{\mathrm{mcmc}}{\sigma }_{{f}_{0}}}{{f}_{0}^{2}}\right)}^{2}}.\end{eqnarray} \tag{ 8b }$$

We define the detection threshold of S/N to be 3. ²⁹ That is to say, whenever ${f}_{\mathrm{ratio}}\gt 3\times {\sigma }_{{f}_{\mathrm{ratio}}}$, the conversion from flux to magnitude can be applied:

$$\begin{eqnarray}&&m=-2.5\times \mathrm{log}{f}_{\mathrm{ratio}}\end{eqnarray} \tag{ 9a }$$

$$\begin{eqnarray}&&{\sigma }_{m-}=\,2.5\times \mathrm{log}(1+{\sigma }_{{f}_{\mathrm{ratio}}}/{f}_{\mathrm{ratio}})\ \mathrm{brighter}\,\mathrm{end}\end{eqnarray} \tag{ 9b }$$

$$\begin{eqnarray}&&{\sigma }_{m+}=-2.5\times \mathrm{log}(1-{\sigma }_{{f}_{\mathrm{ratio}}}/{f}_{\mathrm{ratio}})\ \mathrm{fainter}\,\mathrm{end}.\end{eqnarray} \tag{ 9c }$$

For non-detections, we compute 5σ upper limits as

$$\begin{eqnarray}&&{m}_{\mathrm{lim}}=-2.5\times \mathrm{log}(5\times {\sigma }_{{f}_{\mathrm{ratio}}}).\end{eqnarray} \tag{ 10 }$$

With the 154 targets selected in Section 2.2, we further apply the cuts illustrated in steps 5–7 of Table 1. Steps 5 and 6 are made to ensure that targets included in our sample have both early-time detections and relatively dense light-curve sampling. The requirement in step 7 is to ensure that epochs of maximum light in g and r can be accurately estimated (in Section 4.3). In the end, 127 SNe Ia were finally retained in our sample. Table 2 provides general information on these targets. Table 3 summarizes additional photometric properties of this sample, and Table 5 provides their forced-PSF photometry light curves. Photometric and spectroscopic observations of sources rejected by our sample selection criteria will be published in a separate study on the full sample of SNe Ia found by ZTF.

The redshift distribution of all targets in our sample is plotted in Figure 6. Shown in black are 46 SNe with host-galaxy redshifts from the NASA/IPAC Extragalactic Database (NED), while redshifts of the 16 shown in gray are measured from host-galaxy lines in the SN spectrum or from a spectrum of the host galaxy itself. Redshifts of the remaining 65 targets shown in blue are inferred from the SN spectrum (see Section 4.2 for details). Redshifts estimated directly from the SN spectrum have a typical uncertainty of ∼0.004 (Fremling et al. 2019). The 16th, 50th, and 84th percentiles of the redshift distribution are z = 0.051, 0.074, and 0.106.

Zoom In Zoom Out Reset image size

We summarize early-time photometric samples of SNe Ia with low to intermediate redshift from multiple surveys in Table 4. The table is divided into two, with the top half listing surveys focused on the follow-up of SNe Ia, while the bottom half lists surveys that both discover and follow up SNe Ia. We use this split to better highlight the number of SNe with early observations, because these numbers are not directly comparable between surveys that discover SNe and those that only perform follow-up observations. Hereafter we only compare the ZTF sample with the LOSS, SDSS-II, iPTF/PTF, and TESS samples.

Table 4. Samples of SNe Ia with Low to Intermediate Redshift

Catalog	Size	Sample Redshift	Nearly a	Obs. Nights	Time Span	Bands
(1)	(2)	(3)	(4)	(5)	(6)	(7)
CfA3	185	0.01–0.085 (0.027)	9	12	2001–2008	${BVRIr}^{\prime} i^{\prime}$
CfA4	94	0.0055–0.073 (0.029)	3	16	2006–2011	(u'U)BVr'i'
CSP-I	134	0.0037–0.0835 (0.0241)	14	28	2004–2009	uBgVriYJH
CSP-II	214	0.0036–0.1376 (0.0341)	⋯	⋯	2011–2015	uBgVriYJH
Foundation-I	225	0.004–0.11 (0.033)	23	7	2015–2017	grizyP1
LOSS	165	0.002–0.095 (0.0194)	32	21	1998–2008	BVRI
SDSS-II b	327	0.037–0.4 (∼0.21)	72	9	2005-2007	ugriz
PTF/iPTF	265	0.00068–0.19 (0.083)	138	20	2009–2014	R
TESS-2018	18	0.0163–0.09 (0.04)	16	18	2018	iTESS
ZTF-2018	336	0.01815–0.164 (0.074)	127	43	2018	gr

Notes. Column (2): total number of objects in each catalog. Column (3): redshift range with the median value shown in parenthesis. Column (4): number of targets with early observations. Column (5): median number of nights of observation per SN (upper limits not included). Column (6): survey period. Column (7): observing bands, those shown in parenthesis indicating that less than half of the targets were observed with the corresponding bands. Some estimates cannot be made due to our limited access to data. References: the Harvard-Smithsonian Center for Astrophysics SNe Ia sample (CfA3, Hicken et al. 2009; CfA4 Hicken et al. 2012), the Carnegie Supernova Project I (CSP-I) low-redshift sample (Hamuy et al. 2006; Contreras et al. 2010; Stritzinger et al. 2011; Krisciunas et al. 2017), CSP-II (Phillips et al. 2019), the Foundation Supernovae Survey data release I (Foley et al. 2018), the Sloan Digital Sky Survey II Supernova Survey (SDSS-II; Frieman et al. 2008), the Lick Observatory Supernova Search (LOSS, Filippenko et al. 2001) follow-up photometry program (Ganeshalingam et al. 2010), the (intermediate) Palomar Transient Factory (PTF/iPTF, Papadogiannakis et al. 2019), and SNe Ia observed in the first six sectors of the Transiting Exoplanet Survey Satellite (TESS) with pre-explosion observations (Fausnaugh et al. 2019).

^a The number of SNe Ia with early observations, N_early, is defined as the number of targets with detections earlier than 10 days in the rest frame relative to the epoch of B-band peak luminosity. For SDSS-II this estimate is made relative to the time of g-band maximum light, while for the CfA3 and LOSS samples we use the observer-frame phase. ^b The size of the SDSS-II sample was reported to be 327 in Frieman et al. (2008), and increased to ∼500 later (Hayden et al. 2010a, 2010b). Sako et al. (2018) claimed 1364 SNe Ia from SDSS with spectroscopic redshifts (though some of these SNe were identified photometrically). The statistics shown for the SDSS-II sample are based on Frieman et al. (2008).

Download table as:  ASCIITypeset image

Table 5. P48 Photometry of 127 SNe Ia

ZTF Name	JD	programid	fieldid	ccdid	qid	filterid	Seeing	zp	σzp	fmcmc	C	$\sqrt{{\chi }_{\nu }^{2}}$
(ZTF18)							(arcsec)	(mag)	(mag)	(DN)	(DN)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)
aazblzy	2458291.7770833	2	722	3	4	2	2.164	26.185502	4.7941 ×10−6	1361.0505270 ± 37.7493381	−0.393	1.018
aazblzy	2458291.7992593	2	679	15	1	2	2.240	26.170234	7.9630 ×10−6	1367.4679899 ± 36.4484999	7.251	1.113
aazblzy	2458291.7997338	2	722	3	4	2	2.057	26.179769	4.9365 ×10−6	1377.8058619 ± 33.4542310	−0.393	1.018
aazblzy	2458291.8392708	2	722	3	4	1	1.970	26.274518	8.9916 ×10−6	1630.3413509 ± 35.3272129	−3.349	0.904
aazblzy	2458292.7180556	2	722	3	4	1	2.103	26.299129	10.4533 ×10−6	1634.6671366 ± 51.8378991	−3.349	0.904
aaqcozd	2458257.7669097	1	716	11	2	2	2.565	26.275000	15.3278 ×10−6	1159.2163294 ± 29.4045185	−0.981	0.965
aaqcozd	2458257.7678472	2	716	11	2	2	2.554	26.275000	14.1952 ×10−6	1233.6421626 ± 28.5476163	−0.981	0.965
aaqcozd	2458257.7778472	3	716	11	2	2	2.695	26.275000	12.6417 ×10−6	1212.3373769 ± 32.0352867	−0.981	0.965
aaqcozd	2458257.7787963	1	716	11	2	2	2.643	26.275000	14.0979 ×10−6	1151.8020575 ± 30.9927667	−0.981	0.965
aaqcozd	2458257.7797338	2	716	11	2	2	2.541	26.275000	14.5513 ×10−6	1182.5142907 ± 29.5918902	−0.981	0.965
abdpvnd	2458364.8118171	1	646	13	2	2	1.916	26.106877	3.3710 ×10−6	1082.7538462 ± 24.8383520	−999	−999
abdpvnd	2458364.8239120	2	692	1	4	2	2.217	25.958831	2.8078 ×10−6	988.7527352 ± 25.3953545	−999	−999
abdpvnd	2458364.8460764	2	692	1	4	2	2.296	25.948320	3.5620 ×10−6	982.4542010 ± 27.9368325	−999	−999
abdpvnd	2458365.8068634	2	692	1	4	1	2.323	26.026621	6.2705 ×10−6	307.9495909 ± 16.4243875	−999	−999
abdpvnd	2458365.8400579	2	692	1	4	2	2.442	26.006744	2.9185 ×10−6	963.6859996 ± 24.3100430	−999	−999

Note. Column (3): program identifier (1 = public survey, 2 = partnership survey, 3 = Caltech survey). Column (4): fieldid = ZTF field identifier. Column (5): ccdid = CCD identifier (from 1 to 16). Column (6): qid = quadrant (CCD-amplifier) identifier (from 1 to 4). Column (7): filterid = filter identifier (1 = g_ZTF, 2 = r_ZTF). The fcqf ID (Equation (1)) can be calculated with Columns (3)–(7). Column (8): photometric seeing (FWHM) at the Palomar Observatory at the time of observation. Columns (9) and (10): photometric zero-point. Column (11): forced PSF-fit flux for the difference image. Note that this is the direct measurement from Section 3.3. Baseline correction described in Section 3.5 is not applied to these values. Column (12): history offset in the baseline region. Column (13): square root of the reduced chi-square statistics (Equation (6)). Note that Columns (12) and (13) are set to −999 if N_base < 30. See Section 3.5 for details. Only 15 observations of three objects are shown to present the format of this table, which is available in its entirety in a FITS file.

Download table as:  ASCIITypeset image

Figure 7 shows the distribution of first-detection epoch relative to B- or g-band maximum light for ZTF, PTF/iPTF, SDSS, and LOSS. SNe with no pre-maximum detections are not shown in the figure. Figure 8 shows the histogram of the number of nights that each target was observed (upper limits are not included, intra-night observations are counted as one night). The TESS-2018 sample is not plotted because it has a relatively small size. We note that Column (5) of Table 4 may not be appropriate for this sample, since TESS is a space satellite that provides light curves with a cadence of 30 minutes (Ricker et al. 2015). Among the 18 TESS SNe, seven were observed in two sectors and 11 were covered in one sector (27 days per sector). Ten events were detected at least 14 days prior to maximum light (see Figure 1 of Fausnaugh et al. 2019).

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

LOSS is a targeted survey that uses the Katzman Automatic Imaging Telescope (KAIT, Filippenko et al. 2001; Li et al. 2003) as its discovery engine. As shown in Figure 7, this sample contains the smallest number of events observed prior to −12 days, likely as a result of KAIT's relatively small aperture (m_lim ≈ 19 mag) and slower cadence (∼3.5 days).

The SDSS-II survey provides one of the largest samples, which has a higher median redshift due to its large aperture (m_lim ≈ 22.2 mag). However, Figure 8 implies that the intervals between consecutive observations are relatively long due to the cadence of 4.5 days.

PTF/iPTF observations were carried out at a variety of cadences between 1 and 4 days. Although the number of events with early-time photometry is comparable to that in the ZTF sample (Figure 7), only 27 (4) objects have more than 40 (60) nights of observations (Figure 8). Furthermore, the PTF/iPTF photometry is only in the R band. In comparison, from the first 7 months of the ZTF high-cadence experiment, the number of objects with 40 or more nights of observation is 71, and the number of objects with 60 or more is 35. Only 11 targets were observed on fewer than 20 nights.

Among the 127 ZTF SNe Ia in this study, 50 were discovered at least 14 days prior to t_B,max, with nine being detected >17 days before t_B,max. Among the latter nine events, three are peculiar events with longer rise time than normal SNe Ia (ZTF18aaykjei, ZTF18abdpvnd, and ZTF18abhpgje; see Section 5 for details), four are at very low redshift (ZTF18aasdted, ZTF18abcflnz, ZTF18abfhryc, and ZTF18abauprj, all within z = 0.04), and two have possible early-time flux excess (ZTF18abxxssh at z = 0.064 and ZTF18aavrwhu at z = 0.062, a detailed analysis of these two will be presented elsewhere). In short, it is the rich information contained in the multi-band, well-sampled, early light curves that distinguishes ZTF as a unique survey for the study of early-time SNe Ia.

For the majority of SNe Ia the width of the light curve is related to the peak luminosity (Phillips 1993). Smaller subclasses can be characterized by their peculiar spectroscopic and photometric properties. For example, the overluminous 91T-like events (Filippenko et al. 1992b) and 99aa-like events (Li et al. 2001) have distinct Fe iii lines dominating their early spectra; while the subluminous 91bg-like events (Filippenko et al. 1992a) and 86G-like events (Phillips et al. 1987) display pronounced Si ii and Ti ii lines. Recent reviews of the observational characteristics and physical interpretation of different subtypes can be found in the literature (e.g., Parrent et al. 2014; Maeda & Terada 2016; Taubenberger 2017).

4.2.1. Spectroscopic Observations

A large fraction of our spectroscopic follow-up observations were conducted by the Spectral Energy Distribution Machine (SEDM, Blagorodnova et al. 2018; Rigault et al. 2019) on the robotic Palomar 60 inch telescope (P60, Cenko et al. 2006). Other follow-up instruments include the Double Spectrograph (DBSP; Oke & Gunn 1982) on the Palomar 200 inch telescope (P200), the Low-Resolution Imaging Spectrometer (LRIS; Oke et al. 1995) on the Keck I 10 m telescope, the Andalucia Faint Object Spectrograph and Camera (ALFOSC) on the 2.56 m Nordic Optical Telescope (NOT), the Dual Imaging Spectrograph (DIS) on the Astrophysical Research Consortium (ARC) 3.5 m telescope at Apache Point Observatory (APO), the SPectrograph for the Rapid Acquisition of Transients (SPRAT) on the 2.0 m Liverpool Telescope (LT), and the Deveny spectrograph on the 4.3 m Discovery Channel Telescope (DCT; Bida et al. 2014).

Within our sample, 95 objects have one spectrum; 22 have two, five have three, one has four, two have five, and one has 10. The classification of ZTF18abptsco was reported via The Astronomer's Telegram (Gomez et al. 2018). If an object has more than one spectrum, we choose the one of highest S/N or closest to maximum light for classification. The spectral phase for individual SNe is shown in Column (7) of Table 2. Figure 9 shows the distribution of rest-frame epoch relative to g-band maximum light (the estimation of t_g,max is illustrated in Section 4.3) used to determine the spectral subtype.

Zoom In Zoom Out Reset image size

Within our sample, 92 SNe are classified solely with SEDM spectra. These spectra will be described in detail in M. Rigault et al. (2019, in preparation). ³⁰ Below we describe our method for SN subtype classification. Table 6 provides information on 37 non-SEDM spectra of 34 targets, for which the subtype determination was not solely dependent on SEDM. ³¹ A subset of these spectra are shown in Figure 10.

Zoom In Zoom Out Reset image size

Table 6. Summary of Spectroscopic Observations

ZTF Name	Telescope	UT Date	Observers/Reducers
(ZTF18)
aapqwyv	DCT	2018 May 6	C. Ward/T. Hung
aaqcozd	NOT	2018 May 11	F. Taddia
aaqcqkv	P200	2018 May 17	A. Ho, Y. Sharma/A. Ho
aaqqoqs	P200	2018 May 17	A. Ho, Y. Sharma/A. Ho
aarldnh	P200	2018 May 17	A. Ho, Y. Sharma/A. Ho
aarqnje	P200	2018 May 17	A. Ho, Y. Sharma/A. Ho
aasesgl	P200	2018 May 17	A. Ho, Y. Sharma/A. Ho
aaslhxt	LT	2018 May 23	D. Perley
aatzygk	DCT	2018 May 21	P. Gatkine/B. Cenko
aauhxce	NOT	2018 Jun 4	F. Taddia
aaumeys	DCT	2018 May 21	P. Gatkine/B. Cenko
aaxcntm	APO	2018 Jun 13	M. Graham, D. Bektesevic/M. Graham
aaxdrjn	LT	2018 Jun 3	D. Perley
aaxqyki	P200	2018 Jun 8	A. Ho, Y. Sharma/A. Ho
aaxrvzj	APO	2018 Jun 20	J. Davenport/M. Graham
aaxsioa	P200	2018 Jun 8	A. Ho, Y. Sharma/A. Ho
aaydmkh	P200	2018 Jun 8	A. Ho, Y. Sharma/A. Ho
aaytovs	P200	2018 Jul 8	A. Ho
aazabmh	P200	2018 Jun 12	M. Kuhn, Y. Sharma/C. Fremling
aazblzy	P200	2018 Jun 12	M. Kuhn, Y. Sharma/C. Fremling
aazixbw	NOT	2018 Jun 11	F. Taddia
abatffv	Keck I	2018 Jun 17	N. Blagorodnova, K. Burdge, K. De, S. Kulkarni/K. De
abauprj	NOT	2018 Jun 26	F. Taddia
abdmgab	Keck I	2018 Jul 13	C. Fremling, H. Ko/C. Fremling
abfhryc	P200	2018 Jul 08	A. Ho
abgmcmv	Keck I	2018 Jul 13	C. Fremling, H. Ko/C. Fremling
abixjey	P200	2018 Sep 13	S. Adams, M. Hankins, I. Andreoni/K. De
abkifng	P200	2018 Aug 21	C. Fremling, A. Dugas/C. Fremling
abqjvyl	P200	2018 Sep 12	A. Dugas/C. Fremling
aaykjei	APO	2018 Jun 13	M. Graham, D. Bektesevicc/M. Graham
aaykjei	P200	2018 Sep 12	A. Dugas/C. Fremling
abclfee	LT	2018 Jul 4	D. Perley/K. Taggart
abclfee	P200	2018 Jul 8	A. Ho
abclfee	P200	2018 Aug 4	K. De
abddmrf	P200	2018 Aug 13	L. Yan/Z. Zhuang
abdpvnd	NOT	2018 Sep 17	F. Taddia
abhpgje	P200	2018 Oct 10	A. Dugas/A. Ho, Y. Yao

Note. Only non-SEDM spectra are included in this table. SEDM spectra will be described in detail by one of us (M. Rigault et al. 2019, in preparation).

Download table as:  ASCIITypeset image

4.2.2. Classification Based on SNID

4.2.3. Subtype Modifications and Reliability

Forced photometry for the 127 SNe Ia in our sample is shown in Figures 11 and 12. We adopted Equations (9) and (10) to convert f_ratio into the observed magnitude. The absolute magnitude is determined by correcting for the distance modulus and Galactic extinction E(B − V) estimated by Schlafly & Finkbeiner (2011), which builds upon Schlegel et al. (1998). We assume R_V = 3.1, and integrate the reddening law from Cardelli et al. (1989) over the ZTF filters.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

In order to estimate the time of g-band maximum (t_g,max), observed peak magnitude (m_g,max), and the decline-rate parameter expressed by the decline within 15 days from maximum in the g band (Δm₁₅(g)), we fit light curves of normal(∗), 99aa-like(∗), 91T-like(∗), and 86G-like objects with SALT2 (as shown by the overplotted solid lines in Figure 11). For the 02cx-like, Ia-CSM, and SC(∗) SNe we fit the light curves with low-order polynomial functions (as shown by the overplotted solid lines in Figure 12). We convert m_g,max into absolute peak magnitude M_g,max using the same method as above.

We separate the sample into two groups because SALT2 is currently not suitable to satisfactorily determine light-curve features of peculiar events. Our choice of low-order polynomial functions follows the fitting technique adopted by Foley et al. (2013) and Miller et al. (2017). Estimated parameters are reported in Table 3.

4.3.1. Light-curve Fitting with SALT2

To attempt the SALT2 fits, we assumed R_V  = 3.1, adopted the Galactic extinction estimate of E(B − V) from Schlafly & Finkbeiner (2011), and added a Milky Way dust model (CCM89Dust) (Cardelli et al. 1989) to the SN model (SALT2Model) in sncosmo (Barbary et al. 2016). SALT2 characterizes the flux density for a given SN as a function of phase p and rest-frame wavelength λ as

$$\begin{eqnarray}&&f(p,\lambda )={x}_{0}\left[{{ \mathcal M }}_{0}(p,\lambda )+{x}_{1}{{ \mathcal M }}_{1}(p,\lambda )\right]{e}^{c\cdot {{ \mathcal C }}_{{\rm{L}}}(\lambda )}\end{eqnarray} \tag{ 11 }$$

where x₀, x₁, and c are the normalization, shape, and color parameters, respectively. The mean spectral sequence ${{ \mathcal M }}_{0}$, the first-order deviation around the mean sequence ${{ \mathcal M }}_{1}$, and the average color-correction law ${{ \mathcal C }}_{{\rm{L}}}$ were trained on photometric and spectroscopic data of known SNe Ia (see Guy et al. 2007 for details).

In addition to ${t}_{g,\max }$, M_g,max, and Δm₁₅(g), we also obtained the expected Δm₁₅(B) and M_B,max from the SALT2 fitted parameters for objects shown in Figure 11.

4.3.2. Light-curve Fitting with Polynomial Functions

4.3.3. The Selection Effect

Figure 13 shows the distribution of 127 SNe in the plane of the light-curve shape parameter SALT2 x₁ versus redshift. Larger x₁ indicates a broader light curve and greater maximum luminosity. We note that the correlation between x₁ and Δm₁₅(g) is sufficiently strong that x₁ can be used as a proxy for the rate of decline of the light curve and thus the peak luminosity (see Figure 15). The median of x₁ should be around zero for an unbiased sample. For our sample, x₁ is centered at ∼0 for 100 SNe with z ≤ 0.1 (median x₁ = 0.007), but shifts to greater values for the 27 objects with z > 0.1 (median x₁ = 0.729). This is a consequence of Malmquist bias (Malmquist 1922)—at higher redshift, only targets intrinsically more luminous can be detected early enough. The Malmquist bias had been predicted at about the same level from the PTF/iPTF work (see Figure 11 of Papadogiannakis et al. 2019).

Zoom In Zoom Out Reset image size

4.3.4. The Luminosity–Decline Relation

Accurate estimates of host extinction are critical for the luminosity–decline relation of SNe Ia (Phillips 1993). An empirical way to get the absolute B-band magnitude corrected for host extinction is to subtract 3.1 times the SALT2 color parameter (c) from M_B,max corrected for Galactic extinction (Betoule et al. 2014). The c-corrected M_B,max is plotted against the rate of decline of the light curve Δm₁₅(B) for 121 SNe in Figure 14. Peculiar events shown in Figure 12 are not included since their light curves cannot be well fitted by SALT2. There is a fairly tight correlation between luminosity and decline rate for normal SNe Ia plotted as filled black circles.

Zoom In Zoom Out Reset image size

Ia-CSM is a subclass of SNe Ia showing evidence of interaction between the ejecta and the dense circumstellar medium (Dilday et al. 2012). As can be seen in Figure 16, the spectra of ZTF18aaykjei are dominated by Hα emission at all epochs. Its early-time APO spectrum matches the prototype of Ia-CSM SNe (SN 2002ic), whose spectral features resembled 1991T-like events, but diluted in strength (Hamuy et al. 2003). Absorption and emission lines of intermediate-mass elements and iron-peak elements (IPEs) are present in the blue portion of the two spectra at −4 and +3 days, but the Si ii lines commonly seen in normal SNe Ia spectra are "veiled" by continuum radiation. The noisy SEDM spectrum at +18 days only matches to an Sb-type galaxy spectrum in the SNID database. Its late-time DBSP spectrum matches the Ia-CSM object SN 2005gj (Aldering et al. 2006), where emission lines from overlapping IPEs (mostly Fe ii) are prominent.

Zoom In Zoom Out Reset image size

The redshift (z = 0.0970) of ZTF18aaykjei is measured from the Hα, [N ii] λλ6548, 6583, and [S ii] λλ6716, 6731 (nebular) lines in the spectrum of its host galaxy (SDSS J161938.91+491104.7) obtained by DBSP on 2019 May 24. At +81 days, the Hα emission line profiles have a narrow component on top of a broad (FWHM ≈ 1020 km s⁻¹) base, much greater than the Hα FWHM of the host-only spectrum (97 km s⁻¹). The spectra presented here have relatively low resolution, so we do not expect to resolve the P-Cygni profiles seen in some other Ia-CSM SNe.

We show the light curve of ZTF18aaykjei in the middle left panel of Figure 12. It peaked at −19.19 ± 0.04 mag in g and −19.65 ± 0.04 mag in r (only Galactic extinction is corrected in these estimates). Its red color even at early times suggests that the host extinction may be non-negligible. The peak luminosity of ZTF18aaykjei is consistent with other objects in the Ia-CSM class (−21.3 mag ≤M_R  ≤ −19 mag, Silverman et al. 2013).

There are four events in our sample with x₁ ≈ 3: ZTF18abhpgje, ZTF18abdpvnd, ZTF18aawpcel, and ZTF18abddmrf. Their light curves are displayed in Figure 12. Among them, the former two events are considered to be super-Chandrasekhar mass explosions (termed "SC" in Table 2) with evidence from spectroscopy, while the latter two events are classified as candidate super-Chandrasekhar SNe (denoted as "SC∗" in Table 2) based only on their light curves.

5.2.1. ZTF18abhpgje (SN 2018eul)

The redshift of ZTF18abhpgje was measured to be 0.134 from the host Hα emission in its DBSP SN spectrum (upper panel of Figure 17). After correcting for Galactic extinction, it peaked at −19.99 ± 0.04 mag in g and at −19.74 ± 0.03 mag in r. Si ii λ6355 and C ii λλ6580, 7234 absorption features can be identified in its SEDM spectrum, with velocities of ∼8000 km s⁻¹. The measured velocity is slower than normal SNe Ia (∼10,000 km s⁻¹) but similar to some other super-Chandrasekhar mass SN candidates: at +12 days, SN 2007if has v(Si ii λ6355) ∼ 8600 km s⁻¹ (Scalzo et al. 2010) and SN 2009dc has v(Si ii λ6355) ∼ 7500 km s⁻¹ (Yamanaka et al. 2009). The extreme luminosity and low velocity have been interpreted as the result of either high gravitational binding energy (Howell et al. 2006) or the deceleration of the outer layers of ejecta by a massive envelope surrounding the progenitor (Scalzo et al. 2010). The best match to its late-time DBSP spectrum is SN 2017if at +67 days (also shown in the upper panel of Figure 17 for comparison), which further supports the argument that ZTF18abhpgje has a super-Chandrasekhar mass progenitor.

Zoom In Zoom Out Reset image size

5.2.2. ZTF18abdpvnd (SN 2018dvf)

5.2.3. ZTF18aawpcel (SN 2018cir) and ZTF18abddmrf (SN 2018dsx)

ZTF18abclfee is an 02cx-like event at z = 0.029 (redshift measured from host Hα emission in its +35 days DBSP spectrum). This subclass is also termed "Type Iax supernovae" (SNe Iax) (Foley et al. 2013). Its photometric and spectroscopic properties are concordant with the criteria of this subclass (Foley et al. 2013; White et al. 2015): (1) there is no evidence of hydrogen in any spectra; (2) the velocity of Si ii λ6355 in the +2 days SEDM spectrum is ∼6000 km s⁻¹, which is much slower than normal SNe Ia; (3) it shows spectral similarity with other 02cx-like events, as can be seen in Figure 18; (4) it is a fast-declining, low-luminosity event.

Zoom In Zoom Out Reset image size

We do not detect narrow Na i D at the redshift of 0.029 in any of our spectra, and therefore we assume that host-galaxy extinction is negligible. This assumption is supported by the observed blue color of ZTF18abclfee at peak (upper left panel of Figure 12). After correcting for foreground Galactic extinction, we find that ZTF18abclfee peaked at M_g,max = −16.93 ± 0.06 mag, M_r,max = −16.85 ± 0.02 mag. The decline rates inferred from polynomial fits are Δm₁₅(g) =1.76 ± 0.08 mag and Δm₁₅(r) = 0.56 ± 0.02 mag, which are consistent with other 02cx-like objects (see Figure 8 of Miller et al. 2017). The color evolution of ZTF18abclfee is also consistent with the relations shown in Figure 9 of Miller et al. (2017): at maximum light this event has (g − r)${}_{\max }\,\approx -0.1$ mag, which is bluer than 91bg-like events and similar to normal SNe Ia; ${\rm{\Delta }}{\left(g-r\right)}_{10}\,={\left(g-r\right)}_{+10\mathrm{days}}-{\left(g-r\right)}_{\max }\,\approx 0.8$ mag, which is similar to 91bg-like events but much greater than Δ(g − r)₁₀ of normal SNe Ia.