# The Zwicky Transient Facility Type Ia supernova survey: first data release
and results

S. Dhawan,1,2 A. Goobar,1 M.Smith,3 J.Johansson,1 M.Rigault,3 J.Nordin,4 R.
Biswas,1 D.Goldstein,5 P. Nugent,5,6 Y.-L. Kim,3 A. A. Miller,7,8 M.J.
Graham,9 M. Medford,5,6 M. M. Kasliwal,9 S. R. Kulkarni,9 Dmitry A. Duev,9 E.
Bellm,10 P. Rosnet,11 R. Riddle,12 J. Sollerman13
1The Oskar Klein Centre for Cosmoparticle Physics, Department of Physics,
Stockholm University, SE-10691 Stockholm, Sweden
2Kavli Institute for Cosmology and Institute of Astronomy, University of
Cambridge, Madingley Road, Cambridge CB3 0HA, UK
3Université de Lyon, Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon,
F-69622, Villeurbanne, France.
4Institute of Physics, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489
Berlin, Germany
5E.O. Lawrence Berkeley National Laboratory, 1 Cyclotron Rd., Berkeley, CA,
94720
6Department of Astronomy, University of California, Berkeley, CA 94720-3411,
USA
7 CIERA and Department of Physics and Astronomy, Northwestern University, 1800
Sherman Road, Evanston, IL 60201, USA
8The Adler Planetarium, Chicago, IL 60605, USA
9 Division of Physics, Mathematics, and Astronomy, California Institute of
Technology, Pasadena,USA
10 DIRAC Institute, Department of Astronomy, University of Washington, 3910
15th Avenue NE, Seattle, WA 98195, USA
11 Universite Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
12 Caltech Optical Observatories, California Institute of Technology,
Pasadena, CA 91125, USA
13 The Oskar Klein Centre for Cosmoparticle Physics, Department of Astronomy,
Stockholm University, AlbaNova, SE-10691 Stockholm, Sweden
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Type Ia supernovae (SNe Ia) in the nearby Hubble flow are excellent distance
indicators in cosmology. The Zwicky Transient Facility (ZTF) has observed a
large sample of supernovae from an untargeted, rolling survey, reaching
$20.8,20.6,20.3$ mag in $g$ $r$, and $i$-band, respectively. With a FoV of 47
sq.deg, ZTF discovered $>$ 3000 SNe Ia in a little over 2.5 years. Here, we
report on the sample of 761 spectroscopically classified SNe Ia from the first
year of operations (DR1). The sample has a median redshift $\bar{z}=$ 0.057,
nearly a factor of two higher than the current low-$z$ sample. Our sample has
a total of 934 spectra, of which 632 were obtained with the robotic SEDm on
Palomar P60. We assess the potential for precision cosmology for a total of
305 SNe with redshifts from host galaxy spectra. The sample is already
comparable in size to the entire combined literature low-$z$ anchor sample.
The median first detection is 13.5 days before maximum light, about 10 days
earlier than the median in the literature. Furthermore, six SNe from our
sample are at $D_{L}<80$ Mpc, for which host galaxy distances can be obtained
in the JWST era, such that we have calibrator and Hubble flow SNe observed
with the same instrument. In the entire duration of ZTF-I, we have observed
nearly fifty SNe for which we can obtain calibrator distances, key for percent
level distance scale measurements.

###### keywords:

supernovae:general – surveys – distance scale

††pubyear: 2021††pagerange: The Zwicky Transient Facility Type Ia supernova
survey: first data release and results–A.3

##  1 Introduction

In the two decades since the discovery of the accelerated expansion of the
universe (Riess et al., 1998; Perlmutter et al., 1999), thought to be driven
by the as yet poorly understood “dark energy" component (see Goobar &
Leibundgut, 2011, for a review), Type Ia supernovae (SNe Ia) have been
developed to become mature cosmological probes (Betoule et al., 2014; Scolnic
et al., 2018; Brout et al., 2019). Despite the progress in SN Ia observations,
the nature of the underlying physical mechanism driving acceleration remains
an open question, with several potential explanations (see e.g., Dhawan et
al., 2017; Lonappan et al., 2018). Increasing sample sizes of SNe Ia decreases
statistical errors; hence, improving our understanding of dark energy relies
on similarly reducing systematic uncertainties. Recent studies find that the
systematic and statistical uncertainties on the measurement of the dark energy
equation of state, $w$, are approximately equal (Conley et al., 2011; Scolnic
et al., 2018; Brout et al., 2019; Jones et al., 2019). Apart from measuring
dark energy properties, SNe Ia in the nearby Hubble flow, i.e. redshift range
$z\lesssim 0.1$ (hereafter, also referred to as “low-$z$") are also critical
for measuring the present day expansion rate, i.e. the Hubble constant
($H_{0}$) precisely. Over the last decade, several improvements in the
measurements of $H_{0}$ (Riess et al., 2019a) have revealed a $>4\sigma$
tension between the local measurement of $H_{0}$ based on Cepheid calibrated
SNe Ia and the value inferred from the early universe (Planck Collaboration et
al., 2018).

This discrepancy could be an indicator of novel cosmological physics, e.g.
early dark energy, additional relativistic neutrino species (Knox & Millea,
2020, present a summary of possible explanations). However, the tension could
be caused by poorly understood astrophysical systematics (e.g. see, Scolnic et
al., 2019; Mortsell et al., 2021a, b; Freedman, 2021). There is significant
debate regarding the impact of SN Ia environments and host galaxy properties
on the inferred SN Ia luminosity, and hence, $H_{0}$ (Rigault et al., 2015;
Jones et al., 2018a; Rigault et al., 2020). Conclusively testing the extent of
the bias on $H_{0}$ requires probing the underlying distribution of SN Ia host
galaxy properties, which is not possible with observing campaigns targeted to
specific host galaxy types. Having a sample of SNe Ia discovered and followed-
up by the same, untargeted survey is, therefore, crucial to observe the entire
range of SN Ia environmental properties and test for possible biases in
inferring cosmological parameters.

Dark energy inference with SNe Ia relies on relative distances. The high-$z$
SNe Ia magnitude redshift relation needs to be “anchored" at low-$z$. The
current low-$z$ anchor sample is compiled heterogeneously from several
different photometric systems, each with its own set of systematic
uncertainties, which can be correlated in a way that is extremely difficult to
predict. Some of the surveys in the low-$z$ anchor sample targeted pre-
selected galaxies (e.g. the Lick Observatory Supernova Survey; Filippenko et
al., 2001) and their sample selection and follow-up criteria are heterogeneous
and sometimes not well documented. This leads to several systematic
uncertainties relating to observational and selection biases. SN Ia samples at
high redshifts ($z\gtrsim 0.1$) e.g. from Sloan Digital Sky Survey (SDSS;
Kessler et al., 2009), Supernova Legacy Survey (SNLS; Conley et al., 2011;
Sullivan et al., 2011), Panoramic Survey Telescope and Rapid Response System
(Pan-STARRS; Rest et al., 2014; Jones et al., 2019) and Dark Energy Survey
(DES; Brout et al., 2019), however, are homogeneously observed on single
photometric systems. Hence, the low-$z$ sample, counter-intuitively,
contributes most significantly to the systematics error budget for dark energy
inference from SNe Ia (see also Foley et al., 2018). Beyond their use as
probes of the expansion history, SNe Ia have previously been used as tracers
of local large scale structure (LSS), e.g. for measuring bulk flows (Feindt et
al., 2013; Mathews et al., 2016), the product of the growth rate and amplitude
of mass fluctuation, i.e. $f\sigma_{8}$ (Huterer et al., 2017). SNe Ia are
significantly more precise distance indicators compared to methods using
galaxy distance, e.g. the Tully-Fisher relation, (Kourkchi et al., 2020), and
are therefore, an exciting route to infer properties of local LSS. So far, SNe
Ia samples have been very sparse, which is the largest limitation of current
datasets for precision constraints on local LSS with SNe Ia.

The advent of modern, wide field surveys has greatly increased the SN
discovery rate almost by an order of magnitude (e.g., see Shappee et al.,
2014; Tonry et al., 2018; Graham et al., 2019; Jones et al., 2021), making it
possible to overcome the aforementioned uncertainties. The Zwicky Transient
Facility (ZTF), using the 48-inch telescope at Palomar, is the widest field
transient survey in the optical for SN discovery and follow-up. ZTF, in
phase-I of operations (hereafter ZTF-I) scanned the entire Northern night sky
in the $g$,$r$ filters, reaching $\sim 20.5$ mag/pointing (Bellm et al.,
2019a, b; Graham et al., 2019; Dekany et al., 2020), with a three-day cadence.
To create a definitive data-set of low-$z$ SNe Ia distances, the main survey
was complemented by ZTF partnership surveys, including observations of a large
fraction of the sky in the $i$-band. The ZTF SN Ia survey discovers and
provides well-sampled lightcurves, for a large sample of spectroscopically
classified SNe Ia in the $z\lesssim 0.1$ range. This large sample of well-
characterised SN Ia lightcurves from a single, rolling untargeted survey
allows for a unique control of the systematics from photometric calibration,
observational and astrophysical bias in SN cosmology. This is critical for
overcoming the systematics in $H_{0}$ and dark energy studies. Moreover, the
large statistics and uniform sky coverage, will help overcome existing
uncertainties in inferring the growth of structure from SNe Ia (see e.g.
Graziani et al., 2020).

In this paper, we present the data-set from the first year of operations and
first results from the ZTF SN Ia survey. The ZTF SNe Ia sample aims to: (1)
anchor current and future high-$z$ SN Ia sample for dark energy studies, (2)
unlock the study of large scale structure in the nearby universe and (3)
measure $H_{0}$ using a unique, self-consistent, calibrator and Hubble-flow
sample. With the anticipated deluge of well-observed high-$z$ SNe Ia from the
Vera Rubin Observatory Legacy Survey of Space and time (see The LSST Dark
Energy Science Collaboration et al., 2018, for the science requirements
document ), the large, homogeneously measured, untargeted low-$z$ sample of
SNe Ia from ZTF has the potential to be a definitive data-set for cosmology in
the coming decade.

The paper is structured as follows. In section 2, we describe the survey
strategy, dataset and processing methodology. In section 3 we describe the
analysis and results from the first data release. We present a discussion and
our conclusions in section 4.

Figure 1:  (Left) The number of observations during the first year of
operations in the $g$ (green), $r$ (red), and $i$ (orange) filters. The number
of SNe Ia in each ZTF field are shown on the ZTF field grid in the bottom
panel. (Center) An example lightcurve of an SN Ia at $z\sim 0.07$ and $z\sim
0.03$ to show the typical sampling of the lightcurves in our sample. (Right) A
histogram number of SNe with at least one lightcurve point (top) and spectra
(bottom) in each phase bin along with an example of the spectrum at $z\sim
0.033$.

##  2 Survey, Dataset and Methodology

The survey design and science objectives for ZTF are described in detail in
Bellm et al. (2019a, b) and Graham et al. (2019). In this section, we
summarise the aspects of the survey relevant for the SN Ia first data release
(hereafter, DR1) sample. This includes the extragalactic partnership survey,
the selection and classification for our sample, association of the host
galaxy and the source of the spectroscopic redshift. We also describe the
pipeline used for obtaining multi-band photometry for the SNe.

###  2.1 Survey Strategy

ZTF uses a 47 deg2 field with a 600 megapixel camera to scan the entire
northern visible sky at rates of $\sim 3760$ square degrees per hour (Bellm et
al., 2019a). This is more than an order of magnitude improvement in survey
speed relative to its predecessor survey the Palomar Transient Factory (Rau et
al., 2009). ZTF reaches 5$\sigma$ depth of $\sim$ 20.8 mag in $g$ and $\sim$
20.6 mag in $r$ band (AB mag) in 30s exposures. The median seeing for the
survey is 2.17", 2.01" and 1.82" in the $g,r,i$ bands respectively.

ZTF, in phase-I of observations from March 2018 to November 2020, operated a
unique survey strategy with 40$\%$ of its time for public surveys financed by
the American’s National Science Foundation as part of its Mid-scale
Innovations Program (MSIP), 40$\%$ for partnership observations and 20$\%$ for
Caltech programs. In this paper, we focus on the first year of observations,
hence, unless mentioned otherwise, we refer to ZTF phase-I as ZTF. The SN Ia
cosmology program derives its dataset from a combination of public and
partnership observations. During its MSIP time, ZTF observed the entire
visible sky from Palomar in $g$ and $r$ filters every three nights with a
fiducial exposure time of 30s (Fremling et al., 2020). The distribution of the
SNe across the sky is shown in Figure 1, which also presents a graphical
overview of the DR1 survey, including lightcurve and spectral sampling.
Crucially for studies pertaining to the measurement of local large scale
structure, the SNe are distributed all across the sky (e.g. Feindt et al.,
2013; Graziani et al., 2020).

###  2.2 The partnership survey

The MSIP survey is complemented with ZTF partnership surveys. As part of these
surveys, high-cadence data was obtained in the $g$ and $r$ bands as well as a
wide-area $i$-band survey (Bellm et al., 2019b; Graham et al., 2019). The
high-cadence survey, in the first year of operations, observed a total of
$\sim 2500$ deg 2 with 3 visits per night in the $g$ and $r$ bands, aimed at
finding SNe in their infancy. This survey has been critical for early
discoveries of SNe Ia (Yao et al., 2019), to characterise their rise times
(Miller et al., 2020) and use the early colours as a test for explosion models
and multiple populations (Bulla et al., 2020). The survey also provides
densely sampled lightcurves in the $g$ and $r$ bands for the sample presented
here.

The $i$-band survey involves 30s long exposures with a four-day cadence, over
a footprint of 6700 square degrees, approximately one-quarter of the sky area
of the MSIP survey, to a median nightly depth of 20.3 mag. The three filter
photometry allows us to improve the constraints on the measured colour and is
crucial to quantify colour calibration systematics. Previous studies extending
the SN Ia Hubble diagram in the restframe $i$-band to high-$z$ ($z\sim 0.5$
and higher) find a reduced contribution of systematics errors compared to the
optical and argue for independent distances in the $i$-band to the same SN Ia
(Nobili et al., 2005; Freedman et al., 2009). At low-redshifts, observations
of SNe Ia in the $i$-band have also been used to precisely estimate $H_{0}$
(Burns et al., 2018).

Table 1: The SNe Ia in the complete Year 1 sample along with their coordinates, classification, first observation date, instrument from which the spectrum has been obtained, approximate resolution of the instrument and date of first spectroscopic observation. (Table has been truncated to improve the presentation, the table in its entirety is available online) Name | IAU Name | RA (deg) | Dec (deg) | Classification | Obs Date | Instrument | Resolution | Date of Spectrum
---|---|---|---|---|---|---|---|---
ZTF18aaadqua | SN2018lq | 26.7987 | 18.7986 | SN Ia | 2018-1-14 | P200 | 100-10000 | 20180122
ZTF18aabasml | SN2018tz | 166.4864679 | 37.6251311 | SN Ia | 2018-2-9 | P60 |  100 | 20180221
ZTF18aabqgnb | SN2018yc | 178.1895182 | 37.8542631 | SN Ia | 2018-2-9 | Lijiang2.4m |  300 | 20180228
ZTF18aabssme | SN2018aca | 155.7115261 | 14.054786 | SN Ia | 2018-3-5 | P60 |  100 | 20180307
ZTF18aabstmw | SN2018aaz | 153.4511418 | 38.7630928 | SN Ia 91bg-like | 2018-3-5 | P60 |  100 | 20180307

SNe Ia show a diverse morphology at late times in the redder wavelengths
($izYJHK$ filters). In the $i$-band, the SNe rebrighten $\sim 2$ weeks after
the first peak, showing a characteristic second maximum, which is also an
important diagnostic for SN Ia explosion properties (Hamuy et al., 1996;
Folatelli et al., 2010). The double-peaked behaviour over the timescales of a
few weeks makes them distinguishable from other SN types. In future
photometric SN Ia surveys, having $i$-band and redder coverage will be crucial
to improve photometric classification. The ZTF $gri$ dataset is, therefore, an
ideal testbed for such classification algorithms. Moreover, the second maximum
in the near infrared (NIR), has also been proposed as an alternate metric for
standardisation (Shariff et al., 2016). Hence, observations in the $i$-band
have several advantages for SN cosmology and will be a unique test of
systematic errors.

###  2.3 Spectroscopy and Sample Selection

In this study, we focus on the sample of spectroscopically classified SNe Ia
discovered in 2018, i.e. the first year of operations for ZTF. To include SNe
Ia that were first detected in 2018 but continued to rise after the end of the
year, we conservatively take SNe Ia that peaked before 1 February 2019. This
compilation, hereafter known as the DR1 sample, consists of a total of 761
spectroscopically classified SNe Ia. These SNe Ia are on 340 unique ZTF fields
corresponding to $\sim 2.2$ SNe per field. Accounting for downtime in the
survey operations during the first year, this corresponds to $\sim 2.5$ SNe
per field per year.

A summary of the first year of operations in presented in Figure 1. In the
left panels, the ZTF field grid shows the number of $g$ (green), $r$ (red) and
$i$ (orange) band observations along with the number of SNe per field.The
extragalactic fields with a large number of $g$ and $r$ observations
correspond to the high-cadence survey described in section 2.2. We show an
example lightcurve of an SN Ia with only MSIP and one with MSIP and
partnership data to illustrate the typical sampling in the three filters. We
show a histogram distribution of the number of SNe with at least one
observation for each phase with a 1 day bin size. We find a significant
fraction of SNe Ia have at least one observations before -7 days.

Table 2: SN names, heliocentric frame redshift and coordinates (in degrees) for the SNe Ia in our sample. The table has been truncated for formatting reasons. Full table is available online.  SN Name | $z_{\rm helio}$ | RA | Dec
---|---|---|---
|  | (Deg) | (Deg)
ZTF18aabdgik | 0.021604 | 175.5987 | 10.2641
ZTF18aabstmw | 0.02308648 | 153.4511 | 38.7631
ZTF18aabsyqp | 0.07667208 | 162.8185 | 22.4776
ZTF18aabtaor | 0.07983481 | 172.0952 | 44.7490
ZTF18aabxrjp | 0.07917714 | 185.5432 | 26.9946
Figure 2: Histogram distribution of the redshifts from the DR1 sample with
host galaxy redshifts (red) and the total sample with redshifts from any
source, including fitting the SNID template to the SN spectrum (black)
compared to the current low-$z$ sample in the literature (green). The redshift
distribution of our DR1 sample has a median $z=0.057$ that is $\sim$ twice
higher than the median from the literature sample, hence, making this sample
significantly less sensitive to the uncertainties from peculiar velocity
corrections.

A large fraction of these SNe Ia were classified using the SEDmachine (Ben-Ami
et al., 2012; Blagorodnova et al., 2018; Rigault et al., 2019), a low-
resolution (R $\sim 100$) integral field unit (IFU) spectrograph on the
robotic Palomar 60" telescope (Cenko et al., 2006) as part of the ZTF Bright
Transient Survey (BTS), with the goal to spectroscopically classify and
publicly report every extragalactic transient in the Northern sky with
$r<18.5$ mag discovered by the ZTF public surveys. The SEDm is capable of
classifying $>10$ SNe (of any type) per night in the 18.5 - 19 magnitude
range. Details of the BTS program can be found in Fremling et al. (2020);
Perley et al. (2020). The data are reduced uniformly and consistently as part
of the automated PYSEDM pipeline (Rigault et al., 2019).

For the complete sample of 761 objects, we have obtained a total of 934
spectra, hosted on the GROWTH marshal (Kasliwal et al., 2019). Out of the
total, 632 spectra are obtained with the SED machine, which corresponds to
$\sim 68\%$ of the total sample of spectra. We present a distribution of the
phase at which the spectra were obtained in Figure 1 (top right). A example of
a high S/N spectrum for an SN at $z=0.0335$ in shown in the bottom right panel
of Figure 1.

###  2.4 Host galaxy redshifts

In our study, we want to infer the lightcurve parameters for the SNe Ia in the
DR1 sample and quantify the scatter in the Hubble residuals. This requires a
robust, spectroscopic determination of the redshift to the SN host galaxy. We
compile the SN Ia host galaxy redshifts here. A large fraction of these host
galaxy redshifts are obtained from the Sloan Digital Sky Survey (SDSS)
sixteenth data release (Ahumada et al., 2020). For SNe Ia that do not have a
redshift for the host galaxy in SDSS, we obtain the redshift from the NASA
Extragalactic Database (NED)111https://ned.ipac.caltech.edu/. In addition to
host galaxy redshift constraints, we restrict the sample to SNe with
sufficient data around and before maximum light from the alert pipeline. This
is required to have a robust initial estimate of the time of maximum for
creating custom reference and difference images to perform forced photometry
(see section 2.5 for details). The final sample with these constraints has 305
SNe Ia. The coordinates and redshifts for SNe Ia in this sample, are presented
in Table 2. Hereafter, we refer to this as the host-$z$ sample.

We emphasise that while this criterion selects less than half ($\sim 40\%$)
the total sample of SNe Ia (Fremling et al., 2020, consistent with the
findings of BTS), host galaxy redshifts are not time critical. These can be
obtained after the completion of the survey. Several surveys using multi-
object spectrographs e.g. the Dark Energy Spectroscopic Instrument (DESI; DESI
Collaboration et al., 2016) and/or the 4MOST consortium extragalactic surveys
(de Jong et al., 2019; Swann et al., 2019) can obtain spectra for galaxies
that hosted ZTF observed SNe Ia, from which redshifts can be derived. Despite
the incompleteness of available host redshifts, we note that even the host-$z$
sample is larger than the entire, combined low-$z$ anchor in current SN
cosmology studies (e.g. Scolnic et al., 2018).

Our sample presented here has a median redshift of 0.057 which is nearly twice
that of the median for the sample in the literature. Hence, the inferred
cosmological parameters from this sample will be less prone to systematic
errors from peculiar velocity corrections (see, e.g. Huterer, 2020). The
resulting redshift distribution for our sample is shown in Figure 2. For the
complete sample as well as the host-$z$ only sample, we can see that median
redshift is $\sim$ twice the median of the current literature low-$z$ sample
(with All ZTF Y1 having a higher median $z$ of 0.069).

###  2.5 Photometry pipeline

In this section, we describe the pipeline used for generating the photometry
for our sample of SNe Ia. Since we want to measure lightcurve model parameters
and Hubble residuals, we focus on the host-$z$ sample. While this is a custom-
based pipeline for creating reference images, image subtraction and source
photometry, it uses certain aspects for the ZTF data products made available
by the Image Processing and Analysis Center (IPAC) at Caltech, hence, we
summarise those aspects here. The ZTF data processing, products, and archive
are described in detail in Masci et al. (2019). IPAC provides alert packets
with photometry as well as a forced photometry service at a predetermined
locations. We note that for a substantial fraction of the DR1 sample, building
of reference images began during the survey operations and hence, overlapped
in time with the discovery of astrophysical transients. Therefore, the alert
and IPAC forced photometry for several SNe Ia had contamination from the live
transient in the reference image. This required a reprocessing of the data to
make customised references for the regions of the sky where the SNe Ia were
discovered.

We use a state-of-the-art image processing pipeline, written using well-tested
and widely used astronomical image processing tools for processing data from
the ZTF Uniform Depth Survey (ZUDS) 222https://github.com/zuds-survey/zuds-
pipeline. While the pipeline was designed for discovering slowly evolving
faint transients on deep coadds of science frames, its versatile functionality
makes it ideal for creating image subtractions and computing lightcurves using
single exposures. Details of the individual components of the pipeline are
presented in Appendix A. We summarise the pipeline features in this section.

Using the ZUDS pipeline, we create references for each ZTF field and CCD in
which an SN Ia in our sample has been observed (see section 3 of Masci et al.,
2019, for details about the ZTF CCDs). They are generated using the SWARP
(Bertin et al., 2002) software for coaddition. The associated reference mask
is created with the mask images provided for each exposure by IPAC, using a
bitwise logical AND (see Appendix A). When sufficient number of exposures are
available, reference images are created by coadding epochs from before the SN
explodes (which we determine as epochs 30 or more days before the time of
maximum inferred from photometry provided by IPAC). For making the reference
image we only use images that were obtained in seeing conditions between
1.7"and 3" and have a deeper magnitude limit than 19.2 mag. If there are
insufficient number of exposures ($<20$) for which the nightly conditions do
not meet these criteria, the pre-SN exposures were combined with post-
explosion images from $>400$ days after the time of maximum inferred from the
alert photometry.

Figure 3: An example of fitting the SALT2 model to ZTF18aaumeys, as
implemented in sncosmo. The SN is at redshift 0.033, well into the Hubble flow
and the lightcurve is sampled extremely well on the rising part, which also
allows us to explore beyond the conventional standardisation parameters. Data
for this SN extends beyond +50 days, the validity limit of the SALT2 model.
Hence, we can use SNe in our sample to retrain the SALT2 model and extend to
later phases. We note here that the SALT2 model has only been fitted to the
$g$ and $r$ band data, whereas the for $i$-band only the predicted model
lightcurve is overplotted on the data.

We generate difference images using the HOTPANTS image subtraction software
(Becker, 2015). The subtraction is normalised to the science image and
convolved to the template image. Details of the convolution kernel, half width
substamp, and the setup for the HOTPANTS subtractions are described in Section
A.

We use the PhotUtils astropy package (Bradley et al., 2019) for performing
aperture photometry at the SN position, determined from the alert photometry
provided by IPAC. For each epoch, the zero point is derived from a combination
of the nightly zero point and aperture correction provided by IPAC (see Masci
et al., 2019, for details).

Figure 4: Lightcurves for the DR1 host-$z$ sample in the $g$,$r$,$i$ filters
for SNe Ia that peak within 2 months of 15 June 2018 (shown as days from 1
June 2018). The SALT2 model fits to only the $g$ and $r$ band data are
overplotted as solid lines.

##  3 Analysis and Results

We analyse the host-$z$ sample in this section, describe the spectroscopic
properties and the sample demographics, in comparison with the literature
sample. We also present the sample of SNe Ia that are at feasible distances to
build a calibrator sample for local $H_{0}$ measurements.

###  3.1 Lightcurve fitting

To be used for cosmology, SNe Ia need to be standardised, using relations
between their luminosity and the light curve shape and colour, for measuring
accurate distances (see Leibundgut & Sullivan, 2018, for a review of how SNe
Ia are used in cosmology). Here we describe the procedure for fitting the
lightcurves generated using the pipeline described in section 2.5, to derive
the peak apparent brightness, lightcurve width and colour.

There are several algorithms in the literature to estimate distances from SN
lightcurves, e.g. MLCS (Jha et al., 2007), SiFTO (Conley et al., 2008), BayeSN
(Mandel et al., 2009; Mandel et al., 2011; Mandel et al., 2020), SNooPy (Burns
et al., 2011), BaSALT (Scolnic et al., 2014). Each lightcurve fitting method
makes a correction to the SN luminosity for the lightcurve shape and colour.
The colour correction, however, can be applied in two principly different
ways. The first uses an empirical correlation between the observed colour and
the uncorrected Hubble residuals, whereas the second assumes that the observed
colour is a combination of intrinsic SN colour, photometric errors and
reddening due to dust, e.g. in the SN Ia host galaxy. The former is more model
independent, whereas the latter is more physically motivated. In-depth
comparisons of different lightcurve fitters in the literature (e.g. Kessler et
al., 2009), find that in general they agree reasonably well given the same
input assumptions.

Currently, the most widely used lightcurve fitting algorithm is the Spectral
Adaptive Lightcurve Template - 2 (SALT2; Guy et al., 2007), based on the SALT
method (Guy et al., 2005) and we use this in our analysis. The SALT2 model
treats the colour entirely empirically and is used to find a global colour-
luminosity relation. We use the most updated, published version of SALT2
(SALT2.4, see Guy et al., 2010) as implemented in sncosmo v2.1.0
333https://sncosmo.readthedocs.io/en/v2.1.x/ (Barbary et al., 2016). In the
fitting procedure, we correct the SN fluxes for extinction due to dust in the
Milky Way (MW). We use extinction values for the SN coordinates (presented in
Table 2) derived in Schlafly & Finkbeiner (2011). These are updated galactic
extinction maps that find that the extinction values from Schlegel et al.
(1998) were overestimated. We use the widely applied galactic reddening law,
proposed in (Cardelli et al., 1989), known as the “CCM" law to correct for MW
extinction. For the extinction corrections, we use the canonical value for the
total-to-selective absorption, $R_{V}=3.1$. The SALT2 model assumes a
parametrisation from Tripp (1998)

$\mu_{\rm B}=m_{\rm B}+\alpha x_{1}-\beta c-M_{\rm B}$ (1)

Figure 5: (Left): Phase distribution of the spectra in the host-$z$ sample
from all instruments (red) and from SEDm alone (blue). Similar to the complete
DR1 sample, $68\%$ of all spectra are obtained using SEDm. (Right) The
histogram distribution of the errors on the Si II 6355Å line velocity (in km
s-1) from only the SEDm spectra for the SNe in our sample, inferred using the
spextractor software. We find a median error of $\sim 700$ km s-1.

where $\mu_{\rm B}$ is the distance modulus inferred from restframe $B$-band
parameters, determined for each SN given the observed $B$-band brightness,
$m_{\rm B}$, light-curve shape, $x_{1}$, and an observed colour, $c$.
$\alpha$, $\beta$ and $M_{\rm B}$ are nuisance parameters, namely, the slope
of the width-luminosity and colour luminosity relations and the absolute
magnitude of the SNe Ia in the $B$-band for a fiducial SN Ia with $x_{1}=c=0$.
In our analyses, we do not use any independent, absolute calibration for the
SN Ia luminosity, hence, the $M_{B}$ term is effectively, only the intercept
of the magnitude-redshift relation, $a_{B}$. All nuisance parameters are
globally fit for the sample. We note that since the SALT2.4 model is not
appropriate for wavelengths redder than 7000 Å we only fit the $g$ and $r$
band lightcurves for the host-$z$ sample.

We fit the SALT2 model to each SN Ia in two steps. Firstly, we fit without the
SALT2 model covariance to obtain an initial guess for the time of maximum,
$t_{0}$. We select the data in the phase range -20 to +50 days relative to the
initial guess $t_{0}$, corresponding to the phase range in which the SALT2
model is defined. For the fit, we use an error floor of 2$\%$ of the flux,
corresponding to the the typical photometric calibration accuracy with respect
to Pan-STARRS1 reported in Masci et al. (2019). We note that this is
appropriate since we use the zeropoint report by IPAC in Masci et al. (2019)
for fitting the fluxes computed from the photometry.

We then fit the data only in this phase range along with the model covariance
to get the final fit parameters. The resulting parameters are reported in
Table 3. As we can see in Figure 3, ZTF18aaumeys, shown as an illustrative
example SN, has a significant number of detections on the rising part of the
lightcurve. This can be used to improve the standardisation relative to just
the standard stretch and colour corrections (as in eq. 1), and ultimately
reduce the intrinsic dispersion in the sample. It has been proposed in the
literature that separating the lightcurve width parameter $x_{1}$, into an
$x_{1}$ from the rising and falling parts of the lightcurve, $x_{1}^{r}$
(labeled as the rising width in Figure 3) and $x_{1}^{f}$, can improve the
lightcurve fit. Since it has been shown that for a given decline rate, the
rise times vary significantly (Ganeshalingam et al., 2011; Firth et al., 2015;
Miller et al., 2020), we expect to gain in the precision of the distance
measurement by using information in rising part of the lightcurve. It has been
shown that this method of two lightcurve widths instead of one yields a
smaller scatter than if only using a single lightcurve width (Hayden et al.,
2019). ZTF18aaumeys is also an example SNe Ia that has data extending beyond
the range of phases for which the SALT2 model is valid, which makes it
interesting to use this data for further extending the SALT2 model beyond the
phase range of +50 days. The dataset presented here allows us to test these
novel standardisation procedures in the future.

Table 3: Output SALT2 fit parameters for SNe in our sample along with the CMB frame redshift ($z_{\rm CMB}$; see text for the CMB frame conversion). We report the $m_{B}$, $x_{1}$ and $c$ parameters used to compute the Hubble residuals (Full table available online; fit outputs including covariances between the fit parameters are provided in the github repo) ZTF Name | $z_{\rm CMB}$ | $m_{B}$ | $x_{1}$ | $c$
---|---|---|---|---
|  | (mag) |  |
ZTF18aabdgik | 0.022775296 | 15.516 ($pm$ 0.047) | 0.096 ($\pm$ 0.218) | 0.034 ($\pm$ 0.038)
ZTF18aabstmw | 0.023919309 | 18.005 ($\pm$ 0.066) | -1.302 ($\pm$ 0.148) | 0.433 ($\pm$ 0.048)
ZTF18aabsyqp | 0.077744924 | 18.579 ($\pm$ 0.121) | 0.556 ($\pm$ 0.221) | 0.193 ($\pm$ 0.091)
ZTF18aabtaor | 0.080599043 | 18.397 ($\pm$ 0.075) | 0.659 ($\pm$ 0.451) | -0.045 ($\pm$ 0.057)
ZTF18aabxrjp | 0.080152526 | 18.479 ($\pm$ 0.070) | -0.732 ($\pm$ 0.433) | 0.022 ($\pm$ 0.053)

###  3.2 The $gri$-sample

For the host-$z$ sample, we have a total of 170 SNe Ia with at least one
observation in the $i$-band between -15 and +15 days relative to the
$T_{\max}$ inferred from the SALT2 fits to the $g$ and $r$ band data. However,
to get robust detections, we need deep references to create good difference
images. Therefore, we further require at least 15 frames in the $i$-band
either the phase range before -30 days or after +400 days to make the
reference image. Hence, for the $i$-band, we further impose the cut of the
number of frames to create a reference image. We note that for our host-$z$
sample, out of the 305 SNe, 122 have at least 1 detection in the $i$-band.
This corresponds to $\sim 40\%$ of the SNe in the sample, which is consistent
with the predictions from Feindt et al. (2019). We emphasize that this is a
lower limit, with the number expected to increase with an increase in the
number of observations after the SN has faded, for making a reference image.

The lightcurve fits for the SNe that peaked within 60 days since 15 June 2018
are shown in Figure 4. We note that the fit is only to the $g$ and $r$-band
data and the solid black lines in the bottom panel are the SALT2 model
predictions in the $i$-band overplotted on the data. The sample parameters are
discussed in Section 3.4 along with further selection cuts in Table 4.

###  3.3 Spectroscopic properties

The sample presented here is comprised entirely of spectroscopically
classified SNe Ia. This is critical to remove contamination from core-collapse
SNe and other non-SN Ia transients. Several studies in the literature have
demonstrated that SNe Ia can be divided into subclasses based on spectral line
velocities near maximum light, with potential implications for distance
measurements (Wang et al., 2009; Foley & Kasen, 2011; Folatelli et al., 2013;
Siebert et al., 2020; Dettman et al., 2021). Therefore, having spectra is
important for improving cosmological inference with SNe Ia. The phase
distribution for the spectra of the SNe Ia in the host-$z$ sample is shown in
Figure 5. We find no significant difference in the phase distribution of the
spectra from all instruments and the SEDm alone. 50$\%$ of all spectra (and
50$\%$ of all SEDm spectra) are obtained before maximum light, while 23$\%$
(20$\%$ for SEDm) are obtained before -7 d. Here, measure the accuracy of the
line velocities from spectra obtained with the SEDm.

Since we aim to measure the accuracy of line velocities, we require an
independent determination of the redshift and hence, we use the host-$z$
sample of 305 SNe Ia, which is a lower limit since the host redshift are not
time critical (see section 2.4). In this analysis, we only focus on the
ubiquitous Si II 6355 Å feature, since the velocity of this feature has been
most widely proposed in the literature as a metric for subclassifying SNe and
improving distances. We reiterate that a large fraction (68$\%$) of the
spectra for our sample are obtained with a single instrument, i.e. SEDmachine,
extracted uniformly with the PySEDM pipeline (Rigault et al., 2019).

For our line velocity measurements we use a fully automated and public code
for spectral fitting, spextractor(Papadogiannakis, 2019)
444https://github.com/astrobarn/spextractor. The code uses a non-parametric,
gaussian process (GP) regression (Rasmussen & Williams, 2005) to get the
minima for the individual features. It is based on the publically available
python package GPy (GPy, 2012) and uses a Matern 3/2 kernel for smoothing the
spectra.

The median error in the inferred $v_{\rm Si}$ is $\sim 700$ km s-1. We
emphasize that this method has fewer model assumptions than methods used in
the literature. Hence, we expect the median errors to be higher compared to
e.g. a fit assuming multiple gaussians describe the line profile. However,
even with such precision on the velocity measurements, we can clearly
distinguish high- and low-velocity subtypes to test improvements in the
distance measurements with our sample. A detailed analysis of the method and
the spectral sample, as well as relations with lightcurve and host galaxy
parameters will be presented in a followup study (Johansson et al. in prep).

###  3.4 Sample cuts and demographics

In this section, we describe quality cuts on the host-$z$ sample. We perform
cuts based on the SN Ia spectral subtyping, redshift range and lightcurves
parameters to get the final sample with which to compute the Hubble residuals.
We then compare the lightcurve fit parameters and the Hubble residuals to the
current low-$z$ from the literature.

The first selection cut is to remove peculiar SNe from the final analyses.
These include SNe Ia that are spectroscopically similar to the class of SNe
Iax (Jha et al., 2006; Foley et al., 2013) the eponymous subluminous and fast-
declining SN 1991bg (Filippenko et al., 1992; Leibundgut et al., 1993) or Ia-
CSM, similar to the prototype SN 2002ic (Hamuy et al., 2003; Wood-Vasey et
al., 2004). This is because such peculiar SNe might not follow the width-
luminosity relation (Phillips, 1993) or they may not be adequately described
by the SALT2 model. However, we do not remove SNe Ia in the subclass similar
to SN 1991T. This is for two reasons. Their peculiarities are shown to be
almost exclusively spectroscopic, and they are shown to obey the width-
luminosity relation (see Taubenberger, 2017, for a discussion on the extremes
of thermonuclear supernovae). Furthermore, we note that 91bg-like objects
might not be inherently incalibratable, since there are fitting algorithms
other than SALT2, e.g. MLCS2k2 (Jha et al., 2007) with which it is possible
that can estimate distances for this subclass of SNe Ia, however, for our
current analyses we remove them from the cosmological sample, but possibly
might include them in the future.

Figure 6: (Top) SALT2 lightcurve width ($x_{1}$), (middle) colour ($c$)
parameters and (bottom) the Hubble residuals computed after fitting the
nuisance parameters for the ZTF DR1 sample (red, solid) compared to the low-z
sample used for cosmological studies in the literature (green, dashed). We
find that the $x_{1}$-distributions for the ZTF and literature sample appear
to be drawn from different parent populations, however, the $c$-distribution
for the ZTF sample, within the $|c|>0.3$ does not. We note, however, that the
sample has a larger fraction of $c>0.3$ SNe Ia compared to the literature (see
Table 4) The $\sigma_{\rm rms}$ of the Hubble residuals is 0.17 mag, which is
very similar to the $\sigma_{\rm rms}$ of the literature sample.

We apply cuts based on the redshift of the host galaxy. Since this sample is
uniquely discovered, followed-up and characterised with a single telescope and
instrument, we do not have an a priori truncation on the redshift range. We
apply a lower limit on the redshift distribution of $z\geq 0.015$, to minimize
errors from peculiar velocity corrections, as done in previous studies in the
literature (for e.g. see Foley et al., 2018). The ZTF BTS reports a
completeness of 97$\%$ at $m<18$ mag and 93$\%$ $m<18.5$ mag (Perley et al.,
2020). The ZTF BTS is $\gtrsim 70\%$ complete till $m<19$ mag, corresponding
to a $z\lesssim 0.1$ threshold, hence, we apply an upper limit on the redshift
of $z\leq 0.1$.

Table 4: Selection criteria for the DR1 sample. The final sample, after
quality cuts is used to compute the Hubble residuals. The strongest cut is for
an available host galaxy redshift, which are not time-critical.

Criterion |  $\\#$ of SNe | Cumulative $\\#$ of SNe | Remaining SNe
---|---|---|---
| not passing | not passing |
All DR1 | $\ldots$ | $\ldots$ | 761
Host-$z$ | 456 | 456 | 305
Spectroscopically peculiar, | 11 | 467 | 294
$z>=0.015$, | 5 | 472 | 289
$z<=0.1$, | 23 | 495 | 266
$>3$ points between -10 and +10 days | 26 | 521 | 240
$\sigma(x_{1})<1$, $\sigma(t_{0})<1$ | 11 | 532 | 229
$-3<x_{1}<3$ | 2 | 534 | 227
$-0.3<c<0.3$ | 25 | 559 | 202
Chauvenet’s criterion ($>4\sigma$ outlier) | 2 | 561 | 200

In our analysis we want to robustly determine the lightcurve fit parameters,
hence, we restrict the sample to SNe with at least 3 points in the lightcurve
within 10 days of maximum light. Furthermore we remove poor SALT fits, defined
as having $\sigma(x_{1})>1$ or $\sigma(t_{0})>1$ day. For the final sample, we
also remove SNe with extremely slow or fast declining lightcurves, i.e.
$|x_{1}|>3$ and SNe with extremely blue or red colours, i.e. $|c|>0.3$. We
note that these SNe are of interest to SN Ia explosion physics, environmental
properties and reddening due to dust in the host galaxy (e.g. Bulla et al.,
2018), but are removed when computing the Hubble residuals. Finally, we apply
Chauvenet’s criterion on the sample. The selection cuts are summarised below

  * •

Spectroscopically classified as a normal SN Ia, i.e. not spectroscopically
similar to SNe Iax (Jha et al., 2006; Foley et al., 2013), SN 1991bg
(Filippenko et al., 1992; Leibundgut et al., 1993) or Ia-CSM (Hamuy et al.,
2003; Wood-Vasey et al., 2004).

  * •

$0.015\leq z\leq 0.1$

  * •

At least 3 points between -10 and +10 days

  * •

The uncertainty on $x_{1}$ is $<1$

  * •

$-3<x_{1}<3$

  * •

$-0.3<c<0.3$

  * •

Chauvenet’s criterion to exclude systematic outliers.

Here, we describe the objects in our sample removed with each of the above
selection cuts. Our sample includes a total of 11 spectroscopically peculiar
SNe Ia, 9 of which belong to the subclass of 91bg-likes, 1 Type Iax SN and 1
SN Ia-CSM. For the 91bg-likes which have sufficient coverage between -10 and
+10 days, we derive the SALT2 lightcurve parameters. For 5 of the 7 SNe Ia,
the SALT2 $c>0.3$, consistent with the observation in the literature that
91bg-likes are redder than normal SNe Ia.

We remove 27 SNe which don’t have enough observations near maximum light and 9
SNe which do not have an accurately measured $x_{1}$. Only 2 SNe are outside
the range of $x_{1}$ values for cosmologically viable SNe Ia. We find 25 SNe
with $|c|>0.3$, 23 of which are reddened with a $c>0.3$. We find more reddened
SNe in our sample than in other low-$z$, cosmological samples in the
literature. Additionally, even within the cosmological sample, there are more
SNe Ia in the range $0.25<c<0.3$ compared to the existing low-$z$. The larger
number of high-$c$ SNe could be due to the fact that our sample is derived
from an untargeted survey, where we don’t a priori reject reddened SNe when
building a lightcurve, however, we will explore this in detail in future
works. We finally apply Chauvenet’s criterion and find only 2 SNe removed with
this cut, ZTF18ablqkud and ZTF18aarcypa. They have a $\delta\mu$ of 0.76 and
0.77 mag respectively, making them both significantly fainter than the other
SNe in the sample. While faint, ZTF18ablqkud does not show an spectroscopic
features similar to the class of SN 1991bg-like SNe and has a broad $r$-band
lightcurve, which is consistent with normal SN Ia. It has an inferred
$x_{1}=0.88\pm 0.22$ and $c=0.129\pm 0.034$ which are also consistent with the
values for normal SNe Ia. ZTF18aarcypa similarly does not show spectroscopic
features similar to SN 1991bg, and it shows a shoulder in the $r$-band,
however, it has a low $x_{1}=-2.89\pm 0.29$, which is consistent with the
class of transitional fast decliners (Hsiao et al., 2015). A summary of the
number of objects removed after each cut is presented in Table 4.

We compare the $x_{1}$ and $c$ distribution for our sample (top and middle
panel Figure 6) with the low-$z$ anchor sample for dark energy studies in the
literature (Scolnic et al., 2018). Using a Kolmogorov-Smirnov test we find a
$p-$ value of 0.03 and 0.6 for the $x_{1}$ and $c$ distribution. For the
$x_{1}$ parameter, we can tentatively reject, the hypothesis that both
distributions are drawn from the same parent population. We will investigate
this in detail in future works. We cannot reject the null hypothesis that both
$c$ distributions come from the same parent population, however, we find a
larger fraction of $c>0.3$ SNe Ia in our sample compared to the low-$z$
samples in the literature.

Figure 7:  Log of the host stellar mass distribution for the DR1 host-$z$
sample (red), DR1 all-$z$ sample (i.e. including SNe where the redshift is
determined from the SN spectrum itself) (blue) and the current low-$z$ SN Ia
sample (green). The Y1 sample has $48.1\%$ of all SNe Ia in low mass host
galaxies compared to 23.8$\%$ for the current low-$z$ distribution.

####  3.4.1 Host galaxy mass

Here we compute stellar masses ($M_{\rm stellar}$) for the host galaxies of
SNe Ia in our host-$z$ sample. We take the host galaxy photometry from
PanSTARRS legacy imaging (Chambers et al., 2016) and identify the host galaxy
using the ‘Directional Light Radius’ (DLR; Sullivan et al., 2006; Smith et
al., 2012) methodology, requiring DLR$<5$. SNe with no host satistfying this
criteria (5; 2%) are considered hostless. Stellar masses are computed by
comparing measured griz-band fluxes to those of spectral energy distribution
(SED) model at the redshift of the SN. For this, we use the spectral synthesis
code, PÉGASE2 (Fioc & Rocca-Volmerange, 1997; Le Borgne & Rocca-Volmerange,
2002) combined with a Kroupa (2001) initial mass function (IMF) to calculate
synthetic SEDs. We consider 9 exponentially declining star formation histories
(SFHs) evaluated at 102 time-steps with ${\rm SFR}(t)={\rm
exp}^{-t/\tau}/\tau$, where $t$ is the age of the galaxy and $\tau$ is the
e-folding time, each with 7 foreground dust screens (see Smith et al., 2020,
for more details). We present the $M_{\rm stellar}$ distribution for our
sample in Figure 7. For comparison, we also analyse the host galaxies of the
current low-$z$ sample with the same procedure. We find a slightly larger
fraction of low (log $\frac{M_{\rm stellar}}{{\rm M}_{\odot}}<10$ ) mass hosts
compared to the literature sample. However, we note that requiring a
spectroscopic redshift from the literature could lead to some preference
against fainter and even lower mass hosts in the host-$z$ sample compared to
the entire DR1 sample. Therefore, we also compute the masses for the entire
DR1 sample. We find that compared to the 23.8$\%$ of SNe Ia in low mass
galaxies in the current low-$z$, the ZTF Y1 spec-$z$ sample has 31.6$\%$ of
the SNe Ia in low mass galaxies and ZTF Y1 all-$z$ has 48.1$\%$ of the SNe Ia
in low mass galaxies. A detailed analysis of the host galaxies of all SNe Ia
in the DR1 sample will be presented in a follow-up study (Smith et al. in
preparation). This furthermore emphasizes the need for post-survey SN Ia host
spectroscopy to obtain redshifts.

####  3.4.2 Hubble residuals

For the sample after the selection cuts described above we derive the
distribution of the Hubble residuals. From the fit to the magnitude-redshift
relation, we derive the the rms ($\sigma_{\rm rms}$) and intrinsic scatter
($\sigma_{\rm int}$) values. The $\sigma_{\rm int}$ value is fitted
simultaneously with the coefficient of the width-luminosity and colour
luminosity relations, which allows us to robustly infer $\sigma_{\rm int}$,
instead of fixing it to give an adequate goodness of fit.

While for the lightcurve fitting we fix the SN model redshift to the
heliocentric frame, for our inference of the Hubble residuals use CMB frame
redshifts. We convert the heliocentric redshifts to CMB frame using the
standard conversion formula and the dipole velocity and position of the CMB
from Fixsen et al. (1996). Since we cannot constrain $\Omega_{\rm M}$ from
low-$z$ SNe Ia themselves, we fix it to the value from _Planck_ of 0.307
(Planck Collaboration et al., 2018).

In our fit, the error propagated for each SN is the sum of the fit uncertainty
from the SALT2 covariance matrix ($\sigma_{\rm fit}$), the peculiar velocity
error ($\sigma_{\rm pec}$) and $\sigma_{\rm int}$. To get the error on the fit
from the covariance matrix, we sample over the $\alpha$ and $\beta$ nuisance
parameters along with the intercept of the Hubble diagram and the intrinsic
scatter.

$\sigma^{2}_{\rm m}=\sigma^{2}_{\rm fit}+\sigma^{2}_{\rm pec}+\sigma^{2}_{\rm
int}$ (2)

The $\sigma_{\rm pec}$ magnitude error is derived assuming a stochastic
peculiar velocity error value of 300 km s-1 (Carrick et al., 2015), and
$\sigma_{\rm int}$ to account for the intrinsic scatter of the SNe Ia. Here,
the $\sigma_{\rm fit}$ error term is derived from the output covariance matrix
of the SALT2 model fit, for a given value of $\alpha$ and $\beta$. Hence, in
our inference, we fit the magnitude redshift relation with four free
parameters, namely, the intercept of the magnitude-redshift relation,
$\alpha$, $\beta$, $\sigma_{\rm int}$ with uninformative priors on each. We
use PyMultiNest (Buchner et al., 2014), a python wrapper to MultiNest (Feroz
et al., 2009) to derive the posterior distribution on the parameters.

For the best fit parameter estimates, we obtain a $\sigma_{\rm rms}$ of 0.17
mag. We note that this is comparable to the lightcurve scatter from other
low-$z$ samples in the literature, when analysed with the SALT2 model (e.g.,
see Thorp et al., 2021) as well as low-$z$ sample of SNe Ia used in
cosmological studies (e.g. Scolnic et al., 2018). Moreover, if we don’t apply
the final selection cut of the Chauvenet criterion and keep the 2 SNe Ia that
don’t pass the cut in the sample, the $\sigma_{\rm rms}=0.18$ mag, hence, the
rms scatter is not impacted significantly by the removal of outliers. A
comparison of the Hubble residuals with the current low-$z$ sample from the
literature is shown in Figure 6 (bottom panel). Our sample has a $\sigma_{\rm
int}=0.15$ mag. We note that the rms dispersion and $\sigma_{\rm int}$ are
higher than report values for high-$z$ sample (e.g. Scolnic et al., 2018;
Abbott et al., 2019) We emphasise that the intrinsic scatter term is not
derived for a complete treatment of the systematic uncertainties, but rather
only includes a statistical error term that is a combination of the fit error
and the peculiar velocity error. We would expect the intrinsic scatter value
to be lower when including a complete systematics uncertainty budget.

Figure 8: Sky distribution of the entire DR1 sample (DR1) with the subsample
having host galaxy spec-z highlighted in orange. Known local overdensities,
e.g. Coma (black circle), Virgo (red square), Great Attractor (yellow
diamond), Shapley concentration (blue star), Pisces-Perseus cluster (green
circle), Centaurus (magenta square) are highlighted for comparison.

We emphasize that since there are ongoing improvement to the data processing
pipeline, the inferred root mean square (RMS) and intrinsic scatter values
should be considered as preliminary upper limits, expected to improve in
subsequent analyses. We caution against using the reported fit values for
inferring cosmological parameters and conducting more detailed cosmological
analyses, e.g. for $H_{0}$ or dark energy properties We have not yet produced
a complete systematics error budget. Therefore, at this stage in our analyses
we are blind to the parameters governing the width-luminosity and colour
luminosity relations as well as the intercept of the Hubble diagram till such
a complete systematics analysis has been performed.

###  3.5 Potential calibrator sample SNe Ia

In the sections above, we have focussed on the SNe Ia at higher redshift in
our sample. While the lowest redshift SNe in our dataset cannot be used for
the Hubble flow rung of the distance ladder, with future ground and spaced
based observatories, we can expect measurements of independent, calibrated
distances to their host galaxies, using secondary distance indicators. This
would be possible to distances of $D_{\rm L}\sim 80$ Mpc or approximately
translating to $z\sim 0.02$ (e.g., see Beaton et al., 2019). Such measurements
in the literature use Cepheid variables (Riess et al., 2019b), TRGB stars
(Freedman et al., 2019), JAGB stars (for e.g. Freedman & Madore, 2020; Lee et
al., 2020) or Mira variables (Huang et al., 2020).

The large uncertainty from heterogeneously calibrated instruments and
photometric systems also impacts the local $H_{0}$ measurement via the
calibrator sample of SNe Ia. Hence, the ZTF sample offers a unique opportunity
to have a homogeneously observed calibrator sample of SNe Ia, on the same
instrument as the Hubble flow SNe Ia.

In our sample, we have 14 SNe at $z<0.02$. When applying the criteria for the
final sample selection as in section 3.4, we find that 6 SNe pass the cuts. Of
the SNe rejected by the cuts, there is one spectroscopically peculiar (91bg-
like), three have high reddening ($c>0.3$) and four do not have sufficient
sampling near peak. We emphasize that these six SNe are from the host-z
sample. Since independent distances in the calibrator rung of the distance
ladder do not require a precise redshift, for the complete DR1 sample we
expect this nearby sample to $\sim$ twice as large, i.e. $\sim$ 10 SNe Ia in
the DR1 sample alone that we can get independent distances to the host
galaxies in the near future.

ZTF-I has transitioned to phase-II of operations (ZTF-II) from fall 2020. With
ZTF-II ongoing, we expect to find a few tens of SNe Ia in the redshift range
$z<0.02$ (ZTF-I + II combined) which would be a large sample, of order the
current number of calibrator distances with all SNe on a single photometric
system, which is the same as the system on which the Hubble flow SNe are
observed.

##  4 Discussion and Conclusions

We presented the first year dataset and results from the ZTF SN Ia survey. The
sample includes 761 spectroscopically confirmed SNe Ia, 305 of which have
spectroscopic redshifts from the host galaxy. The large sample statistics,
early discovery and dense sampling make it a unique sample for cosmology with
a uniformly measured low-$z$ SN Ia sample. In the coming years, with the aid
of multi-fibre spectroscopic surveys, we will complete the redshift
measurements for the remaining sample of SN Ia hosts. We note that the
complete DR1 sample is $\sim$ factor of 3 larger than the current combined
low-$z$ anchor and the host-$z$ subsample we present is by itself larger than
the combined low-$z$ anchor as well. ZTF has discovered $\sim$ 2.5 SNe Ia per
field, which, for an FoV of 47 deg2, implies a discovery rate of $\sim$ 0.06
SNe deg-2yr-1, accounting for survey downtime in the first year of operations.

Our SN Ia sample is created from an untargeted search and follow-up program.
This specifically allows us to probe the underlying distribution of SN Ia
environment properties, which will be presented in companion studies. Hence,
we can test the impact of SN Ia luminosity - host galaxy correlations on the
inferred cosmological parameters. This single system search and follow-up
system matches very well with, and is complementary to, future SN cosmology
programs e.g. Rubin Observatory (Ivezić et al., 2019), Roman Space Telescope
(Hounsell et al., 2018), which are attuned to high-$z$ SNe Ia.

Figure 9: Number of SNe Ia with sufficient data for measuring distances
discovered by ZTF-I and expected to be discovered by the ongoing ZTF-II as a
function of time since the beginning of ZTF-I. The vertical lines mark the DR1
sample (present here) and the total ZTF-I sample.

We present well-sampled lightcurves for the 305 SNe Ia in the host-$z$ sample.
From the multi-band data we derive lightcurve parameters and distance
estimates. After applying selection cuts, we compute the Hubble residuals
using 200 SNe that pass the cuts. This is already a competitive sample,
discovered by an untargeted survey, which is homogeneously observed on a
single photometric system. The sample is also larger than the combined low-$z$
anchor sample used in the literature for cosmological constraints. Moreover,
the median redshift of our sample is $\sim$ twice that of the current low-$z$
anchor sample. This is important to study local large scale structure are
greater depths than with current samples. Recent studies (e.g. Feindt et al.,
2013) look into constraining the origin of the local bulk flow with low-$z$
SNe Ia. There are tentative suggestions that a combination of the Shapley
concentration (Shapley, 1930; Raychaudhury et al., 1991) and Sloan Great Wall
could explain the size of dipole velocity (see Figure 8 for positions of known
local overdensities, overlaid on the SNe in our sample). With the current
host-$z$ sample alone, in the highest redshift shell ($0.06<z<0.1$), which
encompasses the Sloan Great Wall ($z\sim 0.07-0.08$) we have $\sim$ factor 2
improvement in sample statistics compared to the current SN Ia compilations.
With the entire DR1 sample, this can be an improvement of up to a factor of 4,
important to test what is the origin of the local flow velocity.

Our sample uniquely features very early discoveries, with a median first
detection epoch of -13.5 days, and densely sampled lightcurves. Recent studies
in the literature (e.g. Hayden et al., 2019) propose improved standardisation
models using SN Ia data on the rise. They split the canonical lightcurve shape
parameter in SALT2 into $x_{1}^{\rm r}$ and $x_{1}^{\rm f}$ for the rising and
falling part of the lightcurve and find that the two lightcurve width model
decreases the luminosity scatter. Our sample presented here is ideal for
testing such novel standardisation procedures which will be explored in
follow-up studies on improving lightcurve fitting algorithms.

We presented the SALT2 $x_{1}$ and $c$ parameter distributions in Figure 6. We
compared the distribution to the sample from the literature using a KS-test
and found a low $p$-value for the $x_{1}$ distributions suggesting that they
are not drawn from the same parent population. For the $c$-distribution we
find that the $p$-value is high indicating that, for the $-0.3<c<0.3$ the
distributions are drawn from the same parent population. However, we find a
larger fraction of $c>0.3$ SNe Ia compared to the literature samples. We also
present the stellar masses of the SN Ia host galaxies. We find a slightly
larger fraction of low $M_{\rm stellar}$ host galaxies compared to the
literature sample. We note that our requirement of having a spectroscopic
redshift of the host can introduce selection effects in our host-$z$ sample
and will present a detail study of the entire DR1 host galaxy properties in a
companion paper. For our sample, we compute the Hubble residuals and find an
rms dispersion of 0.17 mag, comparable to the current state-of-the-art in the
literature. We emphasize that with ongoing improvements in the data processing
this is expected to an upper limit on the scatter. We also simultaneously fit
for $\sigma_{\rm int}$ using only the statistical errors from the lightcurve
fit and peculiar velocity errors and find a value of 0.15 mag.

ZTF completed phase I of observations in October 2020, discovering and
spectroscopically classifying $>$ 3000 SNe Ia. In Figure 9 we present the
number of SNe discovered as a function of the time at which they peak
(relative to the beginning of ZTF-I). We present these values for the entire
ZTF-I using the photometry from the alerts computed by IPAC (see Masci et al.,
2019, for details). We restrict the sample with quality cuts to the lightcurve
sampling as presented above and only show the SNe with an uncertainty on the
inferred time of maximum of $<$ 1 day. The full DR1 sample of 761 SNe Ia is
already large enough we can start to test for anisotropies of the luminosity
distance-redshift relation (e.g. Macpherson & Heinesen, 2021). The complete
ZTF-I sample after the quality cuts on the number of lightcurve points and
$\sigma(t_{0})$ has $>2400$ SNe Ia. After applying the selection cuts for the
gold sample based on SALT2 parameters, there are $>1800$ SNe Ia. We emphasise
that these sample sizes are derived based on alert photometry which has very
restrictive criteria and hence, with the photometry pipeline described in this
work, we expect these numbers to improve further. With these large sample
statistics, the already obtained ZTF-I data is competitve to measure local
large scale structure properties, e.g. the growth rate, parametrised as $fD$
(see Graziani et al., 2020, for more details). Analysing subsamples, based on
host galaxy properties, from the complete ZTF-I dataset based on host galaxy
properties will be critical to study the origin of environmental systematics
in SN Ia cosmology (Rigault et al., 2020; Jones et al., 2018b).

We have ongoing efforts to improve the data reduction pipeline, obtain host
galaxy spectroscopic redshifts, quantify systematic uncertainties and finally
constrain cosmological parameters. We expect the inferred intrinsic and rms
dispersion values to decrease with improvements in the data processing. The
size of the host-$z$ as well as the complete DR1 samples is already at a stage
where, with the improvements mentioned above, we can improve constraints on
dark energy, measure $H_{0}$ and the local bulk flow velocity. With the entire
ZTF-I sample already acquired, we have sufficient number of SNe to obtain
constraints on the growth of structure. This makes the ZTF dataset exciting
for answering various questions in cosmology.

## Acknowledgements

S.D. is supported by the Isaac Newton Trust and the Kavli Foundation through
the Newton-Kavli fellowship and acknowledges a research fellowship at Lucy
Cavendish College. A.G acknowledges support from the Swedish Research Council
under Dnr VR 2016-03274 and 2020-03444. M.S., M.R., and Y.-L.K. have received
funding from the European Research Council (ERC) under the European Unions
Horizon 2020 research and innovation program (grant agreement No. 759194 -
USNAC).

Based on observations obtained with the Samuel Oschin Telescope 48-inch and
the 60-inch Telescope at the Palomar Observatory as part of the Zwicky
Transient Facility project. ZTF is supported by the National Science
Foundation under Grant No. AST-1440341 and a collaboration including Caltech,
IPAC, the Weizmann Institute for Science, the Oskar Klein Center at Stockholm
University, the University of Maryland, the University of Washington,
Deutsches Elektronen-Synchrotron and Humboldt University, Los Alamos National
Laboratories, the TANGO Consortium of Taiwan, the University of Wisconsin at
Milwaukee, and Lawrence Berkeley National Laboratories. Operations are
conducted by COO, IPAC, and UW.

SED Machine is based upon work supported by the National Science Foundation
under Grant No. 1106171. The ZTF forced-photometry service was funded under
the Heising-Simons Foundation grant. This work was supported by the GROWTH
project funded by the National Science Foundation under Grant No 1545949.

software: Numpy (van der Walt et al., 2011), Astropy (Astropy Collaboration et
al., 2013, 2018), sncosmo (Barbary et al., 2016), PhotUtils (Bradley et al.,
2019), ZTFQuery (Rigault, 2018), SWARP (Bertin, 2010), HOTPANTS (Becker,
2015), ZUDS, fringez (Medford et al., 2021), matplotlib (Hunter, 2007), IPAC
forced Photometry Service, spextractor (Papadogiannakis, 2019).

## Data Availability

The data used in this study are made available on github here:
https://github.com/ZwickyTransientFacility/ztfcosmodr

## References

  * Abbott et al. (2019) Abbott T. M. C., et al., 2019, ApJ, 872, L30
  * Ahumada et al. (2020) Ahumada R., et al., 2020, ApJS, 249, 3
  * Astropy Collaboration et al. (2013) Astropy Collaboration et al., 2013, A&A, 558, A33
  * Astropy Collaboration et al. (2018) Astropy Collaboration et al., 2018, AJ, 156, 123
  * Barbary et al. (2016) Barbary K., et al., 2016, SNCosmo: Python library for supernova cosmology (ascl:1611.017)
  * Beaton et al. (2019) Beaton R. L., et al., 2019, BAAS, 51, 456
  * Becker (2015) Becker A., 2015, HOTPANTS: High Order Transform of PSF ANd Template Subtraction (ascl:1504.004)
  * Bellm et al. (2019a) Bellm E. C., et al., 2019a, PASP, 131, 018002
  * Bellm et al. (2019b) Bellm E. C., et al., 2019b, PASP, 131, 068003
  * Ben-Ami et al. (2012) Ben-Ami S., Konidaris N., Quimby R., Davis J. T., Ngeow C. C., Ritter A., Rudy A., 2012, in Ground-based and Airborne Instrumentation for Astronomy IV. p. 844686, doi:10.1117/12.926317
  * Bertin (2010) Bertin E., 2010, SWarp: Resampling and Co-adding FITS Images Together (ascl:1010.068)
  * Bertin et al. (2002) Bertin E., Mellier Y., Radovich M., Missonnier G., Didelon P., Morin B., 2002, in Bohlender D. A., Durand D., Handley T. H., eds, Astronomical Society of the Pacific Conference Series Vol. 281, Astronomical Data Analysis Software and Systems XI. p. 228
  * Betoule et al. (2014) Betoule M., et al., 2014, A&A, 568, A22
  * Blagorodnova et al. (2018) Blagorodnova N., et al., 2018, PASP, 130, 035003
  * Bradley et al. (2019) Bradley L., et al., 2019, astropy/photutils: v0.6, doi:10.5281/zenodo.2533376, https://doi.org/10.5281/zenodo.2533376
  * Brout et al. (2019) Brout D., et al., 2019, The Astrophysical Journal, 874, 106
  * Buchner et al. (2014) Buchner J., et al., 2014, A&A, 564, A125
  * Bulla et al. (2018) Bulla M., Goobar A., Dhawan S., 2018, MNRAS, 479, 3663
  * Bulla et al. (2020) Bulla M., et al., 2020, ApJ, 902, 48
  * Burns et al. (2011) Burns C. R., et al., 2011, AJ, 141, 19
  * Burns et al. (2018) Burns C. R., et al., 2018, ApJ, 869, 56
  * Cardelli et al. (1989) Cardelli J. A., Clayton G. C., Mathis J. S., 1989, ApJ, 345, 245
  * Carrick et al. (2015) Carrick J., Turnbull S. J., Lavaux G., Hudson M. J., 2015, MNRAS, 450, 317
  * Cenko et al. (2006) Cenko S. B., et al., 2006, PASP, 118, 1396
  * Chambers et al. (2016) Chambers K. C., et al., 2016, arXiv e-prints, p. arXiv:1612.05560
  * Conley et al. (2008) Conley A., et al., 2008, ApJ, 681, 482
  * Conley et al. (2011) Conley A., et al., 2011, ApJS, 192, 1
  * DESI Collaboration et al. (2016) DESI Collaboration et al., 2016, arXiv e-prints, p. arXiv:1611.00036
  * Dekany et al. (2020) Dekany R., et al., 2020, PASP, 132, 038001
  * Dettman et al. (2021) Dettman K. G., et al., 2021, arXiv e-prints, p. arXiv:2102.06524
  * Dhawan et al. (2017) Dhawan S., Goobar A., Mörtsell E., Amanullah R., Feindt U., 2017, J. Cosmology Astropart. Phys., 2017, 040
  * Feindt et al. (2013) Feindt U., et al., 2013, A&A, 560, A90
  * Feindt et al. (2019) Feindt U., Nordin J., Rigault M., Brinnel V., Dhawan S., Goobar A., Kowalski M., 2019, J. Cosmology Astropart. Phys., 2019, 005
  * Feroz et al. (2009) Feroz F., Hobson M. P., Bridges M., 2009, MNRAS, 398, 1601
  * Filippenko et al. (1992) Filippenko A. V., et al., 1992, AJ, 104, 1543
  * Filippenko et al. (2001) Filippenko A. V., Li W. D., Treffers R. R., Modjaz M., 2001, in Paczynski B., Chen W.-P., Lemme C., eds, Astronomical Society of the Pacific Conference Series Vol. 246, IAU Colloq. 183: Small Telescope Astronomy on Global Scales. p. 121
  * Fioc & Rocca-Volmerange (1997) Fioc M., Rocca-Volmerange B., 1997, A&A, 500, 507
  * Firth et al. (2015) Firth R. E., et al., 2015, MNRAS, 446, 3895
  * Fixsen et al. (1996) Fixsen D. J., Cheng E. S., Gales J. M., Mather J. C., Shafer R. A., Wright E. L., 1996, ApJ, 473, 576
  * Folatelli et al. (2010) Folatelli G., et al., 2010, AJ, 139, 120
  * Folatelli et al. (2013) Folatelli G., et al., 2013, ApJ, 773, 53
  * Foley & Kasen (2011) Foley R. J., Kasen D., 2011, ApJ, 729, 55
  * Foley et al. (2013) Foley R. J., et al., 2013, ApJ, 767, 57
  * Foley et al. (2018) Foley R. J., et al., 2018, MNRAS, 475, 193
  * Freedman (2021) Freedman W. L., 2021, arXiv e-prints, p. arXiv:2106.15656
  * Freedman & Madore (2020) Freedman W. L., Madore B. F., 2020, ApJ, 899, 67
  * Freedman et al. (2009) Freedman W. L., et al., 2009, ApJ, 704, 1036
  * Freedman et al. (2019) Freedman W. L., et al., 2019, ApJ, 882, 34
  * Fremling et al. (2020) Fremling C., et al., 2020, ApJ, 895, 32
  * GPy (2012) GPy since 2012, GPy: A Gaussian process framework in python, http://github.com/SheffieldML/GPy
  * Ganeshalingam et al. (2011) Ganeshalingam M., Li W., Filippenko A. V., 2011, MNRAS, 416, 2607
  * Goobar & Leibundgut (2011) Goobar A., Leibundgut B., 2011, Annual Review of Nuclear and Particle Science, 61, 251
  * Graham et al. (2019) Graham M. J., et al., 2019, PASP, 131, 078001
  * Graziani et al. (2020) Graziani R., et al., 2020, arXiv e-prints, p. arXiv:2001.09095
  * Guy et al. (2005) Guy J., Astier P., Nobili S., Regnault N., Pain R., 2005, A&A, 443, 781
  * Guy et al. (2007) Guy J., et al., 2007, A&A, 466, 11
  * Guy et al. (2010) Guy J., et al., 2010, A&A, 523, A7
  * Hamuy et al. (1996) Hamuy M., Phillips M. M., Suntzeff N. B., Schommer R. A., Maza J., Smith R. C., Lira P., Aviles R., 1996, AJ, 112, 2438
  * Hamuy et al. (2003) Hamuy M., et al., 2003, Nature, 424, 651
  * Hayden et al. (2019) Hayden B., Rubin D., Strovink M., 2019, ApJ, 871, 219
  * Hounsell et al. (2018) Hounsell R., et al., 2018, ApJ, 867, 23
  * Hsiao et al. (2015) Hsiao E. Y., et al., 2015, A&A, 578, A9
  * Huang et al. (2020) Huang C. D., et al., 2020, ApJ, 889, 5
  * Hunter (2007) Hunter J. D., 2007, Computing in Science and Engineering, 9, 90
  * Huterer (2020) Huterer D., 2020, arXiv e-prints, p. arXiv:2010.05765
  * Huterer et al. (2017) Huterer D., Shafer D. L., Scolnic D. M., Schmidt F., 2017, J. Cosmology Astropart. Phys., 2017, 015
  * Ivezić et al. (2019) Ivezić Ž., et al., 2019, ApJ, 873, 111
  * Jha et al. (2006) Jha S., Branch D., Chornock R., Foley R. J., Li W., Swift B. J., Casebeer D., Filippenko A. V., 2006, AJ, 132, 189
  * Jha et al. (2007) Jha S., Riess A. G., Kirshner R. P., 2007, ApJ, 659, 122
  * Jones et al. (2018a) Jones D. O., et al., 2018a, The Astrophysical Journal, 867, 108
  * Jones et al. (2018b) Jones D. O., et al., 2018b, ApJ, 867, 108
  * Jones et al. (2019) Jones D. O., et al., 2019, ApJ, 881, 19
  * Jones et al. (2021) Jones D. O., et al., 2021, ApJ, 908, 143
  * Kasliwal et al. (2019) Kasliwal M. M., et al., 2019, PASP, 131, 038003
  * Kessler et al. (2009) Kessler R., et al., 2009, ApJS, 185, 32
  * Knox & Millea (2020) Knox L., Millea M., 2020, Phys. Rev. D, 101, 043533
  * Kourkchi et al. (2020) Kourkchi E., et al., 2020, ApJ, 902, 145
  * Kroupa (2001) Kroupa P., 2001, MNRAS, 322, 231
  * Le Borgne & Rocca-Volmerange (2002) Le Borgne D., Rocca-Volmerange B., 2002, A&A, 386, 446
  * Lee et al. (2020) Lee A. J., Freedman W. L., Madore B. F., Owens K. A., Monson A. J., Hoyt T. J., 2020, arXiv e-prints, p. arXiv:2012.04536
  * Leibundgut & Sullivan (2018) Leibundgut B., Sullivan M., 2018, Space Sci. Rev., 214, 57
  * Leibundgut et al. (1993) Leibundgut B., et al., 1993, AJ, 105, 301
  * Lonappan et al. (2018) Lonappan A. I., Kumar S., Ruchika Dinda B. R., Sen A. A., 2018, Phys. Rev. D, 97, 043524
  * Macpherson & Heinesen (2021) Macpherson H. J., Heinesen A., 2021, arXiv e-prints, p. arXiv:2103.11918
  * Mandel et al. (2009) Mandel K. S., Wood-Vasey W. M., Friedman A. S., Kirshner R. P., 2009, ApJ, 704, 629
  * Mandel et al. (2011) Mandel K. S., Narayan G., Kirshner R. P., 2011, ApJ, 731, 120
  * Mandel et al. (2020) Mandel K. S., Thorp S., Narayan G., Friedman A. S., Avelino A., 2020, arXiv e-prints, p. arXiv:2008.07538
  * Masci et al. (2019) Masci F. J., et al., 2019, PASP, 131, 018003
  * Mathews et al. (2016) Mathews G. J., Rose B. M., Garnavich P. M., Yamazaki D. G., Kajino T., 2016, ApJ, 827, 60
  * Medford et al. (2021) Medford M. S., et al., 2021, arXiv e-prints, p. arXiv:2102.10738
  * Miller et al. (2020) Miller A. A., et al., 2020, ApJ, 902, 47
  * Mortsell et al. (2021a) Mortsell E., Goobar A., Johansson J., Dhawan S., 2021a, arXiv e-prints, p. arXiv:2105.11461
  * Mortsell et al. (2021b) Mortsell E., Goobar A., Johansson J., Dhawan S., 2021b, arXiv e-prints, p. arXiv:2106.09400
  * Nobili et al. (2005) Nobili S., et al., 2005, A&A, 437, 789
  * Papadogiannakis (2019) Papadogiannakis S., 2019, PhD thesis, Stockholm University, Department of Physics
  * Perley et al. (2020) Perley D. A., et al., 2020, ApJ, 904, 35
  * Perlmutter et al. (1999) Perlmutter S., et al., 1999, ApJ, 517, 565
  * Phillips (1993) Phillips M. M., 1993, ApJ, 413, L105
  * Planck Collaboration et al. (2018) Planck Collaboration et al., 2018, arXiv e-prints, p. arXiv:1807.06209
  * Rasmussen & Williams (2005) Rasmussen C. E., Williams C. K. I., 2005, Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning). The MIT Press
  * Rau et al. (2009) Rau A., et al., 2009, PASP, 121, 1334
  * Raychaudhury et al. (1991) Raychaudhury S., Fabian A. C., Edge A. C., Jones C., Forman W., 1991, MNRAS, 248, 101
  * Rest et al. (2014) Rest A., et al., 2014, The Astrophysical Journal, 795, 44
  * Riess et al. (1998) Riess A. G., et al., 1998, AJ, 116, 1009
  * Riess et al. (2019a) Riess A. G., Casertano S., Yuan W., Macri L. M., Scolnic D., 2019a, ApJ, 876, 85
  * Riess et al. (2019b) Riess A. G., Casertano S., Yuan W., Macri L. M., Scolnic D., 2019b, ApJ, 876, 85
  * Rigault (2018) Rigault M., 2018, ztfquery, a python tool to access ZTF data, doi:10.5281/zenodo.1345222
  * Rigault et al. (2015) Rigault M., et al., 2015, ApJ, 802, 20
  * Rigault et al. (2019) Rigault M., et al., 2019, A&A, 627, A115
  * Rigault et al. (2020) Rigault M., et al., 2020, A&A, 644, A176
  * Schlafly & Finkbeiner (2011) Schlafly E. F., Finkbeiner D. P., 2011, ApJ, 737, 103
  * Schlegel et al. (1998) Schlegel D. J., Finkbeiner D. P., Davis M., 1998, ApJ, 500, 525
  * Scolnic et al. (2014) Scolnic D. M., Riess A. G., Foley R. J., Rest A., Rodney S. A., Brout D. J., Jones D. O., 2014, ApJ, 780, 37
  * Scolnic et al. (2018) Scolnic D. M., et al., 2018, ApJ, 859, 101
  * Scolnic et al. (2019) Scolnic D., et al., 2019, Astro2020: Decadal Survey on Astronomy and Astrophysics, 2020, 270
  * Shapley (1930) Shapley H., 1930, Harvard College Observatory Bulletin, 874, 9
  * Shappee et al. (2014) Shappee B. J., et al., 2014, ApJ, 788, 48
  * Shariff et al. (2016) Shariff H., Dhawan S., Jiao X., Leibundgut B., Trotta R., van Dyk D. A., 2016, MNRAS, 463, 4311
  * Siebert et al. (2020) Siebert M. R., Foley R. J., Jones D. O., Davis K. W., 2020, MNRAS, 493, 5713
  * Smith et al. (2012) Smith M., et al., 2012, ApJ, 755, 61
  * Smith et al. (2020) Smith M., et al., 2020, MNRAS, 494, 4426
  * Sullivan et al. (2006) Sullivan M., et al., 2006, ApJ, 648, 868
  * Sullivan et al. (2011) Sullivan M., et al., 2011, The Astrophysical Journal, 737, 102
  * Swann et al. (2019) Swann E., et al., 2019, The Messenger, 175, 58
  * Taubenberger (2017) Taubenberger S., 2017, The Extremes of Thermonuclear Supernovae. p. 317, doi:10.1007/978-3-319-21846-5_37
  * The LSST Dark Energy Science Collaboration et al. (2018) The LSST Dark Energy Science Collaboration et al., 2018, arXiv e-prints, p. arXiv:1809.01669
  * Thorp et al. (2021) Thorp S., Mandel K. S., Jones D. O., Ward S. M., Narayan G., 2021, arXiv e-prints, p. arXiv:2102.05678
  * Tonry et al. (2018) Tonry J. L., et al., 2018, PASP, 130, 064505
  * Tripp (1998) Tripp R., 1998, A&A, 331, 815
  * Wang et al. (2009) Wang X., et al., 2009, ApJ, 699, L139
  * Wood-Vasey et al. (2004) Wood-Vasey W. M., Wang L., Aldering G., 2004, ApJ, 616, 339
  * Yao et al. (2019) Yao Y., et al., 2019, ApJ, 886, 152
  * de Jong et al. (2019) de Jong R. S., et al., 2019, The Messenger, 175, 3
  * van der Walt et al. (2011) van der Walt S., Colbert S. C., Varoquaux G., 2011, Computing in Science and Engineering, 13, 22

##  Appendix A Photometry pipeline description

In this section, we present a detailed description of the photometric pipeline
parameters. As described in section 2.5, the pipeline can be divided into
three broad components, namely, reference building, image subtraction and
forced photometry. Here, we describe each individual process.

###  A.1 Reference building

Since the SNe Ia in our sample were discovered in 2018, in a fraction of the
cases, the references for each field and readout channel were created during
the lifetime of the SN, which manifests itself as non-zero flux significantly
before and after the inferred time of maximum. For example, some SNe Ia show
negative flux in their forced photometry lightcurves before -30 days from the
SALT2 $t_{0}$ time, since there is SN flux in the reference image. In our
custom pipeline, we use images at least 30 days before peak to make deep
references. For SNe with insufficient data ($<30$ frames) in the phase range
before -30 days, we also use data from $>400$ days after peak. For each
reference image, we have quality control selection cuts such that only images
within the seeing range 1.7" and 3" and a nightly magnitude limit fainter than
19.2 mag are used in the final reference creation.

We use SWARP on the processed images from IPAC to make the reference. For each
input image, we create a test weight map with the mask image from IPAC as an
input (Masci et al., 2019). The weight map is passed as an to SExtractor to
create an rms map for each input image that goes into making the final
reference image. Each associated weight map, derived from the SExtractor
output rms map, is input along with the image to make the reference coadd.
Before coadding, the input images are all scaled to a common zero-point
magnitude of 25. The associated reference mask is produced by using the
logical AND function with SWARP to combine the individual epoch masks. This is
because logical OR coaddition is extremely restrictive at masking the
reference image.

###  A.2 Image Subtraction

The individual science frame, and the associated mask and rms file, along with
the reference coadd and its associated mask and rms file are input to the
image subtraction routine. As described in section 2.5, we use HOTPANTS
(Becker, 2015) for the difference imaging part of the pipeline. For both the
science image and the reference, we fix the lower valid data count as the
computed background minus 10 times the standard deviation. For the
differencing, we use a convolution kernel with a half-width that is 2.5 times
the seeing and a half width of the substamp to extract around each centroid as
6 times the seeing. We set the normalisation to the science image and convolve
to the reference image.

###  A.3 Forced photometry

We use the astropy package photutils (Bradley et al., 2019) to perform
aperture photometry. We define the aperture using the SkyCircularAperture
function with a 6 pixel diameter aperture. The location is defined as the
median coordinate in each filter, derived from the alert packets (see Fremling
et al., 2020, for details). We apply a correction for a six pixel aperture to
the final zero point for the observed fluxes, as provided in the IPAC data
products.